Subgroups — C₃₁×#62121 #21518880

Order 7936.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3350	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3349	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3315	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3252	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3236	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3080	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#557	C₂²	1	1	yes	characteristic
25	C₃₁×#557	C₂²	1	1	yes	characteristic
26	C₃₁×#556	C₂²	1	2	yes	—
27	C₃₁×#556	C₂²	1	1	yes	characteristic
28	C₃₁×#554	C₂²	1	1	yes	characteristic
29	C₃₁×#554	C₂²	1	1	yes	characteristic
30	C₃₁×#553	C₂²	1	2	yes	—
31	C₃₁×#552	—	2	1	no	—
32	C₃₁×#552	—	2	2	no	—
33	C₃₁×#552	—	2	2	no	—
34	C₃₁×#552	—	2	1	no	—
35	C₃₁×#552	C₂²	1	2	yes	—
36	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#548	—	2	1	no	—
38	C₃₁×#547	—	2	1	no	—
39	C₃₁×#547	C₂²	1	1	yes	characteristic
40	C₃₁×#547	C₂²	1	2	yes	—
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#541	—	2	1	no	—
43	C₃₁×#539	—	2	2	no	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#533	C₂²	1	2	yes	—
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₃₁×#529	—	2	1	no	—
48	C₃₁×#529	—	2	2	no	—
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₃₁×#529	C₂²	1	2	yes	—
51	C₂×C₃₁×#125	C₂²	1	2	yes	—
52	C₃₁×#520	—	2	1	no	—
53	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₃₁	C₂²	1	2	yes	—
55	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
57	C₃₁×#501	C₂²	1	2	yes	—
58	C₃₁×#501	C₂²	1	2	yes	—
59	C₃₁×#500	C₂²	1	1	yes	characteristic
60	C₃₁×#498	C₂²	1	1	yes	characteristic
61	C₃₁×#491	C₂²	1	2	yes	—
62	C₃₁×#491	C₂²	1	2	yes	—
63	C₃₁×#487	C₂²	1	1	yes	characteristic
64	C₃₁×#487	C₂²	1	1	yes	characteristic
65	C₃₁×#485	C₂²	1	1	yes	characteristic
66	C₃₁×#485	C₂²	1	2	yes	—
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#484	C₂²	1	2	yes	—
70	C₃₁×#484	C₂²	1	2	yes	—
71	C₃₁×#483	C₂²	1	2	yes	—
72	C₃₁×#483	C₂²	1	2	yes	—
73	C₃₁×#482	C₂²	1	1	yes	characteristic
74	C₃₁×#482	C₂²	1	2	yes	—
75	C₃₁×#479	C₂²	1	2	yes	—
76	C₃₁×#479	C₂²	1	2	yes	—
77	C₃₁×#479	C₂²	1	2	yes	—
78	C₃₁×#479	C₂²	1	2	yes	—
79	C₃₁×#479	C₂²	1	2	yes	—
80	C₃₁×#479	C₂²	1	1	yes	characteristic
81	C₃₁×#479	C₂²	1	2	yes	—
82	C₃₁×#478	C₂²	1	2	yes	—
83	C₃₁×#478	C₂²	1	1	yes	characteristic
84	C₃₁×#478	C₂²	1	2	yes	—
85	C₃₁×#478	C₂²	1	2	yes	—
86	C₃₁×#477	C₂²	1	1	yes	characteristic
87	C₃₁×#477	C₂²	1	2	yes	—
88	C₃₁×#476	C₂²	1	1	yes	characteristic
89	C₃₁×#476	C₂²	1	2	yes	—
90	C₃₁×#475	C₂²	1	1	yes	characteristic
91	C₃₁×#475	C₂²	1	1	yes	characteristic
92	C₃₁×#474	C₂²	1	1	yes	characteristic
93	C₃₁×#474	C₂²	1	1	yes	characteristic
94	C₃₁×#470	C₂²	1	2	yes	—
95	C₃₁×#470	C₂²	1	2	yes	—
96	C₃₁×#468	C₂²	1	2	yes	—
97	C₃₁×#468	C₂²	1	2	yes	—
98	C₃₁×#467	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	—
100	C₃₁×#464	C₂²	1	1	yes	characteristic
101	C₃₁×#464	C₂²	1	2	yes	—
102	C₃₁×#463	C₂²	1	1	yes	characteristic
103	C₃₁×#462	C₂²	1	1	yes	characteristic
104	C₃₁×#462	C₂²	1	2	yes	—
105	C₃₁×#461	C₂²	1	1	yes	characteristic
106	C₃₁×#461	C₂²	1	2	yes	—
107	C₃₁×#452	C₂²	1	2	yes	—
108	C₃₁×#452	C₂²	1	1	yes	characteristic
109	C₃₁×#449	C₂²	1	1	yes	characteristic
110	C₃₁×#449	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic
112	C₃₁×#446	C₂²	1	1	yes	characteristic
113	C₃₁×#442	C₂²	1	2	yes	—
114	C₃₁×#441	C₂²	1	2	yes	—
115	C₃₁×#440	C₂²	1	2	yes	—
116	C₃₁×#440	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	1	yes	characteristic
123	C₃₁×#435	C₂²	1	2	yes	—
124	C₃₁×#435	C₂²	1	2	yes	—
125	C₃₁×#432	C₂²	1	2	yes	—
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	—
128	C₃₁×#428	C₂²	1	2	yes	—
129	C₃₁×#427	C₂²	1	2	yes	—
130	C₃₁×#423	C₂²	1	2	yes	—
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
132	C₃₁×#417	C₂²	1	2	yes	—
133	C₃₁×#417	C₂²	1	2	yes	—
134	C₃₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
149	C₃₁×C₄⋊Q₈	—	2	1	no	—
150	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃₁×#126	—	2	2	no	—
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	—	2	1	no	—
163	C₃₁×#125	—	2	1	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	—	2	1	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	2	no	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	1	no	—
172	C₃₁×#125	C₂³	1	1	yes	characteristic
173	C₃₁×#125	C₂³	1	2	yes	—
174	C₃₁×#125	C₂³	1	2	yes	—
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	C₂³	1	1	yes	characteristic
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	1	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
198	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	C₂³	1	1	yes	characteristic
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₄×Q₈×C₃₁	—	2	1	no	—
208	C₄×Q₈×C₃₁	—	2	1	no	—
209	C₄×Q₈×C₃₁	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	2	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₃₁	—	2	1	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
232	C₄×D₄×C₃₁	D₄	1	2	yes	—
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	C₂³	1	2	yes	—
236	C₄×D₄×C₃₁	C₂³	1	2	yes	—
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₃₁×#117	—	2	2	no	—
241	C₃₁×#117	—	2	1	no	—
242	C₃₁×#117	—	2	2	no	—
243	C₃₁×#117	—	2	2	no	—
244	C₃₁×#117	—	2	1	no	—
245	C₃₁×#117	—	2	1	no	—
246	C₃₁×#117	—	2	2	no	—
247	C₃₁×#117	D₄	1	1	yes	characteristic
248	C₃₁×#117	D₄	1	2	yes	—
249	C₃₁×#117	C₂³	1	2	yes	—
250	C₃₁×#117	C₂³	1	1	yes	characteristic
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄²×C₃₁	—	2	1	no	—
260	C₂×C₄²×C₃₁	—	2	2	no	—
261	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
263	C₃₁×#107	C₂³	1	2	yes	—
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	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	2	yes	—
270	C₃₁×#106	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	#41×C₃₁	—	2	2	no	—
313	#41×C₃₁	—	2	4	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	1	no	—
316	#41×C₃₁	—	4	2	no	—
317	#41×C₃₁	—	4	4	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	4	4	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₃₁	—	2	1	no	—
328	C₂×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
333	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	2	no	—
340	C₂²×C₄×C₃₁	—	2	2	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	1	no	—
343	C₂²×C₄×C₃₁	—	2	2	no	—
344	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
346	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
347	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	Q₁₆×C₃₁	—	4	2	no	—
351	Q₁₆×C₃₁	—	4	1	no	—
352	SD₁₆×C₃₁	—	2	2	no	—
353	SD₁₆×C₃₁	—	4	2	no	—
354	SD₁₆×C₃₁	—	4	1	no	—
355	D₈×C₃₁	—	2	2	no	—
356	M₁₆×C₃₁	—	4	2	no	—
357	M₁₆×C₃₁	—	4	2	no	—
358	C₂×C₈×C₃₁	—	4	2	no	—
359	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
364	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	1	no	—
367	C₄⋊C₄×C₃₁	—	2	1	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	1	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	2	no	—
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
425	C₄²×C₃₁	—	2	1	no	—
426	C₄²×C₃₁	—	2	2	no	—
427	C₄²×C₃₁	—	2	1	no	—
428	C₄²×C₃₁	—	2	2	no	—
429	C₄²×C₃₁	—	2	2	no	—
430	C₄²×C₃₁	—	2	1	no	—
431	C₄²×C₃₁	—	2	2	no	—
432	C₄²×C₃₁	—	2	2	no	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₃₁	C₂×D₄	1	2	yes	—
436	C₄²×C₃₁	C₂×D₄	1	2	yes	—
437	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
439	C₄²×C₃₁	C₂⁴	1	2	yes	—
440	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
441	#62121	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₂³×C₃₁	—	2	1	no	—
443	C₂³×C₃₁	—	2	1	no	—
444	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
445	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
446	Q₈×C₃₁	—	2	2	no	—
447	Q₈×C₃₁	—	2	1	no	—
448	Q₈×C₃₁	—	2	1	no	—
449	Q₈×C₃₁	—	2	2	no	—
450	Q₈×C₃₁	—	2	2	no	—
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	2	1	no	—
453	Q₈×C₃₁	—	4	4	no	—
454	Q₈×C₃₁	—	4	2	no	—
455	Q₈×C₃₁	—	4	2	no	—
456	Q₈×C₃₁	—	8	1	no	—
457	D₄×C₃₁	—	2	2	no	—
458	D₄×C₃₁	—	2	1	no	—
459	D₄×C₃₁	—	2	1	no	—
460	D₄×C₃₁	—	2	1	no	—
461	D₄×C₃₁	—	4	2	no	—
462	D₄×C₃₁	—	4	2	no	—
463	D₄×C₃₁	—	4	4	no	—
464	D₄×C₃₁	—	4	4	no	—
465	D₄×C₃₁	—	8	1	no	—
466	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
467	C₂×C₄×C₃₁	—	2	2	no	—
468	C₂×C₄×C₃₁	—	2	2	no	—
469	C₂×C₄×C₃₁	—	2	1	no	—
470	C₂×C₄×C₃₁	—	2	1	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	2	no	—
477	C₂×C₄×C₃₁	—	2	1	no	—
478	C₂×C₄×C₃₁	—	2	2	no	—
479	C₂×C₄×C₃₁	—	2	2	no	—
480	C₂×C₄×C₃₁	—	2	1	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	4	2	no	—
483	C₂×C₄×C₃₁	—	4	1	no	—
484	C₂×C₄×C₃₁	—	4	2	no	—
485	C₂×C₄×C₃₁	—	4	2	no	—
486	C₂×C₄×C₃₁	—	4	4	no	—
487	C₂×C₄×C₃₁	—	4	2	no	—
488	C₂×C₄×C₃₁	—	4	4	no	—
489	C₂×C₄×C₃₁	—	4	4	no	—
490	C₂×C₄×C₃₁	—	4	2	no	—
491	C₂×C₄×C₃₁	—	4	2	no	—
492	C₂×C₄×C₃₁	—	8	2	no	—
493	C₂×C₄×C₃₁	—	8	2	no	—
494	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
503	C₈×C₃₁	—	2	1	no	—
504	C₈×C₃₁	—	2	1	no	—
505	C₈×C₃₁	—	2	2	no	—
506	C₈×C₃₁	—	2	2	no	—
507	C₈×C₃₁	—	2	1	no	—
508	C₈×C₃₁	—	2	1	no	—
509	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#3356	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3353	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3350	C₂×C₃₁	1	2	yes	complemented
518	#3349	C₂×C₃₁	1	2	yes	complemented
519	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3315	C₂×C₃₁	1	2	yes	complemented
522	#3307	C₂×C₃₁	1	2	yes	complemented
523	#3252	C₂×C₃₁	1	2	yes	complemented
524	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3236	C₂×C₃₁	1	2	yes	complemented
526	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3111	C₂×C₃₁	1	2	yes	complemented
528	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3080	C₂×C₃₁	1	2	yes	complemented
530	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
532	C₂²×C₃₁	—	2	2	no	—
533	C₂²×C₃₁	—	2	1	no	—
534	C₂²×C₃₁	—	2	1	no	—
535	C₂²×C₃₁	—	2	2	no	—
536	C₂²×C₃₁	—	2	2	no	—
537	C₂²×C₃₁	—	2	1	no	—
538	C₂²×C₃₁	—	2	2	no	—
539	C₂²×C₃₁	—	4	1	no	—
540	C₂²×C₃₁	—	4	1	no	—
541	C₂²×C₃₁	—	4	1	no	—
542	C₂²×C₃₁	—	4	1	no	—
543	C₂²×C₃₁	—	4	1	no	—
544	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
545	C₄×C₃₁	—	2	1	no	—
546	C₄×C₃₁	—	2	2	no	—
547	C₄×C₃₁	—	2	1	no	—
548	C₄×C₃₁	—	2	1	no	—
549	C₄×C₃₁	—	2	2	no	—
550	C₄×C₃₁	—	2	1	no	—
551	C₄×C₃₁	—	2	2	no	—
552	C₄×C₃₁	—	4	1	no	—
553	C₄×C₃₁	—	4	1	no	—
554	C₄×C₃₁	—	4	2	no	—
555	C₄×C₃₁	—	4	2	no	—
556	C₄×C₃₁	—	4	1	no	—
557	C₄×C₃₁	—	4	1	no	—
558	C₄×C₃₁	—	4	1	no	—
559	C₄×C₃₁	—	4	2	no	—
560	C₄×C₃₁	—	4	2	no	—
561	C₄×C₃₁	—	4	1	no	—
562	C₄×C₃₁	#575	1	2	yes	—
563	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
564	C₄×C₃₁	#585	1	1	yes	characteristic
565	#557	C₂²×C₃₁	1	1	yes	characteristic
566	#557	C₂²×C₃₁	1	1	yes	characteristic
567	#556	C₂²×C₃₁	1	2	yes	—
568	#556	C₂²×C₃₁	1	1	yes	characteristic
569	#554	C₂²×C₃₁	1	1	yes	characteristic
570	#554	C₂²×C₃₁	1	1	yes	characteristic
571	#553	C₂²×C₃₁	1	2	yes	—
572	#552	—	2	1	no	—
573	#552	—	2	2	no	—
574	#552	—	2	2	no	—
575	#552	—	2	1	no	—
576	#552	C₂²×C₃₁	1	2	yes	—
577	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
578	#548	—	2	1	no	—
579	#547	—	2	1	no	—
580	#547	C₂²×C₃₁	1	1	yes	characteristic
581	#547	C₂²×C₃₁	1	2	yes	—
582	#547	C₂²×C₃₁	1	1	yes	characteristic
583	#541	—	2	1	no	—
584	#539	—	2	2	no	—
585	#533	C₂²×C₃₁	1	1	yes	characteristic
586	#533	C₂²×C₃₁	1	2	yes	—
587	#533	C₂²×C₃₁	1	1	yes	characteristic
588	#529	—	2	1	no	—
589	#529	—	2	2	no	—
590	#529	C₂²×C₃₁	1	1	yes	characteristic
591	#529	C₂²×C₃₁	1	2	yes	—
592	C₂×#125	C₂²×C₃₁	1	2	yes	—
593	#520	—	2	1	no	—
594	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
595	C₄×#41	C₂²×C₃₁	1	2	yes	—
596	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
597	C₂×C₄×Q₈	—	2	1	no	—
598	#501	C₂²×C₃₁	1	2	yes	—
599	#501	C₂²×C₃₁	1	2	yes	—
600	#500	C₂²×C₃₁	1	1	yes	characteristic
601	#498	C₂²×C₃₁	1	1	yes	characteristic
602	#491	C₂²×C₃₁	1	2	yes	—
603	#491	C₂²×C₃₁	1	2	yes	—
604	#487	C₂²×C₃₁	1	1	yes	characteristic
605	#487	C₂²×C₃₁	1	1	yes	characteristic
606	#485	C₂²×C₃₁	1	1	yes	characteristic
607	#485	C₂²×C₃₁	1	2	yes	—
608	#485	C₂²×C₃₁	1	2	yes	—
609	#485	C₂²×C₃₁	1	2	yes	—
610	#484	C₂²×C₃₁	1	2	yes	—
611	#484	C₂²×C₃₁	1	2	yes	—
612	#483	C₂²×C₃₁	1	2	yes	—
613	#483	C₂²×C₃₁	1	2	yes	—
614	#482	C₂²×C₃₁	1	1	yes	characteristic
615	#482	C₂²×C₃₁	1	2	yes	—
616	#479	C₂²×C₃₁	1	2	yes	—
617	#479	C₂²×C₃₁	1	2	yes	—
618	#479	C₂²×C₃₁	1	2	yes	—
619	#479	C₂²×C₃₁	1	2	yes	—
620	#479	C₂²×C₃₁	1	2	yes	—
621	#479	C₂²×C₃₁	1	1	yes	characteristic
622	#479	C₂²×C₃₁	1	2	yes	—
623	#478	C₂²×C₃₁	1	2	yes	—
624	#478	C₂²×C₃₁	1	1	yes	characteristic
625	#478	C₂²×C₃₁	1	2	yes	—
626	#478	C₂²×C₃₁	1	2	yes	—
627	#477	C₂²×C₃₁	1	1	yes	characteristic
628	#477	C₂²×C₃₁	1	2	yes	—
629	#476	C₂²×C₃₁	1	1	yes	characteristic
630	#476	C₂²×C₃₁	1	2	yes	—
631	#475	C₂²×C₃₁	1	1	yes	characteristic
632	#475	C₂²×C₃₁	1	1	yes	characteristic
633	#474	C₂²×C₃₁	1	1	yes	characteristic
634	#474	C₂²×C₃₁	1	1	yes	characteristic
635	#470	C₂²×C₃₁	1	2	yes	—
636	#470	C₂²×C₃₁	1	2	yes	—
637	#468	C₂²×C₃₁	1	2	yes	—
638	#468	C₂²×C₃₁	1	2	yes	—
639	#467	C₂²×C₃₁	1	2	yes	—
640	#465	C₂²×C₃₁	1	2	yes	—
641	#464	C₂²×C₃₁	1	1	yes	characteristic
642	#464	C₂²×C₃₁	1	2	yes	—
643	#463	C₂²×C₃₁	1	1	yes	characteristic
644	#462	C₂²×C₃₁	1	1	yes	characteristic
645	#462	C₂²×C₃₁	1	2	yes	—
646	#461	C₂²×C₃₁	1	1	yes	characteristic
647	#461	C₂²×C₃₁	1	2	yes	—
648	#452	C₂²×C₃₁	1	2	yes	—
649	#452	C₂²×C₃₁	1	1	yes	characteristic
650	#449	C₂²×C₃₁	1	2	yes	—
651	#449	C₂²×C₃₁	1	1	yes	characteristic
652	#446	C₂²×C₃₁	1	1	yes	characteristic
653	#446	C₂²×C₃₁	1	1	yes	characteristic
654	#442	C₂²×C₃₁	1	2	yes	—
655	#441	C₂²×C₃₁	1	2	yes	—
656	#440	C₂²×C₃₁	1	2	yes	—
657	#440	C₂²×C₃₁	1	2	yes	—
658	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
659	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
660	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
661	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
662	#436	C₂²×C₃₁	1	1	yes	characteristic
663	#436	C₂²×C₃₁	1	1	yes	characteristic
664	#435	C₂²×C₃₁	1	2	yes	—
665	#435	C₂²×C₃₁	1	2	yes	—
666	#432	C₂²×C₃₁	1	2	yes	—
667	#431	C₂²×C₃₁	1	1	yes	characteristic
668	#428	C₂²×C₃₁	1	2	yes	—
669	#428	C₂²×C₃₁	1	2	yes	—
670	#427	C₂²×C₃₁	1	2	yes	—
671	#423	C₂²×C₃₁	1	2	yes	—
672	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
673	#417	C₂²×C₃₁	1	2	yes	—
674	#417	C₂²×C₃₁	1	2	yes	—
675	#416	C₂²×C₃₁	1	2	yes	—
676	C₂×C₃₁	—	4	2	no	—
677	C₂×C₃₁	—	4	1	no	—
678	C₂×C₃₁	—	4	2	no	—
679	C₂×C₃₁	—	8	1	no	—
680	C₂×C₃₁	#3489	1	1	yes	characteristic
681	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
682	C₂×C₃₁	#3586	1	1	yes	characteristic
683	C₂×#41	—	2	1	no	—
684	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
685	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×#41	C₂³×C₃₁	1	2	yes	—
687	C₂²×Q₈	—	2	1	no	—
688	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
690	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
691	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
692	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
693	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
695	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
696	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
697	C₄⋊Q₈	—	2	1	no	—
698	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
700	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	1	no	—
711	#125	—	2	1	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	1	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	1	no	—
720	#125	C₂³×C₃₁	1	1	yes	characteristic
721	#125	C₂³×C₃₁	1	2	yes	—
722	#125	C₂³×C₃₁	1	2	yes	—
723	#125	C₂³×C₃₁	1	2	yes	—
724	#124	—	2	1	no	—
725	#124	—	2	2	no	—
726	#124	C₂³×C₃₁	1	1	yes	characteristic
727	#123	—	2	2	no	—
728	#123	—	2	1	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	C₂²⋊Q₈	—	2	1	no	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	1	no	—
738	C₂²⋊Q₈	—	2	1	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
746	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
747	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
748	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
749	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
750	#121	—	2	1	no	—
751	#121	—	2	2	no	—
752	#121	—	2	2	no	—
753	#121	C₂³×C₃₁	1	2	yes	—
754	#121	C₂³×C₃₁	1	1	yes	characteristic
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	2	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	2	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
766	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
768	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
769	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
771	C₄×D₄	—	2	1	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
780	C₄×D₄	D₄×C₃₁	1	2	yes	—
781	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
782	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
783	C₄×D₄	C₂³×C₃₁	1	2	yes	—
784	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
785	C₄×D₄	C₂³×C₃₁	1	2	yes	—
786	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
787	C₄×D₄	C₂³×C₃₁	1	2	yes	—
788	#117	—	2	2	no	—
789	#117	—	2	1	no	—
790	#117	—	2	2	no	—
791	#117	—	2	2	no	—
792	#117	—	2	1	no	—
793	#117	—	2	1	no	—
794	#117	—	2	2	no	—
795	#117	D₄×C₃₁	1	1	yes	characteristic
796	#117	D₄×C₃₁	1	2	yes	—
797	#117	C₂³×C₃₁	1	1	yes	characteristic
798	#117	C₂³×C₃₁	1	2	yes	—
799	#117	C₂³×C₃₁	1	2	yes	—
800	C₂×C₄⋊C₄	—	2	2	no	—
801	C₂×C₄⋊C₄	—	2	2	no	—
802	C₂×C₄⋊C₄	—	2	1	no	—
803	C₂×C₄⋊C₄	—	2	2	no	—
804	C₂×C₄⋊C₄	—	2	1	no	—
805	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
806	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
807	C₂×C₄²	—	2	1	no	—
808	C₂×C₄²	—	2	2	no	—
809	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
810	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
811	#107	C₂³×C₃₁	1	2	yes	—
812	#107	C₂³×C₃₁	1	2	yes	—
813	#107	C₂³×C₃₁	1	1	yes	characteristic
814	#107	C₂³×C₃₁	1	2	yes	—
815	#107	C₂³×C₃₁	1	2	yes	—
816	#107	C₂³×C₃₁	1	1	yes	characteristic
817	#107	C₂³×C₃₁	1	2	yes	—
818	#106	C₂³×C₃₁	1	2	yes	—
819	#106	C₂³×C₃₁	1	2	yes	—
820	#106	C₂³×C₃₁	1	1	yes	characteristic
821	#106	C₂³×C₃₁	1	2	yes	—
822	#106	C₂³×C₃₁	1	2	yes	—
823	#106	C₂³×C₃₁	1	1	yes	characteristic
824	#106	C₂³×C₃₁	1	2	yes	—
825	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
826	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
830	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
831	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
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	#103	C₂³×C₃₁	1	1	yes	characteristic
842	#103	C₂³×C₃₁	1	2	yes	—
843	#103	C₂³×C₃₁	1	2	yes	—
844	#103	C₂³×C₃₁	1	2	yes	—
845	#102	C₂³×C₃₁	1	2	yes	—
846	#102	C₂³×C₃₁	1	2	yes	—
847	#102	C₂³×C₃₁	1	1	yes	characteristic
848	#102	C₂³×C₃₁	1	1	yes	characteristic
849	#102	C₂³×C₃₁	1	1	yes	characteristic
850	#102	C₂³×C₃₁	1	1	yes	characteristic
851	#102	C₂³×C₃₁	1	2	yes	—
852	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
854	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
855	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
856	#97	C₂³×C₃₁	1	2	yes	—
857	#97	C₂³×C₃₁	1	2	yes	—
858	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
859	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₃₁	#62121	1	1	yes	characteristic, direct product factor, Sylow
861	#41	—	2	2	no	—
862	#41	—	2	4	no	—
863	#41	—	4	2	no	—
864	#41	—	4	1	no	—
865	#41	—	4	2	no	—
866	#41	—	4	4	no	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	4	4	no	—
872	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
873	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
874	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
875	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
876	C₂×D₄	—	2	1	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	2	1	no	—
880	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
881	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
882	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
883	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	1	no	—
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
894	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
895	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
896	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
898	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
899	Q₁₆	—	4	2	no	—
900	Q₁₆	—	4	1	no	—
901	SD₁₆	—	2	2	no	—
902	SD₁₆	—	4	2	no	—
903	SD₁₆	—	4	1	no	—
904	D₈	—	2	2	no	—
905	M₁₆	—	4	2	no	—
906	M₁₆	—	4	2	no	—
907	C₂×C₈	—	4	2	no	—
908	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
912	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
913	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
914	C₄⋊C₄	—	2	2	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	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	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	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
944	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
954	C₂²⋊C₄	—	2	2	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	1	no	—
962	C₂²⋊C₄	—	2	1	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	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
973	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	1	no	—
983	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
984	C₄²	C₂×D₄×C₃₁	1	2	yes	—
985	C₄²	C₂×D₄×C₃₁	1	2	yes	—
986	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
987	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₄²	C₂⁴×C₃₁	1	2	yes	—
989	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
993	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
994	Q₈	—	2	2	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	2	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	2	1	no	—
1001	Q₈	—	4	4	no	—
1002	Q₈	—	4	2	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	8	1	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	4	2	no	—
1010	D₄	—	4	2	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	4	4	no	—
1013	D₄	—	8	1	no	—
1014	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	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	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	4	1	no	—
1032	C₂×C₄	—	4	2	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	4	2	no	—
1036	C₂×C₄	—	4	4	no	—
1037	C₂×C₄	—	4	4	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1045	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1046	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1047	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1050	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1051	C₈	—	2	1	no	—
1052	C₈	—	2	1	no	—
1053	C₈	—	2	2	no	—
1054	C₈	—	2	2	no	—
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	4	2	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	2	no	—
1087	C₄	C₃₁×#575	1	2	yes	—
1088	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1089	C₄	C₃₁×#585	1	1	yes	characteristic
1090	C₂	—	4	1	no	—
1091	C₂	—	4	2	no	—
1092	C₂	—	4	2	no	—
1093	C₂	—	8	1	no	—
1094	C₂	C₃₁×#3489	1	1	yes	characteristic
1095	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1096	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3515	C₂	semidirect
2. C₃₁×#3482	C₂	semidirect
3. C₃₁×#3386	C₂	semidirect
4. C₃₁×#3384	C₂	semidirect
5. C₃₁×#3374	C₂	semidirect
6. C₃₁×#3372	C₂	semidirect
7. C₃₁×#3356	C₂	semidirect
8. C₃₁×#3353	C₂	semidirect
9. C₃₁×#3350	C₂	semidirect
10. C₃₁×#3349	C₂	semidirect
11. C₃₁×#3331	C₂	semidirect
12. C₃₁×#3330	C₂	semidirect
13. C₃₁×#3315	C₂	semidirect
14. C₃₁×#3307	C₂	semidirect
15. C₃₁×#3252	C₂	semidirect
16. C₃₁×#3248	C₂	semidirect
17. C₃₁×#3236	C₂	semidirect
18. C₃₁×#3231	C₂	semidirect
19. C₃₁×#3111	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3080	C₂	semidirect
22. C₃₁×#3076	C₂	semidirect
23. C₃₁×#2989	C₂	semidirect
441. #62121	C₃₁	direct (N × H)
509. #3515	C₂×C₃₁	semidirect
510. #3482	C₂×C₃₁	semidirect
511. #3386	C₂×C₃₁	semidirect
512. #3384	C₂×C₃₁	semidirect
513. #3374	C₂×C₃₁	semidirect
514. #3372	C₂×C₃₁	semidirect
515. #3356	C₂×C₃₁	semidirect
516. #3353	C₂×C₃₁	semidirect
517. #3350	C₂×C₃₁	semidirect
518. #3349	C₂×C₃₁	semidirect
519. #3331	C₂×C₃₁	semidirect
520. #3330	C₂×C₃₁	semidirect
521. #3315	C₂×C₃₁	semidirect
522. #3307	C₂×C₃₁	semidirect
523. #3252	C₂×C₃₁	semidirect
524. #3248	C₂×C₃₁	semidirect
525. #3236	C₂×C₃₁	semidirect
526. #3231	C₂×C₃₁	semidirect
527. #3111	C₂×C₃₁	semidirect
528. #3102	C₂×C₃₁	semidirect
529. #3080	C₂×C₃₁	semidirect
530. #3076	C₂×C₃₁	semidirect
531. #2989	C₂×C₃₁	semidirect
860. C₃₁	#62121	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×#3515	2
C₃₁×#3482	2
C₃₁×#3386	2
C₃₁×#3384	2
C₃₁×#3374	2
C₃₁×#3372	2
C₃₁×#3356	2
C₃₁×#3353	2
C₃₁×#3350	2
C₃₁×#3349	2
C₃₁×#3331	2
C₃₁×#3330	2
C₃₁×#3315	2
C₃₁×#3307	2
C₃₁×#3252	2
C₃₁×#3248	2
C₃₁×#3236	2
C₃₁×#3231	2
C₃₁×#3111	2
C₃₁×#3102	2
C₃₁×#3080	2
C₃₁×#3076	2
C₃₁×#2989	2
#62121	31

Subgroups — C31×#62121 #21518880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62121 #21518880