Subgroups — C₃₁×#61921 #21518680

Order 7936.

1760 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3397	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3368	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3224	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3222	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
21	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#559	C₂²	1	1	yes	characteristic
26	C₃₁×#559	C₂²	1	2	yes	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic
28	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#557	C₂²	1	2	yes	complemented
31	C₃₁×#556	—	2	1	no	—
32	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#556	C₂²	1	2	yes	complemented
34	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#552	—	2	1	no	—
36	C₃₁×#550	C₂²	1	1	yes	characteristic
37	C₃₁×#550	C₂²	1	1	yes	characteristic
38	C₃₁×#550	C₂²	1	2	yes	—
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	—	2	2	no	—
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#542	C₂²	1	2	yes	—
44	C₃₁×#541	—	2	1	no	—
45	C₃₁×#541	—	2	2	no	—
46	C₃₁×#541	C₂²	1	2	yes	—
47	C₃₁×#540	—	2	2	no	—
48	C₃₁×#535	C₂²	1	2	yes	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#532	—	2	1	no	—
52	C₃₁×#532	—	2	1	no	—
53	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
54	C₃₁×#529	C₂²	1	1	yes	characteristic
55	C₃₁×#518	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#497	C₂²	1	2	yes	complemented
58	C₃₁×#496	C₂²	1	2	yes	—
59	C₃₁×#496	C₂²	1	2	yes	complemented
60	C₃₁×#495	C₂²	1	2	yes	complemented
61	C₃₁×#492	C₂²	1	1	yes	characteristic
62	C₃₁×#492	C₂²	1	1	yes	characteristic
63	C₃₁×#492	C₂²	1	2	yes	complemented
64	C₃₁×#490	C₂²	1	2	yes	—
65	C₃₁×#490	C₂²	1	2	yes	complemented
66	C₃₁×#489	C₂²	1	2	yes	complemented
67	C₃₁×#488	C₂²	1	2	yes	complemented
68	C₃₁×#486	C₂²	1	1	yes	characteristic
69	C₃₁×#486	C₂²	1	1	yes	characteristic
70	C₃₁×#486	C₂²	1	2	yes	complemented
71	C₃₁×#485	C₂²	1	1	yes	characteristic
72	C₃₁×#485	C₂²	1	2	yes	—
73	C₃₁×#482	C₂²	1	1	yes	characteristic
74	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#478	C₂²	1	2	yes	complemented
78	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#476	C₂²	1	2	yes	complemented
81	C₃₁×#474	C₂²	1	2	yes	complemented
82	C₃₁×#464	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#464	C₂²	1	2	yes	complemented
84	C₃₁×#464	C₂²	1	2	yes	complemented
85	C₃₁×#464	C₂²	1	2	yes	complemented
86	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#463	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#461	C₂²	1	2	yes	complemented
93	C₃₁×#461	C₂²	1	2	yes	complemented
94	C₃₁×#460	C₂²	1	1	yes	characteristic
95	C₃₁×#460	C₂²	1	2	yes	—
96	C₃₁×#460	C₂²	1	2	yes	—
97	C₃₁×#460	C₂²	1	1	yes	characteristic
98	C₃₁×#460	C₂²	1	2	yes	complemented
99	C₃₁×#460	C₂²	1	2	yes	complemented
100	C₃₁×#460	C₂²	1	2	yes	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×#452	C₂²	1	1	yes	characteristic
105	C₃₁×#452	C₂²	1	2	yes	—
106	C₃₁×#450	C₂²	1	2	yes	—
107	C₃₁×#450	C₂²	1	2	yes	—
108	C₃₁×#450	C₂²	1	2	yes	—
109	C₃₁×#449	C₂²	1	1	yes	characteristic
110	C₃₁×#447	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#446	C₂²	1	2	yes	complemented
113	C₃₁×#446	C₂²	1	2	yes	complemented
114	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#442	C₂²	1	2	yes	complemented
118	C₃₁×#441	C₂²	1	2	yes	complemented
119	C₃₁×#440	C₂²	1	2	yes	complemented
120	C₃₁×#440	C₂²	1	2	yes	complemented
121	C₃₁×#440	C₂²	1	2	yes	complemented
122	C₃₁×#440	C₂²	1	2	yes	complemented
123	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
126	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
127	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
128	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
129	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
130	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
131	C₃₁×#433	C₂²	1	2	yes	—
132	C₃₁×#433	C₂²	1	2	yes	—
133	C₃₁×#432	C₂²	1	1	yes	characteristic
134	C₃₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	2	no	—
138	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×D₈×C₃₁	C₂³	1	2	yes	—
154	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	—	2	2	no	—
157	C₃₁×C₄⋊Q₈	—	2	2	no	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×#127	—	2	1	no	—
166	C₃₁×#127	—	2	1	no	—
167	C₃₁×#127	C₂³	1	1	yes	characteristic
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#127	C₂³	1	2	yes	—
170	C₃₁×#127	C₂³	1	2	yes	—
171	C₃₁×#127	C₂³	1	2	yes	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#126	—	2	1	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	2	no	—
182	C₃₁×#125	—	2	2	no	—
183	C₃₁×#125	—	2	2	no	—
184	C₃₁×#125	—	2	1	no	—
185	C₃₁×#125	—	2	1	no	—
186	C₃₁×#125	D₄	1	2	yes	—
187	C₃₁×#125	C₂³	1	2	yes	—
188	C₃₁×#125	C₂³	1	1	yes	characteristic
189	C₃₁×#124	—	2	1	no	—
190	C₃₁×#124	—	2	1	no	—
191	C₃₁×#124	—	2	2	no	—
192	C₃₁×#124	—	2	2	no	—
193	C₃₁×#124	C₂³	1	2	yes	—
194	C₃₁×#124	C₂³	1	2	yes	—
195	C₃₁×#124	C₂³	1	1	yes	characteristic
196	C₃₁×#124	C₂³	1	2	yes	—
197	C₃₁×#123	—	2	1	no	—
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×#123	—	2	2	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	1	no	—
204	C₃₁×C₂²⋊Q₈	—	2	1	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	1	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	D₄	1	1	yes	characteristic
211	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
212	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	1	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	C₂³	1	1	yes	characteristic
224	C₃₁×#120	—	2	2	no	—
225	C₃₁×#120	—	2	2	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	—	2	1	no	—
228	C₄×Q₈×C₃₁	—	2	2	no	—
229	C₄×Q₈×C₃₁	—	2	1	no	—
230	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	2	no	—
244	C₄×D₄×C₃₁	—	2	2	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	—	2	2	no	—
248	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	2	yes	—
255	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	—	2	1	no	—
259	C₃₁×#117	—	2	1	no	—
260	C₃₁×#117	—	2	1	no	—
261	C₃₁×#117	C₂³	1	1	yes	characteristic
262	C₃₁×#117	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	—	2	1	no	—
267	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
268	C₃₁×#107	C₂³	1	2	yes	—
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	1	yes	characteristic
272	C₃₁×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
277	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×#103	C₂³	1	1	yes	characteristic
283	C₃₁×#103	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×#97	C₂³	1	2	yes	—
306	C₃₁×#97	C₂³	1	2	yes	—
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	1	no	—
314	#41×C₃₁	—	4	1	no	—
315	#41×C₃₁	—	8	2	no	—
316	#41×C₃₁	—	8	2	no	—
317	#41×C₃₁	—	8	4	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
323	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
326	C₂×D₄×C₃₁	—	2	1	no	—
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	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	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	—	4	2	no	—
340	C₂×D₄×C₃₁	—	4	2	no	—
341	C₂×D₄×C₃₁	—	8	2	no	—
342	C₂×D₄×C₃₁	—	8	2	no	—
343	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
344	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
345	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
359	Q₁₆×C₃₁	—	4	2	no	—
360	Q₁₆×C₃₁	—	4	1	no	—
361	SD₁₆×C₃₁	—	4	2	no	—
362	SD₁₆×C₃₁	—	4	2	no	—
363	SD₁₆×C₃₁	—	4	2	no	—
364	SD₁₆×C₃₁	—	4	2	no	—
365	SD₁₆×C₃₁	—	4	1	no	—
366	SD₁₆×C₃₁	—	4	2	no	—
367	SD₁₆×C₃₁	—	4	1	no	—
368	SD₁₆×C₃₁	—	4	2	no	—
369	SD₁₆×C₃₁	—	4	2	no	—
370	D₈×C₃₁	—	4	1	no	—
371	D₈×C₃₁	—	4	2	no	—
372	D₈×C₃₁	—	4	2	no	—
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
377	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	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	1	yes	characteristic
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	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	2	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	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	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₄²×C₃₁	—	2	1	no	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
445	C₄²×C₃₁	C₂⁴	1	2	yes	—
446	C₄²×C₃₁	C₂⁴	1	2	yes	—
447	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
448	#61921	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
449	C₂³×C₃₁	—	2	1	no	—
450	C₂³×C₃₁	—	2	2	no	—
451	C₂³×C₃₁	—	2	2	no	—
452	C₂³×C₃₁	—	2	1	no	—
453	C₂³×C₃₁	—	4	4	no	—
454	C₂³×C₃₁	—	8	2	no	—
455	C₂³×C₃₁	—	8	2	no	—
456	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
457	Q₈×C₃₁	—	2	2	no	—
458	Q₈×C₃₁	—	2	2	no	—
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	1	no	—
464	Q₈×C₃₁	—	2	1	no	—
465	Q₈×C₃₁	—	4	2	no	—
466	Q₈×C₃₁	—	8	1	no	—
467	Q₈×C₃₁	—	8	2	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	2	no	—
471	D₄×C₃₁	—	2	2	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	2	2	no	—
475	D₄×C₃₁	—	2	1	no	—
476	D₄×C₃₁	—	4	4	no	—
477	D₄×C₃₁	—	4	4	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	2	no	—
486	D₄×C₃₁	—	8	2	no	—
487	D₄×C₃₁	—	8	2	no	—
488	D₄×C₃₁	—	8	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	2	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	1	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	2	no	—
500	C₂×C₄×C₃₁	—	4	1	no	—
501	C₂×C₄×C₃₁	—	4	2	no	—
502	C₂×C₄×C₃₁	—	4	2	no	—
503	C₂×C₄×C₃₁	—	4	2	no	—
504	C₂×C₄×C₃₁	—	4	2	no	—
505	C₂×C₄×C₃₁	—	8	2	no	—
506	C₂×C₄×C₃₁	—	8	2	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	2	no	—
509	C₂×C₄×C₃₁	—	8	2	no	—
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
520	C₈×C₃₁	—	2	2	no	—
521	C₈×C₃₁	—	2	1	no	—
522	C₈×C₃₁	—	2	2	no	—
523	C₈×C₃₁	—	2	1	no	—
524	C₈×C₃₁	—	2	1	no	—
525	C₈×C₃₁	—	2	1	no	—
526	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3401	C₂×C₃₁	1	2	yes	complemented
529	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3397	C₂×C₃₁	1	2	yes	complemented
532	#3394	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3392	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3375	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3371	C₂×C₃₁	1	2	yes	complemented
536	#3368	C₂×C₃₁	1	2	yes	complemented
537	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3362	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3224	C₂×C₃₁	1	2	yes	complemented
541	#3222	C₂×C₃₁	1	2	yes	complemented
542	#3217	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3208	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3123	C₂×C₃₁	1	2	yes	complemented
545	#3118	C₂×C₃₁	1	2	yes	complemented
546	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#2985	C₂×C₃₁	1	1	yes	characteristic, complemented
549	C₂²×C₃₁	—	2	1	no	—
550	C₂²×C₃₁	—	2	1	no	—
551	C₂²×C₃₁	—	2	1	no	—
552	C₂²×C₃₁	—	4	1	no	—
553	C₂²×C₃₁	—	4	1	no	—
554	C₂²×C₃₁	—	4	2	no	—
555	C₂²×C₃₁	—	4	2	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	—	4	2	no	—
558	C₂²×C₃₁	—	4	2	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	1	no	—
562	C₂²×C₃₁	—	4	2	no	—
563	C₂²×C₃₁	—	4	2	no	—
564	C₂²×C₃₁	—	16	4	no	—
565	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
566	C₄×C₃₁	—	2	1	no	—
567	C₄×C₃₁	—	2	1	no	—
568	C₄×C₃₁	—	2	2	no	—
569	C₄×C₃₁	—	2	2	no	—
570	C₄×C₃₁	—	2	1	no	—
571	C₄×C₃₁	—	2	1	no	—
572	C₄×C₃₁	—	2	2	no	—
573	C₄×C₃₁	—	2	2	no	—
574	C₄×C₃₁	—	4	1	no	—
575	C₄×C₃₁	—	4	2	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	1	no	—
578	C₄×C₃₁	—	4	2	no	—
579	C₄×C₃₁	—	4	1	no	—
580	C₄×C₃₁	—	4	1	no	—
581	C₄×C₃₁	—	4	1	no	—
582	C₄×C₃₁	#577	1	2	yes	—
583	C₄×C₃₁	#585	1	1	yes	characteristic
584	C₄×C₃₁	#585	1	1	yes	characteristic
585	#563	—	2	2	no	—
586	#559	C₂²×C₃₁	1	1	yes	characteristic
587	#559	C₂²×C₃₁	1	2	yes	—
588	#559	C₂²×C₃₁	1	1	yes	characteristic
589	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
590	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
591	#557	C₂²×C₃₁	1	2	yes	complemented
592	#556	—	2	1	no	—
593	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
594	#556	C₂²×C₃₁	1	2	yes	complemented
595	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
596	#552	—	2	1	no	—
597	#550	C₂²×C₃₁	1	1	yes	characteristic
598	#550	C₂²×C₃₁	1	1	yes	characteristic
599	#550	C₂²×C₃₁	1	2	yes	—
600	#546	—	2	1	no	—
601	#546	—	2	1	no	—
602	#546	—	2	2	no	—
603	#544	—	2	1	no	—
604	#542	C₂²×C₃₁	1	2	yes	—
605	#541	—	2	1	no	—
606	#541	—	2	2	no	—
607	#541	C₂²×C₃₁	1	2	yes	—
608	#540	—	2	2	no	—
609	#535	C₂²×C₃₁	1	2	yes	—
610	#533	C₂²×C₃₁	1	1	yes	characteristic
611	#533	C₂²×C₃₁	1	1	yes	characteristic
612	#532	—	2	1	no	—
613	#532	—	2	1	no	—
614	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
615	#529	C₂²×C₃₁	1	1	yes	characteristic
616	#518	C₂²×C₃₁	1	2	yes	—
617	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
618	#497	C₂²×C₃₁	1	2	yes	complemented
619	#496	C₂²×C₃₁	1	2	yes	—
620	#496	C₂²×C₃₁	1	2	yes	complemented
621	#495	C₂²×C₃₁	1	2	yes	complemented
622	#492	C₂²×C₃₁	1	1	yes	characteristic
623	#492	C₂²×C₃₁	1	1	yes	characteristic
624	#492	C₂²×C₃₁	1	2	yes	complemented
625	#490	C₂²×C₃₁	1	2	yes	—
626	#490	C₂²×C₃₁	1	2	yes	complemented
627	#489	C₂²×C₃₁	1	2	yes	complemented
628	#488	C₂²×C₃₁	1	2	yes	complemented
629	#486	C₂²×C₃₁	1	1	yes	characteristic
630	#486	C₂²×C₃₁	1	1	yes	characteristic
631	#486	C₂²×C₃₁	1	2	yes	complemented
632	#485	C₂²×C₃₁	1	1	yes	characteristic
633	#485	C₂²×C₃₁	1	2	yes	—
634	#482	C₂²×C₃₁	1	1	yes	characteristic
635	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	#478	C₂²×C₃₁	1	2	yes	complemented
638	#478	C₂²×C₃₁	1	2	yes	complemented
639	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#476	C₂²×C₃₁	1	2	yes	complemented
642	#474	C₂²×C₃₁	1	2	yes	complemented
643	#464	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#464	C₂²×C₃₁	1	2	yes	complemented
645	#464	C₂²×C₃₁	1	2	yes	complemented
646	#464	C₂²×C₃₁	1	2	yes	complemented
647	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#463	C₂²×C₃₁	1	2	yes	complemented
649	#463	C₂²×C₃₁	1	2	yes	complemented
650	#463	C₂²×C₃₁	1	2	yes	complemented
651	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#461	C₂²×C₃₁	1	2	yes	complemented
654	#461	C₂²×C₃₁	1	2	yes	complemented
655	#460	C₂²×C₃₁	1	1	yes	characteristic
656	#460	C₂²×C₃₁	1	2	yes	—
657	#460	C₂²×C₃₁	1	2	yes	—
658	#460	C₂²×C₃₁	1	1	yes	characteristic
659	#460	C₂²×C₃₁	1	2	yes	complemented
660	#460	C₂²×C₃₁	1	2	yes	complemented
661	#460	C₂²×C₃₁	1	2	yes	complemented
662	#459	C₂²×C₃₁	1	1	yes	characteristic
663	#459	C₂²×C₃₁	1	1	yes	characteristic
664	#459	C₂²×C₃₁	1	2	yes	complemented
665	#452	C₂²×C₃₁	1	1	yes	characteristic
666	#452	C₂²×C₃₁	1	2	yes	—
667	#450	C₂²×C₃₁	1	2	yes	—
668	#450	C₂²×C₃₁	1	2	yes	—
669	#450	C₂²×C₃₁	1	2	yes	—
670	#449	C₂²×C₃₁	1	1	yes	characteristic
671	#447	C₂²×C₃₁	1	2	yes	—
672	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#446	C₂²×C₃₁	1	2	yes	complemented
674	#446	C₂²×C₃₁	1	2	yes	complemented
675	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#442	C₂²×C₃₁	1	2	yes	complemented
679	#441	C₂²×C₃₁	1	2	yes	complemented
680	#440	C₂²×C₃₁	1	2	yes	complemented
681	#440	C₂²×C₃₁	1	2	yes	complemented
682	#440	C₂²×C₃₁	1	2	yes	complemented
683	#440	C₂²×C₃₁	1	2	yes	complemented
684	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
688	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
689	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
690	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
692	#433	C₂²×C₃₁	1	2	yes	—
693	#433	C₂²×C₃₁	1	2	yes	—
694	#432	C₂²×C₃₁	1	1	yes	characteristic
695	#431	C₂²×C₃₁	1	1	yes	characteristic
696	C₂×C₃₁	—	4	1	no	—
697	C₂×C₃₁	—	8	1	no	—
698	C₂×C₃₁	—	8	1	no	—
699	C₂×C₃₁	—	8	2	no	—
700	C₂×C₃₁	—	8	2	no	—
701	C₂×C₃₁	#3487	1	1	yes	characteristic
702	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
703	C₂×C₃₁	#3585	1	1	yes	characteristic
704	C₂×#41	—	2	1	no	—
705	C₂×#41	—	2	1	no	—
706	C₂×#41	—	2	2	no	—
707	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
708	C₂²×D₄	—	2	1	no	—
709	C₂²×D₄	—	2	1	no	—
710	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
712	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
718	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
722	C₂×D₈	C₂³×C₃₁	1	2	yes	—
723	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₃₁	1	2	yes	—
725	C₄⋊Q₈	—	2	2	no	—
726	C₄⋊Q₈	—	2	2	no	—
727	C₄⋊Q₈	—	2	1	no	—
728	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
729	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
730	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
731	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
732	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
733	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
734	#127	—	2	1	no	—
735	#127	—	2	1	no	—
736	#127	C₂³×C₃₁	1	1	yes	characteristic
737	#127	C₂³×C₃₁	1	1	yes	characteristic
738	#127	C₂³×C₃₁	1	2	yes	—
739	#127	C₂³×C₃₁	1	2	yes	—
740	#127	C₂³×C₃₁	1	2	yes	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	1	no	—
748	#125	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	2	no	—
752	#125	—	2	2	no	—
753	#125	—	2	1	no	—
754	#125	—	2	1	no	—
755	#125	D₄×C₃₁	1	2	yes	—
756	#125	C₂³×C₃₁	1	1	yes	characteristic
757	#125	C₂³×C₃₁	1	2	yes	—
758	#124	—	2	1	no	—
759	#124	—	2	1	no	—
760	#124	—	2	2	no	—
761	#124	—	2	2	no	—
762	#124	C₂³×C₃₁	1	1	yes	characteristic
763	#124	C₂³×C₃₁	1	2	yes	—
764	#124	C₂³×C₃₁	1	2	yes	—
765	#124	C₂³×C₃₁	1	2	yes	—
766	#123	—	2	1	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
779	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
780	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
781	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
782	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	C₂³×C₃₁	1	1	yes	characteristic
793	#120	—	2	2	no	—
794	#120	—	2	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	2	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
803	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
804	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
805	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
806	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
808	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₃₁	1	2	yes	—
820	C₄×D₄	C₂³×C₃₁	1	2	yes	—
821	C₄×D₄	C₂³×C₃₁	1	2	yes	—
822	C₄×D₄	C₂³×C₃₁	1	2	yes	—
823	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₃₁	1	2	yes	—
825	#117	—	2	1	no	—
826	#117	—	2	2	no	—
827	#117	—	2	1	no	—
828	#117	—	2	1	no	—
829	#117	—	2	1	no	—
830	#117	C₂³×C₃₁	1	1	yes	characteristic
831	#117	C₂³×C₃₁	1	2	yes	—
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₂²⋊C₄	—	2	2	no	—
834	C₂×C₂²⋊C₄	—	2	2	no	—
835	C₂×C₄²	—	2	1	no	—
836	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
837	#107	C₂³×C₃₁	1	2	yes	—
838	#107	C₂³×C₃₁	1	1	yes	characteristic
839	#107	C₂³×C₃₁	1	1	yes	characteristic
840	#106	C₂³×C₃₁	1	1	yes	characteristic
841	#106	C₂³×C₃₁	1	1	yes	characteristic
842	#106	C₂³×C₃₁	1	2	yes	—
843	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
848	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
849	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
850	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
851	#103	C₂³×C₃₁	1	1	yes	characteristic
852	#103	C₂³×C₃₁	1	2	yes	—
853	#103	C₂³×C₃₁	1	2	yes	—
854	#103	C₂³×C₃₁	1	1	yes	characteristic
855	#103	C₂³×C₃₁	1	1	yes	characteristic
856	#103	C₂³×C₃₁	1	1	yes	characteristic
857	#103	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	1	yes	characteristic
859	#102	C₂³×C₃₁	1	1	yes	characteristic
860	#102	C₂³×C₃₁	1	2	yes	—
861	#102	C₂³×C₃₁	1	1	yes	characteristic
862	#102	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
868	#102	C₂³×C₃₁	1	2	yes	—
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
874	#97	C₂³×C₃₁	1	2	yes	—
875	#97	C₂³×C₃₁	1	2	yes	—
876	#97	C₂³×C₃₁	1	2	yes	—
877	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
879	C₄×C₈	C₂³×C₃₁	1	2	yes	—
880	C₄×C₈	C₂³×C₃₁	1	2	yes	—
881	C₃₁	#61921	1	1	yes	characteristic, direct product factor, Sylow
882	C₂⁴	—	2	2	no	—
883	#41	—	4	1	no	—
884	#41	—	4	1	no	—
885	#41	—	8	2	no	—
886	#41	—	8	2	no	—
887	#41	—	8	4	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
891	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
892	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
893	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	—	4	2	no	—
911	C₂×D₄	—	8	2	no	—
912	C₂×D₄	—	8	2	no	—
913	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
914	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
915	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
927	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
928	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
929	Q₁₆	—	4	2	no	—
930	Q₁₆	—	4	1	no	—
931	SD₁₆	—	4	2	no	—
932	SD₁₆	—	4	2	no	—
933	SD₁₆	—	4	2	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	1	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	1	no	—
938	SD₁₆	—	4	2	no	—
939	SD₁₆	—	4	2	no	—
940	D₈	—	4	1	no	—
941	D₈	—	4	2	no	—
942	D₈	—	4	2	no	—
943	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
947	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
973	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
974	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
979	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1013	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1014	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1015	C₄²	C₂⁴×C₃₁	1	2	yes	—
1016	C₄²	C₂⁴×C₃₁	1	2	yes	—
1017	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	2	no	—
1020	C₂³	—	2	2	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	4	4	no	—
1023	C₂³	—	8	2	no	—
1024	C₂³	—	8	2	no	—
1025	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	2	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	2	2	no	—
1032	Q₈	—	2	1	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	1	no	—
1036	Q₈	—	8	2	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	4	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	1	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1082	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1084	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1085	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1088	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1089	C₈	—	2	2	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	2	2	no	—
1092	C₈	—	2	1	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	1	no	—
1103	C₂²	—	4	1	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	16	4	no	—
1111	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	2	1	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	C₃₁×#577	1	2	yes	—
1129	C₄	C₃₁×#585	1	1	yes	characteristic
1130	C₄	C₃₁×#585	1	1	yes	characteristic
1131	C₂	—	4	1	no	—
1132	C₂	—	8	2	no	—
1133	C₂	—	8	2	no	—
1134	C₂	—	8	1	no	—
1135	C₂	—	8	1	no	—
1136	C₂	C₃₁×#3487	1	1	yes	characteristic
1137	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1138	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3555	C₂	semidirect
2. C₃₁×#3508	C₂	semidirect
3. C₃₁×#3401	C₂	semidirect
4. C₃₁×#3400	C₂	semidirect
5. C₃₁×#3397	C₂	semidirect
6. C₃₁×#3397	C₂	semidirect
7. C₃₁×#3394	C₂	semidirect
8. C₃₁×#3392	C₂	semidirect
9. C₃₁×#3375	C₂	semidirect
10. C₃₁×#3371	C₂	semidirect
11. C₃₁×#3368	C₂	semidirect
12. C₃₁×#3366	C₂	semidirect
13. C₃₁×#3362	C₂	semidirect
14. C₃₁×#3361	C₂	semidirect
15. C₃₁×#3224	C₂	semidirect
16. C₃₁×#3222	C₂	semidirect
17. C₃₁×#3217	C₂	semidirect
18. C₃₁×#3208	C₂	semidirect
19. C₃₁×#3123	C₂	semidirect
20. C₃₁×#3118	C₂	semidirect
21. C₃₁×#3116	C₂	semidirect
22. C₃₁×#3102	C₂	semidirect
23. C₃₁×#2985	C₂	semidirect
28. Q₈²×C₃₁	C₂²	semidirect
29. C₃₁×#557	C₂²	semidirect
30. C₃₁×#557	C₂²	semidirect
32. C₃₁×#556	C₂²	semidirect
33. C₃₁×#556	C₂²	semidirect
34. C₃₁×#554	C₂²	semidirect
57. C₃₁×#497	C₂²	semidirect
59. C₃₁×#496	C₂²	semidirect
60. C₃₁×#495	C₂²	semidirect
63. C₃₁×#492	C₂²	semidirect
65. C₃₁×#490	C₂²	semidirect
66. C₃₁×#489	C₂²	semidirect
67. C₃₁×#488	C₂²	semidirect
70. C₃₁×#486	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#478	C₂²	semidirect
78. C₃₁×#477	C₂²	semidirect
79. C₃₁×#476	C₂²	semidirect
80. C₃₁×#476	C₂²	semidirect
81. C₃₁×#474	C₂²	semidirect
82. C₃₁×#464	C₂²	semidirect
83. C₃₁×#464	C₂²	semidirect
84. C₃₁×#464	C₂²	semidirect
85. C₃₁×#464	C₂²	semidirect
86. C₃₁×#463	C₂²	semidirect
87. C₃₁×#463	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
90. C₃₁×#462	C₂²	semidirect
91. C₃₁×#461	C₂²	semidirect
92. C₃₁×#461	C₂²	semidirect
93. C₃₁×#461	C₂²	semidirect
98. C₃₁×#460	C₂²	semidirect
99. C₃₁×#460	C₂²	semidirect
100. C₃₁×#460	C₂²	semidirect
103. C₃₁×#459	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₃₁×#446	C₂²	semidirect
113. C₃₁×#446	C₂²	semidirect
114. C₃₁×#446	C₂²	semidirect
115. C₈×Q₈×C₃₁	C₂²	semidirect
116. C₈×Q₈×C₃₁	C₂²	semidirect
117. C₃₁×#442	C₂²	semidirect
118. C₃₁×#441	C₂²	semidirect
119. C₃₁×#440	C₂²	semidirect
120. C₃₁×#440	C₂²	semidirect
121. C₃₁×#440	C₂²	semidirect
122. C₃₁×#440	C₂²	semidirect
123. C₄×Q₁₆×C₃₁	C₂²	semidirect
124. C₄×SD₁₆×C₃₁	C₂²	semidirect
125. C₄×SD₁₆×C₃₁	C₂²	semidirect
126. C₄×SD₁₆×C₃₁	C₂²	semidirect
127. C₄×SD₁₆×C₃₁	C₂²	semidirect
128. C₄×SD₁₆×C₃₁	C₂²	semidirect
129. C₄×D₈×C₃₁	C₂²	semidirect
130. C₄×D₈×C₃₁	C₂²	semidirect
448. #61921	C₃₁	direct (N × H)
526. #3555	C₂×C₃₁	semidirect
527. #3508	C₂×C₃₁	semidirect
528. #3401	C₂×C₃₁	semidirect
529. #3400	C₂×C₃₁	semidirect
530. #3397	C₂×C₃₁	semidirect
531. #3397	C₂×C₃₁	semidirect
532. #3394	C₂×C₃₁	semidirect
533. #3392	C₂×C₃₁	semidirect
534. #3375	C₂×C₃₁	semidirect
535. #3371	C₂×C₃₁	semidirect
536. #3368	C₂×C₃₁	semidirect
537. #3366	C₂×C₃₁	semidirect
538. #3362	C₂×C₃₁	semidirect
539. #3361	C₂×C₃₁	semidirect
540. #3224	C₂×C₃₁	semidirect
541. #3222	C₂×C₃₁	semidirect
542. #3217	C₂×C₃₁	semidirect
543. #3208	C₂×C₃₁	semidirect
544. #3123	C₂×C₃₁	semidirect
545. #3118	C₂×C₃₁	semidirect
546. #3116	C₂×C₃₁	semidirect
547. #3102	C₂×C₃₁	semidirect
548. #2985	C₂×C₃₁	semidirect
589. Q₈²	C₂²×C₃₁	semidirect
590. #557	C₂²×C₃₁	semidirect
591. #557	C₂²×C₃₁	semidirect
593. #556	C₂²×C₃₁	semidirect
594. #556	C₂²×C₃₁	semidirect
595. #554	C₂²×C₃₁	semidirect
618. #497	C₂²×C₃₁	semidirect
620. #496	C₂²×C₃₁	semidirect
621. #495	C₂²×C₃₁	semidirect
624. #492	C₂²×C₃₁	semidirect
626. #490	C₂²×C₃₁	semidirect
627. #489	C₂²×C₃₁	semidirect
628. #488	C₂²×C₃₁	semidirect
631. #486	C₂²×C₃₁	semidirect
635. #479	C₂²×C₃₁	semidirect
636. #478	C₂²×C₃₁	semidirect
637. #478	C₂²×C₃₁	semidirect
638. #478	C₂²×C₃₁	semidirect
639. #477	C₂²×C₃₁	semidirect
640. #476	C₂²×C₃₁	semidirect
641. #476	C₂²×C₃₁	semidirect
642. #474	C₂²×C₃₁	semidirect
643. #464	C₂²×C₃₁	semidirect
644. #464	C₂²×C₃₁	semidirect
645. #464	C₂²×C₃₁	semidirect
646. #464	C₂²×C₃₁	semidirect
647. #463	C₂²×C₃₁	semidirect
648. #463	C₂²×C₃₁	semidirect
649. #463	C₂²×C₃₁	semidirect
650. #463	C₂²×C₃₁	semidirect
651. #462	C₂²×C₃₁	semidirect
652. #461	C₂²×C₃₁	semidirect
653. #461	C₂²×C₃₁	semidirect
654. #461	C₂²×C₃₁	semidirect
659. #460	C₂²×C₃₁	semidirect
660. #460	C₂²×C₃₁	semidirect
661. #460	C₂²×C₃₁	semidirect
664. #459	C₂²×C₃₁	semidirect
672. #446	C₂²×C₃₁	semidirect
673. #446	C₂²×C₃₁	semidirect
674. #446	C₂²×C₃₁	semidirect
675. #446	C₂²×C₃₁	semidirect
676. C₈×Q₈	C₂²×C₃₁	semidirect
677. C₈×Q₈	C₂²×C₃₁	semidirect
678. #442	C₂²×C₃₁	semidirect
679. #441	C₂²×C₃₁	semidirect
680. #440	C₂²×C₃₁	semidirect
681. #440	C₂²×C₃₁	semidirect
682. #440	C₂²×C₃₁	semidirect
683. #440	C₂²×C₃₁	semidirect
684. C₄×Q₁₆	C₂²×C₃₁	semidirect
685. C₄×SD₁₆	C₂²×C₃₁	semidirect
686. C₄×SD₁₆	C₂²×C₃₁	semidirect
687. C₄×SD₁₆	C₂²×C₃₁	semidirect
688. C₄×SD₁₆	C₂²×C₃₁	semidirect
689. C₄×SD₁₆	C₂²×C₃₁	semidirect
690. C₄×D₈	C₂²×C₃₁	semidirect
691. C₄×D₈	C₂²×C₃₁	semidirect
881. C₃₁	#61921	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×#3555	2
C₃₁×#3508	2
C₃₁×#3401	2
C₃₁×#3400	2
C₃₁×#3397	2
C₃₁×#3394	2
C₃₁×#3392	2
C₃₁×#3375	2
C₃₁×#3371	2
C₃₁×#3368	2
C₃₁×#3366	2
C₃₁×#3362	2
C₃₁×#3361	2
C₃₁×#3224	2
C₃₁×#3222	2
C₃₁×#3217	2
C₃₁×#3208	2
C₃₁×#3123	2
C₃₁×#3118	2
C₃₁×#3116	2
C₃₁×#3102	2
C₃₁×#2985	2
#61921	31

Subgroups — C31×#61921 #21518680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61921 #21518680