Subgroups — C₃₁×#62218 #21518977

Order 7936.

1698 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3384	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×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3348	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3337	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3303	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3260	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3084	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#562	—	2	2	no	—
25	C₃₁×#557	C₂²	1	1	yes	characteristic
26	C₃₁×#555	C₂²	1	2	yes	—
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×#553	—	2	1	no	—
32	C₃₁×#553	C₂²	1	2	yes	—
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	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#548	—	2	1	no	—
39	C₃₁×#547	C₂²	1	2	yes	—
40	C₃₁×#547	C₂²	1	1	yes	characteristic
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#544	C₂²	1	2	yes	—
43	C₃₁×#542	—	2	2	no	—
44	C₃₁×#541	C₂²	1	2	yes	—
45	C₃₁×#540	C₂²	1	2	yes	—
46	C₃₁×#539	—	2	2	no	—
47	C₃₁×#537	—	2	1	no	—
48	C₃₁×#536	—	2	1	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#532	C₂²	1	1	yes	characteristic
52	C₃₁×#529	—	2	1	no	—
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×#499	C₂²	1	2	yes	—
60	C₃₁×#498	C₂²	1	1	yes	characteristic
61	C₃₁×#491	C₂²	1	2	yes	—
62	C₃₁×#487	C₂²	1	1	yes	characteristic
63	C₃₁×#487	C₂²	1	2	yes	—
64	C₃₁×#487	C₂²	1	1	yes	characteristic
65	C₃₁×#485	C₂²	1	2	yes	—
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×#483	C₂²	1	2	yes	—
71	C₃₁×#482	C₂²	1	1	yes	characteristic
72	C₃₁×#482	C₂²	1	1	yes	characteristic
73	C₃₁×#481	C₂²	1	2	yes	—
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	2	yes	—
79	C₃₁×#478	C₂²	1	2	yes	—
80	C₃₁×#478	C₂²	1	2	yes	—
81	C₃₁×#478	C₂²	1	2	yes	—
82	C₃₁×#478	C₂²	1	2	yes	—
83	C₃₁×#477	C₂²	1	1	yes	characteristic
84	C₃₁×#477	C₂²	1	1	yes	characteristic
85	C₃₁×#476	C₂²	1	1	yes	characteristic
86	C₃₁×#476	C₂²	1	1	yes	characteristic
87	C₃₁×#476	C₂²	1	1	yes	characteristic
88	C₃₁×#476	C₂²	1	2	yes	—
89	C₃₁×#476	C₂²	1	1	yes	characteristic
90	C₃₁×#475	C₂²	1	1	yes	characteristic
91	C₃₁×#475	C₂²	1	2	yes	—
92	C₃₁×#475	C₂²	1	2	yes	—
93	C₃₁×#474	C₂²	1	1	yes	characteristic
94	C₃₁×#468	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	—
96	C₃₁×#465	C₂²	1	2	yes	—
97	C₃₁×#465	C₂²	1	2	yes	—
98	C₃₁×#465	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	—
100	C₃₁×#461	C₂²	1	1	yes	characteristic
101	C₃₁×#461	C₂²	1	2	yes	—
102	C₃₁×#461	C₂²	1	1	yes	characteristic
103	C₃₁×#461	C₂²	1	2	yes	—
104	C₃₁×#460	C₂²	1	1	yes	characteristic
105	C₃₁×#460	C₂²	1	2	yes	—
106	C₃₁×#459	C₂²	1	1	yes	characteristic
107	C₃₁×#449	C₂²	1	1	yes	characteristic
108	C₃₁×#449	C₂²	1	1	yes	characteristic
109	C₃₁×#449	C₂²	1	2	yes	—
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×#442	C₂²	1	2	yes	—
114	C₃₁×#440	C₂²	1	2	yes	—
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×D₈×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×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₃₁	C₂²	1	2	yes	—
125	C₃₁×#433	C₂²	1	2	yes	—
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	—
128	C₃₁×#427	C₂²	1	2	yes	—
129	C₂×C₃₁×#106	C₂²	1	2	yes	—
130	C₃₁×#424	C₂²	1	2	yes	—
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
132	C₃₁×#417	C₂²	1	2	yes	—
133	C₃₁×#416	C₂²	1	2	yes	—
134	C₃₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
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×D₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
148	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
149	C₃₁×C₄⋊Q₈	—	2	2	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	2	yes	—
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×#127	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
163	C₃₁×#125	—	2	2	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	—	2	1	no	—
166	C₃₁×#125	—	2	1	no	—
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	2	no	—
170	C₃₁×#125	—	2	1	no	—
171	C₃₁×#125	D₄	1	1	yes	characteristic
172	C₃₁×#125	C₂³	1	2	yes	—
173	C₃₁×#125	C₂³	1	2	yes	—
174	C₃₁×#125	C₂³	1	2	yes	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	1	no	—
179	C₃₁×#124	D₄	1	1	yes	characteristic
180	C₃₁×#123	—	2	2	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×#123	—	2	2	no	—
188	C₃₁×#123	D₄	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	D₄	1	1	yes	characteristic
215	C₃₁×#121	C₂³	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	1	yes	characteristic
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	—	2	1	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	2	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	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	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₃₁×#117	—	2	1	no	—
245	C₃₁×#117	—	2	2	no	—
246	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	2	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	C₂³	1	2	yes	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	1	yes	characteristic
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
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	2	yes	—
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	1	yes	characteristic
267	C₃₁×#107	C₂³	1	1	yes	characteristic
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#106	C₂³	1	1	yes	characteristic
270	C₃₁×#106	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	2	yes	—
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	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
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	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	2	no	—
313	#41×C₃₁	—	2	4	no	—
314	#41×C₃₁	—	4	1	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	8	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	8	2	no	—
324	C₂×Q₈×C₃₁	C₂×D₄	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	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	—	2	2	no	—
341	C₂²×C₄×C₃₁	—	2	2	no	—
342	C₂²×C₄×C₃₁	—	2	1	no	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
355	SD₁₆×C₃₁	—	4	1	no	—
356	SD₁₆×C₃₁	—	4	2	no	—
357	SD₁₆×C₃₁	—	4	2	no	—
358	SD₁₆×C₃₁	—	4	1	no	—
359	D₈×C₃₁	—	2	2	no	—
360	D₈×C₃₁	—	2	2	no	—
361	M₁₆×C₃₁	—	4	2	no	—
362	C₂×C₈×C₃₁	—	4	2	no	—
363	C₂×C₈×C₃₁	—	4	2	no	—
364	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
368	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	1	no	—
372	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	2	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	2	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	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂×D₄	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	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
429	C₄²×C₃₁	—	2	1	no	—
430	C₄²×C₃₁	—	2	1	no	—
431	C₄²×C₃₁	—	2	1	no	—
432	C₄²×C₃₁	—	2	2	no	—
433	C₄²×C₃₁	—	2	2	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
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	#62218	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	—	2	1	no	—
445	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
446	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
447	Q₈×C₃₁	—	2	2	no	—
448	Q₈×C₃₁	—	2	2	no	—
449	Q₈×C₃₁	—	2	1	no	—
450	Q₈×C₃₁	—	2	2	no	—
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	4	2	no	—
453	Q₈×C₃₁	—	8	1	no	—
454	Q₈×C₃₁	—	8	1	no	—
455	Q₈×C₃₁	—	8	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	—	2	1	no	—
462	D₄×C₃₁	—	2	1	no	—
463	D₄×C₃₁	—	4	2	no	—
464	D₄×C₃₁	—	4	2	no	—
465	D₄×C₃₁	—	4	4	no	—
466	D₄×C₃₁	—	8	1	no	—
467	D₄×C₃₁	—	8	1	no	—
468	D₄×C₃₁	—	8	2	no	—
469	D₄×C₃₁	—	8	1	no	—
470	D₄×C₃₁	—	8	1	no	—
471	D₄×C₃₁	—	8	2	no	—
472	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	2	1	no	—
479	C₂×C₄×C₃₁	—	2	1	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	1	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	2	2	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	4	1	no	—
488	C₂×C₄×C₃₁	—	4	2	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	—	4	2	no	—
493	C₂×C₄×C₃₁	—	8	1	no	—
494	C₂×C₄×C₃₁	—	8	2	no	—
495	C₂×C₄×C₃₁	—	8	2	no	—
496	C₂×C₄×C₃₁	—	8	2	no	—
497	C₂×C₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	8	2	no	—
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	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
508	C₈×C₃₁	—	2	1	no	—
509	C₈×C₃₁	—	2	1	no	—
510	C₈×C₃₁	—	2	1	no	—
511	C₈×C₃₁	—	2	2	no	—
512	C₈×C₃₁	—	2	2	no	—
513	C₈×C₃₁	—	2	1	no	—
514	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#3515	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3359	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3357	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3348	C₂×C₃₁	1	2	yes	complemented
522	#3337	C₂×C₃₁	1	2	yes	complemented
523	#3335	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3307	C₂×C₃₁	1	2	yes	complemented
526	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3303	C₂×C₃₁	1	2	yes	complemented
528	#3260	C₂×C₃₁	1	2	yes	complemented
529	#3246	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3242	C₂×C₃₁	1	2	yes	complemented
531	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3119	C₂×C₃₁	1	2	yes	complemented
533	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3084	C₂×C₃₁	1	2	yes	complemented
535	#3076	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#2994	C₂×C₃₁	1	1	yes	characteristic, complemented
537	C₂²×C₃₁	—	2	1	no	—
538	C₂²×C₃₁	—	2	2	no	—
539	C₂²×C₃₁	—	2	1	no	—
540	C₂²×C₃₁	—	2	2	no	—
541	C₂²×C₃₁	—	2	2	no	—
542	C₂²×C₃₁	—	2	1	no	—
543	C₂²×C₃₁	—	2	2	no	—
544	C₂²×C₃₁	—	4	1	no	—
545	C₂²×C₃₁	—	4	1	no	—
546	C₂²×C₃₁	—	4	1	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	—	4	1	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
553	C₄×C₃₁	—	2	1	no	—
554	C₄×C₃₁	—	2	1	no	—
555	C₄×C₃₁	—	2	2	no	—
556	C₄×C₃₁	—	2	1	no	—
557	C₄×C₃₁	—	2	2	no	—
558	C₄×C₃₁	—	2	1	no	—
559	C₄×C₃₁	—	2	2	no	—
560	C₄×C₃₁	—	4	1	no	—
561	C₄×C₃₁	—	4	2	no	—
562	C₄×C₃₁	—	4	2	no	—
563	C₄×C₃₁	—	4	1	no	—
564	C₄×C₃₁	—	4	2	no	—
565	C₄×C₃₁	—	4	1	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	2	no	—
569	C₄×C₃₁	#577	1	2	yes	—
570	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
571	C₄×C₃₁	#585	1	1	yes	characteristic
572	#562	—	2	2	no	—
573	#557	C₂²×C₃₁	1	1	yes	characteristic
574	#555	C₂²×C₃₁	1	2	yes	—
575	#555	C₂²×C₃₁	1	1	yes	characteristic
576	#554	C₂²×C₃₁	1	1	yes	characteristic
577	#554	C₂²×C₃₁	1	1	yes	characteristic
578	#554	C₂²×C₃₁	1	1	yes	characteristic
579	#553	—	2	1	no	—
580	#553	C₂²×C₃₁	1	2	yes	—
581	#552	—	2	2	no	—
582	#552	—	2	1	no	—
583	#552	—	2	1	no	—
584	#552	C₂²×C₃₁	1	2	yes	—
585	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
586	#548	—	2	1	no	—
587	#547	C₂²×C₃₁	1	1	yes	characteristic
588	#547	C₂²×C₃₁	1	2	yes	—
589	#547	C₂²×C₃₁	1	1	yes	characteristic
590	#544	C₂²×C₃₁	1	2	yes	—
591	#542	—	2	2	no	—
592	#541	C₂²×C₃₁	1	2	yes	—
593	#540	C₂²×C₃₁	1	2	yes	—
594	#539	—	2	2	no	—
595	#537	—	2	1	no	—
596	#536	—	2	1	no	—
597	#533	C₂²×C₃₁	1	1	yes	characteristic
598	#533	C₂²×C₃₁	1	1	yes	characteristic
599	#532	C₂²×C₃₁	1	1	yes	characteristic
600	#529	—	2	1	no	—
601	#529	C₂²×C₃₁	1	1	yes	characteristic
602	C₂×#125	—	2	1	no	—
603	#520	C₂²×C₃₁	1	2	yes	—
604	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
605	#501	C₂²×C₃₁	1	2	yes	—
606	#500	C₂²×C₃₁	1	1	yes	characteristic
607	#499	C₂²×C₃₁	1	2	yes	—
608	#498	C₂²×C₃₁	1	1	yes	characteristic
609	#491	C₂²×C₃₁	1	2	yes	—
610	#487	C₂²×C₃₁	1	1	yes	characteristic
611	#487	C₂²×C₃₁	1	2	yes	—
612	#487	C₂²×C₃₁	1	1	yes	characteristic
613	#485	C₂²×C₃₁	1	2	yes	—
614	#485	C₂²×C₃₁	1	2	yes	—
615	#485	C₂²×C₃₁	1	2	yes	—
616	#485	C₂²×C₃₁	1	2	yes	—
617	#484	C₂²×C₃₁	1	2	yes	—
618	#483	C₂²×C₃₁	1	2	yes	—
619	#482	C₂²×C₃₁	1	1	yes	characteristic
620	#482	C₂²×C₃₁	1	1	yes	characteristic
621	#481	C₂²×C₃₁	1	2	yes	—
622	#480	C₂²×C₃₁	1	2	yes	—
623	#479	C₂²×C₃₁	1	2	yes	—
624	#479	C₂²×C₃₁	1	2	yes	—
625	#479	C₂²×C₃₁	1	2	yes	—
626	#479	C₂²×C₃₁	1	2	yes	—
627	#478	C₂²×C₃₁	1	2	yes	—
628	#478	C₂²×C₃₁	1	2	yes	—
629	#478	C₂²×C₃₁	1	2	yes	—
630	#478	C₂²×C₃₁	1	2	yes	—
631	#477	C₂²×C₃₁	1	1	yes	characteristic
632	#477	C₂²×C₃₁	1	1	yes	characteristic
633	#476	C₂²×C₃₁	1	1	yes	characteristic
634	#476	C₂²×C₃₁	1	1	yes	characteristic
635	#476	C₂²×C₃₁	1	1	yes	characteristic
636	#476	C₂²×C₃₁	1	2	yes	—
637	#476	C₂²×C₃₁	1	1	yes	characteristic
638	#475	C₂²×C₃₁	1	1	yes	characteristic
639	#475	C₂²×C₃₁	1	2	yes	—
640	#475	C₂²×C₃₁	1	2	yes	—
641	#474	C₂²×C₃₁	1	1	yes	characteristic
642	#468	C₂²×C₃₁	1	2	yes	—
643	#468	C₂²×C₃₁	1	2	yes	—
644	#465	C₂²×C₃₁	1	2	yes	—
645	#465	C₂²×C₃₁	1	2	yes	—
646	#465	C₂²×C₃₁	1	2	yes	—
647	#465	C₂²×C₃₁	1	2	yes	—
648	#461	C₂²×C₃₁	1	1	yes	characteristic
649	#461	C₂²×C₃₁	1	1	yes	characteristic
650	#461	C₂²×C₃₁	1	2	yes	—
651	#461	C₂²×C₃₁	1	2	yes	—
652	#460	C₂²×C₃₁	1	1	yes	characteristic
653	#460	C₂²×C₃₁	1	2	yes	—
654	#459	C₂²×C₃₁	1	1	yes	characteristic
655	#449	C₂²×C₃₁	1	2	yes	—
656	#449	C₂²×C₃₁	1	1	yes	characteristic
657	#449	C₂²×C₃₁	1	1	yes	characteristic
658	#449	C₂²×C₃₁	1	2	yes	—
659	#446	C₂²×C₃₁	1	1	yes	characteristic
660	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
661	#442	C₂²×C₃₁	1	2	yes	—
662	#440	C₂²×C₃₁	1	2	yes	—
663	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
664	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
665	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
666	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
667	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
668	C₄×D₈	C₂²×C₃₁	1	2	yes	—
669	#436	C₂²×C₃₁	1	1	yes	characteristic
670	#435	C₂²×C₃₁	1	2	yes	—
671	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
672	C₈×D₄	C₂²×C₃₁	1	2	yes	—
673	#433	C₂²×C₃₁	1	2	yes	—
674	#431	C₂²×C₃₁	1	1	yes	characteristic
675	#428	C₂²×C₃₁	1	2	yes	—
676	#427	C₂²×C₃₁	1	2	yes	—
677	C₂×#106	C₂²×C₃₁	1	2	yes	—
678	#424	C₂²×C₃₁	1	2	yes	—
679	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
680	#417	C₂²×C₃₁	1	2	yes	—
681	#416	C₂²×C₃₁	1	2	yes	—
682	#416	C₂²×C₃₁	1	2	yes	—
683	C₂×C₃₁	—	4	1	no	—
684	C₂×C₃₁	—	4	2	no	—
685	C₂×C₃₁	—	4	2	no	—
686	C₂×C₃₁	—	8	1	no	—
687	C₂×C₃₁	—	8	1	no	—
688	C₂×C₃₁	#3489	1	1	yes	characteristic
689	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
690	C₂×C₃₁	#3584	1	1	yes	characteristic
691	C₂×#41	—	2	1	no	—
692	C₂×#41	—	2	1	no	—
693	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×#41	C₂³×C₃₁	1	2	yes	—
695	C₂²×Q₈	—	2	1	no	—
696	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
698	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
699	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
700	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
703	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
704	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
705	C₄⋊Q₈	—	2	2	no	—
706	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
708	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
713	#127	C₂³×C₃₁	1	1	yes	characteristic
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	D₄×C₃₁	1	2	yes	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	1	no	—
722	#125	—	2	1	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	1	no	—
727	#125	D₄×C₃₁	1	1	yes	characteristic
728	#125	C₂³×C₃₁	1	2	yes	—
729	#125	C₂³×C₃₁	1	2	yes	—
730	#125	C₂³×C₃₁	1	2	yes	—
731	#124	—	2	2	no	—
732	#124	—	2	2	no	—
733	#124	—	2	2	no	—
734	#124	—	2	1	no	—
735	#124	D₄×C₃₁	1	1	yes	characteristic
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	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	D₄×C₃₁	1	2	yes	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
762	#121	—	2	1	no	—
763	#121	—	2	1	no	—
764	#121	—	2	2	no	—
765	#121	—	2	2	no	—
766	#121	—	2	2	no	—
767	#121	—	2	1	no	—
768	#121	—	2	2	no	—
769	#121	—	2	2	no	—
770	#121	D₄×C₃₁	1	1	yes	characteristic
771	#121	C₂³×C₃₁	1	1	yes	characteristic
772	#121	C₂³×C₃₁	1	1	yes	characteristic
773	#121	C₂³×C₃₁	1	2	yes	—
774	#121	C₂³×C₃₁	1	2	yes	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
782	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
783	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
793	C₄×D₄	C₂³×C₃₁	1	2	yes	—
794	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₃₁	1	2	yes	—
797	C₄×D₄	C₂³×C₃₁	1	2	yes	—
798	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₃₁	1	2	yes	—
800	#117	—	2	1	no	—
801	#117	—	2	2	no	—
802	#117	—	2	1	no	—
803	#117	—	2	2	no	—
804	#117	—	2	2	no	—
805	#117	—	2	1	no	—
806	#117	C₂³×C₃₁	1	1	yes	characteristic
807	#117	C₂³×C₃₁	1	2	yes	—
808	#117	C₂³×C₃₁	1	2	yes	—
809	#117	C₂³×C₃₁	1	2	yes	—
810	C₂×C₄⋊C₄	—	2	2	no	—
811	C₂×C₄⋊C₄	—	2	1	no	—
812	C₂×C₄⋊C₄	—	2	2	no	—
813	C₂×C₄⋊C₄	—	2	1	no	—
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
816	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
817	C₂×C₄²	—	2	1	no	—
818	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
819	#107	C₂³×C₃₁	1	2	yes	—
820	#107	C₂³×C₃₁	1	2	yes	—
821	#107	C₂³×C₃₁	1	2	yes	—
822	#107	C₂³×C₃₁	1	1	yes	characteristic
823	#107	C₂³×C₃₁	1	1	yes	characteristic
824	#107	C₂³×C₃₁	1	2	yes	—
825	#106	C₂³×C₃₁	1	1	yes	characteristic
826	#106	C₂³×C₃₁	1	2	yes	—
827	#106	C₂³×C₃₁	1	2	yes	—
828	#106	C₂³×C₃₁	1	2	yes	—
829	#106	C₂³×C₃₁	1	2	yes	—
830	#106	C₂³×C₃₁	1	1	yes	characteristic
831	#106	C₂³×C₃₁	1	2	yes	—
832	#106	C₂³×C₃₁	1	2	yes	—
833	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
834	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
835	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
836	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
839	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
840	#103	C₂³×C₃₁	1	2	yes	—
841	#103	C₂³×C₃₁	1	2	yes	—
842	#103	C₂³×C₃₁	1	2	yes	—
843	#103	C₂³×C₃₁	1	2	yes	—
844	#103	C₂³×C₃₁	1	2	yes	—
845	#103	C₂³×C₃₁	1	2	yes	—
846	#103	C₂³×C₃₁	1	1	yes	characteristic
847	#103	C₂³×C₃₁	1	1	yes	characteristic
848	#103	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	2	yes	—
850	#102	C₂³×C₃₁	1	1	yes	characteristic
851	#102	C₂³×C₃₁	1	2	yes	—
852	#102	C₂³×C₃₁	1	2	yes	—
853	#102	C₂³×C₃₁	1	1	yes	characteristic
854	#102	C₂³×C₃₁	1	2	yes	—
855	#102	C₂³×C₃₁	1	1	yes	characteristic
856	#102	C₂³×C₃₁	1	1	yes	characteristic
857	#102	C₂³×C₃₁	1	1	yes	characteristic
858	#102	C₂³×C₃₁	1	1	yes	characteristic
859	#102	C₂³×C₃₁	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
864	#97	C₂³×C₃₁	1	2	yes	—
865	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₃₁	1	2	yes	—
868	C₃₁	#62218	1	1	yes	characteristic, direct product factor, Sylow
869	#41	—	2	2	no	—
870	#41	—	2	4	no	—
871	#41	—	4	1	no	—
872	#41	—	4	2	no	—
873	#41	—	8	2	no	—
874	#41	—	8	2	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	2	1	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	8	2	no	—
881	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
882	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
883	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
893	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
894	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
896	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
909	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
912	SD₁₆	—	4	1	no	—
913	SD₁₆	—	4	2	no	—
914	SD₁₆	—	4	2	no	—
915	SD₁₆	—	4	1	no	—
916	D₈	—	2	2	no	—
917	D₈	—	2	2	no	—
918	M₁₆	—	4	2	no	—
919	C₂×C₈	—	4	2	no	—
920	C₂×C₈	—	4	2	no	—
921	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
924	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
925	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
926	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
952	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
953	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
954	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
955	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
956	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
957	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
959	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
960	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
961	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
962	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
982	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
983	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
984	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
985	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
994	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
995	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₄²	C₂⁴×C₃₁	1	2	yes	—
997	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
998	C₂³	—	2	1	no	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	1	no	—
1001	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1002	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1003	Q₈	—	2	2	no	—
1004	Q₈	—	2	2	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	1	no	—
1008	Q₈	—	4	2	no	—
1009	Q₈	—	8	1	no	—
1010	Q₈	—	8	1	no	—
1011	Q₈	—	8	2	no	—
1012	Q₈	—	8	1	no	—
1013	D₄	—	2	2	no	—
1014	D₄	—	2	1	no	—
1015	D₄	—	2	1	no	—
1016	D₄	—	2	1	no	—
1017	D₄	—	2	1	no	—
1018	D₄	—	2	1	no	—
1019	D₄	—	4	2	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	4	no	—
1022	D₄	—	8	1	no	—
1023	D₄	—	8	1	no	—
1024	D₄	—	8	2	no	—
1025	D₄	—	8	1	no	—
1026	D₄	—	8	1	no	—
1027	D₄	—	8	2	no	—
1028	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	4	1	no	—
1044	C₂×C₄	—	4	2	no	—
1045	C₂×C₄	—	4	4	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	8	1	no	—
1050	C₂×C₄	—	8	2	no	—
1051	C₂×C₄	—	8	2	no	—
1052	C₂×C₄	—	8	2	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1056	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1057	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1059	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1061	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1062	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1063	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	2	1	no	—
1067	C₈	—	2	2	no	—
1068	C₈	—	2	2	no	—
1069	C₈	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	2	2	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1086	C₄	—	2	1	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	2	no	—
1102	C₄	C₃₁×#577	1	2	yes	—
1103	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1104	C₄	C₃₁×#585	1	1	yes	characteristic
1105	C₂	—	4	1	no	—
1106	C₂	—	4	2	no	—
1107	C₂	—	4	2	no	—
1108	C₂	—	8	1	no	—
1109	C₂	—	8	1	no	—
1110	C₂	C₃₁×#3489	1	1	yes	characteristic
1111	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1112	C₂	C₃₁×#3584	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×#3547	C₂	semidirect
2. C₃₁×#3515	C₂	semidirect
3. C₃₁×#3384	C₂	semidirect
4. C₃₁×#3380	C₂	semidirect
5. C₃₁×#3372	C₂	semidirect
6. C₃₁×#3359	C₂	semidirect
7. C₃₁×#3357	C₂	semidirect
8. C₃₁×#3348	C₂	semidirect
9. C₃₁×#3337	C₂	semidirect
10. C₃₁×#3335	C₂	semidirect
11. C₃₁×#3330	C₂	semidirect
12. C₃₁×#3307	C₂	semidirect
13. C₃₁×#3303	C₂	semidirect
14. C₃₁×#3303	C₂	semidirect
15. C₃₁×#3260	C₂	semidirect
16. C₃₁×#3246	C₂	semidirect
17. C₃₁×#3242	C₂	semidirect
18. C₃₁×#3231	C₂	semidirect
19. C₃₁×#3119	C₂	semidirect
20. C₃₁×#3106	C₂	semidirect
21. C₃₁×#3084	C₂	semidirect
22. C₃₁×#3076	C₂	semidirect
23. C₃₁×#2994	C₂	semidirect
441. #62218	C₃₁	direct (N × H)
514. #3547	C₂×C₃₁	semidirect
515. #3515	C₂×C₃₁	semidirect
516. #3384	C₂×C₃₁	semidirect
517. #3380	C₂×C₃₁	semidirect
518. #3372	C₂×C₃₁	semidirect
519. #3359	C₂×C₃₁	semidirect
520. #3357	C₂×C₃₁	semidirect
521. #3348	C₂×C₃₁	semidirect
522. #3337	C₂×C₃₁	semidirect
523. #3335	C₂×C₃₁	semidirect
524. #3330	C₂×C₃₁	semidirect
525. #3307	C₂×C₃₁	semidirect
526. #3303	C₂×C₃₁	semidirect
527. #3303	C₂×C₃₁	semidirect
528. #3260	C₂×C₃₁	semidirect
529. #3246	C₂×C₃₁	semidirect
530. #3242	C₂×C₃₁	semidirect
531. #3231	C₂×C₃₁	semidirect
532. #3119	C₂×C₃₁	semidirect
533. #3106	C₂×C₃₁	semidirect
534. #3084	C₂×C₃₁	semidirect
535. #3076	C₂×C₃₁	semidirect
536. #2994	C₂×C₃₁	semidirect
868. C₃₁	#62218	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×#3547	2
C₃₁×#3515	2
C₃₁×#3384	2
C₃₁×#3380	2
C₃₁×#3372	2
C₃₁×#3359	2
C₃₁×#3357	2
C₃₁×#3348	2
C₃₁×#3337	2
C₃₁×#3335	2
C₃₁×#3330	2
C₃₁×#3307	2
C₃₁×#3303	2
C₃₁×#3260	2
C₃₁×#3246	2
C₃₁×#3242	2
C₃₁×#3231	2
C₃₁×#3119	2
C₃₁×#3106	2
C₃₁×#3084	2
C₃₁×#3076	2
C₃₁×#2994	2
#62218	31

Subgroups — C31×#62218 #21518977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62218 #21518977