Subgroups — C₃₁×#62163 #21518922

Order 7936.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3389	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3366	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3347	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3259	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	1	no	—
21	C₃₁×#562	—	2	1	no	—
22	C₃₁×#555	C₂²	1	1	yes	characteristic
23	C₃₁×#554	C₂²	1	1	yes	characteristic
24	C₃₁×#554	C₂²	1	2	yes	complemented
25	C₃₁×#553	—	2	1	no	—
26	C₃₁×#553	C₂²	1	2	yes	—
27	C₃₁×#553	C₂²	1	2	yes	complemented
28	C₃₁×#553	C₂²	1	2	yes	complemented
29	C₃₁×#550	C₂²	1	1	yes	characteristic
30	C₃₁×#547	—	2	2	no	—
31	C₃₁×#547	C₂²	1	2	yes	complemented
32	C₃₁×#546	—	2	1	no	—
33	C₃₁×#546	—	2	2	no	—
34	D₄²×C₃₁	C₂²	1	2	yes	—
35	D₄²×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#544	C₂²	1	2	yes	complemented
37	C₃₁×#540	C₂²	1	2	yes	—
38	C₃₁×#540	C₂²	1	2	yes	complemented
39	C₃₁×#539	—	2	2	no	—
40	C₃₁×#539	—	2	1	no	—
41	C₃₁×#538	—	2	2	no	—
42	C₃₁×#537	—	2	1	no	—
43	C₃₁×#532	C₂²	1	1	yes	characteristic
44	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#529	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#525	—	2	1	no	—
48	C₂×C₃₁×#121	—	2	1	no	—
49	C₃₁×#518	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#501	C₂²	1	2	yes	complemented
53	C₃₁×#499	C₂²	1	2	yes	complemented
54	C₃₁×#490	C₂²	1	2	yes	complemented
55	C₃₁×#490	C₂²	1	2	yes	complemented
56	C₃₁×#486	C₂²	1	2	yes	complemented
57	C₃₁×#482	C₂²	1	2	yes	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×#481	C₂²	1	2	yes	complemented
62	C₃₁×#481	C₂²	1	2	yes	complemented
63	C₃₁×#481	C₂²	1	2	yes	complemented
64	C₃₁×#480	C₂²	1	2	yes	complemented
65	C₃₁×#480	C₂²	1	2	yes	complemented
66	C₃₁×#478	C₂²	1	2	yes	—
67	C₃₁×#478	C₂²	1	2	yes	—
68	C₃₁×#478	C₂²	1	2	yes	—
69	C₃₁×#478	C₂²	1	2	yes	complemented
70	C₃₁×#478	C₂²	1	2	yes	complemented
71	C₃₁×#478	C₂²	1	2	yes	complemented
72	C₃₁×#478	C₂²	1	2	yes	complemented
73	C₃₁×#478	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	2	yes	complemented
76	C₃₁×#476	C₂²	1	1	yes	characteristic
77	C₃₁×#476	C₂²	1	2	yes	complemented
78	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#474	C₂²	1	2	yes	—
80	C₃₁×#474	C₂²	1	2	yes	complemented
81	C₃₁×#474	C₂²	1	2	yes	complemented
82	C₃₁×#469	C₂²	1	2	yes	complemented
83	C₃₁×#469	C₂²	1	2	yes	complemented
84	C₃₁×#466	C₂²	1	2	yes	complemented
85	C₃₁×#466	C₂²	1	2	yes	complemented
86	C₃₁×#466	C₂²	1	2	yes	complemented
87	C₃₁×#466	C₂²	1	2	yes	complemented
88	C₃₁×#459	C₂²	1	1	yes	characteristic
89	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#459	C₂²	1	2	yes	complemented
91	C₃₁×#459	C₂²	1	2	yes	complemented
92	C₃₁×#459	C₂²	1	2	yes	complemented
93	C₃₁×#459	C₂²	1	2	yes	complemented
94	C₃₁×#447	C₂²	1	2	yes	—
95	C₃₁×#447	C₂²	1	2	yes	—
96	C₃₁×#447	C₂²	1	2	yes	—
97	C₃₁×#446	C₂²	1	2	yes	complemented
98	C₃₁×#442	C₂²	1	2	yes	—
99	C₃₁×#442	C₂²	1	2	yes	—
100	C₃₁×#442	C₂²	1	2	yes	complemented
101	C₃₁×#442	C₂²	1	2	yes	complemented
102	C₄×D₈×C₃₁	C₂²	1	2	yes	—
103	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
104	C₃₁×#435	C₂²	1	2	yes	complemented
105	C₃₁×#435	C₂²	1	2	yes	complemented
106	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
107	C₃₁×#433	C₂²	1	2	yes	complemented
108	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
109	C₃₁×#428	C₂²	1	2	yes	complemented
110	C₃₁×#427	C₂²	1	2	yes	complemented
111	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#424	C₂²	1	2	yes	complemented
114	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#418	C₂²	1	2	yes	—
116	C₂×C₃₁×#102	C₂²	1	2	yes	—
117	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	—	2	2	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	—	2	1	no	—
123	C₂²×D₄×C₃₁	—	2	1	no	—
124	C₂²×D₄×C₃₁	—	2	2	no	—
125	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂³×C₄×C₃₁	—	2	1	no	—
128	C₂×D₈×C₃₁	C₂³	1	2	yes	—
129	C₂×D₈×C₃₁	C₂³	1	2	yes	—
130	C₂×D₈×C₃₁	C₂³	1	2	yes	—
131	C₂×D₈×C₃₁	C₂³	1	2	yes	—
132	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
136	C₃₁×C₄⋊Q₈	—	2	2	no	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₃₁×#127	C₂³	1	1	yes	characteristic
141	C₃₁×#127	C₂³	1	2	yes	—
142	C₃₁×#127	C₂³	1	1	yes	characteristic
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	D₄	1	2	yes	—
147	C₃₁×#125	—	2	2	no	—
148	C₃₁×#125	—	2	1	no	—
149	C₃₁×#125	—	2	1	no	—
150	C₃₁×#125	D₄	1	1	yes	characteristic
151	C₃₁×#125	C₂³	1	2	yes	—
152	C₃₁×#125	C₂³	1	2	yes	—
153	C₃₁×#125	C₂³	1	2	yes	—
154	C₃₁×#125	C₂³	1	2	yes	—
155	C₃₁×#124	—	2	2	no	—
156	C₃₁×#124	—	2	1	no	—
157	C₃₁×#124	—	2	1	no	—
158	C₃₁×#124	D₄	1	1	yes	characteristic
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	2	no	—
162	C₃₁×#123	—	2	2	no	—
163	C₃₁×#123	—	2	2	no	—
164	C₃₁×#123	—	2	2	no	—
165	C₃₁×#123	—	2	2	no	—
166	C₃₁×#123	—	2	2	no	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	D₄	1	2	yes	—
169	C₃₁×C₂²⋊Q₈	—	2	1	no	—
170	C₃₁×C₂²⋊Q₈	—	2	2	no	—
171	C₃₁×C₂²⋊Q₈	—	2	2	no	—
172	C₃₁×C₂²⋊Q₈	—	2	2	no	—
173	C₃₁×C₂²⋊Q₈	—	2	2	no	—
174	C₃₁×C₂²⋊Q₈	—	2	2	no	—
175	C₃₁×C₂²⋊Q₈	—	2	2	no	—
176	C₃₁×C₂²⋊Q₈	—	2	2	no	—
177	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
178	C₃₁×#121	—	2	2	no	—
179	C₃₁×#121	—	2	1	no	—
180	C₃₁×#121	—	2	2	no	—
181	C₃₁×#121	—	2	2	no	—
182	C₃₁×#121	—	2	1	no	—
183	C₃₁×#121	—	2	1	no	—
184	C₃₁×#121	—	2	1	no	—
185	C₃₁×#121	—	2	1	no	—
186	C₃₁×#121	—	2	2	no	—
187	C₃₁×#121	—	2	2	no	—
188	C₃₁×#121	—	2	2	no	—
189	C₃₁×#121	—	2	2	no	—
190	C₃₁×#121	—	2	2	no	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	D₄	1	1	yes	characteristic
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×#121	C₂³	1	2	yes	—
198	C₃₁×#121	C₂³	1	2	yes	—
199	C₃₁×#120	—	2	2	no	—
200	C₃₁×#120	—	2	2	no	—
201	C₃₁×#120	—	2	2	no	—
202	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
203	C₄×D₄×C₃₁	—	2	2	no	—
204	C₄×D₄×C₃₁	—	2	2	no	—
205	C₄×D₄×C₃₁	—	2	2	no	—
206	C₄×D₄×C₃₁	—	2	2	no	—
207	C₄×D₄×C₃₁	—	2	2	no	—
208	C₄×D₄×C₃₁	—	2	1	no	—
209	C₄×D₄×C₃₁	—	2	1	no	—
210	C₄×D₄×C₃₁	—	2	1	no	—
211	C₄×D₄×C₃₁	—	2	1	no	—
212	C₄×D₄×C₃₁	C₂³	1	2	yes	—
213	C₄×D₄×C₃₁	C₂³	1	2	yes	—
214	C₄×D₄×C₃₁	C₂³	1	2	yes	—
215	C₄×D₄×C₃₁	C₂³	1	2	yes	—
216	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₃₁	C₂³	1	2	yes	—
218	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₃₁	C₂³	1	2	yes	—
221	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₃₁	C₂³	1	2	yes	—
223	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
224	C₃₁×#117	—	2	1	no	—
225	C₃₁×#117	C₂³	1	2	yes	—
226	C₃₁×#117	C₂³	1	2	yes	—
227	C₃₁×#117	C₂³	1	2	yes	—
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	—	2	2	no	—
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
237	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
239	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×#97	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	2	no	—
282	#41×C₃₁	—	8	2	no	—
283	#41×C₃₁	—	8	2	no	—
284	#41×C₃₁	—	8	4	no	—
285	#41×C₃₁	—	8	2	no	—
286	C₂×Q₈×C₃₁	—	2	2	no	—
287	C₂×Q₈×C₃₁	—	2	1	no	—
288	C₂×Q₈×C₃₁	—	2	1	no	—
289	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
290	C₂×D₄×C₃₁	—	2	2	no	—
291	C₂×D₄×C₃₁	—	2	4	no	—
292	C₂×D₄×C₃₁	—	2	2	no	—
293	C₂×D₄×C₃₁	—	2	2	no	—
294	C₂×D₄×C₃₁	—	2	2	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	1	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	1	no	—
304	C₂×D₄×C₃₁	—	2	2	no	—
305	C₂×D₄×C₃₁	—	2	1	no	—
306	C₂×D₄×C₃₁	—	4	1	no	—
307	C₂×D₄×C₃₁	—	4	2	no	—
308	C₂×D₄×C₃₁	—	8	2	no	—
309	C₂×D₄×C₃₁	—	8	4	no	—
310	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
311	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
312	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
313	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
314	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
315	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₃₁	—	2	1	no	—
317	C₂²×C₄×C₃₁	—	2	1	no	—
318	C₂²×C₄×C₃₁	—	2	1	no	—
319	C₂²×C₄×C₃₁	—	2	2	no	—
320	C₂²×C₄×C₃₁	—	2	1	no	—
321	C₂²×C₄×C₃₁	—	2	1	no	—
322	C₂²×C₄×C₃₁	—	2	1	no	—
323	C₂²×C₄×C₃₁	—	2	2	no	—
324	C₂²×C₄×C₃₁	—	2	2	no	—
325	C₂²×C₄×C₃₁	—	2	2	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	—	2	2	no	—
328	C₂²×C₄×C₃₁	—	2	2	no	—
329	C₂²×C₄×C₃₁	—	2	1	no	—
330	C₂²×C₄×C₃₁	—	8	2	no	—
331	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
335	D₈×C₃₁	—	2	4	no	—
336	D₈×C₃₁	—	4	2	no	—
337	D₈×C₃₁	—	4	2	no	—
338	D₈×C₃₁	—	4	2	no	—
339	M₁₆×C₃₁	—	4	2	no	—
340	C₂×C₈×C₃₁	—	4	1	no	—
341	C₂×C₈×C₃₁	—	4	2	no	—
342	C₂×C₈×C₃₁	—	4	1	no	—
343	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
344	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
345	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
346	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₃₁	—	2	2	no	—
348	C₄⋊C₄×C₃₁	—	2	1	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	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	2	no	—
355	C₄⋊C₄×C₃₁	—	2	1	no	—
356	C₄⋊C₄×C₃₁	—	2	1	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	1	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	1	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
368	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	1	no	—
377	C₂²⋊C₄×C₃₁	—	2	2	no	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	no	—
380	C₂²⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
403	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
404	#62163	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
405	C₂³×C₃₁	—	2	1	no	—
406	C₂³×C₃₁	—	2	2	no	—
407	C₂³×C₃₁	—	2	1	no	—
408	C₂³×C₃₁	—	2	2	no	—
409	C₂³×C₃₁	—	4	2	no	—
410	C₂³×C₃₁	—	4	4	no	—
411	C₂³×C₃₁	—	4	2	no	—
412	C₂³×C₃₁	—	8	1	no	—
413	C₂³×C₃₁	—	8	2	no	—
414	C₂³×C₃₁	—	8	2	no	—
415	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
416	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
417	Q₈×C₃₁	—	4	1	no	—
418	Q₈×C₃₁	—	8	1	no	—
419	Q₈×C₃₁	—	8	1	no	—
420	Q₈×C₃₁	—	8	2	no	—
421	D₄×C₃₁	—	2	4	no	—
422	D₄×C₃₁	—	2	2	no	—
423	D₄×C₃₁	—	2	1	no	—
424	D₄×C₃₁	—	2	2	no	—
425	D₄×C₃₁	—	2	1	no	—
426	D₄×C₃₁	—	2	2	no	—
427	D₄×C₃₁	—	2	1	no	—
428	D₄×C₃₁	—	2	2	no	—
429	D₄×C₃₁	—	4	1	no	—
430	D₄×C₃₁	—	4	2	no	—
431	D₄×C₃₁	—	4	4	no	—
432	D₄×C₃₁	—	4	2	no	—
433	D₄×C₃₁	—	4	4	no	—
434	D₄×C₃₁	—	4	4	no	—
435	D₄×C₃₁	—	8	1	no	—
436	D₄×C₃₁	—	8	2	no	—
437	D₄×C₃₁	—	8	2	no	—
438	D₄×C₃₁	—	8	1	no	—
439	D₄×C₃₁	—	8	1	no	—
440	D₄×C₃₁	—	8	2	no	—
441	D₄×C₃₁	—	8	2	no	—
442	D₄×C₃₁	—	8	2	no	—
443	D₄×C₃₁	—	8	2	no	—
444	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
445	C₂×C₄×C₃₁	—	2	2	no	—
446	C₂×C₄×C₃₁	—	2	1	no	—
447	C₂×C₄×C₃₁	—	2	2	no	—
448	C₂×C₄×C₃₁	—	2	1	no	—
449	C₂×C₄×C₃₁	—	2	2	no	—
450	C₂×C₄×C₃₁	—	2	1	no	—
451	C₂×C₄×C₃₁	—	2	2	no	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	1	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	4	1	no	—
457	C₂×C₄×C₃₁	—	4	2	no	—
458	C₂×C₄×C₃₁	—	4	2	no	—
459	C₂×C₄×C₃₁	—	4	2	no	—
460	C₂×C₄×C₃₁	—	8	2	no	—
461	C₂×C₄×C₃₁	—	8	1	no	—
462	C₂×C₄×C₃₁	—	8	1	no	—
463	C₂×C₄×C₃₁	—	8	2	no	—
464	C₂×C₄×C₃₁	—	8	2	no	—
465	C₂×C₄×C₃₁	—	8	2	no	—
466	C₂×C₄×C₃₁	—	8	2	no	—
467	C₂×C₄×C₃₁	—	8	2	no	—
468	C₂×C₄×C₃₁	—	8	1	no	—
469	C₂×C₄×C₃₁	—	8	1	no	—
470	C₂×C₄×C₃₁	—	8	2	no	—
471	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
480	C₈×C₃₁	—	2	2	no	—
481	C₈×C₃₁	—	2	2	no	—
482	C₈×C₃₁	—	2	2	no	—
483	C₈×C₃₁	—	2	2	no	—
484	#3559	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#3519	C₂×C₃₁	1	1	yes	characteristic, complemented
486	#3389	C₂×C₃₁	1	2	yes	complemented
487	#3366	C₂×C₃₁	1	2	yes	complemented
488	#3347	C₂×C₃₁	1	2	yes	complemented
489	#3345	C₂×C₃₁	1	2	yes	complemented
490	#3339	C₂×C₃₁	1	2	yes	complemented
491	#3318	C₂×C₃₁	1	2	yes	complemented
492	#3318	C₂×C₃₁	1	2	yes	complemented
493	#3294	C₂×C₃₁	1	2	yes	complemented
494	#3259	C₂×C₃₁	1	2	yes	complemented
495	#3245	C₂×C₃₁	1	1	yes	characteristic, complemented
496	#3241	C₂×C₃₁	1	2	yes	complemented
497	#3234	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#3122	C₂×C₃₁	1	2	yes	complemented
499	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#3081	C₂×C₃₁	1	2	yes	complemented
501	C₂×#478	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
503	C₂²×C₃₁	—	2	1	no	—
504	C₂²×C₃₁	—	2	1	no	—
505	C₂²×C₃₁	—	2	2	no	—
506	C₂²×C₃₁	—	2	2	no	—
507	C₂²×C₃₁	—	2	2	no	—
508	C₂²×C₃₁	—	2	2	no	—
509	C₂²×C₃₁	—	4	1	no	—
510	C₂²×C₃₁	—	4	1	no	—
511	C₂²×C₃₁	—	4	1	no	—
512	C₂²×C₃₁	—	4	2	no	—
513	C₂²×C₃₁	—	4	2	no	—
514	C₂²×C₃₁	—	4	1	no	—
515	C₂²×C₃₁	—	4	2	no	—
516	C₂²×C₃₁	—	4	2	no	—
517	C₂²×C₃₁	—	4	2	no	—
518	C₂²×C₃₁	—	4	2	no	—
519	C₂²×C₃₁	—	4	1	no	—
520	C₂²×C₃₁	—	8	4	no	—
521	C₂²×C₃₁	—	16	4	no	—
522	C₂²×C₃₁	#576	1	2	yes	—
523	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
524	C₄×C₃₁	—	2	1	no	—
525	C₄×C₃₁	—	2	1	no	—
526	C₄×C₃₁	—	2	2	no	—
527	C₄×C₃₁	—	2	1	no	—
528	C₄×C₃₁	—	2	2	no	—
529	C₄×C₃₁	—	2	1	no	—
530	C₄×C₃₁	—	2	1	no	—
531	C₄×C₃₁	—	2	2	no	—
532	C₄×C₃₁	—	4	1	no	—
533	C₄×C₃₁	—	4	1	no	—
534	C₄×C₃₁	—	4	2	no	—
535	C₄×C₃₁	—	4	2	no	—
536	C₄×C₃₁	—	4	2	no	—
537	C₄×C₃₁	—	4	2	no	—
538	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
539	C₄×C₃₁	#585	1	1	yes	characteristic
540	#563	—	2	1	no	—
541	#562	—	2	1	no	—
542	#555	C₂²×C₃₁	1	1	yes	characteristic
543	#554	C₂²×C₃₁	1	1	yes	characteristic
544	#554	C₂²×C₃₁	1	2	yes	complemented
545	#553	—	2	1	no	—
546	#553	C₂²×C₃₁	1	2	yes	—
547	#553	C₂²×C₃₁	1	2	yes	complemented
548	#553	C₂²×C₃₁	1	2	yes	complemented
549	#550	C₂²×C₃₁	1	1	yes	characteristic
550	#547	—	2	2	no	—
551	#547	C₂²×C₃₁	1	2	yes	complemented
552	#546	—	2	1	no	—
553	#546	—	2	2	no	—
554	D₄²	C₂²×C₃₁	1	2	yes	—
555	D₄²	C₂²×C₃₁	1	1	yes	characteristic
556	#544	C₂²×C₃₁	1	2	yes	complemented
557	#540	C₂²×C₃₁	1	2	yes	—
558	#540	C₂²×C₃₁	1	2	yes	complemented
559	#539	—	2	2	no	—
560	#539	—	2	1	no	—
561	#538	—	2	2	no	—
562	#537	—	2	1	no	—
563	#532	C₂²×C₃₁	1	1	yes	characteristic
564	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
565	#529	C₂²×C₃₁	1	1	yes	characteristic
566	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
567	#525	—	2	1	no	—
568	C₂×#121	—	2	1	no	—
569	#518	C₂²×C₃₁	1	2	yes	—
570	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
571	#501	C₂²×C₃₁	1	2	yes	complemented
572	#501	C₂²×C₃₁	1	2	yes	complemented
573	#499	C₂²×C₃₁	1	2	yes	complemented
574	#490	C₂²×C₃₁	1	2	yes	complemented
575	#490	C₂²×C₃₁	1	2	yes	complemented
576	#486	C₂²×C₃₁	1	2	yes	complemented
577	#482	C₂²×C₃₁	1	2	yes	complemented
578	#482	C₂²×C₃₁	1	2	yes	complemented
579	#482	C₂²×C₃₁	1	2	yes	complemented
580	#482	C₂²×C₃₁	1	2	yes	complemented
581	#481	C₂²×C₃₁	1	2	yes	complemented
582	#481	C₂²×C₃₁	1	2	yes	complemented
583	#481	C₂²×C₃₁	1	2	yes	complemented
584	#480	C₂²×C₃₁	1	2	yes	complemented
585	#480	C₂²×C₃₁	1	2	yes	complemented
586	#478	C₂²×C₃₁	1	2	yes	—
587	#478	C₂²×C₃₁	1	2	yes	—
588	#478	C₂²×C₃₁	1	2	yes	—
589	#478	C₂²×C₃₁	1	2	yes	complemented
590	#478	C₂²×C₃₁	1	2	yes	complemented
591	#478	C₂²×C₃₁	1	2	yes	complemented
592	#478	C₂²×C₃₁	1	2	yes	complemented
593	#478	C₂²×C₃₁	1	2	yes	complemented
594	#478	C₂²×C₃₁	1	2	yes	complemented
595	#478	C₂²×C₃₁	1	2	yes	complemented
596	#476	C₂²×C₃₁	1	1	yes	characteristic
597	#476	C₂²×C₃₁	1	2	yes	complemented
598	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	#474	C₂²×C₃₁	1	2	yes	—
600	#474	C₂²×C₃₁	1	2	yes	complemented
601	#474	C₂²×C₃₁	1	2	yes	complemented
602	#469	C₂²×C₃₁	1	2	yes	complemented
603	#469	C₂²×C₃₁	1	2	yes	complemented
604	#466	C₂²×C₃₁	1	2	yes	complemented
605	#466	C₂²×C₃₁	1	2	yes	complemented
606	#466	C₂²×C₃₁	1	2	yes	complemented
607	#466	C₂²×C₃₁	1	2	yes	complemented
608	#459	C₂²×C₃₁	1	1	yes	characteristic
609	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
610	#459	C₂²×C₃₁	1	2	yes	complemented
611	#459	C₂²×C₃₁	1	2	yes	complemented
612	#459	C₂²×C₃₁	1	2	yes	complemented
613	#459	C₂²×C₃₁	1	2	yes	complemented
614	#447	C₂²×C₃₁	1	2	yes	—
615	#447	C₂²×C₃₁	1	2	yes	—
616	#447	C₂²×C₃₁	1	2	yes	—
617	#446	C₂²×C₃₁	1	2	yes	complemented
618	#442	C₂²×C₃₁	1	2	yes	—
619	#442	C₂²×C₃₁	1	2	yes	—
620	#442	C₂²×C₃₁	1	2	yes	complemented
621	#442	C₂²×C₃₁	1	2	yes	complemented
622	C₄×D₈	C₂²×C₃₁	1	2	yes	—
623	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
624	#435	C₂²×C₃₁	1	2	yes	complemented
625	#435	C₂²×C₃₁	1	2	yes	complemented
626	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
627	#433	C₂²×C₃₁	1	2	yes	complemented
628	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#428	C₂²×C₃₁	1	2	yes	complemented
630	#427	C₂²×C₃₁	1	2	yes	complemented
631	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#424	C₂²×C₃₁	1	2	yes	complemented
634	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#418	C₂²×C₃₁	1	2	yes	—
636	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
637	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
638	C₂×#102	C₂²×C₃₁	1	2	yes	—
639	C₂×C₃₁	—	2	2	no	—
640	C₂×C₃₁	—	4	2	no	—
641	C₂×C₃₁	—	4	2	no	—
642	C₂×C₃₁	—	8	2	no	—
643	C₂×C₃₁	—	8	1	no	—
644	C₂×C₃₁	—	8	2	no	—
645	C₂×C₃₁	#3489	1	1	yes	characteristic
646	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
647	C₂×C₃₁	#3585	1	1	yes	characteristic
648	C₂×#41	—	2	1	no	—
649	C₂×#41	—	2	2	no	—
650	C₂×#41	—	2	1	no	—
651	C₂×#41	—	2	1	no	—
652	C₂²×D₄	—	2	1	no	—
653	C₂²×D₄	—	2	2	no	—
654	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
655	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
656	C₂³×C₄	—	2	1	no	—
657	C₂×D₈	C₂³×C₃₁	1	2	yes	—
658	C₂×D₈	C₂³×C₃₁	1	2	yes	—
659	C₂×D₈	C₂³×C₃₁	1	2	yes	—
660	C₂×D₈	C₂³×C₃₁	1	2	yes	—
661	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
662	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
663	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
664	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
665	C₄⋊Q₈	—	2	2	no	—
666	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
667	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
668	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
669	#127	C₂³×C₃₁	1	1	yes	characteristic
670	#127	C₂³×C₃₁	1	1	yes	characteristic
671	#127	C₂³×C₃₁	1	2	yes	—
672	#126	—	2	2	no	—
673	#126	—	2	2	no	—
674	#126	—	2	2	no	—
675	#126	D₄×C₃₁	1	2	yes	—
676	#125	—	2	2	no	—
677	#125	—	2	1	no	—
678	#125	—	2	1	no	—
679	#125	D₄×C₃₁	1	1	yes	characteristic
680	#125	C₂³×C₃₁	1	2	yes	—
681	#125	C₂³×C₃₁	1	2	yes	—
682	#125	C₂³×C₃₁	1	2	yes	—
683	#125	C₂³×C₃₁	1	2	yes	—
684	#124	—	2	2	no	—
685	#124	—	2	1	no	—
686	#124	—	2	1	no	—
687	#124	D₄×C₃₁	1	1	yes	characteristic
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	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	D₄×C₃₁	1	2	yes	—
698	C₂²⋊Q₈	—	2	1	no	—
699	C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
706	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
707	#121	—	2	2	no	—
708	#121	—	2	1	no	—
709	#121	—	2	2	no	—
710	#121	—	2	2	no	—
711	#121	—	2	1	no	—
712	#121	—	2	1	no	—
713	#121	—	2	1	no	—
714	#121	—	2	1	no	—
715	#121	—	2	2	no	—
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	—	2	2	no	—
721	#121	D₄×C₃₁	1	1	yes	characteristic
722	#121	C₂³×C₃₁	1	2	yes	—
723	#121	C₂³×C₃₁	1	2	yes	—
724	#121	C₂³×C₃₁	1	2	yes	—
725	#121	C₂³×C₃₁	1	2	yes	—
726	#121	C₂³×C₃₁	1	2	yes	—
727	#121	C₂³×C₃₁	1	2	yes	—
728	#120	—	2	2	no	—
729	#120	—	2	2	no	—
730	#120	—	2	2	no	—
731	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	2	no	—
735	C₄×D₄	—	2	2	no	—
736	C₄×D₄	—	2	2	no	—
737	C₄×D₄	—	2	1	no	—
738	C₄×D₄	—	2	1	no	—
739	C₄×D₄	—	2	1	no	—
740	C₄×D₄	—	2	1	no	—
741	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
742	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
743	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
744	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
745	C₄×D₄	C₂³×C₃₁	1	2	yes	—
746	C₄×D₄	C₂³×C₃₁	1	2	yes	—
747	C₄×D₄	C₂³×C₃₁	1	2	yes	—
748	C₄×D₄	C₂³×C₃₁	1	2	yes	—
749	C₄×D₄	C₂³×C₃₁	1	2	yes	—
750	C₄×D₄	C₂³×C₃₁	1	2	yes	—
751	C₄×D₄	C₂³×C₃₁	1	2	yes	—
752	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
753	#117	—	2	1	no	—
754	#117	C₂³×C₃₁	1	2	yes	—
755	#117	C₂³×C₃₁	1	2	yes	—
756	#117	C₂³×C₃₁	1	2	yes	—
757	C₂×C₄⋊C₄	—	2	1	no	—
758	C₂×C₄⋊C₄	—	2	1	no	—
759	C₂×C₄⋊C₄	—	2	1	no	—
760	C₂×C₄⋊C₄	—	2	2	no	—
761	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
762	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
765	C₂×C₂²⋊C₄	—	2	1	no	—
766	C₂×C₂²⋊C₄	—	2	2	no	—
767	C₂×C₂²⋊C₄	—	2	2	no	—
768	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
769	#107	C₂³×C₃₁	1	2	yes	—
770	#107	C₂³×C₃₁	1	2	yes	—
771	#107	C₂³×C₃₁	1	2	yes	—
772	#107	C₂³×C₃₁	1	2	yes	—
773	#107	C₂³×C₃₁	1	2	yes	—
774	#107	C₂³×C₃₁	1	2	yes	—
775	#106	C₂³×C₃₁	1	2	yes	—
776	#106	C₂³×C₃₁	1	2	yes	—
777	#106	C₂³×C₃₁	1	2	yes	—
778	#106	C₂³×C₃₁	1	2	yes	—
779	#106	C₂³×C₃₁	1	2	yes	—
780	#106	C₂³×C₃₁	1	2	yes	—
781	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
782	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
783	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
785	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
786	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
787	#102	C₂³×C₃₁	1	2	yes	—
788	#102	C₂³×C₃₁	1	2	yes	—
789	#102	C₂³×C₃₁	1	2	yes	—
790	#102	C₂³×C₃₁	1	2	yes	—
791	#102	C₂³×C₃₁	1	2	yes	—
792	#102	C₂³×C₃₁	1	2	yes	—
793	#102	C₂³×C₃₁	1	2	yes	—
794	#102	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	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
804	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
805	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
806	#97	C₂³×C₃₁	1	2	yes	—
807	#97	C₂³×C₃₁	1	2	yes	—
808	C₄×C₈	C₂³×C₃₁	1	2	yes	—
809	C₃₁	#62163	1	1	yes	characteristic, direct product factor, Sylow
810	C₂⁴	—	2	1	no	—
811	C₂⁴	—	2	2	no	—
812	#41	—	8	2	no	—
813	#41	—	8	2	no	—
814	#41	—	8	4	no	—
815	#41	—	8	2	no	—
816	C₂×Q₈	—	2	2	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	4	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	1	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	4	1	no	—
837	C₂×D₄	—	4	2	no	—
838	C₂×D₄	—	8	2	no	—
839	C₂×D₄	—	8	4	no	—
840	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
841	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
842	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
843	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
844	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
845	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	1	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	8	2	no	—
861	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
862	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
863	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
864	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
865	D₈	—	2	4	no	—
866	D₈	—	4	2	no	—
867	D₈	—	4	2	no	—
868	D₈	—	4	2	no	—
869	M₁₆	—	4	2	no	—
870	C₂×C₈	—	4	1	no	—
871	C₂×C₈	—	4	2	no	—
872	C₂×C₈	—	4	1	no	—
873	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
874	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
875	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
876	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
893	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
894	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
895	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
896	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
897	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
898	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
899	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
900	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
901	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
902	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	1	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	1	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	1	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	1	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	2	no	—
921	C₂²⋊C₄	—	2	2	no	—
922	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
923	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
924	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
925	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
926	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	2	no	—
929	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
930	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
931	C₄²	C₂⁴×C₃₁	1	2	yes	—
932	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₂³	—	2	1	no	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	4	2	no	—
939	C₂³	—	4	4	no	—
940	C₂³	—	4	2	no	—
941	C₂³	—	8	1	no	—
942	C₂³	—	8	2	no	—
943	C₂³	—	8	2	no	—
944	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
945	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
946	Q₈	—	4	1	no	—
947	Q₈	—	8	1	no	—
948	Q₈	—	8	1	no	—
949	Q₈	—	8	2	no	—
950	D₄	—	2	4	no	—
951	D₄	—	2	2	no	—
952	D₄	—	2	1	no	—
953	D₄	—	2	2	no	—
954	D₄	—	2	1	no	—
955	D₄	—	2	2	no	—
956	D₄	—	2	1	no	—
957	D₄	—	2	2	no	—
958	D₄	—	4	1	no	—
959	D₄	—	4	2	no	—
960	D₄	—	4	4	no	—
961	D₄	—	4	2	no	—
962	D₄	—	4	4	no	—
963	D₄	—	4	4	no	—
964	D₄	—	8	1	no	—
965	D₄	—	8	2	no	—
966	D₄	—	8	1	no	—
967	D₄	—	8	1	no	—
968	D₄	—	8	2	no	—
969	D₄	—	8	2	no	—
970	D₄	—	8	2	no	—
971	D₄	—	8	2	no	—
972	D₄	—	8	2	no	—
973	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	4	1	no	—
986	C₂×C₄	—	4	2	no	—
987	C₂×C₄	—	4	2	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	8	2	no	—
990	C₂×C₄	—	8	1	no	—
991	C₂×C₄	—	8	1	no	—
992	C₂×C₄	—	8	2	no	—
993	C₂×C₄	—	8	2	no	—
994	C₂×C₄	—	8	2	no	—
995	C₂×C₄	—	8	2	no	—
996	C₂×C₄	—	8	2	no	—
997	C₂×C₄	—	8	1	no	—
998	C₂×C₄	—	8	1	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1001	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1004	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1005	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1006	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1007	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1008	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1009	C₈	—	2	2	no	—
1010	C₈	—	2	2	no	—
1011	C₈	—	2	2	no	—
1012	C₈	—	2	2	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	8	4	no	—
1031	C₂²	—	16	4	no	—
1032	C₂²	C₃₁×#576	1	2	yes	—
1033	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1034	C₄	—	2	1	no	—
1035	C₄	—	2	2	no	—
1036	C₄	—	2	1	no	—
1037	C₄	—	2	1	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	1	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	—	4	1	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	2	no	—
1048	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1049	C₄	C₃₁×#585	1	1	yes	characteristic
1050	C₂	—	2	2	no	—
1051	C₂	—	4	2	no	—
1052	C₂	—	4	2	no	—
1053	C₂	—	8	1	no	—
1054	C₂	—	8	2	no	—
1055	C₂	—	8	2	no	—
1056	C₂	C₃₁×#3489	1	1	yes	characteristic
1057	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1058	C₂	C₃₁×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3559	C₂	semidirect
2. C₃₁×#3519	C₂	semidirect
3. C₃₁×#3389	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3347	C₂	semidirect
6. C₃₁×#3345	C₂	semidirect
7. C₃₁×#3339	C₂	semidirect
8. C₃₁×#3318	C₂	semidirect
9. C₃₁×#3318	C₂	semidirect
10. C₃₁×#3294	C₂	semidirect
11. C₃₁×#3259	C₂	semidirect
12. C₃₁×#3245	C₂	semidirect
13. C₃₁×#3241	C₂	semidirect
14. C₃₁×#3234	C₂	semidirect
15. C₃₁×#3122	C₂	semidirect
16. C₃₁×#3109	C₂	semidirect
17. C₃₁×#3081	C₂	semidirect
18. C₂×C₃₁×#478	C₂	semidirect
19. C₃₁×#2992	C₂	semidirect
24. C₃₁×#554	C₂²	semidirect
27. C₃₁×#553	C₂²	semidirect
28. C₃₁×#553	C₂²	semidirect
31. C₃₁×#547	C₂²	semidirect
36. C₃₁×#544	C₂²	semidirect
38. C₃₁×#540	C₂²	semidirect
44. C₃₁×#532	C₂²	semidirect
46. C₂×C₃₁×#125	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#501	C₂²	semidirect
53. C₃₁×#499	C₂²	semidirect
54. C₃₁×#490	C₂²	semidirect
55. C₃₁×#490	C₂²	semidirect
56. C₃₁×#486	C₂²	semidirect
57. C₃₁×#482	C₂²	semidirect
58. C₃₁×#482	C₂²	semidirect
59. C₃₁×#482	C₂²	semidirect
60. C₃₁×#482	C₂²	semidirect
61. C₃₁×#481	C₂²	semidirect
62. C₃₁×#481	C₂²	semidirect
63. C₃₁×#481	C₂²	semidirect
64. C₃₁×#480	C₂²	semidirect
65. C₃₁×#480	C₂²	semidirect
69. C₃₁×#478	C₂²	semidirect
70. C₃₁×#478	C₂²	semidirect
71. C₃₁×#478	C₂²	semidirect
72. C₃₁×#478	C₂²	semidirect
73. C₃₁×#478	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
77. C₃₁×#476	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#474	C₂²	semidirect
82. C₃₁×#469	C₂²	semidirect
83. C₃₁×#469	C₂²	semidirect
84. C₃₁×#466	C₂²	semidirect
85. C₃₁×#466	C₂²	semidirect
86. C₃₁×#466	C₂²	semidirect
87. C₃₁×#466	C₂²	semidirect
89. C₃₁×#459	C₂²	semidirect
90. C₃₁×#459	C₂²	semidirect
91. C₃₁×#459	C₂²	semidirect
92. C₃₁×#459	C₂²	semidirect
93. C₃₁×#459	C₂²	semidirect
97. C₃₁×#446	C₂²	semidirect
100. C₃₁×#442	C₂²	semidirect
101. C₃₁×#442	C₂²	semidirect
103. C₄×D₈×C₃₁	C₂²	semidirect
104. C₃₁×#435	C₂²	semidirect
105. C₃₁×#435	C₂²	semidirect
106. C₈×D₄×C₃₁	C₂²	semidirect
107. C₃₁×#433	C₂²	semidirect
108. C₃₁×#432	C₂²	semidirect
109. C₃₁×#428	C₂²	semidirect
110. C₃₁×#427	C₂²	semidirect
111. C₂×C₃₁×#107	C₂²	semidirect
112. C₂×C₃₁×#106	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
114. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
404. #62163	C₃₁	direct (N × H)
484. #3559	C₂×C₃₁	semidirect
485. #3519	C₂×C₃₁	semidirect
486. #3389	C₂×C₃₁	semidirect
487. #3366	C₂×C₃₁	semidirect
488. #3347	C₂×C₃₁	semidirect
489. #3345	C₂×C₃₁	semidirect
490. #3339	C₂×C₃₁	semidirect
491. #3318	C₂×C₃₁	semidirect
492. #3318	C₂×C₃₁	semidirect
493. #3294	C₂×C₃₁	semidirect
494. #3259	C₂×C₃₁	semidirect
495. #3245	C₂×C₃₁	semidirect
496. #3241	C₂×C₃₁	semidirect
497. #3234	C₂×C₃₁	semidirect
498. #3122	C₂×C₃₁	semidirect
499. #3109	C₂×C₃₁	semidirect
500. #3081	C₂×C₃₁	semidirect
501. C₂×#478	C₂×C₃₁	semidirect
502. #2992	C₂×C₃₁	semidirect
544. #554	C₂²×C₃₁	semidirect
547. #553	C₂²×C₃₁	semidirect
548. #553	C₂²×C₃₁	semidirect
551. #547	C₂²×C₃₁	semidirect
556. #544	C₂²×C₃₁	semidirect
558. #540	C₂²×C₃₁	semidirect
564. #532	C₂²×C₃₁	semidirect
566. C₂×#125	C₂²×C₃₁	semidirect
571. #501	C₂²×C₃₁	semidirect
572. #501	C₂²×C₃₁	semidirect
573. #499	C₂²×C₃₁	semidirect
574. #490	C₂²×C₃₁	semidirect
575. #490	C₂²×C₃₁	semidirect
576. #486	C₂²×C₃₁	semidirect
577. #482	C₂²×C₃₁	semidirect
578. #482	C₂²×C₃₁	semidirect
579. #482	C₂²×C₃₁	semidirect
580. #482	C₂²×C₃₁	semidirect
581. #481	C₂²×C₃₁	semidirect
582. #481	C₂²×C₃₁	semidirect
583. #481	C₂²×C₃₁	semidirect
584. #480	C₂²×C₃₁	semidirect
585. #480	C₂²×C₃₁	semidirect
589. #478	C₂²×C₃₁	semidirect
590. #478	C₂²×C₃₁	semidirect
591. #478	C₂²×C₃₁	semidirect
592. #478	C₂²×C₃₁	semidirect
593. #478	C₂²×C₃₁	semidirect
594. #478	C₂²×C₃₁	semidirect
595. #478	C₂²×C₃₁	semidirect
597. #476	C₂²×C₃₁	semidirect
598. #476	C₂²×C₃₁	semidirect
600. #474	C₂²×C₃₁	semidirect
601. #474	C₂²×C₃₁	semidirect
602. #469	C₂²×C₃₁	semidirect
603. #469	C₂²×C₃₁	semidirect
604. #466	C₂²×C₃₁	semidirect
605. #466	C₂²×C₃₁	semidirect
606. #466	C₂²×C₃₁	semidirect
607. #466	C₂²×C₃₁	semidirect
609. #459	C₂²×C₃₁	semidirect
610. #459	C₂²×C₃₁	semidirect
611. #459	C₂²×C₃₁	semidirect
612. #459	C₂²×C₃₁	semidirect
613. #459	C₂²×C₃₁	semidirect
617. #446	C₂²×C₃₁	semidirect
620. #442	C₂²×C₃₁	semidirect
621. #442	C₂²×C₃₁	semidirect
623. C₄×D₈	C₂²×C₃₁	semidirect
624. #435	C₂²×C₃₁	semidirect
625. #435	C₂²×C₃₁	semidirect
626. C₈×D₄	C₂²×C₃₁	semidirect
627. #433	C₂²×C₃₁	semidirect
628. #432	C₂²×C₃₁	semidirect
629. #428	C₂²×C₃₁	semidirect
630. #427	C₂²×C₃₁	semidirect
631. C₂×#107	C₂²×C₃₁	semidirect
632. C₂×#106	C₂²×C₃₁	semidirect
633. #424	C₂²×C₃₁	semidirect
634. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
809. C₃₁	#62163	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×#3559	2
C₃₁×#3519	2
C₃₁×#3389	2
C₃₁×#3366	2
C₃₁×#3347	2
C₃₁×#3345	2
C₃₁×#3339	2
C₃₁×#3318	2
C₃₁×#3294	2
C₃₁×#3259	2
C₃₁×#3245	2
C₃₁×#3241	2
C₃₁×#3234	2
C₃₁×#3122	2
C₃₁×#3109	2
C₃₁×#3081	2
C₂×C₃₁×#478	2
C₃₁×#2992	2
#62163	31

Subgroups — C31×#62163 #21518922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62163 #21518922