Subgroups — C₃₁×#62240 #21518999

Order 7936.

1632 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3518	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3387	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3356	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3349	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3327	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3316	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3127	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3082	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3080	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#564	—	2	1	no	—
21	C₃₁×#563	—	2	1	no	—
22	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×#557	C₂²	1	2	yes	—
24	C₃₁×#556	—	2	2	no	—
25	C₃₁×#556	—	2	1	no	—
26	C₃₁×#556	C₂²	1	1	yes	characteristic
27	C₃₁×#556	C₂²	1	2	yes	—
28	C₃₁×#555	—	2	1	no	—
29	C₃₁×#555	C₂²	1	1	yes	characteristic
30	C₃₁×#554	C₂²	1	2	yes	—
31	C₃₁×#552	—	2	2	no	—
32	C₃₁×#552	C₂²	1	2	yes	—
33	C₃₁×#552	C₂²	1	2	yes	—
34	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#548	C₂²	1	2	yes	—
36	C₃₁×#544	—	2	1	no	—
37	C₃₁×#544	C₂²	1	2	yes	—
38	C₃₁×#542	—	2	2	no	—
39	C₃₁×#542	C₂²	1	2	yes	—
40	C₃₁×#541	—	2	2	no	—
41	C₃₁×#541	C₂²	1	2	yes	—
42	C₃₁×#539	—	2	1	no	—
43	C₃₁×#533	—	2	1	no	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#533	C₂²	1	1	yes	characteristic
46	C₃₁×#529	—	2	1	no	—
47	C₃₁×#529	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
49	C₃₁×#519	C₂²	1	2	yes	—
50	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	—
52	C₃₁×#501	C₂²	1	2	yes	—
53	C₃₁×#498	C₂²	1	2	yes	—
54	C₃₁×#491	C₂²	1	2	yes	—
55	C₃₁×#489	C₂²	1	2	yes	—
56	C₃₁×#488	C₂²	1	2	yes	—
57	C₃₁×#485	C₂²	1	2	yes	—
58	C₃₁×#485	C₂²	1	2	yes	—
59	C₃₁×#485	C₂²	1	2	yes	—
60	C₃₁×#485	C₂²	1	2	yes	—
61	C₃₁×#484	C₂²	1	2	yes	—
62	C₃₁×#483	C₂²	1	2	yes	—
63	C₃₁×#483	C₂²	1	2	yes	—
64	C₃₁×#482	C₂²	1	2	yes	—
65	C₃₁×#481	C₂²	1	2	yes	—
66	C₃₁×#479	C₂²	1	2	yes	—
67	C₃₁×#479	C₂²	1	2	yes	—
68	C₃₁×#479	C₂²	1	2	yes	—
69	C₃₁×#479	C₂²	1	2	yes	—
70	C₃₁×#479	C₂²	1	2	yes	—
71	C₃₁×#479	C₂²	1	2	yes	—
72	C₃₁×#478	C₂²	1	2	yes	—
73	C₃₁×#478	C₂²	1	2	yes	—
74	C₃₁×#477	C₂²	1	1	yes	characteristic
75	C₃₁×#477	C₂²	1	2	yes	—
76	C₃₁×#477	C₂²	1	2	yes	—
77	C₃₁×#476	C₂²	1	1	yes	characteristic
78	C₃₁×#475	C₂²	1	2	yes	—
79	C₃₁×#475	C₂²	1	2	yes	—
80	C₃₁×#475	C₂²	1	2	yes	—
81	C₃₁×#475	C₂²	1	2	yes	—
82	C₃₁×#470	C₂²	1	2	yes	—
83	C₃₁×#470	C₂²	1	2	yes	—
84	C₃₁×#470	C₂²	1	2	yes	—
85	C₃₁×#468	C₂²	1	2	yes	—
86	C₃₁×#467	C₂²	1	2	yes	—
87	C₃₁×#465	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#464	C₂²	1	2	yes	—
90	C₃₁×#462	C₂²	1	1	yes	characteristic
91	C₃₁×#462	C₂²	1	2	yes	—
92	C₃₁×#462	C₂²	1	2	yes	—
93	C₃₁×#461	C₂²	1	1	yes	characteristic
94	C₃₁×#452	C₂²	1	2	yes	—
95	C₃₁×#451	C₂²	1	2	yes	—
96	C₃₁×#451	C₂²	1	2	yes	—
97	C₃₁×#446	C₂²	1	2	yes	—
98	C₃₁×#441	C₂²	1	2	yes	—
99	C₃₁×#441	C₂²	1	2	yes	—
100	C₃₁×#441	C₂²	1	2	yes	—
101	C₃₁×#440	C₂²	1	2	yes	—
102	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
103	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
104	C₃₁×#436	C₂²	1	2	yes	—
105	C₃₁×#435	C₂²	1	2	yes	—
106	C₃₁×#435	C₂²	1	2	yes	—
107	C₃₁×#433	C₂²	1	2	yes	—
108	C₃₁×#432	C₂²	1	1	yes	characteristic
109	C₃₁×#428	C₂²	1	1	yes	characteristic
110	C₃₁×#428	C₂²	1	1	yes	characteristic
111	C₃₁×#428	C₂²	1	2	yes	—
112	C₃₁×#427	C₂²	1	2	yes	—
113	C₃₁×#424	C₂²	1	2	yes	—
114	C₃₁×#423	C₂²	1	1	yes	characteristic
115	C₃₁×#419	C₂²	1	2	yes	—
116	C₃₁×#417	C₂²	1	1	yes	characteristic
117	C₃₁×#417	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×#103	C₂²	1	2	yes	—
119	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
129	C₃₁×C₄⋊Q₈	—	2	2	no	—
130	C₃₁×C₄⋊Q₈	—	2	1	no	—
131	C₃₁×C₄⋊Q₈	—	2	1	no	—
132	C₃₁×C₄⋊Q₈	—	2	2	no	—
133	C₃₁×C₄⋊Q₈	—	2	2	no	—
134	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#126	—	2	2	no	—
148	C₃₁×#126	D₄	1	2	yes	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	—	2	2	no	—
153	C₃₁×#125	—	2	2	no	—
154	C₃₁×#125	—	2	2	no	—
155	C₃₁×#125	—	2	2	no	—
156	C₃₁×#125	—	2	2	no	—
157	C₃₁×#125	—	2	1	no	—
158	C₃₁×#125	—	2	1	no	—
159	C₃₁×#125	—	2	1	no	—
160	C₃₁×#125	—	2	1	no	—
161	C₃₁×#125	D₄	1	1	yes	characteristic
162	C₃₁×#125	C₂³	1	2	yes	—
163	C₃₁×#125	C₂³	1	2	yes	—
164	C₃₁×#125	C₂³	1	2	yes	—
165	C₃₁×#124	—	2	2	no	—
166	C₃₁×#124	—	2	2	no	—
167	C₃₁×#124	—	2	2	no	—
168	C₃₁×#124	—	2	2	no	—
169	C₃₁×#124	D₄	1	1	yes	characteristic
170	C₃₁×#124	C₂³	1	2	yes	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	—	2	2	no	—
173	C₃₁×#123	—	2	2	no	—
174	C₃₁×#123	D₄	1	2	yes	—
175	C₃₁×C₂²⋊Q₈	—	2	1	no	—
176	C₃₁×C₂²⋊Q₈	—	2	1	no	—
177	C₃₁×C₂²⋊Q₈	—	2	1	no	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
186	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₃₁×#121	—	2	1	no	—
192	C₃₁×#121	—	2	2	no	—
193	C₃₁×#121	D₄	1	1	yes	characteristic
194	C₃₁×#121	C₂³	1	2	yes	—
195	C₄×Q₈×C₃₁	—	2	1	no	—
196	C₄×Q₈×C₃₁	—	2	2	no	—
197	C₄×Q₈×C₃₁	—	2	2	no	—
198	C₄×Q₈×C₃₁	—	2	2	no	—
199	C₄×Q₈×C₃₁	—	2	2	no	—
200	C₄×Q₈×C₃₁	—	2	1	no	—
201	C₄×Q₈×C₃₁	—	2	1	no	—
202	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
203	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
204	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
205	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
206	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
207	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
210	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₄×D₄×C₃₁	—	2	1	no	—
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	—	2	1	no	—
214	C₄×D₄×C₃₁	—	2	1	no	—
215	C₄×D₄×C₃₁	—	2	2	no	—
216	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₃₁	C₂³	1	2	yes	—
220	C₃₁×#117	—	2	1	no	—
221	C₃₁×#117	—	2	1	no	—
222	C₃₁×#117	—	2	1	no	—
223	C₃₁×#117	—	2	1	no	—
224	C₃₁×#117	—	2	2	no	—
225	C₃₁×#117	—	2	2	no	—
226	C₃₁×#117	—	2	2	no	—
227	C₃₁×#117	—	2	2	no	—
228	C₃₁×#117	—	2	1	no	—
229	C₃₁×#117	C₂³	1	2	yes	—
230	C₃₁×#117	C₂³	1	2	yes	—
231	C₃₁×#117	C₂³	1	1	yes	characteristic
232	C₃₁×#117	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
234	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₃₁	—	2	1	no	—
239	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#107	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×#106	C₂³	1	2	yes	—
249	C₃₁×#106	C₂³	1	2	yes	—
250	C₃₁×#106	C₂³	1	2	yes	—
251	C₃₁×#106	C₂³	1	2	yes	—
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#103	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₃₁×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	#41×C₃₁	—	2	2	no	—
281	#41×C₃₁	—	4	1	no	—
282	C₂×Q₈×C₃₁	—	2	2	no	—
283	C₂×Q₈×C₃₁	—	2	1	no	—
284	C₂×Q₈×C₃₁	—	2	2	no	—
285	C₂×Q₈×C₃₁	—	2	1	no	—
286	C₂×Q₈×C₃₁	—	2	2	no	—
287	C₂×Q₈×C₃₁	—	2	4	no	—
288	C₂×Q₈×C₃₁	—	4	2	no	—
289	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
290	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
291	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
293	C₂×D₄×C₃₁	—	2	1	no	—
294	C₂×D₄×C₃₁	—	2	2	no	—
295	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
297	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	—	2	1	no	—
299	C₂²×C₄×C₃₁	—	2	2	no	—
300	C₂²×C₄×C₃₁	—	2	1	no	—
301	C₂²×C₄×C₃₁	—	2	2	no	—
302	C₂²×C₄×C₃₁	—	2	1	no	—
303	C₂²×C₄×C₃₁	—	2	1	no	—
304	C₂²×C₄×C₃₁	—	2	1	no	—
305	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
309	Q₁₆×C₃₁	—	2	4	no	—
310	Q₁₆×C₃₁	—	4	2	no	—
311	Q₁₆×C₃₁	—	4	2	no	—
312	SD₁₆×C₃₁	—	4	2	no	—
313	M₁₆×C₃₁	—	4	2	no	—
314	M₁₆×C₃₁	—	4	1	no	—
315	M₁₆×C₃₁	—	4	1	no	—
316	C₂×C₈×C₃₁	—	4	2	no	—
317	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
318	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
319	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
320	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₃₁	—	2	2	no	—
322	C₄⋊C₄×C₃₁	—	2	2	no	—
323	C₄⋊C₄×C₃₁	—	2	2	no	—
324	C₄⋊C₄×C₃₁	—	2	2	no	—
325	C₄⋊C₄×C₃₁	—	2	1	no	—
326	C₄⋊C₄×C₃₁	—	2	2	no	—
327	C₄⋊C₄×C₃₁	—	2	1	no	—
328	C₄⋊C₄×C₃₁	—	2	1	no	—
329	C₄⋊C₄×C₃₁	—	2	1	no	—
330	C₄⋊C₄×C₃₁	—	2	1	no	—
331	C₄⋊C₄×C₃₁	—	2	1	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	—	2	1	no	—
336	C₄⋊C₄×C₃₁	—	2	2	no	—
337	C₄⋊C₄×C₃₁	—	2	2	no	—
338	C₄⋊C₄×C₃₁	—	2	2	no	—
339	C₄⋊C₄×C₃₁	—	2	1	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	1	no	—
343	C₄⋊C₄×C₃₁	—	2	2	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	1	no	—
347	C₄⋊C₄×C₃₁	—	2	2	no	—
348	C₄⋊C₄×C₃₁	—	2	2	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
352	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
355	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
359	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂²⋊C₄×C₃₁	—	2	2	no	—
364	C₂²⋊C₄×C₃₁	—	2	2	no	—
365	C₂²⋊C₄×C₃₁	—	2	2	no	—
366	C₂²⋊C₄×C₃₁	—	2	2	no	—
367	C₂²⋊C₄×C₃₁	—	2	1	no	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	2	no	—
370	C₂²⋊C₄×C₃₁	—	2	2	no	—
371	C₂²⋊C₄×C₃₁	—	2	1	no	—
372	C₂²⋊C₄×C₃₁	—	2	1	no	—
373	C₂²⋊C₄×C₃₁	—	2	2	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	no	—
376	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
377	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
378	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
379	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
380	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
381	C₄²×C₃₁	—	2	1	no	—
382	C₄²×C₃₁	—	2	1	no	—
383	C₄²×C₃₁	—	2	1	no	—
384	C₄²×C₃₁	—	2	2	no	—
385	C₄²×C₃₁	—	2	2	no	—
386	C₄²×C₃₁	—	2	2	no	—
387	C₄²×C₃₁	—	2	2	no	—
388	C₄²×C₃₁	—	2	2	no	—
389	C₄²×C₃₁	—	2	2	no	—
390	C₄²×C₃₁	—	2	2	no	—
391	C₄²×C₃₁	—	2	2	no	—
392	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₃₁	C₂⁴	1	2	yes	—
395	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
397	#62240	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
398	C₂³×C₃₁	—	2	1	no	—
399	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
400	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
401	Q₈×C₃₁	—	2	1	no	—
402	Q₈×C₃₁	—	2	2	no	—
403	Q₈×C₃₁	—	2	2	no	—
404	Q₈×C₃₁	—	2	2	no	—
405	Q₈×C₃₁	—	2	2	no	—
406	Q₈×C₃₁	—	4	1	no	—
407	Q₈×C₃₁	—	4	4	no	—
408	Q₈×C₃₁	—	8	1	no	—
409	Q₈×C₃₁	—	8	1	no	—
410	Q₈×C₃₁	—	8	2	no	—
411	Q₈×C₃₁	—	8	2	no	—
412	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
413	D₄×C₃₁	—	2	1	no	—
414	D₄×C₃₁	—	2	1	no	—
415	D₄×C₃₁	—	4	1	no	—
416	D₄×C₃₁	—	4	2	no	—
417	D₄×C₃₁	—	4	2	no	—
418	D₄×C₃₁	—	8	2	no	—
419	C₂×C₄×C₃₁	—	2	1	no	—
420	C₂×C₄×C₃₁	—	2	2	no	—
421	C₂×C₄×C₃₁	—	2	1	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	1	no	—
424	C₂×C₄×C₃₁	—	2	1	no	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	2	2	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	1	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	2	2	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	4	1	no	—
433	C₂×C₄×C₃₁	—	4	1	no	—
434	C₂×C₄×C₃₁	—	4	2	no	—
435	C₂×C₄×C₃₁	—	4	4	no	—
436	C₂×C₄×C₃₁	—	4	2	no	—
437	C₂×C₄×C₃₁	—	4	2	no	—
438	C₂×C₄×C₃₁	—	8	1	no	—
439	C₂×C₄×C₃₁	—	8	1	no	—
440	C₂×C₄×C₃₁	—	8	2	no	—
441	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
450	C₈×C₃₁	—	2	2	no	—
451	C₈×C₃₁	—	2	2	no	—
452	C₈×C₃₁	—	2	2	no	—
453	C₈×C₃₁	—	2	2	no	—
454	#3563	C₂×C₃₁	1	1	yes	characteristic, complemented
455	#3518	C₂×C₃₁	1	1	yes	characteristic
456	#3387	C₂×C₃₁	1	2	yes	complemented
457	#3377	C₂×C₃₁	1	2	yes	complemented
458	#3356	C₂×C₃₁	1	2	yes	complemented
459	#3349	C₂×C₃₁	1	2	yes	complemented
460	#3348	C₂×C₃₁	1	2	yes	complemented
461	#3327	C₂×C₃₁	1	2	yes	complemented
462	#3316	C₂×C₃₁	1	2	yes	complemented
463	#3312	C₂×C₃₁	1	2	yes	complemented
464	#3258	C₂×C₃₁	1	2	yes	complemented
465	#3255	C₂×C₃₁	1	1	yes	characteristic, complemented
466	#3244	C₂×C₃₁	1	2	yes	complemented
467	#3236	C₂×C₃₁	1	1	yes	characteristic, complemented
468	#3127	C₂×C₃₁	1	2	yes	complemented
469	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
470	#3082	C₂×C₃₁	1	2	yes	complemented
471	#3080	C₂×C₃₁	1	1	yes	characteristic, complemented
472	#2995	C₂×C₃₁	1	1	yes	characteristic, complemented
473	C₂²×C₃₁	—	2	1	no	—
474	C₂²×C₃₁	—	2	1	no	—
475	C₂²×C₃₁	—	2	2	no	—
476	C₂²×C₃₁	—	2	2	no	—
477	C₂²×C₃₁	—	2	2	no	—
478	C₂²×C₃₁	—	2	1	no	—
479	C₂²×C₃₁	—	4	1	no	—
480	C₂²×C₃₁	—	4	1	no	—
481	C₂²×C₃₁	—	4	1	no	—
482	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
483	C₄×C₃₁	—	2	1	no	—
484	C₄×C₃₁	—	2	1	no	—
485	C₄×C₃₁	—	2	1	no	—
486	C₄×C₃₁	—	2	1	no	—
487	C₄×C₃₁	—	2	2	no	—
488	C₄×C₃₁	—	2	2	no	—
489	C₄×C₃₁	—	2	1	no	—
490	C₄×C₃₁	—	2	2	no	—
491	C₄×C₃₁	—	2	2	no	—
492	C₄×C₃₁	—	4	1	no	—
493	C₄×C₃₁	—	4	2	no	—
494	C₄×C₃₁	—	4	2	no	—
495	C₄×C₃₁	—	4	1	no	—
496	C₄×C₃₁	—	4	2	no	—
497	C₄×C₃₁	—	4	2	no	—
498	C₄×C₃₁	—	4	2	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
501	C₄×C₃₁	#585	1	1	yes	characteristic
502	#564	—	2	1	no	—
503	#563	—	2	1	no	—
504	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
505	#557	C₂²×C₃₁	1	2	yes	—
506	#556	—	2	2	no	—
507	#556	—	2	1	no	—
508	#556	C₂²×C₃₁	1	1	yes	characteristic
509	#556	C₂²×C₃₁	1	2	yes	—
510	#555	—	2	1	no	—
511	#555	C₂²×C₃₁	1	1	yes	characteristic
512	#554	C₂²×C₃₁	1	2	yes	—
513	#552	—	2	2	no	—
514	#552	C₂²×C₃₁	1	2	yes	—
515	#552	C₂²×C₃₁	1	2	yes	—
516	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
517	#548	C₂²×C₃₁	1	2	yes	—
518	#544	—	2	1	no	—
519	#544	C₂²×C₃₁	1	2	yes	—
520	#542	—	2	2	no	—
521	#542	C₂²×C₃₁	1	2	yes	—
522	#541	—	2	2	no	—
523	#541	C₂²×C₃₁	1	2	yes	—
524	#539	—	2	1	no	—
525	#533	—	2	1	no	—
526	#533	C₂²×C₃₁	1	1	yes	characteristic
527	#533	C₂²×C₃₁	1	1	yes	characteristic
528	#529	—	2	1	no	—
529	#529	C₂²×C₃₁	1	1	yes	characteristic
530	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
531	#519	C₂²×C₃₁	1	2	yes	—
532	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
533	#501	C₂²×C₃₁	1	2	yes	—
534	#501	C₂²×C₃₁	1	2	yes	—
535	#498	C₂²×C₃₁	1	2	yes	—
536	#491	C₂²×C₃₁	1	2	yes	—
537	#489	C₂²×C₃₁	1	2	yes	—
538	#488	C₂²×C₃₁	1	2	yes	—
539	#485	C₂²×C₃₁	1	2	yes	—
540	#485	C₂²×C₃₁	1	2	yes	—
541	#485	C₂²×C₃₁	1	2	yes	—
542	#485	C₂²×C₃₁	1	2	yes	—
543	#484	C₂²×C₃₁	1	2	yes	—
544	#483	C₂²×C₃₁	1	2	yes	—
545	#483	C₂²×C₃₁	1	2	yes	—
546	#482	C₂²×C₃₁	1	2	yes	—
547	#481	C₂²×C₃₁	1	2	yes	—
548	#479	C₂²×C₃₁	1	2	yes	—
549	#479	C₂²×C₃₁	1	2	yes	—
550	#479	C₂²×C₃₁	1	2	yes	—
551	#479	C₂²×C₃₁	1	2	yes	—
552	#479	C₂²×C₃₁	1	2	yes	—
553	#479	C₂²×C₃₁	1	2	yes	—
554	#478	C₂²×C₃₁	1	2	yes	—
555	#478	C₂²×C₃₁	1	2	yes	—
556	#477	C₂²×C₃₁	1	1	yes	characteristic
557	#477	C₂²×C₃₁	1	2	yes	—
558	#477	C₂²×C₃₁	1	2	yes	—
559	#476	C₂²×C₃₁	1	1	yes	characteristic
560	#475	C₂²×C₃₁	1	2	yes	—
561	#475	C₂²×C₃₁	1	2	yes	—
562	#475	C₂²×C₃₁	1	2	yes	—
563	#475	C₂²×C₃₁	1	2	yes	—
564	#470	C₂²×C₃₁	1	2	yes	—
565	#470	C₂²×C₃₁	1	2	yes	—
566	#470	C₂²×C₃₁	1	2	yes	—
567	#468	C₂²×C₃₁	1	2	yes	—
568	#467	C₂²×C₃₁	1	2	yes	—
569	#465	C₂²×C₃₁	1	2	yes	—
570	#464	C₂²×C₃₁	1	2	yes	—
571	#464	C₂²×C₃₁	1	2	yes	—
572	#462	C₂²×C₃₁	1	1	yes	characteristic
573	#462	C₂²×C₃₁	1	2	yes	—
574	#462	C₂²×C₃₁	1	2	yes	—
575	#461	C₂²×C₃₁	1	1	yes	characteristic
576	#452	C₂²×C₃₁	1	2	yes	—
577	#451	C₂²×C₃₁	1	2	yes	—
578	#451	C₂²×C₃₁	1	2	yes	—
579	#446	C₂²×C₃₁	1	2	yes	—
580	#441	C₂²×C₃₁	1	2	yes	—
581	#441	C₂²×C₃₁	1	2	yes	—
582	#441	C₂²×C₃₁	1	2	yes	—
583	#440	C₂²×C₃₁	1	2	yes	—
584	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
585	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
586	#436	C₂²×C₃₁	1	2	yes	—
587	#435	C₂²×C₃₁	1	2	yes	—
588	#435	C₂²×C₃₁	1	2	yes	—
589	#433	C₂²×C₃₁	1	2	yes	—
590	#432	C₂²×C₃₁	1	1	yes	characteristic
591	#428	C₂²×C₃₁	1	1	yes	characteristic
592	#428	C₂²×C₃₁	1	1	yes	characteristic
593	#428	C₂²×C₃₁	1	2	yes	—
594	#427	C₂²×C₃₁	1	2	yes	—
595	#424	C₂²×C₃₁	1	2	yes	—
596	#423	C₂²×C₃₁	1	1	yes	characteristic
597	#419	C₂²×C₃₁	1	2	yes	—
598	#417	C₂²×C₃₁	1	1	yes	characteristic
599	#417	C₂²×C₃₁	1	1	yes	characteristic
600	C₂×#103	C₂²×C₃₁	1	2	yes	—
601	C₂×C₃₁	—	4	1	no	—
602	C₂×C₃₁	—	4	2	no	—
603	C₂×C₃₁	—	8	1	no	—
604	C₂×C₃₁	#3489	1	1	yes	characteristic
605	C₂×C₃₁	#3586	1	1	yes	characteristic
606	C₂×C₃₁	#3586	1	1	yes	characteristic
607	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
608	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
609	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
610	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
611	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
612	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
613	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
614	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
615	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
616	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
617	C₄⋊Q₈	—	2	2	no	—
618	C₄⋊Q₈	—	2	1	no	—
619	C₄⋊Q₈	—	2	1	no	—
620	C₄⋊Q₈	—	2	2	no	—
621	C₄⋊Q₈	—	2	2	no	—
622	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
623	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
625	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
626	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
627	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
628	#126	—	2	2	no	—
629	#126	—	2	2	no	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#126	D₄×C₃₁	1	2	yes	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	—	2	2	no	—
641	#125	—	2	2	no	—
642	#125	—	2	2	no	—
643	#125	—	2	2	no	—
644	#125	—	2	2	no	—
645	#125	—	2	1	no	—
646	#125	—	2	1	no	—
647	#125	—	2	1	no	—
648	#125	—	2	1	no	—
649	#125	D₄×C₃₁	1	1	yes	characteristic
650	#125	C₂³×C₃₁	1	2	yes	—
651	#125	C₂³×C₃₁	1	2	yes	—
652	#125	C₂³×C₃₁	1	2	yes	—
653	#124	—	2	2	no	—
654	#124	—	2	2	no	—
655	#124	—	2	2	no	—
656	#124	—	2	2	no	—
657	#124	D₄×C₃₁	1	1	yes	characteristic
658	#124	C₂³×C₃₁	1	2	yes	—
659	#123	—	2	2	no	—
660	#123	—	2	2	no	—
661	#123	—	2	2	no	—
662	#123	D₄×C₃₁	1	2	yes	—
663	C₂²⋊Q₈	—	2	1	no	—
664	C₂²⋊Q₈	—	2	1	no	—
665	C₂²⋊Q₈	—	2	1	no	—
666	C₂²⋊Q₈	—	2	2	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
674	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
675	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
676	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
677	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
678	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
679	#121	—	2	1	no	—
680	#121	—	2	2	no	—
681	#121	D₄×C₃₁	1	1	yes	characteristic
682	#121	C₂³×C₃₁	1	2	yes	—
683	C₄×Q₈	—	2	1	no	—
684	C₄×Q₈	—	2	2	no	—
685	C₄×Q₈	—	2	2	no	—
686	C₄×Q₈	—	2	2	no	—
687	C₄×Q₈	—	2	2	no	—
688	C₄×Q₈	—	2	1	no	—
689	C₄×Q₈	—	2	1	no	—
690	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
692	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
693	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
694	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
695	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
696	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
697	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
698	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
699	C₄×D₄	—	2	1	no	—
700	C₄×D₄	—	2	2	no	—
701	C₄×D₄	—	2	1	no	—
702	C₄×D₄	—	2	1	no	—
703	C₄×D₄	—	2	2	no	—
704	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
705	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
706	C₄×D₄	C₂³×C₃₁	1	2	yes	—
707	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
708	#117	—	2	1	no	—
709	#117	—	2	1	no	—
710	#117	—	2	1	no	—
711	#117	—	2	1	no	—
712	#117	—	2	2	no	—
713	#117	—	2	2	no	—
714	#117	—	2	2	no	—
715	#117	—	2	2	no	—
716	#117	—	2	1	no	—
717	#117	C₂³×C₃₁	1	1	yes	characteristic
718	#117	C₂³×C₃₁	1	2	yes	—
719	#117	C₂³×C₃₁	1	2	yes	—
720	#117	C₂³×C₃₁	1	2	yes	—
721	C₂×C₄⋊C₄	—	2	1	no	—
722	C₂×C₄⋊C₄	—	2	1	no	—
723	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
726	C₂×C₄²	—	2	1	no	—
727	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
728	#107	C₂³×C₃₁	1	2	yes	—
729	#107	C₂³×C₃₁	1	2	yes	—
730	#107	C₂³×C₃₁	1	2	yes	—
731	#107	C₂³×C₃₁	1	2	yes	—
732	#107	C₂³×C₃₁	1	2	yes	—
733	#106	C₂³×C₃₁	1	2	yes	—
734	#106	C₂³×C₃₁	1	2	yes	—
735	#106	C₂³×C₃₁	1	2	yes	—
736	#106	C₂³×C₃₁	1	2	yes	—
737	#106	C₂³×C₃₁	1	2	yes	—
738	#106	C₂³×C₃₁	1	2	yes	—
739	#106	C₂³×C₃₁	1	2	yes	—
740	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
741	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
742	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
743	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
744	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
745	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
746	#103	C₂³×C₃₁	1	2	yes	—
747	#103	C₂³×C₃₁	1	2	yes	—
748	#103	C₂³×C₃₁	1	2	yes	—
749	#103	C₂³×C₃₁	1	2	yes	—
750	#103	C₂³×C₃₁	1	2	yes	—
751	#103	C₂³×C₃₁	1	2	yes	—
752	#103	C₂³×C₃₁	1	2	yes	—
753	#103	C₂³×C₃₁	1	2	yes	—
754	#103	C₂³×C₃₁	1	2	yes	—
755	#103	C₂³×C₃₁	1	2	yes	—
756	#103	C₂³×C₃₁	1	2	yes	—
757	#103	C₂³×C₃₁	1	2	yes	—
758	#103	C₂³×C₃₁	1	2	yes	—
759	#102	C₂³×C₃₁	1	2	yes	—
760	#102	C₂³×C₃₁	1	2	yes	—
761	#102	C₂³×C₃₁	1	2	yes	—
762	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
763	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
765	#97	C₂³×C₃₁	1	2	yes	—
766	#97	C₂³×C₃₁	1	2	yes	—
767	C₄×C₈	C₂³×C₃₁	1	2	yes	—
768	C₃₁	#62240	1	1	yes	characteristic, direct product factor, Sylow
769	#41	—	2	2	no	—
770	#41	—	4	1	no	—
771	C₂×Q₈	—	2	2	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	2	1	no	—
775	C₂×Q₈	—	2	2	no	—
776	C₂×Q₈	—	2	4	no	—
777	C₂×Q₈	—	4	2	no	—
778	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
779	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
780	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
781	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
785	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
786	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
787	C₂²×C₄	—	2	1	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	1	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
798	Q₁₆	—	2	4	no	—
799	Q₁₆	—	4	2	no	—
800	Q₁₆	—	4	2	no	—
801	SD₁₆	—	4	2	no	—
802	M₁₆	—	4	2	no	—
803	M₁₆	—	4	1	no	—
804	M₁₆	—	4	1	no	—
805	C₂×C₈	—	4	2	no	—
806	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
807	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
808	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
809	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	1	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	1	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
841	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
842	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
843	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
844	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
845	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
846	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
847	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
848	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
849	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
850	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
851	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	1	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	1	no	—
861	C₂²⋊C₄	—	2	1	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
866	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
867	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
868	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
869	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
870	C₄²	—	2	1	no	—
871	C₄²	—	2	1	no	—
872	C₄²	—	2	1	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	2	no	—
880	C₄²	—	2	2	no	—
881	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
882	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
883	C₄²	C₂⁴×C₃₁	1	2	yes	—
884	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
885	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
886	C₂³	—	2	1	no	—
887	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
888	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
889	Q₈	—	2	1	no	—
890	Q₈	—	2	2	no	—
891	Q₈	—	2	2	no	—
892	Q₈	—	2	2	no	—
893	Q₈	—	2	2	no	—
894	Q₈	—	4	1	no	—
895	Q₈	—	4	4	no	—
896	Q₈	—	8	1	no	—
897	Q₈	—	8	1	no	—
898	Q₈	—	8	2	no	—
899	Q₈	—	8	2	no	—
900	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
901	D₄	—	2	1	no	—
902	D₄	—	2	1	no	—
903	D₄	—	4	1	no	—
904	D₄	—	4	2	no	—
905	D₄	—	4	2	no	—
906	D₄	—	8	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	4	2	no	—
926	C₂×C₄	—	8	1	no	—
927	C₂×C₄	—	8	1	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
933	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
934	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
937	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
938	C₈	—	2	2	no	—
939	C₈	—	2	2	no	—
940	C₈	—	2	2	no	—
941	C₈	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	1	no	—
951	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
952	C₄	—	2	1	no	—
953	C₄	—	2	2	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	1	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
970	C₄	C₃₁×#585	1	1	yes	characteristic
971	C₂	—	4	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	8	1	no	—
974	C₂	C₃₁×#3489	1	1	yes	characteristic
975	C₂	C₃₁×#3586	1	1	yes	characteristic
976	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×#3518	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3563	C₂	semidirect
3. C₃₁×#3387	C₂	semidirect
4. C₃₁×#3377	C₂	semidirect
5. C₃₁×#3356	C₂	semidirect
6. C₃₁×#3349	C₂	semidirect
7. C₃₁×#3348	C₂	semidirect
8. C₃₁×#3327	C₂	semidirect
9. C₃₁×#3316	C₂	semidirect
10. C₃₁×#3312	C₂	semidirect
11. C₃₁×#3258	C₂	semidirect
12. C₃₁×#3255	C₂	semidirect
13. C₃₁×#3244	C₂	semidirect
14. C₃₁×#3236	C₂	semidirect
15. C₃₁×#3127	C₂	semidirect
16. C₃₁×#3116	C₂	semidirect
17. C₃₁×#3082	C₂	semidirect
18. C₃₁×#3080	C₂	semidirect
19. C₃₁×#2995	C₂	semidirect
397. #62240	C₃₁	direct (N × H)
454. #3563	C₂×C₃₁	semidirect
456. #3387	C₂×C₃₁	semidirect
457. #3377	C₂×C₃₁	semidirect
458. #3356	C₂×C₃₁	semidirect
459. #3349	C₂×C₃₁	semidirect
460. #3348	C₂×C₃₁	semidirect
461. #3327	C₂×C₃₁	semidirect
462. #3316	C₂×C₃₁	semidirect
463. #3312	C₂×C₃₁	semidirect
464. #3258	C₂×C₃₁	semidirect
465. #3255	C₂×C₃₁	semidirect
466. #3244	C₂×C₃₁	semidirect
467. #3236	C₂×C₃₁	semidirect
468. #3127	C₂×C₃₁	semidirect
469. #3116	C₂×C₃₁	semidirect
470. #3082	C₂×C₃₁	semidirect
471. #3080	C₂×C₃₁	semidirect
472. #2995	C₂×C₃₁	semidirect
768. C₃₁	#62240	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×#3563	2
C₃₁×#3518	2
C₃₁×#3387	2
C₃₁×#3377	2
C₃₁×#3356	2
C₃₁×#3349	2
C₃₁×#3348	2
C₃₁×#3327	2
C₃₁×#3316	2
C₃₁×#3312	2
C₃₁×#3258	2
C₃₁×#3255	2
C₃₁×#3244	2
C₃₁×#3236	2
C₃₁×#3127	2
C₃₁×#3116	2
C₃₁×#3082	2
C₃₁×#3080	2
C₃₁×#2995	2
#62240	31

Subgroups — C31×#62240 #21518999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62240 #21518999