Subgroups — C₃₁×#62599 #21519358

Order 7936.

1648 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×#3552	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3374	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3316	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3315	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3223	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3181	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3177	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#491	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2968	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#564	—	2	1	no	—
21	C₃₁×#563	—	2	2	no	—
22	C₃₁×#563	—	2	1	no	—
23	C₃₁×#557	C₂²	1	1	yes	characteristic
24	C₃₁×#557	C₂²	1	2	yes	—
25	C₃₁×#556	C₂²	1	1	yes	characteristic
26	C₃₁×#554	—	2	1	no	—
27	C₃₁×#554	C₂²	1	2	yes	—
28	C₃₁×#553	—	2	1	no	—
29	C₃₁×#552	—	2	2	no	—
30	C₃₁×#552	C₂²	1	2	yes	—
31	C₃₁×#552	C₂²	1	2	yes	—
32	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
33	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#548	C₂²	1	2	yes	—
35	C₃₁×#547	C₂²	1	1	yes	characteristic
36	C₃₁×#544	—	2	1	no	—
37	C₃₁×#544	—	2	1	no	—
38	C₃₁×#544	C₂²	1	2	yes	—
39	C₃₁×#542	—	2	1	no	—
40	C₃₁×#541	—	2	2	no	—
41	C₃₁×#541	C₂²	1	2	yes	—
42	C₃₁×#541	C₂²	1	2	yes	—
43	C₃₁×#539	—	2	2	no	—
44	C₃₁×#539	—	2	1	no	—
45	C₃₁×#536	C₂²	1	2	yes	—
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
48	C₃₁×#529	C₂²	1	1	yes	characteristic
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	1	yes	characteristic
52	C₃₁×#499	C₂²	1	2	yes	—
53	C₃₁×#497	C₂²	1	1	yes	characteristic
54	C₃₁×#494	C₂²	1	2	yes	—
55	C₃₁×#491	C₂²	1	2	yes	—
56	C₃₁×#491	C₂²	1	2	yes	—
57	C₃₁×#491	C₂²	1	2	yes	—
58	C₃₁×#491	C₂²	1	2	yes	—
59	C₃₁×#491	C₂²	1	2	yes	—
60	C₃₁×#491	C₂²	1	1	yes	characteristic
61	C₃₁×#489	C₂²	1	2	yes	—
62	C₃₁×#489	C₂²	1	1	yes	characteristic
63	C₃₁×#488	C₂²	1	2	yes	—
64	C₃₁×#488	C₂²	1	2	yes	—
65	C₃₁×#487	C₂²	1	2	yes	—
66	C₃₁×#487	C₂²	1	2	yes	—
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#484	C₂²	1	1	yes	characteristic
70	C₃₁×#484	C₂²	1	2	yes	—
71	C₃₁×#483	C₂²	1	1	yes	characteristic
72	C₃₁×#483	C₂²	1	2	yes	—
73	C₃₁×#481	C₂²	1	1	yes	characteristic
74	C₃₁×#480	C₂²	1	1	yes	characteristic
75	C₃₁×#479	C₂²	1	2	yes	—
76	C₃₁×#479	C₂²	1	2	yes	—
77	C₃₁×#479	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#477	C₂²	1	2	yes	—
80	C₃₁×#475	C₂²	1	2	yes	—
81	C₃₁×#470	C₂²	1	2	yes	—
82	C₃₁×#470	C₂²	1	2	yes	—
83	C₃₁×#467	C₂²	1	2	yes	—
84	C₃₁×#467	C₂²	1	2	yes	—
85	C₃₁×#467	C₂²	1	2	yes	—
86	C₃₁×#465	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#462	C₂²	1	2	yes	—
90	C₃₁×#462	C₂²	1	2	yes	—
91	C₃₁×#462	C₂²	1	2	yes	—
92	C₃₁×#462	C₂²	1	2	yes	—
93	C₃₁×#452	C₂²	1	2	yes	—
94	C₃₁×#452	C₂²	1	2	yes	—
95	C₃₁×#451	C₂²	1	2	yes	—
96	C₃₁×#451	C₂²	1	2	yes	—
97	C₃₁×#451	C₂²	1	2	yes	—
98	C₃₁×#451	C₂²	1	2	yes	—
99	C₃₁×#446	C₂²	1	2	yes	—
100	C₃₁×#441	C₂²	1	2	yes	—
101	C₃₁×#441	C₂²	1	2	yes	—
102	C₃₁×#441	C₂²	1	2	yes	—
103	C₃₁×#440	C₂²	1	2	yes	—
104	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
105	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
106	C₃₁×#435	C₂²	1	2	yes	—
107	C₃₁×#435	C₂²	1	2	yes	—
108	C₈×D₄×C₃₁	C₂²	1	2	yes	—
109	C₃₁×#433	C₂²	1	2	yes	—
110	C₃₁×#431	C₂²	1	1	yes	characteristic
111	C₃₁×#419	C₂²	1	2	yes	—
112	C₃₁×#417	C₂²	1	2	yes	—
113	C₃₁×#416	C₂²	1	2	yes	—
114	C₂×C₃₁×#103	C₂²	1	2	yes	—
115	C₂×C₃₁×#103	C₂²	1	2	yes	—
116	C₂×C₃₁×#103	C₂²	1	2	yes	—
117	C₃₁×#405	C₂²	1	2	yes	—
118	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	C₂³	1	2	yes	—
120	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
121	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
130	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
131	C₃₁×C₄⋊Q₈	—	2	2	no	—
132	C₃₁×C₄⋊Q₈	—	2	2	no	—
133	C₃₁×C₄⋊Q₈	—	2	1	no	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	—	2	1	no	—
136	C₃₁×C₄⋊Q₈	—	2	1	no	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
143	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
149	C₃₁×#126	—	2	2	no	—
150	C₃₁×#126	—	2	2	no	—
151	C₃₁×#126	—	2	1	no	—
152	C₃₁×#126	D₄	1	2	yes	—
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	2	no	—
158	C₃₁×#125	—	2	2	no	—
159	C₃₁×#125	—	2	2	no	—
160	C₃₁×#125	—	2	2	no	—
161	C₃₁×#125	—	2	2	no	—
162	C₃₁×#125	—	2	2	no	—
163	C₃₁×#125	—	2	1	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	—	2	1	no	—
166	C₃₁×#125	—	2	1	no	—
167	C₃₁×#125	—	2	1	no	—
168	C₃₁×#125	D₄	1	1	yes	characteristic
169	C₃₁×#125	C₂³	1	2	yes	—
170	C₃₁×#125	C₂³	1	2	yes	—
171	C₃₁×#125	C₂³	1	2	yes	—
172	C₃₁×#125	C₂³	1	1	yes	characteristic
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	D₄	1	1	yes	characteristic
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#124	C₂³	1	1	yes	characteristic
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	1	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	D₄	1	2	yes	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	D₄	1	1	yes	characteristic
206	C₃₁×#121	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₃₁	—	2	1	no	—
208	C₄×Q₈×C₃₁	—	2	2	no	—
209	C₄×Q₈×C₃₁	—	2	1	no	—
210	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
213	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
214	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₃₁	—	2	2	no	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	1	no	—
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₃₁	C₂³	1	2	yes	—
224	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
225	C₃₁×#117	—	2	1	no	—
226	C₃₁×#117	—	2	1	no	—
227	C₃₁×#117	—	2	2	no	—
228	C₃₁×#117	—	2	2	no	—
229	C₃₁×#117	—	2	1	no	—
230	C₃₁×#117	C₂³	1	2	yes	—
231	C₃₁×#117	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
233	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
234	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
235	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
236	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
240	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
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×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₃₁×#97	C₂³	1	1	yes	characteristic
275	C₃₁×#97	C₂³	1	1	yes	characteristic
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₃₁	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	#41×C₃₁	—	4	2	no	—
281	#41×C₃₁	—	4	2	no	—
282	C₂×Q₈×C₃₁	—	2	1	no	—
283	C₂×Q₈×C₃₁	—	2	2	no	—
284	C₂×Q₈×C₃₁	—	2	2	no	—
285	C₂×Q₈×C₃₁	—	2	2	no	—
286	C₂×Q₈×C₃₁	—	4	2	no	—
287	C₂×Q₈×C₃₁	—	4	2	no	—
288	C₂×Q₈×C₃₁	—	4	2	no	—
289	C₂×Q₈×C₃₁	—	4	2	no	—
290	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
293	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
295	C₂×D₄×C₃₁	—	2	1	no	—
296	C₂×D₄×C₃₁	—	2	2	no	—
297	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
298	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	—	2	1	no	—
301	C₂²×C₄×C₃₁	—	2	1	no	—
302	C₂²×C₄×C₃₁	—	2	2	no	—
303	C₂²×C₄×C₃₁	—	2	2	no	—
304	C₂²×C₄×C₃₁	—	2	2	no	—
305	C₂²×C₄×C₃₁	—	2	1	no	—
306	C₂²×C₄×C₃₁	—	2	2	no	—
307	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
311	Q₁₆×C₃₁	—	4	2	no	—
312	Q₁₆×C₃₁	—	4	2	no	—
313	Q₁₆×C₃₁	—	4	2	no	—
314	Q₁₆×C₃₁	—	4	2	no	—
315	Q₁₆×C₃₁	—	4	2	no	—
316	SD₁₆×C₃₁	—	4	2	no	—
317	M₁₆×C₃₁	—	4	2	no	—
318	C₂×C₈×C₃₁	—	4	2	no	—
319	C₂×C₈×C₃₁	—	4	2	no	—
320	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
321	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
322	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
323	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
324	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
329	C₄⋊C₄×C₃₁	—	2	2	no	—
330	C₄⋊C₄×C₃₁	—	2	2	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
338	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
343	C₄⋊C₄×C₃₁	—	2	1	no	—
344	C₄⋊C₄×C₃₁	—	2	1	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	2	no	—
347	C₄⋊C₄×C₃₁	—	2	2	no	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	1	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	1	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂²⋊C₄×C₃₁	—	2	2	no	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	—	2	1	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	—	2	2	no	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	1	no	—
380	C₂²⋊C₄×C₃₁	—	2	1	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	1	no	—
383	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
388	C₄²×C₃₁	—	2	2	no	—
389	C₄²×C₃₁	—	2	2	no	—
390	C₄²×C₃₁	—	2	1	no	—
391	C₄²×C₃₁	—	2	2	no	—
392	C₄²×C₃₁	—	2	2	no	—
393	C₄²×C₃₁	—	2	2	no	—
394	C₄²×C₃₁	—	2	2	no	—
395	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₄²×C₃₁	C₂⁴	1	2	yes	—
399	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
400	#62599	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
401	C₂³×C₃₁	—	2	1	no	—
402	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
403	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
404	Q₈×C₃₁	—	2	2	no	—
405	Q₈×C₃₁	—	2	2	no	—
406	Q₈×C₃₁	—	2	2	no	—
407	Q₈×C₃₁	—	2	2	no	—
408	Q₈×C₃₁	—	2	2	no	—
409	Q₈×C₃₁	—	2	2	no	—
410	Q₈×C₃₁	—	2	2	no	—
411	Q₈×C₃₁	—	4	1	no	—
412	Q₈×C₃₁	—	8	1	no	—
413	Q₈×C₃₁	—	8	2	no	—
414	Q₈×C₃₁	—	8	2	no	—
415	Q₈×C₃₁	—	8	2	no	—
416	D₄×C₃₁	—	2	4	no	—
417	D₄×C₃₁	—	2	2	no	—
418	D₄×C₃₁	—	4	1	no	—
419	D₄×C₃₁	—	4	2	no	—
420	D₄×C₃₁	—	8	2	no	—
421	C₂×C₄×C₃₁	—	2	2	no	—
422	C₂×C₄×C₃₁	—	2	2	no	—
423	C₂×C₄×C₃₁	—	2	2	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	2	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	1	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	2	1	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	2	no	—
434	C₂×C₄×C₃₁	—	4	1	no	—
435	C₂×C₄×C₃₁	—	4	2	no	—
436	C₂×C₄×C₃₁	—	4	2	no	—
437	C₂×C₄×C₃₁	—	8	2	no	—
438	C₂×C₄×C₃₁	—	8	1	no	—
439	C₂×C₄×C₃₁	—	8	2	no	—
440	C₂×C₄×C₃₁	—	8	2	no	—
441	C₂×C₄×C₃₁	—	8	2	no	—
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	1	yes	characteristic
446	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
451	C₈×C₃₁	—	2	2	no	—
452	C₈×C₃₁	—	2	2	no	—
453	C₈×C₃₁	—	2	2	no	—
454	C₈×C₃₁	—	2	2	no	—
455	#3563	C₂×C₃₁	1	1	yes	characteristic, complemented
456	#3552	C₂×C₃₁	1	1	yes	characteristic
457	#3377	C₂×C₃₁	1	2	yes	complemented
458	#3374	C₂×C₃₁	1	2	yes	complemented
459	#3316	C₂×C₃₁	1	2	yes	complemented
460	#3315	C₂×C₃₁	1	2	yes	complemented
461	#3312	C₂×C₃₁	1	2	yes	complemented
462	#3312	C₂×C₃₁	1	2	yes	complemented
463	#3300	C₂×C₃₁	1	2	yes	complemented
464	#3299	C₂×C₃₁	1	2	yes	complemented
465	#3242	C₂×C₃₁	1	2	yes	complemented
466	#3232	C₂×C₃₁	1	1	yes	characteristic, complemented
467	#3223	C₂×C₃₁	1	2	yes	complemented
468	#3209	C₂×C₃₁	1	1	yes	characteristic, complemented
469	#3181	C₂×C₃₁	1	1	yes	characteristic, complemented
470	#3177	C₂×C₃₁	1	2	yes	complemented
471	#3137	C₂×C₃₁	1	2	yes	complemented
472	C₂×#491	C₂×C₃₁	1	1	yes	characteristic, complemented
473	#2968	C₂×C₃₁	1	1	yes	characteristic, complemented
474	C₂²×C₃₁	—	2	1	no	—
475	C₂²×C₃₁	—	2	1	no	—
476	C₂²×C₃₁	—	2	2	no	—
477	C₂²×C₃₁	—	2	2	no	—
478	C₂²×C₃₁	—	2	2	no	—
479	C₂²×C₃₁	—	4	1	no	—
480	C₂²×C₃₁	—	4	1	no	—
481	C₂²×C₃₁	—	4	1	no	—
482	C₂²×C₃₁	#578	1	2	yes	—
483	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
484	C₄×C₃₁	—	2	1	no	—
485	C₄×C₃₁	—	2	1	no	—
486	C₄×C₃₁	—	2	2	no	—
487	C₄×C₃₁	—	2	2	no	—
488	C₄×C₃₁	—	2	1	no	—
489	C₄×C₃₁	—	2	1	no	—
490	C₄×C₃₁	—	2	1	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	2	no	—
496	C₄×C₃₁	—	4	1	no	—
497	C₄×C₃₁	—	4	2	no	—
498	C₄×C₃₁	—	4	2	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	—	4	1	no	—
501	C₄×C₃₁	#585	1	2	yes	—
502	#564	—	2	1	no	—
503	#563	—	2	2	no	—
504	#563	—	2	1	no	—
505	#557	C₂²×C₃₁	1	1	yes	characteristic
506	#557	C₂²×C₃₁	1	2	yes	—
507	#556	C₂²×C₃₁	1	1	yes	characteristic
508	#554	—	2	1	no	—
509	#554	C₂²×C₃₁	1	2	yes	—
510	#553	—	2	1	no	—
511	#552	—	2	2	no	—
512	#552	C₂²×C₃₁	1	2	yes	—
513	#552	C₂²×C₃₁	1	2	yes	—
514	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
515	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
516	#548	C₂²×C₃₁	1	2	yes	—
517	#547	C₂²×C₃₁	1	1	yes	characteristic
518	#544	—	2	1	no	—
519	#544	—	2	1	no	—
520	#544	C₂²×C₃₁	1	2	yes	—
521	#542	—	2	1	no	—
522	#541	—	2	2	no	—
523	#541	C₂²×C₃₁	1	2	yes	—
524	#541	C₂²×C₃₁	1	2	yes	—
525	#539	—	2	2	no	—
526	#539	—	2	1	no	—
527	#536	C₂²×C₃₁	1	2	yes	—
528	#533	C₂²×C₃₁	1	1	yes	characteristic
529	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
530	#529	C₂²×C₃₁	1	1	yes	characteristic
531	#529	C₂²×C₃₁	1	1	yes	characteristic
532	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
533	#501	C₂²×C₃₁	1	1	yes	characteristic
534	#499	C₂²×C₃₁	1	2	yes	—
535	#497	C₂²×C₃₁	1	1	yes	characteristic
536	#494	C₂²×C₃₁	1	2	yes	—
537	#491	C₂²×C₃₁	1	2	yes	—
538	#491	C₂²×C₃₁	1	2	yes	—
539	#491	C₂²×C₃₁	1	2	yes	—
540	#491	C₂²×C₃₁	1	2	yes	—
541	#491	C₂²×C₃₁	1	2	yes	—
542	#491	C₂²×C₃₁	1	1	yes	characteristic
543	#489	C₂²×C₃₁	1	2	yes	—
544	#489	C₂²×C₃₁	1	1	yes	characteristic
545	#488	C₂²×C₃₁	1	2	yes	—
546	#488	C₂²×C₃₁	1	2	yes	—
547	#487	C₂²×C₃₁	1	2	yes	—
548	#487	C₂²×C₃₁	1	2	yes	—
549	#485	C₂²×C₃₁	1	2	yes	—
550	#485	C₂²×C₃₁	1	2	yes	—
551	#484	C₂²×C₃₁	1	1	yes	characteristic
552	#484	C₂²×C₃₁	1	2	yes	—
553	#483	C₂²×C₃₁	1	1	yes	characteristic
554	#483	C₂²×C₃₁	1	2	yes	—
555	#481	C₂²×C₃₁	1	1	yes	characteristic
556	#480	C₂²×C₃₁	1	1	yes	characteristic
557	#479	C₂²×C₃₁	1	2	yes	—
558	#479	C₂²×C₃₁	1	2	yes	—
559	#479	C₂²×C₃₁	1	2	yes	—
560	#478	C₂²×C₃₁	1	2	yes	—
561	#477	C₂²×C₃₁	1	2	yes	—
562	#475	C₂²×C₃₁	1	2	yes	—
563	#470	C₂²×C₃₁	1	2	yes	—
564	#470	C₂²×C₃₁	1	2	yes	—
565	#467	C₂²×C₃₁	1	2	yes	—
566	#467	C₂²×C₃₁	1	2	yes	—
567	#467	C₂²×C₃₁	1	2	yes	—
568	#465	C₂²×C₃₁	1	2	yes	—
569	#464	C₂²×C₃₁	1	2	yes	—
570	#464	C₂²×C₃₁	1	2	yes	—
571	#462	C₂²×C₃₁	1	2	yes	—
572	#462	C₂²×C₃₁	1	2	yes	—
573	#462	C₂²×C₃₁	1	2	yes	—
574	#462	C₂²×C₃₁	1	2	yes	—
575	#452	C₂²×C₃₁	1	2	yes	—
576	#452	C₂²×C₃₁	1	2	yes	—
577	#451	C₂²×C₃₁	1	2	yes	—
578	#451	C₂²×C₃₁	1	2	yes	—
579	#451	C₂²×C₃₁	1	2	yes	—
580	#451	C₂²×C₃₁	1	2	yes	—
581	#446	C₂²×C₃₁	1	2	yes	—
582	#441	C₂²×C₃₁	1	2	yes	—
583	#441	C₂²×C₃₁	1	2	yes	—
584	#441	C₂²×C₃₁	1	2	yes	—
585	#440	C₂²×C₃₁	1	2	yes	—
586	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
587	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
588	#435	C₂²×C₃₁	1	2	yes	—
589	#435	C₂²×C₃₁	1	2	yes	—
590	C₈×D₄	C₂²×C₃₁	1	2	yes	—
591	#433	C₂²×C₃₁	1	2	yes	—
592	#431	C₂²×C₃₁	1	1	yes	characteristic
593	#419	C₂²×C₃₁	1	2	yes	—
594	#417	C₂²×C₃₁	1	2	yes	—
595	#416	C₂²×C₃₁	1	2	yes	—
596	C₂×#103	C₂²×C₃₁	1	2	yes	—
597	C₂×#103	C₂²×C₃₁	1	2	yes	—
598	C₂×#103	C₂²×C₃₁	1	2	yes	—
599	#405	C₂²×C₃₁	1	2	yes	—
600	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
601	C₂×C₃₁	—	2	2	no	—
602	C₂×C₃₁	—	4	2	no	—
603	C₂×C₃₁	—	8	1	no	—
604	C₂×C₃₁	#3500	1	1	yes	characteristic
605	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
606	C₂×C₃₁	#3586	1	1	yes	characteristic
607	C₂×#41	C₂³×C₃₁	1	2	yes	—
608	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
609	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
610	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
611	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
612	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
613	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
614	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
615	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
616	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
617	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
618	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
619	C₄⋊Q₈	—	2	2	no	—
620	C₄⋊Q₈	—	2	2	no	—
621	C₄⋊Q₈	—	2	1	no	—
622	C₄⋊Q₈	—	2	2	no	—
623	C₄⋊Q₈	—	2	1	no	—
624	C₄⋊Q₈	—	2	1	no	—
625	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
626	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
627	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
628	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
629	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
630	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
631	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#126	—	2	2	no	—
637	#126	—	2	2	no	—
638	#126	—	2	2	no	—
639	#126	—	2	1	no	—
640	#126	D₄×C₃₁	1	2	yes	—
641	#125	—	2	2	no	—
642	#125	—	2	2	no	—
643	#125	—	2	2	no	—
644	#125	—	2	2	no	—
645	#125	—	2	2	no	—
646	#125	—	2	2	no	—
647	#125	—	2	2	no	—
648	#125	—	2	2	no	—
649	#125	—	2	2	no	—
650	#125	—	2	2	no	—
651	#125	—	2	1	no	—
652	#125	—	2	2	no	—
653	#125	—	2	1	no	—
654	#125	—	2	1	no	—
655	#125	—	2	1	no	—
656	#125	D₄×C₃₁	1	1	yes	characteristic
657	#125	C₂³×C₃₁	1	2	yes	—
658	#125	C₂³×C₃₁	1	2	yes	—
659	#125	C₂³×C₃₁	1	1	yes	characteristic
660	#125	C₂³×C₃₁	1	2	yes	—
661	#124	—	2	2	no	—
662	#124	D₄×C₃₁	1	1	yes	characteristic
663	#124	C₂³×C₃₁	1	1	yes	characteristic
664	#124	C₂³×C₃₁	1	2	yes	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	1	no	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	D₄×C₃₁	1	2	yes	—
672	C₂²⋊Q₈	—	2	1	no	—
673	C₂²⋊Q₈	—	2	1	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
685	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
686	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
688	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
689	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
690	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
691	#121	—	2	2	no	—
692	#121	—	2	1	no	—
693	#121	D₄×C₃₁	1	1	yes	characteristic
694	#121	C₂³×C₃₁	1	1	yes	characteristic
695	C₄×Q₈	—	2	1	no	—
696	C₄×Q₈	—	2	2	no	—
697	C₄×Q₈	—	2	1	no	—
698	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
699	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
700	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
701	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
702	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
703	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
704	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
705	C₄×D₄	—	2	2	no	—
706	C₄×D₄	—	2	2	no	—
707	C₄×D₄	—	2	1	no	—
708	C₄×D₄	—	2	1	no	—
709	C₄×D₄	—	2	2	no	—
710	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
711	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
712	C₄×D₄	C₂³×C₃₁	1	2	yes	—
713	#117	—	2	1	no	—
714	#117	—	2	1	no	—
715	#117	—	2	2	no	—
716	#117	—	2	2	no	—
717	#117	—	2	1	no	—
718	#117	C₂³×C₃₁	1	2	yes	—
719	#117	C₂³×C₃₁	1	2	yes	—
720	C₂×C₄⋊C₄	—	2	1	no	—
721	C₂×C₄⋊C₄	—	2	1	no	—
722	C₂×C₄⋊C₄	—	2	1	no	—
723	C₂×C₄⋊C₄	—	2	1	no	—
724	C₂×C₄⋊C₄	—	2	1	no	—
725	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
728	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
729	#107	C₂³×C₃₁	1	2	yes	—
730	#107	C₂³×C₃₁	1	2	yes	—
731	#107	C₂³×C₃₁	1	2	yes	—
732	#106	C₂³×C₃₁	1	2	yes	—
733	#106	C₂³×C₃₁	1	2	yes	—
734	#106	C₂³×C₃₁	1	2	yes	—
735	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
736	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
737	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
738	#103	C₂³×C₃₁	1	2	yes	—
739	#103	C₂³×C₃₁	1	2	yes	—
740	#103	C₂³×C₃₁	1	2	yes	—
741	#103	C₂³×C₃₁	1	2	yes	—
742	#103	C₂³×C₃₁	1	2	yes	—
743	#103	C₂³×C₃₁	1	2	yes	—
744	#103	C₂³×C₃₁	1	2	yes	—
745	#103	C₂³×C₃₁	1	2	yes	—
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	#102	C₂³×C₃₁	1	2	yes	—
756	#102	C₂³×C₃₁	1	2	yes	—
757	#102	C₂³×C₃₁	1	2	yes	—
758	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
759	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
760	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
761	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
762	#97	C₂³×C₃₁	1	1	yes	characteristic
763	#97	C₂³×C₃₁	1	1	yes	characteristic
764	#97	C₂³×C₃₁	1	2	yes	—
765	#97	C₂³×C₃₁	1	2	yes	—
766	C₄×C₈	C₂³×C₃₁	1	2	yes	—
767	C₄×C₈	C₂³×C₃₁	1	2	yes	—
768	C₃₁	#62599	1	1	yes	characteristic, direct product factor, Sylow
769	#41	—	4	2	no	—
770	#41	—	4	2	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	4	2	no	—
776	C₂×Q₈	—	4	2	no	—
777	C₂×Q₈	—	4	2	no	—
778	C₂×Q₈	—	4	2	no	—
779	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
780	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
781	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
782	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
783	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
787	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
788	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	2	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
800	Q₁₆	—	4	2	no	—
801	Q₁₆	—	4	2	no	—
802	Q₁₆	—	4	2	no	—
803	Q₁₆	—	4	2	no	—
804	Q₁₆	—	4	2	no	—
805	SD₁₆	—	4	2	no	—
806	M₁₆	—	4	2	no	—
807	C₂×C₈	—	4	2	no	—
808	C₂×C₈	—	4	2	no	—
809	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
810	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
811	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
812	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	1	no	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	1	no	—
833	C₄⋊C₄	—	2	1	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
849	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
850	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
851	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
852	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
853	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
854	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
855	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
856	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
857	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
858	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	1	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	1	no	—
868	C₂²⋊C₄	—	2	1	no	—
869	C₂²⋊C₄	—	2	1	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	1	no	—
872	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
873	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
874	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
875	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
876	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	—	2	1	no	—
880	C₄²	—	2	2	no	—
881	C₄²	—	2	2	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	2	no	—
884	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
885	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
886	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
887	C₄²	C₂⁴×C₃₁	1	2	yes	—
888	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₂³	—	2	1	no	—
890	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
891	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
892	Q₈	—	2	2	no	—
893	Q₈	—	2	2	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	2	2	no	—
896	Q₈	—	2	2	no	—
897	Q₈	—	2	2	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	4	1	no	—
900	Q₈	—	8	1	no	—
901	Q₈	—	8	2	no	—
902	Q₈	—	8	2	no	—
903	Q₈	—	8	2	no	—
904	D₄	—	2	4	no	—
905	D₄	—	2	2	no	—
906	D₄	—	4	1	no	—
907	D₄	—	4	2	no	—
908	D₄	—	8	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	8	2	no	—
926	C₂×C₄	—	8	1	no	—
927	C₂×C₄	—	8	2	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	—	8	2	no	—
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	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
935	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
937	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
938	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
939	C₈	—	2	2	no	—
940	C₈	—	2	2	no	—
941	C₈	—	2	2	no	—
942	C₈	—	2	2	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	2	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	C₃₁×#578	1	2	yes	—
952	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
953	C₄	—	2	2	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	2	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	1	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	C₃₁×#585	1	2	yes	—
971	C₂	—	2	2	no	—
972	C₂	—	4	2	no	—
973	C₂	—	8	1	no	—
974	C₂	C₃₁×#3500	1	1	yes	characteristic
975	C₂	C₂×C₃₁×#578	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×#3552	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×#3377	C₂	semidirect
4. C₃₁×#3374	C₂	semidirect
5. C₃₁×#3316	C₂	semidirect
6. C₃₁×#3315	C₂	semidirect
7. C₃₁×#3312	C₂	semidirect
8. C₃₁×#3312	C₂	semidirect
9. C₃₁×#3300	C₂	semidirect
10. C₃₁×#3299	C₂	semidirect
11. C₃₁×#3242	C₂	semidirect
12. C₃₁×#3232	C₂	semidirect
13. C₃₁×#3223	C₂	semidirect
14. C₃₁×#3209	C₂	semidirect
15. C₃₁×#3181	C₂	semidirect
16. C₃₁×#3177	C₂	semidirect
17. C₃₁×#3137	C₂	semidirect
18. C₂×C₃₁×#491	C₂	semidirect
19. C₃₁×#2968	C₂	semidirect
400. #62599	C₃₁	direct (N × H)
455. #3563	C₂×C₃₁	semidirect
457. #3377	C₂×C₃₁	semidirect
458. #3374	C₂×C₃₁	semidirect
459. #3316	C₂×C₃₁	semidirect
460. #3315	C₂×C₃₁	semidirect
461. #3312	C₂×C₃₁	semidirect
462. #3312	C₂×C₃₁	semidirect
463. #3300	C₂×C₃₁	semidirect
464. #3299	C₂×C₃₁	semidirect
465. #3242	C₂×C₃₁	semidirect
466. #3232	C₂×C₃₁	semidirect
467. #3223	C₂×C₃₁	semidirect
468. #3209	C₂×C₃₁	semidirect
469. #3181	C₂×C₃₁	semidirect
470. #3177	C₂×C₃₁	semidirect
471. #3137	C₂×C₃₁	semidirect
472. C₂×#491	C₂×C₃₁	semidirect
473. #2968	C₂×C₃₁	semidirect
768. C₃₁	#62599	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×#3552	2
C₃₁×#3377	2
C₃₁×#3374	2
C₃₁×#3316	2
C₃₁×#3315	2
C₃₁×#3312	2
C₃₁×#3300	2
C₃₁×#3299	2
C₃₁×#3242	2
C₃₁×#3232	2
C₃₁×#3223	2
C₃₁×#3209	2
C₃₁×#3181	2
C₃₁×#3177	2
C₃₁×#3137	2
C₂×C₃₁×#491	2
C₃₁×#2968	2
#62599	31

Subgroups — C31×#62599 #21519358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62599 #21519358