Subgroups — C₃₁×#62181 #21518940

Order 7936.

1684 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3352	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3330	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3315	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#557	C₂²	1	1	yes	characteristic
27	C₃₁×#555	C₂²	1	1	yes	characteristic
28	C₃₁×#554	C₂²	1	1	yes	characteristic
29	C₃₁×#554	C₂²	1	1	yes	characteristic
30	C₃₁×#554	C₂²	1	1	yes	characteristic
31	C₃₁×#554	C₂²	1	1	yes	characteristic
32	C₃₁×#553	—	2	1	no	—
33	C₃₁×#552	—	2	2	no	—
34	C₃₁×#552	—	2	1	no	—
35	C₃₁×#552	—	2	1	no	—
36	C₃₁×#552	C₂²	1	2	yes	—
37	C₃₁×#552	C₂²	1	2	yes	—
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	2	yes	—
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#544	C₂²	1	2	yes	—
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#542	C₂²	1	2	yes	—
46	C₃₁×#541	C₂²	1	2	yes	—
47	C₃₁×#539	—	2	2	no	—
48	C₃₁×#536	—	2	2	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
51	C₃₁×#529	—	2	1	no	—
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#529	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×#125	—	2	1	no	—
55	C₃₁×#520	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	—
58	C₃₁×#500	C₂²	1	1	yes	characteristic
59	C₃₁×#500	C₂²	1	1	yes	characteristic
60	C₃₁×#499	C₂²	1	2	yes	—
61	C₃₁×#491	C₂²	1	2	yes	—
62	C₃₁×#487	C₂²	1	1	yes	characteristic
63	C₃₁×#487	C₂²	1	1	yes	characteristic
64	C₃₁×#487	C₂²	1	2	yes	—
65	C₃₁×#485	C₂²	1	1	yes	characteristic
66	C₃₁×#485	C₂²	1	2	yes	—
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#484	C₂²	1	2	yes	—
69	C₃₁×#484	C₂²	1	2	yes	—
70	C₃₁×#484	C₂²	1	2	yes	—
71	C₃₁×#484	C₂²	1	2	yes	—
72	C₃₁×#483	C₂²	1	2	yes	—
73	C₃₁×#482	C₂²	1	1	yes	characteristic
74	C₃₁×#480	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	1	yes	characteristic
79	C₃₁×#478	C₂²	1	1	yes	characteristic
80	C₃₁×#478	C₂²	1	2	yes	—
81	C₃₁×#478	C₂²	1	2	yes	—
82	C₃₁×#477	C₂²	1	1	yes	characteristic
83	C₃₁×#477	C₂²	1	1	yes	characteristic
84	C₃₁×#477	C₂²	1	1	yes	characteristic
85	C₃₁×#477	C₂²	1	2	yes	—
86	C₃₁×#477	C₂²	1	2	yes	—
87	C₃₁×#477	C₂²	1	2	yes	—
88	C₃₁×#476	C₂²	1	1	yes	characteristic
89	C₃₁×#476	C₂²	1	1	yes	characteristic
90	C₃₁×#476	C₂²	1	1	yes	characteristic
91	C₃₁×#475	C₂²	1	2	yes	—
92	C₃₁×#474	C₂²	1	2	yes	—
93	C₃₁×#474	C₂²	1	2	yes	—
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	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
113	C₃₁×#440	C₂²	1	2	yes	—
114	C₃₁×#440	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	2	yes	—
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	2	yes	—
123	C₃₁×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₃₁×#433	C₂²	1	2	yes	—
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	—
128	C₃₁×#428	C₂²	1	2	yes	—
129	C₂×C₃₁×#107	C₂²	1	2	yes	—
130	C₃₁×#424	C₂²	1	2	yes	—
131	C₃₁×#423	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	2	no	—
136	C₂×#41×C₃₁	C₂³	1	2	yes	—
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
148	C₃₁×C₄⋊Q₈	—	2	2	no	—
149	C₃₁×C₄⋊Q₈	—	2	2	no	—
150	C₃₁×C₄⋊Q₈	—	2	1	no	—
151	C₃₁×C₄⋊Q₈	—	2	1	no	—
152	C₃₁×C₄⋊Q₈	—	2	1	no	—
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×#126	—	2	2	no	—
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	1	no	—
166	C₃₁×#126	D₄	1	2	yes	—
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	1	no	—
170	C₃₁×#125	—	2	1	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	1	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	1	no	—
177	C₃₁×#125	D₄	1	1	yes	characteristic
178	C₃₁×#125	C₂³	1	1	yes	characteristic
179	C₃₁×#125	C₂³	1	2	yes	—
180	C₃₁×#125	C₂³	1	2	yes	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	D₄	1	1	yes	characteristic
184	C₃₁×#124	C₂³	1	1	yes	characteristic
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	1	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	D₄	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
209	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	D₄	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	—	2	1	no	—
219	C₄×Q₈×C₃₁	—	2	1	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₃₁	—	2	1	no	—
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₃₁×#117	—	2	1	no	—
243	C₃₁×#117	—	2	2	no	—
244	C₃₁×#117	—	2	1	no	—
245	C₃₁×#117	—	2	2	no	—
246	C₃₁×#117	—	2	2	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	1	no	—
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	1	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	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
261	C₂×C₄²×C₃₁	—	2	1	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	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	2	yes	—
276	C₃₁×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
294	C₃₁×#103	C₂³	1	1	yes	characteristic
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	1	yes	characteristic
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	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	#41×C₃₁	—	2	4	no	—
313	#41×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	1	no	—
316	#41×C₃₁	—	8	4	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	8	2	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	2	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	2	no	—
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	1	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	—	2	2	no	—
345	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
349	Q₁₆×C₃₁	—	4	1	no	—
350	Q₁₆×C₃₁	—	4	2	no	—
351	SD₁₆×C₃₁	—	2	2	no	—
352	SD₁₆×C₃₁	—	4	2	no	—
353	SD₁₆×C₃₁	—	4	1	no	—
354	D₈×C₃₁	—	2	2	no	—
355	M₁₆×C₃₁	—	4	2	no	—
356	M₁₆×C₃₁	—	4	2	no	—
357	C₂×C₈×C₃₁	—	4	2	no	—
358	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₃₁	—	2	1	no	—
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	1	no	—
369	C₄⋊C₄×C₃₁	—	2	2	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	2	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	1	no	—
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
406	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	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	1	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	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
427	C₄²×C₃₁	—	2	1	no	—
428	C₄²×C₃₁	—	2	1	no	—
429	C₄²×C₃₁	—	2	1	no	—
430	C₄²×C₃₁	—	2	2	no	—
431	C₄²×C₃₁	—	2	2	no	—
432	C₄²×C₃₁	—	2	2	no	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
438	C₄²×C₃₁	C₂⁴	1	2	yes	—
439	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
440	#62181	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
441	C₂³×C₃₁	—	2	1	no	—
442	C₂³×C₃₁	—	2	1	no	—
443	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
444	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
445	Q₈×C₃₁	—	2	2	no	—
446	Q₈×C₃₁	—	2	1	no	—
447	Q₈×C₃₁	—	2	2	no	—
448	Q₈×C₃₁	—	2	1	no	—
449	Q₈×C₃₁	—	2	2	no	—
450	Q₈×C₃₁	—	2	1	no	—
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	8	1	no	—
453	Q₈×C₃₁	—	8	2	no	—
454	Q₈×C₃₁	—	8	1	no	—
455	Q₈×C₃₁	—	8	1	no	—
456	Q₈×C₃₁	—	8	2	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	4	no	—
463	D₄×C₃₁	—	4	2	no	—
464	D₄×C₃₁	—	4	2	no	—
465	D₄×C₃₁	—	8	2	no	—
466	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
467	C₂×C₄×C₃₁	—	2	2	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	2	2	no	—
470	C₂×C₄×C₃₁	—	2	2	no	—
471	C₂×C₄×C₃₁	—	2	1	no	—
472	C₂×C₄×C₃₁	—	2	1	no	—
473	C₂×C₄×C₃₁	—	2	1	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	2	1	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	2	2	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	2	no	—
482	C₂×C₄×C₃₁	—	4	1	no	—
483	C₂×C₄×C₃₁	—	4	2	no	—
484	C₂×C₄×C₃₁	—	4	4	no	—
485	C₂×C₄×C₃₁	—	4	4	no	—
486	C₂×C₄×C₃₁	—	4	2	no	—
487	C₂×C₄×C₃₁	—	4	2	no	—
488	C₂×C₄×C₃₁	—	8	1	no	—
489	C₂×C₄×C₃₁	—	8	2	no	—
490	C₂×C₄×C₃₁	—	8	2	no	—
491	C₂×C₄×C₃₁	—	8	2	no	—
492	C₂×C₄×C₃₁	—	8	2	no	—
493	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
502	C₈×C₃₁	—	2	1	no	—
503	C₈×C₃₁	—	2	1	no	—
504	C₈×C₃₁	—	2	1	no	—
505	C₈×C₃₁	—	2	2	no	—
506	C₈×C₃₁	—	2	1	no	—
507	C₈×C₃₁	—	2	2	no	—
508	#3544	C₂×C₃₁	1	1	yes	characteristic, complemented
509	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#3363	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#3357	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#3352	C₂×C₃₁	1	2	yes	complemented
516	#3343	C₂×C₃₁	1	2	yes	complemented
517	#3338	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3330	C₂×C₃₁	1	2	yes	complemented
520	#3315	C₂×C₃₁	1	2	yes	complemented
521	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3258	C₂×C₃₁	1	2	yes	complemented
523	#3252	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3242	C₂×C₃₁	1	2	yes	complemented
525	#3230	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3124	C₂×C₃₁	1	2	yes	complemented
527	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3083	C₂×C₃₁	1	2	yes	complemented
529	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#2993	C₂×C₃₁	1	1	yes	characteristic, complemented
531	C₂²×C₃₁	—	2	1	no	—
532	C₂²×C₃₁	—	2	2	no	—
533	C₂²×C₃₁	—	2	2	no	—
534	C₂²×C₃₁	—	2	1	no	—
535	C₂²×C₃₁	—	2	2	no	—
536	C₂²×C₃₁	—	2	1	no	—
537	C₂²×C₃₁	—	2	2	no	—
538	C₂²×C₃₁	—	4	1	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	C₂³×D₄	1	1	yes	characteristic
544	C₄×C₃₁	—	2	1	no	—
545	C₄×C₃₁	—	2	1	no	—
546	C₄×C₃₁	—	2	2	no	—
547	C₄×C₃₁	—	2	2	no	—
548	C₄×C₃₁	—	2	1	no	—
549	C₄×C₃₁	—	2	1	no	—
550	C₄×C₃₁	—	2	2	no	—
551	C₄×C₃₁	—	4	2	no	—
552	C₄×C₃₁	—	4	2	no	—
553	C₄×C₃₁	—	4	1	no	—
554	C₄×C₃₁	—	4	1	no	—
555	C₄×C₃₁	—	4	2	no	—
556	C₄×C₃₁	—	4	1	no	—
557	C₄×C₃₁	—	4	2	no	—
558	C₄×C₃₁	—	4	1	no	—
559	C₄×C₃₁	—	4	1	no	—
560	C₄×C₃₁	—	4	1	no	—
561	C₄×C₃₁	#578	1	2	yes	—
562	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
563	C₄×C₃₁	#585	1	1	yes	characteristic
564	#563	—	2	2	no	—
565	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
566	#557	C₂²×C₃₁	1	1	yes	characteristic
567	#555	C₂²×C₃₁	1	1	yes	characteristic
568	#554	C₂²×C₃₁	1	1	yes	characteristic
569	#554	C₂²×C₃₁	1	1	yes	characteristic
570	#554	C₂²×C₃₁	1	1	yes	characteristic
571	#554	C₂²×C₃₁	1	1	yes	characteristic
572	#553	—	2	1	no	—
573	#552	—	2	2	no	—
574	#552	—	2	1	no	—
575	#552	—	2	1	no	—
576	#552	C₂²×C₃₁	1	2	yes	—
577	#552	C₂²×C₃₁	1	2	yes	—
578	#547	—	2	1	no	—
579	#547	C₂²×C₃₁	1	2	yes	—
580	#547	C₂²×C₃₁	1	1	yes	characteristic
581	#547	C₂²×C₃₁	1	2	yes	—
582	#544	—	2	1	no	—
583	#544	C₂²×C₃₁	1	2	yes	—
584	#542	—	2	1	no	—
585	#542	C₂²×C₃₁	1	2	yes	—
586	#541	C₂²×C₃₁	1	2	yes	—
587	#539	—	2	2	no	—
588	#536	—	2	2	no	—
589	#533	C₂²×C₃₁	1	1	yes	characteristic
590	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
591	#529	—	2	1	no	—
592	#529	C₂²×C₃₁	1	1	yes	characteristic
593	#529	C₂²×C₃₁	1	1	yes	characteristic
594	C₂×#125	—	2	1	no	—
595	#520	C₂²×C₃₁	1	2	yes	—
596	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
597	#501	C₂²×C₃₁	1	2	yes	—
598	#500	C₂²×C₃₁	1	1	yes	characteristic
599	#500	C₂²×C₃₁	1	1	yes	characteristic
600	#499	C₂²×C₃₁	1	2	yes	—
601	#491	C₂²×C₃₁	1	2	yes	—
602	#487	C₂²×C₃₁	1	2	yes	—
603	#487	C₂²×C₃₁	1	1	yes	characteristic
604	#487	C₂²×C₃₁	1	1	yes	characteristic
605	#485	C₂²×C₃₁	1	1	yes	characteristic
606	#485	C₂²×C₃₁	1	2	yes	—
607	#485	C₂²×C₃₁	1	2	yes	—
608	#484	C₂²×C₃₁	1	2	yes	—
609	#484	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	#482	C₂²×C₃₁	1	1	yes	characteristic
614	#480	C₂²×C₃₁	1	2	yes	—
615	#479	C₂²×C₃₁	1	2	yes	—
616	#479	C₂²×C₃₁	1	2	yes	—
617	#479	C₂²×C₃₁	1	2	yes	—
618	#479	C₂²×C₃₁	1	1	yes	characteristic
619	#478	C₂²×C₃₁	1	1	yes	characteristic
620	#478	C₂²×C₃₁	1	2	yes	—
621	#478	C₂²×C₃₁	1	2	yes	—
622	#477	C₂²×C₃₁	1	1	yes	characteristic
623	#477	C₂²×C₃₁	1	1	yes	characteristic
624	#477	C₂²×C₃₁	1	1	yes	characteristic
625	#477	C₂²×C₃₁	1	2	yes	—
626	#477	C₂²×C₃₁	1	2	yes	—
627	#477	C₂²×C₃₁	1	2	yes	—
628	#476	C₂²×C₃₁	1	1	yes	characteristic
629	#476	C₂²×C₃₁	1	1	yes	characteristic
630	#476	C₂²×C₃₁	1	1	yes	characteristic
631	#475	C₂²×C₃₁	1	2	yes	—
632	#474	C₂²×C₃₁	1	2	yes	—
633	#474	C₂²×C₃₁	1	2	yes	—
634	#470	C₂²×C₃₁	1	2	yes	—
635	#470	C₂²×C₃₁	1	2	yes	—
636	#468	C₂²×C₃₁	1	2	yes	—
637	#468	C₂²×C₃₁	1	2	yes	—
638	#467	C₂²×C₃₁	1	2	yes	—
639	#465	C₂²×C₃₁	1	2	yes	—
640	#464	C₂²×C₃₁	1	1	yes	characteristic
641	#464	C₂²×C₃₁	1	2	yes	—
642	#463	C₂²×C₃₁	1	1	yes	characteristic
643	#462	C₂²×C₃₁	1	1	yes	characteristic
644	#462	C₂²×C₃₁	1	2	yes	—
645	#461	C₂²×C₃₁	1	2	yes	—
646	#461	C₂²×C₃₁	1	1	yes	characteristic
647	#452	C₂²×C₃₁	1	2	yes	—
648	#452	C₂²×C₃₁	1	1	yes	characteristic
649	#449	C₂²×C₃₁	1	1	yes	characteristic
650	#449	C₂²×C₃₁	1	2	yes	—
651	#446	C₂²×C₃₁	1	1	yes	characteristic
652	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
653	#440	C₂²×C₃₁	1	2	yes	—
654	#440	C₂²×C₃₁	1	2	yes	—
655	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
656	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
657	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
658	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
659	C₄×D₈	C₂²×C₃₁	1	2	yes	—
660	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
661	#436	C₂²×C₃₁	1	2	yes	—
662	#436	C₂²×C₃₁	1	1	yes	characteristic
663	#435	C₂²×C₃₁	1	2	yes	—
664	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
665	#433	C₂²×C₃₁	1	2	yes	—
666	#431	C₂²×C₃₁	1	1	yes	characteristic
667	#428	C₂²×C₃₁	1	2	yes	—
668	#428	C₂²×C₃₁	1	2	yes	—
669	C₂×#107	C₂²×C₃₁	1	2	yes	—
670	#424	C₂²×C₃₁	1	2	yes	—
671	#423	C₂²×C₃₁	1	1	yes	characteristic
672	#417	C₂²×C₃₁	1	2	yes	—
673	#417	C₂²×C₃₁	1	2	yes	—
674	#416	C₂²×C₃₁	1	2	yes	—
675	C₂×C₃₁	—	4	1	no	—
676	C₂×C₃₁	—	4	2	no	—
677	C₂×C₃₁	—	4	2	no	—
678	C₂×C₃₁	—	8	1	no	—
679	C₂×C₃₁	#3489	1	1	yes	characteristic
680	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
681	C₂×C₃₁	#3585	1	1	yes	characteristic
682	C₂×#41	—	2	2	no	—
683	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×#41	C₂³×C₃₁	1	2	yes	—
685	C₂²×Q₈	—	2	1	no	—
686	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
690	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
691	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
692	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
693	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
694	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
695	C₄⋊Q₈	—	2	2	no	—
696	C₄⋊Q₈	—	2	2	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	2	yes	—
702	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	1	no	—
713	#126	D₄×C₃₁	1	2	yes	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	1	no	—
717	#125	—	2	1	no	—
718	#125	—	2	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	1	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	1	no	—
724	#125	D₄×C₃₁	1	1	yes	characteristic
725	#125	C₂³×C₃₁	1	1	yes	characteristic
726	#125	C₂³×C₃₁	1	2	yes	—
727	#125	C₂³×C₃₁	1	2	yes	—
728	#124	—	2	2	no	—
729	#124	—	2	2	no	—
730	#124	D₄×C₃₁	1	1	yes	characteristic
731	#124	C₂³×C₃₁	1	1	yes	characteristic
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	1	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	D₄×C₃₁	1	2	yes	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
754	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
755	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
756	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
759	#121	—	2	1	no	—
760	#121	—	2	2	no	—
761	#121	—	2	1	no	—
762	#121	D₄×C₃₁	1	1	yes	characteristic
763	#121	C₂³×C₃₁	1	1	yes	characteristic
764	#121	C₂³×C₃₁	1	2	yes	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
771	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
772	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
774	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
783	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×D₄	C₂³×C₃₁	1	2	yes	—
785	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
786	C₄×D₄	C₂³×C₃₁	1	2	yes	—
787	C₄×D₄	C₂³×C₃₁	1	2	yes	—
788	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
789	#117	—	2	1	no	—
790	#117	—	2	2	no	—
791	#117	—	2	1	no	—
792	#117	—	2	2	no	—
793	#117	—	2	2	no	—
794	#117	—	2	1	no	—
795	#117	—	2	1	no	—
796	#117	C₂³×C₃₁	1	1	yes	characteristic
797	#117	C₂³×C₃₁	1	2	yes	—
798	#117	C₂³×C₃₁	1	2	yes	—
799	C₂×C₄⋊C₄	—	2	1	no	—
800	C₂×C₄⋊C₄	—	2	2	no	—
801	C₂×C₄⋊C₄	—	2	1	no	—
802	C₂×C₄⋊C₄	—	2	2	no	—
803	C₂×C₄⋊C₄	—	2	1	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×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
808	C₂×C₄²	—	2	1	no	—
809	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
810	#107	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	2	yes	—
814	#107	C₂³×C₃₁	1	2	yes	—
815	#107	C₂³×C₃₁	1	2	yes	—
816	#107	C₂³×C₃₁	1	2	yes	—
817	#107	C₂³×C₃₁	1	1	yes	characteristic
818	#107	C₂³×C₃₁	1	2	yes	—
819	#106	C₂³×C₃₁	1	1	yes	characteristic
820	#106	C₂³×C₃₁	1	2	yes	—
821	#106	C₂³×C₃₁	1	2	yes	—
822	#106	C₂³×C₃₁	1	2	yes	—
823	#106	C₂³×C₃₁	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
825	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
828	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
829	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
830	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
831	#103	C₂³×C₃₁	1	2	yes	—
832	#103	C₂³×C₃₁	1	2	yes	—
833	#103	C₂³×C₃₁	1	2	yes	—
834	#103	C₂³×C₃₁	1	2	yes	—
835	#103	C₂³×C₃₁	1	2	yes	—
836	#103	C₂³×C₃₁	1	2	yes	—
837	#103	C₂³×C₃₁	1	1	yes	characteristic
838	#103	C₂³×C₃₁	1	1	yes	characteristic
839	#103	C₂³×C₃₁	1	1	yes	characteristic
840	#103	C₂³×C₃₁	1	2	yes	—
841	#103	C₂³×C₃₁	1	1	yes	characteristic
842	#103	C₂³×C₃₁	1	2	yes	—
843	#103	C₂³×C₃₁	1	2	yes	—
844	#102	C₂³×C₃₁	1	1	yes	characteristic
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	2	yes	—
850	#102	C₂³×C₃₁	1	1	yes	characteristic
851	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
854	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
855	#97	C₂³×C₃₁	1	2	yes	—
856	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
857	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
858	C₄×C₈	C₂³×C₃₁	1	2	yes	—
859	C₃₁	#62181	1	1	yes	characteristic, direct product factor, Sylow
860	#41	—	2	2	no	—
861	#41	—	2	4	no	—
862	#41	—	4	2	no	—
863	#41	—	4	1	no	—
864	#41	—	8	4	no	—
865	C₂×Q₈	—	2	1	no	—
866	C₂×Q₈	—	2	1	no	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	2	2	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	8	2	no	—
871	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
872	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
873	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
874	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	1	no	—
877	C₂×D₄	—	2	1	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
880	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
881	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
882	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
883	C₂²×C₄	—	2	2	no	—
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	1	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
894	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
897	Q₁₆	—	4	1	no	—
898	Q₁₆	—	4	2	no	—
899	SD₁₆	—	2	2	no	—
900	SD₁₆	—	4	2	no	—
901	SD₁₆	—	4	1	no	—
902	D₈	—	2	2	no	—
903	M₁₆	—	4	2	no	—
904	M₁₆	—	4	2	no	—
905	C₂×C₈	—	4	2	no	—
906	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
907	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
908	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
909	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	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	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	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	1	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	2	no	—
941	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
943	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₃₁	1	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	1	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	2	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	2	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
971	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
973	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
974	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	2	no	—
983	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
984	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
985	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₄²	C₂⁴×C₃₁	1	2	yes	—
987	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₂³	—	2	1	no	—
989	C₂³	—	2	1	no	—
990	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
991	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	2	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	8	1	no	—
1000	Q₈	—	8	2	no	—
1001	Q₈	—	8	1	no	—
1002	Q₈	—	8	1	no	—
1003	Q₈	—	8	2	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	1	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	4	2	no	—
1009	D₄	—	4	4	no	—
1010	D₄	—	4	2	no	—
1011	D₄	—	4	2	no	—
1012	D₄	—	8	2	no	—
1013	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	4	1	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	4	2	no	—
1035	C₂×C₄	—	8	1	no	—
1036	C₂×C₄	—	8	2	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
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	1	yes	characteristic
1046	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1047	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1048	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1049	C₈	—	2	1	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	2	1	no	—
1052	C₈	—	2	2	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	1	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1068	C₄	—	2	2	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	1	no	—
1084	C₄	—	4	2	no	—
1085	C₄	C₃₁×#578	1	2	yes	—
1086	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1087	C₄	C₃₁×#585	1	1	yes	characteristic
1088	C₂	—	4	1	no	—
1089	C₂	—	4	2	no	—
1090	C₂	—	4	2	no	—
1091	C₂	—	8	1	no	—
1092	C₂	C₃₁×#3489	1	1	yes	characteristic
1093	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1094	C₂	C₃₁×#3585	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×#3544	C₂	semidirect
2. C₃₁×#3515	C₂	semidirect
3. C₃₁×#3385	C₂	semidirect
4. C₃₁×#3380	C₂	semidirect
5. C₃₁×#3372	C₂	semidirect
6. C₃₁×#3363	C₂	semidirect
7. C₃₁×#3357	C₂	semidirect
8. C₃₁×#3352	C₂	semidirect
9. C₃₁×#3343	C₂	semidirect
10. C₃₁×#3338	C₂	semidirect
11. C₃₁×#3331	C₂	semidirect
12. C₃₁×#3330	C₂	semidirect
13. C₃₁×#3315	C₂	semidirect
14. C₃₁×#3303	C₂	semidirect
15. C₃₁×#3258	C₂	semidirect
16. C₃₁×#3252	C₂	semidirect
17. C₃₁×#3242	C₂	semidirect
18. C₃₁×#3230	C₂	semidirect
19. C₃₁×#3124	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3083	C₂	semidirect
22. C₃₁×#3079	C₂	semidirect
23. C₃₁×#2993	C₂	semidirect
440. #62181	C₃₁	direct (N × H)
508. #3544	C₂×C₃₁	semidirect
509. #3515	C₂×C₃₁	semidirect
510. #3385	C₂×C₃₁	semidirect
511. #3380	C₂×C₃₁	semidirect
512. #3372	C₂×C₃₁	semidirect
513. #3363	C₂×C₃₁	semidirect
514. #3357	C₂×C₃₁	semidirect
515. #3352	C₂×C₃₁	semidirect
516. #3343	C₂×C₃₁	semidirect
517. #3338	C₂×C₃₁	semidirect
518. #3331	C₂×C₃₁	semidirect
519. #3330	C₂×C₃₁	semidirect
520. #3315	C₂×C₃₁	semidirect
521. #3303	C₂×C₃₁	semidirect
522. #3258	C₂×C₃₁	semidirect
523. #3252	C₂×C₃₁	semidirect
524. #3242	C₂×C₃₁	semidirect
525. #3230	C₂×C₃₁	semidirect
526. #3124	C₂×C₃₁	semidirect
527. #3102	C₂×C₃₁	semidirect
528. #3083	C₂×C₃₁	semidirect
529. #3079	C₂×C₃₁	semidirect
530. #2993	C₂×C₃₁	semidirect
859. C₃₁	#62181	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×#3544	2
C₃₁×#3515	2
C₃₁×#3385	2
C₃₁×#3380	2
C₃₁×#3372	2
C₃₁×#3363	2
C₃₁×#3357	2
C₃₁×#3352	2
C₃₁×#3343	2
C₃₁×#3338	2
C₃₁×#3331	2
C₃₁×#3330	2
C₃₁×#3315	2
C₃₁×#3303	2
C₃₁×#3258	2
C₃₁×#3252	2
C₃₁×#3242	2
C₃₁×#3230	2
C₃₁×#3124	2
C₃₁×#3102	2
C₃₁×#3083	2
C₃₁×#3079	2
C₃₁×#2993	2
#62181	31

Subgroups — C31×#62181 #21518940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62181 #21518940