Subgroups — C₃₁×#62113 #21518872

Order 7936.

1684 conjugacy classes of subgroups.

The subgroup lattice has 836 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
2	Q₈×#41×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3387	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3374	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3356	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3344	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3328	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3312	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3255	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3237	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3113	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3078	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic
18	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#557	—	2	1	no	—
20	C₃₁×#557	—	2	1	no	—
21	C₃₁×#557	C₂²	1	1	yes	characteristic
22	C₃₁×#557	C₂²	1	2	yes	—
23	C₃₁×#556	—	2	1	no	—
24	C₃₁×#556	C₂²	1	2	yes	—
25	C₃₁×#554	—	2	2	no	—
26	C₃₁×#554	—	2	1	no	—
27	C₃₁×#554	C₂²	1	2	yes	—
28	C₃₁×#554	C₂²	1	1	yes	characteristic
29	C₃₁×#552	—	2	2	no	—
30	C₃₁×#552	C₂²	1	4	yes	—
31	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
32	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#541	—	2	2	no	—
34	C₃₁×#536	—	2	1	no	—
35	C₃₁×#533	—	2	1	no	—
36	C₃₁×#533	—	2	2	no	—
37	C₃₁×#533	C₂²	1	1	yes	characteristic
38	C₃₁×#533	C₂²	1	2	yes	—
39	C₃₁×#533	C₂²	1	1	yes	characteristic
40	C₃₁×#533	C₂²	1	2	yes	—
41	C₃₁×#533	C₂²	1	2	yes	—
42	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃₁×#519	—	2	1	no	—
44	C₄×#41×C₃₁	—	2	1	no	—
45	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
48	C₃₁×#501	C₂²	1	4	yes	—
49	C₃₁×#498	C₂²	1	2	yes	—
50	C₃₁×#491	C₂²	1	4	yes	—
51	C₃₁×#487	C₂²	1	2	yes	—
52	C₃₁×#485	C₂²	1	4	yes	—
53	C₃₁×#485	C₂²	1	4	yes	—
54	C₃₁×#484	C₂²	1	2	yes	—
55	C₃₁×#483	C₂²	1	4	yes	—
56	C₃₁×#483	C₂²	1	4	yes	—
57	C₃₁×#479	C₂²	1	4	yes	—
58	C₃₁×#479	C₂²	1	4	yes	—
59	C₃₁×#477	C₂²	1	1	yes	characteristic
60	C₃₁×#477	C₂²	1	2	yes	—
61	C₃₁×#477	C₂²	1	2	yes	—
62	C₃₁×#477	C₂²	1	1	yes	characteristic
63	C₃₁×#475	C₂²	1	2	yes	—
64	C₃₁×#475	C₂²	1	2	yes	—
65	C₃₁×#475	C₂²	1	4	yes	—
66	C₃₁×#475	C₂²	1	2	yes	—
67	C₃₁×#475	C₂²	1	2	yes	—
68	C₃₁×#475	C₂²	1	2	yes	—
69	C₃₁×#475	C₂²	1	2	yes	—
70	C₃₁×#470	C₂²	1	4	yes	—
71	C₃₁×#470	C₂²	1	4	yes	—
72	C₃₁×#467	C₂²	1	4	yes	—
73	C₃₁×#462	C₂²	1	1	yes	characteristic
74	C₃₁×#462	C₂²	1	1	yes	characteristic
75	C₃₁×#462	C₂²	1	2	yes	—
76	C₃₁×#462	C₂²	1	2	yes	—
77	C₃₁×#462	C₂²	1	4	yes	—
78	C₃₁×#451	C₂²	1	2	yes	—
79	C₃₁×#451	C₂²	1	4	yes	—
80	C₃₁×#446	C₂²	1	2	yes	—
81	C₃₁×#441	C₂²	1	4	yes	—
82	C₃₁×#441	C₂²	1	4	yes	—
83	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
84	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
85	C₃₁×#436	C₂²	1	2	yes	—
86	C₃₁×#435	C₂²	1	4	yes	—
87	C₃₁×#432	C₂²	1	2	yes	—
88	C₃₁×#431	C₂²	1	1	yes	characteristic
89	C₃₁×#428	C₂²	1	4	yes	—
90	C₂×C₃₁×#106	C₂²	1	2	yes	—
91	C₃₁×#423	C₂²	1	2	yes	—
92	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
93	C₃₁×#419	C₂²	1	4	yes	—
94	C₂×C₃₁×#103	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
96	C₂²×Q₈×C₃₁	—	2	1	no	—
97	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
99	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
103	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
104	C₃₁×C₄⋊Q₈	—	2	2	no	—
105	C₃₁×C₄⋊Q₈	—	2	1	no	—
106	C₃₁×C₄⋊Q₈	—	2	2	no	—
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	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃₁×#126	—	2	4	no	—
120	C₃₁×#126	—	2	4	no	—
121	C₃₁×#125	—	2	1	no	—
122	C₃₁×#125	—	2	2	no	—
123	C₃₁×#125	—	2	1	no	—
124	C₃₁×#125	—	2	2	no	—
125	C₃₁×#125	—	2	4	no	—
126	C₃₁×#125	—	2	4	no	—
127	C₃₁×#125	—	2	1	no	—
128	C₃₁×#125	—	2	2	no	—
129	C₃₁×#125	—	2	2	no	—
130	C₃₁×#125	—	2	1	no	—
131	C₃₁×#125	C₂³	1	4	yes	—
132	C₃₁×#124	—	2	2	no	—
133	C₃₁×#123	—	2	4	no	—
134	C₃₁×C₂²⋊Q₈	—	2	2	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	1	no	—
137	C₃₁×C₂²⋊Q₈	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	—	2	1	no	—
139	C₃₁×C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
144	C₃₁×C₂²⋊Q₈	—	2	2	no	—
145	C₃₁×C₂²⋊Q₈	—	2	2	no	—
146	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₄×Q₈×C₃₁	—	2	1	no	—
152	C₄×Q₈×C₃₁	—	2	1	no	—
153	C₄×Q₈×C₃₁	—	2	2	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	2	no	—
158	C₄×Q₈×C₃₁	—	2	1	no	—
159	C₄×Q₈×C₃₁	—	2	2	no	—
160	C₄×Q₈×C₃₁	—	2	2	no	—
161	C₄×Q₈×C₃₁	—	2	2	no	—
162	C₄×Q₈×C₃₁	—	2	1	no	—
163	C₄×Q₈×C₃₁	—	2	2	no	—
164	C₄×Q₈×C₃₁	—	2	1	no	—
165	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
167	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
170	C₄×Q₈×C₃₁	C₂³	1	2	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×Q₈×C₃₁	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₃₁	—	2	2	no	—
177	C₄×D₄×C₃₁	—	2	1	no	—
178	C₄×D₄×C₃₁	—	2	2	no	—
179	C₄×D₄×C₃₁	—	2	1	no	—
180	C₄×D₄×C₃₁	D₄	1	2	yes	—
181	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
182	C₄×D₄×C₃₁	C₂³	1	2	yes	—
183	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₃₁×#117	—	2	2	no	—
185	C₃₁×#117	—	2	1	no	—
186	C₃₁×#117	—	2	1	no	—
187	C₃₁×#117	—	2	2	no	—
188	C₃₁×#117	—	2	4	no	—
189	C₃₁×#117	D₄	1	1	yes	characteristic
190	C₃₁×#117	D₄	1	2	yes	—
191	C₃₁×#117	C₂³	1	4	yes	—
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	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₃₁	—	2	2	no	—
199	C₂×C₄²×C₃₁	—	2	1	no	—
200	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
202	C₃₁×#107	C₂³	1	2	yes	—
203	C₃₁×#107	C₂³	1	4	yes	—
204	C₃₁×#107	C₂³	1	2	yes	—
205	C₃₁×#106	C₂³	1	4	yes	—
206	C₃₁×#106	C₂³	1	4	yes	—
207	C₃₁×#106	C₂³	1	4	yes	—
208	C₃₁×#106	C₂³	1	4	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
211	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	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×#103	C₂³	1	2	yes	—
222	C₃₁×#103	C₂³	1	4	yes	—
223	C₃₁×#103	C₂³	1	4	yes	—
224	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₃₁×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₃₁	C₂³	1	2	yes	—
228	#41×C₃₁	—	2	4	no	—
229	C₂×Q₈×C₃₁	—	2	1	no	—
230	C₂×Q₈×C₃₁	—	2	2	no	—
231	C₂×Q₈×C₃₁	—	2	1	no	—
232	C₂×Q₈×C₃₁	—	2	2	no	—
233	C₂×Q₈×C₃₁	—	2	2	no	—
234	C₂×Q₈×C₃₁	—	2	2	no	—
235	C₂×Q₈×C₃₁	—	2	1	no	—
236	C₂×Q₈×C₃₁	—	2	2	no	—
237	C₂×Q₈×C₃₁	—	2	4	no	—
238	C₂×Q₈×C₃₁	—	4	1	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	C₂⁴	1	1	yes	characteristic
243	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
247	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₃₁	—	2	2	no	—
249	C₂²×C₄×C₃₁	—	2	1	no	—
250	C₂²×C₄×C₃₁	—	2	2	no	—
251	C₂²×C₄×C₃₁	—	2	2	no	—
252	C₂²×C₄×C₃₁	—	2	1	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	2	yes	—
256	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
259	Q₁₆×C₃₁	—	2	4	no	—
260	Q₁₆×C₃₁	—	4	4	no	—
261	Q₁₆×C₃₁	—	4	2	no	—
262	M₁₆×C₃₁	—	4	4	no	—
263	C₂×C₈×C₃₁	—	4	2	no	—
264	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
265	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
266	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
267	C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₄⋊C₄×C₃₁	—	2	2	no	—
269	C₄⋊C₄×C₃₁	—	2	2	no	—
270	C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
277	C₄⋊C₄×C₃₁	—	2	1	no	—
278	C₄⋊C₄×C₃₁	—	2	2	no	—
279	C₄⋊C₄×C₃₁	—	2	1	no	—
280	C₄⋊C₄×C₃₁	—	2	2	no	—
281	C₄⋊C₄×C₃₁	—	2	1	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	4	no	—
287	C₄⋊C₄×C₃₁	—	2	4	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	1	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	2	no	—
293	C₄⋊C₄×C₃₁	—	2	4	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	4	no	—
296	C₄⋊C₄×C₃₁	—	2	2	no	—
297	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
306	C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	2	no	—
309	C₂²⋊C₄×C₃₁	—	2	2	no	—
310	C₂²⋊C₄×C₃₁	—	2	4	no	—
311	C₂²⋊C₄×C₃₁	—	2	4	no	—
312	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
313	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
314	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
315	C₄²×C₃₁	—	2	1	no	—
316	C₄²×C₃₁	—	2	2	no	—
317	C₄²×C₃₁	—	2	1	no	—
318	C₄²×C₃₁	—	2	2	no	—
319	C₄²×C₃₁	—	2	1	no	—
320	C₄²×C₃₁	—	2	2	no	—
321	C₄²×C₃₁	—	2	1	no	—
322	C₄²×C₃₁	—	2	4	no	—
323	C₄²×C₃₁	—	2	4	no	—
324	C₄²×C₃₁	—	2	2	no	—
325	C₄²×C₃₁	C₂×D₄	1	2	yes	—
326	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₃₁	C₂×D₄	1	2	yes	—
328	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₄²×C₃₁	C₂⁴	1	2	yes	—
331	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
332	#62113	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
334	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
335	Q₈×C₃₁	—	2	2	no	—
336	Q₈×C₃₁	—	2	1	no	—
337	Q₈×C₃₁	—	2	2	no	—
338	Q₈×C₃₁	—	2	1	no	—
339	Q₈×C₃₁	—	2	2	no	—
340	Q₈×C₃₁	—	2	2	no	—
341	Q₈×C₃₁	—	2	2	no	—
342	Q₈×C₃₁	—	2	1	no	—
343	Q₈×C₃₁	—	4	2	no	—
344	Q₈×C₃₁	—	4	4	no	—
345	Q₈×C₃₁	—	4	2	no	—
346	Q₈×C₃₁	—	4	4	no	—
347	Q₈×C₃₁	—	4	4	no	—
348	Q₈×C₃₁	—	8	2	no	—
349	Q₈×C₃₁	—	8	1	no	—
350	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
351	D₄×C₃₁	—	2	4	no	—
352	D₄×C₃₁	—	2	2	no	—
353	C₂×C₄×C₃₁	—	2	1	no	—
354	C₂×C₄×C₃₁	—	2	4	no	—
355	C₂×C₄×C₃₁	—	2	1	no	—
356	C₂×C₄×C₃₁	—	2	2	no	—
357	C₂×C₄×C₃₁	—	2	1	no	—
358	C₂×C₄×C₃₁	—	2	2	no	—
359	C₂×C₄×C₃₁	—	2	1	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	1	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	1	no	—
366	C₂×C₄×C₃₁	—	2	4	no	—
367	C₂×C₄×C₃₁	—	4	1	no	—
368	C₂×C₄×C₃₁	—	4	2	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	—	8	1	no	—
373	C₂×C₄×C₃₁	—	8	2	no	—
374	C₂×C₄×C₃₁	#137	1	4	yes	—
375	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
384	C₈×C₃₁	—	2	2	no	—
385	C₈×C₃₁	—	2	4	no	—
386	C₈×C₃₁	—	2	2	no	—
387	#3509	C₂×C₃₁	1	1	yes	characteristic
388	Q₈×#41	C₂×C₃₁	1	1	yes	characteristic
389	#3387	C₂×C₃₁	1	2	yes	complemented
390	#3374	C₂×C₃₁	1	2	yes	complemented
391	#3356	C₂×C₃₁	1	2	yes	complemented
392	#3344	C₂×C₃₁	1	4	yes	complemented
393	#3328	C₂×C₃₁	1	2	yes	complemented
394	#3312	C₂×C₃₁	1	4	yes	complemented
395	#3255	C₂×C₃₁	1	2	yes	complemented
396	#3249	C₂×C₃₁	1	1	yes	characteristic, complemented
397	#3237	C₂×C₃₁	1	2	yes	complemented
398	#3229	C₂×C₃₁	1	1	yes	characteristic, complemented
399	#3113	C₂×C₃₁	1	2	yes	complemented
400	#3104	C₂×C₃₁	1	1	yes	characteristic, complemented
401	#3078	C₂×C₃₁	1	2	yes	complemented
402	C₂×#475	C₂×C₃₁	1	1	yes	characteristic, complemented
403	#2989	C₂×C₃₁	1	1	yes	characteristic
404	C₂²×C₃₁	—	2	1	no	—
405	C₂²×C₃₁	—	2	1	no	—
406	C₂²×C₃₁	—	2	2	no	—
407	C₂²×C₃₁	—	2	2	no	—
408	C₂²×C₃₁	—	2	2	no	—
409	C₂²×C₃₁	C₂×#137	1	2	yes	—
410	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
411	C₄×C₃₁	—	2	1	no	—
412	C₄×C₃₁	—	2	2	no	—
413	C₄×C₃₁	—	2	1	no	—
414	C₄×C₃₁	—	2	1	no	—
415	C₄×C₃₁	—	2	2	no	—
416	C₄×C₃₁	—	2	2	no	—
417	C₄×C₃₁	—	2	2	no	—
418	C₄×C₃₁	—	4	1	no	—
419	C₄×C₃₁	—	4	1	no	—
420	C₄×C₃₁	—	4	2	no	—
421	C₄×C₃₁	—	4	2	no	—
422	C₄×C₃₁	—	4	1	no	—
423	C₄×C₃₁	—	4	2	no	—
424	C₄×C₃₁	—	4	2	no	—
425	C₄×C₃₁	—	4	4	no	—
426	C₄×C₃₁	C₂×#137	1	2	yes	—
427	C₄×C₃₁	C₂×#137	1	2	yes	—
428	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
429	C₄×C₃₁	#585	1	1	yes	characteristic
430	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
431	#557	—	2	1	no	—
432	#557	—	2	1	no	—
433	#557	C₂²×C₃₁	1	1	yes	characteristic
434	#557	C₂²×C₃₁	1	2	yes	—
435	#556	—	2	1	no	—
436	#556	C₂²×C₃₁	1	2	yes	—
437	#554	—	2	2	no	—
438	#554	—	2	1	no	—
439	#554	C₂²×C₃₁	1	2	yes	—
440	#554	C₂²×C₃₁	1	1	yes	characteristic
441	#552	—	2	2	no	—
442	#552	C₂²×C₃₁	1	4	yes	—
443	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
444	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
445	#541	—	2	2	no	—
446	#536	—	2	1	no	—
447	#533	—	2	1	no	—
448	#533	—	2	2	no	—
449	#533	C₂²×C₃₁	1	1	yes	characteristic
450	#533	C₂²×C₃₁	1	2	yes	—
451	#533	C₂²×C₃₁	1	1	yes	characteristic
452	#533	C₂²×C₃₁	1	2	yes	—
453	#533	C₂²×C₃₁	1	2	yes	—
454	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
455	#519	—	2	1	no	—
456	C₄×#41	—	2	1	no	—
457	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
459	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
460	#501	C₂²×C₃₁	1	4	yes	—
461	#498	C₂²×C₃₁	1	2	yes	—
462	#491	C₂²×C₃₁	1	4	yes	—
463	#487	C₂²×C₃₁	1	2	yes	—
464	#485	C₂²×C₃₁	1	4	yes	—
465	#485	C₂²×C₃₁	1	4	yes	—
466	#484	C₂²×C₃₁	1	2	yes	—
467	#483	C₂²×C₃₁	1	4	yes	—
468	#483	C₂²×C₃₁	1	4	yes	—
469	#479	C₂²×C₃₁	1	4	yes	—
470	#479	C₂²×C₃₁	1	4	yes	—
471	#477	C₂²×C₃₁	1	1	yes	characteristic
472	#477	C₂²×C₃₁	1	2	yes	—
473	#477	C₂²×C₃₁	1	2	yes	—
474	#477	C₂²×C₃₁	1	1	yes	characteristic
475	#475	C₂²×C₃₁	1	2	yes	—
476	#475	C₂²×C₃₁	1	2	yes	—
477	#475	C₂²×C₃₁	1	2	yes	—
478	#475	C₂²×C₃₁	1	2	yes	—
479	#475	C₂²×C₃₁	1	2	yes	—
480	#475	C₂²×C₃₁	1	4	yes	—
481	#475	C₂²×C₃₁	1	2	yes	—
482	#470	C₂²×C₃₁	1	4	yes	—
483	#470	C₂²×C₃₁	1	4	yes	—
484	#467	C₂²×C₃₁	1	4	yes	—
485	#462	C₂²×C₃₁	1	2	yes	—
486	#462	C₂²×C₃₁	1	1	yes	characteristic
487	#462	C₂²×C₃₁	1	1	yes	characteristic
488	#462	C₂²×C₃₁	1	2	yes	—
489	#462	C₂²×C₃₁	1	4	yes	—
490	#451	C₂²×C₃₁	1	4	yes	—
491	#451	C₂²×C₃₁	1	2	yes	—
492	#446	C₂²×C₃₁	1	2	yes	—
493	#441	C₂²×C₃₁	1	4	yes	—
494	#441	C₂²×C₃₁	1	4	yes	—
495	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
496	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
497	#436	C₂²×C₃₁	1	2	yes	—
498	#435	C₂²×C₃₁	1	4	yes	—
499	#432	C₂²×C₃₁	1	2	yes	—
500	#431	C₂²×C₃₁	1	1	yes	characteristic
501	#428	C₂²×C₃₁	1	4	yes	—
502	C₂×#106	C₂²×C₃₁	1	2	yes	—
503	#423	C₂²×C₃₁	1	2	yes	—
504	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
505	#419	C₂²×C₃₁	1	4	yes	—
506	C₂×#103	C₂²×C₃₁	1	2	yes	—
507	C₂×C₃₁	—	2	2	no	—
508	C₂×C₃₁	—	4	2	no	—
509	C₂×C₃₁	#3489	1	1	yes	characteristic
510	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
511	C₂×C₃₁	#3586	1	1	yes	characteristic
512	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
513	C₂²×Q₈	—	2	1	no	—
514	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
515	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
516	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
517	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
518	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
519	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
520	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
521	C₄⋊Q₈	—	2	2	no	—
522	C₄⋊Q₈	—	2	1	no	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	—	2	1	no	—
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	—	2	1	no	—
528	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
536	#126	—	2	4	no	—
537	#126	—	2	4	no	—
538	#125	—	2	1	no	—
539	#125	—	2	2	no	—
540	#125	—	2	1	no	—
541	#125	—	2	2	no	—
542	#125	—	2	4	no	—
543	#125	—	2	4	no	—
544	#125	—	2	1	no	—
545	#125	—	2	2	no	—
546	#125	—	2	2	no	—
547	#125	—	2	1	no	—
548	#125	C₂³×C₃₁	1	4	yes	—
549	#124	—	2	2	no	—
550	#123	—	2	4	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	1	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
564	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
565	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
566	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
567	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
568	C₄×Q₈	—	2	1	no	—
569	C₄×Q₈	—	2	1	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	—	2	2	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	—	2	1	no	—
582	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
583	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
584	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
585	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
586	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
588	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
589	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
590	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
591	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
592	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	D₄×C₃₁	1	2	yes	—
598	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
599	C₄×D₄	C₂³×C₃₁	1	2	yes	—
600	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
601	#117	—	2	2	no	—
602	#117	—	2	1	no	—
603	#117	—	2	1	no	—
604	#117	—	2	2	no	—
605	#117	—	2	4	no	—
606	#117	D₄×C₃₁	1	1	yes	characteristic
607	#117	D₄×C₃₁	1	2	yes	—
608	#117	C₂³×C₃₁	1	4	yes	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	2	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
615	C₂×C₄²	—	2	2	no	—
616	C₂×C₄²	—	2	1	no	—
617	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
619	#107	C₂³×C₃₁	1	2	yes	—
620	#107	C₂³×C₃₁	1	4	yes	—
621	#107	C₂³×C₃₁	1	2	yes	—
622	#106	C₂³×C₃₁	1	4	yes	—
623	#106	C₂³×C₃₁	1	4	yes	—
624	#106	C₂³×C₃₁	1	4	yes	—
625	#106	C₂³×C₃₁	1	4	yes	—
626	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
627	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
628	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
629	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
630	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
631	#103	C₂³×C₃₁	1	4	yes	—
632	#103	C₂³×C₃₁	1	4	yes	—
633	#103	C₂³×C₃₁	1	2	yes	—
634	#103	C₂³×C₃₁	1	4	yes	—
635	#103	C₂³×C₃₁	1	4	yes	—
636	#103	C₂³×C₃₁	1	2	yes	—
637	#103	C₂³×C₃₁	1	2	yes	—
638	#103	C₂³×C₃₁	1	2	yes	—
639	#103	C₂³×C₃₁	1	4	yes	—
640	#103	C₂³×C₃₁	1	4	yes	—
641	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
642	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
643	#97	C₂³×C₃₁	1	4	yes	—
644	C₄×C₈	C₂³×C₃₁	1	2	yes	—
645	C₃₁	#62113	1	1	yes	characteristic, direct product factor, Sylow
646	#41	—	2	4	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	2	no	—
649	C₂×Q₈	—	2	1	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	4	no	—
656	C₂×Q₈	—	4	1	no	—
657	C₂×Q₈	—	4	2	no	—
658	C₂×Q₈	—	4	4	no	—
659	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
660	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
661	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
662	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
663	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
664	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
665	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
672	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
674	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
677	Q₁₆	—	2	4	no	—
678	Q₁₆	—	4	4	no	—
679	Q₁₆	—	4	2	no	—
680	M₁₆	—	4	4	no	—
681	C₂×C₈	—	4	2	no	—
682	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
683	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
684	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
716	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
717	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
718	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
720	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
722	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
723	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
731	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
732	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	1	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	4	no	—
741	C₄²	—	2	4	no	—
742	C₄²	—	2	2	no	—
743	C₄²	C₂×D₄×C₃₁	1	2	yes	—
744	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₃₁	1	2	yes	—
746	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
747	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
748	C₄²	C₂⁴×C₃₁	1	2	yes	—
749	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
750	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
751	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
752	Q₈	—	2	2	no	—
753	Q₈	—	2	1	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	2	1	no	—
756	Q₈	—	2	2	no	—
757	Q₈	—	2	2	no	—
758	Q₈	—	2	2	no	—
759	Q₈	—	2	1	no	—
760	Q₈	—	4	2	no	—
761	Q₈	—	4	4	no	—
762	Q₈	—	4	2	no	—
763	Q₈	—	4	4	no	—
764	Q₈	—	4	4	no	—
765	Q₈	—	8	2	no	—
766	Q₈	—	8	1	no	—
767	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
768	D₄	—	2	4	no	—
769	D₄	—	2	2	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	8	1	no	—
790	C₂×C₄	—	8	2	no	—
791	C₂×C₄	C₃₁×#137	1	4	yes	—
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	2	yes	—
795	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
800	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
801	C₈	—	2	2	no	—
802	C₈	—	2	4	no	—
803	C₈	—	2	2	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	C₂×C₃₁×#137	1	2	yes	—
810	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
811	C₄	—	2	1	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	4	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	C₂×C₃₁×#137	1	2	yes	—
827	C₄	C₂×C₃₁×#137	1	2	yes	—
828	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
829	C₄	C₃₁×#585	1	1	yes	characteristic
830	C₂	—	2	2	no	—
831	C₂	—	4	2	no	—
832	C₂	C₃₁×#3489	1	1	yes	characteristic
833	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic
834	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	C₂×#41×C₃₁	D₄
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
3. C₃₁×#3387	C₂	semidirect
4. C₃₁×#3374	C₂	semidirect
5. C₃₁×#3356	C₂	semidirect
6. C₃₁×#3344	C₂	semidirect
7. C₃₁×#3328	C₂	semidirect
8. C₃₁×#3312	C₂	semidirect
9. C₃₁×#3255	C₂	semidirect
10. C₃₁×#3249	C₂	semidirect
11. C₃₁×#3237	C₂	semidirect
12. C₃₁×#3229	C₂	semidirect
13. C₃₁×#3113	C₂	semidirect
14. C₃₁×#3104	C₂	semidirect
15. C₃₁×#3078	C₂	semidirect
16. C₂×C₃₁×#475	C₂	semidirect
332. #62113	C₃₁	direct (N × H)
389. #3387	C₂×C₃₁	semidirect
390. #3374	C₂×C₃₁	semidirect
391. #3356	C₂×C₃₁	semidirect
392. #3344	C₂×C₃₁	semidirect
393. #3328	C₂×C₃₁	semidirect
394. #3312	C₂×C₃₁	semidirect
395. #3255	C₂×C₃₁	semidirect
396. #3249	C₂×C₃₁	semidirect
397. #3237	C₂×C₃₁	semidirect
398. #3229	C₂×C₃₁	semidirect
399. #3113	C₂×C₃₁	semidirect
400. #3104	C₂×C₃₁	semidirect
401. #3078	C₂×C₃₁	semidirect
402. C₂×#475	C₂×C₃₁	semidirect
645. C₃₁	#62113	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
Q₈×#41×C₃₁	2
C₃₁×#3387	2
C₃₁×#3374	2
C₃₁×#3356	2
C₃₁×#3344	2
C₃₁×#3328	2
C₃₁×#3312	2
C₃₁×#3255	2
C₃₁×#3249	2
C₃₁×#3237	2
C₃₁×#3229	2
C₃₁×#3113	2
C₃₁×#3104	2
C₃₁×#3078	2
C₂×C₃₁×#475	2
C₃₁×#2989	2
#62113	31

Subgroups — C31×#62113 #21518872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62113 #21518872