Subgroups — C₃₁×#61281 #21518040

Order 7936.

1796 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3356	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3353	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3348	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3344	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3342	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3335	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3099	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3063	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2912	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#131	C₂²	1	2	yes	—
20	C₃₁×#559	—	2	1	no	—
21	C₃₁×#557	—	2	1	no	—
22	C₃₁×#556	—	2	2	no	—
23	C₃₁×#556	C₂²	1	2	yes	—
24	C₃₁×#556	C₂²	1	2	yes	—
25	C₃₁×#555	C₂²	1	2	yes	—
26	C₃₁×#554	C₂²	1	2	yes	—
27	C₃₁×#554	C₂²	1	2	yes	—
28	C₃₁×#553	—	2	2	no	—
29	C₃₁×#552	C₂²	1	4	yes	—
30	C₃₁×#548	—	2	2	no	—
31	C₃₁×#547	C₂²	1	2	yes	—
32	C₃₁×#542	—	2	2	no	—
33	C₃₁×#539	—	2	2	no	—
34	C₃₁×#537	C₂²	1	2	yes	—
35	C₃₁×#536	C₂²	1	2	yes	—
36	C₃₁×#533	—	2	1	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#532	—	2	1	no	—
39	C₃₁×#532	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₃₁×#529	—	2	2	no	—
42	C₃₁×#520	C₂²	1	2	yes	—
43	C₃₁×#520	C₂²	1	2	yes	—
44	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
46	C₃₁×#501	C₂²	1	4	yes	—
47	C₃₁×#500	C₂²	1	2	yes	—
48	C₃₁×#498	C₂²	1	2	yes	—
49	C₃₁×#485	C₂²	1	4	yes	—
50	C₃₁×#485	C₂²	1	4	yes	—
51	C₃₁×#485	C₂²	1	4	yes	—
52	C₃₁×#484	C₂²	1	4	yes	—
53	C₃₁×#483	C₂²	1	4	yes	—
54	C₃₁×#483	C₂²	1	4	yes	—
55	C₃₁×#482	C₂²	1	4	yes	—
56	C₃₁×#481	C₂²	1	4	yes	—
57	C₃₁×#479	C₂²	1	2	yes	—
58	C₃₁×#478	C₂²	1	2	yes	—
59	C₃₁×#477	C₂²	1	1	yes	characteristic
60	C₃₁×#476	C₂²	1	1	yes	characteristic
61	C₃₁×#475	C₂²	1	1	yes	characteristic
62	C₃₁×#475	C₂²	1	2	yes	—
63	C₃₁×#475	C₂²	1	4	yes	—
64	C₃₁×#475	C₂²	1	2	yes	—
65	C₃₁×#474	C₂²	1	1	yes	characteristic
66	C₃₁×#470	C₂²	1	4	yes	—
67	C₃₁×#468	C₂²	1	4	yes	—
68	C₃₁×#467	C₂²	1	4	yes	—
69	C₃₁×#465	C₂²	1	4	yes	—
70	C₃₁×#441	C₂²	1	2	yes	—
71	C₃₁×#440	C₂²	1	2	yes	—
72	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
73	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
74	C₃₁×#436	C₂²	1	2	yes	—
75	C₃₁×#435	C₂²	1	4	yes	—
76	C₈×D₄×C₃₁	C₂²	1	2	yes	—
77	C₃₁×#428	C₂²	1	4	yes	—
78	C₃₁×#428	C₂²	1	4	yes	—
79	C₃₁×#428	C₂²	1	2	yes	—
80	C₃₁×#428	C₂²	1	2	yes	—
81	C₃₁×#428	C₂²	1	1	yes	characteristic
82	C₃₁×#427	C₂²	1	2	yes	—
83	C₃₁×#427	C₂²	1	4	yes	—
84	C₂×C₃₁×#106	C₂²	1	4	yes	—
85	C₂×C₃₁×#106	C₂²	1	2	yes	—
86	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₃₁×#419	C₂²	1	1	yes	characteristic
88	C₃₁×#417	C₂²	1	1	yes	characteristic
89	C₃₁×#416	C₂²	1	2	yes	—
90	C₂×C₃₁×#103	C₂²	1	2	yes	—
91	C₃₁×#408	C₂²	1	2	yes	—
92	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
93	C₂×#41×C₃₁	—	2	2	no	—
94	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
95	C₂×#41×C₃₁	C₂³	1	2	yes	—
96	C₂²×Q₈×C₃₁	—	2	1	no	—
97	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
98	C₃₁×#137	—	2	4	no	—
99	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
101	C₃₁×#131	—	2	8	no	—
102	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
104	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×#127	D₄	1	1	yes	characteristic
116	C₃₁×#126	—	2	4	no	—
117	C₃₁×#126	—	2	4	no	—
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#125	—	2	2	no	—
120	C₃₁×#125	—	2	2	no	—
121	C₃₁×#125	—	2	4	no	—
122	C₃₁×#125	C₂³	1	2	yes	—
123	C₃₁×#124	—	2	2	no	—
124	C₃₁×#124	—	2	2	no	—
125	C₃₁×#124	—	2	2	no	—
126	C₃₁×#124	—	2	4	no	—
127	C₃₁×#124	D₄	1	2	yes	—
128	C₃₁×#123	—	2	4	no	—
129	C₃₁×#123	—	2	4	no	—
130	C₃₁×#123	—	2	4	no	—
131	C₃₁×C₂²⋊Q₈	—	2	2	no	—
132	C₃₁×C₂²⋊Q₈	—	2	1	no	—
133	C₃₁×C₂²⋊Q₈	—	2	1	no	—
134	C₃₁×C₂²⋊Q₈	—	2	2	no	—
135	C₃₁×C₂²⋊Q₈	—	2	4	no	—
136	C₃₁×C₂²⋊Q₈	—	2	4	no	—
137	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₃₁×#121	—	2	2	no	—
141	C₃₁×#121	—	2	2	no	—
142	C₃₁×#121	—	2	4	no	—
143	C₃₁×#121	D₄	1	2	yes	—
144	C₃₁×#121	D₄	1	2	yes	—
145	C₃₁×#121	C₂³	1	4	yes	—
146	C₄×Q₈×C₃₁	—	2	2	no	—
147	C₄×Q₈×C₃₁	—	2	2	no	—
148	C₄×Q₈×C₃₁	—	2	2	no	—
149	C₄×Q₈×C₃₁	—	2	2	no	—
150	C₄×Q₈×C₃₁	—	2	1	no	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	1	no	—
154	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
155	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
158	C₄×D₄×C₃₁	—	2	4	no	—
159	C₄×D₄×C₃₁	—	2	2	no	—
160	C₄×D₄×C₃₁	—	2	4	no	—
161	C₄×D₄×C₃₁	—	2	2	no	—
162	C₄×D₄×C₃₁	—	2	2	no	—
163	C₄×D₄×C₃₁	—	2	2	no	—
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
168	C₄×D₄×C₃₁	C₂³	1	2	yes	—
169	C₄×D₄×C₃₁	C₂³	1	2	yes	—
170	C₃₁×#117	—	2	2	no	—
171	C₃₁×#117	—	2	4	no	—
172	C₃₁×#117	—	2	1	no	—
173	C₃₁×#117	C₂³	1	2	yes	—
174	C₃₁×#117	C₂³	1	1	yes	characteristic
175	C₃₁×#117	C₂³	1	4	yes	—
176	C₃₁×#117	C₂³	1	4	yes	—
177	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
178	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
183	C₂×C₄²×C₃₁	—	2	1	no	—
184	C₂×C₄²×C₃₁	—	2	1	no	—
185	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
186	C₃₁×#107	C₂³	1	2	yes	—
187	C₃₁×#107	C₂³	1	4	yes	—
188	C₃₁×#107	C₂³	1	2	yes	—
189	C₃₁×#107	C₂³	1	2	yes	—
190	C₃₁×#107	C₂³	1	4	yes	—
191	C₃₁×#106	C₂³	1	4	yes	—
192	C₃₁×#106	C₂³	1	2	yes	—
193	C₃₁×#106	C₂³	1	2	yes	—
194	C₃₁×#106	C₂³	1	4	yes	—
195	C₃₁×#106	C₂³	1	4	yes	—
196	C₃₁×#106	C₂³	1	2	yes	—
197	C₃₁×#106	C₂³	1	4	yes	—
198	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
199	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
200	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₃₁×#103	C₂³	1	4	yes	—
202	C₃₁×#103	C₂³	1	4	yes	—
203	C₃₁×#103	C₂³	1	2	yes	—
204	C₃₁×#103	C₂³	1	2	yes	—
205	C₃₁×#103	C₂³	1	2	yes	—
206	C₃₁×#103	C₂³	1	2	yes	—
207	C₃₁×#103	C₂³	1	2	yes	—
208	C₃₁×#102	C₂³	1	2	yes	—
209	C₃₁×#102	C₂³	1	2	yes	—
210	C₃₁×#102	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
212	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₃₁×#97	C₂³	1	2	yes	—
214	C₄×C₈×C₃₁	C₂³	1	2	yes	—
215	#41×C₃₁	—	2	4	no	—
216	#41×C₃₁	—	2	4	no	—
217	#41×C₃₁	—	2	2	no	—
218	#41×C₃₁	—	2	2	no	—
219	#41×C₃₁	—	8	4	no	—
220	C₂×Q₈×C₃₁	—	2	1	no	—
221	C₂×Q₈×C₃₁	—	2	1	no	—
222	C₂×Q₈×C₃₁	—	2	2	no	—
223	C₂×Q₈×C₃₁	—	2	1	no	—
224	C₂×Q₈×C₃₁	—	2	2	no	—
225	C₂×Q₈×C₃₁	—	2	2	no	—
226	C₂×Q₈×C₃₁	—	2	2	no	—
227	C₂×Q₈×C₃₁	—	8	2	no	—
228	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
230	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₂×D₄×C₃₁	—	2	1	no	—
232	C₂×D₄×C₃₁	—	2	4	no	—
233	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
234	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₃₁	—	2	1	no	—
239	C₂²×C₄×C₃₁	—	2	1	no	—
240	C₂²×C₄×C₃₁	—	2	2	no	—
241	C₂²×C₄×C₃₁	—	2	4	no	—
242	C₂²×C₄×C₃₁	—	2	4	no	—
243	C₂²×C₄×C₃₁	—	2	1	no	—
244	C₂²×C₄×C₃₁	—	2	1	no	—
245	C₂²×C₄×C₃₁	—	2	1	no	—
246	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	Q₁₆×C₃₁	—	2	4	no	—
251	SD₁₆×C₃₁	—	2	4	no	—
252	M₁₆×C₃₁	—	2	2	no	—
253	M₁₆×C₃₁	—	2	8	no	—
254	M₁₆×C₃₁	#41	1	4	yes	complemented
255	C₂×C₈×C₃₁	—	2	4	no	—
256	C₂×C₈×C₃₁	—	2	8	no	—
257	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
258	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
259	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
260	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₄⋊C₄×C₃₁	—	2	2	no	—
263	C₄⋊C₄×C₃₁	—	2	2	no	—
264	C₄⋊C₄×C₃₁	—	2	2	no	—
265	C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₄⋊C₄×C₃₁	—	2	4	no	—
268	C₄⋊C₄×C₃₁	—	2	4	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₄⋊C₄×C₃₁	—	2	1	no	—
272	C₄⋊C₄×C₃₁	—	2	4	no	—
273	C₄⋊C₄×C₃₁	—	2	1	no	—
274	C₄⋊C₄×C₃₁	—	2	4	no	—
275	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	—	2	1	no	—
277	C₄⋊C₄×C₃₁	—	2	4	no	—
278	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₂²⋊C₄×C₃₁	—	2	4	no	—
287	C₂²⋊C₄×C₃₁	—	2	1	no	—
288	C₂²⋊C₄×C₃₁	—	2	4	no	—
289	C₂²⋊C₄×C₃₁	—	2	2	no	—
290	C₂²⋊C₄×C₃₁	—	2	4	no	—
291	C₂²⋊C₄×C₃₁	—	2	4	no	—
292	C₂²⋊C₄×C₃₁	—	2	4	no	—
293	C₂²⋊C₄×C₃₁	—	2	1	no	—
294	C₂²⋊C₄×C₃₁	—	2	1	no	—
295	C₂²⋊C₄×C₃₁	—	2	4	no	—
296	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
297	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
298	C₄²×C₃₁	—	2	2	no	—
299	C₄²×C₃₁	—	2	1	no	—
300	C₄²×C₃₁	—	2	1	no	—
301	C₄²×C₃₁	—	2	1	no	—
302	C₄²×C₃₁	—	2	2	no	—
303	C₄²×C₃₁	—	2	4	no	—
304	C₄²×C₃₁	—	2	4	no	—
305	C₄²×C₃₁	—	2	2	no	—
306	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
310	#61281	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
311	C₂³×C₃₁	—	2	1	no	—
312	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
313	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
314	Q₈×C₃₁	—	2	4	no	—
315	Q₈×C₃₁	—	2	2	no	—
316	Q₈×C₃₁	—	2	1	no	—
317	Q₈×C₃₁	—	2	2	no	—
318	Q₈×C₃₁	—	2	1	no	—
319	Q₈×C₃₁	—	4	2	no	—
320	Q₈×C₃₁	—	4	2	no	—
321	Q₈×C₃₁	—	4	4	no	—
322	Q₈×C₃₁	—	8	1	no	—
323	Q₈×C₃₁	—	8	2	no	—
324	D₄×C₃₁	—	2	8	no	—
325	D₄×C₃₁	—	2	4	no	—
326	D₄×C₃₁	—	2	4	no	—
327	D₄×C₃₁	—	2	1	no	—
328	D₄×C₃₁	—	2	1	no	—
329	D₄×C₃₁	—	4	2	no	—
330	D₄×C₃₁	—	4	2	no	—
331	D₄×C₃₁	—	8	4	no	—
332	C₂×C₄×C₃₁	—	2	2	no	—
333	C₂×C₄×C₃₁	—	2	4	no	—
334	C₂×C₄×C₃₁	—	2	4	no	—
335	C₂×C₄×C₃₁	—	2	1	no	—
336	C₂×C₄×C₃₁	—	2	2	no	—
337	C₂×C₄×C₃₁	—	2	2	no	—
338	C₂×C₄×C₃₁	—	2	1	no	—
339	C₂×C₄×C₃₁	—	2	2	no	—
340	C₂×C₄×C₃₁	—	2	1	no	—
341	C₂×C₄×C₃₁	—	2	2	no	—
342	C₂×C₄×C₃₁	—	2	4	no	—
343	C₂×C₄×C₃₁	—	4	1	no	—
344	C₂×C₄×C₃₁	—	4	2	no	—
345	C₂×C₄×C₃₁	—	4	2	no	—
346	C₂×C₄×C₃₁	—	4	2	no	—
347	C₂×C₄×C₃₁	—	4	2	no	—
348	C₂×C₄×C₃₁	—	8	1	no	—
349	C₂×C₄×C₃₁	—	8	4	no	—
350	C₂×C₄×C₃₁	—	8	2	no	—
351	C₂×C₄×C₃₁	—	8	4	no	—
352	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
354	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
359	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
360	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
361	C₈×C₃₁	—	2	2	no	—
362	C₈×C₃₁	—	2	2	no	—
363	C₈×C₃₁	—	2	2	no	—
364	C₈×C₃₁	C₂×#41	1	4	yes	—
365	#3511	C₂×C₃₁	1	1	yes	characteristic
366	#3507	C₂×C₃₁	1	1	yes	characteristic, complemented
367	#3356	C₂×C₃₁	1	2	yes	complemented
368	#3353	C₂×C₃₁	1	2	yes	complemented
369	#3348	C₂×C₃₁	1	4	yes	complemented
370	#3344	C₂×C₃₁	1	4	yes	complemented
371	#3342	C₂×C₃₁	1	2	yes	complemented
372	#3335	C₂×C₃₁	1	2	yes	complemented
373	#3165	C₂×C₃₁	1	1	yes	characteristic, complemented
374	#3099	C₂×C₃₁	1	2	yes	complemented
375	#3097	C₂×C₃₁	1	2	yes	complemented
376	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
377	C₂×#475	C₂×C₃₁	1	1	yes	characteristic, complemented
378	#3063	C₂×C₃₁	1	2	yes	complemented
379	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
380	#2935	C₂×C₃₁	1	1	yes	characteristic, complemented
381	#2912	C₂×C₃₁	1	2	yes	complemented
382	C₂²×C₃₁	—	2	1	no	—
383	C₂²×C₃₁	—	2	1	no	—
384	C₂²×C₃₁	—	2	4	no	—
385	C₂²×C₃₁	—	2	4	no	—
386	C₂²×C₃₁	—	2	4	no	—
387	C₂²×C₃₁	—	4	1	no	—
388	C₂²×C₃₁	—	4	1	no	—
389	C₂²×C₃₁	—	4	1	no	—
390	C₂²×C₃₁	#547	1	2	yes	—
391	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
392	C₄×C₃₁	—	2	1	no	—
393	C₄×C₃₁	—	2	1	no	—
394	C₄×C₃₁	—	2	4	no	—
395	C₄×C₃₁	—	2	1	no	—
396	C₄×C₃₁	—	4	1	no	—
397	C₄×C₃₁	—	4	2	no	—
398	C₄×C₃₁	—	4	2	no	—
399	C₄×C₃₁	—	4	1	no	—
400	C₄×C₃₁	—	4	2	no	—
401	C₄×C₃₁	—	4	1	no	—
402	C₄×C₃₁	—	4	4	no	—
403	C₄×C₃₁	—	4	2	no	—
404	C₄×C₃₁	#547	1	2	yes	—
405	C₄×C₃₁	#577	1	2	yes	—
406	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
407	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
408	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
409	C₂×#131	C₂²×C₃₁	1	2	yes	—
410	#559	—	2	1	no	—
411	#557	—	2	1	no	—
412	#556	—	2	2	no	—
413	#556	C₂²×C₃₁	1	2	yes	—
414	#556	C₂²×C₃₁	1	2	yes	—
415	#555	C₂²×C₃₁	1	2	yes	—
416	#554	C₂²×C₃₁	1	2	yes	—
417	#554	C₂²×C₃₁	1	2	yes	—
418	#553	—	2	2	no	—
419	#552	C₂²×C₃₁	1	4	yes	—
420	#548	—	2	2	no	—
421	#547	C₂²×C₃₁	1	2	yes	—
422	#542	—	2	2	no	—
423	#539	—	2	2	no	—
424	#537	C₂²×C₃₁	1	2	yes	—
425	#536	C₂²×C₃₁	1	2	yes	—
426	#533	—	2	1	no	—
427	#533	C₂²×C₃₁	1	1	yes	characteristic
428	#532	—	2	1	no	—
429	#532	C₂²×C₃₁	1	1	yes	characteristic
430	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
431	#529	—	2	2	no	—
432	#520	C₂²×C₃₁	1	2	yes	—
433	#520	C₂²×C₃₁	1	2	yes	—
434	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
435	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
436	#501	C₂²×C₃₁	1	4	yes	—
437	#500	C₂²×C₃₁	1	2	yes	—
438	#498	C₂²×C₃₁	1	2	yes	—
439	#485	C₂²×C₃₁	1	4	yes	—
440	#485	C₂²×C₃₁	1	4	yes	—
441	#485	C₂²×C₃₁	1	4	yes	—
442	#484	C₂²×C₃₁	1	4	yes	—
443	#483	C₂²×C₃₁	1	4	yes	—
444	#483	C₂²×C₃₁	1	4	yes	—
445	#482	C₂²×C₃₁	1	4	yes	—
446	#481	C₂²×C₃₁	1	4	yes	—
447	#479	C₂²×C₃₁	1	2	yes	—
448	#478	C₂²×C₃₁	1	2	yes	—
449	#477	C₂²×C₃₁	1	1	yes	characteristic
450	#476	C₂²×C₃₁	1	1	yes	characteristic
451	#475	C₂²×C₃₁	1	2	yes	—
452	#475	C₂²×C₃₁	1	4	yes	—
453	#475	C₂²×C₃₁	1	2	yes	—
454	#475	C₂²×C₃₁	1	1	yes	characteristic
455	#474	C₂²×C₃₁	1	1	yes	characteristic
456	#470	C₂²×C₃₁	1	4	yes	—
457	#468	C₂²×C₃₁	1	4	yes	—
458	#467	C₂²×C₃₁	1	4	yes	—
459	#465	C₂²×C₃₁	1	4	yes	—
460	#441	C₂²×C₃₁	1	2	yes	—
461	#440	C₂²×C₃₁	1	2	yes	—
462	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
463	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
464	#436	C₂²×C₃₁	1	2	yes	—
465	#435	C₂²×C₃₁	1	4	yes	—
466	C₈×D₄	C₂²×C₃₁	1	2	yes	—
467	#428	C₂²×C₃₁	1	4	yes	—
468	#428	C₂²×C₃₁	1	4	yes	—
469	#428	C₂²×C₃₁	1	2	yes	—
470	#428	C₂²×C₃₁	1	2	yes	—
471	#428	C₂²×C₃₁	1	1	yes	characteristic
472	#427	C₂²×C₃₁	1	2	yes	—
473	#427	C₂²×C₃₁	1	4	yes	—
474	C₂×#106	C₂²×C₃₁	1	2	yes	—
475	C₂×#106	C₂²×C₃₁	1	4	yes	—
476	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
477	#419	C₂²×C₃₁	1	1	yes	characteristic
478	#417	C₂²×C₃₁	1	1	yes	characteristic
479	#416	C₂²×C₃₁	1	2	yes	—
480	C₂×#103	C₂²×C₃₁	1	2	yes	—
481	#408	C₂²×C₃₁	1	2	yes	—
482	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
483	C₂×C₃₁	—	2	2	no	—
484	C₂×C₃₁	—	4	4	no	—
485	C₂×C₃₁	—	8	1	no	—
486	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
487	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
488	C₂×C₃₁	#3586	1	1	yes	characteristic
489	C₂×#41	—	2	2	no	—
490	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
491	C₂×#41	C₂³×C₃₁	1	2	yes	—
492	C₂²×Q₈	—	2	1	no	—
493	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
494	#137	—	2	4	no	—
495	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
496	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
497	#131	—	2	8	no	—
498	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
499	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
500	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
502	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
503	C₄⋊Q₈	—	2	2	no	—
504	C₄⋊Q₈	—	2	1	no	—
505	C₄⋊Q₈	—	2	1	no	—
506	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
508	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
509	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
511	#127	D₄×C₃₁	1	1	yes	characteristic
512	#126	—	2	4	no	—
513	#126	—	2	4	no	—
514	#126	—	2	4	no	—
515	#125	—	2	2	no	—
516	#125	—	2	2	no	—
517	#125	—	2	4	no	—
518	#125	C₂³×C₃₁	1	2	yes	—
519	#124	—	2	2	no	—
520	#124	—	2	2	no	—
521	#124	—	2	2	no	—
522	#124	—	2	4	no	—
523	#124	D₄×C₃₁	1	2	yes	—
524	#123	—	2	4	no	—
525	#123	—	2	4	no	—
526	#123	—	2	4	no	—
527	C₂²⋊Q₈	—	2	2	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	4	no	—
532	C₂²⋊Q₈	—	2	4	no	—
533	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
534	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
535	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
536	#121	—	2	2	no	—
537	#121	—	2	2	no	—
538	#121	—	2	4	no	—
539	#121	D₄×C₃₁	1	2	yes	—
540	#121	D₄×C₃₁	1	2	yes	—
541	#121	C₂³×C₃₁	1	4	yes	—
542	C₄×Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	—	2	1	no	—
550	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
551	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
552	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
553	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
554	C₄×D₄	—	2	4	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	4	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
563	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
564	C₄×D₄	C₂³×C₃₁	1	2	yes	—
565	C₄×D₄	C₂³×C₃₁	1	2	yes	—
566	#117	—	2	2	no	—
567	#117	—	2	4	no	—
568	#117	—	2	1	no	—
569	#117	C₂³×C₃₁	1	1	yes	characteristic
570	#117	C₂³×C₃₁	1	2	yes	—
571	#117	C₂³×C₃₁	1	4	yes	—
572	#117	C₂³×C₃₁	1	4	yes	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
578	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
579	C₂×C₄²	—	2	1	no	—
580	C₂×C₄²	—	2	1	no	—
581	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
582	#107	C₂³×C₃₁	1	2	yes	—
583	#107	C₂³×C₃₁	1	4	yes	—
584	#107	C₂³×C₃₁	1	2	yes	—
585	#107	C₂³×C₃₁	1	2	yes	—
586	#107	C₂³×C₃₁	1	4	yes	—
587	#106	C₂³×C₃₁	1	4	yes	—
588	#106	C₂³×C₃₁	1	2	yes	—
589	#106	C₂³×C₃₁	1	2	yes	—
590	#106	C₂³×C₃₁	1	4	yes	—
591	#106	C₂³×C₃₁	1	4	yes	—
592	#106	C₂³×C₃₁	1	2	yes	—
593	#106	C₂³×C₃₁	1	4	yes	—
594	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
595	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
596	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
597	#103	C₂³×C₃₁	1	4	yes	—
598	#103	C₂³×C₃₁	1	4	yes	—
599	#103	C₂³×C₃₁	1	2	yes	—
600	#103	C₂³×C₃₁	1	2	yes	—
601	#103	C₂³×C₃₁	1	2	yes	—
602	#103	C₂³×C₃₁	1	2	yes	—
603	#103	C₂³×C₃₁	1	2	yes	—
604	#102	C₂³×C₃₁	1	2	yes	—
605	#102	C₂³×C₃₁	1	2	yes	—
606	#102	C₂³×C₃₁	1	2	yes	—
607	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
608	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
609	#97	C₂³×C₃₁	1	2	yes	—
610	C₄×C₈	C₂³×C₃₁	1	2	yes	—
611	C₃₁	#61281	1	1	yes	characteristic, direct product factor, Sylow
612	#41	—	2	4	no	—
613	#41	—	2	4	no	—
614	#41	—	2	2	no	—
615	#41	—	2	2	no	—
616	#41	—	8	4	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	2	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	2	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	2	2	no	—
624	C₂×Q₈	—	8	2	no	—
625	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
626	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
627	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
631	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
632	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
633	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
634	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
646	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
647	Q₁₆	—	2	4	no	—
648	SD₁₆	—	2	4	no	—
649	M₁₆	—	2	2	no	—
650	M₁₆	—	2	8	no	—
651	M₁₆	#41×C₃₁	1	4	yes	complemented
652	C₂×C₈	—	2	4	no	—
653	C₂×C₈	—	2	8	no	—
654	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
655	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
656	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
657	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
678	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
679	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
681	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
682	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	1	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
694	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	1	no	—
697	C₄²	—	2	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	4	no	—
702	C₄²	—	2	2	no	—
703	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
704	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
705	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
706	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
707	C₂³	—	2	1	no	—
708	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
709	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
710	Q₈	—	2	4	no	—
711	Q₈	—	2	2	no	—
712	Q₈	—	2	1	no	—
713	Q₈	—	2	2	no	—
714	Q₈	—	2	1	no	—
715	Q₈	—	4	2	no	—
716	Q₈	—	4	2	no	—
717	Q₈	—	4	4	no	—
718	Q₈	—	8	1	no	—
719	Q₈	—	8	2	no	—
720	D₄	—	2	8	no	—
721	D₄	—	2	4	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	1	no	—
724	D₄	—	2	1	no	—
725	D₄	—	4	2	no	—
726	D₄	—	4	2	no	—
727	D₄	—	8	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	8	1	no	—
745	C₂×C₄	—	8	4	no	—
746	C₂×C₄	—	8	2	no	—
747	C₂×C₄	—	8	4	no	—
748	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
750	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
751	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
754	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
755	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
756	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
757	C₈	—	2	2	no	—
758	C₈	—	2	2	no	—
759	C₈	—	2	2	no	—
760	C₈	C₂×#41×C₃₁	1	4	yes	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	2	4	no	—
765	C₂²	—	2	4	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	C₃₁×#547	1	2	yes	—
770	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
771	C₄	—	2	4	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	1	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	4	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	C₃₁×#547	1	2	yes	—
784	C₄	C₃₁×#577	1	2	yes	—
785	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
786	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
787	C₂	—	2	2	no	—
788	C₂	—	4	4	no	—
789	C₂	—	8	1	no	—
790	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
791	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
792	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3511	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3507	C₂	semidirect
3. C₃₁×#3356	C₂	semidirect
4. C₃₁×#3353	C₂	semidirect
5. C₃₁×#3348	C₂	semidirect
6. C₃₁×#3344	C₂	semidirect
7. C₃₁×#3342	C₂	semidirect
8. C₃₁×#3335	C₂	semidirect
9. C₃₁×#3165	C₂	semidirect
10. C₃₁×#3099	C₂	semidirect
11. C₃₁×#3097	C₂	semidirect
12. C₃₁×#3076	C₂	semidirect
13. C₂×C₃₁×#475	C₂	semidirect
14. C₃₁×#3063	C₂	semidirect
15. C₄×C₃₁×#137	C₂	semidirect
16. C₃₁×#2935	C₂	semidirect
17. C₃₁×#2912	C₂	semidirect
254. M₁₆×C₃₁	#41	semidirect
310. #61281	C₃₁	direct (N × H)
366. #3507	C₂×C₃₁	semidirect
367. #3356	C₂×C₃₁	semidirect
368. #3353	C₂×C₃₁	semidirect
369. #3348	C₂×C₃₁	semidirect
370. #3344	C₂×C₃₁	semidirect
371. #3342	C₂×C₃₁	semidirect
372. #3335	C₂×C₃₁	semidirect
373. #3165	C₂×C₃₁	semidirect
374. #3099	C₂×C₃₁	semidirect
375. #3097	C₂×C₃₁	semidirect
376. #3076	C₂×C₃₁	semidirect
377. C₂×#475	C₂×C₃₁	semidirect
378. #3063	C₂×C₃₁	semidirect
379. C₄×#137	C₂×C₃₁	semidirect
380. #2935	C₂×C₃₁	semidirect
381. #2912	C₂×C₃₁	semidirect
611. C₃₁	#61281	direct (N × H)
651. M₁₆	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3511	2
C₃₁×#3507	2
C₃₁×#3356	2
C₃₁×#3353	2
C₃₁×#3348	2
C₃₁×#3344	2
C₃₁×#3342	2
C₃₁×#3335	2
C₃₁×#3165	2
C₃₁×#3099	2
C₃₁×#3097	2
C₃₁×#3076	2
C₂×C₃₁×#475	2
C₃₁×#3063	2
C₄×C₃₁×#137	2
C₃₁×#2935	2
C₃₁×#2912	2
#61281	31

Subgroups — C31×#61281 #21518040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61281 #21518040