Subgroups — C₃₁×#3562 #16843495

Order 3968.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#562	C₂	1	2	yes	maximal, complemented
2	C₃₁×#560	C₂	1	2	yes	maximal, complemented
3	C₃₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#553	C₂	1	2	yes	maximal, complemented
6	C₃₁×#551	C₂	1	2	yes	maximal, complemented
7	C₃₁×#550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#541	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#540	C₂	1	2	yes	maximal, complemented
16	C₃₁×#539	C₂	1	2	yes	maximal, complemented
17	C₃₁×#538	C₂	1	2	yes	maximal, complemented
18	C₃₁×#538	C₂	1	2	yes	maximal, complemented
19	C₃₁×#536	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
26	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#127	C₂²	1	1	yes	characteristic
33	C₃₁×#127	C₂²	1	1	yes	characteristic
34	C₃₁×#127	C₂²	1	2	yes	complemented
35	C₃₁×#126	C₂²	1	1	yes	characteristic
36	C₃₁×#126	C₂²	1	2	yes	—
37	C₃₁×#126	C₂²	1	2	yes	—
38	C₃₁×#126	C₂²	1	2	yes	complemented
39	C₃₁×#126	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#126	C₂²	1	2	yes	complemented
41	C₃₁×#126	C₂²	1	2	yes	complemented
42	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#125	C₂²	1	2	yes	complemented
45	C₃₁×#125	C₂²	1	2	yes	complemented
46	C₃₁×#124	C₂²	1	1	yes	characteristic
47	C₃₁×#124	C₂²	1	1	yes	characteristic
48	C₃₁×#124	C₂²	1	1	yes	characteristic
49	C₃₁×#124	C₂²	1	1	yes	characteristic
50	C₃₁×#124	C₂²	1	1	yes	characteristic
51	C₃₁×#124	C₂²	1	2	yes	—
52	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#124	C₂²	1	2	yes	complemented
54	C₃₁×#124	C₂²	1	2	yes	complemented
55	C₃₁×#123	C₂²	1	1	yes	characteristic
56	C₃₁×#123	C₂²	1	2	yes	—
57	C₃₁×#123	C₂²	1	2	yes	—
58	C₃₁×#123	C₂²	1	2	yes	—
59	C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#123	C₂²	1	2	yes	complemented
61	C₃₁×#123	C₂²	1	2	yes	complemented
62	C₃₁×#123	C₂²	1	2	yes	complemented
63	C₃₁×#123	C₂²	1	2	yes	complemented
64	C₃₁×#123	C₂²	1	2	yes	complemented
65	C₃₁×#123	C₂²	1	2	yes	complemented
66	C₃₁×#123	C₂²	1	2	yes	complemented
67	C₃₁×#123	C₂²	1	2	yes	complemented
68	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
69	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
70	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
73	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
74	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
75	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
76	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₃₁×#121	C₂²	1	1	yes	characteristic
78	C₃₁×#121	C₂²	1	1	yes	characteristic
79	C₃₁×#121	C₂²	1	2	yes	—
80	C₃₁×#121	C₂²	1	2	yes	—
81	C₃₁×#121	C₂²	1	2	yes	—
82	C₃₁×#121	C₂²	1	2	yes	—
83	C₃₁×#121	C₂²	1	1	yes	characteristic
84	C₃₁×#121	C₂²	1	2	yes	—
85	C₃₁×#121	C₂²	1	2	yes	—
86	C₃₁×#121	C₂²	1	2	yes	complemented
87	C₃₁×#121	C₂²	1	2	yes	complemented
88	C₃₁×#121	C₂²	1	2	yes	complemented
89	C₃₁×#121	C₂²	1	2	yes	complemented
90	C₃₁×#121	C₂²	1	2	yes	complemented
91	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#121	C₂²	1	2	yes	complemented
93	C₃₁×#121	C₂²	1	2	yes	complemented
94	C₃₁×#120	C₂²	1	2	yes	—
95	C₃₁×#120	C₂²	1	2	yes	—
96	C₃₁×#120	C₂²	1	2	yes	—
97	C₃₁×#120	C₂²	1	2	yes	—
98	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
99	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
100	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
103	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
105	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
107	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
109	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
110	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
111	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
112	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
113	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
115	C₃₁×#117	C₂²	1	1	yes	characteristic
116	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#117	C₂²	1	2	yes	complemented
118	C₃₁×#117	C₂²	1	2	yes	complemented
119	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
120	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
121	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
122	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₃₁	C₂³	1	2	yes	—
124	#41×C₃₁	—	4	2	no	—
125	#41×C₃₁	—	4	2	no	—
126	#41×C₃₁	—	4	2	no	—
127	#41×C₃₁	—	4	2	no	—
128	C₂×Q₈×C₃₁	—	4	2	no	—
129	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
133	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
134	C₂×D₄×C₃₁	—	4	2	no	—
135	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₃₁	C₂³	1	2	yes	—
141	C₂×D₄×C₃₁	C₂³	1	2	yes	—
142	C₂×D₄×C₃₁	C₂³	1	2	yes	—
143	C₂×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂×D₄×C₃₁	C₂³	1	2	yes	—
145	C₂×D₄×C₃₁	C₂³	1	2	yes	—
146	C₂×D₄×C₃₁	C₂³	1	2	yes	—
147	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×D₄×C₃₁	C₂³	1	2	yes	—
149	C₂×D₄×C₃₁	C₂³	1	2	yes	—
150	C₂×D₄×C₃₁	C₂³	1	2	yes	—
151	C₂×D₄×C₃₁	C₂³	1	2	yes	—
152	C₂×D₄×C₃₁	C₂³	1	2	yes	—
153	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
155	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
156	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
157	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
158	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
159	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
160	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
161	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
162	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
163	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
164	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
165	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
166	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
199	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
200	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
203	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
204	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
205	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
206	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
207	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
208	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
209	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
210	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
211	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
212	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
213	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
214	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
219	C₄²×C₃₁	C₂³	1	1	yes	characteristic
220	C₄²×C₃₁	C₂³	1	1	yes	characteristic
221	C₄²×C₃₁	C₂³	1	1	yes	characteristic
222	C₄²×C₃₁	C₂³	1	1	yes	characteristic
223	C₄²×C₃₁	C₂³	1	1	yes	characteristic
224	C₄²×C₃₁	C₂³	1	2	yes	—
225	C₄²×C₃₁	C₂³	1	1	yes	characteristic
226	C₄²×C₃₁	C₂³	1	2	yes	—
227	C₄²×C₃₁	C₂³	1	2	yes	—
228	C₂³×C₃₁	—	4	2	no	—
229	C₂³×C₃₁	—	4	2	no	—
230	C₂³×C₃₁	—	4	2	no	—
231	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
232	C₂³×C₃₁	C₂⁴	1	2	yes	—
233	C₂³×C₃₁	C₂⁴	1	2	yes	—
234	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
235	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
236	C₂³×C₃₁	C₂⁴	1	2	yes	—
237	Q₈×C₃₁	—	2	2	no	—
238	Q₈×C₃₁	—	2	2	no	—
239	Q₈×C₃₁	—	2	2	no	—
240	Q₈×C₃₁	—	4	2	no	—
241	Q₈×C₃₁	—	4	1	no	—
242	D₄×C₃₁	—	2	2	no	—
243	D₄×C₃₁	—	2	2	no	—
244	D₄×C₃₁	—	2	2	no	—
245	D₄×C₃₁	—	4	2	no	—
246	D₄×C₃₁	—	4	1	no	—
247	D₄×C₃₁	—	4	2	no	—
248	D₄×C₃₁	—	4	2	no	—
249	D₄×C₃₁	—	4	2	no	—
250	D₄×C₃₁	—	4	2	no	—
251	D₄×C₃₁	—	4	2	no	—
252	D₄×C₃₁	—	4	1	no	—
253	D₄×C₃₁	—	4	2	no	—
254	D₄×C₃₁	—	4	1	no	—
255	D₄×C₃₁	—	4	2	no	—
256	D₄×C₃₁	—	4	2	no	—
257	D₄×C₃₁	—	4	2	no	—
258	D₄×C₃₁	—	4	2	no	—
259	D₄×C₃₁	—	4	2	no	—
260	C₂×C₄×C₃₁	—	2	2	no	—
261	C₂×C₄×C₃₁	—	2	2	no	—
262	C₂×C₄×C₃₁	—	2	2	no	—
263	C₂×C₄×C₃₁	—	4	2	no	—
264	C₂×C₄×C₃₁	—	4	1	no	—
265	C₂×C₄×C₃₁	—	4	2	no	—
266	C₂×C₄×C₃₁	—	4	2	no	—
267	C₂×C₄×C₃₁	—	4	1	no	—
268	C₂×C₄×C₃₁	—	4	2	no	—
269	C₂×C₄×C₃₁	—	4	2	no	—
270	C₂×C₄×C₃₁	—	4	2	no	—
271	C₂×C₄×C₃₁	—	4	2	no	—
272	C₂×C₄×C₃₁	—	4	2	no	—
273	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
285	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
286	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
287	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	#3562	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂²×C₃₁	—	2	1	no	—
292	C₂²×C₃₁	—	2	1	no	—
293	C₂²×C₃₁	—	2	1	no	—
294	C₂²×C₃₁	—	2	2	no	—
295	C₂²×C₃₁	—	2	2	no	—
296	C₂²×C₃₁	—	2	2	no	—
297	C₂²×C₃₁	—	2	1	no	—
298	C₂²×C₃₁	—	2	1	no	—
299	C₂²×C₃₁	—	2	2	no	—
300	C₂²×C₃₁	—	2	2	no	—
301	C₂²×C₃₁	—	2	2	no	—
302	C₂²×C₃₁	—	2	1	no	—
303	C₂²×C₃₁	—	2	1	no	—
304	C₂²×C₃₁	—	2	2	no	—
305	C₂²×C₃₁	—	2	2	no	—
306	C₂²×C₃₁	—	2	2	no	—
307	C₂²×C₃₁	—	2	1	no	—
308	C₂²×C₃₁	—	2	1	no	—
309	C₂²×C₃₁	—	8	4	no	—
310	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
311	C₄×C₃₁	—	2	1	no	—
312	C₄×C₃₁	—	2	1	no	—
313	C₄×C₃₁	—	2	1	no	—
314	C₄×C₃₁	—	2	2	no	—
315	C₄×C₃₁	—	2	2	no	—
316	C₄×C₃₁	—	2	2	no	—
317	C₄×C₃₁	—	2	1	no	—
318	C₄×C₃₁	—	2	2	no	—
319	C₄×C₃₁	—	2	1	no	—
320	C₄×C₃₁	—	2	1	no	—
321	C₄×C₃₁	—	2	1	no	—
322	C₄×C₃₁	—	2	2	no	—
323	C₄×C₃₁	—	2	1	no	—
324	C₄×C₃₁	—	2	1	no	—
325	C₄×C₃₁	—	2	1	no	—
326	C₄×C₃₁	—	2	1	no	—
327	C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
328	#562	C₂×C₃₁	1	2	yes	complemented
329	#560	C₂×C₃₁	1	2	yes	complemented
330	#559	C₂×C₃₁	1	1	yes	characteristic, complemented
331	#556	C₂×C₃₁	1	1	yes	characteristic, complemented
332	#553	C₂×C₃₁	1	2	yes	complemented
333	#551	C₂×C₃₁	1	2	yes	complemented
334	#550	C₂×C₃₁	1	1	yes	characteristic, complemented
335	#548	C₂×C₃₁	1	1	yes	characteristic, complemented
336	#548	C₂×C₃₁	1	1	yes	characteristic, complemented
337	#547	C₂×C₃₁	1	1	yes	characteristic, complemented
338	#546	C₂×C₃₁	1	1	yes	characteristic, complemented
339	#546	C₂×C₃₁	1	1	yes	characteristic, complemented
340	#541	C₂×C₃₁	1	1	yes	characteristic, complemented
341	#540	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#540	C₂×C₃₁	1	2	yes	complemented
343	#539	C₂×C₃₁	1	2	yes	complemented
344	#538	C₂×C₃₁	1	2	yes	complemented
345	#538	C₂×C₃₁	1	2	yes	complemented
346	#536	C₂×C₃₁	1	1	yes	characteristic, complemented
347	#535	C₂×C₃₁	1	1	yes	characteristic, complemented
348	#532	C₂×C₃₁	1	1	yes	characteristic, complemented
349	#529	C₂×C₃₁	1	1	yes	characteristic, complemented
350	#529	C₂×C₃₁	1	1	yes	characteristic, complemented
351	C₂×C₃₁	—	4	1	no	—
352	C₂×C₃₁	—	4	1	no	—
353	C₂×C₃₁	—	4	2	no	—
354	C₂×C₃₁	—	4	2	no	—
355	C₂×C₃₁	—	4	2	no	—
356	C₂×C₃₁	—	4	1	no	—
357	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₃₁	#585	1	1	yes	characteristic
359	C₂×C₃₁	#585	1	1	yes	characteristic
360	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic
361	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic
362	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic
363	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
364	C₂²×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
365	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
366	C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
367	C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
368	#127	C₂²×C₃₁	1	1	yes	characteristic
369	#127	C₂²×C₃₁	1	1	yes	characteristic
370	#127	C₂²×C₃₁	1	2	yes	complemented
371	#126	C₂²×C₃₁	1	1	yes	characteristic
372	#126	C₂²×C₃₁	1	2	yes	—
373	#126	C₂²×C₃₁	1	2	yes	—
374	#126	C₂²×C₃₁	1	2	yes	complemented
375	#126	C₂²×C₃₁	1	1	yes	characteristic, complemented
376	#126	C₂²×C₃₁	1	2	yes	complemented
377	#126	C₂²×C₃₁	1	2	yes	complemented
378	#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
379	#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
380	#125	C₂²×C₃₁	1	2	yes	complemented
381	#125	C₂²×C₃₁	1	2	yes	complemented
382	#124	C₂²×C₃₁	1	1	yes	characteristic
383	#124	C₂²×C₃₁	1	1	yes	characteristic
384	#124	C₂²×C₃₁	1	1	yes	characteristic
385	#124	C₂²×C₃₁	1	1	yes	characteristic
386	#124	C₂²×C₃₁	1	1	yes	characteristic
387	#124	C₂²×C₃₁	1	2	yes	—
388	#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
389	#124	C₂²×C₃₁	1	2	yes	complemented
390	#124	C₂²×C₃₁	1	2	yes	complemented
391	#123	C₂²×C₃₁	1	1	yes	characteristic
392	#123	C₂²×C₃₁	1	2	yes	—
393	#123	C₂²×C₃₁	1	2	yes	—
394	#123	C₂²×C₃₁	1	2	yes	—
395	#123	C₂²×C₃₁	1	1	yes	characteristic, complemented
396	#123	C₂²×C₃₁	1	2	yes	complemented
397	#123	C₂²×C₃₁	1	2	yes	complemented
398	#123	C₂²×C₃₁	1	2	yes	complemented
399	#123	C₂²×C₃₁	1	2	yes	complemented
400	#123	C₂²×C₃₁	1	2	yes	complemented
401	#123	C₂²×C₃₁	1	2	yes	complemented
402	#123	C₂²×C₃₁	1	2	yes	complemented
403	#123	C₂²×C₃₁	1	2	yes	complemented
404	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
405	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
406	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
407	C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
408	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
409	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
410	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
411	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
412	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
413	#121	C₂²×C₃₁	1	1	yes	characteristic
414	#121	C₂²×C₃₁	1	1	yes	characteristic
415	#121	C₂²×C₃₁	1	2	yes	—
416	#121	C₂²×C₃₁	1	2	yes	—
417	#121	C₂²×C₃₁	1	2	yes	—
418	#121	C₂²×C₃₁	1	2	yes	—
419	#121	C₂²×C₃₁	1	1	yes	characteristic
420	#121	C₂²×C₃₁	1	2	yes	—
421	#121	C₂²×C₃₁	1	2	yes	—
422	#121	C₂²×C₃₁	1	2	yes	complemented
423	#121	C₂²×C₃₁	1	2	yes	complemented
424	#121	C₂²×C₃₁	1	2	yes	complemented
425	#121	C₂²×C₃₁	1	2	yes	complemented
426	#121	C₂²×C₃₁	1	2	yes	complemented
427	#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
428	#121	C₂²×C₃₁	1	2	yes	complemented
429	#121	C₂²×C₃₁	1	2	yes	complemented
430	#120	C₂²×C₃₁	1	2	yes	—
431	#120	C₂²×C₃₁	1	2	yes	—
432	#120	C₂²×C₃₁	1	2	yes	—
433	#120	C₂²×C₃₁	1	2	yes	—
434	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
435	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
436	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
437	C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
438	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
439	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
440	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
441	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
442	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
443	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
444	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
445	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
446	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
447	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
448	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
449	C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
450	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
451	#117	C₂²×C₃₁	1	1	yes	characteristic
452	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
453	#117	C₂²×C₃₁	1	2	yes	complemented
454	#117	C₂²×C₃₁	1	2	yes	complemented
455	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
456	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
458	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
459	C₃₁	#3562	1	1	yes	characteristic, direct product factor, Sylow
460	C₂⁴	C₂³×C₃₁	1	2	yes	—
461	#41	—	4	2	no	—
462	#41	—	4	2	no	—
463	#41	—	4	2	no	—
464	#41	—	4	2	no	—
465	C₂×Q₈	—	4	2	no	—
466	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
467	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
468	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
469	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
470	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
471	C₂×D₄	—	4	2	no	—
472	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
473	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
474	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
475	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
476	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
477	C₂×D₄	C₂³×C₃₁	1	2	yes	—
478	C₂×D₄	C₂³×C₃₁	1	2	yes	—
479	C₂×D₄	C₂³×C₃₁	1	2	yes	—
480	C₂×D₄	C₂³×C₃₁	1	2	yes	—
481	C₂×D₄	C₂³×C₃₁	1	2	yes	—
482	C₂×D₄	C₂³×C₃₁	1	2	yes	—
483	C₂×D₄	C₂³×C₃₁	1	2	yes	—
484	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
485	C₂×D₄	C₂³×C₃₁	1	2	yes	—
486	C₂×D₄	C₂³×C₃₁	1	2	yes	—
487	C₂×D₄	C₂³×C₃₁	1	2	yes	—
488	C₂×D₄	C₂³×C₃₁	1	2	yes	—
489	C₂×D₄	C₂³×C₃₁	1	2	yes	—
490	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
491	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
492	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
493	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
494	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
495	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
496	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
497	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
498	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
499	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
500	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
501	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
502	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
503	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
504	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
505	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
506	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
507	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
508	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
509	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
510	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
511	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
512	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
513	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
514	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
515	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
516	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
517	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
518	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
519	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
520	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
521	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
522	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
523	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
524	C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
525	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
526	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
527	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
528	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
529	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
530	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
531	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
532	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
533	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
534	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
535	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
536	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
537	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
538	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
539	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
540	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
541	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
542	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
543	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
544	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
546	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
547	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
548	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
549	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
550	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
551	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
552	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
553	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
554	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
555	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
556	C₄²	C₂³×C₃₁	1	1	yes	characteristic
557	C₄²	C₂³×C₃₁	1	1	yes	characteristic
558	C₄²	C₂³×C₃₁	1	1	yes	characteristic
559	C₄²	C₂³×C₃₁	1	1	yes	characteristic
560	C₄²	C₂³×C₃₁	1	1	yes	characteristic
561	C₄²	C₂³×C₃₁	1	2	yes	—
562	C₄²	C₂³×C₃₁	1	1	yes	characteristic
563	C₄²	C₂³×C₃₁	1	2	yes	—
564	C₄²	C₂³×C₃₁	1	2	yes	—
565	C₂³	—	4	2	no	—
566	C₂³	—	4	2	no	—
567	C₂³	—	4	2	no	—
568	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
569	C₂³	C₂⁴×C₃₁	1	2	yes	—
570	C₂³	C₂⁴×C₃₁	1	2	yes	—
571	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
572	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
573	C₂³	C₂⁴×C₃₁	1	2	yes	—
574	Q₈	—	2	2	no	—
575	Q₈	—	2	2	no	—
576	Q₈	—	2	2	no	—
577	Q₈	—	4	2	no	—
578	Q₈	—	4	1	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
611	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
612	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
613	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
614	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
615	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
616	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
617	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
618	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
619	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
620	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
621	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
622	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
623	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
624	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
625	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
626	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	8	4	no	—
646	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
664	C₂	—	4	1	no	—
665	C₂	—	4	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	1	no	—
668	C₂	—	4	1	no	—
669	C₂	—	4	2	no	—
670	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂	C₃₁×#585	1	1	yes	characteristic
672	C₂	C₃₁×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#562	C₂	semidirect
2. C₃₁×#560	C₂	semidirect
3. C₃₁×#559	C₂	semidirect
4. C₃₁×#556	C₂	semidirect
5. C₃₁×#553	C₂	semidirect
6. C₃₁×#551	C₂	semidirect
7. C₃₁×#550	C₂	semidirect
8. C₃₁×#548	C₂	semidirect
9. C₃₁×#548	C₂	semidirect
10. C₃₁×#547	C₂	semidirect
11. C₃₁×#546	C₂	semidirect
12. C₃₁×#546	C₂	semidirect
13. C₃₁×#541	C₂	semidirect
14. C₃₁×#540	C₂	semidirect
15. C₃₁×#540	C₂	semidirect
16. C₃₁×#539	C₂	semidirect
17. C₃₁×#538	C₂	semidirect
18. C₃₁×#538	C₂	semidirect
19. C₃₁×#536	C₂	semidirect
20. C₃₁×#535	C₂	semidirect
21. C₃₁×#532	C₂	semidirect
22. C₃₁×#529	C₂	semidirect
23. C₃₁×#529	C₂	semidirect
27. C₂×#41×C₃₁	C₂²	semidirect
28. C₂²×Q₈×C₃₁	C₂²	semidirect
30. C₃₁×C₄⋊Q₈	C₂²	semidirect
31. C₃₁×C₄⋊Q₈	C₂²	semidirect
34. C₃₁×#127	C₂²	semidirect
38. C₃₁×#126	C₂²	semidirect
39. C₃₁×#126	C₂²	semidirect
40. C₃₁×#126	C₂²	semidirect
41. C₃₁×#126	C₂²	semidirect
42. C₃₁×#125	C₂²	semidirect
43. C₃₁×#125	C₂²	semidirect
44. C₃₁×#125	C₂²	semidirect
45. C₃₁×#125	C₂²	semidirect
52. C₃₁×#124	C₂²	semidirect
53. C₃₁×#124	C₂²	semidirect
54. C₃₁×#124	C₂²	semidirect
59. C₃₁×#123	C₂²	semidirect
60. C₃₁×#123	C₂²	semidirect
61. C₃₁×#123	C₂²	semidirect
62. C₃₁×#123	C₂²	semidirect
63. C₃₁×#123	C₂²	semidirect
64. C₃₁×#123	C₂²	semidirect
65. C₃₁×#123	C₂²	semidirect
66. C₃₁×#123	C₂²	semidirect
67. C₃₁×#123	C₂²	semidirect
70. C₃₁×C₂²⋊Q₈	C₂²	semidirect
71. C₃₁×C₂²⋊Q₈	C₂²	semidirect
72. C₃₁×C₂²⋊Q₈	C₂²	semidirect
73. C₃₁×C₂²⋊Q₈	C₂²	semidirect
74. C₃₁×C₂²⋊Q₈	C₂²	semidirect
75. C₃₁×C₂²⋊Q₈	C₂²	semidirect
76. C₃₁×C₂²⋊Q₈	C₂²	semidirect
86. C₃₁×#121	C₂²	semidirect
87. C₃₁×#121	C₂²	semidirect
88. C₃₁×#121	C₂²	semidirect
89. C₃₁×#121	C₂²	semidirect
90. C₃₁×#121	C₂²	semidirect
91. C₃₁×#121	C₂²	semidirect
92. C₃₁×#121	C₂²	semidirect
93. C₃₁×#121	C₂²	semidirect
98. C₄×Q₈×C₃₁	C₂²	semidirect
99. C₄×Q₈×C₃₁	C₂²	semidirect
100. C₄×Q₈×C₃₁	C₂²	semidirect
101. C₄×Q₈×C₃₁	C₂²	semidirect
106. C₄×D₄×C₃₁	C₂²	semidirect
107. C₄×D₄×C₃₁	C₂²	semidirect
108. C₄×D₄×C₃₁	C₂²	semidirect
109. C₄×D₄×C₃₁	C₂²	semidirect
110. C₄×D₄×C₃₁	C₂²	semidirect
111. C₄×D₄×C₃₁	C₂²	semidirect
112. C₄×D₄×C₃₁	C₂²	semidirect
113. C₄×D₄×C₃₁	C₂²	semidirect
114. C₄×D₄×C₃₁	C₂²	semidirect
116. C₃₁×#117	C₂²	semidirect
117. C₃₁×#117	C₂²	semidirect
118. C₃₁×#117	C₂²	semidirect
119. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
122. C₂×C₄²×C₃₁	C₂²	semidirect
290. #3562	C₃₁	direct (N × H)
328. #562	C₂×C₃₁	semidirect
329. #560	C₂×C₃₁	semidirect
330. #559	C₂×C₃₁	semidirect
331. #556	C₂×C₃₁	semidirect
332. #553	C₂×C₃₁	semidirect
333. #551	C₂×C₃₁	semidirect
334. #550	C₂×C₃₁	semidirect
335. #548	C₂×C₃₁	semidirect
336. #548	C₂×C₃₁	semidirect
337. #547	C₂×C₃₁	semidirect
338. #546	C₂×C₃₁	semidirect
339. #546	C₂×C₃₁	semidirect
340. #541	C₂×C₃₁	semidirect
341. #540	C₂×C₃₁	semidirect
342. #540	C₂×C₃₁	semidirect
343. #539	C₂×C₃₁	semidirect
344. #538	C₂×C₃₁	semidirect
345. #538	C₂×C₃₁	semidirect
346. #536	C₂×C₃₁	semidirect
347. #535	C₂×C₃₁	semidirect
348. #532	C₂×C₃₁	semidirect
349. #529	C₂×C₃₁	semidirect
350. #529	C₂×C₃₁	semidirect
363. C₂×#41	C₂²×C₃₁	semidirect
364. C₂²×Q₈	C₂²×C₃₁	semidirect
366. C₄⋊Q₈	C₂²×C₃₁	semidirect
367. C₄⋊Q₈	C₂²×C₃₁	semidirect
370. #127	C₂²×C₃₁	semidirect
374. #126	C₂²×C₃₁	semidirect
375. #126	C₂²×C₃₁	semidirect
376. #126	C₂²×C₃₁	semidirect
377. #126	C₂²×C₃₁	semidirect
378. #125	C₂²×C₃₁	semidirect
379. #125	C₂²×C₃₁	semidirect
380. #125	C₂²×C₃₁	semidirect
381. #125	C₂²×C₃₁	semidirect
388. #124	C₂²×C₃₁	semidirect
389. #124	C₂²×C₃₁	semidirect
390. #124	C₂²×C₃₁	semidirect
395. #123	C₂²×C₃₁	semidirect
396. #123	C₂²×C₃₁	semidirect
397. #123	C₂²×C₃₁	semidirect
398. #123	C₂²×C₃₁	semidirect
399. #123	C₂²×C₃₁	semidirect
400. #123	C₂²×C₃₁	semidirect
401. #123	C₂²×C₃₁	semidirect
402. #123	C₂²×C₃₁	semidirect
403. #123	C₂²×C₃₁	semidirect
406. C₂²⋊Q₈	C₂²×C₃₁	semidirect
407. C₂²⋊Q₈	C₂²×C₃₁	semidirect
408. C₂²⋊Q₈	C₂²×C₃₁	semidirect
409. C₂²⋊Q₈	C₂²×C₃₁	semidirect
410. C₂²⋊Q₈	C₂²×C₃₁	semidirect
411. C₂²⋊Q₈	C₂²×C₃₁	semidirect
412. C₂²⋊Q₈	C₂²×C₃₁	semidirect
422. #121	C₂²×C₃₁	semidirect
423. #121	C₂²×C₃₁	semidirect
424. #121	C₂²×C₃₁	semidirect
425. #121	C₂²×C₃₁	semidirect
426. #121	C₂²×C₃₁	semidirect
427. #121	C₂²×C₃₁	semidirect
428. #121	C₂²×C₃₁	semidirect
429. #121	C₂²×C₃₁	semidirect
434. C₄×Q₈	C₂²×C₃₁	semidirect
435. C₄×Q₈	C₂²×C₃₁	semidirect
436. C₄×Q₈	C₂²×C₃₁	semidirect
437. C₄×Q₈	C₂²×C₃₁	semidirect
442. C₄×D₄	C₂²×C₃₁	semidirect
443. C₄×D₄	C₂²×C₃₁	semidirect
444. C₄×D₄	C₂²×C₃₁	semidirect
445. C₄×D₄	C₂²×C₃₁	semidirect
446. C₄×D₄	C₂²×C₃₁	semidirect
447. C₄×D₄	C₂²×C₃₁	semidirect
448. C₄×D₄	C₂²×C₃₁	semidirect
449. C₄×D₄	C₂²×C₃₁	semidirect
450. C₄×D₄	C₂²×C₃₁	semidirect
452. #117	C₂²×C₃₁	semidirect
453. #117	C₂²×C₃₁	semidirect
454. #117	C₂²×C₃₁	semidirect
455. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
458. C₂×C₄²	C₂²×C₃₁	semidirect
459. C₃₁	#3562	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×#562	2
C₃₁×#560	2
C₃₁×#559	2
C₃₁×#556	2
C₃₁×#553	2
C₃₁×#551	2
C₃₁×#550	2
C₃₁×#548	2
C₃₁×#547	2
C₃₁×#546	2
C₃₁×#541	2
C₃₁×#540	2
C₃₁×#539	2
C₃₁×#538	2
C₃₁×#536	2
C₃₁×#535	2
C₃₁×#532	2
C₃₁×#529	2
#3562	31

Subgroups — C31×#3562 #16843495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3562 #16843495