Subgroups — C₃₁×#61482 #21518241

Order 7936.

1882 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3520	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3338	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3330	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3314	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3280	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3175	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3124	C₂	1	4	yes	maximal, complemented
14	C₃₁×#3110	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#2951	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#135	C₂²	1	2	yes	—
19	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#556	C₂²	1	2	yes	complemented
21	C₃₁×#554	C₂²	1	4	yes	—
22	C₃₁×#552	—	2	2	no	—
23	C₃₁×#551	—	2	4	no	—
24	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
25	C₃₁×#548	—	2	2	no	—
26	C₃₁×#547	C₂²	1	2	yes	complemented
27	C₃₁×#547	C₂²	1	2	yes	complemented
28	C₃₁×#546	C₂²	1	4	yes	—
29	C₃₁×#542	C₂²	1	4	yes	complemented
30	C₃₁×#539	—	2	4	no	—
31	C₃₁×#533	C₂²	1	2	yes	—
32	C₃₁×#529	C₂²	1	1	yes	characteristic
33	C₃₁×#525	—	2	2	no	—
34	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
35	C₃₁×#520	C₂²	1	4	yes	complemented
36	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
37	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#500	C₂²	1	2	yes	complemented
39	C₃₁×#495	C₂²	1	2	yes	—
40	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#489	C₂²	1	4	yes	complemented
42	C₃₁×#487	C₂²	1	2	yes	complemented
43	C₃₁×#484	C₂²	1	4	yes	—
44	C₃₁×#484	C₂²	1	4	yes	complemented
45	C₃₁×#480	C₂²	1	4	yes	complemented
46	C₃₁×#477	C₂²	1	4	yes	complemented
47	C₃₁×#474	C₂²	1	2	yes	complemented
48	C₃₁×#474	C₂²	1	2	yes	complemented
49	C₃₁×#474	C₂²	1	4	yes	complemented
50	C₃₁×#468	C₂²	1	4	yes	complemented
51	C₃₁×#467	C₂²	1	2	yes	—
52	C₃₁×#467	C₂²	1	2	yes	—
53	C₃₁×#467	C₂²	1	2	yes	complemented
54	C₃₁×#466	C₂²	1	2	yes	—
55	C₃₁×#464	C₂²	1	4	yes	complemented
56	C₃₁×#463	C₂²	1	4	yes	—
57	C₃₁×#461	C₂²	1	2	yes	complemented
58	C₃₁×#461	C₂²	1	2	yes	complemented
59	C₃₁×#452	C₂²	1	4	yes	complemented
60	C₃₁×#450	C₂²	1	4	yes	—
61	C₃₁×#449	C₂²	1	4	yes	—
62	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#440	C₂²	1	4	yes	complemented
65	C₃₁×#440	C₂²	1	4	yes	complemented
66	C₃₁×#440	C₂²	1	4	yes	complemented
67	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
68	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
69	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
70	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
71	C₄×D₈×C₃₁	C₂²	1	2	yes	—
72	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
73	C₄×D₈×C₃₁	C₂²	1	2	yes	—
74	C₄×D₈×C₃₁	C₂²	1	2	yes	—
75	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
76	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
77	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#435	C₂²	1	2	yes	—
79	C₈×D₄×C₃₁	C₂²	1	2	yes	—
80	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#433	C₂²	1	2	yes	complemented
82	C₃₁×#432	C₂²	1	1	yes	characteristic
83	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
84	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
85	C₃₁×#417	C₂²	1	4	yes	complemented
86	C₂×C₃₁×#102	C₂²	1	2	yes	—
87	C₃₁×#405	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
89	C₂×#41×C₃₁	—	2	2	no	—
90	C₂×#41×C₃₁	C₂³	1	4	yes	—
91	C₂²×Q₈×C₃₁	—	2	2	no	—
92	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₃₁	—	2	2	no	—
94	C₃₁×#135	—	2	8	no	—
95	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
96	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
97	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
99	C₂×D₈×C₃₁	—	2	4	no	—
100	C₂×D₈×C₃₁	C₂³	1	2	yes	—
101	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
102	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
106	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
107	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₃₁×#126	—	2	4	no	—
111	C₃₁×#126	—	2	4	no	—
112	C₃₁×#126	D₄	1	2	yes	—
113	C₃₁×#125	—	2	4	no	—
114	C₃₁×#125	—	2	2	no	—
115	C₃₁×#125	D₄	1	1	yes	characteristic
116	C₃₁×#124	—	2	4	no	—
117	C₃₁×#124	D₄	1	1	yes	characteristic
118	C₃₁×#124	C₂³	1	4	yes	—
119	C₃₁×#123	—	2	4	no	—
120	C₃₁×#123	—	2	4	no	—
121	C₃₁×#123	—	2	4	no	—
122	C₃₁×#123	—	2	4	no	—
123	C₃₁×#123	D₄	1	2	yes	—
124	C₃₁×C₂²⋊Q₈	—	2	2	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	2	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	D₄	1	1	yes	characteristic
133	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₃₁×#121	—	2	2	no	—
136	C₃₁×#121	—	2	4	no	—
137	C₃₁×#121	D₄	1	1	yes	characteristic
138	C₃₁×#121	C₂³	1	4	yes	—
139	C₃₁×#120	—	2	4	no	—
140	C₄×Q₈×C₃₁	—	2	2	no	—
141	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
142	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
143	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
144	C₄×D₄×C₃₁	—	2	4	no	—
145	C₄×D₄×C₃₁	—	2	4	no	—
146	C₄×D₄×C₃₁	—	2	4	no	—
147	C₄×D₄×C₃₁	—	2	2	no	—
148	C₄×D₄×C₃₁	—	2	2	no	—
149	C₄×D₄×C₃₁	C₂³	1	2	yes	—
150	C₄×D₄×C₃₁	C₂³	1	2	yes	—
151	C₄×D₄×C₃₁	C₂³	1	2	yes	—
152	C₄×D₄×C₃₁	C₂³	1	2	yes	—
153	C₄×D₄×C₃₁	C₂³	1	4	yes	—
154	C₄×D₄×C₃₁	C₂³	1	2	yes	—
155	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₃₁×#117	—	2	2	no	—
157	C₃₁×#117	—	2	4	no	—
158	C₃₁×#117	—	2	2	no	—
159	C₃₁×#117	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
161	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
162	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
165	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
166	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
167	C₃₁×#107	C₂³	1	1	yes	characteristic
168	C₃₁×#107	C₂³	1	1	yes	characteristic
169	C₃₁×#107	C₂³	1	2	yes	—
170	C₃₁×#107	C₂³	1	2	yes	—
171	C₃₁×#107	C₂³	1	4	yes	—
172	C₃₁×#107	C₂³	1	2	yes	—
173	C₃₁×#107	C₂³	1	4	yes	—
174	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
177	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
178	C₃₁×#103	C₂³	1	4	yes	—
179	C₃₁×#103	C₂³	1	4	yes	—
180	C₃₁×#103	C₂³	1	4	yes	—
181	C₃₁×#103	C₂³	1	4	yes	—
182	C₃₁×#102	C₂³	1	2	yes	—
183	C₃₁×#102	C₂³	1	2	yes	—
184	C₃₁×#102	C₂³	1	2	yes	—
185	C₃₁×#102	C₂³	1	2	yes	—
186	C₃₁×#102	C₂³	1	4	yes	—
187	C₃₁×#102	C₂³	1	4	yes	—
188	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₃₁×#97	C₂³	1	2	yes	—
192	C₃₁×#97	C₂³	1	2	yes	—
193	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₃₁	C₂³	1	2	yes	—
198	C₂⁴×C₃₁	—	2	2	no	—
199	#41×C₃₁	—	2	8	no	—
200	#41×C₃₁	—	4	4	no	—
201	#41×C₃₁	—	8	4	no	—
202	C₂×Q₈×C₃₁	—	2	2	no	—
203	C₂×Q₈×C₃₁	—	2	4	no	—
204	C₂×Q₈×C₃₁	—	8	4	no	—
205	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
206	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
207	C₂×D₄×C₃₁	—	2	4	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	—	2	4	no	—
210	C₂×D₄×C₃₁	—	2	2	no	—
211	C₂×D₄×C₃₁	—	4	2	no	—
212	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
213	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
214	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
215	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₃₁	—	2	2	no	—
217	C₂²×C₄×C₃₁	—	2	4	no	—
218	C₂²×C₄×C₃₁	—	2	4	no	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	—	2	2	no	—
221	C₂²×C₄×C₃₁	—	2	4	no	—
222	C₂²×C₄×C₃₁	—	2	2	no	—
223	C₂²×C₄×C₃₁	—	2	2	no	—
224	C₂²×C₄×C₃₁	—	8	4	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	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
229	Q₁₆×C₃₁	—	2	4	no	—
230	Q₁₆×C₃₁	—	4	2	no	—
231	SD₁₆×C₃₁	—	2	8	no	—
232	SD₁₆×C₃₁	—	4	4	no	—
233	D₈×C₃₁	—	2	4	no	—
234	D₈×C₃₁	—	2	2	no	—
235	D₈×C₃₁	#41	1	4	yes	complemented
236	M₁₆×C₃₁	—	4	2	no	—
237	C₂×C₈×C₃₁	—	2	2	no	—
238	C₂×C₈×C₃₁	—	2	4	no	—
239	C₂×C₈×C₃₁	—	4	1	no	—
240	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
244	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
245	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
246	C₄⋊C₄×C₃₁	—	2	4	no	—
247	C₄⋊C₄×C₃₁	—	2	2	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	4	no	—
250	C₄⋊C₄×C₃₁	—	2	4	no	—
251	C₄⋊C₄×C₃₁	—	2	2	no	—
252	C₄⋊C₄×C₃₁	—	2	2	no	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	—	2	4	no	—
255	C₄⋊C₄×C₃₁	—	2	4	no	—
256	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
258	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
260	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂²⋊C₄×C₃₁	—	2	4	no	—
272	C₂²⋊C₄×C₃₁	—	2	4	no	—
273	C₂²⋊C₄×C₃₁	—	2	4	no	—
274	C₂²⋊C₄×C₃₁	—	2	4	no	—
275	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
276	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
278	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
279	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
280	C₄²×C₃₁	—	2	4	no	—
281	C₄²×C₃₁	—	2	4	no	—
282	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
286	C₄²×C₃₁	C₂⁴	1	2	yes	—
287	#61482	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	2	2	no	—
290	C₂³×C₃₁	—	4	4	no	—
291	C₂³×C₃₁	—	4	4	no	—
292	C₂³×C₃₁	—	8	2	no	—
293	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
294	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₃₁	—	2	2	no	—
296	Q₈×C₃₁	—	2	4	no	—
297	Q₈×C₃₁	—	2	4	no	—
298	Q₈×C₃₁	—	4	4	no	—
299	Q₈×C₃₁	—	8	4	no	—
300	D₄×C₃₁	—	2	4	no	—
301	D₄×C₃₁	—	2	2	no	—
302	D₄×C₃₁	—	2	2	no	—
303	D₄×C₃₁	—	2	2	no	—
304	D₄×C₃₁	—	2	2	no	—
305	D₄×C₃₁	—	4	4	no	—
306	D₄×C₃₁	—	4	8	no	—
307	D₄×C₃₁	—	8	4	no	—
308	D₄×C₃₁	C₂×#41	1	4	yes	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	1	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	1	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	4	no	—
316	C₂×C₄×C₃₁	—	2	2	no	—
317	C₂×C₄×C₃₁	—	2	4	no	—
318	C₂×C₄×C₃₁	—	2	2	no	—
319	C₂×C₄×C₃₁	—	4	8	no	—
320	C₂×C₄×C₃₁	—	4	4	no	—
321	C₂×C₄×C₃₁	—	4	4	no	—
322	C₂×C₄×C₃₁	—	8	2	no	—
323	C₂×C₄×C₃₁	—	8	2	no	—
324	C₂×C₄×C₃₁	—	8	4	no	—
325	C₂×C₄×C₃₁	—	8	2	no	—
326	C₂×C₄×C₃₁	—	8	4	no	—
327	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
336	C₈×C₃₁	—	2	1	no	—
337	C₈×C₃₁	—	2	2	no	—
338	C₈×C₃₁	—	2	1	no	—
339	C₈×C₃₁	—	2	1	no	—
340	C₈×C₃₁	—	2	2	no	—
341	C₈×C₃₁	C₂×#41	1	2	yes	—
342	#3520	C₂×C₃₁	1	2	yes	complemented
343	#3393	C₂×C₃₁	1	1	yes	characteristic, complemented
344	Q₈×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#3367	C₂×C₃₁	1	2	yes	complemented
346	#3338	C₂×C₃₁	1	2	yes	complemented
347	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
348	#3330	C₂×C₃₁	1	2	yes	complemented
349	#3314	C₂×C₃₁	1	4	yes	complemented
350	#3283	C₂×C₃₁	1	1	yes	characteristic, complemented
351	#3280	C₂×C₃₁	1	2	yes	complemented
352	#3175	C₂×C₃₁	1	2	yes	complemented
353	#3170	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3124	C₂×C₃₁	1	4	yes	complemented
355	#3110	C₂×C₃₁	1	2	yes	complemented
356	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#2951	C₂×C₃₁	1	2	yes	complemented
358	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
359	C₂²×C₃₁	—	2	1	no	—
360	C₂²×C₃₁	—	2	1	no	—
361	C₂²×C₃₁	—	2	2	no	—
362	C₂²×C₃₁	—	2	4	no	—
363	C₂²×C₃₁	—	2	2	no	—
364	C₂²×C₃₁	—	2	2	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	2	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	—	4	2	no	—
369	C₂²×C₃₁	—	4	2	no	—
370	C₂²×C₃₁	—	8	8	no	—
371	C₂²×C₃₁	#578	1	2	yes	—
372	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
373	C₄×C₃₁	—	2	2	no	—
374	C₄×C₃₁	—	2	1	no	—
375	C₄×C₃₁	—	2	1	no	—
376	C₄×C₃₁	—	2	2	no	—
377	C₄×C₃₁	—	2	1	no	—
378	C₄×C₃₁	—	2	1	no	—
379	C₄×C₃₁	—	2	2	no	—
380	C₄×C₃₁	—	4	4	no	—
381	C₄×C₃₁	—	4	2	no	—
382	C₄×C₃₁	—	4	2	no	—
383	C₄×C₃₁	—	4	4	no	—
384	C₄×C₃₁	#576	1	2	yes	—
385	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
386	C₄×C₃₁	#585	1	1	yes	characteristic
387	C₂×#135	C₂²×C₃₁	1	2	yes	—
388	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
389	#556	C₂²×C₃₁	1	2	yes	complemented
390	#554	C₂²×C₃₁	1	4	yes	—
391	#552	—	2	2	no	—
392	#551	—	2	4	no	—
393	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
394	#548	—	2	2	no	—
395	#547	C₂²×C₃₁	1	2	yes	complemented
396	#547	C₂²×C₃₁	1	2	yes	complemented
397	#546	C₂²×C₃₁	1	4	yes	—
398	#542	C₂²×C₃₁	1	4	yes	complemented
399	#539	—	2	4	no	—
400	#533	C₂²×C₃₁	1	2	yes	—
401	#529	C₂²×C₃₁	1	1	yes	characteristic
402	#525	—	2	2	no	—
403	C₂×C₂²⋊Q₈	—	2	2	no	—
404	#520	C₂²×C₃₁	1	4	yes	complemented
405	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
406	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
407	#500	C₂²×C₃₁	1	2	yes	complemented
408	#495	C₂²×C₃₁	1	2	yes	—
409	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
410	#489	C₂²×C₃₁	1	4	yes	complemented
411	#487	C₂²×C₃₁	1	2	yes	complemented
412	#484	C₂²×C₃₁	1	4	yes	—
413	#484	C₂²×C₃₁	1	4	yes	complemented
414	#480	C₂²×C₃₁	1	4	yes	complemented
415	#477	C₂²×C₃₁	1	4	yes	complemented
416	#474	C₂²×C₃₁	1	2	yes	complemented
417	#474	C₂²×C₃₁	1	2	yes	complemented
418	#474	C₂²×C₃₁	1	4	yes	complemented
419	#468	C₂²×C₃₁	1	4	yes	complemented
420	#467	C₂²×C₃₁	1	2	yes	—
421	#467	C₂²×C₃₁	1	2	yes	—
422	#467	C₂²×C₃₁	1	2	yes	complemented
423	#466	C₂²×C₃₁	1	2	yes	—
424	#464	C₂²×C₃₁	1	4	yes	complemented
425	#463	C₂²×C₃₁	1	4	yes	—
426	#461	C₂²×C₃₁	1	2	yes	complemented
427	#461	C₂²×C₃₁	1	2	yes	complemented
428	#452	C₂²×C₃₁	1	4	yes	complemented
429	#450	C₂²×C₃₁	1	4	yes	—
430	#449	C₂²×C₃₁	1	4	yes	—
431	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
432	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
433	#440	C₂²×C₃₁	1	4	yes	complemented
434	#440	C₂²×C₃₁	1	4	yes	complemented
435	#440	C₂²×C₃₁	1	4	yes	complemented
436	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
437	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
438	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
439	C₄×D₈	C₂²×C₃₁	1	2	yes	—
440	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
441	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
442	C₄×D₈	C₂²×C₃₁	1	2	yes	—
443	C₄×D₈	C₂²×C₃₁	1	2	yes	—
444	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
445	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
446	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
447	#435	C₂²×C₃₁	1	2	yes	—
448	C₈×D₄	C₂²×C₃₁	1	2	yes	—
449	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	#433	C₂²×C₃₁	1	2	yes	complemented
451	#432	C₂²×C₃₁	1	1	yes	characteristic
452	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
453	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
454	#417	C₂²×C₃₁	1	4	yes	complemented
455	C₂×#102	C₂²×C₃₁	1	2	yes	—
456	#405	C₂²×C₃₁	1	2	yes	complemented
457	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×C₃₁	—	2	2	no	—
459	C₂×C₃₁	—	4	2	no	—
460	C₂×C₃₁	—	4	4	no	—
461	C₂×C₃₁	—	8	2	no	—
462	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
463	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
464	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
465	C₂×#41	—	2	2	no	—
466	C₂×#41	C₂³×C₃₁	1	4	yes	—
467	C₂²×Q₈	—	2	2	no	—
468	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
469	C₂³×C₄	—	2	2	no	—
470	#135	—	2	8	no	—
471	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
472	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
473	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
474	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
475	C₂×D₈	—	2	4	no	—
476	C₂×D₈	C₂³×C₃₁	1	2	yes	—
477	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
478	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
479	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
480	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
482	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
483	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
484	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
485	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
486	#126	—	2	4	no	—
487	#126	—	2	4	no	—
488	#126	D₄×C₃₁	1	2	yes	—
489	#125	—	2	4	no	—
490	#125	—	2	2	no	—
491	#125	D₄×C₃₁	1	1	yes	characteristic
492	#124	—	2	4	no	—
493	#124	D₄×C₃₁	1	1	yes	characteristic
494	#124	C₂³×C₃₁	1	4	yes	—
495	#123	—	2	4	no	—
496	#123	—	2	4	no	—
497	#123	—	2	4	no	—
498	#123	—	2	4	no	—
499	#123	D₄×C₃₁	1	2	yes	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	—	2	2	no	—
505	C₂²⋊Q₈	—	2	4	no	—
506	C₂²⋊Q₈	—	2	4	no	—
507	C₂²⋊Q₈	—	2	4	no	—
508	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
509	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
510	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
511	#121	—	2	2	no	—
512	#121	—	2	4	no	—
513	#121	D₄×C₃₁	1	1	yes	characteristic
514	#121	C₂³×C₃₁	1	4	yes	—
515	#120	—	2	4	no	—
516	C₄×Q₈	—	2	2	no	—
517	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
518	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
519	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
520	C₄×D₄	—	2	4	no	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	C₂³×C₃₁	1	2	yes	—
526	C₄×D₄	C₂³×C₃₁	1	2	yes	—
527	C₄×D₄	C₂³×C₃₁	1	2	yes	—
528	C₄×D₄	C₂³×C₃₁	1	2	yes	—
529	C₄×D₄	C₂³×C₃₁	1	4	yes	—
530	C₄×D₄	C₂³×C₃₁	1	2	yes	—
531	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
532	#117	—	2	2	no	—
533	#117	—	2	4	no	—
534	#117	—	2	2	no	—
535	#117	C₂³×C₃₁	1	2	yes	—
536	C₂×C₄⋊C₄	—	2	4	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
540	C₂×C₂²⋊C₄	—	2	2	no	—
541	C₂×C₂²⋊C₄	—	2	4	no	—
542	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
543	#107	C₂³×C₃₁	1	1	yes	characteristic
544	#107	C₂³×C₃₁	1	1	yes	characteristic
545	#107	C₂³×C₃₁	1	2	yes	—
546	#107	C₂³×C₃₁	1	2	yes	—
547	#107	C₂³×C₃₁	1	4	yes	—
548	#107	C₂³×C₃₁	1	2	yes	—
549	#107	C₂³×C₃₁	1	4	yes	—
550	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
551	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
552	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
553	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
554	#103	C₂³×C₃₁	1	4	yes	—
555	#103	C₂³×C₃₁	1	4	yes	—
556	#103	C₂³×C₃₁	1	4	yes	—
557	#103	C₂³×C₃₁	1	4	yes	—
558	#102	C₂³×C₃₁	1	2	yes	—
559	#102	C₂³×C₃₁	1	2	yes	—
560	#102	C₂³×C₃₁	1	2	yes	—
561	#102	C₂³×C₃₁	1	2	yes	—
562	#102	C₂³×C₃₁	1	4	yes	—
563	#102	C₂³×C₃₁	1	4	yes	—
564	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
565	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
566	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
567	#97	C₂³×C₃₁	1	2	yes	—
568	#97	C₂³×C₃₁	1	2	yes	—
569	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
570	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
572	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
573	C₄×C₈	C₂³×C₃₁	1	2	yes	—
574	C₃₁	#61482	1	1	yes	characteristic, direct product factor, Sylow
575	C₂⁴	—	2	2	no	—
576	#41	—	2	8	no	—
577	#41	—	4	4	no	—
578	#41	—	8	4	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	8	4	no	—
582	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
583	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	4	2	no	—
589	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
590	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
591	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
592	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	8	4	no	—
602	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
604	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
605	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
606	Q₁₆	—	2	4	no	—
607	Q₁₆	—	4	2	no	—
608	SD₁₆	—	2	8	no	—
609	SD₁₆	—	4	4	no	—
610	D₈	—	2	4	no	—
611	D₈	—	2	2	no	—
612	D₈	#41×C₃₁	1	4	yes	complemented
613	M₁₆	—	4	2	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	4	no	—
616	C₂×C₈	—	4	1	no	—
617	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
618	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
619	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
621	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
622	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
636	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
637	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
638	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
653	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
654	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
655	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
656	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
660	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
661	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
662	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
663	C₄²	C₂⁴×C₃₁	1	2	yes	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	4	4	no	—
667	C₂³	—	4	4	no	—
668	C₂³	—	8	2	no	—
669	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
670	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
671	Q₈	—	2	2	no	—
672	Q₈	—	2	4	no	—
673	Q₈	—	2	4	no	—
674	Q₈	—	4	4	no	—
675	Q₈	—	8	4	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	4	4	no	—
682	D₄	—	4	8	no	—
683	D₄	—	8	4	no	—
684	D₄	C₂×#41×C₃₁	1	4	yes	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	4	8	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	—	8	2	no	—
700	C₂×C₄	—	8	4	no	—
701	C₂×C₄	—	8	2	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
705	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
710	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
711	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
712	C₈	—	2	1	no	—
713	C₈	—	2	2	no	—
714	C₈	—	2	1	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	2	no	—
717	C₈	C₂×#41×C₃₁	1	2	yes	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	8	8	no	—
730	C₂²	C₃₁×#578	1	2	yes	—
731	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
732	C₄	—	2	2	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	2	no	—
739	C₄	—	4	4	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	4	no	—
743	C₄	C₃₁×#576	1	2	yes	—
744	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
745	C₄	C₃₁×#585	1	1	yes	characteristic
746	C₂	—	2	2	no	—
747	C₂	—	4	2	no	—
748	C₂	—	4	4	no	—
749	C₂	—	8	2	no	—
750	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
751	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
752	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3520	C₂	semidirect
2. C₃₁×#3393	C₂	semidirect
3. Q₈×D₈×C₃₁	C₂	semidirect
4. C₃₁×#3367	C₂	semidirect
5. C₃₁×#3338	C₂	semidirect
6. C₃₁×#3334	C₂	semidirect
7. C₃₁×#3330	C₂	semidirect
8. C₃₁×#3314	C₂	semidirect
9. C₃₁×#3283	C₂	semidirect
10. C₃₁×#3280	C₂	semidirect
11. C₃₁×#3175	C₂	semidirect
12. C₃₁×#3170	C₂	semidirect
13. C₃₁×#3124	C₂	semidirect
14. C₃₁×#3110	C₂	semidirect
15. C₃₁×#2966	C₂	semidirect
16. C₃₁×#2951	C₂	semidirect
17. C₂×C₄×D₈×C₃₁	C₂	semidirect
20. C₃₁×#556	C₂²	semidirect
24. D₄×Q₈×C₃₁	C₂²	semidirect
26. C₃₁×#547	C₂²	semidirect
27. C₃₁×#547	C₂²	semidirect
29. C₃₁×#542	C₂²	semidirect
35. C₃₁×#520	C₂²	semidirect
37. C₃₁×#500	C₂²	semidirect
38. C₃₁×#500	C₂²	semidirect
40. C₃₁×#494	C₂²	semidirect
41. C₃₁×#489	C₂²	semidirect
42. C₃₁×#487	C₂²	semidirect
44. C₃₁×#484	C₂²	semidirect
45. C₃₁×#480	C₂²	semidirect
46. C₃₁×#477	C₂²	semidirect
47. C₃₁×#474	C₂²	semidirect
48. C₃₁×#474	C₂²	semidirect
49. C₃₁×#474	C₂²	semidirect
50. C₃₁×#468	C₂²	semidirect
53. C₃₁×#467	C₂²	semidirect
55. C₃₁×#464	C₂²	semidirect
57. C₃₁×#461	C₂²	semidirect
58. C₃₁×#461	C₂²	semidirect
59. C₃₁×#452	C₂²	semidirect
62. C₃₁×#446	C₂²	semidirect
63. C₈×Q₈×C₃₁	C₂²	semidirect
64. C₃₁×#440	C₂²	semidirect
65. C₃₁×#440	C₂²	semidirect
66. C₃₁×#440	C₂²	semidirect
67. C₄×Q₁₆×C₃₁	C₂²	semidirect
68. C₄×Q₁₆×C₃₁	C₂²	semidirect
69. C₄×Q₁₆×C₃₁	C₂²	semidirect
77. C₃₁×#436	C₂²	semidirect
80. C₈×D₄×C₃₁	C₂²	semidirect
81. C₃₁×#433	C₂²	semidirect
84. C₂×C₃₁×#107	C₂²	semidirect
85. C₃₁×#417	C₂²	semidirect
87. C₃₁×#405	C₂²	semidirect
235. D₈×C₃₁	#41	semidirect
287. #61482	C₃₁	direct (N × H)
342. #3520	C₂×C₃₁	semidirect
343. #3393	C₂×C₃₁	semidirect
344. Q₈×D₈	C₂×C₃₁	semidirect
345. #3367	C₂×C₃₁	semidirect
346. #3338	C₂×C₃₁	semidirect
347. #3334	C₂×C₃₁	semidirect
348. #3330	C₂×C₃₁	semidirect
349. #3314	C₂×C₃₁	semidirect
350. #3283	C₂×C₃₁	semidirect
351. #3280	C₂×C₃₁	semidirect
352. #3175	C₂×C₃₁	semidirect
353. #3170	C₂×C₃₁	semidirect
354. #3124	C₂×C₃₁	semidirect
355. #3110	C₂×C₃₁	semidirect
356. #2966	C₂×C₃₁	semidirect
357. #2951	C₂×C₃₁	semidirect
358. C₂×C₄×D₈	C₂×C₃₁	semidirect
389. #556	C₂²×C₃₁	semidirect
393. D₄×Q₈	C₂²×C₃₁	semidirect
395. #547	C₂²×C₃₁	semidirect
396. #547	C₂²×C₃₁	semidirect
398. #542	C₂²×C₃₁	semidirect
404. #520	C₂²×C₃₁	semidirect
406. #500	C₂²×C₃₁	semidirect
407. #500	C₂²×C₃₁	semidirect
409. #494	C₂²×C₃₁	semidirect
410. #489	C₂²×C₃₁	semidirect
411. #487	C₂²×C₃₁	semidirect
413. #484	C₂²×C₃₁	semidirect
414. #480	C₂²×C₃₁	semidirect
415. #477	C₂²×C₃₁	semidirect
416. #474	C₂²×C₃₁	semidirect
417. #474	C₂²×C₃₁	semidirect
418. #474	C₂²×C₃₁	semidirect
419. #468	C₂²×C₃₁	semidirect
422. #467	C₂²×C₃₁	semidirect
424. #464	C₂²×C₃₁	semidirect
426. #461	C₂²×C₃₁	semidirect
427. #461	C₂²×C₃₁	semidirect
428. #452	C₂²×C₃₁	semidirect
431. #446	C₂²×C₃₁	semidirect
432. C₈×Q₈	C₂²×C₃₁	semidirect
433. #440	C₂²×C₃₁	semidirect
434. #440	C₂²×C₃₁	semidirect
435. #440	C₂²×C₃₁	semidirect
436. C₄×Q₁₆	C₂²×C₃₁	semidirect
437. C₄×Q₁₆	C₂²×C₃₁	semidirect
438. C₄×Q₁₆	C₂²×C₃₁	semidirect
446. #436	C₂²×C₃₁	semidirect
449. C₈×D₄	C₂²×C₃₁	semidirect
450. #433	C₂²×C₃₁	semidirect
453. C₂×#107	C₂²×C₃₁	semidirect
454. #417	C₂²×C₃₁	semidirect
456. #405	C₂²×C₃₁	semidirect
574. C₃₁	#61482	direct (N × H)
612. D₈	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3520	2
C₃₁×#3393	2
Q₈×D₈×C₃₁	2
C₃₁×#3367	2
C₃₁×#3338	2
C₃₁×#3334	2
C₃₁×#3330	2
C₃₁×#3314	2
C₃₁×#3283	2
C₃₁×#3280	2
C₃₁×#3175	2
C₃₁×#3170	2
C₃₁×#3124	2
C₃₁×#3110	2
C₃₁×#2966	2
C₃₁×#2951	2
C₂×C₄×D₈×C₃₁	2
#61482	31

Subgroups — C31×#61482 #21518241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61482 #21518241