Subgroups — C₃₁×#62192 #21518951

Order 7936.

1626 conjugacy classes of subgroups.

The subgroup lattice has 1064 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
2	C₃₁×#3523	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3383	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3352	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3349	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3328	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3261	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3242	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3127	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3082	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2993	C₂	1	1	yes	maximal, characteristic
24	C₃₁×#563	—	2	2	no	—
25	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#557	—	2	1	no	—
27	C₃₁×#557	—	2	1	no	—
28	C₃₁×#557	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	1	yes	characteristic
30	C₃₁×#557	C₂²	1	1	yes	characteristic
31	C₃₁×#556	—	2	1	no	—
32	C₃₁×#556	—	2	1	no	—
33	C₃₁×#556	C₂²	1	1	yes	characteristic
34	C₃₁×#556	C₂²	1	1	yes	characteristic
35	C₃₁×#556	C₂²	1	2	yes	—
36	C₃₁×#554	C₂²	1	1	yes	characteristic
37	C₃₁×#552	—	2	2	no	—
38	C₃₁×#552	C₂²	1	2	yes	—
39	C₃₁×#552	C₂²	1	2	yes	—
40	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
42	C₃₁×#544	C₂²	1	2	yes	—
43	C₃₁×#542	—	2	1	no	—
44	C₃₁×#541	—	2	2	no	—
45	C₃₁×#541	—	2	2	no	—
46	C₃₁×#541	—	2	1	no	—
47	C₃₁×#541	C₂²	1	2	yes	—
48	C₃₁×#541	C₂²	1	2	yes	—
49	C₃₁×#533	—	2	1	no	—
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#533	C₂²	1	1	yes	characteristic
52	C₃₁×#533	C₂²	1	1	yes	characteristic
53	C₃₁×#529	—	2	1	no	—
54	C₃₁×#529	C₂²	1	1	yes	characteristic
55	C₃₁×#519	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	—
58	C₃₁×#500	C₂²	1	1	yes	characteristic
59	C₃₁×#499	C₂²	1	2	yes	—
60	C₃₁×#498	C₂²	1	1	yes	characteristic
61	C₃₁×#491	C₂²	1	2	yes	—
62	C₃₁×#487	C₂²	1	1	yes	characteristic
63	C₃₁×#487	C₂²	1	2	yes	—
64	C₃₁×#487	C₂²	1	1	yes	characteristic
65	C₃₁×#485	C₂²	1	2	yes	—
66	C₃₁×#485	C₂²	1	2	yes	—
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	—
69	C₃₁×#485	C₂²	1	2	yes	—
70	C₃₁×#485	C₂²	1	2	yes	—
71	C₃₁×#484	C₂²	1	1	yes	characteristic
72	C₃₁×#484	C₂²	1	1	yes	characteristic
73	C₃₁×#484	C₂²	1	2	yes	—
74	C₃₁×#483	C₂²	1	2	yes	—
75	C₃₁×#479	C₂²	1	2	yes	—
76	C₃₁×#479	C₂²	1	2	yes	—
77	C₃₁×#479	C₂²	1	2	yes	—
78	C₃₁×#479	C₂²	1	2	yes	—
79	C₃₁×#479	C₂²	1	2	yes	—
80	C₃₁×#479	C₂²	1	2	yes	—
81	C₃₁×#479	C₂²	1	2	yes	—
82	C₃₁×#479	C₂²	1	2	yes	—
83	C₃₁×#477	C₂²	1	1	yes	characteristic
84	C₃₁×#477	C₂²	1	1	yes	characteristic
85	C₃₁×#477	C₂²	1	1	yes	characteristic
86	C₃₁×#477	C₂²	1	2	yes	—
87	C₃₁×#477	C₂²	1	1	yes	characteristic
88	C₃₁×#475	C₂²	1	1	yes	characteristic
89	C₃₁×#475	C₂²	1	1	yes	characteristic
90	C₃₁×#475	C₂²	1	2	yes	—
91	C₃₁×#475	C₂²	1	2	yes	—
92	C₃₁×#475	C₂²	1	1	yes	characteristic
93	C₃₁×#475	C₂²	1	1	yes	characteristic
94	C₃₁×#470	C₂²	1	2	yes	—
95	C₃₁×#470	C₂²	1	2	yes	—
96	C₃₁×#470	C₂²	1	2	yes	—
97	C₃₁×#470	C₂²	1	2	yes	—
98	C₃₁×#467	C₂²	1	2	yes	—
99	C₃₁×#467	C₂²	1	2	yes	—
100	C₃₁×#462	C₂²	1	1	yes	characteristic
101	C₃₁×#462	C₂²	1	1	yes	characteristic
102	C₃₁×#462	C₂²	1	1	yes	characteristic
103	C₃₁×#462	C₂²	1	2	yes	—
104	C₃₁×#462	C₂²	1	1	yes	characteristic
105	C₃₁×#462	C₂²	1	2	yes	—
106	C₃₁×#462	C₂²	1	2	yes	—
107	C₃₁×#451	C₂²	1	1	yes	characteristic
108	C₃₁×#451	C₂²	1	1	yes	characteristic
109	C₃₁×#451	C₂²	1	2	yes	—
110	C₃₁×#451	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×#441	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
121	C₃₁×#436	C₂²	1	2	yes	—
122	C₃₁×#436	C₂²	1	1	yes	characteristic
123	C₃₁×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₃₁×#433	C₂²	1	2	yes	—
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	—
128	C₃₁×#428	C₂²	1	2	yes	—
129	C₃₁×#427	C₂²	1	2	yes	—
130	C₃₁×#424	C₂²	1	2	yes	—
131	C₃₁×#423	C₂²	1	1	yes	characteristic
132	C₃₁×#419	C₂²	1	2	yes	—
133	C₃₁×#419	C₂²	1	2	yes	—
134	C₂×C₃₁×#103	C₂²	1	2	yes	—
135	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
136	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
146	C₃₁×C₄⋊Q₈	—	2	1	no	—
147	C₃₁×C₄⋊Q₈	—	2	1	no	—
148	C₃₁×C₄⋊Q₈	—	2	1	no	—
149	C₃₁×C₄⋊Q₈	—	2	2	no	—
150	C₃₁×C₄⋊Q₈	—	2	2	no	—
151	C₃₁×C₄⋊Q₈	—	2	1	no	—
152	C₃₁×C₄⋊Q₈	—	2	2	no	—
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	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	1	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	1	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	1	yes	characteristic
187	C₃₁×#125	C₂³	1	2	yes	—
188	C₃₁×#125	C₂³	1	2	yes	—
189	C₃₁×#125	C₂³	1	2	yes	—
190	C₃₁×#124	—	2	1	no	—
191	C₃₁×#124	—	2	1	no	—
192	C₃₁×#124	—	2	2	no	—
193	C₃₁×#124	D₄	1	1	yes	characteristic
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	D₄	1	2	yes	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₃₁×#121	D₄	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	—	2	1	no	—
218	C₄×Q₈×C₃₁	—	2	2	no	—
219	C₄×Q₈×C₃₁	—	2	2	no	—
220	C₄×Q₈×C₃₁	—	2	1	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	2	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	—	2	1	no	—
228	C₄×Q₈×C₃₁	—	2	1	no	—
229	C₄×Q₈×C₃₁	—	2	1	no	—
230	C₄×Q₈×C₃₁	—	2	1	no	—
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
237	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	—	2	2	no	—
253	C₃₁×#117	—	2	2	no	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	2	yes	—
256	C₃₁×#117	C₂³	1	2	yes	—
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₄²×C₃₁	—	2	1	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	1	yes	characteristic
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
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×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#103	C₂³	1	1	yes	characteristic
298	C₃₁×#103	C₂³	1	2	yes	—
299	C₃₁×#103	C₂³	1	1	yes	characteristic
300	C₃₁×#103	C₂³	1	2	yes	—
301	C₃₁×#103	C₂³	1	1	yes	characteristic
302	C₃₁×#103	C₂³	1	2	yes	—
303	C₃₁×#103	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂×Q₈×C₃₁	—	2	1	no	—
313	C₂×Q₈×C₃₁	—	2	1	no	—
314	C₂×Q₈×C₃₁	—	2	1	no	—
315	C₂×Q₈×C₃₁	—	2	2	no	—
316	C₂×Q₈×C₃₁	—	2	1	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	4	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	4	2	no	—
322	C₂×Q₈×C₃₁	—	4	1	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
331	C₂²×C₄×C₃₁	—	2	1	no	—
332	C₂²×C₄×C₃₁	—	2	1	no	—
333	C₂²×C₄×C₃₁	—	2	2	no	—
334	C₂²×C₄×C₃₁	—	2	2	no	—
335	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
339	Q₁₆×C₃₁	—	2	2	no	—
340	Q₁₆×C₃₁	—	2	2	no	—
341	Q₁₆×C₃₁	—	4	1	no	—
342	Q₁₆×C₃₁	—	4	2	no	—
343	Q₁₆×C₃₁	—	4	2	no	—
344	Q₁₆×C₃₁	—	4	1	no	—
345	M₁₆×C₃₁	—	4	2	no	—
346	M₁₆×C₃₁	—	4	2	no	—
347	C₂×C₈×C₃₁	—	4	2	no	—
348	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
352	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₃₁	—	2	1	no	—
355	C₄⋊C₄×C₃₁	—	2	1	no	—
356	C₄⋊C₄×C₃₁	—	2	1	no	—
357	C₄⋊C₄×C₃₁	—	2	1	no	—
358	C₄⋊C₄×C₃₁	—	2	1	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	1	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	1	no	—
365	C₄⋊C₄×C₃₁	—	2	1	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	1	no	—
369	C₄⋊C₄×C₃₁	—	2	1	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	1	no	—
372	C₄⋊C₄×C₃₁	—	2	1	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
379	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₂²⋊C₄×C₃₁	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	—	2	1	no	—
407	C₂²⋊C₄×C₃₁	—	2	1	no	—
408	C₂²⋊C₄×C₃₁	—	2	2	no	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
415	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
416	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
417	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
418	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
419	C₄²×C₃₁	—	2	1	no	—
420	C₄²×C₃₁	—	2	1	no	—
421	C₄²×C₃₁	—	2	1	no	—
422	C₄²×C₃₁	—	2	1	no	—
423	C₄²×C₃₁	—	2	2	no	—
424	C₄²×C₃₁	—	2	2	no	—
425	C₄²×C₃₁	—	2	2	no	—
426	C₄²×C₃₁	—	2	2	no	—
427	C₄²×C₃₁	—	2	2	no	—
428	C₄²×C₃₁	—	2	1	no	—
429	C₄²×C₃₁	—	2	1	no	—
430	C₄²×C₃₁	—	2	2	no	—
431	C₄²×C₃₁	—	2	2	no	—
432	C₄²×C₃₁	—	2	2	no	—
433	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
436	C₄²×C₃₁	C₂⁴	1	2	yes	—
437	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
438	#62192	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
440	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
441	Q₈×C₃₁	—	2	2	no	—
442	Q₈×C₃₁	—	2	1	no	—
443	Q₈×C₃₁	—	2	1	no	—
444	Q₈×C₃₁	—	2	1	no	—
445	Q₈×C₃₁	—	2	2	no	—
446	Q₈×C₃₁	—	2	1	no	—
447	Q₈×C₃₁	—	2	1	no	—
448	Q₈×C₃₁	—	2	1	no	—
449	Q₈×C₃₁	—	2	1	no	—
450	Q₈×C₃₁	—	2	2	no	—
451	Q₈×C₃₁	—	4	4	no	—
452	Q₈×C₃₁	—	4	2	no	—
453	Q₈×C₃₁	—	4	2	no	—
454	Q₈×C₃₁	—	4	2	no	—
455	Q₈×C₃₁	—	8	1	no	—
456	Q₈×C₃₁	—	8	1	no	—
457	Q₈×C₃₁	—	8	2	no	—
458	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
459	D₄×C₃₁	—	2	2	no	—
460	D₄×C₃₁	—	4	2	no	—
461	C₂×C₄×C₃₁	—	2	1	no	—
462	C₂×C₄×C₃₁	—	2	2	no	—
463	C₂×C₄×C₃₁	—	2	1	no	—
464	C₂×C₄×C₃₁	—	2	2	no	—
465	C₂×C₄×C₃₁	—	2	2	no	—
466	C₂×C₄×C₃₁	—	2	1	no	—
467	C₂×C₄×C₃₁	—	2	1	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	2	1	no	—
470	C₂×C₄×C₃₁	—	2	2	no	—
471	C₂×C₄×C₃₁	—	2	2	no	—
472	C₂×C₄×C₃₁	—	2	1	no	—
473	C₂×C₄×C₃₁	—	2	1	no	—
474	C₂×C₄×C₃₁	—	2	1	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	2	2	no	—
477	C₂×C₄×C₃₁	—	2	1	no	—
478	C₂×C₄×C₃₁	—	4	1	no	—
479	C₂×C₄×C₃₁	—	4	2	no	—
480	C₂×C₄×C₃₁	—	4	4	no	—
481	C₂×C₄×C₃₁	—	4	2	no	—
482	C₂×C₄×C₃₁	—	8	2	no	—
483	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
487	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
492	C₈×C₃₁	—	2	1	no	—
493	C₈×C₃₁	—	2	1	no	—
494	C₈×C₃₁	—	2	1	no	—
495	C₈×C₃₁	—	2	2	no	—
496	C₈×C₃₁	—	2	1	no	—
497	C₈×C₃₁	—	2	2	no	—
498	#3555	C₂×C₃₁	1	1	yes	characteristic
499	#3523	C₂×C₃₁	1	1	yes	characteristic
500	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
501	#3383	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
503	#3363	C₂×C₃₁	1	1	yes	characteristic, complemented
504	#3356	C₂×C₃₁	1	1	yes	characteristic, complemented
505	#3352	C₂×C₃₁	1	2	yes	complemented
506	#3349	C₂×C₃₁	1	2	yes	complemented
507	#3342	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#3328	C₂×C₃₁	1	1	yes	characteristic, complemented
509	#3328	C₂×C₃₁	1	2	yes	complemented
510	#3312	C₂×C₃₁	1	2	yes	complemented
511	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3261	C₂×C₃₁	1	2	yes	complemented
513	#3255	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#3242	C₂×C₃₁	1	2	yes	complemented
515	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3127	C₂×C₃₁	1	2	yes	complemented
517	#3104	C₂×C₃₁	1	1	yes	characteristic, complemented
518	#3082	C₂×C₃₁	1	2	yes	complemented
519	#3078	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#2993	C₂×C₃₁	1	1	yes	characteristic
521	C₂²×C₃₁	—	2	1	no	—
522	C₂²×C₃₁	—	2	2	no	—
523	C₂²×C₃₁	—	2	2	no	—
524	C₂²×C₃₁	—	2	1	no	—
525	C₂²×C₃₁	—	2	1	no	—
526	C₂²×C₃₁	—	2	2	no	—
527	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
528	C₄×C₃₁	—	2	1	no	—
529	C₄×C₃₁	—	2	1	no	—
530	C₄×C₃₁	—	2	2	no	—
531	C₄×C₃₁	—	2	2	no	—
532	C₄×C₃₁	—	2	1	no	—
533	C₄×C₃₁	—	2	2	no	—
534	C₄×C₃₁	—	2	1	no	—
535	C₄×C₃₁	—	2	2	no	—
536	C₄×C₃₁	—	4	1	no	—
537	C₄×C₃₁	—	4	1	no	—
538	C₄×C₃₁	—	4	1	no	—
539	C₄×C₃₁	—	4	2	no	—
540	C₄×C₃₁	—	4	1	no	—
541	C₄×C₃₁	—	4	1	no	—
542	C₄×C₃₁	—	4	2	no	—
543	C₄×C₃₁	—	4	1	no	—
544	C₄×C₃₁	—	4	1	no	—
545	C₄×C₃₁	—	4	2	no	—
546	C₄×C₃₁	—	4	2	no	—
547	C₄×C₃₁	#578	1	2	yes	—
548	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
549	C₄×C₃₁	#585	1	1	yes	characteristic
550	#563	—	2	2	no	—
551	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
552	#557	—	2	1	no	—
553	#557	—	2	1	no	—
554	#557	C₂²×C₃₁	1	1	yes	characteristic
555	#557	C₂²×C₃₁	1	1	yes	characteristic
556	#557	C₂²×C₃₁	1	1	yes	characteristic
557	#556	—	2	1	no	—
558	#556	—	2	1	no	—
559	#556	C₂²×C₃₁	1	1	yes	characteristic
560	#556	C₂²×C₃₁	1	2	yes	—
561	#556	C₂²×C₃₁	1	1	yes	characteristic
562	#554	C₂²×C₃₁	1	1	yes	characteristic
563	#552	—	2	2	no	—
564	#552	C₂²×C₃₁	1	2	yes	—
565	#552	C₂²×C₃₁	1	2	yes	—
566	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
567	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
568	#544	C₂²×C₃₁	1	2	yes	—
569	#542	—	2	1	no	—
570	#541	—	2	2	no	—
571	#541	—	2	2	no	—
572	#541	—	2	1	no	—
573	#541	C₂²×C₃₁	1	2	yes	—
574	#541	C₂²×C₃₁	1	2	yes	—
575	#533	—	2	1	no	—
576	#533	C₂²×C₃₁	1	1	yes	characteristic
577	#533	C₂²×C₃₁	1	1	yes	characteristic
578	#533	C₂²×C₃₁	1	1	yes	characteristic
579	#529	—	2	1	no	—
580	#529	C₂²×C₃₁	1	1	yes	characteristic
581	#519	C₂²×C₃₁	1	2	yes	—
582	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
583	#501	C₂²×C₃₁	1	2	yes	—
584	#500	C₂²×C₃₁	1	1	yes	characteristic
585	#499	C₂²×C₃₁	1	2	yes	—
586	#498	C₂²×C₃₁	1	1	yes	characteristic
587	#491	C₂²×C₃₁	1	2	yes	—
588	#487	C₂²×C₃₁	1	2	yes	—
589	#487	C₂²×C₃₁	1	1	yes	characteristic
590	#487	C₂²×C₃₁	1	1	yes	characteristic
591	#485	C₂²×C₃₁	1	2	yes	—
592	#485	C₂²×C₃₁	1	2	yes	—
593	#485	C₂²×C₃₁	1	2	yes	—
594	#485	C₂²×C₃₁	1	2	yes	—
595	#485	C₂²×C₃₁	1	2	yes	—
596	#485	C₂²×C₃₁	1	2	yes	—
597	#484	C₂²×C₃₁	1	1	yes	characteristic
598	#484	C₂²×C₃₁	1	1	yes	characteristic
599	#484	C₂²×C₃₁	1	2	yes	—
600	#483	C₂²×C₃₁	1	2	yes	—
601	#479	C₂²×C₃₁	1	2	yes	—
602	#479	C₂²×C₃₁	1	2	yes	—
603	#479	C₂²×C₃₁	1	2	yes	—
604	#479	C₂²×C₃₁	1	2	yes	—
605	#479	C₂²×C₃₁	1	2	yes	—
606	#479	C₂²×C₃₁	1	2	yes	—
607	#479	C₂²×C₃₁	1	2	yes	—
608	#479	C₂²×C₃₁	1	2	yes	—
609	#477	C₂²×C₃₁	1	1	yes	characteristic
610	#477	C₂²×C₃₁	1	1	yes	characteristic
611	#477	C₂²×C₃₁	1	1	yes	characteristic
612	#477	C₂²×C₃₁	1	2	yes	—
613	#477	C₂²×C₃₁	1	1	yes	characteristic
614	#475	C₂²×C₃₁	1	1	yes	characteristic
615	#475	C₂²×C₃₁	1	2	yes	—
616	#475	C₂²×C₃₁	1	1	yes	characteristic
617	#475	C₂²×C₃₁	1	2	yes	—
618	#475	C₂²×C₃₁	1	1	yes	characteristic
619	#475	C₂²×C₃₁	1	1	yes	characteristic
620	#470	C₂²×C₃₁	1	2	yes	—
621	#470	C₂²×C₃₁	1	2	yes	—
622	#470	C₂²×C₃₁	1	2	yes	—
623	#470	C₂²×C₃₁	1	2	yes	—
624	#467	C₂²×C₃₁	1	2	yes	—
625	#467	C₂²×C₃₁	1	2	yes	—
626	#462	C₂²×C₃₁	1	1	yes	characteristic
627	#462	C₂²×C₃₁	1	2	yes	—
628	#462	C₂²×C₃₁	1	1	yes	characteristic
629	#462	C₂²×C₃₁	1	1	yes	characteristic
630	#462	C₂²×C₃₁	1	2	yes	—
631	#462	C₂²×C₃₁	1	1	yes	characteristic
632	#462	C₂²×C₃₁	1	2	yes	—
633	#451	C₂²×C₃₁	1	1	yes	characteristic
634	#451	C₂²×C₃₁	1	2	yes	—
635	#451	C₂²×C₃₁	1	2	yes	—
636	#451	C₂²×C₃₁	1	1	yes	characteristic
637	#446	C₂²×C₃₁	1	1	yes	characteristic
638	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
639	#441	C₂²×C₃₁	1	2	yes	—
640	#441	C₂²×C₃₁	1	2	yes	—
641	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
642	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
643	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
644	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
645	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
646	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
647	#436	C₂²×C₃₁	1	2	yes	—
648	#436	C₂²×C₃₁	1	1	yes	characteristic
649	#435	C₂²×C₃₁	1	2	yes	—
650	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
651	#433	C₂²×C₃₁	1	2	yes	—
652	#431	C₂²×C₃₁	1	1	yes	characteristic
653	#428	C₂²×C₃₁	1	2	yes	—
654	#428	C₂²×C₃₁	1	2	yes	—
655	#427	C₂²×C₃₁	1	2	yes	—
656	#424	C₂²×C₃₁	1	2	yes	—
657	#423	C₂²×C₃₁	1	1	yes	characteristic
658	#419	C₂²×C₃₁	1	2	yes	—
659	#419	C₂²×C₃₁	1	2	yes	—
660	C₂×#103	C₂²×C₃₁	1	2	yes	—
661	C₂×C₃₁	—	4	1	no	—
662	C₂×C₃₁	—	4	2	no	—
663	C₂×C₃₁	#3489	1	1	yes	characteristic
664	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
665	C₂×C₃₁	#3586	1	1	yes	characteristic
666	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
667	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
668	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
669	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
670	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
671	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
672	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
673	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
674	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
675	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
676	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
677	C₄⋊Q₈	—	2	1	no	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	—	2	2	no	—
681	C₄⋊Q₈	—	2	2	no	—
682	C₄⋊Q₈	—	2	1	no	—
683	C₄⋊Q₈	—	2	2	no	—
684	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
685	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
686	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
687	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
688	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
689	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
690	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
692	#126	—	2	2	no	—
693	#126	—	2	2	no	—
694	#126	—	2	2	no	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	D₄×C₃₁	1	2	yes	—
703	#125	—	2	1	no	—
704	#125	—	2	2	no	—
705	#125	—	2	2	no	—
706	#125	—	2	2	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	1	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	1	no	—
716	#125	—	2	1	no	—
717	#125	D₄×C₃₁	1	1	yes	characteristic
718	#125	C₂³×C₃₁	1	2	yes	—
719	#125	C₂³×C₃₁	1	2	yes	—
720	#125	C₂³×C₃₁	1	2	yes	—
721	#124	—	2	1	no	—
722	#124	—	2	1	no	—
723	#124	—	2	2	no	—
724	#124	D₄×C₃₁	1	1	yes	characteristic
725	#123	—	2	2	no	—
726	#123	—	2	2	no	—
727	#123	D₄×C₃₁	1	2	yes	—
728	C₂²⋊Q₈	—	2	1	no	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
739	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
740	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
741	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
742	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
743	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
744	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
745	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
746	#121	D₄×C₃₁	1	1	yes	characteristic
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	2	no	—
750	C₄×Q₈	—	2	2	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	2	no	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
767	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
768	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
769	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
772	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
773	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	C₂³×C₃₁	1	2	yes	—
778	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
779	#117	—	2	1	no	—
780	#117	—	2	1	no	—
781	#117	—	2	2	no	—
782	#117	—	2	2	no	—
783	#117	—	2	2	no	—
784	#117	—	2	2	no	—
785	#117	C₂³×C₃₁	1	2	yes	—
786	#117	C₂³×C₃₁	1	2	yes	—
787	#117	C₂³×C₃₁	1	2	yes	—
788	#117	C₂³×C₃₁	1	2	yes	—
789	C₂×C₄⋊C₄	—	2	1	no	—
790	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
791	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
792	C₂×C₄²	—	2	1	no	—
793	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
794	#107	C₂³×C₃₁	1	1	yes	characteristic
795	#107	C₂³×C₃₁	1	2	yes	—
796	#107	C₂³×C₃₁	1	2	yes	—
797	#107	C₂³×C₃₁	1	1	yes	characteristic
798	#107	C₂³×C₃₁	1	2	yes	—
799	#107	C₂³×C₃₁	1	1	yes	characteristic
800	#107	C₂³×C₃₁	1	1	yes	characteristic
801	#107	C₂³×C₃₁	1	2	yes	—
802	#106	C₂³×C₃₁	1	2	yes	—
803	#106	C₂³×C₃₁	1	2	yes	—
804	#106	C₂³×C₃₁	1	2	yes	—
805	#106	C₂³×C₃₁	1	2	yes	—
806	#106	C₂³×C₃₁	1	2	yes	—
807	#106	C₂³×C₃₁	1	2	yes	—
808	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
809	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
813	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
814	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
815	#103	C₂³×C₃₁	1	1	yes	characteristic
816	#103	C₂³×C₃₁	1	2	yes	—
817	#103	C₂³×C₃₁	1	2	yes	—
818	#103	C₂³×C₃₁	1	2	yes	—
819	#103	C₂³×C₃₁	1	1	yes	characteristic
820	#103	C₂³×C₃₁	1	2	yes	—
821	#103	C₂³×C₃₁	1	2	yes	—
822	#103	C₂³×C₃₁	1	2	yes	—
823	#103	C₂³×C₃₁	1	2	yes	—
824	#103	C₂³×C₃₁	1	2	yes	—
825	#103	C₂³×C₃₁	1	1	yes	characteristic
826	#103	C₂³×C₃₁	1	1	yes	characteristic
827	#103	C₂³×C₃₁	1	1	yes	characteristic
828	#103	C₂³×C₃₁	1	1	yes	characteristic
829	#103	C₂³×C₃₁	1	2	yes	—
830	#103	C₂³×C₃₁	1	1	yes	characteristic
831	#103	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	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
836	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
837	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
838	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
839	#97	C₂³×C₃₁	1	2	yes	—
840	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
841	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₄×C₈	C₂³×C₃₁	1	2	yes	—
843	C₃₁	#62192	1	1	yes	characteristic, direct product factor, Sylow
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	2	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	1	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	2	4	no	—
853	C₂×Q₈	—	4	2	no	—
854	C₂×Q₈	—	4	1	no	—
855	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
856	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
857	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
858	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
859	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
860	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
861	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
862	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
868	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
871	Q₁₆	—	2	2	no	—
872	Q₁₆	—	2	2	no	—
873	Q₁₆	—	4	1	no	—
874	Q₁₆	—	4	2	no	—
875	Q₁₆	—	4	2	no	—
876	Q₁₆	—	4	1	no	—
877	M₁₆	—	4	2	no	—
878	M₁₆	—	4	2	no	—
879	C₂×C₈	—	4	2	no	—
880	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
881	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
882	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
883	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
884	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
885	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
924	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
925	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
926	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
927	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
928	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
931	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
932	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
935	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
947	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
948	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
949	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
950	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
951	C₄²	—	2	1	no	—
952	C₄²	—	2	1	no	—
953	C₄²	—	2	1	no	—
954	C₄²	—	2	1	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
966	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
967	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₄²	C₂⁴×C₃₁	1	2	yes	—
969	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
971	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
972	Q₈	—	2	2	no	—
973	Q₈	—	2	1	no	—
974	Q₈	—	2	1	no	—
975	Q₈	—	2	1	no	—
976	Q₈	—	2	1	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	1	no	—
980	Q₈	—	2	1	no	—
981	Q₈	—	2	2	no	—
982	Q₈	—	4	4	no	—
983	Q₈	—	4	2	no	—
984	Q₈	—	4	2	no	—
985	Q₈	—	4	2	no	—
986	Q₈	—	8	1	no	—
987	Q₈	—	8	1	no	—
988	Q₈	—	8	2	no	—
989	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
990	D₄	—	2	2	no	—
991	D₄	—	4	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	4	1	no	—
1010	C₂×C₄	—	4	2	no	—
1011	C₂×C₄	—	4	4	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	8	2	no	—
1014	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1015	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1016	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1018	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1019	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1020	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1022	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1023	C₈	—	2	1	no	—
1024	C₈	—	2	1	no	—
1025	C₈	—	2	1	no	—
1026	C₈	—	2	2	no	—
1027	C₈	—	2	1	no	—
1028	C₈	—	2	2	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	2	1	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	2	no	—
1033	C₂²	—	2	1	no	—
1034	C₂²	—	2	2	no	—
1035	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1036	C₄	—	2	2	no	—
1037	C₄	—	2	1	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	1	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	C₃₁×#578	1	2	yes	—
1056	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1057	C₄	C₃₁×#585	1	1	yes	characteristic
1058	C₂	—	4	1	no	—
1059	C₂	—	4	2	no	—
1060	C₂	C₃₁×#3489	1	1	yes	characteristic
1061	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1062	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#121	D₄
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
3. C₃₁×#3387	C₂	semidirect
4. C₃₁×#3383	C₂	semidirect
5. C₃₁×#3374	C₂	semidirect
6. C₃₁×#3363	C₂	semidirect
7. C₃₁×#3356	C₂	semidirect
8. C₃₁×#3352	C₂	semidirect
9. C₃₁×#3349	C₂	semidirect
10. C₃₁×#3342	C₂	semidirect
11. C₃₁×#3328	C₂	semidirect
12. C₃₁×#3328	C₂	semidirect
13. C₃₁×#3312	C₂	semidirect
14. C₃₁×#3299	C₂	semidirect
15. C₃₁×#3261	C₂	semidirect
16. C₃₁×#3255	C₂	semidirect
17. C₃₁×#3242	C₂	semidirect
18. C₃₁×#3231	C₂	semidirect
19. C₃₁×#3127	C₂	semidirect
20. C₃₁×#3104	C₂	semidirect
21. C₃₁×#3082	C₂	semidirect
22. C₃₁×#3078	C₂	semidirect
438. #62192	C₃₁	direct (N × H)
500. #3387	C₂×C₃₁	semidirect
501. #3383	C₂×C₃₁	semidirect
502. #3374	C₂×C₃₁	semidirect
503. #3363	C₂×C₃₁	semidirect
504. #3356	C₂×C₃₁	semidirect
505. #3352	C₂×C₃₁	semidirect
506. #3349	C₂×C₃₁	semidirect
507. #3342	C₂×C₃₁	semidirect
508. #3328	C₂×C₃₁	semidirect
509. #3328	C₂×C₃₁	semidirect
510. #3312	C₂×C₃₁	semidirect
511. #3299	C₂×C₃₁	semidirect
512. #3261	C₂×C₃₁	semidirect
513. #3255	C₂×C₃₁	semidirect
514. #3242	C₂×C₃₁	semidirect
515. #3231	C₂×C₃₁	semidirect
516. #3127	C₂×C₃₁	semidirect
517. #3104	C₂×C₃₁	semidirect
518. #3082	C₂×C₃₁	semidirect
519. #3078	C₂×C₃₁	semidirect
843. C₃₁	#62192	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×#3523	2
C₃₁×#3387	2
C₃₁×#3383	2
C₃₁×#3374	2
C₃₁×#3363	2
C₃₁×#3356	2
C₃₁×#3352	2
C₃₁×#3349	2
C₃₁×#3342	2
C₃₁×#3328	2
C₃₁×#3312	2
C₃₁×#3299	2
C₃₁×#3261	2
C₃₁×#3255	2
C₃₁×#3242	2
C₃₁×#3231	2
C₃₁×#3127	2
C₃₁×#3104	2
C₃₁×#3082	2
C₃₁×#3078	2
C₃₁×#2993	2
#62192	31

Subgroups — C31×#62192 #21518951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62192 #21518951