Subgroups — C₂×C₃₁×#2361 #21490892

Order 7936.

4782 conjugacy classes of subgroups.

The subgroup lattice has 664 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	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₃₁	C₂	1	2	yes	maximal, complemented
4	C₂³×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2361	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×#385	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
14	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
17	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×#121	C₄	1	16	yes	complemented
19	C₂×C₃₁×#121	C₂²	1	8	yes	—
20	C₂×C₄×D₄×C₃₁	—	2	8	no	—
21	C₂×C₄×D₄×C₃₁	—	2	16	no	—
22	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
23	C₂×C₄×D₄×C₃₁	C₂²	1	16	yes	complemented
24	C₂²×C₄⋊C₄×C₃₁	—	2	8	no	—
25	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₃₁	C₂²	1	8	yes	complemented
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	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
35	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×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	C₃₁×#390	C₂²	1	8	yes	complemented
41	C₃₁×#389	C₂²	1	8	yes	complemented
42	C₃₁×#388	C₂²	1	16	yes	complemented
43	C₃₁×#386	C₂²	1	16	yes	complemented
44	C₃₁×#385	C₂²	1	16	yes	complemented
45	C₄×C₄⋊C₄×C₃₁	C₂²	1	8	yes	complemented
46	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
47	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#95	C₂²	1	1	yes	characteristic
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	8	no	—
64	C₂³×C₄×C₃₁	—	2	8	no	—
65	C₂³×C₄×C₃₁	—	2	8	no	—
66	C₂³×C₄×C₃₁	—	2	8	no	—
67	C₂³×C₄×C₃₁	—	4	4	no	—
68	C₂³×C₄×C₃₁	—	4	4	no	—
69	C₂³×C₄×C₃₁	C₂×C₄	1	8	yes	complemented
70	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
73	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
74	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
75	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
76	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
78	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
80	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
82	C₃₁×#121	C₂×C₄	1	64	yes	complemented
83	C₄×D₄×C₃₁	—	2	32	no	—
84	C₄×D₄×C₃₁	—	2	64	no	—
85	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
86	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
87	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
88	C₂×C₄⋊C₄×C₃₁	—	2	32	no	—
89	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
90	C₂×C₄⋊C₄×C₃₁	D₄	1	8	yes	complemented
91	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
92	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
94	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
97	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
98	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
99	C₂×C₂²⋊C₄×C₃₁	—	4	4	no	—
100	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	16	yes	complemented
101	C₂×C₂²⋊C₄×C₃₁	D₄	1	8	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	4	yes	—
105	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
106	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
108	C₂×C₄²×C₃₁	—	2	8	no	—
109	C₂×C₄²×C₃₁	—	2	4	no	—
110	C₂×C₄²×C₃₁	—	2	4	no	—
111	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
112	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
113	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
114	C₃₁×#95	C₂³	1	4	yes	—
115	C₃₁×#95	C₂³	1	4	yes	—
116	C₃₁×#95	C₂³	1	8	yes	—
117	C₃₁×#95	C₂³	1	8	yes	—
118	C₂⁴×C₃₁	—	2	2	no	—
119	C₂⁴×C₃₁	—	2	2	no	—
120	C₂⁴×C₃₁	—	2	2	no	—
121	C₂⁴×C₃₁	—	2	2	no	—
122	C₂⁴×C₃₁	—	2	4	no	—
123	C₂⁴×C₃₁	—	2	4	no	—
124	C₂⁴×C₃₁	—	2	4	no	—
125	C₂⁴×C₃₁	—	2	4	no	—
126	C₂⁴×C₃₁	—	2	4	no	—
127	C₂⁴×C₃₁	—	2	4	no	—
128	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
129	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
130	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
131	C₂⁴×C₃₁	#41	1	4	yes	—
132	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
133	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
134	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
135	C₂×D₄×C₃₁	—	2	64	no	—
136	C₂×D₄×C₃₁	—	2	16	no	—
137	C₂×D₄×C₃₁	—	2	16	no	—
138	C₂×D₄×C₃₁	—	2	32	no	—
139	C₂×D₄×C₃₁	—	2	8	no	—
140	C₂×D₄×C₃₁	—	2	8	no	—
141	C₂×D₄×C₃₁	C₂²×C₄	1	32	yes	complemented
142	C₂×D₄×C₃₁	C₂²×C₄	1	16	yes	complemented
143	C₂²×C₄×C₃₁	—	2	4	no	—
144	C₂²×C₄×C₃₁	—	2	4	no	—
145	C₂²×C₄×C₃₁	—	2	2	no	—
146	C₂²×C₄×C₃₁	—	2	2	no	—
147	C₂²×C₄×C₃₁	—	2	2	no	—
148	C₂²×C₄×C₃₁	—	2	2	no	—
149	C₂²×C₄×C₃₁	—	2	4	no	—
150	C₂²×C₄×C₃₁	—	2	2	no	—
151	C₂²×C₄×C₃₁	—	2	4	no	—
152	C₂²×C₄×C₃₁	—	2	2	no	—
153	C₂²×C₄×C₃₁	—	2	32	no	—
154	C₂²×C₄×C₃₁	—	2	8	no	—
155	C₂²×C₄×C₃₁	—	2	8	no	—
156	C₂²×C₄×C₃₁	—	2	2	no	—
157	C₂²×C₄×C₃₁	—	2	4	no	—
158	C₂²×C₄×C₃₁	—	2	4	no	—
159	C₂²×C₄×C₃₁	—	2	16	no	—
160	C₂²×C₄×C₃₁	—	2	2	no	—
161	C₂²×C₄×C₃₁	—	2	2	no	—
162	C₂²×C₄×C₃₁	—	2	2	no	—
163	C₂²×C₄×C₃₁	—	2	2	no	—
164	C₂²×C₄×C₃₁	—	2	4	no	—
165	C₂²×C₄×C₃₁	—	2	2	no	—
166	C₂²×C₄×C₃₁	—	2	16	no	—
167	C₂²×C₄×C₃₁	—	2	16	no	—
168	C₂²×C₄×C₃₁	—	2	16	no	—
169	C₂²×C₄×C₃₁	—	4	8	no	—
170	C₂²×C₄×C₃₁	—	4	8	no	—
171	C₂²×C₄×C₃₁	—	4	32	no	—
172	C₂²×C₄×C₃₁	—	4	32	no	—
173	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
175	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
176	C₂²×C₄×C₃₁	C₂²×C₄	1	16	yes	complemented
177	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
179	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₃₁	#41	1	4	yes	—
182	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
191	C₄⋊C₄×C₃₁	—	2	16	no	—
192	C₄⋊C₄×C₃₁	—	2	8	no	—
193	C₄⋊C₄×C₃₁	—	2	16	no	—
194	C₄⋊C₄×C₃₁	C₂²×C₄	1	16	yes	complemented
195	C₄⋊C₄×C₃₁	C₂×D₄	1	16	yes	complemented
196	C₂²⋊C₄×C₃₁	—	2	8	no	—
197	C₂²⋊C₄×C₃₁	—	2	16	no	—
198	C₂²⋊C₄×C₃₁	—	2	16	no	—
199	C₂²⋊C₄×C₃₁	—	4	8	no	—
200	C₂²⋊C₄×C₃₁	C₂²×C₄	1	32	yes	complemented
201	C₂²⋊C₄×C₃₁	C₂×D₄	1	16	yes	complemented
202	C₄²×C₃₁	—	2	16	no	—
203	C₄²×C₃₁	—	2	8	no	—
204	C₄²×C₃₁	—	2	8	no	—
205	C₂×#2361	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂³×C₃₁	—	2	8	no	—
207	C₂³×C₃₁	—	2	8	no	—
208	C₂³×C₃₁	—	2	8	no	—
209	C₂³×C₃₁	—	2	8	no	—
210	C₂³×C₃₁	—	2	8	no	—
211	C₂³×C₃₁	—	2	8	no	—
212	C₂³×C₃₁	—	2	2	no	—
213	C₂³×C₃₁	—	2	2	no	—
214	C₂³×C₃₁	—	2	2	no	—
215	C₂³×C₃₁	—	2	2	no	—
216	C₂³×C₃₁	—	2	16	no	—
217	C₂³×C₃₁	—	2	16	no	—
218	C₂³×C₃₁	—	2	16	no	—
219	C₂³×C₃₁	—	2	4	no	—
220	C₂³×C₃₁	—	2	4	no	—
221	C₂³×C₃₁	—	2	4	no	—
222	C₂³×C₃₁	—	2	4	no	—
223	C₂³×C₃₁	—	2	4	no	—
224	C₂³×C₃₁	—	2	4	no	—
225	C₂³×C₃₁	—	4	8	no	—
226	C₂³×C₃₁	—	4	8	no	—
227	C₂³×C₃₁	—	4	8	no	—
228	C₂³×C₃₁	—	4	8	no	—
229	C₂³×C₃₁	C₄×D₄	1	16	yes	complemented
230	C₂³×C₃₁	C₂³×C₄	1	8	yes	—
231	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
232	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
233	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
234	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
235	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
236	C₂³×C₃₁	C₂×#41	1	4	yes	—
237	C₂³×C₃₁	C₂×#41	1	2	yes	—
238	C₂³×C₃₁	C₂×#41	1	2	yes	—
239	C₂³×C₃₁	H(5,𝔽₂)	1	2	yes	—
240	C₂³×C₃₁	2₋¹⁺⁴	1	2	yes	—
241	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
242	D₄×C₃₁	—	2	64	no	—
243	D₄×C₃₁	—	2	32	no	—
244	C₂×C₄×C₃₁	—	2	8	no	—
245	C₂×C₄×C₃₁	—	2	16	no	—
246	C₂×C₄×C₃₁	—	2	8	no	—
247	C₂×C₄×C₃₁	—	2	16	no	—
248	C₂×C₄×C₃₁	—	2	8	no	—
249	C₂×C₄×C₃₁	—	2	4	no	—
250	C₂×C₄×C₃₁	—	2	4	no	—
251	C₂×C₄×C₃₁	—	2	2	no	—
252	C₂×C₄×C₃₁	—	2	2	no	—
253	C₂×C₄×C₃₁	—	2	2	no	—
254	C₂×C₄×C₃₁	—	2	2	no	—
255	C₂×C₄×C₃₁	—	2	4	no	—
256	C₂×C₄×C₃₁	—	2	2	no	—
257	C₂×C₄×C₃₁	—	2	4	no	—
258	C₂×C₄×C₃₁	—	2	2	no	—
259	C₂×C₄×C₃₁	—	2	32	no	—
260	C₂×C₄×C₃₁	—	2	2	no	—
261	C₂×C₄×C₃₁	—	2	4	no	—
262	C₂×C₄×C₃₁	—	2	4	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	2	no	—
267	C₂×C₄×C₃₁	—	2	4	no	—
268	C₂×C₄×C₃₁	—	2	2	no	—
269	C₂×C₄×C₃₁	—	4	32	no	—
270	C₂×C₄×C₃₁	—	4	32	no	—
271	C₂×C₄×C₃₁	—	4	8	no	—
272	C₂×C₄×C₃₁	—	4	4	no	—
273	C₂×C₄×C₃₁	—	4	4	no	—
274	C₂×C₄×C₃₁	C₄×D₄	1	16	yes	complemented
275	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
276	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
277	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
278	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
279	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
280	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
281	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
282	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
283	C₂²×#121	C₂×C₃₁	1	1	yes	characteristic
284	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
285	C₂²×C₄×D₄	C₂×C₃₁	1	2	yes	complemented
286	C₂³×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
287	#2361	C₂×C₃₁	1	16	yes	direct product factor
288	C₂×#390	C₂×C₃₁	1	1	yes	characteristic, complemented
289	C₂×#389	C₂×C₃₁	1	1	yes	characteristic, complemented
290	C₂×#388	C₂×C₃₁	1	2	yes	complemented
291	C₂×#386	C₂×C₃₁	1	2	yes	complemented
292	C₂×#385	C₂×C₃₁	1	2	yes	complemented
293	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
294	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
295	C₂²×C₃₁	—	2	32	no	—
296	C₂²×C₃₁	—	2	4	no	—
297	C₂²×C₃₁	—	2	4	no	—
298	C₂²×C₃₁	—	2	4	no	—
299	C₂²×C₃₁	—	2	4	no	—
300	C₂²×C₃₁	—	2	4	no	—
301	C₂²×C₃₁	—	2	4	no	—
302	C₂²×C₃₁	—	2	8	no	—
303	C₂²×C₃₁	—	2	8	no	—
304	C₂²×C₃₁	—	2	8	no	—
305	C₂²×C₃₁	—	4	32	no	—
306	C₂²×C₃₁	—	4	4	no	—
307	C₂²×C₃₁	—	4	4	no	—
308	C₂²×C₃₁	—	4	4	no	—
309	C₂²×C₃₁	—	4	4	no	—
310	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
311	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
312	C₂²×C₃₁	C₂×C₄×D₄	1	8	yes	complemented
313	C₂²×C₃₁	#520	1	4	yes	—
314	C₂²×C₃₁	D₄²	1	4	yes	—
315	C₂²×C₃₁	#547	1	4	yes	—
316	C₂²×C₃₁	#548	1	4	yes	—
317	C₂²×C₃₁	#553	1	4	yes	—
318	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
319	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
320	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
321	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
322	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
323	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
325	C₄×C₃₁	—	2	4	no	—
326	C₄×C₃₁	—	2	8	no	—
327	C₄×C₃₁	—	2	4	no	—
328	C₄×C₃₁	—	2	8	no	—
329	C₄×C₃₁	—	2	4	no	—
330	C₄×C₃₁	—	4	4	no	—
331	C₄×C₃₁	—	4	2	no	—
332	C₄×C₃₁	—	4	2	no	—
333	C₄×C₃₁	C₂×C₄×D₄	1	8	yes	complemented
334	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
335	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
336	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
337	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
338	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
339	C₂×#121	C₄×C₃₁	1	16	yes	complemented
340	C₂×#121	C₂²×C₃₁	1	8	yes	—
341	C₂×C₄×D₄	—	2	8	no	—
342	C₂×C₄×D₄	—	2	16	no	—
343	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
344	C₂×C₄×D₄	C₂²×C₃₁	1	16	yes	complemented
345	C₂²×C₄⋊C₄	—	2	8	no	—
346	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
347	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
348	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
349	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
350	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
351	C₂²×C₄⋊C₄	C₂²×C₃₁	1	8	yes	complemented
352	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
353	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
354	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
356	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
357	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
358	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
359	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
360	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
361	#390	C₂²×C₃₁	1	8	yes	complemented
362	#389	C₂²×C₃₁	1	8	yes	complemented
363	#388	C₂²×C₃₁	1	16	yes	complemented
364	#386	C₂²×C₃₁	1	16	yes	complemented
365	#385	C₂²×C₃₁	1	16	yes	complemented
366	C₄×C₄⋊C₄	C₂²×C₃₁	1	8	yes	complemented
367	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
368	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
369	C₂×#95	C₂²×C₃₁	1	1	yes	characteristic
370	C₂×#95	C₂²×C₃₁	1	2	yes	—
371	C₂×#95	C₂²×C₃₁	1	2	yes	—
372	C₂×C₃₁	—	2	8	no	—
373	C₂×C₃₁	—	4	8	no	—
374	C₂×C₃₁	#2361	1	8	yes	direct product factor
375	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
376	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
377	C₂×C₃₁	C₂×#520	1	1	yes	characteristic
378	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
379	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
380	C₂×C₃₁	C₂×#548	1	1	yes	characteristic
381	C₂×C₃₁	C₂×#553	1	1	yes	characteristic
382	C₂⁵	C₂³×C₃₁	1	2	yes	—
383	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
384	C₂²×D₄	—	2	8	no	—
385	C₂²×D₄	—	2	8	no	—
386	C₂²×D₄	—	2	4	no	—
387	C₂²×D₄	—	2	4	no	—
388	C₂²×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
389	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
390	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
391	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
392	C₂³×C₄	—	2	4	no	—
393	C₂³×C₄	—	2	4	no	—
394	C₂³×C₄	—	2	8	no	—
395	C₂³×C₄	—	2	8	no	—
396	C₂³×C₄	—	2	8	no	—
397	C₂³×C₄	—	2	8	no	—
398	C₂³×C₄	—	4	4	no	—
399	C₂³×C₄	—	4	4	no	—
400	C₂³×C₄	C₂×C₄×C₃₁	1	8	yes	complemented
401	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
404	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
405	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
406	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
408	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
409	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
410	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
411	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
412	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
413	#121	C₂×C₄×C₃₁	1	64	yes	complemented
414	C₄×D₄	—	2	32	no	—
415	C₄×D₄	—	2	64	no	—
416	C₂×C₄⋊C₄	—	2	8	no	—
417	C₂×C₄⋊C₄	—	2	4	no	—
418	C₂×C₄⋊C₄	—	2	8	no	—
419	C₂×C₄⋊C₄	—	2	32	no	—
420	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
421	C₂×C₄⋊C₄	D₄×C₃₁	1	8	yes	complemented
422	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
423	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
425	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
426	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
427	C₂×C₂²⋊C₄	—	2	4	no	—
428	C₂×C₂²⋊C₄	—	2	8	no	—
429	C₂×C₂²⋊C₄	—	2	8	no	—
430	C₂×C₂²⋊C₄	—	4	4	no	—
431	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	16	yes	complemented
432	C₂×C₂²⋊C₄	D₄×C₃₁	1	8	yes	complemented
433	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
439	C₂×C₄²	—	2	8	no	—
440	C₂×C₄²	—	2	4	no	—
441	C₂×C₄²	—	2	4	no	—
442	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
443	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
444	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
445	#95	C₂³×C₃₁	1	4	yes	—
446	#95	C₂³×C₃₁	1	4	yes	—
447	#95	C₂³×C₃₁	1	8	yes	—
448	#95	C₂³×C₃₁	1	8	yes	—
449	C₃₁	C₂×#2361	1	1	yes	characteristic, direct product factor, Sylow
450	C₂⁴	—	2	2	no	—
451	C₂⁴	—	2	2	no	—
452	C₂⁴	—	2	2	no	—
453	C₂⁴	—	2	2	no	—
454	C₂⁴	—	2	4	no	—
455	C₂⁴	—	2	4	no	—
456	C₂⁴	—	2	4	no	—
457	C₂⁴	—	2	4	no	—
458	C₂⁴	—	2	4	no	—
459	C₂⁴	—	2	4	no	—
460	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
461	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
462	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
463	C₂⁴	#41×C₃₁	1	4	yes	—
464	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
465	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
466	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
467	C₂×D₄	—	2	64	no	—
468	C₂×D₄	—	2	16	no	—
469	C₂×D₄	—	2	16	no	—
470	C₂×D₄	—	2	32	no	—
471	C₂×D₄	—	2	8	no	—
472	C₂×D₄	—	2	8	no	—
473	C₂×D₄	C₂²×C₄×C₃₁	1	32	yes	complemented
474	C₂×D₄	C₂²×C₄×C₃₁	1	16	yes	complemented
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	32	no	—
486	C₂²×C₄	—	2	8	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	16	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	4	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	16	no	—
499	C₂²×C₄	—	2	16	no	—
500	C₂²×C₄	—	2	16	no	—
501	C₂²×C₄	—	4	8	no	—
502	C₂²×C₄	—	4	8	no	—
503	C₂²×C₄	—	4	32	no	—
504	C₂²×C₄	—	4	32	no	—
505	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
506	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
507	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
508	C₂²×C₄	C₂²×C₄×C₃₁	1	16	yes	complemented
509	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
510	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
511	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
512	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
513	C₂²×C₄	#41×C₃₁	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
515	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
517	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
518	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
521	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
523	C₄⋊C₄	—	2	16	no	—
524	C₄⋊C₄	—	2	8	no	—
525	C₄⋊C₄	—	2	16	no	—
526	C₄⋊C₄	C₂²×C₄×C₃₁	1	16	yes	complemented
527	C₄⋊C₄	C₂×D₄×C₃₁	1	16	yes	complemented
528	C₂²⋊C₄	—	2	8	no	—
529	C₂²⋊C₄	—	2	16	no	—
530	C₂²⋊C₄	—	2	16	no	—
531	C₂²⋊C₄	—	4	8	no	—
532	C₂²⋊C₄	C₂²×C₄×C₃₁	1	32	yes	complemented
533	C₂²⋊C₄	C₂×D₄×C₃₁	1	16	yes	complemented
534	C₄²	—	2	16	no	—
535	C₄²	—	2	8	no	—
536	C₄²	—	2	8	no	—
537	C₂³	—	2	8	no	—
538	C₂³	—	2	8	no	—
539	C₂³	—	2	8	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	2	8	no	—
542	C₂³	—	2	8	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	16	no	—
548	C₂³	—	2	16	no	—
549	C₂³	—	2	16	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	4	no	—
552	C₂³	—	2	4	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	4	8	no	—
557	C₂³	—	4	8	no	—
558	C₂³	—	4	8	no	—
559	C₂³	—	4	8	no	—
560	C₂³	C₄×D₄×C₃₁	1	16	yes	complemented
561	C₂³	C₂³×C₄×C₃₁	1	8	yes	—
562	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
563	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
564	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
565	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
566	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
567	C₂³	C₂×#41×C₃₁	1	4	yes	—
568	C₂³	C₂×#41×C₃₁	1	2	yes	—
569	C₂³	C₂×#41×C₃₁	1	2	yes	—
570	C₂³	C₃₁×H(5,𝔽₂)	1	2	yes	—
571	C₂³	C₃₁×2₋¹⁺⁴	1	2	yes	—
572	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
573	D₄	—	2	64	no	—
574	D₄	—	2	32	no	—
575	C₂×C₄	—	2	8	no	—
576	C₂×C₄	—	2	16	no	—
577	C₂×C₄	—	2	8	no	—
578	C₂×C₄	—	2	16	no	—
579	C₂×C₄	—	2	8	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	32	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	32	no	—
601	C₂×C₄	—	4	32	no	—
602	C₂×C₄	—	4	8	no	—
603	C₂×C₄	—	4	4	no	—
604	C₂×C₄	—	4	4	no	—
605	C₂×C₄	C₄×D₄×C₃₁	1	16	yes	complemented
606	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
607	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
608	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
609	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
610	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
611	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
612	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
613	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
614	C₂²	—	2	32	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	2	4	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	2	4	no	—
619	C₂²	—	2	4	no	—
620	C₂²	—	2	4	no	—
621	C₂²	—	2	8	no	—
622	C₂²	—	2	8	no	—
623	C₂²	—	2	8	no	—
624	C₂²	—	4	32	no	—
625	C₂²	—	4	4	no	—
626	C₂²	—	4	4	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	4	4	no	—
629	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
630	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
631	C₂²	C₂×C₄×D₄×C₃₁	1	8	yes	complemented
632	C₂²	C₃₁×#520	1	4	yes	—
633	C₂²	D₄²×C₃₁	1	4	yes	—
634	C₂²	C₃₁×#547	1	4	yes	—
635	C₂²	C₃₁×#548	1	4	yes	—
636	C₂²	C₃₁×#553	1	4	yes	—
637	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
638	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
639	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
640	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
641	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
642	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
644	C₄	—	2	4	no	—
645	C₄	—	2	8	no	—
646	C₄	—	2	4	no	—
647	C₄	—	2	8	no	—
648	C₄	—	2	4	no	—
649	C₄	—	4	4	no	—
650	C₄	—	4	2	no	—
651	C₄	—	4	2	no	—
652	C₄	C₂×C₄×D₄×C₃₁	1	8	yes	complemented
653	C₂	—	2	8	no	—
654	C₂	—	4	8	no	—
655	C₂	C₃₁×#2361	1	8	yes	direct product factor
656	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
657	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
658	C₂	C₂×C₃₁×#520	1	1	yes	characteristic
659	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
660	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
661	C₂	C₂×C₃₁×#548	1	1	yes	characteristic
662	C₂	C₂×C₃₁×#553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×C₃₁×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×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×C₄⋊C₄×C₃₁	C₂	semidirect
5. C₃₁×#2361	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×#385	C₂	semidirect
11. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
18. C₂×C₃₁×#121	C₄	semidirect
22. C₂×C₄×D₄×C₃₁	C₂²	semidirect
23. C₂×C₄×D₄×C₃₁	C₂²	semidirect
30. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
40. C₃₁×#390	C₂²	semidirect
41. C₃₁×#389	C₂²	semidirect
42. C₃₁×#388	C₂²	semidirect
43. C₃₁×#386	C₂²	semidirect
44. C₃₁×#385	C₂²	semidirect
45. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
46. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
57. C₂²×D₄×C₃₁	C₂×C₄	semidirect
58. C₂²×D₄×C₃₁	C₂×C₄	semidirect
69. C₂³×C₄×C₃₁	C₂×C₄	semidirect
82. C₃₁×#121	C₂×C₄	semidirect
89. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
90. C₂×C₄⋊C₄×C₃₁	D₄	semidirect
100. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
101. C₂×C₂²⋊C₄×C₃₁	D₄	semidirect
141. C₂×D₄×C₃₁	C₂²×C₄	semidirect
142. C₂×D₄×C₃₁	C₂²×C₄	semidirect
176. C₂²×C₄×C₃₁	C₂²×C₄	semidirect
194. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
195. C₄⋊C₄×C₃₁	C₂×D₄	semidirect
200. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
201. C₂²⋊C₄×C₃₁	C₂×D₄	semidirect
205. C₂×#2361	C₃₁	direct (N × H)
229. C₂³×C₃₁	C₄×D₄	semidirect
274. C₂×C₄×C₃₁	C₄×D₄	semidirect
284. C₂²×C₄×D₄	C₂×C₃₁	semidirect
285. C₂²×C₄×D₄	C₂×C₃₁	semidirect
286. C₂³×C₄⋊C₄	C₂×C₃₁	semidirect
287. #2361	C₂×C₃₁	direct (N × H)
288. C₂×#390	C₂×C₃₁	semidirect
289. C₂×#389	C₂×C₃₁	semidirect
290. C₂×#388	C₂×C₃₁	semidirect
291. C₂×#386	C₂×C₃₁	semidirect
292. C₂×#385	C₂×C₃₁	semidirect
293. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
294. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
312. C₂²×C₃₁	C₂×C₄×D₄	semidirect
333. C₄×C₃₁	C₂×C₄×D₄	semidirect
339. C₂×#121	C₄×C₃₁	semidirect
343. C₂×C₄×D₄	C₂²×C₃₁	semidirect
344. C₂×C₄×D₄	C₂²×C₃₁	semidirect
351. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
361. #390	C₂²×C₃₁	semidirect
362. #389	C₂²×C₃₁	semidirect
363. #388	C₂²×C₃₁	semidirect
364. #386	C₂²×C₃₁	semidirect
365. #385	C₂²×C₃₁	semidirect
366. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
367. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
374. C₂×C₃₁	#2361	direct (N × H)
388. C₂²×D₄	C₂×C₄×C₃₁	semidirect
389. C₂²×D₄	C₂×C₄×C₃₁	semidirect
400. C₂³×C₄	C₂×C₄×C₃₁	semidirect
413. #121	C₂×C₄×C₃₁	semidirect
420. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
421. C₂×C₄⋊C₄	D₄×C₃₁	semidirect
431. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
432. C₂×C₂²⋊C₄	D₄×C₃₁	semidirect
449. C₃₁	C₂×#2361	direct (N × H)
473. C₂×D₄	C₂²×C₄×C₃₁	semidirect
474. C₂×D₄	C₂²×C₄×C₃₁	semidirect
508. C₂²×C₄	C₂²×C₄×C₃₁	semidirect
526. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
527. C₄⋊C₄	C₂×D₄×C₃₁	semidirect
532. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
533. C₂²⋊C₄	C₂×D₄×C₃₁	semidirect
560. C₂³	C₄×D₄×C₃₁	semidirect
605. C₂×C₄	C₄×D₄×C₃₁	semidirect
631. C₂²	C₂×C₄×D₄×C₃₁	semidirect
652. C₄	C₂×C₄×D₄×C₃₁	semidirect
655. C₂	C₃₁×#2361	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×C₄⋊C₄×C₃₁	2
C₃₁×#2361	2
C₂×C₃₁×#390	2
C₂×C₃₁×#389	2
C₂×C₃₁×#388	2
C₂×C₃₁×#386	2
C₂×C₃₁×#385	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₂×#2361	31

Subgroups — C2×C31×#2361 #21490892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2361 #21490892