Subgroups — C₃₁×#61784 #21518543

Order 7936.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3355	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3199	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3098	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3096	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#560	—	2	2	no	—
25	C₃₁×#559	—	2	2	no	—
26	C₃₁×#556	—	2	1	no	—
27	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#555	C₂²	1	1	yes	characteristic
29	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#553	C₂²	1	2	yes	complemented
31	C₃₁×#553	C₂²	1	2	yes	complemented
32	C₃₁×#553	C₂²	1	2	yes	complemented
33	C₃₁×#550	—	2	1	no	—
34	C₃₁×#550	—	2	1	no	—
35	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#547	C₂²	1	1	yes	characteristic
37	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	C₂²	1	2	yes	complemented
41	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#542	—	2	1	no	—
43	C₃₁×#538	—	2	2	no	—
44	C₃₁×#538	—	2	2	no	—
45	C₃₁×#537	C₂²	1	2	yes	—
46	C₃₁×#535	—	2	1	no	—
47	C₃₁×#535	C₂²	1	2	yes	—
48	C₃₁×#535	C₂²	1	2	yes	complemented
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
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	1	no	—
54	C₃₁×#525	—	2	1	no	—
55	C₃₁×#520	C₂²	1	2	yes	complemented
56	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#499	C₂²	1	2	yes	complemented
59	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#488	C₂²	1	2	yes	complemented
61	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#485	C₂²	1	2	yes	complemented
64	C₃₁×#485	C₂²	1	2	yes	complemented
65	C₃₁×#484	C₂²	1	2	yes	complemented
66	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#482	C₂²	1	2	yes	—
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×#482	C₂²	1	2	yes	complemented
72	C₃₁×#482	C₂²	1	2	yes	complemented
73	C₃₁×#482	C₂²	1	2	yes	complemented
74	C₃₁×#482	C₂²	1	2	yes	complemented
75	C₃₁×#481	C₂²	1	1	yes	characteristic
76	C₃₁×#481	C₂²	1	2	yes	complemented
77	C₃₁×#481	C₂²	1	2	yes	complemented
78	C₃₁×#480	C₂²	1	2	yes	complemented
79	C₃₁×#480	C₂²	1	2	yes	complemented
80	C₃₁×#480	C₂²	1	2	yes	complemented
81	C₃₁×#480	C₂²	1	2	yes	complemented
82	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#478	C₂²	1	2	yes	complemented
84	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#478	C₂²	1	2	yes	complemented
86	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#469	C₂²	1	2	yes	—
93	C₃₁×#469	C₂²	1	2	yes	—
94	C₃₁×#469	C₂²	1	2	yes	complemented
95	C₃₁×#468	C₂²	1	2	yes	complemented
96	C₃₁×#466	C₂²	1	2	yes	—
97	C₃₁×#466	C₂²	1	2	yes	—
98	C₃₁×#466	C₂²	1	2	yes	complemented
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#463	C₂²	1	1	yes	characteristic
101	C₃₁×#463	C₂²	1	1	yes	characteristic
102	C₃₁×#459	C₂²	1	1	yes	characteristic
103	C₃₁×#459	C₂²	1	1	yes	characteristic
104	C₃₁×#450	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#449	C₂²	1	2	yes	complemented
106	C₃₁×#449	C₂²	1	2	yes	complemented
107	C₃₁×#447	C₂²	1	1	yes	characteristic
108	C₃₁×#447	C₂²	1	2	yes	—
109	C₃₁×#447	C₂²	1	2	yes	—
110	C₃₁×#447	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
116	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
117	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
118	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#436	C₂²	1	2	yes	complemented
120	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
122	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#428	C₂²	1	2	yes	complemented
126	C₃₁×#428	C₂²	1	2	yes	complemented
127	C₃₁×#427	C₂²	1	2	yes	complemented
128	C₂×C₃₁×#107	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×#408	C₂²	1	2	yes	complemented
134	C₃₁×#408	C₂²	1	2	yes	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	—	2	1	no	—
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₃₁	—	2	1	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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×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	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
155	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×#127	—	2	1	no	—
160	C₃₁×#127	—	2	2	no	—
161	C₃₁×#127	—	2	2	no	—
162	C₃₁×#127	D₄	1	1	yes	characteristic
163	C₃₁×#127	C₂³	1	1	yes	characteristic
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	1	no	—
169	C₃₁×#125	C₂³	1	2	yes	—
170	C₃₁×#125	C₂³	1	1	yes	characteristic
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	2	no	—
173	C₃₁×#124	—	2	1	no	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	—	2	1	no	—
177	C₃₁×#124	D₄	1	2	yes	—
178	C₃₁×#124	C₂³	1	1	yes	characteristic
179	C₃₁×#123	—	2	1	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	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	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	1	no	—
193	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×#121	—	2	1	no	—
196	C₃₁×#121	—	2	1	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	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	2	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	D₄	1	1	yes	characteristic
208	C₃₁×#121	D₄	1	1	yes	characteristic
209	C₃₁×#121	D₄	1	2	yes	—
210	C₃₁×#121	C₂³	1	2	yes	—
211	C₃₁×#121	C₂³	1	2	yes	—
212	C₃₁×#121	C₂³	1	1	yes	characteristic
213	C₃₁×#121	C₂³	1	2	yes	—
214	C₃₁×#121	C₂³	1	2	yes	—
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#120	—	2	2	no	—
220	C₃₁×#120	—	2	2	no	—
221	C₃₁×#120	—	2	2	no	—
222	C₃₁×#120	—	2	2	no	—
223	C₃₁×#120	—	2	2	no	—
224	C₃₁×#120	—	2	2	no	—
225	C₄×Q₈×C₃₁	—	2	2	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	—	2	1	no	—
228	C₄×Q₈×C₃₁	—	2	1	no	—
229	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	—	2	1	no	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	2	yes	—
256	C₃₁×#117	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	1	yes	characteristic
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	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	1	yes	characteristic
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	1	yes	characteristic
294	C₃₁×#102	C₂³	1	2	yes	—
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	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	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	—	4	2	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	4	2	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	8	2	no	—
319	#41×C₃₁	—	8	2	no	—
320	#41×C₃₁	—	8	2	no	—
321	#41×C₃₁	—	8	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₃₁	—	2	1	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	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	4	1	no	—
342	C₂×D₄×C₃₁	—	4	1	no	—
343	C₂×D₄×C₃₁	—	4	2	no	—
344	C₂×D₄×C₃₁	—	4	2	no	—
345	C₂×D₄×C₃₁	—	8	2	no	—
346	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
354	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	2	2	no	—
364	C₂²×C₄×C₃₁	—	2	2	no	—
365	C₂²×C₄×C₃₁	—	2	1	no	—
366	C₂²×C₄×C₃₁	—	2	1	no	—
367	C₂²×C₄×C₃₁	—	8	2	no	—
368	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
373	SD₁₆×C₃₁	—	4	1	no	—
374	SD₁₆×C₃₁	—	4	1	no	—
375	D₈×C₃₁	—	4	2	no	—
376	D₈×C₃₁	—	4	1	no	—
377	D₈×C₃₁	—	4	2	no	—
378	D₈×C₃₁	—	4	1	no	—
379	M₁₆×C₃₁	—	4	2	no	—
380	M₁₆×C₃₁	—	4	2	no	—
381	C₂×C₈×C₃₁	—	4	2	no	—
382	C₂×C₈×C₃₁	—	4	2	no	—
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
387	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	1	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	2	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
448	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
449	#61784	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
450	C₂³×C₃₁	—	2	1	no	—
451	C₂³×C₃₁	—	2	1	no	—
452	C₂³×C₃₁	—	2	1	no	—
453	C₂³×C₃₁	—	2	2	no	—
454	C₂³×C₃₁	—	4	2	no	—
455	C₂³×C₃₁	—	8	1	no	—
456	C₂³×C₃₁	—	8	1	no	—
457	C₂³×C₃₁	—	8	2	no	—
458	C₂³×C₃₁	—	8	2	no	—
459	C₂³×C₃₁	—	8	2	no	—
460	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
461	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
462	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
463	Q₈×C₃₁	—	2	1	no	—
464	Q₈×C₃₁	—	2	1	no	—
465	Q₈×C₃₁	—	4	2	no	—
466	Q₈×C₃₁	—	4	2	no	—
467	Q₈×C₃₁	—	4	2	no	—
468	Q₈×C₃₁	—	8	1	no	—
469	D₄×C₃₁	—	2	2	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	1	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	2	2	no	—
478	D₄×C₃₁	—	2	2	no	—
479	D₄×C₃₁	—	4	2	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	4	2	no	—
482	D₄×C₃₁	—	4	2	no	—
483	D₄×C₃₁	—	4	2	no	—
484	D₄×C₃₁	—	4	2	no	—
485	D₄×C₃₁	—	8	1	no	—
486	D₄×C₃₁	—	8	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	2	no	—
492	D₄×C₃₁	—	8	2	no	—
493	D₄×C₃₁	—	8	2	no	—
494	D₄×C₃₁	—	8	2	no	—
495	D₄×C₃₁	—	8	2	no	—
496	D₄×C₃₁	—	8	2	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	2	no	—
501	C₂×C₄×C₃₁	—	2	2	no	—
502	C₂×C₄×C₃₁	—	2	1	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	1	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	1	no	—
509	C₂×C₄×C₃₁	—	2	2	no	—
510	C₂×C₄×C₃₁	—	2	2	no	—
511	C₂×C₄×C₃₁	—	2	1	no	—
512	C₂×C₄×C₃₁	—	4	1	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	4	2	no	—
515	C₂×C₄×C₃₁	—	4	2	no	—
516	C₂×C₄×C₃₁	—	8	1	no	—
517	C₂×C₄×C₃₁	—	8	1	no	—
518	C₂×C₄×C₃₁	—	8	2	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	—	8	1	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	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
532	C₈×C₃₁	—	2	1	no	—
533	C₈×C₃₁	—	2	2	no	—
534	C₈×C₃₁	—	2	1	no	—
535	C₈×C₃₁	—	2	1	no	—
536	C₈×C₃₁	—	2	2	no	—
537	C₈×C₃₁	—	2	1	no	—
538	#3546	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3506	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	#3353	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3340	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3339	C₂×C₃₁	1	2	yes	complemented
545	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3332	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3325	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3322	C₂×C₃₁	1	2	yes	complemented
549	#3305	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3297	C₂×C₃₁	1	2	yes	complemented
551	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3228	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3199	C₂×C₃₁	1	2	yes	complemented
555	#3198	C₂×C₃₁	1	2	yes	complemented
556	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3100	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3098	C₂×C₃₁	1	2	yes	complemented
559	#3096	C₂×C₃₁	1	2	yes	complemented
560	#2979	C₂×C₃₁	1	1	yes	characteristic, complemented
561	C₂²×C₃₁	—	2	1	no	—
562	C₂²×C₃₁	—	2	2	no	—
563	C₂²×C₃₁	—	2	2	no	—
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	2	no	—
569	C₂²×C₃₁	—	2	2	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	—	4	1	no	—
572	C₂²×C₃₁	—	4	2	no	—
573	C₂²×C₃₁	—	4	1	no	—
574	C₂²×C₃₁	—	4	2	no	—
575	C₂²×C₃₁	—	4	1	no	—
576	C₂²×C₃₁	—	4	1	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	2	no	—
582	C₂²×C₃₁	—	8	4	no	—
583	C₂²×C₃₁	—	16	4	no	—
584	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
585	C₄×C₃₁	—	2	1	no	—
586	C₄×C₃₁	—	2	1	no	—
587	C₄×C₃₁	—	2	2	no	—
588	C₄×C₃₁	—	2	1	no	—
589	C₄×C₃₁	—	2	2	no	—
590	C₄×C₃₁	—	2	1	no	—
591	C₄×C₃₁	—	4	1	no	—
592	C₄×C₃₁	—	4	2	no	—
593	C₄×C₃₁	—	4	1	no	—
594	C₄×C₃₁	—	4	1	no	—
595	C₄×C₃₁	—	4	1	no	—
596	C₄×C₃₁	—	4	1	no	—
597	C₄×C₃₁	—	4	2	no	—
598	C₄×C₃₁	—	4	2	no	—
599	C₄×C₃₁	#576	1	2	yes	—
600	C₄×C₃₁	#585	1	1	yes	characteristic
601	C₄×C₃₁	#585	1	1	yes	characteristic
602	#560	—	2	2	no	—
603	#559	—	2	2	no	—
604	#556	—	2	1	no	—
605	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
606	#555	C₂²×C₃₁	1	1	yes	characteristic
607	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	#553	C₂²×C₃₁	1	2	yes	complemented
609	#553	C₂²×C₃₁	1	2	yes	complemented
610	#553	C₂²×C₃₁	1	2	yes	complemented
611	#550	—	2	1	no	—
612	#550	—	2	1	no	—
613	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	#547	C₂²×C₃₁	1	1	yes	characteristic
615	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
617	#546	—	2	1	no	—
618	#546	C₂²×C₃₁	1	2	yes	complemented
619	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#542	—	2	1	no	—
621	#538	—	2	2	no	—
622	#538	—	2	2	no	—
623	#537	C₂²×C₃₁	1	2	yes	—
624	#535	—	2	1	no	—
625	#535	C₂²×C₃₁	1	2	yes	—
626	#535	C₂²×C₃₁	1	2	yes	complemented
627	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
628	#532	C₂²×C₃₁	1	1	yes	characteristic
629	#532	C₂²×C₃₁	1	1	yes	characteristic
630	#529	C₂²×C₃₁	1	1	yes	characteristic
631	#525	—	2	1	no	—
632	#525	—	2	1	no	—
633	#520	C₂²×C₃₁	1	2	yes	complemented
634	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#499	C₂²×C₃₁	1	2	yes	complemented
637	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#488	C₂²×C₃₁	1	2	yes	complemented
639	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#485	C₂²×C₃₁	1	2	yes	complemented
642	#485	C₂²×C₃₁	1	2	yes	complemented
643	#484	C₂²×C₃₁	1	2	yes	complemented
644	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#482	C₂²×C₃₁	1	2	yes	—
646	#482	C₂²×C₃₁	1	2	yes	complemented
647	#482	C₂²×C₃₁	1	2	yes	complemented
648	#482	C₂²×C₃₁	1	2	yes	complemented
649	#482	C₂²×C₃₁	1	2	yes	complemented
650	#482	C₂²×C₃₁	1	2	yes	complemented
651	#482	C₂²×C₃₁	1	2	yes	complemented
652	#482	C₂²×C₃₁	1	2	yes	complemented
653	#481	C₂²×C₃₁	1	1	yes	characteristic
654	#481	C₂²×C₃₁	1	2	yes	complemented
655	#481	C₂²×C₃₁	1	2	yes	complemented
656	#480	C₂²×C₃₁	1	2	yes	complemented
657	#480	C₂²×C₃₁	1	2	yes	complemented
658	#480	C₂²×C₃₁	1	2	yes	complemented
659	#480	C₂²×C₃₁	1	2	yes	complemented
660	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#478	C₂²×C₃₁	1	2	yes	complemented
662	#478	C₂²×C₃₁	1	1	yes	characteristic, 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	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#469	C₂²×C₃₁	1	2	yes	—
671	#469	C₂²×C₃₁	1	2	yes	—
672	#469	C₂²×C₃₁	1	2	yes	complemented
673	#468	C₂²×C₃₁	1	2	yes	complemented
674	#466	C₂²×C₃₁	1	2	yes	—
675	#466	C₂²×C₃₁	1	2	yes	—
676	#466	C₂²×C₃₁	1	2	yes	complemented
677	#465	C₂²×C₃₁	1	2	yes	complemented
678	#463	C₂²×C₃₁	1	1	yes	characteristic
679	#463	C₂²×C₃₁	1	1	yes	characteristic
680	#459	C₂²×C₃₁	1	1	yes	characteristic
681	#459	C₂²×C₃₁	1	1	yes	characteristic
682	#450	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	#449	C₂²×C₃₁	1	2	yes	complemented
684	#449	C₂²×C₃₁	1	2	yes	complemented
685	#447	C₂²×C₃₁	1	1	yes	characteristic
686	#447	C₂²×C₃₁	1	2	yes	—
687	#447	C₂²×C₃₁	1	2	yes	—
688	#447	C₂²×C₃₁	1	2	yes	complemented
689	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
692	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
693	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
694	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
695	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
696	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
697	#436	C₂²×C₃₁	1	2	yes	complemented
698	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
700	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	#428	C₂²×C₃₁	1	2	yes	complemented
704	#428	C₂²×C₃₁	1	2	yes	complemented
705	#427	C₂²×C₃₁	1	2	yes	complemented
706	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
707	#418	C₂²×C₃₁	1	2	yes	complemented
708	#417	C₂²×C₃₁	1	2	yes	complemented
709	#416	C₂²×C₃₁	1	2	yes	complemented
710	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
711	#408	C₂²×C₃₁	1	2	yes	complemented
712	#408	C₂²×C₃₁	1	2	yes	complemented
713	C₂×C₃₁	—	4	2	no	—
714	C₂×C₃₁	—	4	1	no	—
715	C₂×C₃₁	—	4	2	no	—
716	C₂×C₃₁	—	8	1	no	—
717	C₂×C₃₁	—	8	1	no	—
718	C₂×C₃₁	—	8	2	no	—
719	C₂×C₃₁	—	8	1	no	—
720	C₂×C₃₁	#3485	1	1	yes	characteristic
721	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
722	C₂×C₃₁	#3584	1	1	yes	characteristic
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	2	1	no	—
725	C₂×#41	—	2	1	no	—
726	C₂×#41	—	2	1	no	—
727	C₂×#41	C₂³×C₃₁	1	2	yes	—
728	C₂×#41	C₂³×C₃₁	1	2	yes	—
729	C₂²×D₄	—	2	1	no	—
730	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
731	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
732	C₂³×C₄	—	2	1	no	—
733	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
734	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
735	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
736	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×D₈	C₂³×C₃₁	1	2	yes	—
738	C₂×D₈	C₂³×C₃₁	1	2	yes	—
739	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
740	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
741	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
742	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
743	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
744	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
747	#127	—	2	1	no	—
748	#127	—	2	2	no	—
749	#127	—	2	2	no	—
750	#127	D₄×C₃₁	1	1	yes	characteristic
751	#127	C₂³×C₃₁	1	1	yes	characteristic
752	#126	—	2	2	no	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	1	no	—
757	#125	C₂³×C₃₁	1	1	yes	characteristic
758	#125	C₂³×C₃₁	1	2	yes	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	—	2	1	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	1	no	—
765	#124	D₄×C₃₁	1	2	yes	—
766	#124	C₂³×C₃₁	1	1	yes	characteristic
767	#123	—	2	1	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
782	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
783	#121	—	2	1	no	—
784	#121	—	2	1	no	—
785	#121	—	2	2	no	—
786	#121	—	2	2	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	D₄×C₃₁	1	1	yes	characteristic
796	#121	D₄×C₃₁	1	1	yes	characteristic
797	#121	D₄×C₃₁	1	2	yes	—
798	#121	C₂³×C₃₁	1	1	yes	characteristic
799	#121	C₂³×C₃₁	1	2	yes	—
800	#121	C₂³×C₃₁	1	2	yes	—
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	#121	C₂³×C₃₁	1	2	yes	—
806	#121	C₂³×C₃₁	1	2	yes	—
807	#120	—	2	2	no	—
808	#120	—	2	2	no	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	C₄×Q₈	—	2	2	no	—
814	C₄×Q₈	—	2	1	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₃₁	1	2	yes	—
835	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₃₁	1	2	yes	—
837	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	C₂³×C₃₁	1	2	yes	—
842	#117	C₂³×C₃₁	1	2	yes	—
843	#117	C₂³×C₃₁	1	2	yes	—
844	#117	C₂³×C₃₁	1	2	yes	—
845	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
846	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
847	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
848	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
849	C₂×C₂²⋊C₄	—	2	1	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
852	#107	C₂³×C₃₁	1	1	yes	characteristic
853	#107	C₂³×C₃₁	1	2	yes	—
854	#107	C₂³×C₃₁	1	2	yes	—
855	#107	C₂³×C₃₁	1	2	yes	—
856	#107	C₂³×C₃₁	1	2	yes	—
857	#107	C₂³×C₃₁	1	1	yes	characteristic
858	#107	C₂³×C₃₁	1	2	yes	—
859	#107	C₂³×C₃₁	1	2	yes	—
860	#106	C₂³×C₃₁	1	1	yes	characteristic
861	#106	C₂³×C₃₁	1	2	yes	—
862	#106	C₂³×C₃₁	1	1	yes	characteristic
863	#106	C₂³×C₃₁	1	2	yes	—
864	#106	C₂³×C₃₁	1	2	yes	—
865	#106	C₂³×C₃₁	1	2	yes	—
866	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
869	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
870	#103	C₂³×C₃₁	1	1	yes	characteristic
871	#103	C₂³×C₃₁	1	2	yes	—
872	#103	C₂³×C₃₁	1	1	yes	characteristic
873	#103	C₂³×C₃₁	1	2	yes	—
874	#102	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
885	#102	C₂³×C₃₁	1	1	yes	characteristic
886	#102	C₂³×C₃₁	1	2	yes	—
887	#102	C₂³×C₃₁	1	2	yes	—
888	#102	C₂³×C₃₁	1	1	yes	characteristic
889	#102	C₂³×C₃₁	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
892	C₂²⋊C₈	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	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
897	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
898	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
899	C₄×C₈	C₂³×C₃₁	1	2	yes	—
900	C₃₁	#61784	1	1	yes	characteristic, direct product factor, Sylow
901	C₂⁴	—	2	1	no	—
902	C₂⁴	—	2	2	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	8	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	1	no	—
914	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	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	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	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	—	4	1	no	—
931	C₂×D₄	—	4	1	no	—
932	C₂×D₄	—	4	2	no	—
933	C₂×D₄	—	4	2	no	—
934	C₂×D₄	—	8	2	no	—
935	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
936	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
937	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
938	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
939	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
940	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
941	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
942	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
943	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂²×C₄	—	2	1	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	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	8	2	no	—
957	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
958	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
961	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
962	SD₁₆	—	4	1	no	—
963	SD₁₆	—	4	1	no	—
964	D₈	—	4	2	no	—
965	D₈	—	4	1	no	—
966	D₈	—	4	2	no	—
967	D₈	—	4	1	no	—
968	M₁₆	—	4	2	no	—
969	M₁₆	—	4	2	no	—
970	C₂×C₈	—	4	2	no	—
971	C₂×C₈	—	4	2	no	—
972	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
976	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₃₁	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	4	2	no	—
1043	C₂³	—	8	1	no	—
1044	C₂³	—	8	1	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	—	8	2	no	—
1048	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1049	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1050	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	4	2	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	8	1	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	8	1	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	1	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	1	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	—	8	1	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1114	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1115	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1117	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1119	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1120	C₈	—	2	1	no	—
1121	C₈	—	2	2	no	—
1122	C₈	—	2	1	no	—
1123	C₈	—	2	1	no	—
1124	C₈	—	2	2	no	—
1125	C₈	—	2	1	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	4	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	8	4	no	—
1148	C₂²	—	16	4	no	—
1149	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1150	C₄	—	2	2	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	2	no	—
1164	C₄	C₃₁×#576	1	2	yes	—
1165	C₄	C₃₁×#585	1	1	yes	characteristic
1166	C₄	C₃₁×#585	1	1	yes	characteristic
1167	C₂	—	4	1	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	4	2	no	—
1170	C₂	—	8	1	no	—
1171	C₂	—	8	1	no	—
1172	C₂	—	8	1	no	—
1173	C₂	—	8	2	no	—
1174	C₂	C₃₁×#3485	1	1	yes	characteristic
1175	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1176	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3546	C₂	semidirect
2. C₃₁×#3506	C₂	semidirect
3. C₃₁×#3355	C₂	semidirect
4. C₃₁×#3354	C₂	semidirect
5. C₃₁×#3353	C₂	semidirect
6. C₃₁×#3340	C₂	semidirect
7. C₃₁×#3339	C₂	semidirect
8. C₃₁×#3334	C₂	semidirect
9. C₃₁×#3332	C₂	semidirect
10. C₃₁×#3325	C₂	semidirect
11. C₃₁×#3322	C₂	semidirect
12. C₃₁×#3305	C₂	semidirect
13. C₃₁×#3297	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3233	C₂	semidirect
16. C₃₁×#3228	C₂	semidirect
17. C₃₁×#3199	C₂	semidirect
18. C₃₁×#3198	C₂	semidirect
19. C₃₁×#3105	C₂	semidirect
20. C₃₁×#3100	C₂	semidirect
21. C₃₁×#3098	C₂	semidirect
22. C₃₁×#3096	C₂	semidirect
23. C₃₁×#2979	C₂	semidirect
27. C₃₁×#556	C₂²	semidirect
29. C₃₁×#555	C₂²	semidirect
30. C₃₁×#553	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
32. C₃₁×#553	C₂²	semidirect
35. C₃₁×#550	C₂²	semidirect
37. C₃₁×#547	C₂²	semidirect
38. C₃₁×#547	C₂²	semidirect
40. C₃₁×#546	C₂²	semidirect
41. D₄²×C₃₁	C₂²	semidirect
48. C₃₁×#535	C₂²	semidirect
49. C₃₁×#533	C₂²	semidirect
55. C₃₁×#520	C₂²	semidirect
56. C₂×C₄×D₄×C₃₁	C₂²	semidirect
57. C₃₁×#500	C₂²	semidirect
58. C₃₁×#499	C₂²	semidirect
59. C₃₁×#498	C₂²	semidirect
60. C₃₁×#488	C₂²	semidirect
61. C₃₁×#486	C₂²	semidirect
62. C₃₁×#486	C₂²	semidirect
63. C₃₁×#485	C₂²	semidirect
64. C₃₁×#485	C₂²	semidirect
65. C₃₁×#484	C₂²	semidirect
66. C₃₁×#484	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
72. C₃₁×#482	C₂²	semidirect
73. C₃₁×#482	C₂²	semidirect
74. C₃₁×#482	C₂²	semidirect
76. C₃₁×#481	C₂²	semidirect
77. C₃₁×#481	C₂²	semidirect
78. C₃₁×#480	C₂²	semidirect
79. C₃₁×#480	C₂²	semidirect
80. C₃₁×#480	C₂²	semidirect
81. C₃₁×#480	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
83. C₃₁×#478	C₂²	semidirect
84. C₃₁×#478	C₂²	semidirect
85. C₃₁×#478	C₂²	semidirect
86. C₃₁×#477	C₂²	semidirect
87. C₃₁×#476	C₂²	semidirect
88. C₃₁×#475	C₂²	semidirect
89. C₃₁×#474	C₂²	semidirect
90. C₃₁×#474	C₂²	semidirect
91. C₃₁×#474	C₂²	semidirect
94. C₃₁×#469	C₂²	semidirect
95. C₃₁×#468	C₂²	semidirect
98. C₃₁×#466	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
104. C₃₁×#450	C₂²	semidirect
105. C₃₁×#449	C₂²	semidirect
106. C₃₁×#449	C₂²	semidirect
110. C₃₁×#447	C₂²	semidirect
111. C₄×SD₁₆×C₃₁	C₂²	semidirect
112. C₄×SD₁₆×C₃₁	C₂²	semidirect
115. C₄×D₈×C₃₁	C₂²	semidirect
116. C₄×D₈×C₃₁	C₂²	semidirect
117. C₃₁×#436	C₂²	semidirect
118. C₃₁×#436	C₂²	semidirect
119. C₃₁×#436	C₂²	semidirect
120. C₈×D₄×C₃₁	C₂²	semidirect
121. C₈×D₄×C₃₁	C₂²	semidirect
122. C₈×D₄×C₃₁	C₂²	semidirect
123. C₃₁×#431	C₂²	semidirect
124. C₃₁×#431	C₂²	semidirect
125. C₃₁×#428	C₂²	semidirect
126. C₃₁×#428	C₂²	semidirect
127. C₃₁×#427	C₂²	semidirect
128. C₂×C₃₁×#107	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×#408	C₂²	semidirect
134. C₃₁×#408	C₂²	semidirect
449. #61784	C₃₁	direct (N × H)
538. #3546	C₂×C₃₁	semidirect
539. #3506	C₂×C₃₁	semidirect
540. #3355	C₂×C₃₁	semidirect
541. #3354	C₂×C₃₁	semidirect
542. #3353	C₂×C₃₁	semidirect
543. #3340	C₂×C₃₁	semidirect
544. #3339	C₂×C₃₁	semidirect
545. #3334	C₂×C₃₁	semidirect
546. #3332	C₂×C₃₁	semidirect
547. #3325	C₂×C₃₁	semidirect
548. #3322	C₂×C₃₁	semidirect
549. #3305	C₂×C₃₁	semidirect
550. #3297	C₂×C₃₁	semidirect
551. #3294	C₂×C₃₁	semidirect
552. #3233	C₂×C₃₁	semidirect
553. #3228	C₂×C₃₁	semidirect
554. #3199	C₂×C₃₁	semidirect
555. #3198	C₂×C₃₁	semidirect
556. #3105	C₂×C₃₁	semidirect
557. #3100	C₂×C₃₁	semidirect
558. #3098	C₂×C₃₁	semidirect
559. #3096	C₂×C₃₁	semidirect
560. #2979	C₂×C₃₁	semidirect
605. #556	C₂²×C₃₁	semidirect
607. #555	C₂²×C₃₁	semidirect
608. #553	C₂²×C₃₁	semidirect
609. #553	C₂²×C₃₁	semidirect
610. #553	C₂²×C₃₁	semidirect
613. #550	C₂²×C₃₁	semidirect
615. #547	C₂²×C₃₁	semidirect
616. #547	C₂²×C₃₁	semidirect
618. #546	C₂²×C₃₁	semidirect
619. D₄²	C₂²×C₃₁	semidirect
626. #535	C₂²×C₃₁	semidirect
627. #533	C₂²×C₃₁	semidirect
633. #520	C₂²×C₃₁	semidirect
634. C₂×C₄×D₄	C₂²×C₃₁	semidirect
635. #500	C₂²×C₃₁	semidirect
636. #499	C₂²×C₃₁	semidirect
637. #498	C₂²×C₃₁	semidirect
638. #488	C₂²×C₃₁	semidirect
639. #486	C₂²×C₃₁	semidirect
640. #486	C₂²×C₃₁	semidirect
641. #485	C₂²×C₃₁	semidirect
642. #485	C₂²×C₃₁	semidirect
643. #484	C₂²×C₃₁	semidirect
644. #484	C₂²×C₃₁	semidirect
646. #482	C₂²×C₃₁	semidirect
647. #482	C₂²×C₃₁	semidirect
648. #482	C₂²×C₃₁	semidirect
649. #482	C₂²×C₃₁	semidirect
650. #482	C₂²×C₃₁	semidirect
651. #482	C₂²×C₃₁	semidirect
652. #482	C₂²×C₃₁	semidirect
654. #481	C₂²×C₃₁	semidirect
655. #481	C₂²×C₃₁	semidirect
656. #480	C₂²×C₃₁	semidirect
657. #480	C₂²×C₃₁	semidirect
658. #480	C₂²×C₃₁	semidirect
659. #480	C₂²×C₃₁	semidirect
660. #478	C₂²×C₃₁	semidirect
661. #478	C₂²×C₃₁	semidirect
662. #478	C₂²×C₃₁	semidirect
663. #478	C₂²×C₃₁	semidirect
664. #477	C₂²×C₃₁	semidirect
665. #476	C₂²×C₃₁	semidirect
666. #475	C₂²×C₃₁	semidirect
667. #474	C₂²×C₃₁	semidirect
668. #474	C₂²×C₃₁	semidirect
669. #474	C₂²×C₃₁	semidirect
672. #469	C₂²×C₃₁	semidirect
673. #468	C₂²×C₃₁	semidirect
676. #466	C₂²×C₃₁	semidirect
677. #465	C₂²×C₃₁	semidirect
682. #450	C₂²×C₃₁	semidirect
683. #449	C₂²×C₃₁	semidirect
684. #449	C₂²×C₃₁	semidirect
688. #447	C₂²×C₃₁	semidirect
689. C₄×SD₁₆	C₂²×C₃₁	semidirect
690. C₄×SD₁₆	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. #436	C₂²×C₃₁	semidirect
698. C₈×D₄	C₂²×C₃₁	semidirect
699. C₈×D₄	C₂²×C₃₁	semidirect
700. C₈×D₄	C₂²×C₃₁	semidirect
701. #431	C₂²×C₃₁	semidirect
702. #431	C₂²×C₃₁	semidirect
703. #428	C₂²×C₃₁	semidirect
704. #428	C₂²×C₃₁	semidirect
705. #427	C₂²×C₃₁	semidirect
706. C₂×#107	C₂²×C₃₁	semidirect
707. #418	C₂²×C₃₁	semidirect
708. #417	C₂²×C₃₁	semidirect
709. #416	C₂²×C₃₁	semidirect
710. C₂×#102	C₂²×C₃₁	semidirect
711. #408	C₂²×C₃₁	semidirect
712. #408	C₂²×C₃₁	semidirect
900. C₃₁	#61784	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×#3546	2
C₃₁×#3506	2
C₃₁×#3355	2
C₃₁×#3354	2
C₃₁×#3353	2
C₃₁×#3340	2
C₃₁×#3339	2
C₃₁×#3334	2
C₃₁×#3332	2
C₃₁×#3325	2
C₃₁×#3322	2
C₃₁×#3305	2
C₃₁×#3297	2
C₃₁×#3294	2
C₃₁×#3233	2
C₃₁×#3228	2
C₃₁×#3199	2
C₃₁×#3198	2
C₃₁×#3105	2
C₃₁×#3100	2
C₃₁×#3098	2
C₃₁×#3096	2
C₃₁×#2979	2
#61784	31

Subgroups — C31×#61784 #21518543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61784 #21518543