Subgroups — C₃₁×#61068 #21517827

Order 7936.

2772 conjugacy classes of subgroups.

The subgroup lattice has 1580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3285	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3282	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3277	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3275	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3271	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3270	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3269	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3265	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3153	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3056	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3055	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3006	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3005	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3004	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#575	—	2	8	no	—
29	C₂×C₃₁×#137	—	2	8	no	—
30	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
36	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
37	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
38	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
42	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
44	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
45	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
46	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
47	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
48	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
50	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#548	—	2	1	no	—
52	C₃₁×#548	—	2	1	no	—
53	C₃₁×#548	—	2	1	no	—
54	C₃₁×#548	—	2	1	no	—
55	C₃₁×#548	C₂²	1	2	yes	—
56	C₃₁×#548	C₂²	1	2	yes	complemented
57	C₃₁×#548	C₂²	1	2	yes	complemented
58	C₃₁×#548	C₂²	1	2	yes	complemented
59	C₃₁×#548	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#548	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#547	—	2	1	no	—
62	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#546	—	2	1	no	—
64	C₃₁×#546	—	2	1	no	—
65	C₃₁×#546	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#546	C₂²	1	1	yes	characteristic, complemented
67	D₄²×C₃₁	—	2	1	no	—
68	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#532	—	2	1	no	—
70	C₃₁×#532	C₂²	1	1	yes	characteristic
71	C₂×C₃₁×#124	—	2	1	no	—
72	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#525	—	2	1	no	—
74	C₃₁×#525	—	2	1	no	—
75	C₃₁×#525	C₂²	1	1	yes	characteristic
76	C₃₁×#525	C₂²	1	1	yes	characteristic
77	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
78	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₃₁×#121	—	2	1	no	—
80	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
81	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
82	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×D₄×C₃₁	—	2	1	no	—
84	C₂×C₄×D₄×C₃₁	—	2	1	no	—
85	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
86	C₃₁×#497	C₂²	1	2	yes	complemented
87	C₃₁×#496	C₂²	1	2	yes	complemented
88	C₃₁×#495	C₂²	1	2	yes	complemented
89	C₃₁×#495	C₂²	1	2	yes	complemented
90	C₃₁×#470	C₂²	1	2	yes	complemented
91	C₃₁×#469	C₂²	1	2	yes	complemented
92	C₃₁×#468	C₂²	1	2	yes	complemented
93	C₃₁×#468	C₂²	1	2	yes	complemented
94	C₃₁×#467	C₂²	1	2	yes	complemented
95	C₃₁×#466	C₂²	1	2	yes	complemented
96	C₃₁×#465	C₂²	1	2	yes	complemented
97	C₃₁×#465	C₂²	1	2	yes	complemented
98	C₃₁×#464	C₂²	1	2	yes	complemented
99	C₃₁×#464	C₂²	1	2	yes	complemented
100	C₃₁×#464	C₂²	1	2	yes	complemented
101	C₃₁×#464	C₂²	1	2	yes	complemented
102	C₃₁×#463	C₂²	1	2	yes	complemented
103	C₃₁×#463	C₂²	1	2	yes	complemented
104	C₃₁×#462	C₂²	1	2	yes	complemented
105	C₃₁×#460	C₂²	1	2	yes	complemented
106	C₃₁×#452	C₂²	1	2	yes	complemented
107	C₃₁×#452	C₂²	1	2	yes	complemented
108	C₃₁×#452	C₂²	1	2	yes	complemented
109	C₃₁×#452	C₂²	1	2	yes	complemented
110	C₃₁×#451	C₂²	1	2	yes	complemented
111	C₃₁×#451	C₂²	1	2	yes	complemented
112	C₃₁×#451	C₂²	1	2	yes	complemented
113	C₃₁×#450	C₂²	1	2	yes	complemented
114	C₃₁×#449	C₂²	1	2	yes	complemented
115	C₃₁×#449	C₂²	1	2	yes	complemented
116	C₃₁×#449	C₂²	1	2	yes	complemented
117	C₃₁×#449	C₂²	1	2	yes	complemented
118	C₃₁×#448	C₂²	1	2	yes	complemented
119	C₃₁×#448	C₂²	1	2	yes	complemented
120	C₃₁×#448	C₂²	1	2	yes	complemented
121	C₃₁×#447	C₂²	1	2	yes	complemented
122	C₃₁×#441	C₂²	1	2	yes	complemented
123	C₃₁×#440	C₂²	1	2	yes	complemented
124	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
126	C₃₁×#436	C₂²	1	2	yes	complemented
127	C₃₁×#435	C₂²	1	2	yes	complemented
128	C₃₁×#435	C₂²	1	2	yes	complemented
129	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
130	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#418	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×#417	C₂²	1	1	yes	characteristic
136	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
138	C₃₁×#407	C₂²	1	1	yes	characteristic, complemented
139	C₃₁×#407	C₂²	1	1	yes	characteristic, complemented
140	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
141	C₂×#41×C₃₁	—	2	1	no	—
142	C₂×#41×C₃₁	—	2	1	no	—
143	C₂×#41×C₃₁	—	2	1	no	—
144	C₂×#41×C₃₁	—	2	1	no	—
145	C₂×#41×C₃₁	—	2	1	no	—
146	C₂×#41×C₃₁	—	2	1	no	—
147	C₂×#41×C₃₁	—	2	4	no	—
148	C₂×#41×C₃₁	—	2	4	no	—
149	C₂×#41×C₃₁	—	2	4	no	—
150	C₂×#41×C₃₁	—	4	2	no	—
151	C₂×#41×C₃₁	—	4	2	no	—
152	C₂×#41×C₃₁	—	4	2	no	—
153	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×#41×C₃₁	C₂³	1	2	yes	—
158	C₂×#41×C₃₁	C₂³	1	2	yes	—
159	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
162	C₂²×Q₈×C₃₁	—	2	1	no	—
163	C₂²×Q₈×C₃₁	—	2	1	no	—
164	C₂²×Q₈×C₃₁	—	2	1	no	—
165	C₂²×Q₈×C₃₁	—	2	4	no	—
166	C₂²×Q₈×C₃₁	—	4	2	no	—
167	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
169	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
170	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
171	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
172	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₂²×D₄×C₃₁	—	2	1	no	—
174	C₂²×D₄×C₃₁	—	2	1	no	—
175	C₂²×D₄×C₃₁	—	2	1	no	—
176	C₂²×D₄×C₃₁	—	2	1	no	—
177	C₂²×D₄×C₃₁	—	2	1	no	—
178	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
179	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₂³×C₄×C₃₁	—	2	1	no	—
183	C₂³×C₄×C₃₁	—	2	1	no	—
184	C₂³×C₄×C₃₁	—	2	1	no	—
185	C₂³×C₄×C₃₁	—	2	1	no	—
186	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₃₁×#137	—	2	4	no	—
189	C₃₁×#137	—	2	4	no	—
190	C₃₁×#137	—	2	4	no	—
191	C₃₁×#137	—	2	8	no	—
192	C₃₁×#137	—	2	8	no	—
193	C₃₁×#137	—	2	8	no	—
194	C₃₁×#137	—	2	4	no	—
195	C₃₁×#137	—	4	2	no	—
196	C₃₁×#137	D₄	1	8	yes	complemented
197	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
198	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
199	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
200	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
201	C₃₁×#135	—	2	8	no	—
202	C₃₁×#135	—	2	8	no	—
203	C₂×Q₁₆×C₃₁	—	2	8	no	—
204	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
205	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
206	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
207	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
208	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
209	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
210	C₂×SD₁₆×C₃₁	—	2	8	no	—
211	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
212	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
213	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
214	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
215	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
216	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
217	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
218	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
219	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
220	C₂×D₈×C₃₁	C₂³	1	2	yes	—
221	C₂×D₈×C₃₁	C₂³	1	2	yes	—
222	C₂×D₈×C₃₁	C₂³	1	2	yes	—
223	C₂×M₁₆×C₃₁	—	2	4	no	—
224	C₂×M₁₆×C₃₁	—	2	4	no	—
225	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
226	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
227	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
228	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
229	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
230	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
231	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
232	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
233	C₃₁×C₄⋊Q₈	—	2	1	no	—
234	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
235	C₃₁×#127	—	2	1	no	—
236	C₃₁×#127	C₂³	1	1	yes	characteristic
237	C₃₁×#124	—	2	2	no	—
238	C₃₁×#124	—	2	2	no	—
239	C₃₁×#124	—	2	2	no	—
240	C₃₁×#124	—	2	2	no	—
241	C₃₁×#124	—	2	1	no	—
242	C₃₁×#124	—	2	1	no	—
243	C₃₁×#124	—	2	1	no	—
244	C₃₁×#124	—	2	1	no	—
245	C₃₁×#124	C₂³	1	2	yes	—
246	C₃₁×#124	C₂³	1	2	yes	—
247	C₃₁×#124	C₂³	1	1	yes	characteristic
248	C₃₁×#124	C₂³	1	1	yes	characteristic
249	C₃₁×#123	—	2	1	no	—
250	C₃₁×#123	—	2	1	no	—
251	C₃₁×#123	—	2	1	no	—
252	C₃₁×#123	—	2	1	no	—
253	C₃₁×#123	—	2	1	no	—
254	C₃₁×#123	—	2	1	no	—
255	C₃₁×C₂²⋊Q₈	—	2	1	no	—
256	C₃₁×C₂²⋊Q₈	—	2	1	no	—
257	C₃₁×C₂²⋊Q₈	—	2	2	no	—
258	C₃₁×C₂²⋊Q₈	—	2	2	no	—
259	C₃₁×C₂²⋊Q₈	—	2	2	no	—
260	C₃₁×C₂²⋊Q₈	—	2	2	no	—
261	C₃₁×C₂²⋊Q₈	—	2	1	no	—
262	C₃₁×C₂²⋊Q₈	—	2	1	no	—
263	C₃₁×C₂²⋊Q₈	—	2	1	no	—
264	C₃₁×C₂²⋊Q₈	—	2	1	no	—
265	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
266	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
267	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
268	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
269	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
270	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
271	C₃₁×#121	—	2	2	no	—
272	C₃₁×#121	—	2	2	no	—
273	C₃₁×#121	—	2	2	no	—
274	C₃₁×#121	—	2	2	no	—
275	C₃₁×#121	—	2	1	no	—
276	C₃₁×#121	—	2	1	no	—
277	C₃₁×#121	—	2	1	no	—
278	C₃₁×#121	—	2	1	no	—
279	C₃₁×#121	—	2	1	no	—
280	C₃₁×#121	—	2	1	no	—
281	C₃₁×#121	—	2	1	no	—
282	C₃₁×#121	—	2	1	no	—
283	C₃₁×#121	—	2	1	no	—
284	C₃₁×#121	—	2	1	no	—
285	C₃₁×#121	—	2	1	no	—
286	C₃₁×#121	—	2	1	no	—
287	C₃₁×#121	C₂³	1	2	yes	—
288	C₃₁×#121	C₂³	1	1	yes	characteristic
289	C₃₁×#121	C₂³	1	1	yes	characteristic
290	C₃₁×#121	C₂³	1	1	yes	characteristic
291	C₃₁×#121	C₂³	1	1	yes	characteristic
292	C₃₁×#121	C₂³	1	2	yes	—
293	C₃₁×#120	—	2	1	no	—
294	C₃₁×#120	—	2	1	no	—
295	C₃₁×#120	—	2	1	no	—
296	C₃₁×#120	—	2	1	no	—
297	C₃₁×#120	—	2	1	no	—
298	C₃₁×#120	—	2	1	no	—
299	C₄×Q₈×C₃₁	—	2	1	no	—
300	C₄×Q₈×C₃₁	—	2	1	no	—
301	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
302	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
303	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
304	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
305	C₄×D₄×C₃₁	—	2	1	no	—
306	C₄×D₄×C₃₁	—	2	1	no	—
307	C₄×D₄×C₃₁	—	2	1	no	—
308	C₄×D₄×C₃₁	—	2	1	no	—
309	C₄×D₄×C₃₁	—	2	1	no	—
310	C₄×D₄×C₃₁	—	2	1	no	—
311	C₄×D₄×C₃₁	—	2	1	no	—
312	C₄×D₄×C₃₁	—	2	1	no	—
313	C₄×D₄×C₃₁	—	2	1	no	—
314	C₄×D₄×C₃₁	—	2	1	no	—
315	C₄×D₄×C₃₁	—	2	2	no	—
316	C₄×D₄×C₃₁	—	2	2	no	—
317	C₄×D₄×C₃₁	—	2	2	no	—
318	C₄×D₄×C₃₁	—	2	2	no	—
319	C₄×D₄×C₃₁	—	2	1	no	—
320	C₄×D₄×C₃₁	—	2	1	no	—
321	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
322	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
323	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
324	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
325	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
326	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
327	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
328	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
329	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
330	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
331	C₃₁×#117	—	2	1	no	—
332	C₃₁×#117	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
334	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
335	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
336	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
339	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
340	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
341	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
342	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
343	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
344	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
346	C₂×C₄²×C₃₁	—	2	1	no	—
347	C₂×C₄²×C₃₁	—	2	1	no	—
348	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
349	C₃₁×#107	C₂³	1	2	yes	—
350	C₃₁×#106	C₂³	1	2	yes	—
351	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
352	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
353	C₃₁×#103	C₂³	1	2	yes	—
354	C₃₁×#103	C₂³	1	2	yes	—
355	C₃₁×#103	C₂³	1	2	yes	—
356	C₃₁×#103	C₂³	1	2	yes	—
357	C₃₁×#103	C₂³	1	2	yes	—
358	C₃₁×#103	C₂³	1	2	yes	—
359	C₃₁×#103	C₂³	1	2	yes	—
360	C₃₁×#102	C₂³	1	2	yes	—
361	C₃₁×#102	C₂³	1	2	yes	—
362	C₃₁×#102	C₂³	1	2	yes	—
363	C₃₁×#102	C₂³	1	2	yes	—
364	C₃₁×#102	C₂³	1	2	yes	—
365	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
366	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
367	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
368	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
369	C₃₁×#97	C₂³	1	2	yes	—
370	C₄×C₈×C₃₁	C₂³	1	2	yes	—
371	C₂⁴×C₃₁	—	2	1	no	—
372	C₂⁴×C₃₁	—	2	1	no	—
373	C₂⁴×C₃₁	—	2	1	no	—
374	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
376	#41×C₃₁	—	2	2	no	—
377	#41×C₃₁	—	2	4	no	—
378	#41×C₃₁	—	2	2	no	—
379	#41×C₃₁	—	2	4	no	—
380	#41×C₃₁	—	2	2	no	—
381	#41×C₃₁	—	2	2	no	—
382	#41×C₃₁	—	2	2	no	—
383	#41×C₃₁	—	2	2	no	—
384	#41×C₃₁	—	2	2	no	—
385	#41×C₃₁	—	2	2	no	—
386	#41×C₃₁	—	2	2	no	—
387	#41×C₃₁	—	4	4	no	—
388	#41×C₃₁	—	4	4	no	—
389	#41×C₃₁	—	4	2	no	—
390	#41×C₃₁	—	4	1	no	—
391	#41×C₃₁	—	4	1	no	—
392	#41×C₃₁	—	4	2	no	—
393	#41×C₃₁	—	4	1	no	—
394	#41×C₃₁	—	4	1	no	—
395	#41×C₃₁	—	4	4	no	—
396	#41×C₃₁	—	4	4	no	—
397	#41×C₃₁	—	4	4	no	—
398	#41×C₃₁	—	4	4	no	—
399	#41×C₃₁	C₂×D₄	1	4	yes	—
400	C₂×Q₈×C₃₁	—	2	1	no	—
401	C₂×Q₈×C₃₁	—	2	2	no	—
402	C₂×Q₈×C₃₁	—	2	2	no	—
403	C₂×Q₈×C₃₁	—	2	1	no	—
404	C₂×Q₈×C₃₁	—	2	1	no	—
405	C₂×Q₈×C₃₁	—	2	1	no	—
406	C₂×Q₈×C₃₁	—	2	2	no	—
407	C₂×Q₈×C₃₁	—	2	4	no	—
408	C₂×Q₈×C₃₁	—	2	2	no	—
409	C₂×Q₈×C₃₁	—	2	4	no	—
410	C₂×Q₈×C₃₁	—	2	2	no	—
411	C₂×Q₈×C₃₁	—	2	2	no	—
412	C₂×Q₈×C₃₁	—	2	2	no	—
413	C₂×Q₈×C₃₁	—	4	4	no	—
414	C₂×Q₈×C₃₁	—	4	2	no	—
415	C₂×Q₈×C₃₁	—	4	2	no	—
416	C₂×Q₈×C₃₁	—	4	1	no	—
417	C₂×Q₈×C₃₁	—	4	1	no	—
418	C₂×Q₈×C₃₁	—	4	4	no	—
419	C₂×Q₈×C₃₁	—	4	4	no	—
420	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	complemented
421	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
422	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
425	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
426	C₂×D₄×C₃₁	—	2	1	no	—
427	C₂×D₄×C₃₁	—	2	2	no	—
428	C₂×D₄×C₃₁	—	2	2	no	—
429	C₂×D₄×C₃₁	—	2	1	no	—
430	C₂×D₄×C₃₁	—	2	1	no	—
431	C₂×D₄×C₃₁	—	2	2	no	—
432	C₂×D₄×C₃₁	—	2	2	no	—
433	C₂×D₄×C₃₁	—	2	1	no	—
434	C₂×D₄×C₃₁	—	2	1	no	—
435	C₂×D₄×C₃₁	—	2	1	no	—
436	C₂×D₄×C₃₁	—	2	1	no	—
437	C₂×D₄×C₃₁	—	2	2	no	—
438	C₂×D₄×C₃₁	—	2	2	no	—
439	C₂×D₄×C₃₁	—	2	1	no	—
440	C₂×D₄×C₃₁	—	2	1	no	—
441	C₂×D₄×C₃₁	—	2	1	no	—
442	C₂×D₄×C₃₁	—	2	1	no	—
443	C₂×D₄×C₃₁	—	2	2	no	—
444	C₂×D₄×C₃₁	—	2	1	no	—
445	C₂×D₄×C₃₁	—	2	1	no	—
446	C₂×D₄×C₃₁	—	2	1	no	—
447	C₂×D₄×C₃₁	—	2	1	no	—
448	C₂×D₄×C₃₁	—	2	1	no	—
449	C₂×D₄×C₃₁	—	2	2	no	—
450	C₂×D₄×C₃₁	—	4	1	no	—
451	C₂×D₄×C₃₁	—	4	1	no	—
452	C₂×D₄×C₃₁	—	4	4	no	—
453	C₂×D₄×C₃₁	—	4	2	no	—
454	C₂×D₄×C₃₁	—	4	4	no	—
455	C₂×D₄×C₃₁	—	4	4	no	—
456	C₂×D₄×C₃₁	—	4	4	no	—
457	C₂×D₄×C₃₁	—	4	4	no	—
458	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
459	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
460	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
461	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
462	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
463	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
464	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
465	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
466	C₂²×C₄×C₃₁	—	2	1	no	—
467	C₂²×C₄×C₃₁	—	2	1	no	—
468	C₂²×C₄×C₃₁	—	2	2	no	—
469	C₂²×C₄×C₃₁	—	2	2	no	—
470	C₂²×C₄×C₃₁	—	2	2	no	—
471	C₂²×C₄×C₃₁	—	2	2	no	—
472	C₂²×C₄×C₃₁	—	2	1	no	—
473	C₂²×C₄×C₃₁	—	2	1	no	—
474	C₂²×C₄×C₃₁	—	2	2	no	—
475	C₂²×C₄×C₃₁	—	2	2	no	—
476	C₂²×C₄×C₃₁	—	2	1	no	—
477	C₂²×C₄×C₃₁	—	2	1	no	—
478	C₂²×C₄×C₃₁	—	2	1	no	—
479	C₂²×C₄×C₃₁	—	2	1	no	—
480	C₂²×C₄×C₃₁	—	2	1	no	—
481	C₂²×C₄×C₃₁	—	2	1	no	—
482	C₂²×C₄×C₃₁	—	2	1	no	—
483	C₂²×C₄×C₃₁	—	2	1	no	—
484	C₂²×C₄×C₃₁	—	2	1	no	—
485	C₂²×C₄×C₃₁	—	2	2	no	—
486	C₂²×C₄×C₃₁	—	2	2	no	—
487	C₂²×C₄×C₃₁	—	2	1	no	—
488	C₂²×C₄×C₃₁	—	4	4	no	—
489	C₂²×C₄×C₃₁	—	4	4	no	—
490	C₂²×C₄×C₃₁	—	4	4	no	—
491	C₂²×C₄×C₃₁	—	4	4	no	—
492	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
493	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
494	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
495	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
496	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
497	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
498	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
499	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
500	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
501	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
502	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
503	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
504	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
505	Q₁₆×C₃₁	—	2	4	no	—
506	Q₁₆×C₃₁	—	2	4	no	—
507	Q₁₆×C₃₁	—	2	4	no	—
508	Q₁₆×C₃₁	—	2	4	no	—
509	Q₁₆×C₃₁	—	4	2	no	—
510	Q₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
511	SD₁₆×C₃₁	—	2	4	no	—
512	SD₁₆×C₃₁	—	2	4	no	—
513	SD₁₆×C₃₁	—	2	4	no	—
514	SD₁₆×C₃₁	—	2	4	no	—
515	SD₁₆×C₃₁	—	2	4	no	—
516	SD₁₆×C₃₁	—	2	4	no	—
517	SD₁₆×C₃₁	—	4	2	no	—
518	SD₁₆×C₃₁	—	4	2	no	—
519	SD₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
520	D₈×C₃₁	—	2	4	no	—
521	D₈×C₃₁	—	2	4	no	—
522	D₈×C₃₁	—	4	2	no	—
523	M₁₆×C₃₁	—	2	2	no	—
524	M₁₆×C₃₁	—	2	2	no	—
525	M₁₆×C₃₁	—	2	2	no	—
526	M₁₆×C₃₁	—	2	4	no	—
527	M₁₆×C₃₁	—	2	4	no	—
528	M₁₆×C₃₁	C₂×D₄	1	4	yes	complemented
529	C₂×C₈×C₃₁	—	2	4	no	—
530	C₂×C₈×C₃₁	—	2	4	no	—
531	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
532	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
533	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
534	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
535	C₄⋊C₄×C₃₁	—	2	1	no	—
536	C₄⋊C₄×C₃₁	—	2	2	no	—
537	C₄⋊C₄×C₃₁	—	2	2	no	—
538	C₄⋊C₄×C₃₁	—	2	1	no	—
539	C₄⋊C₄×C₃₁	—	2	1	no	—
540	C₄⋊C₄×C₃₁	—	2	2	no	—
541	C₄⋊C₄×C₃₁	—	2	2	no	—
542	C₄⋊C₄×C₃₁	—	2	1	no	—
543	C₄⋊C₄×C₃₁	—	2	1	no	—
544	C₄⋊C₄×C₃₁	—	2	1	no	—
545	C₄⋊C₄×C₃₁	—	2	1	no	—
546	C₄⋊C₄×C₃₁	—	2	1	no	—
547	C₄⋊C₄×C₃₁	—	2	1	no	—
548	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
549	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
550	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
551	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
552	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
553	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
554	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
555	C₂²⋊C₄×C₃₁	—	2	1	no	—
556	C₂²⋊C₄×C₃₁	—	2	1	no	—
557	C₂²⋊C₄×C₃₁	—	2	2	no	—
558	C₂²⋊C₄×C₃₁	—	2	2	no	—
559	C₂²⋊C₄×C₃₁	—	2	1	no	—
560	C₂²⋊C₄×C₃₁	—	2	1	no	—
561	C₂²⋊C₄×C₃₁	—	2	1	no	—
562	C₂²⋊C₄×C₃₁	—	2	1	no	—
563	C₂²⋊C₄×C₃₁	—	2	1	no	—
564	C₂²⋊C₄×C₃₁	—	2	1	no	—
565	C₂²⋊C₄×C₃₁	—	2	1	no	—
566	C₂²⋊C₄×C₃₁	—	2	2	no	—
567	C₂²⋊C₄×C₃₁	—	2	2	no	—
568	C₂²⋊C₄×C₃₁	—	2	2	no	—
569	C₂²⋊C₄×C₃₁	—	2	2	no	—
570	C₂²⋊C₄×C₃₁	—	2	2	no	—
571	C₂²⋊C₄×C₃₁	—	2	2	no	—
572	C₂²⋊C₄×C₃₁	—	2	1	no	—
573	C₂²⋊C₄×C₃₁	—	2	1	no	—
574	C₂²⋊C₄×C₃₁	—	2	1	no	—
575	C₂²⋊C₄×C₃₁	—	2	1	no	—
576	C₂²⋊C₄×C₃₁	—	2	1	no	—
577	C₂²⋊C₄×C₃₁	—	2	1	no	—
578	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
579	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
580	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
581	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
582	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
583	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
584	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
585	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
586	C₄²×C₃₁	—	2	1	no	—
587	C₄²×C₃₁	—	2	1	no	—
588	C₄²×C₃₁	—	2	1	no	—
589	C₄²×C₃₁	—	2	2	no	—
590	C₄²×C₃₁	—	2	2	no	—
591	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
592	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
593	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
594	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
595	#61068	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
596	C₂³×C₃₁	—	2	2	no	—
597	C₂³×C₃₁	—	2	2	no	—
598	C₂³×C₃₁	—	2	1	no	—
599	C₂³×C₃₁	—	2	2	no	—
600	C₂³×C₃₁	—	2	2	no	—
601	C₂³×C₃₁	—	2	1	no	—
602	C₂³×C₃₁	—	2	1	no	—
603	C₂³×C₃₁	—	4	1	no	—
604	C₂³×C₃₁	—	4	1	no	—
605	C₂³×C₃₁	—	4	1	no	—
606	C₂³×C₃₁	—	4	2	no	—
607	C₂³×C₃₁	—	4	2	no	—
608	C₂³×C₃₁	—	4	2	no	—
609	C₂³×C₃₁	—	4	2	no	—
610	C₂³×C₃₁	—	4	2	no	—
611	C₂³×C₃₁	—	4	2	no	—
612	C₂³×C₃₁	—	4	2	no	—
613	C₂³×C₃₁	—	8	1	no	—
614	C₂³×C₃₁	—	8	1	no	—
615	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
616	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
617	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
618	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
619	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
620	Q₈×C₃₁	—	2	4	no	—
621	Q₈×C₃₁	—	2	2	no	—
622	Q₈×C₃₁	—	2	1	no	—
623	Q₈×C₃₁	—	2	2	no	—
624	Q₈×C₃₁	—	2	1	no	—
625	Q₈×C₃₁	—	2	1	no	—
626	Q₈×C₃₁	—	2	1	no	—
627	Q₈×C₃₁	—	2	2	no	—
628	Q₈×C₃₁	—	2	1	no	—
629	Q₈×C₃₁	—	4	4	no	—
630	Q₈×C₃₁	—	4	4	no	—
631	Q₈×C₃₁	—	4	2	no	—
632	Q₈×C₃₁	—	4	2	no	—
633	Q₈×C₃₁	—	4	2	no	—
634	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
635	Q₈×C₃₁	C₂²×D₄	1	2	yes	—
636	D₄×C₃₁	—	2	4	no	—
637	D₄×C₃₁	—	2	2	no	—
638	D₄×C₃₁	—	2	2	no	—
639	D₄×C₃₁	—	2	2	no	—
640	D₄×C₃₁	—	2	1	no	—
641	D₄×C₃₁	—	2	1	no	—
642	D₄×C₃₁	—	2	1	no	—
643	D₄×C₃₁	—	2	1	no	—
644	D₄×C₃₁	—	2	2	no	—
645	D₄×C₃₁	—	2	1	no	—
646	D₄×C₃₁	—	4	1	no	—
647	D₄×C₃₁	—	4	1	no	—
648	D₄×C₃₁	—	4	2	no	—
649	D₄×C₃₁	—	4	2	no	—
650	D₄×C₃₁	—	4	2	no	—
651	D₄×C₃₁	—	4	2	no	—
652	D₄×C₃₁	—	4	4	no	—
653	D₄×C₃₁	—	4	4	no	—
654	D₄×C₃₁	—	4	2	no	—
655	D₄×C₃₁	—	4	2	no	—
656	D₄×C₃₁	—	4	2	no	—
657	D₄×C₃₁	—	4	2	no	—
658	D₄×C₃₁	—	4	4	no	—
659	D₄×C₃₁	—	4	2	no	—
660	D₄×C₃₁	—	4	2	no	—
661	D₄×C₃₁	—	4	2	no	—
662	D₄×C₃₁	—	4	4	no	—
663	D₄×C₃₁	—	4	2	no	—
664	D₄×C₃₁	—	8	1	no	—
665	D₄×C₃₁	—	8	1	no	—
666	D₄×C₃₁	—	8	1	no	—
667	D₄×C₃₁	C₂²×D₄	1	2	yes	—
668	C₂×C₄×C₃₁	—	2	2	no	—
669	C₂×C₄×C₃₁	—	2	2	no	—
670	C₂×C₄×C₃₁	—	2	4	no	—
671	C₂×C₄×C₃₁	—	2	1	no	—
672	C₂×C₄×C₃₁	—	2	2	no	—
673	C₂×C₄×C₃₁	—	2	2	no	—
674	C₂×C₄×C₃₁	—	2	2	no	—
675	C₂×C₄×C₃₁	—	2	2	no	—
676	C₂×C₄×C₃₁	—	2	2	no	—
677	C₂×C₄×C₃₁	—	2	4	no	—
678	C₂×C₄×C₃₁	—	2	1	no	—
679	C₂×C₄×C₃₁	—	2	1	no	—
680	C₂×C₄×C₃₁	—	2	1	no	—
681	C₂×C₄×C₃₁	—	2	1	no	—
682	C₂×C₄×C₃₁	—	2	1	no	—
683	C₂×C₄×C₃₁	—	2	1	no	—
684	C₂×C₄×C₃₁	—	2	1	no	—
685	C₂×C₄×C₃₁	—	2	1	no	—
686	C₂×C₄×C₃₁	—	2	1	no	—
687	C₂×C₄×C₃₁	—	2	1	no	—
688	C₂×C₄×C₃₁	—	2	2	no	—
689	C₂×C₄×C₃₁	—	2	2	no	—
690	C₂×C₄×C₃₁	—	2	1	no	—
691	C₂×C₄×C₃₁	—	2	1	no	—
692	C₂×C₄×C₃₁	—	4	1	no	—
693	C₂×C₄×C₃₁	—	4	1	no	—
694	C₂×C₄×C₃₁	—	4	2	no	—
695	C₂×C₄×C₃₁	—	4	4	no	—
696	C₂×C₄×C₃₁	—	4	4	no	—
697	C₂×C₄×C₃₁	—	4	2	no	—
698	C₂×C₄×C₃₁	—	4	2	no	—
699	C₂×C₄×C₃₁	—	4	2	no	—
700	C₂×C₄×C₃₁	—	4	4	no	—
701	C₂×C₄×C₃₁	—	4	4	no	—
702	C₂×C₄×C₃₁	—	4	2	no	—
703	C₂×C₄×C₃₁	—	4	2	no	—
704	C₂×C₄×C₃₁	—	4	2	no	—
705	C₂×C₄×C₃₁	—	4	2	no	—
706	C₂×C₄×C₃₁	—	4	2	no	—
707	C₂×C₄×C₃₁	—	4	2	no	—
708	C₂×C₄×C₃₁	—	4	2	no	—
709	C₂×C₄×C₃₁	—	8	1	no	—
710	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
711	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
712	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
713	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
714	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
715	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
716	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
717	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
718	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
719	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
720	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
721	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
722	C₈×C₃₁	—	2	2	no	—
723	C₈×C₃₁	—	2	2	no	—
724	C₈×C₃₁	—	2	2	no	—
725	C₈×C₃₁	C₂²×D₄	1	4	yes	—
726	C₂×#575	C₂×C₃₁	1	1	yes	characteristic, complemented
727	C₂²×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
728	D₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
729	C₂×#548	C₂×C₃₁	1	1	yes	characteristic, complemented
730	#3285	C₂×C₃₁	1	2	yes	complemented
731	#3282	C₂×C₃₁	1	2	yes	complemented
732	#3277	C₂×C₃₁	1	2	yes	complemented
733	#3275	C₂×C₃₁	1	2	yes	complemented
734	#3271	C₂×C₃₁	1	2	yes	complemented
735	#3270	C₂×C₃₁	1	2	yes	complemented
736	#3269	C₂×C₃₁	1	2	yes	complemented
737	#3265	C₂×C₃₁	1	2	yes	complemented
738	#3153	C₂×C₃₁	1	1	yes	characteristic, complemented
739	#3056	C₂×C₃₁	1	1	yes	characteristic, complemented
740	#3055	C₂×C₃₁	1	1	yes	characteristic, complemented
741	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
742	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
743	#3007	C₂×C₃₁	1	1	yes	characteristic, complemented
744	#3006	C₂×C₃₁	1	1	yes	characteristic, complemented
745	#3005	C₂×C₃₁	1	1	yes	characteristic, complemented
746	#3004	C₂×C₃₁	1	1	yes	characteristic, complemented
747	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
748	D₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
749	C₂²×C₃₁	—	2	1	no	—
750	C₂²×C₃₁	—	2	1	no	—
751	C₂²×C₃₁	—	2	1	no	—
752	C₂²×C₃₁	—	2	1	no	—
753	C₂²×C₃₁	—	2	1	no	—
754	C₂²×C₃₁	—	2	1	no	—
755	C₂²×C₃₁	—	2	1	no	—
756	C₂²×C₃₁	—	2	1	no	—
757	C₂²×C₃₁	—	2	1	no	—
758	C₂²×C₃₁	—	2	1	no	—
759	C₂²×C₃₁	—	2	2	no	—
760	C₂²×C₃₁	—	2	1	no	—
761	C₂²×C₃₁	—	2	1	no	—
762	C₂²×C₃₁	—	2	1	no	—
763	C₂²×C₃₁	—	4	4	no	—
764	C₂²×C₃₁	—	4	1	no	—
765	C₂²×C₃₁	—	4	1	no	—
766	C₂²×C₃₁	—	4	1	no	—
767	C₂²×C₃₁	—	4	1	no	—
768	C₂²×C₃₁	—	4	2	no	—
769	C₂²×C₃₁	—	4	2	no	—
770	C₂²×C₃₁	—	4	1	no	—
771	C₂²×C₃₁	—	4	1	no	—
772	C₂²×C₃₁	—	4	1	no	—
773	C₂²×C₃₁	—	4	1	no	—
774	C₂²×C₃₁	—	4	2	no	—
775	C₂²×C₃₁	—	8	2	no	—
776	C₂²×C₃₁	—	8	4	no	—
777	C₂²×C₃₁	—	8	4	no	—
778	C₂²×C₃₁	—	8	4	no	—
779	C₂²×C₃₁	D₄²	1	2	yes	—
780	C₂²×C₃₁	#575	1	2	yes	complemented
781	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
782	C₄×C₃₁	—	2	1	no	—
783	C₄×C₃₁	—	2	1	no	—
784	C₄×C₃₁	—	2	1	no	—
785	C₄×C₃₁	—	2	1	no	—
786	C₄×C₃₁	—	2	1	no	—
787	C₄×C₃₁	—	2	1	no	—
788	C₄×C₃₁	—	2	2	no	—
789	C₄×C₃₁	—	2	4	no	—
790	C₄×C₃₁	—	2	1	no	—
791	C₄×C₃₁	—	2	1	no	—
792	C₄×C₃₁	—	4	1	no	—
793	C₄×C₃₁	—	4	1	no	—
794	C₄×C₃₁	—	4	1	no	—
795	C₄×C₃₁	—	4	2	no	—
796	C₄×C₃₁	—	4	1	no	—
797	C₄×C₃₁	—	4	2	no	—
798	C₄×C₃₁	D₄²	1	2	yes	—
799	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
800	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
801	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
802	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
803	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
804	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
805	#575	—	2	8	no	—
806	C₂×#137	—	2	8	no	—
807	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
808	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
809	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
810	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
811	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
812	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
813	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
814	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
815	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
816	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
817	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
818	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
819	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
820	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
821	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
822	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
823	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
824	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
825	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
826	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
827	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
828	#548	—	2	1	no	—
829	#548	—	2	1	no	—
830	#548	—	2	1	no	—
831	#548	—	2	1	no	—
832	#548	C₂²×C₃₁	1	2	yes	—
833	#548	C₂²×C₃₁	1	2	yes	complemented
834	#548	C₂²×C₃₁	1	2	yes	complemented
835	#548	C₂²×C₃₁	1	2	yes	complemented
836	#548	C₂²×C₃₁	1	1	yes	characteristic, complemented
837	#548	C₂²×C₃₁	1	1	yes	characteristic, complemented
838	#547	—	2	1	no	—
839	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
840	#546	—	2	1	no	—
841	#546	—	2	1	no	—
842	#546	C₂²×C₃₁	1	1	yes	characteristic, complemented
843	#546	C₂²×C₃₁	1	1	yes	characteristic, complemented
844	D₄²	—	2	1	no	—
845	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
846	#532	—	2	1	no	—
847	#532	C₂²×C₃₁	1	1	yes	characteristic
848	C₂×#124	—	2	1	no	—
849	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
850	#525	—	2	1	no	—
851	#525	—	2	1	no	—
852	#525	C₂²×C₃₁	1	1	yes	characteristic
853	#525	C₂²×C₃₁	1	1	yes	characteristic
854	C₂×C₂²⋊Q₈	—	2	1	no	—
855	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
856	C₂×#121	—	2	1	no	—
857	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
858	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
859	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
860	C₂×C₄×D₄	—	2	1	no	—
861	C₂×C₄×D₄	—	2	1	no	—
862	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
863	#497	C₂²×C₃₁	1	2	yes	complemented
864	#496	C₂²×C₃₁	1	2	yes	complemented
865	#495	C₂²×C₃₁	1	2	yes	complemented
866	#495	C₂²×C₃₁	1	2	yes	complemented
867	#470	C₂²×C₃₁	1	2	yes	complemented
868	#469	C₂²×C₃₁	1	2	yes	complemented
869	#468	C₂²×C₃₁	1	2	yes	complemented
870	#468	C₂²×C₃₁	1	2	yes	complemented
871	#467	C₂²×C₃₁	1	2	yes	complemented
872	#466	C₂²×C₃₁	1	2	yes	complemented
873	#465	C₂²×C₃₁	1	2	yes	complemented
874	#465	C₂²×C₃₁	1	2	yes	complemented
875	#464	C₂²×C₃₁	1	2	yes	complemented
876	#464	C₂²×C₃₁	1	2	yes	complemented
877	#464	C₂²×C₃₁	1	2	yes	complemented
878	#464	C₂²×C₃₁	1	2	yes	complemented
879	#463	C₂²×C₃₁	1	2	yes	complemented
880	#463	C₂²×C₃₁	1	2	yes	complemented
881	#462	C₂²×C₃₁	1	2	yes	complemented
882	#460	C₂²×C₃₁	1	2	yes	complemented
883	#452	C₂²×C₃₁	1	2	yes	complemented
884	#452	C₂²×C₃₁	1	2	yes	complemented
885	#452	C₂²×C₃₁	1	2	yes	complemented
886	#452	C₂²×C₃₁	1	2	yes	complemented
887	#451	C₂²×C₃₁	1	2	yes	complemented
888	#451	C₂²×C₃₁	1	2	yes	complemented
889	#451	C₂²×C₃₁	1	2	yes	complemented
890	#450	C₂²×C₃₁	1	2	yes	complemented
891	#449	C₂²×C₃₁	1	2	yes	complemented
892	#449	C₂²×C₃₁	1	2	yes	complemented
893	#449	C₂²×C₃₁	1	2	yes	complemented
894	#449	C₂²×C₃₁	1	2	yes	complemented
895	#448	C₂²×C₃₁	1	2	yes	complemented
896	#448	C₂²×C₃₁	1	2	yes	complemented
897	#448	C₂²×C₃₁	1	2	yes	complemented
898	#447	C₂²×C₃₁	1	2	yes	complemented
899	#441	C₂²×C₃₁	1	2	yes	complemented
900	#440	C₂²×C₃₁	1	2	yes	complemented
901	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
902	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
903	#436	C₂²×C₃₁	1	2	yes	complemented
904	#435	C₂²×C₃₁	1	2	yes	complemented
905	#435	C₂²×C₃₁	1	2	yes	complemented
906	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
907	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
908	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
909	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
910	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
911	#418	C₂²×C₃₁	1	1	yes	characteristic, complemented
912	#417	C₂²×C₃₁	1	1	yes	characteristic
913	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
914	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
915	#407	C₂²×C₃₁	1	1	yes	characteristic, complemented
916	#407	C₂²×C₃₁	1	1	yes	characteristic, complemented
917	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
918	C₂×C₃₁	—	2	2	no	—
919	C₂×C₃₁	—	2	2	no	—
920	C₂×C₃₁	—	4	1	no	—
921	C₂×C₃₁	—	4	1	no	—
922	C₂×C₃₁	—	4	1	no	—
923	C₂×C₃₁	—	4	2	no	—
924	C₂×C₃₁	—	8	1	no	—
925	C₂×C₃₁	—	8	1	no	—
926	C₂×C₃₁	—	8	2	no	—
927	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
928	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
929	C₂×C₃₁	#3586	1	1	yes	characteristic
930	C₂×#41	—	2	1	no	—
931	C₂×#41	—	2	1	no	—
932	C₂×#41	—	2	1	no	—
933	C₂×#41	—	2	1	no	—
934	C₂×#41	—	2	1	no	—
935	C₂×#41	—	2	1	no	—
936	C₂×#41	—	2	4	no	—
937	C₂×#41	—	2	4	no	—
938	C₂×#41	—	2	4	no	—
939	C₂×#41	—	4	2	no	—
940	C₂×#41	—	4	2	no	—
941	C₂×#41	—	4	2	no	—
942	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
943	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
944	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
945	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
946	C₂×#41	C₂³×C₃₁	1	2	yes	—
947	C₂×#41	C₂³×C₃₁	1	2	yes	—
948	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
949	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
950	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
951	C₂²×Q₈	—	2	1	no	—
952	C₂²×Q₈	—	2	1	no	—
953	C₂²×Q₈	—	2	1	no	—
954	C₂²×Q₈	—	2	4	no	—
955	C₂²×Q₈	—	4	2	no	—
956	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
957	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
958	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
959	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
960	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
961	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
962	C₂²×D₄	—	2	1	no	—
963	C₂²×D₄	—	2	1	no	—
964	C₂²×D₄	—	2	1	no	—
965	C₂²×D₄	—	2	1	no	—
966	C₂²×D₄	—	2	1	no	—
967	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
968	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
969	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
970	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
971	C₂³×C₄	—	2	1	no	—
972	C₂³×C₄	—	2	1	no	—
973	C₂³×C₄	—	2	1	no	—
974	C₂³×C₄	—	2	1	no	—
975	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
976	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
977	#137	—	2	4	no	—
978	#137	—	2	4	no	—
979	#137	—	2	4	no	—
980	#137	—	2	8	no	—
981	#137	—	2	8	no	—
982	#137	—	2	8	no	—
983	#137	—	2	4	no	—
984	#137	—	4	2	no	—
985	#137	D₄×C₃₁	1	8	yes	complemented
986	AGL(1,ℤ/8)	—	2	4	no	—
987	AGL(1,ℤ/8)	—	2	8	no	—
988	AGL(1,ℤ/8)	—	2	4	no	—
989	AGL(1,ℤ/8)	—	4	2	no	—
990	#135	—	2	8	no	—
991	#135	—	2	8	no	—
992	C₂×Q₁₆	—	2	8	no	—
993	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
994	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
995	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
996	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
997	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
998	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
999	C₂×SD₁₆	—	2	8	no	—
1000	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
1001	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
1002	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
1003	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
1004	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
1005	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
1006	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
1007	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
1008	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
1009	C₂×D₈	C₂³×C₃₁	1	2	yes	—
1010	C₂×D₈	C₂³×C₃₁	1	2	yes	—
1011	C₂×D₈	C₂³×C₃₁	1	2	yes	—
1012	C₂×M₁₆	—	2	4	no	—
1013	C₂×M₁₆	—	2	4	no	—
1014	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1015	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
1016	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1017	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
1018	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1019	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
1020	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
1021	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
1022	C₄⋊Q₈	—	2	1	no	—
1023	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1024	#127	—	2	1	no	—
1025	#127	C₂³×C₃₁	1	1	yes	characteristic
1026	#124	—	2	2	no	—
1027	#124	—	2	2	no	—
1028	#124	—	2	2	no	—
1029	#124	—	2	2	no	—
1030	#124	—	2	1	no	—
1031	#124	—	2	1	no	—
1032	#124	—	2	1	no	—
1033	#124	—	2	1	no	—
1034	#124	C₂³×C₃₁	1	2	yes	—
1035	#124	C₂³×C₃₁	1	2	yes	—
1036	#124	C₂³×C₃₁	1	1	yes	characteristic
1037	#124	C₂³×C₃₁	1	1	yes	characteristic
1038	#123	—	2	1	no	—
1039	#123	—	2	1	no	—
1040	#123	—	2	1	no	—
1041	#123	—	2	1	no	—
1042	#123	—	2	1	no	—
1043	#123	—	2	1	no	—
1044	C₂²⋊Q₈	—	2	1	no	—
1045	C₂²⋊Q₈	—	2	1	no	—
1046	C₂²⋊Q₈	—	2	2	no	—
1047	C₂²⋊Q₈	—	2	2	no	—
1048	C₂²⋊Q₈	—	2	2	no	—
1049	C₂²⋊Q₈	—	2	2	no	—
1050	C₂²⋊Q₈	—	2	1	no	—
1051	C₂²⋊Q₈	—	2	1	no	—
1052	C₂²⋊Q₈	—	2	1	no	—
1053	C₂²⋊Q₈	—	2	1	no	—
1054	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
1055	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
1056	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1057	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1058	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1059	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
1060	#121	—	2	2	no	—
1061	#121	—	2	2	no	—
1062	#121	—	2	2	no	—
1063	#121	—	2	2	no	—
1064	#121	—	2	1	no	—
1065	#121	—	2	1	no	—
1066	#121	—	2	1	no	—
1067	#121	—	2	1	no	—
1068	#121	—	2	1	no	—
1069	#121	—	2	1	no	—
1070	#121	—	2	1	no	—
1071	#121	—	2	1	no	—
1072	#121	—	2	1	no	—
1073	#121	—	2	1	no	—
1074	#121	—	2	1	no	—
1075	#121	—	2	1	no	—
1076	#121	C₂³×C₃₁	1	2	yes	—
1077	#121	C₂³×C₃₁	1	2	yes	—
1078	#121	C₂³×C₃₁	1	1	yes	characteristic
1079	#121	C₂³×C₃₁	1	1	yes	characteristic
1080	#121	C₂³×C₃₁	1	1	yes	characteristic
1081	#121	C₂³×C₃₁	1	1	yes	characteristic
1082	#120	—	2	1	no	—
1083	#120	—	2	1	no	—
1084	#120	—	2	1	no	—
1085	#120	—	2	1	no	—
1086	#120	—	2	1	no	—
1087	#120	—	2	1	no	—
1088	C₄×Q₈	—	2	1	no	—
1089	C₄×Q₈	—	2	1	no	—
1090	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
1091	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
1092	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1093	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
1094	C₄×D₄	—	2	1	no	—
1095	C₄×D₄	—	2	1	no	—
1096	C₄×D₄	—	2	1	no	—
1097	C₄×D₄	—	2	1	no	—
1098	C₄×D₄	—	2	1	no	—
1099	C₄×D₄	—	2	1	no	—
1100	C₄×D₄	—	2	1	no	—
1101	C₄×D₄	—	2	1	no	—
1102	C₄×D₄	—	2	1	no	—
1103	C₄×D₄	—	2	1	no	—
1104	C₄×D₄	—	2	2	no	—
1105	C₄×D₄	—	2	2	no	—
1106	C₄×D₄	—	2	2	no	—
1107	C₄×D₄	—	2	2	no	—
1108	C₄×D₄	—	2	1	no	—
1109	C₄×D₄	—	2	1	no	—
1110	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
1111	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
1112	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
1113	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
1114	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1115	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1116	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1117	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1118	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1119	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
1120	#117	—	2	1	no	—
1121	#117	C₂³×C₃₁	1	1	yes	characteristic
1122	C₂×C₄⋊C₄	—	2	1	no	—
1123	C₂×C₄⋊C₄	—	2	1	no	—
1124	C₂×C₄⋊C₄	—	2	1	no	—
1125	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
1126	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1127	C₂×C₂²⋊C₄	—	2	1	no	—
1128	C₂×C₂²⋊C₄	—	2	1	no	—
1129	C₂×C₂²⋊C₄	—	2	1	no	—
1130	C₂×C₂²⋊C₄	—	2	1	no	—
1131	C₂×C₂²⋊C₄	—	2	1	no	—
1132	C₂×C₂²⋊C₄	—	2	1	no	—
1133	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
1134	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
1135	C₂×C₄²	—	2	1	no	—
1136	C₂×C₄²	—	2	1	no	—
1137	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
1138	#107	C₂³×C₃₁	1	2	yes	—
1139	#106	C₂³×C₃₁	1	2	yes	—
1140	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
1141	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
1142	#103	C₂³×C₃₁	1	2	yes	—
1143	#103	C₂³×C₃₁	1	2	yes	—
1144	#103	C₂³×C₃₁	1	2	yes	—
1145	#103	C₂³×C₃₁	1	2	yes	—
1146	#103	C₂³×C₃₁	1	2	yes	—
1147	#103	C₂³×C₃₁	1	2	yes	—
1148	#103	C₂³×C₃₁	1	2	yes	—
1149	#102	C₂³×C₃₁	1	2	yes	—
1150	#102	C₂³×C₃₁	1	2	yes	—
1151	#102	C₂³×C₃₁	1	2	yes	—
1152	#102	C₂³×C₃₁	1	2	yes	—
1153	#102	C₂³×C₃₁	1	2	yes	—
1154	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1155	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1156	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1157	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1158	#97	C₂³×C₃₁	1	2	yes	—
1159	C₄×C₈	C₂³×C₃₁	1	2	yes	—
1160	C₃₁	#61068	1	1	yes	characteristic, direct product factor, Sylow
1161	C₂⁴	—	2	1	no	—
1162	C₂⁴	—	2	1	no	—
1163	C₂⁴	—	2	1	no	—
1164	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
1165	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
1166	#41	—	2	2	no	—
1167	#41	—	2	4	no	—
1168	#41	—	2	2	no	—
1169	#41	—	2	4	no	—
1170	#41	—	2	2	no	—
1171	#41	—	2	2	no	—
1172	#41	—	2	2	no	—
1173	#41	—	2	2	no	—
1174	#41	—	2	2	no	—
1175	#41	—	2	2	no	—
1176	#41	—	2	2	no	—
1177	#41	—	4	4	no	—
1178	#41	—	4	4	no	—
1179	#41	—	4	2	no	—
1180	#41	—	4	1	no	—
1181	#41	—	4	1	no	—
1182	#41	—	4	2	no	—
1183	#41	—	4	1	no	—
1184	#41	—	4	1	no	—
1185	#41	—	4	4	no	—
1186	#41	—	4	4	no	—
1187	#41	—	4	4	no	—
1188	#41	—	4	4	no	—
1189	#41	C₂×D₄×C₃₁	1	4	yes	—
1190	C₂×Q₈	—	2	1	no	—
1191	C₂×Q₈	—	2	2	no	—
1192	C₂×Q₈	—	2	2	no	—
1193	C₂×Q₈	—	2	1	no	—
1194	C₂×Q₈	—	2	1	no	—
1195	C₂×Q₈	—	2	1	no	—
1196	C₂×Q₈	—	2	2	no	—
1197	C₂×Q₈	—	2	4	no	—
1198	C₂×Q₈	—	2	2	no	—
1199	C₂×Q₈	—	2	4	no	—
1200	C₂×Q₈	—	2	2	no	—
1201	C₂×Q₈	—	2	2	no	—
1202	C₂×Q₈	—	2	2	no	—
1203	C₂×Q₈	—	4	4	no	—
1204	C₂×Q₈	—	4	2	no	—
1205	C₂×Q₈	—	4	2	no	—
1206	C₂×Q₈	—	4	1	no	—
1207	C₂×Q₈	—	4	1	no	—
1208	C₂×Q₈	—	4	4	no	—
1209	C₂×Q₈	—	4	4	no	—
1210	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	complemented
1211	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1212	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1213	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1214	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1215	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1216	C₂×D₄	—	2	1	no	—
1217	C₂×D₄	—	2	2	no	—
1218	C₂×D₄	—	2	2	no	—
1219	C₂×D₄	—	2	1	no	—
1220	C₂×D₄	—	2	1	no	—
1221	C₂×D₄	—	2	2	no	—
1222	C₂×D₄	—	2	2	no	—
1223	C₂×D₄	—	2	1	no	—
1224	C₂×D₄	—	2	1	no	—
1225	C₂×D₄	—	2	1	no	—
1226	C₂×D₄	—	2	1	no	—
1227	C₂×D₄	—	2	2	no	—
1228	C₂×D₄	—	2	2	no	—
1229	C₂×D₄	—	2	1	no	—
1230	C₂×D₄	—	2	1	no	—
1231	C₂×D₄	—	2	1	no	—
1232	C₂×D₄	—	2	1	no	—
1233	C₂×D₄	—	2	2	no	—
1234	C₂×D₄	—	2	1	no	—
1235	C₂×D₄	—	2	1	no	—
1236	C₂×D₄	—	2	1	no	—
1237	C₂×D₄	—	2	1	no	—
1238	C₂×D₄	—	2	1	no	—
1239	C₂×D₄	—	2	2	no	—
1240	C₂×D₄	—	4	1	no	—
1241	C₂×D₄	—	4	1	no	—
1242	C₂×D₄	—	4	4	no	—
1243	C₂×D₄	—	4	2	no	—
1244	C₂×D₄	—	4	4	no	—
1245	C₂×D₄	—	4	4	no	—
1246	C₂×D₄	—	4	4	no	—
1247	C₂×D₄	—	4	4	no	—
1248	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1249	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1250	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1251	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1252	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1253	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1254	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1255	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1256	C₂²×C₄	—	2	1	no	—
1257	C₂²×C₄	—	2	1	no	—
1258	C₂²×C₄	—	2	2	no	—
1259	C₂²×C₄	—	2	2	no	—
1260	C₂²×C₄	—	2	2	no	—
1261	C₂²×C₄	—	2	2	no	—
1262	C₂²×C₄	—	2	1	no	—
1263	C₂²×C₄	—	2	1	no	—
1264	C₂²×C₄	—	2	2	no	—
1265	C₂²×C₄	—	2	2	no	—
1266	C₂²×C₄	—	2	1	no	—
1267	C₂²×C₄	—	2	1	no	—
1268	C₂²×C₄	—	2	1	no	—
1269	C₂²×C₄	—	2	1	no	—
1270	C₂²×C₄	—	2	1	no	—
1271	C₂²×C₄	—	2	1	no	—
1272	C₂²×C₄	—	2	1	no	—
1273	C₂²×C₄	—	2	1	no	—
1274	C₂²×C₄	—	2	1	no	—
1275	C₂²×C₄	—	2	2	no	—
1276	C₂²×C₄	—	2	2	no	—
1277	C₂²×C₄	—	2	1	no	—
1278	C₂²×C₄	—	4	4	no	—
1279	C₂²×C₄	—	4	4	no	—
1280	C₂²×C₄	—	4	4	no	—
1281	C₂²×C₄	—	4	4	no	—
1282	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1283	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1284	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1285	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1286	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1287	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1288	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1289	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1290	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1291	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1292	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1293	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1294	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1295	Q₁₆	—	2	4	no	—
1296	Q₁₆	—	2	4	no	—
1297	Q₁₆	—	2	4	no	—
1298	Q₁₆	—	2	4	no	—
1299	Q₁₆	—	4	2	no	—
1300	Q₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
1301	SD₁₆	—	2	4	no	—
1302	SD₁₆	—	2	4	no	—
1303	SD₁₆	—	2	4	no	—
1304	SD₁₆	—	2	4	no	—
1305	SD₁₆	—	2	4	no	—
1306	SD₁₆	—	2	4	no	—
1307	SD₁₆	—	4	2	no	—
1308	SD₁₆	—	4	2	no	—
1309	SD₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
1310	D₈	—	2	4	no	—
1311	D₈	—	2	4	no	—
1312	D₈	—	4	2	no	—
1313	M₁₆	—	2	2	no	—
1314	M₁₆	—	2	2	no	—
1315	M₁₆	—	2	2	no	—
1316	M₁₆	—	2	4	no	—
1317	M₁₆	—	2	4	no	—
1318	M₁₆	C₂×D₄×C₃₁	1	4	yes	complemented
1319	C₂×C₈	—	2	4	no	—
1320	C₂×C₈	—	2	4	no	—
1321	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1322	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1323	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1324	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1325	C₄⋊C₄	—	2	1	no	—
1326	C₄⋊C₄	—	2	2	no	—
1327	C₄⋊C₄	—	2	2	no	—
1328	C₄⋊C₄	—	2	1	no	—
1329	C₄⋊C₄	—	2	1	no	—
1330	C₄⋊C₄	—	2	2	no	—
1331	C₄⋊C₄	—	2	2	no	—
1332	C₄⋊C₄	—	2	1	no	—
1333	C₄⋊C₄	—	2	1	no	—
1334	C₄⋊C₄	—	2	1	no	—
1335	C₄⋊C₄	—	2	1	no	—
1336	C₄⋊C₄	—	2	1	no	—
1337	C₄⋊C₄	—	2	1	no	—
1338	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1339	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1340	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1341	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1342	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1343	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1344	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1345	C₂²⋊C₄	—	2	1	no	—
1346	C₂²⋊C₄	—	2	1	no	—
1347	C₂²⋊C₄	—	2	2	no	—
1348	C₂²⋊C₄	—	2	2	no	—
1349	C₂²⋊C₄	—	2	1	no	—
1350	C₂²⋊C₄	—	2	1	no	—
1351	C₂²⋊C₄	—	2	1	no	—
1352	C₂²⋊C₄	—	2	1	no	—
1353	C₂²⋊C₄	—	2	1	no	—
1354	C₂²⋊C₄	—	2	1	no	—
1355	C₂²⋊C₄	—	2	1	no	—
1356	C₂²⋊C₄	—	2	2	no	—
1357	C₂²⋊C₄	—	2	2	no	—
1358	C₂²⋊C₄	—	2	2	no	—
1359	C₂²⋊C₄	—	2	2	no	—
1360	C₂²⋊C₄	—	2	2	no	—
1361	C₂²⋊C₄	—	2	2	no	—
1362	C₂²⋊C₄	—	2	1	no	—
1363	C₂²⋊C₄	—	2	1	no	—
1364	C₂²⋊C₄	—	2	1	no	—
1365	C₂²⋊C₄	—	2	1	no	—
1366	C₂²⋊C₄	—	2	1	no	—
1367	C₂²⋊C₄	—	2	1	no	—
1368	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1369	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1370	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1371	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1372	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1373	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1374	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1375	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1376	C₄²	—	2	1	no	—
1377	C₄²	—	2	1	no	—
1378	C₄²	—	2	1	no	—
1379	C₄²	—	2	2	no	—
1380	C₄²	—	2	2	no	—
1381	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1382	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1383	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1384	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1385	C₂³	—	2	2	no	—
1386	C₂³	—	2	2	no	—
1387	C₂³	—	2	1	no	—
1388	C₂³	—	2	2	no	—
1389	C₂³	—	2	2	no	—
1390	C₂³	—	2	1	no	—
1391	C₂³	—	2	1	no	—
1392	C₂³	—	4	1	no	—
1393	C₂³	—	4	1	no	—
1394	C₂³	—	4	1	no	—
1395	C₂³	—	4	2	no	—
1396	C₂³	—	4	2	no	—
1397	C₂³	—	4	2	no	—
1398	C₂³	—	4	2	no	—
1399	C₂³	—	4	2	no	—
1400	C₂³	—	4	2	no	—
1401	C₂³	—	4	2	no	—
1402	C₂³	—	8	1	no	—
1403	C₂³	—	8	1	no	—
1404	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1405	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1406	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1407	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1408	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1409	Q₈	—	2	4	no	—
1410	Q₈	—	2	2	no	—
1411	Q₈	—	2	1	no	—
1412	Q₈	—	2	2	no	—
1413	Q₈	—	2	1	no	—
1414	Q₈	—	2	1	no	—
1415	Q₈	—	2	1	no	—
1416	Q₈	—	2	2	no	—
1417	Q₈	—	2	1	no	—
1418	Q₈	—	4	4	no	—
1419	Q₈	—	4	4	no	—
1420	Q₈	—	4	2	no	—
1421	Q₈	—	4	2	no	—
1422	Q₈	—	4	2	no	—
1423	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
1424	Q₈	C₂²×D₄×C₃₁	1	2	yes	—
1425	D₄	—	2	4	no	—
1426	D₄	—	2	2	no	—
1427	D₄	—	2	2	no	—
1428	D₄	—	2	2	no	—
1429	D₄	—	2	1	no	—
1430	D₄	—	2	1	no	—
1431	D₄	—	2	1	no	—
1432	D₄	—	2	1	no	—
1433	D₄	—	2	2	no	—
1434	D₄	—	2	1	no	—
1435	D₄	—	4	1	no	—
1436	D₄	—	4	1	no	—
1437	D₄	—	4	2	no	—
1438	D₄	—	4	2	no	—
1439	D₄	—	4	2	no	—
1440	D₄	—	4	2	no	—
1441	D₄	—	4	4	no	—
1442	D₄	—	4	4	no	—
1443	D₄	—	4	2	no	—
1444	D₄	—	4	2	no	—
1445	D₄	—	4	2	no	—
1446	D₄	—	4	2	no	—
1447	D₄	—	4	4	no	—
1448	D₄	—	4	2	no	—
1449	D₄	—	4	2	no	—
1450	D₄	—	4	2	no	—
1451	D₄	—	4	4	no	—
1452	D₄	—	4	2	no	—
1453	D₄	—	8	1	no	—
1454	D₄	—	8	1	no	—
1455	D₄	—	8	1	no	—
1456	D₄	C₂²×D₄×C₃₁	1	2	yes	—
1457	C₂×C₄	—	2	2	no	—
1458	C₂×C₄	—	2	2	no	—
1459	C₂×C₄	—	2	4	no	—
1460	C₂×C₄	—	2	1	no	—
1461	C₂×C₄	—	2	2	no	—
1462	C₂×C₄	—	2	2	no	—
1463	C₂×C₄	—	2	2	no	—
1464	C₂×C₄	—	2	2	no	—
1465	C₂×C₄	—	2	2	no	—
1466	C₂×C₄	—	2	4	no	—
1467	C₂×C₄	—	2	1	no	—
1468	C₂×C₄	—	2	1	no	—
1469	C₂×C₄	—	2	1	no	—
1470	C₂×C₄	—	2	1	no	—
1471	C₂×C₄	—	2	1	no	—
1472	C₂×C₄	—	2	1	no	—
1473	C₂×C₄	—	2	1	no	—
1474	C₂×C₄	—	2	1	no	—
1475	C₂×C₄	—	2	1	no	—
1476	C₂×C₄	—	2	1	no	—
1477	C₂×C₄	—	2	2	no	—
1478	C₂×C₄	—	2	2	no	—
1479	C₂×C₄	—	2	1	no	—
1480	C₂×C₄	—	2	1	no	—
1481	C₂×C₄	—	4	1	no	—
1482	C₂×C₄	—	4	1	no	—
1483	C₂×C₄	—	4	2	no	—
1484	C₂×C₄	—	4	4	no	—
1485	C₂×C₄	—	4	4	no	—
1486	C₂×C₄	—	4	2	no	—
1487	C₂×C₄	—	4	2	no	—
1488	C₂×C₄	—	4	2	no	—
1489	C₂×C₄	—	4	4	no	—
1490	C₂×C₄	—	4	4	no	—
1491	C₂×C₄	—	4	2	no	—
1492	C₂×C₄	—	4	2	no	—
1493	C₂×C₄	—	4	2	no	—
1494	C₂×C₄	—	4	2	no	—
1495	C₂×C₄	—	4	2	no	—
1496	C₂×C₄	—	4	2	no	—
1497	C₂×C₄	—	4	2	no	—
1498	C₂×C₄	—	8	1	no	—
1499	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1500	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1501	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1502	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1503	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1504	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1505	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1506	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1507	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1508	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1509	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1510	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1511	C₈	—	2	2	no	—
1512	C₈	—	2	2	no	—
1513	C₈	—	2	2	no	—
1514	C₈	C₂²×D₄×C₃₁	1	4	yes	—
1515	C₂²	—	2	1	no	—
1516	C₂²	—	2	1	no	—
1517	C₂²	—	2	1	no	—
1518	C₂²	—	2	1	no	—
1519	C₂²	—	2	1	no	—
1520	C₂²	—	2	1	no	—
1521	C₂²	—	2	1	no	—
1522	C₂²	—	2	2	no	—
1523	C₂²	—	2	1	no	—
1524	C₂²	—	2	1	no	—
1525	C₂²	—	2	1	no	—
1526	C₂²	—	2	1	no	—
1527	C₂²	—	2	1	no	—
1528	C₂²	—	2	1	no	—
1529	C₂²	—	4	4	no	—
1530	C₂²	—	4	1	no	—
1531	C₂²	—	4	1	no	—
1532	C₂²	—	4	2	no	—
1533	C₂²	—	4	1	no	—
1534	C₂²	—	4	1	no	—
1535	C₂²	—	4	1	no	—
1536	C₂²	—	4	1	no	—
1537	C₂²	—	4	2	no	—
1538	C₂²	—	4	1	no	—
1539	C₂²	—	4	1	no	—
1540	C₂²	—	4	2	no	—
1541	C₂²	—	8	2	no	—
1542	C₂²	—	8	4	no	—
1543	C₂²	—	8	4	no	—
1544	C₂²	—	8	4	no	—
1545	C₂²	D₄²×C₃₁	1	2	yes	—
1546	C₂²	C₃₁×#575	1	2	yes	complemented
1547	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1548	C₄	—	2	1	no	—
1549	C₄	—	2	1	no	—
1550	C₄	—	2	1	no	—
1551	C₄	—	2	1	no	—
1552	C₄	—	2	2	no	—
1553	C₄	—	2	4	no	—
1554	C₄	—	2	1	no	—
1555	C₄	—	2	1	no	—
1556	C₄	—	2	1	no	—
1557	C₄	—	2	1	no	—
1558	C₄	—	4	1	no	—
1559	C₄	—	4	1	no	—
1560	C₄	—	4	2	no	—
1561	C₄	—	4	1	no	—
1562	C₄	—	4	2	no	—
1563	C₄	—	4	1	no	—
1564	C₄	D₄²×C₃₁	1	2	yes	—
1565	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
1566	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1567	C₂	—	2	2	no	—
1568	C₂	—	2	2	no	—
1569	C₂	—	4	1	no	—
1570	C₂	—	4	1	no	—
1571	C₂	—	4	1	no	—
1572	C₂	—	4	2	no	—
1573	C₂	—	8	1	no	—
1574	C₂	—	8	1	no	—
1575	C₂	—	8	2	no	—
1576	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
1577	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1578	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃₁×#575	C₂	semidirect
2. C₂²×C₃₁×#137	C₂	semidirect
3. D₄×#41×C₃₁	C₂	semidirect
4. C₂×C₃₁×#548	C₂	semidirect
5. C₃₁×#3285	C₂	semidirect
6. C₃₁×#3282	C₂	semidirect
7. C₃₁×#3277	C₂	semidirect
8. C₃₁×#3275	C₂	semidirect
9. C₃₁×#3271	C₂	semidirect
10. C₃₁×#3270	C₂	semidirect
11. C₃₁×#3269	C₂	semidirect
12. C₃₁×#3265	C₂	semidirect
13. C₃₁×#3153	C₂	semidirect
14. C₃₁×#3056	C₂	semidirect
15. C₃₁×#3055	C₂	semidirect
16. C₃₁×#3040	C₂	semidirect
17. C₃₁×#3037	C₂	semidirect
18. C₃₁×#3007	C₂	semidirect
19. C₃₁×#3006	C₂	semidirect
20. C₃₁×#3005	C₂	semidirect
21. C₃₁×#3004	C₂	semidirect
22. C₄×C₃₁×#137	C₂	semidirect
23. D₄×M₁₆×C₃₁	C₂	semidirect
26. C₂²×#41×C₃₁	C₂²	semidirect
27. C₂³×Q₈×C₃₁	C₂²	semidirect
32. C₂×C₃₁×#137	C₂²	semidirect
33. C₂×C₃₁×#137	C₂²	semidirect
34. C₂×C₃₁×#137	C₂²	semidirect
35. C₂×C₃₁×#137	C₂²	semidirect
36. C₂×C₃₁×#137	C₂²	semidirect
37. C₂×C₃₁×#137	C₂²	semidirect
38. C₂×C₃₁×#137	C₂²	semidirect
40. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
41. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
42. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
43. C₂×C₃₁×#135	C₂²	semidirect
44. C₂×C₃₁×#135	C₂²	semidirect
45. C₂²×Q₁₆×C₃₁	C₂²	semidirect
46. C₂²×SD₁₆×C₃₁	C₂²	semidirect
47. C₂²×M₁₆×C₃₁	C₂²	semidirect
48. C₂²×M₁₆×C₃₁	C₂²	semidirect
49. C₃₁×#550	C₂²	semidirect
50. D₄×Q₈×C₃₁	C₂²	semidirect
56. C₃₁×#548	C₂²	semidirect
57. C₃₁×#548	C₂²	semidirect
58. C₃₁×#548	C₂²	semidirect
59. C₃₁×#548	C₂²	semidirect
60. C₃₁×#548	C₂²	semidirect
62. C₃₁×#547	C₂²	semidirect
65. C₃₁×#546	C₂²	semidirect
66. C₃₁×#546	C₂²	semidirect
68. D₄²×C₃₁	C₂²	semidirect
72. C₂×C₃₁×#124	C₂²	semidirect
78. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
80. C₂×C₃₁×#121	C₂²	semidirect
82. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
86. C₃₁×#497	C₂²	semidirect
87. C₃₁×#496	C₂²	semidirect
88. C₃₁×#495	C₂²	semidirect
89. C₃₁×#495	C₂²	semidirect
90. C₃₁×#470	C₂²	semidirect
91. C₃₁×#469	C₂²	semidirect
92. C₃₁×#468	C₂²	semidirect
93. C₃₁×#468	C₂²	semidirect
94. C₃₁×#467	C₂²	semidirect
95. C₃₁×#466	C₂²	semidirect
96. C₃₁×#465	C₂²	semidirect
97. C₃₁×#465	C₂²	semidirect
98. C₃₁×#464	C₂²	semidirect
99. C₃₁×#464	C₂²	semidirect
100. C₃₁×#464	C₂²	semidirect
101. C₃₁×#464	C₂²	semidirect
102. C₃₁×#463	C₂²	semidirect
103. C₃₁×#463	C₂²	semidirect
104. C₃₁×#462	C₂²	semidirect
105. C₃₁×#460	C₂²	semidirect
106. C₃₁×#452	C₂²	semidirect
107. C₃₁×#452	C₂²	semidirect
108. C₃₁×#452	C₂²	semidirect
109. C₃₁×#452	C₂²	semidirect
110. C₃₁×#451	C₂²	semidirect
111. C₃₁×#451	C₂²	semidirect
112. C₃₁×#451	C₂²	semidirect
113. C₃₁×#450	C₂²	semidirect
114. C₃₁×#449	C₂²	semidirect
115. C₃₁×#449	C₂²	semidirect
116. C₃₁×#449	C₂²	semidirect
117. C₃₁×#449	C₂²	semidirect
118. C₃₁×#448	C₂²	semidirect
119. C₃₁×#448	C₂²	semidirect
120. C₃₁×#448	C₂²	semidirect
121. C₃₁×#447	C₂²	semidirect
122. C₃₁×#441	C₂²	semidirect
123. C₃₁×#440	C₂²	semidirect
124. C₄×Q₁₆×C₃₁	C₂²	semidirect
125. C₄×SD₁₆×C₃₁	C₂²	semidirect
126. C₃₁×#436	C₂²	semidirect
127. C₃₁×#435	C₂²	semidirect
128. C₃₁×#435	C₂²	semidirect
129. C₈×D₄×C₃₁	C₂²	semidirect
130. C₃₁×#428	C₂²	semidirect
131. C₃₁×#423	C₂²	semidirect
132. C₃₁×#419	C₂²	semidirect
133. C₃₁×#419	C₂²	semidirect
134. C₃₁×#418	C₂²	semidirect
136. C₃₁×#417	C₂²	semidirect
137. C₃₁×#417	C₂²	semidirect
138. C₃₁×#407	C₂²	semidirect
139. C₃₁×#407	C₂²	semidirect
140. C₄×M₁₆×C₃₁	C₂²	semidirect
196. C₃₁×#137	D₄	semidirect
420. C₂×Q₈×C₃₁	C₂×D₄	semidirect
510. Q₁₆×C₃₁	C₂×D₄	semidirect
519. SD₁₆×C₃₁	C₂×D₄	semidirect
528. M₁₆×C₃₁	C₂×D₄	semidirect
595. #61068	C₃₁	direct (N × H)
726. C₂×#575	C₂×C₃₁	semidirect
727. C₂²×#137	C₂×C₃₁	semidirect
728. D₄×#41	C₂×C₃₁	semidirect
729. C₂×#548	C₂×C₃₁	semidirect
730. #3285	C₂×C₃₁	semidirect
731. #3282	C₂×C₃₁	semidirect
732. #3277	C₂×C₃₁	semidirect
733. #3275	C₂×C₃₁	semidirect
734. #3271	C₂×C₃₁	semidirect
735. #3270	C₂×C₃₁	semidirect
736. #3269	C₂×C₃₁	semidirect
737. #3265	C₂×C₃₁	semidirect
738. #3153	C₂×C₃₁	semidirect
739. #3056	C₂×C₃₁	semidirect
740. #3055	C₂×C₃₁	semidirect
741. #3040	C₂×C₃₁	semidirect
742. #3037	C₂×C₃₁	semidirect
743. #3007	C₂×C₃₁	semidirect
744. #3006	C₂×C₃₁	semidirect
745. #3005	C₂×C₃₁	semidirect
746. #3004	C₂×C₃₁	semidirect
747. C₄×#137	C₂×C₃₁	semidirect
748. D₄×M₁₆	C₂×C₃₁	semidirect
780. C₂²×C₃₁	#575	semidirect
803. C₂²×#41	C₂²×C₃₁	semidirect
804. C₂³×Q₈	C₂²×C₃₁	semidirect
809. C₂×#137	C₂²×C₃₁	semidirect
810. C₂×#137	C₂²×C₃₁	semidirect
811. C₂×#137	C₂²×C₃₁	semidirect
812. C₂×#137	C₂²×C₃₁	semidirect
813. C₂×#137	C₂²×C₃₁	semidirect
814. C₂×#137	C₂²×C₃₁	semidirect
815. C₂×#137	C₂²×C₃₁	semidirect
817. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
818. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
819. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
820. C₂×#135	C₂²×C₃₁	semidirect
821. C₂×#135	C₂²×C₃₁	semidirect
822. C₂²×Q₁₆	C₂²×C₃₁	semidirect
823. C₂²×SD₁₆	C₂²×C₃₁	semidirect
824. C₂²×M₁₆	C₂²×C₃₁	semidirect
825. C₂²×M₁₆	C₂²×C₃₁	semidirect
826. #550	C₂²×C₃₁	semidirect
827. D₄×Q₈	C₂²×C₃₁	semidirect
833. #548	C₂²×C₃₁	semidirect
834. #548	C₂²×C₃₁	semidirect
835. #548	C₂²×C₃₁	semidirect
836. #548	C₂²×C₃₁	semidirect
837. #548	C₂²×C₃₁	semidirect
839. #547	C₂²×C₃₁	semidirect
842. #546	C₂²×C₃₁	semidirect
843. #546	C₂²×C₃₁	semidirect
845. D₄²	C₂²×C₃₁	semidirect
849. C₂×#124	C₂²×C₃₁	semidirect
855. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
857. C₂×#121	C₂²×C₃₁	semidirect
859. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
863. #497	C₂²×C₃₁	semidirect
864. #496	C₂²×C₃₁	semidirect
865. #495	C₂²×C₃₁	semidirect
866. #495	C₂²×C₃₁	semidirect
867. #470	C₂²×C₃₁	semidirect
868. #469	C₂²×C₃₁	semidirect
869. #468	C₂²×C₃₁	semidirect
870. #468	C₂²×C₃₁	semidirect
871. #467	C₂²×C₃₁	semidirect
872. #466	C₂²×C₃₁	semidirect
873. #465	C₂²×C₃₁	semidirect
874. #465	C₂²×C₃₁	semidirect
875. #464	C₂²×C₃₁	semidirect
876. #464	C₂²×C₃₁	semidirect
877. #464	C₂²×C₃₁	semidirect
878. #464	C₂²×C₃₁	semidirect
879. #463	C₂²×C₃₁	semidirect
880. #463	C₂²×C₃₁	semidirect
881. #462	C₂²×C₃₁	semidirect
882. #460	C₂²×C₃₁	semidirect
883. #452	C₂²×C₃₁	semidirect
884. #452	C₂²×C₃₁	semidirect
885. #452	C₂²×C₃₁	semidirect
886. #452	C₂²×C₃₁	semidirect
887. #451	C₂²×C₃₁	semidirect
888. #451	C₂²×C₃₁	semidirect
889. #451	C₂²×C₃₁	semidirect
890. #450	C₂²×C₃₁	semidirect
891. #449	C₂²×C₃₁	semidirect
892. #449	C₂²×C₃₁	semidirect
893. #449	C₂²×C₃₁	semidirect
894. #449	C₂²×C₃₁	semidirect
895. #448	C₂²×C₃₁	semidirect
896. #448	C₂²×C₃₁	semidirect
897. #448	C₂²×C₃₁	semidirect
898. #447	C₂²×C₃₁	semidirect
899. #441	C₂²×C₃₁	semidirect
900. #440	C₂²×C₃₁	semidirect
901. C₄×Q₁₆	C₂²×C₃₁	semidirect
902. C₄×SD₁₆	C₂²×C₃₁	semidirect
903. #436	C₂²×C₃₁	semidirect
904. #435	C₂²×C₃₁	semidirect
905. #435	C₂²×C₃₁	semidirect
906. C₈×D₄	C₂²×C₃₁	semidirect
907. #428	C₂²×C₃₁	semidirect
908. #423	C₂²×C₃₁	semidirect
909. #419	C₂²×C₃₁	semidirect
910. #419	C₂²×C₃₁	semidirect
911. #418	C₂²×C₃₁	semidirect
913. #417	C₂²×C₃₁	semidirect
914. #417	C₂²×C₃₁	semidirect
915. #407	C₂²×C₃₁	semidirect
916. #407	C₂²×C₃₁	semidirect
917. C₄×M₁₆	C₂²×C₃₁	semidirect
985. #137	D₄×C₃₁	semidirect
1160. C₃₁	#61068	direct (N × H)
1210. C₂×Q₈	C₂×D₄×C₃₁	semidirect
1300. Q₁₆	C₂×D₄×C₃₁	semidirect
1309. SD₁₆	C₂×D₄×C₃₁	semidirect
1318. M₁₆	C₂×D₄×C₃₁	semidirect
1546. C₂²	C₃₁×#575	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃₁×#575	2
C₂²×C₃₁×#137	2
D₄×#41×C₃₁	2
C₂×C₃₁×#548	2
C₃₁×#3285	2
C₃₁×#3282	2
C₃₁×#3277	2
C₃₁×#3275	2
C₃₁×#3271	2
C₃₁×#3270	2
C₃₁×#3269	2
C₃₁×#3265	2
C₃₁×#3153	2
C₃₁×#3056	2
C₃₁×#3055	2
C₃₁×#3040	2
C₃₁×#3037	2
C₃₁×#3007	2
C₃₁×#3006	2
C₃₁×#3005	2
C₃₁×#3004	2
C₄×C₃₁×#137	2
D₄×M₁₆×C₃₁	2
#61068	31

Subgroups — C31×#61068 #21517827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61068 #21517827