Subgroups — C₃₁×#61766 #21518525

Order 7936.

1858 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3337	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3295	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3188	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3188	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3096	C₂	1	2	yes	maximal, complemented
17	C₂×C₃₁×#481	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2977	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#560	—	2	2	no	—
21	C₃₁×#554	—	2	1	no	—
22	C₃₁×#554	C₂²	1	2	yes	complemented
23	C₃₁×#553	—	2	1	no	—
24	C₃₁×#553	C₂²	1	2	yes	—
25	C₃₁×#553	C₂²	1	2	yes	—
26	C₃₁×#553	C₂²	1	2	yes	complemented
27	C₃₁×#552	—	2	1	no	—
28	C₃₁×#552	C₂²	1	2	yes	complemented
29	C₃₁×#547	—	2	1	no	—
30	C₃₁×#547	C₂²	1	2	yes	complemented
31	D₄²×C₃₁	—	2	2	no	—
32	D₄²×C₃₁	C₂²	1	2	yes	—
33	D₄²×C₃₁	C₂²	1	2	yes	—
34	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#540	C₂²	1	2	yes	—
36	C₃₁×#539	—	2	2	no	—
37	C₃₁×#538	—	2	1	no	—
38	C₃₁×#538	—	2	1	no	—
39	C₃₁×#537	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#535	C₂²	1	2	yes	—
41	C₃₁×#534	—	2	1	no	—
42	C₃₁×#534	—	2	1	no	—
43	C₃₁×#525	—	2	2	no	—
44	C₃₁×#525	C₂²	1	1	yes	characteristic
45	C₃₁×#525	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
48	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#499	C₂²	1	2	yes	complemented
53	C₃₁×#490	C₂²	1	2	yes	complemented
54	C₃₁×#486	C₂²	1	2	yes	complemented
55	C₃₁×#485	C₂²	1	2	yes	complemented
56	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#482	C₂²	1	2	yes	complemented
59	C₃₁×#482	C₂²	1	2	yes	complemented
60	C₃₁×#482	C₂²	1	2	yes	complemented
61	C₃₁×#482	C₂²	1	2	yes	complemented
62	C₃₁×#482	C₂²	1	2	yes	complemented
63	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#481	C₂²	1	2	yes	complemented
65	C₃₁×#481	C₂²	1	2	yes	complemented
66	C₃₁×#481	C₂²	1	2	yes	complemented
67	C₃₁×#481	C₂²	1	2	yes	complemented
68	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#481	C₂²	1	2	yes	complemented
70	C₃₁×#480	C₂²	1	2	yes	complemented
71	C₃₁×#480	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#480	C₂²	1	2	yes	complemented
74	C₃₁×#480	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#478	C₂²	1	2	yes	complemented
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#476	C₂²	1	2	yes	complemented
80	C₃₁×#474	C₂²	1	2	yes	complemented
81	C₃₁×#469	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#466	C₂²	1	2	yes	complemented
84	C₃₁×#466	C₂²	1	2	yes	complemented
85	C₃₁×#466	C₂²	1	2	yes	complemented
86	C₃₁×#465	C₂²	1	2	yes	complemented
87	C₃₁×#465	C₂²	1	2	yes	complemented
88	C₃₁×#465	C₂²	1	2	yes	complemented
89	C₃₁×#460	C₂²	1	2	yes	complemented
90	C₃₁×#459	C₂²	1	2	yes	complemented
91	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#450	C₂²	1	2	yes	complemented
94	C₃₁×#449	C₂²	1	2	yes	complemented
95	C₃₁×#449	C₂²	1	2	yes	complemented
96	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#447	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#447	C₂²	1	2	yes	complemented
99	C₃₁×#442	C₂²	1	2	yes	complemented
100	C₃₁×#440	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
103	C₃₁×#435	C₂²	1	2	yes	complemented
104	C₃₁×#435	C₂²	1	2	yes	complemented
105	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
106	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
107	C₃₁×#433	C₂²	1	2	yes	complemented
108	C₃₁×#428	C₂²	1	2	yes	complemented
109	C₃₁×#427	C₂²	1	2	yes	complemented
110	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
111	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
112	C₃₁×#418	C₂²	1	2	yes	complemented
113	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
114	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
115	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
116	C₃₁×#408	C₂²	1	2	yes	complemented
117	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₃₁	—	2	2	no	—
120	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₃₁	—	2	1	no	—
123	C₂²×D₄×C₃₁	—	2	1	no	—
124	C₂²×D₄×C₃₁	—	2	2	no	—
125	C₂²×D₄×C₃₁	—	2	2	no	—
126	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₃₁	—	2	1	no	—
130	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
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×M₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
137	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
138	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
139	C₃₁×C₄⋊Q₈	—	2	1	no	—
140	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₃₁×#127	—	2	2	no	—
142	C₃₁×#127	C₂³	1	2	yes	—
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	2	no	—
149	C₃₁×#125	—	2	1	no	—
150	C₃₁×#125	C₂³	1	2	yes	—
151	C₃₁×#125	C₂³	1	2	yes	—
152	C₃₁×#124	—	2	2	no	—
153	C₃₁×#123	—	2	2	no	—
154	C₃₁×#123	—	2	1	no	—
155	C₃₁×#123	—	2	2	no	—
156	C₃₁×#123	—	2	2	no	—
157	C₃₁×#123	—	2	2	no	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	2	no	—
162	C₃₁×#123	D₄	1	2	yes	—
163	C₃₁×C₂²⋊Q₈	—	2	1	no	—
164	C₃₁×C₂²⋊Q₈	—	2	2	no	—
165	C₃₁×C₂²⋊Q₈	—	2	2	no	—
166	C₃₁×C₂²⋊Q₈	—	2	2	no	—
167	C₃₁×C₂²⋊Q₈	—	2	2	no	—
168	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
169	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
170	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
171	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
172	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×#121	—	2	2	no	—
174	C₃₁×#121	—	2	2	no	—
175	C₃₁×#121	—	2	2	no	—
176	C₃₁×#121	—	2	2	no	—
177	C₃₁×#121	—	2	1	no	—
178	C₃₁×#121	—	2	1	no	—
179	C₃₁×#121	—	2	1	no	—
180	C₃₁×#121	—	2	1	no	—
181	C₃₁×#121	—	2	1	no	—
182	C₃₁×#121	—	2	2	no	—
183	C₃₁×#121	—	2	2	no	—
184	C₃₁×#121	—	2	2	no	—
185	C₃₁×#121	—	2	2	no	—
186	C₃₁×#121	D₄	1	1	yes	characteristic
187	C₃₁×#121	D₄	1	1	yes	characteristic
188	C₃₁×#121	C₂³	1	1	yes	characteristic
189	C₃₁×#121	C₂³	1	1	yes	characteristic
190	C₃₁×#121	C₂³	1	2	yes	—
191	C₃₁×#121	C₂³	1	2	yes	—
192	C₃₁×#121	C₂³	1	2	yes	—
193	C₃₁×#121	C₂³	1	2	yes	—
194	C₃₁×#121	C₂³	1	2	yes	—
195	C₃₁×#121	C₂³	1	2	yes	—
196	C₃₁×#121	C₂³	1	2	yes	—
197	C₃₁×#120	—	2	1	no	—
198	C₃₁×#120	—	2	2	no	—
199	C₃₁×#120	—	2	2	no	—
200	C₃₁×#120	—	2	2	no	—
201	C₃₁×#120	—	2	2	no	—
202	C₃₁×#120	—	2	2	no	—
203	C₃₁×#120	—	2	2	no	—
204	C₃₁×#120	D₄	1	2	yes	—
205	C₄×Q₈×C₃₁	—	2	1	no	—
206	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
207	C₄×D₄×C₃₁	—	2	2	no	—
208	C₄×D₄×C₃₁	—	2	1	no	—
209	C₄×D₄×C₃₁	—	2	2	no	—
210	C₄×D₄×C₃₁	—	2	1	no	—
211	C₄×D₄×C₃₁	—	2	1	no	—
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	—	2	2	no	—
214	C₄×D₄×C₃₁	—	2	2	no	—
215	C₄×D₄×C₃₁	—	2	2	no	—
216	C₄×D₄×C₃₁	C₂³	1	2	yes	—
217	C₄×D₄×C₃₁	C₂³	1	2	yes	—
218	C₄×D₄×C₃₁	C₂³	1	2	yes	—
219	C₄×D₄×C₃₁	C₂³	1	2	yes	—
220	C₄×D₄×C₃₁	C₂³	1	2	yes	—
221	C₃₁×#117	—	2	1	no	—
222	C₃₁×#117	—	2	2	no	—
223	C₃₁×#117	C₂³	1	2	yes	—
224	C₃₁×#117	C₂³	1	2	yes	—
225	C₃₁×#117	C₂³	1	1	yes	characteristic
226	C₃₁×#117	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
228	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
229	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
230	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
240	C₃₁×#107	C₂³	1	2	yes	—
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×#107	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×#106	C₂³	1	2	yes	—
249	C₃₁×#106	C₂³	1	2	yes	—
250	C₃₁×#106	C₂³	1	2	yes	—
251	C₃₁×#106	C₂³	1	2	yes	—
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#102	C₂³	1	2	yes	—
257	C₃₁×#102	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	2	yes	—
271	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
272	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₃₁×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	C₂⁴×C₃₁	—	2	1	no	—
282	C₂⁴×C₃₁	—	2	2	no	—
283	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
284	#41×C₃₁	—	4	2	no	—
285	#41×C₃₁	—	4	2	no	—
286	#41×C₃₁	—	8	4	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
289	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
290	C₂×D₄×C₃₁	—	2	1	no	—
291	C₂×D₄×C₃₁	—	2	1	no	—
292	C₂×D₄×C₃₁	—	2	2	no	—
293	C₂×D₄×C₃₁	—	2	2	no	—
294	C₂×D₄×C₃₁	—	2	1	no	—
295	C₂×D₄×C₃₁	—	2	2	no	—
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	2	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	—	4	2	no	—
309	C₂×D₄×C₃₁	—	8	4	no	—
310	C₂×D₄×C₃₁	—	8	4	no	—
311	C₂×D₄×C₃₁	—	8	2	no	—
312	C₂×D₄×C₃₁	—	8	2	no	—
313	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
315	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
317	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
318	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
319	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₃₁	—	2	2	no	—
321	C₂²×C₄×C₃₁	—	2	1	no	—
322	C₂²×C₄×C₃₁	—	2	1	no	—
323	C₂²×C₄×C₃₁	—	2	1	no	—
324	C₂²×C₄×C₃₁	—	2	2	no	—
325	C₂²×C₄×C₃₁	—	2	1	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	—	2	1	no	—
328	C₂²×C₄×C₃₁	—	2	2	no	—
329	C₂²×C₄×C₃₁	—	2	2	no	—
330	C₂²×C₄×C₃₁	—	2	2	no	—
331	C₂²×C₄×C₃₁	—	4	2	no	—
332	C₂²×C₄×C₃₁	—	8	2	no	—
333	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
340	SD₁₆×C₃₁	—	4	2	no	—
341	SD₁₆×C₃₁	—	4	2	no	—
342	D₈×C₃₁	—	4	2	no	—
343	D₈×C₃₁	—	4	2	no	—
344	M₁₆×C₃₁	—	4	2	no	—
345	C₂×C₈×C₃₁	—	4	2	no	—
346	C₂×C₈×C₃₁	—	4	2	no	—
347	C₂×C₈×C₃₁	—	4	2	no	—
348	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
349	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
350	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
351	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
352	C₄⋊C₄×C₃₁	—	2	1	no	—
353	C₄⋊C₄×C₃₁	—	2	1	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	1	no	—
359	C₄⋊C₄×C₃₁	—	2	1	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	1	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	1	no	—
368	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
369	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
372	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
373	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	1	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	1	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	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	1	no	—
393	C₂²⋊C₄×C₃₁	—	2	1	no	—
394	C₂²⋊C₄×C₃₁	—	2	2	no	—
395	C₂²⋊C₄×C₃₁	—	2	2	no	—
396	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₄²×C₃₁	—	2	2	no	—
402	C₄²×C₃₁	—	2	2	no	—
403	C₄²×C₃₁	—	2	1	no	—
404	C₄²×C₃₁	—	2	2	no	—
405	C₄²×C₃₁	C₂⁴	1	2	yes	—
406	#61766	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂³×C₃₁	—	2	2	no	—
408	C₂³×C₃₁	—	2	2	no	—
409	C₂³×C₃₁	—	2	1	no	—
410	C₂³×C₃₁	—	2	2	no	—
411	C₂³×C₃₁	—	2	2	no	—
412	C₂³×C₃₁	—	4	1	no	—
413	C₂³×C₃₁	—	4	2	no	—
414	C₂³×C₃₁	—	4	2	no	—
415	C₂³×C₃₁	—	8	1	no	—
416	C₂³×C₃₁	—	8	1	no	—
417	C₂³×C₃₁	—	8	2	no	—
418	C₂³×C₃₁	—	8	1	no	—
419	C₂³×C₃₁	—	8	1	no	—
420	C₂³×C₃₁	—	8	2	no	—
421	C₂³×C₃₁	—	8	2	no	—
422	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
423	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
424	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
425	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
426	Q₈×C₃₁	—	2	2	no	—
427	Q₈×C₃₁	—	4	1	no	—
428	Q₈×C₃₁	—	8	2	no	—
429	D₄×C₃₁	—	2	4	no	—
430	D₄×C₃₁	—	2	4	no	—
431	D₄×C₃₁	—	2	2	no	—
432	D₄×C₃₁	—	2	2	no	—
433	D₄×C₃₁	—	2	2	no	—
434	D₄×C₃₁	—	2	2	no	—
435	D₄×C₃₁	—	2	2	no	—
436	D₄×C₃₁	—	4	1	no	—
437	D₄×C₃₁	—	4	2	no	—
438	D₄×C₃₁	—	4	2	no	—
439	D₄×C₃₁	—	4	4	no	—
440	D₄×C₃₁	—	4	2	no	—
441	D₄×C₃₁	—	4	2	no	—
442	D₄×C₃₁	—	4	4	no	—
443	D₄×C₃₁	—	8	1	no	—
444	D₄×C₃₁	—	8	1	no	—
445	D₄×C₃₁	—	8	2	no	—
446	D₄×C₃₁	—	8	2	no	—
447	D₄×C₃₁	—	8	2	no	—
448	D₄×C₃₁	—	8	2	no	—
449	D₄×C₃₁	—	8	2	no	—
450	D₄×C₃₁	—	8	2	no	—
451	D₄×C₃₁	—	8	2	no	—
452	D₄×C₃₁	—	8	2	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	2	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	2	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	2	1	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	2	no	—
463	C₂×C₄×C₃₁	—	2	1	no	—
464	C₂×C₄×C₃₁	—	2	2	no	—
465	C₂×C₄×C₃₁	—	4	1	no	—
466	C₂×C₄×C₃₁	—	4	1	no	—
467	C₂×C₄×C₃₁	—	4	1	no	—
468	C₂×C₄×C₃₁	—	4	2	no	—
469	C₂×C₄×C₃₁	—	4	4	no	—
470	C₂×C₄×C₃₁	—	8	2	no	—
471	C₂×C₄×C₃₁	—	8	2	no	—
472	C₂×C₄×C₃₁	—	8	2	no	—
473	C₂×C₄×C₃₁	—	8	1	no	—
474	C₂×C₄×C₃₁	—	8	2	no	—
475	C₂×C₄×C₃₁	—	8	1	no	—
476	C₂×C₄×C₃₁	—	8	1	no	—
477	C₂×C₄×C₃₁	—	8	1	no	—
478	C₂×C₄×C₃₁	—	8	2	no	—
479	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
486	C₈×C₃₁	—	2	2	no	—
487	C₈×C₃₁	—	2	2	no	—
488	C₈×C₃₁	—	2	2	no	—
489	C₈×C₃₁	—	2	2	no	—
490	#3537	C₂×C₃₁	1	1	yes	characteristic, complemented
491	#3492	C₂×C₃₁	1	1	yes	characteristic, complemented
492	#3346	C₂×C₃₁	1	2	yes	complemented
493	#3345	C₂×C₃₁	1	2	yes	complemented
494	#3339	C₂×C₃₁	1	2	yes	complemented
495	#3337	C₂×C₃₁	1	2	yes	complemented
496	#3318	C₂×C₃₁	1	2	yes	complemented
497	#3310	C₂×C₃₁	1	2	yes	complemented
498	#3295	C₂×C₃₁	1	2	yes	complemented
499	#3294	C₂×C₃₁	1	2	yes	complemented
500	#3241	C₂×C₃₁	1	2	yes	complemented
501	#3198	C₂×C₃₁	1	2	yes	complemented
502	#3188	C₂×C₃₁	1	1	yes	characteristic, complemented
503	#3188	C₂×C₃₁	1	1	yes	characteristic, complemented
504	#3119	C₂×C₃₁	1	2	yes	complemented
505	#3096	C₂×C₃₁	1	2	yes	complemented
506	C₂×#481	C₂×C₃₁	1	1	yes	characteristic, complemented
507	C₂×#480	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#2977	C₂×C₃₁	1	1	yes	characteristic, complemented
509	C₂²×C₃₁	—	2	1	no	—
510	C₂²×C₃₁	—	2	1	no	—
511	C₂²×C₃₁	—	2	1	no	—
512	C₂²×C₃₁	—	2	1	no	—
513	C₂²×C₃₁	—	2	1	no	—
514	C₂²×C₃₁	—	2	2	no	—
515	C₂²×C₃₁	—	2	1	no	—
516	C₂²×C₃₁	—	2	2	no	—
517	C₂²×C₃₁	—	2	2	no	—
518	C₂²×C₃₁	—	2	1	no	—
519	C₂²×C₃₁	—	4	4	no	—
520	C₂²×C₃₁	—	4	1	no	—
521	C₂²×C₃₁	—	4	2	no	—
522	C₂²×C₃₁	—	4	2	no	—
523	C₂²×C₃₁	—	4	1	no	—
524	C₂²×C₃₁	—	4	2	no	—
525	C₂²×C₃₁	—	4	2	no	—
526	C₂²×C₃₁	—	4	2	no	—
527	C₂²×C₃₁	—	4	2	no	—
528	C₂²×C₃₁	—	4	1	no	—
529	C₂²×C₃₁	—	16	2	no	—
530	C₂²×C₃₁	—	16	2	no	—
531	C₂²×C₃₁	—	16	4	no	—
532	C₂²×C₃₁	#576	1	2	yes	—
533	C₂²×C₃₁	#577	1	2	yes	—
534	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
535	C₄×C₃₁	—	2	1	no	—
536	C₄×C₃₁	—	2	1	no	—
537	C₄×C₃₁	—	2	1	no	—
538	C₄×C₃₁	—	2	2	no	—
539	C₄×C₃₁	—	2	2	no	—
540	C₄×C₃₁	—	2	2	no	—
541	C₄×C₃₁	—	4	1	no	—
542	C₄×C₃₁	—	4	2	no	—
543	C₄×C₃₁	—	4	2	no	—
544	C₄×C₃₁	—	4	2	no	—
545	C₄×C₃₁	—	4	1	no	—
546	C₄×C₃₁	—	4	2	no	—
547	C₄×C₃₁	—	4	1	no	—
548	C₄×C₃₁	#585	1	2	yes	—
549	#560	—	2	2	no	—
550	#554	—	2	1	no	—
551	#554	C₂²×C₃₁	1	2	yes	complemented
552	#553	—	2	1	no	—
553	#553	C₂²×C₃₁	1	2	yes	—
554	#553	C₂²×C₃₁	1	2	yes	—
555	#553	C₂²×C₃₁	1	2	yes	complemented
556	#552	—	2	1	no	—
557	#552	C₂²×C₃₁	1	2	yes	complemented
558	#547	—	2	1	no	—
559	#547	C₂²×C₃₁	1	2	yes	complemented
560	D₄²	—	2	2	no	—
561	D₄²	C₂²×C₃₁	1	2	yes	—
562	D₄²	C₂²×C₃₁	1	2	yes	—
563	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
564	#540	C₂²×C₃₁	1	2	yes	—
565	#539	—	2	2	no	—
566	#538	—	2	1	no	—
567	#538	—	2	1	no	—
568	#537	C₂²×C₃₁	1	1	yes	characteristic, complemented
569	#535	C₂²×C₃₁	1	2	yes	—
570	#534	—	2	1	no	—
571	#534	—	2	1	no	—
572	#525	—	2	2	no	—
573	#525	C₂²×C₃₁	1	1	yes	characteristic
574	#525	C₂²×C₃₁	1	1	yes	characteristic, complemented
575	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
576	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
577	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
578	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
579	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
580	#501	C₂²×C₃₁	1	2	yes	complemented
581	#499	C₂²×C₃₁	1	2	yes	complemented
582	#490	C₂²×C₃₁	1	2	yes	complemented
583	#486	C₂²×C₃₁	1	2	yes	complemented
584	#485	C₂²×C₃₁	1	2	yes	complemented
585	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
586	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	#482	C₂²×C₃₁	1	2	yes	complemented
588	#482	C₂²×C₃₁	1	2	yes	complemented
589	#482	C₂²×C₃₁	1	2	yes	complemented
590	#482	C₂²×C₃₁	1	2	yes	complemented
591	#482	C₂²×C₃₁	1	2	yes	complemented
592	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
593	#481	C₂²×C₃₁	1	2	yes	complemented
594	#481	C₂²×C₃₁	1	2	yes	complemented
595	#481	C₂²×C₃₁	1	2	yes	complemented
596	#481	C₂²×C₃₁	1	2	yes	complemented
597	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
598	#481	C₂²×C₃₁	1	2	yes	complemented
599	#480	C₂²×C₃₁	1	2	yes	complemented
600	#480	C₂²×C₃₁	1	2	yes	complemented
601	#480	C₂²×C₃₁	1	2	yes	complemented
602	#480	C₂²×C₃₁	1	2	yes	complemented
603	#480	C₂²×C₃₁	1	2	yes	complemented
604	#479	C₂²×C₃₁	1	2	yes	complemented
605	#478	C₂²×C₃₁	1	2	yes	complemented
606	#478	C₂²×C₃₁	1	2	yes	complemented
607	#478	C₂²×C₃₁	1	2	yes	complemented
608	#476	C₂²×C₃₁	1	2	yes	complemented
609	#474	C₂²×C₃₁	1	2	yes	complemented
610	#469	C₂²×C₃₁	1	2	yes	complemented
611	#468	C₂²×C₃₁	1	2	yes	complemented
612	#466	C₂²×C₃₁	1	2	yes	complemented
613	#466	C₂²×C₃₁	1	2	yes	complemented
614	#466	C₂²×C₃₁	1	2	yes	complemented
615	#465	C₂²×C₃₁	1	2	yes	complemented
616	#465	C₂²×C₃₁	1	2	yes	complemented
617	#465	C₂²×C₃₁	1	2	yes	complemented
618	#460	C₂²×C₃₁	1	2	yes	complemented
619	#459	C₂²×C₃₁	1	2	yes	complemented
620	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
621	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#450	C₂²×C₃₁	1	2	yes	complemented
623	#449	C₂²×C₃₁	1	2	yes	complemented
624	#449	C₂²×C₃₁	1	2	yes	complemented
625	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#447	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#447	C₂²×C₃₁	1	2	yes	complemented
628	#442	C₂²×C₃₁	1	2	yes	complemented
629	#440	C₂²×C₃₁	1	2	yes	complemented
630	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
631	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
632	#435	C₂²×C₃₁	1	2	yes	complemented
633	#435	C₂²×C₃₁	1	2	yes	complemented
634	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
635	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
636	#433	C₂²×C₃₁	1	2	yes	complemented
637	#428	C₂²×C₃₁	1	2	yes	complemented
638	#427	C₂²×C₃₁	1	2	yes	complemented
639	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
640	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
641	#418	C₂²×C₃₁	1	2	yes	complemented
642	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
643	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
644	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
645	#408	C₂²×C₃₁	1	2	yes	complemented
646	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	C₂×C₃₁	—	2	2	no	—
649	C₂×C₃₁	—	2	2	no	—
650	C₂×C₃₁	—	4	1	no	—
651	C₂×C₃₁	—	4	2	no	—
652	C₂×C₃₁	—	8	1	no	—
653	C₂×C₃₁	—	8	2	no	—
654	C₂×C₃₁	—	8	2	no	—
655	C₂×C₃₁	#3485	1	1	yes	characteristic
656	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
657	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
658	C₂×#41	—	2	2	no	—
659	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
660	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
661	C₂²×D₄	—	2	1	no	—
662	C₂²×D₄	—	2	1	no	—
663	C₂²×D₄	—	2	2	no	—
664	C₂²×D₄	—	2	2	no	—
665	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
666	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
667	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
668	C₂³×C₄	—	2	1	no	—
669	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
670	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
671	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
672	C₂×D₈	C₂³×C₃₁	1	2	yes	—
673	C₂×D₈	C₂³×C₃₁	1	2	yes	—
674	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
675	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
676	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
677	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
680	#127	—	2	2	no	—
681	#127	C₂³×C₃₁	1	2	yes	—
682	#126	—	2	2	no	—
683	#126	—	2	2	no	—
684	#126	—	2	2	no	—
685	#126	—	2	2	no	—
686	#125	—	2	2	no	—
687	#125	—	2	2	no	—
688	#125	—	2	1	no	—
689	#125	C₂³×C₃₁	1	2	yes	—
690	#125	C₂³×C₃₁	1	2	yes	—
691	#124	—	2	2	no	—
692	#123	—	2	2	no	—
693	#123	—	2	1	no	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	—	2	2	no	—
698	#123	—	2	2	no	—
699	#123	—	2	2	no	—
700	#123	—	2	2	no	—
701	#123	D₄×C₃₁	1	2	yes	—
702	C₂²⋊Q₈	—	2	1	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	2	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
708	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
709	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
710	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
712	#121	—	2	2	no	—
713	#121	—	2	2	no	—
714	#121	—	2	2	no	—
715	#121	—	2	2	no	—
716	#121	—	2	1	no	—
717	#121	—	2	1	no	—
718	#121	—	2	1	no	—
719	#121	—	2	1	no	—
720	#121	—	2	1	no	—
721	#121	—	2	2	no	—
722	#121	—	2	2	no	—
723	#121	—	2	2	no	—
724	#121	—	2	2	no	—
725	#121	D₄×C₃₁	1	1	yes	characteristic
726	#121	D₄×C₃₁	1	1	yes	characteristic
727	#121	C₂³×C₃₁	1	2	yes	—
728	#121	C₂³×C₃₁	1	2	yes	—
729	#121	C₂³×C₃₁	1	2	yes	—
730	#121	C₂³×C₃₁	1	2	yes	—
731	#121	C₂³×C₃₁	1	1	yes	characteristic
732	#121	C₂³×C₃₁	1	1	yes	characteristic
733	#121	C₂³×C₃₁	1	2	yes	—
734	#121	C₂³×C₃₁	1	2	yes	—
735	#121	C₂³×C₃₁	1	2	yes	—
736	#120	—	2	1	no	—
737	#120	—	2	2	no	—
738	#120	—	2	2	no	—
739	#120	—	2	2	no	—
740	#120	—	2	2	no	—
741	#120	—	2	2	no	—
742	#120	—	2	2	no	—
743	#120	D₄×C₃₁	1	2	yes	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	1	no	—
748	C₄×D₄	—	2	2	no	—
749	C₄×D₄	—	2	1	no	—
750	C₄×D₄	—	2	1	no	—
751	C₄×D₄	—	2	2	no	—
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	C₂³×C₃₁	1	2	yes	—
756	C₄×D₄	C₂³×C₃₁	1	2	yes	—
757	C₄×D₄	C₂³×C₃₁	1	2	yes	—
758	C₄×D₄	C₂³×C₃₁	1	2	yes	—
759	C₄×D₄	C₂³×C₃₁	1	2	yes	—
760	#117	—	2	1	no	—
761	#117	—	2	2	no	—
762	#117	C₂³×C₃₁	1	1	yes	characteristic
763	#117	C₂³×C₃₁	1	2	yes	—
764	#117	C₂³×C₃₁	1	2	yes	—
765	#117	C₂³×C₃₁	1	1	yes	characteristic
766	C₂×C₄⋊C₄	—	2	1	no	—
767	C₂×C₄⋊C₄	—	2	1	no	—
768	C₂×C₄⋊C₄	—	2	1	no	—
769	C₂×C₄⋊C₄	—	2	1	no	—
770	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
771	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
772	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
773	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
774	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
775	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
776	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
777	C₂×C₂²⋊C₄	—	2	1	no	—
778	C₂×C₂²⋊C₄	—	2	1	no	—
779	#107	C₂³×C₃₁	1	2	yes	—
780	#107	C₂³×C₃₁	1	2	yes	—
781	#107	C₂³×C₃₁	1	2	yes	—
782	#107	C₂³×C₃₁	1	2	yes	—
783	#107	C₂³×C₃₁	1	2	yes	—
784	#107	C₂³×C₃₁	1	2	yes	—
785	#106	C₂³×C₃₁	1	2	yes	—
786	#106	C₂³×C₃₁	1	2	yes	—
787	#106	C₂³×C₃₁	1	2	yes	—
788	#106	C₂³×C₃₁	1	2	yes	—
789	#106	C₂³×C₃₁	1	2	yes	—
790	#106	C₂³×C₃₁	1	2	yes	—
791	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
792	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
793	#103	C₂³×C₃₁	1	2	yes	—
794	#103	C₂³×C₃₁	1	2	yes	—
795	#102	C₂³×C₃₁	1	2	yes	—
796	#102	C₂³×C₃₁	1	2	yes	—
797	#102	C₂³×C₃₁	1	2	yes	—
798	#102	C₂³×C₃₁	1	2	yes	—
799	#102	C₂³×C₃₁	1	2	yes	—
800	#102	C₂³×C₃₁	1	2	yes	—
801	#102	C₂³×C₃₁	1	2	yes	—
802	#102	C₂³×C₃₁	1	2	yes	—
803	#102	C₂³×C₃₁	1	2	yes	—
804	#102	C₂³×C₃₁	1	2	yes	—
805	#102	C₂³×C₃₁	1	2	yes	—
806	#102	C₂³×C₃₁	1	2	yes	—
807	#102	C₂³×C₃₁	1	2	yes	—
808	#102	C₂³×C₃₁	1	2	yes	—
809	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
810	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
811	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
813	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
814	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
815	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
816	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
817	#97	C₂³×C₃₁	1	2	yes	—
818	C₄×C₈	C₂³×C₃₁	1	2	yes	—
819	C₃₁	#61766	1	1	yes	characteristic, direct product factor, Sylow
820	C₂⁴	—	2	1	no	—
821	C₂⁴	—	2	1	no	—
822	C₂⁴	—	2	2	no	—
823	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
824	#41	—	4	2	no	—
825	#41	—	4	2	no	—
826	#41	—	8	4	no	—
827	C₂×Q₈	—	2	2	no	—
828	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
829	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
830	C₂×D₄	—	2	1	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	2	1	no	—
841	C₂×D₄	—	2	1	no	—
842	C₂×D₄	—	2	2	no	—
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	4	2	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	—	4	2	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	8	4	no	—
850	C₂×D₄	—	8	4	no	—
851	C₂×D₄	—	8	2	no	—
852	C₂×D₄	—	8	2	no	—
853	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
854	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
855	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
856	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
857	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
858	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
859	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	8	2	no	—
873	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
874	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
875	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
876	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
880	SD₁₆	—	4	2	no	—
881	SD₁₆	—	4	2	no	—
882	D₈	—	4	2	no	—
883	D₈	—	4	2	no	—
884	M₁₆	—	4	2	no	—
885	C₂×C₈	—	4	2	no	—
886	C₂×C₈	—	4	2	no	—
887	C₂×C₈	—	4	2	no	—
888	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
889	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
890	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
891	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
909	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
910	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
911	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
912	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
913	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
914	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
917	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
918	C₂²⋊C₄	—	2	1	no	—
919	C₂²⋊C₄	—	2	1	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	—	2	1	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	1	no	—
933	C₂²⋊C₄	—	2	1	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
937	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
938	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
939	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
940	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
941	C₄²	—	2	2	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	1	no	—
944	C₄²	—	2	2	no	—
945	C₄²	C₂⁴×C₃₁	1	2	yes	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	2	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	4	1	no	—
952	C₂³	—	4	2	no	—
953	C₂³	—	4	2	no	—
954	C₂³	—	8	1	no	—
955	C₂³	—	8	1	no	—
956	C₂³	—	8	2	no	—
957	C₂³	—	8	1	no	—
958	C₂³	—	8	1	no	—
959	C₂³	—	8	2	no	—
960	C₂³	—	8	2	no	—
961	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
962	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
963	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
964	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
965	Q₈	—	2	2	no	—
966	Q₈	—	4	1	no	—
967	Q₈	—	8	2	no	—
968	D₄	—	2	4	no	—
969	D₄	—	2	4	no	—
970	D₄	—	2	2	no	—
971	D₄	—	2	2	no	—
972	D₄	—	2	2	no	—
973	D₄	—	2	2	no	—
974	D₄	—	2	2	no	—
975	D₄	—	4	1	no	—
976	D₄	—	4	2	no	—
977	D₄	—	4	2	no	—
978	D₄	—	4	4	no	—
979	D₄	—	4	2	no	—
980	D₄	—	4	2	no	—
981	D₄	—	4	4	no	—
982	D₄	—	8	1	no	—
983	D₄	—	8	1	no	—
984	D₄	—	8	2	no	—
985	D₄	—	8	2	no	—
986	D₄	—	8	2	no	—
987	D₄	—	8	2	no	—
988	D₄	—	8	2	no	—
989	D₄	—	8	2	no	—
990	D₄	—	8	2	no	—
991	D₄	—	8	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	1	no	—
1006	C₂×C₄	—	4	1	no	—
1007	C₂×C₄	—	4	2	no	—
1008	C₂×C₄	—	4	4	no	—
1009	C₂×C₄	—	8	2	no	—
1010	C₂×C₄	—	8	2	no	—
1011	C₂×C₄	—	8	2	no	—
1012	C₂×C₄	—	8	1	no	—
1013	C₂×C₄	—	8	2	no	—
1014	C₂×C₄	—	8	1	no	—
1015	C₂×C₄	—	8	1	no	—
1016	C₂×C₄	—	8	1	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1019	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1020	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1022	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1024	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1025	C₈	—	2	2	no	—
1026	C₈	—	2	2	no	—
1027	C₈	—	2	2	no	—
1028	C₈	—	2	2	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	1	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	1	no	—
1033	C₂²	—	2	1	no	—
1034	C₂²	—	2	2	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	4	4	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	2	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	—	16	2	no	—
1050	C₂²	—	16	2	no	—
1051	C₂²	—	16	4	no	—
1052	C₂²	C₃₁×#576	1	2	yes	—
1053	C₂²	C₃₁×#577	1	2	yes	—
1054	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	2	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	1	no	—
1068	C₄	C₃₁×#585	1	2	yes	—
1069	C₂	—	2	2	no	—
1070	C₂	—	2	2	no	—
1071	C₂	—	4	1	no	—
1072	C₂	—	4	2	no	—
1073	C₂	—	8	2	no	—
1074	C₂	—	8	2	no	—
1075	C₂	—	8	1	no	—
1076	C₂	C₃₁×#3485	1	1	yes	characteristic
1077	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1078	C₂	C₂×C₃₁×#577	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3537	C₂	semidirect
2. C₃₁×#3492	C₂	semidirect
3. C₃₁×#3346	C₂	semidirect
4. C₃₁×#3345	C₂	semidirect
5. C₃₁×#3339	C₂	semidirect
6. C₃₁×#3337	C₂	semidirect
7. C₃₁×#3318	C₂	semidirect
8. C₃₁×#3310	C₂	semidirect
9. C₃₁×#3295	C₂	semidirect
10. C₃₁×#3294	C₂	semidirect
11. C₃₁×#3241	C₂	semidirect
12. C₃₁×#3198	C₂	semidirect
13. C₃₁×#3188	C₂	semidirect
14. C₃₁×#3188	C₂	semidirect
15. C₃₁×#3119	C₂	semidirect
16. C₃₁×#3096	C₂	semidirect
17. C₂×C₃₁×#481	C₂	semidirect
18. C₂×C₃₁×#480	C₂	semidirect
19. C₃₁×#2977	C₂	semidirect
22. C₃₁×#554	C₂²	semidirect
26. C₃₁×#553	C₂²	semidirect
28. C₃₁×#552	C₂²	semidirect
30. C₃₁×#547	C₂²	semidirect
34. C₃₁×#544	C₂²	semidirect
39. C₃₁×#537	C₂²	semidirect
45. C₃₁×#525	C₂²	semidirect
48. C₃₁×#520	C₂²	semidirect
49. C₃₁×#520	C₂²	semidirect
50. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#499	C₂²	semidirect
53. C₃₁×#490	C₂²	semidirect
54. C₃₁×#486	C₂²	semidirect
55. C₃₁×#485	C₂²	semidirect
56. C₃₁×#484	C₂²	semidirect
57. C₃₁×#484	C₂²	semidirect
58. C₃₁×#482	C₂²	semidirect
59. C₃₁×#482	C₂²	semidirect
60. C₃₁×#482	C₂²	semidirect
61. C₃₁×#482	C₂²	semidirect
62. C₃₁×#482	C₂²	semidirect
63. C₃₁×#481	C₂²	semidirect
64. C₃₁×#481	C₂²	semidirect
65. C₃₁×#481	C₂²	semidirect
66. C₃₁×#481	C₂²	semidirect
67. C₃₁×#481	C₂²	semidirect
68. C₃₁×#481	C₂²	semidirect
69. C₃₁×#481	C₂²	semidirect
70. C₃₁×#480	C₂²	semidirect
71. C₃₁×#480	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#480	C₂²	semidirect
74. C₃₁×#480	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#478	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#476	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#469	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#466	C₂²	semidirect
84. C₃₁×#466	C₂²	semidirect
85. C₃₁×#466	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
87. C₃₁×#465	C₂²	semidirect
88. C₃₁×#465	C₂²	semidirect
89. C₃₁×#460	C₂²	semidirect
90. C₃₁×#459	C₂²	semidirect
91. C₃₁×#450	C₂²	semidirect
92. C₃₁×#450	C₂²	semidirect
93. C₃₁×#450	C₂²	semidirect
94. C₃₁×#449	C₂²	semidirect
95. C₃₁×#449	C₂²	semidirect
96. C₃₁×#447	C₂²	semidirect
97. C₃₁×#447	C₂²	semidirect
98. C₃₁×#447	C₂²	semidirect
99. C₃₁×#442	C₂²	semidirect
100. C₃₁×#440	C₂²	semidirect
101. C₄×SD₁₆×C₃₁	C₂²	semidirect
102. C₄×D₈×C₃₁	C₂²	semidirect
103. C₃₁×#435	C₂²	semidirect
104. C₃₁×#435	C₂²	semidirect
105. C₈×D₄×C₃₁	C₂²	semidirect
106. C₈×D₄×C₃₁	C₂²	semidirect
107. C₃₁×#433	C₂²	semidirect
108. C₃₁×#428	C₂²	semidirect
109. C₃₁×#427	C₂²	semidirect
110. C₂×C₃₁×#107	C₂²	semidirect
111. C₂×C₃₁×#106	C₂²	semidirect
112. C₃₁×#418	C₂²	semidirect
113. C₂×C₃₁×#102	C₂²	semidirect
114. C₂×C₃₁×#102	C₂²	semidirect
115. C₂×C₃₁×#102	C₂²	semidirect
116. C₃₁×#408	C₂²	semidirect
117. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
118. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
406. #61766	C₃₁	direct (N × H)
490. #3537	C₂×C₃₁	semidirect
491. #3492	C₂×C₃₁	semidirect
492. #3346	C₂×C₃₁	semidirect
493. #3345	C₂×C₃₁	semidirect
494. #3339	C₂×C₃₁	semidirect
495. #3337	C₂×C₃₁	semidirect
496. #3318	C₂×C₃₁	semidirect
497. #3310	C₂×C₃₁	semidirect
498. #3295	C₂×C₃₁	semidirect
499. #3294	C₂×C₃₁	semidirect
500. #3241	C₂×C₃₁	semidirect
501. #3198	C₂×C₃₁	semidirect
502. #3188	C₂×C₃₁	semidirect
503. #3188	C₂×C₃₁	semidirect
504. #3119	C₂×C₃₁	semidirect
505. #3096	C₂×C₃₁	semidirect
506. C₂×#481	C₂×C₃₁	semidirect
507. C₂×#480	C₂×C₃₁	semidirect
508. #2977	C₂×C₃₁	semidirect
551. #554	C₂²×C₃₁	semidirect
555. #553	C₂²×C₃₁	semidirect
557. #552	C₂²×C₃₁	semidirect
559. #547	C₂²×C₃₁	semidirect
563. #544	C₂²×C₃₁	semidirect
568. #537	C₂²×C₃₁	semidirect
574. #525	C₂²×C₃₁	semidirect
577. #520	C₂²×C₃₁	semidirect
578. #520	C₂²×C₃₁	semidirect
579. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
580. #501	C₂²×C₃₁	semidirect
581. #499	C₂²×C₃₁	semidirect
582. #490	C₂²×C₃₁	semidirect
583. #486	C₂²×C₃₁	semidirect
584. #485	C₂²×C₃₁	semidirect
585. #484	C₂²×C₃₁	semidirect
586. #484	C₂²×C₃₁	semidirect
587. #482	C₂²×C₃₁	semidirect
588. #482	C₂²×C₃₁	semidirect
589. #482	C₂²×C₃₁	semidirect
590. #482	C₂²×C₃₁	semidirect
591. #482	C₂²×C₃₁	semidirect
592. #481	C₂²×C₃₁	semidirect
593. #481	C₂²×C₃₁	semidirect
594. #481	C₂²×C₃₁	semidirect
595. #481	C₂²×C₃₁	semidirect
596. #481	C₂²×C₃₁	semidirect
597. #481	C₂²×C₃₁	semidirect
598. #481	C₂²×C₃₁	semidirect
599. #480	C₂²×C₃₁	semidirect
600. #480	C₂²×C₃₁	semidirect
601. #480	C₂²×C₃₁	semidirect
602. #480	C₂²×C₃₁	semidirect
603. #480	C₂²×C₃₁	semidirect
604. #479	C₂²×C₃₁	semidirect
605. #478	C₂²×C₃₁	semidirect
606. #478	C₂²×C₃₁	semidirect
607. #478	C₂²×C₃₁	semidirect
608. #476	C₂²×C₃₁	semidirect
609. #474	C₂²×C₃₁	semidirect
610. #469	C₂²×C₃₁	semidirect
611. #468	C₂²×C₃₁	semidirect
612. #466	C₂²×C₃₁	semidirect
613. #466	C₂²×C₃₁	semidirect
614. #466	C₂²×C₃₁	semidirect
615. #465	C₂²×C₃₁	semidirect
616. #465	C₂²×C₃₁	semidirect
617. #465	C₂²×C₃₁	semidirect
618. #460	C₂²×C₃₁	semidirect
619. #459	C₂²×C₃₁	semidirect
620. #450	C₂²×C₃₁	semidirect
621. #450	C₂²×C₃₁	semidirect
622. #450	C₂²×C₃₁	semidirect
623. #449	C₂²×C₃₁	semidirect
624. #449	C₂²×C₃₁	semidirect
625. #447	C₂²×C₃₁	semidirect
626. #447	C₂²×C₃₁	semidirect
627. #447	C₂²×C₃₁	semidirect
628. #442	C₂²×C₃₁	semidirect
629. #440	C₂²×C₃₁	semidirect
630. C₄×SD₁₆	C₂²×C₃₁	semidirect
631. C₄×D₈	C₂²×C₃₁	semidirect
632. #435	C₂²×C₃₁	semidirect
633. #435	C₂²×C₃₁	semidirect
634. C₈×D₄	C₂²×C₃₁	semidirect
635. C₈×D₄	C₂²×C₃₁	semidirect
636. #433	C₂²×C₃₁	semidirect
637. #428	C₂²×C₃₁	semidirect
638. #427	C₂²×C₃₁	semidirect
639. C₂×#107	C₂²×C₃₁	semidirect
640. C₂×#106	C₂²×C₃₁	semidirect
641. #418	C₂²×C₃₁	semidirect
642. C₂×#102	C₂²×C₃₁	semidirect
643. C₂×#102	C₂²×C₃₁	semidirect
644. C₂×#102	C₂²×C₃₁	semidirect
645. #408	C₂²×C₃₁	semidirect
646. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
647. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
819. C₃₁	#61766	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×#3537	2
C₃₁×#3492	2
C₃₁×#3346	2
C₃₁×#3345	2
C₃₁×#3339	2
C₃₁×#3337	2
C₃₁×#3318	2
C₃₁×#3310	2
C₃₁×#3295	2
C₃₁×#3294	2
C₃₁×#3241	2
C₃₁×#3198	2
C₃₁×#3188	2
C₃₁×#3119	2
C₃₁×#3096	2
C₂×C₃₁×#481	2
C₂×C₃₁×#480	2
C₃₁×#2977	2
#61766	31

Subgroups — C31×#61766 #21518525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61766 #21518525