Subgroups — C₃₁×#62611 #21519370

Order 7936.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3552	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3328	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3327	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3313	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3223	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3177	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3172	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#563	—	2	2	no	—
26	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#557	—	2	1	no	—
28	C₃₁×#557	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	1	yes	characteristic
30	C₃₁×#556	—	2	1	no	—
31	C₃₁×#556	C₂²	1	1	yes	characteristic
32	C₃₁×#556	C₂²	1	1	yes	characteristic
33	C₃₁×#556	C₂²	1	2	yes	—
34	C₃₁×#554	—	2	1	no	—
35	C₃₁×#554	C₂²	1	1	yes	characteristic
36	C₃₁×#553	—	2	1	no	—
37	C₃₁×#552	C₂²	1	2	yes	—
38	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
40	C₃₁×#548	C₂²	1	2	yes	—
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#544	C₂²	1	2	yes	—
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#542	—	2	1	no	—
46	C₃₁×#541	—	2	2	no	—
47	C₃₁×#541	—	2	1	no	—
48	C₃₁×#541	C₂²	1	2	yes	—
49	C₃₁×#541	C₂²	1	2	yes	—
50	C₃₁×#539	—	2	2	no	—
51	C₃₁×#536	C₂²	1	2	yes	—
52	C₃₁×#533	C₂²	1	1	yes	characteristic
53	C₃₁×#533	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
55	C₃₁×#529	C₂²	1	1	yes	characteristic
56	C₃₁×#529	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	1	yes	characteristic
58	C₃₁×#499	C₂²	1	2	yes	—
59	C₃₁×#497	C₂²	1	1	yes	characteristic
60	C₃₁×#494	C₂²	1	2	yes	—
61	C₃₁×#491	C₂²	1	2	yes	—
62	C₃₁×#491	C₂²	1	2	yes	—
63	C₃₁×#491	C₂²	1	2	yes	—
64	C₃₁×#491	C₂²	1	1	yes	characteristic
65	C₃₁×#489	C₂²	1	2	yes	—
66	C₃₁×#489	C₂²	1	1	yes	characteristic
67	C₃₁×#488	C₂²	1	2	yes	—
68	C₃₁×#488	C₂²	1	2	yes	—
69	C₃₁×#487	C₂²	1	1	yes	characteristic
70	C₃₁×#487	C₂²	1	2	yes	—
71	C₃₁×#487	C₂²	1	1	yes	characteristic
72	C₃₁×#487	C₂²	1	1	yes	characteristic
73	C₃₁×#487	C₂²	1	1	yes	characteristic
74	C₃₁×#487	C₂²	1	2	yes	—
75	C₃₁×#485	C₂²	1	2	yes	—
76	C₃₁×#485	C₂²	1	2	yes	—
77	C₃₁×#485	C₂²	1	2	yes	—
78	C₃₁×#484	C₂²	1	2	yes	—
79	C₃₁×#483	C₂²	1	2	yes	—
80	C₃₁×#482	C₂²	1	2	yes	—
81	C₃₁×#479	C₂²	1	2	yes	—
82	C₃₁×#479	C₂²	1	2	yes	—
83	C₃₁×#477	C₂²	1	1	yes	characteristic
84	C₃₁×#477	C₂²	1	2	yes	—
85	C₃₁×#476	C₂²	1	1	yes	characteristic
86	C₃₁×#475	C₂²	1	2	yes	—
87	C₃₁×#475	C₂²	1	1	yes	characteristic
88	C₃₁×#474	C₂²	1	1	yes	characteristic
89	C₃₁×#470	C₂²	1	2	yes	—
90	C₃₁×#470	C₂²	1	1	yes	characteristic
91	C₃₁×#470	C₂²	1	1	yes	characteristic
92	C₃₁×#470	C₂²	1	2	yes	—
93	C₃₁×#468	C₂²	1	1	yes	characteristic
94	C₃₁×#468	C₂²	1	1	yes	characteristic
95	C₃₁×#467	C₂²	1	2	yes	—
96	C₃₁×#467	C₂²	1	2	yes	—
97	C₃₁×#464	C₂²	1	2	yes	—
98	C₃₁×#464	C₂²	1	2	yes	—
99	C₃₁×#462	C₂²	1	1	yes	characteristic
100	C₃₁×#462	C₂²	1	1	yes	characteristic
101	C₃₁×#462	C₂²	1	2	yes	—
102	C₃₁×#462	C₂²	1	1	yes	characteristic
103	C₃₁×#462	C₂²	1	1	yes	characteristic
104	C₃₁×#462	C₂²	1	2	yes	—
105	C₃₁×#452	C₂²	1	2	yes	—
106	C₃₁×#452	C₂²	1	2	yes	—
107	C₃₁×#451	C₂²	1	2	yes	—
108	C₃₁×#451	C₂²	1	2	yes	—
109	C₃₁×#451	C₂²	1	2	yes	—
110	C₃₁×#451	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
113	C₃₁×#441	C₂²	1	2	yes	—
114	C₃₁×#441	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	2	yes	—
123	C₃₁×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₃₁×#433	C₂²	1	2	yes	—
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#419	C₂²	1	2	yes	—
128	C₃₁×#419	C₂²	1	2	yes	—
129	C₃₁×#419	C₂²	1	2	yes	—
130	C₃₁×#417	C₂²	1	2	yes	—
131	C₃₁×#416	C₂²	1	2	yes	—
132	C₂×C₃₁×#103	C₂²	1	2	yes	—
133	C₃₁×#405	C₂²	1	2	yes	—
134	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	C₂³	1	2	yes	—
136	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
137	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
138	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
150	C₃₁×C₄⋊Q₈	—	2	1	no	—
151	C₃₁×C₄⋊Q₈	—	2	2	no	—
152	C₃₁×C₄⋊Q₈	—	2	1	no	—
153	C₃₁×C₄⋊Q₈	—	2	1	no	—
154	C₃₁×C₄⋊Q₈	—	2	2	no	—
155	C₃₁×C₄⋊Q₈	—	2	2	no	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	1	no	—
177	C₃₁×#126	D₄	1	2	yes	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	2	no	—
182	C₃₁×#125	—	2	2	no	—
183	C₃₁×#125	—	2	1	no	—
184	C₃₁×#125	—	2	2	no	—
185	C₃₁×#125	—	2	2	no	—
186	C₃₁×#125	—	2	2	no	—
187	C₃₁×#125	—	2	1	no	—
188	C₃₁×#125	—	2	1	no	—
189	C₃₁×#125	D₄	1	1	yes	characteristic
190	C₃₁×#125	C₂³	1	2	yes	—
191	C₃₁×#125	C₂³	1	2	yes	—
192	C₃₁×#125	C₂³	1	1	yes	characteristic
193	C₃₁×#124	—	2	1	no	—
194	C₃₁×#124	—	2	2	no	—
195	C₃₁×#124	—	2	2	no	—
196	C₃₁×#124	D₄	1	1	yes	characteristic
197	C₃₁×#124	C₂³	1	2	yes	—
198	C₃₁×#124	C₂³	1	1	yes	characteristic
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	1	no	—
201	C₃₁×#123	—	2	2	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×#123	—	2	2	no	—
204	C₃₁×#123	D₄	1	2	yes	—
205	C₃₁×C₂²⋊Q₈	—	2	1	no	—
206	C₃₁×C₂²⋊Q₈	—	2	1	no	—
207	C₃₁×C₂²⋊Q₈	—	2	1	no	—
208	C₃₁×C₂²⋊Q₈	—	2	1	no	—
209	C₃₁×C₂²⋊Q₈	—	2	2	no	—
210	C₃₁×C₂²⋊Q₈	—	2	2	no	—
211	C₃₁×C₂²⋊Q₈	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	2	no	—
213	C₃₁×C₂²⋊Q₈	—	2	2	no	—
214	C₃₁×C₂²⋊Q₈	—	2	2	no	—
215	C₃₁×C₂²⋊Q₈	—	2	2	no	—
216	C₃₁×C₂²⋊Q₈	—	2	2	no	—
217	C₃₁×C₂²⋊Q₈	—	2	2	no	—
218	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
219	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₃₁×#121	—	2	2	no	—
227	C₃₁×#121	—	2	1	no	—
228	C₃₁×#121	D₄	1	1	yes	characteristic
229	C₃₁×#121	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₃₁	—	2	1	no	—
231	C₄×Q₈×C₃₁	—	2	1	no	—
232	C₄×Q₈×C₃₁	—	2	2	no	—
233	C₄×Q₈×C₃₁	—	2	1	no	—
234	C₄×Q₈×C₃₁	—	2	1	no	—
235	C₄×Q₈×C₃₁	—	2	1	no	—
236	C₄×Q₈×C₃₁	—	2	1	no	—
237	C₄×Q₈×C₃₁	—	2	1	no	—
238	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
242	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
243	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
244	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
245	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	—	2	2	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	—	2	1	no	—
249	C₄×D₄×C₃₁	—	2	1	no	—
250	C₄×D₄×C₃₁	—	2	2	no	—
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	1	no	—
256	C₃₁×#117	—	2	2	no	—
257	C₃₁×#117	—	2	1	no	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₃₁×#117	C₂³	1	2	yes	—
260	C₃₁×#117	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
265	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×#103	C₂³	1	1	yes	characteristic
279	C₃₁×#103	C₂³	1	2	yes	—
280	C₃₁×#103	C₂³	1	2	yes	—
281	C₃₁×#103	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	2	yes	—
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	1	yes	characteristic
295	C₃₁×#103	C₂³	1	1	yes	characteristic
296	C₃₁×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#103	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×#97	C₂³	1	1	yes	characteristic
306	C₃₁×#97	C₂³	1	1	yes	characteristic
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	#41×C₃₁	—	4	2	no	—
313	#41×C₃₁	—	4	2	no	—
314	C₂×Q₈×C₃₁	—	2	1	no	—
315	C₂×Q₈×C₃₁	—	2	1	no	—
316	C₂×Q₈×C₃₁	—	2	1	no	—
317	C₂×Q₈×C₃₁	—	2	2	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	4	2	no	—
321	C₂×Q₈×C₃₁	—	4	2	no	—
322	C₂×Q₈×C₃₁	—	4	2	no	—
323	C₂×Q₈×C₃₁	—	4	2	no	—
324	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
333	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₃₁	—	2	2	no	—
336	C₂²×C₄×C₃₁	—	2	2	no	—
337	C₂²×C₄×C₃₁	—	2	2	no	—
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	2	no	—
340	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
344	Q₁₆×C₃₁	—	4	2	no	—
345	Q₁₆×C₃₁	—	4	2	no	—
346	Q₁₆×C₃₁	—	4	1	no	—
347	Q₁₆×C₃₁	—	4	1	no	—
348	Q₁₆×C₃₁	—	4	2	no	—
349	Q₁₆×C₃₁	—	4	2	no	—
350	SD₁₆×C₃₁	—	4	1	no	—
351	SD₁₆×C₃₁	—	4	1	no	—
352	M₁₆×C₃₁	—	4	1	no	—
353	M₁₆×C₃₁	—	4	1	no	—
354	M₁₆×C₃₁	—	4	2	no	—
355	C₂×C₈×C₃₁	—	4	2	no	—
356	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
358	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
360	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₃₁	—	2	1	no	—
363	C₄⋊C₄×C₃₁	—	2	1	no	—
364	C₄⋊C₄×C₃₁	—	2	1	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	1	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	1	no	—
371	C₄⋊C₄×C₃₁	—	2	1	no	—
372	C₄⋊C₄×C₃₁	—	2	1	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	1	no	—
375	C₄⋊C₄×C₃₁	—	2	1	no	—
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	1	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
429	C₄²×C₃₁	—	2	2	no	—
430	C₄²×C₃₁	—	2	1	no	—
431	C₄²×C₃₁	—	2	1	no	—
432	C₄²×C₃₁	—	2	2	no	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
441	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
442	C₄²×C₃₁	C₂⁴	1	2	yes	—
443	#62611	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₃₁	—	2	1	no	—
445	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
446	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
447	Q₈×C₃₁	—	2	2	no	—
448	Q₈×C₃₁	—	2	1	no	—
449	Q₈×C₃₁	—	2	1	no	—
450	Q₈×C₃₁	—	2	1	no	—
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	2	2	no	—
453	Q₈×C₃₁	—	2	1	no	—
454	Q₈×C₃₁	—	2	1	no	—
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	2	no	—
457	Q₈×C₃₁	—	2	2	no	—
458	Q₈×C₃₁	—	4	2	no	—
459	Q₈×C₃₁	—	8	1	no	—
460	Q₈×C₃₁	—	8	1	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	Q₈×C₃₁	—	8	2	no	—
463	Q₈×C₃₁	—	8	2	no	—
464	D₄×C₃₁	—	2	2	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	2	1	no	—
467	D₄×C₃₁	—	4	2	no	—
468	D₄×C₃₁	—	4	2	no	—
469	D₄×C₃₁	—	8	2	no	—
470	C₂×C₄×C₃₁	—	2	2	no	—
471	C₂×C₄×C₃₁	—	2	2	no	—
472	C₂×C₄×C₃₁	—	2	1	no	—
473	C₂×C₄×C₃₁	—	2	1	no	—
474	C₂×C₄×C₃₁	—	2	2	no	—
475	C₂×C₄×C₃₁	—	2	1	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	2	1	no	—
478	C₂×C₄×C₃₁	—	2	2	no	—
479	C₂×C₄×C₃₁	—	2	1	no	—
480	C₂×C₄×C₃₁	—	2	1	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	2	no	—
486	C₂×C₄×C₃₁	—	4	1	no	—
487	C₂×C₄×C₃₁	—	4	2	no	—
488	C₂×C₄×C₃₁	—	8	2	no	—
489	C₂×C₄×C₃₁	—	8	2	no	—
490	C₂×C₄×C₃₁	—	8	2	no	—
491	C₂×C₄×C₃₁	—	8	2	no	—
492	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
501	C₈×C₃₁	—	2	1	no	—
502	C₈×C₃₁	—	2	2	no	—
503	C₈×C₃₁	—	2	1	no	—
504	C₈×C₃₁	—	2	1	no	—
505	C₈×C₃₁	—	2	1	no	—
506	C₈×C₃₁	—	2	2	no	—
507	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#3552	C₂×C₃₁	1	1	yes	characteristic
509	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3363	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#3328	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#3328	C₂×C₃₁	1	2	yes	complemented
516	#3327	C₂×C₃₁	1	2	yes	complemented
517	#3313	C₂×C₃₁	1	2	yes	complemented
518	#3312	C₂×C₃₁	1	2	yes	complemented
519	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3242	C₂×C₃₁	1	2	yes	complemented
522	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3223	C₂×C₃₁	1	2	yes	complemented
524	#3209	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3177	C₂×C₃₁	1	2	yes	complemented
526	#3172	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3139	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3137	C₂×C₃₁	1	2	yes	complemented
529	#2969	C₂×C₃₁	1	1	yes	characteristic, complemented
530	C₂²×C₃₁	—	2	1	no	—
531	C₂²×C₃₁	—	2	2	no	—
532	C₂²×C₃₁	—	2	1	no	—
533	C₂²×C₃₁	—	2	2	no	—
534	C₂²×C₃₁	—	2	1	no	—
535	C₂²×C₃₁	—	2	2	no	—
536	C₂²×C₃₁	—	4	1	no	—
537	C₂²×C₃₁	—	4	1	no	—
538	C₂²×C₃₁	—	4	1	no	—
539	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
540	C₄×C₃₁	—	2	1	no	—
541	C₄×C₃₁	—	2	1	no	—
542	C₄×C₃₁	—	2	2	no	—
543	C₄×C₃₁	—	2	2	no	—
544	C₄×C₃₁	—	2	1	no	—
545	C₄×C₃₁	—	2	1	no	—
546	C₄×C₃₁	—	2	2	no	—
547	C₄×C₃₁	—	4	1	no	—
548	C₄×C₃₁	—	4	2	no	—
549	C₄×C₃₁	—	4	1	no	—
550	C₄×C₃₁	—	4	1	no	—
551	C₄×C₃₁	—	4	2	no	—
552	C₄×C₃₁	—	4	1	no	—
553	C₄×C₃₁	—	4	2	no	—
554	C₄×C₃₁	—	4	1	no	—
555	C₄×C₃₁	—	4	1	no	—
556	C₄×C₃₁	—	4	1	no	—
557	C₄×C₃₁	—	4	2	no	—
558	C₄×C₃₁	#578	1	2	yes	—
559	C₄×C₃₁	#585	1	1	yes	characteristic
560	C₄×C₃₁	#585	1	1	yes	characteristic
561	#563	—	2	2	no	—
562	#563	—	2	2	no	—
563	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
564	#557	—	2	1	no	—
565	#557	C₂²×C₃₁	1	1	yes	characteristic
566	#557	C₂²×C₃₁	1	1	yes	characteristic
567	#556	—	2	1	no	—
568	#556	C₂²×C₃₁	1	1	yes	characteristic
569	#556	C₂²×C₃₁	1	1	yes	characteristic
570	#556	C₂²×C₃₁	1	2	yes	—
571	#554	—	2	1	no	—
572	#554	C₂²×C₃₁	1	1	yes	characteristic
573	#553	—	2	1	no	—
574	#552	C₂²×C₃₁	1	2	yes	—
575	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
576	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
577	#548	C₂²×C₃₁	1	2	yes	—
578	#547	C₂²×C₃₁	1	1	yes	characteristic
579	#544	—	2	1	no	—
580	#544	C₂²×C₃₁	1	2	yes	—
581	#542	—	2	1	no	—
582	#542	—	2	1	no	—
583	#541	—	2	2	no	—
584	#541	—	2	1	no	—
585	#541	C₂²×C₃₁	1	2	yes	—
586	#541	C₂²×C₃₁	1	2	yes	—
587	#539	—	2	2	no	—
588	#536	C₂²×C₃₁	1	2	yes	—
589	#533	C₂²×C₃₁	1	1	yes	characteristic
590	#533	C₂²×C₃₁	1	1	yes	characteristic
591	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
592	#529	C₂²×C₃₁	1	1	yes	characteristic
593	#529	C₂²×C₃₁	1	1	yes	characteristic
594	#501	C₂²×C₃₁	1	1	yes	characteristic
595	#499	C₂²×C₃₁	1	2	yes	—
596	#497	C₂²×C₃₁	1	1	yes	characteristic
597	#494	C₂²×C₃₁	1	2	yes	—
598	#491	C₂²×C₃₁	1	2	yes	—
599	#491	C₂²×C₃₁	1	2	yes	—
600	#491	C₂²×C₃₁	1	2	yes	—
601	#491	C₂²×C₃₁	1	1	yes	characteristic
602	#489	C₂²×C₃₁	1	2	yes	—
603	#489	C₂²×C₃₁	1	1	yes	characteristic
604	#488	C₂²×C₃₁	1	2	yes	—
605	#488	C₂²×C₃₁	1	2	yes	—
606	#487	C₂²×C₃₁	1	2	yes	—
607	#487	C₂²×C₃₁	1	1	yes	characteristic
608	#487	C₂²×C₃₁	1	1	yes	characteristic
609	#487	C₂²×C₃₁	1	1	yes	characteristic
610	#487	C₂²×C₃₁	1	1	yes	characteristic
611	#487	C₂²×C₃₁	1	2	yes	—
612	#485	C₂²×C₃₁	1	2	yes	—
613	#485	C₂²×C₃₁	1	2	yes	—
614	#485	C₂²×C₃₁	1	2	yes	—
615	#484	C₂²×C₃₁	1	2	yes	—
616	#483	C₂²×C₃₁	1	2	yes	—
617	#482	C₂²×C₃₁	1	2	yes	—
618	#479	C₂²×C₃₁	1	2	yes	—
619	#479	C₂²×C₃₁	1	2	yes	—
620	#477	C₂²×C₃₁	1	1	yes	characteristic
621	#477	C₂²×C₃₁	1	2	yes	—
622	#476	C₂²×C₃₁	1	1	yes	characteristic
623	#475	C₂²×C₃₁	1	2	yes	—
624	#475	C₂²×C₃₁	1	1	yes	characteristic
625	#474	C₂²×C₃₁	1	1	yes	characteristic
626	#470	C₂²×C₃₁	1	1	yes	characteristic
627	#470	C₂²×C₃₁	1	2	yes	—
628	#470	C₂²×C₃₁	1	2	yes	—
629	#470	C₂²×C₃₁	1	1	yes	characteristic
630	#468	C₂²×C₃₁	1	1	yes	characteristic
631	#468	C₂²×C₃₁	1	1	yes	characteristic
632	#467	C₂²×C₃₁	1	2	yes	—
633	#467	C₂²×C₃₁	1	2	yes	—
634	#464	C₂²×C₃₁	1	2	yes	—
635	#464	C₂²×C₃₁	1	2	yes	—
636	#462	C₂²×C₃₁	1	1	yes	characteristic
637	#462	C₂²×C₃₁	1	2	yes	—
638	#462	C₂²×C₃₁	1	1	yes	characteristic
639	#462	C₂²×C₃₁	1	1	yes	characteristic
640	#462	C₂²×C₃₁	1	2	yes	—
641	#462	C₂²×C₃₁	1	1	yes	characteristic
642	#452	C₂²×C₃₁	1	2	yes	—
643	#452	C₂²×C₃₁	1	2	yes	—
644	#451	C₂²×C₃₁	1	2	yes	—
645	#451	C₂²×C₃₁	1	2	yes	—
646	#451	C₂²×C₃₁	1	2	yes	—
647	#451	C₂²×C₃₁	1	2	yes	—
648	#446	C₂²×C₃₁	1	1	yes	characteristic
649	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
650	#441	C₂²×C₃₁	1	2	yes	—
651	#441	C₂²×C₃₁	1	2	yes	—
652	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
653	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
654	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
655	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
656	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
657	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
658	#436	C₂²×C₃₁	1	1	yes	characteristic
659	#436	C₂²×C₃₁	1	2	yes	—
660	#435	C₂²×C₃₁	1	2	yes	—
661	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
662	#433	C₂²×C₃₁	1	2	yes	—
663	#431	C₂²×C₃₁	1	1	yes	characteristic
664	#419	C₂²×C₃₁	1	2	yes	—
665	#419	C₂²×C₃₁	1	2	yes	—
666	#419	C₂²×C₃₁	1	2	yes	—
667	#417	C₂²×C₃₁	1	2	yes	—
668	#416	C₂²×C₃₁	1	2	yes	—
669	C₂×#103	C₂²×C₃₁	1	2	yes	—
670	#405	C₂²×C₃₁	1	2	yes	—
671	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
672	C₂×C₃₁	—	4	1	no	—
673	C₂×C₃₁	—	4	2	no	—
674	C₂×C₃₁	—	8	1	no	—
675	C₂×C₃₁	#3500	1	1	yes	characteristic
676	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
677	C₂×C₃₁	#3586	1	1	yes	characteristic
678	C₂×#41	C₂³×C₃₁	1	2	yes	—
679	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
680	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
681	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
682	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
684	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
685	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
686	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
688	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
691	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
692	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	2	no	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	1	no	—
697	C₄⋊Q₈	—	2	2	no	—
698	C₄⋊Q₈	—	2	2	no	—
699	C₄⋊Q₈	—	2	1	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	1	no	—
720	#126	D₄×C₃₁	1	2	yes	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	1	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	1	no	—
731	#125	—	2	1	no	—
732	#125	D₄×C₃₁	1	1	yes	characteristic
733	#125	C₂³×C₃₁	1	1	yes	characteristic
734	#125	C₂³×C₃₁	1	2	yes	—
735	#125	C₂³×C₃₁	1	2	yes	—
736	#124	—	2	1	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	D₄×C₃₁	1	1	yes	characteristic
740	#124	C₂³×C₃₁	1	1	yes	characteristic
741	#124	C₂³×C₃₁	1	2	yes	—
742	#123	—	2	2	no	—
743	#123	—	2	1	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	D₄×C₃₁	1	2	yes	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
762	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
764	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
765	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
766	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
769	#121	—	2	2	no	—
770	#121	—	2	1	no	—
771	#121	D₄×C₃₁	1	1	yes	characteristic
772	#121	C₂³×C₃₁	1	1	yes	characteristic
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
785	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
786	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
787	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₃₁	1	2	yes	—
797	#117	—	2	1	no	—
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	—	2	1	no	—
801	#117	C₂³×C₃₁	1	2	yes	—
802	#117	C₂³×C₃₁	1	2	yes	—
803	#117	C₂³×C₃₁	1	2	yes	—
804	C₂×C₄⋊C₄	—	2	1	no	—
805	C₂×C₄⋊C₄	—	2	1	no	—
806	C₂×C₄⋊C₄	—	2	1	no	—
807	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
808	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
809	#107	C₂³×C₃₁	1	2	yes	—
810	#107	C₂³×C₃₁	1	2	yes	—
811	#107	C₂³×C₃₁	1	1	yes	characteristic
812	#107	C₂³×C₃₁	1	1	yes	characteristic
813	#106	C₂³×C₃₁	1	1	yes	characteristic
814	#106	C₂³×C₃₁	1	1	yes	characteristic
815	#106	C₂³×C₃₁	1	2	yes	—
816	#106	C₂³×C₃₁	1	2	yes	—
817	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
820	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
821	#103	C₂³×C₃₁	1	1	yes	characteristic
822	#103	C₂³×C₃₁	1	2	yes	—
823	#103	C₂³×C₃₁	1	2	yes	—
824	#103	C₂³×C₃₁	1	2	yes	—
825	#103	C₂³×C₃₁	1	2	yes	—
826	#103	C₂³×C₃₁	1	2	yes	—
827	#103	C₂³×C₃₁	1	2	yes	—
828	#103	C₂³×C₃₁	1	2	yes	—
829	#103	C₂³×C₃₁	1	1	yes	characteristic
830	#103	C₂³×C₃₁	1	2	yes	—
831	#103	C₂³×C₃₁	1	2	yes	—
832	#103	C₂³×C₃₁	1	2	yes	—
833	#103	C₂³×C₃₁	1	2	yes	—
834	#103	C₂³×C₃₁	1	2	yes	—
835	#103	C₂³×C₃₁	1	2	yes	—
836	#103	C₂³×C₃₁	1	2	yes	—
837	#103	C₂³×C₃₁	1	1	yes	characteristic
838	#103	C₂³×C₃₁	1	1	yes	characteristic
839	#103	C₂³×C₃₁	1	1	yes	characteristic
840	#103	C₂³×C₃₁	1	1	yes	characteristic
841	#102	C₂³×C₃₁	1	1	yes	characteristic
842	#102	C₂³×C₃₁	1	2	yes	—
843	#102	C₂³×C₃₁	1	1	yes	characteristic
844	#102	C₂³×C₃₁	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
846	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
848	#97	C₂³×C₃₁	1	1	yes	characteristic
849	#97	C₂³×C₃₁	1	1	yes	characteristic
850	#97	C₂³×C₃₁	1	2	yes	—
851	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₄×C₈	C₂³×C₃₁	1	2	yes	—
854	C₄×C₈	C₂³×C₃₁	1	2	yes	—
855	C₃₁	#62611	1	1	yes	characteristic, direct product factor, Sylow
856	#41	—	4	2	no	—
857	#41	—	4	2	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	4	2	no	—
865	C₂×Q₈	—	4	2	no	—
866	C₂×Q₈	—	4	2	no	—
867	C₂×Q₈	—	4	2	no	—
868	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
869	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
870	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
871	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
872	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
873	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
877	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
878	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
885	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
888	Q₁₆	—	4	2	no	—
889	Q₁₆	—	4	2	no	—
890	Q₁₆	—	4	1	no	—
891	Q₁₆	—	4	1	no	—
892	Q₁₆	—	4	2	no	—
893	Q₁₆	—	4	2	no	—
894	SD₁₆	—	4	1	no	—
895	SD₁₆	—	4	1	no	—
896	M₁₆	—	4	1	no	—
897	M₁₆	—	4	1	no	—
898	M₁₆	—	4	2	no	—
899	C₂×C₈	—	4	2	no	—
900	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
902	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
904	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
943	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
950	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
969	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
970	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
971	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
983	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
984	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₄²	C₂⁴×C₃₁	1	2	yes	—
987	C₂³	—	2	1	no	—
988	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
989	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
990	Q₈	—	2	2	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	2	1	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	2	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	2	2	no	—
1000	Q₈	—	2	2	no	—
1001	Q₈	—	4	2	no	—
1002	Q₈	—	8	1	no	—
1003	Q₈	—	8	1	no	—
1004	Q₈	—	8	2	no	—
1005	Q₈	—	8	2	no	—
1006	Q₈	—	8	2	no	—
1007	D₄	—	2	2	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	4	2	no	—
1011	D₄	—	4	2	no	—
1012	D₄	—	8	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	4	1	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1039	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1040	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1042	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1043	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1044	C₈	—	2	1	no	—
1045	C₈	—	2	2	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1060	C₄	—	2	2	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	C₃₁×#578	1	2	yes	—
1079	C₄	C₃₁×#585	1	1	yes	characteristic
1080	C₄	C₃₁×#585	1	1	yes	characteristic
1081	C₂	—	4	1	no	—
1082	C₂	—	4	2	no	—
1083	C₂	—	8	1	no	—
1084	C₂	C₃₁×#3500	1	1	yes	characteristic
1085	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1086	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×#3555	C₂	semidirect
3. C₃₁×#3374	C₂	semidirect
4. C₃₁×#3369	C₂	semidirect
5. C₃₁×#3364	C₂	semidirect
6. C₃₁×#3363	C₂	semidirect
7. C₃₁×#3331	C₂	semidirect
8. C₃₁×#3328	C₂	semidirect
9. C₃₁×#3328	C₂	semidirect
10. C₃₁×#3327	C₂	semidirect
11. C₃₁×#3313	C₂	semidirect
12. C₃₁×#3312	C₂	semidirect
13. C₃₁×#3302	C₂	semidirect
14. C₃₁×#3299	C₂	semidirect
15. C₃₁×#3242	C₂	semidirect
16. C₃₁×#3233	C₂	semidirect
17. C₃₁×#3223	C₂	semidirect
18. C₃₁×#3209	C₂	semidirect
19. C₃₁×#3177	C₂	semidirect
20. C₃₁×#3172	C₂	semidirect
21. C₃₁×#3139	C₂	semidirect
22. C₃₁×#3137	C₂	semidirect
23. C₃₁×#2969	C₂	semidirect
443. #62611	C₃₁	direct (N × H)
507. #3555	C₂×C₃₁	semidirect
509. #3374	C₂×C₃₁	semidirect
510. #3369	C₂×C₃₁	semidirect
511. #3364	C₂×C₃₁	semidirect
512. #3363	C₂×C₃₁	semidirect
513. #3331	C₂×C₃₁	semidirect
514. #3328	C₂×C₃₁	semidirect
515. #3328	C₂×C₃₁	semidirect
516. #3327	C₂×C₃₁	semidirect
517. #3313	C₂×C₃₁	semidirect
518. #3312	C₂×C₃₁	semidirect
519. #3302	C₂×C₃₁	semidirect
520. #3299	C₂×C₃₁	semidirect
521. #3242	C₂×C₃₁	semidirect
522. #3233	C₂×C₃₁	semidirect
523. #3223	C₂×C₃₁	semidirect
524. #3209	C₂×C₃₁	semidirect
525. #3177	C₂×C₃₁	semidirect
526. #3172	C₂×C₃₁	semidirect
527. #3139	C₂×C₃₁	semidirect
528. #3137	C₂×C₃₁	semidirect
529. #2969	C₂×C₃₁	semidirect
855. C₃₁	#62611	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×#3555	2
C₃₁×#3552	2
C₃₁×#3374	2
C₃₁×#3369	2
C₃₁×#3364	2
C₃₁×#3363	2
C₃₁×#3331	2
C₃₁×#3328	2
C₃₁×#3327	2
C₃₁×#3313	2
C₃₁×#3312	2
C₃₁×#3302	2
C₃₁×#3299	2
C₃₁×#3242	2
C₃₁×#3233	2
C₃₁×#3223	2
C₃₁×#3209	2
C₃₁×#3177	2
C₃₁×#3172	2
C₃₁×#3139	2
C₃₁×#3137	2
C₃₁×#2969	2
#62611	31

Subgroups — C31×#62611 #21519370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62611 #21519370