Subgroups — C₃₁×#62561 #21519320

Order 7936.

1780 conjugacy classes of subgroups.

The subgroup lattice has 1172 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×#3546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3309	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3305	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3303	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×#3243	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3220	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3214	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3131	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#562	—	2	2	no	—
25	C₃₁×#560	—	2	2	no	—
26	C₃₁×#556	C₂²	1	1	yes	characteristic
27	C₃₁×#555	C₂²	1	1	yes	characteristic
28	C₃₁×#555	C₂²	1	2	yes	complemented
29	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#553	—	2	1	no	—
31	C₃₁×#553	C₂²	1	2	yes	complemented
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#550	C₂²	1	2	yes	—
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
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	—	2	2	no	—
44	C₃₁×#542	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×#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×#533	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#532	C₂²	1	1	yes	characteristic
54	C₃₁×#532	C₂²	1	1	yes	characteristic
55	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#529	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#496	C₂²	1	2	yes	complemented
60	C₃₁×#493	C₂²	1	1	yes	characteristic
61	C₃₁×#490	C₂²	1	2	yes	—
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×#488	C₂²	1	2	yes	—
66	C₃₁×#488	C₂²	1	2	yes	complemented
67	C₃₁×#488	C₂²	1	2	yes	complemented
68	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
70	C₃₁×#486	C₂²	1	1	yes	characteristic
71	C₃₁×#486	C₂²	1	1	yes	characteristic
72	C₃₁×#486	C₂²	1	1	yes	characteristic
73	C₃₁×#486	C₂²	1	2	yes	complemented
74	C₃₁×#486	C₂²	1	1	yes	characteristic, 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×#482	C₂²	1	2	yes	—
79	C₃₁×#482	C₂²	1	2	yes	complemented
80	C₃₁×#480	C₂²	1	2	yes	—
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×#476	C₂²	1	1	yes	characteristic
85	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#474	C₂²	1	1	yes	characteristic
87	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#474	C₂²	1	2	yes	complemented
89	C₃₁×#469	C₂²	1	2	yes	—
90	C₃₁×#468	C₂²	1	2	yes	complemented
91	C₃₁×#466	C₂²	1	1	yes	characteristic
92	C₃₁×#466	C₂²	1	1	yes	characteristic
93	C₃₁×#466	C₂²	1	2	yes	—
94	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
96	C₃₁×#465	C₂²	1	2	yes	complemented
97	C₃₁×#463	C₂²	1	2	yes	—
98	C₃₁×#463	C₂²	1	2	yes	—
99	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#459	C₂²	1	1	yes	characteristic
102	C₃₁×#459	C₂²	1	1	yes	characteristic
103	C₃₁×#459	C₂²	1	2	yes	complemented
104	C₃₁×#459	C₂²	1	2	yes	complemented
105	C₃₁×#449	C₂²	1	2	yes	complemented
106	C₃₁×#449	C₂²	1	2	yes	complemented
107	C₃₁×#449	C₂²	1	2	yes	complemented
108	C₃₁×#449	C₂²	1	2	yes	complemented
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	complemented
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
116	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#418	C₂²	1	2	yes	—
128	C₃₁×#417	C₂²	1	2	yes	complemented
129	C₃₁×#416	C₂²	1	2	yes	complemented
130	C₃₁×#416	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	C₂×C₄×C₈×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	—	2	1	no	—
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂²×Q₈×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	—	2	1	no	—
143	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×D₈×C₃₁	C₂³	1	2	yes	—
149	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×D₈×C₃₁	C₂³	1	2	yes	—
152	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	—	2	2	no	—
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
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×#127	—	2	2	no	—
164	C₃₁×#127	C₂³	1	1	yes	characteristic
165	C₃₁×#127	C₂³	1	2	yes	—
166	C₃₁×#127	C₂³	1	1	yes	characteristic
167	C₃₁×#127	C₂³	1	1	yes	characteristic
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	D₄	1	2	yes	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	D₄	1	1	yes	characteristic
174	C₃₁×#125	C₂³	1	2	yes	—
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	1	no	—
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	D₄	1	1	yes	characteristic
183	C₃₁×#124	C₂³	1	2	yes	—
184	C₃₁×#124	C₂³	1	2	yes	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	D₄	1	2	yes	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
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	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
205	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	—	2	1	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	—	2	2	no	—
224	C₃₁×#121	D₄	1	1	yes	characteristic
225	C₃₁×#121	C₂³	1	2	yes	—
226	C₃₁×#121	C₂³	1	2	yes	—
227	C₃₁×#121	C₂³	1	1	yes	characteristic
228	C₃₁×#121	C₂³	1	1	yes	characteristic
229	C₃₁×#121	C₂³	1	1	yes	characteristic
230	C₃₁×#121	C₂³	1	2	yes	—
231	C₃₁×#121	C₂³	1	1	yes	characteristic
232	C₃₁×#120	—	2	2	no	—
233	C₃₁×#120	—	2	2	no	—
234	C₃₁×#120	—	2	2	no	—
235	C₃₁×#120	—	2	2	no	—
236	C₄×Q₈×C₃₁	—	2	1	no	—
237	C₄×Q₈×C₃₁	—	2	1	no	—
238	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₃₁	C₂³	1	2	yes	—
255	C₃₁×#117	—	2	1	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₃₁×#117	C₂³	1	2	yes	—
260	C₃₁×#117	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
266	C₃₁×#107	C₂³	1	1	yes	characteristic
267	C₃₁×#107	C₂³	1	1	yes	characteristic
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×#107	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×#103	C₂³	1	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×#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	1	yes	characteristic
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×#97	C₂³	1	2	yes	—
306	C₃₁×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
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	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	#41×C₃₁	—	8	2	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	2	1	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×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	1	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	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	1	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	2	1	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	2	1	no	—
347	C₂×D₄×C₃₁	—	4	2	no	—
348	C₂×D₄×C₃₁	—	4	2	no	—
349	C₂×D₄×C₃₁	—	8	2	no	—
350	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	2	no	—
363	C₂²×C₄×C₃₁	—	2	2	no	—
364	C₂²×C₄×C₃₁	—	2	2	no	—
365	C₂²×C₄×C₃₁	—	2	2	no	—
366	C₂²×C₄×C₃₁	—	2	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	SD₁₆×C₃₁	—	4	2	no	—
372	SD₁₆×C₃₁	—	4	2	no	—
373	D₈×C₃₁	—	4	1	no	—
374	D₈×C₃₁	—	4	1	no	—
375	D₈×C₃₁	—	4	1	no	—
376	D₈×C₃₁	—	4	1	no	—
377	D₈×C₃₁	—	4	2	no	—
378	D₈×C₃₁	—	4	2	no	—
379	M₁₆×C₃₁	—	4	2	no	—
380	C₂×C₈×C₃₁	—	4	1	no	—
381	C₂×C₈×C₃₁	—	4	2	no	—
382	C₂×C₈×C₃₁	—	4	1	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	1	yes	characteristic
387	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
388	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
402	C₄⋊C₄×C₃₁	—	2	2	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	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	no	—
435	C₂²⋊C₄×C₃₁	—	2	1	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	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	#62561	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	—	2	1	no	—
455	C₂³×C₃₁	—	8	2	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	—	2	2	no	—
462	Q₈×C₃₁	—	2	2	no	—
463	Q₈×C₃₁	—	4	2	no	—
464	Q₈×C₃₁	—	8	1	no	—
465	Q₈×C₃₁	—	8	2	no	—
466	Q₈×C₃₁	—	8	1	no	—
467	Q₈×C₃₁	—	8	1	no	—
468	D₄×C₃₁	—	2	2	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	1	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	—	2	2	no	—
477	D₄×C₃₁	—	2	1	no	—
478	D₄×C₃₁	—	2	1	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	1	no	—
484	D₄×C₃₁	—	8	2	no	—
485	D₄×C₃₁	—	8	2	no	—
486	D₄×C₃₁	—	8	1	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	1	no	—
494	D₄×C₃₁	—	8	1	no	—
495	D₄×C₃₁	—	8	1	no	—
496	D₄×C₃₁	—	8	1	no	—
497	D₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	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	—	2	2	no	—
507	C₂×C₄×C₃₁	—	2	2	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	1	no	—
510	C₂×C₄×C₃₁	—	4	1	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	4	2	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	4	2	no	—
515	C₂×C₄×C₃₁	—	8	2	no	—
516	C₂×C₄×C₃₁	—	8	2	no	—
517	C₂×C₄×C₃₁	—	8	2	no	—
518	C₂×C₄×C₃₁	—	8	2	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
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	2	yes	—
524	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
530	C₈×C₃₁	—	2	1	no	—
531	C₈×C₃₁	—	2	1	no	—
532	C₈×C₃₁	—	2	1	no	—
533	C₈×C₃₁	—	2	1	no	—
534	C₈×C₃₁	—	2	2	no	—
535	C₈×C₃₁	—	2	2	no	—
536	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3546	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3360	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3358	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3325	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3319	C₂×C₃₁	1	2	yes	complemented
545	#3309	C₂×C₃₁	1	2	yes	complemented
546	#3305	C₂×C₃₁	1	2	yes	complemented
547	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3297	C₂×C₃₁	1	2	yes	complemented
549	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3243	C₂×C₃₁	1	2	yes	complemented
551	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3220	C₂×C₃₁	1	2	yes	complemented
553	#3214	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3179	C₂×C₃₁	1	2	yes	complemented
555	#3169	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3136	C₂×C₃₁	1	2	yes	complemented
557	#3131	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
559	C₂²×C₃₁	—	2	1	no	—
560	C₂²×C₃₁	—	2	2	no	—
561	C₂²×C₃₁	—	2	1	no	—
562	C₂²×C₃₁	—	2	2	no	—
563	C₂²×C₃₁	—	2	1	no	—
564	C₂²×C₃₁	—	2	2	no	—
565	C₂²×C₃₁	—	4	1	no	—
566	C₂²×C₃₁	—	4	1	no	—
567	C₂²×C₃₁	—	4	1	no	—
568	C₂²×C₃₁	—	4	2	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	1	no	—
578	C₂²×C₃₁	—	4	1	no	—
579	C₂²×C₃₁	—	4	2	no	—
580	C₂²×C₃₁	—	16	4	no	—
581	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
582	C₄×C₃₁	—	2	1	no	—
583	C₄×C₃₁	—	2	1	no	—
584	C₄×C₃₁	—	2	2	no	—
585	C₄×C₃₁	—	2	1	no	—
586	C₄×C₃₁	—	2	2	no	—
587	C₄×C₃₁	—	2	1	no	—
588	C₄×C₃₁	—	2	2	no	—
589	C₄×C₃₁	—	4	2	no	—
590	C₄×C₃₁	—	4	2	no	—
591	C₄×C₃₁	—	4	1	no	—
592	C₄×C₃₁	—	4	1	no	—
593	C₄×C₃₁	—	4	1	no	—
594	C₄×C₃₁	—	4	1	no	—
595	C₄×C₃₁	—	4	2	no	—
596	C₄×C₃₁	#576	1	2	yes	—
597	C₄×C₃₁	#585	1	1	yes	characteristic
598	C₄×C₃₁	#585	1	1	yes	characteristic
599	#562	—	2	2	no	—
600	#560	—	2	2	no	—
601	#556	C₂²×C₃₁	1	1	yes	characteristic
602	#555	C₂²×C₃₁	1	1	yes	characteristic
603	#555	C₂²×C₃₁	1	2	yes	complemented
604	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
605	#553	—	2	1	no	—
606	#553	C₂²×C₃₁	1	2	yes	complemented
607	#552	—	2	1	no	—
608	#550	C₂²×C₃₁	1	2	yes	—
609	#550	C₂²×C₃₁	1	1	yes	characteristic
610	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	#548	—	2	1	no	—
612	#547	C₂²×C₃₁	1	1	yes	characteristic
613	#547	C₂²×C₃₁	1	1	yes	characteristic
614	#546	—	2	1	no	—
615	#546	C₂²×C₃₁	1	2	yes	—
616	D₄²	C₂²×C₃₁	1	1	yes	characteristic
617	#544	C₂²×C₃₁	1	2	yes	complemented
618	#542	—	2	2	no	—
619	#542	C₂²×C₃₁	1	2	yes	—
620	#540	C₂²×C₃₁	1	2	yes	complemented
621	#538	—	2	2	no	—
622	#537	—	2	1	no	—
623	#537	—	2	1	no	—
624	#536	—	2	1	no	—
625	#535	—	2	1	no	—
626	#535	C₂²×C₃₁	1	2	yes	—
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	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
631	#529	C₂²×C₃₁	1	1	yes	characteristic
632	#501	C₂²×C₃₁	1	2	yes	complemented
633	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#496	C₂²×C₃₁	1	2	yes	complemented
635	#493	C₂²×C₃₁	1	1	yes	characteristic
636	#490	C₂²×C₃₁	1	2	yes	—
637	#490	C₂²×C₃₁	1	2	yes	complemented
638	#489	C₂²×C₃₁	1	2	yes	—
639	#489	C₂²×C₃₁	1	2	yes	complemented
640	#488	C₂²×C₃₁	1	2	yes	—
641	#488	C₂²×C₃₁	1	2	yes	complemented
642	#488	C₂²×C₃₁	1	2	yes	complemented
643	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#486	C₂²×C₃₁	1	1	yes	characteristic
646	#486	C₂²×C₃₁	1	1	yes	characteristic
647	#486	C₂²×C₃₁	1	1	yes	characteristic
648	#486	C₂²×C₃₁	1	2	yes	complemented
649	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#485	C₂²×C₃₁	1	2	yes	complemented
651	#484	C₂²×C₃₁	1	2	yes	complemented
652	#482	C₂²×C₃₁	1	2	yes	—
653	#482	C₂²×C₃₁	1	2	yes	—
654	#482	C₂²×C₃₁	1	2	yes	complemented
655	#480	C₂²×C₃₁	1	2	yes	—
656	#479	C₂²×C₃₁	1	2	yes	complemented
657	#478	C₂²×C₃₁	1	2	yes	complemented
658	#477	C₂²×C₃₁	1	2	yes	complemented
659	#476	C₂²×C₃₁	1	1	yes	characteristic
660	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	#474	C₂²×C₃₁	1	1	yes	characteristic
662	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#474	C₂²×C₃₁	1	2	yes	complemented
664	#469	C₂²×C₃₁	1	2	yes	—
665	#468	C₂²×C₃₁	1	2	yes	complemented
666	#466	C₂²×C₃₁	1	1	yes	characteristic
667	#466	C₂²×C₃₁	1	1	yes	characteristic
668	#466	C₂²×C₃₁	1	2	yes	—
669	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#465	C₂²×C₃₁	1	2	yes	complemented
672	#463	C₂²×C₃₁	1	2	yes	—
673	#463	C₂²×C₃₁	1	2	yes	—
674	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#459	C₂²×C₃₁	1	1	yes	characteristic
677	#459	C₂²×C₃₁	1	1	yes	characteristic
678	#459	C₂²×C₃₁	1	2	yes	complemented
679	#459	C₂²×C₃₁	1	2	yes	complemented
680	#449	C₂²×C₃₁	1	2	yes	complemented
681	#449	C₂²×C₃₁	1	2	yes	complemented
682	#449	C₂²×C₃₁	1	2	yes	complemented
683	#449	C₂²×C₃₁	1	2	yes	complemented
684	#447	C₂²×C₃₁	1	2	yes	—
685	#447	C₂²×C₃₁	1	2	yes	—
686	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#442	C₂²×C₃₁	1	2	yes	complemented
689	#440	C₂²×C₃₁	1	2	yes	complemented
690	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	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	1	yes	characteristic, complemented
694	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
696	#436	C₂²×C₃₁	1	1	yes	characteristic
697	#435	C₂²×C₃₁	1	2	yes	complemented
698	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
699	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
700	#433	C₂²×C₃₁	1	2	yes	complemented
701	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	#418	C₂²×C₃₁	1	2	yes	—
703	#417	C₂²×C₃₁	1	2	yes	complemented
704	#416	C₂²×C₃₁	1	2	yes	complemented
705	#416	C₂²×C₃₁	1	2	yes	complemented
706	#416	C₂²×C₃₁	1	2	yes	complemented
707	C₂×#102	C₂²×C₃₁	1	2	yes	—
708	#405	C₂²×C₃₁	1	2	yes	complemented
709	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
710	C₂×C₃₁	—	4	1	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	—	8	1	no	—
717	C₂×C₃₁	#3500	1	1	yes	characteristic
718	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
719	C₂×C₃₁	#3584	1	1	yes	characteristic
720	C₂×#41	—	2	1	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	C₂³×C₃₁	1	2	yes	—
725	C₂×#41	C₂³×C₃₁	1	2	yes	—
726	C₂²×Q₈	—	2	1	no	—
727	C₂²×D₄	—	2	1	no	—
728	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
735	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
736	C₂×D₈	C₂³×C₃₁	1	2	yes	—
737	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
738	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
740	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
741	C₄⋊Q₈	—	2	2	no	—
742	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×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	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
748	#127	—	2	2	no	—
749	#127	C₂³×C₃₁	1	1	yes	characteristic
750	#127	C₂³×C₃₁	1	1	yes	characteristic
751	#127	C₂³×C₃₁	1	1	yes	characteristic
752	#127	C₂³×C₃₁	1	2	yes	—
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	D₄×C₃₁	1	2	yes	—
757	#125	—	2	2	no	—
758	#125	D₄×C₃₁	1	1	yes	characteristic
759	#125	C₂³×C₃₁	1	2	yes	—
760	#125	C₂³×C₃₁	1	2	yes	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	1	no	—
766	#124	—	2	1	no	—
767	#124	D₄×C₃₁	1	1	yes	characteristic
768	#124	C₂³×C₃₁	1	2	yes	—
769	#124	C₂³×C₃₁	1	2	yes	—
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	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	D₄×C₃₁	1	2	yes	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
790	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	1	no	—
796	#121	—	2	1	no	—
797	#121	—	2	1	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	D₄×C₃₁	1	1	yes	characteristic
810	#121	C₂³×C₃₁	1	1	yes	characteristic
811	#121	C₂³×C₃₁	1	1	yes	characteristic
812	#121	C₂³×C₃₁	1	1	yes	characteristic
813	#121	C₂³×C₃₁	1	1	yes	characteristic
814	#121	C₂³×C₃₁	1	2	yes	—
815	#121	C₂³×C₃₁	1	2	yes	—
816	#121	C₂³×C₃₁	1	2	yes	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	C₄×Q₈	—	2	1	no	—
822	C₄×Q₈	—	2	1	no	—
823	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
824	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
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	1	yes	characteristic
835	C₄×D₄	C₂³×C₃₁	1	2	yes	—
836	C₄×D₄	C₂³×C₃₁	1	2	yes	—
837	C₄×D₄	C₂³×C₃₁	1	2	yes	—
838	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₃₁	1	2	yes	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	2	no	—
843	#117	C₂³×C₃₁	1	2	yes	—
844	#117	C₂³×C₃₁	1	2	yes	—
845	#117	C₂³×C₃₁	1	2	yes	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
851	#107	C₂³×C₃₁	1	1	yes	characteristic
852	#107	C₂³×C₃₁	1	1	yes	characteristic
853	#107	C₂³×C₃₁	1	1	yes	characteristic
854	#107	C₂³×C₃₁	1	1	yes	characteristic
855	#107	C₂³×C₃₁	1	2	yes	—
856	#107	C₂³×C₃₁	1	2	yes	—
857	#106	C₂³×C₃₁	1	2	yes	—
858	#106	C₂³×C₃₁	1	2	yes	—
859	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
862	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
863	#103	C₂³×C₃₁	1	2	yes	—
864	#103	C₂³×C₃₁	1	2	yes	—
865	#103	C₂³×C₃₁	1	2	yes	—
866	#103	C₂³×C₃₁	1	2	yes	—
867	#103	C₂³×C₃₁	1	2	yes	—
868	#103	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	1	yes	characteristic
874	#102	C₂³×C₃₁	1	2	yes	—
875	#102	C₂³×C₃₁	1	2	yes	—
876	#102	C₂³×C₃₁	1	2	yes	—
877	#102	C₂³×C₃₁	1	2	yes	—
878	#102	C₂³×C₃₁	1	1	yes	characteristic
879	#102	C₂³×C₃₁	1	2	yes	—
880	#102	C₂³×C₃₁	1	1	yes	characteristic
881	#102	C₂³×C₃₁	1	2	yes	—
882	#102	C₂³×C₃₁	1	2	yes	—
883	#102	C₂³×C₃₁	1	1	yes	characteristic
884	#102	C₂³×C₃₁	1	1	yes	characteristic
885	#102	C₂³×C₃₁	1	1	yes	characteristic
886	#102	C₂³×C₃₁	1	1	yes	characteristic
887	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
890	#97	C₂³×C₃₁	1	2	yes	—
891	#97	C₂³×C₃₁	1	2	yes	—
892	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₃₁	1	2	yes	—
897	C₃₁	#62561	1	1	yes	characteristic, direct product factor, Sylow
898	C₂⁴	—	2	2	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	4	2	no	—
903	#41	—	8	2	no	—
904	#41	—	8	2	no	—
905	#41	—	8	2	no	—
906	#41	—	8	2	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	2	1	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	2	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	8	2	no	—
913	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
915	C₂×D₄	—	2	2	no	—
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	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	4	2	no	—
934	C₂×D₄	—	4	2	no	—
935	C₂×D₄	—	8	2	no	—
936	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
937	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
938	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
940	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
942	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
954	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	2	no	—
959	D₈	—	4	1	no	—
960	D₈	—	4	1	no	—
961	D₈	—	4	1	no	—
962	D₈	—	4	1	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	M₁₆	—	4	2	no	—
966	C₂×C₈	—	4	1	no	—
967	C₂×C₈	—	4	2	no	—
968	C₂×C₈	—	4	1	no	—
969	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
974	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
991	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
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	2	yes	—
998	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	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	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	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	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1031	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₃₁	1	2	yes	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	8	2	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1044	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	8	1	no	—
1050	Q₈	—	8	2	no	—
1051	Q₈	—	8	1	no	—
1052	Q₈	—	8	1	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	2	1	no	—
1055	D₄	—	2	1	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	8	1	no	—
1067	D₄	—	8	1	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	1	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	1	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	1	no	—
1081	D₄	—	8	1	no	—
1082	D₄	—	8	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1114	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	2	no	—
1120	C₈	—	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	—	2	1	no	—
1126	C₂²	—	2	2	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	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	2	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	16	4	no	—
1143	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	4	2	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	2	no	—
1158	C₄	C₃₁×#576	1	2	yes	—
1159	C₄	C₃₁×#585	1	1	yes	characteristic
1160	C₄	C₃₁×#585	1	1	yes	characteristic
1161	C₂	—	4	2	no	—
1162	C₂	—	4	1	no	—
1163	C₂	—	8	1	no	—
1164	C₂	—	8	2	no	—
1165	C₂	—	8	1	no	—
1166	C₂	—	8	1	no	—
1167	C₂	—	8	1	no	—
1168	C₂	C₃₁×#3500	1	1	yes	characteristic
1169	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1170	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×#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×#3546	C₂	semidirect
3. C₃₁×#3367	C₂	semidirect
4. C₃₁×#3366	C₂	semidirect
5. C₃₁×#3360	C₂	semidirect
6. C₃₁×#3358	C₂	semidirect
7. C₃₁×#3330	C₂	semidirect
8. C₃₁×#3325	C₂	semidirect
9. C₃₁×#3319	C₂	semidirect
10. C₃₁×#3309	C₂	semidirect
11. C₃₁×#3305	C₂	semidirect
12. C₃₁×#3303	C₂	semidirect
13. C₃₁×#3297	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3243	C₂	semidirect
16. C₃₁×#3235	C₂	semidirect
17. C₃₁×#3220	C₂	semidirect
18. C₃₁×#3214	C₂	semidirect
19. C₃₁×#3179	C₂	semidirect
20. C₃₁×#3169	C₂	semidirect
21. C₃₁×#3136	C₂	semidirect
22. C₃₁×#3131	C₂	semidirect
23. C₃₁×#2966	C₂	semidirect
28. C₃₁×#555	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
45. C₃₁×#540	C₂²	semidirect
52. C₃₁×#533	C₂²	semidirect
55. C₃₁×#532	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
59. C₃₁×#496	C₂²	semidirect
62. C₃₁×#490	C₂²	semidirect
64. C₃₁×#489	C₂²	semidirect
66. C₃₁×#488	C₂²	semidirect
67. C₃₁×#488	C₂²	semidirect
68. C₃₁×#487	C₂²	semidirect
69. C₃₁×#487	C₂²	semidirect
73. C₃₁×#486	C₂²	semidirect
74. C₃₁×#486	C₂²	semidirect
75. C₃₁×#485	C₂²	semidirect
76. C₃₁×#484	C₂²	semidirect
79. C₃₁×#482	C₂²	semidirect
81. C₃₁×#479	C₂²	semidirect
82. C₃₁×#478	C₂²	semidirect
83. C₃₁×#477	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
87. C₃₁×#474	C₂²	semidirect
88. C₃₁×#474	C₂²	semidirect
90. C₃₁×#468	C₂²	semidirect
94. C₃₁×#466	C₂²	semidirect
95. C₃₁×#466	C₂²	semidirect
96. C₃₁×#465	C₂²	semidirect
99. C₃₁×#461	C₂²	semidirect
100. C₃₁×#461	C₂²	semidirect
103. C₃₁×#459	C₂²	semidirect
104. C₃₁×#459	C₂²	semidirect
105. C₃₁×#449	C₂²	semidirect
106. C₃₁×#449	C₂²	semidirect
107. C₃₁×#449	C₂²	semidirect
108. C₃₁×#449	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
113. C₃₁×#442	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
115. C₄×SD₁₆×C₃₁	C₂²	semidirect
118. C₄×D₈×C₃₁	C₂²	semidirect
119. C₄×D₈×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
128. C₃₁×#417	C₂²	semidirect
129. C₃₁×#416	C₂²	semidirect
130. C₃₁×#416	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
449. #62561	C₃₁	direct (N × H)
536. #3547	C₂×C₃₁	semidirect
537. #3546	C₂×C₃₁	semidirect
538. #3367	C₂×C₃₁	semidirect
539. #3366	C₂×C₃₁	semidirect
540. #3360	C₂×C₃₁	semidirect
541. #3358	C₂×C₃₁	semidirect
542. #3330	C₂×C₃₁	semidirect
543. #3325	C₂×C₃₁	semidirect
544. #3319	C₂×C₃₁	semidirect
545. #3309	C₂×C₃₁	semidirect
546. #3305	C₂×C₃₁	semidirect
547. #3303	C₂×C₃₁	semidirect
548. #3297	C₂×C₃₁	semidirect
549. #3294	C₂×C₃₁	semidirect
550. #3243	C₂×C₃₁	semidirect
551. #3235	C₂×C₃₁	semidirect
552. #3220	C₂×C₃₁	semidirect
553. #3214	C₂×C₃₁	semidirect
554. #3179	C₂×C₃₁	semidirect
555. #3169	C₂×C₃₁	semidirect
556. #3136	C₂×C₃₁	semidirect
557. #3131	C₂×C₃₁	semidirect
558. #2966	C₂×C₃₁	semidirect
603. #555	C₂²×C₃₁	semidirect
604. #554	C₂²×C₃₁	semidirect
606. #553	C₂²×C₃₁	semidirect
610. D₄×Q₈	C₂²×C₃₁	semidirect
617. #544	C₂²×C₃₁	semidirect
620. #540	C₂²×C₃₁	semidirect
627. #533	C₂²×C₃₁	semidirect
630. #532	C₂²×C₃₁	semidirect
632. #501	C₂²×C₃₁	semidirect
633. #500	C₂²×C₃₁	semidirect
634. #496	C₂²×C₃₁	semidirect
637. #490	C₂²×C₃₁	semidirect
639. #489	C₂²×C₃₁	semidirect
641. #488	C₂²×C₃₁	semidirect
642. #488	C₂²×C₃₁	semidirect
643. #487	C₂²×C₃₁	semidirect
644. #487	C₂²×C₃₁	semidirect
648. #486	C₂²×C₃₁	semidirect
649. #486	C₂²×C₃₁	semidirect
650. #485	C₂²×C₃₁	semidirect
651. #484	C₂²×C₃₁	semidirect
654. #482	C₂²×C₃₁	semidirect
656. #479	C₂²×C₃₁	semidirect
657. #478	C₂²×C₃₁	semidirect
658. #477	C₂²×C₃₁	semidirect
660. #476	C₂²×C₃₁	semidirect
662. #474	C₂²×C₃₁	semidirect
663. #474	C₂²×C₃₁	semidirect
665. #468	C₂²×C₃₁	semidirect
669. #466	C₂²×C₃₁	semidirect
670. #466	C₂²×C₃₁	semidirect
671. #465	C₂²×C₃₁	semidirect
674. #461	C₂²×C₃₁	semidirect
675. #461	C₂²×C₃₁	semidirect
678. #459	C₂²×C₃₁	semidirect
679. #459	C₂²×C₃₁	semidirect
680. #449	C₂²×C₃₁	semidirect
681. #449	C₂²×C₃₁	semidirect
682. #449	C₂²×C₃₁	semidirect
683. #449	C₂²×C₃₁	semidirect
686. #446	C₂²×C₃₁	semidirect
687. C₈×Q₈	C₂²×C₃₁	semidirect
688. #442	C₂²×C₃₁	semidirect
689. #440	C₂²×C₃₁	semidirect
690. C₄×SD₁₆	C₂²×C₃₁	semidirect
693. C₄×D₈	C₂²×C₃₁	semidirect
694. C₄×D₈	C₂²×C₃₁	semidirect
695. C₄×D₈	C₂²×C₃₁	semidirect
697. #435	C₂²×C₃₁	semidirect
699. C₈×D₄	C₂²×C₃₁	semidirect
700. #433	C₂²×C₃₁	semidirect
701. #432	C₂²×C₃₁	semidirect
703. #417	C₂²×C₃₁	semidirect
704. #416	C₂²×C₃₁	semidirect
705. #416	C₂²×C₃₁	semidirect
706. #416	C₂²×C₃₁	semidirect
708. #405	C₂²×C₃₁	semidirect
709. C₂×C₄×C₈	C₂²×C₃₁	semidirect
897. C₃₁	#62561	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×#3546	2
C₃₁×#3367	2
C₃₁×#3366	2
C₃₁×#3360	2
C₃₁×#3358	2
C₃₁×#3330	2
C₃₁×#3325	2
C₃₁×#3319	2
C₃₁×#3309	2
C₃₁×#3305	2
C₃₁×#3303	2
C₃₁×#3297	2
C₃₁×#3294	2
C₃₁×#3243	2
C₃₁×#3235	2
C₃₁×#3220	2
C₃₁×#3214	2
C₃₁×#3179	2
C₃₁×#3169	2
C₃₁×#3136	2
C₃₁×#3131	2
C₃₁×#2966	2
#62561	31

Subgroups — C31×#62561 #21519320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62561 #21519320