Subgroups — C₃₁×#62570 #21519329

Order 7936.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3373	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3326	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3325	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3220	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3136	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2967	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#562	—	2	1	no	—
21	C₃₁×#562	—	2	2	no	—
22	C₃₁×H(3,𝔽₄)	—	2	1	no	—
23	C₃₁×#559	C₂²	1	2	yes	—
24	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#555	C₂²	1	2	yes	complemented
26	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#553	C₂²	1	2	yes	complemented
28	C₃₁×#552	—	2	1	no	—
29	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#548	—	2	1	no	—
31	C₃₁×#548	C₂²	1	2	yes	—
32	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#546	—	2	2	no	—
34	C₃₁×#546	C₂²	1	2	yes	—
35	D₄²×C₃₁	C₂²	1	2	yes	—
36	C₃₁×#544	C₂²	1	2	yes	complemented
37	C₃₁×#542	—	2	2	no	—
38	C₃₁×#542	C₂²	1	2	yes	—
39	C₃₁×#540	C₂²	1	2	yes	complemented
40	C₃₁×#538	—	2	2	no	—
41	C₃₁×#538	—	2	1	no	—
42	C₃₁×#537	—	2	1	no	—
43	C₃₁×#536	—	2	1	no	—
44	C₃₁×#535	C₂²	1	2	yes	—
45	C₃₁×#534	—	2	1	no	—
46	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#532	C₂²	1	1	yes	characteristic
48	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#496	C₂²	1	2	yes	complemented
54	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#490	C₂²	1	2	yes	—
56	C₃₁×#490	C₂²	1	2	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	complemented
58	C₃₁×#489	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	complemented
60	C₃₁×#489	C₂²	1	2	yes	complemented
61	C₃₁×#488	C₂²	1	2	yes	complemented
62	C₃₁×#488	C₂²	1	2	yes	complemented
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#486	C₂²	1	2	yes	—
65	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#483	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	—
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#481	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#476	C₂²	1	2	yes	complemented
76	C₃₁×#476	C₂²	1	2	yes	complemented
77	C₃₁×#475	C₂²	1	2	yes	complemented
78	C₃₁×#474	C₂²	1	2	yes	complemented
79	C₃₁×#469	C₂²	1	2	yes	—
80	C₃₁×#469	C₂²	1	2	yes	complemented
81	C₃₁×#469	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#466	C₂²	1	2	yes	—
84	C₃₁×#465	C₂²	1	2	yes	complemented
85	C₃₁×#463	C₂²	1	2	yes	complemented
86	C₃₁×#463	C₂²	1	2	yes	complemented
87	C₃₁×#463	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#459	C₂²	1	2	yes	—
90	C₃₁×#459	C₂²	1	2	yes	—
91	C₃₁×#449	C₂²	1	2	yes	complemented
92	C₃₁×#449	C₂²	1	2	yes	complemented
93	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#447	C₂²	1	1	yes	characteristic
96	C₃₁×#447	C₂²	1	1	yes	characteristic
97	C₃₁×#447	C₂²	1	2	yes	complemented
98	C₃₁×#447	C₂²	1	2	yes	complemented
99	C₃₁×#446	C₂²	1	2	yes	complemented
100	C₃₁×#442	C₂²	1	2	yes	complemented
101	C₃₁×#442	C₂²	1	2	yes	complemented
102	C₃₁×#442	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
105	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
106	C₃₁×#436	C₂²	1	2	yes	complemented
107	C₃₁×#435	C₂²	1	2	yes	complemented
108	C₃₁×#435	C₂²	1	2	yes	complemented
109	C₃₁×#433	C₂²	1	2	yes	complemented
110	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#419	C₂²	1	2	yes	complemented
112	C₃₁×#418	C₂²	1	2	yes	—
113	C₃₁×#418	C₂²	1	2	yes	complemented
114	C₃₁×#417	C₂²	1	2	yes	complemented
115	C₃₁×#416	C₂²	1	2	yes	complemented
116	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
117	C₃₁×#405	C₂²	1	2	yes	complemented
118	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	—	2	1	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	C₂³	1	2	yes	—
123	C₂²×Q₈×C₃₁	—	2	1	no	—
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₃₁	—	2	2	no	—
126	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×D₈×C₃₁	C₂³	1	2	yes	—
131	C₂×D₈×C₃₁	C₂³	1	2	yes	—
132	C₂×D₈×C₃₁	C₂³	1	2	yes	—
133	C₂×D₈×C₃₁	C₂³	1	2	yes	—
134	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
135	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	—	2	2	no	—
138	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
142	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
143	C₃₁×#127	C₂³	1	2	yes	—
144	C₃₁×#127	C₂³	1	1	yes	characteristic
145	C₃₁×#127	C₂³	1	1	yes	characteristic
146	C₃₁×#126	—	2	2	no	—
147	C₃₁×#126	—	2	2	no	—
148	C₃₁×#126	D₄	1	2	yes	—
149	C₃₁×#125	—	2	2	no	—
150	C₃₁×#125	D₄	1	1	yes	characteristic
151	C₃₁×#125	C₂³	1	2	yes	—
152	C₃₁×#125	C₂³	1	2	yes	—
153	C₃₁×#124	—	2	2	no	—
154	C₃₁×#124	—	2	2	no	—
155	C₃₁×#124	—	2	2	no	—
156	C₃₁×#124	—	2	2	no	—
157	C₃₁×#124	—	2	2	no	—
158	C₃₁×#124	—	2	2	no	—
159	C₃₁×#124	—	2	1	no	—
160	C₃₁×#124	—	2	1	no	—
161	C₃₁×#124	—	2	1	no	—
162	C₃₁×#124	—	2	1	no	—
163	C₃₁×#124	D₄	1	1	yes	characteristic
164	C₃₁×#124	C₂³	1	2	yes	—
165	C₃₁×#124	C₂³	1	2	yes	—
166	C₃₁×#124	C₂³	1	2	yes	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	—	2	2	no	—
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	—	2	2	no	—
173	C₃₁×#123	—	2	2	no	—
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	D₄	1	2	yes	—
176	C₃₁×C₂²⋊Q₈	—	2	1	no	—
177	C₃₁×C₂²⋊Q₈	—	2	1	no	—
178	C₃₁×C₂²⋊Q₈	—	2	1	no	—
179	C₃₁×C₂²⋊Q₈	—	2	1	no	—
180	C₃₁×C₂²⋊Q₈	—	2	1	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	—	2	2	no	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
188	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₃₁×#121	—	2	2	no	—
190	C₃₁×#121	—	2	1	no	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	—	2	2	no	—
193	C₃₁×#121	—	2	1	no	—
194	C₃₁×#121	—	2	1	no	—
195	C₃₁×#121	—	2	2	no	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	D₄	1	1	yes	characteristic
202	C₃₁×#121	C₂³	1	1	yes	characteristic
203	C₃₁×#121	C₂³	1	1	yes	characteristic
204	C₃₁×#121	C₂³	1	2	yes	—
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#121	C₂³	1	2	yes	—
208	C₃₁×#120	—	2	2	no	—
209	C₃₁×#120	—	2	2	no	—
210	C₃₁×#120	—	2	2	no	—
211	C₃₁×#120	—	2	2	no	—
212	C₃₁×#120	—	2	2	no	—
213	C₄×Q₈×C₃₁	—	2	1	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₃₁	—	2	2	no	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	—	2	1	no	—
222	C₄×D₄×C₃₁	C₂³	1	2	yes	—
223	C₄×D₄×C₃₁	C₂³	1	2	yes	—
224	C₄×D₄×C₃₁	C₂³	1	2	yes	—
225	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₃₁	C₂³	1	2	yes	—
228	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₃₁	C₂³	1	2	yes	—
230	C₃₁×#117	—	2	1	no	—
231	C₃₁×#117	—	2	2	no	—
232	C₃₁×#117	C₂³	1	2	yes	—
233	C₃₁×#117	C₂³	1	2	yes	—
234	C₃₁×#117	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
240	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#106	C₂³	1	2	yes	—
244	C₃₁×#106	C₂³	1	2	yes	—
245	C₃₁×#106	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
248	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
249	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#102	C₂³	1	2	yes	—
257	C₃₁×#102	C₂³	1	2	yes	—
258	C₃₁×#102	C₂³	1	2	yes	—
259	C₃₁×#102	C₂³	1	2	yes	—
260	C₃₁×#102	C₂³	1	2	yes	—
261	C₃₁×#102	C₂³	1	2	yes	—
262	C₃₁×#102	C₂³	1	2	yes	—
263	C₃₁×#102	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₃₁×#97	C₂³	1	2	yes	—
275	C₃₁×#97	C₂³	1	2	yes	—
276	C₃₁×#97	C₂³	1	2	yes	—
277	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
278	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	C₂⁴×C₃₁	—	2	2	no	—
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	4	2	no	—
284	#41×C₃₁	—	8	2	no	—
285	#41×C₃₁	—	8	2	no	—
286	#41×C₃₁	—	8	2	no	—
287	C₂×Q₈×C₃₁	—	2	1	no	—
288	C₂×Q₈×C₃₁	—	2	1	no	—
289	C₂×Q₈×C₃₁	—	2	1	no	—
290	C₂×Q₈×C₃₁	—	2	1	no	—
291	C₂×Q₈×C₃₁	—	2	2	no	—
292	C₂×Q₈×C₃₁	—	2	1	no	—
293	C₂×Q₈×C₃₁	—	4	2	no	—
294	C₂×Q₈×C₃₁	—	8	2	no	—
295	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
296	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
297	C₂×D₄×C₃₁	—	2	2	no	—
298	C₂×D₄×C₃₁	—	2	2	no	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	—	2	2	no	—
301	C₂×D₄×C₃₁	—	2	1	no	—
302	C₂×D₄×C₃₁	—	2	2	no	—
303	C₂×D₄×C₃₁	—	2	1	no	—
304	C₂×D₄×C₃₁	—	2	2	no	—
305	C₂×D₄×C₃₁	—	2	1	no	—
306	C₂×D₄×C₃₁	—	2	1	no	—
307	C₂×D₄×C₃₁	—	2	1	no	—
308	C₂×D₄×C₃₁	—	2	1	no	—
309	C₂×D₄×C₃₁	—	2	2	no	—
310	C₂×D₄×C₃₁	—	2	2	no	—
311	C₂×D₄×C₃₁	—	2	1	no	—
312	C₂×D₄×C₃₁	—	4	2	no	—
313	C₂×D₄×C₃₁	—	4	2	no	—
314	C₂×D₄×C₃₁	—	4	2	no	—
315	C₂×D₄×C₃₁	—	8	4	no	—
316	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
317	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
318	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
319	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
320	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₃₁	—	2	1	no	—
323	C₂²×C₄×C₃₁	—	2	2	no	—
324	C₂²×C₄×C₃₁	—	2	1	no	—
325	C₂²×C₄×C₃₁	—	2	1	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	—	2	2	no	—
328	C₂²×C₄×C₃₁	—	2	2	no	—
329	C₂²×C₄×C₃₁	—	2	2	no	—
330	C₂²×C₄×C₃₁	—	2	2	no	—
331	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
335	SD₁₆×C₃₁	—	4	2	no	—
336	SD₁₆×C₃₁	—	4	2	no	—
337	D₈×C₃₁	—	4	2	no	—
338	D₈×C₃₁	—	4	2	no	—
339	D₈×C₃₁	—	4	2	no	—
340	D₈×C₃₁	—	4	2	no	—
341	M₁₆×C₃₁	—	4	2	no	—
342	M₁₆×C₃₁	—	4	2	no	—
343	C₂×C₈×C₃₁	—	4	2	no	—
344	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
345	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
346	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
347	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	—	2	2	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	1	no	—
354	C₄⋊C₄×C₃₁	—	2	1	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	1	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	—	2	2	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	—	2	2	no	—
378	C₂²⋊C₄×C₃₁	—	2	2	no	—
379	C₂²⋊C₄×C₃₁	—	2	1	no	—
380	C₂²⋊C₄×C₃₁	—	2	2	no	—
381	C₂²⋊C₄×C₃₁	—	2	2	no	—
382	C₂²⋊C₄×C₃₁	—	2	1	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	1	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	1	no	—
392	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₄²×C₃₁	—	2	2	no	—
398	C₄²×C₃₁	—	2	2	no	—
399	C₄²×C₃₁	—	2	2	no	—
400	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄²×C₃₁	C₂⁴	1	2	yes	—
404	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
405	#62570	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
406	C₂³×C₃₁	—	2	1	no	—
407	C₂³×C₃₁	—	2	1	no	—
408	C₂³×C₃₁	—	2	2	no	—
409	C₂³×C₃₁	—	2	2	no	—
410	C₂³×C₃₁	—	4	2	no	—
411	C₂³×C₃₁	—	8	1	no	—
412	C₂³×C₃₁	—	8	2	no	—
413	C₂³×C₃₁	—	8	2	no	—
414	C₂³×C₃₁	—	8	1	no	—
415	C₂³×C₃₁	—	8	2	no	—
416	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
417	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
418	Q₈×C₃₁	—	2	2	no	—
419	Q₈×C₃₁	—	2	2	no	—
420	Q₈×C₃₁	—	4	1	no	—
421	Q₈×C₃₁	—	4	2	no	—
422	Q₈×C₃₁	—	8	1	no	—
423	Q₈×C₃₁	—	8	1	no	—
424	Q₈×C₃₁	—	8	2	no	—
425	Q₈×C₃₁	—	8	1	no	—
426	Q₈×C₃₁	—	8	1	no	—
427	D₄×C₃₁	—	2	2	no	—
428	D₄×C₃₁	—	2	2	no	—
429	D₄×C₃₁	—	2	2	no	—
430	D₄×C₃₁	—	2	2	no	—
431	D₄×C₃₁	—	2	2	no	—
432	D₄×C₃₁	—	2	2	no	—
433	D₄×C₃₁	—	4	2	no	—
434	D₄×C₃₁	—	4	1	no	—
435	D₄×C₃₁	—	4	4	no	—
436	D₄×C₃₁	—	8	1	no	—
437	D₄×C₃₁	—	8	1	no	—
438	D₄×C₃₁	—	8	2	no	—
439	D₄×C₃₁	—	8	2	no	—
440	D₄×C₃₁	—	8	1	no	—
441	D₄×C₃₁	—	8	2	no	—
442	D₄×C₃₁	—	8	1	no	—
443	D₄×C₃₁	—	8	1	no	—
444	D₄×C₃₁	—	8	2	no	—
445	D₄×C₃₁	—	8	2	no	—
446	D₄×C₃₁	—	8	2	no	—
447	D₄×C₃₁	—	8	1	no	—
448	D₄×C₃₁	—	8	1	no	—
449	D₄×C₃₁	—	8	2	no	—
450	C₂×C₄×C₃₁	—	2	2	no	—
451	C₂×C₄×C₃₁	—	2	2	no	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	1	no	—
455	C₂×C₄×C₃₁	—	2	2	no	—
456	C₂×C₄×C₃₁	—	2	2	no	—
457	C₂×C₄×C₃₁	—	2	2	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	4	1	no	—
460	C₂×C₄×C₃₁	—	4	1	no	—
461	C₂×C₄×C₃₁	—	4	2	no	—
462	C₂×C₄×C₃₁	—	4	2	no	—
463	C₂×C₄×C₃₁	—	8	2	no	—
464	C₂×C₄×C₃₁	—	8	2	no	—
465	C₂×C₄×C₃₁	—	8	2	no	—
466	C₂×C₄×C₃₁	—	8	2	no	—
467	C₂×C₄×C₃₁	—	8	2	no	—
468	C₂×C₄×C₃₁	—	8	1	no	—
469	C₂×C₄×C₃₁	—	8	2	no	—
470	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
479	C₈×C₃₁	—	2	2	no	—
480	C₈×C₃₁	—	2	2	no	—
481	C₈×C₃₁	—	2	2	no	—
482	C₈×C₃₁	—	2	2	no	—
483	#3558	C₂×C₃₁	1	1	yes	characteristic, complemented
484	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#3373	C₂×C₃₁	1	2	yes	complemented
486	#3370	C₂×C₃₁	1	2	yes	complemented
487	#3326	C₂×C₃₁	1	2	yes	complemented
488	#3325	C₂×C₃₁	1	2	yes	complemented
489	#3321	C₂×C₃₁	1	2	yes	complemented
490	#3319	C₂×C₃₁	1	2	yes	complemented
491	#3318	C₂×C₃₁	1	2	yes	complemented
492	#3306	C₂×C₃₁	1	2	yes	complemented
493	#3244	C₂×C₃₁	1	2	yes	complemented
494	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#3220	C₂×C₃₁	1	2	yes	complemented
496	#3213	C₂×C₃₁	1	1	yes	characteristic, complemented
497	#3184	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#3179	C₂×C₃₁	1	2	yes	complemented
499	#3140	C₂×C₃₁	1	1	yes	characteristic, complemented
500	#3136	C₂×C₃₁	1	2	yes	complemented
501	#2967	C₂×C₃₁	1	1	yes	characteristic, complemented
502	C₂²×C₃₁	—	2	1	no	—
503	C₂²×C₃₁	—	2	1	no	—
504	C₂²×C₃₁	—	2	2	no	—
505	C₂²×C₃₁	—	2	2	no	—
506	C₂²×C₃₁	—	2	1	no	—
507	C₂²×C₃₁	—	2	2	no	—
508	C₂²×C₃₁	—	4	1	no	—
509	C₂²×C₃₁	—	4	1	no	—
510	C₂²×C₃₁	—	4	1	no	—
511	C₂²×C₃₁	—	4	2	no	—
512	C₂²×C₃₁	—	4	2	no	—
513	C₂²×C₃₁	—	4	1	no	—
514	C₂²×C₃₁	—	4	2	no	—
515	C₂²×C₃₁	—	4	2	no	—
516	C₂²×C₃₁	—	4	2	no	—
517	C₂²×C₃₁	—	4	2	no	—
518	C₂²×C₃₁	—	4	1	no	—
519	C₂²×C₃₁	—	4	1	no	—
520	C₂²×C₃₁	—	16	2	no	—
521	C₂²×C₃₁	—	16	4	no	—
522	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
523	C₄×C₃₁	—	2	1	no	—
524	C₄×C₃₁	—	2	1	no	—
525	C₄×C₃₁	—	2	1	no	—
526	C₄×C₃₁	—	2	1	no	—
527	C₄×C₃₁	—	2	2	no	—
528	C₄×C₃₁	—	2	2	no	—
529	C₄×C₃₁	—	2	2	no	—
530	C₄×C₃₁	—	2	1	no	—
531	C₄×C₃₁	—	4	1	no	—
532	C₄×C₃₁	—	4	1	no	—
533	C₄×C₃₁	—	4	2	no	—
534	C₄×C₃₁	—	4	2	no	—
535	C₄×C₃₁	—	4	2	no	—
536	C₄×C₃₁	—	4	2	no	—
537	C₄×C₃₁	#585	1	2	yes	—
538	#562	—	2	1	no	—
539	#562	—	2	2	no	—
540	H(3,𝔽₄)	—	2	1	no	—
541	#559	C₂²×C₃₁	1	2	yes	—
542	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
543	#555	C₂²×C₃₁	1	2	yes	complemented
544	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
545	#553	C₂²×C₃₁	1	2	yes	complemented
546	#552	—	2	1	no	—
547	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	#548	—	2	1	no	—
549	#548	C₂²×C₃₁	1	2	yes	—
550	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
551	#546	—	2	2	no	—
552	#546	C₂²×C₃₁	1	2	yes	—
553	D₄²	C₂²×C₃₁	1	2	yes	—
554	#544	C₂²×C₃₁	1	2	yes	complemented
555	#542	—	2	2	no	—
556	#542	C₂²×C₃₁	1	2	yes	—
557	#540	C₂²×C₃₁	1	2	yes	complemented
558	#538	—	2	2	no	—
559	#538	—	2	1	no	—
560	#537	—	2	1	no	—
561	#536	—	2	1	no	—
562	#535	C₂²×C₃₁	1	2	yes	—
563	#534	—	2	1	no	—
564	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
565	#532	C₂²×C₃₁	1	1	yes	characteristic
566	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
567	#529	C₂²×C₃₁	1	1	yes	characteristic
568	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
569	#501	C₂²×C₃₁	1	2	yes	complemented
570	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
571	#496	C₂²×C₃₁	1	2	yes	complemented
572	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
573	#490	C₂²×C₃₁	1	2	yes	—
574	#490	C₂²×C₃₁	1	2	yes	complemented
575	#489	C₂²×C₃₁	1	2	yes	complemented
576	#489	C₂²×C₃₁	1	2	yes	complemented
577	#489	C₂²×C₃₁	1	2	yes	complemented
578	#489	C₂²×C₃₁	1	2	yes	complemented
579	#488	C₂²×C₃₁	1	2	yes	complemented
580	#488	C₂²×C₃₁	1	2	yes	complemented
581	#488	C₂²×C₃₁	1	2	yes	complemented
582	#486	C₂²×C₃₁	1	2	yes	—
583	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
585	#485	C₂²×C₃₁	1	2	yes	complemented
586	#483	C₂²×C₃₁	1	2	yes	complemented
587	#482	C₂²×C₃₁	1	2	yes	—
588	#482	C₂²×C₃₁	1	2	yes	complemented
589	#482	C₂²×C₃₁	1	2	yes	complemented
590	#481	C₂²×C₃₁	1	2	yes	—
591	#479	C₂²×C₃₁	1	2	yes	complemented
592	#478	C₂²×C₃₁	1	2	yes	complemented
593	#476	C₂²×C₃₁	1	2	yes	complemented
594	#476	C₂²×C₃₁	1	2	yes	complemented
595	#475	C₂²×C₃₁	1	2	yes	complemented
596	#474	C₂²×C₃₁	1	2	yes	complemented
597	#469	C₂²×C₃₁	1	2	yes	—
598	#469	C₂²×C₃₁	1	2	yes	complemented
599	#469	C₂²×C₃₁	1	2	yes	complemented
600	#468	C₂²×C₃₁	1	2	yes	complemented
601	#466	C₂²×C₃₁	1	2	yes	—
602	#465	C₂²×C₃₁	1	2	yes	complemented
603	#463	C₂²×C₃₁	1	2	yes	complemented
604	#463	C₂²×C₃₁	1	2	yes	complemented
605	#463	C₂²×C₃₁	1	2	yes	complemented
606	#463	C₂²×C₃₁	1	2	yes	complemented
607	#459	C₂²×C₃₁	1	2	yes	—
608	#459	C₂²×C₃₁	1	2	yes	—
609	#449	C₂²×C₃₁	1	2	yes	complemented
610	#449	C₂²×C₃₁	1	2	yes	complemented
611	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#447	C₂²×C₃₁	1	1	yes	characteristic
614	#447	C₂²×C₃₁	1	1	yes	characteristic
615	#447	C₂²×C₃₁	1	2	yes	complemented
616	#447	C₂²×C₃₁	1	2	yes	complemented
617	#446	C₂²×C₃₁	1	2	yes	complemented
618	#442	C₂²×C₃₁	1	2	yes	complemented
619	#442	C₂²×C₃₁	1	2	yes	complemented
620	#442	C₂²×C₃₁	1	2	yes	complemented
621	#440	C₂²×C₃₁	1	2	yes	complemented
622	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
623	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
624	#436	C₂²×C₃₁	1	2	yes	complemented
625	#435	C₂²×C₃₁	1	2	yes	complemented
626	#435	C₂²×C₃₁	1	2	yes	complemented
627	#433	C₂²×C₃₁	1	2	yes	complemented
628	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#419	C₂²×C₃₁	1	2	yes	complemented
630	#418	C₂²×C₃₁	1	2	yes	—
631	#418	C₂²×C₃₁	1	2	yes	complemented
632	#417	C₂²×C₃₁	1	2	yes	complemented
633	#416	C₂²×C₃₁	1	2	yes	complemented
634	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
635	#405	C₂²×C₃₁	1	2	yes	complemented
636	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	C₂×C₃₁	—	4	1	no	—
638	C₂×C₃₁	—	4	2	no	—
639	C₂×C₃₁	—	8	1	no	—
640	C₂×C₃₁	—	8	1	no	—
641	C₂×C₃₁	—	8	2	no	—
642	C₂×C₃₁	—	8	2	no	—
643	C₂×C₃₁	#3500	1	1	yes	characteristic
644	C₂×C₃₁	#3585	1	1	yes	characteristic
645	C₂×C₃₁	#3585	1	1	yes	characteristic
646	C₂×#41	—	2	1	no	—
647	C₂×#41	—	2	1	no	—
648	C₂×#41	—	2	1	no	—
649	C₂×#41	C₂³×C₃₁	1	2	yes	—
650	C₂²×Q₈	—	2	1	no	—
651	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
652	C₂²×D₄	—	2	2	no	—
653	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
654	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
655	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
656	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
657	C₂×D₈	C₂³×C₃₁	1	2	yes	—
658	C₂×D₈	C₂³×C₃₁	1	2	yes	—
659	C₂×D₈	C₂³×C₃₁	1	2	yes	—
660	C₂×D₈	C₂³×C₃₁	1	2	yes	—
661	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
662	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
663	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
664	C₄⋊Q₈	—	2	2	no	—
665	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
666	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
667	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
668	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
669	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
670	#127	C₂³×C₃₁	1	1	yes	characteristic
671	#127	C₂³×C₃₁	1	1	yes	characteristic
672	#127	C₂³×C₃₁	1	2	yes	—
673	#126	—	2	2	no	—
674	#126	—	2	2	no	—
675	#126	D₄×C₃₁	1	2	yes	—
676	#125	—	2	2	no	—
677	#125	D₄×C₃₁	1	1	yes	characteristic
678	#125	C₂³×C₃₁	1	2	yes	—
679	#125	C₂³×C₃₁	1	2	yes	—
680	#124	—	2	2	no	—
681	#124	—	2	2	no	—
682	#124	—	2	2	no	—
683	#124	—	2	2	no	—
684	#124	—	2	2	no	—
685	#124	—	2	2	no	—
686	#124	—	2	1	no	—
687	#124	—	2	1	no	—
688	#124	—	2	1	no	—
689	#124	—	2	1	no	—
690	#124	D₄×C₃₁	1	1	yes	characteristic
691	#124	C₂³×C₃₁	1	2	yes	—
692	#124	C₂³×C₃₁	1	2	yes	—
693	#124	C₂³×C₃₁	1	2	yes	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	—	2	2	no	—
698	#123	—	2	2	no	—
699	#123	—	2	2	no	—
700	#123	—	2	2	no	—
701	#123	—	2	2	no	—
702	#123	D₄×C₃₁	1	2	yes	—
703	C₂²⋊Q₈	—	2	1	no	—
704	C₂²⋊Q₈	—	2	1	no	—
705	C₂²⋊Q₈	—	2	1	no	—
706	C₂²⋊Q₈	—	2	1	no	—
707	C₂²⋊Q₈	—	2	1	no	—
708	C₂²⋊Q₈	—	2	2	no	—
709	C₂²⋊Q₈	—	2	2	no	—
710	C₂²⋊Q₈	—	2	2	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	—	2	2	no	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
715	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
716	#121	—	2	2	no	—
717	#121	—	2	1	no	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	—	2	1	no	—
721	#121	—	2	1	no	—
722	#121	—	2	2	no	—
723	#121	—	2	2	no	—
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	—	2	2	no	—
728	#121	D₄×C₃₁	1	1	yes	characteristic
729	#121	C₂³×C₃₁	1	2	yes	—
730	#121	C₂³×C₃₁	1	1	yes	characteristic
731	#121	C₂³×C₃₁	1	1	yes	characteristic
732	#121	C₂³×C₃₁	1	2	yes	—
733	#121	C₂³×C₃₁	1	2	yes	—
734	#121	C₂³×C₃₁	1	2	yes	—
735	#120	—	2	2	no	—
736	#120	—	2	2	no	—
737	#120	—	2	2	no	—
738	#120	—	2	2	no	—
739	#120	—	2	2	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	—	2	1	no	—
742	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
743	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
744	C₄×D₄	—	2	2	no	—
745	C₄×D₄	—	2	2	no	—
746	C₄×D₄	—	2	2	no	—
747	C₄×D₄	—	2	1	no	—
748	C₄×D₄	—	2	1	no	—
749	C₄×D₄	C₂³×C₃₁	1	2	yes	—
750	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
751	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
752	C₄×D₄	C₂³×C₃₁	1	2	yes	—
753	C₄×D₄	C₂³×C₃₁	1	2	yes	—
754	C₄×D₄	C₂³×C₃₁	1	2	yes	—
755	C₄×D₄	C₂³×C₃₁	1	2	yes	—
756	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
757	#117	—	2	1	no	—
758	#117	—	2	2	no	—
759	#117	C₂³×C₃₁	1	2	yes	—
760	#117	C₂³×C₃₁	1	2	yes	—
761	#117	C₂³×C₃₁	1	2	yes	—
762	C₂×C₄⋊C₄	—	2	1	no	—
763	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
764	C₂×C₂²⋊C₄	—	2	1	no	—
765	C₂×C₂²⋊C₄	—	2	1	no	—
766	C₂×C₂²⋊C₄	—	2	2	no	—
767	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
768	#107	C₂³×C₃₁	1	2	yes	—
769	#107	C₂³×C₃₁	1	2	yes	—
770	#106	C₂³×C₃₁	1	2	yes	—
771	#106	C₂³×C₃₁	1	2	yes	—
772	#106	C₂³×C₃₁	1	2	yes	—
773	#106	C₂³×C₃₁	1	2	yes	—
774	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
775	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
776	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
777	#103	C₂³×C₃₁	1	2	yes	—
778	#103	C₂³×C₃₁	1	2	yes	—
779	#103	C₂³×C₃₁	1	2	yes	—
780	#103	C₂³×C₃₁	1	2	yes	—
781	#103	C₂³×C₃₁	1	2	yes	—
782	#103	C₂³×C₃₁	1	2	yes	—
783	#102	C₂³×C₃₁	1	2	yes	—
784	#102	C₂³×C₃₁	1	2	yes	—
785	#102	C₂³×C₃₁	1	2	yes	—
786	#102	C₂³×C₃₁	1	2	yes	—
787	#102	C₂³×C₃₁	1	2	yes	—
788	#102	C₂³×C₃₁	1	2	yes	—
789	#102	C₂³×C₃₁	1	2	yes	—
790	#102	C₂³×C₃₁	1	2	yes	—
791	#102	C₂³×C₃₁	1	2	yes	—
792	#102	C₂³×C₃₁	1	2	yes	—
793	#102	C₂³×C₃₁	1	2	yes	—
794	#102	C₂³×C₃₁	1	2	yes	—
795	#102	C₂³×C₃₁	1	2	yes	—
796	#102	C₂³×C₃₁	1	2	yes	—
797	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
798	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
799	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
800	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
801	#97	C₂³×C₃₁	1	2	yes	—
802	#97	C₂³×C₃₁	1	2	yes	—
803	#97	C₂³×C₃₁	1	2	yes	—
804	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
805	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×C₈	C₂³×C₃₁	1	2	yes	—
807	C₃₁	#62570	1	1	yes	characteristic, direct product factor, Sylow
808	C₂⁴	—	2	1	no	—
809	C₂⁴	—	2	2	no	—
810	#41	—	4	2	no	—
811	#41	—	4	2	no	—
812	#41	—	8	2	no	—
813	#41	—	8	2	no	—
814	#41	—	8	2	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	2	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	4	2	no	—
822	C₂×Q₈	—	8	2	no	—
823	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
824	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	2	1	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	1	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	8	4	no	—
844	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
845	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
846	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
847	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
848	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
849	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	2	no	—
856	C₂²×C₄	—	2	2	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
860	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
862	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
863	SD₁₆	—	4	2	no	—
864	SD₁₆	—	4	2	no	—
865	D₈	—	4	2	no	—
866	D₈	—	4	2	no	—
867	D₈	—	4	2	no	—
868	D₈	—	4	2	no	—
869	M₁₆	—	4	2	no	—
870	M₁₆	—	4	2	no	—
871	C₂×C₈	—	4	2	no	—
872	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
873	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
874	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
875	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
889	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
890	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
891	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
892	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
893	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
894	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
896	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
897	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
898	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	1	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	1	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	1	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	1	no	—
920	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
921	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
922	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
923	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
924	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
929	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
930	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₄²	C₂⁴×C₃₁	1	2	yes	—
932	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	4	2	no	—
938	C₂³	—	8	1	no	—
939	C₂³	—	8	2	no	—
940	C₂³	—	8	2	no	—
941	C₂³	—	8	1	no	—
942	C₂³	—	8	2	no	—
943	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
944	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
945	Q₈	—	2	2	no	—
946	Q₈	—	2	2	no	—
947	Q₈	—	4	1	no	—
948	Q₈	—	4	2	no	—
949	Q₈	—	8	1	no	—
950	Q₈	—	8	1	no	—
951	Q₈	—	8	2	no	—
952	Q₈	—	8	1	no	—
953	Q₈	—	8	1	no	—
954	D₄	—	2	2	no	—
955	D₄	—	2	2	no	—
956	D₄	—	2	2	no	—
957	D₄	—	2	2	no	—
958	D₄	—	2	2	no	—
959	D₄	—	2	2	no	—
960	D₄	—	4	2	no	—
961	D₄	—	4	1	no	—
962	D₄	—	4	4	no	—
963	D₄	—	8	1	no	—
964	D₄	—	8	1	no	—
965	D₄	—	8	2	no	—
966	D₄	—	8	2	no	—
967	D₄	—	8	1	no	—
968	D₄	—	8	2	no	—
969	D₄	—	8	1	no	—
970	D₄	—	8	1	no	—
971	D₄	—	8	2	no	—
972	D₄	—	8	2	no	—
973	D₄	—	8	2	no	—
974	D₄	—	8	1	no	—
975	D₄	—	8	1	no	—
976	D₄	—	8	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	4	1	no	—
987	C₂×C₄	—	4	1	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	4	2	no	—
990	C₂×C₄	—	8	2	no	—
991	C₂×C₄	—	8	2	no	—
992	C₂×C₄	—	8	2	no	—
993	C₂×C₄	—	8	2	no	—
994	C₂×C₄	—	8	2	no	—
995	C₂×C₄	—	8	1	no	—
996	C₂×C₄	—	8	2	no	—
997	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
998	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
999	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1000	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1001	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1004	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1005	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1006	C₈	—	2	2	no	—
1007	C₈	—	2	2	no	—
1008	C₈	—	2	2	no	—
1009	C₈	—	2	2	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	4	2	no	—
1017	C₂²	—	4	2	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	16	2	no	—
1029	C₂²	—	16	4	no	—
1030	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1031	C₄	—	2	2	no	—
1032	C₄	—	2	1	no	—
1033	C₄	—	2	1	no	—
1034	C₄	—	2	1	no	—
1035	C₄	—	2	1	no	—
1036	C₄	—	2	1	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	4	2	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	C₃₁×#585	1	2	yes	—
1046	C₂	—	4	1	no	—
1047	C₂	—	4	2	no	—
1048	C₂	—	8	2	no	—
1049	C₂	—	8	2	no	—
1050	C₂	—	8	1	no	—
1051	C₂	—	8	1	no	—
1052	C₂	C₃₁×#3500	1	1	yes	characteristic
1053	C₂	C₃₁×#3585	1	1	yes	characteristic
1054	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3558	C₂	semidirect
2. C₃₁×#3547	C₂	semidirect
3. C₃₁×#3373	C₂	semidirect
4. C₃₁×#3370	C₂	semidirect
5. C₃₁×#3326	C₂	semidirect
6. C₃₁×#3325	C₂	semidirect
7. C₃₁×#3321	C₂	semidirect
8. C₃₁×#3319	C₂	semidirect
9. C₃₁×#3318	C₂	semidirect
10. C₃₁×#3306	C₂	semidirect
11. C₃₁×#3244	C₂	semidirect
12. C₃₁×#3235	C₂	semidirect
13. C₃₁×#3220	C₂	semidirect
14. C₃₁×#3213	C₂	semidirect
15. C₃₁×#3184	C₂	semidirect
16. C₃₁×#3179	C₂	semidirect
17. C₃₁×#3140	C₂	semidirect
18. C₃₁×#3136	C₂	semidirect
19. C₃₁×#2967	C₂	semidirect
24. C₃₁×#555	C₂²	semidirect
25. C₃₁×#555	C₂²	semidirect
26. C₃₁×#554	C₂²	semidirect
27. C₃₁×#553	C₂²	semidirect
29. D₄×Q₈×C₃₁	C₂²	semidirect
32. C₃₁×#547	C₂²	semidirect
36. C₃₁×#544	C₂²	semidirect
39. C₃₁×#540	C₂²	semidirect
46. C₃₁×#533	C₂²	semidirect
48. C₃₁×#532	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#498	C₂²	semidirect
53. C₃₁×#496	C₂²	semidirect
54. C₃₁×#493	C₂²	semidirect
56. C₃₁×#490	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#489	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
60. C₃₁×#489	C₂²	semidirect
61. C₃₁×#488	C₂²	semidirect
62. C₃₁×#488	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
65. C₃₁×#486	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#483	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#476	C₂²	semidirect
76. C₃₁×#476	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
78. C₃₁×#474	C₂²	semidirect
80. C₃₁×#469	C₂²	semidirect
81. C₃₁×#469	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
84. C₃₁×#465	C₂²	semidirect
85. C₃₁×#463	C₂²	semidirect
86. C₃₁×#463	C₂²	semidirect
87. C₃₁×#463	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
91. C₃₁×#449	C₂²	semidirect
92. C₃₁×#449	C₂²	semidirect
93. C₃₁×#448	C₂²	semidirect
94. C₃₁×#448	C₂²	semidirect
97. C₃₁×#447	C₂²	semidirect
98. C₃₁×#447	C₂²	semidirect
99. C₃₁×#446	C₂²	semidirect
100. C₃₁×#442	C₂²	semidirect
101. C₃₁×#442	C₂²	semidirect
102. C₃₁×#442	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₄×SD₁₆×C₃₁	C₂²	semidirect
105. C₄×D₈×C₃₁	C₂²	semidirect
106. C₃₁×#436	C₂²	semidirect
107. C₃₁×#435	C₂²	semidirect
108. C₃₁×#435	C₂²	semidirect
109. C₃₁×#433	C₂²	semidirect
110. C₃₁×#432	C₂²	semidirect
111. C₃₁×#419	C₂²	semidirect
113. C₃₁×#418	C₂²	semidirect
114. C₃₁×#417	C₂²	semidirect
115. C₃₁×#416	C₂²	semidirect
116. C₂×C₃₁×#102	C₂²	semidirect
117. C₃₁×#405	C₂²	semidirect
118. C₄×M₁₆×C₃₁	C₂²	semidirect
405. #62570	C₃₁	direct (N × H)
483. #3558	C₂×C₃₁	semidirect
484. #3547	C₂×C₃₁	semidirect
485. #3373	C₂×C₃₁	semidirect
486. #3370	C₂×C₃₁	semidirect
487. #3326	C₂×C₃₁	semidirect
488. #3325	C₂×C₃₁	semidirect
489. #3321	C₂×C₃₁	semidirect
490. #3319	C₂×C₃₁	semidirect
491. #3318	C₂×C₃₁	semidirect
492. #3306	C₂×C₃₁	semidirect
493. #3244	C₂×C₃₁	semidirect
494. #3235	C₂×C₃₁	semidirect
495. #3220	C₂×C₃₁	semidirect
496. #3213	C₂×C₃₁	semidirect
497. #3184	C₂×C₃₁	semidirect
498. #3179	C₂×C₃₁	semidirect
499. #3140	C₂×C₃₁	semidirect
500. #3136	C₂×C₃₁	semidirect
501. #2967	C₂×C₃₁	semidirect
542. #555	C₂²×C₃₁	semidirect
543. #555	C₂²×C₃₁	semidirect
544. #554	C₂²×C₃₁	semidirect
545. #553	C₂²×C₃₁	semidirect
547. D₄×Q₈	C₂²×C₃₁	semidirect
550. #547	C₂²×C₃₁	semidirect
554. #544	C₂²×C₃₁	semidirect
557. #540	C₂²×C₃₁	semidirect
564. #533	C₂²×C₃₁	semidirect
566. #532	C₂²×C₃₁	semidirect
569. #501	C₂²×C₃₁	semidirect
570. #498	C₂²×C₃₁	semidirect
571. #496	C₂²×C₃₁	semidirect
572. #493	C₂²×C₃₁	semidirect
574. #490	C₂²×C₃₁	semidirect
575. #489	C₂²×C₃₁	semidirect
576. #489	C₂²×C₃₁	semidirect
577. #489	C₂²×C₃₁	semidirect
578. #489	C₂²×C₃₁	semidirect
579. #488	C₂²×C₃₁	semidirect
580. #488	C₂²×C₃₁	semidirect
581. #488	C₂²×C₃₁	semidirect
583. #486	C₂²×C₃₁	semidirect
584. #486	C₂²×C₃₁	semidirect
585. #485	C₂²×C₃₁	semidirect
586. #483	C₂²×C₃₁	semidirect
588. #482	C₂²×C₃₁	semidirect
589. #482	C₂²×C₃₁	semidirect
591. #479	C₂²×C₃₁	semidirect
592. #478	C₂²×C₃₁	semidirect
593. #476	C₂²×C₃₁	semidirect
594. #476	C₂²×C₃₁	semidirect
595. #475	C₂²×C₃₁	semidirect
596. #474	C₂²×C₃₁	semidirect
598. #469	C₂²×C₃₁	semidirect
599. #469	C₂²×C₃₁	semidirect
600. #468	C₂²×C₃₁	semidirect
602. #465	C₂²×C₃₁	semidirect
603. #463	C₂²×C₃₁	semidirect
604. #463	C₂²×C₃₁	semidirect
605. #463	C₂²×C₃₁	semidirect
606. #463	C₂²×C₃₁	semidirect
609. #449	C₂²×C₃₁	semidirect
610. #449	C₂²×C₃₁	semidirect
611. #448	C₂²×C₃₁	semidirect
612. #448	C₂²×C₃₁	semidirect
615. #447	C₂²×C₃₁	semidirect
616. #447	C₂²×C₃₁	semidirect
617. #446	C₂²×C₃₁	semidirect
618. #442	C₂²×C₃₁	semidirect
619. #442	C₂²×C₃₁	semidirect
620. #442	C₂²×C₃₁	semidirect
621. #440	C₂²×C₃₁	semidirect
622. C₄×SD₁₆	C₂²×C₃₁	semidirect
623. C₄×D₈	C₂²×C₃₁	semidirect
624. #436	C₂²×C₃₁	semidirect
625. #435	C₂²×C₃₁	semidirect
626. #435	C₂²×C₃₁	semidirect
627. #433	C₂²×C₃₁	semidirect
628. #432	C₂²×C₃₁	semidirect
629. #419	C₂²×C₃₁	semidirect
631. #418	C₂²×C₃₁	semidirect
632. #417	C₂²×C₃₁	semidirect
633. #416	C₂²×C₃₁	semidirect
634. C₂×#102	C₂²×C₃₁	semidirect
635. #405	C₂²×C₃₁	semidirect
636. C₄×M₁₆	C₂²×C₃₁	semidirect
807. C₃₁	#62570	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×#3558	2
C₃₁×#3547	2
C₃₁×#3373	2
C₃₁×#3370	2
C₃₁×#3326	2
C₃₁×#3325	2
C₃₁×#3321	2
C₃₁×#3319	2
C₃₁×#3318	2
C₃₁×#3306	2
C₃₁×#3244	2
C₃₁×#3235	2
C₃₁×#3220	2
C₃₁×#3213	2
C₃₁×#3184	2
C₃₁×#3179	2
C₃₁×#3140	2
C₃₁×#3136	2
C₃₁×#2967	2
#62570	31

Subgroups — C31×#62570 #21519329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62570 #21519329