Subgroups — C₃₁×#62610 #21519369

Order 7936.

1830 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3543	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3220	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3176	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3171	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#562	—	2	2	no	—
25	C₃₁×#560	—	2	2	no	—
26	C₃₁×#559	C₂²	1	1	yes	characteristic
27	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#555	C₂²	1	2	yes	complemented
29	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#553	C₂²	1	2	yes	complemented
31	C₃₁×#552	—	2	1	no	—
32	C₃₁×#550	C₂²	1	1	yes	characteristic
33	C₃₁×#550	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#548	—	2	1	no	—
36	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#546	—	2	1	no	—
38	C₃₁×#546	C₂²	1	2	yes	—
39	D₄²×C₃₁	—	2	1	no	—
40	D₄²×C₃₁	C₂²	1	1	yes	characteristic
41	D₄²×C₃₁	C₂²	1	2	yes	—
42	C₃₁×#544	C₂²	1	2	yes	complemented
43	C₃₁×#542	—	2	2	no	—
44	C₃₁×#540	—	2	1	no	—
45	C₃₁×#540	C₂²	1	2	yes	—
46	C₃₁×#540	C₂²	1	2	yes	complemented
47	C₃₁×#537	—	2	1	no	—
48	C₃₁×#536	—	2	1	no	—
49	C₃₁×#535	—	2	1	no	—
50	C₃₁×#535	C₂²	1	2	yes	—
51	C₃₁×#534	—	2	2	no	—
52	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
55	C₃₁×#529	C₂²	1	1	yes	characteristic
56	C₃₁×#529	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#499	C₂²	1	2	yes	complemented
59	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#493	C₂²	1	2	yes	complemented
61	C₃₁×#490	C₂²	1	2	yes	complemented
62	C₃₁×#490	C₂²	1	2	yes	complemented
63	C₃₁×#490	C₂²	1	2	yes	complemented
64	C₃₁×#490	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#489	C₂²	1	2	yes	complemented
66	C₃₁×#489	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#488	C₂²	1	2	yes	complemented
68	C₃₁×#488	C₂²	1	2	yes	complemented
69	C₃₁×#486	C₂²	1	1	yes	characteristic
70	C₃₁×#486	C₂²	1	1	yes	characteristic
71	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#486	C₂²	1	2	yes	complemented
73	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#486	C₂²	1	2	yes	complemented
75	C₃₁×#485	C₂²	1	2	yes	complemented
76	C₃₁×#482	C₂²	1	2	yes	—
77	C₃₁×#482	C₂²	1	2	yes	complemented
78	C₃₁×#482	C₂²	1	2	yes	complemented
79	C₃₁×#481	C₂²	1	2	yes	complemented
80	C₃₁×#480	C₂²	1	2	yes	complemented
81	C₃₁×#478	C₂²	1	2	yes	complemented
82	C₃₁×#478	C₂²	1	2	yes	complemented
83	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#476	C₂²	1	2	yes	complemented
86	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#474	C₂²	1	2	yes	complemented
89	C₃₁×#469	C₂²	1	1	yes	characteristic
90	C₃₁×#469	C₂²	1	1	yes	characteristic
91	C₃₁×#469	C₂²	1	2	yes	complemented
92	C₃₁×#469	C₂²	1	2	yes	complemented
93	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#466	C₂²	1	2	yes	complemented
96	C₃₁×#466	C₂²	1	2	yes	complemented
97	C₃₁×#463	C₂²	1	2	yes	complemented
98	C₃₁×#463	C₂²	1	2	yes	complemented
99	C₃₁×#459	C₂²	1	1	yes	characteristic
100	C₃₁×#459	C₂²	1	1	yes	characteristic
101	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#459	C₂²	1	2	yes	complemented
104	C₃₁×#459	C₂²	1	2	yes	complemented
105	C₃₁×#449	C₂²	1	2	yes	complemented
106	C₃₁×#449	C₂²	1	2	yes	complemented
107	C₃₁×#447	C₂²	1	2	yes	complemented
108	C₃₁×#447	C₂²	1	2	yes	complemented
109	C₃₁×#447	C₂²	1	2	yes	complemented
110	C₃₁×#447	C₂²	1	2	yes	complemented
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#442	C₂²	1	2	yes	complemented
114	C₃₁×#442	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
119	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#436	C₂²	1	2	yes	complemented
123	C₃₁×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#418	C₂²	1	2	yes	complemented
128	C₃₁×#418	C₂²	1	2	yes	complemented
129	C₃₁×#418	C₂²	1	2	yes	complemented
130	C₃₁×#417	C₂²	1	2	yes	complemented
131	C₃₁×#416	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
133	C₃₁×#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	—	2	2	no	—
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	—	2	1	no	—
143	C₂²×D₄×C₃₁	—	2	1	no	—
144	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
145	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₃₁	C₂³	1	2	yes	—
149	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×D₈×C₃₁	C₂³	1	2	yes	—
152	C₂×D₈×C₃₁	C₂³	1	2	yes	—
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	—	2	2	no	—
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×#127	—	2	1	no	—
164	C₃₁×#127	—	2	1	no	—
165	C₃₁×#127	—	2	1	no	—
166	C₃₁×#127	C₂³	1	1	yes	characteristic
167	C₃₁×#127	C₂³	1	1	yes	characteristic
168	C₃₁×#127	C₂³	1	2	yes	—
169	C₃₁×#127	C₂³	1	2	yes	—
170	C₃₁×#127	C₂³	1	1	yes	characteristic
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	1	no	—
173	C₃₁×#126	D₄	1	2	yes	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	D₄	1	1	yes	characteristic
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#125	C₂³	1	2	yes	—
178	C₃₁×#125	C₂³	1	1	yes	characteristic
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	—	2	2	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	D₄	1	1	yes	characteristic
185	C₃₁×#124	C₂³	1	2	yes	—
186	C₃₁×#124	C₂³	1	1	yes	characteristic
187	C₃₁×#123	—	2	1	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	D₄	1	2	yes	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	1	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	1	no	—
216	C₃₁×#121	—	2	1	no	—
217	C₃₁×#121	—	2	2	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	—	2	2	no	—
224	C₃₁×#121	D₄	1	1	yes	characteristic
225	C₃₁×#121	C₂³	1	1	yes	characteristic
226	C₃₁×#121	C₂³	1	1	yes	characteristic
227	C₃₁×#121	C₂³	1	2	yes	—
228	C₃₁×#121	C₂³	1	2	yes	—
229	C₃₁×#121	C₂³	1	2	yes	—
230	C₃₁×#121	C₂³	1	2	yes	—
231	C₃₁×#121	C₂³	1	1	yes	characteristic
232	C₃₁×#120	—	2	2	no	—
233	C₃₁×#120	—	2	2	no	—
234	C₃₁×#120	—	2	2	no	—
235	C₃₁×#120	—	2	2	no	—
236	C₃₁×#120	—	2	2	no	—
237	C₃₁×#120	—	2	2	no	—
238	C₄×Q₈×C₃₁	—	2	1	no	—
239	C₄×Q₈×C₃₁	—	2	1	no	—
240	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	2	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₃₁	C₂³	1	2	yes	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	—	2	1	no	—
259	C₃₁×#117	C₂³	1	2	yes	—
260	C₃₁×#117	C₂³	1	2	yes	—
261	C₃₁×#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×#103	C₂³	1	1	yes	characteristic
279	C₃₁×#103	C₂³	1	2	yes	—
280	C₃₁×#103	C₂³	1	1	yes	characteristic
281	C₃₁×#103	C₂³	1	2	yes	—
282	C₃₁×#102	C₂³	1	1	yes	characteristic
283	C₃₁×#102	C₂³	1	2	yes	—
284	C₃₁×#102	C₂³	1	2	yes	—
285	C₃₁×#102	C₂³	1	2	yes	—
286	C₃₁×#102	C₂³	1	2	yes	—
287	C₃₁×#102	C₂³	1	2	yes	—
288	C₃₁×#102	C₂³	1	2	yes	—
289	C₃₁×#102	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	1	yes	characteristic
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×#97	C₂³	1	1	yes	characteristic
306	C₃₁×#97	C₂³	1	1	yes	characteristic
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	2	no	—
313	C₂⁴×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	8	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	#41×C₃₁	—	8	2	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	8	2	no	—
324	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₃₁	—	2	1	no	—
327	C₂×D₄×C₃₁	—	2	2	no	—
328	C₂×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	2	1	no	—
345	C₂×D₄×C₃₁	—	2	1	no	—
346	C₂×D₄×C₃₁	—	4	2	no	—
347	C₂×D₄×C₃₁	—	4	2	no	—
348	C₂×D₄×C₃₁	—	4	2	no	—
349	C₂×D₄×C₃₁	—	4	2	no	—
350	C₂×D₄×C₃₁	—	8	2	no	—
351	C₂×D₄×C₃₁	—	8	2	no	—
352	C₂×D₄×C₃₁	—	8	2	no	—
353	C₂×D₄×C₃₁	—	8	4	no	—
354	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
356	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
358	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
359	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	2	1	no	—
364	C₂²×C₄×C₃₁	—	2	1	no	—
365	C₂²×C₄×C₃₁	—	2	2	no	—
366	C₂²×C₄×C₃₁	—	2	2	no	—
367	C₂²×C₄×C₃₁	—	2	2	no	—
368	C₂²×C₄×C₃₁	—	2	2	no	—
369	C₂²×C₄×C₃₁	—	2	2	no	—
370	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
372	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
374	SD₁₆×C₃₁	—	4	1	no	—
375	SD₁₆×C₃₁	—	4	1	no	—
376	D₈×C₃₁	—	4	2	no	—
377	D₈×C₃₁	—	4	2	no	—
378	D₈×C₃₁	—	4	2	no	—
379	D₈×C₃₁	—	4	2	no	—
380	D₈×C₃₁	—	4	1	no	—
381	D₈×C₃₁	—	4	1	no	—
382	M₁₆×C₃₁	—	4	1	no	—
383	M₁₆×C₃₁	—	4	2	no	—
384	M₁₆×C₃₁	—	4	1	no	—
385	C₂×C₈×C₃₁	—	4	2	no	—
386	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
388	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	1	no	—
404	C₄⋊C₄×C₃₁	—	2	1	no	—
405	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	1	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	1	no	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
443	C₄²×C₃₁	—	2	2	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	—	2	1	no	—
446	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
449	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
450	C₄²×C₃₁	C₂⁴	1	2	yes	—
451	#62610	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂³×C₃₁	—	2	1	no	—
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	2	2	no	—
455	C₂³×C₃₁	—	2	1	no	—
456	C₂³×C₃₁	—	2	2	no	—
457	C₂³×C₃₁	—	4	4	no	—
458	C₂³×C₃₁	—	8	2	no	—
459	C₂³×C₃₁	—	8	2	no	—
460	C₂³×C₃₁	—	8	2	no	—
461	C₂³×C₃₁	—	8	2	no	—
462	C₂³×C₃₁	—	8	2	no	—
463	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
464	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
465	Q₈×C₃₁	—	2	2	no	—
466	Q₈×C₃₁	—	2	1	no	—
467	Q₈×C₃₁	—	2	1	no	—
468	Q₈×C₃₁	—	4	2	no	—
469	Q₈×C₃₁	—	8	1	no	—
470	Q₈×C₃₁	—	8	2	no	—
471	Q₈×C₃₁	—	8	1	no	—
472	D₄×C₃₁	—	2	2	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	1	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	2	2	no	—
478	D₄×C₃₁	—	2	1	no	—
479	D₄×C₃₁	—	2	2	no	—
480	D₄×C₃₁	—	2	1	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	2	2	no	—
483	D₄×C₃₁	—	4	2	no	—
484	D₄×C₃₁	—	4	2	no	—
485	D₄×C₃₁	—	4	2	no	—
486	D₄×C₃₁	—	4	2	no	—
487	D₄×C₃₁	—	8	1	no	—
488	D₄×C₃₁	—	8	2	no	—
489	D₄×C₃₁	—	8	2	no	—
490	D₄×C₃₁	—	8	2	no	—
491	D₄×C₃₁	—	8	1	no	—
492	D₄×C₃₁	—	8	1	no	—
493	D₄×C₃₁	—	8	2	no	—
494	D₄×C₃₁	—	8	2	no	—
495	D₄×C₃₁	—	8	1	no	—
496	D₄×C₃₁	—	8	2	no	—
497	D₄×C₃₁	—	8	2	no	—
498	D₄×C₃₁	—	8	2	no	—
499	D₄×C₃₁	—	8	2	no	—
500	D₄×C₃₁	—	8	2	no	—
501	D₄×C₃₁	—	8	1	no	—
502	D₄×C₃₁	—	8	1	no	—
503	D₄×C₃₁	—	8	2	no	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	2	2	no	—
506	C₂×C₄×C₃₁	—	2	1	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	2	no	—
509	C₂×C₄×C₃₁	—	2	2	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	1	no	—
512	C₂×C₄×C₃₁	—	2	1	no	—
513	C₂×C₄×C₃₁	—	2	2	no	—
514	C₂×C₄×C₃₁	—	2	1	no	—
515	C₂×C₄×C₃₁	—	2	1	no	—
516	C₂×C₄×C₃₁	—	4	1	no	—
517	C₂×C₄×C₃₁	—	4	2	no	—
518	C₂×C₄×C₃₁	—	4	2	no	—
519	C₂×C₄×C₃₁	—	4	2	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
521	C₂×C₄×C₃₁	—	8	2	no	—
522	C₂×C₄×C₃₁	—	8	2	no	—
523	C₂×C₄×C₃₁	—	8	2	no	—
524	C₂×C₄×C₃₁	—	8	2	no	—
525	C₂×C₄×C₃₁	—	8	2	no	—
526	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
535	C₈×C₃₁	—	2	1	no	—
536	C₈×C₃₁	—	2	2	no	—
537	C₈×C₃₁	—	2	1	no	—
538	C₈×C₃₁	—	2	2	no	—
539	C₈×C₃₁	—	2	1	no	—
540	C₈×C₃₁	—	2	1	no	—
541	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3543	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3373	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3358	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3332	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3325	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3325	C₂×C₃₁	1	2	yes	complemented
550	#3322	C₂×C₃₁	1	2	yes	complemented
551	#3319	C₂×C₃₁	1	2	yes	complemented
552	#3318	C₂×C₃₁	1	2	yes	complemented
553	#3305	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3241	C₂×C₃₁	1	2	yes	complemented
556	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3220	C₂×C₃₁	1	2	yes	complemented
558	#3205	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3176	C₂×C₃₁	1	2	yes	complemented
560	#3171	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#3138	C₂×C₃₁	1	1	yes	characteristic, complemented
562	#3136	C₂×C₃₁	1	2	yes	complemented
563	#2969	C₂×C₃₁	1	1	yes	characteristic, complemented
564	C₂²×C₃₁	—	2	1	no	—
565	C₂²×C₃₁	—	2	2	no	—
566	C₂²×C₃₁	—	2	2	no	—
567	C₂²×C₃₁	—	2	1	no	—
568	C₂²×C₃₁	—	2	1	no	—
569	C₂²×C₃₁	—	2	2	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	—	4	2	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	2	no	—
574	C₂²×C₃₁	—	4	1	no	—
575	C₂²×C₃₁	—	4	2	no	—
576	C₂²×C₃₁	—	4	2	no	—
577	C₂²×C₃₁	—	4	1	no	—
578	C₂²×C₃₁	—	4	1	no	—
579	C₂²×C₃₁	—	4	1	no	—
580	C₂²×C₃₁	—	4	1	no	—
581	C₂²×C₃₁	—	4	1	no	—
582	C₂²×C₃₁	—	4	1	no	—
583	C₂²×C₃₁	—	4	2	no	—
584	C₂²×C₃₁	—	4	2	no	—
585	C₂²×C₃₁	—	16	4	no	—
586	C₂²×C₃₁	—	16	4	no	—
587	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
588	C₄×C₃₁	—	2	1	no	—
589	C₄×C₃₁	—	2	1	no	—
590	C₄×C₃₁	—	2	2	no	—
591	C₄×C₃₁	—	2	2	no	—
592	C₄×C₃₁	—	2	1	no	—
593	C₄×C₃₁	—	2	1	no	—
594	C₄×C₃₁	—	2	2	no	—
595	C₄×C₃₁	—	4	1	no	—
596	C₄×C₃₁	—	4	2	no	—
597	C₄×C₃₁	—	4	1	no	—
598	C₄×C₃₁	—	4	1	no	—
599	C₄×C₃₁	—	4	1	no	—
600	C₄×C₃₁	—	4	1	no	—
601	C₄×C₃₁	—	4	2	no	—
602	C₄×C₃₁	#576	1	2	yes	—
603	C₄×C₃₁	#585	1	1	yes	characteristic
604	C₄×C₃₁	#585	1	1	yes	characteristic
605	#562	—	2	2	no	—
606	#560	—	2	2	no	—
607	#559	C₂²×C₃₁	1	1	yes	characteristic
608	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	#555	C₂²×C₃₁	1	2	yes	complemented
610	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	#553	C₂²×C₃₁	1	2	yes	complemented
612	#552	—	2	1	no	—
613	#550	C₂²×C₃₁	1	1	yes	characteristic
614	#550	C₂²×C₃₁	1	1	yes	characteristic
615	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#548	—	2	1	no	—
617	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#546	—	2	1	no	—
619	#546	C₂²×C₃₁	1	2	yes	—
620	D₄²	—	2	1	no	—
621	D₄²	C₂²×C₃₁	1	1	yes	characteristic
622	D₄²	C₂²×C₃₁	1	2	yes	—
623	#544	C₂²×C₃₁	1	2	yes	complemented
624	#542	—	2	2	no	—
625	#540	—	2	1	no	—
626	#540	C₂²×C₃₁	1	2	yes	—
627	#540	C₂²×C₃₁	1	2	yes	complemented
628	#537	—	2	1	no	—
629	#536	—	2	1	no	—
630	#535	—	2	1	no	—
631	#535	C₂²×C₃₁	1	2	yes	—
632	#534	—	2	2	no	—
633	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
636	#529	C₂²×C₃₁	1	1	yes	characteristic
637	#529	C₂²×C₃₁	1	1	yes	characteristic
638	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#499	C₂²×C₃₁	1	2	yes	complemented
640	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#493	C₂²×C₃₁	1	2	yes	complemented
642	#490	C₂²×C₃₁	1	2	yes	complemented
643	#490	C₂²×C₃₁	1	2	yes	complemented
644	#490	C₂²×C₃₁	1	2	yes	complemented
645	#490	C₂²×C₃₁	1	1	yes	characteristic, complemented
646	#489	C₂²×C₃₁	1	2	yes	complemented
647	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#488	C₂²×C₃₁	1	2	yes	complemented
649	#488	C₂²×C₃₁	1	2	yes	complemented
650	#486	C₂²×C₃₁	1	1	yes	characteristic
651	#486	C₂²×C₃₁	1	1	yes	characteristic
652	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#486	C₂²×C₃₁	1	2	yes	complemented
654	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#486	C₂²×C₃₁	1	2	yes	complemented
656	#485	C₂²×C₃₁	1	2	yes	complemented
657	#482	C₂²×C₃₁	1	2	yes	—
658	#482	C₂²×C₃₁	1	2	yes	complemented
659	#482	C₂²×C₃₁	1	2	yes	complemented
660	#481	C₂²×C₃₁	1	2	yes	complemented
661	#480	C₂²×C₃₁	1	2	yes	complemented
662	#478	C₂²×C₃₁	1	2	yes	complemented
663	#478	C₂²×C₃₁	1	2	yes	complemented
664	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#476	C₂²×C₃₁	1	2	yes	complemented
667	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#474	C₂²×C₃₁	1	2	yes	complemented
670	#469	C₂²×C₃₁	1	1	yes	characteristic
671	#469	C₂²×C₃₁	1	1	yes	characteristic
672	#469	C₂²×C₃₁	1	2	yes	complemented
673	#469	C₂²×C₃₁	1	2	yes	complemented
674	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#466	C₂²×C₃₁	1	2	yes	complemented
677	#466	C₂²×C₃₁	1	2	yes	complemented
678	#463	C₂²×C₃₁	1	2	yes	complemented
679	#463	C₂²×C₃₁	1	2	yes	complemented
680	#459	C₂²×C₃₁	1	1	yes	characteristic
681	#459	C₂²×C₃₁	1	1	yes	characteristic
682	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#459	C₂²×C₃₁	1	2	yes	complemented
685	#459	C₂²×C₃₁	1	2	yes	complemented
686	#449	C₂²×C₃₁	1	2	yes	complemented
687	#449	C₂²×C₃₁	1	2	yes	complemented
688	#447	C₂²×C₃₁	1	2	yes	complemented
689	#447	C₂²×C₃₁	1	2	yes	complemented
690	#447	C₂²×C₃₁	1	2	yes	complemented
691	#447	C₂²×C₃₁	1	2	yes	complemented
692	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#442	C₂²×C₃₁	1	2	yes	complemented
695	#442	C₂²×C₃₁	1	2	yes	complemented
696	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
697	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
700	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
701	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	#436	C₂²×C₃₁	1	2	yes	complemented
704	#435	C₂²×C₃₁	1	2	yes	complemented
705	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#433	C₂²×C₃₁	1	2	yes	complemented
707	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
708	#418	C₂²×C₃₁	1	2	yes	complemented
709	#418	C₂²×C₃₁	1	2	yes	complemented
710	#418	C₂²×C₃₁	1	2	yes	complemented
711	#417	C₂²×C₃₁	1	2	yes	complemented
712	#416	C₂²×C₃₁	1	2	yes	complemented
713	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
714	#405	C₂²×C₃₁	1	2	yes	complemented
715	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	C₂×C₃₁	—	4	2	no	—
717	C₂×C₃₁	—	4	1	no	—
718	C₂×C₃₁	—	8	1	no	—
719	C₂×C₃₁	—	8	1	no	—
720	C₂×C₃₁	—	8	2	no	—
721	C₂×C₃₁	—	8	2	no	—
722	C₂×C₃₁	—	8	1	no	—
723	C₂×C₃₁	#3500	1	1	yes	characteristic
724	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
725	C₂×C₃₁	#3585	1	1	yes	characteristic
726	C₂×#41	—	2	1	no	—
727	C₂×#41	—	2	1	no	—
728	C₂×#41	—	2	1	no	—
729	C₂×#41	C₂³×C₃₁	1	2	yes	—
730	C₂²×Q₈	—	2	1	no	—
731	C₂²×D₄	—	2	2	no	—
732	C₂²×D₄	—	2	1	no	—
733	C₂²×D₄	—	2	1	no	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
736	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
739	C₂×D₈	C₂³×C₃₁	1	2	yes	—
740	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
741	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×D₈	C₂³×C₃₁	1	2	yes	—
743	C₂×D₈	C₂³×C₃₁	1	2	yes	—
744	C₂×D₈	C₂³×C₃₁	1	2	yes	—
745	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
746	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
747	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
748	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
749	C₄⋊Q₈	—	2	2	no	—
750	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
753	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
754	#127	—	2	1	no	—
755	#127	—	2	1	no	—
756	#127	—	2	1	no	—
757	#127	C₂³×C₃₁	1	2	yes	—
758	#127	C₂³×C₃₁	1	1	yes	characteristic
759	#127	C₂³×C₃₁	1	1	yes	characteristic
760	#127	C₂³×C₃₁	1	1	yes	characteristic
761	#127	C₂³×C₃₁	1	2	yes	—
762	#126	—	2	2	no	—
763	#126	—	2	1	no	—
764	#126	D₄×C₃₁	1	2	yes	—
765	#125	—	2	2	no	—
766	#125	D₄×C₃₁	1	1	yes	characteristic
767	#125	C₂³×C₃₁	1	1	yes	characteristic
768	#125	C₂³×C₃₁	1	2	yes	—
769	#125	C₂³×C₃₁	1	2	yes	—
770	#124	—	2	1	no	—
771	#124	—	2	2	no	—
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	—	2	1	no	—
775	#124	D₄×C₃₁	1	1	yes	characteristic
776	#124	C₂³×C₃₁	1	1	yes	characteristic
777	#124	C₂³×C₃₁	1	2	yes	—
778	#123	—	2	1	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	D₄×C₃₁	1	2	yes	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
798	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
799	#121	—	2	1	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	1	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	D₄×C₃₁	1	1	yes	characteristic
816	#121	C₂³×C₃₁	1	1	yes	characteristic
817	#121	C₂³×C₃₁	1	1	yes	characteristic
818	#121	C₂³×C₃₁	1	1	yes	characteristic
819	#121	C₂³×C₃₁	1	2	yes	—
820	#121	C₂³×C₃₁	1	2	yes	—
821	#121	C₂³×C₃₁	1	2	yes	—
822	#121	C₂³×C₃₁	1	2	yes	—
823	#120	—	2	2	no	—
824	#120	—	2	2	no	—
825	#120	—	2	2	no	—
826	#120	—	2	2	no	—
827	#120	—	2	2	no	—
828	#120	—	2	2	no	—
829	C₄×Q₈	—	2	1	no	—
830	C₄×Q₈	—	2	1	no	—
831	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
832	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₃₁	1	2	yes	—
842	C₄×D₄	C₂³×C₃₁	1	2	yes	—
843	C₄×D₄	C₂³×C₃₁	1	2	yes	—
844	C₄×D₄	C₂³×C₃₁	1	2	yes	—
845	C₄×D₄	C₂³×C₃₁	1	2	yes	—
846	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
847	#117	—	2	1	no	—
848	#117	—	2	2	no	—
849	#117	—	2	1	no	—
850	#117	C₂³×C₃₁	1	2	yes	—
851	#117	C₂³×C₃₁	1	2	yes	—
852	#117	C₂³×C₃₁	1	2	yes	—
853	C₂×C₄⋊C₄	—	2	1	no	—
854	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
855	C₂×C₂²⋊C₄	—	2	2	no	—
856	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
857	#107	C₂³×C₃₁	1	2	yes	—
858	#107	C₂³×C₃₁	1	2	yes	—
859	#107	C₂³×C₃₁	1	1	yes	characteristic
860	#107	C₂³×C₃₁	1	1	yes	characteristic
861	#106	C₂³×C₃₁	1	1	yes	characteristic
862	#106	C₂³×C₃₁	1	1	yes	characteristic
863	#106	C₂³×C₃₁	1	2	yes	—
864	#106	C₂³×C₃₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
868	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
869	#103	C₂³×C₃₁	1	1	yes	characteristic
870	#103	C₂³×C₃₁	1	2	yes	—
871	#103	C₂³×C₃₁	1	1	yes	characteristic
872	#103	C₂³×C₃₁	1	2	yes	—
873	#102	C₂³×C₃₁	1	1	yes	characteristic
874	#102	C₂³×C₃₁	1	2	yes	—
875	#102	C₂³×C₃₁	1	2	yes	—
876	#102	C₂³×C₃₁	1	2	yes	—
877	#102	C₂³×C₃₁	1	2	yes	—
878	#102	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	2	yes	—
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	1	yes	characteristic
882	#102	C₂³×C₃₁	1	2	yes	—
883	#102	C₂³×C₃₁	1	2	yes	—
884	#102	C₂³×C₃₁	1	2	yes	—
885	#102	C₂³×C₃₁	1	2	yes	—
886	#102	C₂³×C₃₁	1	2	yes	—
887	#102	C₂³×C₃₁	1	2	yes	—
888	#102	C₂³×C₃₁	1	2	yes	—
889	#102	C₂³×C₃₁	1	1	yes	characteristic
890	#102	C₂³×C₃₁	1	1	yes	characteristic
891	#102	C₂³×C₃₁	1	1	yes	characteristic
892	#102	C₂³×C₃₁	1	1	yes	characteristic
893	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
894	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
895	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
896	#97	C₂³×C₃₁	1	1	yes	characteristic
897	#97	C₂³×C₃₁	1	1	yes	characteristic
898	#97	C₂³×C₃₁	1	2	yes	—
899	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
900	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₃₁	1	2	yes	—
902	C₄×C₈	C₂³×C₃₁	1	2	yes	—
903	C₃₁	#62610	1	1	yes	characteristic, direct product factor, Sylow
904	C₂⁴	—	2	2	no	—
905	C₂⁴	—	2	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	2	no	—
908	#41	—	8	2	no	—
909	#41	—	8	2	no	—
910	#41	—	8	2	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	2	2	no	—
914	C₂×Q₈	—	2	1	no	—
915	C₂×Q₈	—	8	2	no	—
916	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	4	2	no	—
939	C₂×D₄	—	4	2	no	—
940	C₂×D₄	—	4	2	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	8	2	no	—
943	C₂×D₄	—	8	2	no	—
944	C₂×D₄	—	8	2	no	—
945	C₂×D₄	—	8	4	no	—
946	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
947	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
948	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
949	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
950	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
951	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
966	SD₁₆	—	4	1	no	—
967	SD₁₆	—	4	1	no	—
968	D₈	—	4	2	no	—
969	D₈	—	4	2	no	—
970	D₈	—	4	2	no	—
971	D₈	—	4	2	no	—
972	D₈	—	4	1	no	—
973	D₈	—	4	1	no	—
974	M₁₆	—	4	1	no	—
975	M₁₆	—	4	2	no	—
976	M₁₆	—	4	1	no	—
977	C₂×C₈	—	4	2	no	—
978	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
980	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1000	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1001	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1002	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1006	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1031	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1033	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1034	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1039	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1040	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1042	C₄²	C₂⁴×C₃₁	1	2	yes	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	2	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	4	4	no	—
1049	C₂³	—	8	2	no	—
1050	C₂³	—	8	2	no	—
1051	C₂³	—	8	2	no	—
1052	C₂³	—	8	2	no	—
1053	C₂³	—	8	2	no	—
1054	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1055	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	4	2	no	—
1060	Q₈	—	8	1	no	—
1061	Q₈	—	8	2	no	—
1062	Q₈	—	8	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	4	2	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	8	1	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	1	no	—
1084	D₄	—	8	1	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	1	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	1	no	—
1093	D₄	—	8	1	no	—
1094	D₄	—	8	2	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1119	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1121	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1124	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1125	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1126	C₈	—	2	1	no	—
1127	C₈	—	2	2	no	—
1128	C₈	—	2	1	no	—
1129	C₈	—	2	2	no	—
1130	C₈	—	2	1	no	—
1131	C₈	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	2	1	no	—
1137	C₂²	—	2	2	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	16	4	no	—
1154	C₂²	—	16	4	no	—
1155	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1156	C₄	—	2	2	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	2	no	—
1170	C₄	C₃₁×#576	1	2	yes	—
1171	C₄	C₃₁×#585	1	1	yes	characteristic
1172	C₄	C₃₁×#585	1	1	yes	characteristic
1173	C₂	—	4	1	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	8	1	no	—
1176	C₂	—	8	2	no	—
1177	C₂	—	8	2	no	—
1178	C₂	—	8	1	no	—
1179	C₂	—	8	1	no	—
1180	C₂	C₃₁×#3500	1	1	yes	characteristic
1181	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1182	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×#3547	C₂	semidirect
2. C₃₁×#3543	C₂	semidirect
3. C₃₁×#3373	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3361	C₂	semidirect
6. C₃₁×#3358	C₂	semidirect
7. C₃₁×#3332	C₂	semidirect
8. C₃₁×#3325	C₂	semidirect
9. C₃₁×#3325	C₂	semidirect
10. C₃₁×#3322	C₂	semidirect
11. C₃₁×#3319	C₂	semidirect
12. C₃₁×#3318	C₂	semidirect
13. C₃₁×#3305	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3241	C₂	semidirect
16. C₃₁×#3233	C₂	semidirect
17. C₃₁×#3220	C₂	semidirect
18. C₃₁×#3205	C₂	semidirect
19. C₃₁×#3176	C₂	semidirect
20. C₃₁×#3171	C₂	semidirect
21. C₃₁×#3138	C₂	semidirect
22. C₃₁×#3136	C₂	semidirect
23. C₃₁×#2969	C₂	semidirect
27. C₃₁×#555	C₂²	semidirect
28. C₃₁×#555	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
30. C₃₁×#553	C₂²	semidirect
34. D₄×Q₈×C₃₁	C₂²	semidirect
36. C₃₁×#547	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
46. C₃₁×#540	C₂²	semidirect
52. C₃₁×#533	C₂²	semidirect
53. C₃₁×#532	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#499	C₂²	semidirect
59. C₃₁×#496	C₂²	semidirect
60. C₃₁×#493	C₂²	semidirect
61. C₃₁×#490	C₂²	semidirect
62. C₃₁×#490	C₂²	semidirect
63. C₃₁×#490	C₂²	semidirect
64. C₃₁×#490	C₂²	semidirect
65. C₃₁×#489	C₂²	semidirect
66. C₃₁×#489	C₂²	semidirect
67. C₃₁×#488	C₂²	semidirect
68. C₃₁×#488	C₂²	semidirect
71. C₃₁×#486	C₂²	semidirect
72. C₃₁×#486	C₂²	semidirect
73. C₃₁×#486	C₂²	semidirect
74. C₃₁×#486	C₂²	semidirect
75. C₃₁×#485	C₂²	semidirect
77. C₃₁×#482	C₂²	semidirect
78. C₃₁×#482	C₂²	semidirect
79. C₃₁×#481	C₂²	semidirect
80. C₃₁×#480	C₂²	semidirect
81. C₃₁×#478	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
83. C₃₁×#477	C₂²	semidirect
84. C₃₁×#476	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
86. C₃₁×#475	C₂²	semidirect
87. C₃₁×#474	C₂²	semidirect
88. C₃₁×#474	C₂²	semidirect
91. C₃₁×#469	C₂²	semidirect
92. C₃₁×#469	C₂²	semidirect
93. C₃₁×#468	C₂²	semidirect
94. C₃₁×#468	C₂²	semidirect
95. C₃₁×#466	C₂²	semidirect
96. C₃₁×#466	C₂²	semidirect
97. C₃₁×#463	C₂²	semidirect
98. C₃₁×#463	C₂²	semidirect
101. C₃₁×#459	C₂²	semidirect
102. C₃₁×#459	C₂²	semidirect
103. C₃₁×#459	C₂²	semidirect
104. C₃₁×#459	C₂²	semidirect
105. C₃₁×#449	C₂²	semidirect
106. C₃₁×#449	C₂²	semidirect
107. C₃₁×#447	C₂²	semidirect
108. C₃₁×#447	C₂²	semidirect
109. C₃₁×#447	C₂²	semidirect
110. C₃₁×#447	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
113. C₃₁×#442	C₂²	semidirect
114. C₃₁×#442	C₂²	semidirect
115. C₄×SD₁₆×C₃₁	C₂²	semidirect
116. C₄×SD₁₆×C₃₁	C₂²	semidirect
117. C₄×D₈×C₃₁	C₂²	semidirect
118. C₄×D₈×C₃₁	C₂²	semidirect
119. C₄×D₈×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
123. C₃₁×#435	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#431	C₂²	semidirect
127. C₃₁×#418	C₂²	semidirect
128. C₃₁×#418	C₂²	semidirect
129. C₃₁×#418	C₂²	semidirect
130. C₃₁×#417	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
132. C₂×C₃₁×#102	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₄×M₁₆×C₃₁	C₂²	semidirect
451. #62610	C₃₁	direct (N × H)
541. #3547	C₂×C₃₁	semidirect
542. #3543	C₂×C₃₁	semidirect
543. #3373	C₂×C₃₁	semidirect
544. #3366	C₂×C₃₁	semidirect
545. #3361	C₂×C₃₁	semidirect
546. #3358	C₂×C₃₁	semidirect
547. #3332	C₂×C₃₁	semidirect
548. #3325	C₂×C₃₁	semidirect
549. #3325	C₂×C₃₁	semidirect
550. #3322	C₂×C₃₁	semidirect
551. #3319	C₂×C₃₁	semidirect
552. #3318	C₂×C₃₁	semidirect
553. #3305	C₂×C₃₁	semidirect
554. #3294	C₂×C₃₁	semidirect
555. #3241	C₂×C₃₁	semidirect
556. #3233	C₂×C₃₁	semidirect
557. #3220	C₂×C₃₁	semidirect
558. #3205	C₂×C₃₁	semidirect
559. #3176	C₂×C₃₁	semidirect
560. #3171	C₂×C₃₁	semidirect
561. #3138	C₂×C₃₁	semidirect
562. #3136	C₂×C₃₁	semidirect
563. #2969	C₂×C₃₁	semidirect
608. #555	C₂²×C₃₁	semidirect
609. #555	C₂²×C₃₁	semidirect
610. #554	C₂²×C₃₁	semidirect
611. #553	C₂²×C₃₁	semidirect
615. D₄×Q₈	C₂²×C₃₁	semidirect
617. #547	C₂²×C₃₁	semidirect
623. #544	C₂²×C₃₁	semidirect
627. #540	C₂²×C₃₁	semidirect
633. #533	C₂²×C₃₁	semidirect
634. #532	C₂²×C₃₁	semidirect
638. #501	C₂²×C₃₁	semidirect
639. #499	C₂²×C₃₁	semidirect
640. #496	C₂²×C₃₁	semidirect
641. #493	C₂²×C₃₁	semidirect
642. #490	C₂²×C₃₁	semidirect
643. #490	C₂²×C₃₁	semidirect
644. #490	C₂²×C₃₁	semidirect
645. #490	C₂²×C₃₁	semidirect
646. #489	C₂²×C₃₁	semidirect
647. #489	C₂²×C₃₁	semidirect
648. #488	C₂²×C₃₁	semidirect
649. #488	C₂²×C₃₁	semidirect
652. #486	C₂²×C₃₁	semidirect
653. #486	C₂²×C₃₁	semidirect
654. #486	C₂²×C₃₁	semidirect
655. #486	C₂²×C₃₁	semidirect
656. #485	C₂²×C₃₁	semidirect
658. #482	C₂²×C₃₁	semidirect
659. #482	C₂²×C₃₁	semidirect
660. #481	C₂²×C₃₁	semidirect
661. #480	C₂²×C₃₁	semidirect
662. #478	C₂²×C₃₁	semidirect
663. #478	C₂²×C₃₁	semidirect
664. #477	C₂²×C₃₁	semidirect
665. #476	C₂²×C₃₁	semidirect
666. #476	C₂²×C₃₁	semidirect
667. #475	C₂²×C₃₁	semidirect
668. #474	C₂²×C₃₁	semidirect
669. #474	C₂²×C₃₁	semidirect
672. #469	C₂²×C₃₁	semidirect
673. #469	C₂²×C₃₁	semidirect
674. #468	C₂²×C₃₁	semidirect
675. #468	C₂²×C₃₁	semidirect
676. #466	C₂²×C₃₁	semidirect
677. #466	C₂²×C₃₁	semidirect
678. #463	C₂²×C₃₁	semidirect
679. #463	C₂²×C₃₁	semidirect
682. #459	C₂²×C₃₁	semidirect
683. #459	C₂²×C₃₁	semidirect
684. #459	C₂²×C₃₁	semidirect
685. #459	C₂²×C₃₁	semidirect
686. #449	C₂²×C₃₁	semidirect
687. #449	C₂²×C₃₁	semidirect
688. #447	C₂²×C₃₁	semidirect
689. #447	C₂²×C₃₁	semidirect
690. #447	C₂²×C₃₁	semidirect
691. #447	C₂²×C₃₁	semidirect
692. #446	C₂²×C₃₁	semidirect
693. C₈×Q₈	C₂²×C₃₁	semidirect
694. #442	C₂²×C₃₁	semidirect
695. #442	C₂²×C₃₁	semidirect
696. C₄×SD₁₆	C₂²×C₃₁	semidirect
697. C₄×SD₁₆	C₂²×C₃₁	semidirect
698. C₄×D₈	C₂²×C₃₁	semidirect
699. C₄×D₈	C₂²×C₃₁	semidirect
700. C₄×D₈	C₂²×C₃₁	semidirect
701. C₄×D₈	C₂²×C₃₁	semidirect
702. #436	C₂²×C₃₁	semidirect
703. #436	C₂²×C₃₁	semidirect
704. #435	C₂²×C₃₁	semidirect
705. C₈×D₄	C₂²×C₃₁	semidirect
706. #433	C₂²×C₃₁	semidirect
707. #431	C₂²×C₃₁	semidirect
708. #418	C₂²×C₃₁	semidirect
709. #418	C₂²×C₃₁	semidirect
710. #418	C₂²×C₃₁	semidirect
711. #417	C₂²×C₃₁	semidirect
712. #416	C₂²×C₃₁	semidirect
713. C₂×#102	C₂²×C₃₁	semidirect
714. #405	C₂²×C₃₁	semidirect
715. C₄×M₁₆	C₂²×C₃₁	semidirect
903. C₃₁	#62610	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×#3547	2
C₃₁×#3543	2
C₃₁×#3373	2
C₃₁×#3366	2
C₃₁×#3361	2
C₃₁×#3358	2
C₃₁×#3332	2
C₃₁×#3325	2
C₃₁×#3322	2
C₃₁×#3319	2
C₃₁×#3318	2
C₃₁×#3305	2
C₃₁×#3294	2
C₃₁×#3241	2
C₃₁×#3233	2
C₃₁×#3220	2
C₃₁×#3205	2
C₃₁×#3176	2
C₃₁×#3171	2
C₃₁×#3138	2
C₃₁×#3136	2
C₃₁×#2969	2
#62610	31

Subgroups — C31×#62610 #21519369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62610 #21519369