Subgroups — C₂×C₃₁×#1762 #21477168

Order 7936.

2118 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#102	C₂	1	2	yes	maximal
3	C₂²×C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1762	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×#340	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₃₁	—	2	1	no	—
9	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₃₁	—	2	2	no	—
11	C₂×C₄×D₄×C₃₁	—	2	4	no	—
12	C₂×C₄×D₄×C₃₁	C₄	1	8	yes	complemented
13	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₃₁	—	2	1	no	—
17	C₂²×C₄²×C₃₁	—	2	1	no	—
18	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#102	C₄	1	16	yes	complemented
20	C₂×C₃₁×#102	C₂²	1	8	yes	—
21	C₂×C₃₁×#97	—	2	4	no	—
22	C₂×C₃₁×#97	C₂²	1	4	yes	complemented
23	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
24	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
25	C₂×C₃₁×#95	—	2	1	no	—
26	C₃₁×#340	C₂²	1	8	yes	complemented
27	C₂⁵×C₃₁	—	2	1	no	—
28	C₂²×D₄×C₃₁	—	2	1	no	—
29	C₂²×D₄×C₃₁	—	2	2	no	—
30	C₂²×D₄×C₃₁	—	2	4	no	—
31	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	—
32	C₂²×D₄×C₃₁	C₂×C₄	1	4	yes	—
33	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
34	C₂³×C₄×C₃₁	—	2	2	no	—
35	C₂³×C₄×C₃₁	—	2	1	no	—
36	C₂³×C₄×C₃₁	—	2	8	no	—
37	C₂³×C₄×C₃₁	—	2	4	no	—
38	C₂³×C₄×C₃₁	—	4	8	no	—
39	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₁	—	2	4	no	—
43	C₂²×C₈×C₃₁	—	2	4	no	—
44	C₂²×C₈×C₃₁	C₂×C₄	1	8	yes	complemented
45	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
46	C₄×D₄×C₃₁	—	2	16	no	—
47	C₄×D₄×C₃₁	—	2	8	no	—
48	C₄×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
49	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
57	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
58	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
59	C₂×C₄²×C₃₁	—	2	4	no	—
60	C₂×C₄²×C₃₁	—	4	4	no	—
61	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₃₁	D₄	1	2	yes	—
63	C₂×C₄²×C₃₁	D₄	1	4	yes	—
64	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
65	C₃₁×#102	C₂×C₄	1	32	yes	complemented
66	C₃₁×#97	—	2	8	no	—
67	C₃₁×#95	—	2	4	no	—
68	C₂⁴×C₃₁	—	2	4	no	—
69	C₂⁴×C₃₁	—	2	8	no	—
70	C₂⁴×C₃₁	—	2	2	no	—
71	C₂⁴×C₃₁	—	4	4	no	—
72	C₂⁴×C₃₁	—	4	2	no	—
73	C₂⁴×C₃₁	—	4	2	no	—
74	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
75	C₂×D₄×C₃₁	—	2	4	no	—
76	C₂×D₄×C₃₁	—	2	8	no	—
77	C₂×D₄×C₃₁	—	2	16	no	—
78	C₂×D₄×C₃₁	—	2	8	no	—
79	C₂×D₄×C₃₁	—	2	2	no	—
80	C₂×D₄×C₃₁	—	2	4	no	—
81	C₂×D₄×C₃₁	C₄²	1	16	yes	complemented
82	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
83	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	2	4	no	—
86	C₂²×C₄×C₃₁	—	2	2	no	—
87	C₂²×C₄×C₃₁	—	2	4	no	—
88	C₂²×C₄×C₃₁	—	2	8	no	—
89	C₂²×C₄×C₃₁	—	2	4	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	—	2	16	no	—
92	C₂²×C₄×C₃₁	—	4	16	no	—
93	C₂²×C₄×C₃₁	—	4	32	no	—
94	C₂²×C₄×C₃₁	—	4	4	no	—
95	C₂²×C₄×C₃₁	—	4	4	no	—
96	C₂²×C₄×C₃₁	—	4	4	no	—
97	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₃₁	#41	1	4	yes	—
106	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₃₁	—	2	16	no	—
108	C₂×C₈×C₃₁	—	2	4	no	—
109	C₂×C₈×C₃₁	—	2	4	no	—
110	C₂×C₈×C₃₁	C₂²×C₄	1	8	yes	complemented
111	C₄⋊C₄×C₃₁	—	2	4	no	—
112	C₄⋊C₄×C₃₁	—	2	8	no	—
113	C₄⋊C₄×C₃₁	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	2	4	no	—
115	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
116	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
117	C₂²⋊C₄×C₃₁	—	2	16	no	—
118	C₄²×C₃₁	—	4	8	no	—
119	C₄²×C₃₁	C₂²⋊C₄	1	8	yes	—
120	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
121	C₄²×C₃₁	C₂×D₄	1	4	yes	—
122	C₂×#1762	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₃₁	—	2	4	no	—
124	C₂³×C₃₁	—	2	8	no	—
125	C₂³×C₃₁	—	2	16	no	—
126	C₂³×C₃₁	—	4	4	no	—
127	C₂³×C₃₁	—	4	2	no	—
128	C₂³×C₃₁	—	4	2	no	—
129	C₂³×C₃₁	—	4	8	no	—
130	C₂³×C₃₁	—	4	8	no	—
131	C₂³×C₃₁	—	4	16	no	—
132	C₂³×C₃₁	—	4	16	no	—
133	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×C₃₁	C₄×D₄	1	4	yes	—
135	C₂³×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
136	C₂³×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
137	C₂³×C₃₁	#137	1	2	yes	—
138	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
139	D₄×C₃₁	—	2	4	no	—
140	D₄×C₃₁	—	2	8	no	—
141	D₄×C₃₁	—	2	16	no	—
142	D₄×C₃₁	C₂×C₄²	1	8	yes	complemented
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	4	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	8	no	—
147	C₂×C₄×C₃₁	—	2	8	no	—
148	C₂×C₄×C₃₁	—	2	4	no	—
149	C₂×C₄×C₃₁	—	2	8	no	—
150	C₂×C₄×C₃₁	—	4	32	no	—
151	C₂×C₄×C₃₁	—	4	4	no	—
152	C₂×C₄×C₃₁	—	4	4	no	—
153	C₂×C₄×C₃₁	—	4	4	no	—
154	C₂×C₄×C₃₁	—	4	8	no	—
155	C₂×C₄×C₃₁	—	4	16	no	—
156	C₂×C₄×C₃₁	C₂×C₄²	1	4	yes	—
157	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
158	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
159	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₃₁	#117	1	4	yes	—
161	C₂×C₄×C₃₁	C₄×D₄	1	8	yes	—
162	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
165	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
167	C₈×C₃₁	—	2	8	no	—
168	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic
169	C₂²×#102	C₂×C₃₁	1	2	yes	—
170	C₂²×#97	C₂×C₃₁	1	1	yes	characteristic, complemented
171	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
172	#1762	C₂×C₃₁	1	8	yes	direct product factor
173	C₂×#340	C₂×C₃₁	1	2	yes	complemented
174	C₂²×C₃₁	—	2	8	no	—
175	C₂²×C₃₁	—	4	4	no	—
176	C₂²×C₃₁	—	4	4	no	—
177	C₂²×C₃₁	—	4	8	no	—
178	C₂²×C₃₁	—	4	8	no	—
179	C₂²×C₃₁	—	4	32	no	—
180	C₂²×C₃₁	C₄×C₂²⋊C₄	1	4	yes	—
181	C₂²×C₃₁	#417	1	4	yes	—
182	C₂²×C₃₁	#418	1	4	yes	—
183	C₂²×C₃₁	#440	1	8	yes	—
184	C₂²×C₃₁	#442	1	8	yes	—
185	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₃₁	C₂×C₄×D₄	1	2	yes	—
187	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
188	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
190	C₄×C₃₁	—	2	4	no	—
191	C₄×C₃₁	—	2	4	no	—
192	C₄×C₃₁	—	4	4	no	—
193	C₄×C₃₁	—	4	8	no	—
194	C₄×C₃₁	C₄×C₂²⋊C₄	1	4	yes	—
195	C₄×C₃₁	C₂²×C₄²	1	1	yes	characteristic
196	C₄×C₃₁	C₂×#117	1	1	yes	characteristic
197	C₄×C₃₁	C₂×C₄×D₄	1	2	yes	—
198	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
199	C₂⁴×C₄	—	2	1	no	—
200	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
201	C₂×C₄×D₄	—	2	2	no	—
202	C₂×C₄×D₄	—	2	4	no	—
203	C₂×C₄×D₄	C₄×C₃₁	1	8	yes	complemented
204	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
207	C₂²×C₂²⋊C₄	—	2	1	no	—
208	C₂²×C₄²	—	2	1	no	—
209	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
210	C₂×#102	C₄×C₃₁	1	16	yes	complemented
211	C₂×#102	C₂²×C₃₁	1	8	yes	—
212	C₂×#97	—	2	4	no	—
213	C₂×#97	C₂²×C₃₁	1	4	yes	complemented
214	C₄×C₄⋊C₄	—	2	2	no	—
215	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
216	C₂×#95	—	2	1	no	—
217	#340	C₂²×C₃₁	1	8	yes	complemented
218	C₂×C₃₁	—	4	8	no	—
219	C₂×C₃₁	#1762	1	8	yes	direct product factor
220	C₂×C₃₁	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₃₁	C₂×#418	1	1	yes	characteristic
222	C₂×C₃₁	C₂×#417	1	1	yes	characteristic
223	C₂×C₃₁	C₂×#440	1	2	yes	—
224	C₂×C₃₁	C₂×#442	1	2	yes	—
225	C₂⁵	—	2	1	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	—	2	4	no	—
229	C₂²×D₄	C₂×C₄×C₃₁	1	4	yes	—
230	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	—
231	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	—	2	8	no	—
235	C₂³×C₄	—	2	4	no	—
236	C₂³×C₄	—	4	8	no	—
237	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
238	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
240	C₂²×C₈	—	2	4	no	—
241	C₂²×C₈	—	2	4	no	—
242	C₂²×C₈	C₂×C₄×C₃₁	1	8	yes	complemented
243	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
244	C₄×D₄	—	2	16	no	—
245	C₄×D₄	—	2	8	no	—
246	C₄×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
253	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
255	C₂×C₂²⋊C₄	—	2	8	no	—
256	C₂×C₂²⋊C₄	—	2	4	no	—
257	C₂×C₄²	—	2	4	no	—
258	C₂×C₄²	—	4	4	no	—
259	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
260	C₂×C₄²	D₄×C₃₁	1	2	yes	—
261	C₂×C₄²	D₄×C₃₁	1	4	yes	—
262	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
263	#102	C₂×C₄×C₃₁	1	32	yes	complemented
264	#97	—	2	8	no	—
265	#95	—	2	4	no	—
266	C₃₁	C₂×#1762	1	1	yes	characteristic, direct product factor, Sylow
267	C₂⁴	—	2	4	no	—
268	C₂⁴	—	2	8	no	—
269	C₂⁴	—	2	2	no	—
270	C₂⁴	—	4	4	no	—
271	C₂⁴	—	4	2	no	—
272	C₂⁴	—	4	2	no	—
273	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	8	no	—
276	C₂×D₄	—	2	16	no	—
277	C₂×D₄	—	2	8	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	C₄²×C₃₁	1	16	yes	complemented
281	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
282	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	16	no	—
291	C₂²×C₄	—	4	32	no	—
292	C₂²×C₄	—	4	16	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	—	4	4	no	—
296	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
297	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
298	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
300	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
304	C₂²×C₄	#41×C₃₁	1	4	yes	—
305	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
306	C₂×C₈	—	2	16	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	C₂²×C₄×C₃₁	1	8	yes	complemented
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
315	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
316	C₂²⋊C₄	—	2	16	no	—
317	C₄²	—	4	8	no	—
318	C₄²	C₂²⋊C₄×C₃₁	1	8	yes	—
319	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
320	C₄²	C₂×D₄×C₃₁	1	4	yes	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	8	no	—
323	C₂³	—	2	16	no	—
324	C₂³	—	4	8	no	—
325	C₂³	—	4	8	no	—
326	C₂³	—	4	16	no	—
327	C₂³	—	4	16	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
332	C₂³	C₄×D₄×C₃₁	1	4	yes	—
333	C₂³	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
334	C₂³	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
335	C₂³	C₃₁×#137	1	2	yes	—
336	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
337	D₄	—	2	4	no	—
338	D₄	—	2	8	no	—
339	D₄	—	2	16	no	—
340	D₄	C₂×C₄²×C₃₁	1	8	yes	complemented
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	4	32	no	—
349	C₂×C₄	—	4	8	no	—
350	C₂×C₄	—	4	16	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	C₂×C₄²×C₃₁	1	4	yes	—
355	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
356	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
357	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
358	C₂×C₄	C₃₁×#117	1	4	yes	—
359	C₂×C₄	C₄×D₄×C₃₁	1	8	yes	—
360	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
361	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
362	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
363	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
364	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
365	C₈	—	2	8	no	—
366	C₂²	—	2	8	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	8	no	—
370	C₂²	—	4	8	no	—
371	C₂²	—	4	32	no	—
372	C₂²	C₄×C₂²⋊C₄×C₃₁	1	4	yes	—
373	C₂²	C₃₁×#417	1	4	yes	—
374	C₂²	C₃₁×#418	1	4	yes	—
375	C₂²	C₃₁×#440	1	8	yes	—
376	C₂²	C₃₁×#442	1	8	yes	—
377	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
378	C₂²	C₂×C₄×D₄×C₃₁	1	2	yes	—
379	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
380	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
381	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
382	C₄	—	2	4	no	—
383	C₄	—	2	4	no	—
384	C₄	—	4	4	no	—
385	C₄	—	4	8	no	—
386	C₄	C₄×C₂²⋊C₄×C₃₁	1	4	yes	—
387	C₄	C₂²×C₄²×C₃₁	1	1	yes	characteristic
388	C₄	C₂×C₃₁×#117	1	1	yes	characteristic
389	C₄	C₂×C₄×D₄×C₃₁	1	2	yes	—
390	C₂	—	4	8	no	—
391	C₂	C₃₁×#1762	1	8	yes	direct product factor
392	C₂	C₂×C₄×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
393	C₂	C₂×C₃₁×#418	1	1	yes	characteristic
394	C₂	C₂×C₃₁×#417	1	1	yes	characteristic
395	C₂	C₂×C₃₁×#440	1	2	yes	—
396	C₂	C₂×C₃₁×#442	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂×D₄
commutator	C₄	C₂²×C₄²×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂³×D₄×C₃₁	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₃₁×#97	C₂	semidirect
4. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
5. C₃₁×#1762	C₂	direct (N × H)
6. C₂×C₃₁×#340	C₂	semidirect
12. C₂×C₄×D₄×C₃₁	C₄	semidirect
19. C₂×C₃₁×#102	C₄	semidirect
22. C₂×C₃₁×#97	C₂²	semidirect
24. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
26. C₃₁×#340	C₂²	semidirect
44. C₂²×C₈×C₃₁	C₂×C₄	semidirect
48. C₄×D₄×C₃₁	C₂×C₄	semidirect
54. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
65. C₃₁×#102	C₂×C₄	semidirect
81. C₂×D₄×C₃₁	C₄²	semidirect
110. C₂×C₈×C₃₁	C₂²×C₄	semidirect
116. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
122. C₂×#1762	C₃₁	direct (N × H)
142. D₄×C₃₁	C₂×C₄²	semidirect
170. C₂²×#97	C₂×C₃₁	semidirect
171. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
172. #1762	C₂×C₃₁	direct (N × H)
173. C₂×#340	C₂×C₃₁	semidirect
203. C₂×C₄×D₄	C₄×C₃₁	semidirect
210. C₂×#102	C₄×C₃₁	semidirect
213. C₂×#97	C₂²×C₃₁	semidirect
215. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
217. #340	C₂²×C₃₁	semidirect
219. C₂×C₃₁	#1762	direct (N × H)
242. C₂²×C₈	C₂×C₄×C₃₁	semidirect
246. C₄×D₄	C₂×C₄×C₃₁	semidirect
252. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
263. #102	C₂×C₄×C₃₁	semidirect
266. C₃₁	C₂×#1762	direct (N × H)
280. C₂×D₄	C₄²×C₃₁	semidirect
309. C₂×C₈	C₂²×C₄×C₃₁	semidirect
315. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
340. D₄	C₂×C₄²×C₃₁	semidirect
391. C₂	C₃₁×#1762	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×C₄×D₄×C₃₁	2
C₂²×C₃₁×#102	2
C₂²×C₃₁×#97	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₃₁×#1762	2
C₂×C₃₁×#340	2
C₂×#1762	31

Subgroups — C2×C31×#1762 #21477168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1762 #21477168