Subgroups — C₃₁×#62553 #21519312

Order 7936.

1698 conjugacy classes of subgroups.

The subgroup lattice has 1110 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×#3552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3374	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×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3320	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3316	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3218	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3137	C₂	1	2	yes	maximal, complemented
22	C₂×C₃₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#563	—	2	2	no	—
26	C₃₁×#557	C₂²	1	1	yes	characteristic
27	C₃₁×#557	C₂²	1	1	yes	characteristic
28	C₃₁×#556	C₂²	1	1	yes	characteristic
29	C₃₁×#556	C₂²	1	1	yes	characteristic
30	C₃₁×#554	—	2	1	no	—
31	C₃₁×#554	C₂²	1	2	yes	—
32	C₃₁×#553	—	2	1	no	—
33	C₃₁×#553	C₂²	1	2	yes	—
34	D₄×Q₈×C₃₁	—	2	1	no	—
35	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
37	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#548	—	2	1	no	—
39	C₃₁×#548	C₂²	1	2	yes	—
40	C₃₁×#547	C₂²	1	1	yes	characteristic
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#544	C₂²	1	2	yes	—
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#542	C₂²	1	2	yes	—
46	C₃₁×#541	—	2	1	no	—
47	C₃₁×#541	C₂²	1	2	yes	—
48	C₃₁×#539	—	2	2	no	—
49	C₃₁×#539	—	2	2	no	—
50	C₃₁×#536	—	2	1	no	—
51	C₃₁×#536	C₂²	1	2	yes	—
52	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₃₁×#529	C₂²	1	1	yes	characteristic
55	C₃₁×#529	C₂²	1	1	yes	characteristic
56	C₃₁×#529	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	—
58	C₃₁×#499	C₂²	1	1	yes	characteristic
59	C₃₁×#497	C₂²	1	2	yes	—
60	C₃₁×#495	C₂²	1	1	yes	characteristic
61	C₃₁×#491	C₂²	1	2	yes	—
62	C₃₁×#491	C₂²	1	2	yes	—
63	C₃₁×#489	C₂²	1	2	yes	—
64	C₃₁×#489	C₂²	1	2	yes	—
65	C₃₁×#488	C₂²	1	2	yes	—
66	C₃₁×#488	C₂²	1	1	yes	characteristic
67	C₃₁×#488	C₂²	1	1	yes	characteristic
68	C₃₁×#487	C₂²	1	1	yes	characteristic
69	C₃₁×#487	C₂²	1	2	yes	—
70	C₃₁×#487	C₂²	1	1	yes	characteristic
71	C₃₁×#487	C₂²	1	1	yes	characteristic
72	C₃₁×#487	C₂²	1	1	yes	characteristic
73	C₃₁×#487	C₂²	1	2	yes	—
74	C₃₁×#487	C₂²	1	2	yes	—
75	C₃₁×#485	C₂²	1	2	yes	—
76	C₃₁×#485	C₂²	1	2	yes	—
77	C₃₁×#484	C₂²	1	2	yes	—
78	C₃₁×#484	C₂²	1	2	yes	—
79	C₃₁×#483	C₂²	1	2	yes	—
80	C₃₁×#481	C₂²	1	2	yes	—
81	C₃₁×#479	C₂²	1	2	yes	—
82	C₃₁×#479	C₂²	1	2	yes	—
83	C₃₁×#477	C₂²	1	2	yes	—
84	C₃₁×#475	C₂²	1	1	yes	characteristic
85	C₃₁×#475	C₂²	1	2	yes	—
86	C₃₁×#475	C₂²	1	1	yes	characteristic
87	C₃₁×#474	C₂²	1	1	yes	characteristic
88	C₃₁×#474	C₂²	1	1	yes	characteristic
89	C₃₁×#470	C₂²	1	2	yes	—
90	C₃₁×#468	C₂²	1	2	yes	—
91	C₃₁×#467	C₂²	1	1	yes	characteristic
92	C₃₁×#467	C₂²	1	2	yes	—
93	C₃₁×#466	C₂²	1	1	yes	characteristic
94	C₃₁×#465	C₂²	1	1	yes	characteristic
95	C₃₁×#465	C₂²	1	1	yes	characteristic
96	C₃₁×#465	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
100	C₃₁×#462	C₂²	1	1	yes	characteristic
101	C₃₁×#462	C₂²	1	2	yes	—
102	C₃₁×#461	C₂²	1	1	yes	characteristic
103	C₃₁×#461	C₂²	1	2	yes	—
104	C₃₁×#461	C₂²	1	1	yes	characteristic
105	C₃₁×#452	C₂²	1	2	yes	—
106	C₃₁×#451	C₂²	1	2	yes	—
107	C₃₁×#451	C₂²	1	2	yes	—
108	C₃₁×#449	C₂²	1	2	yes	—
109	C₃₁×#448	C₂²	1	2	yes	—
110	C₃₁×#448	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
113	C₃₁×#441	C₂²	1	2	yes	—
114	C₃₁×#440	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
116	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₃₁	C₂²	1	2	yes	—
125	C₃₁×#433	C₂²	1	2	yes	—
126	C₃₁×#432	C₂²	1	1	yes	characteristic
127	C₃₁×#419	C₂²	1	2	yes	—
128	C₃₁×#417	C₂²	1	2	yes	—
129	C₃₁×#416	C₂²	1	2	yes	—
130	C₂×C₃₁×#103	C₂²	1	2	yes	—
131	C₂×C₃₁×#103	C₂²	1	2	yes	—
132	C₂×C₃₁×#103	C₂²	1	2	yes	—
133	C₃₁×#405	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	C₂³	1	2	yes	—
137	C₂²×Q₈×C₃₁	—	2	1	no	—
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
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	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
153	C₃₁×C₄⋊Q₈	—	2	1	no	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	—	2	2	no	—
156	C₃₁×C₄⋊Q₈	—	2	2	no	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₃₁×#126	—	2	2	no	—
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	—	2	1	no	—
177	C₃₁×#126	D₄	1	2	yes	—
178	C₃₁×#125	—	2	2	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	D₄	1	1	yes	characteristic
186	C₃₁×#125	C₂³	1	2	yes	—
187	C₃₁×#125	C₂³	1	1	yes	characteristic
188	C₃₁×#125	C₂³	1	1	yes	characteristic
189	C₃₁×#124	—	2	1	no	—
190	C₃₁×#124	—	2	2	no	—
191	C₃₁×#124	—	2	2	no	—
192	C₃₁×#124	D₄	1	1	yes	characteristic
193	C₃₁×#124	C₂³	1	2	yes	—
194	C₃₁×#124	C₂³	1	1	yes	characteristic
195	C₃₁×#124	C₂³	1	1	yes	characteristic
196	C₃₁×#123	—	2	1	no	—
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×#123	—	2	2	no	—
204	C₃₁×#123	D₄	1	2	yes	—
205	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	1	no	—
210	C₃₁×C₂²⋊Q₈	—	2	1	no	—
211	C₃₁×C₂²⋊Q₈	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	2	no	—
213	C₃₁×C₂²⋊Q₈	—	2	2	no	—
214	C₃₁×C₂²⋊Q₈	—	2	2	no	—
215	C₃₁×C₂²⋊Q₈	—	2	2	no	—
216	C₃₁×C₂²⋊Q₈	—	2	2	no	—
217	C₃₁×C₂²⋊Q₈	—	2	2	no	—
218	C₃₁×C₂²⋊Q₈	—	2	2	no	—
219	C₃₁×C₂²⋊Q₈	—	2	2	no	—
220	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
221	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₃₁×#121	—	2	2	no	—
227	C₃₁×#121	—	2	2	no	—
228	C₃₁×#121	—	2	1	no	—
229	C₃₁×#121	D₄	1	1	yes	characteristic
230	C₃₁×#121	C₂³	1	1	yes	characteristic
231	C₃₁×#121	C₂³	1	2	yes	—
232	C₃₁×#121	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₃₁	—	2	1	no	—
234	C₄×Q₈×C₃₁	—	2	1	no	—
235	C₄×Q₈×C₃₁	—	2	1	no	—
236	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
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	2	no	—
244	C₄×D₄×C₃₁	—	2	1	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	—	2	2	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	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	1	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
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×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	2	yes	—
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	1	yes	characteristic
295	C₃₁×#103	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	1	yes	characteristic
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	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	#41×C₃₁	—	4	2	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	8	2	no	—
315	C₂×Q₈×C₃₁	—	2	1	no	—
316	C₂×Q₈×C₃₁	—	2	1	no	—
317	C₂×Q₈×C₃₁	—	2	2	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	4	2	no	—
322	C₂×Q₈×C₃₁	—	4	2	no	—
323	C₂×Q₈×C₃₁	—	4	2	no	—
324	C₂×Q₈×C₃₁	—	4	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	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
337	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	—	2	2	no	—
341	C₂²×C₄×C₃₁	—	2	2	no	—
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	—	2	2	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	2	no	—
348	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
352	Q₁₆×C₃₁	—	4	1	no	—
353	Q₁₆×C₃₁	—	4	2	no	—
354	Q₁₆×C₃₁	—	4	2	no	—
355	SD₁₆×C₃₁	—	4	1	no	—
356	SD₁₆×C₃₁	—	4	1	no	—
357	SD₁₆×C₃₁	—	4	2	no	—
358	SD₁₆×C₃₁	—	4	2	no	—
359	D₈×C₃₁	—	4	1	no	—
360	M₁₆×C₃₁	—	4	2	no	—
361	C₂×C₈×C₃₁	—	4	1	no	—
362	C₂×C₈×C₃₁	—	4	2	no	—
363	C₂×C₈×C₃₁	—	4	1	no	—
364	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
369	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₃₁	—	2	1	no	—
371	C₄⋊C₄×C₃₁	—	2	1	no	—
372	C₄⋊C₄×C₃₁	—	2	1	no	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	1	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	2	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	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	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	1	no	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
445	C₄²×C₃₁	C₂⁴	1	2	yes	—
446	#62553	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₃₁	—	2	1	no	—
448	C₂³×C₃₁	—	2	1	no	—
449	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
450	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
451	Q₈×C₃₁	—	2	2	no	—
452	Q₈×C₃₁	—	2	1	no	—
453	Q₈×C₃₁	—	2	2	no	—
454	Q₈×C₃₁	—	2	1	no	—
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	2	1	no	—
458	Q₈×C₃₁	—	2	2	no	—
459	Q₈×C₃₁	—	2	2	no	—
460	Q₈×C₃₁	—	4	2	no	—
461	Q₈×C₃₁	—	4	2	no	—
462	Q₈×C₃₁	—	8	2	no	—
463	Q₈×C₃₁	—	8	2	no	—
464	Q₈×C₃₁	—	8	2	no	—
465	Q₈×C₃₁	—	8	2	no	—
466	D₄×C₃₁	—	2	4	no	—
467	D₄×C₃₁	—	2	2	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	1	no	—
471	D₄×C₃₁	—	2	1	no	—
472	D₄×C₃₁	—	4	2	no	—
473	D₄×C₃₁	—	4	2	no	—
474	D₄×C₃₁	—	8	2	no	—
475	D₄×C₃₁	—	8	2	no	—
476	C₂×C₄×C₃₁	—	2	2	no	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	2	1	no	—
479	C₂×C₄×C₃₁	—	2	1	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	4	2	no	—
493	C₂×C₄×C₃₁	—	4	2	no	—
494	C₂×C₄×C₃₁	—	8	2	no	—
495	C₂×C₄×C₃₁	—	8	2	no	—
496	C₂×C₄×C₃₁	—	8	2	no	—
497	C₂×C₄×C₃₁	—	8	2	no	—
498	C₂×C₄×C₃₁	—	8	2	no	—
499	C₂×C₄×C₃₁	—	8	2	no	—
500	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
509	C₈×C₃₁	—	2	1	no	—
510	C₈×C₃₁	—	2	1	no	—
511	C₈×C₃₁	—	2	1	no	—
512	C₈×C₃₁	—	2	1	no	—
513	C₈×C₃₁	—	2	2	no	—
514	C₈×C₃₁	—	2	2	no	—
515	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3367	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3359	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3328	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3320	C₂×C₃₁	1	2	yes	complemented
524	#3316	C₂×C₃₁	1	2	yes	complemented
525	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3301	C₂×C₃₁	1	2	yes	complemented
527	#3299	C₂×C₃₁	1	2	yes	complemented
528	#3298	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3242	C₂×C₃₁	1	2	yes	complemented
530	#3239	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3225	C₂×C₃₁	1	2	yes	complemented
532	#3218	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3178	C₂×C₃₁	1	2	yes	complemented
534	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3137	C₂×C₃₁	1	2	yes	complemented
536	C₂×#487	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
538	C₂²×C₃₁	—	2	1	no	—
539	C₂²×C₃₁	—	2	1	no	—
540	C₂²×C₃₁	—	2	2	no	—
541	C₂²×C₃₁	—	2	2	no	—
542	C₂²×C₃₁	—	2	2	no	—
543	C₂²×C₃₁	—	4	1	no	—
544	C₂²×C₃₁	—	4	1	no	—
545	C₂²×C₃₁	—	4	1	no	—
546	C₂²×C₃₁	—	4	1	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	#578	1	2	yes	—
550	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
551	C₄×C₃₁	—	2	2	no	—
552	C₄×C₃₁	—	2	1	no	—
553	C₄×C₃₁	—	2	1	no	—
554	C₄×C₃₁	—	2	2	no	—
555	C₄×C₃₁	—	2	1	no	—
556	C₄×C₃₁	—	2	1	no	—
557	C₄×C₃₁	—	2	2	no	—
558	C₄×C₃₁	—	4	2	no	—
559	C₄×C₃₁	—	4	1	no	—
560	C₄×C₃₁	—	4	2	no	—
561	C₄×C₃₁	—	4	1	no	—
562	C₄×C₃₁	—	4	1	no	—
563	C₄×C₃₁	—	4	1	no	—
564	C₄×C₃₁	—	4	2	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	#577	1	2	yes	—
569	C₄×C₃₁	#585	1	1	yes	characteristic
570	C₄×C₃₁	#585	1	1	yes	characteristic
571	#563	—	2	2	no	—
572	#563	—	2	2	no	—
573	#557	C₂²×C₃₁	1	1	yes	characteristic
574	#557	C₂²×C₃₁	1	1	yes	characteristic
575	#556	C₂²×C₃₁	1	1	yes	characteristic
576	#556	C₂²×C₃₁	1	1	yes	characteristic
577	#554	—	2	1	no	—
578	#554	C₂²×C₃₁	1	2	yes	—
579	#553	—	2	1	no	—
580	#553	C₂²×C₃₁	1	2	yes	—
581	D₄×Q₈	—	2	1	no	—
582	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
583	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
584	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
585	#548	—	2	1	no	—
586	#548	C₂²×C₃₁	1	2	yes	—
587	#547	C₂²×C₃₁	1	1	yes	characteristic
588	#547	C₂²×C₃₁	1	1	yes	characteristic
589	#544	—	2	1	no	—
590	#544	C₂²×C₃₁	1	2	yes	—
591	#542	—	2	1	no	—
592	#542	C₂²×C₃₁	1	2	yes	—
593	#541	—	2	1	no	—
594	#541	C₂²×C₃₁	1	2	yes	—
595	#539	—	2	2	no	—
596	#539	—	2	2	no	—
597	#536	—	2	1	no	—
598	#536	C₂²×C₃₁	1	2	yes	—
599	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
600	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
601	#529	C₂²×C₃₁	1	1	yes	characteristic
602	#529	C₂²×C₃₁	1	1	yes	characteristic
603	#529	C₂²×C₃₁	1	1	yes	characteristic
604	#501	C₂²×C₃₁	1	2	yes	—
605	#499	C₂²×C₃₁	1	1	yes	characteristic
606	#497	C₂²×C₃₁	1	2	yes	—
607	#495	C₂²×C₃₁	1	1	yes	characteristic
608	#491	C₂²×C₃₁	1	2	yes	—
609	#491	C₂²×C₃₁	1	2	yes	—
610	#489	C₂²×C₃₁	1	2	yes	—
611	#489	C₂²×C₃₁	1	2	yes	—
612	#488	C₂²×C₃₁	1	2	yes	—
613	#488	C₂²×C₃₁	1	1	yes	characteristic
614	#488	C₂²×C₃₁	1	1	yes	characteristic
615	#487	C₂²×C₃₁	1	1	yes	characteristic
616	#487	C₂²×C₃₁	1	1	yes	characteristic
617	#487	C₂²×C₃₁	1	1	yes	characteristic
618	#487	C₂²×C₃₁	1	2	yes	—
619	#487	C₂²×C₃₁	1	1	yes	characteristic
620	#487	C₂²×C₃₁	1	2	yes	—
621	#487	C₂²×C₃₁	1	2	yes	—
622	#485	C₂²×C₃₁	1	2	yes	—
623	#485	C₂²×C₃₁	1	2	yes	—
624	#484	C₂²×C₃₁	1	2	yes	—
625	#484	C₂²×C₃₁	1	2	yes	—
626	#483	C₂²×C₃₁	1	2	yes	—
627	#481	C₂²×C₃₁	1	2	yes	—
628	#479	C₂²×C₃₁	1	2	yes	—
629	#479	C₂²×C₃₁	1	2	yes	—
630	#477	C₂²×C₃₁	1	2	yes	—
631	#475	C₂²×C₃₁	1	1	yes	characteristic
632	#475	C₂²×C₃₁	1	2	yes	—
633	#475	C₂²×C₃₁	1	1	yes	characteristic
634	#474	C₂²×C₃₁	1	1	yes	characteristic
635	#474	C₂²×C₃₁	1	1	yes	characteristic
636	#470	C₂²×C₃₁	1	2	yes	—
637	#468	C₂²×C₃₁	1	2	yes	—
638	#467	C₂²×C₃₁	1	1	yes	characteristic
639	#467	C₂²×C₃₁	1	2	yes	—
640	#466	C₂²×C₃₁	1	1	yes	characteristic
641	#465	C₂²×C₃₁	1	1	yes	characteristic
642	#465	C₂²×C₃₁	1	1	yes	characteristic
643	#465	C₂²×C₃₁	1	2	yes	—
644	#464	C₂²×C₃₁	1	2	yes	—
645	#463	C₂²×C₃₁	1	2	yes	—
646	#462	C₂²×C₃₁	1	1	yes	characteristic
647	#462	C₂²×C₃₁	1	1	yes	characteristic
648	#462	C₂²×C₃₁	1	2	yes	—
649	#461	C₂²×C₃₁	1	1	yes	characteristic
650	#461	C₂²×C₃₁	1	2	yes	—
651	#461	C₂²×C₃₁	1	1	yes	characteristic
652	#452	C₂²×C₃₁	1	2	yes	—
653	#451	C₂²×C₃₁	1	2	yes	—
654	#451	C₂²×C₃₁	1	2	yes	—
655	#449	C₂²×C₃₁	1	2	yes	—
656	#448	C₂²×C₃₁	1	2	yes	—
657	#448	C₂²×C₃₁	1	2	yes	—
658	#446	C₂²×C₃₁	1	1	yes	characteristic
659	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
660	#441	C₂²×C₃₁	1	2	yes	—
661	#440	C₂²×C₃₁	1	2	yes	—
662	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
663	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
664	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
665	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
666	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
667	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
668	#436	C₂²×C₃₁	1	1	yes	characteristic
669	#435	C₂²×C₃₁	1	2	yes	—
670	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
671	C₈×D₄	C₂²×C₃₁	1	2	yes	—
672	#433	C₂²×C₃₁	1	2	yes	—
673	#432	C₂²×C₃₁	1	1	yes	characteristic
674	#419	C₂²×C₃₁	1	2	yes	—
675	#417	C₂²×C₃₁	1	2	yes	—
676	#416	C₂²×C₃₁	1	2	yes	—
677	C₂×#103	C₂²×C₃₁	1	2	yes	—
678	C₂×#103	C₂²×C₃₁	1	2	yes	—
679	C₂×#103	C₂²×C₃₁	1	2	yes	—
680	#405	C₂²×C₃₁	1	2	yes	—
681	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
682	C₂×C₃₁	—	2	2	no	—
683	C₂×C₃₁	—	4	2	no	—
684	C₂×C₃₁	—	8	1	no	—
685	C₂×C₃₁	—	8	1	no	—
686	C₂×C₃₁	#3500	1	1	yes	characteristic
687	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
688	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
689	C₂×#41	—	2	1	no	—
690	C₂×#41	C₂³×C₃₁	1	2	yes	—
691	C₂²×Q₈	—	2	1	no	—
692	C₂²×Q₈	—	2	1	no	—
693	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
694	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
695	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
697	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
698	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
699	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
700	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
702	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
703	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
704	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
705	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
706	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	2	1	no	—
709	C₄⋊Q₈	—	2	2	no	—
710	C₄⋊Q₈	—	2	2	no	—
711	C₄⋊Q₈	—	2	1	no	—
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	—	2	1	no	—
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
716	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
717	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
719	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
720	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	1	no	—
730	#126	—	2	1	no	—
731	#126	D₄×C₃₁	1	2	yes	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	D₄×C₃₁	1	1	yes	characteristic
740	#125	C₂³×C₃₁	1	1	yes	characteristic
741	#125	C₂³×C₃₁	1	1	yes	characteristic
742	#125	C₂³×C₃₁	1	2	yes	—
743	#124	—	2	1	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	D₄×C₃₁	1	1	yes	characteristic
747	#124	C₂³×C₃₁	1	1	yes	characteristic
748	#124	C₂³×C₃₁	1	1	yes	characteristic
749	#124	C₂³×C₃₁	1	2	yes	—
750	#123	—	2	1	no	—
751	#123	—	2	1	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	D₄×C₃₁	1	2	yes	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
775	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	1	no	—
783	#121	D₄×C₃₁	1	1	yes	characteristic
784	#121	C₂³×C₃₁	1	1	yes	characteristic
785	#121	C₂³×C₃₁	1	1	yes	characteristic
786	#121	C₂³×C₃₁	1	2	yes	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
793	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
794	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
795	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₃₁	1	2	yes	—
806	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₃₁	1	2	yes	—
808	#117	—	2	1	no	—
809	#117	—	2	1	no	—
810	#117	—	2	1	no	—
811	#117	C₂³×C₃₁	1	2	yes	—
812	#117	C₂³×C₃₁	1	2	yes	—
813	C₂×C₄⋊C₄	—	2	1	no	—
814	C₂×C₄⋊C₄	—	2	1	no	—
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
818	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
819	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
820	#107	C₂³×C₃₁	1	1	yes	characteristic
821	#107	C₂³×C₃₁	1	1	yes	characteristic
822	#107	C₂³×C₃₁	1	2	yes	—
823	#107	C₂³×C₃₁	1	2	yes	—
824	#106	C₂³×C₃₁	1	1	yes	characteristic
825	#106	C₂³×C₃₁	1	1	yes	characteristic
826	#106	C₂³×C₃₁	1	2	yes	—
827	#106	C₂³×C₃₁	1	2	yes	—
828	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
831	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
832	#103	C₂³×C₃₁	1	1	yes	characteristic
833	#103	C₂³×C₃₁	1	2	yes	—
834	#103	C₂³×C₃₁	1	2	yes	—
835	#103	C₂³×C₃₁	1	2	yes	—
836	#103	C₂³×C₃₁	1	2	yes	—
837	#103	C₂³×C₃₁	1	2	yes	—
838	#103	C₂³×C₃₁	1	2	yes	—
839	#103	C₂³×C₃₁	1	2	yes	—
840	#103	C₂³×C₃₁	1	2	yes	—
841	#103	C₂³×C₃₁	1	2	yes	—
842	#103	C₂³×C₃₁	1	2	yes	—
843	#103	C₂³×C₃₁	1	2	yes	—
844	#103	C₂³×C₃₁	1	2	yes	—
845	#103	C₂³×C₃₁	1	1	yes	characteristic
846	#103	C₂³×C₃₁	1	2	yes	—
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	1	yes	characteristic
849	#103	C₂³×C₃₁	1	1	yes	characteristic
850	#102	C₂³×C₃₁	1	1	yes	characteristic
851	#102	C₂³×C₃₁	1	2	yes	—
852	#102	C₂³×C₃₁	1	1	yes	characteristic
853	#102	C₂³×C₃₁	1	2	yes	—
854	#102	C₂³×C₃₁	1	1	yes	characteristic
855	#102	C₂³×C₃₁	1	1	yes	characteristic
856	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
857	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
859	#97	C₂³×C₃₁	1	2	yes	—
860	#97	C₂³×C₃₁	1	2	yes	—
861	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
865	C₄×C₈	C₂³×C₃₁	1	2	yes	—
866	C₃₁	#62553	1	1	yes	characteristic, direct product factor, Sylow
867	#41	—	4	2	no	—
868	#41	—	4	2	no	—
869	#41	—	8	2	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	2	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	2	no	—
876	C₂×Q₈	—	4	2	no	—
877	C₂×Q₈	—	4	2	no	—
878	C₂×Q₈	—	4	2	no	—
879	C₂×Q₈	—	4	2	no	—
880	C₂×Q₈	—	8	2	no	—
881	C₂×Q₈	—	8	2	no	—
882	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
884	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
885	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
886	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
892	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
893	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	2	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
904	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
907	Q₁₆	—	4	1	no	—
908	Q₁₆	—	4	2	no	—
909	Q₁₆	—	4	2	no	—
910	SD₁₆	—	4	1	no	—
911	SD₁₆	—	4	1	no	—
912	SD₁₆	—	4	2	no	—
913	SD₁₆	—	4	2	no	—
914	D₈	—	4	1	no	—
915	M₁₆	—	4	2	no	—
916	C₂×C₈	—	4	1	no	—
917	C₂×C₈	—	4	2	no	—
918	C₂×C₈	—	4	1	no	—
919	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
924	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
956	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
957	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
959	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
963	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
986	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
987	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
988	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
989	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	2	no	—
996	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
997	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
998	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
999	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1000	C₄²	C₂⁴×C₃₁	1	2	yes	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	1	no	—
1003	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1004	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1005	Q₈	—	2	2	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	1	no	—
1011	Q₈	—	2	1	no	—
1012	Q₈	—	2	2	no	—
1013	Q₈	—	2	2	no	—
1014	Q₈	—	4	2	no	—
1015	Q₈	—	4	2	no	—
1016	Q₈	—	8	2	no	—
1017	Q₈	—	8	2	no	—
1018	Q₈	—	8	2	no	—
1019	Q₈	—	8	2	no	—
1020	D₄	—	2	4	no	—
1021	D₄	—	2	2	no	—
1022	D₄	—	2	1	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	1	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	4	2	no	—
1028	D₄	—	8	2	no	—
1029	D₄	—	8	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	8	2	no	—
1049	C₂×C₄	—	8	2	no	—
1050	C₂×C₄	—	8	2	no	—
1051	C₂×C₄	—	8	2	no	—
1052	C₂×C₄	—	8	2	no	—
1053	C₂×C₄	—	8	2	no	—
1054	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1055	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1056	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1057	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1059	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1060	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1061	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1062	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1063	C₈	—	2	1	no	—
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	2	1	no	—
1067	C₈	—	2	2	no	—
1068	C₈	—	2	2	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	2	no	—
1072	C₂²	—	2	2	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	C₃₁×#578	1	2	yes	—
1081	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1082	C₄	—	2	2	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	1	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	1	no	—
1099	C₄	C₃₁×#577	1	2	yes	—
1100	C₄	C₃₁×#585	1	1	yes	characteristic
1101	C₄	C₃₁×#585	1	1	yes	characteristic
1102	C₂	—	2	2	no	—
1103	C₂	—	4	2	no	—
1104	C₂	—	8	1	no	—
1105	C₂	—	8	1	no	—
1106	C₂	C₃₁×#3500	1	1	yes	characteristic
1107	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1108	C₂	C₂×C₃₁×#578	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×#3552	C₂	semidirect
3. C₃₁×#3374	C₂	semidirect
4. C₃₁×#3367	C₂	semidirect
5. C₃₁×#3364	C₂	semidirect
6. C₃₁×#3359	C₂	semidirect
7. C₃₁×#3330	C₂	semidirect
8. C₃₁×#3328	C₂	semidirect
9. C₃₁×#3320	C₂	semidirect
10. C₃₁×#3316	C₂	semidirect
11. C₃₁×#3302	C₂	semidirect
12. C₃₁×#3301	C₂	semidirect
13. C₃₁×#3299	C₂	semidirect
14. C₃₁×#3298	C₂	semidirect
15. C₃₁×#3242	C₂	semidirect
16. C₃₁×#3239	C₂	semidirect
17. C₃₁×#3225	C₂	semidirect
18. C₃₁×#3218	C₂	semidirect
19. C₃₁×#3178	C₂	semidirect
20. C₃₁×#3168	C₂	semidirect
21. C₃₁×#3137	C₂	semidirect
22. C₂×C₃₁×#487	C₂	semidirect
23. C₃₁×#2966	C₂	semidirect
446. #62553	C₃₁	direct (N × H)
515. #3552	C₂×C₃₁	semidirect
516. #3552	C₂×C₃₁	semidirect
517. #3374	C₂×C₃₁	semidirect
518. #3367	C₂×C₃₁	semidirect
519. #3364	C₂×C₃₁	semidirect
520. #3359	C₂×C₃₁	semidirect
521. #3330	C₂×C₃₁	semidirect
522. #3328	C₂×C₃₁	semidirect
523. #3320	C₂×C₃₁	semidirect
524. #3316	C₂×C₃₁	semidirect
525. #3302	C₂×C₃₁	semidirect
526. #3301	C₂×C₃₁	semidirect
527. #3299	C₂×C₃₁	semidirect
528. #3298	C₂×C₃₁	semidirect
529. #3242	C₂×C₃₁	semidirect
530. #3239	C₂×C₃₁	semidirect
531. #3225	C₂×C₃₁	semidirect
532. #3218	C₂×C₃₁	semidirect
533. #3178	C₂×C₃₁	semidirect
534. #3168	C₂×C₃₁	semidirect
535. #3137	C₂×C₃₁	semidirect
536. C₂×#487	C₂×C₃₁	semidirect
537. #2966	C₂×C₃₁	semidirect
866. C₃₁	#62553	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×#3374	2
C₃₁×#3367	2
C₃₁×#3364	2
C₃₁×#3359	2
C₃₁×#3330	2
C₃₁×#3328	2
C₃₁×#3320	2
C₃₁×#3316	2
C₃₁×#3302	2
C₃₁×#3301	2
C₃₁×#3299	2
C₃₁×#3298	2
C₃₁×#3242	2
C₃₁×#3239	2
C₃₁×#3225	2
C₃₁×#3218	2
C₃₁×#3178	2
C₃₁×#3168	2
C₃₁×#3137	2
C₂×C₃₁×#487	2
C₃₁×#2966	2
#62553	31

Subgroups — C31×#62553 #21519312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62553 #21519312