Subgroups — C₃₁×#62597 #21519356

Order 7936.

1704 conjugacy classes of subgroups.

The subgroup lattice has 1004 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, complemented
2	C₃₁×#3552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3372	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3221	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3180	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3174	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#491	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2968	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	2	no	—
21	C₃₁×#563	—	2	1	no	—
22	C₃₁×#562	—	2	1	no	—
23	C₃₁×#557	C₂²	1	1	yes	characteristic
24	C₃₁×#556	C₂²	1	1	yes	characteristic
25	C₃₁×#554	—	2	1	no	—
26	C₃₁×#554	C₂²	1	2	yes	—
27	C₃₁×#553	—	2	1	no	—
28	C₃₁×#553	C₂²	1	2	yes	—
29	C₃₁×#553	C₂²	1	2	yes	—
30	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
31	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#548	C₂²	1	2	yes	—
33	C₃₁×#547	—	2	2	no	—
34	C₃₁×#547	C₂²	1	1	yes	characteristic
35	C₃₁×#547	C₂²	1	2	yes	—
36	C₃₁×#544	—	2	1	no	—
37	C₃₁×#544	C₂²	1	2	yes	—
38	C₃₁×#542	—	2	1	no	—
39	C₃₁×#541	C₂²	1	2	yes	—
40	C₃₁×#540	C₂²	1	2	yes	—
41	C₃₁×#539	—	2	2	no	—
42	C₃₁×#539	—	2	2	no	—
43	C₃₁×#539	—	2	1	no	—
44	C₃₁×#537	—	2	1	no	—
45	C₃₁×#536	C₂²	1	2	yes	—
46	C₃₁×#532	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
48	C₃₁×#529	C₂²	1	1	yes	characteristic
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	1	yes	characteristic
52	C₃₁×#499	C₂²	1	2	yes	—
53	C₃₁×#496	C₂²	1	1	yes	characteristic
54	C₃₁×#492	C₂²	1	2	yes	—
55	C₃₁×#491	C₂²	1	2	yes	—
56	C₃₁×#491	C₂²	1	2	yes	—
57	C₃₁×#491	C₂²	1	2	yes	—
58	C₃₁×#491	C₂²	1	2	yes	—
59	C₃₁×#491	C₂²	1	2	yes	—
60	C₃₁×#490	C₂²	1	1	yes	characteristic
61	C₃₁×#489	C₂²	1	2	yes	—
62	C₃₁×#489	C₂²	1	1	yes	characteristic
63	C₃₁×#488	C₂²	1	2	yes	—
64	C₃₁×#488	C₂²	1	2	yes	—
65	C₃₁×#487	C₂²	1	2	yes	—
66	C₃₁×#487	C₂²	1	2	yes	—
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#484	C₂²	1	1	yes	characteristic
70	C₃₁×#484	C₂²	1	2	yes	—
71	C₃₁×#483	C₂²	1	1	yes	characteristic
72	C₃₁×#483	C₂²	1	2	yes	—
73	C₃₁×#481	C₂²	1	1	yes	characteristic
74	C₃₁×#480	C₂²	1	1	yes	characteristic
75	C₃₁×#479	C₂²	1	2	yes	—
76	C₃₁×#479	C₂²	1	2	yes	—
77	C₃₁×#479	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#477	C₂²	1	2	yes	—
80	C₃₁×#475	C₂²	1	2	yes	—
81	C₃₁×#468	C₂²	1	2	yes	—
82	C₃₁×#468	C₂²	1	2	yes	—
83	C₃₁×#466	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×#463	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#461	C₂²	1	2	yes	—
90	C₃₁×#461	C₂²	1	2	yes	—
91	C₃₁×#461	C₂²	1	2	yes	—
92	C₃₁×#461	C₂²	1	2	yes	—
93	C₃₁×#449	C₂²	1	2	yes	—
94	C₃₁×#449	C₂²	1	2	yes	—
95	C₃₁×#448	C₂²	1	2	yes	—
96	C₃₁×#448	C₂²	1	2	yes	—
97	C₃₁×#448	C₂²	1	2	yes	—
98	C₃₁×#448	C₂²	1	2	yes	—
99	C₃₁×#446	C₂²	1	2	yes	—
100	C₃₁×#442	C₂²	1	2	yes	—
101	C₃₁×#440	C₂²	1	2	yes	—
102	C₃₁×#440	C₂²	1	2	yes	—
103	C₃₁×#440	C₂²	1	2	yes	—
104	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
105	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
106	C₃₁×#435	C₂²	1	2	yes	—
107	C₃₁×#435	C₂²	1	2	yes	—
108	C₈×D₄×C₃₁	C₂²	1	2	yes	—
109	C₃₁×#433	C₂²	1	2	yes	—
110	C₃₁×#431	C₂²	1	1	yes	characteristic
111	C₃₁×#419	C₂²	1	2	yes	—
112	C₃₁×#417	C₂²	1	2	yes	—
113	C₃₁×#416	C₂²	1	2	yes	—
114	C₂×C₃₁×#103	C₂²	1	2	yes	—
115	C₂×C₃₁×#103	C₂²	1	2	yes	—
116	C₂×C₃₁×#103	C₂²	1	2	yes	—
117	C₃₁×#405	C₂²	1	2	yes	—
118	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	2	no	—
120	C₂×#41×C₃₁	—	2	1	no	—
121	C₂×#41×C₃₁	C₂³	1	2	yes	—
122	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
123	C₂²×Q₈×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×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×D₈×C₃₁	C₂³	1	2	yes	—
130	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
132	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
133	C₃₁×C₄⋊Q₈	—	2	1	no	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	—	2	1	no	—
137	C₃₁×C₄⋊Q₈	—	2	1	no	—
138	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
143	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₃₁×#127	C₂³	1	1	yes	characteristic
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#126	—	2	2	no	—
148	C₃₁×#126	—	2	2	no	—
149	C₃₁×#126	—	2	2	no	—
150	C₃₁×#126	—	2	1	no	—
151	C₃₁×#126	D₄	1	2	yes	—
152	C₃₁×#125	—	2	2	no	—
153	C₃₁×#125	—	2	2	no	—
154	C₃₁×#125	—	2	2	no	—
155	C₃₁×#125	—	2	2	no	—
156	C₃₁×#125	—	2	1	no	—
157	C₃₁×#125	—	2	1	no	—
158	C₃₁×#125	—	2	1	no	—
159	C₃₁×#125	D₄	1	1	yes	characteristic
160	C₃₁×#125	C₂³	1	2	yes	—
161	C₃₁×#125	C₂³	1	2	yes	—
162	C₃₁×#125	C₂³	1	2	yes	—
163	C₃₁×#125	C₂³	1	1	yes	characteristic
164	C₃₁×#124	—	2	2	no	—
165	C₃₁×#124	—	2	1	no	—
166	C₃₁×#124	D₄	1	1	yes	characteristic
167	C₃₁×#124	C₂³	1	2	yes	—
168	C₃₁×#124	C₂³	1	1	yes	characteristic
169	C₃₁×#123	—	2	1	no	—
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	—	2	2	no	—
173	C₃₁×#123	—	2	2	no	—
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	—	2	2	no	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	D₄	1	2	yes	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	1	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	1	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	D₄	1	1	yes	characteristic
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#121	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₃₁	—	2	1	no	—
210	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₃₁	—	2	2	no	—
215	C₄×D₄×C₃₁	—	2	1	no	—
216	C₄×D₄×C₃₁	—	2	1	no	—
217	C₄×D₄×C₃₁	—	2	2	no	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	C₂³	1	2	yes	—
222	C₄×D₄×C₃₁	C₂³	1	2	yes	—
223	C₄×D₄×C₃₁	C₂³	1	2	yes	—
224	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₃₁	C₂³	1	2	yes	—
226	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
227	C₃₁×#117	—	2	1	no	—
228	C₃₁×#117	—	2	1	no	—
229	C₃₁×#117	C₂³	1	2	yes	—
230	C₃₁×#117	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
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	—	2	1	no	—
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
240	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₃₁×#97	C₂³	1	1	yes	characteristic
275	C₃₁×#97	C₂³	1	1	yes	characteristic
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₃₁	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	#41×C₃₁	—	4	2	no	—
281	#41×C₃₁	—	4	2	no	—
282	#41×C₃₁	—	8	2	no	—
283	#41×C₃₁	—	8	4	no	—
284	C₂×Q₈×C₃₁	—	2	2	no	—
285	C₂×Q₈×C₃₁	—	2	2	no	—
286	C₂×Q₈×C₃₁	—	2	2	no	—
287	C₂×Q₈×C₃₁	—	2	1	no	—
288	C₂×Q₈×C₃₁	—	4	2	no	—
289	C₂×Q₈×C₃₁	—	4	2	no	—
290	C₂×Q₈×C₃₁	—	4	2	no	—
291	C₂×Q₈×C₃₁	—	4	2	no	—
292	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
296	C₂×D₄×C₃₁	—	2	1	no	—
297	C₂×D₄×C₃₁	—	2	2	no	—
298	C₂×D₄×C₃₁	—	2	2	no	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	—	2	2	no	—
301	C₂×D₄×C₃₁	—	2	1	no	—
302	C₂×D₄×C₃₁	—	2	1	no	—
303	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
304	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
305	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₃₁	—	2	1	no	—
308	C₂²×C₄×C₃₁	—	2	1	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	—	2	1	no	—
313	C₂²×C₄×C₃₁	—	2	2	no	—
314	C₂²×C₄×C₃₁	—	2	2	no	—
315	C₂²×C₄×C₃₁	—	2	2	no	—
316	C₂²×C₄×C₃₁	—	2	2	no	—
317	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
321	SD₁₆×C₃₁	—	4	2	no	—
322	SD₁₆×C₃₁	—	4	2	no	—
323	SD₁₆×C₃₁	—	4	2	no	—
324	SD₁₆×C₃₁	—	4	2	no	—
325	SD₁₆×C₃₁	—	4	2	no	—
326	D₈×C₃₁	—	4	2	no	—
327	M₁₆×C₃₁	—	4	2	no	—
328	C₂×C₈×C₃₁	—	4	2	no	—
329	C₂×C₈×C₃₁	—	4	2	no	—
330	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
331	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
333	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₃₁	—	2	2	no	—
335	C₄⋊C₄×C₃₁	—	2	1	no	—
336	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
343	C₄⋊C₄×C₃₁	—	2	2	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	1	no	—
347	C₄⋊C₄×C₃₁	—	2	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	1	no	—
352	C₄⋊C₄×C₃₁	—	2	1	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	1	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	1	no	—
361	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	—	2	1	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	—	2	1	no	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	1	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	1	no	—
388	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₄²×C₃₁	—	2	1	no	—
394	C₄²×C₃₁	—	2	2	no	—
395	C₄²×C₃₁	—	2	2	no	—
396	C₄²×C₃₁	—	2	2	no	—
397	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄²×C₃₁	C₂⁴	1	2	yes	—
401	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
402	#62597	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂³×C₃₁	—	2	1	no	—
404	C₂³×C₃₁	—	2	2	no	—
405	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
406	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
407	Q₈×C₃₁	—	2	2	no	—
408	Q₈×C₃₁	—	2	2	no	—
409	Q₈×C₃₁	—	2	2	no	—
410	Q₈×C₃₁	—	2	2	no	—
411	Q₈×C₃₁	—	2	2	no	—
412	Q₈×C₃₁	—	4	1	no	—
413	Q₈×C₃₁	—	8	2	no	—
414	Q₈×C₃₁	—	8	2	no	—
415	Q₈×C₃₁	—	8	1	no	—
416	Q₈×C₃₁	—	8	2	no	—
417	D₄×C₃₁	—	2	4	no	—
418	D₄×C₃₁	—	2	2	no	—
419	D₄×C₃₁	—	2	2	no	—
420	D₄×C₃₁	—	2	2	no	—
421	D₄×C₃₁	—	4	1	no	—
422	D₄×C₃₁	—	4	2	no	—
423	D₄×C₃₁	—	4	4	no	—
424	D₄×C₃₁	—	8	1	no	—
425	D₄×C₃₁	—	8	1	no	—
426	D₄×C₃₁	—	8	2	no	—
427	D₄×C₃₁	—	8	2	no	—
428	D₄×C₃₁	—	8	2	no	—
429	C₂×C₄×C₃₁	—	2	2	no	—
430	C₂×C₄×C₃₁	—	2	2	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	1	no	—
434	C₂×C₄×C₃₁	—	2	1	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	1	no	—
437	C₂×C₄×C₃₁	—	2	2	no	—
438	C₂×C₄×C₃₁	—	2	2	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	2	no	—
441	C₂×C₄×C₃₁	—	4	1	no	—
442	C₂×C₄×C₃₁	—	4	2	no	—
443	C₂×C₄×C₃₁	—	4	2	no	—
444	C₂×C₄×C₃₁	—	8	2	no	—
445	C₂×C₄×C₃₁	—	8	2	no	—
446	C₂×C₄×C₃₁	—	8	2	no	—
447	C₂×C₄×C₃₁	—	8	2	no	—
448	C₂×C₄×C₃₁	—	8	1	no	—
449	C₂×C₄×C₃₁	—	8	2	no	—
450	C₂×C₄×C₃₁	—	8	2	no	—
451	C₂×C₄×C₃₁	—	8	2	no	—
452	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
461	C₈×C₃₁	—	2	2	no	—
462	C₈×C₃₁	—	2	2	no	—
463	C₈×C₃₁	—	2	2	no	—
464	C₈×C₃₁	—	2	2	no	—
465	#3559	C₂×C₃₁	1	1	yes	characteristic, complemented
466	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
467	#3376	C₂×C₃₁	1	2	yes	complemented
468	#3372	C₂×C₃₁	1	2	yes	complemented
469	#3320	C₂×C₃₁	1	2	yes	complemented
470	#3320	C₂×C₃₁	1	2	yes	complemented
471	#3308	C₂×C₃₁	1	2	yes	complemented
472	#3307	C₂×C₃₁	1	2	yes	complemented
473	#3301	C₂×C₃₁	1	2	yes	complemented
474	#3298	C₂×C₃₁	1	2	yes	complemented
475	#3242	C₂×C₃₁	1	2	yes	complemented
476	#3232	C₂×C₃₁	1	1	yes	characteristic, complemented
477	#3221	C₂×C₃₁	1	2	yes	complemented
478	#3206	C₂×C₃₁	1	1	yes	characteristic, complemented
479	#3180	C₂×C₃₁	1	1	yes	characteristic, complemented
480	#3174	C₂×C₃₁	1	2	yes	complemented
481	#3137	C₂×C₃₁	1	2	yes	complemented
482	C₂×#491	C₂×C₃₁	1	1	yes	characteristic, complemented
483	#2968	C₂×C₃₁	1	1	yes	characteristic, complemented
484	C₂²×C₃₁	—	2	1	no	—
485	C₂²×C₃₁	—	2	1	no	—
486	C₂²×C₃₁	—	2	2	no	—
487	C₂²×C₃₁	—	2	2	no	—
488	C₂²×C₃₁	—	2	2	no	—
489	C₂²×C₃₁	—	4	1	no	—
490	C₂²×C₃₁	—	4	2	no	—
491	C₂²×C₃₁	—	4	1	no	—
492	C₂²×C₃₁	—	4	2	no	—
493	C₂²×C₃₁	—	4	2	no	—
494	C₂²×C₃₁	—	4	1	no	—
495	C₂²×C₃₁	#577	1	2	yes	—
496	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
497	C₄×C₃₁	—	2	1	no	—
498	C₄×C₃₁	—	2	1	no	—
499	C₄×C₃₁	—	2	2	no	—
500	C₄×C₃₁	—	2	2	no	—
501	C₄×C₃₁	—	2	1	no	—
502	C₄×C₃₁	—	2	1	no	—
503	C₄×C₃₁	—	2	1	no	—
504	C₄×C₃₁	—	2	2	no	—
505	C₄×C₃₁	—	4	1	no	—
506	C₄×C₃₁	—	4	2	no	—
507	C₄×C₃₁	—	4	2	no	—
508	C₄×C₃₁	—	4	1	no	—
509	C₄×C₃₁	—	4	2	no	—
510	C₄×C₃₁	—	4	2	no	—
511	C₄×C₃₁	—	4	2	no	—
512	C₄×C₃₁	—	4	1	no	—
513	C₄×C₃₁	#585	1	2	yes	—
514	#563	—	2	2	no	—
515	#563	—	2	1	no	—
516	#562	—	2	1	no	—
517	#557	C₂²×C₃₁	1	1	yes	characteristic
518	#556	C₂²×C₃₁	1	1	yes	characteristic
519	#554	—	2	1	no	—
520	#554	C₂²×C₃₁	1	2	yes	—
521	#553	—	2	1	no	—
522	#553	C₂²×C₃₁	1	2	yes	—
523	#553	C₂²×C₃₁	1	2	yes	—
524	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
525	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
526	#548	C₂²×C₃₁	1	2	yes	—
527	#547	—	2	2	no	—
528	#547	C₂²×C₃₁	1	1	yes	characteristic
529	#547	C₂²×C₃₁	1	2	yes	—
530	#544	—	2	1	no	—
531	#544	C₂²×C₃₁	1	2	yes	—
532	#542	—	2	1	no	—
533	#541	C₂²×C₃₁	1	2	yes	—
534	#540	C₂²×C₃₁	1	2	yes	—
535	#539	—	2	2	no	—
536	#539	—	2	2	no	—
537	#539	—	2	1	no	—
538	#537	—	2	1	no	—
539	#536	C₂²×C₃₁	1	2	yes	—
540	#532	C₂²×C₃₁	1	1	yes	characteristic
541	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
542	#529	C₂²×C₃₁	1	1	yes	characteristic
543	#529	C₂²×C₃₁	1	1	yes	characteristic
544	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
545	#501	C₂²×C₃₁	1	1	yes	characteristic
546	#499	C₂²×C₃₁	1	2	yes	—
547	#496	C₂²×C₃₁	1	1	yes	characteristic
548	#492	C₂²×C₃₁	1	2	yes	—
549	#491	C₂²×C₃₁	1	2	yes	—
550	#491	C₂²×C₃₁	1	2	yes	—
551	#491	C₂²×C₃₁	1	2	yes	—
552	#491	C₂²×C₃₁	1	2	yes	—
553	#491	C₂²×C₃₁	1	2	yes	—
554	#490	C₂²×C₃₁	1	1	yes	characteristic
555	#489	C₂²×C₃₁	1	2	yes	—
556	#489	C₂²×C₃₁	1	1	yes	characteristic
557	#488	C₂²×C₃₁	1	2	yes	—
558	#488	C₂²×C₃₁	1	2	yes	—
559	#487	C₂²×C₃₁	1	2	yes	—
560	#487	C₂²×C₃₁	1	2	yes	—
561	#485	C₂²×C₃₁	1	2	yes	—
562	#485	C₂²×C₃₁	1	2	yes	—
563	#484	C₂²×C₃₁	1	1	yes	characteristic
564	#484	C₂²×C₃₁	1	2	yes	—
565	#483	C₂²×C₃₁	1	1	yes	characteristic
566	#483	C₂²×C₃₁	1	2	yes	—
567	#481	C₂²×C₃₁	1	1	yes	characteristic
568	#480	C₂²×C₃₁	1	1	yes	characteristic
569	#479	C₂²×C₃₁	1	2	yes	—
570	#479	C₂²×C₃₁	1	2	yes	—
571	#479	C₂²×C₃₁	1	2	yes	—
572	#478	C₂²×C₃₁	1	2	yes	—
573	#477	C₂²×C₃₁	1	2	yes	—
574	#475	C₂²×C₃₁	1	2	yes	—
575	#468	C₂²×C₃₁	1	2	yes	—
576	#468	C₂²×C₃₁	1	2	yes	—
577	#466	C₂²×C₃₁	1	2	yes	—
578	#465	C₂²×C₃₁	1	2	yes	—
579	#465	C₂²×C₃₁	1	2	yes	—
580	#465	C₂²×C₃₁	1	2	yes	—
581	#463	C₂²×C₃₁	1	2	yes	—
582	#463	C₂²×C₃₁	1	2	yes	—
583	#461	C₂²×C₃₁	1	2	yes	—
584	#461	C₂²×C₃₁	1	2	yes	—
585	#461	C₂²×C₃₁	1	2	yes	—
586	#461	C₂²×C₃₁	1	2	yes	—
587	#449	C₂²×C₃₁	1	2	yes	—
588	#449	C₂²×C₃₁	1	2	yes	—
589	#448	C₂²×C₃₁	1	2	yes	—
590	#448	C₂²×C₃₁	1	2	yes	—
591	#448	C₂²×C₃₁	1	2	yes	—
592	#448	C₂²×C₃₁	1	2	yes	—
593	#446	C₂²×C₃₁	1	2	yes	—
594	#442	C₂²×C₃₁	1	2	yes	—
595	#440	C₂²×C₃₁	1	2	yes	—
596	#440	C₂²×C₃₁	1	2	yes	—
597	#440	C₂²×C₃₁	1	2	yes	—
598	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
599	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
600	#435	C₂²×C₃₁	1	2	yes	—
601	#435	C₂²×C₃₁	1	2	yes	—
602	C₈×D₄	C₂²×C₃₁	1	2	yes	—
603	#433	C₂²×C₃₁	1	2	yes	—
604	#431	C₂²×C₃₁	1	1	yes	characteristic
605	#419	C₂²×C₃₁	1	2	yes	—
606	#417	C₂²×C₃₁	1	2	yes	—
607	#416	C₂²×C₃₁	1	2	yes	—
608	C₂×#103	C₂²×C₃₁	1	2	yes	—
609	C₂×#103	C₂²×C₃₁	1	2	yes	—
610	C₂×#103	C₂²×C₃₁	1	2	yes	—
611	#405	C₂²×C₃₁	1	2	yes	—
612	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
613	C₂×C₃₁	—	2	2	no	—
614	C₂×C₃₁	—	4	2	no	—
615	C₂×C₃₁	—	8	1	no	—
616	C₂×C₃₁	—	8	2	no	—
617	C₂×C₃₁	#3500	1	1	yes	characteristic
618	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
619	C₂×C₃₁	#3586	1	1	yes	characteristic
620	C₂×#41	—	2	2	no	—
621	C₂×#41	—	2	1	no	—
622	C₂×#41	C₂³×C₃₁	1	2	yes	—
623	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
624	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
625	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
626	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
627	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
628	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
629	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
630	C₂×D₈	C₂³×C₃₁	1	2	yes	—
631	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
632	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
633	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
634	C₄⋊Q₈	—	2	1	no	—
635	C₄⋊Q₈	—	2	2	no	—
636	C₄⋊Q₈	—	2	2	no	—
637	C₄⋊Q₈	—	2	1	no	—
638	C₄⋊Q₈	—	2	1	no	—
639	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
640	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
641	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
642	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
643	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
644	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
645	#127	C₂³×C₃₁	1	1	yes	characteristic
646	#126	—	2	2	no	—
647	#126	—	2	2	no	—
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	—	2	2	no	—
651	#126	—	2	1	no	—
652	#126	D₄×C₃₁	1	2	yes	—
653	#125	—	2	2	no	—
654	#125	—	2	2	no	—
655	#125	—	2	2	no	—
656	#125	—	2	2	no	—
657	#125	—	2	1	no	—
658	#125	—	2	1	no	—
659	#125	—	2	1	no	—
660	#125	D₄×C₃₁	1	1	yes	characteristic
661	#125	C₂³×C₃₁	1	2	yes	—
662	#125	C₂³×C₃₁	1	2	yes	—
663	#125	C₂³×C₃₁	1	1	yes	characteristic
664	#125	C₂³×C₃₁	1	2	yes	—
665	#124	—	2	2	no	—
666	#124	—	2	1	no	—
667	#124	D₄×C₃₁	1	1	yes	characteristic
668	#124	C₂³×C₃₁	1	1	yes	characteristic
669	#124	C₂³×C₃₁	1	2	yes	—
670	#123	—	2	1	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	D₄×C₃₁	1	2	yes	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	1	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
695	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
696	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
697	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
698	#121	—	2	2	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	1	no	—
702	#121	—	2	1	no	—
703	#121	—	2	2	no	—
704	#121	—	2	2	no	—
705	#121	D₄×C₃₁	1	1	yes	characteristic
706	#121	C₂³×C₃₁	1	1	yes	characteristic
707	#121	C₂³×C₃₁	1	2	yes	—
708	#121	C₂³×C₃₁	1	2	yes	—
709	#121	C₂³×C₃₁	1	2	yes	—
710	C₄×Q₈	—	2	1	no	—
711	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
712	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
713	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
714	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
715	C₄×D₄	—	2	2	no	—
716	C₄×D₄	—	2	1	no	—
717	C₄×D₄	—	2	1	no	—
718	C₄×D₄	—	2	2	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	1	no	—
722	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
723	C₄×D₄	C₂³×C₃₁	1	2	yes	—
724	C₄×D₄	C₂³×C₃₁	1	2	yes	—
725	C₄×D₄	C₂³×C₃₁	1	2	yes	—
726	C₄×D₄	C₂³×C₃₁	1	2	yes	—
727	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
728	#117	—	2	1	no	—
729	#117	—	2	1	no	—
730	#117	C₂³×C₃₁	1	2	yes	—
731	#117	C₂³×C₃₁	1	2	yes	—
732	C₂×C₄⋊C₄	—	2	1	no	—
733	C₂×C₄⋊C₄	—	2	1	no	—
734	C₂×C₄⋊C₄	—	2	1	no	—
735	C₂×C₄⋊C₄	—	2	1	no	—
736	C₂×C₄⋊C₄	—	2	2	no	—
737	C₂×C₄⋊C₄	—	2	1	no	—
738	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
741	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
742	#107	C₂³×C₃₁	1	2	yes	—
743	#107	C₂³×C₃₁	1	2	yes	—
744	#107	C₂³×C₃₁	1	2	yes	—
745	#106	C₂³×C₃₁	1	2	yes	—
746	#106	C₂³×C₃₁	1	2	yes	—
747	#106	C₂³×C₃₁	1	2	yes	—
748	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
749	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
750	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
751	#103	C₂³×C₃₁	1	2	yes	—
752	#103	C₂³×C₃₁	1	2	yes	—
753	#103	C₂³×C₃₁	1	2	yes	—
754	#103	C₂³×C₃₁	1	2	yes	—
755	#103	C₂³×C₃₁	1	2	yes	—
756	#103	C₂³×C₃₁	1	2	yes	—
757	#103	C₂³×C₃₁	1	2	yes	—
758	#103	C₂³×C₃₁	1	2	yes	—
759	#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	#103	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	#102	C₂³×C₃₁	1	2	yes	—
770	#102	C₂³×C₃₁	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
772	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
773	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
775	#97	C₂³×C₃₁	1	1	yes	characteristic
776	#97	C₂³×C₃₁	1	1	yes	characteristic
777	#97	C₂³×C₃₁	1	2	yes	—
778	#97	C₂³×C₃₁	1	2	yes	—
779	C₄×C₈	C₂³×C₃₁	1	2	yes	—
780	C₄×C₈	C₂³×C₃₁	1	2	yes	—
781	C₃₁	#62597	1	1	yes	characteristic, direct product factor, Sylow
782	#41	—	4	2	no	—
783	#41	—	4	2	no	—
784	#41	—	8	2	no	—
785	#41	—	8	4	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	2	2	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	4	2	no	—
791	C₂×Q₈	—	4	2	no	—
792	C₂×Q₈	—	4	2	no	—
793	C₂×Q₈	—	4	2	no	—
794	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
795	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
796	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
797	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
806	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
807	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
820	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
823	SD₁₆	—	4	2	no	—
824	SD₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	SD₁₆	—	4	2	no	—
827	SD₁₆	—	4	2	no	—
828	D₈	—	4	2	no	—
829	M₁₆	—	4	2	no	—
830	C₂×C₈	—	4	2	no	—
831	C₂×C₈	—	4	2	no	—
832	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
833	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
834	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
835	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	1	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	1	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
864	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
866	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
868	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
870	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
871	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
872	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
873	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	1	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	1	no	—
880	C₂²⋊C₄	—	2	1	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	1	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
891	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
892	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
893	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
894	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
895	C₄²	—	2	1	no	—
896	C₄²	—	2	2	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
900	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
901	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
902	C₄²	C₂⁴×C₃₁	1	2	yes	—
903	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
904	C₂³	—	2	1	no	—
905	C₂³	—	2	2	no	—
906	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
907	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
908	Q₈	—	2	2	no	—
909	Q₈	—	2	2	no	—
910	Q₈	—	2	2	no	—
911	Q₈	—	2	2	no	—
912	Q₈	—	2	2	no	—
913	Q₈	—	4	1	no	—
914	Q₈	—	8	2	no	—
915	Q₈	—	8	2	no	—
916	Q₈	—	8	1	no	—
917	Q₈	—	8	2	no	—
918	D₄	—	2	4	no	—
919	D₄	—	2	2	no	—
920	D₄	—	2	2	no	—
921	D₄	—	2	2	no	—
922	D₄	—	4	1	no	—
923	D₄	—	4	2	no	—
924	D₄	—	4	4	no	—
925	D₄	—	8	1	no	—
926	D₄	—	8	1	no	—
927	D₄	—	8	2	no	—
928	D₄	—	8	2	no	—
929	D₄	—	8	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	4	1	no	—
943	C₂×C₄	—	4	2	no	—
944	C₂×C₄	—	4	2	no	—
945	C₂×C₄	—	8	2	no	—
946	C₂×C₄	—	8	2	no	—
947	C₂×C₄	—	8	2	no	—
948	C₂×C₄	—	8	2	no	—
949	C₂×C₄	—	8	1	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	2	no	—
952	C₂×C₄	—	8	2	no	—
953	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
954	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
955	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
956	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
958	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
961	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
962	C₈	—	2	2	no	—
963	C₈	—	2	2	no	—
964	C₈	—	2	2	no	—
965	C₈	—	2	2	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	2	no	—
977	C₂²	C₃₁×#577	1	2	yes	—
978	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
979	C₄	—	2	2	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	1	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	1	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	C₃₁×#585	1	2	yes	—
996	C₂	—	2	2	no	—
997	C₂	—	4	2	no	—
998	C₂	—	8	1	no	—
999	C₂	—	8	2	no	—
1000	C₂	C₃₁×#3500	1	1	yes	characteristic
1001	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1002	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
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×#3559	C₂	semidirect
2. C₃₁×#3552	C₂	semidirect
3. C₃₁×#3376	C₂	semidirect
4. C₃₁×#3372	C₂	semidirect
5. C₃₁×#3320	C₂	semidirect
6. C₃₁×#3320	C₂	semidirect
7. C₃₁×#3308	C₂	semidirect
8. C₃₁×#3307	C₂	semidirect
9. C₃₁×#3301	C₂	semidirect
10. C₃₁×#3298	C₂	semidirect
11. C₃₁×#3242	C₂	semidirect
12. C₃₁×#3232	C₂	semidirect
13. C₃₁×#3221	C₂	semidirect
14. C₃₁×#3206	C₂	semidirect
15. C₃₁×#3180	C₂	semidirect
16. C₃₁×#3174	C₂	semidirect
17. C₃₁×#3137	C₂	semidirect
18. C₂×C₃₁×#491	C₂	semidirect
19. C₃₁×#2968	C₂	semidirect
402. #62597	C₃₁	direct (N × H)
465. #3559	C₂×C₃₁	semidirect
466. #3552	C₂×C₃₁	semidirect
467. #3376	C₂×C₃₁	semidirect
468. #3372	C₂×C₃₁	semidirect
469. #3320	C₂×C₃₁	semidirect
470. #3320	C₂×C₃₁	semidirect
471. #3308	C₂×C₃₁	semidirect
472. #3307	C₂×C₃₁	semidirect
473. #3301	C₂×C₃₁	semidirect
474. #3298	C₂×C₃₁	semidirect
475. #3242	C₂×C₃₁	semidirect
476. #3232	C₂×C₃₁	semidirect
477. #3221	C₂×C₃₁	semidirect
478. #3206	C₂×C₃₁	semidirect
479. #3180	C₂×C₃₁	semidirect
480. #3174	C₂×C₃₁	semidirect
481. #3137	C₂×C₃₁	semidirect
482. C₂×#491	C₂×C₃₁	semidirect
483. #2968	C₂×C₃₁	semidirect
781. C₃₁	#62597	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×#3552	2
C₃₁×#3376	2
C₃₁×#3372	2
C₃₁×#3320	2
C₃₁×#3308	2
C₃₁×#3307	2
C₃₁×#3301	2
C₃₁×#3298	2
C₃₁×#3242	2
C₃₁×#3232	2
C₃₁×#3221	2
C₃₁×#3206	2
C₃₁×#3180	2
C₃₁×#3174	2
C₃₁×#3137	2
C₂×C₃₁×#491	2
C₃₁×#2968	2
#62597	31

Subgroups — C31×#62597 #21519356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62597 #21519356