Subgroups — C₃₁×#61450 #21518209

Order 7936.

1884 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3271	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3171	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3103	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	2	yes	maximal, complemented
21	C₃₁×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#137	C₂	1	2	yes	maximal, complemented
23	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	—
25	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
26	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#557	C₂²	1	1	yes	characteristic
28	C₃₁×#556	—	2	1	no	—
29	C₃₁×#556	C₂²	1	1	yes	characteristic
30	C₃₁×#555	—	2	2	no	—
31	C₃₁×#555	—	2	1	no	—
32	C₃₁×#555	C₂²	1	2	yes	—
33	C₃₁×#555	C₂²	1	1	yes	characteristic
34	C₃₁×#552	—	2	2	no	—
35	C₃₁×#552	C₂²	1	2	yes	—
36	C₃₁×#550	—	2	1	no	—
37	C₃₁×#550	C₂²	1	1	yes	characteristic
38	C₃₁×#550	C₂²	1	2	yes	—
39	C₃₁×#550	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#548	C₂²	1	2	yes	—
42	C₃₁×#547	—	2	1	no	—
43	C₃₁×#547	C₂²	1	1	yes	characteristic
44	C₃₁×#533	—	2	1	no	—
45	C₃₁×#533	C₂²	1	1	yes	characteristic
46	C₃₁×#532	—	2	1	no	—
47	C₃₁×#532	—	2	2	no	—
48	C₃₁×#532	C₂²	1	2	yes	—
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#529	—	2	2	no	—
51	C₃₁×#529	C₂²	1	2	yes	—
52	C₄×#41×C₃₁	—	2	1	no	—
53	C₄×#41×C₃₁	—	2	1	no	—
54	C₄×#41×C₃₁	C₂²	1	2	yes	—
55	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
59	C₃₁×#501	C₂²	1	2	yes	—
60	C₃₁×#498	C₂²	1	1	yes	characteristic
61	C₃₁×#496	C₂²	1	2	yes	—
62	C₃₁×#492	C₂²	1	1	yes	characteristic
63	C₃₁×#490	C₂²	1	2	yes	—
64	C₃₁×#489	C₂²	1	2	yes	—
65	C₃₁×#487	C₂²	1	1	yes	characteristic
66	C₃₁×#486	C₂²	1	1	yes	characteristic
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#482	C₂²	1	2	yes	—
71	C₃₁×#481	C₂²	1	2	yes	—
72	C₃₁×#481	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	—
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#477	C₂²	1	1	yes	characteristic
76	C₃₁×#476	C₂²	1	1	yes	characteristic
77	C₃₁×#475	C₂²	1	1	yes	characteristic
78	C₃₁×#475	C₂²	1	2	yes	—
79	C₃₁×#475	C₂²	1	2	yes	—
80	C₃₁×#474	C₂²	1	1	yes	characteristic
81	C₃₁×#469	C₂²	1	2	yes	—
82	C₃₁×#469	C₂²	1	2	yes	—
83	C₃₁×#468	C₂²	1	2	yes	—
84	C₃₁×#468	C₂²	1	2	yes	—
85	C₃₁×#465	C₂²	1	2	yes	—
86	C₃₁×#465	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#462	C₂²	1	1	yes	characteristic
90	C₃₁×#461	C₂²	1	1	yes	characteristic
91	C₃₁×#460	C₂²	1	2	yes	—
92	C₃₁×#460	C₂²	1	2	yes	—
93	C₃₁×#460	C₂²	1	1	yes	characteristic
94	C₃₁×#459	C₂²	1	1	yes	characteristic
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#452	C₂²	1	2	yes	—
97	C₃₁×#449	C₂²	1	2	yes	—
98	C₃₁×#449	C₂²	1	2	yes	—
99	C₃₁×#448	C₂²	1	2	yes	—
100	C₃₁×#448	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	1	yes	characteristic
102	C₃₁×#446	C₂²	1	1	yes	characteristic
103	C₃₁×#441	C₂²	1	2	yes	—
104	C₃₁×#441	C₂²	1	2	yes	—
105	C₃₁×#440	C₂²	1	2	yes	—
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
108	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
118	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₃₁	C₂²	1	2	yes	—
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	1	yes	characteristic
123	C₃₁×#435	C₂²	1	2	yes	—
124	C₃₁×#435	C₂²	1	2	yes	—
125	C₃₁×#431	C₂²	1	2	yes	—
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	—
128	C₃₁×#427	C₂²	1	1	yes	characteristic
129	C₃₁×#419	C₂²	1	2	yes	—
130	C₃₁×#417	C₂²	1	2	yes	—
131	C₃₁×#416	C₂²	1	1	yes	characteristic
132	C₃₁×#416	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	2	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
140	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	2	yes	—
143	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
144	C₃₁×#137	—	2	8	no	—
145	C₃₁×#135	—	2	4	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
161	C₃₁×C₄⋊Q₈	—	2	1	no	—
162	C₃₁×C₄⋊Q₈	—	2	2	no	—
163	C₃₁×C₄⋊Q₈	—	2	1	no	—
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃₁×#127	—	2	1	no	—
169	C₃₁×#127	—	2	2	no	—
170	C₃₁×#127	C₂³	1	1	yes	characteristic
171	C₃₁×#127	C₂³	1	2	yes	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	C₂³	1	2	yes	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	C₂³	1	2	yes	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	1	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	1	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#121	C₂³	1	2	yes	—
209	C₃₁×#121	C₂³	1	2	yes	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	2	no	—
213	C₄×Q₈×C₃₁	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
223	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	2	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	D₄	1	1	yes	characteristic
239	C₄×D₄×C₃₁	D₄	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	2	no	—
257	C₃₁×#117	D₄	1	2	yes	—
258	C₃₁×#117	D₄	1	1	yes	characteristic
259	C₃₁×#117	C₂³	1	1	yes	characteristic
260	C₃₁×#117	C₂³	1	1	yes	characteristic
261	C₃₁×#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₄²×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	—	2	1	no	—
266	C₂×C₄²×C₃₁	—	2	2	no	—
267	C₂×C₄²×C₃₁	—	2	1	no	—
268	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	1	yes	characteristic
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	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	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
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×#97	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	#41×C₃₁	—	2	2	no	—
315	#41×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	4	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	1	no	—
319	#41×C₃₁	—	4	1	no	—
320	#41×C₃₁	—	4	2	no	—
321	#41×C₃₁	—	4	4	no	—
322	#41×C₃₁	—	4	4	no	—
323	#41×C₃₁	—	8	4	no	—
324	#41×C₃₁	—	8	2	no	—
325	C₂×Q₈×C₃₁	—	2	2	no	—
326	C₂×Q₈×C₃₁	—	2	1	no	—
327	C₂×Q₈×C₃₁	—	2	2	no	—
328	C₂×Q₈×C₃₁	—	2	1	no	—
329	C₂×Q₈×C₃₁	—	2	4	no	—
330	C₂×Q₈×C₃₁	—	4	2	no	—
331	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	2	1	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	2	1	no	—
346	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
367	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	Q₁₆×C₃₁	—	2	4	no	—
369	Q₁₆×C₃₁	#41	1	4	yes	complemented
370	SD₁₆×C₃₁	—	2	2	no	—
371	SD₁₆×C₃₁	—	2	2	no	—
372	SD₁₆×C₃₁	—	2	4	no	—
373	SD₁₆×C₃₁	—	2	4	no	—
374	SD₁₆×C₃₁	—	4	2	no	—
375	SD₁₆×C₃₁	—	4	2	no	—
376	D₈×C₃₁	—	2	2	no	—
377	D₈×C₃₁	—	4	2	no	—
378	M₁₆×C₃₁	—	2	4	no	—
379	M₁₆×C₃₁	—	4	2	no	—
380	C₂×C₈×C₃₁	—	2	2	no	—
381	C₂×C₈×C₃₁	—	4	1	no	—
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
386	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
387	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	1	no	—
405	C₄⋊C₄×C₃₁	—	2	2	no	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	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	2	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	1	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	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	—	2	1	no	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	2	no	—
444	C₄²×C₃₁	—	2	1	no	—
445	C₄²×C₃₁	—	2	1	no	—
446	C₄²×C₃₁	—	2	2	no	—
447	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₃₁	C₂×D₄	1	2	yes	—
449	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₃₁	C₂×D₄	1	2	yes	—
451	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
452	C₄²×C₃₁	C₂⁴	1	2	yes	—
453	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
454	#61450	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂³×C₃₁	—	2	1	no	—
456	C₂³×C₃₁	—	2	1	no	—
457	C₂³×C₃₁	—	2	2	no	—
458	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
460	Q₈×C₃₁	—	2	2	no	—
461	Q₈×C₃₁	—	2	1	no	—
462	Q₈×C₃₁	—	2	1	no	—
463	Q₈×C₃₁	—	2	2	no	—
464	Q₈×C₃₁	—	2	2	no	—
465	Q₈×C₃₁	—	4	4	no	—
466	Q₈×C₃₁	—	4	2	no	—
467	Q₈×C₃₁	—	8	2	no	—
468	Q₈×C₃₁	—	8	1	no	—
469	Q₈×C₃₁	C₂×#41	1	2	yes	—
470	Q₈×C₃₁	C₂×#41	1	2	yes	—
471	D₄×C₃₁	—	2	2	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	2	2	no	—
475	D₄×C₃₁	—	2	1	no	—
476	D₄×C₃₁	—	2	2	no	—
477	D₄×C₃₁	—	2	1	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	4	4	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	4	2	no	—
482	D₄×C₃₁	—	4	4	no	—
483	D₄×C₃₁	—	4	4	no	—
484	D₄×C₃₁	—	4	2	no	—
485	D₄×C₃₁	—	8	2	no	—
486	D₄×C₃₁	—	8	1	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	—	8	2	no	—
489	D₄×C₃₁	—	8	2	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	4	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	2	2	no	—
506	C₂×C₄×C₃₁	—	4	2	no	—
507	C₂×C₄×C₃₁	—	4	2	no	—
508	C₂×C₄×C₃₁	—	4	2	no	—
509	C₂×C₄×C₃₁	—	4	4	no	—
510	C₂×C₄×C₃₁	—	4	4	no	—
511	C₂×C₄×C₃₁	—	4	4	no	—
512	C₂×C₄×C₃₁	—	4	4	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	4	2	no	—
515	C₂×C₄×C₃₁	—	4	2	no	—
516	C₂×C₄×C₃₁	—	4	2	no	—
517	C₂×C₄×C₃₁	—	4	4	no	—
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
527	C₈×C₃₁	—	2	1	no	—
528	C₈×C₃₁	—	2	2	no	—
529	C₈×C₃₁	—	2	1	no	—
530	C₈×C₃₁	—	2	1	no	—
531	C₈×C₃₁	—	2	2	no	—
532	C₈×C₃₁	C₂×#41	1	2	yes	—
533	#3483	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3354	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3348	C₂×C₃₁	1	2	yes	complemented
541	#3332	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3329	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3321	C₂×C₃₁	1	2	yes	complemented
544	#3317	C₂×C₃₁	1	2	yes	complemented
545	#3278	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3271	C₂×C₃₁	1	2	yes	complemented
547	#3171	C₂×C₃₁	1	2	yes	complemented
548	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3103	C₂×C₃₁	1	2	yes	complemented
552	#3102	C₂×C₃₁	1	2	yes	complemented
553	#2965	C₂×C₃₁	1	1	yes	characteristic, complemented
554	C₄×#137	C₂×C₃₁	1	2	yes	complemented
555	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
556	C₂²×C₃₁	—	2	2	no	—
557	C₂²×C₃₁	—	2	1	no	—
558	C₂²×C₃₁	—	2	1	no	—
559	C₂²×C₃₁	—	2	2	no	—
560	C₂²×C₃₁	—	2	1	no	—
561	C₂²×C₃₁	—	2	2	no	—
562	C₂²×C₃₁	—	4	1	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	—	4	2	no	—
565	C₂²×C₃₁	—	4	2	no	—
566	C₂²×C₃₁	—	4	1	no	—
567	C₂²×C₃₁	—	4	1	no	—
568	C₂²×C₃₁	—	4	1	no	—
569	C₂²×C₃₁	—	4	2	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
572	C₄×C₃₁	—	2	1	no	—
573	C₄×C₃₁	—	2	2	no	—
574	C₄×C₃₁	—	2	2	no	—
575	C₄×C₃₁	—	2	2	no	—
576	C₄×C₃₁	—	2	1	no	—
577	C₄×C₃₁	—	2	2	no	—
578	C₄×C₃₁	—	2	2	no	—
579	C₄×C₃₁	—	2	1	no	—
580	C₄×C₃₁	—	4	2	no	—
581	C₄×C₃₁	—	4	1	no	—
582	C₄×C₃₁	—	4	1	no	—
583	C₄×C₃₁	—	4	2	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	—	4	1	no	—
586	C₄×C₃₁	—	4	2	no	—
587	C₄×C₃₁	#575	1	2	yes	—
588	C₄×C₃₁	#577	1	2	yes	—
589	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
590	C₄×C₃₁	#585	1	1	yes	characteristic
591	C₂×#137	C₂²×C₃₁	1	2	yes	—
592	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
593	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
594	#557	C₂²×C₃₁	1	1	yes	characteristic
595	#556	—	2	1	no	—
596	#556	C₂²×C₃₁	1	1	yes	characteristic
597	#555	—	2	2	no	—
598	#555	—	2	1	no	—
599	#555	C₂²×C₃₁	1	1	yes	characteristic
600	#555	C₂²×C₃₁	1	2	yes	—
601	#552	—	2	2	no	—
602	#552	C₂²×C₃₁	1	2	yes	—
603	#550	—	2	1	no	—
604	#550	C₂²×C₃₁	1	1	yes	characteristic
605	#550	C₂²×C₃₁	1	2	yes	—
606	#550	C₂²×C₃₁	1	1	yes	characteristic
607	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
608	#548	C₂²×C₃₁	1	2	yes	—
609	#547	—	2	1	no	—
610	#547	C₂²×C₃₁	1	1	yes	characteristic
611	#533	—	2	1	no	—
612	#533	C₂²×C₃₁	1	1	yes	characteristic
613	#532	—	2	1	no	—
614	#532	—	2	2	no	—
615	#532	C₂²×C₃₁	1	2	yes	—
616	#532	C₂²×C₃₁	1	1	yes	characteristic
617	#529	—	2	2	no	—
618	#529	C₂²×C₃₁	1	2	yes	—
619	C₄×#41	—	2	1	no	—
620	C₄×#41	—	2	1	no	—
621	C₄×#41	C₂²×C₃₁	1	2	yes	—
622	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
623	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
624	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
625	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
626	#501	C₂²×C₃₁	1	2	yes	—
627	#498	C₂²×C₃₁	1	1	yes	characteristic
628	#496	C₂²×C₃₁	1	2	yes	—
629	#492	C₂²×C₃₁	1	1	yes	characteristic
630	#490	C₂²×C₃₁	1	2	yes	—
631	#489	C₂²×C₃₁	1	2	yes	—
632	#487	C₂²×C₃₁	1	1	yes	characteristic
633	#486	C₂²×C₃₁	1	1	yes	characteristic
634	#485	C₂²×C₃₁	1	2	yes	—
635	#485	C₂²×C₃₁	1	2	yes	—
636	#482	C₂²×C₃₁	1	2	yes	—
637	#482	C₂²×C₃₁	1	2	yes	—
638	#481	C₂²×C₃₁	1	2	yes	—
639	#481	C₂²×C₃₁	1	2	yes	—
640	#479	C₂²×C₃₁	1	2	yes	—
641	#478	C₂²×C₃₁	1	2	yes	—
642	#477	C₂²×C₃₁	1	1	yes	characteristic
643	#476	C₂²×C₃₁	1	1	yes	characteristic
644	#475	C₂²×C₃₁	1	1	yes	characteristic
645	#475	C₂²×C₃₁	1	2	yes	—
646	#475	C₂²×C₃₁	1	2	yes	—
647	#474	C₂²×C₃₁	1	1	yes	characteristic
648	#469	C₂²×C₃₁	1	2	yes	—
649	#469	C₂²×C₃₁	1	2	yes	—
650	#468	C₂²×C₃₁	1	2	yes	—
651	#468	C₂²×C₃₁	1	2	yes	—
652	#465	C₂²×C₃₁	1	2	yes	—
653	#465	C₂²×C₃₁	1	2	yes	—
654	#464	C₂²×C₃₁	1	2	yes	—
655	#463	C₂²×C₃₁	1	2	yes	—
656	#462	C₂²×C₃₁	1	1	yes	characteristic
657	#461	C₂²×C₃₁	1	1	yes	characteristic
658	#460	C₂²×C₃₁	1	2	yes	—
659	#460	C₂²×C₃₁	1	2	yes	—
660	#460	C₂²×C₃₁	1	1	yes	characteristic
661	#459	C₂²×C₃₁	1	1	yes	characteristic
662	#452	C₂²×C₃₁	1	2	yes	—
663	#452	C₂²×C₃₁	1	2	yes	—
664	#449	C₂²×C₃₁	1	2	yes	—
665	#449	C₂²×C₃₁	1	2	yes	—
666	#448	C₂²×C₃₁	1	2	yes	—
667	#448	C₂²×C₃₁	1	2	yes	—
668	#446	C₂²×C₃₁	1	1	yes	characteristic
669	#446	C₂²×C₃₁	1	1	yes	characteristic
670	#441	C₂²×C₃₁	1	2	yes	—
671	#441	C₂²×C₃₁	1	2	yes	—
672	#440	C₂²×C₃₁	1	2	yes	—
673	#440	C₂²×C₃₁	1	2	yes	—
674	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
675	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
676	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
678	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
679	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
681	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
682	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
683	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
684	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
685	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
686	C₄×D₈	C₂²×C₃₁	1	2	yes	—
687	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
688	#436	C₂²×C₃₁	1	1	yes	characteristic
689	#436	C₂²×C₃₁	1	1	yes	characteristic
690	#435	C₂²×C₃₁	1	2	yes	—
691	#435	C₂²×C₃₁	1	2	yes	—
692	#431	C₂²×C₃₁	1	2	yes	—
693	#431	C₂²×C₃₁	1	1	yes	characteristic
694	#428	C₂²×C₃₁	1	2	yes	—
695	#427	C₂²×C₃₁	1	1	yes	characteristic
696	#419	C₂²×C₃₁	1	2	yes	—
697	#417	C₂²×C₃₁	1	2	yes	—
698	#416	C₂²×C₃₁	1	1	yes	characteristic
699	#416	C₂²×C₃₁	1	1	yes	characteristic
700	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
701	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
702	C₂×C₃₁	—	4	2	no	—
703	C₂×C₃₁	—	4	1	no	—
704	C₂×C₃₁	—	8	1	no	—
705	C₂×C₃₁	—	8	2	no	—
706	C₂×C₃₁	—	8	1	no	—
707	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
708	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
709	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
710	C₂×#41	—	2	1	no	—
711	C₂×#41	—	2	1	no	—
712	C₂×#41	—	2	2	no	—
713	C₂×#41	—	2	1	no	—
714	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
715	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×#41	C₂³×C₃₁	1	2	yes	—
718	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
719	#137	—	2	8	no	—
720	#135	—	2	4	no	—
721	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
722	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
729	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
730	C₂×D₈	C₂³×C₃₁	1	2	yes	—
731	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
732	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
733	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
734	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	—	2	2	no	—
738	C₄⋊Q₈	—	2	1	no	—
739	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
741	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
743	#127	—	2	1	no	—
744	#127	—	2	2	no	—
745	#127	C₂³×C₃₁	1	1	yes	characteristic
746	#127	C₂³×C₃₁	1	2	yes	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	2	no	—
752	#125	—	2	1	no	—
753	#125	C₂³×C₃₁	1	2	yes	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	1	no	—
759	#124	—	2	2	no	—
760	#124	C₂³×C₃₁	1	2	yes	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
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	2	no	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	C₂³×C₃₁	1	2	yes	—
782	#121	C₂³×C₃₁	1	2	yes	—
783	#121	C₂³×C₃₁	1	2	yes	—
784	#121	C₂³×C₃₁	1	2	yes	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	2	no	—
788	C₄×Q₈	—	2	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
793	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
794	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
795	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
799	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
814	C₄×D₄	D₄×C₃₁	1	2	yes	—
815	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₃₁	1	2	yes	—
817	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₃₁	1	2	yes	—
821	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₃₁	1	2	yes	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	—	2	2	no	—
828	#117	—	2	1	no	—
829	#117	—	2	1	no	—
830	#117	—	2	2	no	—
831	#117	—	2	2	no	—
832	#117	D₄×C₃₁	1	2	yes	—
833	#117	D₄×C₃₁	1	1	yes	characteristic
834	#117	C₂³×C₃₁	1	1	yes	characteristic
835	#117	C₂³×C₃₁	1	1	yes	characteristic
836	#117	C₂³×C₃₁	1	2	yes	—
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
839	C₂×C₄²	—	2	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	—	2	2	no	—
842	C₂×C₄²	—	2	1	no	—
843	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
844	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
845	#107	C₂³×C₃₁	1	1	yes	characteristic
846	#107	C₂³×C₃₁	1	1	yes	characteristic
847	#107	C₂³×C₃₁	1	2	yes	—
848	#107	C₂³×C₃₁	1	2	yes	—
849	#106	C₂³×C₃₁	1	1	yes	characteristic
850	#106	C₂³×C₃₁	1	1	yes	characteristic
851	#106	C₂³×C₃₁	1	2	yes	—
852	#106	C₂³×C₃₁	1	2	yes	—
853	#106	C₂³×C₃₁	1	2	yes	—
854	#106	C₂³×C₃₁	1	2	yes	—
855	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
856	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
857	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
859	#103	C₂³×C₃₁	1	1	yes	characteristic
860	#103	C₂³×C₃₁	1	1	yes	characteristic
861	#103	C₂³×C₃₁	1	1	yes	characteristic
862	#103	C₂³×C₃₁	1	1	yes	characteristic
863	#103	C₂³×C₃₁	1	2	yes	—
864	#103	C₂³×C₃₁	1	2	yes	—
865	#103	C₂³×C₃₁	1	2	yes	—
866	#103	C₂³×C₃₁	1	2	yes	—
867	#103	C₂³×C₃₁	1	2	yes	—
868	#103	C₂³×C₃₁	1	2	yes	—
869	#102	C₂³×C₃₁	1	1	yes	characteristic
870	#102	C₂³×C₃₁	1	1	yes	characteristic
871	#102	C₂³×C₃₁	1	1	yes	characteristic
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	2	yes	—
874	#102	C₂³×C₃₁	1	2	yes	—
875	#102	C₂³×C₃₁	1	2	yes	—
876	#102	C₂³×C₃₁	1	2	yes	—
877	#102	C₂³×C₃₁	1	2	yes	—
878	#102	C₂³×C₃₁	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
882	#97	C₂³×C₃₁	1	2	yes	—
883	#97	C₂³×C₃₁	1	2	yes	—
884	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
887	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
888	C₄×C₈	C₂³×C₃₁	1	2	yes	—
889	C₃₁	#61450	1	1	yes	characteristic, direct product factor, Sylow
890	#41	—	2	2	no	—
891	#41	—	2	2	no	—
892	#41	—	2	4	no	—
893	#41	—	4	2	no	—
894	#41	—	4	1	no	—
895	#41	—	4	1	no	—
896	#41	—	4	2	no	—
897	#41	—	4	4	no	—
898	#41	—	4	4	no	—
899	#41	—	8	4	no	—
900	#41	—	8	2	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	4	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
908	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
909	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
923	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
924	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
925	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
926	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
939	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
941	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
942	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
943	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
944	Q₁₆	—	2	4	no	—
945	Q₁₆	#41×C₃₁	1	4	yes	complemented
946	SD₁₆	—	2	2	no	—
947	SD₁₆	—	2	2	no	—
948	SD₁₆	—	2	4	no	—
949	SD₁₆	—	2	4	no	—
950	SD₁₆	—	4	2	no	—
951	SD₁₆	—	4	2	no	—
952	D₈	—	2	2	no	—
953	D₈	—	4	2	no	—
954	M₁₆	—	2	4	no	—
955	M₁₆	—	4	2	no	—
956	C₂×C₈	—	2	2	no	—
957	C₂×C₈	—	4	1	no	—
958	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
962	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
963	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
983	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
984	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
985	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
986	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
988	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1011	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1024	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1025	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1026	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1027	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1028	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₃₁	1	2	yes	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1034	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	4	4	no	—
1041	Q₈	—	4	2	no	—
1042	Q₈	—	8	2	no	—
1043	Q₈	—	8	1	no	—
1044	Q₈	C₂×#41×C₃₁	1	2	yes	—
1045	Q₈	C₂×#41×C₃₁	1	2	yes	—
1046	D₄	—	2	2	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	4	4	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	4	no	—
1058	D₄	—	4	4	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	1	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	4	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	4	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	4	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1096	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1101	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1102	C₈	—	2	1	no	—
1103	C₈	—	2	2	no	—
1104	C₈	—	2	1	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	2	2	no	—
1107	C₈	C₂×#41×C₃₁	1	2	yes	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1124	C₄	—	2	1	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	C₃₁×#575	1	2	yes	—
1140	C₄	C₃₁×#577	1	2	yes	—
1141	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1142	C₄	C₃₁×#585	1	1	yes	characteristic
1143	C₂	—	4	2	no	—
1144	C₂	—	4	1	no	—
1145	C₂	—	8	1	no	—
1146	C₂	—	8	2	no	—
1147	C₂	—	8	1	no	—
1148	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1149	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1150	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
socle	C₂²×C₃₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3483	C₂	semidirect
2. C₃₁×#3482	C₂	semidirect
3. C₃₁×#3397	C₂	semidirect
4. C₃₁×#3387	C₂	semidirect
5. C₃₁×#3369	C₂	semidirect
6. C₃₁×#3368	C₂	semidirect
7. C₃₁×#3354	C₂	semidirect
8. C₃₁×#3348	C₂	semidirect
9. C₃₁×#3332	C₂	semidirect
10. C₃₁×#3329	C₂	semidirect
11. C₃₁×#3321	C₂	semidirect
12. C₃₁×#3317	C₂	semidirect
13. C₃₁×#3278	C₂	semidirect
14. C₃₁×#3271	C₂	semidirect
15. C₃₁×#3171	C₂	semidirect
16. C₃₁×#3167	C₂	semidirect
17. C₃₁×#3107	C₂	semidirect
18. C₃₁×#3106	C₂	semidirect
19. C₃₁×#3103	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#2965	C₂	semidirect
22. C₄×C₃₁×#137	C₂	semidirect
23. C₄×C₃₁×#135	C₂	semidirect
369. Q₁₆×C₃₁	#41	semidirect
454. #61450	C₃₁	direct (N × H)
533. #3483	C₂×C₃₁	semidirect
534. #3482	C₂×C₃₁	semidirect
535. #3397	C₂×C₃₁	semidirect
536. #3387	C₂×C₃₁	semidirect
537. #3369	C₂×C₃₁	semidirect
538. #3368	C₂×C₃₁	semidirect
539. #3354	C₂×C₃₁	semidirect
540. #3348	C₂×C₃₁	semidirect
541. #3332	C₂×C₃₁	semidirect
542. #3329	C₂×C₃₁	semidirect
543. #3321	C₂×C₃₁	semidirect
544. #3317	C₂×C₃₁	semidirect
545. #3278	C₂×C₃₁	semidirect
546. #3271	C₂×C₃₁	semidirect
547. #3171	C₂×C₃₁	semidirect
548. #3167	C₂×C₃₁	semidirect
549. #3107	C₂×C₃₁	semidirect
550. #3106	C₂×C₃₁	semidirect
551. #3103	C₂×C₃₁	semidirect
552. #3102	C₂×C₃₁	semidirect
553. #2965	C₂×C₃₁	semidirect
554. C₄×#137	C₂×C₃₁	semidirect
555. C₄×#135	C₂×C₃₁	semidirect
889. C₃₁	#61450	direct (N × H)
945. Q₁₆	#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×#3483	2
C₃₁×#3482	2
C₃₁×#3397	2
C₃₁×#3387	2
C₃₁×#3369	2
C₃₁×#3368	2
C₃₁×#3354	2
C₃₁×#3348	2
C₃₁×#3332	2
C₃₁×#3329	2
C₃₁×#3321	2
C₃₁×#3317	2
C₃₁×#3278	2
C₃₁×#3271	2
C₃₁×#3171	2
C₃₁×#3167	2
C₃₁×#3107	2
C₃₁×#3106	2
C₃₁×#3103	2
C₃₁×#3102	2
C₃₁×#2965	2
C₄×C₃₁×#137	2
C₄×C₃₁×#135	2
#61450	31

Subgroups — C31×#61450 #21518209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61450 #21518209