Subgroups — C₃₁×#61785 #21518544

Order 7936.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3351	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3337	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3326	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3200	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3099	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3097	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#562	—	2	2	no	—
25	C₃₁×#559	—	2	2	no	—
26	C₃₁×#556	—	2	1	no	—
27	C₃₁×#555	—	2	1	no	—
28	C₃₁×#555	C₂²	1	1	yes	characteristic
29	C₃₁×#555	C₂²	1	1	yes	characteristic
30	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#553	—	2	1	no	—
33	C₃₁×#553	C₂²	1	2	yes	—
34	C₃₁×#553	C₂²	1	2	yes	—
35	C₃₁×#552	C₂²	1	2	yes	complemented
36	C₃₁×#550	—	2	1	no	—
37	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#548	C₂²	1	2	yes	complemented
39	C₃₁×#547	C₂²	1	1	yes	characteristic
40	C₃₁×#547	C₂²	1	1	yes	characteristic
41	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#542	—	2	2	no	—
44	C₃₁×#540	—	2	1	no	—
45	C₃₁×#538	—	2	2	no	—
46	C₃₁×#537	C₂²	1	2	yes	—
47	C₃₁×#536	C₂²	1	2	yes	—
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	C₂²	1	1	yes	characteristic
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	1	no	—
54	C₃₁×#525	—	2	1	no	—
55	C₃₁×#520	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#499	C₂²	1	2	yes	complemented
59	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#488	C₂²	1	2	yes	complemented
61	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#485	C₂²	1	2	yes	—
64	C₃₁×#485	C₂²	1	2	yes	—
65	C₃₁×#485	C₂²	1	2	yes	—
66	C₃₁×#485	C₂²	1	2	yes	complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#484	C₂²	1	1	yes	characteristic
70	C₃₁×#484	C₂²	1	2	yes	complemented
71	C₃₁×#483	C₂²	1	2	yes	—
72	C₃₁×#483	C₂²	1	2	yes	complemented
73	C₃₁×#483	C₂²	1	2	yes	complemented
74	C₃₁×#482	C₂²	1	2	yes	—
75	C₃₁×#482	C₂²	1	2	yes	—
76	C₃₁×#482	C₂²	1	2	yes	—
77	C₃₁×#482	C₂²	1	2	yes	complemented
78	C₃₁×#481	C₂²	1	2	yes	—
79	C₃₁×#481	C₂²	1	1	yes	characteristic
80	C₃₁×#481	C₂²	1	2	yes	complemented
81	C₃₁×#480	C₂²	1	2	yes	—
82	C₃₁×#479	C₂²	1	2	yes	complemented
83	C₃₁×#479	C₂²	1	2	yes	complemented
84	C₃₁×#478	C₂²	1	1	yes	characteristic
85	C₃₁×#478	C₂²	1	1	yes	characteristic
86	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
87	C₃₁×#476	C₂²	1	1	yes	characteristic
88	C₃₁×#476	C₂²	1	1	yes	characteristic
89	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#469	C₂²	1	2	yes	—
93	C₃₁×#468	C₂²	1	2	yes	—
94	C₃₁×#468	C₂²	1	2	yes	—
95	C₃₁×#468	C₂²	1	2	yes	—
96	C₃₁×#466	C₂²	1	2	yes	—
97	C₃₁×#465	C₂²	1	2	yes	—
98	C₃₁×#465	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	—
100	C₃₁×#463	C₂²	1	1	yes	characteristic
101	C₃₁×#463	C₂²	1	1	yes	characteristic
102	C₃₁×#461	C₂²	1	1	yes	characteristic
103	C₃₁×#461	C₂²	1	1	yes	characteristic
104	C₃₁×#450	C₂²	1	2	yes	—
105	C₃₁×#450	C₂²	1	1	yes	characteristic
106	C₃₁×#449	C₂²	1	2	yes	—
107	C₃₁×#449	C₂²	1	2	yes	—
108	C₃₁×#448	C₂²	1	2	yes	—
109	C₃₁×#448	C₂²	1	2	yes	—
110	C₃₁×#447	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
117	C₃₁×#436	C₂²	1	2	yes	complemented
118	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
120	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
122	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#431	C₂²	1	1	yes	characteristic
124	C₃₁×#431	C₂²	1	1	yes	characteristic
125	C₃₁×#428	C₂²	1	2	yes	complemented
126	C₃₁×#428	C₂²	1	2	yes	complemented
127	C₃₁×#427	C₂²	1	2	yes	complemented
128	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
129	C₃₁×#419	C₂²	1	2	yes	complemented
130	C₃₁×#417	C₂²	1	2	yes	complemented
131	C₃₁×#416	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
133	C₃₁×#408	C₂²	1	2	yes	—
134	C₃₁×#408	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	—	2	1	no	—
142	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
152	C₃₁×C₄⋊Q₈	—	2	2	no	—
153	C₃₁×C₄⋊Q₈	—	2	1	no	—
154	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#127	—	2	2	no	—
160	C₃₁×#127	D₄	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	1	no	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	—	2	1	no	—
167	C₃₁×#125	—	2	1	no	—
168	C₃₁×#125	C₂³	1	1	yes	characteristic
169	C₃₁×#125	C₂³	1	2	yes	—
170	C₃₁×#124	—	2	2	no	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	2	no	—
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	D₄	1	2	yes	—
177	C₃₁×#124	C₂³	1	1	yes	characteristic
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	1	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
198	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×#121	—	2	1	no	—
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	D₄	1	1	yes	characteristic
212	C₃₁×#121	D₄	1	1	yes	characteristic
213	C₃₁×#121	D₄	1	2	yes	—
214	C₃₁×#121	C₂³	1	1	yes	characteristic
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#120	—	2	2	no	—
221	C₃₁×#120	—	2	2	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	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	2	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	—	2	1	no	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₃₁×#117	C₂³	1	2	yes	—
256	C₃₁×#117	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	1	yes	characteristic
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	2	yes	—
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
277	C₃₁×#106	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	1	yes	characteristic
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	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	1	yes	characteristic
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	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	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
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×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	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	C₂⁴×C₃₁	—	2	1	no	—
313	#41×C₃₁	—	4	2	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	4	2	no	—
317	#41×C₃₁	—	8	2	no	—
318	#41×C₃₁	—	8	2	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	4	2	no	—
324	C₂×Q₈×C₃₁	—	4	2	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	4	1	no	—
337	C₂×D₄×C₃₁	—	4	1	no	—
338	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	8	2	no	—
359	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
364	SD₁₆×C₃₁	—	4	1	no	—
365	SD₁₆×C₃₁	—	4	2	no	—
366	SD₁₆×C₃₁	—	4	1	no	—
367	SD₁₆×C₃₁	—	4	2	no	—
368	D₈×C₃₁	—	4	1	no	—
369	D₈×C₃₁	—	4	1	no	—
370	M₁₆×C₃₁	—	4	2	no	—
371	M₁₆×C₃₁	—	4	2	no	—
372	C₂×C₈×C₃₁	—	4	2	no	—
373	C₂×C₈×C₃₁	—	4	2	no	—
374	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
376	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
378	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	1	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	1	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	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	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	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	—	2	2	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	1	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	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₄²×C₃₁	—	2	2	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	2	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	1	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	1	yes	characteristic
446	#61785	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	—	2	1	no	—
450	C₂³×C₃₁	—	4	2	no	—
451	C₂³×C₃₁	—	8	1	no	—
452	C₂³×C₃₁	—	8	1	no	—
453	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
454	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
455	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
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	1	no	—
463	Q₈×C₃₁	—	8	1	no	—
464	Q₈×C₃₁	—	8	2	no	—
465	D₄×C₃₁	—	2	2	no	—
466	D₄×C₃₁	—	2	2	no	—
467	D₄×C₃₁	—	2	1	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	—	2	1	no	—
473	D₄×C₃₁	—	4	2	no	—
474	D₄×C₃₁	—	4	2	no	—
475	D₄×C₃₁	—	4	2	no	—
476	D₄×C₃₁	—	4	2	no	—
477	D₄×C₃₁	—	4	2	no	—
478	D₄×C₃₁	—	8	1	no	—
479	D₄×C₃₁	—	8	2	no	—
480	D₄×C₃₁	—	8	2	no	—
481	D₄×C₃₁	—	8	2	no	—
482	D₄×C₃₁	—	8	2	no	—
483	D₄×C₃₁	—	8	2	no	—
484	D₄×C₃₁	—	8	2	no	—
485	C₂×C₄×C₃₁	—	2	2	no	—
486	C₂×C₄×C₃₁	—	2	2	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	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	2	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	—	2	2	no	—
501	C₂×C₄×C₃₁	—	4	1	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	1	no	—
506	C₂×C₄×C₃₁	—	8	1	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	2	no	—
509	C₂×C₄×C₃₁	—	8	1	no	—
510	C₂×C₄×C₃₁	—	8	2	no	—
511	C₂×C₄×C₃₁	—	8	2	no	—
512	C₂×C₄×C₃₁	—	8	2	no	—
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
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	C₈×C₃₁	—	2	2	no	—
527	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3506	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3357	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3354	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3351	C₂×C₃₁	1	2	yes	complemented
532	#3341	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3337	C₂×C₃₁	1	2	yes	complemented
534	#3335	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3329	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3326	C₂×C₃₁	1	2	yes	complemented
538	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3301	C₂×C₃₁	1	2	yes	complemented
540	#3298	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3233	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3200	C₂×C₃₁	1	2	yes	complemented
544	#3198	C₂×C₃₁	1	2	yes	complemented
545	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3101	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3099	C₂×C₃₁	1	2	yes	complemented
548	#3097	C₂×C₃₁	1	2	yes	complemented
549	#2979	C₂×C₃₁	1	1	yes	characteristic, complemented
550	C₂²×C₃₁	—	2	1	no	—
551	C₂²×C₃₁	—	2	2	no	—
552	C₂²×C₃₁	—	2	2	no	—
553	C₂²×C₃₁	—	2	2	no	—
554	C₂²×C₃₁	—	2	1	no	—
555	C₂²×C₃₁	—	2	2	no	—
556	C₂²×C₃₁	—	2	1	no	—
557	C₂²×C₃₁	—	2	2	no	—
558	C₂²×C₃₁	—	2	2	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	1	no	—
562	C₂²×C₃₁	—	4	1	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	4	1	no	—
566	C₂²×C₃₁	—	4	1	no	—
567	C₂²×C₃₁	—	4	1	no	—
568	C₂²×C₃₁	—	8	4	no	—
569	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
570	C₄×C₃₁	—	2	1	no	—
571	C₄×C₃₁	—	2	1	no	—
572	C₄×C₃₁	—	2	2	no	—
573	C₄×C₃₁	—	2	1	no	—
574	C₄×C₃₁	—	2	2	no	—
575	C₄×C₃₁	—	2	1	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	2	no	—
578	C₄×C₃₁	—	4	2	no	—
579	C₄×C₃₁	—	4	2	no	—
580	C₄×C₃₁	—	4	1	no	—
581	C₄×C₃₁	—	4	1	no	—
582	C₄×C₃₁	—	4	1	no	—
583	C₄×C₃₁	—	4	1	no	—
584	C₄×C₃₁	—	4	2	no	—
585	C₄×C₃₁	#577	1	2	yes	—
586	C₄×C₃₁	#585	1	1	yes	characteristic
587	C₄×C₃₁	#585	1	1	yes	characteristic
588	#562	—	2	2	no	—
589	#559	—	2	2	no	—
590	#556	—	2	1	no	—
591	#555	—	2	1	no	—
592	#555	C₂²×C₃₁	1	1	yes	characteristic
593	#555	C₂²×C₃₁	1	1	yes	characteristic
594	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
595	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
596	#553	—	2	1	no	—
597	#553	C₂²×C₃₁	1	2	yes	—
598	#553	C₂²×C₃₁	1	2	yes	—
599	#552	C₂²×C₃₁	1	2	yes	complemented
600	#550	—	2	1	no	—
601	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#548	C₂²×C₃₁	1	2	yes	complemented
603	#547	C₂²×C₃₁	1	1	yes	characteristic
604	#547	C₂²×C₃₁	1	1	yes	characteristic
605	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
606	#544	—	2	1	no	—
607	#542	—	2	2	no	—
608	#540	—	2	1	no	—
609	#538	—	2	2	no	—
610	#537	C₂²×C₃₁	1	2	yes	—
611	#536	C₂²×C₃₁	1	2	yes	—
612	#535	C₂²×C₃₁	1	2	yes	—
613	#533	C₂²×C₃₁	1	1	yes	characteristic
614	#533	C₂²×C₃₁	1	1	yes	characteristic
615	#532	C₂²×C₃₁	1	1	yes	characteristic
616	#529	C₂²×C₃₁	1	1	yes	characteristic
617	#525	—	2	1	no	—
618	#525	—	2	1	no	—
619	#520	C₂²×C₃₁	1	2	yes	—
620	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
621	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#499	C₂²×C₃₁	1	2	yes	complemented
623	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#488	C₂²×C₃₁	1	2	yes	complemented
625	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#485	C₂²×C₃₁	1	2	yes	—
628	#485	C₂²×C₃₁	1	2	yes	—
629	#485	C₂²×C₃₁	1	2	yes	—
630	#485	C₂²×C₃₁	1	2	yes	complemented
631	#485	C₂²×C₃₁	1	2	yes	complemented
632	#485	C₂²×C₃₁	1	2	yes	complemented
633	#484	C₂²×C₃₁	1	1	yes	characteristic
634	#484	C₂²×C₃₁	1	2	yes	complemented
635	#483	C₂²×C₃₁	1	2	yes	—
636	#483	C₂²×C₃₁	1	2	yes	complemented
637	#483	C₂²×C₃₁	1	2	yes	complemented
638	#482	C₂²×C₃₁	1	2	yes	—
639	#482	C₂²×C₃₁	1	2	yes	—
640	#482	C₂²×C₃₁	1	2	yes	—
641	#482	C₂²×C₃₁	1	2	yes	complemented
642	#481	C₂²×C₃₁	1	2	yes	—
643	#481	C₂²×C₃₁	1	1	yes	characteristic
644	#481	C₂²×C₃₁	1	2	yes	complemented
645	#480	C₂²×C₃₁	1	2	yes	—
646	#479	C₂²×C₃₁	1	2	yes	complemented
647	#479	C₂²×C₃₁	1	2	yes	complemented
648	#478	C₂²×C₃₁	1	1	yes	characteristic
649	#478	C₂²×C₃₁	1	1	yes	characteristic
650	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#476	C₂²×C₃₁	1	1	yes	characteristic
652	#476	C₂²×C₃₁	1	1	yes	characteristic
653	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#469	C₂²×C₃₁	1	2	yes	—
657	#468	C₂²×C₃₁	1	2	yes	—
658	#468	C₂²×C₃₁	1	2	yes	—
659	#468	C₂²×C₃₁	1	2	yes	—
660	#466	C₂²×C₃₁	1	2	yes	—
661	#465	C₂²×C₃₁	1	2	yes	—
662	#465	C₂²×C₃₁	1	2	yes	—
663	#465	C₂²×C₃₁	1	2	yes	—
664	#463	C₂²×C₃₁	1	1	yes	characteristic
665	#463	C₂²×C₃₁	1	1	yes	characteristic
666	#461	C₂²×C₃₁	1	1	yes	characteristic
667	#461	C₂²×C₃₁	1	1	yes	characteristic
668	#450	C₂²×C₃₁	1	2	yes	—
669	#450	C₂²×C₃₁	1	1	yes	characteristic
670	#449	C₂²×C₃₁	1	2	yes	—
671	#449	C₂²×C₃₁	1	2	yes	—
672	#448	C₂²×C₃₁	1	2	yes	—
673	#448	C₂²×C₃₁	1	2	yes	—
674	#447	C₂²×C₃₁	1	1	yes	characteristic
675	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
676	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
677	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
678	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
679	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
680	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
681	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
683	#436	C₂²×C₃₁	1	2	yes	complemented
684	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
686	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#431	C₂²×C₃₁	1	1	yes	characteristic
688	#431	C₂²×C₃₁	1	1	yes	characteristic
689	#428	C₂²×C₃₁	1	2	yes	complemented
690	#428	C₂²×C₃₁	1	2	yes	complemented
691	#427	C₂²×C₃₁	1	2	yes	complemented
692	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
693	#419	C₂²×C₃₁	1	2	yes	complemented
694	#417	C₂²×C₃₁	1	2	yes	complemented
695	#416	C₂²×C₃₁	1	2	yes	complemented
696	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
697	#408	C₂²×C₃₁	1	2	yes	—
698	#408	C₂²×C₃₁	1	2	yes	—
699	C₂×C₃₁	—	4	2	no	—
700	C₂×C₃₁	—	4	2	no	—
701	C₂×C₃₁	—	4	1	no	—
702	C₂×C₃₁	—	8	1	no	—
703	C₂×C₃₁	—	8	1	no	—
704	C₂×C₃₁	—	8	1	no	—
705	C₂×C₃₁	#3485	1	1	yes	characteristic
706	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
707	C₂×C₃₁	#3584	1	1	yes	characteristic
708	C₂×#41	—	2	1	no	—
709	C₂×#41	—	2	1	no	—
710	C₂×#41	C₂³×C₃₁	1	2	yes	—
711	C₂×#41	C₂³×C₃₁	1	2	yes	—
712	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
713	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
714	C₂³×C₄	—	2	1	no	—
715	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
719	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
722	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
723	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
724	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
725	C₄⋊Q₈	—	2	2	no	—
726	C₄⋊Q₈	—	2	1	no	—
727	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
729	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
730	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
731	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
732	#127	—	2	2	no	—
733	#127	D₄×C₃₁	1	1	yes	characteristic
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	1	no	—
738	#125	—	2	2	no	—
739	#125	—	2	1	no	—
740	#125	—	2	1	no	—
741	#125	C₂³×C₃₁	1	1	yes	characteristic
742	#125	C₂³×C₃₁	1	2	yes	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	—	2	2	no	—
746	#124	—	2	2	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	D₄×C₃₁	1	2	yes	—
750	#124	C₂³×C₃₁	1	1	yes	characteristic
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	1	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
770	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
771	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
774	#121	—	2	1	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	—	2	2	no	—
779	#121	—	2	2	no	—
780	#121	—	2	2	no	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	1	no	—
784	#121	D₄×C₃₁	1	1	yes	characteristic
785	#121	D₄×C₃₁	1	1	yes	characteristic
786	#121	D₄×C₃₁	1	2	yes	—
787	#121	C₂³×C₃₁	1	1	yes	characteristic
788	#121	C₂³×C₃₁	1	2	yes	—
789	#121	C₂³×C₃₁	1	2	yes	—
790	#121	C₂³×C₃₁	1	2	yes	—
791	#121	C₂³×C₃₁	1	2	yes	—
792	#121	C₂³×C₃₁	1	2	yes	—
793	#120	—	2	2	no	—
794	#120	—	2	2	no	—
795	C₄×Q₈	—	2	2	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
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	#117	—	2	1	no	—
821	#117	—	2	1	no	—
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	C₂³×C₃₁	1	2	yes	—
827	#117	C₂³×C₃₁	1	2	yes	—
828	#117	C₂³×C₃₁	1	2	yes	—
829	#117	C₂³×C₃₁	1	2	yes	—
830	C₂×C₄⋊C₄	—	2	1	no	—
831	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
832	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
833	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
834	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
835	C₂×C₂²⋊C₄	—	2	1	no	—
836	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
837	#107	C₂³×C₃₁	1	1	yes	characteristic
838	#107	C₂³×C₃₁	1	2	yes	—
839	#107	C₂³×C₃₁	1	1	yes	characteristic
840	#107	C₂³×C₃₁	1	2	yes	—
841	#107	C₂³×C₃₁	1	2	yes	—
842	#107	C₂³×C₃₁	1	2	yes	—
843	#106	C₂³×C₃₁	1	1	yes	characteristic
844	#106	C₂³×C₃₁	1	2	yes	—
845	#106	C₂³×C₃₁	1	2	yes	—
846	#106	C₂³×C₃₁	1	2	yes	—
847	#106	C₂³×C₃₁	1	2	yes	—
848	#106	C₂³×C₃₁	1	2	yes	—
849	#106	C₂³×C₃₁	1	1	yes	characteristic
850	#106	C₂³×C₃₁	1	2	yes	—
851	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
855	#103	C₂³×C₃₁	1	1	yes	characteristic
856	#103	C₂³×C₃₁	1	2	yes	—
857	#103	C₂³×C₃₁	1	2	yes	—
858	#103	C₂³×C₃₁	1	2	yes	—
859	#103	C₂³×C₃₁	1	2	yes	—
860	#103	C₂³×C₃₁	1	2	yes	—
861	#103	C₂³×C₃₁	1	2	yes	—
862	#103	C₂³×C₃₁	1	1	yes	characteristic
863	#103	C₂³×C₃₁	1	2	yes	—
864	#103	C₂³×C₃₁	1	2	yes	—
865	#102	C₂³×C₃₁	1	1	yes	characteristic
866	#102	C₂³×C₃₁	1	2	yes	—
867	#102	C₂³×C₃₁	1	1	yes	characteristic
868	#102	C₂³×C₃₁	1	2	yes	—
869	#102	C₂³×C₃₁	1	1	yes	characteristic
870	#102	C₂³×C₃₁	1	1	yes	characteristic
871	#102	C₂³×C₃₁	1	1	yes	characteristic
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	2	yes	—
874	#102	C₂³×C₃₁	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
882	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₃₁	1	2	yes	—
885	C₃₁	#61785	1	1	yes	characteristic, direct product factor, Sylow
886	C₂⁴	—	2	1	no	—
887	#41	—	4	2	no	—
888	#41	—	4	2	no	—
889	#41	—	4	2	no	—
890	#41	—	4	2	no	—
891	#41	—	8	2	no	—
892	#41	—	8	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	4	2	no	—
898	C₂×Q₈	—	4	2	no	—
899	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
900	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	4	1	no	—
911	C₂×D₄	—	4	1	no	—
912	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
913	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
914	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
915	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
916	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
917	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
918	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
921	C₂²×C₄	—	2	1	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	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	8	2	no	—
933	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
934	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
935	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
938	SD₁₆	—	4	1	no	—
939	SD₁₆	—	4	2	no	—
940	SD₁₆	—	4	1	no	—
941	SD₁₆	—	4	2	no	—
942	D₈	—	4	1	no	—
943	D₈	—	4	1	no	—
944	M₁₆	—	4	2	no	—
945	M₁₆	—	4	2	no	—
946	C₂×C₈	—	4	2	no	—
947	C₂×C₈	—	4	2	no	—
948	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
950	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
952	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
953	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
984	C₂²⋊C₄	—	2	2	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	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1017	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1018	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1019	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	—	2	1	no	—
1023	C₂³	—	4	2	no	—
1024	C₂³	—	8	1	no	—
1025	C₂³	—	8	1	no	—
1026	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1027	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1028	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	2	2	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	4	2	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	1	no	—
1036	Q₈	—	8	1	no	—
1037	Q₈	—	8	2	no	—
1038	D₄	—	2	2	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	1	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	—	8	2	no	—
1057	D₄	—	8	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	4	1	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	—	8	1	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1092	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1093	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1094	C₈	—	2	1	no	—
1095	C₈	—	2	2	no	—
1096	C₈	—	2	1	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	8	4	no	—
1119	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	—	4	2	no	—
1135	C₄	C₃₁×#577	1	2	yes	—
1136	C₄	C₃₁×#585	1	1	yes	characteristic
1137	C₄	C₃₁×#585	1	1	yes	characteristic
1138	C₂	—	4	1	no	—
1139	C₂	—	4	2	no	—
1140	C₂	—	4	2	no	—
1141	C₂	—	8	1	no	—
1142	C₂	—	8	1	no	—
1143	C₂	—	8	1	no	—
1144	C₂	C₃₁×#3485	1	1	yes	characteristic
1145	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1146	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3547	C₂	semidirect
2. C₃₁×#3506	C₂	semidirect
3. C₃₁×#3357	C₂	semidirect
4. C₃₁×#3354	C₂	semidirect
5. C₃₁×#3351	C₂	semidirect
6. C₃₁×#3341	C₂	semidirect
7. C₃₁×#3337	C₂	semidirect
8. C₃₁×#3335	C₂	semidirect
9. C₃₁×#3330	C₂	semidirect
10. C₃₁×#3329	C₂	semidirect
11. C₃₁×#3326	C₂	semidirect
12. C₃₁×#3303	C₂	semidirect
13. C₃₁×#3301	C₂	semidirect
14. C₃₁×#3298	C₂	semidirect
15. C₃₁×#3233	C₂	semidirect
16. C₃₁×#3231	C₂	semidirect
17. C₃₁×#3200	C₂	semidirect
18. C₃₁×#3198	C₂	semidirect
19. C₃₁×#3105	C₂	semidirect
20. C₃₁×#3101	C₂	semidirect
21. C₃₁×#3099	C₂	semidirect
22. C₃₁×#3097	C₂	semidirect
23. C₃₁×#2979	C₂	semidirect
30. C₃₁×#555	C₂²	semidirect
31. C₃₁×#554	C₂²	semidirect
35. C₃₁×#552	C₂²	semidirect
37. D₄×Q₈×C₃₁	C₂²	semidirect
38. C₃₁×#548	C₂²	semidirect
41. C₃₁×#547	C₂²	semidirect
57. C₃₁×#500	C₂²	semidirect
58. C₃₁×#499	C₂²	semidirect
59. C₃₁×#498	C₂²	semidirect
60. C₃₁×#488	C₂²	semidirect
61. C₃₁×#487	C₂²	semidirect
62. C₃₁×#487	C₂²	semidirect
66. C₃₁×#485	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
70. C₃₁×#484	C₂²	semidirect
72. C₃₁×#483	C₂²	semidirect
73. C₃₁×#483	C₂²	semidirect
77. C₃₁×#482	C₂²	semidirect
80. C₃₁×#481	C₂²	semidirect
82. C₃₁×#479	C₂²	semidirect
83. C₃₁×#479	C₂²	semidirect
86. C₃₁×#477	C₂²	semidirect
89. C₃₁×#476	C₂²	semidirect
90. C₃₁×#475	C₂²	semidirect
91. C₃₁×#474	C₂²	semidirect
117. C₃₁×#436	C₂²	semidirect
118. C₃₁×#436	C₂²	semidirect
119. C₃₁×#436	C₂²	semidirect
120. C₈×D₄×C₃₁	C₂²	semidirect
121. C₈×D₄×C₃₁	C₂²	semidirect
122. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#428	C₂²	semidirect
126. C₃₁×#428	C₂²	semidirect
127. C₃₁×#427	C₂²	semidirect
128. C₂×C₃₁×#106	C₂²	semidirect
129. C₃₁×#419	C₂²	semidirect
130. C₃₁×#417	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
132. C₂×C₃₁×#103	C₂²	semidirect
446. #61785	C₃₁	direct (N × H)
527. #3547	C₂×C₃₁	semidirect
528. #3506	C₂×C₃₁	semidirect
529. #3357	C₂×C₃₁	semidirect
530. #3354	C₂×C₃₁	semidirect
531. #3351	C₂×C₃₁	semidirect
532. #3341	C₂×C₃₁	semidirect
533. #3337	C₂×C₃₁	semidirect
534. #3335	C₂×C₃₁	semidirect
535. #3330	C₂×C₃₁	semidirect
536. #3329	C₂×C₃₁	semidirect
537. #3326	C₂×C₃₁	semidirect
538. #3303	C₂×C₃₁	semidirect
539. #3301	C₂×C₃₁	semidirect
540. #3298	C₂×C₃₁	semidirect
541. #3233	C₂×C₃₁	semidirect
542. #3231	C₂×C₃₁	semidirect
543. #3200	C₂×C₃₁	semidirect
544. #3198	C₂×C₃₁	semidirect
545. #3105	C₂×C₃₁	semidirect
546. #3101	C₂×C₃₁	semidirect
547. #3099	C₂×C₃₁	semidirect
548. #3097	C₂×C₃₁	semidirect
549. #2979	C₂×C₃₁	semidirect
594. #555	C₂²×C₃₁	semidirect
595. #554	C₂²×C₃₁	semidirect
599. #552	C₂²×C₃₁	semidirect
601. D₄×Q₈	C₂²×C₃₁	semidirect
602. #548	C₂²×C₃₁	semidirect
605. #547	C₂²×C₃₁	semidirect
621. #500	C₂²×C₃₁	semidirect
622. #499	C₂²×C₃₁	semidirect
623. #498	C₂²×C₃₁	semidirect
624. #488	C₂²×C₃₁	semidirect
625. #487	C₂²×C₃₁	semidirect
626. #487	C₂²×C₃₁	semidirect
630. #485	C₂²×C₃₁	semidirect
631. #485	C₂²×C₃₁	semidirect
632. #485	C₂²×C₃₁	semidirect
634. #484	C₂²×C₃₁	semidirect
636. #483	C₂²×C₃₁	semidirect
637. #483	C₂²×C₃₁	semidirect
641. #482	C₂²×C₃₁	semidirect
644. #481	C₂²×C₃₁	semidirect
646. #479	C₂²×C₃₁	semidirect
647. #479	C₂²×C₃₁	semidirect
650. #477	C₂²×C₃₁	semidirect
653. #476	C₂²×C₃₁	semidirect
654. #475	C₂²×C₃₁	semidirect
655. #474	C₂²×C₃₁	semidirect
681. #436	C₂²×C₃₁	semidirect
682. #436	C₂²×C₃₁	semidirect
683. #436	C₂²×C₃₁	semidirect
684. C₈×D₄	C₂²×C₃₁	semidirect
685. C₈×D₄	C₂²×C₃₁	semidirect
686. C₈×D₄	C₂²×C₃₁	semidirect
689. #428	C₂²×C₃₁	semidirect
690. #428	C₂²×C₃₁	semidirect
691. #427	C₂²×C₃₁	semidirect
692. C₂×#106	C₂²×C₃₁	semidirect
693. #419	C₂²×C₃₁	semidirect
694. #417	C₂²×C₃₁	semidirect
695. #416	C₂²×C₃₁	semidirect
696. C₂×#103	C₂²×C₃₁	semidirect
885. C₃₁	#61785	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3547	2
C₃₁×#3506	2
C₃₁×#3357	2
C₃₁×#3354	2
C₃₁×#3351	2
C₃₁×#3341	2
C₃₁×#3337	2
C₃₁×#3335	2
C₃₁×#3330	2
C₃₁×#3329	2
C₃₁×#3326	2
C₃₁×#3303	2
C₃₁×#3301	2
C₃₁×#3298	2
C₃₁×#3233	2
C₃₁×#3231	2
C₃₁×#3200	2
C₃₁×#3198	2
C₃₁×#3105	2
C₃₁×#3101	2
C₃₁×#3099	2
C₃₁×#3097	2
C₃₁×#2979	2
#61785	31

Subgroups — C31×#61785 #21518544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61785 #21518544