Subgroups — C₃₁×#61076 #21517835

Order 7936.

2672 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3486	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×Q₁₆×C₃₁	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×#3276	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3270	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×#3266	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3156	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3002	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₃₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2933	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
27	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#578	—	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
33	C₂×C₃₁×#137	C₂²	1	2	yes	—
34	C₂×C₃₁×#137	C₂²	1	2	yes	—
35	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
38	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
39	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
41	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
42	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
43	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
44	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
45	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
46	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
47	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic, complemented
48	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
49	D₄×Q₈×C₃₁	—	2	1	no	—
50	D₄×Q₈×C₃₁	—	2	1	no	—
51	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
52	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
53	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
54	C₃₁×#548	—	2	1	no	—
55	C₃₁×#548	—	2	1	no	—
56	C₃₁×#548	C₂²	1	2	yes	—
57	C₃₁×#548	C₂²	1	2	yes	—
58	C₃₁×#548	C₂²	1	2	yes	complemented
59	C₃₁×#547	—	2	2	no	—
60	C₃₁×#547	C₂²	1	2	yes	—
61	C₃₁×#546	—	2	2	no	—
62	C₃₁×#546	C₂²	1	2	yes	—
63	C₃₁×#537	—	2	1	no	—
64	C₃₁×#537	C₂²	1	1	yes	characteristic
65	C₃₁×#536	—	2	2	no	—
66	C₃₁×#536	—	2	1	no	—
67	C₃₁×#536	C₂²	1	1	yes	characteristic
68	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#525	—	2	1	no	—
71	C₃₁×#525	—	2	2	no	—
72	C₃₁×#525	C₂²	1	1	yes	characteristic
73	C₃₁×#525	C₂²	1	1	yes	characteristic
74	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
75	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
76	C₃₁×#520	C₂²	1	1	yes	characteristic
77	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#497	C₂²	1	2	yes	complemented
79	C₃₁×#497	C₂²	1	2	yes	complemented
80	C₃₁×#495	C₂²	1	2	yes	complemented
81	C₃₁×#494	C₂²	1	2	yes	complemented
82	C₃₁×#470	C₂²	1	2	yes	complemented
83	C₃₁×#470	C₂²	1	2	yes	complemented
84	C₃₁×#468	C₂²	1	2	yes	complemented
85	C₃₁×#468	C₂²	1	2	yes	complemented
86	C₃₁×#467	C₂²	1	2	yes	—
87	C₃₁×#467	C₂²	1	2	yes	complemented
88	C₃₁×#465	C₂²	1	2	yes	—
89	C₃₁×#465	C₂²	1	2	yes	complemented
90	C₃₁×#464	C₂²	1	2	yes	complemented
91	C₃₁×#464	C₂²	1	2	yes	complemented
92	C₃₁×#464	C₂²	1	2	yes	complemented
93	C₃₁×#463	C₂²	1	2	yes	complemented
94	C₃₁×#462	C₂²	1	2	yes	complemented
95	C₃₁×#462	C₂²	1	2	yes	complemented
96	C₃₁×#462	C₂²	1	2	yes	complemented
97	C₃₁×#461	C₂²	1	2	yes	complemented
98	C₃₁×#452	C₂²	1	1	yes	characteristic
99	C₃₁×#452	C₂²	1	1	yes	characteristic
100	C₃₁×#452	C₂²	1	2	yes	complemented
101	C₃₁×#452	C₂²	1	2	yes	complemented
102	C₃₁×#452	C₂²	1	2	yes	complemented
103	C₃₁×#451	C₂²	1	2	yes	—
104	C₃₁×#451	C₂²	1	2	yes	—
105	C₃₁×#451	C₂²	1	1	yes	characteristic
106	C₃₁×#451	C₂²	1	2	yes	complemented
107	C₃₁×#451	C₂²	1	2	yes	complemented
108	C₃₁×#451	C₂²	1	2	yes	complemented
109	C₃₁×#451	C₂²	1	2	yes	complemented
110	C₃₁×#451	C₂²	1	2	yes	complemented
111	C₃₁×#450	C₂²	1	1	yes	characteristic
112	C₃₁×#449	C₂²	1	1	yes	characteristic
113	C₃₁×#449	C₂²	1	1	yes	characteristic
114	C₃₁×#449	C₂²	1	2	yes	complemented
115	C₃₁×#448	C₂²	1	1	yes	characteristic
116	C₃₁×#448	C₂²	1	2	yes	complemented
117	C₃₁×#447	C₂²	1	1	yes	characteristic
118	C₃₁×#441	C₂²	1	2	yes	complemented
119	C₃₁×#440	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
122	C₃₁×#436	C₂²	1	2	yes	complemented
123	C₃₁×#435	C₂²	1	2	yes	—
124	C₃₁×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₃₁	C₂²	1	2	yes	—
126	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#416	C₂²	1	1	yes	characteristic
131	C₃₁×#416	C₂²	1	1	yes	characteristic
132	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
136	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
137	C₃₁×2₋¹⁺⁴	—	2	4	no	—
138	C₃₁×2₋¹⁺⁴	—	2	4	no	—
139	C₃₁×2₋¹⁺⁴	—	4	2	no	—
140	C₃₁×2₋¹⁺⁴	—	4	2	no	—
141	C₂×#41×C₃₁	—	2	2	no	—
142	C₂×#41×C₃₁	—	2	1	no	—
143	C₂×#41×C₃₁	—	2	2	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	—	4	2	no	—
149	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×#41×C₃₁	C₂³	1	2	yes	—
154	C₂×#41×C₃₁	C₂³	1	2	yes	—
155	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
157	C₂²×Q₈×C₃₁	—	2	1	no	—
158	C₂²×Q₈×C₃₁	—	2	1	no	—
159	C₂²×Q₈×C₃₁	—	2	1	no	—
160	C₂²×Q₈×C₃₁	—	2	1	no	—
161	C₂²×Q₈×C₃₁	—	2	1	no	—
162	C₂²×Q₈×C₃₁	—	2	4	no	—
163	C₂²×Q₈×C₃₁	—	4	2	no	—
164	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
166	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
168	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
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×D₄×C₃₁	—	2	1	no	—
173	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
174	C₂³×C₄×C₃₁	—	2	1	no	—
175	C₂³×C₄×C₃₁	—	2	1	no	—
176	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₃₁×#137	—	2	4	no	—
178	C₃₁×#137	—	2	4	no	—
179	C₃₁×#137	—	2	8	no	—
180	C₃₁×#137	—	2	8	no	—
181	C₃₁×#137	—	2	8	no	—
182	C₃₁×#137	—	2	8	no	—
183	C₃₁×#137	—	2	4	no	—
184	C₃₁×#137	—	2	4	no	—
185	C₃₁×#137	D₄	1	8	yes	complemented
186	C₃₁×#135	—	2	4	no	—
187	C₃₁×#135	—	2	8	no	—
188	C₃₁×#135	—	4	2	no	—
189	C₂×Q₁₆×C₃₁	—	2	4	no	—
190	C₂×Q₁₆×C₃₁	—	2	8	no	—
191	C₂×Q₁₆×C₃₁	—	2	8	no	—
192	C₂×Q₁₆×C₃₁	—	4	2	no	—
193	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
194	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
195	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
197	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
198	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
199	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
200	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
202	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
203	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
204	C₂×SD₁₆×C₃₁	—	2	8	no	—
205	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
207	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
209	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
210	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
211	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
212	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
214	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
215	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₃₁×#131	—	2	4	no	—
217	C₂×M₁₆×C₃₁	—	2	4	no	—
218	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
219	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
220	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
221	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
222	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
225	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
226	C₃₁×C₄⋊Q₈	—	2	1	no	—
227	C₃₁×C₄⋊Q₈	—	2	2	no	—
228	C₃₁×C₄⋊Q₈	—	2	2	no	—
229	C₃₁×C₄⋊Q₈	—	2	2	no	—
230	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
231	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
232	C₃₁×#124	—	2	1	no	—
233	C₃₁×#124	—	2	2	no	—
234	C₃₁×#124	—	2	2	no	—
235	C₃₁×#124	—	2	2	no	—
236	C₃₁×#124	C₂³	1	2	yes	—
237	C₃₁×#124	C₂³	1	2	yes	—
238	C₃₁×#123	—	2	2	no	—
239	C₃₁×#123	—	2	1	no	—
240	C₃₁×#123	—	2	2	no	—
241	C₃₁×#123	—	2	2	no	—
242	C₃₁×#123	—	2	2	no	—
243	C₃₁×#123	—	2	2	no	—
244	C₃₁×#123	—	2	2	no	—
245	C₃₁×#123	D₄	1	2	yes	—
246	C₃₁×C₂²⋊Q₈	—	2	1	no	—
247	C₃₁×C₂²⋊Q₈	—	2	1	no	—
248	C₃₁×C₂²⋊Q₈	—	2	1	no	—
249	C₃₁×C₂²⋊Q₈	—	2	1	no	—
250	C₃₁×C₂²⋊Q₈	—	2	2	no	—
251	C₃₁×C₂²⋊Q₈	—	2	1	no	—
252	C₃₁×C₂²⋊Q₈	—	2	2	no	—
253	C₃₁×C₂²⋊Q₈	—	2	2	no	—
254	C₃₁×C₂²⋊Q₈	—	2	1	no	—
255	C₃₁×C₂²⋊Q₈	—	2	1	no	—
256	C₃₁×C₂²⋊Q₈	—	2	2	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	2	no	—
262	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
263	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
264	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
265	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
266	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
267	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
268	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
269	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
271	C₃₁×#121	—	2	1	no	—
272	C₃₁×#121	—	2	2	no	—
273	C₃₁×#121	—	2	2	no	—
274	C₃₁×#121	—	2	2	no	—
275	C₃₁×#121	—	2	2	no	—
276	C₃₁×#121	—	2	2	no	—
277	C₃₁×#121	—	2	2	no	—
278	C₃₁×#121	D₄	1	1	yes	characteristic
279	C₃₁×#121	D₄	1	1	yes	characteristic
280	C₃₁×#121	C₂³	1	1	yes	characteristic
281	C₃₁×#121	C₂³	1	2	yes	—
282	C₃₁×#121	C₂³	1	1	yes	characteristic
283	C₃₁×#120	—	2	1	no	—
284	C₃₁×#120	—	2	2	no	—
285	C₃₁×#120	D₄	1	2	yes	—
286	C₄×Q₈×C₃₁	—	2	1	no	—
287	C₄×Q₈×C₃₁	—	2	1	no	—
288	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
289	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
290	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
291	C₄×D₄×C₃₁	—	2	2	no	—
292	C₄×D₄×C₃₁	—	2	2	no	—
293	C₄×D₄×C₃₁	—	2	2	no	—
294	C₄×D₄×C₃₁	—	2	1	no	—
295	C₄×D₄×C₃₁	—	2	1	no	—
296	C₄×D₄×C₃₁	—	2	2	no	—
297	C₄×D₄×C₃₁	—	2	2	no	—
298	C₄×D₄×C₃₁	—	2	2	no	—
299	C₄×D₄×C₃₁	—	2	2	no	—
300	C₄×D₄×C₃₁	C₂³	1	2	yes	—
301	C₄×D₄×C₃₁	C₂³	1	2	yes	—
302	C₄×D₄×C₃₁	C₂³	1	2	yes	—
303	C₃₁×#117	—	2	1	no	—
304	C₃₁×#117	—	2	2	no	—
305	C₃₁×#117	C₂³	1	1	yes	characteristic
306	C₃₁×#117	C₂³	1	1	yes	characteristic
307	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
308	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
309	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
310	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
312	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₃₁×#107	C₂³	1	2	yes	—
314	C₃₁×#106	C₂³	1	2	yes	—
315	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
316	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
317	C₃₁×#103	C₂³	1	2	yes	—
318	C₃₁×#103	C₂³	1	2	yes	—
319	C₃₁×#103	C₂³	1	2	yes	—
320	C₃₁×#103	C₂³	1	2	yes	—
321	C₃₁×#103	C₂³	1	1	yes	characteristic
322	C₃₁×#103	C₂³	1	1	yes	characteristic
323	C₃₁×#103	C₂³	1	1	yes	characteristic
324	C₃₁×#103	C₂³	1	1	yes	characteristic
325	C₃₁×#103	C₂³	1	2	yes	—
326	C₃₁×#103	C₂³	1	2	yes	—
327	C₃₁×#103	C₂³	1	2	yes	—
328	C₃₁×#102	C₂³	1	1	yes	characteristic
329	C₃₁×#102	C₂³	1	1	yes	characteristic
330	C₃₁×#102	C₂³	1	1	yes	characteristic
331	C₃₁×#102	C₂³	1	1	yes	characteristic
332	C₃₁×#102	C₂³	1	2	yes	—
333	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
334	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
335	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
336	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
337	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₃₁×#97	C₂³	1	2	yes	—
340	C₄×C₈×C₃₁	C₂³	1	2	yes	—
341	C₂⁴×C₃₁	—	2	1	no	—
342	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
343	#41×C₃₁	—	2	2	no	—
344	#41×C₃₁	—	2	2	no	—
345	#41×C₃₁	—	2	2	no	—
346	#41×C₃₁	—	2	4	no	—
347	#41×C₃₁	—	2	2	no	—
348	#41×C₃₁	—	2	4	no	—
349	#41×C₃₁	—	2	2	no	—
350	#41×C₃₁	—	2	2	no	—
351	#41×C₃₁	—	2	2	no	—
352	#41×C₃₁	—	2	2	no	—
353	#41×C₃₁	—	2	2	no	—
354	#41×C₃₁	—	4	4	no	—
355	#41×C₃₁	—	4	1	no	—
356	#41×C₃₁	—	4	1	no	—
357	#41×C₃₁	—	4	2	no	—
358	#41×C₃₁	—	4	2	no	—
359	#41×C₃₁	—	4	4	no	—
360	#41×C₃₁	—	4	8	no	—
361	#41×C₃₁	—	4	4	no	—
362	#41×C₃₁	—	4	8	no	—
363	#41×C₃₁	—	4	4	no	—
364	#41×C₃₁	C₂×D₄	1	4	yes	—
365	C₂×Q₈×C₃₁	—	2	1	no	—
366	C₂×Q₈×C₃₁	—	2	1	no	—
367	C₂×Q₈×C₃₁	—	2	2	no	—
368	C₂×Q₈×C₃₁	—	2	2	no	—
369	C₂×Q₈×C₃₁	—	2	1	no	—
370	C₂×Q₈×C₃₁	—	2	2	no	—
371	C₂×Q₈×C₃₁	—	2	2	no	—
372	C₂×Q₈×C₃₁	—	2	1	no	—
373	C₂×Q₈×C₃₁	—	2	2	no	—
374	C₂×Q₈×C₃₁	—	2	4	no	—
375	C₂×Q₈×C₃₁	—	2	2	no	—
376	C₂×Q₈×C₃₁	—	2	4	no	—
377	C₂×Q₈×C₃₁	—	2	4	no	—
378	C₂×Q₈×C₃₁	—	2	4	no	—
379	C₂×Q₈×C₃₁	—	2	2	no	—
380	C₂×Q₈×C₃₁	—	2	2	no	—
381	C₂×Q₈×C₃₁	—	2	2	no	—
382	C₂×Q₈×C₃₁	—	2	2	no	—
383	C₂×Q₈×C₃₁	—	4	4	no	—
384	C₂×Q₈×C₃₁	—	4	2	no	—
385	C₂×Q₈×C₃₁	—	4	2	no	—
386	C₂×Q₈×C₃₁	—	4	1	no	—
387	C₂×Q₈×C₃₁	—	4	2	no	—
388	C₂×Q₈×C₃₁	—	4	2	no	—
389	C₂×Q₈×C₃₁	—	4	4	no	—
390	C₂×Q₈×C₃₁	—	4	4	no	—
391	C₂×Q₈×C₃₁	—	4	4	no	—
392	C₂×Q₈×C₃₁	—	4	4	no	—
393	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
394	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
396	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
397	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
400	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₂×D₄×C₃₁	—	2	1	no	—
402	C₂×D₄×C₃₁	—	2	2	no	—
403	C₂×D₄×C₃₁	—	2	1	no	—
404	C₂×D₄×C₃₁	—	2	1	no	—
405	C₂×D₄×C₃₁	—	2	2	no	—
406	C₂×D₄×C₃₁	—	2	1	no	—
407	C₂×D₄×C₃₁	—	2	1	no	—
408	C₂×D₄×C₃₁	—	2	1	no	—
409	C₂×D₄×C₃₁	—	2	1	no	—
410	C₂×D₄×C₃₁	—	2	2	no	—
411	C₂×D₄×C₃₁	—	2	2	no	—
412	C₂×D₄×C₃₁	—	2	1	no	—
413	C₂×D₄×C₃₁	—	4	1	no	—
414	C₂×D₄×C₃₁	—	4	4	no	—
415	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
416	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
417	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
418	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
419	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
420	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
421	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₃₁	—	2	1	no	—
423	C₂²×C₄×C₃₁	—	2	1	no	—
424	C₂²×C₄×C₃₁	—	2	2	no	—
425	C₂²×C₄×C₃₁	—	2	2	no	—
426	C₂²×C₄×C₃₁	—	2	1	no	—
427	C₂²×C₄×C₃₁	—	2	2	no	—
428	C₂²×C₄×C₃₁	—	2	2	no	—
429	C₂²×C₄×C₃₁	—	2	2	no	—
430	C₂²×C₄×C₃₁	—	2	1	no	—
431	C₂²×C₄×C₃₁	—	2	2	no	—
432	C₂²×C₄×C₃₁	—	2	1	no	—
433	C₂²×C₄×C₃₁	—	2	1	no	—
434	C₂²×C₄×C₃₁	—	2	2	no	—
435	C₂²×C₄×C₃₁	—	2	1	no	—
436	C₂²×C₄×C₃₁	—	2	1	no	—
437	C₂²×C₄×C₃₁	—	2	2	no	—
438	C₂²×C₄×C₃₁	—	2	1	no	—
439	C₂²×C₄×C₃₁	—	2	1	no	—
440	C₂²×C₄×C₃₁	—	2	2	no	—
441	C₂²×C₄×C₃₁	—	4	4	no	—
442	C₂²×C₄×C₃₁	—	4	4	no	—
443	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
444	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
445	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
447	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
448	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
450	Q₁₆×C₃₁	—	2	4	no	—
451	Q₁₆×C₃₁	—	2	2	no	—
452	Q₁₆×C₃₁	—	2	4	no	—
453	Q₁₆×C₃₁	—	2	4	no	—
454	Q₁₆×C₃₁	—	2	4	no	—
455	Q₁₆×C₃₁	—	2	4	no	—
456	Q₁₆×C₃₁	—	2	4	no	—
457	Q₁₆×C₃₁	—	4	2	no	—
458	Q₁₆×C₃₁	—	4	2	no	—
459	Q₁₆×C₃₁	—	4	1	no	—
460	Q₁₆×C₃₁	C₂×D₄	1	8	yes	—
461	SD₁₆×C₃₁	—	2	4	no	—
462	SD₁₆×C₃₁	—	2	2	no	—
463	SD₁₆×C₃₁	—	2	4	no	—
464	SD₁₆×C₃₁	—	2	2	no	—
465	SD₁₆×C₃₁	—	2	4	no	—
466	SD₁₆×C₃₁	—	2	4	no	—
467	SD₁₆×C₃₁	—	4	1	no	—
468	SD₁₆×C₃₁	—	4	1	no	—
469	SD₁₆×C₃₁	C₂×D₄	1	8	yes	—
470	D₈×C₃₁	—	2	2	no	—
471	D₈×C₃₁	—	4	1	no	—
472	M₁₆×C₃₁	—	2	2	no	—
473	M₁₆×C₃₁	—	2	4	no	—
474	M₁₆×C₃₁	—	2	4	no	—
475	M₁₆×C₃₁	C₂×D₄	1	4	yes	—
476	C₂×C₈×C₃₁	—	2	2	no	—
477	C₂×C₈×C₃₁	—	2	2	no	—
478	C₂×C₈×C₃₁	—	2	4	no	—
479	C₂×C₈×C₃₁	—	2	4	no	—
480	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
481	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
482	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
483	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
484	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
485	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
486	C₄⋊C₄×C₃₁	—	2	2	no	—
487	C₄⋊C₄×C₃₁	—	2	1	no	—
488	C₄⋊C₄×C₃₁	—	2	2	no	—
489	C₄⋊C₄×C₃₁	—	2	2	no	—
490	C₄⋊C₄×C₃₁	—	2	2	no	—
491	C₄⋊C₄×C₃₁	—	2	2	no	—
492	C₄⋊C₄×C₃₁	—	2	2	no	—
493	C₄⋊C₄×C₃₁	—	2	2	no	—
494	C₄⋊C₄×C₃₁	—	2	2	no	—
495	C₄⋊C₄×C₃₁	—	2	2	no	—
496	C₄⋊C₄×C₃₁	—	2	2	no	—
497	C₄⋊C₄×C₃₁	—	2	2	no	—
498	C₄⋊C₄×C₃₁	—	2	1	no	—
499	C₄⋊C₄×C₃₁	—	2	1	no	—
500	C₄⋊C₄×C₃₁	—	2	2	no	—
501	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
502	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
503	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
504	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
505	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
506	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
507	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
508	C₂²⋊C₄×C₃₁	—	2	2	no	—
509	C₂²⋊C₄×C₃₁	—	2	2	no	—
510	C₂²⋊C₄×C₃₁	—	2	1	no	—
511	C₂²⋊C₄×C₃₁	—	2	1	no	—
512	C₂²⋊C₄×C₃₁	—	2	1	no	—
513	C₂²⋊C₄×C₃₁	—	2	2	no	—
514	C₂²⋊C₄×C₃₁	—	2	2	no	—
515	C₂²⋊C₄×C₃₁	—	2	2	no	—
516	C₂²⋊C₄×C₃₁	—	2	2	no	—
517	C₂²⋊C₄×C₃₁	—	2	2	no	—
518	C₂²⋊C₄×C₃₁	—	2	2	no	—
519	C₂²⋊C₄×C₃₁	—	2	2	no	—
520	C₂²⋊C₄×C₃₁	—	2	2	no	—
521	C₂²⋊C₄×C₃₁	—	2	2	no	—
522	C₂²⋊C₄×C₃₁	—	2	1	no	—
523	C₂²⋊C₄×C₃₁	—	2	1	no	—
524	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
525	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
526	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
527	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
528	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
529	C₄²×C₃₁	—	2	2	no	—
530	C₄²×C₃₁	—	2	2	no	—
531	C₄²×C₃₁	—	2	2	no	—
532	C₄²×C₃₁	—	2	1	no	—
533	C₄²×C₃₁	C₂⁴	1	2	yes	—
534	#61076	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
535	C₂³×C₃₁	—	2	2	no	—
536	C₂³×C₃₁	—	2	2	no	—
537	C₂³×C₃₁	—	2	1	no	—
538	C₂³×C₃₁	—	2	1	no	—
539	C₂³×C₃₁	—	2	1	no	—
540	C₂³×C₃₁	—	4	1	no	—
541	C₂³×C₃₁	—	4	2	no	—
542	C₂³×C₃₁	—	4	2	no	—
543	C₂³×C₃₁	—	8	1	no	—
544	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
545	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
546	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
547	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
548	Q₈×C₃₁	—	2	4	no	—
549	Q₈×C₃₁	—	2	2	no	—
550	Q₈×C₃₁	—	2	2	no	—
551	Q₈×C₃₁	—	2	1	no	—
552	Q₈×C₃₁	—	2	2	no	—
553	Q₈×C₃₁	—	2	1	no	—
554	Q₈×C₃₁	—	2	2	no	—
555	Q₈×C₃₁	—	2	1	no	—
556	Q₈×C₃₁	—	2	1	no	—
557	Q₈×C₃₁	—	2	1	no	—
558	Q₈×C₃₁	—	2	2	no	—
559	Q₈×C₃₁	—	2	2	no	—
560	Q₈×C₃₁	—	4	4	no	—
561	Q₈×C₃₁	—	4	4	no	—
562	Q₈×C₃₁	—	4	4	no	—
563	Q₈×C₃₁	—	4	4	no	—
564	Q₈×C₃₁	—	4	2	no	—
565	Q₈×C₃₁	—	4	2	no	—
566	Q₈×C₃₁	—	4	2	no	—
567	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
568	Q₈×C₃₁	C₂²×D₄	1	2	yes	—
569	D₄×C₃₁	—	2	4	no	—
570	D₄×C₃₁	—	2	4	no	—
571	D₄×C₃₁	—	2	4	no	—
572	D₄×C₃₁	—	2	2	no	—
573	D₄×C₃₁	—	2	1	no	—
574	D₄×C₃₁	—	2	1	no	—
575	D₄×C₃₁	—	2	1	no	—
576	D₄×C₃₁	—	2	1	no	—
577	D₄×C₃₁	—	2	1	no	—
578	D₄×C₃₁	—	4	2	no	—
579	D₄×C₃₁	—	4	2	no	—
580	D₄×C₃₁	—	4	2	no	—
581	D₄×C₃₁	—	4	4	no	—
582	D₄×C₃₁	—	4	2	no	—
583	D₄×C₃₁	—	4	4	no	—
584	D₄×C₃₁	—	4	2	no	—
585	D₄×C₃₁	—	4	2	no	—
586	D₄×C₃₁	—	4	2	no	—
587	D₄×C₃₁	—	4	2	no	—
588	D₄×C₃₁	—	8	2	no	—
589	D₄×C₃₁	C₂²×D₄	1	2	yes	—
590	C₂×C₄×C₃₁	—	2	2	no	—
591	C₂×C₄×C₃₁	—	2	4	no	—
592	C₂×C₄×C₃₁	—	2	1	no	—
593	C₂×C₄×C₃₁	—	2	2	no	—
594	C₂×C₄×C₃₁	—	2	2	no	—
595	C₂×C₄×C₃₁	—	2	2	no	—
596	C₂×C₄×C₃₁	—	2	4	no	—
597	C₂×C₄×C₃₁	—	2	1	no	—
598	C₂×C₄×C₃₁	—	2	2	no	—
599	C₂×C₄×C₃₁	—	2	1	no	—
600	C₂×C₄×C₃₁	—	2	1	no	—
601	C₂×C₄×C₃₁	—	2	1	no	—
602	C₂×C₄×C₃₁	—	2	2	no	—
603	C₂×C₄×C₃₁	—	2	1	no	—
604	C₂×C₄×C₃₁	—	2	1	no	—
605	C₂×C₄×C₃₁	—	2	2	no	—
606	C₂×C₄×C₃₁	—	2	2	no	—
607	C₂×C₄×C₃₁	—	2	2	no	—
608	C₂×C₄×C₃₁	—	2	1	no	—
609	C₂×C₄×C₃₁	—	2	1	no	—
610	C₂×C₄×C₃₁	—	4	2	no	—
611	C₂×C₄×C₃₁	—	4	4	no	—
612	C₂×C₄×C₃₁	—	4	2	no	—
613	C₂×C₄×C₃₁	—	4	4	no	—
614	C₂×C₄×C₃₁	—	4	4	no	—
615	C₂×C₄×C₃₁	—	4	2	no	—
616	C₂×C₄×C₃₁	—	4	4	no	—
617	C₂×C₄×C₃₁	—	4	4	no	—
618	C₂×C₄×C₃₁	—	4	4	no	—
619	C₂×C₄×C₃₁	—	4	2	no	—
620	C₂×C₄×C₃₁	—	4	2	no	—
621	C₂×C₄×C₃₁	—	4	2	no	—
622	C₂×C₄×C₃₁	—	4	2	no	—
623	C₂×C₄×C₃₁	—	8	2	no	—
624	C₂×C₄×C₃₁	—	8	1	no	—
625	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
626	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
627	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
628	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
629	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
630	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
631	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
632	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
633	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
634	C₈×C₃₁	—	2	1	no	—
635	C₈×C₃₁	—	2	1	no	—
636	C₈×C₃₁	—	2	2	no	—
637	C₈×C₃₁	—	2	1	no	—
638	C₈×C₃₁	—	2	1	no	—
639	C₈×C₃₁	C₂²×D₄	1	4	yes	—
640	C₂×#578	C₂×C₃₁	1	1	yes	characteristic, complemented
641	C₂²×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
642	#3489	C₂×C₃₁	1	1	yes	characteristic, complemented
643	#3486	C₂×C₃₁	1	1	yes	characteristic, complemented
644	D₄×Q₁₆	C₂×C₃₁	1	2	yes	complemented
645	#3282	C₂×C₃₁	1	2	yes	complemented
646	#3277	C₂×C₃₁	1	2	yes	complemented
647	#3276	C₂×C₃₁	1	2	yes	complemented
648	#3270	C₂×C₃₁	1	2	yes	complemented
649	#3270	C₂×C₃₁	1	2	yes	complemented
650	#3269	C₂×C₃₁	1	2	yes	complemented
651	#3266	C₂×C₃₁	1	2	yes	complemented
652	#3156	C₂×C₃₁	1	1	yes	characteristic, complemented
653	#3063	C₂×C₃₁	1	1	yes	characteristic, complemented
654	#3056	C₂×C₃₁	1	1	yes	characteristic, complemented
655	#3046	C₂×C₃₁	1	1	yes	characteristic, complemented
656	#3044	C₂×C₃₁	1	1	yes	characteristic, complemented
657	#3013	C₂×C₃₁	1	1	yes	characteristic, complemented
658	#3011	C₂×C₃₁	1	1	yes	characteristic, complemented
659	#3002	C₂×C₃₁	1	1	yes	characteristic, complemented
660	C₂×#451	C₂×C₃₁	1	1	yes	characteristic, complemented
661	#2947	C₂×C₃₁	1	1	yes	characteristic, complemented
662	#2933	C₂×C₃₁	1	1	yes	characteristic, complemented
663	C₂²×C₃₁	—	2	1	no	—
664	C₂²×C₃₁	—	2	1	no	—
665	C₂²×C₃₁	—	2	1	no	—
666	C₂²×C₃₁	—	2	1	no	—
667	C₂²×C₃₁	—	2	1	no	—
668	C₂²×C₃₁	—	2	2	no	—
669	C₂²×C₃₁	—	2	1	no	—
670	C₂²×C₃₁	—	2	2	no	—
671	C₂²×C₃₁	—	2	2	no	—
672	C₂²×C₃₁	—	2	2	no	—
673	C₂²×C₃₁	—	2	1	no	—
674	C₂²×C₃₁	—	4	4	no	—
675	C₂²×C₃₁	—	4	1	no	—
676	C₂²×C₃₁	—	4	1	no	—
677	C₂²×C₃₁	—	4	1	no	—
678	C₂²×C₃₁	—	4	1	no	—
679	C₂²×C₃₁	—	4	1	no	—
680	C₂²×C₃₁	—	4	1	no	—
681	C₂²×C₃₁	—	4	1	no	—
682	C₂²×C₃₁	—	4	1	no	—
683	C₂²×C₃₁	—	8	4	no	—
684	C₂²×C₃₁	D₄²	1	2	yes	—
685	C₂²×C₃₁	#578	1	2	yes	complemented
686	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
687	C₄×C₃₁	—	2	2	no	—
688	C₄×C₃₁	—	2	1	no	—
689	C₄×C₃₁	—	2	1	no	—
690	C₄×C₃₁	—	2	2	no	—
691	C₄×C₃₁	—	2	4	no	—
692	C₄×C₃₁	—	2	2	no	—
693	C₄×C₃₁	—	2	2	no	—
694	C₄×C₃₁	—	4	2	no	—
695	C₄×C₃₁	—	4	1	no	—
696	C₄×C₃₁	—	4	1	no	—
697	C₄×C₃₁	—	4	2	no	—
698	C₄×C₃₁	—	4	1	no	—
699	C₄×C₃₁	—	4	2	no	—
700	C₄×C₃₁	—	4	1	no	—
701	C₄×C₃₁	D₄²	1	2	yes	—
702	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
703	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
705	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
707	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
708	#578	—	2	8	no	—
709	C₂×#137	—	2	8	no	—
710	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
711	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
712	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
713	C₂×#137	C₂²×C₃₁	1	2	yes	—
714	C₂×#137	C₂²×C₃₁	1	2	yes	—
715	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
716	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
717	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
718	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
719	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
720	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
721	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
722	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
723	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
724	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
725	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
726	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
727	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic, complemented
728	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
729	D₄×Q₈	—	2	1	no	—
730	D₄×Q₈	—	2	1	no	—
731	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
732	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
733	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
734	#548	—	2	1	no	—
735	#548	—	2	1	no	—
736	#548	C₂²×C₃₁	1	2	yes	—
737	#548	C₂²×C₃₁	1	2	yes	—
738	#548	C₂²×C₃₁	1	2	yes	complemented
739	#547	—	2	2	no	—
740	#547	C₂²×C₃₁	1	2	yes	—
741	#546	—	2	2	no	—
742	#546	C₂²×C₃₁	1	2	yes	—
743	#537	—	2	1	no	—
744	#537	C₂²×C₃₁	1	1	yes	characteristic
745	#536	—	2	2	no	—
746	#536	—	2	1	no	—
747	#536	C₂²×C₃₁	1	1	yes	characteristic
748	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
749	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
750	#525	—	2	1	no	—
751	#525	—	2	2	no	—
752	#525	C₂²×C₃₁	1	1	yes	characteristic
753	#525	C₂²×C₃₁	1	1	yes	characteristic
754	C₂×C₂²⋊Q₈	—	2	1	no	—
755	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
756	#520	C₂²×C₃₁	1	1	yes	characteristic
757	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
758	#497	C₂²×C₃₁	1	2	yes	complemented
759	#497	C₂²×C₃₁	1	2	yes	complemented
760	#495	C₂²×C₃₁	1	2	yes	complemented
761	#494	C₂²×C₃₁	1	2	yes	complemented
762	#470	C₂²×C₃₁	1	2	yes	complemented
763	#470	C₂²×C₃₁	1	2	yes	complemented
764	#468	C₂²×C₃₁	1	2	yes	complemented
765	#468	C₂²×C₃₁	1	2	yes	complemented
766	#467	C₂²×C₃₁	1	2	yes	—
767	#467	C₂²×C₃₁	1	2	yes	complemented
768	#465	C₂²×C₃₁	1	2	yes	—
769	#465	C₂²×C₃₁	1	2	yes	complemented
770	#464	C₂²×C₃₁	1	2	yes	complemented
771	#464	C₂²×C₃₁	1	2	yes	complemented
772	#464	C₂²×C₃₁	1	2	yes	complemented
773	#463	C₂²×C₃₁	1	2	yes	complemented
774	#462	C₂²×C₃₁	1	2	yes	complemented
775	#462	C₂²×C₃₁	1	2	yes	complemented
776	#462	C₂²×C₃₁	1	2	yes	complemented
777	#461	C₂²×C₃₁	1	2	yes	complemented
778	#452	C₂²×C₃₁	1	1	yes	characteristic
779	#452	C₂²×C₃₁	1	1	yes	characteristic
780	#452	C₂²×C₃₁	1	2	yes	complemented
781	#452	C₂²×C₃₁	1	2	yes	complemented
782	#452	C₂²×C₃₁	1	2	yes	complemented
783	#451	C₂²×C₃₁	1	2	yes	—
784	#451	C₂²×C₃₁	1	2	yes	—
785	#451	C₂²×C₃₁	1	1	yes	characteristic
786	#451	C₂²×C₃₁	1	2	yes	complemented
787	#451	C₂²×C₃₁	1	2	yes	complemented
788	#451	C₂²×C₃₁	1	2	yes	complemented
789	#451	C₂²×C₃₁	1	2	yes	complemented
790	#451	C₂²×C₃₁	1	2	yes	complemented
791	#450	C₂²×C₃₁	1	1	yes	characteristic
792	#449	C₂²×C₃₁	1	1	yes	characteristic
793	#449	C₂²×C₃₁	1	1	yes	characteristic
794	#449	C₂²×C₃₁	1	2	yes	complemented
795	#448	C₂²×C₃₁	1	1	yes	characteristic
796	#448	C₂²×C₃₁	1	2	yes	complemented
797	#447	C₂²×C₃₁	1	1	yes	characteristic
798	#441	C₂²×C₃₁	1	2	yes	complemented
799	#440	C₂²×C₃₁	1	2	yes	complemented
800	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
801	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
802	#436	C₂²×C₃₁	1	2	yes	complemented
803	#435	C₂²×C₃₁	1	2	yes	—
804	#435	C₂²×C₃₁	1	2	yes	complemented
805	C₈×D₄	C₂²×C₃₁	1	2	yes	—
806	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
807	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
808	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
809	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
810	#416	C₂²×C₃₁	1	1	yes	characteristic
811	#416	C₂²×C₃₁	1	1	yes	characteristic
812	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
813	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
814	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
815	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
816	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
817	C₂×C₃₁	—	2	2	no	—
818	C₂×C₃₁	—	2	2	no	—
819	C₂×C₃₁	—	4	2	no	—
820	C₂×C₃₁	—	4	1	no	—
821	C₂×C₃₁	—	4	2	no	—
822	C₂×C₃₁	—	8	1	no	—
823	C₂×C₃₁	—	8	1	no	—
824	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
825	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
826	C₂×C₃₁	#3586	1	1	yes	characteristic
827	2₋¹⁺⁴	—	2	4	no	—
828	2₋¹⁺⁴	—	2	4	no	—
829	2₋¹⁺⁴	—	4	2	no	—
830	2₋¹⁺⁴	—	4	2	no	—
831	C₂×#41	—	2	2	no	—
832	C₂×#41	—	2	1	no	—
833	C₂×#41	—	2	2	no	—
834	C₂×#41	—	2	1	no	—
835	C₂×#41	—	2	1	no	—
836	C₂×#41	—	2	1	no	—
837	C₂×#41	—	2	4	no	—
838	C₂×#41	—	4	2	no	—
839	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
840	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
841	C₂×#41	C₂³×C₃₁	1	2	yes	—
842	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
843	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
844	C₂×#41	C₂³×C₃₁	1	2	yes	—
845	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
846	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
847	C₂²×Q₈	—	2	1	no	—
848	C₂²×Q₈	—	2	1	no	—
849	C₂²×Q₈	—	2	1	no	—
850	C₂²×Q₈	—	2	1	no	—
851	C₂²×Q₈	—	2	1	no	—
852	C₂²×Q₈	—	2	4	no	—
853	C₂²×Q₈	—	4	2	no	—
854	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
855	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
856	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
857	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
858	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
859	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
861	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₂²×D₄	—	2	1	no	—
863	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
864	C₂³×C₄	—	2	1	no	—
865	C₂³×C₄	—	2	1	no	—
866	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
867	#137	—	2	4	no	—
868	#137	—	2	4	no	—
869	#137	—	2	8	no	—
870	#137	—	2	8	no	—
871	#137	—	2	8	no	—
872	#137	—	2	8	no	—
873	#137	—	2	4	no	—
874	#137	—	2	4	no	—
875	#137	D₄×C₃₁	1	8	yes	complemented
876	#135	—	2	4	no	—
877	#135	—	2	8	no	—
878	#135	—	4	2	no	—
879	C₂×Q₁₆	—	2	4	no	—
880	C₂×Q₁₆	—	2	8	no	—
881	C₂×Q₁₆	—	2	8	no	—
882	C₂×Q₁₆	—	4	2	no	—
883	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
884	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
885	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
886	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
887	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
888	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
889	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
890	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
891	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
892	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
893	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
894	C₂×SD₁₆	—	2	8	no	—
895	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
896	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
897	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
898	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
899	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
900	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
901	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
902	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
903	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
904	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
905	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
906	#131	—	2	4	no	—
907	C₂×M₁₆	—	2	4	no	—
908	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
909	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
910	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
911	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
912	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
913	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
914	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
915	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
916	C₄⋊Q₈	—	2	1	no	—
917	C₄⋊Q₈	—	2	2	no	—
918	C₄⋊Q₈	—	2	2	no	—
919	C₄⋊Q₈	—	2	2	no	—
920	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
921	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
922	#124	—	2	1	no	—
923	#124	—	2	2	no	—
924	#124	—	2	2	no	—
925	#124	—	2	2	no	—
926	#124	C₂³×C₃₁	1	2	yes	—
927	#124	C₂³×C₃₁	1	2	yes	—
928	#123	—	2	2	no	—
929	#123	—	2	1	no	—
930	#123	—	2	2	no	—
931	#123	—	2	2	no	—
932	#123	—	2	2	no	—
933	#123	—	2	2	no	—
934	#123	—	2	2	no	—
935	#123	D₄×C₃₁	1	2	yes	—
936	C₂²⋊Q₈	—	2	1	no	—
937	C₂²⋊Q₈	—	2	1	no	—
938	C₂²⋊Q₈	—	2	1	no	—
939	C₂²⋊Q₈	—	2	1	no	—
940	C₂²⋊Q₈	—	2	2	no	—
941	C₂²⋊Q₈	—	2	1	no	—
942	C₂²⋊Q₈	—	2	2	no	—
943	C₂²⋊Q₈	—	2	2	no	—
944	C₂²⋊Q₈	—	2	1	no	—
945	C₂²⋊Q₈	—	2	1	no	—
946	C₂²⋊Q₈	—	2	2	no	—
947	C₂²⋊Q₈	—	2	2	no	—
948	C₂²⋊Q₈	—	2	2	no	—
949	C₂²⋊Q₈	—	2	2	no	—
950	C₂²⋊Q₈	—	2	2	no	—
951	C₂²⋊Q₈	—	2	2	no	—
952	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
953	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
954	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
955	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
956	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
957	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
958	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
959	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
960	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
961	#121	—	2	1	no	—
962	#121	—	2	2	no	—
963	#121	—	2	2	no	—
964	#121	—	2	2	no	—
965	#121	—	2	2	no	—
966	#121	—	2	2	no	—
967	#121	—	2	2	no	—
968	#121	D₄×C₃₁	1	1	yes	characteristic
969	#121	D₄×C₃₁	1	1	yes	characteristic
970	#121	C₂³×C₃₁	1	1	yes	characteristic
971	#121	C₂³×C₃₁	1	1	yes	characteristic
972	#121	C₂³×C₃₁	1	2	yes	—
973	#120	—	2	1	no	—
974	#120	—	2	2	no	—
975	#120	D₄×C₃₁	1	2	yes	—
976	C₄×Q₈	—	2	1	no	—
977	C₄×Q₈	—	2	1	no	—
978	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
979	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
980	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
981	C₄×D₄	—	2	2	no	—
982	C₄×D₄	—	2	2	no	—
983	C₄×D₄	—	2	2	no	—
984	C₄×D₄	—	2	1	no	—
985	C₄×D₄	—	2	1	no	—
986	C₄×D₄	—	2	2	no	—
987	C₄×D₄	—	2	2	no	—
988	C₄×D₄	—	2	2	no	—
989	C₄×D₄	—	2	2	no	—
990	C₄×D₄	C₂³×C₃₁	1	2	yes	—
991	C₄×D₄	C₂³×C₃₁	1	2	yes	—
992	C₄×D₄	C₂³×C₃₁	1	2	yes	—
993	#117	—	2	1	no	—
994	#117	—	2	2	no	—
995	#117	C₂³×C₃₁	1	1	yes	characteristic
996	#117	C₂³×C₃₁	1	1	yes	characteristic
997	C₂×C₄⋊C₄	—	2	1	no	—
998	C₂×C₄⋊C₄	—	2	1	no	—
999	C₂×C₄⋊C₄	—	2	2	no	—
1000	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
1001	C₂×C₂²⋊C₄	—	2	1	no	—
1002	C₂×C₂²⋊C₄	—	2	2	no	—
1003	#107	C₂³×C₃₁	1	2	yes	—
1004	#106	C₂³×C₃₁	1	2	yes	—
1005	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
1006	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
1007	#103	C₂³×C₃₁	1	2	yes	—
1008	#103	C₂³×C₃₁	1	2	yes	—
1009	#103	C₂³×C₃₁	1	2	yes	—
1010	#103	C₂³×C₃₁	1	2	yes	—
1011	#103	C₂³×C₃₁	1	1	yes	characteristic
1012	#103	C₂³×C₃₁	1	1	yes	characteristic
1013	#103	C₂³×C₃₁	1	1	yes	characteristic
1014	#103	C₂³×C₃₁	1	1	yes	characteristic
1015	#103	C₂³×C₃₁	1	2	yes	—
1016	#103	C₂³×C₃₁	1	2	yes	—
1017	#103	C₂³×C₃₁	1	2	yes	—
1018	#102	C₂³×C₃₁	1	1	yes	characteristic
1019	#102	C₂³×C₃₁	1	1	yes	characteristic
1020	#102	C₂³×C₃₁	1	1	yes	characteristic
1021	#102	C₂³×C₃₁	1	1	yes	characteristic
1022	#102	C₂³×C₃₁	1	2	yes	—
1023	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1024	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1025	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1026	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
1027	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1028	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1029	#97	C₂³×C₃₁	1	2	yes	—
1030	C₄×C₈	C₂³×C₃₁	1	2	yes	—
1031	C₃₁	#61076	1	1	yes	characteristic, direct product factor, Sylow
1032	C₂⁴	—	2	1	no	—
1033	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
1034	#41	—	2	2	no	—
1035	#41	—	2	2	no	—
1036	#41	—	2	2	no	—
1037	#41	—	2	4	no	—
1038	#41	—	2	2	no	—
1039	#41	—	2	4	no	—
1040	#41	—	2	2	no	—
1041	#41	—	2	2	no	—
1042	#41	—	2	2	no	—
1043	#41	—	2	2	no	—
1044	#41	—	2	2	no	—
1045	#41	—	4	4	no	—
1046	#41	—	4	1	no	—
1047	#41	—	4	1	no	—
1048	#41	—	4	2	no	—
1049	#41	—	4	2	no	—
1050	#41	—	4	4	no	—
1051	#41	—	4	8	no	—
1052	#41	—	4	4	no	—
1053	#41	—	4	8	no	—
1054	#41	—	4	4	no	—
1055	#41	C₂×D₄×C₃₁	1	4	yes	—
1056	C₂×Q₈	—	2	1	no	—
1057	C₂×Q₈	—	2	1	no	—
1058	C₂×Q₈	—	2	2	no	—
1059	C₂×Q₈	—	2	2	no	—
1060	C₂×Q₈	—	2	1	no	—
1061	C₂×Q₈	—	2	2	no	—
1062	C₂×Q₈	—	2	2	no	—
1063	C₂×Q₈	—	2	1	no	—
1064	C₂×Q₈	—	2	2	no	—
1065	C₂×Q₈	—	2	4	no	—
1066	C₂×Q₈	—	2	2	no	—
1067	C₂×Q₈	—	2	4	no	—
1068	C₂×Q₈	—	2	4	no	—
1069	C₂×Q₈	—	2	4	no	—
1070	C₂×Q₈	—	2	2	no	—
1071	C₂×Q₈	—	2	2	no	—
1072	C₂×Q₈	—	2	2	no	—
1073	C₂×Q₈	—	2	2	no	—
1074	C₂×Q₈	—	4	4	no	—
1075	C₂×Q₈	—	4	2	no	—
1076	C₂×Q₈	—	4	2	no	—
1077	C₂×Q₈	—	4	1	no	—
1078	C₂×Q₈	—	4	2	no	—
1079	C₂×Q₈	—	4	2	no	—
1080	C₂×Q₈	—	4	4	no	—
1081	C₂×Q₈	—	4	4	no	—
1082	C₂×Q₈	—	4	4	no	—
1083	C₂×Q₈	—	4	4	no	—
1084	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
1085	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1086	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1087	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1088	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1089	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1090	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1091	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1092	C₂×D₄	—	2	1	no	—
1093	C₂×D₄	—	2	2	no	—
1094	C₂×D₄	—	2	1	no	—
1095	C₂×D₄	—	2	1	no	—
1096	C₂×D₄	—	2	2	no	—
1097	C₂×D₄	—	2	1	no	—
1098	C₂×D₄	—	2	1	no	—
1099	C₂×D₄	—	2	1	no	—
1100	C₂×D₄	—	2	1	no	—
1101	C₂×D₄	—	2	2	no	—
1102	C₂×D₄	—	2	2	no	—
1103	C₂×D₄	—	2	1	no	—
1104	C₂×D₄	—	4	1	no	—
1105	C₂×D₄	—	4	4	no	—
1106	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1107	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1108	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1109	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1110	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1111	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1112	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1113	C₂²×C₄	—	2	1	no	—
1114	C₂²×C₄	—	2	1	no	—
1115	C₂²×C₄	—	2	2	no	—
1116	C₂²×C₄	—	2	2	no	—
1117	C₂²×C₄	—	2	1	no	—
1118	C₂²×C₄	—	2	2	no	—
1119	C₂²×C₄	—	2	2	no	—
1120	C₂²×C₄	—	2	2	no	—
1121	C₂²×C₄	—	2	1	no	—
1122	C₂²×C₄	—	2	2	no	—
1123	C₂²×C₄	—	2	1	no	—
1124	C₂²×C₄	—	2	1	no	—
1125	C₂²×C₄	—	2	2	no	—
1126	C₂²×C₄	—	2	1	no	—
1127	C₂²×C₄	—	2	1	no	—
1128	C₂²×C₄	—	2	2	no	—
1129	C₂²×C₄	—	2	1	no	—
1130	C₂²×C₄	—	2	1	no	—
1131	C₂²×C₄	—	2	2	no	—
1132	C₂²×C₄	—	4	4	no	—
1133	C₂²×C₄	—	4	4	no	—
1134	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1135	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1136	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1137	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1138	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1139	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1140	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1141	Q₁₆	—	2	4	no	—
1142	Q₁₆	—	2	2	no	—
1143	Q₁₆	—	2	4	no	—
1144	Q₁₆	—	2	4	no	—
1145	Q₁₆	—	2	4	no	—
1146	Q₁₆	—	2	4	no	—
1147	Q₁₆	—	2	4	no	—
1148	Q₁₆	—	4	2	no	—
1149	Q₁₆	—	4	2	no	—
1150	Q₁₆	—	4	1	no	—
1151	Q₁₆	C₂×D₄×C₃₁	1	8	yes	—
1152	SD₁₆	—	2	4	no	—
1153	SD₁₆	—	2	2	no	—
1154	SD₁₆	—	2	4	no	—
1155	SD₁₆	—	2	2	no	—
1156	SD₁₆	—	2	4	no	—
1157	SD₁₆	—	2	4	no	—
1158	SD₁₆	—	4	1	no	—
1159	SD₁₆	—	4	1	no	—
1160	SD₁₆	C₂×D₄×C₃₁	1	8	yes	—
1161	D₈	—	2	2	no	—
1162	D₈	—	4	1	no	—
1163	M₁₆	—	2	2	no	—
1164	M₁₆	—	2	4	no	—
1165	M₁₆	—	2	4	no	—
1166	M₁₆	C₂×D₄×C₃₁	1	4	yes	—
1167	C₂×C₈	—	2	2	no	—
1168	C₂×C₈	—	2	2	no	—
1169	C₂×C₈	—	2	4	no	—
1170	C₂×C₈	—	2	4	no	—
1171	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1172	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1173	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1174	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1175	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1176	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1177	C₄⋊C₄	—	2	2	no	—
1178	C₄⋊C₄	—	2	1	no	—
1179	C₄⋊C₄	—	2	2	no	—
1180	C₄⋊C₄	—	2	2	no	—
1181	C₄⋊C₄	—	2	2	no	—
1182	C₄⋊C₄	—	2	2	no	—
1183	C₄⋊C₄	—	2	2	no	—
1184	C₄⋊C₄	—	2	2	no	—
1185	C₄⋊C₄	—	2	2	no	—
1186	C₄⋊C₄	—	2	2	no	—
1187	C₄⋊C₄	—	2	2	no	—
1188	C₄⋊C₄	—	2	2	no	—
1189	C₄⋊C₄	—	2	1	no	—
1190	C₄⋊C₄	—	2	1	no	—
1191	C₄⋊C₄	—	2	2	no	—
1192	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1193	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1194	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1195	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1196	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1197	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1198	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1199	C₂²⋊C₄	—	2	2	no	—
1200	C₂²⋊C₄	—	2	2	no	—
1201	C₂²⋊C₄	—	2	1	no	—
1202	C₂²⋊C₄	—	2	1	no	—
1203	C₂²⋊C₄	—	2	1	no	—
1204	C₂²⋊C₄	—	2	2	no	—
1205	C₂²⋊C₄	—	2	2	no	—
1206	C₂²⋊C₄	—	2	2	no	—
1207	C₂²⋊C₄	—	2	2	no	—
1208	C₂²⋊C₄	—	2	2	no	—
1209	C₂²⋊C₄	—	2	2	no	—
1210	C₂²⋊C₄	—	2	2	no	—
1211	C₂²⋊C₄	—	2	2	no	—
1212	C₂²⋊C₄	—	2	2	no	—
1213	C₂²⋊C₄	—	2	1	no	—
1214	C₂²⋊C₄	—	2	1	no	—
1215	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1216	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1217	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1218	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1219	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1220	C₄²	—	2	2	no	—
1221	C₄²	—	2	2	no	—
1222	C₄²	—	2	2	no	—
1223	C₄²	—	2	1	no	—
1224	C₄²	C₂⁴×C₃₁	1	2	yes	—
1225	C₂³	—	2	2	no	—
1226	C₂³	—	2	2	no	—
1227	C₂³	—	2	1	no	—
1228	C₂³	—	2	1	no	—
1229	C₂³	—	2	1	no	—
1230	C₂³	—	4	1	no	—
1231	C₂³	—	4	2	no	—
1232	C₂³	—	4	2	no	—
1233	C₂³	—	8	1	no	—
1234	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1235	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1236	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1237	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1238	Q₈	—	2	4	no	—
1239	Q₈	—	2	2	no	—
1240	Q₈	—	2	2	no	—
1241	Q₈	—	2	1	no	—
1242	Q₈	—	2	2	no	—
1243	Q₈	—	2	1	no	—
1244	Q₈	—	2	2	no	—
1245	Q₈	—	2	1	no	—
1246	Q₈	—	2	1	no	—
1247	Q₈	—	2	1	no	—
1248	Q₈	—	2	2	no	—
1249	Q₈	—	2	2	no	—
1250	Q₈	—	4	4	no	—
1251	Q₈	—	4	4	no	—
1252	Q₈	—	4	4	no	—
1253	Q₈	—	4	4	no	—
1254	Q₈	—	4	2	no	—
1255	Q₈	—	4	2	no	—
1256	Q₈	—	4	2	no	—
1257	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
1258	Q₈	C₂²×D₄×C₃₁	1	2	yes	—
1259	D₄	—	2	4	no	—
1260	D₄	—	2	4	no	—
1261	D₄	—	2	4	no	—
1262	D₄	—	2	2	no	—
1263	D₄	—	2	1	no	—
1264	D₄	—	2	1	no	—
1265	D₄	—	2	1	no	—
1266	D₄	—	2	1	no	—
1267	D₄	—	2	1	no	—
1268	D₄	—	4	2	no	—
1269	D₄	—	4	2	no	—
1270	D₄	—	4	2	no	—
1271	D₄	—	4	4	no	—
1272	D₄	—	4	2	no	—
1273	D₄	—	4	4	no	—
1274	D₄	—	4	2	no	—
1275	D₄	—	4	2	no	—
1276	D₄	—	4	2	no	—
1277	D₄	—	4	2	no	—
1278	D₄	—	8	2	no	—
1279	D₄	C₂²×D₄×C₃₁	1	2	yes	—
1280	C₂×C₄	—	2	2	no	—
1281	C₂×C₄	—	2	4	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	2	no	—
1284	C₂×C₄	—	2	2	no	—
1285	C₂×C₄	—	2	2	no	—
1286	C₂×C₄	—	2	4	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	2	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	2	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	2	no	—
1296	C₂×C₄	—	2	2	no	—
1297	C₂×C₄	—	2	2	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	4	2	no	—
1301	C₂×C₄	—	4	4	no	—
1302	C₂×C₄	—	4	2	no	—
1303	C₂×C₄	—	4	4	no	—
1304	C₂×C₄	—	4	4	no	—
1305	C₂×C₄	—	4	2	no	—
1306	C₂×C₄	—	4	4	no	—
1307	C₂×C₄	—	4	4	no	—
1308	C₂×C₄	—	4	4	no	—
1309	C₂×C₄	—	4	2	no	—
1310	C₂×C₄	—	4	2	no	—
1311	C₂×C₄	—	4	2	no	—
1312	C₂×C₄	—	4	2	no	—
1313	C₂×C₄	—	8	2	no	—
1314	C₂×C₄	—	8	1	no	—
1315	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1316	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1317	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1318	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1319	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1320	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1321	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1322	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1323	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1324	C₈	—	2	1	no	—
1325	C₈	—	2	1	no	—
1326	C₈	—	2	2	no	—
1327	C₈	—	2	1	no	—
1328	C₈	—	2	1	no	—
1329	C₈	C₂²×D₄×C₃₁	1	4	yes	—
1330	C₂²	—	2	1	no	—
1331	C₂²	—	2	1	no	—
1332	C₂²	—	2	1	no	—
1333	C₂²	—	2	1	no	—
1334	C₂²	—	2	1	no	—
1335	C₂²	—	2	2	no	—
1336	C₂²	—	2	2	no	—
1337	C₂²	—	2	2	no	—
1338	C₂²	—	2	1	no	—
1339	C₂²	—	2	1	no	—
1340	C₂²	—	2	2	no	—
1341	C₂²	—	4	4	no	—
1342	C₂²	—	4	1	no	—
1343	C₂²	—	4	1	no	—
1344	C₂²	—	4	1	no	—
1345	C₂²	—	4	1	no	—
1346	C₂²	—	4	1	no	—
1347	C₂²	—	4	1	no	—
1348	C₂²	—	4	1	no	—
1349	C₂²	—	4	1	no	—
1350	C₂²	—	8	4	no	—
1351	C₂²	D₄²×C₃₁	1	2	yes	—
1352	C₂²	C₃₁×#578	1	2	yes	complemented
1353	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1354	C₄	—	2	1	no	—
1355	C₄	—	2	1	no	—
1356	C₄	—	2	2	no	—
1357	C₄	—	2	4	no	—
1358	C₄	—	2	2	no	—
1359	C₄	—	2	2	no	—
1360	C₄	—	2	2	no	—
1361	C₄	—	4	1	no	—
1362	C₄	—	4	2	no	—
1363	C₄	—	4	1	no	—
1364	C₄	—	4	2	no	—
1365	C₄	—	4	1	no	—
1366	C₄	—	4	2	no	—
1367	C₄	—	4	1	no	—
1368	C₄	D₄²×C₃₁	1	2	yes	—
1369	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
1370	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1371	C₂	—	2	2	no	—
1372	C₂	—	2	2	no	—
1373	C₂	—	4	1	no	—
1374	C₂	—	4	2	no	—
1375	C₂	—	4	2	no	—
1376	C₂	—	8	1	no	—
1377	C₂	—	8	1	no	—
1378	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
1379	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1380	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 ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#578	C₂	semidirect
2. C₂²×C₃₁×#137	C₂	semidirect
3. C₃₁×#3489	C₂	semidirect
4. C₃₁×#3486	C₂	semidirect
5. D₄×Q₁₆×C₃₁	C₂	semidirect
6. C₃₁×#3282	C₂	semidirect
7. C₃₁×#3277	C₂	semidirect
8. C₃₁×#3276	C₂	semidirect
9. C₃₁×#3270	C₂	semidirect
10. C₃₁×#3270	C₂	semidirect
11. C₃₁×#3269	C₂	semidirect
12. C₃₁×#3266	C₂	semidirect
13. C₃₁×#3156	C₂	semidirect
14. C₃₁×#3063	C₂	semidirect
15. C₃₁×#3056	C₂	semidirect
16. C₃₁×#3046	C₂	semidirect
17. C₃₁×#3044	C₂	semidirect
18. C₃₁×#3013	C₂	semidirect
19. C₃₁×#3011	C₂	semidirect
20. C₃₁×#3002	C₂	semidirect
21. C₂×C₃₁×#451	C₂	semidirect
22. C₃₁×#2947	C₂	semidirect
23. C₃₁×#2933	C₂	semidirect
25. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
36. C₂×C₃₁×#137	C₂²	semidirect
37. C₂×C₃₁×#137	C₂²	semidirect
38. C₂×C₃₁×#137	C₂²	semidirect
41. C₂×C₃₁×#135	C₂²	semidirect
43. C₂²×Q₁₆×C₃₁	C₂²	semidirect
44. C₂²×Q₁₆×C₃₁	C₂²	semidirect
45. C₂²×Q₁₆×C₃₁	C₂²	semidirect
47. C₂×C₃₁×#131	C₂²	semidirect
53. D₄×Q₈×C₃₁	C₂²	semidirect
58. C₃₁×#548	C₂²	semidirect
68. C₃₁×#536	C₂²	semidirect
69. C₃₁×#536	C₂²	semidirect
77. C₃₁×#519	C₂²	semidirect
78. C₃₁×#497	C₂²	semidirect
79. C₃₁×#497	C₂²	semidirect
80. C₃₁×#495	C₂²	semidirect
81. C₃₁×#494	C₂²	semidirect
82. C₃₁×#470	C₂²	semidirect
83. C₃₁×#470	C₂²	semidirect
84. C₃₁×#468	C₂²	semidirect
85. C₃₁×#468	C₂²	semidirect
87. C₃₁×#467	C₂²	semidirect
89. C₃₁×#465	C₂²	semidirect
90. C₃₁×#464	C₂²	semidirect
91. C₃₁×#464	C₂²	semidirect
92. C₃₁×#464	C₂²	semidirect
93. C₃₁×#463	C₂²	semidirect
94. C₃₁×#462	C₂²	semidirect
95. C₃₁×#462	C₂²	semidirect
96. C₃₁×#462	C₂²	semidirect
97. C₃₁×#461	C₂²	semidirect
100. C₃₁×#452	C₂²	semidirect
101. C₃₁×#452	C₂²	semidirect
102. C₃₁×#452	C₂²	semidirect
106. C₃₁×#451	C₂²	semidirect
107. C₃₁×#451	C₂²	semidirect
108. C₃₁×#451	C₂²	semidirect
109. C₃₁×#451	C₂²	semidirect
110. C₃₁×#451	C₂²	semidirect
114. C₃₁×#449	C₂²	semidirect
116. C₃₁×#448	C₂²	semidirect
118. C₃₁×#441	C₂²	semidirect
119. C₃₁×#440	C₂²	semidirect
120. C₄×Q₁₆×C₃₁	C₂²	semidirect
121. C₄×SD₁₆×C₃₁	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
124. C₃₁×#435	C₂²	semidirect
126. C₃₁×#428	C₂²	semidirect
127. C₃₁×#424	C₂²	semidirect
128. C₃₁×#419	C₂²	semidirect
129. C₃₁×#417	C₂²	semidirect
132. C₂×C₃₁×#103	C₂²	semidirect
133. C₂×C₃₁×#103	C₂²	semidirect
134. C₃₁×#408	C₂²	semidirect
136. C₃₁×#405	C₂²	semidirect
185. C₃₁×#137	D₄	semidirect
534. #61076	C₃₁	direct (N × H)
640. C₂×#578	C₂×C₃₁	semidirect
641. C₂²×#137	C₂×C₃₁	semidirect
642. #3489	C₂×C₃₁	semidirect
643. #3486	C₂×C₃₁	semidirect
644. D₄×Q₁₆	C₂×C₃₁	semidirect
645. #3282	C₂×C₃₁	semidirect
646. #3277	C₂×C₃₁	semidirect
647. #3276	C₂×C₃₁	semidirect
648. #3270	C₂×C₃₁	semidirect
649. #3270	C₂×C₃₁	semidirect
650. #3269	C₂×C₃₁	semidirect
651. #3266	C₂×C₃₁	semidirect
652. #3156	C₂×C₃₁	semidirect
653. #3063	C₂×C₃₁	semidirect
654. #3056	C₂×C₃₁	semidirect
655. #3046	C₂×C₃₁	semidirect
656. #3044	C₂×C₃₁	semidirect
657. #3013	C₂×C₃₁	semidirect
658. #3011	C₂×C₃₁	semidirect
659. #3002	C₂×C₃₁	semidirect
660. C₂×#451	C₂×C₃₁	semidirect
661. #2947	C₂×C₃₁	semidirect
662. #2933	C₂×C₃₁	semidirect
685. C₂²×C₃₁	#578	semidirect
705. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
716. C₂×#137	C₂²×C₃₁	semidirect
717. C₂×#137	C₂²×C₃₁	semidirect
718. C₂×#137	C₂²×C₃₁	semidirect
721. C₂×#135	C₂²×C₃₁	semidirect
723. C₂²×Q₁₆	C₂²×C₃₁	semidirect
724. C₂²×Q₁₆	C₂²×C₃₁	semidirect
725. C₂²×Q₁₆	C₂²×C₃₁	semidirect
727. C₂×#131	C₂²×C₃₁	semidirect
733. D₄×Q₈	C₂²×C₃₁	semidirect
738. #548	C₂²×C₃₁	semidirect
748. #536	C₂²×C₃₁	semidirect
749. #536	C₂²×C₃₁	semidirect
757. #519	C₂²×C₃₁	semidirect
758. #497	C₂²×C₃₁	semidirect
759. #497	C₂²×C₃₁	semidirect
760. #495	C₂²×C₃₁	semidirect
761. #494	C₂²×C₃₁	semidirect
762. #470	C₂²×C₃₁	semidirect
763. #470	C₂²×C₃₁	semidirect
764. #468	C₂²×C₃₁	semidirect
765. #468	C₂²×C₃₁	semidirect
767. #467	C₂²×C₃₁	semidirect
769. #465	C₂²×C₃₁	semidirect
770. #464	C₂²×C₃₁	semidirect
771. #464	C₂²×C₃₁	semidirect
772. #464	C₂²×C₃₁	semidirect
773. #463	C₂²×C₃₁	semidirect
774. #462	C₂²×C₃₁	semidirect
775. #462	C₂²×C₃₁	semidirect
776. #462	C₂²×C₃₁	semidirect
777. #461	C₂²×C₃₁	semidirect
780. #452	C₂²×C₃₁	semidirect
781. #452	C₂²×C₃₁	semidirect
782. #452	C₂²×C₃₁	semidirect
786. #451	C₂²×C₃₁	semidirect
787. #451	C₂²×C₃₁	semidirect
788. #451	C₂²×C₃₁	semidirect
789. #451	C₂²×C₃₁	semidirect
790. #451	C₂²×C₃₁	semidirect
794. #449	C₂²×C₃₁	semidirect
796. #448	C₂²×C₃₁	semidirect
798. #441	C₂²×C₃₁	semidirect
799. #440	C₂²×C₃₁	semidirect
800. C₄×Q₁₆	C₂²×C₃₁	semidirect
801. C₄×SD₁₆	C₂²×C₃₁	semidirect
802. #436	C₂²×C₃₁	semidirect
804. #435	C₂²×C₃₁	semidirect
806. #428	C₂²×C₃₁	semidirect
807. #424	C₂²×C₃₁	semidirect
808. #419	C₂²×C₃₁	semidirect
809. #417	C₂²×C₃₁	semidirect
812. C₂×#103	C₂²×C₃₁	semidirect
813. C₂×#103	C₂²×C₃₁	semidirect
814. #408	C₂²×C₃₁	semidirect
816. #405	C₂²×C₃₁	semidirect
875. #137	D₄×C₃₁	semidirect
1031. C₃₁	#61076	direct (N × H)
1352. C₂²	C₃₁×#578	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#578	2
C₂²×C₃₁×#137	2
C₃₁×#3489	2
C₃₁×#3486	2
D₄×Q₁₆×C₃₁	2
C₃₁×#3282	2
C₃₁×#3277	2
C₃₁×#3276	2
C₃₁×#3270	2
C₃₁×#3269	2
C₃₁×#3266	2
C₃₁×#3156	2
C₃₁×#3063	2
C₃₁×#3056	2
C₃₁×#3046	2
C₃₁×#3044	2
C₃₁×#3013	2
C₃₁×#3011	2
C₃₁×#3002	2
C₂×C₃₁×#451	2
C₃₁×#2947	2
C₃₁×#2933	2
#61076	31

Subgroups — C31×#61076 #21517835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61076 #21517835