Subgroups — C₂²×C₃₁×#435 #21516890

Order 7936.

3350 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×#435	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₃₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₃₁	C₄	1	1	yes	characteristic
10	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₃₁	—	2	8	no	—
13	C₂²×M₁₆×C₃₁	C₂²	1	12	yes	complemented
14	C₂³×C₈×C₃₁	—	2	8	no	—
15	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₃₁	C₂²	1	12	yes	complemented
20	C₂×C₄×D₄×C₃₁	C₄	1	12	yes	—
21	C₂×C₄×D₄×C₃₁	C₂²	1	12	yes	—
22	C₂²×C₄⋊C₄×C₃₁	C₄	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₃₁	C₄	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₃₁	C₄	1	1	yes	characteristic
25	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#435	C₂²	1	64	yes	direct product factor
27	C₂×C₃₁×C₄⋊C₈	C₂²	1	12	yes	complemented
28	C₂×C₃₁×C₂²⋊C₈	C₂²	1	12	yes	complemented
29	C₂×C₃₁×C₂²⋊C₈	C₂²	1	12	yes	complemented
30	C₂×C₃₁×#97	C₂²	1	12	yes	complemented
31	C₂⁵×C₃₁	C₂×C₄	1	1	yes	characteristic
32	C₂⁵×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×D₄×C₃₁	—	2	8	no	—
34	C₂²×D₄×C₃₁	C₂×C₄	1	12	yes	—
35	C₂³×C₄×C₃₁	—	2	4	no	—
36	C₂³×C₄×C₃₁	—	2	4	no	—
37	C₂³×C₄×C₃₁	—	2	4	no	—
38	C₂³×C₄×C₃₁	—	2	4	no	—
39	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₃₁	C₂×C₄	1	6	yes	—
44	C₂³×C₄×C₃₁	C₂×C₄	1	6	yes	—
45	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
46	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
47	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₃₁	—	2	48	no	—
49	C₂×M₁₆×C₃₁	C₂³	1	16	yes	complemented
50	C₂²×C₈×C₃₁	—	2	4	no	—
51	C₂²×C₈×C₃₁	—	2	4	no	—
52	C₂²×C₈×C₃₁	—	2	4	no	—
53	C₂²×C₈×C₃₁	—	2	48	no	—
54	C₂²×C₈×C₃₁	D₄	1	8	yes	complemented
55	C₂²×C₈×C₃₁	C₂³	1	6	yes	—
56	C₂²×C₈×C₃₁	C₂³	1	6	yes	—
57	C₂²×C₈×C₃₁	C₂³	1	6	yes	—
58	C₂²×C₈×C₃₁	C₂³	1	6	yes	—
59	C₂²×C₈×C₃₁	C₂³	1	16	yes	complemented
60	C₄×D₄×C₃₁	C₂×C₄	1	48	yes	—
61	C₄×D₄×C₃₁	C₂³	1	16	yes	—
62	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	12	yes	—
63	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	12	yes	—
64	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	12	yes	—
65	C₂×C₄²×C₃₁	C₂×C₄	1	6	yes	—
66	C₂×C₄²×C₃₁	C₂³	1	6	yes	—
67	C₃₁×C₄⋊C₈	C₂³	1	16	yes	complemented
68	C₃₁×C₂²⋊C₈	C₂³	1	16	yes	complemented
69	C₃₁×C₂²⋊C₈	C₂³	1	16	yes	complemented
70	C₃₁×#97	C₂³	1	16	yes	complemented
71	C₂⁴×C₃₁	—	2	4	no	—
72	C₂⁴×C₃₁	—	2	4	no	—
73	C₂⁴×C₃₁	—	2	4	no	—
74	C₂⁴×C₃₁	—	2	4	no	—
75	C₂⁴×C₃₁	—	2	4	no	—
76	C₂⁴×C₃₁	M₁₆	1	8	yes	complemented
77	C₂⁴×C₃₁	C₂²×C₄	1	6	yes	—
78	C₂⁴×C₃₁	C₂²×C₄	1	6	yes	—
79	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
80	C₂×D₄×C₃₁	—	2	48	no	—
81	C₂×D₄×C₃₁	C₂²×C₄	1	16	yes	—
82	C₂²×C₄×C₃₁	—	2	4	no	—
83	C₂²×C₄×C₃₁	—	2	4	no	—
84	C₂²×C₄×C₃₁	—	2	4	no	—
85	C₂²×C₄×C₃₁	—	2	4	no	—
86	C₂²×C₄×C₃₁	—	2	24	no	—
87	C₂²×C₄×C₃₁	—	2	24	no	—
88	C₂²×C₄×C₃₁	—	2	12	no	—
89	C₂²×C₄×C₃₁	—	2	12	no	—
90	C₂²×C₄×C₃₁	—	2	12	no	—
91	C₂²×C₄×C₃₁	—	2	12	no	—
92	C₂²×C₄×C₃₁	C₂²×C₄	1	6	yes	—
93	C₂²×C₄×C₃₁	C₂²×C₄	1	6	yes	—
94	C₂²×C₄×C₃₁	C₂²×C₄	1	6	yes	—
95	C₂²×C₄×C₃₁	C₂²×C₄	1	6	yes	—
96	C₂²×C₄×C₃₁	C₂²×C₄	1	12	yes	—
97	C₂²×C₄×C₃₁	C₂²×C₄	1	12	yes	—
98	C₂²×C₄×C₃₁	C₂²×C₄	1	3	yes	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₃₁	#41	1	4	yes	—
101	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
102	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
104	M₁₆×C₃₁	—	2	32	no	—
105	C₂×C₈×C₃₁	—	2	12	no	—
106	C₂×C₈×C₃₁	—	2	12	no	—
107	C₂×C₈×C₃₁	—	2	12	no	—
108	C₂×C₈×C₃₁	—	2	32	no	—
109	C₂×C₈×C₃₁	C₂×D₄	1	24	yes	complemented
110	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
111	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
112	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
113	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
114	C₄⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
115	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
116	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
117	C₄²×C₃₁	C₂²×C₄	1	12	yes	—
118	C₄²×C₃₁	C₂⁴	1	4	yes	—
119	C₂²×#435	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₃₁	—	2	12	no	—
121	C₂³×C₃₁	—	2	12	no	—
122	C₂³×C₃₁	—	2	32	no	—
123	C₂³×C₃₁	—	2	12	no	—
124	C₂³×C₃₁	—	2	12	no	—
125	C₂³×C₃₁	—	2	12	no	—
126	C₂³×C₃₁	—	4	16	no	—
127	C₂³×C₃₁	C₄×D₄	1	4	yes	—
128	C₂³×C₃₁	C₂×M₁₆	1	4	yes	—
129	C₂³×C₃₁	C₂×M₁₆	1	24	yes	complemented
130	C₂³×C₃₁	#131	1	4	yes	—
131	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
132	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
133	C₂³×C₃₁	C₂³×C₄	1	3	yes	—
134	D₄×C₃₁	—	2	32	no	—
135	C₂×C₄×C₃₁	—	2	12	no	—
136	C₂×C₄×C₃₁	—	2	12	no	—
137	C₂×C₄×C₃₁	—	2	12	no	—
138	C₂×C₄×C₃₁	—	2	12	no	—
139	C₂×C₄×C₃₁	—	2	24	no	—
140	C₂×C₄×C₃₁	—	2	24	no	—
141	C₂×C₄×C₃₁	—	2	4	no	—
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	2	4	no	—
144	C₂×C₄×C₃₁	—	2	4	no	—
145	C₂×C₄×C₃₁	C₄×D₄	1	12	yes	—
146	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
147	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
148	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
149	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
150	C₂×C₄×C₃₁	C₂³×C₄	1	3	yes	—
151	C₂×C₄×C₃₁	C₂²×D₄	1	6	yes	—
152	C₂×C₄×C₃₁	C₂×#41	1	6	yes	—
153	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
154	C₈×C₃₁	—	2	4	no	—
155	C₈×C₃₁	—	2	4	no	—
156	C₈×C₃₁	—	2	4	no	—
157	C₈×C₃₁	C₂²×D₄	1	8	yes	complemented
158	C₂³×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
159	C₂⁴×C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
160	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic
161	C₂×#435	C₂×C₃₁	1	24	yes	direct product factor
162	C₂²×C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
163	C₂²×C₂²⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
164	C₂²×C₂²⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
165	C₂²×#97	C₂×C₃₁	1	1	yes	characteristic, complemented
166	C₂²×C₃₁	—	2	4	no	—
167	C₂²×C₃₁	—	2	48	no	—
168	C₂²×C₃₁	—	2	4	no	—
169	C₂²×C₃₁	—	2	4	no	—
170	C₂²×C₃₁	—	2	4	no	—
171	C₂²×C₃₁	—	2	4	no	—
172	C₂²×C₃₁	—	4	24	no	—
173	C₂²×C₃₁	#435	1	16	yes	direct product factor
174	C₂²×C₃₁	C₂×C₄×D₄	1	6	yes	—
175	C₂²×C₃₁	C₂²×M₁₆	1	6	yes	—
176	C₂²×C₃₁	C₂²×M₁₆	1	8	yes	complemented
177	C₂²×C₃₁	C₂×#131	1	6	yes	—
178	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
179	C₄×C₃₁	—	2	4	no	—
180	C₄×C₃₁	—	2	4	no	—
181	C₄×C₃₁	—	2	4	no	—
182	C₄×C₃₁	—	2	4	no	—
183	C₄×C₃₁	C₂×C₄×D₄	1	6	yes	—
184	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
185	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
186	C₂³×D₄	C₄×C₃₁	1	1	yes	characteristic
187	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
188	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
189	C₂²×M₁₆	—	2	8	no	—
190	C₂²×M₁₆	C₂²×C₃₁	1	12	yes	complemented
191	C₂³×C₈	—	2	8	no	—
192	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
193	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
194	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
195	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₃₁	1	12	yes	complemented
197	C₂×C₄×D₄	C₄×C₃₁	1	12	yes	—
198	C₂×C₄×D₄	C₂²×C₃₁	1	12	yes	—
199	C₂²×C₄⋊C₄	C₄×C₃₁	1	1	yes	characteristic
200	C₂²×C₂²⋊C₄	C₄×C₃₁	1	1	yes	characteristic
201	C₂²×C₂²⋊C₄	C₄×C₃₁	1	1	yes	characteristic
202	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
203	#435	C₂²×C₃₁	1	64	yes	direct product factor
204	C₂×C₄⋊C₈	C₂²×C₃₁	1	12	yes	complemented
205	C₂×C₂²⋊C₈	C₂²×C₃₁	1	12	yes	complemented
206	C₂×C₂²⋊C₈	C₂²×C₃₁	1	12	yes	complemented
207	C₂×#97	C₂²×C₃₁	1	12	yes	complemented
208	C₂×C₃₁	—	2	8	no	—
209	C₂×C₃₁	—	4	4	no	—
210	C₂×C₃₁	C₂×#435	1	12	yes	direct product factor
211	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
212	C₂×C₃₁	C₂³×M₁₆	1	1	yes	characteristic
213	C₂×C₃₁	C₂²×#131	1	1	yes	characteristic
214	C₂⁵	C₂×C₄×C₃₁	1	1	yes	characteristic
215	C₂⁵	C₂×C₄×C₃₁	1	1	yes	characteristic
216	C₂²×D₄	—	2	8	no	—
217	C₂²×D₄	C₂×C₄×C₃₁	1	12	yes	—
218	C₂³×C₄	—	2	4	no	—
219	C₂³×C₄	—	2	4	no	—
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	—	2	4	no	—
222	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
223	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
224	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
225	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
226	C₂³×C₄	C₂×C₄×C₃₁	1	6	yes	—
227	C₂³×C₄	C₂×C₄×C₃₁	1	6	yes	—
228	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
229	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
230	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
231	C₂×M₁₆	—	2	48	no	—
232	C₂×M₁₆	C₂³×C₃₁	1	16	yes	complemented
233	C₂²×C₈	—	2	4	no	—
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	—	2	4	no	—
236	C₂²×C₈	—	2	48	no	—
237	C₂²×C₈	D₄×C₃₁	1	8	yes	complemented
238	C₂²×C₈	C₂³×C₃₁	1	6	yes	—
239	C₂²×C₈	C₂³×C₃₁	1	6	yes	—
240	C₂²×C₈	C₂³×C₃₁	1	6	yes	—
241	C₂²×C₈	C₂³×C₃₁	1	6	yes	—
242	C₂²×C₈	C₂³×C₃₁	1	16	yes	complemented
243	C₄×D₄	C₂×C₄×C₃₁	1	48	yes	—
244	C₄×D₄	C₂³×C₃₁	1	16	yes	—
245	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	12	yes	—
246	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	12	yes	—
247	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	12	yes	—
248	C₂×C₄²	C₂×C₄×C₃₁	1	6	yes	—
249	C₂×C₄²	C₂³×C₃₁	1	6	yes	—
250	C₄⋊C₈	C₂³×C₃₁	1	16	yes	complemented
251	C₂²⋊C₈	C₂³×C₃₁	1	16	yes	complemented
252	C₂²⋊C₈	C₂³×C₃₁	1	16	yes	complemented
253	#97	C₂³×C₃₁	1	16	yes	complemented
254	C₃₁	C₂²×#435	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	—	2	4	no	—
260	C₂⁴	M₁₆×C₃₁	1	8	yes	complemented
261	C₂⁴	C₂²×C₄×C₃₁	1	6	yes	—
262	C₂⁴	C₂²×C₄×C₃₁	1	6	yes	—
263	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
264	C₂×D₄	—	2	48	no	—
265	C₂×D₄	C₂²×C₄×C₃₁	1	16	yes	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	24	no	—
271	C₂²×C₄	—	2	24	no	—
272	C₂²×C₄	—	2	12	no	—
273	C₂²×C₄	—	2	12	no	—
274	C₂²×C₄	—	2	12	no	—
275	C₂²×C₄	—	2	12	no	—
276	C₂²×C₄	C₂²×C₄×C₃₁	1	6	yes	—
277	C₂²×C₄	C₂²×C₄×C₃₁	1	6	yes	—
278	C₂²×C₄	C₂²×C₄×C₃₁	1	6	yes	—
279	C₂²×C₄	C₂²×C₄×C₃₁	1	6	yes	—
280	C₂²×C₄	C₂²×C₄×C₃₁	1	12	yes	—
281	C₂²×C₄	C₂²×C₄×C₃₁	1	12	yes	—
282	C₂²×C₄	C₂²×C₄×C₃₁	1	3	yes	—
283	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
284	C₂²×C₄	#41×C₃₁	1	4	yes	—
285	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
287	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
288	M₁₆	—	2	32	no	—
289	C₂×C₈	—	2	12	no	—
290	C₂×C₈	—	2	12	no	—
291	C₂×C₈	—	2	12	no	—
292	C₂×C₈	—	2	32	no	—
293	C₂×C₈	C₂×D₄×C₃₁	1	24	yes	complemented
294	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
295	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
296	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
297	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
298	C₄⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
299	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
300	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
301	C₄²	C₂²×C₄×C₃₁	1	12	yes	—
302	C₄²	C₂⁴×C₃₁	1	4	yes	—
303	C₂³	—	2	32	no	—
304	C₂³	—	2	12	no	—
305	C₂³	—	2	12	no	—
306	C₂³	—	2	12	no	—
307	C₂³	—	2	12	no	—
308	C₂³	—	2	12	no	—
309	C₂³	—	4	16	no	—
310	C₂³	C₄×D₄×C₃₁	1	4	yes	—
311	C₂³	C₂×M₁₆×C₃₁	1	4	yes	—
312	C₂³	C₂×M₁₆×C₃₁	1	24	yes	complemented
313	C₂³	C₃₁×#131	1	4	yes	—
314	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
315	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
316	C₂³	C₂³×C₄×C₃₁	1	3	yes	—
317	D₄	—	2	32	no	—
318	C₂×C₄	—	2	12	no	—
319	C₂×C₄	—	2	12	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	12	no	—
322	C₂×C₄	—	2	24	no	—
323	C₂×C₄	—	2	24	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	C₄×D₄×C₃₁	1	12	yes	—
329	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
330	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
331	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
332	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
333	C₂×C₄	C₂³×C₄×C₃₁	1	3	yes	—
334	C₂×C₄	C₂²×D₄×C₃₁	1	6	yes	—
335	C₂×C₄	C₂×#41×C₃₁	1	6	yes	—
336	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
337	C₈	—	2	4	no	—
338	C₈	—	2	4	no	—
339	C₈	—	2	4	no	—
340	C₈	C₂²×D₄×C₃₁	1	8	yes	complemented
341	C₂²	—	2	4	no	—
342	C₂²	—	2	48	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	4	24	no	—
348	C₂²	C₃₁×#435	1	16	yes	direct product factor
349	C₂²	C₂×C₄×D₄×C₃₁	1	6	yes	—
350	C₂²	C₂²×M₁₆×C₃₁	1	6	yes	—
351	C₂²	C₂²×M₁₆×C₃₁	1	8	yes	complemented
352	C₂²	C₂×C₃₁×#131	1	6	yes	—
353	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	4	no	—
358	C₄	C₂×C₄×D₄×C₃₁	1	6	yes	—
359	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
360	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
361	C₂	—	2	8	no	—
362	C₂	—	4	4	no	—
363	C₂	C₂×C₃₁×#435	1	12	yes	direct product factor
364	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
365	C₂	C₂³×M₁₆×C₃₁	1	1	yes	characteristic
366	C₂	C₂²×C₃₁×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₃₁	C₂³
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
socle	C₂⁴×C₃₁	C₂²×C₄
prime radical	C₂³×D₄×C₃₁	C₄
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
1. C₂³×M₁₆×C₃₁	C₂	semidirect
2. C₂⁴×C₈×C₃₁	C₂	semidirect
4. C₂×C₃₁×#435	C₂	direct (N × H)
5. C₂²×C₃₁×C₄⋊C₈	C₂	semidirect
6. C₂²×C₃₁×C₂²⋊C₈	C₂	semidirect
7. C₂²×C₃₁×C₂²⋊C₈	C₂	semidirect
8. C₂²×C₃₁×#97	C₂	semidirect
13. C₂²×M₁₆×C₃₁	C₂²	semidirect
19. C₂³×C₈×C₃₁	C₂²	semidirect
26. C₃₁×#435	C₂²	direct (N × H)
27. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
28. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
29. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
30. C₂×C₃₁×#97	C₂²	semidirect
49. C₂×M₁₆×C₃₁	C₂³	semidirect
54. C₂²×C₈×C₃₁	D₄	semidirect
59. C₂²×C₈×C₃₁	C₂³	semidirect
67. C₃₁×C₄⋊C₈	C₂³	semidirect
68. C₃₁×C₂²⋊C₈	C₂³	semidirect
69. C₃₁×C₂²⋊C₈	C₂³	semidirect
70. C₃₁×#97	C₂³	semidirect
76. C₂⁴×C₃₁	M₁₆	semidirect
109. C₂×C₈×C₃₁	C₂×D₄	semidirect
119. C₂²×#435	C₃₁	direct (N × H)
129. C₂³×C₃₁	C₂×M₁₆	semidirect
157. C₈×C₃₁	C₂²×D₄	semidirect
158. C₂³×M₁₆	C₂×C₃₁	semidirect
159. C₂⁴×C₈	C₂×C₃₁	semidirect
161. C₂×#435	C₂×C₃₁	direct (N × H)
162. C₂²×C₄⋊C₈	C₂×C₃₁	semidirect
163. C₂²×C₂²⋊C₈	C₂×C₃₁	semidirect
164. C₂²×C₂²⋊C₈	C₂×C₃₁	semidirect
165. C₂²×#97	C₂×C₃₁	semidirect
173. C₂²×C₃₁	#435	direct (N × H)
176. C₂²×C₃₁	C₂²×M₁₆	semidirect
190. C₂²×M₁₆	C₂²×C₃₁	semidirect
196. C₂³×C₈	C₂²×C₃₁	semidirect
203. #435	C₂²×C₃₁	direct (N × H)
204. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
205. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
206. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
207. C₂×#97	C₂²×C₃₁	semidirect
210. C₂×C₃₁	C₂×#435	direct (N × H)
232. C₂×M₁₆	C₂³×C₃₁	semidirect
237. C₂²×C₈	D₄×C₃₁	semidirect
242. C₂²×C₈	C₂³×C₃₁	semidirect
250. C₄⋊C₈	C₂³×C₃₁	semidirect
251. C₂²⋊C₈	C₂³×C₃₁	semidirect
252. C₂²⋊C₈	C₂³×C₃₁	semidirect
253. #97	C₂³×C₃₁	semidirect
254. C₃₁	C₂²×#435	direct (N × H)
260. C₂⁴	M₁₆×C₃₁	semidirect
293. C₂×C₈	C₂×D₄×C₃₁	semidirect
312. C₂³	C₂×M₁₆×C₃₁	semidirect
340. C₈	C₂²×D₄×C₃₁	semidirect
348. C₂²	C₃₁×#435	direct (N × H)
351. C₂²	C₂²×M₁₆×C₃₁	semidirect
363. C₂	C₂×C₃₁×#435	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₃₁	2
C₂⁴×C₈×C₃₁	2
C₂²×C₄×D₄×C₃₁	2
C₂×C₃₁×#435	2
C₂²×C₃₁×C₄⋊C₈	2
C₂²×C₃₁×C₂²⋊C₈	2
C₂²×C₃₁×#97	2
C₂²×#435	31

Subgroups — C22×C31×#435 #21516890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃₁×#435 #21516890