Subgroups — C₄×C₃₁×#535 #21490847

Order 7936.

3602 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2328	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2326	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2324	C₂	1	4	yes	maximal, complemented
7	C₃₁×#2321	C₂	1	4	yes	maximal, complemented
8	C₃₁×#2317	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2311	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#2309	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₃₁×#127	C₂	1	2	yes	maximal, complemented
12	C₄×C₃₁×#124	C₂	1	2	yes	maximal, complemented
13	C₄×C₃₁×#121	C₂	1	4	yes	maximal, complemented
14	C₄×C₃₁×#120	C₂	1	4	yes	maximal, complemented
15	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
19	C₃₁×#535	C₄	1	16	yes	direct product factor
20	C₂×C₃₁×#127	C₂²	1	2	yes	—
21	C₂×C₃₁×#124	C₂²	1	2	yes	—
22	C₂×C₃₁×#121	C₂²	1	4	yes	—
23	C₂×C₃₁×#120	C₂²	1	4	yes	—
24	C₄×#41×C₃₁	—	2	8	no	—
25	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×D₄×C₃₁	—	2	8	no	—
28	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
37	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
40	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
41	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
43	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
45	C₃₁×#391	C₂²	1	2	yes	complemented
46	C₃₁×#390	C₂²	1	4	yes	—
47	C₃₁×#390	C₂²	1	2	yes	—
48	C₃₁×#390	C₂²	1	2	yes	—
49	C₃₁×#390	C₂²	1	2	yes	complemented
50	C₃₁×#390	C₂²	1	8	yes	complemented
51	C₃₁×#389	C₂²	1	4	yes	complemented
52	C₃₁×#388	C₂²	1	8	yes	complemented
53	C₃₁×#388	C₂²	1	8	yes	complemented
54	C₃₁×#386	C₂²	1	4	yes	—
55	C₃₁×#386	C₂²	1	8	yes	complemented
56	C₃₁×#386	C₂²	1	8	yes	complemented
57	C₃₁×#385	C₂²	1	4	yes	—
58	C₃₁×#385	C₂²	1	8	yes	complemented
59	C₃₁×#384	C₂²	1	2	yes	complemented
60	C₃₁×#382	C₂²	1	2	yes	complemented
61	C₃₁×#380	C₂²	1	4	yes	complemented
62	C₃₁×#379	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
64	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
66	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
67	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
68	C₃₁×#376	C₂²	1	2	yes	complemented
69	C₄³×C₃₁	C₂²	1	2	yes	complemented
70	C₂⁵×C₃₁	C₂³	1	2	yes	—
71	C₂×#41×C₃₁	—	2	4	no	—
72	C₂×#41×C₃₁	—	2	4	no	—
73	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
74	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₃₁	—	2	4	no	—
76	C₂²×D₄×C₃₁	—	2	4	no	—
77	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
78	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
79	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
80	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
81	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
83	C₂³×C₄×C₃₁	—	2	8	no	—
84	C₂³×C₄×C₃₁	—	4	8	no	—
85	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
86	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
87	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
88	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
90	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
92	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
94	C₃₁×#127	C₂×C₄	1	16	yes	complemented
95	C₃₁×#124	C₂×C₄	1	16	yes	complemented
96	C₃₁×#121	C₂×C₄	1	32	yes	complemented
97	C₃₁×#120	C₂×C₄	1	32	yes	complemented
98	C₄×Q₈×C₃₁	—	2	4	no	—
99	C₄×Q₈×C₃₁	—	2	4	no	—
100	C₄×D₄×C₃₁	—	2	8	no	—
101	C₄×D₄×C₃₁	—	2	8	no	—
102	C₄×D₄×C₃₁	—	2	8	no	—
103	C₄×D₄×C₃₁	—	2	8	no	—
104	C₄×D₄×C₃₁	—	2	8	no	—
105	C₄×D₄×C₃₁	—	2	8	no	—
106	C₄×D₄×C₃₁	—	2	4	no	—
107	C₄×D₄×C₃₁	—	2	4	no	—
108	C₄×D₄×C₃₁	—	4	16	no	—
109	C₃₁×#117	—	2	4	no	—
110	C₃₁×#117	—	2	4	no	—
111	C₃₁×#117	—	2	8	no	—
112	C₃₁×#117	C₂×C₄	1	8	yes	complemented
113	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
114	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
124	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
131	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
132	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
133	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
135	C₂×C₄²×C₃₁	—	2	8	no	—
136	C₂×C₄²×C₃₁	D₄	1	8	yes	complemented
137	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
142	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
143	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
144	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
148	C₃₁×#95	C₂³	1	4	yes	—
149	C₃₁×#95	C₂³	1	4	yes	—
150	C₃₁×#95	C₂³	1	8	yes	—
151	C₃₁×#95	C₂³	1	8	yes	—
152	C₂⁴×C₃₁	—	2	4	no	—
153	C₂⁴×C₃₁	—	2	4	no	—
154	C₂⁴×C₃₁	—	4	4	no	—
155	C₂⁴×C₃₁	—	4	4	no	—
156	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
157	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
158	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
159	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
160	#41×C₃₁	—	2	32	no	—
161	C₂×Q₈×C₃₁	—	2	2	no	—
162	C₂×Q₈×C₃₁	—	2	2	no	—
163	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	complemented
164	C₂×D₄×C₃₁	—	2	4	no	—
165	C₂×D₄×C₃₁	—	2	4	no	—
166	C₂×D₄×C₃₁	—	2	32	no	—
167	C₂×D₄×C₃₁	—	2	4	no	—
168	C₂×D₄×C₃₁	—	2	4	no	—
169	C₂×D₄×C₃₁	—	2	2	no	—
170	C₂×D₄×C₃₁	—	2	4	no	—
171	C₂×D₄×C₃₁	—	2	4	no	—
172	C₂×D₄×C₃₁	—	2	2	no	—
173	C₂×D₄×C₃₁	—	4	8	no	—
174	C₂×D₄×C₃₁	—	4	8	no	—
175	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
176	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
177	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
178	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	complemented
179	C₂×D₄×C₃₁	C₂²×C₄	1	32	yes	complemented
180	C₂²×C₄×C₃₁	—	2	4	no	—
181	C₂²×C₄×C₃₁	—	2	4	no	—
182	C₂²×C₄×C₃₁	—	2	4	no	—
183	C₂²×C₄×C₃₁	—	2	4	no	—
184	C₂²×C₄×C₃₁	—	2	4	no	—
185	C₂²×C₄×C₃₁	—	2	4	no	—
186	C₂²×C₄×C₃₁	—	2	8	no	—
187	C₂²×C₄×C₃₁	—	2	8	no	—
188	C₂²×C₄×C₃₁	—	2	8	no	—
189	C₂²×C₄×C₃₁	—	2	16	no	—
190	C₂²×C₄×C₃₁	—	4	8	no	—
191	C₂²×C₄×C₃₁	—	4	4	no	—
192	C₂²×C₄×C₃₁	—	4	2	no	—
193	C₂²×C₄×C₃₁	—	4	4	no	—
194	C₂²×C₄×C₃₁	—	4	32	no	—
195	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
197	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
198	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
200	C₂²×C₄×C₃₁	#41	1	4	yes	—
201	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
213	C₄⋊C₄×C₃₁	—	2	4	no	—
214	C₄⋊C₄×C₃₁	—	2	4	no	—
215	C₄⋊C₄×C₃₁	—	2	4	no	—
216	C₄⋊C₄×C₃₁	—	2	4	no	—
217	C₄⋊C₄×C₃₁	—	2	2	no	—
218	C₄⋊C₄×C₃₁	—	2	2	no	—
219	C₄⋊C₄×C₃₁	—	2	4	no	—
220	C₄⋊C₄×C₃₁	—	4	8	no	—
221	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
222	C₂²⋊C₄×C₃₁	—	2	4	no	—
223	C₂²⋊C₄×C₃₁	—	2	4	no	—
224	C₂²⋊C₄×C₃₁	—	2	8	no	—
225	C₂²⋊C₄×C₃₁	—	2	8	no	—
226	C₂²⋊C₄×C₃₁	—	2	4	no	—
227	C₂²⋊C₄×C₃₁	—	2	4	no	—
228	C₂²⋊C₄×C₃₁	—	4	8	no	—
229	C₂²⋊C₄×C₃₁	—	4	8	no	—
230	C₂²⋊C₄×C₃₁	—	4	8	no	—
231	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
232	C₂²⋊C₄×C₃₁	C₂²×C₄	1	32	yes	complemented
233	C₄²×C₃₁	—	2	4	no	—
234	C₄²×C₃₁	—	2	4	no	—
235	C₄²×C₃₁	—	2	4	no	—
236	C₄²×C₃₁	—	2	4	no	—
237	C₄²×C₃₁	—	2	8	no	—
238	C₄²×C₃₁	—	4	4	no	—
239	C₄²×C₃₁	C₂²×C₄	1	8	yes	complemented
240	C₄²×C₃₁	C₂×D₄	1	4	yes	—
241	C₄²×C₃₁	C₂×D₄	1	4	yes	—
242	C₄²×C₃₁	C₂×D₄	1	4	yes	—
243	C₄²×C₃₁	C₂×D₄	1	4	yes	—
244	C₄×#535	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂³×C₃₁	—	2	2	no	—
246	C₂³×C₃₁	—	2	2	no	—
247	C₂³×C₃₁	—	2	16	no	—
248	C₂³×C₃₁	—	2	2	no	—
249	C₂³×C₃₁	—	2	4	no	—
250	C₂³×C₃₁	—	2	2	no	—
251	C₂³×C₃₁	—	2	4	no	—
252	C₂³×C₃₁	—	2	4	no	—
253	C₂³×C₃₁	—	2	8	no	—
254	C₂³×C₃₁	—	2	8	no	—
255	C₂³×C₃₁	—	2	4	no	—
256	C₂³×C₃₁	—	4	16	no	—
257	C₂³×C₃₁	—	4	8	no	—
258	C₂³×C₃₁	—	4	8	no	—
259	C₂³×C₃₁	—	4	16	no	—
260	C₂³×C₃₁	C₂³×C₄	1	8	yes	—
261	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
262	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
263	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
264	C₂³×C₃₁	C₂×#41	1	2	yes	—
265	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
266	Q₈×C₃₁	—	2	8	no	—
267	D₄×C₃₁	—	2	16	no	—
268	D₄×C₃₁	—	2	16	no	—
269	D₄×C₃₁	—	2	16	no	—
270	D₄×C₃₁	—	2	8	no	—
271	D₄×C₃₁	—	4	32	no	—
272	C₂×C₄×C₃₁	—	2	2	no	—
273	C₂×C₄×C₃₁	—	2	2	no	—
274	C₂×C₄×C₃₁	—	2	4	no	—
275	C₂×C₄×C₃₁	—	2	2	no	—
276	C₂×C₄×C₃₁	—	2	2	no	—
277	C₂×C₄×C₃₁	—	2	4	no	—
278	C₂×C₄×C₃₁	—	2	2	no	—
279	C₂×C₄×C₃₁	—	2	16	no	—
280	C₂×C₄×C₃₁	—	2	8	no	—
281	C₂×C₄×C₃₁	—	2	2	no	—
282	C₂×C₄×C₃₁	—	2	2	no	—
283	C₂×C₄×C₃₁	—	2	4	no	—
284	C₂×C₄×C₃₁	—	2	4	no	—
285	C₂×C₄×C₃₁	—	2	4	no	—
286	C₂×C₄×C₃₁	—	2	4	no	—
287	C₂×C₄×C₃₁	—	2	8	no	—
288	C₂×C₄×C₃₁	—	2	4	no	—
289	C₂×C₄×C₃₁	—	2	4	no	—
290	C₂×C₄×C₃₁	—	4	4	no	—
291	C₂×C₄×C₃₁	—	4	8	no	—
292	C₂×C₄×C₃₁	—	4	16	no	—
293	C₂×C₄×C₃₁	—	4	8	no	—
294	C₂×C₄×C₃₁	—	4	8	no	—
295	C₂×C₄×C₃₁	—	4	16	no	—
296	C₂×C₄×C₃₁	C₄×D₄	1	16	yes	complemented
297	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
298	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
299	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
300	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
301	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
308	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
309	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
310	C₂×#535	C₂×C₃₁	1	1	yes	characteristic
311	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
312	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
313	#2328	C₂×C₃₁	1	2	yes	complemented
314	#2326	C₂×C₃₁	1	2	yes	complemented
315	#2324	C₂×C₃₁	1	4	yes	complemented
316	#2321	C₂×C₃₁	1	4	yes	complemented
317	#2317	C₂×C₃₁	1	1	yes	characteristic, complemented
318	#2311	C₂×C₃₁	1	1	yes	characteristic, complemented
319	#2309	C₂×C₃₁	1	1	yes	characteristic, complemented
320	C₄×#127	C₂×C₃₁	1	2	yes	complemented
321	C₄×#124	C₂×C₃₁	1	2	yes	complemented
322	C₄×#121	C₂×C₃₁	1	4	yes	complemented
323	C₄×#120	C₂×C₃₁	1	4	yes	complemented
324	C₄×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
325	C₂²×C₃₁	—	2	4	no	—
326	C₂²×C₃₁	—	2	2	no	—
327	C₂²×C₃₁	—	2	2	no	—
328	C₂²×C₃₁	—	2	4	no	—
329	C₂²×C₃₁	—	2	4	no	—
330	C₂²×C₃₁	—	2	8	no	—
331	C₂²×C₃₁	—	2	8	no	—
332	C₂²×C₃₁	—	2	16	no	—
333	C₂²×C₃₁	—	4	32	no	—
334	C₂²×C₃₁	—	4	4	no	—
335	C₂²×C₃₁	—	4	2	no	—
336	C₂²×C₃₁	—	4	2	no	—
337	C₂²×C₃₁	—	4	4	no	—
338	C₂²×C₃₁	—	4	4	no	—
339	C₂²×C₃₁	—	4	8	no	—
340	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
341	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
342	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
343	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
344	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
345	C₂²×C₃₁	#585	1	2	yes	—
346	C₄×C₃₁	—	2	4	no	—
347	C₄×C₃₁	—	2	8	no	—
348	C₄×C₃₁	—	2	2	no	—
349	C₄×C₃₁	—	2	2	no	—
350	C₄×C₃₁	—	2	2	no	—
351	C₄×C₃₁	—	4	2	no	—
352	C₄×C₃₁	—	4	4	no	—
353	C₄×C₃₁	—	4	2	no	—
354	C₄×C₃₁	—	4	4	no	—
355	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
356	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
357	C₄×C₃₁	#535	1	4	yes	direct product factor
358	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
359	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
360	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
361	#535	C₄×C₃₁	1	16	yes	direct product factor
362	C₂×#127	C₂²×C₃₁	1	2	yes	—
363	C₂×#124	C₂²×C₃₁	1	2	yes	—
364	C₂×#121	C₂²×C₃₁	1	4	yes	—
365	C₂×#120	C₂²×C₃₁	1	4	yes	—
366	C₄×#41	—	2	8	no	—
367	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
368	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
369	C₂×C₄×D₄	—	2	8	no	—
370	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
371	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
372	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
374	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
376	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
377	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
378	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
379	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
380	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
381	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
382	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
383	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
384	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
385	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
386	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
387	#391	C₂²×C₃₁	1	2	yes	complemented
388	#390	C₂²×C₃₁	1	2	yes	—
389	#390	C₂²×C₃₁	1	4	yes	—
390	#390	C₂²×C₃₁	1	2	yes	—
391	#390	C₂²×C₃₁	1	2	yes	complemented
392	#390	C₂²×C₃₁	1	8	yes	complemented
393	#389	C₂²×C₃₁	1	4	yes	complemented
394	#388	C₂²×C₃₁	1	8	yes	complemented
395	#388	C₂²×C₃₁	1	8	yes	complemented
396	#386	C₂²×C₃₁	1	4	yes	—
397	#386	C₂²×C₃₁	1	8	yes	complemented
398	#386	C₂²×C₃₁	1	8	yes	complemented
399	#385	C₂²×C₃₁	1	4	yes	—
400	#385	C₂²×C₃₁	1	8	yes	complemented
401	#384	C₂²×C₃₁	1	2	yes	complemented
402	#382	C₂²×C₃₁	1	2	yes	complemented
403	#380	C₂²×C₃₁	1	4	yes	complemented
404	#379	C₂²×C₃₁	1	4	yes	—
405	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
406	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
407	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
408	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
409	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
410	#376	C₂²×C₃₁	1	2	yes	complemented
411	C₄³	C₂²×C₃₁	1	2	yes	complemented
412	C₂×C₃₁	—	2	4	no	—
413	C₂×C₃₁	—	4	4	no	—
414	C₂×C₃₁	—	4	8	no	—
415	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
416	C₂×C₃₁	C₄×H(5,𝔽₂)	1	2	yes	—
417	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
418	C₂×C₃₁	#3449	1	1	yes	characteristic
419	C₂×C₃₁	#3460	1	2	yes	—
420	C₂⁵	C₂³×C₃₁	1	2	yes	—
421	C₂×#41	—	2	4	no	—
422	C₂×#41	—	2	4	no	—
423	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
424	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
425	C₂²×D₄	—	2	4	no	—
426	C₂²×D₄	—	2	4	no	—
427	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
428	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
429	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
430	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
431	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
433	C₂³×C₄	—	2	8	no	—
434	C₂³×C₄	—	4	8	no	—
435	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
436	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
437	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
438	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
440	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
441	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
442	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
444	#127	C₂×C₄×C₃₁	1	16	yes	complemented
445	#124	C₂×C₄×C₃₁	1	16	yes	complemented
446	#121	C₂×C₄×C₃₁	1	32	yes	complemented
447	#120	C₂×C₄×C₃₁	1	32	yes	complemented
448	C₄×Q₈	—	2	4	no	—
449	C₄×Q₈	—	2	4	no	—
450	C₄×D₄	—	2	8	no	—
451	C₄×D₄	—	2	8	no	—
452	C₄×D₄	—	2	8	no	—
453	C₄×D₄	—	2	8	no	—
454	C₄×D₄	—	2	8	no	—
455	C₄×D₄	—	2	8	no	—
456	C₄×D₄	—	2	4	no	—
457	C₄×D₄	—	2	4	no	—
458	C₄×D₄	—	4	16	no	—
459	#117	—	2	4	no	—
460	#117	—	2	4	no	—
461	#117	—	2	8	no	—
462	#117	C₂×C₄×C₃₁	1	8	yes	complemented
463	C₂×C₄⋊C₄	—	2	4	no	—
464	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
472	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
473	C₂×C₂²⋊C₄	—	2	8	no	—
474	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
485	C₂×C₄²	—	2	8	no	—
486	C₂×C₄²	D₄×C₃₁	1	8	yes	complemented
487	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
488	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
489	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
490	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
491	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
492	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
493	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
494	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
498	#95	C₂³×C₃₁	1	4	yes	—
499	#95	C₂³×C₃₁	1	4	yes	—
500	#95	C₂³×C₃₁	1	8	yes	—
501	#95	C₂³×C₃₁	1	8	yes	—
502	C₃₁	C₄×#535	1	1	yes	characteristic, direct product factor, Sylow
503	C₂⁴	—	2	4	no	—
504	C₂⁴	—	2	4	no	—
505	C₂⁴	—	4	4	no	—
506	C₂⁴	—	4	4	no	—
507	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
508	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
509	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
510	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
511	#41	—	2	32	no	—
512	C₂×Q₈	—	2	2	no	—
513	C₂×Q₈	—	2	2	no	—
514	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	complemented
515	C₂×D₄	—	2	4	no	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	32	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	4	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	4	8	no	—
525	C₂×D₄	—	4	8	no	—
526	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
527	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
528	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
529	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	complemented
530	C₂×D₄	C₂²×C₄×C₃₁	1	32	yes	complemented
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	8	no	—
538	C₂²×C₄	—	2	8	no	—
539	C₂²×C₄	—	2	8	no	—
540	C₂²×C₄	—	2	16	no	—
541	C₂²×C₄	—	4	8	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	4	4	no	—
545	C₂²×C₄	—	4	32	no	—
546	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
547	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
548	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
549	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
550	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
551	C₂²×C₄	#41×C₃₁	1	4	yes	—
552	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
555	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
557	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
561	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	4	8	no	—
572	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	8	no	—
576	C₂²⋊C₄	—	2	8	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	4	8	no	—
580	C₂²⋊C₄	—	4	8	no	—
581	C₂²⋊C₄	—	4	8	no	—
582	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
583	C₂²⋊C₄	C₂²×C₄×C₃₁	1	32	yes	complemented
584	C₄²	—	2	4	no	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	8	no	—
589	C₄²	—	4	4	no	—
590	C₄²	C₂²×C₄×C₃₁	1	8	yes	complemented
591	C₄²	C₂×D₄×C₃₁	1	4	yes	—
592	C₄²	C₂×D₄×C₃₁	1	4	yes	—
593	C₄²	C₂×D₄×C₃₁	1	4	yes	—
594	C₄²	C₂×D₄×C₃₁	1	4	yes	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	16	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	4	no	—
602	C₂³	—	2	4	no	—
603	C₂³	—	2	8	no	—
604	C₂³	—	2	8	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	4	16	no	—
607	C₂³	—	4	8	no	—
608	C₂³	—	4	8	no	—
609	C₂³	—	4	16	no	—
610	C₂³	C₂³×C₄×C₃₁	1	8	yes	—
611	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
612	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
613	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
614	C₂³	C₂×#41×C₃₁	1	2	yes	—
615	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
616	Q₈	—	2	8	no	—
617	D₄	—	2	16	no	—
618	D₄	—	2	16	no	—
619	D₄	—	2	16	no	—
620	D₄	—	2	8	no	—
621	D₄	—	4	32	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	16	no	—
630	C₂×C₄	—	2	8	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	8	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	8	no	—
642	C₂×C₄	—	4	16	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	8	no	—
645	C₂×C₄	—	4	16	no	—
646	C₂×C₄	C₄×D₄×C₃₁	1	16	yes	complemented
647	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
648	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
649	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
650	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
652	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
653	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
654	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
655	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
656	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
657	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
658	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
659	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
660	C₂²	—	2	4	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	8	no	—
666	C₂²	—	2	8	no	—
667	C₂²	—	2	16	no	—
668	C₂²	—	4	32	no	—
669	C₂²	—	4	4	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	4	8	no	—
674	C₂²	—	4	4	no	—
675	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
676	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
677	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
678	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
679	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
680	C₂²	C₃₁×#585	1	2	yes	—
681	C₄	—	2	4	no	—
682	C₄	—	2	8	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	4	4	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	4	no	—
690	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
691	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
692	C₄	C₃₁×#535	1	4	yes	direct product factor
693	C₂	—	2	4	no	—
694	C₂	—	4	8	no	—
695	C₂	—	4	4	no	—
696	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
697	C₂	C₄×C₃₁×H(5,𝔽₂)	1	2	yes	—
698	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
699	C₂	C₃₁×#3449	1	1	yes	characteristic
700	C₂	C₃₁×#3460	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂×C₃₁×#535	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₃₁	C₂	semidirect
3. C₂²×C₄×D₄×C₃₁	C₂	semidirect
4. C₃₁×#2328	C₂	semidirect
5. C₃₁×#2326	C₂	semidirect
6. C₃₁×#2324	C₂	semidirect
7. C₃₁×#2321	C₂	semidirect
8. C₃₁×#2317	C₂	semidirect
9. C₃₁×#2311	C₂	semidirect
10. C₃₁×#2309	C₂	semidirect
11. C₄×C₃₁×#127	C₂	semidirect
12. C₄×C₃₁×#124	C₂	semidirect
13. C₄×C₃₁×#121	C₂	semidirect
14. C₄×C₃₁×#120	C₂	semidirect
15. C₄×C₃₁×#117	C₂	semidirect
19. C₃₁×#535	C₄	direct (N × H)
25. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
26. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
34. C₂×C₄×D₄×C₃₁	C₂²	semidirect
35. C₂×C₄×D₄×C₃₁	C₂²	semidirect
36. C₂×C₄×D₄×C₃₁	C₂²	semidirect
40. C₂×C₃₁×#117	C₂²	semidirect
44. C₂²×C₄²×C₃₁	C₂²	semidirect
45. C₃₁×#391	C₂²	semidirect
49. C₃₁×#390	C₂²	semidirect
50. C₃₁×#390	C₂²	semidirect
51. C₃₁×#389	C₂²	semidirect
52. C₃₁×#388	C₂²	semidirect
53. C₃₁×#388	C₂²	semidirect
55. C₃₁×#386	C₂²	semidirect
56. C₃₁×#386	C₂²	semidirect
58. C₃₁×#385	C₂²	semidirect
59. C₃₁×#384	C₂²	semidirect
60. C₃₁×#382	C₂²	semidirect
61. C₃₁×#380	C₂²	semidirect
63. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
64. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
67. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
68. C₃₁×#376	C₂²	semidirect
69. C₄³×C₃₁	C₂²	semidirect
73. C₂×#41×C₃₁	C₂×C₄	semidirect
77. C₂²×D₄×C₃₁	C₂×C₄	semidirect
94. C₃₁×#127	C₂×C₄	semidirect
95. C₃₁×#124	C₂×C₄	semidirect
96. C₃₁×#121	C₂×C₄	semidirect
97. C₃₁×#120	C₂×C₄	semidirect
112. C₃₁×#117	C₂×C₄	semidirect
136. C₂×C₄²×C₃₁	D₄	semidirect
163. C₂×Q₈×C₃₁	C₂²×C₄	semidirect
178. C₂×D₄×C₃₁	C₂²×C₄	semidirect
179. C₂×D₄×C₃₁	C₂²×C₄	semidirect
196. C₂²×C₄×C₃₁	C₂²×C₄	semidirect
221. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
232. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
239. C₄²×C₃₁	C₂²×C₄	semidirect
244. C₄×#535	C₃₁	direct (N × H)
296. C₂×C₄×C₃₁	C₄×D₄	semidirect
311. C₂×C₄×#41	C₂×C₃₁	semidirect
312. C₂²×C₄×D₄	C₂×C₃₁	semidirect
313. #2328	C₂×C₃₁	semidirect
314. #2326	C₂×C₃₁	semidirect
315. #2324	C₂×C₃₁	semidirect
316. #2321	C₂×C₃₁	semidirect
317. #2317	C₂×C₃₁	semidirect
318. #2311	C₂×C₃₁	semidirect
319. #2309	C₂×C₃₁	semidirect
320. C₄×#127	C₂×C₃₁	semidirect
321. C₄×#124	C₂×C₃₁	semidirect
322. C₄×#121	C₂×C₃₁	semidirect
323. C₄×#120	C₂×C₃₁	semidirect
324. C₄×#117	C₂×C₃₁	semidirect
357. C₄×C₃₁	#535	direct (N × H)
361. #535	C₄×C₃₁	direct (N × H)
367. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
368. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
376. C₂×C₄×D₄	C₂²×C₃₁	semidirect
377. C₂×C₄×D₄	C₂²×C₃₁	semidirect
378. C₂×C₄×D₄	C₂²×C₃₁	semidirect
382. C₂×#117	C₂²×C₃₁	semidirect
386. C₂²×C₄²	C₂²×C₃₁	semidirect
387. #391	C₂²×C₃₁	semidirect
391. #390	C₂²×C₃₁	semidirect
392. #390	C₂²×C₃₁	semidirect
393. #389	C₂²×C₃₁	semidirect
394. #388	C₂²×C₃₁	semidirect
395. #388	C₂²×C₃₁	semidirect
397. #386	C₂²×C₃₁	semidirect
398. #386	C₂²×C₃₁	semidirect
400. #385	C₂²×C₃₁	semidirect
401. #384	C₂²×C₃₁	semidirect
402. #382	C₂²×C₃₁	semidirect
403. #380	C₂²×C₃₁	semidirect
405. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
406. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
409. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
410. #376	C₂²×C₃₁	semidirect
411. C₄³	C₂²×C₃₁	semidirect
423. C₂×#41	C₂×C₄×C₃₁	semidirect
427. C₂²×D₄	C₂×C₄×C₃₁	semidirect
444. #127	C₂×C₄×C₃₁	semidirect
445. #124	C₂×C₄×C₃₁	semidirect
446. #121	C₂×C₄×C₃₁	semidirect
447. #120	C₂×C₄×C₃₁	semidirect
462. #117	C₂×C₄×C₃₁	semidirect
486. C₂×C₄²	D₄×C₃₁	semidirect
502. C₃₁	C₄×#535	direct (N × H)
514. C₂×Q₈	C₂²×C₄×C₃₁	semidirect
529. C₂×D₄	C₂²×C₄×C₃₁	semidirect
530. C₂×D₄	C₂²×C₄×C₃₁	semidirect
547. C₂²×C₄	C₂²×C₄×C₃₁	semidirect
572. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
583. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
590. C₄²	C₂²×C₄×C₃₁	semidirect
646. C₂×C₄	C₄×D₄×C₃₁	semidirect
692. C₄	C₃₁×#535	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#535	2
C₂×C₄×#41×C₃₁	2
C₂²×C₄×D₄×C₃₁	2
C₃₁×#2328	2
C₃₁×#2326	2
C₃₁×#2324	2
C₃₁×#2321	2
C₃₁×#2317	2
C₃₁×#2311	2
C₃₁×#2309	2
C₄×C₃₁×#127	2
C₄×C₃₁×#124	2
C₄×C₃₁×#121	2
C₄×C₃₁×#120	2
C₄×C₃₁×#117	2
C₄×#535	31

Subgroups — C4×C31×#535 #21490847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃₁×#535 #21490847