Subgroups — C₃₁×#61994 #21518753

Order 7936.

1860 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3309	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3271	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3269	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3250	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3219	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3035	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	—
25	C₂×C₃₁×#135	C₂²	1	2	yes	—
26	C₂×C₃₁×#135	C₂²	1	2	yes	—
27	C₃₁×#559	—	2	1	no	—
28	C₃₁×#559	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	1	yes	characteristic
30	C₃₁×#557	C₂²	1	1	yes	characteristic
31	C₃₁×#556	—	2	1	no	—
32	C₃₁×#556	C₂²	1	1	yes	characteristic
33	C₃₁×#553	—	2	2	no	—
34	C₃₁×#553	—	2	1	no	—
35	C₃₁×#553	—	2	2	no	—
36	C₃₁×#553	C₂²	1	2	yes	—
37	C₃₁×#550	—	2	1	no	—
38	C₃₁×#550	C₂²	1	1	yes	characteristic
39	C₃₁×#550	C₂²	1	2	yes	—
40	C₃₁×#550	C₂²	1	1	yes	characteristic
41	C₃₁×#550	C₂²	1	1	yes	characteristic
42	C₃₁×#548	C₂²	1	2	yes	—
43	C₃₁×#547	C₂²	1	2	yes	—
44	C₃₁×#547	C₂²	1	1	yes	characteristic
45	C₃₁×#540	—	2	2	no	—
46	C₃₁×#540	—	2	1	no	—
47	C₃₁×#532	—	2	1	no	—
48	C₃₁×#532	C₂²	1	1	yes	characteristic
49	C₃₁×#532	C₂²	1	2	yes	—
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₃₁×#529	—	2	2	no	—
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#529	C₂²	1	2	yes	—
54	C₃₁×#529	C₂²	1	2	yes	—
55	C₃₁×#520	—	2	1	no	—
56	C₄×#41×C₃₁	—	2	1	no	—
57	C₄×#41×C₃₁	C₂²	1	2	yes	—
58	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
59	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
60	C₃₁×#497	C₂²	1	2	yes	—
61	C₃₁×#496	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×#487	C₂²	1	1	yes	characteristic
67	C₃₁×#486	C₂²	1	1	yes	characteristic
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#483	C₂²	1	1	yes	characteristic
70	C₃₁×#482	C₂²	1	2	yes	—
71	C₃₁×#480	C₂²	1	1	yes	characteristic
72	C₃₁×#479	C₂²	1	1	yes	characteristic
73	C₃₁×#479	C₂²	1	1	yes	characteristic
74	C₃₁×#479	C₂²	1	2	yes	—
75	C₃₁×#478	C₂²	1	2	yes	—
76	C₃₁×#478	C₂²	1	2	yes	—
77	C₃₁×#475	C₂²	1	1	yes	characteristic
78	C₃₁×#474	C₂²	1	1	yes	characteristic
79	C₃₁×#469	C₂²	1	2	yes	—
80	C₃₁×#468	C₂²	1	2	yes	—
81	C₃₁×#467	C₂²	1	2	yes	—
82	C₃₁×#466	C₂²	1	2	yes	—
83	C₃₁×#465	C₂²	1	2	yes	—
84	C₃₁×#465	C₂²	1	2	yes	—
85	C₃₁×#464	C₂²	1	1	yes	characteristic
86	C₃₁×#464	C₂²	1	1	yes	characteristic
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#464	C₂²	1	2	yes	—
90	C₃₁×#463	C₂²	1	2	yes	—
91	C₃₁×#463	C₂²	1	2	yes	—
92	C₃₁×#463	C₂²	1	2	yes	—
93	C₃₁×#463	C₂²	1	2	yes	—
94	C₃₁×#462	C₂²	1	2	yes	—
95	C₃₁×#462	C₂²	1	1	yes	characteristic
96	C₃₁×#462	C₂²	1	1	yes	characteristic
97	C₃₁×#461	C₂²	1	2	yes	—
98	C₃₁×#460	C₂²	1	2	yes	—
99	C₃₁×#460	C₂²	1	1	yes	characteristic
100	C₃₁×#460	C₂²	1	1	yes	characteristic
101	C₃₁×#460	C₂²	1	1	yes	characteristic
102	C₃₁×#459	C₂²	1	1	yes	characteristic
103	C₃₁×#459	C₂²	1	2	yes	—
104	C₃₁×#452	C₂²	1	2	yes	—
105	C₃₁×#452	C₂²	1	2	yes	—
106	C₃₁×#452	C₂²	1	2	yes	—
107	C₃₁×#451	C₂²	1	1	yes	characteristic
108	C₃₁×#449	C₂²	1	2	yes	—
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#449	C₂²	1	2	yes	—
111	C₃₁×#449	C₂²	1	2	yes	—
112	C₃₁×#449	C₂²	1	2	yes	—
113	C₃₁×#448	C₂²	1	1	yes	characteristic
114	C₃₁×#446	C₂²	1	1	yes	characteristic
115	C₃₁×#446	C₂²	1	1	yes	characteristic
116	C₃₁×#442	C₂²	1	2	yes	—
117	C₃₁×#441	C₂²	1	2	yes	—
118	C₃₁×#440	C₂²	1	2	yes	—
119	C₃₁×#440	C₂²	1	2	yes	—
120	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
121	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
124	C₃₁×#435	C₂²	1	2	yes	—
125	C₃₁×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
128	C₃₁×#432	C₂²	1	2	yes	—
129	C₃₁×#431	C₂²	1	1	yes	characteristic
130	C₃₁×#423	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
132	C₃₁×#417	C₂²	1	2	yes	—
133	C₃₁×#416	C₂²	1	2	yes	—
134	C₃₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂×#41×C₃₁	C₂³	1	2	yes	—
142	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
143	C₃₁×#137	—	4	4	no	—
144	C₃₁×#135	—	4	4	no	—
145	C₃₁×#135	—	4	4	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×D₈×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	C₂³	1	2	yes	—
159	C₂×D₈×C₃₁	C₂³	1	2	yes	—
160	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	—	2	1	no	—
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×#127	—	2	1	no	—
168	C₃₁×#127	—	2	1	no	—
169	C₃₁×#127	—	2	2	no	—
170	C₃₁×#127	C₂³	1	2	yes	—
171	C₃₁×#127	C₂³	1	1	yes	characteristic
172	C₃₁×#127	C₂³	1	1	yes	characteristic
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	1	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	1	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	C₂³	1	1	yes	characteristic
182	C₃₁×#125	C₂³	1	2	yes	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	—	2	1	no	—
187	C₃₁×#124	C₂³	1	2	yes	—
188	C₃₁×#124	C₂³	1	1	yes	characteristic
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#123	—	2	1	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×#121	—	2	2	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	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	2	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	1	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	2	no	—
244	C₄×D₄×C₃₁	—	2	2	no	—
245	C₄×D₄×C₃₁	—	2	2	no	—
246	C₄×D₄×C₃₁	—	2	2	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	—	2	1	no	—
249	C₄×D₄×C₃₁	—	2	2	no	—
250	C₄×D₄×C₃₁	—	2	1	no	—
251	C₄×D₄×C₃₁	D₄	1	2	yes	—
252	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
253	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₃₁	C₂³	1	2	yes	—
255	C₄×D₄×C₃₁	C₂³	1	2	yes	—
256	C₄×D₄×C₃₁	C₂³	1	2	yes	—
257	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₃₁	C₂³	1	2	yes	—
259	C₃₁×#117	—	2	2	no	—
260	C₃₁×#117	—	2	2	no	—
261	C₃₁×#117	—	2	2	no	—
262	C₃₁×#117	—	2	1	no	—
263	C₃₁×#117	D₄	1	1	yes	characteristic
264	C₃₁×#117	D₄	1	2	yes	—
265	C₃₁×#117	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
267	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
270	C₂×C₄²×C₃₁	—	2	1	no	—
271	C₂×C₄²×C₃₁	—	2	2	no	—
272	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
273	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	1	yes	characteristic
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₃₁×#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	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	1	yes	characteristic
295	C₃₁×#103	C₂³	1	1	yes	characteristic
296	C₃₁×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	2	yes	—
312	C₃₁×#97	C₂³	1	2	yes	—
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
315	#41×C₃₁	—	2	4	no	—
316	#41×C₃₁	—	4	2	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	4	no	—
319	#41×C₃₁	—	4	2	no	—
320	#41×C₃₁	—	4	2	no	—
321	#41×C₃₁	—	4	2	no	—
322	#41×C₃₁	—	4	2	no	—
323	#41×C₃₁	—	4	2	no	—
324	#41×C₃₁	—	4	2	no	—
325	#41×C₃₁	—	4	4	no	—
326	C₂×Q₈×C₃₁	—	2	1	no	—
327	C₂×Q₈×C₃₁	—	2	1	no	—
328	C₂×Q₈×C₃₁	—	2	2	no	—
329	C₂×Q₈×C₃₁	—	4	1	no	—
330	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	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	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	1	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	2	no	—
344	C₂×D₄×C₃₁	—	2	1	no	—
345	C₂×D₄×C₃₁	—	2	1	no	—
346	C₂×D₄×C₃₁	—	2	2	no	—
347	C₂×D₄×C₃₁	—	2	1	no	—
348	C₂×D₄×C₃₁	—	2	1	no	—
349	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
353	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	—	2	2	no	—
363	C₂²×C₄×C₃₁	—	2	2	no	—
364	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
370	Q₁₆×C₃₁	—	2	2	no	—
371	Q₁₆×C₃₁	—	2	4	no	—
372	Q₁₆×C₃₁	—	4	1	no	—
373	Q₁₆×C₃₁	—	4	2	no	—
374	SD₁₆×C₃₁	—	2	2	no	—
375	SD₁₆×C₃₁	—	2	4	no	—
376	SD₁₆×C₃₁	—	4	1	no	—
377	SD₁₆×C₃₁	—	4	2	no	—
378	SD₁₆×C₃₁	—	4	2	no	—
379	SD₁₆×C₃₁	—	4	2	no	—
380	SD₁₆×C₃₁	—	4	2	no	—
381	D₈×C₃₁	—	4	2	no	—
382	D₈×C₃₁	—	4	2	no	—
383	D₈×C₃₁	—	4	2	no	—
384	M₁₆×C₃₁	—	4	2	no	—
385	C₂×C₈×C₃₁	—	4	2	no	—
386	C₂×C₈×C₃₁	—	4	2	no	—
387	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
392	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	1	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	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
405	C₄⋊C₄×C₃₁	—	2	2	no	—
406	C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	1	no	—
409	C₄⋊C₄×C₃₁	—	2	1	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	2	no	—
412	C₄⋊C₄×C₃₁	—	2	1	no	—
413	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	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	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	—	2	2	no	—
439	C₂²⋊C₄×C₃₁	—	2	1	no	—
440	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	1	no	—
445	C₄²×C₃₁	—	2	2	no	—
446	C₄²×C₃₁	—	2	2	no	—
447	C₄²×C₃₁	—	2	1	no	—
448	C₄²×C₃₁	—	2	1	no	—
449	C₄²×C₃₁	—	2	2	no	—
450	C₄²×C₃₁	—	2	1	no	—
451	C₄²×C₃₁	C₂×D₄	1	2	yes	—
452	C₄²×C₃₁	C₂×D₄	1	2	yes	—
453	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₃₁	C₂⁴	1	2	yes	—
457	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
458	#61994	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₂³×C₃₁	—	2	2	no	—
460	C₂³×C₃₁	—	2	1	no	—
461	C₂³×C₃₁	—	2	2	no	—
462	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
463	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
464	Q₈×C₃₁	—	2	2	no	—
465	Q₈×C₃₁	—	2	1	no	—
466	Q₈×C₃₁	—	2	1	no	—
467	Q₈×C₃₁	—	2	1	no	—
468	Q₈×C₃₁	—	2	2	no	—
469	Q₈×C₃₁	—	2	1	no	—
470	Q₈×C₃₁	—	2	2	no	—
471	Q₈×C₃₁	—	2	1	no	—
472	Q₈×C₃₁	—	4	2	no	—
473	Q₈×C₃₁	—	4	2	no	—
474	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
475	D₄×C₃₁	—	2	2	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	2	2	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	2	2	no	—
480	D₄×C₃₁	—	2	2	no	—
481	D₄×C₃₁	—	2	1	no	—
482	D₄×C₃₁	—	4	2	no	—
483	D₄×C₃₁	—	4	4	no	—
484	D₄×C₃₁	—	4	4	no	—
485	D₄×C₃₁	—	4	4	no	—
486	D₄×C₃₁	—	4	2	no	—
487	D₄×C₃₁	—	4	2	no	—
488	D₄×C₃₁	—	8	2	no	—
489	D₄×C₃₁	—	8	1	no	—
490	D₄×C₃₁	—	8	1	no	—
491	D₄×C₃₁	—	8	2	no	—
492	D₄×C₃₁	—	8	1	no	—
493	D₄×C₃₁	—	8	2	no	—
494	D₄×C₃₁	—	8	2	no	—
495	D₄×C₃₁	—	8	2	no	—
496	D₄×C₃₁	—	8	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	2	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	1	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	2	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	2	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	4	1	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	4	4	no	—
515	C₂×C₄×C₃₁	—	4	2	no	—
516	C₂×C₄×C₃₁	—	4	4	no	—
517	C₂×C₄×C₃₁	—	4	4	no	—
518	C₂×C₄×C₃₁	—	4	2	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
521	C₂×C₄×C₃₁	—	8	2	no	—
522	C₂×C₄×C₃₁	—	8	2	no	—
523	C₂×C₄×C₃₁	—	8	1	no	—
524	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
533	C₈×C₃₁	—	2	1	no	—
534	C₈×C₃₁	—	2	1	no	—
535	C₈×C₃₁	—	2	2	no	—
536	C₈×C₃₁	—	2	2	no	—
537	C₈×C₃₁	—	2	1	no	—
538	C₈×C₃₁	—	2	1	no	—
539	#3517	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3480	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3309	C₂×C₃₁	1	2	yes	complemented
546	#3307	C₂×C₃₁	1	2	yes	complemented
547	#3304	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3287	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3284	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3271	C₂×C₃₁	1	2	yes	complemented
552	#3269	C₂×C₃₁	1	2	yes	complemented
553	#3251	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3250	C₂×C₃₁	1	2	yes	complemented
555	#3219	C₂×C₃₁	1	2	yes	complemented
556	#3207	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3111	C₂×C₃₁	1	2	yes	complemented
558	#3108	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#3035	C₂×C₃₁	1	2	yes	complemented
561	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
562	C₂²×C₃₁	—	2	1	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	2	1	no	—
565	C₂²×C₃₁	—	2	2	no	—
566	C₂²×C₃₁	—	2	1	no	—
567	C₂²×C₃₁	—	2	2	no	—
568	C₂²×C₃₁	—	4	2	no	—
569	C₂²×C₃₁	—	4	1	no	—
570	C₂²×C₃₁	—	4	2	no	—
571	C₂²×C₃₁	—	4	2	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	2	no	—
574	C₂²×C₃₁	—	4	2	no	—
575	C₂²×C₃₁	—	4	2	no	—
576	C₂²×C₃₁	—	4	1	no	—
577	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
578	C₄×C₃₁	—	2	1	no	—
579	C₄×C₃₁	—	2	2	no	—
580	C₄×C₃₁	—	2	1	no	—
581	C₄×C₃₁	—	2	2	no	—
582	C₄×C₃₁	—	2	1	no	—
583	C₄×C₃₁	—	2	2	no	—
584	C₄×C₃₁	—	2	1	no	—
585	C₄×C₃₁	—	2	2	no	—
586	C₄×C₃₁	—	4	1	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	—	4	1	no	—
589	C₄×C₃₁	—	4	1	no	—
590	C₄×C₃₁	—	4	1	no	—
591	C₄×C₃₁	—	4	2	no	—
592	C₄×C₃₁	—	4	1	no	—
593	C₄×C₃₁	—	4	2	no	—
594	C₄×C₃₁	#575	1	2	yes	—
595	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
596	C₄×C₃₁	#585	1	1	yes	characteristic
597	C₂×#137	C₂²×C₃₁	1	2	yes	—
598	C₂×#135	C₂²×C₃₁	1	2	yes	—
599	C₂×#135	C₂²×C₃₁	1	2	yes	—
600	#559	—	2	1	no	—
601	#559	C₂²×C₃₁	1	1	yes	characteristic
602	#557	C₂²×C₃₁	1	1	yes	characteristic
603	#557	C₂²×C₃₁	1	1	yes	characteristic
604	#556	—	2	1	no	—
605	#556	C₂²×C₃₁	1	1	yes	characteristic
606	#553	—	2	2	no	—
607	#553	—	2	1	no	—
608	#553	—	2	2	no	—
609	#553	C₂²×C₃₁	1	2	yes	—
610	#550	—	2	1	no	—
611	#550	C₂²×C₃₁	1	1	yes	characteristic
612	#550	C₂²×C₃₁	1	2	yes	—
613	#550	C₂²×C₃₁	1	1	yes	characteristic
614	#550	C₂²×C₃₁	1	1	yes	characteristic
615	#548	C₂²×C₃₁	1	2	yes	—
616	#547	C₂²×C₃₁	1	2	yes	—
617	#547	C₂²×C₃₁	1	1	yes	characteristic
618	#540	—	2	2	no	—
619	#540	—	2	1	no	—
620	#532	—	2	1	no	—
621	#532	C₂²×C₃₁	1	1	yes	characteristic
622	#532	C₂²×C₃₁	1	2	yes	—
623	#532	C₂²×C₃₁	1	1	yes	characteristic
624	#529	—	2	2	no	—
625	#529	C₂²×C₃₁	1	1	yes	characteristic
626	#529	C₂²×C₃₁	1	2	yes	—
627	#529	C₂²×C₃₁	1	2	yes	—
628	#520	—	2	1	no	—
629	C₄×#41	—	2	1	no	—
630	C₄×#41	C₂²×C₃₁	1	2	yes	—
631	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
632	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
633	#497	C₂²×C₃₁	1	2	yes	—
634	#496	C₂²×C₃₁	1	2	yes	—
635	#493	C₂²×C₃₁	1	1	yes	characteristic
636	#492	C₂²×C₃₁	1	1	yes	characteristic
637	#491	C₂²×C₃₁	1	2	yes	—
638	#490	C₂²×C₃₁	1	2	yes	—
639	#487	C₂²×C₃₁	1	1	yes	characteristic
640	#486	C₂²×C₃₁	1	1	yes	characteristic
641	#485	C₂²×C₃₁	1	2	yes	—
642	#483	C₂²×C₃₁	1	1	yes	characteristic
643	#482	C₂²×C₃₁	1	2	yes	—
644	#480	C₂²×C₃₁	1	1	yes	characteristic
645	#479	C₂²×C₃₁	1	1	yes	characteristic
646	#479	C₂²×C₃₁	1	1	yes	characteristic
647	#479	C₂²×C₃₁	1	2	yes	—
648	#478	C₂²×C₃₁	1	2	yes	—
649	#478	C₂²×C₃₁	1	2	yes	—
650	#475	C₂²×C₃₁	1	1	yes	characteristic
651	#474	C₂²×C₃₁	1	1	yes	characteristic
652	#469	C₂²×C₃₁	1	2	yes	—
653	#468	C₂²×C₃₁	1	2	yes	—
654	#467	C₂²×C₃₁	1	2	yes	—
655	#466	C₂²×C₃₁	1	2	yes	—
656	#465	C₂²×C₃₁	1	2	yes	—
657	#465	C₂²×C₃₁	1	2	yes	—
658	#464	C₂²×C₃₁	1	1	yes	characteristic
659	#464	C₂²×C₃₁	1	1	yes	characteristic
660	#464	C₂²×C₃₁	1	2	yes	—
661	#464	C₂²×C₃₁	1	2	yes	—
662	#464	C₂²×C₃₁	1	2	yes	—
663	#463	C₂²×C₃₁	1	2	yes	—
664	#463	C₂²×C₃₁	1	2	yes	—
665	#463	C₂²×C₃₁	1	2	yes	—
666	#463	C₂²×C₃₁	1	2	yes	—
667	#462	C₂²×C₃₁	1	2	yes	—
668	#462	C₂²×C₃₁	1	1	yes	characteristic
669	#462	C₂²×C₃₁	1	1	yes	characteristic
670	#461	C₂²×C₃₁	1	2	yes	—
671	#460	C₂²×C₃₁	1	2	yes	—
672	#460	C₂²×C₃₁	1	1	yes	characteristic
673	#460	C₂²×C₃₁	1	1	yes	characteristic
674	#460	C₂²×C₃₁	1	1	yes	characteristic
675	#459	C₂²×C₃₁	1	1	yes	characteristic
676	#459	C₂²×C₃₁	1	2	yes	—
677	#452	C₂²×C₃₁	1	2	yes	—
678	#452	C₂²×C₃₁	1	2	yes	—
679	#452	C₂²×C₃₁	1	2	yes	—
680	#451	C₂²×C₃₁	1	1	yes	characteristic
681	#449	C₂²×C₃₁	1	2	yes	—
682	#449	C₂²×C₃₁	1	2	yes	—
683	#449	C₂²×C₃₁	1	2	yes	—
684	#449	C₂²×C₃₁	1	2	yes	—
685	#449	C₂²×C₃₁	1	2	yes	—
686	#448	C₂²×C₃₁	1	1	yes	characteristic
687	#446	C₂²×C₃₁	1	1	yes	characteristic
688	#446	C₂²×C₃₁	1	1	yes	characteristic
689	#442	C₂²×C₃₁	1	2	yes	—
690	#441	C₂²×C₃₁	1	2	yes	—
691	#440	C₂²×C₃₁	1	2	yes	—
692	#440	C₂²×C₃₁	1	2	yes	—
693	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
694	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
695	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
696	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
697	#435	C₂²×C₃₁	1	2	yes	—
698	#435	C₂²×C₃₁	1	2	yes	—
699	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
700	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
701	#432	C₂²×C₃₁	1	2	yes	—
702	#431	C₂²×C₃₁	1	1	yes	characteristic
703	#423	C₂²×C₃₁	1	1	yes	characteristic
704	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
705	#417	C₂²×C₃₁	1	2	yes	—
706	#416	C₂²×C₃₁	1	2	yes	—
707	#416	C₂²×C₃₁	1	2	yes	—
708	C₂×C₃₁	—	4	1	no	—
709	C₂×C₃₁	—	4	2	no	—
710	C₂×C₃₁	—	8	2	no	—
711	C₂×C₃₁	—	8	1	no	—
712	C₂×C₃₁	—	8	2	no	—
713	C₂×C₃₁	#3488	1	1	yes	characteristic
714	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
715	C₂×C₃₁	#3584	1	1	yes	characteristic
716	C₂×#41	—	2	1	no	—
717	C₂×#41	—	2	1	no	—
718	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
719	C₂×#41	C₂³×C₃₁	1	2	yes	—
720	C₂×#41	C₂³×C₃₁	1	2	yes	—
721	C₂×#41	C₂³×C₃₁	1	2	yes	—
722	C₂×#41	C₂³×C₃₁	1	2	yes	—
723	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
724	#137	—	4	4	no	—
725	#135	—	4	4	no	—
726	#135	—	4	4	no	—
727	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
730	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
738	C₂×D₈	C₂³×C₃₁	1	2	yes	—
739	C₂×D₈	C₂³×C₃₁	1	2	yes	—
740	C₂×D₈	C₂³×C₃₁	1	2	yes	—
741	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
742	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
743	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
746	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
748	#127	—	2	1	no	—
749	#127	—	2	1	no	—
750	#127	—	2	2	no	—
751	#127	C₂³×C₃₁	1	2	yes	—
752	#127	C₂³×C₃₁	1	1	yes	characteristic
753	#127	C₂³×C₃₁	1	1	yes	characteristic
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	1	no	—
758	#126	—	2	2	no	—
759	#125	—	2	2	no	—
760	#125	—	2	1	no	—
761	#125	—	2	2	no	—
762	#125	C₂³×C₃₁	1	1	yes	characteristic
763	#125	C₂³×C₃₁	1	2	yes	—
764	#124	—	2	1	no	—
765	#124	—	2	1	no	—
766	#124	—	2	2	no	—
767	#124	—	2	1	no	—
768	#124	C₂³×C₃₁	1	1	yes	characteristic
769	#124	C₂³×C₃₁	1	2	yes	—
770	#124	C₂³×C₃₁	1	2	yes	—
771	#123	—	2	1	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
781	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
782	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	1	no	—
786	#121	—	2	2	no	—
787	#121	—	2	1	no	—
788	#121	—	2	2	no	—
789	#121	—	2	1	no	—
790	#121	—	2	2	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	C₂³×C₃₁	1	1	yes	characteristic
799	#121	C₂³×C₃₁	1	2	yes	—
800	#121	C₂³×C₃₁	1	2	yes	—
801	#121	C₂³×C₃₁	1	2	yes	—
802	C₄×Q₈	—	2	1	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
813	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
814	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
815	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	D₄×C₃₁	1	2	yes	—
833	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₃₁	1	2	yes	—
835	C₄×D₄	C₂³×C₃₁	1	2	yes	—
836	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₃₁	1	2	yes	—
838	C₄×D₄	C₂³×C₃₁	1	2	yes	—
839	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
840	#117	—	2	2	no	—
841	#117	—	2	2	no	—
842	#117	—	2	2	no	—
843	#117	—	2	1	no	—
844	#117	D₄×C₃₁	1	1	yes	characteristic
845	#117	D₄×C₃₁	1	2	yes	—
846	#117	C₂³×C₃₁	1	2	yes	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	—	2	2	no	—
850	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
851	C₂×C₄²	—	2	1	no	—
852	C₂×C₄²	—	2	2	no	—
853	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
854	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
855	#107	C₂³×C₃₁	1	1	yes	characteristic
856	#107	C₂³×C₃₁	1	1	yes	characteristic
857	#107	C₂³×C₃₁	1	2	yes	—
858	#106	C₂³×C₃₁	1	1	yes	characteristic
859	#106	C₂³×C₃₁	1	1	yes	characteristic
860	#106	C₂³×C₃₁	1	2	yes	—
861	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
863	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
868	#103	C₂³×C₃₁	1	1	yes	characteristic
869	#103	C₂³×C₃₁	1	2	yes	—
870	#103	C₂³×C₃₁	1	2	yes	—
871	#103	C₂³×C₃₁	1	2	yes	—
872	#103	C₂³×C₃₁	1	2	yes	—
873	#103	C₂³×C₃₁	1	1	yes	characteristic
874	#103	C₂³×C₃₁	1	1	yes	characteristic
875	#103	C₂³×C₃₁	1	1	yes	characteristic
876	#103	C₂³×C₃₁	1	1	yes	characteristic
877	#103	C₂³×C₃₁	1	1	yes	characteristic
878	#103	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	1	yes	characteristic
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	2	yes	—
882	#102	C₂³×C₃₁	1	2	yes	—
883	#102	C₂³×C₃₁	1	2	yes	—
884	#102	C₂³×C₃₁	1	1	yes	characteristic
885	#102	C₂³×C₃₁	1	2	yes	—
886	#102	C₂³×C₃₁	1	2	yes	—
887	#102	C₂³×C₃₁	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
889	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
892	#97	C₂³×C₃₁	1	2	yes	—
893	#97	C₂³×C₃₁	1	2	yes	—
894	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
896	C₃₁	#61994	1	1	yes	characteristic, direct product factor, Sylow
897	#41	—	2	4	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	4	4	no	—
901	#41	—	4	2	no	—
902	#41	—	4	2	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	4	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	2	no	—
911	C₂×Q₈	—	4	1	no	—
912	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
933	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
947	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
948	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
949	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
950	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
951	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
952	Q₁₆	—	2	2	no	—
953	Q₁₆	—	2	4	no	—
954	Q₁₆	—	4	1	no	—
955	Q₁₆	—	4	2	no	—
956	SD₁₆	—	2	2	no	—
957	SD₁₆	—	2	4	no	—
958	SD₁₆	—	4	1	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	2	no	—
962	SD₁₆	—	4	2	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	D₈	—	4	2	no	—
966	M₁₆	—	4	2	no	—
967	C₂×C₈	—	4	2	no	—
968	C₂×C₈	—	4	2	no	—
969	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
974	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1002	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1034	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1035	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₃₁	1	2	yes	—
1039	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1044	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	4	2	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1056	D₄	—	2	2	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	1	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	4	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	4	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1107	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1113	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1114	C₈	—	2	1	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	2	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	2	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	C₃₁×#575	1	2	yes	—
1153	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1154	C₄	C₃₁×#585	1	1	yes	characteristic
1155	C₂	—	4	1	no	—
1156	C₂	—	4	2	no	—
1157	C₂	—	8	2	no	—
1158	C₂	—	8	1	no	—
1159	C₂	—	8	2	no	—
1160	C₂	C₃₁×#3488	1	1	yes	characteristic
1161	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1162	C₂	C₃₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3517	C₂	semidirect
2. C₃₁×#3480	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3399	C₂	semidirect
5. C₃₁×#3374	C₂	semidirect
6. C₃₁×#3368	C₂	semidirect
7. C₃₁×#3309	C₂	semidirect
8. C₃₁×#3307	C₂	semidirect
9. C₃₁×#3304	C₂	semidirect
10. C₃₁×#3302	C₂	semidirect
11. C₃₁×#3287	C₂	semidirect
12. C₃₁×#3284	C₂	semidirect
13. C₃₁×#3271	C₂	semidirect
14. C₃₁×#3269	C₂	semidirect
15. C₃₁×#3251	C₂	semidirect
16. C₃₁×#3250	C₂	semidirect
17. C₃₁×#3219	C₂	semidirect
18. C₃₁×#3207	C₂	semidirect
19. C₃₁×#3111	C₂	semidirect
20. C₃₁×#3108	C₂	semidirect
21. C₃₁×#3037	C₂	semidirect
22. C₃₁×#3035	C₂	semidirect
23. C₃₁×#2990	C₂	semidirect
458. #61994	C₃₁	direct (N × H)
539. #3517	C₂×C₃₁	semidirect
540. #3480	C₂×C₃₁	semidirect
541. #3400	C₂×C₃₁	semidirect
542. #3399	C₂×C₃₁	semidirect
543. #3374	C₂×C₃₁	semidirect
544. #3368	C₂×C₃₁	semidirect
545. #3309	C₂×C₃₁	semidirect
546. #3307	C₂×C₃₁	semidirect
547. #3304	C₂×C₃₁	semidirect
548. #3302	C₂×C₃₁	semidirect
549. #3287	C₂×C₃₁	semidirect
550. #3284	C₂×C₃₁	semidirect
551. #3271	C₂×C₃₁	semidirect
552. #3269	C₂×C₃₁	semidirect
553. #3251	C₂×C₃₁	semidirect
554. #3250	C₂×C₃₁	semidirect
555. #3219	C₂×C₃₁	semidirect
556. #3207	C₂×C₃₁	semidirect
557. #3111	C₂×C₃₁	semidirect
558. #3108	C₂×C₃₁	semidirect
559. #3037	C₂×C₃₁	semidirect
560. #3035	C₂×C₃₁	semidirect
561. #2990	C₂×C₃₁	semidirect
896. C₃₁	#61994	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×#3517	2
C₃₁×#3480	2
C₃₁×#3400	2
C₃₁×#3399	2
C₃₁×#3374	2
C₃₁×#3368	2
C₃₁×#3309	2
C₃₁×#3307	2
C₃₁×#3304	2
C₃₁×#3302	2
C₃₁×#3287	2
C₃₁×#3284	2
C₃₁×#3271	2
C₃₁×#3269	2
C₃₁×#3251	2
C₃₁×#3250	2
C₃₁×#3219	2
C₃₁×#3207	2
C₃₁×#3111	2
C₃₁×#3108	2
C₃₁×#3037	2
C₃₁×#3035	2
C₃₁×#2990	2
#61994	31

Subgroups — C31×#61994 #21518753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61994 #21518753