Subgroups — C₃₁×#61320 #21518079

Order 7936.

1804 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3480	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3377	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3374	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3371	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3368	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3142	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3080	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3037	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₃₁×#137	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#137	C₂²	1	2	yes	—
20	C₃₁×#559	C₂²	1	1	yes	characteristic
21	C₃₁×#559	C₂²	1	2	yes	—
22	C₃₁×#557	—	2	1	no	—
23	C₃₁×#557	—	2	1	no	—
24	C₃₁×#557	—	2	2	no	—
25	C₃₁×#557	C₂²	1	1	yes	characteristic
26	C₃₁×#557	C₂²	1	2	yes	—
27	C₃₁×#557	C₂²	1	2	yes	—
28	C₃₁×#557	C₂²	1	4	yes	—
29	C₃₁×#556	C₂²	1	1	yes	characteristic
30	C₃₁×#556	C₂²	1	2	yes	—
31	C₃₁×#553	—	2	1	no	—
32	C₃₁×#553	—	2	2	no	—
33	C₃₁×#550	C₂²	1	1	yes	characteristic
34	C₃₁×#548	—	2	1	no	—
35	C₃₁×#532	C₂²	1	1	yes	characteristic
36	C₃₁×#532	C₂²	1	2	yes	—
37	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
38	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₃₁×#529	—	2	2	no	—
40	C₃₁×#529	—	2	1	no	—
41	C₂×C₃₁×#125	—	2	2	no	—
42	C₂×C₃₁×#125	C₂²	1	2	yes	—
43	C₄×#41×C₃₁	—	2	1	no	—
44	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
45	C₄×#41×C₃₁	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
47	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
48	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
50	C₃₁×#491	C₂²	1	4	yes	—
51	C₃₁×#490	C₂²	1	4	yes	—
52	C₃₁×#489	C₂²	1	4	yes	—
53	C₃₁×#488	C₂²	1	4	yes	—
54	C₃₁×#488	C₂²	1	4	yes	—
55	C₃₁×#487	C₂²	1	2	yes	—
56	C₃₁×#486	C₂²	1	2	yes	—
57	C₃₁×#479	C₂²	1	4	yes	—
58	C₃₁×#479	C₂²	1	4	yes	—
59	C₃₁×#478	C₂²	1	4	yes	—
60	C₃₁×#478	C₂²	1	4	yes	—
61	C₃₁×#477	C₂²	1	2	yes	—
62	C₃₁×#476	C₂²	1	2	yes	—
63	C₃₁×#475	C₂²	1	2	yes	—
64	C₃₁×#474	C₂²	1	2	yes	—
65	C₃₁×#464	C₂²	1	4	yes	—
66	C₃₁×#464	C₂²	1	4	yes	—
67	C₃₁×#464	C₂²	1	4	yes	—
68	C₃₁×#462	C₂²	1	2	yes	—
69	C₃₁×#462	C₂²	1	4	yes	—
70	C₃₁×#460	C₂²	1	2	yes	—
71	C₃₁×#460	C₂²	1	4	yes	—
72	C₃₁×#446	C₂²	1	2	yes	—
73	C₃₁×#446	C₂²	1	4	yes	—
74	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
75	C₃₁×#441	C₂²	1	4	yes	—
76	C₃₁×#441	C₂²	1	2	yes	—
77	C₃₁×#440	C₂²	1	4	yes	—
78	C₃₁×#440	C₂²	1	2	yes	—
79	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
80	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
82	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
83	C₃₁×#428	C₂²	1	2	yes	—
84	C₃₁×#428	C₂²	1	1	yes	characteristic
85	C₃₁×#423	C₂²	1	1	yes	characteristic
86	C₃₁×#423	C₂²	1	2	yes	—
87	C₃₁×#419	C₂²	1	1	yes	characteristic
88	C₃₁×#417	C₂²	1	2	yes	—
89	C₃₁×#417	C₂²	1	2	yes	—
90	C₃₁×#417	C₂²	1	2	yes	—
91	C₃₁×#417	C₂²	1	2	yes	—
92	C₃₁×#417	C₂²	1	1	yes	characteristic
93	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
97	C₂×#41×C₃₁	C₂³	1	2	yes	—
98	C₂²×Q₈×C₃₁	—	2	1	no	—
99	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
100	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
101	C₃₁×#137	—	2	4	no	—
102	C₃₁×#137	—	2	8	no	—
103	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
104	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
106	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
107	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
110	C₃₁×C₄⋊Q₈	—	2	2	no	—
111	C₃₁×C₄⋊Q₈	—	2	2	no	—
112	C₃₁×C₄⋊Q₈	—	2	4	no	—
113	C₃₁×C₄⋊Q₈	—	2	1	no	—
114	C₃₁×C₄⋊Q₈	—	2	1	no	—
115	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₃₁×#127	C₂³	1	1	yes	characteristic
120	C₃₁×#127	C₂³	1	2	yes	—
121	C₃₁×#126	—	2	2	no	—
122	C₃₁×#126	—	2	2	no	—
123	C₃₁×#126	—	2	2	no	—
124	C₃₁×#125	—	2	4	no	—
125	C₃₁×#125	—	2	4	no	—
126	C₃₁×#125	—	2	4	no	—
127	C₃₁×#125	—	2	4	no	—
128	C₃₁×#125	—	2	1	no	—
129	C₃₁×#125	—	2	2	no	—
130	C₃₁×#125	—	2	2	no	—
131	C₃₁×#125	—	2	2	no	—
132	C₃₁×#125	C₂³	1	4	yes	—
133	C₃₁×#125	C₂³	1	4	yes	—
134	C₃₁×#124	—	2	1	no	—
135	C₃₁×#124	—	2	2	no	—
136	C₃₁×#124	C₂³	1	2	yes	—
137	C₃₁×#124	C₂³	1	2	yes	—
138	C₃₁×#124	C₂³	1	2	yes	—
139	C₃₁×#123	—	2	2	no	—
140	C₃₁×#123	—	2	2	no	—
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×C₂²⋊Q₈	—	2	1	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×#121	—	2	1	no	—
145	C₃₁×#121	—	2	2	no	—
146	C₃₁×#121	—	2	2	no	—
147	C₃₁×#121	—	2	1	no	—
148	C₃₁×#121	—	2	1	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₄×Q₈×C₃₁	—	2	1	no	—
151	C₄×Q₈×C₃₁	—	2	2	no	—
152	C₄×Q₈×C₃₁	—	2	2	no	—
153	C₄×Q₈×C₃₁	—	2	4	no	—
154	C₄×Q₈×C₃₁	—	2	2	no	—
155	C₄×Q₈×C₃₁	—	2	2	no	—
156	C₄×Q₈×C₃₁	—	2	1	no	—
157	C₄×Q₈×C₃₁	—	2	1	no	—
158	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
159	C₄×Q₈×C₃₁	D₄	1	2	yes	—
160	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
162	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
163	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
165	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
166	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
167	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
172	C₄×D₄×C₃₁	—	2	1	no	—
173	C₄×D₄×C₃₁	—	2	2	no	—
174	C₄×D₄×C₃₁	—	2	2	no	—
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	1	no	—
177	C₄×D₄×C₃₁	—	2	2	no	—
178	C₄×D₄×C₃₁	—	2	2	no	—
179	C₄×D₄×C₃₁	—	2	1	no	—
180	C₄×D₄×C₃₁	—	2	2	no	—
181	C₄×D₄×C₃₁	—	2	1	no	—
182	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₃₁	C₂³	1	2	yes	—
184	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₃₁	C₂³	1	2	yes	—
186	C₃₁×#117	—	2	1	no	—
187	C₃₁×#117	—	2	2	no	—
188	C₃₁×#117	—	2	2	no	—
189	C₃₁×#117	—	2	1	no	—
190	C₃₁×#117	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
192	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
193	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
194	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
196	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
198	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂×C₄²×C₃₁	—	2	2	no	—
201	C₂×C₄²×C₃₁	—	2	1	no	—
202	C₂×C₄²×C₃₁	—	2	2	no	—
203	C₂×C₄²×C₃₁	—	2	1	no	—
204	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
205	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
206	C₃₁×#107	C₂³	1	4	yes	—
207	C₃₁×#107	C₂³	1	2	yes	—
208	C₃₁×#106	C₂³	1	4	yes	—
209	C₃₁×#106	C₂³	1	2	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
214	C₃₁×#103	C₂³	1	4	yes	—
215	C₃₁×#103	C₂³	1	2	yes	—
216	C₃₁×#103	C₂³	1	4	yes	—
217	C₃₁×#103	C₂³	1	4	yes	—
218	C₃₁×#103	C₂³	1	4	yes	—
219	C₃₁×#103	C₂³	1	2	yes	—
220	C₃₁×#103	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	2	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×#102	C₂³	1	4	yes	—
225	C₃₁×#102	C₂³	1	4	yes	—
226	C₃₁×#97	C₂³	1	2	yes	—
227	C₃₁×#97	C₂³	1	4	yes	—
228	C₄×C₈×C₃₁	C₂³	1	2	yes	—
229	C₄×C₈×C₃₁	C₂³	1	4	yes	—
230	#41×C₃₁	—	2	2	no	—
231	#41×C₃₁	—	2	4	no	—
232	#41×C₃₁	—	2	2	no	—
233	#41×C₃₁	—	2	4	no	—
234	#41×C₃₁	—	4	4	no	—
235	C₂×Q₈×C₃₁	—	2	1	no	—
236	C₂×Q₈×C₃₁	—	2	2	no	—
237	C₂×Q₈×C₃₁	—	2	2	no	—
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	4	2	no	—
240	C₂×Q₈×C₃₁	—	4	4	no	—
241	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
244	C₂×Q₈×C₃₁	#41	1	4	yes	complemented
245	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
248	C₂×D₄×C₃₁	—	2	1	no	—
249	C₂×D₄×C₃₁	—	2	2	no	—
250	C₂×D₄×C₃₁	—	2	2	no	—
251	C₂×D₄×C₃₁	—	2	1	no	—
252	C₂×D₄×C₃₁	—	2	2	no	—
253	C₂×D₄×C₃₁	—	2	1	no	—
254	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
255	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	—	2	1	no	—
257	C₂²×C₄×C₃₁	—	2	1	no	—
258	C₂²×C₄×C₃₁	—	2	2	no	—
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	—	2	1	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	1	no	—
263	C₂²×C₄×C₃₁	—	2	2	no	—
264	C₂²×C₄×C₃₁	—	2	1	no	—
265	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
270	Q₁₆×C₃₁	—	2	8	no	—
271	Q₁₆×C₃₁	—	2	4	no	—
272	SD₁₆×C₃₁	—	2	4	no	—
273	SD₁₆×C₃₁	—	2	8	no	—
274	M₁₆×C₃₁	—	2	2	no	—
275	M₁₆×C₃₁	—	2	4	no	—
276	M₁₆×C₃₁	—	2	2	no	—
277	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
278	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
279	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
280	C₄⋊C₄×C₃₁	—	2	4	no	—
281	C₄⋊C₄×C₃₁	—	2	4	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	4	no	—
285	C₄⋊C₄×C₃₁	—	2	4	no	—
286	C₄⋊C₄×C₃₁	—	2	2	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	4	no	—
289	C₄⋊C₄×C₃₁	—	2	4	no	—
290	C₄⋊C₄×C₃₁	—	2	1	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	1	no	—
294	C₄⋊C₄×C₃₁	—	2	1	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	—	2	1	no	—
298	C₄⋊C₄×C₃₁	—	2	2	no	—
299	C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
306	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
307	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
309	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₂²⋊C₄×C₃₁	—	2	1	no	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	—	2	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	1	no	—
317	C₂²⋊C₄×C₃₁	—	2	1	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	—	2	2	no	—
322	C₄²×C₃₁	—	2	1	no	—
323	C₄²×C₃₁	—	2	2	no	—
324	C₄²×C₃₁	—	2	1	no	—
325	C₄²×C₃₁	—	2	2	no	—
326	C₄²×C₃₁	—	2	1	no	—
327	C₄²×C₃₁	—	2	4	no	—
328	C₄²×C₃₁	—	2	4	no	—
329	C₄²×C₃₁	—	2	2	no	—
330	C₄²×C₃₁	—	2	2	no	—
331	C₄²×C₃₁	C₂×D₄	1	2	yes	—
332	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₃₁	C₂×D₄	1	2	yes	—
334	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₃₁	C₂⁴	1	2	yes	—
336	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₄²×C₃₁	C₂⁴	1	2	yes	—
339	#61320	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂³×C₃₁	—	2	2	no	—
341	C₂³×C₃₁	—	2	1	no	—
342	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₃₁	—	2	4	no	—
344	Q₈×C₃₁	—	2	2	no	—
345	Q₈×C₃₁	—	2	2	no	—
346	Q₈×C₃₁	—	2	2	no	—
347	Q₈×C₃₁	—	2	2	no	—
348	Q₈×C₃₁	—	2	1	no	—
349	Q₈×C₃₁	—	2	2	no	—
350	Q₈×C₃₁	—	2	1	no	—
351	Q₈×C₃₁	—	4	2	no	—
352	Q₈×C₃₁	—	4	4	no	—
353	Q₈×C₃₁	—	4	4	no	—
354	Q₈×C₃₁	C₂×#41	1	4	yes	—
355	D₄×C₃₁	—	2	2	no	—
356	D₄×C₃₁	—	2	1	no	—
357	D₄×C₃₁	—	2	2	no	—
358	D₄×C₃₁	—	2	1	no	—
359	D₄×C₃₁	—	4	4	no	—
360	D₄×C₃₁	—	4	2	no	—
361	D₄×C₃₁	—	4	4	no	—
362	D₄×C₃₁	—	4	2	no	—
363	D₄×C₃₁	—	8	2	no	—
364	D₄×C₃₁	—	8	1	no	—
365	C₂×C₄×C₃₁	—	2	4	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	2	no	—
368	C₂×C₄×C₃₁	—	2	1	no	—
369	C₂×C₄×C₃₁	—	2	1	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	1	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	4	no	—
374	C₂×C₄×C₃₁	—	4	2	no	—
375	C₂×C₄×C₃₁	—	4	1	no	—
376	C₂×C₄×C₃₁	—	4	2	no	—
377	C₂×C₄×C₃₁	—	4	4	no	—
378	C₂×C₄×C₃₁	—	4	2	no	—
379	C₂×C₄×C₃₁	—	4	4	no	—
380	C₂×C₄×C₃₁	—	4	4	no	—
381	C₂×C₄×C₃₁	—	4	2	no	—
382	C₂×C₄×C₃₁	—	4	2	no	—
383	C₂×C₄×C₃₁	—	8	2	no	—
384	C₂×C₄×C₃₁	—	8	1	no	—
385	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
395	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
396	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
397	C₈×C₃₁	—	2	2	no	—
398	C₈×C₃₁	—	2	4	no	—
399	C₈×C₃₁	—	2	2	no	—
400	#3480	C₂×C₃₁	1	1	yes	characteristic
401	C₂×#557	C₂×C₃₁	1	1	yes	characteristic, complemented
402	#3377	C₂×C₃₁	1	4	yes	complemented
403	#3374	C₂×C₃₁	1	2	yes	complemented
404	#3371	C₂×C₃₁	1	4	yes	complemented
405	#3368	C₂×C₃₁	1	2	yes	complemented
406	#3365	C₂×C₃₁	1	2	yes	complemented
407	#3364	C₂×C₃₁	1	2	yes	complemented
408	#3142	C₂×C₃₁	1	2	yes	complemented
409	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
410	#3080	C₂×C₃₁	1	2	yes	complemented
411	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
413	#3037	C₂×C₃₁	1	2	yes	complemented
414	Q₈×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
415	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
416	C₄×#137	C₂×C₃₁	1	2	yes	complemented
417	C₂²×C₃₁	—	2	1	no	—
418	C₂²×C₃₁	—	2	1	no	—
419	C₂²×C₃₁	—	4	2	no	—
420	C₂²×C₃₁	—	4	1	no	—
421	C₂²×C₃₁	—	4	2	no	—
422	C₂²×C₃₁	—	4	1	no	—
423	C₂²×C₃₁	—	4	2	no	—
424	C₂²×C₃₁	—	4	1	no	—
425	C₂²×C₃₁	#548	1	2	yes	—
426	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₃₁	—	2	2	no	—
428	C₄×C₃₁	—	2	1	no	—
429	C₄×C₃₁	—	2	2	no	—
430	C₄×C₃₁	—	2	1	no	—
431	C₄×C₃₁	—	2	4	no	—
432	C₄×C₃₁	—	2	1	no	—
433	C₄×C₃₁	—	2	2	no	—
434	C₄×C₃₁	—	2	2	no	—
435	C₄×C₃₁	—	4	2	no	—
436	C₄×C₃₁	—	4	1	no	—
437	C₄×C₃₁	—	4	2	no	—
438	C₄×C₃₁	—	4	1	no	—
439	C₄×C₃₁	—	4	1	no	—
440	C₄×C₃₁	—	4	4	no	—
441	C₄×C₃₁	#548	1	2	yes	—
442	C₄×C₃₁	#575	1	2	yes	—
443	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
444	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
445	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
446	C₂×#137	C₂²×C₃₁	1	2	yes	—
447	#559	C₂²×C₃₁	1	1	yes	characteristic
448	#559	C₂²×C₃₁	1	2	yes	—
449	#557	—	2	1	no	—
450	#557	—	2	1	no	—
451	#557	—	2	2	no	—
452	#557	C₂²×C₃₁	1	1	yes	characteristic
453	#557	C₂²×C₃₁	1	2	yes	—
454	#557	C₂²×C₃₁	1	2	yes	—
455	#557	C₂²×C₃₁	1	4	yes	—
456	#556	C₂²×C₃₁	1	1	yes	characteristic
457	#556	C₂²×C₃₁	1	2	yes	—
458	#553	—	2	1	no	—
459	#553	—	2	2	no	—
460	#550	C₂²×C₃₁	1	1	yes	characteristic
461	#548	—	2	1	no	—
462	#532	C₂²×C₃₁	1	1	yes	characteristic
463	#532	C₂²×C₃₁	1	2	yes	—
464	C₂×C₄⋊Q₈	—	2	1	no	—
465	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
466	#529	—	2	2	no	—
467	#529	—	2	1	no	—
468	C₂×#125	—	2	2	no	—
469	C₂×#125	C₂²×C₃₁	1	2	yes	—
470	C₄×#41	—	2	1	no	—
471	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
472	C₄×#41	C₂²×C₃₁	1	2	yes	—
473	C₂×C₄×Q₈	—	2	1	no	—
474	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
475	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
476	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
477	#491	C₂²×C₃₁	1	4	yes	—
478	#490	C₂²×C₃₁	1	4	yes	—
479	#489	C₂²×C₃₁	1	4	yes	—
480	#488	C₂²×C₃₁	1	4	yes	—
481	#488	C₂²×C₃₁	1	4	yes	—
482	#487	C₂²×C₃₁	1	2	yes	—
483	#486	C₂²×C₃₁	1	2	yes	—
484	#479	C₂²×C₃₁	1	4	yes	—
485	#479	C₂²×C₃₁	1	4	yes	—
486	#478	C₂²×C₃₁	1	4	yes	—
487	#478	C₂²×C₃₁	1	4	yes	—
488	#477	C₂²×C₃₁	1	2	yes	—
489	#476	C₂²×C₃₁	1	2	yes	—
490	#475	C₂²×C₃₁	1	2	yes	—
491	#474	C₂²×C₃₁	1	2	yes	—
492	#464	C₂²×C₃₁	1	4	yes	—
493	#464	C₂²×C₃₁	1	4	yes	—
494	#464	C₂²×C₃₁	1	4	yes	—
495	#462	C₂²×C₃₁	1	2	yes	—
496	#462	C₂²×C₃₁	1	4	yes	—
497	#460	C₂²×C₃₁	1	2	yes	—
498	#460	C₂²×C₃₁	1	4	yes	—
499	#446	C₂²×C₃₁	1	2	yes	—
500	#446	C₂²×C₃₁	1	4	yes	—
501	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
502	#441	C₂²×C₃₁	1	4	yes	—
503	#441	C₂²×C₃₁	1	2	yes	—
504	#440	C₂²×C₃₁	1	4	yes	—
505	#440	C₂²×C₃₁	1	2	yes	—
506	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
507	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
508	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
509	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
510	#428	C₂²×C₃₁	1	2	yes	—
511	#428	C₂²×C₃₁	1	1	yes	characteristic
512	#423	C₂²×C₃₁	1	1	yes	characteristic
513	#423	C₂²×C₃₁	1	2	yes	—
514	#419	C₂²×C₃₁	1	1	yes	characteristic
515	#417	C₂²×C₃₁	1	2	yes	—
516	#417	C₂²×C₃₁	1	2	yes	—
517	#417	C₂²×C₃₁	1	2	yes	—
518	#417	C₂²×C₃₁	1	2	yes	—
519	#417	C₂²×C₃₁	1	1	yes	characteristic
520	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
521	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
522	C₂×C₃₁	—	2	2	no	—
523	C₂×C₃₁	—	8	2	no	—
524	C₂×C₃₁	—	8	1	no	—
525	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
526	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
527	C₂×C₃₁	#3586	1	1	yes	characteristic
528	C₂×#41	—	2	1	no	—
529	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
530	C₂×#41	C₂³×C₃₁	1	2	yes	—
531	C₂²×Q₈	—	2	1	no	—
532	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
533	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
534	#137	—	2	4	no	—
535	#137	—	2	8	no	—
536	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
537	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
538	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
539	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
540	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
541	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
542	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
543	C₄⋊Q₈	—	2	2	no	—
544	C₄⋊Q₈	—	2	2	no	—
545	C₄⋊Q₈	—	2	4	no	—
546	C₄⋊Q₈	—	2	1	no	—
547	C₄⋊Q₈	—	2	1	no	—
548	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
552	#127	C₂³×C₃₁	1	1	yes	characteristic
553	#127	C₂³×C₃₁	1	2	yes	—
554	#126	—	2	2	no	—
555	#126	—	2	2	no	—
556	#126	—	2	2	no	—
557	#125	—	2	4	no	—
558	#125	—	2	4	no	—
559	#125	—	2	4	no	—
560	#125	—	2	4	no	—
561	#125	—	2	1	no	—
562	#125	—	2	2	no	—
563	#125	—	2	2	no	—
564	#125	—	2	2	no	—
565	#125	C₂³×C₃₁	1	4	yes	—
566	#125	C₂³×C₃₁	1	4	yes	—
567	#124	—	2	1	no	—
568	#124	—	2	2	no	—
569	#124	C₂³×C₃₁	1	2	yes	—
570	#124	C₂³×C₃₁	1	2	yes	—
571	#124	C₂³×C₃₁	1	2	yes	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	#121	—	2	1	no	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	—	2	1	no	—
581	#121	—	2	1	no	—
582	#121	—	2	2	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	4	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
592	C₄×Q₈	D₄×C₃₁	1	2	yes	—
593	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
595	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
596	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
597	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
598	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
599	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
602	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
604	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₃₁	1	2	yes	—
617	C₄×D₄	C₂³×C₃₁	1	2	yes	—
618	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
619	#117	—	2	1	no	—
620	#117	—	2	2	no	—
621	#117	—	2	2	no	—
622	#117	—	2	1	no	—
623	#117	C₂³×C₃₁	1	1	yes	characteristic
624	C₂×C₄⋊C₄	—	2	2	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	2	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	2	no	—
629	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
630	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₄²	—	2	2	no	—
634	C₂×C₄²	—	2	1	no	—
635	C₂×C₄²	—	2	2	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
638	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
639	#107	C₂³×C₃₁	1	4	yes	—
640	#107	C₂³×C₃₁	1	2	yes	—
641	#106	C₂³×C₃₁	1	4	yes	—
642	#106	C₂³×C₃₁	1	2	yes	—
643	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
644	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
645	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
646	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
647	#103	C₂³×C₃₁	1	4	yes	—
648	#103	C₂³×C₃₁	1	2	yes	—
649	#103	C₂³×C₃₁	1	4	yes	—
650	#103	C₂³×C₃₁	1	4	yes	—
651	#103	C₂³×C₃₁	1	4	yes	—
652	#103	C₂³×C₃₁	1	2	yes	—
653	#103	C₂³×C₃₁	1	2	yes	—
654	#102	C₂³×C₃₁	1	4	yes	—
655	#102	C₂³×C₃₁	1	2	yes	—
656	#102	C₂³×C₃₁	1	4	yes	—
657	#102	C₂³×C₃₁	1	4	yes	—
658	#102	C₂³×C₃₁	1	4	yes	—
659	#97	C₂³×C₃₁	1	2	yes	—
660	#97	C₂³×C₃₁	1	4	yes	—
661	C₄×C₈	C₂³×C₃₁	1	2	yes	—
662	C₄×C₈	C₂³×C₃₁	1	4	yes	—
663	C₃₁	#61320	1	1	yes	characteristic, direct product factor, Sylow
664	#41	—	2	2	no	—
665	#41	—	2	4	no	—
666	#41	—	2	2	no	—
667	#41	—	2	4	no	—
668	#41	—	4	4	no	—
669	C₂×Q₈	—	2	1	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	4	2	no	—
674	C₂×Q₈	—	4	4	no	—
675	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
676	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
677	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
678	C₂×Q₈	#41×C₃₁	1	4	yes	complemented
679	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
680	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
681	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
689	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
700	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
701	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
704	Q₁₆	—	2	8	no	—
705	Q₁₆	—	2	4	no	—
706	SD₁₆	—	2	4	no	—
707	SD₁₆	—	2	8	no	—
708	M₁₆	—	2	2	no	—
709	M₁₆	—	2	4	no	—
710	M₁₆	—	2	2	no	—
711	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
712	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
713	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
735	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
737	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
738	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
739	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
740	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
743	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
744	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	1	no	—
761	C₄²	—	2	4	no	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	C₂×D₄×C₃₁	1	2	yes	—
766	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₃₁	1	2	yes	—
768	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
769	C₄²	C₂⁴×C₃₁	1	2	yes	—
770	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
771	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
772	C₄²	C₂⁴×C₃₁	1	2	yes	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	1	no	—
775	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
776	Q₈	—	2	4	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	2	no	—
783	Q₈	—	2	1	no	—
784	Q₈	—	4	2	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	4	4	no	—
787	Q₈	C₂×#41×C₃₁	1	4	yes	—
788	D₄	—	2	2	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	2	no	—
791	D₄	—	2	1	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	2	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	2	no	—
796	D₄	—	8	2	no	—
797	D₄	—	8	1	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	8	2	no	—
817	C₂×C₄	—	8	1	no	—
818	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
827	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
828	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
829	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
830	C₈	—	2	2	no	—
831	C₈	—	2	4	no	—
832	C₈	—	2	2	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	1	no	—
841	C₂²	C₃₁×#548	1	2	yes	—
842	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
843	C₄	—	2	4	no	—
844	C₄	—	2	1	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	1	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	4	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	1	no	—
857	C₄	C₃₁×#548	1	2	yes	—
858	C₄	C₃₁×#575	1	2	yes	—
859	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
860	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
861	C₂	—	2	2	no	—
862	C₂	—	8	2	no	—
863	C₂	—	8	1	no	—
864	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
865	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
866	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#557	C₂	semidirect
3. C₃₁×#3377	C₂	semidirect
4. C₃₁×#3374	C₂	semidirect
5. C₃₁×#3371	C₂	semidirect
6. C₃₁×#3368	C₂	semidirect
7. C₃₁×#3365	C₂	semidirect
8. C₃₁×#3364	C₂	semidirect
9. C₃₁×#3142	C₂	semidirect
10. C₃₁×#3141	C₂	semidirect
11. C₃₁×#3080	C₂	semidirect
12. C₃₁×#3079	C₂	semidirect
13. C₃₁×#3037	C₂	semidirect
14. C₃₁×#3037	C₂	semidirect
15. Q₈×M₁₆×C₃₁	C₂	semidirect
16. C₄×C₃₁×#137	C₂	semidirect
17. C₄×C₃₁×#137	C₂	semidirect
244. C₂×Q₈×C₃₁	#41	semidirect
339. #61320	C₃₁	direct (N × H)
401. C₂×#557	C₂×C₃₁	semidirect
402. #3377	C₂×C₃₁	semidirect
403. #3374	C₂×C₃₁	semidirect
404. #3371	C₂×C₃₁	semidirect
405. #3368	C₂×C₃₁	semidirect
406. #3365	C₂×C₃₁	semidirect
407. #3364	C₂×C₃₁	semidirect
408. #3142	C₂×C₃₁	semidirect
409. #3141	C₂×C₃₁	semidirect
410. #3080	C₂×C₃₁	semidirect
411. #3079	C₂×C₃₁	semidirect
412. #3037	C₂×C₃₁	semidirect
413. #3037	C₂×C₃₁	semidirect
414. Q₈×M₁₆	C₂×C₃₁	semidirect
415. C₄×#137	C₂×C₃₁	semidirect
416. C₄×#137	C₂×C₃₁	semidirect
663. C₃₁	#61320	direct (N × H)
678. C₂×Q₈	#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×#3480	2
C₂×C₃₁×#557	2
C₃₁×#3377	2
C₃₁×#3374	2
C₃₁×#3371	2
C₃₁×#3368	2
C₃₁×#3365	2
C₃₁×#3364	2
C₃₁×#3142	2
C₃₁×#3141	2
C₃₁×#3080	2
C₃₁×#3079	2
C₃₁×#3037	2
Q₈×M₁₆×C₃₁	2
C₄×C₃₁×#137	2
#61320	31

Subgroups — C31×#61320 #21518079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61320 #21518079