Subgroups — C₃₁×#62618 #21519377

Order 7936.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3333	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3309	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3226	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3175	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3171	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3141	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×#563	—	2	2	no	—
25	C₃₁×#560	—	2	2	no	—
26	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#556	C₂²	1	1	yes	characteristic
28	C₃₁×#556	C₂²	1	1	yes	characteristic
29	C₃₁×#554	C₂²	1	2	yes	complemented
30	C₃₁×#553	—	2	1	no	—
31	C₃₁×#553	C₂²	1	2	yes	complemented
32	C₃₁×#550	C₂²	1	2	yes	—
33	C₃₁×#550	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₃₁	—	2	1	no	—
35	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#547	C₂²	1	1	yes	characteristic
38	C₃₁×#547	C₂²	1	1	yes	characteristic
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	C₂²	1	2	yes	—
41	D₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#544	C₂²	1	2	yes	complemented
43	C₃₁×#542	C₂²	1	2	yes	—
44	C₃₁×#542	C₂²	1	2	yes	complemented
45	C₃₁×#541	—	2	1	no	—
46	C₃₁×#539	—	2	2	no	—
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#537	—	2	1	no	—
49	C₃₁×#536	—	2	1	no	—
50	C₃₁×#535	—	2	1	no	—
51	C₃₁×#535	C₂²	1	2	yes	—
52	C₃₁×#532	C₂²	1	1	yes	characteristic
53	C₃₁×#532	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#529	C₂²	1	1	yes	characteristic
56	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#501	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#500	C₂²	1	2	yes	complemented
59	C₃₁×#496	C₂²	1	1	yes	characteristic
60	C₃₁×#495	C₂²	1	2	yes	complemented
61	C₃₁×#490	C₂²	1	1	yes	characteristic
62	C₃₁×#490	C₂²	1	2	yes	complemented
63	C₃₁×#489	C₂²	1	2	yes	—
64	C₃₁×#489	C₂²	1	2	yes	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	—
68	C₃₁×#488	C₂²	1	2	yes	complemented
69	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#486	C₂²	1	1	yes	characteristic
72	C₃₁×#486	C₂²	1	1	yes	characteristic
73	C₃₁×#486	C₂²	1	2	yes	—
74	C₃₁×#486	C₂²	1	2	yes	complemented
75	C₃₁×#485	C₂²	1	2	yes	complemented
76	C₃₁×#484	C₂²	1	2	yes	complemented
77	C₃₁×#482	C₂²	1	2	yes	—
78	C₃₁×#480	C₂²	1	2	yes	—
79	C₃₁×#480	C₂²	1	2	yes	—
80	C₃₁×#480	C₂²	1	2	yes	complemented
81	C₃₁×#479	C₂²	1	2	yes	complemented
82	C₃₁×#478	C₂²	1	2	yes	complemented
83	C₃₁×#477	C₂²	1	2	yes	complemented
84	C₃₁×#474	C₂²	1	1	yes	characteristic
85	C₃₁×#474	C₂²	1	1	yes	characteristic
86	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#474	C₂²	1	2	yes	complemented
88	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#469	C₂²	1	1	yes	characteristic
90	C₃₁×#469	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#468	C₂²	1	2	yes	—
92	C₃₁×#468	C₂²	1	1	yes	characteristic
93	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#468	C₂²	1	2	yes	complemented
95	C₃₁×#467	C₂²	1	2	yes	complemented
96	C₃₁×#466	C₂²	1	2	yes	—
97	C₃₁×#464	C₂²	1	2	yes	—
98	C₃₁×#463	C₂²	1	2	yes	—
99	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#460	C₂²	1	1	yes	characteristic
102	C₃₁×#460	C₂²	1	2	yes	complemented
103	C₃₁×#459	C₂²	1	1	yes	characteristic
104	C₃₁×#459	C₂²	1	2	yes	complemented
105	C₃₁×#452	C₂²	1	2	yes	complemented
106	C₃₁×#452	C₂²	1	2	yes	complemented
107	C₃₁×#450	C₂²	1	2	yes	—
108	C₃₁×#449	C₂²	1	2	yes	complemented
109	C₃₁×#449	C₂²	1	2	yes	complemented
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×#440	C₂²	1	2	yes	complemented
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
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
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
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#418	C₂²	1	2	yes	—
128	C₃₁×#417	C₂²	1	2	yes	complemented
129	C₃₁×#417	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	—
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	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₃₁	—	2	1	no	—
141	C₂²×Q₈×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	—	2	1	no	—
143	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₃₁	C₂³	1	2	yes	—
151	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	—	2	1	no	—
157	C₃₁×C₄⋊Q₈	—	2	2	no	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×#127	—	2	2	no	—
167	C₃₁×#127	C₂³	1	1	yes	characteristic
168	C₃₁×#127	C₂³	1	2	yes	—
169	C₃₁×#127	C₂³	1	1	yes	characteristic
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	1	no	—
176	C₃₁×#126	D₄	1	2	yes	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	D₄	1	1	yes	characteristic
181	C₃₁×#125	C₂³	1	2	yes	—
182	C₃₁×#125	C₂³	1	1	yes	characteristic
183	C₃₁×#124	—	2	1	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	—	2	1	no	—
187	C₃₁×#124	D₄	1	1	yes	characteristic
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#124	C₂³	1	1	yes	characteristic
191	C₃₁×#123	—	2	1	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	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×#123	D₄	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	1	no	—
203	C₃₁×C₂²⋊Q₈	—	2	1	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	1	no	—
216	C₃₁×#121	—	2	1	no	—
217	C₃₁×#121	—	2	1	no	—
218	C₃₁×#121	—	2	1	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	1	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	—	2	2	no	—
224	C₃₁×#121	—	2	2	no	—
225	C₃₁×#121	—	2	2	no	—
226	C₃₁×#121	D₄	1	1	yes	characteristic
227	C₃₁×#121	C₂³	1	2	yes	—
228	C₃₁×#121	C₂³	1	1	yes	characteristic
229	C₃₁×#121	C₂³	1	2	yes	—
230	C₃₁×#121	C₂³	1	1	yes	characteristic
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	C₄×Q₈×C₃₁	—	2	1	no	—
237	C₄×Q₈×C₃₁	—	2	1	no	—
238	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
241	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	—	2	2	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	2	no	—
245	C₄×D₄×C₃₁	—	2	2	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	—	2	1	no	—
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	1	no	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₃₁×#117	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
279	C₃₁×#103	C₂³	1	2	yes	—
280	C₃₁×#103	C₂³	1	2	yes	—
281	C₃₁×#103	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	2	yes	—
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	1	yes	characteristic
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	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	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	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	4	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	#41×C₃₁	—	8	2	no	—
319	#41×C₃₁	—	8	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	8	2	no	—
326	C₂×Q₈×C₃₁	—	8	2	no	—
327	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	2	1	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	1	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	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	4	2	no	—
345	C₂×D₄×C₃₁	—	4	2	no	—
346	C₂×D₄×C₃₁	—	8	2	no	—
347	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
351	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₃₁	—	2	2	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	2	no	—
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
366	Q₁₆×C₃₁	—	4	2	no	—
367	SD₁₆×C₃₁	—	4	1	no	—
368	SD₁₆×C₃₁	—	4	1	no	—
369	SD₁₆×C₃₁	—	4	2	no	—
370	SD₁₆×C₃₁	—	4	2	no	—
371	D₈×C₃₁	—	4	2	no	—
372	D₈×C₃₁	—	4	1	no	—
373	D₈×C₃₁	—	4	1	no	—
374	M₁₆×C₃₁	—	4	1	no	—
375	M₁₆×C₃₁	—	4	1	no	—
376	M₁₆×C₃₁	—	4	2	no	—
377	C₂×C₈×C₃₁	—	4	2	no	—
378	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
380	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	1	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₂²⋊C₄×C₃₁	—	2	2	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	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	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	1	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	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	2	no	—
444	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
447	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
448	C₄²×C₃₁	C₂⁴	1	2	yes	—
449	#62618	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	2	no	—
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	8	2	no	—
455	C₂³×C₃₁	—	8	2	no	—
456	C₂³×C₃₁	—	8	2	no	—
457	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
458	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	Q₈×C₃₁	—	2	2	no	—
460	Q₈×C₃₁	—	2	1	no	—
461	Q₈×C₃₁	—	2	1	no	—
462	Q₈×C₃₁	—	2	2	no	—
463	Q₈×C₃₁	—	2	2	no	—
464	Q₈×C₃₁	—	4	2	no	—
465	Q₈×C₃₁	—	4	2	no	—
466	Q₈×C₃₁	—	8	2	no	—
467	Q₈×C₃₁	—	8	2	no	—
468	Q₈×C₃₁	—	8	1	no	—
469	D₄×C₃₁	—	2	2	no	—
470	D₄×C₃₁	—	2	1	no	—
471	D₄×C₃₁	—	2	1	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	1	no	—
476	D₄×C₃₁	—	2	2	no	—
477	D₄×C₃₁	—	2	1	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	4	2	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	8	1	no	—
482	D₄×C₃₁	—	8	1	no	—
483	D₄×C₃₁	—	8	2	no	—
484	D₄×C₃₁	—	8	2	no	—
485	D₄×C₃₁	—	8	1	no	—
486	D₄×C₃₁	—	8	2	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	—	8	2	no	—
489	D₄×C₃₁	—	8	2	no	—
490	D₄×C₃₁	—	8	1	no	—
491	D₄×C₃₁	—	8	1	no	—
492	D₄×C₃₁	—	8	2	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	1	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	2	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	4	1	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	2	no	—
512	C₂×C₄×C₃₁	—	8	2	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	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
525	C₈×C₃₁	—	2	1	no	—
526	C₈×C₃₁	—	2	2	no	—
527	C₈×C₃₁	—	2	1	no	—
528	C₈×C₃₁	—	2	1	no	—
529	C₈×C₃₁	—	2	1	no	—
530	C₈×C₃₁	—	2	2	no	—
531	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3546	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3358	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3333	C₂×C₃₁	1	2	yes	complemented
538	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3322	C₂×C₃₁	1	2	yes	complemented
541	#3314	C₂×C₃₁	1	2	yes	complemented
542	#3309	C₂×C₃₁	1	2	yes	complemented
543	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3243	C₂×C₃₁	1	2	yes	complemented
546	#3226	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3224	C₂×C₃₁	1	2	yes	complemented
548	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3175	C₂×C₃₁	1	2	yes	complemented
550	#3171	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3141	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3136	C₂×C₃₁	1	2	yes	complemented
553	#2969	C₂×C₃₁	1	1	yes	characteristic, complemented
554	C₂²×C₃₁	—	2	1	no	—
555	C₂²×C₃₁	—	2	2	no	—
556	C₂²×C₃₁	—	2	1	no	—
557	C₂²×C₃₁	—	2	2	no	—
558	C₂²×C₃₁	—	2	1	no	—
559	C₂²×C₃₁	—	2	2	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	1	no	—
562	C₂²×C₃₁	—	4	2	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	4	2	no	—
566	C₂²×C₃₁	—	4	1	no	—
567	C₂²×C₃₁	—	4	1	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	—	16	4	no	—
573	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
574	C₄×C₃₁	—	2	1	no	—
575	C₄×C₃₁	—	2	1	no	—
576	C₄×C₃₁	—	2	2	no	—
577	C₄×C₃₁	—	2	1	no	—
578	C₄×C₃₁	—	2	2	no	—
579	C₄×C₃₁	—	2	1	no	—
580	C₄×C₃₁	—	2	2	no	—
581	C₄×C₃₁	—	4	1	no	—
582	C₄×C₃₁	—	4	2	no	—
583	C₄×C₃₁	—	4	1	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	—	4	1	no	—
586	C₄×C₃₁	—	4	1	no	—
587	C₄×C₃₁	—	4	2	no	—
588	C₄×C₃₁	—	4	2	no	—
589	C₄×C₃₁	#576	1	2	yes	—
590	C₄×C₃₁	#585	1	1	yes	characteristic
591	C₄×C₃₁	#585	1	1	yes	characteristic
592	#563	—	2	2	no	—
593	#560	—	2	2	no	—
594	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
595	#556	C₂²×C₃₁	1	1	yes	characteristic
596	#556	C₂²×C₃₁	1	1	yes	characteristic
597	#554	C₂²×C₃₁	1	2	yes	complemented
598	#553	—	2	1	no	—
599	#553	C₂²×C₃₁	1	2	yes	complemented
600	#550	C₂²×C₃₁	1	2	yes	—
601	#550	C₂²×C₃₁	1	1	yes	characteristic
602	D₄×Q₈	—	2	1	no	—
603	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
604	#548	—	2	1	no	—
605	#547	C₂²×C₃₁	1	1	yes	characteristic
606	#547	C₂²×C₃₁	1	1	yes	characteristic
607	#546	—	2	1	no	—
608	#546	C₂²×C₃₁	1	2	yes	—
609	D₄²	C₂²×C₃₁	1	1	yes	characteristic
610	#544	C₂²×C₃₁	1	2	yes	complemented
611	#542	C₂²×C₃₁	1	2	yes	—
612	#542	C₂²×C₃₁	1	2	yes	complemented
613	#541	—	2	1	no	—
614	#539	—	2	2	no	—
615	#538	—	2	2	no	—
616	#537	—	2	1	no	—
617	#536	—	2	1	no	—
618	#535	—	2	1	no	—
619	#535	C₂²×C₃₁	1	2	yes	—
620	#532	C₂²×C₃₁	1	1	yes	characteristic
621	#532	C₂²×C₃₁	1	1	yes	characteristic
622	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#529	C₂²×C₃₁	1	1	yes	characteristic
624	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#501	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#500	C₂²×C₃₁	1	2	yes	complemented
627	#496	C₂²×C₃₁	1	1	yes	characteristic
628	#495	C₂²×C₃₁	1	2	yes	complemented
629	#490	C₂²×C₃₁	1	1	yes	characteristic
630	#490	C₂²×C₃₁	1	2	yes	complemented
631	#489	C₂²×C₃₁	1	2	yes	—
632	#489	C₂²×C₃₁	1	2	yes	complemented
633	#489	C₂²×C₃₁	1	2	yes	complemented
634	#489	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#488	C₂²×C₃₁	1	2	yes	—
636	#488	C₂²×C₃₁	1	2	yes	complemented
637	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	#486	C₂²×C₃₁	1	1	yes	characteristic
640	#486	C₂²×C₃₁	1	1	yes	characteristic
641	#486	C₂²×C₃₁	1	2	yes	—
642	#486	C₂²×C₃₁	1	2	yes	complemented
643	#485	C₂²×C₃₁	1	2	yes	complemented
644	#484	C₂²×C₃₁	1	2	yes	complemented
645	#482	C₂²×C₃₁	1	2	yes	—
646	#480	C₂²×C₃₁	1	2	yes	—
647	#480	C₂²×C₃₁	1	2	yes	—
648	#480	C₂²×C₃₁	1	2	yes	complemented
649	#479	C₂²×C₃₁	1	2	yes	complemented
650	#478	C₂²×C₃₁	1	2	yes	complemented
651	#477	C₂²×C₃₁	1	2	yes	complemented
652	#474	C₂²×C₃₁	1	1	yes	characteristic
653	#474	C₂²×C₃₁	1	1	yes	characteristic
654	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#474	C₂²×C₃₁	1	2	yes	complemented
657	#469	C₂²×C₃₁	1	1	yes	characteristic
658	#469	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#468	C₂²×C₃₁	1	2	yes	—
660	#468	C₂²×C₃₁	1	1	yes	characteristic
661	#468	C₂²×C₃₁	1	2	yes	complemented
662	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#467	C₂²×C₃₁	1	2	yes	complemented
664	#466	C₂²×C₃₁	1	2	yes	—
665	#464	C₂²×C₃₁	1	2	yes	—
666	#463	C₂²×C₃₁	1	2	yes	—
667	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#460	C₂²×C₃₁	1	1	yes	characteristic
670	#460	C₂²×C₃₁	1	2	yes	complemented
671	#459	C₂²×C₃₁	1	1	yes	characteristic
672	#459	C₂²×C₃₁	1	2	yes	complemented
673	#452	C₂²×C₃₁	1	2	yes	complemented
674	#452	C₂²×C₃₁	1	2	yes	complemented
675	#450	C₂²×C₃₁	1	2	yes	—
676	#449	C₂²×C₃₁	1	2	yes	complemented
677	#449	C₂²×C₃₁	1	2	yes	complemented
678	#447	C₂²×C₃₁	1	2	yes	—
679	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	#440	C₂²×C₃₁	1	2	yes	complemented
682	#440	C₂²×C₃₁	1	2	yes	complemented
683	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
684	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
687	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
689	#436	C₂²×C₃₁	1	1	yes	characteristic
690	#436	C₂²×C₃₁	1	2	yes	complemented
691	#435	C₂²×C₃₁	1	2	yes	complemented
692	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
693	#433	C₂²×C₃₁	1	2	yes	complemented
694	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	#418	C₂²×C₃₁	1	2	yes	—
696	#417	C₂²×C₃₁	1	2	yes	complemented
697	#417	C₂²×C₃₁	1	2	yes	complemented
698	#417	C₂²×C₃₁	1	2	yes	complemented
699	#416	C₂²×C₃₁	1	2	yes	complemented
700	C₂×#102	C₂²×C₃₁	1	2	yes	—
701	#405	C₂²×C₃₁	1	2	yes	complemented
702	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	C₂×C₃₁	—	4	1	no	—
704	C₂×C₃₁	—	4	2	no	—
705	C₂×C₃₁	—	8	1	no	—
706	C₂×C₃₁	—	8	1	no	—
707	C₂×C₃₁	—	8	2	no	—
708	C₂×C₃₁	—	8	1	no	—
709	C₂×C₃₁	#3500	1	1	yes	characteristic
710	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
711	C₂×C₃₁	#3586	1	1	yes	characteristic
712	C₂×#41	—	2	1	no	—
713	C₂×#41	—	2	1	no	—
714	C₂×#41	—	2	1	no	—
715	C₂×#41	C₂³×C₃₁	1	2	yes	—
716	C₂×#41	C₂³×C₃₁	1	2	yes	—
717	C₂²×Q₈	—	2	1	no	—
718	C₂²×Q₈	—	2	1	no	—
719	C₂²×D₄	—	2	1	no	—
720	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
721	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
726	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×D₈	C₂³×C₃₁	1	2	yes	—
728	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
730	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
732	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
733	C₄⋊Q₈	—	2	1	no	—
734	C₄⋊Q₈	—	2	2	no	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
743	#127	—	2	2	no	—
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	—	2	2	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	1	no	—
753	#126	D₄×C₃₁	1	2	yes	—
754	#125	—	2	2	no	—
755	#125	—	2	2	no	—
756	#125	—	2	2	no	—
757	#125	D₄×C₃₁	1	1	yes	characteristic
758	#125	C₂³×C₃₁	1	1	yes	characteristic
759	#125	C₂³×C₃₁	1	2	yes	—
760	#124	—	2	1	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	1	no	—
764	#124	D₄×C₃₁	1	1	yes	characteristic
765	#124	C₂³×C₃₁	1	1	yes	characteristic
766	#124	C₂³×C₃₁	1	2	yes	—
767	#124	C₂³×C₃₁	1	2	yes	—
768	#123	—	2	1	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	#123	D₄×C₃₁	1	2	yes	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
787	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
788	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
790	#121	—	2	1	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	D₄×C₃₁	1	1	yes	characteristic
804	#121	C₂³×C₃₁	1	1	yes	characteristic
805	#121	C₂³×C₃₁	1	1	yes	characteristic
806	#121	C₂³×C₃₁	1	1	yes	characteristic
807	#121	C₂³×C₃₁	1	2	yes	—
808	#121	C₂³×C₃₁	1	2	yes	—
809	#120	—	2	2	no	—
810	#120	—	2	2	no	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	—	2	1	no	—
815	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
817	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
818	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₃₁	1	2	yes	—
830	C₄×D₄	C₂³×C₃₁	1	2	yes	—
831	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₃₁	1	2	yes	—
833	#117	—	2	1	no	—
834	#117	—	2	1	no	—
835	#117	C₂³×C₃₁	1	2	yes	—
836	#117	C₂³×C₃₁	1	2	yes	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
840	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
841	C₂×C₂²⋊C₄	—	2	2	no	—
842	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
843	#107	C₂³×C₃₁	1	1	yes	characteristic
844	#107	C₂³×C₃₁	1	2	yes	—
845	#107	C₂³×C₃₁	1	1	yes	characteristic
846	#107	C₂³×C₃₁	1	2	yes	—
847	#107	C₂³×C₃₁	1	2	yes	—
848	#107	C₂³×C₃₁	1	2	yes	—
849	#106	C₂³×C₃₁	1	1	yes	characteristic
850	#106	C₂³×C₃₁	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
854	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
855	#103	C₂³×C₃₁	1	2	yes	—
856	#103	C₂³×C₃₁	1	2	yes	—
857	#103	C₂³×C₃₁	1	2	yes	—
858	#103	C₂³×C₃₁	1	2	yes	—
859	#103	C₂³×C₃₁	1	2	yes	—
860	#103	C₂³×C₃₁	1	2	yes	—
861	#103	C₂³×C₃₁	1	1	yes	characteristic
862	#103	C₂³×C₃₁	1	1	yes	characteristic
863	#102	C₂³×C₃₁	1	1	yes	characteristic
864	#102	C₂³×C₃₁	1	2	yes	—
865	#102	C₂³×C₃₁	1	2	yes	—
866	#102	C₂³×C₃₁	1	2	yes	—
867	#102	C₂³×C₃₁	1	1	yes	characteristic
868	#102	C₂³×C₃₁	1	2	yes	—
869	#102	C₂³×C₃₁	1	1	yes	characteristic
870	#102	C₂³×C₃₁	1	2	yes	—
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	2	yes	—
873	#102	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	1	yes	characteristic
878	#102	C₂³×C₃₁	1	1	yes	characteristic
879	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
882	#97	C₂³×C₃₁	1	1	yes	characteristic
883	#97	C₂³×C₃₁	1	1	yes	characteristic
884	#97	C₂³×C₃₁	1	2	yes	—
885	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
887	C₄×C₈	C₂³×C₃₁	1	2	yes	—
888	C₄×C₈	C₂³×C₃₁	1	2	yes	—
889	C₃₁	#62618	1	1	yes	characteristic, direct product factor, Sylow
890	C₂⁴	—	2	2	no	—
891	#41	—	4	2	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	#41	—	4	2	no	—
895	#41	—	8	2	no	—
896	#41	—	8	2	no	—
897	#41	—	8	2	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	1	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	8	2	no	—
904	C₂×Q₈	—	8	2	no	—
905	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
906	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
907	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	8	2	no	—
925	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
926	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
927	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
929	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
941	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
944	Q₁₆	—	4	2	no	—
945	SD₁₆	—	4	1	no	—
946	SD₁₆	—	4	1	no	—
947	SD₁₆	—	4	2	no	—
948	SD₁₆	—	4	2	no	—
949	D₈	—	4	2	no	—
950	D₈	—	4	1	no	—
951	D₈	—	4	1	no	—
952	M₁₆	—	4	1	no	—
953	M₁₆	—	4	1	no	—
954	M₁₆	—	4	2	no	—
955	C₂×C₈	—	4	2	no	—
956	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
958	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
960	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
984	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
985	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
986	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
990	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	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	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	2	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1023	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1025	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1026	C₄²	C₂⁴×C₃₁	1	2	yes	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	8	2	no	—
1032	C₂³	—	8	2	no	—
1033	C₂³	—	8	2	no	—
1034	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1035	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	2	no	—
1041	Q₈	—	4	2	no	—
1042	Q₈	—	4	2	no	—
1043	Q₈	—	8	2	no	—
1044	Q₈	—	8	2	no	—
1045	Q₈	—	8	1	no	—
1046	D₄	—	2	2	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	1	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	8	1	no	—
1059	D₄	—	8	1	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	1	no	—
1063	D₄	—	8	2	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	2	no	—
1066	D₄	—	8	2	no	—
1067	D₄	—	8	1	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	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	—	4	1	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	8	2	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1094	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1101	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1102	C₈	—	2	1	no	—
1103	C₈	—	2	2	no	—
1104	C₈	—	2	1	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	2	1	no	—
1107	C₈	—	2	2	no	—
1108	C₂²	—	2	1	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	2	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	16	4	no	—
1127	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1128	C₄	—	2	1	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	4	2	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	C₃₁×#576	1	2	yes	—
1144	C₄	C₃₁×#585	1	1	yes	characteristic
1145	C₄	C₃₁×#585	1	1	yes	characteristic
1146	C₂	—	4	2	no	—
1147	C₂	—	4	1	no	—
1148	C₂	—	8	1	no	—
1149	C₂	—	8	2	no	—
1150	C₂	—	8	1	no	—
1151	C₂	—	8	1	no	—
1152	C₂	C₃₁×#3500	1	1	yes	characteristic
1153	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1154	C₂	C₃₁×#3586	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×#3552	C₂	semidirect
2. C₃₁×#3546	C₂	semidirect
3. C₃₁×#3368	C₂	semidirect
4. C₃₁×#3367	C₂	semidirect
5. C₃₁×#3364	C₂	semidirect
6. C₃₁×#3358	C₂	semidirect
7. C₃₁×#3333	C₂	semidirect
8. C₃₁×#3330	C₂	semidirect
9. C₃₁×#3324	C₂	semidirect
10. C₃₁×#3322	C₂	semidirect
11. C₃₁×#3314	C₂	semidirect
12. C₃₁×#3309	C₂	semidirect
13. C₃₁×#3302	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3243	C₂	semidirect
16. C₃₁×#3226	C₂	semidirect
17. C₃₁×#3224	C₂	semidirect
18. C₃₁×#3212	C₂	semidirect
19. C₃₁×#3175	C₂	semidirect
20. C₃₁×#3171	C₂	semidirect
21. C₃₁×#3141	C₂	semidirect
22. C₃₁×#3136	C₂	semidirect
23. C₃₁×#2969	C₂	semidirect
26. C₃₁×#557	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
44. C₃₁×#542	C₂²	semidirect
54. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
56. C₃₁×#529	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
60. C₃₁×#495	C₂²	semidirect
62. C₃₁×#490	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
65. C₃₁×#489	C₂²	semidirect
66. C₃₁×#489	C₂²	semidirect
68. C₃₁×#488	C₂²	semidirect
69. C₃₁×#487	C₂²	semidirect
70. C₃₁×#487	C₂²	semidirect
74. C₃₁×#486	C₂²	semidirect
75. C₃₁×#485	C₂²	semidirect
76. C₃₁×#484	C₂²	semidirect
80. C₃₁×#480	C₂²	semidirect
81. C₃₁×#479	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
83. C₃₁×#477	C₂²	semidirect
86. C₃₁×#474	C₂²	semidirect
87. C₃₁×#474	C₂²	semidirect
88. C₃₁×#474	C₂²	semidirect
90. C₃₁×#469	C₂²	semidirect
93. C₃₁×#468	C₂²	semidirect
94. C₃₁×#468	C₂²	semidirect
95. C₃₁×#467	C₂²	semidirect
99. C₃₁×#462	C₂²	semidirect
100. C₃₁×#461	C₂²	semidirect
102. C₃₁×#460	C₂²	semidirect
104. C₃₁×#459	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
106. C₃₁×#452	C₂²	semidirect
108. C₃₁×#449	C₂²	semidirect
109. C₃₁×#449	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
113. C₃₁×#440	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₄×Q₁₆×C₃₁	C₂²	semidirect
117. C₄×SD₁₆×C₃₁	C₂²	semidirect
119. C₄×D₈×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
123. C₃₁×#435	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#431	C₂²	semidirect
128. C₃₁×#417	C₂²	semidirect
129. C₃₁×#417	C₂²	semidirect
130. C₃₁×#417	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₄×M₁₆×C₃₁	C₂²	semidirect
449. #62618	C₃₁	direct (N × H)
531. #3552	C₂×C₃₁	semidirect
532. #3546	C₂×C₃₁	semidirect
533. #3368	C₂×C₃₁	semidirect
534. #3367	C₂×C₃₁	semidirect
535. #3364	C₂×C₃₁	semidirect
536. #3358	C₂×C₃₁	semidirect
537. #3333	C₂×C₃₁	semidirect
538. #3330	C₂×C₃₁	semidirect
539. #3324	C₂×C₃₁	semidirect
540. #3322	C₂×C₃₁	semidirect
541. #3314	C₂×C₃₁	semidirect
542. #3309	C₂×C₃₁	semidirect
543. #3302	C₂×C₃₁	semidirect
544. #3294	C₂×C₃₁	semidirect
545. #3243	C₂×C₃₁	semidirect
546. #3226	C₂×C₃₁	semidirect
547. #3224	C₂×C₃₁	semidirect
548. #3212	C₂×C₃₁	semidirect
549. #3175	C₂×C₃₁	semidirect
550. #3171	C₂×C₃₁	semidirect
551. #3141	C₂×C₃₁	semidirect
552. #3136	C₂×C₃₁	semidirect
553. #2969	C₂×C₃₁	semidirect
594. #557	C₂²×C₃₁	semidirect
597. #554	C₂²×C₃₁	semidirect
599. #553	C₂²×C₃₁	semidirect
603. D₄×Q₈	C₂²×C₃₁	semidirect
610. #544	C₂²×C₃₁	semidirect
612. #542	C₂²×C₃₁	semidirect
622. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
624. #529	C₂²×C₃₁	semidirect
625. #501	C₂²×C₃₁	semidirect
626. #500	C₂²×C₃₁	semidirect
628. #495	C₂²×C₃₁	semidirect
630. #490	C₂²×C₃₁	semidirect
632. #489	C₂²×C₃₁	semidirect
633. #489	C₂²×C₃₁	semidirect
634. #489	C₂²×C₃₁	semidirect
636. #488	C₂²×C₃₁	semidirect
637. #487	C₂²×C₃₁	semidirect
638. #487	C₂²×C₃₁	semidirect
642. #486	C₂²×C₃₁	semidirect
643. #485	C₂²×C₃₁	semidirect
644. #484	C₂²×C₃₁	semidirect
648. #480	C₂²×C₃₁	semidirect
649. #479	C₂²×C₃₁	semidirect
650. #478	C₂²×C₃₁	semidirect
651. #477	C₂²×C₃₁	semidirect
654. #474	C₂²×C₃₁	semidirect
655. #474	C₂²×C₃₁	semidirect
656. #474	C₂²×C₃₁	semidirect
658. #469	C₂²×C₃₁	semidirect
661. #468	C₂²×C₃₁	semidirect
662. #468	C₂²×C₃₁	semidirect
663. #467	C₂²×C₃₁	semidirect
667. #462	C₂²×C₃₁	semidirect
668. #461	C₂²×C₃₁	semidirect
670. #460	C₂²×C₃₁	semidirect
672. #459	C₂²×C₃₁	semidirect
673. #452	C₂²×C₃₁	semidirect
674. #452	C₂²×C₃₁	semidirect
676. #449	C₂²×C₃₁	semidirect
677. #449	C₂²×C₃₁	semidirect
679. #446	C₂²×C₃₁	semidirect
680. C₈×Q₈	C₂²×C₃₁	semidirect
681. #440	C₂²×C₃₁	semidirect
682. #440	C₂²×C₃₁	semidirect
683. C₄×Q₁₆	C₂²×C₃₁	semidirect
685. C₄×SD₁₆	C₂²×C₃₁	semidirect
687. C₄×D₈	C₂²×C₃₁	semidirect
688. C₄×D₈	C₂²×C₃₁	semidirect
690. #436	C₂²×C₃₁	semidirect
691. #435	C₂²×C₃₁	semidirect
693. #433	C₂²×C₃₁	semidirect
694. #431	C₂²×C₃₁	semidirect
696. #417	C₂²×C₃₁	semidirect
697. #417	C₂²×C₃₁	semidirect
698. #417	C₂²×C₃₁	semidirect
699. #416	C₂²×C₃₁	semidirect
701. #405	C₂²×C₃₁	semidirect
702. C₄×M₁₆	C₂²×C₃₁	semidirect
889. C₃₁	#62618	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×#3552	2
C₃₁×#3546	2
C₃₁×#3368	2
C₃₁×#3367	2
C₃₁×#3364	2
C₃₁×#3358	2
C₃₁×#3333	2
C₃₁×#3330	2
C₃₁×#3324	2
C₃₁×#3322	2
C₃₁×#3314	2
C₃₁×#3309	2
C₃₁×#3302	2
C₃₁×#3294	2
C₃₁×#3243	2
C₃₁×#3226	2
C₃₁×#3224	2
C₃₁×#3212	2
C₃₁×#3175	2
C₃₁×#3171	2
C₃₁×#3141	2
C₃₁×#3136	2
C₃₁×#2969	2
#62618	31

Subgroups — C31×#62618 #21519377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62618 #21519377