Subgroups — C₃₁×#62187 #21518946

Order 7936.

1812 conjugacy classes of subgroups.

The subgroup lattice has 1170 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×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3355	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3347	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3259	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3253	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#562	—	2	2	no	—
25	C₃₁×#555	C₂²	1	1	yes	characteristic
26	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#555	C₂²	1	2	yes	complemented
28	C₃₁×#554	C₂²	1	1	yes	characteristic
29	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#553	—	2	1	no	—
31	C₃₁×#553	C₂²	1	2	yes	—
32	C₃₁×#553	C₂²	1	2	yes	complemented
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#550	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#546	—	2	1	no	—
39	C₃₁×#546	—	2	2	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	C₂²	1	2	yes	—
45	C₃₁×#540	C₂²	1	2	yes	complemented
46	C₃₁×#538	—	2	2	no	—
47	C₃₁×#537	—	2	1	no	—
48	C₃₁×#536	—	2	1	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	1	no	—
54	C₂×C₃₁×#121	—	2	1	no	—
55	C₃₁×#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#499	C₂²	1	2	yes	complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#490	C₂²	1	2	yes	complemented
62	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#486	C₂²	1	2	yes	complemented
64	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#482	C₂²	1	2	yes	complemented
66	C₃₁×#482	C₂²	1	2	yes	complemented
67	C₃₁×#482	C₂²	1	2	yes	complemented
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	complemented
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#481	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#480	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#480	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	2	yes	—
76	C₃₁×#478	C₂²	1	2	yes	—
77	C₃₁×#478	C₂²	1	2	yes	complemented
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#478	C₂²	1	2	yes	complemented
80	C₃₁×#478	C₂²	1	2	yes	complemented
81	C₃₁×#478	C₂²	1	2	yes	complemented
82	C₃₁×#478	C₂²	1	2	yes	complemented
83	C₃₁×#476	C₂²	1	1	yes	characteristic
84	C₃₁×#476	C₂²	1	2	yes	—
85	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#476	C₂²	1	2	yes	complemented
87	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#474	C₂²	1	1	yes	characteristic
90	C₃₁×#474	C₂²	1	1	yes	characteristic
91	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#474	C₂²	1	2	yes	complemented
93	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#469	C₂²	1	2	yes	complemented
95	C₃₁×#469	C₂²	1	2	yes	complemented
96	C₃₁×#469	C₂²	1	2	yes	complemented
97	C₃₁×#469	C₂²	1	2	yes	complemented
98	C₃₁×#466	C₂²	1	2	yes	complemented
99	C₃₁×#466	C₂²	1	2	yes	complemented
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	1	yes	characteristic, complemented
105	C₃₁×#459	C₂²	1	2	yes	complemented
106	C₃₁×#459	C₂²	1	2	yes	complemented
107	C₃₁×#447	C₂²	1	1	yes	characteristic
108	C₃₁×#447	C₂²	1	1	yes	characteristic
109	C₃₁×#447	C₂²	1	2	yes	—
110	C₃₁×#447	C₂²	1	2	yes	—
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	—
114	C₃₁×#442	C₂²	1	2	yes	complemented
115	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×D₈×C₃₁	C₂²	1	2	yes	—
118	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₃₁	C₂²	1	2	yes	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×#428	C₂²	1	2	yes	complemented
128	C₃₁×#428	C₂²	1	2	yes	complemented
129	C₃₁×#427	C₂²	1	2	yes	complemented
130	C₃₁×#424	C₂²	1	2	yes	complemented
131	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#418	C₂²	1	2	yes	—
133	C₃₁×#418	C₂²	1	2	yes	—
134	C₂×C₃₁×#102	C₂²	1	2	yes	—
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	—	2	1	no	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	—	2	2	no	—
142	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
143	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₃₁	—	2	1	no	—
145	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₃₁	C₂³	1	2	yes	—
150	C₂×D₈×C₃₁	C₂³	1	2	yes	—
151	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	—	2	2	no	—
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×#127	C₂³	1	1	yes	characteristic
161	C₃₁×#127	C₂³	1	1	yes	characteristic
162	C₃₁×#127	C₂³	1	2	yes	—
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	D₄	1	2	yes	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	D₄	1	1	yes	characteristic
168	C₃₁×#125	C₂³	1	2	yes	—
169	C₃₁×#125	C₂³	1	2	yes	—
170	C₃₁×#125	C₂³	1	2	yes	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	2	no	—
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	—	2	1	no	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	D₄	1	1	yes	characteristic
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	D₄	1	2	yes	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	1	no	—
200	C₃₁×#121	—	2	1	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	1	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	D₄	1	1	yes	characteristic
214	C₃₁×#121	C₂³	1	2	yes	—
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#121	C₂³	1	1	yes	characteristic
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₃₁×#120	—	2	2	no	—
222	C₃₁×#120	—	2	2	no	—
223	C₃₁×#120	—	2	2	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	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×#107	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
289	C₃₁×#102	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	1	no	—
313	C₂⁴×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	8	2	no	—
315	#41×C₃₁	—	8	2	no	—
316	#41×C₃₁	—	8	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	C₂×Q₈×C₃₁	—	2	1	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×D₄×C₃₁	—	2	2	no	—
326	C₂×D₄×C₃₁	—	2	4	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	2	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	1	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	1	no	—
342	C₂×D₄×C₃₁	—	4	2	no	—
343	C₂×D₄×C₃₁	—	4	1	no	—
344	C₂×D₄×C₃₁	—	8	2	no	—
345	C₂×D₄×C₃₁	—	8	4	no	—
346	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
349	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	—	2	2	no	—
363	C₂²×C₄×C₃₁	—	2	2	no	—
364	C₂²×C₄×C₃₁	—	2	1	no	—
365	C₂²×C₄×C₃₁	—	2	2	no	—
366	C₂²×C₄×C₃₁	—	8	2	no	—
367	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
371	D₈×C₃₁	—	2	2	no	—
372	D₈×C₃₁	—	2	2	no	—
373	D₈×C₃₁	—	4	1	no	—
374	D₈×C₃₁	—	4	2	no	—
375	D₈×C₃₁	—	4	1	no	—
376	D₈×C₃₁	—	4	2	no	—
377	M₁₆×C₃₁	—	4	2	no	—
378	M₁₆×C₃₁	—	4	2	no	—
379	C₂×C₈×C₃₁	—	4	2	no	—
380	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
384	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	no	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	2	yes	—
445	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
446	#62187	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₃₁	—	2	1	no	—
448	C₂³×C₃₁	—	2	1	no	—
449	C₂³×C₃₁	—	2	1	no	—
450	C₂³×C₃₁	—	2	2	no	—
451	C₂³×C₃₁	—	2	1	no	—
452	C₂³×C₃₁	—	4	2	no	—
453	C₂³×C₃₁	—	4	4	no	—
454	C₂³×C₃₁	—	4	2	no	—
455	C₂³×C₃₁	—	8	1	no	—
456	C₂³×C₃₁	—	8	2	no	—
457	C₂³×C₃₁	—	8	2	no	—
458	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
459	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₃₁	—	2	2	no	—
461	Q₈×C₃₁	—	4	2	no	—
462	Q₈×C₃₁	—	8	1	no	—
463	Q₈×C₃₁	—	8	2	no	—
464	Q₈×C₃₁	—	8	1	no	—
465	Q₈×C₃₁	—	8	1	no	—
466	D₄×C₃₁	—	2	2	no	—
467	D₄×C₃₁	—	2	1	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	2	no	—
471	D₄×C₃₁	—	2	1	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	2	no	—
476	D₄×C₃₁	—	4	2	no	—
477	D₄×C₃₁	—	4	4	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	4	4	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	8	1	no	—
482	D₄×C₃₁	—	8	2	no	—
483	D₄×C₃₁	—	8	1	no	—
484	D₄×C₃₁	—	8	1	no	—
485	D₄×C₃₁	—	8	2	no	—
486	D₄×C₃₁	—	8	2	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	—	8	2	no	—
489	D₄×C₃₁	—	8	1	no	—
490	D₄×C₃₁	—	8	1	no	—
491	D₄×C₃₁	—	8	2	no	—
492	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	2	no	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	4	1	no	—
506	C₂×C₄×C₃₁	—	4	2	no	—
507	C₂×C₄×C₃₁	—	4	2	no	—
508	C₂×C₄×C₃₁	—	4	2	no	—
509	C₂×C₄×C₃₁	—	4	2	no	—
510	C₂×C₄×C₃₁	—	8	2	no	—
511	C₂×C₄×C₃₁	—	8	1	no	—
512	C₂×C₄×C₃₁	—	8	1	no	—
513	C₂×C₄×C₃₁	—	8	2	no	—
514	C₂×C₄×C₃₁	—	8	2	no	—
515	C₂×C₄×C₃₁	—	8	2	no	—
516	C₂×C₄×C₃₁	—	8	2	no	—
517	C₂×C₄×C₃₁	—	8	1	no	—
518	C₂×C₄×C₃₁	—	8	2	no	—
519	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
528	C₈×C₃₁	—	2	1	no	—
529	C₈×C₃₁	—	2	1	no	—
530	C₈×C₃₁	—	2	1	no	—
531	C₈×C₃₁	—	2	2	no	—
532	C₈×C₃₁	—	2	1	no	—
533	C₈×C₃₁	—	2	2	no	—
534	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3519	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3358	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3355	C₂×C₃₁	1	2	yes	complemented
541	#3354	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3347	C₂×C₃₁	1	2	yes	complemented
543	#3341	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3325	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3325	C₂×C₃₁	1	2	yes	complemented
546	#3318	C₂×C₃₁	1	2	yes	complemented
547	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3259	C₂×C₃₁	1	2	yes	complemented
549	#3253	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3241	C₂×C₃₁	1	2	yes	complemented
551	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3122	C₂×C₃₁	1	2	yes	complemented
553	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3081	C₂×C₃₁	1	2	yes	complemented
555	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#2993	C₂×C₃₁	1	1	yes	characteristic, complemented
557	C₂²×C₃₁	—	2	1	no	—
558	C₂²×C₃₁	—	2	2	no	—
559	C₂²×C₃₁	—	2	1	no	—
560	C₂²×C₃₁	—	2	2	no	—
561	C₂²×C₃₁	—	2	2	no	—
562	C₂²×C₃₁	—	2	1	no	—
563	C₂²×C₃₁	—	2	2	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	4	1	no	—
566	C₂²×C₃₁	—	4	1	no	—
567	C₂²×C₃₁	—	4	2	no	—
568	C₂²×C₃₁	—	4	1	no	—
569	C₂²×C₃₁	—	4	1	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	—	4	2	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	1	no	—
574	C₂²×C₃₁	—	4	1	no	—
575	C₂²×C₃₁	—	4	1	no	—
576	C₂²×C₃₁	—	4	1	no	—
577	C₂²×C₃₁	—	4	2	no	—
578	C₂²×C₃₁	—	8	4	no	—
579	C₂²×C₃₁	—	16	4	no	—
580	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
581	C₄×C₃₁	—	2	1	no	—
582	C₄×C₃₁	—	2	1	no	—
583	C₄×C₃₁	—	2	2	no	—
584	C₄×C₃₁	—	2	2	no	—
585	C₄×C₃₁	—	2	1	no	—
586	C₄×C₃₁	—	2	1	no	—
587	C₄×C₃₁	—	2	2	no	—
588	C₄×C₃₁	—	4	2	no	—
589	C₄×C₃₁	—	4	2	no	—
590	C₄×C₃₁	—	4	1	no	—
591	C₄×C₃₁	—	4	1	no	—
592	C₄×C₃₁	—	4	1	no	—
593	C₄×C₃₁	—	4	1	no	—
594	C₄×C₃₁	—	4	2	no	—
595	C₄×C₃₁	#576	1	2	yes	—
596	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
597	C₄×C₃₁	#585	1	1	yes	characteristic
598	#562	—	2	2	no	—
599	#555	C₂²×C₃₁	1	1	yes	characteristic
600	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
601	#555	C₂²×C₃₁	1	2	yes	complemented
602	#554	C₂²×C₃₁	1	1	yes	characteristic
603	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
604	#553	—	2	1	no	—
605	#553	C₂²×C₃₁	1	2	yes	—
606	#553	C₂²×C₃₁	1	2	yes	complemented
607	#552	—	2	1	no	—
608	#550	C₂²×C₃₁	1	1	yes	characteristic
609	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
610	#548	—	2	1	no	—
611	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#546	—	2	1	no	—
613	#546	—	2	2	no	—
614	D₄²	C₂²×C₃₁	1	1	yes	characteristic
615	D₄²	C₂²×C₃₁	1	2	yes	—
616	#544	C₂²×C₃₁	1	2	yes	complemented
617	#542	—	2	2	no	—
618	#540	C₂²×C₃₁	1	2	yes	—
619	#540	C₂²×C₃₁	1	2	yes	complemented
620	#538	—	2	2	no	—
621	#537	—	2	1	no	—
622	#536	—	2	1	no	—
623	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#532	C₂²×C₃₁	1	1	yes	characteristic
625	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#529	C₂²×C₃₁	1	1	yes	characteristic
627	#525	—	2	1	no	—
628	C₂×#121	—	2	1	no	—
629	#518	C₂²×C₃₁	1	2	yes	—
630	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
631	#501	C₂²×C₃₁	1	2	yes	complemented
632	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#499	C₂²×C₃₁	1	2	yes	complemented
634	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#490	C₂²×C₃₁	1	2	yes	complemented
636	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	#486	C₂²×C₃₁	1	2	yes	complemented
638	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#482	C₂²×C₃₁	1	2	yes	complemented
640	#482	C₂²×C₃₁	1	2	yes	complemented
641	#482	C₂²×C₃₁	1	2	yes	complemented
642	#482	C₂²×C₃₁	1	2	yes	complemented
643	#482	C₂²×C₃₁	1	2	yes	complemented
644	#482	C₂²×C₃₁	1	2	yes	complemented
645	#481	C₂²×C₃₁	1	2	yes	complemented
646	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#480	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#480	C₂²×C₃₁	1	2	yes	complemented
649	#478	C₂²×C₃₁	1	2	yes	—
650	#478	C₂²×C₃₁	1	2	yes	—
651	#478	C₂²×C₃₁	1	2	yes	complemented
652	#478	C₂²×C₃₁	1	2	yes	complemented
653	#478	C₂²×C₃₁	1	2	yes	complemented
654	#478	C₂²×C₃₁	1	2	yes	complemented
655	#478	C₂²×C₃₁	1	2	yes	complemented
656	#478	C₂²×C₃₁	1	2	yes	complemented
657	#476	C₂²×C₃₁	1	1	yes	characteristic
658	#476	C₂²×C₃₁	1	2	yes	—
659	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#476	C₂²×C₃₁	1	2	yes	complemented
661	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#474	C₂²×C₃₁	1	1	yes	characteristic
664	#474	C₂²×C₃₁	1	1	yes	characteristic
665	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#474	C₂²×C₃₁	1	2	yes	complemented
667	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#469	C₂²×C₃₁	1	2	yes	complemented
669	#469	C₂²×C₃₁	1	2	yes	complemented
670	#469	C₂²×C₃₁	1	2	yes	complemented
671	#469	C₂²×C₃₁	1	2	yes	complemented
672	#466	C₂²×C₃₁	1	2	yes	complemented
673	#466	C₂²×C₃₁	1	2	yes	complemented
674	#459	C₂²×C₃₁	1	1	yes	characteristic
675	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	#459	C₂²×C₃₁	1	2	yes	complemented
678	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#459	C₂²×C₃₁	1	2	yes	complemented
680	#459	C₂²×C₃₁	1	2	yes	complemented
681	#447	C₂²×C₃₁	1	1	yes	characteristic
682	#447	C₂²×C₃₁	1	1	yes	characteristic
683	#447	C₂²×C₃₁	1	2	yes	—
684	#447	C₂²×C₃₁	1	2	yes	—
685	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#442	C₂²×C₃₁	1	2	yes	—
688	#442	C₂²×C₃₁	1	2	yes	complemented
689	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
690	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
691	C₄×D₈	C₂²×C₃₁	1	2	yes	—
692	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
695	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
696	#436	C₂²×C₃₁	1	2	yes	complemented
697	#435	C₂²×C₃₁	1	2	yes	complemented
698	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#433	C₂²×C₃₁	1	2	yes	complemented
700	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#428	C₂²×C₃₁	1	2	yes	complemented
702	#428	C₂²×C₃₁	1	2	yes	complemented
703	#427	C₂²×C₃₁	1	2	yes	complemented
704	#424	C₂²×C₃₁	1	2	yes	complemented
705	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#418	C₂²×C₃₁	1	2	yes	—
707	#418	C₂²×C₃₁	1	2	yes	—
708	C₂×#102	C₂²×C₃₁	1	2	yes	—
709	C₂×C₃₁	—	4	1	no	—
710	C₂×C₃₁	—	4	2	no	—
711	C₂×C₃₁	—	4	2	no	—
712	C₂×C₃₁	—	8	1	no	—
713	C₂×C₃₁	—	8	1	no	—
714	C₂×C₃₁	—	8	1	no	—
715	C₂×C₃₁	—	8	2	no	—
716	C₂×C₃₁	#3489	1	1	yes	characteristic
717	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
718	C₂×C₃₁	#3585	1	1	yes	characteristic
719	C₂×#41	—	2	1	no	—
720	C₂×#41	—	2	1	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂²×Q₈	—	2	1	no	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	—	2	2	no	—
726	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
727	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
728	C₂³×C₄	—	2	1	no	—
729	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
730	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
732	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
733	C₂×D₈	C₂³×C₃₁	1	2	yes	—
734	C₂×D₈	C₂³×C₃₁	1	2	yes	—
735	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
737	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
738	C₄⋊Q₈	—	2	2	no	—
739	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
744	#127	C₂³×C₃₁	1	1	yes	characteristic
745	#127	C₂³×C₃₁	1	1	yes	characteristic
746	#127	C₂³×C₃₁	1	2	yes	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	D₄×C₃₁	1	2	yes	—
750	#125	—	2	2	no	—
751	#125	D₄×C₃₁	1	1	yes	characteristic
752	#125	C₂³×C₃₁	1	2	yes	—
753	#125	C₂³×C₃₁	1	2	yes	—
754	#125	C₂³×C₃₁	1	2	yes	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	—	2	1	no	—
760	#124	—	2	1	no	—
761	#124	D₄×C₃₁	1	1	yes	characteristic
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	D₄×C₃₁	1	2	yes	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
782	#121	—	2	2	no	—
783	#121	—	2	1	no	—
784	#121	—	2	1	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	1	no	—
790	#121	—	2	1	no	—
791	#121	—	2	2	no	—
792	#121	—	2	2	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	D₄×C₃₁	1	1	yes	characteristic
798	#121	C₂³×C₃₁	1	2	yes	—
799	#121	C₂³×C₃₁	1	1	yes	characteristic
800	#121	C₂³×C₃₁	1	1	yes	characteristic
801	#121	C₂³×C₃₁	1	2	yes	—
802	#121	C₂³×C₃₁	1	2	yes	—
803	#121	C₂³×C₃₁	1	2	yes	—
804	#121	C₂³×C₃₁	1	2	yes	—
805	#120	—	2	2	no	—
806	#120	—	2	2	no	—
807	#120	—	2	2	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₃₁	1	2	yes	—
824	C₄×D₄	C₂³×C₃₁	1	2	yes	—
825	C₄×D₄	C₂³×C₃₁	1	2	yes	—
826	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₃₁	1	2	yes	—
829	C₄×D₄	C₂³×C₃₁	1	2	yes	—
830	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₃₁	1	2	yes	—
832	#117	—	2	1	no	—
833	#117	—	2	1	no	—
834	#117	—	2	2	no	—
835	#117	C₂³×C₃₁	1	2	yes	—
836	#117	C₂³×C₃₁	1	2	yes	—
837	#117	C₂³×C₃₁	1	2	yes	—
838	#117	C₂³×C₃₁	1	2	yes	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	—	2	1	no	—
841	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
843	C₂×C₂²⋊C₄	—	2	1	no	—
844	C₂×C₂²⋊C₄	—	2	2	no	—
845	C₂×C₂²⋊C₄	—	2	2	no	—
846	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
847	#107	C₂³×C₃₁	1	1	yes	characteristic
848	#107	C₂³×C₃₁	1	2	yes	—
849	#107	C₂³×C₃₁	1	1	yes	characteristic
850	#107	C₂³×C₃₁	1	2	yes	—
851	#107	C₂³×C₃₁	1	2	yes	—
852	#107	C₂³×C₃₁	1	1	yes	characteristic
853	#107	C₂³×C₃₁	1	1	yes	characteristic
854	#107	C₂³×C₃₁	1	2	yes	—
855	#106	C₂³×C₃₁	1	2	yes	—
856	#106	C₂³×C₃₁	1	2	yes	—
857	#106	C₂³×C₃₁	1	2	yes	—
858	#106	C₂³×C₃₁	1	2	yes	—
859	#106	C₂³×C₃₁	1	2	yes	—
860	#106	C₂³×C₃₁	1	2	yes	—
861	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
862	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
866	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
867	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
868	#102	C₂³×C₃₁	1	1	yes	characteristic
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	2	yes	—
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
879	#102	C₂³×C₃₁	1	2	yes	—
880	#102	C₂³×C₃₁	1	1	yes	characteristic
881	#102	C₂³×C₃₁	1	1	yes	characteristic
882	#102	C₂³×C₃₁	1	1	yes	characteristic
883	#102	C₂³×C₃₁	1	1	yes	characteristic
884	#102	C₂³×C₃₁	1	1	yes	characteristic
885	#102	C₂³×C₃₁	1	2	yes	—
886	#102	C₂³×C₃₁	1	2	yes	—
887	#102	C₂³×C₃₁	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
889	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
892	#97	C₂³×C₃₁	1	2	yes	—
893	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₃₁	1	2	yes	—
896	C₃₁	#62187	1	1	yes	characteristic, direct product factor, Sylow
897	C₂⁴	—	2	1	no	—
898	C₂⁴	—	2	2	no	—
899	#41	—	8	2	no	—
900	#41	—	8	2	no	—
901	#41	—	8	2	no	—
902	#41	—	8	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	8	2	no	—
909	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	4	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	1	no	—
929	C₂×D₄	—	8	2	no	—
930	C₂×D₄	—	8	4	no	—
931	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
932	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
933	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
934	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	8	2	no	—
952	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
953	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
956	D₈	—	2	2	no	—
957	D₈	—	2	2	no	—
958	D₈	—	4	1	no	—
959	D₈	—	4	2	no	—
960	D₈	—	4	1	no	—
961	D₈	—	4	2	no	—
962	M₁₆	—	4	2	no	—
963	M₁₆	—	4	2	no	—
964	C₂×C₈	—	4	2	no	—
965	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
969	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
985	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
986	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
987	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
988	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
991	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1019	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1020	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1021	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1027	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1028	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1029	C₄²	C₂⁴×C₃₁	1	2	yes	—
1030	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	4	2	no	—
1037	C₂³	—	4	4	no	—
1038	C₂³	—	4	2	no	—
1039	C₂³	—	8	1	no	—
1040	C₂³	—	8	2	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1043	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1044	Q₈	—	2	2	no	—
1045	Q₈	—	4	2	no	—
1046	Q₈	—	8	1	no	—
1047	Q₈	—	8	2	no	—
1048	Q₈	—	8	1	no	—
1049	Q₈	—	8	1	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	1	no	—
1054	D₄	—	2	2	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	4	2	no	—
1061	D₄	—	4	4	no	—
1062	D₄	—	4	2	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	8	1	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	1	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	1	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	8	2	no	—
1076	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	1	no	—
1096	C₂×C₄	—	8	1	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	1	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1110	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1111	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₈	—	2	2	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	8	4	no	—
1140	C₂²	—	16	4	no	—
1141	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	2	no	—
1154	C₄	—	4	2	no	—
1155	C₄	—	4	2	no	—
1156	C₄	C₃₁×#576	1	2	yes	—
1157	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1158	C₄	C₃₁×#585	1	1	yes	characteristic
1159	C₂	—	4	1	no	—
1160	C₂	—	4	2	no	—
1161	C₂	—	4	2	no	—
1162	C₂	—	8	1	no	—
1163	C₂	—	8	2	no	—
1164	C₂	—	8	1	no	—
1165	C₂	—	8	1	no	—
1166	C₂	C₃₁×#3489	1	1	yes	characteristic
1167	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1168	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×#3519	C₂	semidirect
3. C₃₁×#3384	C₂	semidirect
4. C₃₁×#3380	C₂	semidirect
5. C₃₁×#3366	C₂	semidirect
6. C₃₁×#3358	C₂	semidirect
7. C₃₁×#3355	C₂	semidirect
8. C₃₁×#3354	C₂	semidirect
9. C₃₁×#3347	C₂	semidirect
10. C₃₁×#3341	C₂	semidirect
11. C₃₁×#3325	C₂	semidirect
12. C₃₁×#3325	C₂	semidirect
13. C₃₁×#3318	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3259	C₂	semidirect
16. C₃₁×#3253	C₂	semidirect
17. C₃₁×#3241	C₂	semidirect
18. C₃₁×#3228	C₂	semidirect
19. C₃₁×#3122	C₂	semidirect
20. C₃₁×#3100	C₂	semidirect
21. C₃₁×#3081	C₂	semidirect
22. C₃₁×#3077	C₂	semidirect
23. C₃₁×#2993	C₂	semidirect
26. C₃₁×#555	C₂²	semidirect
27. C₃₁×#555	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
32. C₃₁×#553	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
37. C₃₁×#547	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
45. C₃₁×#540	C₂²	semidirect
49. C₃₁×#533	C₂²	semidirect
51. C₃₁×#532	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
59. C₃₁×#499	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#490	C₂²	semidirect
62. C₃₁×#486	C₂²	semidirect
63. C₃₁×#486	C₂²	semidirect
64. C₃₁×#486	C₂²	semidirect
65. C₃₁×#482	C₂²	semidirect
66. C₃₁×#482	C₂²	semidirect
67. C₃₁×#482	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#481	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#480	C₂²	semidirect
74. C₃₁×#480	C₂²	semidirect
77. C₃₁×#478	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#478	C₂²	semidirect
81. C₃₁×#478	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
86. C₃₁×#476	C₂²	semidirect
87. C₃₁×#476	C₂²	semidirect
88. C₃₁×#476	C₂²	semidirect
91. C₃₁×#474	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
94. C₃₁×#469	C₂²	semidirect
95. C₃₁×#469	C₂²	semidirect
96. C₃₁×#469	C₂²	semidirect
97. C₃₁×#469	C₂²	semidirect
98. C₃₁×#466	C₂²	semidirect
99. C₃₁×#466	C₂²	semidirect
101. C₃₁×#459	C₂²	semidirect
102. C₃₁×#459	C₂²	semidirect
103. C₃₁×#459	C₂²	semidirect
104. C₃₁×#459	C₂²	semidirect
105. C₃₁×#459	C₂²	semidirect
106. C₃₁×#459	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
114. C₃₁×#442	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×#428	C₂²	semidirect
128. C₃₁×#428	C₂²	semidirect
129. C₃₁×#427	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
131. C₃₁×#423	C₂²	semidirect
446. #62187	C₃₁	direct (N × H)
534. #3547	C₂×C₃₁	semidirect
535. #3519	C₂×C₃₁	semidirect
536. #3384	C₂×C₃₁	semidirect
537. #3380	C₂×C₃₁	semidirect
538. #3366	C₂×C₃₁	semidirect
539. #3358	C₂×C₃₁	semidirect
540. #3355	C₂×C₃₁	semidirect
541. #3354	C₂×C₃₁	semidirect
542. #3347	C₂×C₃₁	semidirect
543. #3341	C₂×C₃₁	semidirect
544. #3325	C₂×C₃₁	semidirect
545. #3325	C₂×C₃₁	semidirect
546. #3318	C₂×C₃₁	semidirect
547. #3294	C₂×C₃₁	semidirect
548. #3259	C₂×C₃₁	semidirect
549. #3253	C₂×C₃₁	semidirect
550. #3241	C₂×C₃₁	semidirect
551. #3228	C₂×C₃₁	semidirect
552. #3122	C₂×C₃₁	semidirect
553. #3100	C₂×C₃₁	semidirect
554. #3081	C₂×C₃₁	semidirect
555. #3077	C₂×C₃₁	semidirect
556. #2993	C₂×C₃₁	semidirect
600. #555	C₂²×C₃₁	semidirect
601. #555	C₂²×C₃₁	semidirect
603. #554	C₂²×C₃₁	semidirect
606. #553	C₂²×C₃₁	semidirect
609. D₄×Q₈	C₂²×C₃₁	semidirect
611. #547	C₂²×C₃₁	semidirect
616. #544	C₂²×C₃₁	semidirect
619. #540	C₂²×C₃₁	semidirect
623. #533	C₂²×C₃₁	semidirect
625. #532	C₂²×C₃₁	semidirect
631. #501	C₂²×C₃₁	semidirect
632. #500	C₂²×C₃₁	semidirect
633. #499	C₂²×C₃₁	semidirect
634. #498	C₂²×C₃₁	semidirect
635. #490	C₂²×C₃₁	semidirect
636. #486	C₂²×C₃₁	semidirect
637. #486	C₂²×C₃₁	semidirect
638. #486	C₂²×C₃₁	semidirect
639. #482	C₂²×C₃₁	semidirect
640. #482	C₂²×C₃₁	semidirect
641. #482	C₂²×C₃₁	semidirect
642. #482	C₂²×C₃₁	semidirect
643. #482	C₂²×C₃₁	semidirect
644. #482	C₂²×C₃₁	semidirect
645. #481	C₂²×C₃₁	semidirect
646. #480	C₂²×C₃₁	semidirect
647. #480	C₂²×C₃₁	semidirect
648. #480	C₂²×C₃₁	semidirect
651. #478	C₂²×C₃₁	semidirect
652. #478	C₂²×C₃₁	semidirect
653. #478	C₂²×C₃₁	semidirect
654. #478	C₂²×C₃₁	semidirect
655. #478	C₂²×C₃₁	semidirect
656. #478	C₂²×C₃₁	semidirect
659. #476	C₂²×C₃₁	semidirect
660. #476	C₂²×C₃₁	semidirect
661. #476	C₂²×C₃₁	semidirect
662. #476	C₂²×C₃₁	semidirect
665. #474	C₂²×C₃₁	semidirect
666. #474	C₂²×C₃₁	semidirect
667. #474	C₂²×C₃₁	semidirect
668. #469	C₂²×C₃₁	semidirect
669. #469	C₂²×C₃₁	semidirect
670. #469	C₂²×C₃₁	semidirect
671. #469	C₂²×C₃₁	semidirect
672. #466	C₂²×C₃₁	semidirect
673. #466	C₂²×C₃₁	semidirect
675. #459	C₂²×C₃₁	semidirect
676. #459	C₂²×C₃₁	semidirect
677. #459	C₂²×C₃₁	semidirect
678. #459	C₂²×C₃₁	semidirect
679. #459	C₂²×C₃₁	semidirect
680. #459	C₂²×C₃₁	semidirect
685. #446	C₂²×C₃₁	semidirect
686. C₈×Q₈	C₂²×C₃₁	semidirect
688. #442	C₂²×C₃₁	semidirect
692. C₄×D₈	C₂²×C₃₁	semidirect
693. C₄×D₈	C₂²×C₃₁	semidirect
694. C₄×D₈	C₂²×C₃₁	semidirect
695. #436	C₂²×C₃₁	semidirect
696. #436	C₂²×C₃₁	semidirect
697. #435	C₂²×C₃₁	semidirect
698. C₈×D₄	C₂²×C₃₁	semidirect
699. #433	C₂²×C₃₁	semidirect
700. #431	C₂²×C₃₁	semidirect
701. #428	C₂²×C₃₁	semidirect
702. #428	C₂²×C₃₁	semidirect
703. #427	C₂²×C₃₁	semidirect
704. #424	C₂²×C₃₁	semidirect
705. #423	C₂²×C₃₁	semidirect
896. C₃₁	#62187	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×#3519	2
C₃₁×#3384	2
C₃₁×#3380	2
C₃₁×#3366	2
C₃₁×#3358	2
C₃₁×#3355	2
C₃₁×#3354	2
C₃₁×#3347	2
C₃₁×#3341	2
C₃₁×#3325	2
C₃₁×#3318	2
C₃₁×#3294	2
C₃₁×#3259	2
C₃₁×#3253	2
C₃₁×#3241	2
C₃₁×#3228	2
C₃₁×#3122	2
C₃₁×#3100	2
C₃₁×#3081	2
C₃₁×#3077	2
C₃₁×#2993	2
#62187	31

Subgroups — C31×#62187 #21518946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62187 #21518946