Subgroups — C₃₁×#61896 #21518655

Order 7936.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3403	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3219	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3214	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3115	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
21	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#559	C₂²	1	2	yes	—
25	C₃₁×#559	C₂²	1	1	yes	characteristic
26	C₃₁×#559	C₂²	1	1	yes	characteristic
27	C₃₁×#559	C₂²	1	2	yes	—
28	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	1	yes	characteristic
30	C₃₁×#556	C₂²	1	1	yes	characteristic
31	C₃₁×#556	C₂²	1	2	yes	—
32	C₃₁×#554	C₂²	1	1	yes	characteristic
33	C₃₁×#554	C₂²	1	2	yes	—
34	C₃₁×#553	—	2	1	no	—
35	C₃₁×#553	—	2	2	no	—
36	C₃₁×#550	C₂²	1	1	yes	characteristic
37	C₃₁×#550	C₂²	1	1	yes	characteristic
38	C₃₁×#548	—	2	1	no	—
39	C₃₁×#548	—	2	1	no	—
40	C₃₁×#547	—	2	1	no	—
41	C₃₁×#547	—	2	2	no	—
42	C₃₁×#542	—	2	1	no	—
43	C₃₁×#542	—	2	2	no	—
44	C₃₁×#532	C₂²	1	1	yes	characteristic
45	C₃₁×#532	C₂²	1	2	yes	—
46	C₃₁×#532	C₂²	1	1	yes	characteristic
47	C₃₁×#532	C₂²	1	2	yes	—
48	C₃₁×#529	—	2	1	no	—
49	C₃₁×#529	—	2	2	no	—
50	C₃₁×#529	C₂²	1	1	yes	characteristic
51	C₃₁×#529	C₂²	1	2	yes	—
52	C₃₁×#520	—	2	1	no	—
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	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#497	C₂²	1	2	yes	—
58	C₃₁×#496	C₂²	1	2	yes	—
59	C₃₁×#496	C₂²	1	2	yes	—
60	C₃₁×#496	C₂²	1	2	yes	—
61	C₃₁×#495	C₂²	1	2	yes	—
62	C₃₁×#493	C₂²	1	1	yes	characteristic
63	C₃₁×#492	C₂²	1	1	yes	characteristic
64	C₃₁×#491	C₂²	1	2	yes	—
65	C₃₁×#490	C₂²	1	2	yes	—
66	C₃₁×#489	C₂²	1	2	yes	—
67	C₃₁×#489	C₂²	1	2	yes	—
68	C₃₁×#488	C₂²	1	2	yes	—
69	C₃₁×#487	C₂²	1	1	yes	characteristic
70	C₃₁×#486	C₂²	1	1	yes	characteristic
71	C₃₁×#485	C₂²	1	1	yes	characteristic
72	C₃₁×#482	C₂²	1	1	yes	characteristic
73	C₃₁×#482	C₂²	1	2	yes	—
74	C₃₁×#479	C₂²	1	1	yes	characteristic
75	C₃₁×#479	C₂²	1	2	yes	—
76	C₃₁×#478	C₂²	1	1	yes	characteristic
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#477	C₂²	1	1	yes	characteristic
79	C₃₁×#476	C₂²	1	1	yes	characteristic
80	C₃₁×#475	C₂²	1	2	yes	—
81	C₃₁×#474	C₂²	1	2	yes	—
82	C₃₁×#464	C₂²	1	1	yes	characteristic
83	C₃₁×#464	C₂²	1	2	yes	—
84	C₃₁×#464	C₂²	1	2	yes	—
85	C₃₁×#464	C₂²	1	2	yes	—
86	C₃₁×#463	C₂²	1	1	yes	characteristic
87	C₃₁×#463	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#463	C₂²	1	2	yes	—
90	C₃₁×#463	C₂²	1	2	yes	—
91	C₃₁×#463	C₂²	1	2	yes	—
92	C₃₁×#462	C₂²	1	1	yes	characteristic
93	C₃₁×#461	C₂²	1	1	yes	characteristic
94	C₃₁×#461	C₂²	1	2	yes	—
95	C₃₁×#461	C₂²	1	2	yes	—
96	C₃₁×#460	C₂²	1	1	yes	characteristic
97	C₃₁×#460	C₂²	1	2	yes	—
98	C₃₁×#460	C₂²	1	1	yes	characteristic
99	C₃₁×#459	C₂²	1	1	yes	characteristic
100	C₃₁×#459	C₂²	1	1	yes	characteristic
101	C₃₁×#459	C₂²	1	2	yes	—
102	C₃₁×#459	C₂²	1	2	yes	—
103	C₃₁×#459	C₂²	1	2	yes	—
104	C₃₁×#452	C₂²	1	1	yes	characteristic
105	C₃₁×#452	C₂²	1	2	yes	—
106	C₃₁×#449	C₂²	1	1	yes	characteristic
107	C₃₁×#449	C₂²	1	2	yes	—
108	C₃₁×#449	C₂²	1	2	yes	—
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#449	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic
112	C₃₁×#446	C₂²	1	1	yes	characteristic
113	C₃₁×#446	C₂²	1	2	yes	—
114	C₃₁×#446	C₂²	1	1	yes	characteristic
115	C₃₁×#446	C₂²	1	1	yes	characteristic
116	C₃₁×#446	C₂²	1	2	yes	—
117	C₃₁×#442	C₂²	1	2	yes	—
118	C₃₁×#442	C₂²	1	2	yes	—
119	C₃₁×#442	C₂²	1	2	yes	—
120	C₃₁×#441	C₂²	1	2	yes	—
121	C₃₁×#440	C₂²	1	2	yes	—
122	C₃₁×#440	C₂²	1	2	yes	—
123	C₃₁×#440	C₂²	1	2	yes	—
124	C₃₁×#440	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
129	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₃₁	C₂²	1	2	yes	—
131	C₃₁×#432	C₂²	1	2	yes	—
132	C₃₁×#432	C₂²	1	2	yes	—
133	C₃₁×#431	C₂²	1	1	yes	characteristic
134	C₃₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	—	2	2	no	—
139	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
142	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₃₁	C₂³	1	2	yes	—
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₂×D₈×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	—	2	2	no	—
158	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×#127	C₂³	1	2	yes	—
163	C₃₁×#127	C₂³	1	1	yes	characteristic
164	C₃₁×#127	C₂³	1	1	yes	characteristic
165	C₃₁×#127	C₂³	1	2	yes	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	1	no	—
171	C₃₁×#125	—	2	1	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	C₂³	1	1	yes	characteristic
174	C₃₁×#125	C₂³	1	2	yes	—
175	C₃₁×#124	—	2	1	no	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	1	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	C₂³	1	2	yes	—
182	C₃₁×#124	C₂³	1	2	yes	—
183	C₃₁×#124	C₂³	1	2	yes	—
184	C₃₁×#124	C₂³	1	1	yes	characteristic
185	C₃₁×#124	C₂³	1	2	yes	—
186	C₃₁×#123	—	2	1	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	C₂³	1	1	yes	characteristic
213	C₃₁×#121	C₂³	1	2	yes	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
217	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	D₄	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	2	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	2	yes	—
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	—	2	2	no	—
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	—	2	1	no	—
258	C₃₁×#117	—	2	2	no	—
259	C₃₁×#117	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
264	C₂×C₄²×C₃₁	—	2	1	no	—
265	C₂×C₄²×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
267	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	1	yes	characteristic
274	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	1	yes	characteristic
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
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×#97	C₂³	1	2	yes	—
306	C₃₁×#97	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	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	1	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	4	1	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	4	4	no	—
317	#41×C₃₁	—	4	4	no	—
318	#41×C₃₁	—	8	2	no	—
319	#41×C₃₁	—	8	4	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	4	2	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	—	2	1	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	2	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
360	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
361	Q₁₆×C₃₁	—	4	2	no	—
362	Q₁₆×C₃₁	—	4	1	no	—
363	SD₁₆×C₃₁	—	4	1	no	—
364	SD₁₆×C₃₁	—	4	1	no	—
365	SD₁₆×C₃₁	—	4	2	no	—
366	SD₁₆×C₃₁	—	4	2	no	—
367	SD₁₆×C₃₁	—	4	2	no	—
368	SD₁₆×C₃₁	—	4	2	no	—
369	SD₁₆×C₃₁	—	4	2	no	—
370	D₈×C₃₁	—	4	2	no	—
371	D₈×C₃₁	—	4	2	no	—
372	D₈×C₃₁	—	4	1	no	—
373	D₈×C₃₁	—	4	2	no	—
374	D₈×C₃₁	—	4	2	no	—
375	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
377	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
378	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄×C₃₁	—	2	1	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	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	1	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	1	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	—	2	1	no	—
440	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₃₁	C₂×D₄	1	2	yes	—
442	C₄²×C₃₁	C₂×D₄	1	2	yes	—
443	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
445	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
446	C₄²×C₃₁	C₂⁴	1	2	yes	—
447	C₄²×C₃₁	C₂⁴	1	2	yes	—
448	#61896	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₃₁	—	2	1	no	—
450	C₂³×C₃₁	—	2	2	no	—
451	C₂³×C₃₁	—	2	2	no	—
452	C₂³×C₃₁	—	2	1	no	—
453	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
454	Q₈×C₃₁	—	2	2	no	—
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	2	2	no	—
458	Q₈×C₃₁	—	2	1	no	—
459	Q₈×C₃₁	—	2	1	no	—
460	Q₈×C₃₁	—	2	1	no	—
461	Q₈×C₃₁	—	2	2	no	—
462	Q₈×C₃₁	—	4	2	no	—
463	Q₈×C₃₁	—	8	2	no	—
464	Q₈×C₃₁	—	8	1	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	2	2	no	—
467	D₄×C₃₁	—	2	1	no	—
468	D₄×C₃₁	—	2	2	no	—
469	D₄×C₃₁	—	2	2	no	—
470	D₄×C₃₁	—	2	2	no	—
471	D₄×C₃₁	—	2	1	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	4	4	no	—
474	D₄×C₃₁	—	4	4	no	—
475	D₄×C₃₁	—	4	2	no	—
476	D₄×C₃₁	—	4	4	no	—
477	D₄×C₃₁	—	4	4	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	4	2	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	8	2	no	—
482	D₄×C₃₁	—	8	1	no	—
483	D₄×C₃₁	—	8	2	no	—
484	D₄×C₃₁	—	8	1	no	—
485	C₂×C₄×C₃₁	—	2	2	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	1	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	4	2	no	—
497	C₂×C₄×C₃₁	—	4	1	no	—
498	C₂×C₄×C₃₁	—	4	2	no	—
499	C₂×C₄×C₃₁	—	4	2	no	—
500	C₂×C₄×C₃₁	—	4	4	no	—
501	C₂×C₄×C₃₁	—	4	4	no	—
502	C₂×C₄×C₃₁	—	4	4	no	—
503	C₂×C₄×C₃₁	—	4	2	no	—
504	C₂×C₄×C₃₁	—	4	2	no	—
505	C₂×C₄×C₃₁	—	8	1	no	—
506	C₂×C₄×C₃₁	—	8	2	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	2	no	—
509	C₂×C₄×C₃₁	—	8	2	no	—
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	2	yes	—
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
520	C₈×C₃₁	—	2	1	no	—
521	C₈×C₃₁	—	2	1	no	—
522	C₈×C₃₁	—	2	2	no	—
523	C₈×C₃₁	—	2	1	no	—
524	C₈×C₃₁	—	2	2	no	—
525	C₈×C₃₁	—	2	1	no	—
526	#3522	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3480	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3403	C₂×C₃₁	1	2	yes	complemented
529	#3401	C₂×C₃₁	1	2	yes	complemented
530	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3376	C₂×C₃₁	1	2	yes	complemented
535	#3375	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3370	C₂×C₃₁	1	2	yes	complemented
538	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3219	C₂×C₃₁	1	2	yes	complemented
541	#3214	C₂×C₃₁	1	2	yes	complemented
542	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3207	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3115	C₂×C₃₁	1	2	yes	complemented
545	#3111	C₂×C₃₁	1	2	yes	complemented
546	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#2983	C₂×C₃₁	1	1	yes	characteristic, complemented
549	C₂²×C₃₁	—	2	1	no	—
550	C₂²×C₃₁	—	2	1	no	—
551	C₂²×C₃₁	—	2	1	no	—
552	C₂²×C₃₁	—	4	2	no	—
553	C₂²×C₃₁	—	4	1	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	4	2	no	—
556	C₂²×C₃₁	—	4	2	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	1	no	—
559	C₂²×C₃₁	—	4	2	no	—
560	C₂²×C₃₁	—	4	2	no	—
561	C₂²×C₃₁	—	4	2	no	—
562	C₂²×C₃₁	—	4	1	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
565	C₄×C₃₁	—	2	1	no	—
566	C₄×C₃₁	—	2	2	no	—
567	C₄×C₃₁	—	2	2	no	—
568	C₄×C₃₁	—	2	1	no	—
569	C₄×C₃₁	—	2	1	no	—
570	C₄×C₃₁	—	2	1	no	—
571	C₄×C₃₁	—	2	2	no	—
572	C₄×C₃₁	—	2	2	no	—
573	C₄×C₃₁	—	4	1	no	—
574	C₄×C₃₁	—	4	2	no	—
575	C₄×C₃₁	—	4	1	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	2	no	—
578	C₄×C₃₁	—	4	1	no	—
579	C₄×C₃₁	—	4	1	no	—
580	C₄×C₃₁	—	4	1	no	—
581	C₄×C₃₁	#575	1	2	yes	—
582	C₄×C₃₁	#585	1	1	yes	characteristic
583	C₄×C₃₁	#585	1	1	yes	characteristic
584	#559	C₂²×C₃₁	1	2	yes	—
585	#559	C₂²×C₃₁	1	1	yes	characteristic
586	#559	C₂²×C₃₁	1	1	yes	characteristic
587	#559	C₂²×C₃₁	1	2	yes	—
588	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
589	#557	C₂²×C₃₁	1	1	yes	characteristic
590	#556	C₂²×C₃₁	1	1	yes	characteristic
591	#556	C₂²×C₃₁	1	2	yes	—
592	#554	C₂²×C₃₁	1	1	yes	characteristic
593	#554	C₂²×C₃₁	1	2	yes	—
594	#553	—	2	1	no	—
595	#553	—	2	2	no	—
596	#550	C₂²×C₃₁	1	1	yes	characteristic
597	#550	C₂²×C₃₁	1	1	yes	characteristic
598	#548	—	2	1	no	—
599	#548	—	2	1	no	—
600	#547	—	2	1	no	—
601	#547	—	2	2	no	—
602	#542	—	2	1	no	—
603	#542	—	2	2	no	—
604	#532	C₂²×C₃₁	1	1	yes	characteristic
605	#532	C₂²×C₃₁	1	2	yes	—
606	#532	C₂²×C₃₁	1	1	yes	characteristic
607	#532	C₂²×C₃₁	1	2	yes	—
608	#529	—	2	1	no	—
609	#529	—	2	2	no	—
610	#529	C₂²×C₃₁	1	1	yes	characteristic
611	#529	C₂²×C₃₁	1	2	yes	—
612	#520	—	2	1	no	—
613	C₄×#41	—	2	1	no	—
614	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
615	C₄×#41	C₂²×C₃₁	1	2	yes	—
616	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
617	#497	C₂²×C₃₁	1	2	yes	—
618	#496	C₂²×C₃₁	1	2	yes	—
619	#496	C₂²×C₃₁	1	2	yes	—
620	#496	C₂²×C₃₁	1	2	yes	—
621	#495	C₂²×C₃₁	1	2	yes	—
622	#493	C₂²×C₃₁	1	1	yes	characteristic
623	#492	C₂²×C₃₁	1	1	yes	characteristic
624	#491	C₂²×C₃₁	1	2	yes	—
625	#490	C₂²×C₃₁	1	2	yes	—
626	#489	C₂²×C₃₁	1	2	yes	—
627	#489	C₂²×C₃₁	1	2	yes	—
628	#488	C₂²×C₃₁	1	2	yes	—
629	#487	C₂²×C₃₁	1	1	yes	characteristic
630	#486	C₂²×C₃₁	1	1	yes	characteristic
631	#485	C₂²×C₃₁	1	1	yes	characteristic
632	#482	C₂²×C₃₁	1	1	yes	characteristic
633	#482	C₂²×C₃₁	1	2	yes	—
634	#479	C₂²×C₃₁	1	1	yes	characteristic
635	#479	C₂²×C₃₁	1	2	yes	—
636	#478	C₂²×C₃₁	1	1	yes	characteristic
637	#478	C₂²×C₃₁	1	2	yes	—
638	#477	C₂²×C₃₁	1	1	yes	characteristic
639	#476	C₂²×C₃₁	1	1	yes	characteristic
640	#475	C₂²×C₃₁	1	2	yes	—
641	#474	C₂²×C₃₁	1	2	yes	—
642	#464	C₂²×C₃₁	1	1	yes	characteristic
643	#464	C₂²×C₃₁	1	2	yes	—
644	#464	C₂²×C₃₁	1	2	yes	—
645	#464	C₂²×C₃₁	1	2	yes	—
646	#463	C₂²×C₃₁	1	1	yes	characteristic
647	#463	C₂²×C₃₁	1	2	yes	—
648	#463	C₂²×C₃₁	1	2	yes	—
649	#463	C₂²×C₃₁	1	2	yes	—
650	#463	C₂²×C₃₁	1	2	yes	—
651	#463	C₂²×C₃₁	1	2	yes	—
652	#462	C₂²×C₃₁	1	1	yes	characteristic
653	#461	C₂²×C₃₁	1	1	yes	characteristic
654	#461	C₂²×C₃₁	1	2	yes	—
655	#461	C₂²×C₃₁	1	2	yes	—
656	#460	C₂²×C₃₁	1	1	yes	characteristic
657	#460	C₂²×C₃₁	1	2	yes	—
658	#460	C₂²×C₃₁	1	1	yes	characteristic
659	#459	C₂²×C₃₁	1	1	yes	characteristic
660	#459	C₂²×C₃₁	1	1	yes	characteristic
661	#459	C₂²×C₃₁	1	2	yes	—
662	#459	C₂²×C₃₁	1	2	yes	—
663	#459	C₂²×C₃₁	1	2	yes	—
664	#452	C₂²×C₃₁	1	1	yes	characteristic
665	#452	C₂²×C₃₁	1	2	yes	—
666	#449	C₂²×C₃₁	1	1	yes	characteristic
667	#449	C₂²×C₃₁	1	2	yes	—
668	#449	C₂²×C₃₁	1	2	yes	—
669	#449	C₂²×C₃₁	1	2	yes	—
670	#449	C₂²×C₃₁	1	2	yes	—
671	#446	C₂²×C₃₁	1	1	yes	characteristic
672	#446	C₂²×C₃₁	1	1	yes	characteristic
673	#446	C₂²×C₃₁	1	2	yes	—
674	#446	C₂²×C₃₁	1	1	yes	characteristic
675	#446	C₂²×C₃₁	1	1	yes	characteristic
676	#446	C₂²×C₃₁	1	2	yes	—
677	#442	C₂²×C₃₁	1	2	yes	—
678	#442	C₂²×C₃₁	1	2	yes	—
679	#442	C₂²×C₃₁	1	2	yes	—
680	#441	C₂²×C₃₁	1	2	yes	—
681	#440	C₂²×C₃₁	1	2	yes	—
682	#440	C₂²×C₃₁	1	2	yes	—
683	#440	C₂²×C₃₁	1	2	yes	—
684	#440	C₂²×C₃₁	1	2	yes	—
685	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
686	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
687	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
688	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
689	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
690	C₄×D₈	C₂²×C₃₁	1	2	yes	—
691	#432	C₂²×C₃₁	1	2	yes	—
692	#432	C₂²×C₃₁	1	2	yes	—
693	#431	C₂²×C₃₁	1	1	yes	characteristic
694	#431	C₂²×C₃₁	1	1	yes	characteristic
695	C₂×C₃₁	—	4	1	no	—
696	C₂×C₃₁	—	8	1	no	—
697	C₂×C₃₁	—	8	2	no	—
698	C₂×C₃₁	—	8	2	no	—
699	C₂×C₃₁	—	8	1	no	—
700	C₂×C₃₁	#3487	1	1	yes	characteristic
701	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
702	C₂×C₃₁	#3585	1	1	yes	characteristic
703	C₂×#41	—	2	1	no	—
704	C₂×#41	—	2	1	no	—
705	C₂×#41	—	2	1	no	—
706	C₂×#41	—	2	2	no	—
707	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×#41	C₂³×C₃₁	1	2	yes	—
709	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
710	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
715	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
719	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×D₈	C₂³×C₃₁	1	2	yes	—
721	C₂×D₈	C₂³×C₃₁	1	2	yes	—
722	C₂×D₈	C₂³×C₃₁	1	2	yes	—
723	C₂×D₈	C₂³×C₃₁	1	2	yes	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	—	2	2	no	—
726	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
727	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
729	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
730	#127	C₂³×C₃₁	1	2	yes	—
731	#127	C₂³×C₃₁	1	1	yes	characteristic
732	#127	C₂³×C₃₁	1	1	yes	characteristic
733	#127	C₂³×C₃₁	1	2	yes	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	1	no	—
739	#125	—	2	1	no	—
740	#125	—	2	2	no	—
741	#125	C₂³×C₃₁	1	1	yes	characteristic
742	#125	C₂³×C₃₁	1	2	yes	—
743	#124	—	2	1	no	—
744	#124	—	2	2	no	—
745	#124	—	2	1	no	—
746	#124	—	2	2	no	—
747	#124	—	2	2	no	—
748	#124	—	2	1	no	—
749	#124	C₂³×C₃₁	1	1	yes	characteristic
750	#124	C₂³×C₃₁	1	2	yes	—
751	#124	C₂³×C₃₁	1	2	yes	—
752	#124	C₂³×C₃₁	1	2	yes	—
753	#124	C₂³×C₃₁	1	2	yes	—
754	#123	—	2	1	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
770	#121	—	2	1	no	—
771	#121	—	2	2	no	—
772	#121	—	2	1	no	—
773	#121	—	2	2	no	—
774	#121	—	2	1	no	—
775	#121	—	2	2	no	—
776	#121	—	2	1	no	—
777	#121	—	2	2	no	—
778	#121	—	2	1	no	—
779	#121	—	2	2	no	—
780	#121	C₂³×C₃₁	1	1	yes	characteristic
781	#121	C₂³×C₃₁	1	2	yes	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
785	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
786	C₄×Q₈	D₄×C₃₁	1	2	yes	—
787	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
789	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
791	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
793	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₃₁	1	2	yes	—
814	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₃₁	1	2	yes	—
816	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₃₁	1	2	yes	—
818	C₄×D₄	C₂³×C₃₁	1	2	yes	—
819	C₄×D₄	C₂³×C₃₁	1	2	yes	—
820	C₄×D₄	C₂³×C₃₁	1	2	yes	—
821	#117	—	2	1	no	—
822	#117	—	2	2	no	—
823	#117	—	2	2	no	—
824	#117	—	2	1	no	—
825	#117	—	2	1	no	—
826	#117	—	2	2	no	—
827	#117	C₂³×C₃₁	1	1	yes	characteristic
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	—	2	2	no	—
830	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
831	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	—	2	2	no	—
834	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
835	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
836	#107	C₂³×C₃₁	1	2	yes	—
837	#107	C₂³×C₃₁	1	1	yes	characteristic
838	#107	C₂³×C₃₁	1	1	yes	characteristic
839	#106	C₂³×C₃₁	1	2	yes	—
840	#106	C₂³×C₃₁	1	1	yes	characteristic
841	#106	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	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
847	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
848	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
849	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
850	#103	C₂³×C₃₁	1	1	yes	characteristic
851	#103	C₂³×C₃₁	1	2	yes	—
852	#103	C₂³×C₃₁	1	1	yes	characteristic
853	#103	C₂³×C₃₁	1	1	yes	characteristic
854	#103	C₂³×C₃₁	1	1	yes	characteristic
855	#103	C₂³×C₃₁	1	2	yes	—
856	#103	C₂³×C₃₁	1	2	yes	—
857	#103	C₂³×C₃₁	1	2	yes	—
858	#103	C₂³×C₃₁	1	2	yes	—
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	#102	C₂³×C₃₁	1	1	yes	characteristic
866	#102	C₂³×C₃₁	1	2	yes	—
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	2	yes	—
869	#102	C₂³×C₃₁	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
873	#97	C₂³×C₃₁	1	2	yes	—
874	#97	C₂³×C₃₁	1	2	yes	—
875	#97	C₂³×C₃₁	1	2	yes	—
876	#97	C₂³×C₃₁	1	2	yes	—
877	C₄×C₈	C₂³×C₃₁	1	2	yes	—
878	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
879	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
880	C₃₁	#61896	1	1	yes	characteristic, direct product factor, Sylow
881	#41	—	4	1	no	—
882	#41	—	4	2	no	—
883	#41	—	4	1	no	—
884	#41	—	4	2	no	—
885	#41	—	4	4	no	—
886	#41	—	4	4	no	—
887	#41	—	8	2	no	—
888	#41	—	8	4	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	4	2	no	—
892	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
893	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
894	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
895	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
897	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
912	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
913	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
926	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
927	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
928	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
929	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
930	Q₁₆	—	4	2	no	—
931	Q₁₆	—	4	1	no	—
932	SD₁₆	—	4	1	no	—
933	SD₁₆	—	4	1	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	2	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	2	no	—
938	SD₁₆	—	4	2	no	—
939	D₈	—	4	2	no	—
940	D₈	—	4	2	no	—
941	D₈	—	4	1	no	—
942	D₈	—	4	2	no	—
943	D₈	—	4	2	no	—
944	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
946	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
947	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	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	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
973	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
976	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1010	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1011	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1012	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1013	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₃₁	1	2	yes	—
1016	C₄²	C₂⁴×C₃₁	1	2	yes	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	2	no	—
1021	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	4	2	no	—
1031	Q₈	—	8	2	no	—
1032	Q₈	—	8	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	4	4	no	—
1042	D₄	—	4	4	no	—
1043	D₄	—	4	2	no	—
1044	D₄	—	4	4	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	1	no	—
1051	D₄	—	8	2	no	—
1052	D₄	—	8	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	1	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	4	no	—
1069	C₂×C₄	—	4	4	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1079	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1080	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1081	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1085	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1087	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	2	no	—
1091	C₈	—	2	1	no	—
1092	C₈	—	2	2	no	—
1093	C₈	—	2	1	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	2	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	2	no	—
1125	C₄	—	4	1	no	—
1126	C₄	C₃₁×#575	1	2	yes	—
1127	C₄	C₃₁×#585	1	1	yes	characteristic
1128	C₄	C₃₁×#585	1	1	yes	characteristic
1129	C₂	—	4	1	no	—
1130	C₂	—	8	2	no	—
1131	C₂	—	8	1	no	—
1132	C₂	—	8	1	no	—
1133	C₂	—	8	2	no	—
1134	C₂	C₃₁×#3487	1	1	yes	characteristic
1135	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1136	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 ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3522	C₂	semidirect
2. C₃₁×#3480	C₂	semidirect
3. C₃₁×#3403	C₂	semidirect
4. C₃₁×#3401	C₂	semidirect
5. C₃₁×#3400	C₂	semidirect
6. C₃₁×#3399	C₂	semidirect
7. C₃₁×#3399	C₂	semidirect
8. C₃₁×#3397	C₂	semidirect
9. C₃₁×#3376	C₂	semidirect
10. C₃₁×#3375	C₂	semidirect
11. C₃₁×#3372	C₂	semidirect
12. C₃₁×#3370	C₂	semidirect
13. C₃₁×#3369	C₂	semidirect
14. C₃₁×#3366	C₂	semidirect
15. C₃₁×#3219	C₂	semidirect
16. C₃₁×#3214	C₂	semidirect
17. C₃₁×#3212	C₂	semidirect
18. C₃₁×#3207	C₂	semidirect
19. C₃₁×#3115	C₂	semidirect
20. C₃₁×#3111	C₂	semidirect
21. C₃₁×#3106	C₂	semidirect
22. C₃₁×#3102	C₂	semidirect
23. C₃₁×#2983	C₂	semidirect
448. #61896	C₃₁	direct (N × H)
526. #3522	C₂×C₃₁	semidirect
527. #3480	C₂×C₃₁	semidirect
528. #3403	C₂×C₃₁	semidirect
529. #3401	C₂×C₃₁	semidirect
530. #3400	C₂×C₃₁	semidirect
531. #3399	C₂×C₃₁	semidirect
532. #3399	C₂×C₃₁	semidirect
533. #3397	C₂×C₃₁	semidirect
534. #3376	C₂×C₃₁	semidirect
535. #3375	C₂×C₃₁	semidirect
536. #3372	C₂×C₃₁	semidirect
537. #3370	C₂×C₃₁	semidirect
538. #3369	C₂×C₃₁	semidirect
539. #3366	C₂×C₃₁	semidirect
540. #3219	C₂×C₃₁	semidirect
541. #3214	C₂×C₃₁	semidirect
542. #3212	C₂×C₃₁	semidirect
543. #3207	C₂×C₃₁	semidirect
544. #3115	C₂×C₃₁	semidirect
545. #3111	C₂×C₃₁	semidirect
546. #3106	C₂×C₃₁	semidirect
547. #3102	C₂×C₃₁	semidirect
548. #2983	C₂×C₃₁	semidirect
880. C₃₁	#61896	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×#3522	2
C₃₁×#3480	2
C₃₁×#3403	2
C₃₁×#3401	2
C₃₁×#3400	2
C₃₁×#3399	2
C₃₁×#3397	2
C₃₁×#3376	2
C₃₁×#3375	2
C₃₁×#3372	2
C₃₁×#3370	2
C₃₁×#3369	2
C₃₁×#3366	2
C₃₁×#3219	2
C₃₁×#3214	2
C₃₁×#3212	2
C₃₁×#3207	2
C₃₁×#3115	2
C₃₁×#3111	2
C₃₁×#3106	2
C₃₁×#3102	2
C₃₁×#2983	2
#61896	31

Subgroups — C31×#61896 #21518655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61896 #21518655