Subgroups — C₃₁×#61262 #21518021

Order 7936.

1884 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3494	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3347	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3345	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3341	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3334	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3096	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3094	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3058	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₃₁×#555	C₂²	1	4	yes	complemented
22	C₃₁×#553	C₂²	1	4	yes	complemented
23	C₃₁×#553	C₂²	1	4	yes	complemented
24	C₃₁×#551	—	2	4	no	—
25	C₃₁×#547	C₂²	1	4	yes	complemented
26	C₃₁×#546	—	2	4	no	—
27	C₃₁×#544	C₂²	1	2	yes	—
28	C₃₁×#542	—	2	2	no	—
29	C₃₁×#540	—	2	2	no	—
30	C₃₁×#535	C₂²	1	2	yes	—
31	C₃₁×#532	—	2	2	no	—
32	C₃₁×#529	—	2	2	no	—
33	C₃₁×#525	C₂²	1	1	yes	characteristic
34	C₂×C₃₁×#121	C₂²	1	2	yes	—
35	C₃₁×#520	C₂²	1	2	yes	—
36	C₃₁×#518	C₂²	1	2	yes	—
37	C₂×C₃₁×#117	C₂²	1	2	yes	—
38	C₃₁×#501	C₂²	1	4	yes	complemented
39	C₃₁×#500	C₂²	1	2	yes	complemented
40	C₃₁×#499	C₂²	1	2	yes	complemented
41	C₃₁×#482	C₂²	1	4	yes	complemented
42	C₃₁×#482	C₂²	1	4	yes	complemented
43	C₃₁×#482	C₂²	1	4	yes	complemented
44	C₃₁×#482	C₂²	1	4	yes	complemented
45	C₃₁×#481	C₂²	1	4	yes	complemented
46	C₃₁×#481	C₂²	1	4	yes	complemented
47	C₃₁×#480	C₂²	1	4	yes	complemented
48	C₃₁×#480	C₂²	1	4	yes	complemented
49	C₃₁×#478	C₂²	1	4	yes	complemented
50	C₃₁×#478	C₂²	1	4	yes	complemented
51	C₃₁×#476	C₂²	1	4	yes	complemented
52	C₃₁×#474	C₂²	1	4	yes	complemented
53	C₃₁×#469	C₂²	1	4	yes	complemented
54	C₃₁×#466	C₂²	1	2	yes	—
55	C₃₁×#466	C₂²	1	2	yes	—
56	C₃₁×#466	C₂²	1	2	yes	—
57	C₃₁×#466	C₂²	1	2	yes	—
58	C₃₁×#466	C₂²	1	2	yes	complemented
59	C₃₁×#466	C₂²	1	2	yes	complemented
60	C₃₁×#442	C₂²	1	4	yes	complemented
61	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
62	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
63	C₃₁×#435	C₂²	1	2	yes	complemented
64	C₃₁×#435	C₂²	1	2	yes	complemented
65	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
66	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
67	C₃₁×#428	C₂²	1	2	yes	—
68	C₃₁×#428	C₂²	1	2	yes	—
69	C₃₁×#428	C₂²	1	4	yes	complemented
70	C₃₁×#427	C₂²	1	2	yes	—
71	C₃₁×#427	C₂²	1	1	yes	characteristic
72	C₃₁×#427	C₂²	1	1	yes	characteristic
73	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#427	C₂²	1	2	yes	complemented
75	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#427	C₂²	1	2	yes	complemented
77	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
78	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
80	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
82	C₃₁×#424	C₂²	1	1	yes	characteristic
83	C₃₁×#418	C₂²	1	2	yes	—
84	C₃₁×#418	C₂²	1	2	yes	—
85	C₂×C₃₁×#102	C₂²	1	2	yes	—
86	C₃₁×#408	C₂²	1	1	yes	characteristic
87	C₃₁×#407	C₂²	1	1	yes	characteristic
88	C₃₁×#405	C₂²	1	1	yes	characteristic
89	C₂×#41×C₃₁	—	2	4	no	—
90	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₃₁	—	2	2	no	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₂×D₈×C₃₁	—	2	4	no	—
95	C₂×D₈×C₃₁	C₂³	1	2	yes	—
96	C₂×D₈×C₃₁	C₂³	1	2	yes	—
97	C₃₁×#131	—	2	4	no	—
98	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
101	C₂²×C₈×C₃₁	—	2	4	no	—
102	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
109	C₃₁×C₄⋊Q₈	—	2	2	no	—
110	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
111	C₃₁×#127	—	2	2	no	—
112	C₃₁×#126	—	2	4	no	—
113	C₃₁×#126	—	2	4	no	—
114	C₃₁×#125	—	2	2	no	—
115	C₃₁×#125	C₂³	1	4	yes	—
116	C₃₁×#124	—	2	2	no	—
117	C₃₁×#124	—	2	4	no	—
118	C₃₁×#124	—	2	4	no	—
119	C₃₁×#123	—	2	4	no	—
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×#123	D₄	1	2	yes	—
124	C₃₁×C₂²⋊Q₈	—	2	4	no	—
125	C₃₁×C₂²⋊Q₈	—	2	4	no	—
126	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
128	C₃₁×#121	—	2	4	no	—
129	C₃₁×#121	—	2	4	no	—
130	C₃₁×#121	—	2	4	no	—
131	C₃₁×#121	—	2	2	no	—
132	C₃₁×#121	—	2	2	no	—
133	C₃₁×#121	D₄	1	1	yes	characteristic
134	C₃₁×#121	D₄	1	1	yes	characteristic
135	C₃₁×#121	C₂³	1	4	yes	—
136	C₃₁×#121	C₂³	1	4	yes	—
137	C₃₁×#121	C₂³	1	4	yes	—
138	C₃₁×#121	C₂³	1	4	yes	—
139	C₃₁×#120	—	2	4	no	—
140	C₃₁×#120	D₄	1	2	yes	—
141	C₄×Q₈×C₃₁	—	2	2	no	—
142	C₄×D₄×C₃₁	—	2	2	no	—
143	C₄×D₄×C₃₁	—	2	4	no	—
144	C₄×D₄×C₃₁	—	2	2	no	—
145	C₄×D₄×C₃₁	—	2	2	no	—
146	C₄×D₄×C₃₁	—	2	4	no	—
147	C₄×D₄×C₃₁	—	2	4	no	—
148	C₄×D₄×C₃₁	C₂³	1	4	yes	—
149	C₄×D₄×C₃₁	C₂³	1	4	yes	—
150	C₄×D₄×C₃₁	C₂³	1	2	yes	—
151	C₄×D₄×C₃₁	C₂³	1	2	yes	—
152	C₃₁×#117	—	2	2	no	—
153	C₃₁×#117	—	2	2	no	—
154	C₃₁×#117	—	2	4	no	—
155	C₃₁×#117	C₂³	1	2	yes	—
156	C₃₁×#117	C₂³	1	2	yes	—
157	C₃₁×#117	C₂³	1	2	yes	—
158	C₃₁×#117	C₂³	1	2	yes	—
159	C₃₁×#117	C₂³	1	4	yes	—
160	C₃₁×#117	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
165	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
166	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
167	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
168	C₂×C₄²×C₃₁	—	2	2	no	—
169	C₃₁×#107	C₂³	1	2	yes	—
170	C₃₁×#107	C₂³	1	2	yes	—
171	C₃₁×#107	C₂³	1	1	yes	characteristic
172	C₃₁×#107	C₂³	1	1	yes	characteristic
173	C₃₁×#107	C₂³	1	1	yes	characteristic
174	C₃₁×#107	C₂³	1	1	yes	characteristic
175	C₃₁×#107	C₂³	1	2	yes	—
176	C₃₁×#107	C₂³	1	2	yes	—
177	C₃₁×#107	C₂³	1	4	yes	—
178	C₃₁×#107	C₂³	1	4	yes	—
179	C₃₁×#106	C₂³	1	2	yes	—
180	C₃₁×#106	C₂³	1	2	yes	—
181	C₃₁×#106	C₂³	1	2	yes	—
182	C₃₁×#106	C₂³	1	2	yes	—
183	C₃₁×#106	C₂³	1	4	yes	—
184	C₃₁×#106	C₂³	1	4	yes	—
185	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
186	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
187	C₃₁×#102	C₂³	1	4	yes	—
188	C₃₁×#102	C₂³	1	4	yes	—
189	C₃₁×#102	C₂³	1	4	yes	—
190	C₃₁×#102	C₂³	1	4	yes	—
191	C₃₁×#102	C₂³	1	4	yes	—
192	C₃₁×#102	C₂³	1	4	yes	—
193	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₃₁×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₃₁	C₂³	1	2	yes	—
199	C₂⁴×C₃₁	—	2	2	no	—
200	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
201	#41×C₃₁	—	2	2	no	—
202	#41×C₃₁	—	2	2	no	—
203	#41×C₃₁	—	8	8	no	—
204	C₂×Q₈×C₃₁	—	2	4	no	—
205	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
206	C₂×D₄×C₃₁	—	2	4	no	—
207	C₂×D₄×C₃₁	—	2	4	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	4	no	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	—	2	4	no	—
213	C₂×D₄×C₃₁	—	8	4	no	—
214	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
215	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
218	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	—	2	2	no	—
221	C₂²×C₄×C₃₁	—	2	2	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	2	no	—
224	C₂²×C₄×C₃₁	—	2	4	no	—
225	C₂²×C₄×C₃₁	—	2	4	no	—
226	C₂²×C₄×C₃₁	—	2	4	no	—
227	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
234	D₈×C₃₁	—	2	4	no	—
235	D₈×C₃₁	—	2	4	no	—
236	M₁₆×C₃₁	—	2	2	no	—
237	M₁₆×C₃₁	—	2	2	no	—
238	M₁₆×C₃₁	—	2	4	no	—
239	C₂×C₈×C₃₁	—	2	2	no	—
240	C₂×C₈×C₃₁	—	2	2	no	—
241	C₂×C₈×C₃₁	—	2	2	no	—
242	C₂×C₈×C₃₁	—	2	2	no	—
243	C₂×C₈×C₃₁	—	2	2	no	—
244	C₂×C₈×C₃₁	—	2	4	no	—
245	C₂×C₈×C₃₁	#41	1	4	yes	complemented
246	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
247	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
249	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	—	2	4	no	—
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
261	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
262	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
267	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
268	C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂²⋊C₄×C₃₁	—	2	4	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	4	no	—
275	C₂²⋊C₄×C₃₁	—	2	4	no	—
276	C₂²⋊C₄×C₃₁	—	2	4	no	—
277	C₂²⋊C₄×C₃₁	—	2	4	no	—
278	C₂²⋊C₄×C₃₁	—	2	4	no	—
279	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
281	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
284	C₄²×C₃₁	—	2	2	no	—
285	C₄²×C₃₁	—	2	2	no	—
286	C₄²×C₃₁	—	2	2	no	—
287	C₄²×C₃₁	—	2	2	no	—
288	C₄²×C₃₁	—	2	4	no	—
289	C₄²×C₃₁	C₂⁴	1	2	yes	—
290	#61262	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂³×C₃₁	—	2	2	no	—
292	C₂³×C₃₁	—	2	2	no	—
293	C₂³×C₃₁	—	2	4	no	—
294	C₂³×C₃₁	—	4	1	no	—
295	C₂³×C₃₁	—	4	4	no	—
296	C₂³×C₃₁	—	8	2	no	—
297	C₂³×C₃₁	—	8	2	no	—
298	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
299	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
300	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
301	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₃₁	—	2	2	no	—
303	Q₈×C₃₁	—	8	4	no	—
304	D₄×C₃₁	—	2	4	no	—
305	D₄×C₃₁	—	2	4	no	—
306	D₄×C₃₁	—	2	2	no	—
307	D₄×C₃₁	—	2	4	no	—
308	D₄×C₃₁	—	2	4	no	—
309	D₄×C₃₁	—	4	2	no	—
310	D₄×C₃₁	—	4	8	no	—
311	D₄×C₃₁	—	4	4	no	—
312	D₄×C₃₁	—	8	4	no	—
313	D₄×C₃₁	—	8	4	no	—
314	D₄×C₃₁	—	8	4	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	2	no	—
318	C₂×C₄×C₃₁	—	2	1	no	—
319	C₂×C₄×C₃₁	—	2	1	no	—
320	C₂×C₄×C₃₁	—	2	2	no	—
321	C₂×C₄×C₃₁	—	2	1	no	—
322	C₂×C₄×C₃₁	—	2	1	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	2	no	—
326	C₂×C₄×C₃₁	—	2	2	no	—
327	C₂×C₄×C₃₁	—	2	2	no	—
328	C₂×C₄×C₃₁	—	2	4	no	—
329	C₂×C₄×C₃₁	—	4	4	no	—
330	C₂×C₄×C₃₁	—	8	4	no	—
331	C₂×C₄×C₃₁	—	8	4	no	—
332	C₂×C₄×C₃₁	—	8	2	no	—
333	C₂×C₄×C₃₁	—	8	2	no	—
334	C₂×C₄×C₃₁	—	8	4	no	—
335	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
342	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
343	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
344	C₈×C₃₁	—	2	1	no	—
345	C₈×C₃₁	—	2	1	no	—
346	C₈×C₃₁	—	2	2	no	—
347	C₈×C₃₁	—	2	2	no	—
348	C₈×C₃₁	C₂×#41	1	2	yes	—
349	C₈×C₃₁	C₂×#41	1	2	yes	—
350	#3494	C₂×C₃₁	1	2	yes	complemented
351	#3347	C₂×C₃₁	1	4	yes	complemented
352	#3345	C₂×C₃₁	1	4	yes	complemented
353	#3341	C₂×C₃₁	1	2	yes	complemented
354	#3339	C₂×C₃₁	1	2	yes	complemented
355	#3339	C₂×C₃₁	1	2	yes	complemented
356	#3334	C₂×C₃₁	1	2	yes	complemented
357	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
358	#3096	C₂×C₃₁	1	2	yes	complemented
359	#3094	C₂×C₃₁	1	2	yes	complemented
360	#3081	C₂×C₃₁	1	2	yes	complemented
361	#3058	C₂×C₃₁	1	1	yes	characteristic, complemented
362	C₂×#466	C₂×C₃₁	1	1	yes	characteristic, complemented
363	#2948	C₂×C₃₁	1	1	yes	characteristic, complemented
364	#2929	C₂×C₃₁	1	1	yes	characteristic, complemented
365	#2913	C₂×C₃₁	1	1	yes	characteristic, complemented
366	C₂×#427	C₂×C₃₁	1	1	yes	characteristic, complemented
367	C₂²×C₃₁	—	2	1	no	—
368	C₂²×C₃₁	—	2	1	no	—
369	C₂²×C₃₁	—	2	1	no	—
370	C₂²×C₃₁	—	2	1	no	—
371	C₂²×C₃₁	—	2	1	no	—
372	C₂²×C₃₁	—	2	2	no	—
373	C₂²×C₃₁	—	2	1	no	—
374	C₂²×C₃₁	—	2	2	no	—
375	C₂²×C₃₁	—	2	2	no	—
376	C₂²×C₃₁	—	2	1	no	—
377	C₂²×C₃₁	—	4	4	no	—
378	C₂²×C₃₁	—	4	4	no	—
379	C₂²×C₃₁	—	4	4	no	—
380	C₂²×C₃₁	—	4	4	no	—
381	C₂²×C₃₁	—	16	4	no	—
382	C₂²×C₃₁	#547	1	2	yes	—
383	C₂²×C₃₁	#576	1	2	yes	—
384	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₃₁	—	2	2	no	—
386	C₄×C₃₁	—	2	1	no	—
387	C₄×C₃₁	—	2	1	no	—
388	C₄×C₃₁	—	2	2	no	—
389	C₄×C₃₁	—	2	2	no	—
390	C₄×C₃₁	—	4	2	no	—
391	C₄×C₃₁	—	4	2	no	—
392	C₄×C₃₁	—	4	2	no	—
393	C₄×C₃₁	—	4	2	no	—
394	C₄×C₃₁	—	4	4	no	—
395	C₄×C₃₁	#547	1	2	yes	—
396	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
397	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
398	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
399	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
400	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
401	#555	C₂²×C₃₁	1	4	yes	complemented
402	#553	C₂²×C₃₁	1	4	yes	complemented
403	#553	C₂²×C₃₁	1	4	yes	complemented
404	#551	—	2	4	no	—
405	#547	C₂²×C₃₁	1	4	yes	complemented
406	#546	—	2	4	no	—
407	#544	C₂²×C₃₁	1	2	yes	—
408	#542	—	2	2	no	—
409	#540	—	2	2	no	—
410	#535	C₂²×C₃₁	1	2	yes	—
411	#532	—	2	2	no	—
412	#529	—	2	2	no	—
413	#525	C₂²×C₃₁	1	1	yes	characteristic
414	C₂×#121	C₂²×C₃₁	1	2	yes	—
415	#520	C₂²×C₃₁	1	2	yes	—
416	#518	C₂²×C₃₁	1	2	yes	—
417	C₂×#117	C₂²×C₃₁	1	2	yes	—
418	#501	C₂²×C₃₁	1	4	yes	complemented
419	#500	C₂²×C₃₁	1	2	yes	complemented
420	#499	C₂²×C₃₁	1	2	yes	complemented
421	#482	C₂²×C₃₁	1	4	yes	complemented
422	#482	C₂²×C₃₁	1	4	yes	complemented
423	#482	C₂²×C₃₁	1	4	yes	complemented
424	#482	C₂²×C₃₁	1	4	yes	complemented
425	#481	C₂²×C₃₁	1	4	yes	complemented
426	#481	C₂²×C₃₁	1	4	yes	complemented
427	#480	C₂²×C₃₁	1	4	yes	complemented
428	#480	C₂²×C₃₁	1	4	yes	complemented
429	#478	C₂²×C₃₁	1	4	yes	complemented
430	#478	C₂²×C₃₁	1	4	yes	complemented
431	#476	C₂²×C₃₁	1	4	yes	complemented
432	#474	C₂²×C₃₁	1	4	yes	complemented
433	#469	C₂²×C₃₁	1	4	yes	complemented
434	#466	C₂²×C₃₁	1	2	yes	—
435	#466	C₂²×C₃₁	1	2	yes	—
436	#466	C₂²×C₃₁	1	2	yes	—
437	#466	C₂²×C₃₁	1	2	yes	—
438	#466	C₂²×C₃₁	1	2	yes	complemented
439	#466	C₂²×C₃₁	1	2	yes	complemented
440	#442	C₂²×C₃₁	1	4	yes	complemented
441	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
442	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
443	#435	C₂²×C₃₁	1	2	yes	complemented
444	#435	C₂²×C₃₁	1	2	yes	complemented
445	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
446	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
447	#428	C₂²×C₃₁	1	2	yes	—
448	#428	C₂²×C₃₁	1	2	yes	—
449	#428	C₂²×C₃₁	1	4	yes	complemented
450	#427	C₂²×C₃₁	1	2	yes	—
451	#427	C₂²×C₃₁	1	1	yes	characteristic
452	#427	C₂²×C₃₁	1	1	yes	characteristic
453	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
454	#427	C₂²×C₃₁	1	2	yes	complemented
455	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
456	#427	C₂²×C₃₁	1	2	yes	complemented
457	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
459	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
460	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
461	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
462	#424	C₂²×C₃₁	1	1	yes	characteristic
463	#418	C₂²×C₃₁	1	2	yes	—
464	#418	C₂²×C₃₁	1	2	yes	—
465	C₂×#102	C₂²×C₃₁	1	2	yes	—
466	#408	C₂²×C₃₁	1	1	yes	characteristic
467	#407	C₂²×C₃₁	1	1	yes	characteristic
468	#405	C₂²×C₃₁	1	1	yes	characteristic
469	C₂×C₃₁	—	2	2	no	—
470	C₂×C₃₁	—	2	2	no	—
471	C₂×C₃₁	—	4	2	no	—
472	C₂×C₃₁	—	4	1	no	—
473	C₂×C₃₁	—	8	4	no	—
474	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
475	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
476	C₂×C₃₁	#3584	1	1	yes	characteristic
477	C₂×#41	—	2	4	no	—
478	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
479	C₂²×D₄	—	2	2	no	—
480	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
481	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
482	C₂×D₈	—	2	4	no	—
483	C₂×D₈	C₂³×C₃₁	1	2	yes	—
484	C₂×D₈	C₂³×C₃₁	1	2	yes	—
485	#131	—	2	4	no	—
486	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
487	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
488	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
489	C₂²×C₈	—	2	4	no	—
490	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
496	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
497	C₄⋊Q₈	—	2	2	no	—
498	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
499	#127	—	2	2	no	—
500	#126	—	2	4	no	—
501	#126	—	2	4	no	—
502	#125	—	2	2	no	—
503	#125	C₂³×C₃₁	1	4	yes	—
504	#124	—	2	2	no	—
505	#124	—	2	4	no	—
506	#124	—	2	4	no	—
507	#123	—	2	4	no	—
508	#123	—	2	4	no	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	#123	D₄×C₃₁	1	2	yes	—
512	C₂²⋊Q₈	—	2	4	no	—
513	C₂²⋊Q₈	—	2	4	no	—
514	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
515	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
516	#121	—	2	4	no	—
517	#121	—	2	4	no	—
518	#121	—	2	4	no	—
519	#121	—	2	2	no	—
520	#121	—	2	2	no	—
521	#121	D₄×C₃₁	1	1	yes	characteristic
522	#121	D₄×C₃₁	1	1	yes	characteristic
523	#121	C₂³×C₃₁	1	4	yes	—
524	#121	C₂³×C₃₁	1	4	yes	—
525	#121	C₂³×C₃₁	1	4	yes	—
526	#121	C₂³×C₃₁	1	4	yes	—
527	#120	—	2	4	no	—
528	#120	D₄×C₃₁	1	2	yes	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	4	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	2	no	—
534	C₄×D₄	—	2	4	no	—
535	C₄×D₄	—	2	4	no	—
536	C₄×D₄	C₂³×C₃₁	1	4	yes	—
537	C₄×D₄	C₂³×C₃₁	1	4	yes	—
538	C₄×D₄	C₂³×C₃₁	1	2	yes	—
539	C₄×D₄	C₂³×C₃₁	1	2	yes	—
540	#117	—	2	2	no	—
541	#117	—	2	2	no	—
542	#117	—	2	4	no	—
543	#117	C₂³×C₃₁	1	2	yes	—
544	#117	C₂³×C₃₁	1	2	yes	—
545	#117	C₂³×C₃₁	1	2	yes	—
546	#117	C₂³×C₃₁	1	2	yes	—
547	#117	C₂³×C₃₁	1	4	yes	—
548	#117	C₂³×C₃₁	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
553	C₂×C₂²⋊C₄	—	2	2	no	—
554	C₂×C₂²⋊C₄	—	2	2	no	—
555	C₂×C₂²⋊C₄	—	2	4	no	—
556	C₂×C₄²	—	2	2	no	—
557	#107	C₂³×C₃₁	1	2	yes	—
558	#107	C₂³×C₃₁	1	2	yes	—
559	#107	C₂³×C₃₁	1	1	yes	characteristic
560	#107	C₂³×C₃₁	1	1	yes	characteristic
561	#107	C₂³×C₃₁	1	1	yes	characteristic
562	#107	C₂³×C₃₁	1	1	yes	characteristic
563	#107	C₂³×C₃₁	1	2	yes	—
564	#107	C₂³×C₃₁	1	2	yes	—
565	#107	C₂³×C₃₁	1	4	yes	—
566	#107	C₂³×C₃₁	1	4	yes	—
567	#106	C₂³×C₃₁	1	2	yes	—
568	#106	C₂³×C₃₁	1	2	yes	—
569	#106	C₂³×C₃₁	1	2	yes	—
570	#106	C₂³×C₃₁	1	2	yes	—
571	#106	C₂³×C₃₁	1	4	yes	—
572	#106	C₂³×C₃₁	1	4	yes	—
573	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
574	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
575	#102	C₂³×C₃₁	1	4	yes	—
576	#102	C₂³×C₃₁	1	4	yes	—
577	#102	C₂³×C₃₁	1	4	yes	—
578	#102	C₂³×C₃₁	1	4	yes	—
579	#102	C₂³×C₃₁	1	4	yes	—
580	#102	C₂³×C₃₁	1	4	yes	—
581	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
582	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
583	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
584	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
585	#97	C₂³×C₃₁	1	2	yes	—
586	C₄×C₈	C₂³×C₃₁	1	2	yes	—
587	C₃₁	#61262	1	1	yes	characteristic, direct product factor, Sylow
588	C₂⁴	—	2	2	no	—
589	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
590	#41	—	2	2	no	—
591	#41	—	2	2	no	—
592	#41	—	8	8	no	—
593	C₂×Q₈	—	2	4	no	—
594	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	8	4	no	—
603	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
604	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
605	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
606	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
607	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
623	D₈	—	2	4	no	—
624	D₈	—	2	4	no	—
625	M₁₆	—	2	2	no	—
626	M₁₆	—	2	2	no	—
627	M₁₆	—	2	4	no	—
628	C₂×C₈	—	2	2	no	—
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	4	no	—
634	C₂×C₈	#41×C₃₁	1	4	yes	complemented
635	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
636	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
637	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
638	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
639	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
649	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
650	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
651	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
655	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
656	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
669	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
670	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
671	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
672	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	2	no	—
676	C₄²	—	2	2	no	—
677	C₄²	—	2	4	no	—
678	C₄²	C₂⁴×C₃₁	1	2	yes	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	4	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	8	2	no	—
685	C₂³	—	8	2	no	—
686	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
687	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
688	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
689	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
690	Q₈	—	2	2	no	—
691	Q₈	—	8	4	no	—
692	D₄	—	2	4	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	4	no	—
696	D₄	—	2	4	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	8	no	—
699	D₄	—	4	4	no	—
700	D₄	—	8	4	no	—
701	D₄	—	8	4	no	—
702	D₄	—	8	4	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	8	4	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	4	no	—
723	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
729	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
730	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
731	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
732	C₈	—	2	1	no	—
733	C₈	—	2	1	no	—
734	C₈	—	2	2	no	—
735	C₈	—	2	2	no	—
736	C₈	C₂×#41×C₃₁	1	2	yes	—
737	C₈	C₂×#41×C₃₁	1	2	yes	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	16	4	no	—
753	C₂²	C₃₁×#547	1	2	yes	—
754	C₂²	C₃₁×#576	1	2	yes	—
755	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
756	C₄	—	2	1	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	C₃₁×#547	1	2	yes	—
767	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
768	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
769	C₂	—	2	2	no	—
770	C₂	—	2	2	no	—
771	C₂	—	4	1	no	—
772	C₂	—	4	2	no	—
773	C₂	—	8	4	no	—
774	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
775	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
776	C₂	C₃₁×#3584	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×#3494	C₂	semidirect
2. C₃₁×#3347	C₂	semidirect
3. C₃₁×#3345	C₂	semidirect
4. C₃₁×#3341	C₂	semidirect
5. C₃₁×#3339	C₂	semidirect
6. C₃₁×#3339	C₂	semidirect
7. C₃₁×#3334	C₂	semidirect
8. C₃₁×#3164	C₂	semidirect
9. C₃₁×#3096	C₂	semidirect
10. C₃₁×#3094	C₂	semidirect
11. C₃₁×#3081	C₂	semidirect
12. C₃₁×#3058	C₂	semidirect
13. C₂×C₃₁×#466	C₂	semidirect
14. C₃₁×#2948	C₂	semidirect
15. C₃₁×#2929	C₂	semidirect
16. C₃₁×#2913	C₂	semidirect
17. C₂×C₃₁×#427	C₂	semidirect
21. C₃₁×#555	C₂²	semidirect
22. C₃₁×#553	C₂²	semidirect
23. C₃₁×#553	C₂²	semidirect
25. C₃₁×#547	C₂²	semidirect
38. C₃₁×#501	C₂²	semidirect
39. C₃₁×#500	C₂²	semidirect
40. C₃₁×#499	C₂²	semidirect
41. C₃₁×#482	C₂²	semidirect
42. C₃₁×#482	C₂²	semidirect
43. C₃₁×#482	C₂²	semidirect
44. C₃₁×#482	C₂²	semidirect
45. C₃₁×#481	C₂²	semidirect
46. C₃₁×#481	C₂²	semidirect
47. C₃₁×#480	C₂²	semidirect
48. C₃₁×#480	C₂²	semidirect
49. C₃₁×#478	C₂²	semidirect
50. C₃₁×#478	C₂²	semidirect
51. C₃₁×#476	C₂²	semidirect
52. C₃₁×#474	C₂²	semidirect
53. C₃₁×#469	C₂²	semidirect
58. C₃₁×#466	C₂²	semidirect
59. C₃₁×#466	C₂²	semidirect
60. C₃₁×#442	C₂²	semidirect
61. C₄×D₈×C₃₁	C₂²	semidirect
62. C₄×D₈×C₃₁	C₂²	semidirect
63. C₃₁×#435	C₂²	semidirect
64. C₃₁×#435	C₂²	semidirect
65. C₈×D₄×C₃₁	C₂²	semidirect
66. C₈×D₄×C₃₁	C₂²	semidirect
69. C₃₁×#428	C₂²	semidirect
73. C₃₁×#427	C₂²	semidirect
74. C₃₁×#427	C₂²	semidirect
75. C₃₁×#427	C₂²	semidirect
76. C₃₁×#427	C₂²	semidirect
78. C₂×C₃₁×#107	C₂²	semidirect
79. C₂×C₃₁×#107	C₂²	semidirect
80. C₂×C₃₁×#107	C₂²	semidirect
81. C₂×C₃₁×#106	C₂²	semidirect
245. C₂×C₈×C₃₁	#41	semidirect
290. #61262	C₃₁	direct (N × H)
350. #3494	C₂×C₃₁	semidirect
351. #3347	C₂×C₃₁	semidirect
352. #3345	C₂×C₃₁	semidirect
353. #3341	C₂×C₃₁	semidirect
354. #3339	C₂×C₃₁	semidirect
355. #3339	C₂×C₃₁	semidirect
356. #3334	C₂×C₃₁	semidirect
357. #3164	C₂×C₃₁	semidirect
358. #3096	C₂×C₃₁	semidirect
359. #3094	C₂×C₃₁	semidirect
360. #3081	C₂×C₃₁	semidirect
361. #3058	C₂×C₃₁	semidirect
362. C₂×#466	C₂×C₃₁	semidirect
363. #2948	C₂×C₃₁	semidirect
364. #2929	C₂×C₃₁	semidirect
365. #2913	C₂×C₃₁	semidirect
366. C₂×#427	C₂×C₃₁	semidirect
401. #555	C₂²×C₃₁	semidirect
402. #553	C₂²×C₃₁	semidirect
403. #553	C₂²×C₃₁	semidirect
405. #547	C₂²×C₃₁	semidirect
418. #501	C₂²×C₃₁	semidirect
419. #500	C₂²×C₃₁	semidirect
420. #499	C₂²×C₃₁	semidirect
421. #482	C₂²×C₃₁	semidirect
422. #482	C₂²×C₃₁	semidirect
423. #482	C₂²×C₃₁	semidirect
424. #482	C₂²×C₃₁	semidirect
425. #481	C₂²×C₃₁	semidirect
426. #481	C₂²×C₃₁	semidirect
427. #480	C₂²×C₃₁	semidirect
428. #480	C₂²×C₃₁	semidirect
429. #478	C₂²×C₃₁	semidirect
430. #478	C₂²×C₃₁	semidirect
431. #476	C₂²×C₃₁	semidirect
432. #474	C₂²×C₃₁	semidirect
433. #469	C₂²×C₃₁	semidirect
438. #466	C₂²×C₃₁	semidirect
439. #466	C₂²×C₃₁	semidirect
440. #442	C₂²×C₃₁	semidirect
441. C₄×D₈	C₂²×C₃₁	semidirect
442. C₄×D₈	C₂²×C₃₁	semidirect
443. #435	C₂²×C₃₁	semidirect
444. #435	C₂²×C₃₁	semidirect
445. C₈×D₄	C₂²×C₃₁	semidirect
446. C₈×D₄	C₂²×C₃₁	semidirect
449. #428	C₂²×C₃₁	semidirect
453. #427	C₂²×C₃₁	semidirect
454. #427	C₂²×C₃₁	semidirect
455. #427	C₂²×C₃₁	semidirect
456. #427	C₂²×C₃₁	semidirect
458. C₂×#107	C₂²×C₃₁	semidirect
459. C₂×#107	C₂²×C₃₁	semidirect
460. C₂×#107	C₂²×C₃₁	semidirect
461. C₂×#106	C₂²×C₃₁	semidirect
587. C₃₁	#61262	direct (N × H)
634. C₂×C₈	#41×C₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3494	2
C₃₁×#3347	2
C₃₁×#3345	2
C₃₁×#3341	2
C₃₁×#3339	2
C₃₁×#3334	2
C₃₁×#3164	2
C₃₁×#3096	2
C₃₁×#3094	2
C₃₁×#3081	2
C₃₁×#3058	2
C₂×C₃₁×#466	2
C₃₁×#2948	2
C₃₁×#2929	2
C₃₁×#2913	2
C₂×C₃₁×#427	2
#61262	31

Subgroups — C31×#61262 #21518021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61262 #21518021