Subgroups — C₃₁×#62167 #21518926

Order 7936.

1684 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3559	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3388	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3372	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3350	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3337	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3260	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3126	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3082	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	1	no	—
21	C₃₁×#562	—	2	1	no	—
22	C₃₁×#557	—	2	1	no	—
23	C₃₁×#557	C₂²	1	1	yes	characteristic
24	C₃₁×#557	C₂²	1	1	yes	characteristic
25	C₃₁×#556	—	2	1	no	—
26	C₃₁×#556	C₂²	1	1	yes	characteristic
27	C₃₁×#554	C₂²	1	2	yes	—
28	C₃₁×#553	C₂²	1	2	yes	—
29	C₃₁×#553	C₂²	1	2	yes	—
30	C₃₁×#552	—	2	2	no	—
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×#547	—	2	2	no	—
35	C₃₁×#547	C₂²	1	2	yes	—
36	C₃₁×#544	C₂²	1	2	yes	—
37	C₃₁×#541	—	2	2	no	—
38	C₃₁×#541	C₂²	1	2	yes	—
39	C₃₁×#540	C₂²	1	2	yes	—
40	C₃₁×#539	—	2	2	no	—
41	C₃₁×#539	—	2	1	no	—
42	C₃₁×#537	—	2	1	no	—
43	C₃₁×#533	—	2	1	no	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#532	C₂²	1	1	yes	characteristic
46	C₃₁×#529	—	2	1	no	—
47	C₃₁×#529	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
49	C₃₁×#519	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	—
52	C₃₁×#501	C₂²	1	2	yes	—
53	C₃₁×#499	C₂²	1	2	yes	—
54	C₃₁×#491	C₂²	1	2	yes	—
55	C₃₁×#491	C₂²	1	2	yes	—
56	C₃₁×#487	C₂²	1	2	yes	—
57	C₃₁×#485	C₂²	1	2	yes	—
58	C₃₁×#485	C₂²	1	2	yes	—
59	C₃₁×#484	C₂²	1	2	yes	—
60	C₃₁×#484	C₂²	1	2	yes	—
61	C₃₁×#483	C₂²	1	2	yes	—
62	C₃₁×#483	C₂²	1	2	yes	—
63	C₃₁×#482	C₂²	1	2	yes	—
64	C₃₁×#482	C₂²	1	2	yes	—
65	C₃₁×#480	C₂²	1	2	yes	—
66	C₃₁×#479	C₂²	1	2	yes	—
67	C₃₁×#479	C₂²	1	2	yes	—
68	C₃₁×#479	C₂²	1	2	yes	—
69	C₃₁×#479	C₂²	1	2	yes	—
70	C₃₁×#479	C₂²	1	2	yes	—
71	C₃₁×#479	C₂²	1	2	yes	—
72	C₃₁×#479	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	—
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#478	C₂²	1	2	yes	—
76	C₃₁×#477	C₂²	1	1	yes	characteristic
77	C₃₁×#477	C₂²	1	2	yes	—
78	C₃₁×#477	C₂²	1	1	yes	characteristic
79	C₃₁×#476	C₂²	1	2	yes	—
80	C₃₁×#475	C₂²	1	2	yes	—
81	C₃₁×#475	C₂²	1	2	yes	—
82	C₃₁×#468	C₂²	1	2	yes	—
83	C₃₁×#468	C₂²	1	2	yes	—
84	C₃₁×#465	C₂²	1	2	yes	—
85	C₃₁×#465	C₂²	1	2	yes	—
86	C₃₁×#465	C₂²	1	2	yes	—
87	C₃₁×#465	C₂²	1	2	yes	—
88	C₃₁×#461	C₂²	1	2	yes	—
89	C₃₁×#461	C₂²	1	2	yes	—
90	C₃₁×#461	C₂²	1	2	yes	—
91	C₃₁×#460	C₂²	1	1	yes	characteristic
92	C₃₁×#460	C₂²	1	1	yes	characteristic
93	C₃₁×#460	C₂²	1	2	yes	—
94	C₃₁×#448	C₂²	1	2	yes	—
95	C₃₁×#448	C₂²	1	2	yes	—
96	C₃₁×#448	C₂²	1	2	yes	—
97	C₃₁×#446	C₂²	1	2	yes	—
98	C₃₁×#440	C₂²	1	2	yes	—
99	C₃₁×#440	C₂²	1	2	yes	—
100	C₃₁×#440	C₂²	1	2	yes	—
101	C₃₁×#440	C₂²	1	2	yes	—
102	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
103	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
104	C₃₁×#435	C₂²	1	2	yes	—
105	C₃₁×#435	C₂²	1	2	yes	—
106	C₈×D₄×C₃₁	C₂²	1	2	yes	—
107	C₃₁×#433	C₂²	1	2	yes	—
108	C₃₁×#432	C₂²	1	1	yes	characteristic
109	C₃₁×#428	C₂²	1	2	yes	—
110	C₃₁×#427	C₂²	1	2	yes	—
111	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
112	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
113	C₃₁×#424	C₂²	1	2	yes	—
114	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₃₁×#419	C₂²	1	2	yes	—
116	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
117	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×#103	C₂²	1	2	yes	—
119	C₂×#41×C₃₁	—	2	2	no	—
120	C₂×#41×C₃₁	—	2	1	no	—
121	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
131	C₃₁×C₄⋊Q₈	—	2	1	no	—
132	C₃₁×C₄⋊Q₈	—	2	1	no	—
133	C₃₁×C₄⋊Q₈	—	2	2	no	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×#127	C₂³	1	1	yes	characteristic
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#126	D₄	1	2	yes	—
148	C₃₁×#125	—	2	1	no	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	—	2	2	no	—
151	C₃₁×#125	—	2	2	no	—
152	C₃₁×#125	—	2	2	no	—
153	C₃₁×#125	—	2	2	no	—
154	C₃₁×#125	—	2	2	no	—
155	C₃₁×#125	—	2	1	no	—
156	C₃₁×#125	—	2	1	no	—
157	C₃₁×#125	—	2	1	no	—
158	C₃₁×#125	D₄	1	1	yes	characteristic
159	C₃₁×#125	C₂³	1	2	yes	—
160	C₃₁×#125	C₂³	1	2	yes	—
161	C₃₁×#125	C₂³	1	2	yes	—
162	C₃₁×#125	C₂³	1	2	yes	—
163	C₃₁×#124	—	2	1	no	—
164	C₃₁×#124	—	2	1	no	—
165	C₃₁×#124	D₄	1	1	yes	characteristic
166	C₃₁×#123	—	2	2	no	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	—	2	2	no	—
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	—	2	2	no	—
173	C₃₁×#123	D₄	1	2	yes	—
174	C₃₁×C₂²⋊Q₈	—	2	2	no	—
175	C₃₁×C₂²⋊Q₈	—	2	1	no	—
176	C₃₁×C₂²⋊Q₈	—	2	2	no	—
177	C₃₁×C₂²⋊Q₈	—	2	2	no	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
185	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
186	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
188	C₃₁×#121	—	2	2	no	—
189	C₃₁×#121	—	2	2	no	—
190	C₃₁×#121	—	2	1	no	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	—	2	2	no	—
193	C₃₁×#121	D₄	1	1	yes	characteristic
194	C₃₁×#121	C₂³	1	2	yes	—
195	C₃₁×#121	C₂³	1	2	yes	—
196	C₃₁×#121	C₂³	1	2	yes	—
197	C₄×Q₈×C₃₁	—	2	1	no	—
198	C₄×Q₈×C₃₁	—	2	2	no	—
199	C₄×Q₈×C₃₁	—	2	2	no	—
200	C₄×Q₈×C₃₁	—	2	1	no	—
201	C₄×Q₈×C₃₁	—	2	1	no	—
202	C₄×Q₈×C₃₁	—	2	1	no	—
203	C₄×Q₈×C₃₁	—	2	1	no	—
204	C₄×Q₈×C₃₁	—	2	1	no	—
205	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
206	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
207	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₃₁	—	2	2	no	—
214	C₄×D₄×C₃₁	—	2	1	no	—
215	C₄×D₄×C₃₁	—	2	2	no	—
216	C₄×D₄×C₃₁	—	2	2	no	—
217	C₄×D₄×C₃₁	—	2	1	no	—
218	C₄×D₄×C₃₁	C₂³	1	2	yes	—
219	C₄×D₄×C₃₁	C₂³	1	2	yes	—
220	C₄×D₄×C₃₁	C₂³	1	2	yes	—
221	C₄×D₄×C₃₁	C₂³	1	2	yes	—
222	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
223	C₃₁×#117	—	2	1	no	—
224	C₃₁×#117	—	2	2	no	—
225	C₃₁×#117	—	2	2	no	—
226	C₃₁×#117	—	2	2	no	—
227	C₃₁×#117	C₂³	1	2	yes	—
228	C₃₁×#117	C₂³	1	2	yes	—
229	C₃₁×#117	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
231	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
232	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
233	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₃₁	—	2	1	no	—
239	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#107	C₂³	1	2	yes	—
245	C₃₁×#107	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×#106	C₂³	1	2	yes	—
249	C₃₁×#106	C₂³	1	2	yes	—
250	C₃₁×#106	C₂³	1	2	yes	—
251	C₃₁×#106	C₂³	1	2	yes	—
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₃₁×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	#41×C₃₁	—	8	2	no	—
281	#41×C₃₁	—	8	4	no	—
282	C₂×Q₈×C₃₁	—	2	1	no	—
283	C₂×Q₈×C₃₁	—	2	2	no	—
284	C₂×Q₈×C₃₁	—	2	1	no	—
285	C₂×Q₈×C₃₁	—	2	2	no	—
286	C₂×Q₈×C₃₁	—	2	1	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	—	2	4	no	—
289	C₂×Q₈×C₃₁	—	4	1	no	—
290	C₂×Q₈×C₃₁	—	4	2	no	—
291	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂×D₄×C₃₁	—	2	2	no	—
296	C₂×D₄×C₃₁	—	2	2	no	—
297	C₂×D₄×C₃₁	—	2	2	no	—
298	C₂×D₄×C₃₁	—	2	1	no	—
299	C₂×D₄×C₃₁	—	2	1	no	—
300	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
301	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₃₁	—	2	1	no	—
304	C₂²×C₄×C₃₁	—	2	1	no	—
305	C₂²×C₄×C₃₁	—	2	1	no	—
306	C₂²×C₄×C₃₁	—	2	2	no	—
307	C₂²×C₄×C₃₁	—	2	1	no	—
308	C₂²×C₄×C₃₁	—	2	2	no	—
309	C₂²×C₄×C₃₁	—	2	2	no	—
310	C₂²×C₄×C₃₁	—	2	2	no	—
311	C₂²×C₄×C₃₁	—	2	2	no	—
312	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
316	SD₁₆×C₃₁	—	2	4	no	—
317	SD₁₆×C₃₁	—	4	2	no	—
318	SD₁₆×C₃₁	—	4	2	no	—
319	SD₁₆×C₃₁	—	4	2	no	—
320	M₁₆×C₃₁	—	4	2	no	—
321	C₂×C₈×C₃₁	—	4	1	no	—
322	C₂×C₈×C₃₁	—	4	2	no	—
323	C₂×C₈×C₃₁	—	4	1	no	—
324	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
325	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
326	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
327	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
328	C₄⋊C₄×C₃₁	—	2	2	no	—
329	C₄⋊C₄×C₃₁	—	2	1	no	—
330	C₄⋊C₄×C₃₁	—	2	1	no	—
331	C₄⋊C₄×C₃₁	—	2	1	no	—
332	C₄⋊C₄×C₃₁	—	2	1	no	—
333	C₄⋊C₄×C₃₁	—	2	2	no	—
334	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
339	C₄⋊C₄×C₃₁	—	2	1	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	1	no	—
342	C₄⋊C₄×C₃₁	—	2	2	no	—
343	C₄⋊C₄×C₃₁	—	2	2	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	1	no	—
346	C₄⋊C₄×C₃₁	—	2	2	no	—
347	C₄⋊C₄×C₃₁	—	2	1	no	—
348	C₄⋊C₄×C₃₁	—	2	2	no	—
349	C₄⋊C₄×C₃₁	—	2	1	no	—
350	C₄⋊C₄×C₃₁	—	2	1	no	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
363	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
369	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	2	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	2	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
381	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
382	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
383	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
385	C₄²×C₃₁	—	2	1	no	—
386	C₄²×C₃₁	—	2	1	no	—
387	C₄²×C₃₁	—	2	1	no	—
388	C₄²×C₃₁	—	2	1	no	—
389	C₄²×C₃₁	—	2	2	no	—
390	C₄²×C₃₁	—	2	2	no	—
391	C₄²×C₃₁	—	2	2	no	—
392	C₄²×C₃₁	—	2	2	no	—
393	C₄²×C₃₁	—	2	2	no	—
394	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₃₁	C₂⁴	1	2	yes	—
397	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
399	#62167	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
400	C₂³×C₃₁	—	2	2	no	—
401	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
402	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
403	Q₈×C₃₁	—	2	1	no	—
404	Q₈×C₃₁	—	2	1	no	—
405	Q₈×C₃₁	—	2	2	no	—
406	Q₈×C₃₁	—	2	2	no	—
407	Q₈×C₃₁	—	2	1	no	—
408	Q₈×C₃₁	—	4	1	no	—
409	Q₈×C₃₁	—	4	2	no	—
410	Q₈×C₃₁	—	4	4	no	—
411	Q₈×C₃₁	—	4	2	no	—
412	Q₈×C₃₁	—	8	1	no	—
413	Q₈×C₃₁	—	8	2	no	—
414	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
415	D₄×C₃₁	—	2	4	no	—
416	D₄×C₃₁	—	2	2	no	—
417	D₄×C₃₁	—	2	2	no	—
418	D₄×C₃₁	—	4	1	no	—
419	D₄×C₃₁	—	4	4	no	—
420	D₄×C₃₁	—	8	1	no	—
421	D₄×C₃₁	—	8	1	no	—
422	D₄×C₃₁	—	8	2	no	—
423	D₄×C₃₁	—	8	2	no	—
424	C₂×C₄×C₃₁	—	2	2	no	—
425	C₂×C₄×C₃₁	—	2	1	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	1	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	2	1	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	1	no	—
433	C₂×C₄×C₃₁	—	2	1	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	2	no	—
437	C₂×C₄×C₃₁	—	2	2	no	—
438	C₂×C₄×C₃₁	—	4	1	no	—
439	C₂×C₄×C₃₁	—	4	2	no	—
440	C₂×C₄×C₃₁	—	4	4	no	—
441	C₂×C₄×C₃₁	—	4	2	no	—
442	C₂×C₄×C₃₁	—	4	2	no	—
443	C₂×C₄×C₃₁	—	8	2	no	—
444	C₂×C₄×C₃₁	—	8	2	no	—
445	C₂×C₄×C₃₁	—	8	2	no	—
446	C₂×C₄×C₃₁	—	8	1	no	—
447	C₂×C₄×C₃₁	—	8	2	no	—
448	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
457	C₈×C₃₁	—	2	2	no	—
458	C₈×C₃₁	—	2	2	no	—
459	C₈×C₃₁	—	2	2	no	—
460	C₈×C₃₁	—	2	2	no	—
461	#3559	C₂×C₃₁	1	1	yes	characteristic
462	#3523	C₂×C₃₁	1	1	yes	characteristic, complemented
463	#3388	C₂×C₃₁	1	2	yes	complemented
464	#3372	C₂×C₃₁	1	2	yes	complemented
465	#3350	C₂×C₃₁	1	2	yes	complemented
466	#3343	C₂×C₃₁	1	2	yes	complemented
467	#3337	C₂×C₃₁	1	2	yes	complemented
468	#3320	C₂×C₃₁	1	2	yes	complemented
469	#3320	C₂×C₃₁	1	2	yes	complemented
470	#3298	C₂×C₃₁	1	2	yes	complemented
471	#3260	C₂×C₃₁	1	2	yes	complemented
472	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
473	#3242	C₂×C₃₁	1	2	yes	complemented
474	#3236	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#3126	C₂×C₃₁	1	2	yes	complemented
476	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
477	#3082	C₂×C₃₁	1	2	yes	complemented
478	C₂×#479	C₂×C₃₁	1	1	yes	characteristic, complemented
479	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
480	C₂²×C₃₁	—	2	1	no	—
481	C₂²×C₃₁	—	2	1	no	—
482	C₂²×C₃₁	—	2	2	no	—
483	C₂²×C₃₁	—	2	2	no	—
484	C₂²×C₃₁	—	2	2	no	—
485	C₂²×C₃₁	—	4	2	no	—
486	C₂²×C₃₁	—	4	2	no	—
487	C₂²×C₃₁	—	4	2	no	—
488	C₂²×C₃₁	#577	1	2	yes	—
489	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
490	C₄×C₃₁	—	2	1	no	—
491	C₄×C₃₁	—	2	1	no	—
492	C₄×C₃₁	—	2	2	no	—
493	C₄×C₃₁	—	2	1	no	—
494	C₄×C₃₁	—	2	2	no	—
495	C₄×C₃₁	—	2	2	no	—
496	C₄×C₃₁	—	2	1	no	—
497	C₄×C₃₁	—	2	1	no	—
498	C₄×C₃₁	—	2	2	no	—
499	C₄×C₃₁	—	4	2	no	—
500	C₄×C₃₁	—	4	2	no	—
501	C₄×C₃₁	—	4	1	no	—
502	C₄×C₃₁	—	4	2	no	—
503	C₄×C₃₁	—	4	1	no	—
504	C₄×C₃₁	—	4	1	no	—
505	C₄×C₃₁	—	4	2	no	—
506	C₄×C₃₁	—	4	2	no	—
507	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
508	C₄×C₃₁	#585	1	1	yes	characteristic
509	#563	—	2	1	no	—
510	#562	—	2	1	no	—
511	#557	—	2	1	no	—
512	#557	C₂²×C₃₁	1	1	yes	characteristic
513	#557	C₂²×C₃₁	1	1	yes	characteristic
514	#556	—	2	1	no	—
515	#556	C₂²×C₃₁	1	1	yes	characteristic
516	#554	C₂²×C₃₁	1	2	yes	—
517	#553	C₂²×C₃₁	1	2	yes	—
518	#553	C₂²×C₃₁	1	2	yes	—
519	#552	—	2	2	no	—
520	#552	C₂²×C₃₁	1	2	yes	—
521	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
522	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
523	#547	—	2	2	no	—
524	#547	C₂²×C₃₁	1	2	yes	—
525	#544	C₂²×C₃₁	1	2	yes	—
526	#541	—	2	2	no	—
527	#541	C₂²×C₃₁	1	2	yes	—
528	#540	C₂²×C₃₁	1	2	yes	—
529	#539	—	2	2	no	—
530	#539	—	2	1	no	—
531	#537	—	2	1	no	—
532	#533	—	2	1	no	—
533	#533	C₂²×C₃₁	1	1	yes	characteristic
534	#532	C₂²×C₃₁	1	1	yes	characteristic
535	#529	—	2	1	no	—
536	#529	C₂²×C₃₁	1	1	yes	characteristic
537	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
538	#519	C₂²×C₃₁	1	2	yes	—
539	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
540	#501	C₂²×C₃₁	1	2	yes	—
541	#501	C₂²×C₃₁	1	2	yes	—
542	#499	C₂²×C₃₁	1	2	yes	—
543	#491	C₂²×C₃₁	1	2	yes	—
544	#491	C₂²×C₃₁	1	2	yes	—
545	#487	C₂²×C₃₁	1	2	yes	—
546	#485	C₂²×C₃₁	1	2	yes	—
547	#485	C₂²×C₃₁	1	2	yes	—
548	#484	C₂²×C₃₁	1	2	yes	—
549	#484	C₂²×C₃₁	1	2	yes	—
550	#483	C₂²×C₃₁	1	2	yes	—
551	#483	C₂²×C₃₁	1	2	yes	—
552	#482	C₂²×C₃₁	1	2	yes	—
553	#482	C₂²×C₃₁	1	2	yes	—
554	#480	C₂²×C₃₁	1	2	yes	—
555	#479	C₂²×C₃₁	1	2	yes	—
556	#479	C₂²×C₃₁	1	2	yes	—
557	#479	C₂²×C₃₁	1	2	yes	—
558	#479	C₂²×C₃₁	1	2	yes	—
559	#479	C₂²×C₃₁	1	2	yes	—
560	#479	C₂²×C₃₁	1	2	yes	—
561	#479	C₂²×C₃₁	1	2	yes	—
562	#479	C₂²×C₃₁	1	2	yes	—
563	#478	C₂²×C₃₁	1	2	yes	—
564	#478	C₂²×C₃₁	1	2	yes	—
565	#477	C₂²×C₃₁	1	1	yes	characteristic
566	#477	C₂²×C₃₁	1	2	yes	—
567	#477	C₂²×C₃₁	1	1	yes	characteristic
568	#476	C₂²×C₃₁	1	2	yes	—
569	#475	C₂²×C₃₁	1	2	yes	—
570	#475	C₂²×C₃₁	1	2	yes	—
571	#468	C₂²×C₃₁	1	2	yes	—
572	#468	C₂²×C₃₁	1	2	yes	—
573	#465	C₂²×C₃₁	1	2	yes	—
574	#465	C₂²×C₃₁	1	2	yes	—
575	#465	C₂²×C₃₁	1	2	yes	—
576	#465	C₂²×C₃₁	1	2	yes	—
577	#461	C₂²×C₃₁	1	2	yes	—
578	#461	C₂²×C₃₁	1	2	yes	—
579	#461	C₂²×C₃₁	1	2	yes	—
580	#460	C₂²×C₃₁	1	1	yes	characteristic
581	#460	C₂²×C₃₁	1	1	yes	characteristic
582	#460	C₂²×C₃₁	1	2	yes	—
583	#448	C₂²×C₃₁	1	2	yes	—
584	#448	C₂²×C₃₁	1	2	yes	—
585	#448	C₂²×C₃₁	1	2	yes	—
586	#446	C₂²×C₃₁	1	2	yes	—
587	#440	C₂²×C₃₁	1	2	yes	—
588	#440	C₂²×C₃₁	1	2	yes	—
589	#440	C₂²×C₃₁	1	2	yes	—
590	#440	C₂²×C₃₁	1	2	yes	—
591	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
592	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
593	#435	C₂²×C₃₁	1	2	yes	—
594	#435	C₂²×C₃₁	1	2	yes	—
595	C₈×D₄	C₂²×C₃₁	1	2	yes	—
596	#433	C₂²×C₃₁	1	2	yes	—
597	#432	C₂²×C₃₁	1	1	yes	characteristic
598	#428	C₂²×C₃₁	1	2	yes	—
599	#427	C₂²×C₃₁	1	2	yes	—
600	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
601	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
602	#424	C₂²×C₃₁	1	2	yes	—
603	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
604	#419	C₂²×C₃₁	1	2	yes	—
605	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
606	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
607	C₂×#103	C₂²×C₃₁	1	2	yes	—
608	C₂×C₃₁	—	2	2	no	—
609	C₂×C₃₁	—	4	2	no	—
610	C₂×C₃₁	—	8	2	no	—
611	C₂×C₃₁	#3489	1	1	yes	characteristic
612	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
613	C₂×C₃₁	#3586	1	1	yes	characteristic
614	C₂×#41	—	2	2	no	—
615	C₂×#41	—	2	1	no	—
616	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
617	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
618	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
619	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
620	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
621	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
622	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
623	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
624	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
625	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
626	C₄⋊Q₈	—	2	1	no	—
627	C₄⋊Q₈	—	2	1	no	—
628	C₄⋊Q₈	—	2	2	no	—
629	C₄⋊Q₈	—	2	2	no	—
630	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
631	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
632	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
633	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
634	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
635	#127	C₂³×C₃₁	1	1	yes	characteristic
636	#126	—	2	2	no	—
637	#126	—	2	2	no	—
638	#126	—	2	2	no	—
639	#126	—	2	2	no	—
640	#126	—	2	2	no	—
641	#126	—	2	2	no	—
642	#126	D₄×C₃₁	1	2	yes	—
643	#125	—	2	1	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	1	no	—
651	#125	—	2	1	no	—
652	#125	—	2	1	no	—
653	#125	D₄×C₃₁	1	1	yes	characteristic
654	#125	C₂³×C₃₁	1	2	yes	—
655	#125	C₂³×C₃₁	1	2	yes	—
656	#125	C₂³×C₃₁	1	2	yes	—
657	#125	C₂³×C₃₁	1	2	yes	—
658	#124	—	2	1	no	—
659	#124	—	2	1	no	—
660	#124	D₄×C₃₁	1	1	yes	characteristic
661	#123	—	2	2	no	—
662	#123	—	2	2	no	—
663	#123	—	2	2	no	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	D₄×C₃₁	1	2	yes	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	1	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	—	2	2	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	D₄×C₃₁	1	1	yes	characteristic
680	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
681	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
682	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
683	#121	—	2	2	no	—
684	#121	—	2	2	no	—
685	#121	—	2	1	no	—
686	#121	—	2	2	no	—
687	#121	—	2	2	no	—
688	#121	D₄×C₃₁	1	1	yes	characteristic
689	#121	C₂³×C₃₁	1	2	yes	—
690	#121	C₂³×C₃₁	1	2	yes	—
691	#121	C₂³×C₃₁	1	2	yes	—
692	C₄×Q₈	—	2	1	no	—
693	C₄×Q₈	—	2	2	no	—
694	C₄×Q₈	—	2	2	no	—
695	C₄×Q₈	—	2	1	no	—
696	C₄×Q₈	—	2	1	no	—
697	C₄×Q₈	—	2	1	no	—
698	C₄×Q₈	—	2	1	no	—
699	C₄×Q₈	—	2	1	no	—
700	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
701	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
702	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
703	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
704	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
705	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
706	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
707	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
708	C₄×D₄	—	2	2	no	—
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	—	2	2	no	—
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	1	no	—
713	C₄×D₄	C₂³×C₃₁	1	2	yes	—
714	C₄×D₄	C₂³×C₃₁	1	2	yes	—
715	C₄×D₄	C₂³×C₃₁	1	2	yes	—
716	C₄×D₄	C₂³×C₃₁	1	2	yes	—
717	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
718	#117	—	2	1	no	—
719	#117	—	2	2	no	—
720	#117	—	2	2	no	—
721	#117	—	2	2	no	—
722	#117	C₂³×C₃₁	1	2	yes	—
723	#117	C₂³×C₃₁	1	2	yes	—
724	#117	C₂³×C₃₁	1	2	yes	—
725	C₂×C₄⋊C₄	—	2	1	no	—
726	C₂×C₄⋊C₄	—	2	1	no	—
727	C₂×C₄⋊C₄	—	2	1	no	—
728	C₂×C₄⋊C₄	—	2	2	no	—
729	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
733	C₂×C₄²	—	2	1	no	—
734	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
735	#107	C₂³×C₃₁	1	2	yes	—
736	#107	C₂³×C₃₁	1	2	yes	—
737	#107	C₂³×C₃₁	1	2	yes	—
738	#107	C₂³×C₃₁	1	2	yes	—
739	#107	C₂³×C₃₁	1	2	yes	—
740	#107	C₂³×C₃₁	1	2	yes	—
741	#106	C₂³×C₃₁	1	2	yes	—
742	#106	C₂³×C₃₁	1	2	yes	—
743	#106	C₂³×C₃₁	1	2	yes	—
744	#106	C₂³×C₃₁	1	2	yes	—
745	#106	C₂³×C₃₁	1	2	yes	—
746	#106	C₂³×C₃₁	1	2	yes	—
747	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
748	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
749	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
750	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
751	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
752	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
753	#103	C₂³×C₃₁	1	2	yes	—
754	#103	C₂³×C₃₁	1	2	yes	—
755	#103	C₂³×C₃₁	1	2	yes	—
756	#103	C₂³×C₃₁	1	2	yes	—
757	#103	C₂³×C₃₁	1	2	yes	—
758	#103	C₂³×C₃₁	1	2	yes	—
759	#103	C₂³×C₃₁	1	2	yes	—
760	#103	C₂³×C₃₁	1	2	yes	—
761	#103	C₂³×C₃₁	1	2	yes	—
762	#103	C₂³×C₃₁	1	2	yes	—
763	#103	C₂³×C₃₁	1	2	yes	—
764	#103	C₂³×C₃₁	1	2	yes	—
765	#102	C₂³×C₃₁	1	2	yes	—
766	#102	C₂³×C₃₁	1	2	yes	—
767	#102	C₂³×C₃₁	1	2	yes	—
768	#102	C₂³×C₃₁	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
772	#97	C₂³×C₃₁	1	2	yes	—
773	#97	C₂³×C₃₁	1	2	yes	—
774	C₄×C₈	C₂³×C₃₁	1	2	yes	—
775	C₃₁	#62167	1	1	yes	characteristic, direct product factor, Sylow
776	#41	—	8	2	no	—
777	#41	—	8	4	no	—
778	C₂×Q₈	—	2	1	no	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	2	1	no	—
781	C₂×Q₈	—	2	2	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	2	no	—
784	C₂×Q₈	—	2	4	no	—
785	C₂×Q₈	—	4	1	no	—
786	C₂×Q₈	—	4	2	no	—
787	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
788	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
789	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
790	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
797	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
798	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	2	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
809	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
812	SD₁₆	—	2	4	no	—
813	SD₁₆	—	4	2	no	—
814	SD₁₆	—	4	2	no	—
815	SD₁₆	—	4	2	no	—
816	M₁₆	—	4	2	no	—
817	C₂×C₈	—	4	1	no	—
818	C₂×C₈	—	4	2	no	—
819	C₂×C₈	—	4	1	no	—
820	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
821	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
822	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
823	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	1	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	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	—	2	1	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	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
854	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
855	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
856	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
857	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
858	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
859	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
860	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
861	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
862	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
863	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
864	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
877	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
878	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
879	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
880	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
881	C₄²	—	2	1	no	—
882	C₄²	—	2	1	no	—
883	C₄²	—	2	1	no	—
884	C₄²	—	2	1	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	2	no	—
889	C₄²	—	2	2	no	—
890	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
891	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
892	C₄²	C₂⁴×C₃₁	1	2	yes	—
893	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂³	—	2	2	no	—
896	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
897	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
898	Q₈	—	2	1	no	—
899	Q₈	—	2	1	no	—
900	Q₈	—	2	2	no	—
901	Q₈	—	2	2	no	—
902	Q₈	—	2	1	no	—
903	Q₈	—	4	1	no	—
904	Q₈	—	4	2	no	—
905	Q₈	—	4	4	no	—
906	Q₈	—	4	2	no	—
907	Q₈	—	8	1	no	—
908	Q₈	—	8	2	no	—
909	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
910	D₄	—	2	4	no	—
911	D₄	—	2	2	no	—
912	D₄	—	2	2	no	—
913	D₄	—	4	1	no	—
914	D₄	—	4	4	no	—
915	D₄	—	8	1	no	—
916	D₄	—	8	1	no	—
917	D₄	—	8	2	no	—
918	D₄	—	8	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	2	no	—
935	C₂×C₄	—	4	4	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	—	8	2	no	—
940	C₂×C₄	—	8	2	no	—
941	C₂×C₄	—	8	1	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
944	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
945	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
947	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
948	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
949	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
950	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
951	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
952	C₈	—	2	2	no	—
953	C₈	—	2	2	no	—
954	C₈	—	2	2	no	—
955	C₈	—	2	2	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	2	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	4	2	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	C₃₁×#577	1	2	yes	—
965	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
966	C₄	—	2	1	no	—
967	C₄	—	2	2	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	1	no	—
973	C₄	—	2	1	no	—
974	C₄	—	2	2	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
984	C₄	C₃₁×#585	1	1	yes	characteristic
985	C₂	—	2	2	no	—
986	C₂	—	4	2	no	—
987	C₂	—	8	2	no	—
988	C₂	C₃₁×#3489	1	1	yes	characteristic
989	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
990	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×#3559	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
2. C₃₁×#3523	C₂	semidirect
3. C₃₁×#3388	C₂	semidirect
4. C₃₁×#3372	C₂	semidirect
5. C₃₁×#3350	C₂	semidirect
6. C₃₁×#3343	C₂	semidirect
7. C₃₁×#3337	C₂	semidirect
8. C₃₁×#3320	C₂	semidirect
9. C₃₁×#3320	C₂	semidirect
10. C₃₁×#3298	C₂	semidirect
11. C₃₁×#3260	C₂	semidirect
12. C₃₁×#3246	C₂	semidirect
13. C₃₁×#3242	C₂	semidirect
14. C₃₁×#3236	C₂	semidirect
15. C₃₁×#3126	C₂	semidirect
16. C₃₁×#3112	C₂	semidirect
17. C₃₁×#3082	C₂	semidirect
18. C₂×C₃₁×#479	C₂	semidirect
19. C₃₁×#2992	C₂	semidirect
399. #62167	C₃₁	direct (N × H)
462. #3523	C₂×C₃₁	semidirect
463. #3388	C₂×C₃₁	semidirect
464. #3372	C₂×C₃₁	semidirect
465. #3350	C₂×C₃₁	semidirect
466. #3343	C₂×C₃₁	semidirect
467. #3337	C₂×C₃₁	semidirect
468. #3320	C₂×C₃₁	semidirect
469. #3320	C₂×C₃₁	semidirect
470. #3298	C₂×C₃₁	semidirect
471. #3260	C₂×C₃₁	semidirect
472. #3246	C₂×C₃₁	semidirect
473. #3242	C₂×C₃₁	semidirect
474. #3236	C₂×C₃₁	semidirect
475. #3126	C₂×C₃₁	semidirect
476. #3112	C₂×C₃₁	semidirect
477. #3082	C₂×C₃₁	semidirect
478. C₂×#479	C₂×C₃₁	semidirect
479. #2992	C₂×C₃₁	semidirect
775. C₃₁	#62167	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×#3559	2
C₃₁×#3523	2
C₃₁×#3388	2
C₃₁×#3372	2
C₃₁×#3350	2
C₃₁×#3343	2
C₃₁×#3337	2
C₃₁×#3320	2
C₃₁×#3298	2
C₃₁×#3260	2
C₃₁×#3246	2
C₃₁×#3242	2
C₃₁×#3236	2
C₃₁×#3126	2
C₃₁×#3112	2
C₃₁×#3082	2
C₂×C₃₁×#479	2
C₃₁×#2992	2
#62167	31

Subgroups — C31×#62167 #21518926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62167 #21518926