Subgroups — C₃₁×#61920 #21518679

Order 7936.

1816 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3403	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3399	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3220	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
21	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#562	—	2	2	no	—
25	C₃₁×#559	C₂²	1	1	yes	characteristic
26	C₃₁×#559	C₂²	1	2	yes	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic
28	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#559	C₂²	1	2	yes	complemented
30	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#554	C₂²	1	2	yes	complemented
32	C₃₁×#550	C₂²	1	1	yes	characteristic
33	C₃₁×#550	C₂²	1	2	yes	—
34	C₃₁×#550	C₂²	1	1	yes	characteristic
35	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
36	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#548	—	2	1	no	—
38	C₃₁×#547	—	2	1	no	—
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	—	2	2	no	—
42	C₃₁×#542	—	2	1	no	—
43	C₃₁×#542	C₂²	1	2	yes	—
44	C₃₁×#540	—	2	2	no	—
45	C₃₁×#540	C₂²	1	2	yes	—
46	C₃₁×#539	—	2	2	no	—
47	C₃₁×#536	—	2	1	no	—
48	C₃₁×#535	C₂²	1	2	yes	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#532	—	2	1	no	—
51	C₃₁×#532	—	2	1	no	—
52	C₃₁×#532	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
54	C₃₁×#529	C₂²	1	1	yes	characteristic
55	C₃₁×#518	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#496	C₂²	1	2	yes	—
58	C₃₁×#496	C₂²	1	2	yes	complemented
59	C₃₁×#496	C₂²	1	2	yes	complemented
60	C₃₁×#495	C₂²	1	2	yes	complemented
61	C₃₁×#493	C₂²	1	1	yes	characteristic
62	C₃₁×#493	C₂²	1	1	yes	characteristic
63	C₃₁×#493	C₂²	1	2	yes	complemented
64	C₃₁×#490	C₂²	1	2	yes	—
65	C₃₁×#490	C₂²	1	2	yes	complemented
66	C₃₁×#489	C₂²	1	2	yes	complemented
67	C₃₁×#488	C₂²	1	2	yes	complemented
68	C₃₁×#486	C₂²	1	1	yes	characteristic
69	C₃₁×#486	C₂²	1	1	yes	characteristic
70	C₃₁×#486	C₂²	1	2	yes	complemented
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, complemented
75	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#478	C₂²	1	2	yes	complemented
78	C₃₁×#476	C₂²	1	2	yes	complemented
79	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#474	C₂²	1	2	yes	complemented
82	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#464	C₂²	1	2	yes	complemented
84	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#463	C₂²	1	2	yes	complemented
86	C₃₁×#463	C₂²	1	2	yes	complemented
87	C₃₁×#463	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#460	C₂²	1	1	yes	characteristic
91	C₃₁×#460	C₂²	1	1	yes	characteristic
92	C₃₁×#460	C₂²	1	2	yes	complemented
93	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#459	C₂²	1	1	yes	characteristic
95	C₃₁×#459	C₂²	1	2	yes	—
96	C₃₁×#459	C₂²	1	2	yes	—
97	C₃₁×#459	C₂²	1	1	yes	characteristic
98	C₃₁×#459	C₂²	1	2	yes	complemented
99	C₃₁×#459	C₂²	1	2	yes	complemented
100	C₃₁×#459	C₂²	1	2	yes	complemented
101	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#459	C₂²	1	2	yes	complemented
103	C₃₁×#459	C₂²	1	2	yes	complemented
104	C₃₁×#452	C₂²	1	1	yes	characteristic
105	C₃₁×#450	C₂²	1	2	yes	—
106	C₃₁×#449	C₂²	1	1	yes	characteristic
107	C₃₁×#449	C₂²	1	2	yes	—
108	C₃₁×#447	C₂²	1	2	yes	—
109	C₃₁×#447	C₂²	1	2	yes	—
110	C₃₁×#447	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	2	yes	complemented
112	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#446	C₂²	1	2	yes	complemented
114	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#442	C₂²	1	2	yes	complemented
118	C₃₁×#442	C₂²	1	2	yes	complemented
119	C₃₁×#442	C₂²	1	2	yes	complemented
120	C₃₁×#442	C₂²	1	2	yes	complemented
121	C₃₁×#440	C₂²	1	2	yes	complemented
122	C₃₁×#440	C₂²	1	2	yes	complemented
123	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
126	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
127	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
128	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
129	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
130	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
131	C₃₁×#433	C₂²	1	2	yes	—
132	C₃₁×#433	C₂²	1	2	yes	—
133	C₃₁×#432	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	2	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
141	C₂²×Q₈×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	—	2	1	no	—
143	C₂²×D₄×C₃₁	—	2	1	no	—
144	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×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	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×D₈×C₃₁	C₂³	1	2	yes	—
152	C₂×D₈×C₃₁	C₂³	1	2	yes	—
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	C₂³	1	2	yes	—
157	C₂×D₈×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₃₁×#127	—	2	1	no	—
165	C₃₁×#127	—	2	1	no	—
166	C₃₁×#127	C₂³	1	2	yes	—
167	C₃₁×#127	C₂³	1	1	yes	characteristic
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#127	C₂³	1	2	yes	—
170	C₃₁×#127	C₂³	1	2	yes	—
171	C₃₁×#127	C₂³	1	2	yes	—
172	C₃₁×#127	C₂³	1	1	yes	characteristic
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	1	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	D₄	1	2	yes	—
177	C₃₁×#125	C₂³	1	2	yes	—
178	C₃₁×#125	C₂³	1	1	yes	characteristic
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	1	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	C₂³	1	2	yes	—
187	C₃₁×#124	C₂³	1	2	yes	—
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#124	C₂³	1	1	yes	characteristic
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×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	1	no	—
207	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	1	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	—	2	2	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	1	no	—
223	C₃₁×#121	—	2	2	no	—
224	C₃₁×#121	—	2	2	no	—
225	C₃₁×#121	C₂³	1	1	yes	characteristic
226	C₃₁×#121	C₂³	1	2	yes	—
227	C₃₁×#120	—	2	2	no	—
228	C₃₁×#120	—	2	2	no	—
229	C₄×Q₈×C₃₁	—	2	1	no	—
230	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	2	no	—
245	C₄×D₄×C₃₁	—	2	2	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	C₄×D₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
258	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₃₁×#117	—	2	1	no	—
260	C₃₁×#117	—	2	1	no	—
261	C₃₁×#117	C₂³	1	1	yes	characteristic
262	C₃₁×#117	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	—	2	1	no	—
267	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	2	yes	—
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	1	yes	characteristic
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#102	C₂³	1	1	yes	characteristic
288	C₃₁×#102	C₂³	1	2	yes	—
289	C₃₁×#102	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	1	yes	characteristic
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	2	yes	—
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	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	4	1	no	—
314	#41×C₃₁	—	4	1	no	—
315	#41×C₃₁	—	8	2	no	—
316	#41×C₃₁	—	8	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	#41×C₃₁	—	8	2	no	—
319	#41×C₃₁	—	8	4	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	8	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	1	yes	characteristic
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	1	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	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	1	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	4	2	no	—
347	C₂×D₄×C₃₁	—	4	2	no	—
348	C₂×D₄×C₃₁	—	8	2	no	—
349	C₂×D₄×C₃₁	—	8	2	no	—
350	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
351	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
352	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	2	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	—	2	2	no	—
365	C₂²×C₄×C₃₁	—	2	2	no	—
366	C₂²×C₄×C₃₁	—	2	2	no	—
367	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
370	Q₁₆×C₃₁	—	4	1	no	—
371	SD₁₆×C₃₁	—	4	1	no	—
372	SD₁₆×C₃₁	—	4	2	no	—
373	SD₁₆×C₃₁	—	4	1	no	—
374	SD₁₆×C₃₁	—	4	2	no	—
375	SD₁₆×C₃₁	—	4	2	no	—
376	D₈×C₃₁	—	4	1	no	—
377	D₈×C₃₁	—	4	2	no	—
378	D₈×C₃₁	—	4	2	no	—
379	D₈×C₃₁	—	4	2	no	—
380	D₈×C₃₁	—	4	2	no	—
381	D₈×C₃₁	—	4	2	no	—
382	D₈×C₃₁	—	4	2	no	—
383	D₈×C₃₁	—	4	2	no	—
384	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
387	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
390	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	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	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	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	1	no	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
448	C₄²×C₃₁	C₂⁴	1	2	yes	—
449	C₄²×C₃₁	C₂⁴	1	2	yes	—
450	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
451	#61920	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂³×C₃₁	—	2	2	no	—
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	2	2	no	—
455	C₂³×C₃₁	—	2	2	no	—
456	C₂³×C₃₁	—	2	1	no	—
457	C₂³×C₃₁	—	4	4	no	—
458	C₂³×C₃₁	—	8	2	no	—
459	C₂³×C₃₁	—	8	2	no	—
460	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
461	Q₈×C₃₁	—	2	2	no	—
462	Q₈×C₃₁	—	2	2	no	—
463	Q₈×C₃₁	—	2	1	no	—
464	Q₈×C₃₁	—	2	1	no	—
465	Q₈×C₃₁	—	2	1	no	—
466	Q₈×C₃₁	—	2	1	no	—
467	Q₈×C₃₁	—	4	2	no	—
468	Q₈×C₃₁	—	4	2	no	—
469	Q₈×C₃₁	—	8	2	no	—
470	D₄×C₃₁	—	2	1	no	—
471	D₄×C₃₁	—	2	2	no	—
472	D₄×C₃₁	—	2	2	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	2	2	no	—
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	1	no	—
480	D₄×C₃₁	—	4	4	no	—
481	D₄×C₃₁	—	4	4	no	—
482	D₄×C₃₁	—	4	2	no	—
483	D₄×C₃₁	—	4	2	no	—
484	D₄×C₃₁	—	4	2	no	—
485	D₄×C₃₁	—	4	2	no	—
486	D₄×C₃₁	—	8	1	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	—	8	1	no	—
489	D₄×C₃₁	—	8	1	no	—
490	D₄×C₃₁	—	8	2	no	—
491	D₄×C₃₁	—	8	2	no	—
492	D₄×C₃₁	—	8	2	no	—
493	D₄×C₃₁	—	8	2	no	—
494	D₄×C₃₁	—	8	2	no	—
495	D₄×C₃₁	—	8	2	no	—
496	D₄×C₃₁	—	8	1	no	—
497	D₄×C₃₁	—	8	2	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	1	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	—	4	1	no	—
509	C₂×C₄×C₃₁	—	4	2	no	—
510	C₂×C₄×C₃₁	—	4	2	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	4	2	no	—
513	C₂×C₄×C₃₁	—	8	2	no	—
514	C₂×C₄×C₃₁	—	8	2	no	—
515	C₂×C₄×C₃₁	—	8	2	no	—
516	C₂×C₄×C₃₁	—	8	2	no	—
517	C₂×C₄×C₃₁	—	8	2	no	—
518	C₂×C₄×C₃₁	—	8	2	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
521	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
529	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
531	C₈×C₃₁	—	2	1	no	—
532	C₈×C₃₁	—	2	1	no	—
533	C₈×C₃₁	—	2	1	no	—
534	C₈×C₃₁	—	2	2	no	—
535	C₈×C₃₁	—	2	1	no	—
536	C₈×C₃₁	—	2	2	no	—
537	#3554	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3403	C₂×C₃₁	1	2	yes	complemented
540	#3399	C₂×C₃₁	1	2	yes	complemented
541	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3396	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3391	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3370	C₂×C₃₁	1	2	yes	complemented
547	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3366	C₂×C₃₁	1	2	yes	complemented
549	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3358	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3224	C₂×C₃₁	1	2	yes	complemented
552	#3220	C₂×C₃₁	1	2	yes	complemented
553	#3217	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3122	C₂×C₃₁	1	2	yes	complemented
556	#3118	C₂×C₃₁	1	2	yes	complemented
557	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#2985	C₂×C₃₁	1	1	yes	characteristic, complemented
560	C₂²×C₃₁	—	2	1	no	—
561	C₂²×C₃₁	—	2	1	no	—
562	C₂²×C₃₁	—	2	1	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	—	4	2	no	—
565	C₂²×C₃₁	—	4	2	no	—
566	C₂²×C₃₁	—	4	2	no	—
567	C₂²×C₃₁	—	4	1	no	—
568	C₂²×C₃₁	—	4	1	no	—
569	C₂²×C₃₁	—	4	2	no	—
570	C₂²×C₃₁	—	4	2	no	—
571	C₂²×C₃₁	—	4	2	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	1	no	—
574	C₂²×C₃₁	—	4	1	no	—
575	C₂²×C₃₁	—	4	2	no	—
576	C₂²×C₃₁	—	4	2	no	—
577	C₂²×C₃₁	—	4	2	no	—
578	C₂²×C₃₁	—	16	4	no	—
579	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
580	C₄×C₃₁	—	2	1	no	—
581	C₄×C₃₁	—	2	1	no	—
582	C₄×C₃₁	—	2	2	no	—
583	C₄×C₃₁	—	2	2	no	—
584	C₄×C₃₁	—	2	1	no	—
585	C₄×C₃₁	—	2	1	no	—
586	C₄×C₃₁	—	2	2	no	—
587	C₄×C₃₁	—	2	2	no	—
588	C₄×C₃₁	—	4	1	no	—
589	C₄×C₃₁	—	4	1	no	—
590	C₄×C₃₁	—	4	1	no	—
591	C₄×C₃₁	—	4	1	no	—
592	C₄×C₃₁	—	4	1	no	—
593	C₄×C₃₁	—	4	1	no	—
594	C₄×C₃₁	—	4	2	no	—
595	C₄×C₃₁	#576	1	2	yes	—
596	C₄×C₃₁	#585	1	1	yes	characteristic
597	C₄×C₃₁	#585	1	1	yes	characteristic
598	#562	—	2	2	no	—
599	#559	C₂²×C₃₁	1	1	yes	characteristic
600	#559	C₂²×C₃₁	1	2	yes	—
601	#559	C₂²×C₃₁	1	1	yes	characteristic
602	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	#559	C₂²×C₃₁	1	2	yes	complemented
604	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
605	#554	C₂²×C₃₁	1	2	yes	complemented
606	#550	C₂²×C₃₁	1	1	yes	characteristic
607	#550	C₂²×C₃₁	1	2	yes	—
608	#550	C₂²×C₃₁	1	1	yes	characteristic
609	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
610	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	#548	—	2	1	no	—
612	#547	—	2	1	no	—
613	#546	—	2	1	no	—
614	#546	—	2	1	no	—
615	#546	—	2	2	no	—
616	#542	—	2	1	no	—
617	#542	C₂²×C₃₁	1	2	yes	—
618	#540	—	2	2	no	—
619	#540	C₂²×C₃₁	1	2	yes	—
620	#539	—	2	2	no	—
621	#536	—	2	1	no	—
622	#535	C₂²×C₃₁	1	2	yes	—
623	#533	C₂²×C₃₁	1	1	yes	characteristic
624	#532	—	2	1	no	—
625	#532	—	2	1	no	—
626	#532	C₂²×C₃₁	1	1	yes	characteristic
627	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
628	#529	C₂²×C₃₁	1	1	yes	characteristic
629	#518	C₂²×C₃₁	1	2	yes	—
630	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
631	#496	C₂²×C₃₁	1	2	yes	—
632	#496	C₂²×C₃₁	1	2	yes	complemented
633	#496	C₂²×C₃₁	1	2	yes	complemented
634	#495	C₂²×C₃₁	1	2	yes	complemented
635	#493	C₂²×C₃₁	1	1	yes	characteristic
636	#493	C₂²×C₃₁	1	1	yes	characteristic
637	#493	C₂²×C₃₁	1	2	yes	complemented
638	#490	C₂²×C₃₁	1	2	yes	—
639	#490	C₂²×C₃₁	1	2	yes	complemented
640	#489	C₂²×C₃₁	1	2	yes	complemented
641	#488	C₂²×C₃₁	1	2	yes	complemented
642	#486	C₂²×C₃₁	1	1	yes	characteristic
643	#486	C₂²×C₃₁	1	1	yes	characteristic
644	#486	C₂²×C₃₁	1	2	yes	complemented
645	#485	C₂²×C₃₁	1	1	yes	characteristic
646	#482	C₂²×C₃₁	1	1	yes	characteristic
647	#482	C₂²×C₃₁	1	2	yes	—
648	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#478	C₂²×C₃₁	1	2	yes	complemented
651	#478	C₂²×C₃₁	1	2	yes	complemented
652	#476	C₂²×C₃₁	1	2	yes	complemented
653	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#474	C₂²×C₃₁	1	2	yes	complemented
656	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#464	C₂²×C₃₁	1	2	yes	complemented
658	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#463	C₂²×C₃₁	1	2	yes	complemented
660	#463	C₂²×C₃₁	1	2	yes	complemented
661	#463	C₂²×C₃₁	1	2	yes	complemented
662	#463	C₂²×C₃₁	1	2	yes	complemented
663	#463	C₂²×C₃₁	1	2	yes	complemented
664	#460	C₂²×C₃₁	1	1	yes	characteristic
665	#460	C₂²×C₃₁	1	1	yes	characteristic
666	#460	C₂²×C₃₁	1	2	yes	complemented
667	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#459	C₂²×C₃₁	1	1	yes	characteristic
669	#459	C₂²×C₃₁	1	2	yes	—
670	#459	C₂²×C₃₁	1	2	yes	—
671	#459	C₂²×C₃₁	1	1	yes	characteristic
672	#459	C₂²×C₃₁	1	2	yes	complemented
673	#459	C₂²×C₃₁	1	2	yes	complemented
674	#459	C₂²×C₃₁	1	2	yes	complemented
675	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#459	C₂²×C₃₁	1	2	yes	complemented
677	#459	C₂²×C₃₁	1	2	yes	complemented
678	#452	C₂²×C₃₁	1	1	yes	characteristic
679	#450	C₂²×C₃₁	1	2	yes	—
680	#449	C₂²×C₃₁	1	1	yes	characteristic
681	#449	C₂²×C₃₁	1	2	yes	—
682	#447	C₂²×C₃₁	1	2	yes	—
683	#447	C₂²×C₃₁	1	2	yes	—
684	#447	C₂²×C₃₁	1	2	yes	—
685	#446	C₂²×C₃₁	1	2	yes	complemented
686	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#446	C₂²×C₃₁	1	2	yes	complemented
688	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	#442	C₂²×C₃₁	1	2	yes	complemented
692	#442	C₂²×C₃₁	1	2	yes	complemented
693	#442	C₂²×C₃₁	1	2	yes	complemented
694	#442	C₂²×C₃₁	1	2	yes	complemented
695	#440	C₂²×C₃₁	1	2	yes	complemented
696	#440	C₂²×C₃₁	1	2	yes	complemented
697	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
701	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
703	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
704	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
705	#433	C₂²×C₃₁	1	2	yes	—
706	#433	C₂²×C₃₁	1	2	yes	—
707	#432	C₂²×C₃₁	1	1	yes	characteristic
708	#431	C₂²×C₃₁	1	1	yes	characteristic
709	C₂×C₃₁	—	4	1	no	—
710	C₂×C₃₁	—	8	1	no	—
711	C₂×C₃₁	—	8	2	no	—
712	C₂×C₃₁	—	8	1	no	—
713	C₂×C₃₁	—	8	2	no	—
714	C₂×C₃₁	—	8	2	no	—
715	C₂×C₃₁	#3487	1	1	yes	characteristic
716	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
717	C₂×C₃₁	#3585	1	1	yes	characteristic
718	C₂×#41	—	2	1	no	—
719	C₂×#41	—	2	1	no	—
720	C₂×#41	—	2	2	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
724	C₂²×Q₈	—	2	1	no	—
725	C₂²×D₄	—	2	1	no	—
726	C₂²×D₄	—	2	1	no	—
727	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
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×D₈	C₂³×C₃₁	1	2	yes	—
735	C₂×D₈	C₂³×C₃₁	1	2	yes	—
736	C₂×D₈	C₂³×C₃₁	1	2	yes	—
737	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
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×D₈	C₂³×C₃₁	1	2	yes	—
742	C₄⋊Q₈	—	2	1	no	—
743	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
744	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
747	#127	—	2	1	no	—
748	#127	—	2	1	no	—
749	#127	C₂³×C₃₁	1	2	yes	—
750	#127	C₂³×C₃₁	1	1	yes	characteristic
751	#127	C₂³×C₃₁	1	1	yes	characteristic
752	#127	C₂³×C₃₁	1	1	yes	characteristic
753	#127	C₂³×C₃₁	1	2	yes	—
754	#127	C₂³×C₃₁	1	2	yes	—
755	#127	C₂³×C₃₁	1	2	yes	—
756	#126	—	2	2	no	—
757	#126	—	2	1	no	—
758	#125	—	2	2	no	—
759	#125	D₄×C₃₁	1	2	yes	—
760	#125	C₂³×C₃₁	1	1	yes	characteristic
761	#125	C₂³×C₃₁	1	2	yes	—
762	#124	—	2	1	no	—
763	#124	—	2	1	no	—
764	#124	—	2	2	no	—
765	#124	—	2	1	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	1	no	—
769	#124	C₂³×C₃₁	1	1	yes	characteristic
770	#124	C₂³×C₃₁	1	2	yes	—
771	#124	C₂³×C₃₁	1	2	yes	—
772	#124	C₂³×C₃₁	1	2	yes	—
773	#123	—	2	1	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	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
791	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
792	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	1	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	C₂³×C₃₁	1	1	yes	characteristic
809	#121	C₂³×C₃₁	1	2	yes	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	C₄×Q₈	—	2	1	no	—
813	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
814	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
815	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
817	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₃₁	1	2	yes	—
834	C₄×D₄	C₂³×C₃₁	1	2	yes	—
835	C₄×D₄	C₂³×C₃₁	1	2	yes	—
836	C₄×D₄	C₂³×C₃₁	1	2	yes	—
837	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₃₁	1	2	yes	—
839	C₄×D₄	C₂³×C₃₁	1	2	yes	—
840	C₄×D₄	C₂³×C₃₁	1	2	yes	—
841	C₄×D₄	C₂³×C₃₁	1	2	yes	—
842	#117	—	2	1	no	—
843	#117	—	2	1	no	—
844	#117	C₂³×C₃₁	1	1	yes	characteristic
845	#117	C₂³×C₃₁	1	2	yes	—
846	C₂×C₄⋊C₄	—	2	2	no	—
847	C₂×C₂²⋊C₄	—	2	2	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	C₂×C₄²	—	2	1	no	—
850	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
851	#107	C₂³×C₃₁	1	1	yes	characteristic
852	#107	C₂³×C₃₁	1	1	yes	characteristic
853	#107	C₂³×C₃₁	1	2	yes	—
854	#106	C₂³×C₃₁	1	2	yes	—
855	#106	C₂³×C₃₁	1	1	yes	characteristic
856	#106	C₂³×C₃₁	1	1	yes	characteristic
857	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
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	#103	C₂³×C₃₁	1	1	yes	characteristic
866	#103	C₂³×C₃₁	1	1	yes	characteristic
867	#103	C₂³×C₃₁	1	1	yes	characteristic
868	#103	C₂³×C₃₁	1	1	yes	characteristic
869	#103	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	1	yes	characteristic
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
877	#102	C₂³×C₃₁	1	1	yes	characteristic
878	#102	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	2	yes	—
885	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
886	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
888	#97	C₂³×C₃₁	1	2	yes	—
889	#97	C₂³×C₃₁	1	2	yes	—
890	#97	C₂³×C₃₁	1	2	yes	—
891	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₃₁	1	2	yes	—
894	C₄×C₈	C₂³×C₃₁	1	2	yes	—
895	C₃₁	#61920	1	1	yes	characteristic, direct product factor, Sylow
896	C₂⁴	—	2	2	no	—
897	#41	—	4	1	no	—
898	#41	—	4	1	no	—
899	#41	—	8	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	2	no	—
902	#41	—	8	2	no	—
903	#41	—	8	4	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	8	2	no	—
907	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
908	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
909	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	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	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	4	2	no	—
932	C₂×D₄	—	8	2	no	—
933	C₂×D₄	—	8	2	no	—
934	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
936	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
954	Q₁₆	—	4	1	no	—
955	SD₁₆	—	4	1	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	1	no	—
958	SD₁₆	—	4	2	no	—
959	SD₁₆	—	4	2	no	—
960	D₈	—	4	1	no	—
961	D₈	—	4	2	no	—
962	D₈	—	4	2	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	D₈	—	4	2	no	—
966	D₈	—	4	2	no	—
967	D₈	—	4	2	no	—
968	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
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	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
986	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
987	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
994	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
997	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	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	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1030	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₃₁	1	2	yes	—
1033	C₄²	C₂⁴×C₃₁	1	2	yes	—
1034	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	2	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	4	4	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	4	2	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	8	2	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	2	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	1	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	D₄	—	8	2	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	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	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1109	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1110	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
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	1	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	2	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	16	4	no	—
1139	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1140	C₄	—	2	1	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	1	no	—
1146	C₄	—	2	2	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	C₃₁×#576	1	2	yes	—
1156	C₄	C₃₁×#585	1	1	yes	characteristic
1157	C₄	C₃₁×#585	1	1	yes	characteristic
1158	C₂	—	4	1	no	—
1159	C₂	—	8	2	no	—
1160	C₂	—	8	2	no	—
1161	C₂	—	8	1	no	—
1162	C₂	—	8	1	no	—
1163	C₂	—	8	2	no	—
1164	C₂	C₃₁×#3487	1	1	yes	characteristic
1165	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1166	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3554	C₂	semidirect
2. C₃₁×#3508	C₂	semidirect
3. C₃₁×#3403	C₂	semidirect
4. C₃₁×#3399	C₂	semidirect
5. C₃₁×#3399	C₂	semidirect
6. C₃₁×#3399	C₂	semidirect
7. C₃₁×#3396	C₂	semidirect
8. C₃₁×#3391	C₂	semidirect
9. C₃₁×#3373	C₂	semidirect
10. C₃₁×#3370	C₂	semidirect
11. C₃₁×#3368	C₂	semidirect
12. C₃₁×#3366	C₂	semidirect
13. C₃₁×#3365	C₂	semidirect
14. C₃₁×#3358	C₂	semidirect
15. C₃₁×#3224	C₂	semidirect
16. C₃₁×#3220	C₂	semidirect
17. C₃₁×#3217	C₂	semidirect
18. C₃₁×#3205	C₂	semidirect
19. C₃₁×#3122	C₂	semidirect
20. C₃₁×#3118	C₂	semidirect
21. C₃₁×#3115	C₂	semidirect
22. C₃₁×#3102	C₂	semidirect
23. C₃₁×#2985	C₂	semidirect
28. C₃₁×#559	C₂²	semidirect
29. C₃₁×#559	C₂²	semidirect
30. C₃₁×#557	C₂²	semidirect
31. C₃₁×#554	C₂²	semidirect
35. C₃₁×#550	C₂²	semidirect
36. D₄×Q₈×C₃₁	C₂²	semidirect
58. C₃₁×#496	C₂²	semidirect
59. C₃₁×#496	C₂²	semidirect
60. C₃₁×#495	C₂²	semidirect
63. C₃₁×#493	C₂²	semidirect
65. C₃₁×#490	C₂²	semidirect
66. C₃₁×#489	C₂²	semidirect
67. C₃₁×#488	C₂²	semidirect
70. C₃₁×#486	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#478	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
79. C₃₁×#475	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#474	C₂²	semidirect
82. C₃₁×#464	C₂²	semidirect
83. C₃₁×#464	C₂²	semidirect
84. C₃₁×#463	C₂²	semidirect
85. C₃₁×#463	C₂²	semidirect
86. C₃₁×#463	C₂²	semidirect
87. C₃₁×#463	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
92. C₃₁×#460	C₂²	semidirect
93. C₃₁×#460	C₂²	semidirect
98. C₃₁×#459	C₂²	semidirect
99. C₃₁×#459	C₂²	semidirect
100. C₃₁×#459	C₂²	semidirect
101. C₃₁×#459	C₂²	semidirect
102. C₃₁×#459	C₂²	semidirect
103. C₃₁×#459	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₃₁×#446	C₂²	semidirect
113. C₃₁×#446	C₂²	semidirect
114. C₃₁×#446	C₂²	semidirect
115. C₈×Q₈×C₃₁	C₂²	semidirect
116. C₈×Q₈×C₃₁	C₂²	semidirect
117. C₃₁×#442	C₂²	semidirect
118. C₃₁×#442	C₂²	semidirect
119. C₃₁×#442	C₂²	semidirect
120. C₃₁×#442	C₂²	semidirect
121. C₃₁×#440	C₂²	semidirect
122. C₃₁×#440	C₂²	semidirect
123. C₄×Q₁₆×C₃₁	C₂²	semidirect
124. C₄×SD₁₆×C₃₁	C₂²	semidirect
125. C₄×SD₁₆×C₃₁	C₂²	semidirect
126. C₄×SD₁₆×C₃₁	C₂²	semidirect
127. C₄×D₈×C₃₁	C₂²	semidirect
128. C₄×D₈×C₃₁	C₂²	semidirect
129. C₄×D₈×C₃₁	C₂²	semidirect
130. C₄×D₈×C₃₁	C₂²	semidirect
451. #61920	C₃₁	direct (N × H)
537. #3554	C₂×C₃₁	semidirect
538. #3508	C₂×C₃₁	semidirect
539. #3403	C₂×C₃₁	semidirect
540. #3399	C₂×C₃₁	semidirect
541. #3399	C₂×C₃₁	semidirect
542. #3399	C₂×C₃₁	semidirect
543. #3396	C₂×C₃₁	semidirect
544. #3391	C₂×C₃₁	semidirect
545. #3373	C₂×C₃₁	semidirect
546. #3370	C₂×C₃₁	semidirect
547. #3368	C₂×C₃₁	semidirect
548. #3366	C₂×C₃₁	semidirect
549. #3365	C₂×C₃₁	semidirect
550. #3358	C₂×C₃₁	semidirect
551. #3224	C₂×C₃₁	semidirect
552. #3220	C₂×C₃₁	semidirect
553. #3217	C₂×C₃₁	semidirect
554. #3205	C₂×C₃₁	semidirect
555. #3122	C₂×C₃₁	semidirect
556. #3118	C₂×C₃₁	semidirect
557. #3115	C₂×C₃₁	semidirect
558. #3102	C₂×C₃₁	semidirect
559. #2985	C₂×C₃₁	semidirect
602. #559	C₂²×C₃₁	semidirect
603. #559	C₂²×C₃₁	semidirect
604. #557	C₂²×C₃₁	semidirect
605. #554	C₂²×C₃₁	semidirect
609. #550	C₂²×C₃₁	semidirect
610. D₄×Q₈	C₂²×C₃₁	semidirect
632. #496	C₂²×C₃₁	semidirect
633. #496	C₂²×C₃₁	semidirect
634. #495	C₂²×C₃₁	semidirect
637. #493	C₂²×C₃₁	semidirect
639. #490	C₂²×C₃₁	semidirect
640. #489	C₂²×C₃₁	semidirect
641. #488	C₂²×C₃₁	semidirect
644. #486	C₂²×C₃₁	semidirect
648. #479	C₂²×C₃₁	semidirect
649. #478	C₂²×C₃₁	semidirect
650. #478	C₂²×C₃₁	semidirect
651. #478	C₂²×C₃₁	semidirect
652. #476	C₂²×C₃₁	semidirect
653. #475	C₂²×C₃₁	semidirect
654. #474	C₂²×C₃₁	semidirect
655. #474	C₂²×C₃₁	semidirect
656. #464	C₂²×C₃₁	semidirect
657. #464	C₂²×C₃₁	semidirect
658. #463	C₂²×C₃₁	semidirect
659. #463	C₂²×C₃₁	semidirect
660. #463	C₂²×C₃₁	semidirect
661. #463	C₂²×C₃₁	semidirect
662. #463	C₂²×C₃₁	semidirect
663. #463	C₂²×C₃₁	semidirect
666. #460	C₂²×C₃₁	semidirect
667. #460	C₂²×C₃₁	semidirect
672. #459	C₂²×C₃₁	semidirect
673. #459	C₂²×C₃₁	semidirect
674. #459	C₂²×C₃₁	semidirect
675. #459	C₂²×C₃₁	semidirect
676. #459	C₂²×C₃₁	semidirect
677. #459	C₂²×C₃₁	semidirect
685. #446	C₂²×C₃₁	semidirect
686. #446	C₂²×C₃₁	semidirect
687. #446	C₂²×C₃₁	semidirect
688. #446	C₂²×C₃₁	semidirect
689. C₈×Q₈	C₂²×C₃₁	semidirect
690. C₈×Q₈	C₂²×C₃₁	semidirect
691. #442	C₂²×C₃₁	semidirect
692. #442	C₂²×C₃₁	semidirect
693. #442	C₂²×C₃₁	semidirect
694. #442	C₂²×C₃₁	semidirect
695. #440	C₂²×C₃₁	semidirect
696. #440	C₂²×C₃₁	semidirect
697. C₄×Q₁₆	C₂²×C₃₁	semidirect
698. C₄×SD₁₆	C₂²×C₃₁	semidirect
699. C₄×SD₁₆	C₂²×C₃₁	semidirect
700. C₄×SD₁₆	C₂²×C₃₁	semidirect
701. C₄×D₈	C₂²×C₃₁	semidirect
702. C₄×D₈	C₂²×C₃₁	semidirect
703. C₄×D₈	C₂²×C₃₁	semidirect
704. C₄×D₈	C₂²×C₃₁	semidirect
895. C₃₁	#61920	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×#3554	2
C₃₁×#3508	2
C₃₁×#3403	2
C₃₁×#3399	2
C₃₁×#3396	2
C₃₁×#3391	2
C₃₁×#3373	2
C₃₁×#3370	2
C₃₁×#3368	2
C₃₁×#3366	2
C₃₁×#3365	2
C₃₁×#3358	2
C₃₁×#3224	2
C₃₁×#3220	2
C₃₁×#3217	2
C₃₁×#3205	2
C₃₁×#3122	2
C₃₁×#3118	2
C₃₁×#3115	2
C₃₁×#3102	2
C₃₁×#2985	2
#61920	31

Subgroups — C31×#61920 #21518679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61920 #21518679