Subgroups — C₃₁×#62143 #21518902

Order 7936.

1830 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3380	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3361	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3357	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3355	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3322	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3253	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3251	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3233	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3100	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3077	C₂	1	2	yes	maximal, complemented
17	C₃₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#559	C₂²	1	1	yes	characteristic
19	C₃₁×#556	—	2	1	no	—
20	C₃₁×#555	C₂²	1	2	yes	—
21	C₃₁×#554	C₂²	1	1	yes	characteristic
22	C₃₁×#554	C₂²	1	1	yes	characteristic
23	C₃₁×#554	C₂²	1	2	yes	complemented
24	C₃₁×#553	—	2	1	no	—
25	C₃₁×#553	C₂²	1	2	yes	—
26	C₃₁×#553	C₂²	1	4	yes	complemented
27	C₃₁×#551	—	2	2	no	—
28	C₃₁×#548	—	2	2	no	—
29	C₃₁×#547	—	2	1	no	—
30	C₃₁×#546	—	2	1	no	—
31	C₃₁×#546	C₂²	1	2	yes	—
32	D₄²×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#542	—	2	2	no	—
34	C₃₁×#537	—	2	1	no	—
35	C₃₁×#533	C₂²	1	2	yes	complemented
36	C₃₁×#532	C₂²	1	1	yes	characteristic
37	C₃₁×#532	C₂²	1	2	yes	complemented
38	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#529	—	2	1	no	—
41	C₃₁×#529	C₂²	1	2	yes	—
42	C₃₁×#525	—	2	2	no	—
43	C₃₁×#520	—	2	1	no	—
44	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
45	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₃₁	—	2	1	no	—
47	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
48	C₃₁×#500	C₂²	1	2	yes	complemented
49	C₃₁×#499	C₂²	1	4	yes	complemented
50	C₃₁×#488	C₂²	1	4	yes	complemented
51	C₃₁×#486	C₂²	1	2	yes	—
52	C₃₁×#485	C₂²	1	4	yes	complemented
53	C₃₁×#482	C₂²	1	4	yes	—
54	C₃₁×#482	C₂²	1	2	yes	complemented
55	C₃₁×#480	C₂²	1	4	yes	complemented
56	C₃₁×#480	C₂²	1	4	yes	complemented
57	C₃₁×#478	C₂²	1	4	yes	—
58	C₃₁×#478	C₂²	1	4	yes	complemented
59	C₃₁×#478	C₂²	1	4	yes	complemented
60	C₃₁×#477	C₂²	1	2	yes	complemented
61	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#476	C₂²	1	1	yes	characteristic
63	C₃₁×#476	C₂²	1	2	yes	—
64	C₃₁×#476	C₂²	1	2	yes	complemented
65	C₃₁×#476	C₂²	1	2	yes	complemented
66	C₃₁×#475	C₂²	1	2	yes	complemented
67	C₃₁×#474	C₂²	1	2	yes	—
68	C₃₁×#474	C₂²	1	2	yes	complemented
69	C₃₁×#474	C₂²	1	2	yes	complemented
70	C₃₁×#469	C₂²	1	4	yes	—
71	C₃₁×#469	C₂²	1	4	yes	complemented
72	C₃₁×#468	C₂²	1	4	yes	complemented
73	C₃₁×#463	C₂²	1	4	yes	complemented
74	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×#459	C₂²	1	1	yes	characteristic
76	C₃₁×#459	C₂²	1	2	yes	—
77	C₃₁×#459	C₂²	1	2	yes	complemented
78	C₃₁×#449	C₂²	1	2	yes	—
79	C₃₁×#447	C₂²	1	4	yes	—
80	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
82	C₄×D₈×C₃₁	C₂²	1	4	yes	—
83	C₄×D₈×C₃₁	C₂²	1	2	yes	—
84	C₄×D₈×C₃₁	C₂²	1	4	yes	complemented
85	C₃₁×#436	C₂²	1	2	yes	—
86	C₃₁×#436	C₂²	1	4	yes	complemented
87	C₃₁×#431	C₂²	1	2	yes	complemented
88	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#428	C₂²	1	4	yes	complemented
90	C₃₁×#428	C₂²	1	2	yes	complemented
91	C₃₁×#423	C₂²	1	2	yes	complemented
92	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#418	C₂²	1	4	yes	—
94	C₃₁×#417	C₂²	1	2	yes	—
95	C₂×#41×C₃₁	—	2	1	no	—
96	C₂×#41×C₃₁	—	2	1	no	—
97	C₂×#41×C₃₁	—	2	2	no	—
98	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
99	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₃₁	—	2	1	no	—
101	C₂²×D₄×C₃₁	—	2	1	no	—
102	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
103	C₂³×C₄×C₃₁	—	2	2	no	—
104	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
105	C₂×D₈×C₃₁	C₂³	1	2	yes	—
106	C₂×D₈×C₃₁	C₂³	1	4	yes	—
107	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
108	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
109	C₃₁×C₄⋊Q₈	—	2	1	no	—
110	C₃₁×C₄⋊Q₈	—	2	1	no	—
111	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃₁×#127	C₂³	1	1	yes	characteristic
116	C₃₁×#127	C₂³	1	1	yes	characteristic
117	C₃₁×#126	—	2	2	no	—
118	C₃₁×#126	—	2	4	no	—
119	C₃₁×#126	—	2	2	no	—
120	C₃₁×#125	—	2	1	no	—
121	C₃₁×#125	C₂³	1	4	yes	—
122	C₃₁×#125	C₂³	1	2	yes	—
123	C₃₁×#124	—	2	1	no	—
124	C₃₁×#124	—	2	4	no	—
125	C₃₁×#124	—	2	1	no	—
126	C₃₁×#124	—	2	1	no	—
127	C₃₁×#124	—	2	2	no	—
128	C₃₁×#124	C₂³	1	2	yes	—
129	C₃₁×#123	—	2	2	no	—
130	C₃₁×#123	—	2	2	no	—
131	C₃₁×#123	—	2	2	no	—
132	C₃₁×#123	—	2	2	no	—
133	C₃₁×#123	—	2	4	no	—
134	C₃₁×C₂²⋊Q₈	—	2	1	no	—
135	C₃₁×C₂²⋊Q₈	—	2	2	no	—
136	C₃₁×C₂²⋊Q₈	—	2	2	no	—
137	C₃₁×C₂²⋊Q₈	—	2	2	no	—
138	C₃₁×C₂²⋊Q₈	—	2	2	no	—
139	C₃₁×C₂²⋊Q₈	—	2	4	no	—
140	C₃₁×C₂²⋊Q₈	—	2	2	no	—
141	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₃₁×#121	—	2	2	no	—
143	C₃₁×#121	—	2	2	no	—
144	C₃₁×#121	—	2	4	no	—
145	C₃₁×#121	—	2	1	no	—
146	C₃₁×#121	—	2	2	no	—
147	C₃₁×#121	—	2	1	no	—
148	C₃₁×#121	—	2	1	no	—
149	C₃₁×#121	—	2	2	no	—
150	C₃₁×#121	C₂³	1	4	yes	—
151	C₃₁×#121	C₂³	1	2	yes	—
152	C₃₁×#121	C₂³	1	2	yes	—
153	C₃₁×#121	C₂³	1	2	yes	—
154	C₃₁×#120	—	2	2	no	—
155	C₃₁×#120	—	2	2	no	—
156	C₄×Q₈×C₃₁	—	2	2	no	—
157	C₄×Q₈×C₃₁	—	2	2	no	—
158	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
159	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₄×D₄×C₃₁	—	2	1	no	—
163	C₄×D₄×C₃₁	—	2	2	no	—
164	C₄×D₄×C₃₁	—	2	1	no	—
165	C₄×D₄×C₃₁	—	2	1	no	—
166	C₄×D₄×C₃₁	—	2	1	no	—
167	C₄×D₄×C₃₁	—	2	2	no	—
168	C₄×D₄×C₃₁	—	2	4	no	—
169	C₄×D₄×C₃₁	—	2	1	no	—
170	C₄×D₄×C₃₁	—	2	2	no	—
171	C₄×D₄×C₃₁	—	2	2	no	—
172	C₄×D₄×C₃₁	—	2	2	no	—
173	C₄×D₄×C₃₁	—	2	1	no	—
174	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
175	C₄×D₄×C₃₁	D₄	1	2	yes	—
176	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₃₁	C₂³	1	2	yes	—
178	C₄×D₄×C₃₁	C₂³	1	4	yes	—
179	C₄×D₄×C₃₁	C₂³	1	2	yes	—
180	C₄×D₄×C₃₁	C₂³	1	2	yes	—
181	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₃₁	C₂³	1	2	yes	—
183	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₃₁	C₂³	1	2	yes	—
185	C₃₁×#117	—	2	2	no	—
186	C₃₁×#117	—	2	1	no	—
187	C₃₁×#117	—	2	2	no	—
188	C₃₁×#117	D₄	1	1	yes	characteristic
189	C₃₁×#117	D₄	1	2	yes	—
190	C₃₁×#117	C₂³	1	4	yes	—
191	C₃₁×#117	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
193	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
194	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
195	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
199	C₂×C₄²×C₃₁	—	2	1	no	—
200	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
201	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
202	C₃₁×#107	C₂³	1	4	yes	—
203	C₃₁×#107	C₂³	1	4	yes	—
204	C₃₁×#107	C₂³	1	4	yes	—
205	C₃₁×#107	C₂³	1	2	yes	—
206	C₃₁×#106	C₂³	1	2	yes	—
207	C₃₁×#106	C₂³	1	4	yes	—
208	C₃₁×#106	C₂³	1	4	yes	—
209	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
210	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
212	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
213	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₃₁×#103	C₂³	1	4	yes	—
215	C₃₁×#103	C₂³	1	2	yes	—
216	C₃₁×#102	C₂³	1	4	yes	—
217	C₃₁×#102	C₂³	1	2	yes	—
218	C₃₁×#102	C₂³	1	4	yes	—
219	C₃₁×#102	C₂³	1	4	yes	—
220	C₃₁×#102	C₂³	1	4	yes	—
221	C₃₁×#102	C₂³	1	2	yes	—
222	C₃₁×#102	C₂³	1	2	yes	—
223	C₃₁×#102	C₂³	1	4	yes	—
224	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₄×C₈×C₃₁	C₂³	1	2	yes	—
227	C₄×C₈×C₃₁	C₂³	1	4	yes	—
228	C₂⁴×C₃₁	—	2	2	no	—
229	#41×C₃₁	—	2	2	no	—
230	#41×C₃₁	—	4	2	no	—
231	#41×C₃₁	—	4	1	no	—
232	#41×C₃₁	—	4	4	no	—
233	#41×C₃₁	—	8	2	no	—
234	#41×C₃₁	—	8	4	no	—
235	C₂×Q₈×C₃₁	—	2	1	no	—
236	C₂×Q₈×C₃₁	—	2	2	no	—
237	C₂×Q₈×C₃₁	—	2	1	no	—
238	C₂×Q₈×C₃₁	—	2	2	no	—
239	C₂×Q₈×C₃₁	—	8	2	no	—
240	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₃₁	—	2	4	no	—
243	C₂×D₄×C₃₁	—	2	1	no	—
244	C₂×D₄×C₃₁	—	2	2	no	—
245	C₂×D₄×C₃₁	—	2	2	no	—
246	C₂×D₄×C₃₁	—	2	2	no	—
247	C₂×D₄×C₃₁	—	2	4	no	—
248	C₂×D₄×C₃₁	—	2	2	no	—
249	C₂×D₄×C₃₁	—	2	1	no	—
250	C₂×D₄×C₃₁	—	2	1	no	—
251	C₂×D₄×C₃₁	—	2	1	no	—
252	C₂×D₄×C₃₁	—	2	1	no	—
253	C₂×D₄×C₃₁	—	4	2	no	—
254	C₂×D₄×C₃₁	—	4	4	no	—
255	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
258	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
259	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₃₁	—	2	2	no	—
261	C₂²×C₄×C₃₁	—	2	2	no	—
262	C₂²×C₄×C₃₁	—	2	1	no	—
263	C₂²×C₄×C₃₁	—	2	1	no	—
264	C₂²×C₄×C₃₁	—	2	1	no	—
265	C₂²×C₄×C₃₁	—	2	2	no	—
266	C₂²×C₄×C₃₁	—	2	2	no	—
267	C₂²×C₄×C₃₁	—	2	2	no	—
268	C₂²×C₄×C₃₁	—	2	4	no	—
269	C₂²×C₄×C₃₁	—	2	2	no	—
270	C₂²×C₄×C₃₁	—	8	4	no	—
271	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
277	SD₁₆×C₃₁	—	4	2	no	—
278	D₈×C₃₁	—	2	4	no	—
279	D₈×C₃₁	—	4	4	no	—
280	M₁₆×C₃₁	—	4	2	no	—
281	M₁₆×C₃₁	—	4	4	no	—
282	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
283	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
284	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₃₁	—	2	2	no	—
286	C₄⋊C₄×C₃₁	—	2	1	no	—
287	C₄⋊C₄×C₃₁	—	2	2	no	—
288	C₄⋊C₄×C₃₁	—	2	2	no	—
289	C₄⋊C₄×C₃₁	—	2	4	no	—
290	C₄⋊C₄×C₃₁	—	2	2	no	—
291	C₄⋊C₄×C₃₁	—	2	2	no	—
292	C₄⋊C₄×C₃₁	—	2	1	no	—
293	C₄⋊C₄×C₃₁	—	2	1	no	—
294	C₄⋊C₄×C₃₁	—	2	2	no	—
295	C₄⋊C₄×C₃₁	—	2	2	no	—
296	C₄⋊C₄×C₃₁	—	2	1	no	—
297	C₄⋊C₄×C₃₁	—	2	4	no	—
298	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
299	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₃₁	—	2	2	no	—
308	C₂²⋊C₄×C₃₁	—	2	1	no	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	1	no	—
311	C₂²⋊C₄×C₃₁	—	2	2	no	—
312	C₂²⋊C₄×C₃₁	—	2	2	no	—
313	C₂²⋊C₄×C₃₁	—	2	2	no	—
314	C₂²⋊C₄×C₃₁	—	2	2	no	—
315	C₂²⋊C₄×C₃₁	—	2	2	no	—
316	C₂²⋊C₄×C₃₁	—	2	4	no	—
317	C₂²⋊C₄×C₃₁	—	2	1	no	—
318	C₂²⋊C₄×C₃₁	—	2	2	no	—
319	C₂²⋊C₄×C₃₁	—	2	2	no	—
320	C₂²⋊C₄×C₃₁	—	2	2	no	—
321	C₂²⋊C₄×C₃₁	—	2	4	no	—
322	C₂²⋊C₄×C₃₁	—	2	2	no	—
323	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
326	C₄²×C₃₁	—	2	1	no	—
327	C₄²×C₃₁	—	2	1	no	—
328	C₄²×C₃₁	—	2	1	no	—
329	C₄²×C₃₁	—	2	4	no	—
330	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₃₁	C₂×D₄	1	2	yes	—
333	C₄²×C₃₁	C₂×D₄	1	2	yes	—
334	C₄²×C₃₁	C₂⁴	1	2	yes	—
335	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
337	#62143	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
338	C₂³×C₃₁	—	2	1	no	—
339	C₂³×C₃₁	—	2	2	no	—
340	C₂³×C₃₁	—	2	2	no	—
341	C₂³×C₃₁	—	4	4	no	—
342	C₂³×C₃₁	—	4	4	no	—
343	C₂³×C₃₁	—	8	2	no	—
344	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
345	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
346	Q₈×C₃₁	—	2	2	no	—
347	Q₈×C₃₁	—	2	1	no	—
348	Q₈×C₃₁	—	2	1	no	—
349	Q₈×C₃₁	—	4	2	no	—
350	Q₈×C₃₁	—	4	4	no	—
351	Q₈×C₃₁	—	8	2	no	—
352	Q₈×C₃₁	—	8	1	no	—
353	D₄×C₃₁	—	2	2	no	—
354	D₄×C₃₁	—	2	2	no	—
355	D₄×C₃₁	—	2	2	no	—
356	D₄×C₃₁	—	2	1	no	—
357	D₄×C₃₁	—	2	2	no	—
358	D₄×C₃₁	—	2	2	no	—
359	D₄×C₃₁	—	4	2	no	—
360	D₄×C₃₁	—	4	4	no	—
361	D₄×C₃₁	—	4	2	no	—
362	D₄×C₃₁	—	4	2	no	—
363	D₄×C₃₁	—	4	4	no	—
364	D₄×C₃₁	—	4	4	no	—
365	D₄×C₃₁	—	4	2	no	—
366	D₄×C₃₁	—	4	2	no	—
367	D₄×C₃₁	—	8	1	no	—
368	D₄×C₃₁	—	8	2	no	—
369	D₄×C₃₁	—	8	4	no	—
370	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	4	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	1	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	1	no	—
378	C₂×C₄×C₃₁	—	2	1	no	—
379	C₂×C₄×C₃₁	—	2	1	no	—
380	C₂×C₄×C₃₁	—	2	2	no	—
381	C₂×C₄×C₃₁	—	2	1	no	—
382	C₂×C₄×C₃₁	—	2	4	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	4	2	no	—
385	C₂×C₄×C₃₁	—	4	2	no	—
386	C₂×C₄×C₃₁	—	4	2	no	—
387	C₂×C₄×C₃₁	—	4	4	no	—
388	C₂×C₄×C₃₁	—	4	2	no	—
389	C₂×C₄×C₃₁	—	4	4	no	—
390	C₂×C₄×C₃₁	—	8	2	no	—
391	C₂×C₄×C₃₁	—	8	2	no	—
392	C₂×C₄×C₃₁	—	8	4	no	—
393	C₂×C₄×C₃₁	—	8	2	no	—
394	C₂×C₄×C₃₁	—	8	2	no	—
395	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
404	C₈×C₃₁	—	2	2	no	—
405	C₈×C₃₁	—	2	4	no	—
406	C₈×C₃₁	—	2	2	no	—
407	#3511	C₂×C₃₁	1	1	yes	characteristic, complemented
408	#3481	C₂×C₃₁	1	1	yes	characteristic, complemented
409	#3380	C₂×C₃₁	1	2	yes	complemented
410	#3361	C₂×C₃₁	1	2	yes	complemented
411	#3357	C₂×C₃₁	1	2	yes	complemented
412	#3355	C₂×C₃₁	1	4	yes	complemented
413	#3325	C₂×C₃₁	1	2	yes	complemented
414	#3322	C₂×C₃₁	1	4	yes	complemented
415	#3253	C₂×C₃₁	1	1	yes	characteristic, complemented
416	#3251	C₂×C₃₁	1	2	yes	complemented
417	#3233	C₂×C₃₁	1	2	yes	complemented
418	#3226	C₂×C₃₁	1	1	yes	characteristic, complemented
419	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
420	#3100	C₂×C₃₁	1	2	yes	complemented
421	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
422	#3077	C₂×C₃₁	1	2	yes	complemented
423	#2991	C₂×C₃₁	1	1	yes	characteristic, complemented
424	C₂²×C₃₁	—	2	1	no	—
425	C₂²×C₃₁	—	2	2	no	—
426	C₂²×C₃₁	—	2	2	no	—
427	C₂²×C₃₁	—	2	1	no	—
428	C₂²×C₃₁	—	2	2	no	—
429	C₂²×C₃₁	—	2	1	no	—
430	C₂²×C₃₁	—	2	2	no	—
431	C₂²×C₃₁	—	4	1	no	—
432	C₂²×C₃₁	—	4	1	no	—
433	C₂²×C₃₁	—	4	2	no	—
434	C₂²×C₃₁	—	4	2	no	—
435	C₂²×C₃₁	—	4	2	no	—
436	C₂²×C₃₁	—	4	2	no	—
437	C₂²×C₃₁	—	4	2	no	—
438	C₂²×C₃₁	—	4	2	no	—
439	C₂²×C₃₁	—	8	8	no	—
440	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
441	C₄×C₃₁	—	2	1	no	—
442	C₄×C₃₁	—	2	2	no	—
443	C₄×C₃₁	—	2	1	no	—
444	C₄×C₃₁	—	2	2	no	—
445	C₄×C₃₁	—	2	2	no	—
446	C₄×C₃₁	—	2	1	no	—
447	C₄×C₃₁	—	4	1	no	—
448	C₄×C₃₁	—	4	1	no	—
449	C₄×C₃₁	—	4	2	no	—
450	C₄×C₃₁	—	4	1	no	—
451	C₄×C₃₁	—	4	2	no	—
452	C₄×C₃₁	—	4	4	no	—
453	C₄×C₃₁	#575	1	2	yes	—
454	C₄×C₃₁	#576	1	2	yes	—
455	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
456	C₄×C₃₁	#585	1	1	yes	characteristic
457	#559	C₂²×C₃₁	1	1	yes	characteristic
458	#556	—	2	1	no	—
459	#555	C₂²×C₃₁	1	2	yes	—
460	#554	C₂²×C₃₁	1	1	yes	characteristic
461	#554	C₂²×C₃₁	1	1	yes	characteristic
462	#554	C₂²×C₃₁	1	2	yes	complemented
463	#553	—	2	1	no	—
464	#553	C₂²×C₃₁	1	2	yes	—
465	#553	C₂²×C₃₁	1	4	yes	complemented
466	#551	—	2	2	no	—
467	#548	—	2	2	no	—
468	#547	—	2	1	no	—
469	#546	—	2	1	no	—
470	#546	C₂²×C₃₁	1	2	yes	—
471	D₄²	C₂²×C₃₁	1	1	yes	characteristic
472	#542	—	2	2	no	—
473	#537	—	2	1	no	—
474	#533	C₂²×C₃₁	1	2	yes	complemented
475	#532	C₂²×C₃₁	1	1	yes	characteristic
476	#532	C₂²×C₃₁	1	2	yes	complemented
477	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
478	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
479	#529	—	2	1	no	—
480	#529	C₂²×C₃₁	1	2	yes	—
481	#525	—	2	2	no	—
482	#520	—	2	1	no	—
483	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
484	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
485	C₂×C₄×D₄	—	2	1	no	—
486	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
487	#500	C₂²×C₃₁	1	2	yes	complemented
488	#499	C₂²×C₃₁	1	4	yes	complemented
489	#488	C₂²×C₃₁	1	4	yes	complemented
490	#486	C₂²×C₃₁	1	2	yes	—
491	#485	C₂²×C₃₁	1	4	yes	complemented
492	#482	C₂²×C₃₁	1	4	yes	—
493	#482	C₂²×C₃₁	1	2	yes	complemented
494	#480	C₂²×C₃₁	1	4	yes	complemented
495	#480	C₂²×C₃₁	1	4	yes	complemented
496	#478	C₂²×C₃₁	1	4	yes	—
497	#478	C₂²×C₃₁	1	4	yes	complemented
498	#478	C₂²×C₃₁	1	4	yes	complemented
499	#477	C₂²×C₃₁	1	2	yes	complemented
500	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
501	#476	C₂²×C₃₁	1	1	yes	characteristic
502	#476	C₂²×C₃₁	1	2	yes	—
503	#476	C₂²×C₃₁	1	2	yes	complemented
504	#476	C₂²×C₃₁	1	2	yes	complemented
505	#475	C₂²×C₃₁	1	2	yes	complemented
506	#474	C₂²×C₃₁	1	2	yes	—
507	#474	C₂²×C₃₁	1	2	yes	complemented
508	#474	C₂²×C₃₁	1	2	yes	complemented
509	#469	C₂²×C₃₁	1	4	yes	—
510	#469	C₂²×C₃₁	1	4	yes	complemented
511	#468	C₂²×C₃₁	1	4	yes	complemented
512	#463	C₂²×C₃₁	1	4	yes	complemented
513	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
514	#459	C₂²×C₃₁	1	1	yes	characteristic
515	#459	C₂²×C₃₁	1	2	yes	—
516	#459	C₂²×C₃₁	1	2	yes	complemented
517	#449	C₂²×C₃₁	1	2	yes	—
518	#447	C₂²×C₃₁	1	4	yes	—
519	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
520	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
521	C₄×D₈	C₂²×C₃₁	1	4	yes	—
522	C₄×D₈	C₂²×C₃₁	1	2	yes	—
523	C₄×D₈	C₂²×C₃₁	1	4	yes	complemented
524	#436	C₂²×C₃₁	1	2	yes	—
525	#436	C₂²×C₃₁	1	4	yes	complemented
526	#431	C₂²×C₃₁	1	2	yes	complemented
527	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
528	#428	C₂²×C₃₁	1	4	yes	complemented
529	#428	C₂²×C₃₁	1	2	yes	complemented
530	#423	C₂²×C₃₁	1	2	yes	complemented
531	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
532	#418	C₂²×C₃₁	1	4	yes	—
533	#417	C₂²×C₃₁	1	2	yes	—
534	C₂×C₃₁	—	4	1	no	—
535	C₂×C₃₁	—	4	2	no	—
536	C₂×C₃₁	—	4	2	no	—
537	C₂×C₃₁	—	8	2	no	—
538	C₂×C₃₁	—	8	2	no	—
539	C₂×C₃₁	#3489	1	1	yes	characteristic
540	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
541	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
542	C₂×#41	—	2	1	no	—
543	C₂×#41	—	2	1	no	—
544	C₂×#41	—	2	2	no	—
545	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
546	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
547	C₂²×Q₈	—	2	1	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
550	C₂³×C₄	—	2	2	no	—
551	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
552	C₂×D₈	C₂³×C₃₁	1	2	yes	—
553	C₂×D₈	C₂³×C₃₁	1	4	yes	—
554	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
555	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
559	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
561	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
562	#127	C₂³×C₃₁	1	1	yes	characteristic
563	#127	C₂³×C₃₁	1	1	yes	characteristic
564	#126	—	2	2	no	—
565	#126	—	2	4	no	—
566	#126	—	2	2	no	—
567	#125	—	2	1	no	—
568	#125	C₂³×C₃₁	1	2	yes	—
569	#125	C₂³×C₃₁	1	4	yes	—
570	#124	—	2	1	no	—
571	#124	—	2	4	no	—
572	#124	—	2	1	no	—
573	#124	—	2	1	no	—
574	#124	—	2	2	no	—
575	#124	C₂³×C₃₁	1	2	yes	—
576	#123	—	2	2	no	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	2	no	—
580	#123	—	2	4	no	—
581	C₂²⋊Q₈	—	2	1	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	4	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	—	2	4	no	—
592	#121	—	2	1	no	—
593	#121	—	2	2	no	—
594	#121	—	2	1	no	—
595	#121	—	2	1	no	—
596	#121	—	2	2	no	—
597	#121	C₂³×C₃₁	1	2	yes	—
598	#121	C₂³×C₃₁	1	2	yes	—
599	#121	C₂³×C₃₁	1	2	yes	—
600	#121	C₂³×C₃₁	1	4	yes	—
601	#120	—	2	2	no	—
602	#120	—	2	2	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	4	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
622	C₄×D₄	D₄×C₃₁	1	2	yes	—
623	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₄×D₄	C₂³×C₃₁	1	2	yes	—
625	C₄×D₄	C₂³×C₃₁	1	2	yes	—
626	C₄×D₄	C₂³×C₃₁	1	2	yes	—
627	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₃₁	1	4	yes	—
629	C₄×D₄	C₂³×C₃₁	1	2	yes	—
630	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₃₁	1	2	yes	—
632	#117	—	2	2	no	—
633	#117	—	2	1	no	—
634	#117	—	2	2	no	—
635	#117	D₄×C₃₁	1	1	yes	characteristic
636	#117	D₄×C₃₁	1	2	yes	—
637	#117	C₂³×C₃₁	1	1	yes	characteristic
638	#117	C₂³×C₃₁	1	4	yes	—
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	2	no	—
642	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
644	C₂×C₂²⋊C₄	—	2	2	no	—
645	C₂×C₂²⋊C₄	—	2	2	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
648	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
649	#107	C₂³×C₃₁	1	4	yes	—
650	#107	C₂³×C₃₁	1	4	yes	—
651	#107	C₂³×C₃₁	1	4	yes	—
652	#107	C₂³×C₃₁	1	2	yes	—
653	#106	C₂³×C₃₁	1	2	yes	—
654	#106	C₂³×C₃₁	1	4	yes	—
655	#106	C₂³×C₃₁	1	4	yes	—
656	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
657	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
658	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
659	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
660	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
661	#103	C₂³×C₃₁	1	4	yes	—
662	#103	C₂³×C₃₁	1	2	yes	—
663	#102	C₂³×C₃₁	1	4	yes	—
664	#102	C₂³×C₃₁	1	2	yes	—
665	#102	C₂³×C₃₁	1	4	yes	—
666	#102	C₂³×C₃₁	1	4	yes	—
667	#102	C₂³×C₃₁	1	4	yes	—
668	#102	C₂³×C₃₁	1	2	yes	—
669	#102	C₂³×C₃₁	1	2	yes	—
670	#102	C₂³×C₃₁	1	4	yes	—
671	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
672	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
673	C₄×C₈	C₂³×C₃₁	1	2	yes	—
674	C₄×C₈	C₂³×C₃₁	1	4	yes	—
675	C₃₁	#62143	1	1	yes	characteristic, direct product factor, Sylow
676	C₂⁴	—	2	2	no	—
677	#41	—	2	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	1	no	—
680	#41	—	4	4	no	—
681	#41	—	8	2	no	—
682	#41	—	8	4	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	2	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	8	2	no	—
688	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
689	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
704	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
705	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
706	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
707	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	8	4	no	—
719	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
720	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
721	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
722	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
725	SD₁₆	—	4	2	no	—
726	D₈	—	2	4	no	—
727	D₈	—	4	4	no	—
728	M₁₆	—	4	2	no	—
729	M₁₆	—	4	4	no	—
730	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
731	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
732	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
747	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
749	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
752	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	1	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
773	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
774	C₄²	—	2	1	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	4	no	—
778	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
779	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₃₁	1	2	yes	—
781	C₄²	C₂×D₄×C₃₁	1	2	yes	—
782	C₄²	C₂⁴×C₃₁	1	2	yes	—
783	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
784	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
785	C₂³	—	2	1	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	4	4	no	—
789	C₂³	—	4	4	no	—
790	C₂³	—	8	2	no	—
791	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
792	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
793	Q₈	—	2	2	no	—
794	Q₈	—	2	1	no	—
795	Q₈	—	2	1	no	—
796	Q₈	—	4	2	no	—
797	Q₈	—	4	4	no	—
798	Q₈	—	8	2	no	—
799	Q₈	—	8	1	no	—
800	D₄	—	2	2	no	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	2	no	—
813	D₄	—	4	2	no	—
814	D₄	—	8	1	no	—
815	D₄	—	8	2	no	—
816	D₄	—	8	4	no	—
817	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	—	8	2	no	—
839	C₂×C₄	—	8	4	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	—	8	2	no	—
842	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
846	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
847	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
850	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
851	C₈	—	2	2	no	—
852	C₈	—	2	4	no	—
853	C₈	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	8	8	no	—
870	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
871	C₄	—	2	1	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	2	no	—
876	C₄	—	2	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	4	no	—
883	C₄	C₃₁×#575	1	2	yes	—
884	C₄	C₃₁×#576	1	2	yes	—
885	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
886	C₄	C₃₁×#585	1	1	yes	characteristic
887	C₂	—	4	2	no	—
888	C₂	—	4	1	no	—
889	C₂	—	4	2	no	—
890	C₂	—	8	2	no	—
891	C₂	—	8	2	no	—
892	C₂	C₃₁×#3489	1	1	yes	characteristic
893	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
894	C₂	C₂×C₃₁×#576	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3511	C₂	semidirect
2. C₃₁×#3481	C₂	semidirect
3. C₃₁×#3380	C₂	semidirect
4. C₃₁×#3361	C₂	semidirect
5. C₃₁×#3357	C₂	semidirect
6. C₃₁×#3355	C₂	semidirect
7. C₃₁×#3325	C₂	semidirect
8. C₃₁×#3322	C₂	semidirect
9. C₃₁×#3253	C₂	semidirect
10. C₃₁×#3251	C₂	semidirect
11. C₃₁×#3233	C₂	semidirect
12. C₃₁×#3226	C₂	semidirect
13. C₃₁×#3106	C₂	semidirect
14. C₃₁×#3100	C₂	semidirect
15. C₃₁×#3079	C₂	semidirect
16. C₃₁×#3077	C₂	semidirect
17. C₃₁×#2991	C₂	semidirect
23. C₃₁×#554	C₂²	semidirect
26. C₃₁×#553	C₂²	semidirect
35. C₃₁×#533	C₂²	semidirect
37. C₃₁×#532	C₂²	semidirect
38. C₃₁×#532	C₂²	semidirect
39. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
48. C₃₁×#500	C₂²	semidirect
49. C₃₁×#499	C₂²	semidirect
50. C₃₁×#488	C₂²	semidirect
52. C₃₁×#485	C₂²	semidirect
54. C₃₁×#482	C₂²	semidirect
55. C₃₁×#480	C₂²	semidirect
56. C₃₁×#480	C₂²	semidirect
58. C₃₁×#478	C₂²	semidirect
59. C₃₁×#478	C₂²	semidirect
60. C₃₁×#477	C₂²	semidirect
61. C₃₁×#477	C₂²	semidirect
64. C₃₁×#476	C₂²	semidirect
65. C₃₁×#476	C₂²	semidirect
66. C₃₁×#475	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
69. C₃₁×#474	C₂²	semidirect
71. C₃₁×#469	C₂²	semidirect
72. C₃₁×#468	C₂²	semidirect
73. C₃₁×#463	C₂²	semidirect
74. C₃₁×#460	C₂²	semidirect
77. C₃₁×#459	C₂²	semidirect
80. C₈×Q₈×C₃₁	C₂²	semidirect
81. C₄×SD₁₆×C₃₁	C₂²	semidirect
84. C₄×D₈×C₃₁	C₂²	semidirect
86. C₃₁×#436	C₂²	semidirect
87. C₃₁×#431	C₂²	semidirect
88. C₃₁×#431	C₂²	semidirect
89. C₃₁×#428	C₂²	semidirect
90. C₃₁×#428	C₂²	semidirect
91. C₃₁×#423	C₂²	semidirect
92. C₃₁×#423	C₂²	semidirect
337. #62143	C₃₁	direct (N × H)
407. #3511	C₂×C₃₁	semidirect
408. #3481	C₂×C₃₁	semidirect
409. #3380	C₂×C₃₁	semidirect
410. #3361	C₂×C₃₁	semidirect
411. #3357	C₂×C₃₁	semidirect
412. #3355	C₂×C₃₁	semidirect
413. #3325	C₂×C₃₁	semidirect
414. #3322	C₂×C₃₁	semidirect
415. #3253	C₂×C₃₁	semidirect
416. #3251	C₂×C₃₁	semidirect
417. #3233	C₂×C₃₁	semidirect
418. #3226	C₂×C₃₁	semidirect
419. #3106	C₂×C₃₁	semidirect
420. #3100	C₂×C₃₁	semidirect
421. #3079	C₂×C₃₁	semidirect
422. #3077	C₂×C₃₁	semidirect
423. #2991	C₂×C₃₁	semidirect
462. #554	C₂²×C₃₁	semidirect
465. #553	C₂²×C₃₁	semidirect
474. #533	C₂²×C₃₁	semidirect
476. #532	C₂²×C₃₁	semidirect
477. #532	C₂²×C₃₁	semidirect
478. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
487. #500	C₂²×C₃₁	semidirect
488. #499	C₂²×C₃₁	semidirect
489. #488	C₂²×C₃₁	semidirect
491. #485	C₂²×C₃₁	semidirect
493. #482	C₂²×C₃₁	semidirect
494. #480	C₂²×C₃₁	semidirect
495. #480	C₂²×C₃₁	semidirect
497. #478	C₂²×C₃₁	semidirect
498. #478	C₂²×C₃₁	semidirect
499. #477	C₂²×C₃₁	semidirect
500. #477	C₂²×C₃₁	semidirect
503. #476	C₂²×C₃₁	semidirect
504. #476	C₂²×C₃₁	semidirect
505. #475	C₂²×C₃₁	semidirect
507. #474	C₂²×C₃₁	semidirect
508. #474	C₂²×C₃₁	semidirect
510. #469	C₂²×C₃₁	semidirect
511. #468	C₂²×C₃₁	semidirect
512. #463	C₂²×C₃₁	semidirect
513. #460	C₂²×C₃₁	semidirect
516. #459	C₂²×C₃₁	semidirect
519. C₈×Q₈	C₂²×C₃₁	semidirect
520. C₄×SD₁₆	C₂²×C₃₁	semidirect
523. C₄×D₈	C₂²×C₃₁	semidirect
525. #436	C₂²×C₃₁	semidirect
526. #431	C₂²×C₃₁	semidirect
527. #431	C₂²×C₃₁	semidirect
528. #428	C₂²×C₃₁	semidirect
529. #428	C₂²×C₃₁	semidirect
530. #423	C₂²×C₃₁	semidirect
531. #423	C₂²×C₃₁	semidirect
675. C₃₁	#62143	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×#3511	2
C₃₁×#3481	2
C₃₁×#3380	2
C₃₁×#3361	2
C₃₁×#3357	2
C₃₁×#3355	2
C₃₁×#3325	2
C₃₁×#3322	2
C₃₁×#3253	2
C₃₁×#3251	2
C₃₁×#3233	2
C₃₁×#3226	2
C₃₁×#3106	2
C₃₁×#3100	2
C₃₁×#3079	2
C₃₁×#3077	2
C₃₁×#2991	2
#62143	31

Subgroups — C31×#62143 #21518902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62143 #21518902