Subgroups — C₃₁×#61944 #21518703

Order 7936.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3403	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3402	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3375	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3369	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	1	no	—
21	C₃₁×#563	—	2	1	no	—
22	C₃₁×#559	C₂²	1	2	yes	—
23	C₃₁×#559	C₂²	1	2	yes	—
24	C₃₁×#559	C₂²	1	2	yes	complemented
25	Q₈²×C₃₁	C₂²	1	2	yes	complemented
26	C₃₁×#556	—	2	1	no	—
27	C₃₁×#556	C₂²	1	2	yes	—
28	C₃₁×#556	C₂²	1	2	yes	—
29	C₃₁×#556	C₂²	1	2	yes	complemented
30	C₃₁×#551	—	2	2	no	—
31	C₃₁×#551	—	2	2	no	—
32	D₄×Q₈×C₃₁	—	2	1	no	—
33	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
34	C₃₁×#542	—	2	1	no	—
35	C₃₁×#542	—	2	1	no	—
36	C₃₁×#542	—	2	2	no	—
37	C₃₁×#542	C₂²	1	2	yes	—
38	C₃₁×#542	C₂²	1	2	yes	—
39	C₃₁×#536	—	2	2	no	—
40	C₃₁×#536	C₂²	1	1	yes	characteristic
41	C₃₁×#535	C₂²	1	1	yes	characteristic
42	C₃₁×#533	C₂²	1	1	yes	characteristic
43	C₃₁×#533	C₂²	1	1	yes	characteristic
44	C₃₁×#532	C₂²	1	1	yes	characteristic
45	C₃₁×#529	—	2	1	no	—
46	C₃₁×#529	—	2	1	no	—
47	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
48	C₃₁×#519	C₂²	1	1	yes	characteristic
49	C₃₁×#518	C₂²	1	1	yes	characteristic
50	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#497	C₂²	1	2	yes	—
52	C₃₁×#497	C₂²	1	2	yes	complemented
53	C₃₁×#496	C₂²	1	2	yes	—
54	C₃₁×#496	C₂²	1	2	yes	—
55	C₃₁×#495	C₂²	1	2	yes	—
56	C₃₁×#495	C₂²	1	2	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	—
58	C₃₁×#489	C₂²	1	2	yes	—
59	C₃₁×#489	C₂²	1	2	yes	—
60	C₃₁×#489	C₂²	1	2	yes	complemented
61	C₃₁×#487	C₂²	1	2	yes	complemented
62	C₃₁×#486	C₂²	1	2	yes	—
63	C₃₁×#485	C₂²	1	2	yes	—
64	C₃₁×#482	C₂²	1	2	yes	—
65	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#477	C₂²	1	2	yes	complemented
67	C₃₁×#476	C₂²	1	2	yes	—
68	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#475	C₂²	1	2	yes	complemented
71	C₃₁×#474	C₂²	1	2	yes	—
72	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#464	C₂²	1	2	yes	—
74	C₃₁×#464	C₂²	1	2	yes	—
75	C₃₁×#464	C₂²	1	2	yes	—
76	C₃₁×#464	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#464	C₂²	1	2	yes	complemented
79	C₃₁×#463	C₂²	1	2	yes	—
80	C₃₁×#463	C₂²	1	2	yes	—
81	C₃₁×#463	C₂²	1	2	yes	—
82	C₃₁×#463	C₂²	1	2	yes	—
83	C₃₁×#463	C₂²	1	2	yes	—
84	C₃₁×#463	C₂²	1	2	yes	complemented
85	C₃₁×#462	C₂²	1	2	yes	complemented
86	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#461	C₂²	1	2	yes	complemented
88	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#460	C₂²	1	2	yes	—
90	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#459	C₂²	1	2	yes	—
92	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#452	C₂²	1	2	yes	—
94	C₃₁×#451	C₂²	1	2	yes	—
95	C₃₁×#450	C₂²	1	2	yes	—
96	C₃₁×#449	C₂²	1	2	yes	—
97	C₃₁×#448	C₂²	1	2	yes	—
98	C₃₁×#447	C₂²	1	2	yes	—
99	C₃₁×#446	C₂²	1	2	yes	complemented
100	C₃₁×#446	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#446	C₂²	1	2	yes	complemented
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	2	yes	complemented
105	C₃₁×#441	C₂²	1	2	yes	complemented
106	C₃₁×#441	C₂²	1	2	yes	complemented
107	C₃₁×#440	C₂²	1	2	yes	—
108	C₃₁×#440	C₂²	1	2	yes	complemented
109	C₃₁×#440	C₂²	1	2	yes	complemented
110	C₃₁×#440	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
112	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
114	C₄×D₈×C₃₁	C₂²	1	2	yes	—
115	C₃₁×#433	C₂²	1	2	yes	—
116	C₃₁×#433	C₂²	1	2	yes	—
117	C₃₁×#432	C₂²	1	1	yes	characteristic
118	C₃₁×#432	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₃₁	—	2	2	no	—
122	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
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×SD₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂×D₈×C₃₁	C₂³	1	2	yes	—
134	C₂×D₈×C₃₁	C₂³	1	2	yes	—
135	C₂×D₈×C₃₁	C₂³	1	2	yes	—
136	C₃₁×C₄⋊Q₈	—	2	2	no	—
137	C₃₁×C₄⋊Q₈	—	2	2	no	—
138	C₃₁×C₄⋊Q₈	—	2	2	no	—
139	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
140	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
141	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
142	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
144	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
145	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
146	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
147	C₃₁×#127	C₂³	1	2	yes	—
148	C₃₁×#127	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
154	C₃₁×#126	—	2	2	no	—
155	C₃₁×#126	—	2	2	no	—
156	C₃₁×#126	—	2	2	no	—
157	C₃₁×#125	—	2	1	no	—
158	C₃₁×#125	D₄	1	1	yes	characteristic
159	C₃₁×#125	D₄	1	1	yes	characteristic
160	C₃₁×#124	—	2	2	no	—
161	C₃₁×#124	—	2	2	no	—
162	C₃₁×#124	—	2	2	no	—
163	C₃₁×#124	—	2	2	no	—
164	C₃₁×#124	—	2	2	no	—
165	C₃₁×#124	—	2	1	no	—
166	C₃₁×#124	—	2	1	no	—
167	C₃₁×#124	—	2	1	no	—
168	C₃₁×#124	C₂³	1	2	yes	—
169	C₃₁×#124	C₂³	1	2	yes	—
170	C₃₁×#124	C₂³	1	2	yes	—
171	C₃₁×#124	C₂³	1	2	yes	—
172	C₃₁×#124	C₂³	1	2	yes	—
173	C₃₁×#124	C₂³	1	2	yes	—
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	—	2	2	no	—
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	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×#121	—	2	1	no	—
198	C₃₁×#121	—	2	1	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	C₂³	1	2	yes	—
201	C₃₁×#120	—	2	2	no	—
202	C₄×Q₈×C₃₁	—	2	2	no	—
203	C₄×Q₈×C₃₁	—	2	1	no	—
204	C₄×Q₈×C₃₁	—	2	1	no	—
205	C₄×Q₈×C₃₁	—	2	1	no	—
206	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
207	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
208	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
214	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
215	C₄×D₄×C₃₁	—	2	1	no	—
216	C₄×D₄×C₃₁	—	2	1	no	—
217	C₄×D₄×C₃₁	—	2	1	no	—
218	C₄×D₄×C₃₁	—	2	1	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	—	2	2	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	1	no	—
223	C₄×D₄×C₃₁	C₂³	1	2	yes	—
224	C₄×D₄×C₃₁	C₂³	1	2	yes	—
225	C₄×D₄×C₃₁	C₂³	1	2	yes	—
226	C₄×D₄×C₃₁	C₂³	1	2	yes	—
227	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
230	C₃₁×#117	—	2	1	no	—
231	C₃₁×#117	—	2	2	no	—
232	C₃₁×#117	—	2	2	no	—
233	C₃₁×#117	—	2	2	no	—
234	C₃₁×#117	—	2	2	no	—
235	C₃₁×#117	—	2	1	no	—
236	C₃₁×#117	C₂³	1	1	yes	characteristic
237	C₃₁×#117	C₂³	1	1	yes	characteristic
238	C₃₁×#117	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
240	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
241	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
242	C₂×C₄²×C₃₁	—	2	1	no	—
243	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
244	C₃₁×#107	C₂³	1	2	yes	—
245	C₃₁×#107	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
255	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
258	C₃₁×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	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×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
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	C₃₁×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₃₁	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	#41×C₃₁	—	4	1	no	—
282	#41×C₃₁	—	4	1	no	—
283	#41×C₃₁	—	8	2	no	—
284	C₂×Q₈×C₃₁	—	2	1	no	—
285	C₂×Q₈×C₃₁	—	2	1	no	—
286	C₂×Q₈×C₃₁	—	2	2	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	—	2	1	no	—
289	C₂×Q₈×C₃₁	—	4	1	no	—
290	C₂×Q₈×C₃₁	—	4	1	no	—
291	C₂×Q₈×C₃₁	—	8	4	no	—
292	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
293	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
294	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
295	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
297	C₂×D₄×C₃₁	—	2	1	no	—
298	C₂×D₄×C₃₁	—	2	2	no	—
299	C₂×D₄×C₃₁	—	2	1	no	—
300	C₂×D₄×C₃₁	—	2	1	no	—
301	C₂×D₄×C₃₁	—	2	2	no	—
302	C₂×D₄×C₃₁	—	2	2	no	—
303	C₂×D₄×C₃₁	—	2	1	no	—
304	C₂×D₄×C₃₁	—	4	1	no	—
305	C₂×D₄×C₃₁	—	4	1	no	—
306	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₃₁	—	2	1	no	—
310	C₂²×C₄×C₃₁	—	2	1	no	—
311	C₂²×C₄×C₃₁	—	2	2	no	—
312	C₂²×C₄×C₃₁	—	2	1	no	—
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	Q₁₆×C₃₁	—	4	2	no	—
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	SD₁₆×C₃₁	—	4	2	no	—
329	SD₁₆×C₃₁	—	4	2	no	—
330	D₈×C₃₁	—	4	2	no	—
331	D₈×C₃₁	—	4	2	no	—
332	D₈×C₃₁	—	4	2	no	—
333	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
334	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
335	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
336	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₃₁	—	2	1	no	—
338	C₄⋊C₄×C₃₁	—	2	1	no	—
339	C₄⋊C₄×C₃₁	—	2	1	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	1	no	—
343	C₄⋊C₄×C₃₁	—	2	2	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	1	no	—
346	C₄⋊C₄×C₃₁	—	2	1	no	—
347	C₄⋊C₄×C₃₁	—	2	2	no	—
348	C₄⋊C₄×C₃₁	—	2	2	no	—
349	C₄⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
355	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂²⋊C₄×C₃₁	—	2	1	no	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	2	no	—
370	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
376	C₂²⋊C₄×C₃₁	—	2	1	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	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
391	C₄²×C₃₁	—	2	1	no	—
392	C₄²×C₃₁	—	2	1	no	—
393	C₄²×C₃₁	—	2	1	no	—
394	C₄²×C₃₁	—	2	2	no	—
395	C₄²×C₃₁	—	2	2	no	—
396	C₄²×C₃₁	—	2	2	no	—
397	C₄²×C₃₁	—	2	2	no	—
398	C₄²×C₃₁	—	2	2	no	—
399	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₃₁	C₂⁴	1	2	yes	—
402	C₄²×C₃₁	C₂⁴	1	2	yes	—
403	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
405	#61944	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂³×C₃₁	—	2	2	no	—
407	C₂³×C₃₁	—	2	2	no	—
408	C₂³×C₃₁	—	2	1	no	—
409	C₂³×C₃₁	—	4	2	no	—
410	C₂³×C₃₁	—	8	1	no	—
411	C₂³×C₃₁	—	8	1	no	—
412	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
413	Q₈×C₃₁	—	2	2	no	—
414	Q₈×C₃₁	—	2	1	no	—
415	Q₈×C₃₁	—	2	2	no	—
416	Q₈×C₃₁	—	2	2	no	—
417	Q₈×C₃₁	—	2	2	no	—
418	Q₈×C₃₁	—	2	1	no	—
419	Q₈×C₃₁	—	4	2	no	—
420	Q₈×C₃₁	—	4	2	no	—
421	Q₈×C₃₁	—	4	2	no	—
422	Q₈×C₃₁	—	4	2	no	—
423	Q₈×C₃₁	—	8	2	no	—
424	Q₈×C₃₁	—	8	2	no	—
425	Q₈×C₃₁	—	8	1	no	—
426	D₄×C₃₁	—	2	2	no	—
427	D₄×C₃₁	—	2	1	no	—
428	D₄×C₃₁	—	2	2	no	—
429	D₄×C₃₁	—	2	2	no	—
430	D₄×C₃₁	—	2	2	no	—
431	D₄×C₃₁	—	2	1	no	—
432	D₄×C₃₁	—	4	2	no	—
433	D₄×C₃₁	—	4	2	no	—
434	D₄×C₃₁	—	4	2	no	—
435	D₄×C₃₁	—	8	2	no	—
436	D₄×C₃₁	—	8	2	no	—
437	D₄×C₃₁	—	8	1	no	—
438	D₄×C₃₁	—	8	2	no	—
439	C₂×C₄×C₃₁	—	2	1	no	—
440	C₂×C₄×C₃₁	—	2	1	no	—
441	C₂×C₄×C₃₁	—	2	1	no	—
442	C₂×C₄×C₃₁	—	2	1	no	—
443	C₂×C₄×C₃₁	—	2	2	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	—	4	1	no	—
449	C₂×C₄×C₃₁	—	4	1	no	—
450	C₂×C₄×C₃₁	—	4	4	no	—
451	C₂×C₄×C₃₁	—	4	2	no	—
452	C₂×C₄×C₃₁	—	4	2	no	—
453	C₂×C₄×C₃₁	—	8	1	no	—
454	C₂×C₄×C₃₁	—	8	2	no	—
455	C₂×C₄×C₃₁	—	8	1	no	—
456	C₂×C₄×C₃₁	—	8	2	no	—
457	C₂×C₄×C₃₁	—	8	2	no	—
458	C₂×C₄×C₃₁	—	8	2	no	—
459	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
465	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
469	C₈×C₃₁	—	2	2	no	—
470	C₈×C₃₁	—	2	2	no	—
471	C₈×C₃₁	—	2	2	no	—
472	C₈×C₃₁	—	2	2	no	—
473	#3550	C₂×C₃₁	1	1	yes	characteristic, complemented
474	#3510	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#3403	C₂×C₃₁	1	2	yes	complemented
476	#3402	C₂×C₃₁	1	2	yes	complemented
477	#3401	C₂×C₃₁	1	2	yes	complemented
478	#3401	C₂×C₃₁	1	2	yes	complemented
479	#3375	C₂×C₃₁	1	2	yes	complemented
480	#3373	C₂×C₃₁	1	2	yes	complemented
481	#3369	C₂×C₃₁	1	2	yes	complemented
482	#3367	C₂×C₃₁	1	2	yes	complemented
483	#3225	C₂×C₃₁	1	2	yes	complemented
484	#3224	C₂×C₃₁	1	2	yes	complemented
485	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
486	#3213	C₂×C₃₁	1	1	yes	characteristic, complemented
487	#3121	C₂×C₃₁	1	2	yes	complemented
488	#3118	C₂×C₃₁	1	2	yes	complemented
489	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
490	#3115	C₂×C₃₁	1	1	yes	characteristic, complemented
491	#2987	C₂×C₃₁	1	1	yes	characteristic, complemented
492	C₂²×C₃₁	—	2	1	no	—
493	C₂²×C₃₁	—	2	1	no	—
494	C₂²×C₃₁	—	2	1	no	—
495	C₂²×C₃₁	—	4	2	no	—
496	C₂²×C₃₁	—	4	1	no	—
497	C₂²×C₃₁	—	4	2	no	—
498	C₂²×C₃₁	—	4	1	no	—
499	C₂²×C₃₁	—	4	2	no	—
500	C₂²×C₃₁	—	4	2	no	—
501	C₂²×C₃₁	—	4	1	no	—
502	C₂²×C₃₁	—	4	2	no	—
503	C₂²×C₃₁	—	4	2	no	—
504	C₂²×C₃₁	—	16	2	no	—
505	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
506	C₄×C₃₁	—	2	1	no	—
507	C₄×C₃₁	—	2	1	no	—
508	C₄×C₃₁	—	2	2	no	—
509	C₄×C₃₁	—	2	2	no	—
510	C₄×C₃₁	—	2	1	no	—
511	C₄×C₃₁	—	2	1	no	—
512	C₄×C₃₁	—	2	2	no	—
513	C₄×C₃₁	—	2	2	no	—
514	C₄×C₃₁	—	2	1	no	—
515	C₄×C₃₁	—	4	2	no	—
516	C₄×C₃₁	—	4	1	no	—
517	C₄×C₃₁	—	4	2	no	—
518	C₄×C₃₁	—	4	1	no	—
519	C₄×C₃₁	—	4	1	no	—
520	C₄×C₃₁	—	4	2	no	—
521	C₄×C₃₁	—	4	2	no	—
522	C₄×C₃₁	#585	1	1	yes	characteristic
523	C₄×C₃₁	#585	1	1	yes	characteristic
524	#563	—	2	1	no	—
525	#563	—	2	1	no	—
526	#559	C₂²×C₃₁	1	2	yes	—
527	#559	C₂²×C₃₁	1	2	yes	—
528	#559	C₂²×C₃₁	1	2	yes	complemented
529	Q₈²	C₂²×C₃₁	1	2	yes	complemented
530	#556	—	2	1	no	—
531	#556	C₂²×C₃₁	1	2	yes	—
532	#556	C₂²×C₃₁	1	2	yes	—
533	#556	C₂²×C₃₁	1	2	yes	complemented
534	#551	—	2	2	no	—
535	#551	—	2	2	no	—
536	D₄×Q₈	—	2	1	no	—
537	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
538	#542	—	2	1	no	—
539	#542	—	2	1	no	—
540	#542	—	2	2	no	—
541	#542	C₂²×C₃₁	1	2	yes	—
542	#542	C₂²×C₃₁	1	2	yes	—
543	#536	—	2	2	no	—
544	#536	C₂²×C₃₁	1	1	yes	characteristic
545	#535	C₂²×C₃₁	1	1	yes	characteristic
546	#533	C₂²×C₃₁	1	1	yes	characteristic
547	#533	C₂²×C₃₁	1	1	yes	characteristic
548	#532	C₂²×C₃₁	1	1	yes	characteristic
549	#529	—	2	1	no	—
550	#529	—	2	1	no	—
551	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
552	#519	C₂²×C₃₁	1	1	yes	characteristic
553	#518	C₂²×C₃₁	1	1	yes	characteristic
554	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
555	#497	C₂²×C₃₁	1	2	yes	—
556	#497	C₂²×C₃₁	1	2	yes	complemented
557	#496	C₂²×C₃₁	1	2	yes	—
558	#496	C₂²×C₃₁	1	2	yes	—
559	#495	C₂²×C₃₁	1	2	yes	—
560	#495	C₂²×C₃₁	1	2	yes	complemented
561	#489	C₂²×C₃₁	1	2	yes	—
562	#489	C₂²×C₃₁	1	2	yes	—
563	#489	C₂²×C₃₁	1	2	yes	—
564	#489	C₂²×C₃₁	1	2	yes	complemented
565	#487	C₂²×C₃₁	1	2	yes	complemented
566	#486	C₂²×C₃₁	1	2	yes	—
567	#485	C₂²×C₃₁	1	2	yes	—
568	#482	C₂²×C₃₁	1	2	yes	—
569	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
570	#477	C₂²×C₃₁	1	2	yes	complemented
571	#476	C₂²×C₃₁	1	2	yes	—
572	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
573	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
574	#475	C₂²×C₃₁	1	2	yes	complemented
575	#474	C₂²×C₃₁	1	2	yes	—
576	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
577	#464	C₂²×C₃₁	1	2	yes	—
578	#464	C₂²×C₃₁	1	2	yes	—
579	#464	C₂²×C₃₁	1	2	yes	—
580	#464	C₂²×C₃₁	1	2	yes	complemented
581	#464	C₂²×C₃₁	1	2	yes	complemented
582	#464	C₂²×C₃₁	1	2	yes	complemented
583	#463	C₂²×C₃₁	1	2	yes	—
584	#463	C₂²×C₃₁	1	2	yes	—
585	#463	C₂²×C₃₁	1	2	yes	—
586	#463	C₂²×C₃₁	1	2	yes	—
587	#463	C₂²×C₃₁	1	2	yes	—
588	#463	C₂²×C₃₁	1	2	yes	complemented
589	#462	C₂²×C₃₁	1	2	yes	complemented
590	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
591	#461	C₂²×C₃₁	1	2	yes	complemented
592	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
593	#460	C₂²×C₃₁	1	2	yes	—
594	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
595	#459	C₂²×C₃₁	1	2	yes	—
596	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
597	#452	C₂²×C₃₁	1	2	yes	—
598	#451	C₂²×C₃₁	1	2	yes	—
599	#450	C₂²×C₃₁	1	2	yes	—
600	#449	C₂²×C₃₁	1	2	yes	—
601	#448	C₂²×C₃₁	1	2	yes	—
602	#447	C₂²×C₃₁	1	2	yes	—
603	#446	C₂²×C₃₁	1	2	yes	complemented
604	#446	C₂²×C₃₁	1	2	yes	complemented
605	#446	C₂²×C₃₁	1	2	yes	complemented
606	#446	C₂²×C₃₁	1	2	yes	complemented
607	#442	C₂²×C₃₁	1	2	yes	—
608	#442	C₂²×C₃₁	1	2	yes	complemented
609	#441	C₂²×C₃₁	1	2	yes	complemented
610	#441	C₂²×C₃₁	1	2	yes	complemented
611	#440	C₂²×C₃₁	1	2	yes	—
612	#440	C₂²×C₃₁	1	2	yes	complemented
613	#440	C₂²×C₃₁	1	2	yes	complemented
614	#440	C₂²×C₃₁	1	2	yes	complemented
615	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
616	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
617	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
618	C₄×D₈	C₂²×C₃₁	1	2	yes	—
619	#433	C₂²×C₃₁	1	2	yes	—
620	#433	C₂²×C₃₁	1	2	yes	—
621	#432	C₂²×C₃₁	1	1	yes	characteristic
622	#432	C₂²×C₃₁	1	1	yes	characteristic
623	C₂×C₃₁	—	4	1	no	—
624	C₂×C₃₁	—	8	2	no	—
625	C₂×C₃₁	—	8	1	no	—
626	C₂×C₃₁	—	8	2	no	—
627	C₂×C₃₁	#3487	1	1	yes	characteristic
628	C₂×C₃₁	#3585	1	1	yes	characteristic
629	C₂×C₃₁	#3586	1	1	yes	characteristic
630	C₂×#41	—	2	1	no	—
631	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
632	C₂²×Q₈	—	2	2	no	—
633	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
634	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
635	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
636	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
637	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
638	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
639	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
640	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
641	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
642	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
643	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
644	C₂×D₈	C₂³×C₃₁	1	2	yes	—
645	C₂×D₈	C₂³×C₃₁	1	2	yes	—
646	C₂×D₈	C₂³×C₃₁	1	2	yes	—
647	C₄⋊Q₈	—	2	2	no	—
648	C₄⋊Q₈	—	2	2	no	—
649	C₄⋊Q₈	—	2	2	no	—
650	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
651	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
653	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
654	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
655	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
656	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
657	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
658	#127	C₂³×C₃₁	1	1	yes	characteristic
659	#127	C₂³×C₃₁	1	2	yes	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	—	2	2	no	—
663	#126	—	2	2	no	—
664	#126	—	2	2	no	—
665	#126	—	2	2	no	—
666	#126	—	2	2	no	—
667	#126	—	2	2	no	—
668	#125	—	2	1	no	—
669	#125	D₄×C₃₁	1	1	yes	characteristic
670	#125	D₄×C₃₁	1	1	yes	characteristic
671	#124	—	2	2	no	—
672	#124	—	2	2	no	—
673	#124	—	2	2	no	—
674	#124	—	2	2	no	—
675	#124	—	2	2	no	—
676	#124	—	2	1	no	—
677	#124	—	2	1	no	—
678	#124	—	2	1	no	—
679	#124	C₂³×C₃₁	1	2	yes	—
680	#124	C₂³×C₃₁	1	2	yes	—
681	#124	C₂³×C₃₁	1	2	yes	—
682	#124	C₂³×C₃₁	1	2	yes	—
683	#124	C₂³×C₃₁	1	2	yes	—
684	#124	C₂³×C₃₁	1	2	yes	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	—	2	2	no	—
689	#123	—	2	2	no	—
690	#123	—	2	2	no	—
691	#123	—	2	2	no	—
692	#123	—	2	2	no	—
693	#123	—	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	1	no	—
698	C₂²⋊Q₈	—	2	1	no	—
699	C₂²⋊Q₈	—	2	1	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	2	no	—
705	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
706	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
707	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
708	#121	—	2	1	no	—
709	#121	—	2	1	no	—
710	#121	—	2	1	no	—
711	#121	C₂³×C₃₁	1	2	yes	—
712	#120	—	2	2	no	—
713	C₄×Q₈	—	2	2	no	—
714	C₄×Q₈	—	2	1	no	—
715	C₄×Q₈	—	2	1	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
719	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
720	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
721	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
722	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
723	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
724	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
725	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	—	2	2	no	—
731	C₄×D₄	—	2	2	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	—	2	1	no	—
734	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
735	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
736	C₄×D₄	C₂³×C₃₁	1	2	yes	—
737	C₄×D₄	C₂³×C₃₁	1	2	yes	—
738	C₄×D₄	C₂³×C₃₁	1	2	yes	—
739	C₄×D₄	C₂³×C₃₁	1	2	yes	—
740	C₄×D₄	C₂³×C₃₁	1	2	yes	—
741	#117	—	2	1	no	—
742	#117	—	2	2	no	—
743	#117	—	2	2	no	—
744	#117	—	2	2	no	—
745	#117	—	2	2	no	—
746	#117	—	2	1	no	—
747	#117	C₂³×C₃₁	1	1	yes	characteristic
748	#117	C₂³×C₃₁	1	1	yes	characteristic
749	#117	C₂³×C₃₁	1	1	yes	characteristic
750	C₂×C₂²⋊C₄	—	2	1	no	—
751	C₂×C₂²⋊C₄	—	2	1	no	—
752	C₂×C₂²⋊C₄	—	2	2	no	—
753	C₂×C₄²	—	2	1	no	—
754	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
755	#107	C₂³×C₃₁	1	2	yes	—
756	#107	C₂³×C₃₁	1	2	yes	—
757	#106	C₂³×C₃₁	1	2	yes	—
758	#106	C₂³×C₃₁	1	2	yes	—
759	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
760	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
761	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
762	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
764	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
765	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
766	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
767	#103	C₂³×C₃₁	1	2	yes	—
768	#103	C₂³×C₃₁	1	2	yes	—
769	#103	C₂³×C₃₁	1	2	yes	—
770	#103	C₂³×C₃₁	1	2	yes	—
771	#103	C₂³×C₃₁	1	2	yes	—
772	#103	C₂³×C₃₁	1	2	yes	—
773	#103	C₂³×C₃₁	1	2	yes	—
774	#103	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	#102	C₂³×C₃₁	1	2	yes	—
779	#102	C₂³×C₃₁	1	2	yes	—
780	#102	C₂³×C₃₁	1	2	yes	—
781	#102	C₂³×C₃₁	1	2	yes	—
782	#102	C₂³×C₃₁	1	2	yes	—
783	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
785	#97	C₂³×C₃₁	1	2	yes	—
786	#97	C₂³×C₃₁	1	2	yes	—
787	#97	C₂³×C₃₁	1	2	yes	—
788	#97	C₂³×C₃₁	1	2	yes	—
789	C₄×C₈	C₂³×C₃₁	1	2	yes	—
790	C₄×C₈	C₂³×C₃₁	1	2	yes	—
791	C₃₁	#61944	1	1	yes	characteristic, direct product factor, Sylow
792	C₂⁴	—	2	1	no	—
793	#41	—	4	1	no	—
794	#41	—	4	1	no	—
795	#41	—	8	2	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	2	no	—
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	2	1	no	—
801	C₂×Q₈	—	4	1	no	—
802	C₂×Q₈	—	4	1	no	—
803	C₂×Q₈	—	8	4	no	—
804	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
805	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
806	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
807	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
808	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	4	1	no	—
817	C₂×D₄	—	4	1	no	—
818	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
819	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
820	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
831	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
833	Q₁₆	—	4	2	no	—
834	Q₁₆	—	4	2	no	—
835	Q₁₆	—	4	2	no	—
836	SD₁₆	—	4	2	no	—
837	SD₁₆	—	4	2	no	—
838	SD₁₆	—	4	2	no	—
839	SD₁₆	—	4	2	no	—
840	SD₁₆	—	4	2	no	—
841	SD₁₆	—	4	2	no	—
842	D₈	—	4	2	no	—
843	D₈	—	4	2	no	—
844	D₈	—	4	2	no	—
845	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
846	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
847	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
848	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	1	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	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
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	1	yes	characteristic
869	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
870	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
871	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
872	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
873	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
874	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
875	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
876	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
877	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
878	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
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	1	no	—
888	C₂²⋊C₄	—	2	1	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	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
902	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
903	C₄²	—	2	1	no	—
904	C₄²	—	2	1	no	—
905	C₄²	—	2	1	no	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
912	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
913	C₄²	C₂⁴×C₃₁	1	2	yes	—
914	C₄²	C₂⁴×C₃₁	1	2	yes	—
915	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₂³	—	2	2	no	—
918	C₂³	—	2	2	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	4	2	no	—
921	C₂³	—	8	1	no	—
922	C₂³	—	8	1	no	—
923	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
924	Q₈	—	2	2	no	—
925	Q₈	—	2	1	no	—
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	2	2	no	—
929	Q₈	—	2	1	no	—
930	Q₈	—	4	2	no	—
931	Q₈	—	4	2	no	—
932	Q₈	—	4	2	no	—
933	Q₈	—	4	2	no	—
934	Q₈	—	8	2	no	—
935	Q₈	—	8	2	no	—
936	Q₈	—	8	1	no	—
937	D₄	—	2	2	no	—
938	D₄	—	2	1	no	—
939	D₄	—	2	2	no	—
940	D₄	—	2	2	no	—
941	D₄	—	2	2	no	—
942	D₄	—	2	1	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	2	no	—
945	D₄	—	4	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	—	8	1	no	—
949	D₄	—	8	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	4	1	no	—
960	C₂×C₄	—	4	1	no	—
961	C₂×C₄	—	4	4	no	—
962	C₂×C₄	—	4	2	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	8	1	no	—
965	C₂×C₄	—	8	2	no	—
966	C₂×C₄	—	8	1	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
971	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
972	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
973	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
974	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
975	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
976	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
977	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
979	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
980	C₈	—	2	2	no	—
981	C₈	—	2	2	no	—
982	C₈	—	2	2	no	—
983	C₈	—	2	2	no	—
984	C₂²	—	2	1	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	1	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	—	4	2	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	2	no	—
996	C₂²	—	16	2	no	—
997	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	2	no	—
1002	C₄	—	2	2	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	2	no	—
1007	C₄	—	4	1	no	—
1008	C₄	—	4	2	no	—
1009	C₄	—	4	2	no	—
1010	C₄	—	4	2	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	1	no	—
1014	C₄	C₃₁×#585	1	1	yes	characteristic
1015	C₄	C₃₁×#585	1	1	yes	characteristic
1016	C₂	—	4	1	no	—
1017	C₂	—	8	2	no	—
1018	C₂	—	8	1	no	—
1019	C₂	—	8	2	no	—
1020	C₂	C₃₁×#3487	1	1	yes	characteristic
1021	C₂	C₃₁×#3585	1	1	yes	characteristic
1022	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 ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3550	C₂	semidirect
2. C₃₁×#3510	C₂	semidirect
3. C₃₁×#3403	C₂	semidirect
4. C₃₁×#3402	C₂	semidirect
5. C₃₁×#3401	C₂	semidirect
6. C₃₁×#3401	C₂	semidirect
7. C₃₁×#3375	C₂	semidirect
8. C₃₁×#3373	C₂	semidirect
9. C₃₁×#3369	C₂	semidirect
10. C₃₁×#3367	C₂	semidirect
11. C₃₁×#3225	C₂	semidirect
12. C₃₁×#3224	C₂	semidirect
13. C₃₁×#3215	C₂	semidirect
14. C₃₁×#3213	C₂	semidirect
15. C₃₁×#3121	C₂	semidirect
16. C₃₁×#3118	C₂	semidirect
17. C₃₁×#3116	C₂	semidirect
18. C₃₁×#3115	C₂	semidirect
19. C₃₁×#2987	C₂	semidirect
24. C₃₁×#559	C₂²	semidirect
25. Q₈²×C₃₁	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
33. D₄×Q₈×C₃₁	C₂²	semidirect
52. C₃₁×#497	C₂²	semidirect
56. C₃₁×#495	C₂²	semidirect
60. C₃₁×#489	C₂²	semidirect
61. C₃₁×#487	C₂²	semidirect
65. C₃₁×#477	C₂²	semidirect
66. C₃₁×#477	C₂²	semidirect
68. C₃₁×#476	C₂²	semidirect
69. C₃₁×#475	C₂²	semidirect
70. C₃₁×#475	C₂²	semidirect
72. C₃₁×#474	C₂²	semidirect
76. C₃₁×#464	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
84. C₃₁×#463	C₂²	semidirect
85. C₃₁×#462	C₂²	semidirect
86. C₃₁×#462	C₂²	semidirect
87. C₃₁×#461	C₂²	semidirect
88. C₃₁×#461	C₂²	semidirect
90. C₃₁×#460	C₂²	semidirect
92. C₃₁×#459	C₂²	semidirect
99. C₃₁×#446	C₂²	semidirect
100. C₃₁×#446	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#446	C₂²	semidirect
104. C₃₁×#442	C₂²	semidirect
105. C₃₁×#441	C₂²	semidirect
106. C₃₁×#441	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
109. C₃₁×#440	C₂²	semidirect
110. C₃₁×#440	C₂²	semidirect
111. C₄×Q₁₆×C₃₁	C₂²	semidirect
113. C₄×SD₁₆×C₃₁	C₂²	semidirect
405. #61944	C₃₁	direct (N × H)
473. #3550	C₂×C₃₁	semidirect
474. #3510	C₂×C₃₁	semidirect
475. #3403	C₂×C₃₁	semidirect
476. #3402	C₂×C₃₁	semidirect
477. #3401	C₂×C₃₁	semidirect
478. #3401	C₂×C₃₁	semidirect
479. #3375	C₂×C₃₁	semidirect
480. #3373	C₂×C₃₁	semidirect
481. #3369	C₂×C₃₁	semidirect
482. #3367	C₂×C₃₁	semidirect
483. #3225	C₂×C₃₁	semidirect
484. #3224	C₂×C₃₁	semidirect
485. #3215	C₂×C₃₁	semidirect
486. #3213	C₂×C₃₁	semidirect
487. #3121	C₂×C₃₁	semidirect
488. #3118	C₂×C₃₁	semidirect
489. #3116	C₂×C₃₁	semidirect
490. #3115	C₂×C₃₁	semidirect
491. #2987	C₂×C₃₁	semidirect
528. #559	C₂²×C₃₁	semidirect
529. Q₈²	C₂²×C₃₁	semidirect
533. #556	C₂²×C₃₁	semidirect
537. D₄×Q₈	C₂²×C₃₁	semidirect
556. #497	C₂²×C₃₁	semidirect
560. #495	C₂²×C₃₁	semidirect
564. #489	C₂²×C₃₁	semidirect
565. #487	C₂²×C₃₁	semidirect
569. #477	C₂²×C₃₁	semidirect
570. #477	C₂²×C₃₁	semidirect
572. #476	C₂²×C₃₁	semidirect
573. #475	C₂²×C₃₁	semidirect
574. #475	C₂²×C₃₁	semidirect
576. #474	C₂²×C₃₁	semidirect
580. #464	C₂²×C₃₁	semidirect
581. #464	C₂²×C₃₁	semidirect
582. #464	C₂²×C₃₁	semidirect
588. #463	C₂²×C₃₁	semidirect
589. #462	C₂²×C₃₁	semidirect
590. #462	C₂²×C₃₁	semidirect
591. #461	C₂²×C₃₁	semidirect
592. #461	C₂²×C₃₁	semidirect
594. #460	C₂²×C₃₁	semidirect
596. #459	C₂²×C₃₁	semidirect
603. #446	C₂²×C₃₁	semidirect
604. #446	C₂²×C₃₁	semidirect
605. #446	C₂²×C₃₁	semidirect
606. #446	C₂²×C₃₁	semidirect
608. #442	C₂²×C₃₁	semidirect
609. #441	C₂²×C₃₁	semidirect
610. #441	C₂²×C₃₁	semidirect
612. #440	C₂²×C₃₁	semidirect
613. #440	C₂²×C₃₁	semidirect
614. #440	C₂²×C₃₁	semidirect
615. C₄×Q₁₆	C₂²×C₃₁	semidirect
617. C₄×SD₁₆	C₂²×C₃₁	semidirect
791. C₃₁	#61944	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×#3550	2
C₃₁×#3510	2
C₃₁×#3403	2
C₃₁×#3402	2
C₃₁×#3401	2
C₃₁×#3375	2
C₃₁×#3373	2
C₃₁×#3369	2
C₃₁×#3367	2
C₃₁×#3225	2
C₃₁×#3224	2
C₃₁×#3215	2
C₃₁×#3213	2
C₃₁×#3121	2
C₃₁×#3118	2
C₃₁×#3116	2
C₃₁×#3115	2
C₃₁×#2987	2
#61944	31

Subgroups — C31×#61944 #21518703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61944 #21518703