Subgroups — C₃₁×#62144 #21518903

Order 7936.

1774 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3481	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3381	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3365	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3356	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3351	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3324	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3323	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3252	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3233	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3101	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3077	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#559	C₂²	1	1	yes	characteristic
19	C₃₁×#557	—	2	1	no	—
20	C₃₁×#557	C₂²	1	2	yes	complemented
21	C₃₁×#556	—	2	1	no	—
22	C₃₁×#556	C₂²	1	2	yes	—
23	C₃₁×#554	C₂²	1	1	yes	characteristic
24	C₃₁×#554	C₂²	1	1	yes	characteristic
25	C₃₁×#553	—	2	1	no	—
26	C₃₁×#553	C₂²	1	2	yes	—
27	C₃₁×#552	—	2	2	no	—
28	C₃₁×#552	C₂²	1	4	yes	complemented
29	C₃₁×#551	—	2	2	no	—
30	C₃₁×#546	—	2	1	no	—
31	C₃₁×#546	C₂²	1	2	yes	—
32	D₄²×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#541	—	2	2	no	—
34	C₃₁×#536	—	2	1	no	—
35	C₃₁×#533	C₂²	1	2	yes	complemented
36	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#533	C₂²	1	2	yes	complemented
38	C₃₁×#532	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#529	—	2	1	no	—
41	C₃₁×#529	C₂²	1	2	yes	—
42	C₃₁×#525	—	2	2	no	—
43	C₃₁×#519	—	2	1	no	—
44	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
45	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	—	2	1	no	—
47	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
48	C₃₁×#499	C₂²	1	4	yes	complemented
49	C₃₁×#498	C₂²	1	2	yes	complemented
50	C₃₁×#488	C₂²	1	4	yes	complemented
51	C₃₁×#486	C₂²	1	2	yes	—
52	C₃₁×#485	C₂²	1	2	yes	complemented
53	C₃₁×#485	C₂²	1	4	yes	complemented
54	C₃₁×#483	C₂²	1	4	yes	complemented
55	C₃₁×#482	C₂²	1	4	yes	—
56	C₃₁×#481	C₂²	1	4	yes	complemented
57	C₃₁×#479	C₂²	1	4	yes	complemented
58	C₃₁×#478	C₂²	1	4	yes	—
59	C₃₁×#478	C₂²	1	4	yes	complemented
60	C₃₁×#477	C₂²	1	2	yes	complemented
61	C₃₁×#477	C₂²	1	2	yes	complemented
62	C₃₁×#476	C₂²	1	2	yes	—
63	C₃₁×#476	C₂²	1	2	yes	complemented
64	C₃₁×#476	C₂²	1	2	yes	complemented
65	C₃₁×#475	C₂²	1	2	yes	complemented
66	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#474	C₂²	1	1	yes	characteristic
68	C₃₁×#474	C₂²	1	2	yes	—
69	C₃₁×#474	C₂²	1	2	yes	complemented
70	C₃₁×#470	C₂²	1	4	yes	complemented
71	C₃₁×#468	C₂²	1	4	yes	—
72	C₃₁×#468	C₂²	1	4	yes	complemented
73	C₃₁×#464	C₂²	1	4	yes	complemented
74	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×#461	C₂²	1	1	yes	characteristic
76	C₃₁×#461	C₂²	1	2	yes	complemented
77	C₃₁×#460	C₂²	1	2	yes	—
78	C₃₁×#452	C₂²	1	2	yes	—
79	C₃₁×#450	C₂²	1	4	yes	—
80	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
81	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
83	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
84	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
85	C₃₁×#436	C₂²	1	2	yes	—
86	C₃₁×#436	C₂²	1	4	yes	complemented
87	C₃₁×#431	C₂²	1	2	yes	complemented
88	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#428	C₂²	1	4	yes	complemented
90	C₃₁×#428	C₂²	1	2	yes	complemented
91	C₃₁×#423	C₂²	1	2	yes	complemented
92	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#418	C₂²	1	4	yes	—
94	C₃₁×#417	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
97	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₃₁	—	2	1	no	—
99	C₂²×D₄×C₃₁	—	2	1	no	—
100	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
101	C₂³×C₄×C₃₁	—	2	2	no	—
102	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
106	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
107	C₃₁×C₄⋊Q₈	—	2	2	no	—
108	C₃₁×C₄⋊Q₈	—	2	1	no	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×#127	C₂³	1	1	yes	characteristic
116	C₃₁×#126	—	2	2	no	—
117	C₃₁×#126	—	2	4	no	—
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#126	—	2	2	no	—
120	C₃₁×#125	—	2	1	no	—
121	C₃₁×#125	—	2	4	no	—
122	C₃₁×#125	—	2	4	no	—
123	C₃₁×#125	—	2	1	no	—
124	C₃₁×#125	—	2	2	no	—
125	C₃₁×#125	C₂³	1	4	yes	—
126	C₃₁×#125	C₂³	1	2	yes	—
127	C₃₁×#124	—	2	1	no	—
128	C₃₁×#124	—	2	2	no	—
129	C₃₁×#124	—	2	1	no	—
130	C₃₁×#124	C₂³	1	2	yes	—
131	C₃₁×#123	—	2	4	no	—
132	C₃₁×#123	—	2	2	no	—
133	C₃₁×#123	—	2	2	no	—
134	C₃₁×#123	—	2	2	no	—
135	C₃₁×#123	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	1	no	—
137	C₃₁×C₂²⋊Q₈	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	1	no	—
140	C₃₁×C₂²⋊Q₈	—	2	2	no	—
141	C₃₁×C₂²⋊Q₈	—	2	2	no	—
142	C₃₁×C₂²⋊Q₈	—	2	2	no	—
143	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
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	C₃₁×#121	C₂³	1	2	yes	—
151	C₃₁×#121	C₂³	1	2	yes	—
152	C₃₁×#120	—	2	2	no	—
153	C₃₁×#120	—	2	2	no	—
154	C₄×Q₈×C₃₁	—	2	2	no	—
155	C₄×Q₈×C₃₁	—	2	2	no	—
156	C₄×Q₈×C₃₁	—	2	2	no	—
157	C₄×Q₈×C₃₁	—	2	2	no	—
158	C₄×Q₈×C₃₁	—	2	2	no	—
159	C₄×Q₈×C₃₁	—	2	1	no	—
160	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
162	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
163	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
166	C₄×D₄×C₃₁	—	2	1	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	1	no	—
169	C₄×D₄×C₃₁	—	2	1	no	—
170	C₄×D₄×C₃₁	—	2	1	no	—
171	C₄×D₄×C₃₁	—	2	2	no	—
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	D₄	1	1	yes	characteristic
176	C₄×D₄×C₃₁	D₄	1	2	yes	—
177	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₃₁	C₂³	1	2	yes	—
179	C₄×D₄×C₃₁	C₂³	1	2	yes	—
180	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₃₁	C₂³	1	2	yes	—
182	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₃₁	C₂³	1	2	yes	—
184	C₃₁×#117	—	2	1	no	—
185	C₃₁×#117	—	2	2	no	—
186	C₃₁×#117	—	2	4	no	—
187	C₃₁×#117	—	2	1	no	—
188	C₃₁×#117	—	2	2	no	—
189	C₃₁×#117	D₄	1	1	yes	characteristic
190	C₃₁×#117	D₄	1	2	yes	—
191	C₃₁×#117	C₂³	1	4	yes	—
192	C₃₁×#117	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
194	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₄²×C₃₁	—	2	1	no	—
200	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₃₁×#107	C₂³	1	2	yes	—
203	C₃₁×#107	C₂³	1	4	yes	—
204	C₃₁×#107	C₂³	1	4	yes	—
205	C₃₁×#106	C₂³	1	4	yes	—
206	C₃₁×#106	C₂³	1	4	yes	—
207	C₃₁×#106	C₂³	1	2	yes	—
208	C₃₁×#106	C₂³	1	4	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₃₁×#103	C₂³	1	4	yes	—
215	C₃₁×#103	C₂³	1	4	yes	—
216	C₃₁×#103	C₂³	1	2	yes	—
217	C₃₁×#103	C₂³	1	2	yes	—
218	C₃₁×#103	C₂³	1	2	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	2	yes	—
221	C₃₁×#102	C₂³	1	4	yes	—
222	C₃₁×#102	C₂³	1	4	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₄×C₈×C₃₁	C₂³	1	2	yes	—
227	C₄×C₈×C₃₁	C₂³	1	4	yes	—
228	C₂⁴×C₃₁	—	2	2	no	—
229	#41×C₃₁	—	2	2	no	—
230	#41×C₃₁	—	4	2	no	—
231	#41×C₃₁	—	4	1	no	—
232	#41×C₃₁	—	8	2	no	—
233	C₂×Q₈×C₃₁	—	2	1	no	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂×Q₈×C₃₁	—	2	2	no	—
236	C₂×Q₈×C₃₁	—	2	1	no	—
237	C₂×Q₈×C₃₁	—	4	4	no	—
238	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
241	C₂×D₄×C₃₁	—	2	4	no	—
242	C₂×D₄×C₃₁	—	2	1	no	—
243	C₂×D₄×C₃₁	—	2	2	no	—
244	C₂×D₄×C₃₁	—	2	2	no	—
245	C₂×D₄×C₃₁	—	2	2	no	—
246	C₂×D₄×C₃₁	—	2	1	no	—
247	C₂×D₄×C₃₁	—	2	1	no	—
248	C₂×D₄×C₃₁	—	4	2	no	—
249	C₂×D₄×C₃₁	—	4	4	no	—
250	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
251	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	1	no	—
257	C₂²×C₄×C₃₁	—	2	1	no	—
258	C₂²×C₄×C₃₁	—	2	1	no	—
259	C₂²×C₄×C₃₁	—	2	2	no	—
260	C₂²×C₄×C₃₁	—	2	2	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	8	4	no	—
263	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
269	Q₁₆×C₃₁	—	4	2	no	—
270	SD₁₆×C₃₁	—	2	4	no	—
271	SD₁₆×C₃₁	—	4	4	no	—
272	M₁₆×C₃₁	—	4	2	no	—
273	M₁₆×C₃₁	—	4	4	no	—
274	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
275	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
276	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₄⋊C₄×C₃₁	—	2	1	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	2	no	—
283	C₄⋊C₄×C₃₁	—	2	1	no	—
284	C₄⋊C₄×C₃₁	—	2	1	no	—
285	C₄⋊C₄×C₃₁	—	2	1	no	—
286	C₄⋊C₄×C₃₁	—	2	1	no	—
287	C₄⋊C₄×C₃₁	—	2	1	no	—
288	C₄⋊C₄×C₃₁	—	2	4	no	—
289	C₄⋊C₄×C₃₁	—	2	4	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	4	no	—
293	C₄⋊C₄×C₃₁	—	2	2	no	—
294	C₄⋊C₄×C₃₁	—	2	4	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
301	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂²⋊C₄×C₃₁	—	2	4	no	—
308	C₂²⋊C₄×C₃₁	—	2	1	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	1	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
320	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
321	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
322	C₄²×C₃₁	—	2	1	no	—
323	C₄²×C₃₁	—	2	1	no	—
324	C₄²×C₃₁	—	2	1	no	—
325	C₄²×C₃₁	—	2	4	no	—
326	C₄²×C₃₁	—	2	4	no	—
327	C₄²×C₃₁	—	2	2	no	—
328	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₃₁	C₂×D₄	1	2	yes	—
331	C₄²×C₃₁	C₂×D₄	1	2	yes	—
332	C₄²×C₃₁	C₂⁴	1	2	yes	—
333	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
335	#62144	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂³×C₃₁	—	2	1	no	—
337	C₂³×C₃₁	—	2	2	no	—
338	C₂³×C₃₁	—	4	4	no	—
339	C₂³×C₃₁	—	4	4	no	—
340	C₂³×C₃₁	—	8	2	no	—
341	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
342	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₃₁	—	2	2	no	—
344	Q₈×C₃₁	—	2	2	no	—
345	Q₈×C₃₁	—	2	1	no	—
346	Q₈×C₃₁	—	2	2	no	—
347	Q₈×C₃₁	—	2	1	no	—
348	Q₈×C₃₁	—	4	4	no	—
349	Q₈×C₃₁	—	4	4	no	—
350	Q₈×C₃₁	—	4	2	no	—
351	Q₈×C₃₁	—	8	1	no	—
352	D₄×C₃₁	—	2	2	no	—
353	D₄×C₃₁	—	2	2	no	—
354	D₄×C₃₁	—	2	1	no	—
355	D₄×C₃₁	—	2	2	no	—
356	D₄×C₃₁	—	4	2	no	—
357	D₄×C₃₁	—	4	4	no	—
358	D₄×C₃₁	—	4	2	no	—
359	D₄×C₃₁	—	4	4	no	—
360	D₄×C₃₁	—	4	2	no	—
361	D₄×C₃₁	—	8	1	no	—
362	D₄×C₃₁	—	8	2	no	—
363	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
364	C₂×C₄×C₃₁	—	2	2	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	2	no	—
370	C₂×C₄×C₃₁	—	2	1	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	1	no	—
374	C₂×C₄×C₃₁	—	2	1	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	4	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	4	2	no	—
379	C₂×C₄×C₃₁	—	4	2	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	—	4	4	no	—
384	C₂×C₄×C₃₁	—	8	2	no	—
385	C₂×C₄×C₃₁	—	8	2	no	—
386	C₂×C₄×C₃₁	—	8	2	no	—
387	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
396	C₈×C₃₁	—	2	2	no	—
397	C₈×C₃₁	—	2	4	no	—
398	C₈×C₃₁	—	2	2	no	—
399	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
400	#3481	C₂×C₃₁	1	1	yes	characteristic
401	#3381	C₂×C₃₁	1	2	yes	complemented
402	#3365	C₂×C₃₁	1	2	yes	complemented
403	#3356	C₂×C₃₁	1	2	yes	complemented
404	#3351	C₂×C₃₁	1	4	yes	complemented
405	#3324	C₂×C₃₁	1	2	yes	complemented
406	#3323	C₂×C₃₁	1	4	yes	complemented
407	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
408	#3252	C₂×C₃₁	1	2	yes	complemented
409	#3233	C₂×C₃₁	1	2	yes	complemented
410	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
411	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
412	#3101	C₂×C₃₁	1	2	yes	complemented
413	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
414	#3077	C₂×C₃₁	1	2	yes	complemented
415	#2991	C₂×C₃₁	1	1	yes	characteristic, complemented
416	C₂²×C₃₁	—	2	1	no	—
417	C₂²×C₃₁	—	2	2	no	—
418	C₂²×C₃₁	—	2	2	no	—
419	C₂²×C₃₁	—	2	1	no	—
420	C₂²×C₃₁	—	2	2	no	—
421	C₂²×C₃₁	—	2	2	no	—
422	C₂²×C₃₁	—	2	1	no	—
423	C₂²×C₃₁	—	4	1	no	—
424	C₂²×C₃₁	—	4	1	no	—
425	C₂²×C₃₁	—	4	2	no	—
426	C₂²×C₃₁	—	4	2	no	—
427	C₂²×C₃₁	—	4	2	no	—
428	C₂²×C₃₁	—	8	8	no	—
429	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
430	C₄×C₃₁	—	2	1	no	—
431	C₄×C₃₁	—	2	2	no	—
432	C₄×C₃₁	—	2	1	no	—
433	C₄×C₃₁	—	2	2	no	—
434	C₄×C₃₁	—	2	2	no	—
435	C₄×C₃₁	—	2	1	no	—
436	C₄×C₃₁	—	4	1	no	—
437	C₄×C₃₁	—	4	2	no	—
438	C₄×C₃₁	—	4	1	no	—
439	C₄×C₃₁	—	4	4	no	—
440	C₄×C₃₁	—	4	1	no	—
441	C₄×C₃₁	—	4	2	no	—
442	C₄×C₃₁	—	4	2	no	—
443	C₄×C₃₁	#575	1	2	yes	—
444	C₄×C₃₁	#577	1	2	yes	—
445	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
446	C₄×C₃₁	#585	1	1	yes	characteristic
447	#559	C₂²×C₃₁	1	1	yes	characteristic
448	#557	—	2	1	no	—
449	#557	C₂²×C₃₁	1	2	yes	complemented
450	#556	—	2	1	no	—
451	#556	C₂²×C₃₁	1	2	yes	—
452	#554	C₂²×C₃₁	1	1	yes	characteristic
453	#554	C₂²×C₃₁	1	1	yes	characteristic
454	#553	—	2	1	no	—
455	#553	C₂²×C₃₁	1	2	yes	—
456	#552	—	2	2	no	—
457	#552	C₂²×C₃₁	1	4	yes	complemented
458	#551	—	2	2	no	—
459	#546	—	2	1	no	—
460	#546	C₂²×C₃₁	1	2	yes	—
461	D₄²	C₂²×C₃₁	1	1	yes	characteristic
462	#541	—	2	2	no	—
463	#536	—	2	1	no	—
464	#533	C₂²×C₃₁	1	2	yes	complemented
465	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
466	#533	C₂²×C₃₁	1	2	yes	complemented
467	#532	C₂²×C₃₁	1	1	yes	characteristic
468	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
469	#529	—	2	1	no	—
470	#529	C₂²×C₃₁	1	2	yes	—
471	#525	—	2	2	no	—
472	#519	—	2	1	no	—
473	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
474	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
475	C₂×C₄×D₄	—	2	1	no	—
476	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
477	#499	C₂²×C₃₁	1	4	yes	complemented
478	#498	C₂²×C₃₁	1	2	yes	complemented
479	#488	C₂²×C₃₁	1	4	yes	complemented
480	#486	C₂²×C₃₁	1	2	yes	—
481	#485	C₂²×C₃₁	1	2	yes	complemented
482	#485	C₂²×C₃₁	1	4	yes	complemented
483	#483	C₂²×C₃₁	1	4	yes	complemented
484	#482	C₂²×C₃₁	1	4	yes	—
485	#481	C₂²×C₃₁	1	4	yes	complemented
486	#479	C₂²×C₃₁	1	4	yes	complemented
487	#478	C₂²×C₃₁	1	4	yes	—
488	#478	C₂²×C₃₁	1	4	yes	complemented
489	#477	C₂²×C₃₁	1	2	yes	complemented
490	#477	C₂²×C₃₁	1	2	yes	complemented
491	#476	C₂²×C₃₁	1	2	yes	—
492	#476	C₂²×C₃₁	1	2	yes	complemented
493	#476	C₂²×C₃₁	1	2	yes	complemented
494	#475	C₂²×C₃₁	1	2	yes	complemented
495	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
496	#474	C₂²×C₃₁	1	1	yes	characteristic
497	#474	C₂²×C₃₁	1	2	yes	—
498	#474	C₂²×C₃₁	1	2	yes	complemented
499	#470	C₂²×C₃₁	1	4	yes	complemented
500	#468	C₂²×C₃₁	1	4	yes	—
501	#468	C₂²×C₃₁	1	4	yes	complemented
502	#464	C₂²×C₃₁	1	4	yes	complemented
503	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
504	#461	C₂²×C₃₁	1	1	yes	characteristic
505	#461	C₂²×C₃₁	1	2	yes	complemented
506	#460	C₂²×C₃₁	1	2	yes	—
507	#452	C₂²×C₃₁	1	2	yes	—
508	#450	C₂²×C₃₁	1	4	yes	—
509	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
510	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
511	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
512	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
513	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
514	#436	C₂²×C₃₁	1	2	yes	—
515	#436	C₂²×C₃₁	1	4	yes	complemented
516	#431	C₂²×C₃₁	1	2	yes	complemented
517	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
518	#428	C₂²×C₃₁	1	4	yes	complemented
519	#428	C₂²×C₃₁	1	2	yes	complemented
520	#423	C₂²×C₃₁	1	2	yes	complemented
521	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
522	#418	C₂²×C₃₁	1	4	yes	—
523	#417	C₂²×C₃₁	1	2	yes	—
524	C₂×C₃₁	—	4	1	no	—
525	C₂×C₃₁	—	4	2	no	—
526	C₂×C₃₁	—	4	2	no	—
527	C₂×C₃₁	—	8	2	no	—
528	C₂×C₃₁	#3489	1	1	yes	characteristic
529	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
530	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
531	C₂×#41	—	2	1	no	—
532	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
533	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×D₄	—	2	1	no	—
536	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
537	C₂³×C₄	—	2	2	no	—
538	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
539	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
540	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
541	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
542	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
543	C₄⋊Q₈	—	2	2	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	—	2	1	no	—
546	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
547	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
551	#127	C₂³×C₃₁	1	1	yes	characteristic
552	#126	—	2	2	no	—
553	#126	—	2	4	no	—
554	#126	—	2	4	no	—
555	#126	—	2	2	no	—
556	#125	—	2	1	no	—
557	#125	—	2	4	no	—
558	#125	—	2	4	no	—
559	#125	—	2	1	no	—
560	#125	—	2	2	no	—
561	#125	C₂³×C₃₁	1	2	yes	—
562	#125	C₂³×C₃₁	1	4	yes	—
563	#124	—	2	1	no	—
564	#124	—	2	2	no	—
565	#124	—	2	1	no	—
566	#124	C₂³×C₃₁	1	2	yes	—
567	#123	—	2	4	no	—
568	#123	—	2	2	no	—
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
580	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
581	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
582	#121	—	2	2	no	—
583	#121	—	2	1	no	—
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	C₂³×C₃₁	1	2	yes	—
587	#121	C₂³×C₃₁	1	2	yes	—
588	#120	—	2	2	no	—
589	#120	—	2	2	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
597	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
600	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
601	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
612	C₄×D₄	D₄×C₃₁	1	2	yes	—
613	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₃₁	1	2	yes	—
615	C₄×D₄	C₂³×C₃₁	1	2	yes	—
616	C₄×D₄	C₂³×C₃₁	1	2	yes	—
617	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
619	C₄×D₄	C₂³×C₃₁	1	2	yes	—
620	#117	—	2	1	no	—
621	#117	—	2	2	no	—
622	#117	—	2	4	no	—
623	#117	—	2	1	no	—
624	#117	—	2	2	no	—
625	#117	D₄×C₃₁	1	1	yes	characteristic
626	#117	D₄×C₃₁	1	2	yes	—
627	#117	C₂³×C₃₁	1	1	yes	characteristic
628	#117	C₂³×C₃₁	1	4	yes	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₂²⋊C₄	—	2	2	no	—
634	C₂×C₂²⋊C₄	—	2	2	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
637	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
638	#107	C₂³×C₃₁	1	2	yes	—
639	#107	C₂³×C₃₁	1	4	yes	—
640	#107	C₂³×C₃₁	1	4	yes	—
641	#106	C₂³×C₃₁	1	4	yes	—
642	#106	C₂³×C₃₁	1	4	yes	—
643	#106	C₂³×C₃₁	1	2	yes	—
644	#106	C₂³×C₃₁	1	4	yes	—
645	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
646	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
647	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
648	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
649	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
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	#103	C₂³×C₃₁	1	2	yes	—
655	#102	C₂³×C₃₁	1	4	yes	—
656	#102	C₂³×C₃₁	1	2	yes	—
657	#102	C₂³×C₃₁	1	4	yes	—
658	#102	C₂³×C₃₁	1	4	yes	—
659	#102	C₂³×C₃₁	1	4	yes	—
660	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
661	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
662	C₄×C₈	C₂³×C₃₁	1	2	yes	—
663	C₄×C₈	C₂³×C₃₁	1	4	yes	—
664	C₃₁	#62144	1	1	yes	characteristic, direct product factor, Sylow
665	C₂⁴	—	2	2	no	—
666	#41	—	2	2	no	—
667	#41	—	4	2	no	—
668	#41	—	4	1	no	—
669	#41	—	8	2	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	4	4	no	—
675	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
676	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
677	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	4	2	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
688	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
689	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
690	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	8	4	no	—
700	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
701	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
702	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
703	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
706	Q₁₆	—	4	2	no	—
707	SD₁₆	—	2	4	no	—
708	SD₁₆	—	4	4	no	—
709	M₁₆	—	4	2	no	—
710	M₁₆	—	4	4	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	2	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
734	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
735	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
736	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
738	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
739	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
757	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
758	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	1	no	—
761	C₄²	—	2	1	no	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	2	no	—
765	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
766	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
767	C₄²	C₂×D₄×C₃₁	1	2	yes	—
768	C₄²	C₂×D₄×C₃₁	1	2	yes	—
769	C₄²	C₂⁴×C₃₁	1	2	yes	—
770	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
771	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
772	C₂³	—	2	1	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	8	2	no	—
777	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
778	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	4	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	4	2	no	—
787	Q₈	—	8	1	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	1	no	—
791	D₄	—	2	2	no	—
792	D₄	—	4	2	no	—
793	D₄	—	4	4	no	—
794	D₄	—	4	2	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	2	no	—
797	D₄	—	8	1	no	—
798	D₄	—	8	2	no	—
799	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
828	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
831	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
832	C₈	—	2	2	no	—
833	C₈	—	2	4	no	—
834	C₈	—	2	2	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	8	8	no	—
848	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
849	C₄	—	2	1	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	1	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	4	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	C₃₁×#575	1	2	yes	—
863	C₄	C₃₁×#577	1	2	yes	—
864	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
865	C₄	C₃₁×#585	1	1	yes	characteristic
866	C₂	—	4	2	no	—
867	C₂	—	4	1	no	—
868	C₂	—	4	2	no	—
869	C₂	—	8	2	no	—
870	C₂	C₃₁×#3489	1	1	yes	characteristic
871	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
872	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3481	C₂
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×#3509	C₂	semidirect
3. C₃₁×#3381	C₂	semidirect
4. C₃₁×#3365	C₂	semidirect
5. C₃₁×#3356	C₂	semidirect
6. C₃₁×#3351	C₂	semidirect
7. C₃₁×#3324	C₂	semidirect
8. C₃₁×#3323	C₂	semidirect
9. C₃₁×#3254	C₂	semidirect
10. C₃₁×#3252	C₂	semidirect
11. C₃₁×#3233	C₂	semidirect
12. C₃₁×#3227	C₂	semidirect
13. C₃₁×#3107	C₂	semidirect
14. C₃₁×#3101	C₂	semidirect
15. C₃₁×#3079	C₂	semidirect
16. C₃₁×#3077	C₂	semidirect
17. C₃₁×#2991	C₂	semidirect
20. C₃₁×#557	C₂²	semidirect
28. C₃₁×#552	C₂²	semidirect
35. C₃₁×#533	C₂²	semidirect
36. C₃₁×#533	C₂²	semidirect
37. C₃₁×#533	C₂²	semidirect
39. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
48. C₃₁×#499	C₂²	semidirect
49. C₃₁×#498	C₂²	semidirect
50. C₃₁×#488	C₂²	semidirect
52. C₃₁×#485	C₂²	semidirect
53. C₃₁×#485	C₂²	semidirect
54. C₃₁×#483	C₂²	semidirect
56. C₃₁×#481	C₂²	semidirect
57. C₃₁×#479	C₂²	semidirect
59. C₃₁×#478	C₂²	semidirect
60. C₃₁×#477	C₂²	semidirect
61. C₃₁×#477	C₂²	semidirect
63. C₃₁×#476	C₂²	semidirect
64. C₃₁×#476	C₂²	semidirect
65. C₃₁×#475	C₂²	semidirect
66. C₃₁×#475	C₂²	semidirect
69. C₃₁×#474	C₂²	semidirect
70. C₃₁×#470	C₂²	semidirect
72. C₃₁×#468	C₂²	semidirect
73. C₃₁×#464	C₂²	semidirect
74. C₃₁×#462	C₂²	semidirect
76. C₃₁×#461	C₂²	semidirect
80. C₈×Q₈×C₃₁	C₂²	semidirect
81. C₄×Q₁₆×C₃₁	C₂²	semidirect
84. C₄×SD₁₆×C₃₁	C₂²	semidirect
86. C₃₁×#436	C₂²	semidirect
87. C₃₁×#431	C₂²	semidirect
88. C₃₁×#431	C₂²	semidirect
89. C₃₁×#428	C₂²	semidirect
90. C₃₁×#428	C₂²	semidirect
91. C₃₁×#423	C₂²	semidirect
92. C₃₁×#423	C₂²	semidirect
335. #62144	C₃₁	direct (N × H)
399. #3509	C₂×C₃₁	semidirect
401. #3381	C₂×C₃₁	semidirect
402. #3365	C₂×C₃₁	semidirect
403. #3356	C₂×C₃₁	semidirect
404. #3351	C₂×C₃₁	semidirect
405. #3324	C₂×C₃₁	semidirect
406. #3323	C₂×C₃₁	semidirect
407. #3254	C₂×C₃₁	semidirect
408. #3252	C₂×C₃₁	semidirect
409. #3233	C₂×C₃₁	semidirect
410. #3227	C₂×C₃₁	semidirect
411. #3107	C₂×C₃₁	semidirect
412. #3101	C₂×C₃₁	semidirect
413. #3079	C₂×C₃₁	semidirect
414. #3077	C₂×C₃₁	semidirect
415. #2991	C₂×C₃₁	semidirect
449. #557	C₂²×C₃₁	semidirect
457. #552	C₂²×C₃₁	semidirect
464. #533	C₂²×C₃₁	semidirect
465. #533	C₂²×C₃₁	semidirect
466. #533	C₂²×C₃₁	semidirect
468. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
477. #499	C₂²×C₃₁	semidirect
478. #498	C₂²×C₃₁	semidirect
479. #488	C₂²×C₃₁	semidirect
481. #485	C₂²×C₃₁	semidirect
482. #485	C₂²×C₃₁	semidirect
483. #483	C₂²×C₃₁	semidirect
485. #481	C₂²×C₃₁	semidirect
486. #479	C₂²×C₃₁	semidirect
488. #478	C₂²×C₃₁	semidirect
489. #477	C₂²×C₃₁	semidirect
490. #477	C₂²×C₃₁	semidirect
492. #476	C₂²×C₃₁	semidirect
493. #476	C₂²×C₃₁	semidirect
494. #475	C₂²×C₃₁	semidirect
495. #475	C₂²×C₃₁	semidirect
498. #474	C₂²×C₃₁	semidirect
499. #470	C₂²×C₃₁	semidirect
501. #468	C₂²×C₃₁	semidirect
502. #464	C₂²×C₃₁	semidirect
503. #462	C₂²×C₃₁	semidirect
505. #461	C₂²×C₃₁	semidirect
509. C₈×Q₈	C₂²×C₃₁	semidirect
510. C₄×Q₁₆	C₂²×C₃₁	semidirect
513. C₄×SD₁₆	C₂²×C₃₁	semidirect
515. #436	C₂²×C₃₁	semidirect
516. #431	C₂²×C₃₁	semidirect
517. #431	C₂²×C₃₁	semidirect
518. #428	C₂²×C₃₁	semidirect
519. #428	C₂²×C₃₁	semidirect
520. #423	C₂²×C₃₁	semidirect
521. #423	C₂²×C₃₁	semidirect
664. C₃₁	#62144	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×#3509	2
C₃₁×#3481	2
C₃₁×#3381	2
C₃₁×#3365	2
C₃₁×#3356	2
C₃₁×#3351	2
C₃₁×#3324	2
C₃₁×#3323	2
C₃₁×#3254	2
C₃₁×#3252	2
C₃₁×#3233	2
C₃₁×#3227	2
C₃₁×#3107	2
C₃₁×#3101	2
C₃₁×#3079	2
C₃₁×#3077	2
C₃₁×#2991	2
#62144	31

Subgroups — C31×#62144 #21518903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62144 #21518903