Subgroups — C₃₁×#61816 #21518575

Order 7936.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3349	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3313	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3238	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3203	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3098	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2981	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#562	—	2	2	no	—
25	C₃₁×#556	C₂²	1	2	yes	—
26	C₃₁×#555	—	2	1	no	—
27	C₃₁×#555	C₂²	1	1	yes	characteristic
28	C₃₁×#555	C₂²	1	1	yes	characteristic
29	C₃₁×#555	C₂²	1	1	yes	characteristic
30	C₃₁×#554	C₂²	1	1	yes	characteristic
31	C₃₁×#554	C₂²	1	1	yes	characteristic
32	C₃₁×#554	C₂²	1	1	yes	characteristic
33	C₃₁×#553	—	2	1	no	—
34	C₃₁×#553	—	2	1	no	—
35	C₃₁×#553	—	2	1	no	—
36	C₃₁×#552	C₂²	1	2	yes	—
37	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#548	—	2	2	no	—
39	C₃₁×#548	C₂²	1	2	yes	—
40	C₃₁×#547	C₂²	1	1	yes	characteristic
41	C₃₁×#547	C₂²	1	2	yes	—
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#542	—	2	2	no	—
44	C₃₁×#542	—	2	2	no	—
45	C₃₁×#540	—	2	1	no	—
46	C₃₁×#537	C₂²	1	2	yes	—
47	C₃₁×#537	C₂²	1	2	yes	—
48	C₃₁×#536	C₂²	1	2	yes	—
49	C₃₁×#533	—	2	1	no	—
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#532	—	2	1	no	—
52	C₃₁×#532	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₃₁×#529	C₂²	1	1	yes	characteristic
55	C₃₁×#520	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	—
58	C₃₁×#500	C₂²	1	1	yes	characteristic
59	C₃₁×#500	C₂²	1	1	yes	characteristic
60	C₃₁×#489	C₂²	1	2	yes	—
61	C₃₁×#487	C₂²	1	1	yes	characteristic
62	C₃₁×#487	C₂²	1	1	yes	characteristic
63	C₃₁×#485	C₂²	1	2	yes	—
64	C₃₁×#485	C₂²	1	2	yes	—
65	C₃₁×#485	C₂²	1	2	yes	—
66	C₃₁×#485	C₂²	1	1	yes	characteristic
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#484	C₂²	1	2	yes	—
70	C₃₁×#484	C₂²	1	2	yes	—
71	C₃₁×#484	C₂²	1	2	yes	—
72	C₃₁×#484	C₂²	1	2	yes	—
73	C₃₁×#484	C₂²	1	2	yes	—
74	C₃₁×#483	C₂²	1	2	yes	—
75	C₃₁×#483	C₂²	1	2	yes	—
76	C₃₁×#482	C₂²	1	2	yes	—
77	C₃₁×#482	C₂²	1	2	yes	—
78	C₃₁×#482	C₂²	1	1	yes	characteristic
79	C₃₁×#480	C₂²	1	2	yes	—
80	C₃₁×#480	C₂²	1	2	yes	—
81	C₃₁×#480	C₂²	1	2	yes	—
82	C₃₁×#479	C₂²	1	1	yes	characteristic
83	C₃₁×#478	C₂²	1	1	yes	characteristic
84	C₃₁×#477	C₂²	1	1	yes	characteristic
85	C₃₁×#477	C₂²	1	1	yes	characteristic
86	C₃₁×#477	C₂²	1	2	yes	—
87	C₃₁×#477	C₂²	1	2	yes	—
88	C₃₁×#477	C₂²	1	1	yes	characteristic
89	C₃₁×#476	C₂²	1	1	yes	characteristic
90	C₃₁×#476	C₂²	1	1	yes	characteristic
91	C₃₁×#476	C₂²	1	1	yes	characteristic
92	C₃₁×#470	C₂²	1	2	yes	—
93	C₃₁×#468	C₂²	1	2	yes	—
94	C₃₁×#468	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	—
96	C₃₁×#467	C₂²	1	2	yes	—
97	C₃₁×#467	C₂²	1	2	yes	—
98	C₃₁×#466	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	—
100	C₃₁×#464	C₂²	1	1	yes	characteristic
101	C₃₁×#463	C₂²	1	1	yes	characteristic
102	C₃₁×#462	C₂²	1	1	yes	characteristic
103	C₃₁×#461	C₂²	1	1	yes	characteristic
104	C₃₁×#452	C₂²	1	2	yes	—
105	C₃₁×#452	C₂²	1	1	yes	characteristic
106	C₃₁×#452	C₂²	1	2	yes	—
107	C₃₁×#451	C₂²	1	2	yes	—
108	C₃₁×#449	C₂²	1	1	yes	characteristic
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#448	C₂²	1	2	yes	—
111	C₃₁×#441	C₂²	1	2	yes	—
112	C₃₁×#440	C₂²	1	2	yes	—
113	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
117	C₃₁×#436	C₂²	1	1	yes	characteristic
118	C₃₁×#436	C₂²	1	1	yes	characteristic
119	C₃₁×#435	C₂²	1	2	yes	—
120	C₃₁×#435	C₂²	1	2	yes	—
121	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
123	C₃₁×#432	C₂²	1	1	yes	characteristic
124	C₃₁×#431	C₂²	1	1	yes	characteristic
125	C₃₁×#428	C₂²	1	2	yes	—
126	C₃₁×#428	C₂²	1	2	yes	—
127	C₃₁×#427	C₂²	1	2	yes	—
128	C₂×C₃₁×#107	C₂²	1	2	yes	—
129	C₃₁×#419	C₂²	1	2	yes	—
130	C₃₁×#417	C₂²	1	2	yes	—
131	C₃₁×#416	C₂²	1	2	yes	—
132	C₂×C₃₁×#103	C₂²	1	2	yes	—
133	C₃₁×#408	C₂²	1	2	yes	—
134	C₃₁×#408	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	2	no	—
136	C₂×#41×C₃₁	C₂³	1	2	yes	—
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
151	C₃₁×C₄⋊Q₈	—	2	2	no	—
152	C₃₁×C₄⋊Q₈	—	2	1	no	—
153	C₃₁×C₄⋊Q₈	—	2	1	no	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×#127	D₄	1	1	yes	characteristic
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	1	no	—
166	C₃₁×#125	—	2	1	no	—
167	C₃₁×#125	—	2	1	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	1	no	—
170	C₃₁×#125	—	2	1	no	—
171	C₃₁×#125	C₂³	1	1	yes	characteristic
172	C₃₁×#124	—	2	2	no	—
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	D₄	1	2	yes	—
179	C₃₁×#124	C₂³	1	1	yes	characteristic
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	1	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	D₄	1	2	yes	—
215	C₃₁×#121	D₄	1	1	yes	characteristic
216	C₃₁×#121	D₄	1	1	yes	characteristic
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	1	yes	characteristic
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	—	2	2	no	—
222	C₄×Q₈×C₃₁	—	2	2	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₃₁×#117	—	2	1	no	—
246	C₃₁×#117	—	2	1	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	1	no	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
262	C₂×C₄²×C₃₁	—	2	1	no	—
263	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	1	yes	characteristic
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
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×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	#41×C₃₁	—	4	2	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	4	1	no	—
315	#41×C₃₁	—	4	1	no	—
316	#41×C₃₁	—	4	2	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	8	4	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	4	2	no	—
325	C₂×Q₈×C₃₁	—	4	2	no	—
326	C₂×Q₈×C₃₁	—	8	2	no	—
327	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
360	Q₁₆×C₃₁	—	4	1	no	—
361	Q₁₆×C₃₁	—	4	2	no	—
362	SD₁₆×C₃₁	—	4	2	no	—
363	SD₁₆×C₃₁	—	4	1	no	—
364	SD₁₆×C₃₁	—	4	1	no	—
365	D₈×C₃₁	—	4	1	no	—
366	M₁₆×C₃₁	—	4	2	no	—
367	M₁₆×C₃₁	—	4	2	no	—
368	C₂×C₈×C₃₁	—	4	2	no	—
369	C₂×C₈×C₃₁	—	4	2	no	—
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
375	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	1	no	—
378	C₄⋊C₄×C₃₁	—	2	1	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	1	no	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
445	#61816	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
446	C₂³×C₃₁	—	2	1	no	—
447	C₂³×C₃₁	—	2	1	no	—
448	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
449	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
450	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	2	1	no	—
453	Q₈×C₃₁	—	2	2	no	—
454	Q₈×C₃₁	—	2	1	no	—
455	Q₈×C₃₁	—	2	1	no	—
456	Q₈×C₃₁	—	2	2	no	—
457	Q₈×C₃₁	—	4	2	no	—
458	Q₈×C₃₁	—	4	4	no	—
459	Q₈×C₃₁	—	8	1	no	—
460	Q₈×C₃₁	—	8	2	no	—
461	Q₈×C₃₁	—	8	1	no	—
462	Q₈×C₃₁	—	8	1	no	—
463	D₄×C₃₁	—	2	2	no	—
464	D₄×C₃₁	—	2	2	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	2	1	no	—
467	D₄×C₃₁	—	2	1	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	4	2	no	—
470	D₄×C₃₁	—	4	2	no	—
471	D₄×C₃₁	—	4	2	no	—
472	D₄×C₃₁	—	4	2	no	—
473	D₄×C₃₁	—	4	2	no	—
474	D₄×C₃₁	—	8	1	no	—
475	D₄×C₃₁	—	8	2	no	—
476	D₄×C₃₁	—	8	2	no	—
477	D₄×C₃₁	—	8	2	no	—
478	D₄×C₃₁	—	8	2	no	—
479	C₂×C₄×C₃₁	—	2	2	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	4	1	no	—
497	C₂×C₄×C₃₁	—	4	2	no	—
498	C₂×C₄×C₃₁	—	4	2	no	—
499	C₂×C₄×C₃₁	—	4	2	no	—
500	C₂×C₄×C₃₁	—	4	2	no	—
501	C₂×C₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	—	8	2	no	—
504	C₂×C₄×C₃₁	—	8	2	no	—
505	C₂×C₄×C₃₁	—	8	2	no	—
506	C₂×C₄×C₃₁	—	8	2	no	—
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
515	C₈×C₃₁	—	2	1	no	—
516	C₈×C₃₁	—	2	1	no	—
517	C₈×C₃₁	—	2	2	no	—
518	C₈×C₃₁	—	2	2	no	—
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	—	2	1	no	—
521	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3357	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3357	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3349	C₂×C₃₁	1	2	yes	complemented
526	#3343	C₂×C₃₁	1	2	yes	complemented
527	#3341	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3338	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3329	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3313	C₂×C₃₁	1	2	yes	complemented
532	#3308	C₂×C₃₁	1	2	yes	complemented
533	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3238	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3230	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3203	C₂×C₃₁	1	2	yes	complemented
538	#3201	C₂×C₃₁	1	2	yes	complemented
539	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3098	C₂×C₃₁	1	2	yes	complemented
542	#3097	C₂×C₃₁	1	2	yes	complemented
543	#2981	C₂×C₃₁	1	1	yes	characteristic, complemented
544	C₂²×C₃₁	—	2	1	no	—
545	C₂²×C₃₁	—	2	2	no	—
546	C₂²×C₃₁	—	2	2	no	—
547	C₂²×C₃₁	—	2	2	no	—
548	C₂²×C₃₁	—	2	1	no	—
549	C₂²×C₃₁	—	2	2	no	—
550	C₂²×C₃₁	—	2	1	no	—
551	C₂²×C₃₁	—	2	2	no	—
552	C₂²×C₃₁	—	2	2	no	—
553	C₂²×C₃₁	—	4	1	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	1	no	—
559	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	2	2	no	—
565	C₄×C₃₁	—	2	1	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	2	no	—
569	C₄×C₃₁	—	4	2	no	—
570	C₄×C₃₁	—	4	2	no	—
571	C₄×C₃₁	—	4	1	no	—
572	C₄×C₃₁	—	4	2	no	—
573	C₄×C₃₁	—	4	1	no	—
574	C₄×C₃₁	—	4	1	no	—
575	C₄×C₃₁	—	4	1	no	—
576	C₄×C₃₁	#578	1	2	yes	—
577	C₄×C₃₁	#585	1	1	yes	characteristic
578	C₄×C₃₁	#585	1	1	yes	characteristic
579	#562	—	2	2	no	—
580	#556	C₂²×C₃₁	1	2	yes	—
581	#555	—	2	1	no	—
582	#555	C₂²×C₃₁	1	1	yes	characteristic
583	#555	C₂²×C₃₁	1	1	yes	characteristic
584	#555	C₂²×C₃₁	1	1	yes	characteristic
585	#554	C₂²×C₃₁	1	1	yes	characteristic
586	#554	C₂²×C₃₁	1	1	yes	characteristic
587	#554	C₂²×C₃₁	1	1	yes	characteristic
588	#553	—	2	1	no	—
589	#553	—	2	1	no	—
590	#553	—	2	1	no	—
591	#552	C₂²×C₃₁	1	2	yes	—
592	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
593	#548	—	2	2	no	—
594	#548	C₂²×C₃₁	1	2	yes	—
595	#547	C₂²×C₃₁	1	1	yes	characteristic
596	#547	C₂²×C₃₁	1	2	yes	—
597	#544	—	2	1	no	—
598	#542	—	2	2	no	—
599	#542	—	2	2	no	—
600	#540	—	2	1	no	—
601	#537	C₂²×C₃₁	1	2	yes	—
602	#537	C₂²×C₃₁	1	2	yes	—
603	#536	C₂²×C₃₁	1	2	yes	—
604	#533	—	2	1	no	—
605	#533	C₂²×C₃₁	1	1	yes	characteristic
606	#532	—	2	1	no	—
607	#532	C₂²×C₃₁	1	1	yes	characteristic
608	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
609	#529	C₂²×C₃₁	1	1	yes	characteristic
610	#520	C₂²×C₃₁	1	2	yes	—
611	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
612	#501	C₂²×C₃₁	1	2	yes	—
613	#500	C₂²×C₃₁	1	1	yes	characteristic
614	#500	C₂²×C₃₁	1	1	yes	characteristic
615	#489	C₂²×C₃₁	1	2	yes	—
616	#487	C₂²×C₃₁	1	1	yes	characteristic
617	#487	C₂²×C₃₁	1	1	yes	characteristic
618	#485	C₂²×C₃₁	1	2	yes	—
619	#485	C₂²×C₃₁	1	2	yes	—
620	#485	C₂²×C₃₁	1	2	yes	—
621	#485	C₂²×C₃₁	1	1	yes	characteristic
622	#485	C₂²×C₃₁	1	2	yes	—
623	#485	C₂²×C₃₁	1	2	yes	—
624	#484	C₂²×C₃₁	1	2	yes	—
625	#484	C₂²×C₃₁	1	2	yes	—
626	#484	C₂²×C₃₁	1	2	yes	—
627	#484	C₂²×C₃₁	1	2	yes	—
628	#484	C₂²×C₃₁	1	2	yes	—
629	#483	C₂²×C₃₁	1	2	yes	—
630	#483	C₂²×C₃₁	1	2	yes	—
631	#482	C₂²×C₃₁	1	2	yes	—
632	#482	C₂²×C₃₁	1	2	yes	—
633	#482	C₂²×C₃₁	1	1	yes	characteristic
634	#480	C₂²×C₃₁	1	2	yes	—
635	#480	C₂²×C₃₁	1	2	yes	—
636	#480	C₂²×C₃₁	1	2	yes	—
637	#479	C₂²×C₃₁	1	1	yes	characteristic
638	#478	C₂²×C₃₁	1	1	yes	characteristic
639	#477	C₂²×C₃₁	1	1	yes	characteristic
640	#477	C₂²×C₃₁	1	1	yes	characteristic
641	#477	C₂²×C₃₁	1	2	yes	—
642	#477	C₂²×C₃₁	1	2	yes	—
643	#477	C₂²×C₃₁	1	1	yes	characteristic
644	#476	C₂²×C₃₁	1	1	yes	characteristic
645	#476	C₂²×C₃₁	1	1	yes	characteristic
646	#476	C₂²×C₃₁	1	1	yes	characteristic
647	#470	C₂²×C₃₁	1	2	yes	—
648	#468	C₂²×C₃₁	1	2	yes	—
649	#468	C₂²×C₃₁	1	2	yes	—
650	#468	C₂²×C₃₁	1	2	yes	—
651	#467	C₂²×C₃₁	1	2	yes	—
652	#467	C₂²×C₃₁	1	2	yes	—
653	#466	C₂²×C₃₁	1	2	yes	—
654	#465	C₂²×C₃₁	1	2	yes	—
655	#464	C₂²×C₃₁	1	1	yes	characteristic
656	#463	C₂²×C₃₁	1	1	yes	characteristic
657	#462	C₂²×C₃₁	1	1	yes	characteristic
658	#461	C₂²×C₃₁	1	1	yes	characteristic
659	#452	C₂²×C₃₁	1	2	yes	—
660	#452	C₂²×C₃₁	1	1	yes	characteristic
661	#452	C₂²×C₃₁	1	2	yes	—
662	#451	C₂²×C₃₁	1	2	yes	—
663	#449	C₂²×C₃₁	1	1	yes	characteristic
664	#449	C₂²×C₃₁	1	2	yes	—
665	#448	C₂²×C₃₁	1	2	yes	—
666	#441	C₂²×C₃₁	1	2	yes	—
667	#440	C₂²×C₃₁	1	2	yes	—
668	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
669	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
671	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
672	#436	C₂²×C₃₁	1	1	yes	characteristic
673	#436	C₂²×C₃₁	1	1	yes	characteristic
674	#435	C₂²×C₃₁	1	2	yes	—
675	#435	C₂²×C₃₁	1	2	yes	—
676	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
677	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
678	#432	C₂²×C₃₁	1	1	yes	characteristic
679	#431	C₂²×C₃₁	1	1	yes	characteristic
680	#428	C₂²×C₃₁	1	2	yes	—
681	#428	C₂²×C₃₁	1	2	yes	—
682	#427	C₂²×C₃₁	1	2	yes	—
683	C₂×#107	C₂²×C₃₁	1	2	yes	—
684	#419	C₂²×C₃₁	1	2	yes	—
685	#417	C₂²×C₃₁	1	2	yes	—
686	#416	C₂²×C₃₁	1	2	yes	—
687	C₂×#103	C₂²×C₃₁	1	2	yes	—
688	#408	C₂²×C₃₁	1	2	yes	—
689	#408	C₂²×C₃₁	1	2	yes	—
690	C₂×C₃₁	—	4	1	no	—
691	C₂×C₃₁	—	4	2	no	—
692	C₂×C₃₁	—	4	2	no	—
693	C₂×C₃₁	—	8	1	no	—
694	C₂×C₃₁	—	8	1	no	—
695	C₂×C₃₁	#3485	1	1	yes	characteristic
696	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
697	C₂×C₃₁	#3585	1	1	yes	characteristic
698	C₂×#41	—	2	2	no	—
699	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×#41	C₂³×C₃₁	1	2	yes	—
701	C₂×#41	C₂³×C₃₁	1	2	yes	—
702	C₂²×Q₈	—	2	1	no	—
703	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
704	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
709	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
710	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
711	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
712	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
713	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
714	C₄⋊Q₈	—	2	2	no	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
721	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
724	#127	D₄×C₃₁	1	1	yes	characteristic
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	1	no	—
729	#125	—	2	1	no	—
730	#125	—	2	1	no	—
731	#125	—	2	2	no	—
732	#125	—	2	1	no	—
733	#125	—	2	1	no	—
734	#125	C₂³×C₃₁	1	1	yes	characteristic
735	#124	—	2	2	no	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	—	2	2	no	—
740	#124	—	2	2	no	—
741	#124	D₄×C₃₁	1	2	yes	—
742	#124	C₂³×C₃₁	1	1	yes	characteristic
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	1	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
765	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
766	#121	—	2	2	no	—
767	#121	—	2	1	no	—
768	#121	—	2	1	no	—
769	#121	—	2	2	no	—
770	#121	—	2	2	no	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	1	no	—
775	#121	—	2	2	no	—
776	#121	—	2	1	no	—
777	#121	D₄×C₃₁	1	2	yes	—
778	#121	D₄×C₃₁	1	1	yes	characteristic
779	#121	D₄×C₃₁	1	1	yes	characteristic
780	#121	C₂³×C₃₁	1	1	yes	characteristic
781	#121	C₂³×C₃₁	1	2	yes	—
782	#121	C₂³×C₃₁	1	2	yes	—
783	#121	C₂³×C₃₁	1	2	yes	—
784	C₄×Q₈	—	2	2	no	—
785	C₄×Q₈	—	2	2	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₃₁	1	2	yes	—
806	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
808	#117	—	2	1	no	—
809	#117	—	2	1	no	—
810	#117	—	2	1	no	—
811	#117	—	2	1	no	—
812	#117	—	2	2	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	C₂³×C₃₁	1	1	yes	characteristic
816	#117	C₂³×C₃₁	1	2	yes	—
817	#117	C₂³×C₃₁	1	2	yes	—
818	#117	C₂³×C₃₁	1	2	yes	—
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	—	2	1	no	—
821	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
822	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
823	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
824	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
825	C₂×C₄²	—	2	1	no	—
826	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
827	#107	C₂³×C₃₁	1	1	yes	characteristic
828	#107	C₂³×C₃₁	1	2	yes	—
829	#107	C₂³×C₃₁	1	2	yes	—
830	#107	C₂³×C₃₁	1	2	yes	—
831	#107	C₂³×C₃₁	1	1	yes	characteristic
832	#107	C₂³×C₃₁	1	2	yes	—
833	#107	C₂³×C₃₁	1	2	yes	—
834	#107	C₂³×C₃₁	1	2	yes	—
835	#107	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	2	yes	—
837	#106	C₂³×C₃₁	1	2	yes	—
838	#106	C₂³×C₃₁	1	1	yes	characteristic
839	#106	C₂³×C₃₁	1	1	yes	characteristic
840	#106	C₂³×C₃₁	1	2	yes	—
841	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
845	#103	C₂³×C₃₁	1	1	yes	characteristic
846	#103	C₂³×C₃₁	1	2	yes	—
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	2	yes	—
850	#103	C₂³×C₃₁	1	2	yes	—
851	#103	C₂³×C₃₁	1	2	yes	—
852	#103	C₂³×C₃₁	1	1	yes	characteristic
853	#103	C₂³×C₃₁	1	2	yes	—
854	#103	C₂³×C₃₁	1	2	yes	—
855	#103	C₂³×C₃₁	1	1	yes	characteristic
856	#103	C₂³×C₃₁	1	1	yes	characteristic
857	#103	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	1	yes	characteristic
859	#102	C₂³×C₃₁	1	2	yes	—
860	#102	C₂³×C₃₁	1	1	yes	characteristic
861	#102	C₂³×C₃₁	1	2	yes	—
862	#102	C₂³×C₃₁	1	1	yes	characteristic
863	#102	C₂³×C₃₁	1	1	yes	characteristic
864	#102	C₂³×C₃₁	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
872	#97	C₂³×C₃₁	1	2	yes	—
873	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
875	C₃₁	#61816	1	1	yes	characteristic, direct product factor, Sylow
876	#41	—	4	2	no	—
877	#41	—	4	2	no	—
878	#41	—	4	1	no	—
879	#41	—	4	1	no	—
880	#41	—	4	2	no	—
881	#41	—	4	2	no	—
882	#41	—	8	4	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	4	2	no	—
889	C₂×Q₈	—	4	2	no	—
890	C₂×Q₈	—	8	2	no	—
891	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
892	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
894	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
902	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
903	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
904	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
905	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
906	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
907	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
908	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
920	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
921	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
923	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
924	Q₁₆	—	4	1	no	—
925	Q₁₆	—	4	2	no	—
926	SD₁₆	—	4	2	no	—
927	SD₁₆	—	4	1	no	—
928	SD₁₆	—	4	1	no	—
929	D₈	—	4	1	no	—
930	M₁₆	—	4	2	no	—
931	M₁₆	—	4	2	no	—
932	C₂×C₈	—	4	2	no	—
933	C₂×C₈	—	4	2	no	—
934	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
939	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
964	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
994	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1006	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1012	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1013	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	2	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	4	2	no	—
1021	Q₈	—	4	4	no	—
1022	Q₈	—	8	1	no	—
1023	Q₈	—	8	2	no	—
1024	Q₈	—	8	1	no	—
1025	Q₈	—	8	1	no	—
1026	D₄	—	2	2	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	4	2	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	2	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	8	1	no	—
1038	D₄	—	8	2	no	—
1039	D₄	—	8	2	no	—
1040	D₄	—	8	2	no	—
1041	D₄	—	8	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	4	1	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	4	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	2	no	—
1069	C₂×C₄	—	8	2	no	—
1070	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1075	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1077	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	2	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	C₃₁×#578	1	2	yes	—
1117	C₄	C₃₁×#585	1	1	yes	characteristic
1118	C₄	C₃₁×#585	1	1	yes	characteristic
1119	C₂	—	4	2	no	—
1120	C₂	—	4	1	no	—
1121	C₂	—	4	2	no	—
1122	C₂	—	8	1	no	—
1123	C₂	—	8	1	no	—
1124	C₂	C₃₁×#3485	1	1	yes	characteristic
1125	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1126	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 ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3547	C₂	semidirect
2. C₃₁×#3511	C₂	semidirect
3. C₃₁×#3357	C₂	semidirect
4. C₃₁×#3357	C₂	semidirect
5. C₃₁×#3349	C₂	semidirect
6. C₃₁×#3343	C₂	semidirect
7. C₃₁×#3341	C₂	semidirect
8. C₃₁×#3338	C₂	semidirect
9. C₃₁×#3331	C₂	semidirect
10. C₃₁×#3329	C₂	semidirect
11. C₃₁×#3313	C₂	semidirect
12. C₃₁×#3308	C₂	semidirect
13. C₃₁×#3303	C₂	semidirect
14. C₃₁×#3299	C₂	semidirect
15. C₃₁×#3238	C₂	semidirect
16. C₃₁×#3230	C₂	semidirect
17. C₃₁×#3203	C₂	semidirect
18. C₃₁×#3201	C₂	semidirect
19. C₃₁×#3116	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3098	C₂	semidirect
22. C₃₁×#3097	C₂	semidirect
23. C₃₁×#2981	C₂	semidirect
445. #61816	C₃₁	direct (N × H)
521. #3547	C₂×C₃₁	semidirect
522. #3511	C₂×C₃₁	semidirect
523. #3357	C₂×C₃₁	semidirect
524. #3357	C₂×C₃₁	semidirect
525. #3349	C₂×C₃₁	semidirect
526. #3343	C₂×C₃₁	semidirect
527. #3341	C₂×C₃₁	semidirect
528. #3338	C₂×C₃₁	semidirect
529. #3331	C₂×C₃₁	semidirect
530. #3329	C₂×C₃₁	semidirect
531. #3313	C₂×C₃₁	semidirect
532. #3308	C₂×C₃₁	semidirect
533. #3303	C₂×C₃₁	semidirect
534. #3299	C₂×C₃₁	semidirect
535. #3238	C₂×C₃₁	semidirect
536. #3230	C₂×C₃₁	semidirect
537. #3203	C₂×C₃₁	semidirect
538. #3201	C₂×C₃₁	semidirect
539. #3116	C₂×C₃₁	semidirect
540. #3102	C₂×C₃₁	semidirect
541. #3098	C₂×C₃₁	semidirect
542. #3097	C₂×C₃₁	semidirect
543. #2981	C₂×C₃₁	semidirect
875. C₃₁	#61816	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×#3547	2
C₃₁×#3511	2
C₃₁×#3357	2
C₃₁×#3349	2
C₃₁×#3343	2
C₃₁×#3341	2
C₃₁×#3338	2
C₃₁×#3331	2
C₃₁×#3329	2
C₃₁×#3313	2
C₃₁×#3308	2
C₃₁×#3303	2
C₃₁×#3299	2
C₃₁×#3238	2
C₃₁×#3230	2
C₃₁×#3203	2
C₃₁×#3201	2
C₃₁×#3116	2
C₃₁×#3102	2
C₃₁×#3098	2
C₃₁×#3097	2
C₃₁×#2981	2
#61816	31

Subgroups — C31×#61816 #21518575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61816 #21518575