Subgroups — C₃₁×#61897 #21518656

Order 7936.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3402	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3377	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3219	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3216	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3116	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
21	C₃₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#559	C₂²	1	2	yes	—
25	C₃₁×#559	C₂²	1	1	yes	characteristic
26	C₃₁×#557	C₂²	1	1	yes	characteristic
27	C₃₁×#557	C₂²	1	1	yes	characteristic
28	C₃₁×#557	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	2	yes	—
30	C₃₁×#556	C₂²	1	1	yes	characteristic
31	C₃₁×#556	C₂²	1	2	yes	—
32	C₃₁×#556	C₂²	1	1	yes	characteristic
33	C₃₁×#556	C₂²	1	2	yes	—
34	C₃₁×#553	—	2	1	no	—
35	C₃₁×#553	—	2	2	no	—
36	C₃₁×#552	—	2	1	no	—
37	C₃₁×#552	—	2	2	no	—
38	C₃₁×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₃₁	—	2	1	no	—
40	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#548	—	2	1	no	—
42	C₃₁×#541	—	2	1	no	—
43	C₃₁×#541	—	2	2	no	—
44	C₃₁×#533	C₂²	1	1	yes	characteristic
45	C₃₁×#533	C₂²	1	2	yes	—
46	C₃₁×#532	C₂²	1	1	yes	characteristic
47	C₃₁×#532	C₂²	1	2	yes	—
48	C₃₁×#529	—	2	1	no	—
49	C₃₁×#529	—	2	2	no	—
50	C₃₁×#529	C₂²	1	1	yes	characteristic
51	C₃₁×#529	C₂²	1	2	yes	—
52	C₃₁×#519	—	2	1	no	—
53	C₄×#41×C₃₁	—	2	1	no	—
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₃₁	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#497	C₂²	1	2	yes	—
58	C₃₁×#497	C₂²	1	2	yes	—
59	C₃₁×#497	C₂²	1	2	yes	—
60	C₃₁×#496	C₂²	1	2	yes	—
61	C₃₁×#495	C₂²	1	2	yes	—
62	C₃₁×#494	C₂²	1	1	yes	characteristic
63	C₃₁×#492	C₂²	1	1	yes	characteristic
64	C₃₁×#491	C₂²	1	2	yes	—
65	C₃₁×#490	C₂²	1	2	yes	—
66	C₃₁×#489	C₂²	1	2	yes	—
67	C₃₁×#489	C₂²	1	2	yes	—
68	C₃₁×#488	C₂²	1	2	yes	—
69	C₃₁×#487	C₂²	1	1	yes	characteristic
70	C₃₁×#486	C₂²	1	1	yes	characteristic
71	C₃₁×#485	C₂²	1	1	yes	characteristic
72	C₃₁×#485	C₂²	1	2	yes	—
73	C₃₁×#482	C₂²	1	1	yes	characteristic
74	C₃₁×#479	C₂²	1	1	yes	characteristic
75	C₃₁×#479	C₂²	1	2	yes	—
76	C₃₁×#478	C₂²	1	1	yes	characteristic
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#477	C₂²	1	2	yes	—
79	C₃₁×#476	C₂²	1	2	yes	—
80	C₃₁×#475	C₂²	1	1	yes	characteristic
81	C₃₁×#474	C₂²	1	1	yes	characteristic
82	C₃₁×#464	C₂²	1	1	yes	characteristic
83	C₃₁×#464	C₂²	1	2	yes	—
84	C₃₁×#464	C₂²	1	2	yes	—
85	C₃₁×#464	C₂²	1	2	yes	—
86	C₃₁×#464	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	1	yes	characteristic
89	C₃₁×#463	C₂²	1	2	yes	—
90	C₃₁×#463	C₂²	1	2	yes	—
91	C₃₁×#463	C₂²	1	2	yes	—
92	C₃₁×#462	C₂²	1	1	yes	characteristic
93	C₃₁×#462	C₂²	1	2	yes	—
94	C₃₁×#462	C₂²	1	1	yes	characteristic
95	C₃₁×#462	C₂²	1	2	yes	—
96	C₃₁×#462	C₂²	1	2	yes	—
97	C₃₁×#461	C₂²	1	1	yes	characteristic
98	C₃₁×#461	C₂²	1	1	yes	characteristic
99	C₃₁×#461	C₂²	1	2	yes	—
100	C₃₁×#460	C₂²	1	1	yes	characteristic
101	C₃₁×#460	C₂²	1	2	yes	—
102	C₃₁×#460	C₂²	1	2	yes	—
103	C₃₁×#459	C₂²	1	1	yes	characteristic
104	C₃₁×#452	C₂²	1	1	yes	characteristic
105	C₃₁×#452	C₂²	1	2	yes	—
106	C₃₁×#452	C₂²	1	2	yes	—
107	C₃₁×#452	C₂²	1	2	yes	—
108	C₃₁×#452	C₂²	1	2	yes	—
109	C₃₁×#449	C₂²	1	1	yes	characteristic
110	C₃₁×#449	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic
112	C₃₁×#446	C₂²	1	1	yes	characteristic
113	C₃₁×#446	C₂²	1	2	yes	—
114	C₃₁×#446	C₂²	1	1	yes	characteristic
115	C₃₁×#446	C₂²	1	1	yes	characteristic
116	C₃₁×#446	C₂²	1	2	yes	—
117	C₃₁×#442	C₂²	1	2	yes	—
118	C₃₁×#441	C₂²	1	2	yes	—
119	C₃₁×#441	C₂²	1	2	yes	—
120	C₃₁×#441	C₂²	1	2	yes	—
121	C₃₁×#440	C₂²	1	2	yes	—
122	C₃₁×#440	C₂²	1	2	yes	—
123	C₃₁×#440	C₂²	1	2	yes	—
124	C₃₁×#440	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
126	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
130	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
131	C₃₁×#432	C₂²	1	2	yes	—
132	C₃₁×#432	C₂²	1	2	yes	—
133	C₃₁×#431	C₂²	1	1	yes	characteristic
134	C₃₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
140	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	—	2	2	no	—
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×#127	C₂³	1	1	yes	characteristic
163	C₃₁×#127	C₂³	1	2	yes	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	1	no	—
172	C₃₁×#125	—	2	1	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	1	no	—
181	C₃₁×#125	C₂³	1	1	yes	characteristic
182	C₃₁×#125	C₂³	1	2	yes	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	C₂³	1	2	yes	—
186	C₃₁×#124	C₂³	1	2	yes	—
187	C₃₁×#124	C₂³	1	1	yes	characteristic
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#123	—	2	1	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	1	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
204	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	1	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	C₂³	1	1	yes	characteristic
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	2	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	—	2	2	no	—
218	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	D₄	1	2	yes	—
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	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	—	2	2	no	—
243	C₄×D₄×C₃₁	—	2	2	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	2	yes	—
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	—	2	2	no	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	—	2	2	no	—
255	C₃₁×#117	—	2	1	no	—
256	C₃₁×#117	—	2	2	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	—	2	1	no	—
259	C₃₁×#117	—	2	1	no	—
260	C₃₁×#117	—	2	2	no	—
261	C₃₁×#117	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
264	C₂×C₄²×C₃₁	—	2	1	no	—
265	C₂×C₄²×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
267	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	1	yes	characteristic
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×#97	C₂³	1	2	yes	—
306	C₃₁×#97	C₂³	1	2	yes	—
307	C₃₁×#97	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	—	4	1	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	4	1	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	4	4	no	—
317	C₂×Q₈×C₃₁	—	2	2	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	4	2	no	—
320	C₂×Q₈×C₃₁	—	4	4	no	—
321	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
324	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
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	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
337	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	2	no	—
340	C₂²×C₄×C₃₁	—	2	2	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
349	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
350	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	Q₁₆×C₃₁	—	4	2	no	—
352	Q₁₆×C₃₁	—	4	2	no	—
353	Q₁₆×C₃₁	—	4	1	no	—
354	Q₁₆×C₃₁	—	4	2	no	—
355	Q₁₆×C₃₁	—	4	2	no	—
356	SD₁₆×C₃₁	—	4	2	no	—
357	SD₁₆×C₃₁	—	4	2	no	—
358	SD₁₆×C₃₁	—	4	2	no	—
359	SD₁₆×C₃₁	—	4	2	no	—
360	SD₁₆×C₃₁	—	4	2	no	—
361	SD₁₆×C₃₁	—	4	1	no	—
362	SD₁₆×C₃₁	—	4	1	no	—
363	D₈×C₃₁	—	4	1	no	—
364	D₈×C₃₁	—	4	2	no	—
365	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
369	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	1	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	1	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	1	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	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	2	no	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄×C₃₁	—	2	2	no	—
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	1	no	—
411	C₂²⋊C₄×C₃₁	—	2	1	no	—
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×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	1	no	—
433	C₄²×C₃₁	—	2	2	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₃₁	C₂×D₄	1	2	yes	—
440	C₄²×C₃₁	C₂×D₄	1	2	yes	—
441	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	2	yes	—
445	C₄²×C₃₁	C₂⁴	1	2	yes	—
446	#61897	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₃₁	—	2	1	no	—
448	C₂³×C₃₁	—	2	2	no	—
449	C₂³×C₃₁	—	2	1	no	—
450	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
451	Q₈×C₃₁	—	2	2	no	—
452	Q₈×C₃₁	—	2	2	no	—
453	Q₈×C₃₁	—	2	1	no	—
454	Q₈×C₃₁	—	2	2	no	—
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	2	no	—
457	Q₈×C₃₁	—	2	1	no	—
458	Q₈×C₃₁	—	2	1	no	—
459	Q₈×C₃₁	—	2	1	no	—
460	Q₈×C₃₁	—	2	2	no	—
461	Q₈×C₃₁	—	4	2	no	—
462	Q₈×C₃₁	—	4	4	no	—
463	Q₈×C₃₁	—	4	2	no	—
464	D₄×C₃₁	—	2	1	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	2	1	no	—
467	D₄×C₃₁	—	2	2	no	—
468	D₄×C₃₁	—	2	2	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	4	4	no	—
471	D₄×C₃₁	—	4	2	no	—
472	D₄×C₃₁	—	4	2	no	—
473	D₄×C₃₁	—	4	4	no	—
474	D₄×C₃₁	—	4	2	no	—
475	D₄×C₃₁	—	8	2	no	—
476	D₄×C₃₁	—	8	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	1	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	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	4	1	no	—
490	C₂×C₄×C₃₁	—	4	2	no	—
491	C₂×C₄×C₃₁	—	4	2	no	—
492	C₂×C₄×C₃₁	—	4	4	no	—
493	C₂×C₄×C₃₁	—	4	2	no	—
494	C₂×C₄×C₃₁	—	4	4	no	—
495	C₂×C₄×C₃₁	—	4	4	no	—
496	C₂×C₄×C₃₁	—	4	2	no	—
497	C₂×C₄×C₃₁	—	4	2	no	—
498	C₂×C₄×C₃₁	—	8	1	no	—
499	C₂×C₄×C₃₁	—	8	2	no	—
500	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
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	C₈×C₃₁	—	2	1	no	—
515	C₈×C₃₁	—	2	1	no	—
516	#3523	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3480	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3402	C₂×C₃₁	1	2	yes	complemented
519	#3401	C₂×C₃₁	1	2	yes	complemented
520	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3398	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3398	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3377	C₂×C₃₁	1	2	yes	complemented
525	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3371	C₂×C₃₁	1	2	yes	complemented
528	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3219	C₂×C₃₁	1	2	yes	complemented
531	#3216	C₂×C₃₁	1	2	yes	complemented
532	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3210	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3116	C₂×C₃₁	1	2	yes	complemented
535	#3111	C₂×C₃₁	1	2	yes	complemented
536	#3107	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#2983	C₂×C₃₁	1	1	yes	characteristic, complemented
539	C₂²×C₃₁	—	2	1	no	—
540	C₂²×C₃₁	—	2	1	no	—
541	C₂²×C₃₁	—	2	1	no	—
542	C₂²×C₃₁	—	4	2	no	—
543	C₂²×C₃₁	—	4	1	no	—
544	C₂²×C₃₁	—	4	1	no	—
545	C₂²×C₃₁	—	4	2	no	—
546	C₂²×C₃₁	—	4	1	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	—	4	2	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₃₁	—	2	1	no	—
553	C₄×C₃₁	—	2	2	no	—
554	C₄×C₃₁	—	2	2	no	—
555	C₄×C₃₁	—	2	1	no	—
556	C₄×C₃₁	—	2	1	no	—
557	C₄×C₃₁	—	2	1	no	—
558	C₄×C₃₁	—	2	2	no	—
559	C₄×C₃₁	—	2	2	no	—
560	C₄×C₃₁	—	4	1	no	—
561	C₄×C₃₁	—	4	1	no	—
562	C₄×C₃₁	—	4	1	no	—
563	C₄×C₃₁	—	4	2	no	—
564	C₄×C₃₁	—	4	1	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	2	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	#575	1	2	yes	—
570	C₄×C₃₁	#585	1	1	yes	characteristic
571	C₄×C₃₁	#585	1	1	yes	characteristic
572	#559	C₂²×C₃₁	1	2	yes	—
573	#559	C₂²×C₃₁	1	1	yes	characteristic
574	#557	C₂²×C₃₁	1	1	yes	characteristic
575	#557	C₂²×C₃₁	1	1	yes	characteristic
576	#557	C₂²×C₃₁	1	1	yes	characteristic
577	#557	C₂²×C₃₁	1	2	yes	—
578	#556	C₂²×C₃₁	1	1	yes	characteristic
579	#556	C₂²×C₃₁	1	2	yes	—
580	#556	C₂²×C₃₁	1	1	yes	characteristic
581	#556	C₂²×C₃₁	1	2	yes	—
582	#553	—	2	1	no	—
583	#553	—	2	2	no	—
584	#552	—	2	1	no	—
585	#552	—	2	2	no	—
586	#550	C₂²×C₃₁	1	1	yes	characteristic
587	D₄×Q₈	—	2	1	no	—
588	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
589	#548	—	2	1	no	—
590	#541	—	2	1	no	—
591	#541	—	2	2	no	—
592	#533	C₂²×C₃₁	1	1	yes	characteristic
593	#533	C₂²×C₃₁	1	2	yes	—
594	#532	C₂²×C₃₁	1	1	yes	characteristic
595	#532	C₂²×C₃₁	1	2	yes	—
596	#529	—	2	1	no	—
597	#529	—	2	2	no	—
598	#529	C₂²×C₃₁	1	1	yes	characteristic
599	#529	C₂²×C₃₁	1	2	yes	—
600	#519	—	2	1	no	—
601	C₄×#41	—	2	1	no	—
602	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
603	C₄×#41	C₂²×C₃₁	1	2	yes	—
604	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
605	#497	C₂²×C₃₁	1	2	yes	—
606	#497	C₂²×C₃₁	1	2	yes	—
607	#497	C₂²×C₃₁	1	2	yes	—
608	#496	C₂²×C₃₁	1	2	yes	—
609	#495	C₂²×C₃₁	1	2	yes	—
610	#494	C₂²×C₃₁	1	1	yes	characteristic
611	#492	C₂²×C₃₁	1	1	yes	characteristic
612	#491	C₂²×C₃₁	1	2	yes	—
613	#490	C₂²×C₃₁	1	2	yes	—
614	#489	C₂²×C₃₁	1	2	yes	—
615	#489	C₂²×C₃₁	1	2	yes	—
616	#488	C₂²×C₃₁	1	2	yes	—
617	#487	C₂²×C₃₁	1	1	yes	characteristic
618	#486	C₂²×C₃₁	1	1	yes	characteristic
619	#485	C₂²×C₃₁	1	1	yes	characteristic
620	#485	C₂²×C₃₁	1	2	yes	—
621	#482	C₂²×C₃₁	1	1	yes	characteristic
622	#479	C₂²×C₃₁	1	1	yes	characteristic
623	#479	C₂²×C₃₁	1	2	yes	—
624	#478	C₂²×C₃₁	1	1	yes	characteristic
625	#478	C₂²×C₃₁	1	2	yes	—
626	#477	C₂²×C₃₁	1	2	yes	—
627	#476	C₂²×C₃₁	1	2	yes	—
628	#475	C₂²×C₃₁	1	1	yes	characteristic
629	#474	C₂²×C₃₁	1	1	yes	characteristic
630	#464	C₂²×C₃₁	1	1	yes	characteristic
631	#464	C₂²×C₃₁	1	2	yes	—
632	#464	C₂²×C₃₁	1	2	yes	—
633	#464	C₂²×C₃₁	1	2	yes	—
634	#464	C₂²×C₃₁	1	2	yes	—
635	#464	C₂²×C₃₁	1	2	yes	—
636	#463	C₂²×C₃₁	1	1	yes	characteristic
637	#463	C₂²×C₃₁	1	2	yes	—
638	#463	C₂²×C₃₁	1	2	yes	—
639	#463	C₂²×C₃₁	1	2	yes	—
640	#462	C₂²×C₃₁	1	1	yes	characteristic
641	#462	C₂²×C₃₁	1	2	yes	—
642	#462	C₂²×C₃₁	1	1	yes	characteristic
643	#462	C₂²×C₃₁	1	2	yes	—
644	#462	C₂²×C₃₁	1	2	yes	—
645	#461	C₂²×C₃₁	1	1	yes	characteristic
646	#461	C₂²×C₃₁	1	1	yes	characteristic
647	#461	C₂²×C₃₁	1	2	yes	—
648	#460	C₂²×C₃₁	1	1	yes	characteristic
649	#460	C₂²×C₃₁	1	2	yes	—
650	#460	C₂²×C₃₁	1	2	yes	—
651	#459	C₂²×C₃₁	1	1	yes	characteristic
652	#452	C₂²×C₃₁	1	1	yes	characteristic
653	#452	C₂²×C₃₁	1	2	yes	—
654	#452	C₂²×C₃₁	1	2	yes	—
655	#452	C₂²×C₃₁	1	2	yes	—
656	#452	C₂²×C₃₁	1	2	yes	—
657	#449	C₂²×C₃₁	1	1	yes	characteristic
658	#449	C₂²×C₃₁	1	2	yes	—
659	#446	C₂²×C₃₁	1	1	yes	characteristic
660	#446	C₂²×C₃₁	1	1	yes	characteristic
661	#446	C₂²×C₃₁	1	2	yes	—
662	#446	C₂²×C₃₁	1	1	yes	characteristic
663	#446	C₂²×C₃₁	1	1	yes	characteristic
664	#446	C₂²×C₃₁	1	2	yes	—
665	#442	C₂²×C₃₁	1	2	yes	—
666	#441	C₂²×C₃₁	1	2	yes	—
667	#441	C₂²×C₃₁	1	2	yes	—
668	#441	C₂²×C₃₁	1	2	yes	—
669	#440	C₂²×C₃₁	1	2	yes	—
670	#440	C₂²×C₃₁	1	2	yes	—
671	#440	C₂²×C₃₁	1	2	yes	—
672	#440	C₂²×C₃₁	1	2	yes	—
673	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
674	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
675	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
676	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
678	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
679	#432	C₂²×C₃₁	1	2	yes	—
680	#432	C₂²×C₃₁	1	2	yes	—
681	#431	C₂²×C₃₁	1	1	yes	characteristic
682	#431	C₂²×C₃₁	1	1	yes	characteristic
683	C₂×C₃₁	—	4	1	no	—
684	C₂×C₃₁	—	8	2	no	—
685	C₂×C₃₁	—	8	1	no	—
686	C₂×C₃₁	—	8	1	no	—
687	C₂×C₃₁	#3487	1	1	yes	characteristic
688	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
689	C₂×C₃₁	#3586	1	1	yes	characteristic
690	C₂×#41	—	2	1	no	—
691	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
692	C₂×#41	C₂³×C₃₁	1	2	yes	—
693	C₂²×Q₈	—	2	1	no	—
694	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
695	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
697	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
698	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
699	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
700	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
703	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
707	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×D₈	C₂³×C₃₁	1	2	yes	—
709	C₄⋊Q₈	—	2	1	no	—
710	C₄⋊Q₈	—	2	2	no	—
711	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
712	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
713	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
714	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
715	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
717	#127	C₂³×C₃₁	1	1	yes	characteristic
718	#127	C₂³×C₃₁	1	2	yes	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	1	no	—
727	#125	—	2	1	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	2	no	—
732	#125	—	2	1	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	1	no	—
736	#125	C₂³×C₃₁	1	1	yes	characteristic
737	#125	C₂³×C₃₁	1	2	yes	—
738	#124	—	2	1	no	—
739	#124	—	2	2	no	—
740	#124	C₂³×C₃₁	1	1	yes	characteristic
741	#124	C₂³×C₃₁	1	2	yes	—
742	#124	C₂³×C₃₁	1	2	yes	—
743	#124	C₂³×C₃₁	1	2	yes	—
744	#124	C₂³×C₃₁	1	2	yes	—
745	#123	—	2	1	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
760	#121	—	2	1	no	—
761	#121	—	2	2	no	—
762	#121	—	2	1	no	—
763	#121	—	2	2	no	—
764	#121	—	2	1	no	—
765	#121	—	2	2	no	—
766	#121	C₂³×C₃₁	1	1	yes	characteristic
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	2	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	2	no	—
773	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
774	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
775	C₄×Q₈	D₄×C₃₁	1	2	yes	—
776	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
778	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
784	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
785	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₃₁	1	2	yes	—
802	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₃₁	1	2	yes	—
804	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₃₁	1	2	yes	—
806	#117	—	2	1	no	—
807	#117	—	2	2	no	—
808	#117	—	2	1	no	—
809	#117	—	2	2	no	—
810	#117	—	2	1	no	—
811	#117	—	2	2	no	—
812	#117	—	2	2	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	—	2	2	no	—
816	#117	C₂³×C₃₁	1	1	yes	characteristic
817	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
818	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
819	C₂×C₄²	—	2	1	no	—
820	C₂×C₄²	—	2	2	no	—
821	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
822	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
823	#107	C₂³×C₃₁	1	1	yes	characteristic
824	#107	C₂³×C₃₁	1	2	yes	—
825	#107	C₂³×C₃₁	1	1	yes	characteristic
826	#106	C₂³×C₃₁	1	1	yes	characteristic
827	#106	C₂³×C₃₁	1	1	yes	characteristic
828	#106	C₂³×C₃₁	1	2	yes	—
829	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
834	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
835	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
836	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
837	#103	C₂³×C₃₁	1	1	yes	characteristic
838	#103	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
847	#103	C₂³×C₃₁	1	2	yes	—
848	#102	C₂³×C₃₁	1	1	yes	characteristic
849	#102	C₂³×C₃₁	1	1	yes	characteristic
850	#102	C₂³×C₃₁	1	1	yes	characteristic
851	#102	C₂³×C₃₁	1	1	yes	characteristic
852	#102	C₂³×C₃₁	1	2	yes	—
853	#102	C₂³×C₃₁	1	2	yes	—
854	#102	C₂³×C₃₁	1	2	yes	—
855	#102	C₂³×C₃₁	1	2	yes	—
856	#102	C₂³×C₃₁	1	2	yes	—
857	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
858	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
859	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	#97	C₂³×C₃₁	1	2	yes	—
861	#97	C₂³×C₃₁	1	2	yes	—
862	#97	C₂³×C₃₁	1	2	yes	—
863	#97	C₂³×C₃₁	1	2	yes	—
864	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
865	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₄×C₈	C₂³×C₃₁	1	2	yes	—
867	C₃₁	#61897	1	1	yes	characteristic, direct product factor, Sylow
868	#41	—	4	1	no	—
869	#41	—	4	2	no	—
870	#41	—	4	1	no	—
871	#41	—	4	2	no	—
872	#41	—	4	4	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	2	1	no	—
875	C₂×Q₈	—	4	2	no	—
876	C₂×Q₈	—	4	4	no	—
877	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
878	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
879	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
880	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
881	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
882	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	2	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
892	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
893	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	1	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	C₂×D₄×C₃₁	1	1	yes	characteristic
903	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
904	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
905	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
907	Q₁₆	—	4	2	no	—
908	Q₁₆	—	4	2	no	—
909	Q₁₆	—	4	1	no	—
910	Q₁₆	—	4	2	no	—
911	Q₁₆	—	4	2	no	—
912	SD₁₆	—	4	2	no	—
913	SD₁₆	—	4	2	no	—
914	SD₁₆	—	4	2	no	—
915	SD₁₆	—	4	2	no	—
916	SD₁₆	—	4	2	no	—
917	SD₁₆	—	4	1	no	—
918	SD₁₆	—	4	1	no	—
919	D₈	—	4	1	no	—
920	D₈	—	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	2	yes	—
926	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic
955	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
956	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
957	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
959	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
960	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	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	—	2	1	no	—
994	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
995	C₄²	C₂×D₄×C₃₁	1	2	yes	—
996	C₄²	C₂×D₄×C₃₁	1	2	yes	—
997	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
998	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₄²	C₂⁴×C₃₁	1	2	yes	—
1001	C₄²	C₂⁴×C₃₁	1	2	yes	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	1	no	—
1005	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	2	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	4	2	no	—
1017	Q₈	—	4	4	no	—
1018	Q₈	—	4	2	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	2	no	—
1024	D₄	—	2	1	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	4	2	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	8	2	no	—
1031	D₄	—	8	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	4	1	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	4	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	4	no	—
1050	C₂×C₄	—	4	4	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	8	1	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1056	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
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	2	yes	—
1061	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1064	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1065	C₈	—	2	1	no	—
1066	C₈	—	2	2	no	—
1067	C₈	—	2	2	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	1	no	—
1070	C₈	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	1	no	—
1101	C₄	C₃₁×#575	1	2	yes	—
1102	C₄	C₃₁×#585	1	1	yes	characteristic
1103	C₄	C₃₁×#585	1	1	yes	characteristic
1104	C₂	—	4	1	no	—
1105	C₂	—	8	2	no	—
1106	C₂	—	8	1	no	—
1107	C₂	—	8	1	no	—
1108	C₂	C₃₁×#3487	1	1	yes	characteristic
1109	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1110	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3523	C₂	semidirect
2. C₃₁×#3480	C₂	semidirect
3. C₃₁×#3402	C₂	semidirect
4. C₃₁×#3401	C₂	semidirect
5. C₃₁×#3400	C₂	semidirect
6. C₃₁×#3398	C₂	semidirect
7. C₃₁×#3398	C₂	semidirect
8. C₃₁×#3397	C₂	semidirect
9. C₃₁×#3377	C₂	semidirect
10. C₃₁×#3374	C₂	semidirect
11. C₃₁×#3373	C₂	semidirect
12. C₃₁×#3371	C₂	semidirect
13. C₃₁×#3368	C₂	semidirect
14. C₃₁×#3367	C₂	semidirect
15. C₃₁×#3219	C₂	semidirect
16. C₃₁×#3216	C₂	semidirect
17. C₃₁×#3212	C₂	semidirect
18. C₃₁×#3210	C₂	semidirect
19. C₃₁×#3116	C₂	semidirect
20. C₃₁×#3111	C₂	semidirect
21. C₃₁×#3107	C₂	semidirect
22. C₃₁×#3102	C₂	semidirect
23. C₃₁×#2983	C₂	semidirect
446. #61897	C₃₁	direct (N × H)
516. #3523	C₂×C₃₁	semidirect
517. #3480	C₂×C₃₁	semidirect
518. #3402	C₂×C₃₁	semidirect
519. #3401	C₂×C₃₁	semidirect
520. #3400	C₂×C₃₁	semidirect
521. #3398	C₂×C₃₁	semidirect
522. #3398	C₂×C₃₁	semidirect
523. #3397	C₂×C₃₁	semidirect
524. #3377	C₂×C₃₁	semidirect
525. #3374	C₂×C₃₁	semidirect
526. #3373	C₂×C₃₁	semidirect
527. #3371	C₂×C₃₁	semidirect
528. #3368	C₂×C₃₁	semidirect
529. #3367	C₂×C₃₁	semidirect
530. #3219	C₂×C₃₁	semidirect
531. #3216	C₂×C₃₁	semidirect
532. #3212	C₂×C₃₁	semidirect
533. #3210	C₂×C₃₁	semidirect
534. #3116	C₂×C₃₁	semidirect
535. #3111	C₂×C₃₁	semidirect
536. #3107	C₂×C₃₁	semidirect
537. #3102	C₂×C₃₁	semidirect
538. #2983	C₂×C₃₁	semidirect
867. C₃₁	#61897	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×#3523	2
C₃₁×#3480	2
C₃₁×#3402	2
C₃₁×#3401	2
C₃₁×#3400	2
C₃₁×#3398	2
C₃₁×#3397	2
C₃₁×#3377	2
C₃₁×#3374	2
C₃₁×#3373	2
C₃₁×#3371	2
C₃₁×#3368	2
C₃₁×#3367	2
C₃₁×#3219	2
C₃₁×#3216	2
C₃₁×#3212	2
C₃₁×#3210	2
C₃₁×#3116	2
C₃₁×#3111	2
C₃₁×#3107	2
C₃₁×#3102	2
C₃₁×#2983	2
#61897	31

Subgroups — C31×#61897 #21518656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61897 #21518656