Subgroups — C₃₁×#61905 #21518664

Order 7936.

1724 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3402	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3398	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3393	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3377	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3364	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3215	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3211	C₂	1	2	yes	maximal
12	C₃₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3117	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic
16	C₃₁×#3104	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
19	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
20	C₃₁×#557	C₂²	1	2	yes	complemented
21	C₃₁×#556	—	2	1	no	—
22	C₃₁×#556	—	2	1	no	—
23	C₃₁×#556	—	2	2	no	—
24	C₃₁×#556	C₂²	1	2	yes	—
25	C₃₁×#556	C₂²	1	2	yes	—
26	C₃₁×#556	C₂²	1	4	yes	—
27	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#556	C₂²	1	2	yes	complemented
29	C₃₁×#552	—	2	1	no	—
30	C₃₁×#552	—	2	2	no	—
31	D₄×Q₈×C₃₁	—	2	1	no	—
32	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#541	—	2	1	no	—
34	C₃₁×#541	—	2	2	no	—
35	C₃₁×#533	C₂²	1	2	yes	—
36	C₃₁×#533	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₃₁×#529	C₂²	1	1	yes	characteristic
39	C₃₁×#529	C₂²	1	2	yes	—
40	C₂×C₃₁×#126	—	2	2	no	—
41	C₂×C₃₁×#124	C₂²	1	2	yes	—
42	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
43	C₃₁×#519	—	2	1	no	—
44	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#117	—	2	1	no	—
48	C₃₁×#497	C₂²	1	4	yes	—
49	C₃₁×#497	C₂²	1	2	yes	complemented
50	C₃₁×#495	C₂²	1	4	yes	—
51	C₃₁×#494	C₂²	1	2	yes	complemented
52	C₃₁×#491	C₂²	1	2	yes	complemented
53	C₃₁×#489	C₂²	1	4	yes	—
54	C₃₁×#488	C₂²	1	4	yes	—
55	C₃₁×#487	C₂²	1	2	yes	complemented
56	C₃₁×#484	C₂²	1	1	yes	characteristic
57	C₃₁×#484	C₂²	1	2	yes	—
58	C₃₁×#481	C₂²	1	1	yes	characteristic
59	C₃₁×#479	C₂²	1	4	yes	complemented
60	C₃₁×#478	C₂²	1	2	yes	—
61	C₃₁×#477	C₂²	1	4	yes	complemented
62	C₃₁×#474	C₂²	1	2	yes	—
63	C₃₁×#464	C₂²	1	4	yes	—
64	C₃₁×#464	C₂²	1	4	yes	—
65	C₃₁×#464	C₂²	1	4	yes	—
66	C₃₁×#464	C₂²	1	4	yes	complemented
67	C₃₁×#463	C₂²	1	2	yes	—
68	C₃₁×#463	C₂²	1	4	yes	—
69	C₃₁×#462	C₂²	1	4	yes	complemented
70	C₃₁×#462	C₂²	1	2	yes	complemented
71	C₃₁×#462	C₂²	1	4	yes	complemented
72	C₃₁×#461	C₂²	1	2	yes	—
73	C₃₁×#461	C₂²	1	2	yes	complemented
74	C₃₁×#451	C₂²	1	2	yes	—
75	C₃₁×#451	C₂²	1	2	yes	—
76	C₃₁×#451	C₂²	1	2	yes	—
77	C₃₁×#450	C₂²	1	1	yes	characteristic
78	C₃₁×#450	C₂²	1	2	yes	—
79	C₃₁×#448	C₂²	1	2	yes	—
80	C₃₁×#447	C₂²	1	1	yes	characteristic
81	C₃₁×#446	C₂²	1	2	yes	complemented
82	C₃₁×#446	C₂²	1	4	yes	complemented
83	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
84	C₃₁×#441	C₂²	1	4	yes	complemented
85	C₃₁×#440	C₂²	1	4	yes	—
86	C₃₁×#440	C₂²	1	4	yes	complemented
87	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
88	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
89	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
90	C₄×D₈×C₃₁	C₂²	1	2	yes	—
91	C₃₁×#432	C₂²	1	1	yes	characteristic
92	C₃₁×#432	C₂²	1	2	yes	—
93	C₃₁×#431	C₂²	1	2	yes	—
94	C₃₁×#431	C₂²	1	1	yes	characteristic
95	C₂²×Q₈×C₃₁	—	2	1	no	—
96	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
97	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
98	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₃₁	—	2	1	no	—
100	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
101	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
106	C₂×D₈×C₃₁	C₂³	1	2	yes	—
107	C₃₁×C₄⋊Q₈	—	2	1	no	—
108	C₃₁×C₄⋊Q₈	—	2	2	no	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	—	2	1	no	—
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	2	yes	—
115	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₃₁×#126	—	2	4	no	—
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#126	—	2	4	no	—
121	C₃₁×#126	—	2	2	no	—
122	C₃₁×#126	—	2	2	no	—
123	C₃₁×#126	—	2	2	no	—
124	C₃₁×#126	—	2	1	no	—
125	C₃₁×#126	—	2	2	no	—
126	C₃₁×#125	—	2	2	no	—
127	C₃₁×#125	—	2	2	no	—
128	C₃₁×#125	—	2	2	no	—
129	C₃₁×#125	—	2	1	no	—
130	C₃₁×#125	—	2	2	no	—
131	C₃₁×#125	—	2	1	no	—
132	C₃₁×#125	—	2	2	no	—
133	C₃₁×#125	C₂³	1	1	yes	characteristic
134	C₃₁×#125	C₂³	1	2	yes	—
135	C₃₁×#124	—	2	2	no	—
136	C₃₁×#124	—	2	2	no	—
137	C₃₁×#124	C₂³	1	1	yes	characteristic
138	C₃₁×#124	C₂³	1	4	yes	—
139	C₃₁×#124	C₂³	1	4	yes	—
140	C₃₁×#124	C₂³	1	2	yes	—
141	C₃₁×#123	—	2	2	no	—
142	C₃₁×#123	—	2	1	no	—
143	C₃₁×C₂²⋊Q₈	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	2	no	—
145	C₃₁×C₂²⋊Q₈	—	2	4	no	—
146	C₃₁×C₂²⋊Q₈	—	2	1	no	—
147	C₃₁×C₂²⋊Q₈	—	2	2	no	—
148	C₃₁×C₂²⋊Q₈	—	2	1	no	—
149	C₃₁×C₂²⋊Q₈	—	2	2	no	—
150	C₃₁×C₂²⋊Q₈	—	2	1	no	—
151	C₃₁×C₂²⋊Q₈	—	2	2	no	—
152	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×#121	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₃₁	—	2	1	no	—
156	C₄×Q₈×C₃₁	—	2	1	no	—
157	C₄×Q₈×C₃₁	—	2	2	no	—
158	C₄×Q₈×C₃₁	—	2	2	no	—
159	C₄×Q₈×C₃₁	—	2	2	no	—
160	C₄×Q₈×C₃₁	—	2	1	no	—
161	C₄×Q₈×C₃₁	—	2	2	no	—
162	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₃₁	D₄	1	2	yes	—
165	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
167	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
168	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
169	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
170	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
171	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
172	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
175	C₄×D₄×C₃₁	—	2	1	no	—
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	1	no	—
178	C₄×D₄×C₃₁	—	2	1	no	—
179	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₃₁	C₂³	1	2	yes	—
181	C₄×D₄×C₃₁	C₂³	1	2	yes	—
182	C₄×D₄×C₃₁	C₂³	1	2	yes	—
183	C₃₁×#117	—	2	2	no	—
184	C₃₁×#117	—	2	1	no	—
185	C₃₁×#117	—	2	2	no	—
186	C₃₁×#117	—	2	2	no	—
187	C₃₁×#117	—	2	4	no	—
188	C₃₁×#117	—	2	1	no	—
189	C₃₁×#117	—	2	2	no	—
190	C₃₁×#117	—	2	1	no	—
191	C₃₁×#117	—	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	D₄	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
197	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
201	C₂×C₄²×C₃₁	—	2	2	no	—
202	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
204	C₃₁×#107	C₂³	1	2	yes	—
205	C₃₁×#107	C₂³	1	4	yes	—
206	C₃₁×#106	C₂³	1	2	yes	—
207	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
208	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
211	C₃₁×#103	C₂³	1	2	yes	—
212	C₃₁×#103	C₂³	1	4	yes	—
213	C₃₁×#103	C₂³	1	4	yes	—
214	C₃₁×#103	C₂³	1	4	yes	—
215	C₃₁×#103	C₂³	1	4	yes	—
216	C₃₁×#103	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	2	yes	—
218	C₃₁×#102	C₂³	1	2	yes	—
219	C₃₁×#102	C₂³	1	2	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
224	C₃₁×#97	C₂³	1	2	yes	—
225	C₃₁×#97	C₂³	1	4	yes	—
226	C₄×C₈×C₃₁	C₂³	1	2	yes	—
227	C₄×C₈×C₃₁	C₂³	1	4	yes	—
228	C₂⁴×C₃₁	—	2	1	no	—
229	C₂×Q₈×C₃₁	—	2	2	no	—
230	C₂×Q₈×C₃₁	—	2	1	no	—
231	C₂×Q₈×C₃₁	—	2	2	no	—
232	C₂×Q₈×C₃₁	—	4	2	no	—
233	C₂×Q₈×C₃₁	—	4	4	no	—
234	C₂×Q₈×C₃₁	—	4	4	no	—
235	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
236	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
237	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
238	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
239	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
241	C₂×D₄×C₃₁	—	2	1	no	—
242	C₂×D₄×C₃₁	—	2	1	no	—
243	C₂×D₄×C₃₁	—	4	2	no	—
244	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
245	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₃₁	—	2	1	no	—
247	C₂²×C₄×C₃₁	—	2	2	no	—
248	C₂²×C₄×C₃₁	—	2	2	no	—
249	C₂²×C₄×C₃₁	—	2	2	no	—
250	C₂²×C₄×C₃₁	—	2	2	no	—
251	C₂²×C₄×C₃₁	—	2	1	no	—
252	C₂²×C₄×C₃₁	—	4	4	no	—
253	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	Q₁₆×C₃₁	—	4	4	no	—
259	Q₁₆×C₃₁	—	4	4	no	—
260	Q₁₆×C₃₁	—	4	4	no	—
261	SD₁₆×C₃₁	—	4	4	no	—
262	SD₁₆×C₃₁	—	4	4	no	—
263	SD₁₆×C₃₁	—	4	2	no	—
264	D₈×C₃₁	—	4	2	no	—
265	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
266	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
267	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
268	C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	4	no	—
271	C₄⋊C₄×C₃₁	—	2	4	no	—
272	C₄⋊C₄×C₃₁	—	2	2	no	—
273	C₄⋊C₄×C₃₁	—	2	2	no	—
274	C₄⋊C₄×C₃₁	—	2	1	no	—
275	C₄⋊C₄×C₃₁	—	2	2	no	—
276	C₄⋊C₄×C₃₁	—	2	1	no	—
277	C₄⋊C₄×C₃₁	—	2	1	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	—	2	2	no	—
280	C₄⋊C₄×C₃₁	—	2	1	no	—
281	C₄⋊C₄×C₃₁	—	2	2	no	—
282	C₄⋊C₄×C₃₁	—	2	1	no	—
283	C₄⋊C₄×C₃₁	—	2	2	no	—
284	C₄⋊C₄×C₃₁	—	2	1	no	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	1	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	2	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	1	no	—
292	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₂²⋊C₄×C₃₁	—	2	1	no	—
304	C₂²⋊C₄×C₃₁	—	2	2	no	—
305	C₂²⋊C₄×C₃₁	—	2	4	no	—
306	C₂²⋊C₄×C₃₁	—	2	4	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	4	no	—
311	C₂²⋊C₄×C₃₁	—	2	1	no	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	1	no	—
314	C₂²⋊C₄×C₃₁	—	2	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	1	no	—
316	C₂²⋊C₄×C₃₁	—	2	2	no	—
317	C₂²⋊C₄×C₃₁	—	2	1	no	—
318	C₄²×C₃₁	—	2	4	no	—
319	C₄²×C₃₁	—	2	4	no	—
320	C₄²×C₃₁	—	2	2	no	—
321	C₄²×C₃₁	—	2	2	no	—
322	C₄²×C₃₁	—	2	2	no	—
323	C₄²×C₃₁	—	2	2	no	—
324	C₄²×C₃₁	—	2	1	no	—
325	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₃₁	C₂×D₄	1	2	yes	—
327	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₃₁	C₂×D₄	1	2	yes	—
329	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₄²×C₃₁	C₂⁴	1	2	yes	—
331	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₄²×C₃₁	C₂⁴	1	2	yes	—
333	#61905	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₃₁	—	2	1	no	—
335	C₂³×C₃₁	—	2	2	no	—
336	C₂³×C₃₁	—	4	2	no	—
337	C₂³×C₃₁	—	4	2	no	—
338	C₂³×C₃₁	—	4	2	no	—
339	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₃₁	—	2	2	no	—
341	Q₈×C₃₁	—	2	2	no	—
342	Q₈×C₃₁	—	2	4	no	—
343	Q₈×C₃₁	—	2	2	no	—
344	Q₈×C₃₁	—	2	4	no	—
345	Q₈×C₃₁	—	2	4	no	—
346	Q₈×C₃₁	—	4	2	no	—
347	Q₈×C₃₁	—	4	4	no	—
348	Q₈×C₃₁	—	4	4	no	—
349	Q₈×C₃₁	—	4	2	no	—
350	D₄×C₃₁	—	2	2	no	—
351	D₄×C₃₁	—	2	2	no	—
352	D₄×C₃₁	—	2	2	no	—
353	D₄×C₃₁	—	4	2	no	—
354	D₄×C₃₁	—	4	2	no	—
355	C₂×C₄×C₃₁	—	2	4	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	2	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	1	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	1	no	—
363	C₂×C₄×C₃₁	—	2	4	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	4	2	no	—
367	C₂×C₄×C₃₁	—	4	4	no	—
368	C₂×C₄×C₃₁	—	4	4	no	—
369	C₂×C₄×C₃₁	—	4	2	no	—
370	C₂×C₄×C₃₁	—	4	4	no	—
371	C₂×C₄×C₃₁	—	4	4	no	—
372	C₂×C₄×C₃₁	—	4	2	no	—
373	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
383	C₈×C₃₁	—	2	2	no	—
384	C₈×C₃₁	—	2	4	no	—
385	C₈×C₃₁	—	2	2	no	—
386	#3523	C₂×C₃₁	1	1	yes	characteristic, complemented
387	C₂×#556	C₂×C₃₁	1	1	yes	characteristic, complemented
388	#3402	C₂×C₃₁	1	4	yes	complemented
389	#3398	C₂×C₃₁	1	2	yes	complemented
390	#3393	C₂×C₃₁	1	2	yes	complemented
391	#3377	C₂×C₃₁	1	4	yes	complemented
392	#3367	C₂×C₃₁	1	2	yes	complemented
393	#3364	C₂×C₃₁	1	2	yes	complemented
394	#3218	C₂×C₃₁	1	1	yes	characteristic, complemented
395	#3215	C₂×C₃₁	1	2	yes	complemented
396	#3211	C₂×C₃₁	1	2	yes	—
397	#3209	C₂×C₃₁	1	1	yes	characteristic, complemented
398	#3117	C₂×C₃₁	1	2	yes	complemented
399	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
400	#3105	C₂×C₃₁	1	1	yes	characteristic
401	#3104	C₂×C₃₁	1	2	yes	complemented
402	#2984	C₂×C₃₁	1	1	yes	characteristic, complemented
403	C₂²×C₃₁	—	2	1	no	—
404	C₂²×C₃₁	—	2	1	no	—
405	C₂²×C₃₁	—	4	2	no	—
406	C₂²×C₃₁	—	4	1	no	—
407	C₂²×C₃₁	—	4	1	no	—
408	C₂²×C₃₁	—	4	2	no	—
409	C₂²×C₃₁	—	4	1	no	—
410	C₂²×C₃₁	—	4	2	no	—
411	C₂²×C₃₁	—	8	4	no	—
412	C₂²×C₃₁	#578	1	2	yes	—
413	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
414	C₄×C₃₁	—	2	1	no	—
415	C₄×C₃₁	—	2	1	no	—
416	C₄×C₃₁	—	2	2	no	—
417	C₄×C₃₁	—	2	2	no	—
418	C₄×C₃₁	—	2	2	no	—
419	C₄×C₃₁	—	2	2	no	—
420	C₄×C₃₁	—	2	1	no	—
421	C₄×C₃₁	—	2	1	no	—
422	C₄×C₃₁	—	4	4	no	—
423	C₄×C₃₁	—	4	1	no	—
424	C₄×C₃₁	—	4	2	no	—
425	C₄×C₃₁	—	4	2	no	—
426	C₄×C₃₁	—	4	2	no	—
427	C₄×C₃₁	—	4	1	no	—
428	C₄×C₃₁	—	4	1	no	—
429	C₄×C₃₁	#575	1	2	yes	—
430	C₄×C₃₁	#585	1	2	yes	—
431	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
432	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
433	#557	C₂²×C₃₁	1	2	yes	complemented
434	#556	—	2	1	no	—
435	#556	—	2	1	no	—
436	#556	—	2	2	no	—
437	#556	C₂²×C₃₁	1	2	yes	—
438	#556	C₂²×C₃₁	1	2	yes	—
439	#556	C₂²×C₃₁	1	4	yes	—
440	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
441	#556	C₂²×C₃₁	1	2	yes	complemented
442	#552	—	2	1	no	—
443	#552	—	2	2	no	—
444	D₄×Q₈	—	2	1	no	—
445	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
446	#541	—	2	1	no	—
447	#541	—	2	2	no	—
448	#533	C₂²×C₃₁	1	2	yes	—
449	#533	C₂²×C₃₁	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
451	#529	C₂²×C₃₁	1	1	yes	characteristic
452	#529	C₂²×C₃₁	1	2	yes	—
453	C₂×#126	—	2	2	no	—
454	C₂×#124	C₂²×C₃₁	1	2	yes	—
455	C₂×C₂²⋊Q₈	—	2	1	no	—
456	#519	—	2	1	no	—
457	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
458	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
459	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
460	C₂×#117	—	2	1	no	—
461	#497	C₂²×C₃₁	1	4	yes	—
462	#497	C₂²×C₃₁	1	2	yes	complemented
463	#495	C₂²×C₃₁	1	4	yes	—
464	#494	C₂²×C₃₁	1	2	yes	complemented
465	#491	C₂²×C₃₁	1	2	yes	complemented
466	#489	C₂²×C₃₁	1	4	yes	—
467	#488	C₂²×C₃₁	1	4	yes	—
468	#487	C₂²×C₃₁	1	2	yes	complemented
469	#484	C₂²×C₃₁	1	1	yes	characteristic
470	#484	C₂²×C₃₁	1	2	yes	—
471	#481	C₂²×C₃₁	1	1	yes	characteristic
472	#479	C₂²×C₃₁	1	4	yes	complemented
473	#478	C₂²×C₃₁	1	2	yes	—
474	#477	C₂²×C₃₁	1	4	yes	complemented
475	#474	C₂²×C₃₁	1	2	yes	—
476	#464	C₂²×C₃₁	1	4	yes	—
477	#464	C₂²×C₃₁	1	4	yes	—
478	#464	C₂²×C₃₁	1	4	yes	—
479	#464	C₂²×C₃₁	1	4	yes	complemented
480	#463	C₂²×C₃₁	1	2	yes	—
481	#463	C₂²×C₃₁	1	4	yes	—
482	#462	C₂²×C₃₁	1	4	yes	complemented
483	#462	C₂²×C₃₁	1	2	yes	complemented
484	#462	C₂²×C₃₁	1	4	yes	complemented
485	#461	C₂²×C₃₁	1	2	yes	—
486	#461	C₂²×C₃₁	1	2	yes	complemented
487	#451	C₂²×C₃₁	1	2	yes	—
488	#451	C₂²×C₃₁	1	2	yes	—
489	#451	C₂²×C₃₁	1	2	yes	—
490	#450	C₂²×C₃₁	1	1	yes	characteristic
491	#450	C₂²×C₃₁	1	2	yes	—
492	#448	C₂²×C₃₁	1	2	yes	—
493	#447	C₂²×C₃₁	1	1	yes	characteristic
494	#446	C₂²×C₃₁	1	2	yes	complemented
495	#446	C₂²×C₃₁	1	4	yes	complemented
496	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
497	#441	C₂²×C₃₁	1	4	yes	complemented
498	#440	C₂²×C₃₁	1	4	yes	—
499	#440	C₂²×C₃₁	1	4	yes	complemented
500	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
501	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
502	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
503	C₄×D₈	C₂²×C₃₁	1	2	yes	—
504	#432	C₂²×C₃₁	1	1	yes	characteristic
505	#432	C₂²×C₃₁	1	2	yes	—
506	#431	C₂²×C₃₁	1	2	yes	—
507	#431	C₂²×C₃₁	1	1	yes	characteristic
508	C₂×C₃₁	—	2	2	no	—
509	C₂×C₃₁	—	8	1	no	—
510	C₂×C₃₁	—	8	2	no	—
511	C₂×C₃₁	#3487	1	1	yes	characteristic
512	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
513	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
514	C₂²×Q₈	—	2	1	no	—
515	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
517	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
518	C₂³×C₄	—	2	1	no	—
519	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
520	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
521	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
522	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
523	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
524	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
525	C₂×D₈	C₂³×C₃₁	1	2	yes	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	—	2	2	no	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	—	2	1	no	—
530	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
533	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
534	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
535	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
536	#126	—	2	4	no	—
537	#126	—	2	4	no	—
538	#126	—	2	4	no	—
539	#126	—	2	4	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#126	—	2	2	no	—
543	#126	—	2	1	no	—
544	#126	—	2	2	no	—
545	#125	—	2	2	no	—
546	#125	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	—	2	1	no	—
549	#125	—	2	2	no	—
550	#125	—	2	1	no	—
551	#125	—	2	2	no	—
552	#125	C₂³×C₃₁	1	1	yes	characteristic
553	#125	C₂³×C₃₁	1	2	yes	—
554	#124	—	2	2	no	—
555	#124	—	2	2	no	—
556	#124	C₂³×C₃₁	1	4	yes	—
557	#124	C₂³×C₃₁	1	4	yes	—
558	#124	C₂³×C₃₁	1	1	yes	characteristic
559	#124	C₂³×C₃₁	1	2	yes	—
560	#123	—	2	2	no	—
561	#123	—	2	1	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
572	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
573	#121	C₂³×C₃₁	1	1	yes	characteristic
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
582	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
583	C₄×Q₈	D₄×C₃₁	1	2	yes	—
584	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
585	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
586	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
588	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
589	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
590	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
591	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	C₂³×C₃₁	1	2	yes	—
599	C₄×D₄	C₂³×C₃₁	1	2	yes	—
600	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
601	C₄×D₄	C₂³×C₃₁	1	2	yes	—
602	#117	—	2	2	no	—
603	#117	—	2	1	no	—
604	#117	—	2	2	no	—
605	#117	—	2	2	no	—
606	#117	—	2	4	no	—
607	#117	—	2	1	no	—
608	#117	—	2	2	no	—
609	#117	—	2	1	no	—
610	#117	—	2	2	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	2	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
615	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	—	2	2	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	2	no	—
620	C₂×C₄²	—	2	2	no	—
621	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
623	#107	C₂³×C₃₁	1	2	yes	—
624	#107	C₂³×C₃₁	1	4	yes	—
625	#106	C₂³×C₃₁	1	2	yes	—
626	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
627	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
628	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
629	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
630	#103	C₂³×C₃₁	1	2	yes	—
631	#103	C₂³×C₃₁	1	4	yes	—
632	#103	C₂³×C₃₁	1	4	yes	—
633	#103	C₂³×C₃₁	1	4	yes	—
634	#103	C₂³×C₃₁	1	4	yes	—
635	#103	C₂³×C₃₁	1	4	yes	—
636	#102	C₂³×C₃₁	1	2	yes	—
637	#102	C₂³×C₃₁	1	2	yes	—
638	#102	C₂³×C₃₁	1	2	yes	—
639	#102	C₂³×C₃₁	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
641	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
642	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
643	#97	C₂³×C₃₁	1	2	yes	—
644	#97	C₂³×C₃₁	1	4	yes	—
645	C₄×C₈	C₂³×C₃₁	1	2	yes	—
646	C₄×C₈	C₂³×C₃₁	1	4	yes	—
647	C₃₁	#61905	1	1	yes	characteristic, direct product factor, Sylow
648	C₂⁴	—	2	1	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	4	2	no	—
653	C₂×Q₈	—	4	4	no	—
654	C₂×Q₈	—	4	4	no	—
655	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
656	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
657	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
658	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
659	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
660	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	4	2	no	—
664	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
665	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	4	4	no	—
673	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
674	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
678	Q₁₆	—	4	4	no	—
679	Q₁₆	—	4	4	no	—
680	Q₁₆	—	4	4	no	—
681	SD₁₆	—	4	4	no	—
682	SD₁₆	—	4	4	no	—
683	SD₁₆	—	4	2	no	—
684	D₈	—	4	2	no	—
685	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
686	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
687	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
713	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
714	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
715	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
716	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
717	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
718	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
720	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
721	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	1	no	—
745	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₃₁	1	2	yes	—
747	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₃₁	1	2	yes	—
749	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
750	C₄²	C₂⁴×C₃₁	1	2	yes	—
751	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
752	C₄²	C₂⁴×C₃₁	1	2	yes	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	—	4	2	no	—
758	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	4	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	4	no	—
764	Q₈	—	2	4	no	—
765	Q₈	—	4	2	no	—
766	Q₈	—	4	4	no	—
767	Q₈	—	4	4	no	—
768	Q₈	—	4	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	2	no	—
772	D₄	—	4	2	no	—
773	D₄	—	4	2	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
801	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
802	C₈	—	2	2	no	—
803	C₈	—	2	4	no	—
804	C₈	—	2	2	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	8	4	no	—
814	C₂²	C₃₁×#578	1	2	yes	—
815	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	4	4	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	1	no	—
831	C₄	C₃₁×#575	1	2	yes	—
832	C₄	C₃₁×#585	1	2	yes	—
833	C₂	—	2	2	no	—
834	C₂	—	8	2	no	—
835	C₂	—	8	1	no	—
836	C₂	C₃₁×#3487	1	1	yes	characteristic
837	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
838	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#447	C₂²
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
1. C₃₁×#3523	C₂	semidirect
2. C₂×C₃₁×#556	C₂	semidirect
3. C₃₁×#3402	C₂	semidirect
4. C₃₁×#3398	C₂	semidirect
5. C₃₁×#3393	C₂	semidirect
6. C₃₁×#3377	C₂	semidirect
7. C₃₁×#3367	C₂	semidirect
8. C₃₁×#3364	C₂	semidirect
9. C₃₁×#3218	C₂	semidirect
10. C₃₁×#3215	C₂	semidirect
12. C₃₁×#3209	C₂	semidirect
13. C₃₁×#3117	C₂	semidirect
14. C₃₁×#3110	C₂	semidirect
16. C₃₁×#3104	C₂	semidirect
17. C₃₁×#2984	C₂	semidirect
18. C₃₁×#557	C₂²	semidirect
19. C₃₁×#557	C₂²	semidirect
20. C₃₁×#557	C₂²	semidirect
27. C₃₁×#556	C₂²	semidirect
28. C₃₁×#556	C₂²	semidirect
32. D₄×Q₈×C₃₁	C₂²	semidirect
49. C₃₁×#497	C₂²	semidirect
51. C₃₁×#494	C₂²	semidirect
52. C₃₁×#491	C₂²	semidirect
55. C₃₁×#487	C₂²	semidirect
59. C₃₁×#479	C₂²	semidirect
61. C₃₁×#477	C₂²	semidirect
66. C₃₁×#464	C₂²	semidirect
69. C₃₁×#462	C₂²	semidirect
70. C₃₁×#462	C₂²	semidirect
71. C₃₁×#462	C₂²	semidirect
73. C₃₁×#461	C₂²	semidirect
81. C₃₁×#446	C₂²	semidirect
82. C₃₁×#446	C₂²	semidirect
83. C₈×Q₈×C₃₁	C₂²	semidirect
84. C₃₁×#441	C₂²	semidirect
86. C₃₁×#440	C₂²	semidirect
87. C₄×Q₁₆×C₃₁	C₂²	semidirect
88. C₄×Q₁₆×C₃₁	C₂²	semidirect
333. #61905	C₃₁	direct (N × H)
386. #3523	C₂×C₃₁	semidirect
387. C₂×#556	C₂×C₃₁	semidirect
388. #3402	C₂×C₃₁	semidirect
389. #3398	C₂×C₃₁	semidirect
390. #3393	C₂×C₃₁	semidirect
391. #3377	C₂×C₃₁	semidirect
392. #3367	C₂×C₃₁	semidirect
393. #3364	C₂×C₃₁	semidirect
394. #3218	C₂×C₃₁	semidirect
395. #3215	C₂×C₃₁	semidirect
397. #3209	C₂×C₃₁	semidirect
398. #3117	C₂×C₃₁	semidirect
399. #3110	C₂×C₃₁	semidirect
401. #3104	C₂×C₃₁	semidirect
402. #2984	C₂×C₃₁	semidirect
431. #557	C₂²×C₃₁	semidirect
432. #557	C₂²×C₃₁	semidirect
433. #557	C₂²×C₃₁	semidirect
440. #556	C₂²×C₃₁	semidirect
441. #556	C₂²×C₃₁	semidirect
445. D₄×Q₈	C₂²×C₃₁	semidirect
462. #497	C₂²×C₃₁	semidirect
464. #494	C₂²×C₃₁	semidirect
465. #491	C₂²×C₃₁	semidirect
468. #487	C₂²×C₃₁	semidirect
472. #479	C₂²×C₃₁	semidirect
474. #477	C₂²×C₃₁	semidirect
479. #464	C₂²×C₃₁	semidirect
482. #462	C₂²×C₃₁	semidirect
483. #462	C₂²×C₃₁	semidirect
484. #462	C₂²×C₃₁	semidirect
486. #461	C₂²×C₃₁	semidirect
494. #446	C₂²×C₃₁	semidirect
495. #446	C₂²×C₃₁	semidirect
496. C₈×Q₈	C₂²×C₃₁	semidirect
497. #441	C₂²×C₃₁	semidirect
499. #440	C₂²×C₃₁	semidirect
500. C₄×Q₁₆	C₂²×C₃₁	semidirect
501. C₄×Q₁₆	C₂²×C₃₁	semidirect
647. C₃₁	#61905	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×#3523	2
C₂×C₃₁×#556	2
C₃₁×#3402	2
C₃₁×#3398	2
C₃₁×#3393	2
C₃₁×#3377	2
C₃₁×#3367	2
C₃₁×#3364	2
C₃₁×#3218	2
C₃₁×#3215	2
C₃₁×#3211	2
C₃₁×#3209	2
C₃₁×#3117	2
C₃₁×#3110	2
C₃₁×#3105	2
C₃₁×#3104	2
C₃₁×#2984	2
#61905	31

Subgroups — C31×#61905 #21518664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61905 #21518664