Subgroups — C₃₁×#61849 #21518608

Order 7936.

1716 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3385	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3384	C₂	1	2	yes	maximal, complemented
5	Q₈×D₈×C₃₁	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3370	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3360	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3243	C₂	1	4	yes	maximal, complemented
10	C₃₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3118	C₂	1	4	yes	maximal, complemented
13	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3100	C₂	1	1	yes	maximal, characteristic
15	C₃₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#563	—	2	2	no	—
17	C₃₁×#559	C₂²	1	2	yes	complemented
18	Q₈²×C₃₁	C₂²	1	2	yes	complemented
19	C₃₁×#556	—	2	1	no	—
20	C₃₁×#556	C₂²	1	2	yes	complemented
21	C₃₁×#554	—	2	1	no	—
22	C₃₁×#554	—	2	2	no	—
23	C₃₁×#554	C₂²	1	2	yes	—
24	C₃₁×#554	C₂²	1	4	yes	—
25	D₄×Q₈×C₃₁	—	2	1	no	—
26	D₄×Q₈×C₃₁	—	2	1	no	—
27	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
28	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
29	C₃₁×#544	C₂²	1	2	yes	—
30	C₃₁×#543	—	2	2	no	—
31	C₃₁×#542	—	2	2	no	—
32	C₃₁×#542	C₂²	1	4	yes	—
33	C₃₁×#536	—	2	2	no	—
34	C₃₁×#533	C₂²	1	1	yes	characteristic
35	C₃₁×#533	C₂²	1	1	yes	characteristic
36	C₃₁×#533	C₂²	1	1	yes	characteristic
37	C₃₁×#532	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
39	C₃₁×#518	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#501	C₂²	1	4	yes	complemented
42	C₃₁×#501	C₂²	1	2	yes	complemented
43	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#500	C₂²	1	4	yes	complemented
45	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#490	C₂²	1	2	yes	complemented
47	C₃₁×#489	C₂²	1	4	yes	complemented
48	C₃₁×#488	C₂²	1	4	yes	complemented
49	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#485	C₂²	1	4	yes	—
52	C₃₁×#484	C₂²	1	2	yes	—
53	C₃₁×#482	C₂²	1	4	yes	—
54	C₃₁×#480	C₂²	1	2	yes	—
55	C₃₁×#479	C₂²	1	4	yes	complemented
56	C₃₁×#479	C₂²	1	4	yes	complemented
57	C₃₁×#478	C₂²	1	4	yes	complemented
58	C₃₁×#477	C₂²	1	4	yes	complemented
59	C₃₁×#476	C₂²	1	4	yes	—
60	C₃₁×#476	C₂²	1	2	yes	complemented
61	C₃₁×#474	C₂²	1	2	yes	—
62	C₃₁×#474	C₂²	1	2	yes	—
63	C₃₁×#474	C₂²	1	4	yes	—
64	C₃₁×#474	C₂²	1	2	yes	complemented
65	C₃₁×#474	C₂²	1	4	yes	complemented
66	C₃₁×#463	C₂²	1	4	yes	—
67	C₃₁×#463	C₂²	1	4	yes	—
68	C₃₁×#461	C₂²	1	2	yes	—
69	C₃₁×#459	C₂²	1	2	yes	—
70	C₃₁×#450	C₂²	1	2	yes	—
71	C₃₁×#447	C₂²	1	2	yes	—
72	C₃₁×#446	C₂²	1	2	yes	complemented
73	C₃₁×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₃₁	C₂²	1	2	yes	complemented
75	C₃₁×#442	C₂²	1	4	yes	—
76	C₃₁×#440	C₂²	1	4	yes	—
77	C₃₁×#440	C₂²	1	4	yes	—
78	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	—
79	C₄×D₈×C₃₁	C₂²	1	2	yes	—
80	C₄×D₈×C₃₁	C₂²	1	2	yes	—
81	C₄×D₈×C₃₁	C₂²	1	4	yes	—
82	C₃₁×#433	C₂²	1	4	yes	—
83	C₃₁×#432	C₂²	1	1	yes	characteristic
84	C₃₁×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₃₁	—	2	1	no	—
86	C₂²×Q₈×C₃₁	—	2	2	no	—
87	C₂²×Q₈×C₃₁	—	2	2	no	—
88	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₃₁	—	2	1	no	—
90	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
91	C₂×D₈×C₃₁	C₂³	1	2	yes	—
92	C₂×D₈×C₃₁	C₂³	1	2	yes	—
93	C₃₁×C₄⋊Q₈	—	2	4	no	—
94	C₃₁×C₄⋊Q₈	—	2	2	no	—
95	C₃₁×C₄⋊Q₈	—	2	2	no	—
96	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
97	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
98	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
104	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₃₁×#127	C₂³	1	1	yes	characteristic
106	C₃₁×#126	—	2	4	no	—
107	C₃₁×#126	—	2	4	no	—
108	C₃₁×#125	—	2	2	no	—
109	C₃₁×#125	—	2	1	no	—
110	C₃₁×#125	D₄	1	2	yes	—
111	C₃₁×#125	C₂³	1	4	yes	—
112	C₃₁×#125	C₂³	1	2	yes	—
113	C₃₁×#124	—	2	2	no	—
114	C₃₁×#124	—	2	4	no	—
115	C₃₁×#124	—	2	1	no	—
116	C₃₁×#124	C₂³	1	4	yes	—
117	C₃₁×#123	—	2	4	no	—
118	C₃₁×#123	—	2	4	no	—
119	C₃₁×C₂²⋊Q₈	—	2	2	no	—
120	C₃₁×C₂²⋊Q₈	—	2	2	no	—
121	C₃₁×C₂²⋊Q₈	—	2	4	no	—
122	C₃₁×C₂²⋊Q₈	—	2	1	no	—
123	C₃₁×C₂²⋊Q₈	—	2	1	no	—
124	C₃₁×C₂²⋊Q₈	—	2	1	no	—
125	C₃₁×C₂²⋊Q₈	—	2	2	no	—
126	C₃₁×C₂²⋊Q₈	—	2	4	no	—
127	C₃₁×C₂²⋊Q₈	—	2	2	no	—
128	C₃₁×C₂²⋊Q₈	—	2	4	no	—
129	C₃₁×C₂²⋊Q₈	—	2	4	no	—
130	C₃₁×C₂²⋊Q₈	—	2	4	no	—
131	C₃₁×C₂²⋊Q₈	—	2	4	no	—
132	C₃₁×C₂²⋊Q₈	—	2	4	no	—
133	C₃₁×C₂²⋊Q₈	—	2	4	no	—
134	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
135	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
136	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×#121	—	2	1	no	—
138	C₃₁×#121	C₂³	1	2	yes	—
139	C₄×Q₈×C₃₁	—	2	2	no	—
140	C₄×Q₈×C₃₁	—	2	1	no	—
141	C₄×Q₈×C₃₁	—	2	1	no	—
142	C₄×Q₈×C₃₁	—	2	1	no	—
143	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
144	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
145	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
146	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
147	C₄×D₄×C₃₁	—	2	2	no	—
148	C₄×D₄×C₃₁	—	2	2	no	—
149	C₄×D₄×C₃₁	—	2	2	no	—
150	C₄×D₄×C₃₁	—	2	1	no	—
151	C₄×D₄×C₃₁	—	2	1	no	—
152	C₄×D₄×C₃₁	—	2	1	no	—
153	C₄×D₄×C₃₁	C₂³	1	2	yes	—
154	C₄×D₄×C₃₁	C₂³	1	2	yes	—
155	C₄×D₄×C₃₁	C₂³	1	4	yes	—
156	C₄×D₄×C₃₁	C₂³	1	4	yes	—
157	C₄×D₄×C₃₁	C₂³	1	4	yes	—
158	C₄×D₄×C₃₁	C₂³	1	2	yes	—
159	C₃₁×#117	—	2	1	no	—
160	C₃₁×#117	—	2	2	no	—
161	C₃₁×#117	C₂³	1	2	yes	—
162	C₃₁×#117	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
164	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
165	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
167	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
168	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
169	C₃₁×#107	C₂³	1	4	yes	—
170	C₃₁×#107	C₂³	1	2	yes	—
171	C₃₁×#107	C₂³	1	2	yes	—
172	C₃₁×#107	C₂³	1	4	yes	—
173	C₃₁×#107	C₂³	1	4	yes	—
174	C₃₁×#106	C₂³	1	4	yes	—
175	C₃₁×#106	C₂³	1	4	yes	—
176	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
177	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
178	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
179	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
180	C₃₁×#103	C₂³	1	4	yes	—
181	C₃₁×#103	C₂³	1	4	yes	—
182	C₃₁×#103	C₂³	1	4	yes	—
183	C₃₁×#102	C₂³	1	2	yes	—
184	C₃₁×#102	C₂³	1	2	yes	—
185	C₃₁×#102	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	2	yes	—
187	C₃₁×#102	C₂³	1	2	yes	—
188	C₃₁×#102	C₂³	1	4	yes	—
189	C₃₁×#102	C₂³	1	4	yes	—
190	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₃₁×#97	C₂³	1	2	yes	—
193	C₃₁×#97	C₂³	1	4	yes	—
194	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	4	yes	—
197	C₂⁴×C₃₁	—	2	1	no	—
198	#41×C₃₁	—	8	2	no	—
199	C₂×Q₈×C₃₁	—	2	1	no	—
200	C₂×Q₈×C₃₁	—	2	1	no	—
201	C₂×Q₈×C₃₁	—	2	1	no	—
202	C₂×Q₈×C₃₁	—	2	4	no	—
203	C₂×Q₈×C₃₁	—	2	4	no	—
204	C₂×Q₈×C₃₁	—	2	1	no	—
205	C₂×Q₈×C₃₁	—	8	4	no	—
206	C₂×Q₈×C₃₁	—	8	4	no	—
207	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	2	no	—
212	C₂×D₄×C₃₁	—	2	1	no	—
213	C₂×D₄×C₃₁	—	2	1	no	—
214	C₂×D₄×C₃₁	—	2	1	no	—
215	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
216	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₃₁	—	2	1	no	—
218	C₂²×C₄×C₃₁	—	2	2	no	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	—	2	4	no	—
221	C₂²×C₄×C₃₁	—	2	4	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	4	no	—
224	C₂²×C₄×C₃₁	—	8	2	no	—
225	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
228	SD₁₆×C₃₁	—	2	8	no	—
229	D₈×C₃₁	—	2	4	no	—
230	D₈×C₃₁	—	2	4	no	—
231	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
232	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
233	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
234	C₄⋊C₄×C₃₁	—	2	2	no	—
235	C₄⋊C₄×C₃₁	—	2	1	no	—
236	C₄⋊C₄×C₃₁	—	2	4	no	—
237	C₄⋊C₄×C₃₁	—	2	4	no	—
238	C₄⋊C₄×C₃₁	—	2	4	no	—
239	C₄⋊C₄×C₃₁	—	2	1	no	—
240	C₄⋊C₄×C₃₁	—	2	1	no	—
241	C₄⋊C₄×C₃₁	—	2	1	no	—
242	C₄⋊C₄×C₃₁	—	2	1	no	—
243	C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₄⋊C₄×C₃₁	—	2	2	no	—
245	C₄⋊C₄×C₃₁	—	2	1	no	—
246	C₄⋊C₄×C₃₁	—	2	2	no	—
247	C₄⋊C₄×C₃₁	—	2	4	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	2	no	—
250	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
251	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
252	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
256	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂²⋊C₄×C₃₁	—	2	2	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	2	no	—
266	C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂²⋊C₄×C₃₁	—	2	4	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
273	C₄²×C₃₁	—	2	2	no	—
274	C₄²×C₃₁	—	2	4	no	—
275	C₄²×C₃₁	—	2	2	no	—
276	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₄²×C₃₁	C₂⁴	1	4	yes	—
280	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
281	#61849	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
282	C₂³×C₃₁	—	2	4	no	—
283	C₂³×C₃₁	—	2	2	no	—
284	C₂³×C₃₁	—	2	2	no	—
285	C₂³×C₃₁	—	8	1	no	—
286	C₂³×C₃₁	—	8	1	no	—
287	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
288	Q₈×C₃₁	—	2	4	no	—
289	Q₈×C₃₁	—	2	4	no	—
290	Q₈×C₃₁	—	4	2	no	—
291	Q₈×C₃₁	—	4	2	no	—
292	Q₈×C₃₁	—	4	2	no	—
293	Q₈×C₃₁	—	8	1	no	—
294	Q₈×C₃₁	—	8	4	no	—
295	Q₈×C₃₁	—	8	4	no	—
296	Q₈×C₃₁	—	8	1	no	—
297	D₄×C₃₁	—	2	4	no	—
298	D₄×C₃₁	—	2	2	no	—
299	D₄×C₃₁	—	2	2	no	—
300	D₄×C₃₁	—	2	2	no	—
301	D₄×C₃₁	—	4	2	no	—
302	D₄×C₃₁	—	8	1	no	—
303	D₄×C₃₁	—	8	2	no	—
304	D₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	2	no	—
307	C₂×C₄×C₃₁	—	2	2	no	—
308	C₂×C₄×C₃₁	—	2	2	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	4	1	no	—
314	C₂×C₄×C₃₁	—	4	4	no	—
315	C₂×C₄×C₃₁	—	4	4	no	—
316	C₂×C₄×C₃₁	—	8	4	no	—
317	C₂×C₄×C₃₁	—	8	2	no	—
318	C₂×C₄×C₃₁	—	8	4	no	—
319	C₂×C₄×C₃₁	—	8	4	no	—
320	C₂×C₄×C₃₁	—	8	1	no	—
321	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
324	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
327	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
329	C₈×C₃₁	—	2	2	no	—
330	C₈×C₃₁	—	2	2	no	—
331	C₈×C₃₁	—	2	4	no	—
332	#3550	C₂×C₃₁	1	1	yes	characteristic, complemented
333	#3501	C₂×C₃₁	1	1	yes	characteristic, complemented
334	#3385	C₂×C₃₁	1	4	yes	complemented
335	#3384	C₂×C₃₁	1	2	yes	complemented
336	Q₈×D₈	C₂×C₃₁	1	2	yes	complemented
337	#3370	C₂×C₃₁	1	4	yes	complemented
338	#3367	C₂×C₃₁	1	2	yes	complemented
339	#3360	C₂×C₃₁	1	2	yes	complemented
340	#3243	C₂×C₃₁	1	4	yes	complemented
341	#3235	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
343	#3118	C₂×C₃₁	1	4	yes	complemented
344	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#3100	C₂×C₃₁	1	1	yes	characteristic
346	#2985	C₂×C₃₁	1	1	yes	characteristic, complemented
347	C₂²×C₃₁	—	2	1	no	—
348	C₂²×C₃₁	—	2	1	no	—
349	C₂²×C₃₁	—	2	4	no	—
350	C₂²×C₃₁	—	2	1	no	—
351	C₂²×C₃₁	—	4	2	no	—
352	C₂²×C₃₁	—	4	2	no	—
353	C₂²×C₃₁	—	4	2	no	—
354	C₂²×C₃₁	—	4	2	no	—
355	C₂²×C₃₁	—	4	2	no	—
356	C₂²×C₃₁	—	8	4	no	—
357	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
358	C₄×C₃₁	—	2	1	no	—
359	C₄×C₃₁	—	2	1	no	—
360	C₄×C₃₁	—	2	4	no	—
361	C₄×C₃₁	—	2	1	no	—
362	C₄×C₃₁	—	2	1	no	—
363	C₄×C₃₁	—	2	4	no	—
364	C₄×C₃₁	—	4	2	no	—
365	C₄×C₃₁	—	4	2	no	—
366	C₄×C₃₁	—	4	2	no	—
367	C₄×C₃₁	—	4	2	no	—
368	C₄×C₃₁	—	4	2	no	—
369	C₄×C₃₁	—	4	2	no	—
370	C₄×C₃₁	#576	1	2	yes	—
371	C₄×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
372	#563	—	2	2	no	—
373	#559	C₂²×C₃₁	1	2	yes	complemented
374	Q₈²	C₂²×C₃₁	1	2	yes	complemented
375	#556	—	2	1	no	—
376	#556	C₂²×C₃₁	1	2	yes	complemented
377	#554	—	2	1	no	—
378	#554	—	2	2	no	—
379	#554	C₂²×C₃₁	1	2	yes	—
380	#554	C₂²×C₃₁	1	4	yes	—
381	D₄×Q₈	—	2	1	no	—
382	D₄×Q₈	—	2	1	no	—
383	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
384	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
385	#544	C₂²×C₃₁	1	2	yes	—
386	#543	—	2	2	no	—
387	#542	—	2	2	no	—
388	#542	C₂²×C₃₁	1	4	yes	—
389	#536	—	2	2	no	—
390	#533	C₂²×C₃₁	1	1	yes	characteristic
391	#533	C₂²×C₃₁	1	1	yes	characteristic
392	#533	C₂²×C₃₁	1	1	yes	characteristic
393	#532	C₂²×C₃₁	1	1	yes	characteristic
394	C₂×C₂²⋊Q₈	—	2	2	no	—
395	#518	C₂²×C₃₁	1	2	yes	—
396	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
397	#501	C₂²×C₃₁	1	4	yes	complemented
398	#501	C₂²×C₃₁	1	2	yes	complemented
399	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
400	#500	C₂²×C₃₁	1	4	yes	complemented
401	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
402	#490	C₂²×C₃₁	1	2	yes	complemented
403	#489	C₂²×C₃₁	1	4	yes	complemented
404	#488	C₂²×C₃₁	1	4	yes	complemented
405	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
406	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
407	#485	C₂²×C₃₁	1	4	yes	—
408	#484	C₂²×C₃₁	1	2	yes	—
409	#482	C₂²×C₃₁	1	4	yes	—
410	#480	C₂²×C₃₁	1	2	yes	—
411	#479	C₂²×C₃₁	1	4	yes	complemented
412	#479	C₂²×C₃₁	1	4	yes	complemented
413	#478	C₂²×C₃₁	1	4	yes	complemented
414	#477	C₂²×C₃₁	1	4	yes	complemented
415	#476	C₂²×C₃₁	1	4	yes	—
416	#476	C₂²×C₃₁	1	2	yes	complemented
417	#474	C₂²×C₃₁	1	2	yes	—
418	#474	C₂²×C₃₁	1	2	yes	—
419	#474	C₂²×C₃₁	1	4	yes	—
420	#474	C₂²×C₃₁	1	2	yes	complemented
421	#474	C₂²×C₃₁	1	4	yes	complemented
422	#463	C₂²×C₃₁	1	4	yes	—
423	#463	C₂²×C₃₁	1	4	yes	—
424	#461	C₂²×C₃₁	1	2	yes	—
425	#459	C₂²×C₃₁	1	2	yes	—
426	#450	C₂²×C₃₁	1	2	yes	—
427	#447	C₂²×C₃₁	1	2	yes	—
428	#446	C₂²×C₃₁	1	2	yes	complemented
429	#446	C₂²×C₃₁	1	4	yes	complemented
430	C₈×Q₈	C₂²×C₃₁	1	2	yes	complemented
431	#442	C₂²×C₃₁	1	4	yes	—
432	#440	C₂²×C₃₁	1	4	yes	—
433	#440	C₂²×C₃₁	1	4	yes	—
434	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	—
435	C₄×D₈	C₂²×C₃₁	1	2	yes	—
436	C₄×D₈	C₂²×C₃₁	1	2	yes	—
437	C₄×D₈	C₂²×C₃₁	1	4	yes	—
438	#433	C₂²×C₃₁	1	4	yes	—
439	#432	C₂²×C₃₁	1	1	yes	characteristic
440	#431	C₂²×C₃₁	1	1	yes	characteristic
441	C₂×C₃₁	—	4	1	no	—
442	C₂×C₃₁	—	4	4	no	—
443	C₂×C₃₁	—	8	2	no	—
444	C₂×C₃₁	#3486	1	1	yes	characteristic
445	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
446	C₂×C₃₁	#3586	1	1	yes	characteristic
447	C₂×#41	—	2	1	no	—
448	C₂²×Q₈	—	2	2	no	—
449	C₂²×Q₈	—	2	2	no	—
450	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
451	C₂³×C₄	—	2	1	no	—
452	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
453	C₂×D₈	C₂³×C₃₁	1	2	yes	—
454	C₂×D₈	C₂³×C₃₁	1	2	yes	—
455	C₄⋊Q₈	—	2	4	no	—
456	C₄⋊Q₈	—	2	2	no	—
457	C₄⋊Q₈	—	2	2	no	—
458	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
459	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
460	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
461	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
462	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
466	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
467	#127	C₂³×C₃₁	1	1	yes	characteristic
468	#126	—	2	4	no	—
469	#126	—	2	4	no	—
470	#125	—	2	2	no	—
471	#125	—	2	1	no	—
472	#125	D₄×C₃₁	1	2	yes	—
473	#125	C₂³×C₃₁	1	2	yes	—
474	#125	C₂³×C₃₁	1	4	yes	—
475	#124	—	2	2	no	—
476	#124	—	2	4	no	—
477	#124	—	2	1	no	—
478	#124	C₂³×C₃₁	1	4	yes	—
479	#123	—	2	4	no	—
480	#123	—	2	4	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	4	no	—
484	C₂²⋊Q₈	—	2	1	no	—
485	C₂²⋊Q₈	—	2	1	no	—
486	C₂²⋊Q₈	—	2	1	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	4	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	—	2	4	no	—
494	C₂²⋊Q₈	—	2	4	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
497	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
498	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
499	#121	—	2	1	no	—
500	#121	C₂³×C₃₁	1	2	yes	—
501	C₄×Q₈	—	2	2	no	—
502	C₄×Q₈	—	2	1	no	—
503	C₄×Q₈	—	2	1	no	—
504	C₄×Q₈	—	2	1	no	—
505	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
506	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
507	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
508	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	C₂³×C₃₁	1	2	yes	—
516	C₄×D₄	C₂³×C₃₁	1	2	yes	—
517	C₄×D₄	C₂³×C₃₁	1	4	yes	—
518	C₄×D₄	C₂³×C₃₁	1	4	yes	—
519	C₄×D₄	C₂³×C₃₁	1	2	yes	—
520	C₄×D₄	C₂³×C₃₁	1	4	yes	—
521	#117	—	2	1	no	—
522	#117	—	2	2	no	—
523	#117	C₂³×C₃₁	1	2	yes	—
524	#117	C₂³×C₃₁	1	2	yes	—
525	C₂×C₄⋊C₄	—	2	4	no	—
526	C₂×C₄⋊C₄	—	2	2	no	—
527	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	4	no	—
530	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
531	#107	C₂³×C₃₁	1	4	yes	—
532	#107	C₂³×C₃₁	1	2	yes	—
533	#107	C₂³×C₃₁	1	2	yes	—
534	#107	C₂³×C₃₁	1	4	yes	—
535	#107	C₂³×C₃₁	1	4	yes	—
536	#106	C₂³×C₃₁	1	4	yes	—
537	#106	C₂³×C₃₁	1	4	yes	—
538	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
539	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
540	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
541	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
542	#103	C₂³×C₃₁	1	4	yes	—
543	#103	C₂³×C₃₁	1	4	yes	—
544	#103	C₂³×C₃₁	1	4	yes	—
545	#102	C₂³×C₃₁	1	2	yes	—
546	#102	C₂³×C₃₁	1	2	yes	—
547	#102	C₂³×C₃₁	1	4	yes	—
548	#102	C₂³×C₃₁	1	2	yes	—
549	#102	C₂³×C₃₁	1	2	yes	—
550	#102	C₂³×C₃₁	1	4	yes	—
551	#102	C₂³×C₃₁	1	4	yes	—
552	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
553	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
554	#97	C₂³×C₃₁	1	2	yes	—
555	#97	C₂³×C₃₁	1	4	yes	—
556	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
557	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
558	C₄×C₈	C₂³×C₃₁	1	4	yes	—
559	C₃₁	#61849	1	1	yes	characteristic, direct product factor, Sylow
560	C₂⁴	—	2	1	no	—
561	#41	—	8	2	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	8	4	no	—
569	C₂×Q₈	—	8	4	no	—
570	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
571	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
572	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
579	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	8	2	no	—
588	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
591	SD₁₆	—	2	8	no	—
592	D₈	—	2	4	no	—
593	D₈	—	2	4	no	—
594	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
595	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
596	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
614	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
615	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
616	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
618	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
619	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
620	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
621	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	2	no	—
639	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
641	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
642	C₄²	C₂⁴×C₃₁	1	4	yes	—
643	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
644	C₂³	—	2	4	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	8	1	no	—
648	C₂³	—	8	1	no	—
649	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
650	Q₈	—	2	4	no	—
651	Q₈	—	2	4	no	—
652	Q₈	—	4	2	no	—
653	Q₈	—	4	2	no	—
654	Q₈	—	4	2	no	—
655	Q₈	—	8	1	no	—
656	Q₈	—	8	4	no	—
657	Q₈	—	8	4	no	—
658	Q₈	—	8	1	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	2	2	no	—
663	D₄	—	4	2	no	—
664	D₄	—	8	1	no	—
665	D₄	—	8	2	no	—
666	D₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	—	8	2	no	—
680	C₂×C₄	—	8	4	no	—
681	C₂×C₄	—	8	4	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
685	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
686	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
689	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
690	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
691	C₈	—	2	2	no	—
692	C₈	—	2	2	no	—
693	C₈	—	2	4	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	4	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	8	4	no	—
704	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
705	C₄	—	2	1	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	4	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	C₃₁×#576	1	2	yes	—
718	C₄	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
719	C₂	—	4	1	no	—
720	C₂	—	4	4	no	—
721	C₂	—	8	2	no	—
722	C₂	C₃₁×#3486	1	1	yes	characteristic
723	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
724	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×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3550	C₂	semidirect
2. C₃₁×#3501	C₂	semidirect
3. C₃₁×#3385	C₂	semidirect
4. C₃₁×#3384	C₂	semidirect
5. Q₈×D₈×C₃₁	C₂	semidirect
6. C₃₁×#3370	C₂	semidirect
7. C₃₁×#3367	C₂	semidirect
8. C₃₁×#3360	C₂	semidirect
9. C₃₁×#3243	C₂	semidirect
10. C₃₁×#3235	C₂	semidirect
11. C₃₁×#3231	C₂	semidirect
12. C₃₁×#3118	C₂	semidirect
13. C₃₁×#3110	C₂	semidirect
15. C₃₁×#2985	C₂	semidirect
17. C₃₁×#559	C₂²	semidirect
18. Q₈²×C₃₁	C₂²	semidirect
20. C₃₁×#556	C₂²	semidirect
28. D₄×Q₈×C₃₁	C₂²	semidirect
41. C₃₁×#501	C₂²	semidirect
42. C₃₁×#501	C₂²	semidirect
43. C₃₁×#500	C₂²	semidirect
44. C₃₁×#500	C₂²	semidirect
45. C₃₁×#498	C₂²	semidirect
46. C₃₁×#490	C₂²	semidirect
47. C₃₁×#489	C₂²	semidirect
48. C₃₁×#488	C₂²	semidirect
49. C₃₁×#487	C₂²	semidirect
50. C₃₁×#487	C₂²	semidirect
55. C₃₁×#479	C₂²	semidirect
56. C₃₁×#479	C₂²	semidirect
57. C₃₁×#478	C₂²	semidirect
58. C₃₁×#477	C₂²	semidirect
60. C₃₁×#476	C₂²	semidirect
64. C₃₁×#474	C₂²	semidirect
65. C₃₁×#474	C₂²	semidirect
72. C₃₁×#446	C₂²	semidirect
73. C₃₁×#446	C₂²	semidirect
74. C₈×Q₈×C₃₁	C₂²	semidirect
281. #61849	C₃₁	direct (N × H)
332. #3550	C₂×C₃₁	semidirect
333. #3501	C₂×C₃₁	semidirect
334. #3385	C₂×C₃₁	semidirect
335. #3384	C₂×C₃₁	semidirect
336. Q₈×D₈	C₂×C₃₁	semidirect
337. #3370	C₂×C₃₁	semidirect
338. #3367	C₂×C₃₁	semidirect
339. #3360	C₂×C₃₁	semidirect
340. #3243	C₂×C₃₁	semidirect
341. #3235	C₂×C₃₁	semidirect
342. #3231	C₂×C₃₁	semidirect
343. #3118	C₂×C₃₁	semidirect
344. #3110	C₂×C₃₁	semidirect
346. #2985	C₂×C₃₁	semidirect
373. #559	C₂²×C₃₁	semidirect
374. Q₈²	C₂²×C₃₁	semidirect
376. #556	C₂²×C₃₁	semidirect
384. D₄×Q₈	C₂²×C₃₁	semidirect
397. #501	C₂²×C₃₁	semidirect
398. #501	C₂²×C₃₁	semidirect
399. #500	C₂²×C₃₁	semidirect
400. #500	C₂²×C₃₁	semidirect
401. #498	C₂²×C₃₁	semidirect
402. #490	C₂²×C₃₁	semidirect
403. #489	C₂²×C₃₁	semidirect
404. #488	C₂²×C₃₁	semidirect
405. #487	C₂²×C₃₁	semidirect
406. #487	C₂²×C₃₁	semidirect
411. #479	C₂²×C₃₁	semidirect
412. #479	C₂²×C₃₁	semidirect
413. #478	C₂²×C₃₁	semidirect
414. #477	C₂²×C₃₁	semidirect
416. #476	C₂²×C₃₁	semidirect
420. #474	C₂²×C₃₁	semidirect
421. #474	C₂²×C₃₁	semidirect
428. #446	C₂²×C₃₁	semidirect
429. #446	C₂²×C₃₁	semidirect
430. C₈×Q₈	C₂²×C₃₁	semidirect
559. C₃₁	#61849	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×#3550	2
C₃₁×#3501	2
C₃₁×#3385	2
C₃₁×#3384	2
Q₈×D₈×C₃₁	2
C₃₁×#3370	2
C₃₁×#3367	2
C₃₁×#3360	2
C₃₁×#3243	2
C₃₁×#3235	2
C₃₁×#3231	2
C₃₁×#3118	2
C₃₁×#3110	2
C₃₁×#3100	2
C₃₁×#2985	2
#61849	31

Subgroups — C31×#61849 #21518608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61849 #21518608