Subgroups — C₃₁×#61008 #21517767

Order 7936.

1712 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×#3511	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3258	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3201	C₂	1	4	yes	maximal, complemented
13	C₃₁×#3185	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3121	C₂	1	4	yes	maximal, complemented
18	C₃₁×#3120	C₂	1	4	yes	maximal, complemented
19	C₃₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#557	—	2	1	no	—
21	C₃₁×#557	—	2	1	no	—
22	C₃₁×#556	—	2	1	no	—
23	C₃₁×#556	—	2	1	no	—
24	C₃₁×#556	—	2	1	no	—
25	C₃₁×#555	—	2	1	no	—
26	C₃₁×#554	—	2	1	no	—
27	C₃₁×#553	—	2	1	no	—
28	C₃₁×#553	—	2	1	no	—
29	C₃₁×#552	—	2	1	no	—
30	C₃₁×#552	—	2	1	no	—
31	C₃₁×#552	—	2	1	no	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#548	—	2	1	no	—
34	C₃₁×#548	—	2	1	no	—
35	C₃₁×#547	—	2	1	no	—
36	C₃₁×#542	C₂²	1	2	yes	—
37	C₃₁×#542	C₂²	1	2	yes	—
38	C₃₁×#541	C₂²	1	2	yes	—
39	C₃₁×#541	C₂²	1	2	yes	—
40	C₃₁×#537	C₂²	1	2	yes	—
41	C₃₁×#536	C₂²	1	2	yes	—
42	C₃₁×#533	C₂²	1	1	yes	characteristic
43	C₃₁×#533	C₂²	1	1	yes	characteristic
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#533	C₂²	1	1	yes	characteristic
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₃₁×#533	C₂²	1	1	yes	characteristic
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₃₁×#532	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₃₁×#520	C₂²	1	2	yes	—
55	C₃₁×#519	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#500	C₂²	1	1	yes	characteristic
58	C₃₁×#500	C₂²	1	1	yes	characteristic
59	C₃₁×#498	C₂²	1	1	yes	characteristic
60	C₃₁×#498	C₂²	1	1	yes	characteristic
61	C₃₁×#494	C₂²	1	1	yes	characteristic
62	C₃₁×#494	C₂²	1	1	yes	characteristic
63	C₃₁×#492	C₂²	1	1	yes	characteristic
64	C₃₁×#492	C₂²	1	1	yes	characteristic
65	C₃₁×#487	C₂²	1	1	yes	characteristic
66	C₃₁×#487	C₂²	1	1	yes	characteristic
67	C₃₁×#487	C₂²	1	1	yes	characteristic
68	C₃₁×#487	C₂²	1	1	yes	characteristic
69	C₃₁×#487	C₂²	1	1	yes	characteristic
70	C₃₁×#487	C₂²	1	1	yes	characteristic
71	C₃₁×#486	C₂²	1	1	yes	characteristic
72	C₃₁×#486	C₂²	1	1	yes	characteristic
73	C₃₁×#485	C₂²	1	4	yes	—
74	C₃₁×#484	C₂²	1	4	yes	—
75	C₃₁×#483	C₂²	1	4	yes	—
76	C₃₁×#482	C₂²	1	4	yes	—
77	C₃₁×#479	C₂²	1	4	yes	—
78	C₃₁×#478	C₂²	1	4	yes	—
79	C₃₁×#477	C₂²	1	4	yes	—
80	C₃₁×#475	C₂²	1	4	yes	—
81	C₃₁×#470	C₂²	1	4	yes	—
82	C₃₁×#468	C₂²	1	4	yes	—
83	C₃₁×#467	C₂²	1	4	yes	—
84	C₃₁×#465	C₂²	1	4	yes	—
85	C₃₁×#464	C₂²	1	4	yes	—
86	C₃₁×#464	C₂²	1	4	yes	—
87	C₃₁×#462	C₂²	1	4	yes	—
88	C₃₁×#461	C₂²	1	4	yes	—
89	C₃₁×#452	C₂²	1	4	yes	—
90	C₃₁×#452	C₂²	1	4	yes	—
91	C₃₁×#451	C₂²	1	4	yes	—
92	C₃₁×#448	C₂²	1	4	yes	—
93	C₃₁×#441	C₂²	1	4	yes	—
94	C₃₁×#440	C₂²	1	4	yes	—
95	C₄×Q₁₆×C₃₁	C₂²	1	4	yes	—
96	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
97	C₃₁×#433	C₂²	1	2	yes	—
98	C₃₁×#433	C₂²	1	2	yes	—
99	C₃₁×#431	C₂²	1	1	yes	characteristic
100	C₃₁×#431	C₂²	1	1	yes	characteristic
101	C₃₁×#431	C₂²	1	1	yes	characteristic
102	C₃₁×#431	C₂²	1	1	yes	characteristic
103	C₃₁×#424	C₂²	1	2	yes	—
104	C₃₁×#408	C₂²	1	2	yes	—
105	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
106	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
107	C₂×#41×C₃₁	—	2	1	no	—
108	C₂×#41×C₃₁	—	2	1	no	—
109	C₂×#41×C₃₁	C₂³	1	2	yes	—
110	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₃₁	—	2	1	no	—
112	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
113	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
114	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
117	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
118	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
119	C₃₁×C₄⋊Q₈	—	2	2	no	—
120	C₃₁×C₄⋊Q₈	—	2	1	no	—
121	C₃₁×C₄⋊Q₈	—	2	1	no	—
122	C₃₁×C₄⋊Q₈	—	2	1	no	—
123	C₃₁×C₄⋊Q₈	—	2	1	no	—
124	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
133	C₃₁×#127	C₂³	1	1	yes	characteristic
134	C₃₁×#126	—	2	2	no	—
135	C₃₁×#126	—	2	2	no	—
136	C₃₁×#126	—	2	2	no	—
137	C₃₁×#126	—	2	2	no	—
138	C₃₁×#126	—	2	2	no	—
139	C₃₁×#126	—	2	2	no	—
140	C₃₁×#125	—	2	2	no	—
141	C₃₁×#125	—	2	2	no	—
142	C₃₁×#125	—	2	2	no	—
143	C₃₁×#125	—	2	2	no	—
144	C₃₁×#125	—	2	1	no	—
145	C₃₁×#125	—	2	1	no	—
146	C₃₁×#125	—	2	1	no	—
147	C₃₁×#125	—	2	1	no	—
148	C₃₁×#125	—	2	1	no	—
149	C₃₁×#125	—	2	1	no	—
150	C₃₁×#125	C₂³	1	2	yes	—
151	C₃₁×#124	—	2	2	no	—
152	C₃₁×#124	—	2	2	no	—
153	C₃₁×#124	—	2	2	no	—
154	C₃₁×#124	—	2	1	no	—
155	C₃₁×#124	—	2	1	no	—
156	C₃₁×#124	C₂³	1	2	yes	—
157	C₃₁×#123	—	2	2	no	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×C₂²⋊Q₈	—	2	2	no	—
162	C₃₁×C₂²⋊Q₈	—	2	1	no	—
163	C₃₁×C₂²⋊Q₈	—	2	1	no	—
164	C₃₁×C₂²⋊Q₈	—	2	1	no	—
165	C₃₁×C₂²⋊Q₈	—	2	1	no	—
166	C₃₁×C₂²⋊Q₈	—	2	1	no	—
167	C₃₁×C₂²⋊Q₈	—	2	1	no	—
168	C₃₁×C₂²⋊Q₈	—	2	1	no	—
169	C₃₁×C₂²⋊Q₈	—	2	1	no	—
170	C₃₁×C₂²⋊Q₈	—	2	2	no	—
171	C₃₁×C₂²⋊Q₈	—	2	2	no	—
172	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
175	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₃₁×#121	—	2	2	no	—
179	C₃₁×#121	—	2	2	no	—
180	C₃₁×#121	—	2	2	no	—
181	C₃₁×#121	—	2	1	no	—
182	C₃₁×#121	—	2	1	no	—
183	C₃₁×#121	—	2	1	no	—
184	C₃₁×#121	—	2	1	no	—
185	C₃₁×#121	C₂³	1	2	yes	—
186	C₃₁×#121	C₂³	1	2	yes	—
187	C₄×Q₈×C₃₁	—	2	2	no	—
188	C₄×Q₈×C₃₁	—	2	2	no	—
189	C₄×Q₈×C₃₁	—	2	1	no	—
190	C₄×Q₈×C₃₁	—	2	1	no	—
191	C₄×Q₈×C₃₁	—	2	1	no	—
192	C₄×Q₈×C₃₁	—	2	1	no	—
193	C₄×Q₈×C₃₁	—	2	1	no	—
194	C₄×Q₈×C₃₁	—	2	1	no	—
195	C₄×Q₈×C₃₁	—	2	1	no	—
196	C₄×Q₈×C₃₁	—	2	1	no	—
197	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
198	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
199	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
200	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
201	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
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×D₄×C₃₁	—	2	2	no	—
206	C₄×D₄×C₃₁	—	2	2	no	—
207	C₄×D₄×C₃₁	—	2	1	no	—
208	C₄×D₄×C₃₁	—	2	1	no	—
209	C₄×D₄×C₃₁	—	2	1	no	—
210	C₄×D₄×C₃₁	—	2	1	no	—
211	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
212	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
213	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
214	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
215	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
216	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
217	C₄×D₄×C₃₁	C₂³	1	2	yes	—
218	C₄×D₄×C₃₁	C₂³	1	2	yes	—
219	C₃₁×#117	—	2	1	no	—
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	1	no	—
225	C₃₁×#117	—	2	2	no	—
226	C₃₁×#117	—	2	2	no	—
227	C₃₁×#117	—	2	2	no	—
228	C₃₁×#117	C₂³	1	2	yes	—
229	C₃₁×#117	C₂³	1	1	yes	characteristic
230	C₃₁×#117	C₂³	1	1	yes	characteristic
231	C₃₁×#117	C₂³	1	1	yes	characteristic
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	2	no	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
237	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
240	C₃₁×#107	C₂³	1	4	yes	—
241	C₃₁×#107	C₂³	1	4	yes	—
242	C₃₁×#106	C₂³	1	4	yes	—
243	C₃₁×#106	C₂³	1	4	yes	—
244	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
245	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
246	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
247	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
248	C₃₁×#103	C₂³	1	4	yes	—
249	C₃₁×#103	C₂³	1	4	yes	—
250	C₃₁×#103	C₂³	1	4	yes	—
251	C₃₁×#103	C₂³	1	4	yes	—
252	C₃₁×#103	C₂³	1	4	yes	—
253	C₃₁×#103	C₂³	1	4	yes	—
254	C₃₁×#102	C₂³	1	4	yes	—
255	C₃₁×#102	C₂³	1	4	yes	—
256	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₃₁×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₃₁	C₂³	1	2	yes	—
264	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
266	#41×C₃₁	—	4	2	no	—
267	#41×C₃₁	—	4	4	no	—
268	#41×C₃₁	—	8	2	no	—
269	#41×C₃₁	—	8	2	no	—
270	C₂×Q₈×C₃₁	—	2	1	no	—
271	C₂×Q₈×C₃₁	—	2	1	no	—
272	C₂×Q₈×C₃₁	—	2	2	no	—
273	C₂×Q₈×C₃₁	—	2	1	no	—
274	C₂×Q₈×C₃₁	—	2	1	no	—
275	C₂×Q₈×C₃₁	—	2	2	no	—
276	C₂×Q₈×C₃₁	—	4	4	no	—
277	C₂×Q₈×C₃₁	—	8	2	no	—
278	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
279	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
280	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
281	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
282	C₂×D₄×C₃₁	—	2	2	no	—
283	C₂×D₄×C₃₁	—	2	2	no	—
284	C₂×D₄×C₃₁	—	2	2	no	—
285	C₂×D₄×C₃₁	—	2	1	no	—
286	C₂×D₄×C₃₁	—	2	1	no	—
287	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
288	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
289	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
290	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₃₁	—	2	2	no	—
292	C₂²×C₄×C₃₁	—	2	2	no	—
293	C₂²×C₄×C₃₁	—	2	2	no	—
294	C₂²×C₄×C₃₁	—	2	2	no	—
295	C₂²×C₄×C₃₁	—	2	2	no	—
296	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	Q₁₆×C₃₁	—	4	4	no	—
306	Q₁₆×C₃₁	—	4	4	no	—
307	SD₁₆×C₃₁	—	4	4	no	—
308	SD₁₆×C₃₁	—	4	4	no	—
309	M₁₆×C₃₁	—	4	2	no	—
310	C₂×C₈×C₃₁	—	4	2	no	—
311	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
312	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
313	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
314	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₃₁	—	2	2	no	—
316	C₄⋊C₄×C₃₁	—	2	1	no	—
317	C₄⋊C₄×C₃₁	—	2	1	no	—
318	C₄⋊C₄×C₃₁	—	2	1	no	—
319	C₄⋊C₄×C₃₁	—	2	1	no	—
320	C₄⋊C₄×C₃₁	—	2	1	no	—
321	C₄⋊C₄×C₃₁	—	2	1	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	2	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	2	no	—
331	C₄⋊C₄×C₃₁	—	2	2	no	—
332	C₄⋊C₄×C₃₁	—	2	2	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	1	no	—
335	C₄⋊C₄×C₃₁	—	2	2	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	2	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	C₂×D₄	1	1	yes	characteristic
344	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
345	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
346	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
350	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
351	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
352	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
353	C₂²⋊C₄×C₃₁	—	2	2	no	—
354	C₂²⋊C₄×C₃₁	—	2	2	no	—
355	C₂²⋊C₄×C₃₁	—	2	2	no	—
356	C₂²⋊C₄×C₃₁	—	2	2	no	—
357	C₂²⋊C₄×C₃₁	—	2	2	no	—
358	C₂²⋊C₄×C₃₁	—	2	2	no	—
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	—	2	2	no	—
361	C₂²⋊C₄×C₃₁	—	2	2	no	—
362	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
367	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
368	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
369	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₃₁	—	2	2	no	—
373	C₄²×C₃₁	—	2	2	no	—
374	C₄²×C₃₁	—	2	2	no	—
375	C₄²×C₃₁	—	2	2	no	—
376	C₄²×C₃₁	—	2	2	no	—
377	C₄²×C₃₁	—	2	2	no	—
378	C₄²×C₃₁	—	2	2	no	—
379	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
383	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
384	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
385	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
389	#61008	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₂³×C₃₁	—	2	2	no	—
391	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
392	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
393	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	Q₈×C₃₁	—	2	4	no	—
395	Q₈×C₃₁	—	2	4	no	—
396	Q₈×C₃₁	—	2	4	no	—
397	Q₈×C₃₁	—	4	1	no	—
398	Q₈×C₃₁	—	4	4	no	—
399	Q₈×C₃₁	—	4	2	no	—
400	Q₈×C₃₁	—	4	2	no	—
401	Q₈×C₃₁	—	4	2	no	—
402	Q₈×C₃₁	—	4	2	no	—
403	Q₈×C₃₁	—	8	2	no	—
404	D₄×C₃₁	—	2	4	no	—
405	D₄×C₃₁	—	4	1	no	—
406	D₄×C₃₁	—	4	1	no	—
407	D₄×C₃₁	—	4	1	no	—
408	D₄×C₃₁	—	4	4	no	—
409	D₄×C₃₁	—	4	2	no	—
410	D₄×C₃₁	—	4	2	no	—
411	D₄×C₃₁	—	8	2	no	—
412	D₄×C₃₁	—	8	2	no	—
413	C₂×C₄×C₃₁	—	2	2	no	—
414	C₂×C₄×C₃₁	—	2	2	no	—
415	C₂×C₄×C₃₁	—	2	2	no	—
416	C₂×C₄×C₃₁	—	2	2	no	—
417	C₂×C₄×C₃₁	—	2	2	no	—
418	C₂×C₄×C₃₁	—	2	2	no	—
419	C₂×C₄×C₃₁	—	2	2	no	—
420	C₂×C₄×C₃₁	—	2	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	2	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	2	no	—
429	C₂×C₄×C₃₁	—	4	4	no	—
430	C₂×C₄×C₃₁	—	4	4	no	—
431	C₂×C₄×C₃₁	—	8	2	no	—
432	C₂×C₄×C₃₁	—	8	2	no	—
433	C₂×C₄×C₃₁	—	8	2	no	—
434	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
444	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
446	C₈×C₃₁	—	2	2	no	—
447	C₈×C₃₁	—	2	2	no	—
448	C₈×C₃₁	—	2	2	no	—
449	C₈×C₃₁	—	2	2	no	—
450	#3511	C₂×C₃₁	1	1	yes	characteristic
451	#3509	C₂×C₃₁	1	1	yes	characteristic, complemented
452	#3258	C₂×C₃₁	1	4	yes	complemented
453	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
454	#3230	C₂×C₃₁	1	1	yes	characteristic, complemented
455	#3229	C₂×C₃₁	1	1	yes	characteristic, complemented
456	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
457	#3210	C₂×C₃₁	1	1	yes	characteristic, complemented
458	#3210	C₂×C₃₁	1	1	yes	characteristic, complemented
459	#3209	C₂×C₃₁	1	1	yes	characteristic, complemented
460	#3206	C₂×C₃₁	1	1	yes	characteristic, complemented
461	#3201	C₂×C₃₁	1	4	yes	complemented
462	#3185	C₂×C₃₁	1	1	yes	characteristic, complemented
463	#3182	C₂×C₃₁	1	1	yes	characteristic, complemented
464	#3170	C₂×C₃₁	1	1	yes	characteristic, complemented
465	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
466	#3121	C₂×C₃₁	1	4	yes	complemented
467	#3120	C₂×C₃₁	1	4	yes	complemented
468	#2922	C₂×C₃₁	1	1	yes	characteristic, complemented
469	C₂²×C₃₁	—	2	1	no	—
470	C₂²×C₃₁	—	2	1	no	—
471	C₂²×C₃₁	—	2	1	no	—
472	C₂²×C₃₁	—	2	1	no	—
473	C₂²×C₃₁	—	2	1	no	—
474	C₂²×C₃₁	—	2	1	no	—
475	C₂²×C₃₁	—	2	1	no	—
476	C₂²×C₃₁	—	2	1	no	—
477	C₂²×C₃₁	—	2	1	no	—
478	C₂²×C₃₁	—	4	2	no	—
479	C₂²×C₃₁	—	4	2	no	—
480	C₂²×C₃₁	—	4	2	no	—
481	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
482	C₄×C₃₁	—	2	1	no	—
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	1	no	—
488	C₄×C₃₁	—	2	1	no	—
489	C₄×C₃₁	—	2	1	no	—
490	C₄×C₃₁	—	2	1	no	—
491	C₄×C₃₁	—	4	2	no	—
492	C₄×C₃₁	—	4	2	no	—
493	C₄×C₃₁	—	4	2	no	—
494	C₄×C₃₁	—	4	2	no	—
495	C₄×C₃₁	—	4	2	no	—
496	C₄×C₃₁	—	4	2	no	—
497	C₄×C₃₁	—	4	2	no	—
498	C₄×C₃₁	#577	1	2	yes	—
499	C₄×C₃₁	#578	1	2	yes	—
500	C₄×C₃₁	#585	1	2	yes	—
501	#557	—	2	1	no	—
502	#557	—	2	1	no	—
503	#556	—	2	1	no	—
504	#556	—	2	1	no	—
505	#556	—	2	1	no	—
506	#555	—	2	1	no	—
507	#554	—	2	1	no	—
508	#553	—	2	1	no	—
509	#553	—	2	1	no	—
510	#552	—	2	1	no	—
511	#552	—	2	1	no	—
512	#552	—	2	1	no	—
513	#552	—	2	1	no	—
514	#548	—	2	1	no	—
515	#548	—	2	1	no	—
516	#547	—	2	1	no	—
517	#542	C₂²×C₃₁	1	2	yes	—
518	#542	C₂²×C₃₁	1	2	yes	—
519	#541	C₂²×C₃₁	1	2	yes	—
520	#541	C₂²×C₃₁	1	2	yes	—
521	#537	C₂²×C₃₁	1	2	yes	—
522	#536	C₂²×C₃₁	1	2	yes	—
523	#533	C₂²×C₃₁	1	1	yes	characteristic
524	#533	C₂²×C₃₁	1	1	yes	characteristic
525	#533	C₂²×C₃₁	1	1	yes	characteristic
526	#533	C₂²×C₃₁	1	1	yes	characteristic
527	#533	C₂²×C₃₁	1	1	yes	characteristic
528	#533	C₂²×C₃₁	1	1	yes	characteristic
529	#533	C₂²×C₃₁	1	1	yes	characteristic
530	#532	C₂²×C₃₁	1	1	yes	characteristic
531	#532	C₂²×C₃₁	1	1	yes	characteristic
532	#532	C₂²×C₃₁	1	1	yes	characteristic
533	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
534	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
535	#520	C₂²×C₃₁	1	2	yes	—
536	#519	C₂²×C₃₁	1	2	yes	—
537	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
538	#500	C₂²×C₃₁	1	1	yes	characteristic
539	#500	C₂²×C₃₁	1	1	yes	characteristic
540	#498	C₂²×C₃₁	1	1	yes	characteristic
541	#498	C₂²×C₃₁	1	1	yes	characteristic
542	#494	C₂²×C₃₁	1	1	yes	characteristic
543	#494	C₂²×C₃₁	1	1	yes	characteristic
544	#492	C₂²×C₃₁	1	1	yes	characteristic
545	#492	C₂²×C₃₁	1	1	yes	characteristic
546	#487	C₂²×C₃₁	1	1	yes	characteristic
547	#487	C₂²×C₃₁	1	1	yes	characteristic
548	#487	C₂²×C₃₁	1	1	yes	characteristic
549	#487	C₂²×C₃₁	1	1	yes	characteristic
550	#487	C₂²×C₃₁	1	1	yes	characteristic
551	#487	C₂²×C₃₁	1	1	yes	characteristic
552	#486	C₂²×C₃₁	1	1	yes	characteristic
553	#486	C₂²×C₃₁	1	1	yes	characteristic
554	#485	C₂²×C₃₁	1	4	yes	—
555	#484	C₂²×C₃₁	1	4	yes	—
556	#483	C₂²×C₃₁	1	4	yes	—
557	#482	C₂²×C₃₁	1	4	yes	—
558	#479	C₂²×C₃₁	1	4	yes	—
559	#478	C₂²×C₃₁	1	4	yes	—
560	#477	C₂²×C₃₁	1	4	yes	—
561	#475	C₂²×C₃₁	1	4	yes	—
562	#470	C₂²×C₃₁	1	4	yes	—
563	#468	C₂²×C₃₁	1	4	yes	—
564	#467	C₂²×C₃₁	1	4	yes	—
565	#465	C₂²×C₃₁	1	4	yes	—
566	#464	C₂²×C₃₁	1	4	yes	—
567	#464	C₂²×C₃₁	1	4	yes	—
568	#462	C₂²×C₃₁	1	4	yes	—
569	#461	C₂²×C₃₁	1	4	yes	—
570	#452	C₂²×C₃₁	1	4	yes	—
571	#452	C₂²×C₃₁	1	4	yes	—
572	#451	C₂²×C₃₁	1	4	yes	—
573	#448	C₂²×C₃₁	1	4	yes	—
574	#441	C₂²×C₃₁	1	4	yes	—
575	#440	C₂²×C₃₁	1	4	yes	—
576	C₄×Q₁₆	C₂²×C₃₁	1	4	yes	—
577	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
578	#433	C₂²×C₃₁	1	2	yes	—
579	#433	C₂²×C₃₁	1	2	yes	—
580	#431	C₂²×C₃₁	1	1	yes	characteristic
581	#431	C₂²×C₃₁	1	1	yes	characteristic
582	#431	C₂²×C₃₁	1	1	yes	characteristic
583	#431	C₂²×C₃₁	1	1	yes	characteristic
584	#424	C₂²×C₃₁	1	2	yes	—
585	#408	C₂²×C₃₁	1	2	yes	—
586	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
587	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
588	C₂×C₃₁	—	4	1	no	—
589	C₂×C₃₁	—	4	1	no	—
590	C₂×C₃₁	—	4	1	no	—
591	C₂×C₃₁	—	8	2	no	—
592	C₂×C₃₁	#3449	1	1	yes	characteristic
593	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
594	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
595	C₂×#41	—	2	1	no	—
596	C₂×#41	—	2	1	no	—
597	C₂×#41	C₂³×C₃₁	1	2	yes	—
598	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
599	C₂²×Q₈	—	2	1	no	—
600	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
601	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
602	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
603	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
604	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
605	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
606	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
607	C₄⋊Q₈	—	2	2	no	—
608	C₄⋊Q₈	—	2	1	no	—
609	C₄⋊Q₈	—	2	1	no	—
610	C₄⋊Q₈	—	2	1	no	—
611	C₄⋊Q₈	—	2	1	no	—
612	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
613	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
614	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
615	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
616	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
617	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
618	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
619	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
620	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
621	#127	C₂³×C₃₁	1	1	yes	characteristic
622	#126	—	2	2	no	—
623	#126	—	2	2	no	—
624	#126	—	2	2	no	—
625	#126	—	2	2	no	—
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#125	—	2	2	no	—
629	#125	—	2	2	no	—
630	#125	—	2	2	no	—
631	#125	—	2	2	no	—
632	#125	—	2	1	no	—
633	#125	—	2	1	no	—
634	#125	—	2	1	no	—
635	#125	—	2	1	no	—
636	#125	—	2	1	no	—
637	#125	—	2	1	no	—
638	#125	C₂³×C₃₁	1	2	yes	—
639	#124	—	2	2	no	—
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	—	2	1	no	—
643	#124	—	2	1	no	—
644	#124	C₂³×C₃₁	1	2	yes	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	C₂²⋊Q₈	—	2	2	no	—
650	C₂²⋊Q₈	—	2	1	no	—
651	C₂²⋊Q₈	—	2	1	no	—
652	C₂²⋊Q₈	—	2	1	no	—
653	C₂²⋊Q₈	—	2	1	no	—
654	C₂²⋊Q₈	—	2	1	no	—
655	C₂²⋊Q₈	—	2	1	no	—
656	C₂²⋊Q₈	—	2	1	no	—
657	C₂²⋊Q₈	—	2	1	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
661	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
662	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
663	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
664	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
665	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
666	#121	—	2	2	no	—
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	—	2	1	no	—
670	#121	—	2	1	no	—
671	#121	—	2	1	no	—
672	#121	—	2	1	no	—
673	#121	C₂³×C₃₁	1	2	yes	—
674	#121	C₂³×C₃₁	1	2	yes	—
675	C₄×Q₈	—	2	2	no	—
676	C₄×Q₈	—	2	2	no	—
677	C₄×Q₈	—	2	1	no	—
678	C₄×Q₈	—	2	1	no	—
679	C₄×Q₈	—	2	1	no	—
680	C₄×Q₈	—	2	1	no	—
681	C₄×Q₈	—	2	1	no	—
682	C₄×Q₈	—	2	1	no	—
683	C₄×Q₈	—	2	1	no	—
684	C₄×Q₈	—	2	1	no	—
685	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
686	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
687	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
688	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
689	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
690	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
691	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
692	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	2	no	—
695	C₄×D₄	—	2	1	no	—
696	C₄×D₄	—	2	1	no	—
697	C₄×D₄	—	2	1	no	—
698	C₄×D₄	—	2	1	no	—
699	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
700	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
701	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
702	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
703	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
704	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
705	C₄×D₄	C₂³×C₃₁	1	2	yes	—
706	C₄×D₄	C₂³×C₃₁	1	2	yes	—
707	#117	—	2	1	no	—
708	#117	—	2	1	no	—
709	#117	—	2	1	no	—
710	#117	—	2	1	no	—
711	#117	—	2	1	no	—
712	#117	—	2	1	no	—
713	#117	—	2	2	no	—
714	#117	—	2	2	no	—
715	#117	—	2	2	no	—
716	#117	C₂³×C₃₁	1	2	yes	—
717	#117	C₂³×C₃₁	1	1	yes	characteristic
718	#117	C₂³×C₃₁	1	1	yes	characteristic
719	#117	C₂³×C₃₁	1	1	yes	characteristic
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	2	no	—
724	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
725	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
728	#107	C₂³×C₃₁	1	4	yes	—
729	#107	C₂³×C₃₁	1	4	yes	—
730	#106	C₂³×C₃₁	1	4	yes	—
731	#106	C₂³×C₃₁	1	4	yes	—
732	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
733	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
734	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
735	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
736	#103	C₂³×C₃₁	1	4	yes	—
737	#103	C₂³×C₃₁	1	4	yes	—
738	#103	C₂³×C₃₁	1	4	yes	—
739	#103	C₂³×C₃₁	1	4	yes	—
740	#103	C₂³×C₃₁	1	4	yes	—
741	#103	C₂³×C₃₁	1	4	yes	—
742	#102	C₂³×C₃₁	1	4	yes	—
743	#102	C₂³×C₃₁	1	4	yes	—
744	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
745	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
746	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
747	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
748	#97	C₂³×C₃₁	1	2	yes	—
749	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
750	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
751	C₄×C₈	C₂³×C₃₁	1	2	yes	—
752	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
753	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
754	C₃₁	#61008	1	1	yes	characteristic, direct product factor, Sylow
755	#41	—	4	2	no	—
756	#41	—	4	4	no	—
757	#41	—	8	2	no	—
758	#41	—	8	2	no	—
759	C₂×Q₈	—	2	1	no	—
760	C₂×Q₈	—	2	1	no	—
761	C₂×Q₈	—	2	2	no	—
762	C₂×Q₈	—	2	1	no	—
763	C₂×Q₈	—	2	1	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	—	4	4	no	—
766	C₂×Q₈	—	8	2	no	—
767	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
768	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
769	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
770	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	1	no	—
775	C₂×D₄	—	2	1	no	—
776	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
777	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
778	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
779	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
794	Q₁₆	—	4	4	no	—
795	Q₁₆	—	4	4	no	—
796	SD₁₆	—	4	4	no	—
797	SD₁₆	—	4	4	no	—
798	M₁₆	—	4	2	no	—
799	C₂×C₈	—	4	2	no	—
800	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
801	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
802	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
803	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	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	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
833	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
834	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
835	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
836	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
837	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
838	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
839	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
840	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
841	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
856	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
857	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
858	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
859	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
860	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
869	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
870	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
871	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
872	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
873	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
874	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
875	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
876	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
877	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
878	C₂³	—	2	2	no	—
879	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
880	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
881	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
882	Q₈	—	2	4	no	—
883	Q₈	—	2	4	no	—
884	Q₈	—	2	4	no	—
885	Q₈	—	4	1	no	—
886	Q₈	—	4	4	no	—
887	Q₈	—	4	2	no	—
888	Q₈	—	4	2	no	—
889	Q₈	—	4	2	no	—
890	Q₈	—	4	2	no	—
891	Q₈	—	8	2	no	—
892	D₄	—	2	4	no	—
893	D₄	—	4	1	no	—
894	D₄	—	4	1	no	—
895	D₄	—	4	1	no	—
896	D₄	—	4	4	no	—
897	D₄	—	4	2	no	—
898	D₄	—	4	2	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	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	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
923	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
924	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
925	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
926	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
927	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
932	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
933	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
934	C₈	—	2	2	no	—
935	C₈	—	2	2	no	—
936	C₈	—	2	2	no	—
937	C₈	—	2	2	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	C₃₁×#577	1	2	yes	—
968	C₄	C₃₁×#578	1	2	yes	—
969	C₄	C₃₁×#585	1	2	yes	—
970	C₂	—	4	1	no	—
971	C₂	—	4	1	no	—
972	C₂	—	4	1	no	—
973	C₂	—	8	2	no	—
974	C₂	C₃₁×#3449	1	1	yes	characteristic
975	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
976	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3511	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3509	C₂	semidirect
3. C₃₁×#3258	C₂	semidirect
4. C₃₁×#3231	C₂	semidirect
5. C₃₁×#3230	C₂	semidirect
6. C₃₁×#3229	C₂	semidirect
7. C₃₁×#3228	C₂	semidirect
8. C₃₁×#3210	C₂	semidirect
9. C₃₁×#3210	C₂	semidirect
10. C₃₁×#3209	C₂	semidirect
11. C₃₁×#3206	C₂	semidirect
12. C₃₁×#3201	C₂	semidirect
13. C₃₁×#3185	C₂	semidirect
14. C₃₁×#3182	C₂	semidirect
15. C₃₁×#3170	C₂	semidirect
16. C₃₁×#3167	C₂	semidirect
17. C₃₁×#3121	C₂	semidirect
18. C₃₁×#3120	C₂	semidirect
19. C₃₁×#2922	C₂	semidirect
389. #61008	C₃₁	direct (N × H)
451. #3509	C₂×C₃₁	semidirect
452. #3258	C₂×C₃₁	semidirect
453. #3231	C₂×C₃₁	semidirect
454. #3230	C₂×C₃₁	semidirect
455. #3229	C₂×C₃₁	semidirect
456. #3228	C₂×C₃₁	semidirect
457. #3210	C₂×C₃₁	semidirect
458. #3210	C₂×C₃₁	semidirect
459. #3209	C₂×C₃₁	semidirect
460. #3206	C₂×C₃₁	semidirect
461. #3201	C₂×C₃₁	semidirect
462. #3185	C₂×C₃₁	semidirect
463. #3182	C₂×C₃₁	semidirect
464. #3170	C₂×C₃₁	semidirect
465. #3167	C₂×C₃₁	semidirect
466. #3121	C₂×C₃₁	semidirect
467. #3120	C₂×C₃₁	semidirect
468. #2922	C₂×C₃₁	semidirect
754. C₃₁	#61008	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×#3511	2
C₃₁×#3509	2
C₃₁×#3258	2
C₃₁×#3231	2
C₃₁×#3230	2
C₃₁×#3229	2
C₃₁×#3228	2
C₃₁×#3210	2
C₃₁×#3209	2
C₃₁×#3206	2
C₃₁×#3201	2
C₃₁×#3185	2
C₃₁×#3182	2
C₃₁×#3170	2
C₃₁×#3167	2
C₃₁×#3121	2
C₃₁×#3120	2
C₃₁×#2922	2
#61008	31

Subgroups — C31×#61008 #21517767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61008 #21517767