Subgroups — C₃₁×#62568 #21519327

Order 7936.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3558	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3327	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3324	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3313	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	2	no	—
21	C₃₁×#562	—	2	1	no	—
22	C₃₁×H(3,𝔽₄)	—	2	1	no	—
23	C₃₁×#559	C₂²	1	2	yes	—
24	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#557	—	2	1	no	—
26	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#556	—	2	1	no	—
28	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#556	C₂²	1	2	yes	complemented
30	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#552	C₂²	1	2	yes	complemented
32	C₃₁×#548	C₂²	1	2	yes	—
33	C₃₁×#546	—	2	2	no	—
34	C₃₁×#546	C₂²	1	2	yes	—
35	D₄²×C₃₁	C₂²	1	2	yes	—
36	C₃₁×#544	C₂²	1	2	yes	complemented
37	C₃₁×#542	—	2	1	no	—
38	C₃₁×#542	C₂²	1	2	yes	—
39	C₃₁×#541	—	2	2	no	—
40	C₃₁×#541	—	2	1	no	—
41	C₃₁×#541	C₂²	1	2	yes	complemented
42	C₃₁×#538	—	2	2	no	—
43	C₃₁×#538	—	2	1	no	—
44	C₃₁×#535	C₂²	1	2	yes	—
45	C₃₁×#534	—	2	1	no	—
46	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#532	C₂²	1	1	yes	characteristic
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#497	C₂²	1	2	yes	complemented
54	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#490	C₂²	1	2	yes	—
56	C₃₁×#490	C₂²	1	2	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	complemented
58	C₃₁×#489	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	complemented
60	C₃₁×#489	C₂²	1	2	yes	complemented
61	C₃₁×#488	C₂²	1	2	yes	complemented
62	C₃₁×#488	C₂²	1	2	yes	complemented
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#486	C₂²	1	2	yes	—
66	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#484	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#477	C₂²	1	2	yes	complemented
76	C₃₁×#476	C₂²	1	2	yes	complemented
77	C₃₁×#474	C₂²	1	2	yes	complemented
78	C₃₁×#474	C₂²	1	2	yes	complemented
79	C₃₁×#470	C₂²	1	2	yes	complemented
80	C₃₁×#468	C₂²	1	2	yes	—
81	C₃₁×#468	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#467	C₂²	1	2	yes	complemented
84	C₃₁×#465	C₂²	1	2	yes	—
85	C₃₁×#464	C₂²	1	2	yes	complemented
86	C₃₁×#464	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#464	C₂²	1	2	yes	complemented
89	C₃₁×#460	C₂²	1	2	yes	—
90	C₃₁×#460	C₂²	1	2	yes	—
91	C₃₁×#452	C₂²	1	2	yes	complemented
92	C₃₁×#452	C₂²	1	2	yes	complemented
93	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#450	C₂²	1	1	yes	characteristic
96	C₃₁×#450	C₂²	1	1	yes	characteristic
97	C₃₁×#450	C₂²	1	2	yes	complemented
98	C₃₁×#450	C₂²	1	2	yes	complemented
99	C₃₁×#446	C₂²	1	2	yes	complemented
100	C₃₁×#441	C₂²	1	2	yes	complemented
101	C₃₁×#440	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
106	C₃₁×#436	C₂²	1	2	yes	complemented
107	C₃₁×#435	C₂²	1	2	yes	complemented
108	C₃₁×#435	C₂²	1	2	yes	complemented
109	C₃₁×#433	C₂²	1	2	yes	complemented
110	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#419	C₂²	1	2	yes	complemented
112	C₃₁×#418	C₂²	1	2	yes	—
113	C₃₁×#418	C₂²	1	2	yes	complemented
114	C₃₁×#417	C₂²	1	2	yes	complemented
115	C₃₁×#416	C₂²	1	2	yes	complemented
116	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
117	C₃₁×#405	C₂²	1	2	yes	complemented
118	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₃₁	—	2	2	no	—
123	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
124	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
134	C₃₁×C₄⋊Q₈	—	2	1	no	—
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	—	2	1	no	—
137	C₃₁×C₄⋊Q₈	—	2	2	no	—
138	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₃₁×#127	C₂³	1	2	yes	—
145	C₃₁×#127	C₂³	1	1	yes	characteristic
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#126	—	2	2	no	—
148	C₃₁×#126	—	2	2	no	—
149	C₃₁×#126	—	2	2	no	—
150	C₃₁×#126	—	2	2	no	—
151	C₃₁×#126	—	2	2	no	—
152	C₃₁×#126	—	2	2	no	—
153	C₃₁×#126	D₄	1	2	yes	—
154	C₃₁×#125	—	2	2	no	—
155	C₃₁×#125	—	2	2	no	—
156	C₃₁×#125	—	2	2	no	—
157	C₃₁×#125	—	2	1	no	—
158	C₃₁×#125	—	2	2	no	—
159	C₃₁×#125	—	2	2	no	—
160	C₃₁×#125	—	2	1	no	—
161	C₃₁×#125	D₄	1	1	yes	characteristic
162	C₃₁×#125	C₂³	1	2	yes	—
163	C₃₁×#125	C₂³	1	2	yes	—
164	C₃₁×#124	—	2	2	no	—
165	C₃₁×#124	—	2	1	no	—
166	C₃₁×#124	—	2	2	no	—
167	C₃₁×#124	—	2	2	no	—
168	C₃₁×#124	—	2	2	no	—
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	—	2	1	no	—
171	C₃₁×#124	—	2	1	no	—
172	C₃₁×#124	D₄	1	1	yes	characteristic
173	C₃₁×#124	C₂³	1	2	yes	—
174	C₃₁×#124	C₂³	1	2	yes	—
175	C₃₁×#124	C₂³	1	2	yes	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	D₄	1	2	yes	—
182	C₃₁×C₂²⋊Q₈	—	2	1	no	—
183	C₃₁×C₂²⋊Q₈	—	2	1	no	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
191	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
192	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
193	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	1	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	D₄	1	1	yes	characteristic
203	C₃₁×#121	C₂³	1	2	yes	—
204	C₃₁×#121	C₂³	1	2	yes	—
205	C₃₁×#120	—	2	2	no	—
206	C₃₁×#120	—	2	2	no	—
207	C₃₁×#120	—	2	2	no	—
208	C₃₁×#120	—	2	2	no	—
209	C₃₁×#120	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	1	no	—
211	C₄×Q₈×C₃₁	—	2	2	no	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	C₂³	1	2	yes	—
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₃₁	C₂³	1	2	yes	—
231	C₃₁×#117	—	2	1	no	—
232	C₃₁×#117	—	2	2	no	—
233	C₃₁×#117	C₂³	1	2	yes	—
234	C₃₁×#117	C₂³	1	2	yes	—
235	C₃₁×#117	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
240	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#107	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
258	C₃₁×#102	C₂³	1	2	yes	—
259	C₃₁×#102	C₂³	1	2	yes	—
260	C₃₁×#102	C₂³	1	2	yes	—
261	C₃₁×#102	C₂³	1	2	yes	—
262	C₃₁×#102	C₂³	1	2	yes	—
263	C₃₁×#102	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₃₁×#97	C₂³	1	2	yes	—
275	C₃₁×#97	C₂³	1	2	yes	—
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	C₂⁴×C₃₁	—	2	2	no	—
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	4	2	no	—
284	#41×C₃₁	—	8	2	no	—
285	C₂×Q₈×C₃₁	—	2	1	no	—
286	C₂×Q₈×C₃₁	—	2	1	no	—
287	C₂×Q₈×C₃₁	—	2	1	no	—
288	C₂×Q₈×C₃₁	—	2	2	no	—
289	C₂×Q₈×C₃₁	—	2	1	no	—
290	C₂×Q₈×C₃₁	—	2	1	no	—
291	C₂×Q₈×C₃₁	—	4	2	no	—
292	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂×D₄×C₃₁	—	2	2	no	—
297	C₂×D₄×C₃₁	—	2	2	no	—
298	C₂×D₄×C₃₁	—	2	2	no	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	—	2	1	no	—
301	C₂×D₄×C₃₁	—	2	1	no	—
302	C₂×D₄×C₃₁	—	2	1	no	—
303	C₂×D₄×C₃₁	—	2	2	no	—
304	C₂×D₄×C₃₁	—	2	2	no	—
305	C₂×D₄×C₃₁	—	4	2	no	—
306	C₂×D₄×C₃₁	—	4	2	no	—
307	C₂×D₄×C₃₁	—	4	2	no	—
308	C₂×D₄×C₃₁	—	8	4	no	—
309	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
310	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
311	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
312	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₃₁	—	2	1	no	—
314	C₂²×C₄×C₃₁	—	2	2	no	—
315	C₂²×C₄×C₃₁	—	2	2	no	—
316	C₂²×C₄×C₃₁	—	2	2	no	—
317	C₂²×C₄×C₃₁	—	2	2	no	—
318	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
322	Q₁₆×C₃₁	—	4	2	no	—
323	Q₁₆×C₃₁	—	4	2	no	—
324	SD₁₆×C₃₁	—	4	2	no	—
325	SD₁₆×C₃₁	—	4	2	no	—
326	SD₁₆×C₃₁	—	4	2	no	—
327	SD₁₆×C₃₁	—	4	2	no	—
328	M₁₆×C₃₁	—	4	2	no	—
329	M₁₆×C₃₁	—	4	2	no	—
330	C₂×C₈×C₃₁	—	4	2	no	—
331	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
333	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
334	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₃₁	—	2	2	no	—
336	C₄⋊C₄×C₃₁	—	2	1	no	—
337	C₄⋊C₄×C₃₁	—	2	1	no	—
338	C₄⋊C₄×C₃₁	—	2	2	no	—
339	C₄⋊C₄×C₃₁	—	2	1	no	—
340	C₄⋊C₄×C₃₁	—	2	1	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	1	no	—
343	C₄⋊C₄×C₃₁	—	2	1	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	2	no	—
347	C₄⋊C₄×C₃₁	—	2	2	no	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	1	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	1	no	—
354	C₄⋊C₄×C₃₁	—	2	1	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	1	no	—
370	C₂²⋊C₄×C₃₁	—	2	1	no	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	—	2	2	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	—	2	2	no	—
378	C₂²⋊C₄×C₃₁	—	2	2	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	2	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
390	C₄²×C₃₁	—	2	2	no	—
391	C₄²×C₃₁	—	2	1	no	—
392	C₄²×C₃₁	—	2	1	no	—
393	C₄²×C₃₁	—	2	2	no	—
394	C₄²×C₃₁	—	2	2	no	—
395	C₄²×C₃₁	—	2	2	no	—
396	C₄²×C₃₁	—	2	2	no	—
397	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄²×C₃₁	C₂⁴	1	2	yes	—
401	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
402	#62568	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂³×C₃₁	—	2	2	no	—
404	C₂³×C₃₁	—	2	2	no	—
405	C₂³×C₃₁	—	4	2	no	—
406	C₂³×C₃₁	—	8	1	no	—
407	C₂³×C₃₁	—	8	2	no	—
408	C₂³×C₃₁	—	8	2	no	—
409	C₂³×C₃₁	—	8	1	no	—
410	C₂³×C₃₁	—	8	2	no	—
411	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
412	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
413	Q₈×C₃₁	—	2	2	no	—
414	Q₈×C₃₁	—	2	2	no	—
415	Q₈×C₃₁	—	2	2	no	—
416	Q₈×C₃₁	—	2	2	no	—
417	Q₈×C₃₁	—	4	1	no	—
418	Q₈×C₃₁	—	4	2	no	—
419	Q₈×C₃₁	—	8	1	no	—
420	Q₈×C₃₁	—	8	1	no	—
421	Q₈×C₃₁	—	8	2	no	—
422	Q₈×C₃₁	—	8	1	no	—
423	Q₈×C₃₁	—	8	1	no	—
424	D₄×C₃₁	—	2	2	no	—
425	D₄×C₃₁	—	2	2	no	—
426	D₄×C₃₁	—	2	2	no	—
427	D₄×C₃₁	—	2	2	no	—
428	D₄×C₃₁	—	4	2	no	—
429	D₄×C₃₁	—	4	1	no	—
430	D₄×C₃₁	—	4	4	no	—
431	D₄×C₃₁	—	8	1	no	—
432	D₄×C₃₁	—	8	2	no	—
433	D₄×C₃₁	—	8	2	no	—
434	D₄×C₃₁	—	8	1	no	—
435	D₄×C₃₁	—	8	2	no	—
436	D₄×C₃₁	—	8	1	no	—
437	D₄×C₃₁	—	8	2	no	—
438	D₄×C₃₁	—	8	2	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	2	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	2	1	no	—
443	C₂×C₄×C₃₁	—	2	1	no	—
444	C₂×C₄×C₃₁	—	2	2	no	—
445	C₂×C₄×C₃₁	—	2	1	no	—
446	C₂×C₄×C₃₁	—	2	2	no	—
447	C₂×C₄×C₃₁	—	2	2	no	—
448	C₂×C₄×C₃₁	—	2	2	no	—
449	C₂×C₄×C₃₁	—	2	1	no	—
450	C₂×C₄×C₃₁	—	4	1	no	—
451	C₂×C₄×C₃₁	—	4	1	no	—
452	C₂×C₄×C₃₁	—	8	2	no	—
453	C₂×C₄×C₃₁	—	8	2	no	—
454	C₂×C₄×C₃₁	—	8	2	no	—
455	C₂×C₄×C₃₁	—	8	2	no	—
456	C₂×C₄×C₃₁	—	8	1	no	—
457	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
466	C₈×C₃₁	—	2	2	no	—
467	C₈×C₃₁	—	2	2	no	—
468	C₈×C₃₁	—	2	2	no	—
469	C₈×C₃₁	—	2	2	no	—
470	#3558	C₂×C₃₁	1	1	yes	characteristic
471	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
472	#3375	C₂×C₃₁	1	2	yes	complemented
473	#3371	C₂×C₃₁	1	2	yes	complemented
474	#3327	C₂×C₃₁	1	2	yes	complemented
475	#3324	C₂×C₃₁	1	2	yes	complemented
476	#3314	C₂×C₃₁	1	2	yes	complemented
477	#3313	C₂×C₃₁	1	2	yes	complemented
478	#3311	C₂×C₃₁	1	2	yes	complemented
479	#3310	C₂×C₃₁	1	2	yes	complemented
480	#3243	C₂×C₃₁	1	2	yes	complemented
481	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
482	#3222	C₂×C₃₁	1	2	yes	complemented
483	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
484	#3182	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#3178	C₂×C₃₁	1	2	yes	complemented
486	#3140	C₂×C₃₁	1	1	yes	characteristic, complemented
487	#3136	C₂×C₃₁	1	2	yes	complemented
488	#2967	C₂×C₃₁	1	1	yes	characteristic, complemented
489	C₂²×C₃₁	—	2	1	no	—
490	C₂²×C₃₁	—	2	2	no	—
491	C₂²×C₃₁	—	2	1	no	—
492	C₂²×C₃₁	—	2	2	no	—
493	C₂²×C₃₁	—	2	1	no	—
494	C₂²×C₃₁	—	2	2	no	—
495	C₂²×C₃₁	—	4	2	no	—
496	C₂²×C₃₁	—	4	2	no	—
497	C₂²×C₃₁	—	4	2	no	—
498	C₂²×C₃₁	—	4	2	no	—
499	C₂²×C₃₁	—	4	2	no	—
500	C₂²×C₃₁	—	4	2	no	—
501	C₂²×C₃₁	—	16	2	no	—
502	C₂²×C₃₁	—	16	4	no	—
503	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₃₁	—	2	1	no	—
505	C₄×C₃₁	—	2	1	no	—
506	C₄×C₃₁	—	2	2	no	—
507	C₄×C₃₁	—	2	1	no	—
508	C₄×C₃₁	—	2	1	no	—
509	C₄×C₃₁	—	2	2	no	—
510	C₄×C₃₁	—	2	2	no	—
511	C₄×C₃₁	—	2	1	no	—
512	C₄×C₃₁	—	4	2	no	—
513	C₄×C₃₁	—	4	1	no	—
514	C₄×C₃₁	—	4	2	no	—
515	C₄×C₃₁	—	4	1	no	—
516	C₄×C₃₁	—	4	2	no	—
517	C₄×C₃₁	—	4	2	no	—
518	C₄×C₃₁	—	4	1	no	—
519	C₄×C₃₁	—	4	1	no	—
520	C₄×C₃₁	#585	1	2	yes	—
521	#563	—	2	2	no	—
522	#562	—	2	1	no	—
523	H(3,𝔽₄)	—	2	1	no	—
524	#559	C₂²×C₃₁	1	2	yes	—
525	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
526	#557	—	2	1	no	—
527	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
528	#556	—	2	1	no	—
529	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
530	#556	C₂²×C₃₁	1	2	yes	complemented
531	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	#552	C₂²×C₃₁	1	2	yes	complemented
533	#548	C₂²×C₃₁	1	2	yes	—
534	#546	—	2	2	no	—
535	#546	C₂²×C₃₁	1	2	yes	—
536	D₄²	C₂²×C₃₁	1	2	yes	—
537	#544	C₂²×C₃₁	1	2	yes	complemented
538	#542	—	2	1	no	—
539	#542	C₂²×C₃₁	1	2	yes	—
540	#541	—	2	2	no	—
541	#541	—	2	1	no	—
542	#541	C₂²×C₃₁	1	2	yes	complemented
543	#538	—	2	2	no	—
544	#538	—	2	1	no	—
545	#535	C₂²×C₃₁	1	2	yes	—
546	#534	—	2	1	no	—
547	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
549	#532	C₂²×C₃₁	1	1	yes	characteristic
550	#529	C₂²×C₃₁	1	1	yes	characteristic
551	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
552	#501	C₂²×C₃₁	1	2	yes	complemented
553	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	#497	C₂²×C₃₁	1	2	yes	complemented
555	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
556	#490	C₂²×C₃₁	1	2	yes	—
557	#490	C₂²×C₃₁	1	2	yes	complemented
558	#489	C₂²×C₃₁	1	2	yes	complemented
559	#489	C₂²×C₃₁	1	2	yes	complemented
560	#489	C₂²×C₃₁	1	2	yes	complemented
561	#489	C₂²×C₃₁	1	2	yes	complemented
562	#488	C₂²×C₃₁	1	2	yes	complemented
563	#488	C₂²×C₃₁	1	2	yes	complemented
564	#488	C₂²×C₃₁	1	2	yes	complemented
565	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
566	#486	C₂²×C₃₁	1	2	yes	—
567	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
568	#485	C₂²×C₃₁	1	2	yes	complemented
569	#484	C₂²×C₃₁	1	2	yes	complemented
570	#482	C₂²×C₃₁	1	2	yes	—
571	#482	C₂²×C₃₁	1	2	yes	complemented
572	#482	C₂²×C₃₁	1	2	yes	complemented
573	#480	C₂²×C₃₁	1	2	yes	—
574	#479	C₂²×C₃₁	1	2	yes	complemented
575	#478	C₂²×C₃₁	1	2	yes	complemented
576	#477	C₂²×C₃₁	1	2	yes	complemented
577	#476	C₂²×C₃₁	1	2	yes	complemented
578	#474	C₂²×C₃₁	1	2	yes	complemented
579	#474	C₂²×C₃₁	1	2	yes	complemented
580	#470	C₂²×C₃₁	1	2	yes	complemented
581	#468	C₂²×C₃₁	1	2	yes	—
582	#468	C₂²×C₃₁	1	2	yes	complemented
583	#468	C₂²×C₃₁	1	2	yes	complemented
584	#467	C₂²×C₃₁	1	2	yes	complemented
585	#465	C₂²×C₃₁	1	2	yes	—
586	#464	C₂²×C₃₁	1	2	yes	complemented
587	#464	C₂²×C₃₁	1	2	yes	complemented
588	#464	C₂²×C₃₁	1	2	yes	complemented
589	#464	C₂²×C₃₁	1	2	yes	complemented
590	#460	C₂²×C₃₁	1	2	yes	—
591	#460	C₂²×C₃₁	1	2	yes	—
592	#452	C₂²×C₃₁	1	2	yes	complemented
593	#452	C₂²×C₃₁	1	2	yes	complemented
594	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
595	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
596	#450	C₂²×C₃₁	1	1	yes	characteristic
597	#450	C₂²×C₃₁	1	1	yes	characteristic
598	#450	C₂²×C₃₁	1	2	yes	complemented
599	#450	C₂²×C₃₁	1	2	yes	complemented
600	#446	C₂²×C₃₁	1	2	yes	complemented
601	#441	C₂²×C₃₁	1	2	yes	complemented
602	#440	C₂²×C₃₁	1	2	yes	complemented
603	#440	C₂²×C₃₁	1	2	yes	complemented
604	#440	C₂²×C₃₁	1	2	yes	complemented
605	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
606	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
607	#436	C₂²×C₃₁	1	2	yes	complemented
608	#435	C₂²×C₃₁	1	2	yes	complemented
609	#435	C₂²×C₃₁	1	2	yes	complemented
610	#433	C₂²×C₃₁	1	2	yes	complemented
611	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#419	C₂²×C₃₁	1	2	yes	complemented
613	#418	C₂²×C₃₁	1	2	yes	—
614	#418	C₂²×C₃₁	1	2	yes	complemented
615	#417	C₂²×C₃₁	1	2	yes	complemented
616	#416	C₂²×C₃₁	1	2	yes	complemented
617	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
618	#405	C₂²×C₃₁	1	2	yes	complemented
619	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	C₂×C₃₁	—	4	1	no	—
621	C₂×C₃₁	—	4	2	no	—
622	C₂×C₃₁	—	8	2	no	—
623	C₂×C₃₁	—	8	2	no	—
624	C₂×C₃₁	#3500	1	1	yes	characteristic
625	C₂×C₃₁	#3585	1	1	yes	characteristic
626	C₂×C₃₁	#3586	1	1	yes	characteristic
627	C₂×#41	—	2	1	no	—
628	C₂×#41	C₂³×C₃₁	1	2	yes	—
629	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
630	C₂²×D₄	—	2	2	no	—
631	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
632	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
633	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
634	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
635	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
636	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
637	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
638	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
639	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
640	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
641	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
642	C₄⋊Q₈	—	2	1	no	—
643	C₄⋊Q₈	—	2	2	no	—
644	C₄⋊Q₈	—	2	1	no	—
645	C₄⋊Q₈	—	2	2	no	—
646	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
647	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
648	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
649	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
651	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
652	#127	C₂³×C₃₁	1	1	yes	characteristic
653	#127	C₂³×C₃₁	1	2	yes	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#126	—	2	2	no	—
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	D₄×C₃₁	1	2	yes	—
662	#125	—	2	2	no	—
663	#125	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	1	no	—
666	#125	—	2	2	no	—
667	#125	—	2	2	no	—
668	#125	—	2	1	no	—
669	#125	D₄×C₃₁	1	1	yes	characteristic
670	#125	C₂³×C₃₁	1	2	yes	—
671	#125	C₂³×C₃₁	1	2	yes	—
672	#124	—	2	2	no	—
673	#124	—	2	1	no	—
674	#124	—	2	2	no	—
675	#124	—	2	2	no	—
676	#124	—	2	2	no	—
677	#124	—	2	1	no	—
678	#124	—	2	1	no	—
679	#124	—	2	1	no	—
680	#124	D₄×C₃₁	1	1	yes	characteristic
681	#124	C₂³×C₃₁	1	2	yes	—
682	#124	C₂³×C₃₁	1	2	yes	—
683	#124	C₂³×C₃₁	1	2	yes	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	—	2	2	no	—
689	#123	D₄×C₃₁	1	2	yes	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	1	no	—
692	C₂²⋊Q₈	—	2	1	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
699	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
700	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
701	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
702	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
703	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
704	#121	—	2	2	no	—
705	#121	—	2	1	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	—	2	2	no	—
710	#121	D₄×C₃₁	1	1	yes	characteristic
711	#121	C₂³×C₃₁	1	2	yes	—
712	#121	C₂³×C₃₁	1	2	yes	—
713	#120	—	2	2	no	—
714	#120	—	2	2	no	—
715	#120	—	2	2	no	—
716	#120	—	2	2	no	—
717	#120	—	2	2	no	—
718	C₄×Q₈	—	2	1	no	—
719	C₄×Q₈	—	2	2	no	—
720	C₄×Q₈	—	2	1	no	—
721	C₄×Q₈	—	2	1	no	—
722	C₄×Q₈	—	2	1	no	—
723	C₄×Q₈	—	2	1	no	—
724	C₄×Q₈	—	2	1	no	—
725	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
726	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
728	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
729	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
730	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
731	C₄×D₄	—	2	1	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	1	no	—
735	C₄×D₄	C₂³×C₃₁	1	2	yes	—
736	C₄×D₄	C₂³×C₃₁	1	2	yes	—
737	C₄×D₄	C₂³×C₃₁	1	2	yes	—
738	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
739	#117	—	2	1	no	—
740	#117	—	2	2	no	—
741	#117	C₂³×C₃₁	1	2	yes	—
742	#117	C₂³×C₃₁	1	2	yes	—
743	#117	C₂³×C₃₁	1	2	yes	—
744	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
745	C₂×C₂²⋊C₄	—	2	1	no	—
746	C₂×C₂²⋊C₄	—	2	1	no	—
747	C₂×C₂²⋊C₄	—	2	2	no	—
748	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
749	#107	C₂³×C₃₁	1	2	yes	—
750	#107	C₂³×C₃₁	1	2	yes	—
751	#107	C₂³×C₃₁	1	2	yes	—
752	#107	C₂³×C₃₁	1	2	yes	—
753	#106	C₂³×C₃₁	1	2	yes	—
754	#106	C₂³×C₃₁	1	2	yes	—
755	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
756	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
757	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
758	#103	C₂³×C₃₁	1	2	yes	—
759	#103	C₂³×C₃₁	1	2	yes	—
760	#103	C₂³×C₃₁	1	2	yes	—
761	#103	C₂³×C₃₁	1	2	yes	—
762	#103	C₂³×C₃₁	1	2	yes	—
763	#103	C₂³×C₃₁	1	2	yes	—
764	#103	C₂³×C₃₁	1	2	yes	—
765	#103	C₂³×C₃₁	1	2	yes	—
766	#102	C₂³×C₃₁	1	2	yes	—
767	#102	C₂³×C₃₁	1	2	yes	—
768	#102	C₂³×C₃₁	1	2	yes	—
769	#102	C₂³×C₃₁	1	2	yes	—
770	#102	C₂³×C₃₁	1	2	yes	—
771	#102	C₂³×C₃₁	1	2	yes	—
772	#102	C₂³×C₃₁	1	2	yes	—
773	#102	C₂³×C₃₁	1	2	yes	—
774	#102	C₂³×C₃₁	1	2	yes	—
775	#102	C₂³×C₃₁	1	2	yes	—
776	#102	C₂³×C₃₁	1	2	yes	—
777	#102	C₂³×C₃₁	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
779	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
780	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
782	#97	C₂³×C₃₁	1	2	yes	—
783	#97	C₂³×C₃₁	1	2	yes	—
784	#97	C₂³×C₃₁	1	2	yes	—
785	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₄×C₈	C₂³×C₃₁	1	2	yes	—
788	C₃₁	#62568	1	1	yes	characteristic, direct product factor, Sylow
789	C₂⁴	—	2	1	no	—
790	C₂⁴	—	2	2	no	—
791	#41	—	4	2	no	—
792	#41	—	4	2	no	—
793	#41	—	8	2	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	4	2	no	—
801	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
802	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
803	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
804	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂×D₄	—	8	4	no	—
818	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
819	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
820	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
821	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
828	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
831	Q₁₆	—	4	2	no	—
832	Q₁₆	—	4	2	no	—
833	SD₁₆	—	4	2	no	—
834	SD₁₆	—	4	2	no	—
835	SD₁₆	—	4	2	no	—
836	SD₁₆	—	4	2	no	—
837	M₁₆	—	4	2	no	—
838	M₁₆	—	4	2	no	—
839	C₂×C₈	—	4	2	no	—
840	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
841	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
842	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
843	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
868	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
869	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
870	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
871	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
872	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
873	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
874	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
875	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
876	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	1	no	—
879	C₂²⋊C₄	—	2	1	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
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	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
898	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	1	no	—
901	C₄²	—	2	1	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	2	no	—
905	C₄²	—	2	2	no	—
906	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
907	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
908	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
909	C₄²	C₂⁴×C₃₁	1	2	yes	—
910	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂³	—	2	2	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	4	2	no	—
914	C₂³	—	8	1	no	—
915	C₂³	—	8	2	no	—
916	C₂³	—	8	2	no	—
917	C₂³	—	8	1	no	—
918	C₂³	—	8	2	no	—
919	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
920	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
921	Q₈	—	2	2	no	—
922	Q₈	—	2	2	no	—
923	Q₈	—	2	2	no	—
924	Q₈	—	2	2	no	—
925	Q₈	—	4	1	no	—
926	Q₈	—	4	2	no	—
927	Q₈	—	8	1	no	—
928	Q₈	—	8	1	no	—
929	Q₈	—	8	2	no	—
930	Q₈	—	8	1	no	—
931	Q₈	—	8	1	no	—
932	D₄	—	2	2	no	—
933	D₄	—	2	2	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	2	no	—
936	D₄	—	4	2	no	—
937	D₄	—	4	1	no	—
938	D₄	—	4	4	no	—
939	D₄	—	8	1	no	—
940	D₄	—	8	2	no	—
941	D₄	—	8	2	no	—
942	D₄	—	8	1	no	—
943	D₄	—	8	2	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	4	1	no	—
959	C₂×C₄	—	4	1	no	—
960	C₂×C₄	—	8	2	no	—
961	C₂×C₄	—	8	2	no	—
962	C₂×C₄	—	8	2	no	—
963	C₂×C₄	—	8	2	no	—
964	C₂×C₄	—	8	1	no	—
965	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
966	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
968	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
969	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
970	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
971	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
972	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
973	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
974	C₈	—	2	2	no	—
975	C₈	—	2	2	no	—
976	C₈	—	2	2	no	—
977	C₈	—	2	2	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	2	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	1	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	16	2	no	—
991	C₂²	—	16	4	no	—
992	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
993	C₄	—	2	2	no	—
994	C₄	—	2	1	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	2	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	1	no	—
1003	C₄	—	4	1	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	1	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	1	no	—
1008	C₄	—	4	2	no	—
1009	C₄	C₃₁×#585	1	2	yes	—
1010	C₂	—	4	1	no	—
1011	C₂	—	4	2	no	—
1012	C₂	—	8	2	no	—
1013	C₂	—	8	2	no	—
1014	C₂	C₃₁×#3500	1	1	yes	characteristic
1015	C₂	C₃₁×#3585	1	1	yes	characteristic
1016	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3558	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3555	C₂	semidirect
3. C₃₁×#3375	C₂	semidirect
4. C₃₁×#3371	C₂	semidirect
5. C₃₁×#3327	C₂	semidirect
6. C₃₁×#3324	C₂	semidirect
7. C₃₁×#3314	C₂	semidirect
8. C₃₁×#3313	C₂	semidirect
9. C₃₁×#3311	C₂	semidirect
10. C₃₁×#3310	C₂	semidirect
11. C₃₁×#3243	C₂	semidirect
12. C₃₁×#3235	C₂	semidirect
13. C₃₁×#3222	C₂	semidirect
14. C₃₁×#3215	C₂	semidirect
15. C₃₁×#3182	C₂	semidirect
16. C₃₁×#3178	C₂	semidirect
17. C₃₁×#3140	C₂	semidirect
18. C₃₁×#3136	C₂	semidirect
19. C₃₁×#2967	C₂	semidirect
24. Q₈²×C₃₁	C₂²	semidirect
26. C₃₁×#557	C₂²	semidirect
28. C₃₁×#556	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
31. C₃₁×#552	C₂²	semidirect
36. C₃₁×#544	C₂²	semidirect
41. C₃₁×#541	C₂²	semidirect
46. C₃₁×#533	C₂²	semidirect
47. C₃₁×#533	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#500	C₂²	semidirect
53. C₃₁×#497	C₂²	semidirect
54. C₃₁×#492	C₂²	semidirect
56. C₃₁×#490	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#489	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
60. C₃₁×#489	C₂²	semidirect
61. C₃₁×#488	C₂²	semidirect
62. C₃₁×#488	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#484	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
76. C₃₁×#476	C₂²	semidirect
77. C₃₁×#474	C₂²	semidirect
78. C₃₁×#474	C₂²	semidirect
79. C₃₁×#470	C₂²	semidirect
81. C₃₁×#468	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#467	C₂²	semidirect
85. C₃₁×#464	C₂²	semidirect
86. C₃₁×#464	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
88. C₃₁×#464	C₂²	semidirect
91. C₃₁×#452	C₂²	semidirect
92. C₃₁×#452	C₂²	semidirect
93. C₃₁×#451	C₂²	semidirect
94. C₃₁×#451	C₂²	semidirect
97. C₃₁×#450	C₂²	semidirect
98. C₃₁×#450	C₂²	semidirect
99. C₃₁×#446	C₂²	semidirect
100. C₃₁×#441	C₂²	semidirect
101. C₃₁×#440	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₄×Q₁₆×C₃₁	C₂²	semidirect
105. C₄×SD₁₆×C₃₁	C₂²	semidirect
106. C₃₁×#436	C₂²	semidirect
107. C₃₁×#435	C₂²	semidirect
108. C₃₁×#435	C₂²	semidirect
109. C₃₁×#433	C₂²	semidirect
110. C₃₁×#432	C₂²	semidirect
111. C₃₁×#419	C₂²	semidirect
113. C₃₁×#418	C₂²	semidirect
114. C₃₁×#417	C₂²	semidirect
115. C₃₁×#416	C₂²	semidirect
116. C₂×C₃₁×#102	C₂²	semidirect
117. C₃₁×#405	C₂²	semidirect
118. C₄×M₁₆×C₃₁	C₂²	semidirect
402. #62568	C₃₁	direct (N × H)
471. #3555	C₂×C₃₁	semidirect
472. #3375	C₂×C₃₁	semidirect
473. #3371	C₂×C₃₁	semidirect
474. #3327	C₂×C₃₁	semidirect
475. #3324	C₂×C₃₁	semidirect
476. #3314	C₂×C₃₁	semidirect
477. #3313	C₂×C₃₁	semidirect
478. #3311	C₂×C₃₁	semidirect
479. #3310	C₂×C₃₁	semidirect
480. #3243	C₂×C₃₁	semidirect
481. #3235	C₂×C₃₁	semidirect
482. #3222	C₂×C₃₁	semidirect
483. #3215	C₂×C₃₁	semidirect
484. #3182	C₂×C₃₁	semidirect
485. #3178	C₂×C₃₁	semidirect
486. #3140	C₂×C₃₁	semidirect
487. #3136	C₂×C₃₁	semidirect
488. #2967	C₂×C₃₁	semidirect
525. Q₈²	C₂²×C₃₁	semidirect
527. #557	C₂²×C₃₁	semidirect
529. #556	C₂²×C₃₁	semidirect
530. #556	C₂²×C₃₁	semidirect
531. #554	C₂²×C₃₁	semidirect
532. #552	C₂²×C₃₁	semidirect
537. #544	C₂²×C₃₁	semidirect
542. #541	C₂²×C₃₁	semidirect
547. #533	C₂²×C₃₁	semidirect
548. #533	C₂²×C₃₁	semidirect
552. #501	C₂²×C₃₁	semidirect
553. #500	C₂²×C₃₁	semidirect
554. #497	C₂²×C₃₁	semidirect
555. #492	C₂²×C₃₁	semidirect
557. #490	C₂²×C₃₁	semidirect
558. #489	C₂²×C₃₁	semidirect
559. #489	C₂²×C₃₁	semidirect
560. #489	C₂²×C₃₁	semidirect
561. #489	C₂²×C₃₁	semidirect
562. #488	C₂²×C₃₁	semidirect
563. #488	C₂²×C₃₁	semidirect
564. #488	C₂²×C₃₁	semidirect
565. #487	C₂²×C₃₁	semidirect
567. #486	C₂²×C₃₁	semidirect
568. #485	C₂²×C₃₁	semidirect
569. #484	C₂²×C₃₁	semidirect
571. #482	C₂²×C₃₁	semidirect
572. #482	C₂²×C₃₁	semidirect
574. #479	C₂²×C₃₁	semidirect
575. #478	C₂²×C₃₁	semidirect
576. #477	C₂²×C₃₁	semidirect
577. #476	C₂²×C₃₁	semidirect
578. #474	C₂²×C₃₁	semidirect
579. #474	C₂²×C₃₁	semidirect
580. #470	C₂²×C₃₁	semidirect
582. #468	C₂²×C₃₁	semidirect
583. #468	C₂²×C₃₁	semidirect
584. #467	C₂²×C₃₁	semidirect
586. #464	C₂²×C₃₁	semidirect
587. #464	C₂²×C₃₁	semidirect
588. #464	C₂²×C₃₁	semidirect
589. #464	C₂²×C₃₁	semidirect
592. #452	C₂²×C₃₁	semidirect
593. #452	C₂²×C₃₁	semidirect
594. #451	C₂²×C₃₁	semidirect
595. #451	C₂²×C₃₁	semidirect
598. #450	C₂²×C₃₁	semidirect
599. #450	C₂²×C₃₁	semidirect
600. #446	C₂²×C₃₁	semidirect
601. #441	C₂²×C₃₁	semidirect
602. #440	C₂²×C₃₁	semidirect
603. #440	C₂²×C₃₁	semidirect
604. #440	C₂²×C₃₁	semidirect
605. C₄×Q₁₆	C₂²×C₃₁	semidirect
606. C₄×SD₁₆	C₂²×C₃₁	semidirect
607. #436	C₂²×C₃₁	semidirect
608. #435	C₂²×C₃₁	semidirect
609. #435	C₂²×C₃₁	semidirect
610. #433	C₂²×C₃₁	semidirect
611. #432	C₂²×C₃₁	semidirect
612. #419	C₂²×C₃₁	semidirect
614. #418	C₂²×C₃₁	semidirect
615. #417	C₂²×C₃₁	semidirect
616. #416	C₂²×C₃₁	semidirect
617. C₂×#102	C₂²×C₃₁	semidirect
618. #405	C₂²×C₃₁	semidirect
619. C₄×M₁₆	C₂²×C₃₁	semidirect
788. C₃₁	#62568	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×#3558	2
C₃₁×#3555	2
C₃₁×#3375	2
C₃₁×#3371	2
C₃₁×#3327	2
C₃₁×#3324	2
C₃₁×#3314	2
C₃₁×#3313	2
C₃₁×#3311	2
C₃₁×#3310	2
C₃₁×#3243	2
C₃₁×#3235	2
C₃₁×#3222	2
C₃₁×#3215	2
C₃₁×#3182	2
C₃₁×#3178	2
C₃₁×#3140	2
C₃₁×#3136	2
C₃₁×#2967	2
#62568	31

Subgroups — C31×#62568 #21519327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62568 #21519327