Subgroups — C₂×C₄×C₃₁×#121 #21490787

Order 7936.

5022 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₄×C₃₁	C₂³
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂⁴×C₃₁	C₂⁴
prime radical	C₂²×C₃₁×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₃₁	C₂	semidirect
3. C₂²×C₄×D₄×C₃₁	C₂	semidirect
4. C₂³×C₄²×C₃₁	C₂	semidirect
5. C₄×C₃₁×#121	C₂	direct (N × H)
6. C₂×C₃₁×#390	C₂	semidirect
7. C₂×C₃₁×#389	C₂	semidirect
8. C₂×C₃₁×#388	C₂	semidirect
9. C₂×C₃₁×#386	C₂	semidirect
10. C₂×C₃₁×#380	C₂	semidirect
11. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
19. C₂×C₃₁×#121	C₄	direct (N × H)
23. C₂×C₄×D₄×C₃₁	C₂²	semidirect
24. C₂×C₄×D₄×C₃₁	C₂²	semidirect
40. C₂²×C₄²×C₃₁	C₂²	semidirect
41. C₃₁×#390	C₂²	semidirect
42. C₃₁×#389	C₂²	semidirect
43. C₃₁×#388	C₂²	semidirect
44. C₃₁×#386	C₂²	semidirect
45. C₃₁×#380	C₂²	semidirect
46. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
47. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
57. C₂²×D₄×C₃₁	C₂×C₄	semidirect
58. C₂²×D₄×C₃₁	C₂×C₄	semidirect
71. C₂³×C₄×C₃₁	C₂×C₄	semidirect
72. C₂³×C₄×C₃₁	D₄	semidirect
86. C₃₁×#121	C₂×C₄	direct (N × H)
92. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
101. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
112. C₂×C₄²×C₃₁	D₄	semidirect
144. C₂×D₄×C₃₁	C₂²×C₄	semidirect
145. C₂×D₄×C₃₁	C₂²×C₄	semidirect
179. C₂²×C₄×C₃₁	C₂²×C₄	semidirect
185. C₂²×C₄×C₃₁	C₂×D₄	semidirect
201. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
206. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
211. C₄²×C₃₁	C₂×D₄	semidirect
212. C₂×C₄×#121	C₃₁	direct (N × H)
236. C₂³×C₃₁	C₄×D₄	semidirect
278. C₂×C₄×C₃₁	C₄×D₄	semidirect
279. C₂×C₄×C₃₁	#121	direct (N × H)
292. C₂²×C₄×D₄	C₂×C₃₁	semidirect
293. C₂²×C₄×D₄	C₂×C₃₁	semidirect
294. C₂³×C₄²	C₂×C₃₁	semidirect
295. C₄×#121	C₂×C₃₁	direct (N × H)
296. C₂×#390	C₂×C₃₁	semidirect
297. C₂×#389	C₂×C₃₁	semidirect
298. C₂×#388	C₂×C₃₁	semidirect
299. C₂×#386	C₂×C₃₁	semidirect
300. C₂×#380	C₂×C₃₁	semidirect
301. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
302. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
320. C₂²×C₃₁	C₂×C₄×D₄	semidirect
340. C₄×C₃₁	C₂×C₄×D₄	semidirect
341. C₄×C₃₁	C₂×#121	direct (N × H)
348. C₂×#121	C₄×C₃₁	direct (N × H)
352. C₂×C₄×D₄	C₂²×C₃₁	semidirect
353. C₂×C₄×D₄	C₂²×C₃₁	semidirect
369. C₂²×C₄²	C₂²×C₃₁	semidirect
370. #390	C₂²×C₃₁	semidirect
371. #389	C₂²×C₃₁	semidirect
372. #388	C₂²×C₃₁	semidirect
373. #386	C₂²×C₃₁	semidirect
374. #380	C₂²×C₃₁	semidirect
375. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
376. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
382. C₂×C₃₁	C₄×#121	direct (N × H)
396. C₂²×D₄	C₂×C₄×C₃₁	semidirect
397. C₂²×D₄	C₂×C₄×C₃₁	semidirect
410. C₂³×C₄	C₂×C₄×C₃₁	semidirect
411. C₂³×C₄	D₄×C₃₁	semidirect
425. #121	C₂×C₄×C₃₁	direct (N × H)
431. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
440. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
451. C₂×C₄²	D₄×C₃₁	semidirect
460. C₃₁	C₂×C₄×#121	direct (N × H)
484. C₂×D₄	C₂²×C₄×C₃₁	semidirect
485. C₂×D₄	C₂²×C₄×C₃₁	semidirect
519. C₂²×C₄	C₂²×C₄×C₃₁	semidirect
525. C₂²×C₄	C₂×D₄×C₃₁	semidirect
541. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
546. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
551. C₄²	C₂×D₄×C₃₁	semidirect
575. C₂³	C₄×D₄×C₃₁	semidirect
617. C₂×C₄	C₄×D₄×C₃₁	semidirect
618. C₂×C₄	C₃₁×#121	direct (N × H)
647. C₂²	C₂×C₄×D₄×C₃₁	semidirect
667. C₄	C₂×C₄×D₄×C₃₁	semidirect
668. C₄	C₂×C₃₁×#121	direct (N × H)
671. C₂	C₄×C₃₁×#121	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#121	2
C₂²×C₄×D₄×C₃₁	2
C₂³×C₄²×C₃₁	2
C₄×C₃₁×#121	2
C₂×C₃₁×#390	2
C₂×C₃₁×#389	2
C₂×C₃₁×#388	2
C₂×C₃₁×#386	2
C₂×C₃₁×#380	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₂×C₄×#121	31

Subgroups — C2×C4×C31×#121 #21490787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₃₁×#121 #21490787