Subgroups — C₃₁×#60601 #21517360

Order 7936.

2094 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₃₁×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3114	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3105	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3102	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3099	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3080	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3012	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2946	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
29	C₃₁×#553	—	2	2	no	—
30	C₃₁×#553	—	2	2	no	—
31	C₃₁×#553	—	2	1	no	—
32	C₃₁×#553	—	2	1	no	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#552	—	2	1	no	—
35	C₃₁×#541	C₂²	1	2	yes	complemented
36	C₃₁×#540	C₂²	1	2	yes	complemented
37	C₃₁×#537	C₂²	1	1	yes	characteristic
38	C₃₁×#537	C₂²	1	1	yes	characteristic
39	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#529	C₂²	1	2	yes	complemented
41	C₃₁×#529	C₂²	1	2	yes	complemented
42	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#520	—	2	1	no	—
44	C₃₁×#520	C₂²	1	2	yes	—
45	C₃₁×#520	C₂²	1	1	yes	characteristic
46	C₃₁×#520	C₂²	1	1	yes	characteristic
47	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#518	—	2	2	no	—
50	C₃₁×#518	—	2	1	no	—
51	C₃₁×#518	C₂²	1	2	yes	—
52	C₃₁×#518	C₂²	1	1	yes	characteristic
53	C₄×#41×C₃₁	—	2	1	no	—
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₃₁	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₃₁	—	2	2	no	—
58	C₂×C₄×D₄×C₃₁	—	2	1	no	—
59	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
60	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
61	C₃₁×#485	C₂²	1	2	yes	complemented
62	C₃₁×#485	C₂²	1	2	yes	complemented
63	C₃₁×#484	C₂²	1	2	yes	complemented
64	C₃₁×#483	C₂²	1	2	yes	complemented
65	C₃₁×#482	C₂²	1	2	yes	complemented
66	C₃₁×#482	C₂²	1	2	yes	complemented
67	C₃₁×#481	C₂²	1	2	yes	complemented
68	C₃₁×#480	C₂²	1	2	yes	complemented
69	C₃₁×#479	C₂²	1	2	yes	complemented
70	C₃₁×#479	C₂²	1	2	yes	complemented
71	C₃₁×#478	C₂²	1	2	yes	complemented
72	C₃₁×#478	C₂²	1	2	yes	complemented
73	C₃₁×#478	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#463	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#463	C₂²	1	2	yes	complemented
82	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#461	C₂²	1	2	yes	complemented
85	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#459	C₂²	1	2	yes	complemented
88	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#452	C₂²	1	2	yes	—
90	C₃₁×#452	C₂²	1	2	yes	—
91	C₃₁×#450	C₂²	1	2	yes	—
92	C₃₁×#450	C₂²	1	2	yes	—
93	C₃₁×#449	C₂²	1	2	yes	—
94	C₃₁×#449	C₂²	1	2	yes	—
95	C₃₁×#447	C₂²	1	2	yes	—
96	C₃₁×#447	C₂²	1	2	yes	—
97	C₃₁×#442	C₂²	1	2	yes	complemented
98	C₃₁×#442	C₂²	1	2	yes	complemented
99	C₃₁×#442	C₂²	1	2	yes	complemented
100	C₃₁×#441	C₂²	1	2	yes	complemented
101	C₃₁×#440	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
110	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
111	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
112	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
113	C₃₁×#433	C₂²	1	2	yes	complemented
114	C₃₁×#433	C₂²	1	2	yes	complemented
115	C₃₁×#432	C₂²	1	2	yes	complemented
116	C₃₁×#431	C₂²	1	2	yes	complemented
117	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
118	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#417	C₂²	1	1	yes	characteristic
124	C₃₁×#417	C₂²	1	1	yes	characteristic
125	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
131	C₃₁×#408	C₂²	1	1	yes	characteristic
132	C₃₁×#408	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×H(5,𝔽₂)	—	2	4	no	—
136	C₃₁×H(5,𝔽₂)	—	2	4	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₃₁	—	2	2	no	—
144	C₂²×D₄×C₃₁	—	2	1	no	—
145	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₃₁	—	2	1	no	—
148	C₂³×C₄×C₃₁	—	2	2	no	—
149	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
150	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
151	C₃₁×#135	—	2	4	no	—
152	C₃₁×#135	—	2	4	no	—
153	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×D₈×C₃₁	C₂³	1	2	yes	—
163	C₂×D₈×C₃₁	C₂³	1	2	yes	—
164	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
169	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₃₁×#127	C₂³	1	1	yes	characteristic
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	C₂³	1	2	yes	—
180	C₃₁×#125	C₂³	1	2	yes	—
181	C₃₁×#124	C₂³	1	1	yes	characteristic
182	C₃₁×#124	C₂³	1	1	yes	characteristic
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₃₁×#121	—	2	1	no	—
192	C₃₁×#121	—	2	1	no	—
193	C₃₁×#121	—	2	2	no	—
194	C₃₁×#121	—	2	2	no	—
195	C₃₁×#121	—	2	1	no	—
196	C₃₁×#121	—	2	1	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	C₂³	1	2	yes	—
200	C₃₁×#121	C₂³	1	2	yes	—
201	C₄×Q₈×C₃₁	—	2	1	no	—
202	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
203	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
204	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
205	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
206	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
207	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
209	C₄×D₄×C₃₁	—	2	2	no	—
210	C₄×D₄×C₃₁	—	2	1	no	—
211	C₄×D₄×C₃₁	—	2	1	no	—
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	—	2	1	no	—
214	C₄×D₄×C₃₁	—	2	2	no	—
215	C₄×D₄×C₃₁	—	2	2	no	—
216	C₄×D₄×C₃₁	—	2	2	no	—
217	C₄×D₄×C₃₁	—	2	1	no	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	1	no	—
220	C₄×D₄×C₃₁	—	2	2	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	D₄	1	2	yes	—
233	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
234	C₄×D₄×C₃₁	D₄	1	2	yes	—
235	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	2	yes	—
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₃₁×#117	—	2	1	no	—
246	C₃₁×#117	—	2	2	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	—	2	2	no	—
253	C₃₁×#117	C₂³	1	1	yes	characteristic
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	1	yes	characteristic
256	C₃₁×#117	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
268	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂×C₄²×C₃₁	—	2	2	no	—
273	C₂×C₄²×C₃₁	—	2	1	no	—
274	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#107	C₂³	1	2	yes	—
278	C₃₁×#107	C₂³	1	2	yes	—
279	C₃₁×#107	C₂³	1	2	yes	—
280	C₃₁×#106	C₂³	1	2	yes	—
281	C₃₁×#106	C₂³	1	2	yes	—
282	C₃₁×#106	C₂³	1	2	yes	—
283	C₃₁×#106	C₂³	1	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
289	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	1	yes	characteristic
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×#102	C₂³	1	2	yes	—
309	C₃₁×#102	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₃₁×#97	C₂³	1	2	yes	—
315	C₃₁×#97	C₂³	1	2	yes	—
316	C₄×C₈×C₃₁	C₂³	1	2	yes	—
317	C₄×C₈×C₃₁	C₂³	1	2	yes	—
318	C₂⁴×C₃₁	—	2	2	no	—
319	C₂⁴×C₃₁	—	2	1	no	—
320	#41×C₃₁	—	2	8	no	—
321	#41×C₃₁	—	2	4	no	—
322	#41×C₃₁	—	2	4	no	—
323	#41×C₃₁	—	2	2	no	—
324	#41×C₃₁	—	2	2	no	—
325	#41×C₃₁	—	2	2	no	—
326	#41×C₃₁	—	2	2	no	—
327	#41×C₃₁	—	2	2	no	—
328	#41×C₃₁	—	2	2	no	—
329	#41×C₃₁	—	2	2	no	—
330	#41×C₃₁	#41	1	4	yes	—
331	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₃₁	—	2	16	no	—
336	C₂×D₄×C₃₁	—	2	8	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	—	2	4	no	—
340	C₂×D₄×C₃₁	—	2	4	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	2	1	no	—
347	C₂×D₄×C₃₁	—	2	1	no	—
348	C₂×D₄×C₃₁	—	2	1	no	—
349	C₂×D₄×C₃₁	—	2	2	no	—
350	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₃₁	#41	1	4	yes	—
353	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	2	2	no	—
364	C₂²×C₄×C₃₁	—	2	1	no	—
365	C₂²×C₄×C₃₁	—	2	1	no	—
366	C₂²×C₄×C₃₁	—	2	1	no	—
367	C₂²×C₄×C₃₁	—	2	2	no	—
368	C₂²×C₄×C₃₁	—	2	1	no	—
369	C₂²×C₄×C₃₁	—	2	2	no	—
370	C₂²×C₄×C₃₁	—	2	2	no	—
371	C₂²×C₄×C₃₁	—	2	2	no	—
372	C₂²×C₄×C₃₁	—	2	2	no	—
373	C₂²×C₄×C₃₁	—	2	2	no	—
374	C₂²×C₄×C₃₁	—	8	4	no	—
375	C₂²×C₄×C₃₁	—	8	2	no	—
376	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
378	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
380	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
382	Q₁₆×C₃₁	—	2	2	no	—
383	Q₁₆×C₃₁	—	2	2	no	—
384	SD₁₆×C₃₁	—	2	2	no	—
385	SD₁₆×C₃₁	—	2	2	no	—
386	SD₁₆×C₃₁	—	2	2	no	—
387	SD₁₆×C₃₁	—	2	2	no	—
388	SD₁₆×C₃₁	—	2	4	no	—
389	SD₁₆×C₃₁	—	2	4	no	—
390	D₈×C₃₁	—	2	2	no	—
391	D₈×C₃₁	—	2	2	no	—
392	D₈×C₃₁	—	2	4	no	—
393	D₈×C₃₁	—	2	4	no	—
394	M₁₆×C₃₁	—	2	2	no	—
395	M₁₆×C₃₁	—	2	2	no	—
396	C₂×C₈×C₃₁	—	2	2	no	—
397	C₂×C₈×C₃₁	—	2	2	no	—
398	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
401	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
402	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	—	2	2	no	—
407	C₄⋊C₄×C₃₁	—	2	1	no	—
408	C₄⋊C₄×C₃₁	—	2	1	no	—
409	C₄⋊C₄×C₃₁	—	2	1	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	2	no	—
412	C₄⋊C₄×C₃₁	—	2	2	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	2	no	—
415	C₄⋊C₄×C₃₁	—	2	2	no	—
416	C₄⋊C₄×C₃₁	—	2	1	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	—	2	2	no	—
419	C₄⋊C₄×C₃₁	—	2	1	no	—
420	C₄⋊C₄×C₃₁	—	2	1	no	—
421	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
423	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
424	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
425	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
427	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
429	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	1	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	—	2	2	no	—
439	C₂²⋊C₄×C₃₁	—	2	2	no	—
440	C₂²⋊C₄×C₃₁	—	2	1	no	—
441	C₂²⋊C₄×C₃₁	—	2	1	no	—
442	C₂²⋊C₄×C₃₁	—	2	1	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	—	2	2	no	—
445	C₂²⋊C₄×C₃₁	—	2	2	no	—
446	C₂²⋊C₄×C₃₁	—	2	2	no	—
447	C₂²⋊C₄×C₃₁	—	2	1	no	—
448	C₂²⋊C₄×C₃₁	—	2	1	no	—
449	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
452	C₄²×C₃₁	—	2	1	no	—
453	C₄²×C₃₁	—	2	2	no	—
454	C₄²×C₃₁	—	2	1	no	—
455	C₄²×C₃₁	—	2	2	no	—
456	C₄²×C₃₁	—	2	1	no	—
457	C₄²×C₃₁	—	2	2	no	—
458	C₄²×C₃₁	—	2	2	no	—
459	C₄²×C₃₁	C₂×D₄	1	2	yes	—
460	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
461	C₄²×C₃₁	C₂×D₄	1	2	yes	—
462	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
463	C₄²×C₃₁	C₂⁴	1	2	yes	—
464	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
465	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
466	#60601	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
467	C₂³×C₃₁	—	2	8	no	—
468	C₂³×C₃₁	—	2	2	no	—
469	C₂³×C₃₁	—	2	1	no	—
470	C₂³×C₃₁	—	2	4	no	—
471	C₂³×C₃₁	—	2	1	no	—
472	C₂³×C₃₁	—	2	1	no	—
473	C₂³×C₃₁	—	8	1	no	—
474	C₂³×C₃₁	—	8	2	no	—
475	C₂³×C₃₁	—	8	1	no	—
476	C₂³×C₃₁	—	8	2	no	—
477	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
478	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
479	Q₈×C₃₁	—	2	2	no	—
480	Q₈×C₃₁	—	2	1	no	—
481	Q₈×C₃₁	—	2	1	no	—
482	Q₈×C₃₁	—	2	1	no	—
483	Q₈×C₃₁	—	2	1	no	—
484	Q₈×C₃₁	—	2	1	no	—
485	Q₈×C₃₁	C₂×#41	1	2	yes	—
486	D₄×C₃₁	—	2	8	no	—
487	D₄×C₃₁	—	2	8	no	—
488	D₄×C₃₁	—	2	4	no	—
489	D₄×C₃₁	—	2	4	no	—
490	D₄×C₃₁	—	2	2	no	—
491	D₄×C₃₁	—	2	4	no	—
492	D₄×C₃₁	—	2	2	no	—
493	D₄×C₃₁	—	2	1	no	—
494	D₄×C₃₁	—	2	1	no	—
495	D₄×C₃₁	—	2	1	no	—
496	D₄×C₃₁	—	2	1	no	—
497	D₄×C₃₁	—	2	1	no	—
498	D₄×C₃₁	—	4	2	no	—
499	D₄×C₃₁	—	4	2	no	—
500	D₄×C₃₁	—	8	1	no	—
501	D₄×C₃₁	—	8	1	no	—
502	D₄×C₃₁	—	8	2	no	—
503	D₄×C₃₁	—	8	2	no	—
504	D₄×C₃₁	C₂×#41	1	2	yes	—
505	D₄×C₃₁	C₂×#41	1	4	yes	—
506	C₂×C₄×C₃₁	—	2	8	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	4	no	—
509	C₂×C₄×C₃₁	—	2	2	no	—
510	C₂×C₄×C₃₁	—	2	2	no	—
511	C₂×C₄×C₃₁	—	2	1	no	—
512	C₂×C₄×C₃₁	—	2	1	no	—
513	C₂×C₄×C₃₁	—	2	1	no	—
514	C₂×C₄×C₃₁	—	2	2	no	—
515	C₂×C₄×C₃₁	—	2	1	no	—
516	C₂×C₄×C₃₁	—	2	2	no	—
517	C₂×C₄×C₃₁	—	2	2	no	—
518	C₂×C₄×C₃₁	—	4	2	no	—
519	C₂×C₄×C₃₁	—	4	1	no	—
520	C₂×C₄×C₃₁	—	4	2	no	—
521	C₂×C₄×C₃₁	—	4	1	no	—
522	C₂×C₄×C₃₁	—	4	2	no	—
523	C₂×C₄×C₃₁	—	4	4	no	—
524	C₂×C₄×C₃₁	—	4	2	no	—
525	C₂×C₄×C₃₁	—	4	2	no	—
526	C₂×C₄×C₃₁	—	8	2	no	—
527	C₂×C₄×C₃₁	—	8	2	no	—
528	C₂×C₄×C₃₁	—	8	1	no	—
529	C₂×C₄×C₃₁	—	8	2	no	—
530	C₂×C₄×C₃₁	—	8	2	no	—
531	C₂×C₄×C₃₁	—	8	2	no	—
532	C₂×C₄×C₃₁	—	8	2	no	—
533	C₂×C₄×C₃₁	—	8	1	no	—
534	C₂×C₄×C₃₁	—	8	1	no	—
535	C₂×C₄×C₃₁	—	8	1	no	—
536	C₂×C₄×C₃₁	—	8	2	no	—
537	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
546	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
547	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
548	C₈×C₃₁	—	2	1	no	—
549	C₈×C₃₁	—	2	1	no	—
550	C₈×C₃₁	—	2	1	no	—
551	C₈×C₃₁	—	2	1	no	—
552	C₈×C₃₁	—	2	2	no	—
553	C₈×C₃₁	—	2	2	no	—
554	#3512	C₂×C₃₁	1	1	yes	characteristic, complemented
555	C₄×H(5,𝔽₂)	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3123	C₂×C₃₁	1	2	yes	complemented
557	#3122	C₂×C₃₁	1	2	yes	complemented
558	#3120	C₂×C₃₁	1	2	yes	complemented
559	#3119	C₂×C₃₁	1	2	yes	complemented
560	#3114	C₂×C₃₁	1	2	yes	complemented
561	#3111	C₂×C₃₁	1	2	yes	complemented
562	#3105	C₂×C₃₁	1	2	yes	complemented
563	#3102	C₂×C₃₁	1	2	yes	complemented
564	#3099	C₂×C₃₁	1	1	yes	characteristic, complemented
565	#3098	C₂×C₃₁	1	1	yes	characteristic, complemented
566	#3080	C₂×C₃₁	1	1	yes	characteristic, complemented
567	C₂×#478	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#3036	C₂×C₃₁	1	1	yes	characteristic, complemented
569	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
570	#3012	C₂×C₃₁	1	1	yes	characteristic, complemented
571	#3012	C₂×C₃₁	1	1	yes	characteristic, complemented
572	#2952	C₂×C₃₁	1	1	yes	characteristic, complemented
573	#2951	C₂×C₃₁	1	1	yes	characteristic, complemented
574	#2946	C₂×C₃₁	1	1	yes	characteristic, complemented
575	#2946	C₂×C₃₁	1	1	yes	characteristic, complemented
576	#2925	C₂×C₃₁	1	1	yes	characteristic, complemented
577	C₂²×C₃₁	—	2	1	no	—
578	C₂²×C₃₁	—	2	1	no	—
579	C₂²×C₃₁	—	2	2	no	—
580	C₂²×C₃₁	—	2	2	no	—
581	C₂²×C₃₁	—	2	2	no	—
582	C₂²×C₃₁	—	2	4	no	—
583	C₂²×C₃₁	—	2	2	no	—
584	C₂²×C₃₁	—	4	2	no	—
585	C₂²×C₃₁	—	4	1	no	—
586	C₂²×C₃₁	—	4	2	no	—
587	C₂²×C₃₁	—	4	1	no	—
588	C₂²×C₃₁	—	4	1	no	—
589	C₂²×C₃₁	—	4	1	no	—
590	C₂²×C₃₁	—	4	1	no	—
591	C₂²×C₃₁	—	4	1	no	—
592	C₂²×C₃₁	—	4	1	no	—
593	C₂²×C₃₁	—	4	1	no	—
594	C₂²×C₃₁	—	8	4	no	—
595	C₂²×C₃₁	—	8	8	no	—
596	C₂²×C₃₁	#525	1	2	yes	—
597	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
598	C₄×C₃₁	—	2	1	no	—
599	C₄×C₃₁	—	2	2	no	—
600	C₄×C₃₁	—	2	1	no	—
601	C₄×C₃₁	—	2	1	no	—
602	C₄×C₃₁	—	2	2	no	—
603	C₄×C₃₁	—	2	1	no	—
604	C₄×C₃₁	—	2	2	no	—
605	C₄×C₃₁	—	2	2	no	—
606	C₄×C₃₁	—	4	1	no	—
607	C₄×C₃₁	—	4	2	no	—
608	C₄×C₃₁	—	4	1	no	—
609	C₄×C₃₁	—	4	2	no	—
610	C₄×C₃₁	—	4	2	no	—
611	C₄×C₃₁	—	4	1	no	—
612	C₄×C₃₁	—	4	1	no	—
613	C₄×C₃₁	#525	1	2	yes	—
614	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
615	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
616	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
617	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
618	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
619	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
620	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
621	#553	—	2	2	no	—
622	#553	—	2	2	no	—
623	#553	—	2	1	no	—
624	#553	—	2	1	no	—
625	#552	—	2	1	no	—
626	#552	—	2	1	no	—
627	#541	C₂²×C₃₁	1	2	yes	complemented
628	#540	C₂²×C₃₁	1	2	yes	complemented
629	#537	C₂²×C₃₁	1	1	yes	characteristic
630	#537	C₂²×C₃₁	1	1	yes	characteristic
631	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#529	C₂²×C₃₁	1	2	yes	complemented
633	#529	C₂²×C₃₁	1	2	yes	complemented
634	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#520	—	2	1	no	—
636	#520	C₂²×C₃₁	1	2	yes	—
637	#520	C₂²×C₃₁	1	1	yes	characteristic
638	#520	C₂²×C₃₁	1	1	yes	characteristic
639	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#518	—	2	2	no	—
642	#518	—	2	1	no	—
643	#518	C₂²×C₃₁	1	2	yes	—
644	#518	C₂²×C₃₁	1	1	yes	characteristic
645	C₄×#41	—	2	1	no	—
646	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
647	C₄×#41	C₂²×C₃₁	1	2	yes	—
648	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
649	C₂×C₄×D₄	—	2	2	no	—
650	C₂×C₄×D₄	—	2	1	no	—
651	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
652	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
653	#485	C₂²×C₃₁	1	2	yes	complemented
654	#485	C₂²×C₃₁	1	2	yes	complemented
655	#484	C₂²×C₃₁	1	2	yes	complemented
656	#483	C₂²×C₃₁	1	2	yes	complemented
657	#482	C₂²×C₃₁	1	2	yes	complemented
658	#482	C₂²×C₃₁	1	2	yes	complemented
659	#481	C₂²×C₃₁	1	2	yes	complemented
660	#480	C₂²×C₃₁	1	2	yes	complemented
661	#479	C₂²×C₃₁	1	2	yes	complemented
662	#479	C₂²×C₃₁	1	2	yes	complemented
663	#478	C₂²×C₃₁	1	2	yes	complemented
664	#478	C₂²×C₃₁	1	2	yes	complemented
665	#478	C₂²×C₃₁	1	2	yes	complemented
666	#478	C₂²×C₃₁	1	2	yes	complemented
667	#478	C₂²×C₃₁	1	2	yes	complemented
668	#478	C₂²×C₃₁	1	2	yes	complemented
669	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#463	C₂²×C₃₁	1	2	yes	complemented
672	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#463	C₂²×C₃₁	1	2	yes	complemented
674	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#461	C₂²×C₃₁	1	2	yes	complemented
677	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#459	C₂²×C₃₁	1	2	yes	complemented
680	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	#452	C₂²×C₃₁	1	2	yes	—
682	#452	C₂²×C₃₁	1	2	yes	—
683	#450	C₂²×C₃₁	1	2	yes	—
684	#450	C₂²×C₃₁	1	2	yes	—
685	#449	C₂²×C₃₁	1	2	yes	—
686	#449	C₂²×C₃₁	1	2	yes	—
687	#447	C₂²×C₃₁	1	2	yes	—
688	#447	C₂²×C₃₁	1	2	yes	—
689	#442	C₂²×C₃₁	1	2	yes	complemented
690	#442	C₂²×C₃₁	1	2	yes	complemented
691	#442	C₂²×C₃₁	1	2	yes	complemented
692	#441	C₂²×C₃₁	1	2	yes	complemented
693	#440	C₂²×C₃₁	1	2	yes	complemented
694	#440	C₂²×C₃₁	1	2	yes	complemented
695	#440	C₂²×C₃₁	1	2	yes	complemented
696	#440	C₂²×C₃₁	1	2	yes	complemented
697	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
699	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
700	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
702	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
703	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
704	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
705	#433	C₂²×C₃₁	1	2	yes	complemented
706	#433	C₂²×C₃₁	1	2	yes	complemented
707	#432	C₂²×C₃₁	1	2	yes	complemented
708	#431	C₂²×C₃₁	1	2	yes	complemented
709	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
710	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
711	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
712	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
713	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
715	#417	C₂²×C₃₁	1	1	yes	characteristic
716	#417	C₂²×C₃₁	1	1	yes	characteristic
717	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
719	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
720	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
721	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
722	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
723	#408	C₂²×C₃₁	1	1	yes	characteristic
724	#408	C₂²×C₃₁	1	1	yes	characteristic
725	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
726	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	C₂×C₃₁	—	2	2	no	—
728	C₂×C₃₁	—	4	2	no	—
729	C₂×C₃₁	—	4	4	no	—
730	C₂×C₃₁	—	4	2	no	—
731	C₂×C₃₁	—	8	1	no	—
732	C₂×C₃₁	—	8	1	no	—
733	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
734	C₂×C₃₁	#3584	1	1	yes	characteristic
735	C₂×C₃₁	#3585	1	1	yes	characteristic
736	H(5,𝔽₂)	—	2	4	no	—
737	H(5,𝔽₂)	—	2	4	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	C₂³×C₃₁	1	2	yes	—
740	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
741	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
744	C₂²×D₄	—	2	2	no	—
745	C₂²×D₄	—	2	1	no	—
746	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
747	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
748	C₂³×C₄	—	2	1	no	—
749	C₂³×C₄	—	2	2	no	—
750	AGL(1,ℤ/8)	—	2	4	no	—
751	AGL(1,ℤ/8)	—	2	4	no	—
752	#135	—	2	4	no	—
753	#135	—	2	4	no	—
754	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
755	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
756	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
757	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
758	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
759	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
760	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
762	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
764	C₂×D₈	C₂³×C₃₁	1	2	yes	—
765	C₂×D₈	C₂³×C₃₁	1	2	yes	—
766	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
767	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
768	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
769	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
771	#127	C₂³×C₃₁	1	1	yes	characteristic
772	#126	—	2	2	no	—
773	#126	—	2	2	no	—
774	#126	—	2	2	no	—
775	#126	—	2	2	no	—
776	#125	—	2	2	no	—
777	#125	—	2	2	no	—
778	#125	—	2	1	no	—
779	#125	—	2	1	no	—
780	#125	C₂³×C₃₁	1	2	yes	—
781	#125	C₂³×C₃₁	1	2	yes	—
782	#124	C₂³×C₃₁	1	1	yes	characteristic
783	#124	C₂³×C₃₁	1	1	yes	characteristic
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
791	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	1	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	C₂³×C₃₁	1	2	yes	—
801	#121	C₂³×C₃₁	1	2	yes	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
804	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
807	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	D₄×C₃₁	1	2	yes	—
834	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
835	C₄×D₄	D₄×C₃₁	1	2	yes	—
836	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₃₁	1	2	yes	—
838	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₃₁	1	2	yes	—
840	C₄×D₄	C₂³×C₃₁	1	2	yes	—
841	C₄×D₄	C₂³×C₃₁	1	2	yes	—
842	C₄×D₄	C₂³×C₃₁	1	2	yes	—
843	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₃₁	1	2	yes	—
845	C₄×D₄	C₂³×C₃₁	1	2	yes	—
846	#117	—	2	1	no	—
847	#117	—	2	2	no	—
848	#117	—	2	1	no	—
849	#117	—	2	1	no	—
850	#117	—	2	2	no	—
851	#117	—	2	1	no	—
852	#117	—	2	2	no	—
853	#117	—	2	2	no	—
854	#117	C₂³×C₃₁	1	1	yes	characteristic
855	#117	C₂³×C₃₁	1	2	yes	—
856	#117	C₂³×C₃₁	1	1	yes	characteristic
857	#117	C₂³×C₃₁	1	2	yes	—
858	C₂×C₄⋊C₄	—	2	1	no	—
859	C₂×C₄⋊C₄	—	2	1	no	—
860	C₂×C₄⋊C₄	—	2	1	no	—
861	C₂×C₄⋊C₄	—	2	2	no	—
862	C₂×C₄⋊C₄	—	2	1	no	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
865	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
866	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
867	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
868	C₂×C₂²⋊C₄	—	2	1	no	—
869	C₂×C₂²⋊C₄	—	2	2	no	—
870	C₂×C₂²⋊C₄	—	2	2	no	—
871	C₂×C₂²⋊C₄	—	2	2	no	—
872	C₂×C₂²⋊C₄	—	2	2	no	—
873	C₂×C₄²	—	2	2	no	—
874	C₂×C₄²	—	2	1	no	—
875	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
876	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
877	#107	C₂³×C₃₁	1	2	yes	—
878	#107	C₂³×C₃₁	1	2	yes	—
879	#107	C₂³×C₃₁	1	2	yes	—
880	#107	C₂³×C₃₁	1	2	yes	—
881	#106	C₂³×C₃₁	1	2	yes	—
882	#106	C₂³×C₃₁	1	2	yes	—
883	#106	C₂³×C₃₁	1	2	yes	—
884	#106	C₂³×C₃₁	1	2	yes	—
885	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
886	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
887	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
888	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
889	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
890	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
891	#103	C₂³×C₃₁	1	1	yes	characteristic
892	#103	C₂³×C₃₁	1	1	yes	characteristic
893	#103	C₂³×C₃₁	1	1	yes	characteristic
894	#103	C₂³×C₃₁	1	1	yes	characteristic
895	#103	C₂³×C₃₁	1	2	yes	—
896	#103	C₂³×C₃₁	1	2	yes	—
897	#103	C₂³×C₃₁	1	2	yes	—
898	#103	C₂³×C₃₁	1	2	yes	—
899	#102	C₂³×C₃₁	1	2	yes	—
900	#102	C₂³×C₃₁	1	2	yes	—
901	#102	C₂³×C₃₁	1	2	yes	—
902	#102	C₂³×C₃₁	1	2	yes	—
903	#102	C₂³×C₃₁	1	1	yes	characteristic
904	#102	C₂³×C₃₁	1	1	yes	characteristic
905	#102	C₂³×C₃₁	1	1	yes	characteristic
906	#102	C₂³×C₃₁	1	1	yes	characteristic
907	#102	C₂³×C₃₁	1	2	yes	—
908	#102	C₂³×C₃₁	1	2	yes	—
909	#102	C₂³×C₃₁	1	2	yes	—
910	#102	C₂³×C₃₁	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
913	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
915	#97	C₂³×C₃₁	1	2	yes	—
916	#97	C₂³×C₃₁	1	2	yes	—
917	C₄×C₈	C₂³×C₃₁	1	2	yes	—
918	C₄×C₈	C₂³×C₃₁	1	2	yes	—
919	C₃₁	#60601	1	1	yes	characteristic, direct product factor, Sylow
920	C₂⁴	—	2	2	no	—
921	C₂⁴	—	2	1	no	—
922	#41	—	2	8	no	—
923	#41	—	2	4	no	—
924	#41	—	2	4	no	—
925	#41	—	2	2	no	—
926	#41	—	2	2	no	—
927	#41	—	2	2	no	—
928	#41	—	2	2	no	—
929	#41	—	2	2	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	#41×C₃₁	1	4	yes	—
933	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
934	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₂×D₄	—	2	16	no	—
938	C₂×D₄	—	2	8	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	4	no	—
942	C₂×D₄	—	2	4	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
953	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
954	C₂×D₄	#41×C₃₁	1	4	yes	—
955	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
956	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
958	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	8	4	no	—
977	C₂²×C₄	—	8	2	no	—
978	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
979	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
980	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
981	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
982	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
983	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
984	Q₁₆	—	2	2	no	—
985	Q₁₆	—	2	2	no	—
986	SD₁₆	—	2	2	no	—
987	SD₁₆	—	2	2	no	—
988	SD₁₆	—	2	2	no	—
989	SD₁₆	—	2	2	no	—
990	SD₁₆	—	2	4	no	—
991	SD₁₆	—	2	4	no	—
992	D₈	—	2	2	no	—
993	D₈	—	2	2	no	—
994	D₈	—	2	4	no	—
995	D₈	—	2	4	no	—
996	M₁₆	—	2	2	no	—
997	M₁₆	—	2	2	no	—
998	C₂×C₈	—	2	2	no	—
999	C₂×C₈	—	2	2	no	—
1000	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1001	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1002	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1003	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1004	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1005	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1024	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1025	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1026	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1027	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1028	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1029	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1030	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1031	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1052	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1053	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	2	2	no	—
1056	C₄²	—	2	1	no	—
1057	C₄²	—	2	2	no	—
1058	C₄²	—	2	1	no	—
1059	C₄²	—	2	2	no	—
1060	C₄²	—	2	2	no	—
1061	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1062	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1063	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1064	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1065	C₄²	C₂⁴×C₃₁	1	2	yes	—
1066	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1067	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1068	C₂³	—	2	8	no	—
1069	C₂³	—	2	2	no	—
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	4	no	—
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	1	no	—
1074	C₂³	—	8	1	no	—
1075	C₂³	—	8	2	no	—
1076	C₂³	—	8	1	no	—
1077	C₂³	—	8	2	no	—
1078	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1079	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1080	Q₈	—	2	2	no	—
1081	Q₈	—	2	1	no	—
1082	Q₈	—	2	1	no	—
1083	Q₈	—	2	1	no	—
1084	Q₈	—	2	1	no	—
1085	Q₈	—	2	1	no	—
1086	Q₈	C₂×#41×C₃₁	1	2	yes	—
1087	D₄	—	2	8	no	—
1088	D₄	—	2	8	no	—
1089	D₄	—	2	4	no	—
1090	D₄	—	2	4	no	—
1091	D₄	—	2	2	no	—
1092	D₄	—	2	4	no	—
1093	D₄	—	2	2	no	—
1094	D₄	—	2	1	no	—
1095	D₄	—	2	1	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	1	no	—
1099	D₄	—	4	2	no	—
1100	D₄	—	4	2	no	—
1101	D₄	—	8	1	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	D₄	C₂×#41×C₃₁	1	2	yes	—
1106	D₄	C₂×#41×C₃₁	1	4	yes	—
1107	C₂×C₄	—	2	8	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	4	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	2	no	—
1124	C₂×C₄	—	4	4	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	2	no	—
1131	C₂×C₄	—	8	2	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	2	no	—
1134	C₂×C₄	—	8	1	no	—
1135	C₂×C₄	—	8	1	no	—
1136	C₂×C₄	—	8	1	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1140	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1141	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1142	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1143	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1144	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1145	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1146	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1147	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1148	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1149	C₈	—	2	1	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₈	—	2	2	no	—
1154	C₈	—	2	2	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	1	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	4	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	2	no	—
1161	C₂²	—	2	2	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	8	4	no	—
1173	C₂²	—	8	8	no	—
1174	C₂²	C₃₁×#525	1	2	yes	—
1175	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1176	C₄	—	2	2	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	2	1	no	—
1181	C₄	—	2	1	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	2	no	—
1190	C₄	—	4	2	no	—
1191	C₄	C₃₁×#525	1	2	yes	—
1192	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1193	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1194	C₂	—	2	2	no	—
1195	C₂	—	4	2	no	—
1196	C₂	—	4	4	no	—
1197	C₂	—	4	2	no	—
1198	C₂	—	8	1	no	—
1199	C₂	—	8	1	no	—
1200	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
1201	C₂	C₃₁×#3584	1	1	yes	characteristic
1202	C₂	C₃₁×#3585	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3512	C₂	semidirect
2. C₄×C₃₁×H(5,𝔽₂)	C₂	semidirect
3. C₃₁×#3123	C₂	semidirect
4. C₃₁×#3122	C₂	semidirect
5. C₃₁×#3120	C₂	semidirect
6. C₃₁×#3119	C₂	semidirect
7. C₃₁×#3114	C₂	semidirect
8. C₃₁×#3111	C₂	semidirect
9. C₃₁×#3105	C₂	semidirect
10. C₃₁×#3102	C₂	semidirect
11. C₃₁×#3099	C₂	semidirect
12. C₃₁×#3098	C₂	semidirect
13. C₃₁×#3080	C₂	semidirect
14. C₂×C₃₁×#478	C₂	semidirect
15. C₃₁×#3036	C₂	semidirect
16. C₃₁×#3035	C₂	semidirect
17. C₃₁×#3012	C₂	semidirect
18. C₃₁×#3012	C₂	semidirect
19. C₃₁×#2952	C₂	semidirect
20. C₃₁×#2951	C₂	semidirect
21. C₃₁×#2946	C₂	semidirect
22. C₃₁×#2946	C₂	semidirect
23. C₃₁×#2925	C₂	semidirect
35. C₃₁×#541	C₂²	semidirect
36. C₃₁×#540	C₂²	semidirect
39. C₃₁×#532	C₂²	semidirect
40. C₃₁×#529	C₂²	semidirect
41. C₃₁×#529	C₂²	semidirect
42. C₂×C₃₁×#125	C₂²	semidirect
47. C₃₁×#520	C₂²	semidirect
48. C₃₁×#520	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
62. C₃₁×#485	C₂²	semidirect
63. C₃₁×#484	C₂²	semidirect
64. C₃₁×#483	C₂²	semidirect
65. C₃₁×#482	C₂²	semidirect
66. C₃₁×#482	C₂²	semidirect
67. C₃₁×#481	C₂²	semidirect
68. C₃₁×#480	C₂²	semidirect
69. C₃₁×#479	C₂²	semidirect
70. C₃₁×#479	C₂²	semidirect
71. C₃₁×#478	C₂²	semidirect
72. C₃₁×#478	C₂²	semidirect
73. C₃₁×#478	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
79. C₃₁×#463	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#463	C₂²	semidirect
82. C₃₁×#463	C₂²	semidirect
83. C₃₁×#462	C₂²	semidirect
84. C₃₁×#461	C₂²	semidirect
85. C₃₁×#461	C₂²	semidirect
86. C₃₁×#460	C₂²	semidirect
87. C₃₁×#459	C₂²	semidirect
88. C₃₁×#459	C₂²	semidirect
97. C₃₁×#442	C₂²	semidirect
98. C₃₁×#442	C₂²	semidirect
99. C₃₁×#442	C₂²	semidirect
100. C₃₁×#441	C₂²	semidirect
101. C₃₁×#440	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₄×Q₁₆×C₃₁	C₂²	semidirect
106. C₄×SD₁₆×C₃₁	C₂²	semidirect
107. C₄×SD₁₆×C₃₁	C₂²	semidirect
108. C₄×SD₁₆×C₃₁	C₂²	semidirect
109. C₄×SD₁₆×C₃₁	C₂²	semidirect
110. C₄×D₈×C₃₁	C₂²	semidirect
111. C₄×D₈×C₃₁	C₂²	semidirect
112. C₄×D₈×C₃₁	C₂²	semidirect
113. C₃₁×#433	C₂²	semidirect
114. C₃₁×#433	C₂²	semidirect
115. C₃₁×#432	C₂²	semidirect
116. C₃₁×#431	C₂²	semidirect
117. C₃₁×#428	C₂²	semidirect
118. C₃₁×#428	C₂²	semidirect
119. C₂×C₃₁×#107	C₂²	semidirect
120. C₂×C₃₁×#106	C₂²	semidirect
121. C₃₁×#423	C₂²	semidirect
122. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
125. C₃₁×#417	C₂²	semidirect
126. C₃₁×#417	C₂²	semidirect
127. C₃₁×#416	C₂²	semidirect
128. C₃₁×#416	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₃₁×#405	C₂²	semidirect
466. #60601	C₃₁	direct (N × H)
554. #3512	C₂×C₃₁	semidirect
555. C₄×H(5,𝔽₂)	C₂×C₃₁	semidirect
556. #3123	C₂×C₃₁	semidirect
557. #3122	C₂×C₃₁	semidirect
558. #3120	C₂×C₃₁	semidirect
559. #3119	C₂×C₃₁	semidirect
560. #3114	C₂×C₃₁	semidirect
561. #3111	C₂×C₃₁	semidirect
562. #3105	C₂×C₃₁	semidirect
563. #3102	C₂×C₃₁	semidirect
564. #3099	C₂×C₃₁	semidirect
565. #3098	C₂×C₃₁	semidirect
566. #3080	C₂×C₃₁	semidirect
567. C₂×#478	C₂×C₃₁	semidirect
568. #3036	C₂×C₃₁	semidirect
569. #3035	C₂×C₃₁	semidirect
570. #3012	C₂×C₃₁	semidirect
571. #3012	C₂×C₃₁	semidirect
572. #2952	C₂×C₃₁	semidirect
573. #2951	C₂×C₃₁	semidirect
574. #2946	C₂×C₃₁	semidirect
575. #2946	C₂×C₃₁	semidirect
576. #2925	C₂×C₃₁	semidirect
627. #541	C₂²×C₃₁	semidirect
628. #540	C₂²×C₃₁	semidirect
631. #532	C₂²×C₃₁	semidirect
632. #529	C₂²×C₃₁	semidirect
633. #529	C₂²×C₃₁	semidirect
634. C₂×#125	C₂²×C₃₁	semidirect
639. #520	C₂²×C₃₁	semidirect
640. #520	C₂²×C₃₁	semidirect
653. #485	C₂²×C₃₁	semidirect
654. #485	C₂²×C₃₁	semidirect
655. #484	C₂²×C₃₁	semidirect
656. #483	C₂²×C₃₁	semidirect
657. #482	C₂²×C₃₁	semidirect
658. #482	C₂²×C₃₁	semidirect
659. #481	C₂²×C₃₁	semidirect
660. #480	C₂²×C₃₁	semidirect
661. #479	C₂²×C₃₁	semidirect
662. #479	C₂²×C₃₁	semidirect
663. #478	C₂²×C₃₁	semidirect
664. #478	C₂²×C₃₁	semidirect
665. #478	C₂²×C₃₁	semidirect
666. #478	C₂²×C₃₁	semidirect
667. #478	C₂²×C₃₁	semidirect
668. #478	C₂²×C₃₁	semidirect
669. #464	C₂²×C₃₁	semidirect
670. #464	C₂²×C₃₁	semidirect
671. #463	C₂²×C₃₁	semidirect
672. #463	C₂²×C₃₁	semidirect
673. #463	C₂²×C₃₁	semidirect
674. #463	C₂²×C₃₁	semidirect
675. #462	C₂²×C₃₁	semidirect
676. #461	C₂²×C₃₁	semidirect
677. #461	C₂²×C₃₁	semidirect
678. #460	C₂²×C₃₁	semidirect
679. #459	C₂²×C₃₁	semidirect
680. #459	C₂²×C₃₁	semidirect
689. #442	C₂²×C₃₁	semidirect
690. #442	C₂²×C₃₁	semidirect
691. #442	C₂²×C₃₁	semidirect
692. #441	C₂²×C₃₁	semidirect
693. #440	C₂²×C₃₁	semidirect
694. #440	C₂²×C₃₁	semidirect
695. #440	C₂²×C₃₁	semidirect
696. #440	C₂²×C₃₁	semidirect
697. C₄×Q₁₆	C₂²×C₃₁	semidirect
698. C₄×SD₁₆	C₂²×C₃₁	semidirect
699. C₄×SD₁₆	C₂²×C₃₁	semidirect
700. C₄×SD₁₆	C₂²×C₃₁	semidirect
701. C₄×SD₁₆	C₂²×C₃₁	semidirect
702. C₄×D₈	C₂²×C₃₁	semidirect
703. C₄×D₈	C₂²×C₃₁	semidirect
704. C₄×D₈	C₂²×C₃₁	semidirect
705. #433	C₂²×C₃₁	semidirect
706. #433	C₂²×C₃₁	semidirect
707. #432	C₂²×C₃₁	semidirect
708. #431	C₂²×C₃₁	semidirect
709. #428	C₂²×C₃₁	semidirect
710. #428	C₂²×C₃₁	semidirect
711. C₂×#107	C₂²×C₃₁	semidirect
712. C₂×#106	C₂²×C₃₁	semidirect
713. #423	C₂²×C₃₁	semidirect
714. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
717. #417	C₂²×C₃₁	semidirect
718. #417	C₂²×C₃₁	semidirect
719. #416	C₂²×C₃₁	semidirect
720. #416	C₂²×C₃₁	semidirect
725. #405	C₂²×C₃₁	semidirect
726. #405	C₂²×C₃₁	semidirect
919. C₃₁	#60601	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3512	2
C₄×C₃₁×H(5,𝔽₂)	2
C₃₁×#3123	2
C₃₁×#3122	2
C₃₁×#3120	2
C₃₁×#3119	2
C₃₁×#3114	2
C₃₁×#3111	2
C₃₁×#3105	2
C₃₁×#3102	2
C₃₁×#3099	2
C₃₁×#3098	2
C₃₁×#3080	2
C₂×C₃₁×#478	2
C₃₁×#3036	2
C₃₁×#3035	2
C₃₁×#3012	2
C₃₁×#2952	2
C₃₁×#2951	2
C₃₁×#2946	2
C₃₁×#2925	2
#60601	31

Subgroups — C31×#60601 #21517360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60601 #21517360