Subgroups — C₂×#2352×C₁₃₁ #45719999

Order 33536.

3894 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₄⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2352×C₁₃₁	C₂	1	16	yes	maximal, direct product factor
5	C₂×#388×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	C₂×#387×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	C₂×#386×C₁₃₁	C₂	1	2	yes	maximal
8	C₂×#382×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#380×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#380×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₄⋊C₄×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	1	2	yes	maximal, complemented
13	C₂³×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃₁	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃₁	C₄	1	16	yes	complemented
18	C₂×C₄×D₄×C₁₃₁	C₂²	1	8	yes	—
19	C₂×#117×C₁₃₁	—	2	8	no	—
20	C₂×#117×C₁₃₁	C₂²	1	8	yes	complemented
21	C₂²×C₄⋊C₄×C₁₃₁	—	2	8	no	—
22	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₃₁	C₂²	1	8	yes	complemented
29	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₃₁	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
37	#388×C₁₃₁	C₂²	1	16	yes	complemented
38	#387×C₁₃₁	C₂²	1	16	yes	complemented
39	#386×C₁₃₁	C₂²	1	16	yes	—
40	#382×C₁₃₁	C₂²	1	8	yes	complemented
41	#380×C₁₃₁	C₂²	1	8	yes	complemented
42	#380×C₁₃₁	C₂²	1	8	yes	complemented
43	C₄×C₄⋊C₄×C₁₃₁	C₂²	1	8	yes	complemented
44	C₄×C₂²⋊C₄×C₁₃₁	C₂²	1	16	yes	complemented
45	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
46	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
47	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
48	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
49	C₂×#95×C₁₃₁	C₂²	1	2	yes	—
50	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
51	C₂⁵×C₁₃₁	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃₁	—	2	4	no	—
53	C₂²×D₄×C₁₃₁	—	2	4	no	—
54	C₂²×D₄×C₁₃₁	C₂×C₄	1	8	yes	—
55	C₂²×D₄×C₁₃₁	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₃₁	—	2	4	no	—
57	C₂³×C₄×C₁₃₁	—	2	4	no	—
58	C₂³×C₄×C₁₃₁	—	2	4	no	—
59	C₂³×C₄×C₁₃₁	—	2	4	no	—
60	C₂³×C₄×C₁₃₁	—	2	8	no	—
61	C₂³×C₄×C₁₃₁	—	2	8	no	—
62	C₂³×C₄×C₁₃₁	—	4	4	no	—
63	C₂³×C₄×C₁₃₁	C₂×C₄	1	8	yes	—
64	C₂³×C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
65	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃₁	C₂³	1	8	yes	—
69	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃₁	C₂³	1	4	yes	—
75	C₂³×C₄×C₁₃₁	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
77	C₄×D₄×C₁₃₁	C₂×C₄	1	64	yes	complemented
78	#117×C₁₃₁	—	2	32	no	—
79	C₂×C₄⋊C₄×C₁₃₁	—	2	8	no	—
80	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
81	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
82	C₂×C₄⋊C₄×C₁₃₁	—	2	4	no	—
83	C₂×C₄⋊C₄×C₁₃₁	—	2	32	no	—
84	C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
85	C₂×C₄⋊C₄×C₁₃₁	D₄	1	8	yes	complemented
86	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	8	yes	—
87	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₁₃₁	—	2	8	no	—
93	C₂×C₂²⋊C₄×C₁₃₁	—	2	8	no	—
94	C₂×C₂²⋊C₄×C₁₃₁	—	4	4	no	—
95	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	—
96	C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	1	8	yes	complemented
97	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	8	yes	—
100	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₃₁	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₃₁	—	2	8	no	—
103	C₂×C₄²×C₁₃₁	—	4	4	no	—
104	C₂×C₄²×C₁₃₁	C₂×C₄	1	8	yes	complemented
105	C₂×C₄²×C₁₃₁	C₂³	1	8	yes	—
106	C₂×C₄²×C₁₃₁	C₂³	1	8	yes	—
107	C₂×C₄²×C₁₃₁	C₂³	1	4	yes	—
108	#95×C₁₃₁	C₂³	1	8	yes	—
109	#95×C₁₃₁	C₂³	1	8	yes	—
110	#95×C₁₃₁	C₂³	1	8	yes	—
111	#95×C₁₃₁	C₂³	1	8	yes	—
112	#95×C₁₃₁	C₂³	1	8	yes	—
113	C₂⁴×C₁₃₁	—	2	2	no	—
114	C₂⁴×C₁₃₁	—	2	2	no	—
115	C₂⁴×C₁₃₁	—	2	2	no	—
116	C₂⁴×C₁₃₁	—	2	2	no	—
117	C₂⁴×C₁₃₁	—	2	2	no	—
118	C₂⁴×C₁₃₁	—	2	2	no	—
119	C₂⁴×C₁₃₁	—	2	2	no	—
120	C₂⁴×C₁₃₁	—	2	2	no	—
121	C₂⁴×C₁₃₁	—	2	2	no	—
122	C₂⁴×C₁₃₁	—	2	2	no	—
123	C₂⁴×C₁₃₁	C₂²×C₄	1	4	yes	—
124	C₂⁴×C₁₃₁	C₂²×C₄	1	4	yes	—
125	C₂⁴×C₁₃₁	#41	1	4	yes	—
126	C₂⁴×C₁₃₁	#41	1	4	yes	—
127	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
128	C₂⁴×C₁₃₁	C₂⁴	1	2	yes	—
129	C₂⁴×C₁₃₁	C₂⁴	1	1	yes	characteristic
130	C₂×D₄×C₁₃₁	—	2	32	no	—
131	C₂×D₄×C₁₃₁	—	2	8	no	—
132	C₂×D₄×C₁₃₁	—	2	8	no	—
133	C₂×D₄×C₁₃₁	C₂²×C₄	1	16	yes	—
134	C₂²×C₄×C₁₃₁	—	2	2	no	—
135	C₂²×C₄×C₁₃₁	—	2	2	no	—
136	C₂²×C₄×C₁₃₁	—	2	2	no	—
137	C₂²×C₄×C₁₃₁	—	2	2	no	—
138	C₂²×C₄×C₁₃₁	—	2	4	no	—
139	C₂²×C₄×C₁₃₁	—	2	2	no	—
140	C₂²×C₄×C₁₃₁	—	2	2	no	—
141	C₂²×C₄×C₁₃₁	—	2	2	no	—
142	C₂²×C₄×C₁₃₁	—	2	4	no	—
143	C₂²×C₄×C₁₃₁	—	2	2	no	—
144	C₂²×C₄×C₁₃₁	—	2	32	no	—
145	C₂²×C₄×C₁₃₁	—	2	32	no	—
146	C₂²×C₄×C₁₃₁	—	2	8	no	—
147	C₂²×C₄×C₁₃₁	—	2	8	no	—
148	C₂²×C₄×C₁₃₁	—	2	8	no	—
149	C₂²×C₄×C₁₃₁	—	2	8	no	—
150	C₂²×C₄×C₁₃₁	—	2	4	no	—
151	C₂²×C₄×C₁₃₁	—	2	4	no	—
152	C₂²×C₄×C₁₃₁	—	2	4	no	—
153	C₂²×C₄×C₁₃₁	—	2	4	no	—
154	C₂²×C₄×C₁₃₁	—	2	4	no	—
155	C₂²×C₄×C₁₃₁	—	2	16	no	—
156	C₂²×C₄×C₁₃₁	—	2	4	no	—
157	C₂²×C₄×C₁₃₁	—	2	4	no	—
158	C₂²×C₄×C₁₃₁	—	2	4	no	—
159	C₂²×C₄×C₁₃₁	—	2	4	no	—
160	C₂²×C₄×C₁₃₁	—	2	16	no	—
161	C₂²×C₄×C₁₃₁	—	4	8	no	—
162	C₂²×C₄×C₁₃₁	—	4	32	no	—
163	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
164	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
165	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
166	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
167	C₂²×C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
168	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
169	C₂²×C₄×C₁₃₁	C₂²×C₄	1	16	yes	complemented
170	C₂²×C₄×C₁₃₁	C₂×D₄	1	8	yes	—
171	C₂²×C₄×C₁₃₁	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₃₁	#41	1	4	yes	—
173	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃₁	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃₁	C₂⁴	1	2	yes	—
182	C₄⋊C₄×C₁₃₁	—	2	16	no	—
183	C₄⋊C₄×C₁₃₁	—	2	8	no	—
184	C₄⋊C₄×C₁₃₁	—	2	8	no	—
185	C₄⋊C₄×C₁₃₁	—	2	8	no	—
186	C₄⋊C₄×C₁₃₁	C₂²×C₄	1	16	yes	complemented
187	C₄⋊C₄×C₁₃₁	C₂×D₄	1	16	yes	complemented
188	C₂²⋊C₄×C₁₃₁	—	2	16	no	—
189	C₂²⋊C₄×C₁₃₁	—	2	16	no	—
190	C₂²⋊C₄×C₁₃₁	—	4	8	no	—
191	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	16	yes	—
192	C₂²⋊C₄×C₁₃₁	C₂²×C₄	1	16	yes	complemented
193	C₄²×C₁₃₁	—	2	16	no	—
194	C₄²×C₁₃₁	—	4	8	no	—
195	C₄²×C₁₃₁	C₂²×C₄	1	16	yes	complemented
196	C₂³×C₁₃₁	—	2	8	no	—
197	C₂³×C₁₃₁	—	2	8	no	—
198	C₂³×C₁₃₁	—	2	8	no	—
199	C₂³×C₁₃₁	—	2	8	no	—
200	C₂³×C₁₃₁	—	2	8	no	—
201	C₂³×C₁₃₁	—	2	8	no	—
202	C₂³×C₁₃₁	—	2	2	no	—
203	C₂³×C₁₃₁	—	2	2	no	—
204	C₂³×C₁₃₁	—	2	2	no	—
205	C₂³×C₁₃₁	—	2	2	no	—
206	C₂³×C₁₃₁	—	2	8	no	—
207	C₂³×C₁₃₁	—	2	8	no	—
208	C₂³×C₁₃₁	—	2	8	no	—
209	C₂³×C₁₃₁	—	2	2	no	—
210	C₂³×C₁₃₁	—	2	2	no	—
211	C₂³×C₁₃₁	—	2	2	no	—
212	C₂³×C₁₃₁	—	2	2	no	—
213	C₂³×C₁₃₁	—	2	2	no	—
214	C₂³×C₁₃₁	—	2	2	no	—
215	C₂³×C₁₃₁	—	4	4	no	—
216	C₂³×C₁₃₁	—	4	4	no	—
217	C₂³×C₁₃₁	—	4	4	no	—
218	C₂³×C₁₃₁	—	4	4	no	—
219	C₂³×C₁₃₁	#117	1	16	yes	complemented
220	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
221	C₂³×C₁₃₁	C₂³×C₄	1	4	yes	—
222	C₂³×C₁₃₁	C₂³×C₄	1	2	yes	—
223	C₂³×C₁₃₁	C₂²×D₄	1	2	yes	—
224	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
225	C₂³×C₁₃₁	C₂×#41	1	4	yes	—
226	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
227	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
228	C₂³×C₁₃₁	C₂×#41	1	2	yes	—
229	C₂³×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
230	C₂³×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
231	C₂³×C₁₃₁	C₂⁵	1	1	yes	characteristic
232	D₄×C₁₃₁	—	2	32	no	—
233	C₂×C₄×C₁₃₁	—	2	8	no	—
234	C₂×C₄×C₁₃₁	—	2	8	no	—
235	C₂×C₄×C₁₃₁	—	2	8	no	—
236	C₂×C₄×C₁₃₁	—	2	8	no	—
237	C₂×C₄×C₁₃₁	—	2	16	no	—
238	C₂×C₄×C₁₃₁	—	2	2	no	—
239	C₂×C₄×C₁₃₁	—	2	2	no	—
240	C₂×C₄×C₁₃₁	—	2	2	no	—
241	C₂×C₄×C₁₃₁	—	2	2	no	—
242	C₂×C₄×C₁₃₁	—	2	4	no	—
243	C₂×C₄×C₁₃₁	—	2	2	no	—
244	C₂×C₄×C₁₃₁	—	2	2	no	—
245	C₂×C₄×C₁₃₁	—	2	2	no	—
246	C₂×C₄×C₁₃₁	—	2	4	no	—
247	C₂×C₄×C₁₃₁	—	2	2	no	—
248	C₂×C₄×C₁₃₁	—	2	32	no	—
249	C₂×C₄×C₁₃₁	—	2	32	no	—
250	C₂×C₄×C₁₃₁	—	2	4	no	—
251	C₂×C₄×C₁₃₁	—	2	4	no	—
252	C₂×C₄×C₁₃₁	—	2	4	no	—
253	C₂×C₄×C₁₃₁	—	2	4	no	—
254	C₂×C₄×C₁₃₁	—	2	4	no	—
255	C₂×C₄×C₁₃₁	—	2	4	no	—
256	C₂×C₄×C₁₃₁	—	2	4	no	—
257	C₂×C₄×C₁₃₁	—	2	4	no	—
258	C₂×C₄×C₁₃₁	—	2	4	no	—
259	C₂×C₄×C₁₃₁	—	4	32	no	—
260	C₂×C₄×C₁₃₁	—	4	8	no	—
261	C₂×C₄×C₁₃₁	—	4	8	no	—
262	C₂×C₄×C₁₃₁	—	4	8	no	—
263	C₂×C₄×C₁₃₁	C₄×D₄	1	16	yes	—
264	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
265	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
266	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
267	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
268	C₂×C₄×C₁₃₁	C₂³×C₄	1	4	yes	—
269	C₂×C₄×C₁₃₁	C₂²×D₄	1	8	yes	—
270	C₂×C₄×C₁₃₁	C₂²×D₄	1	4	yes	—
271	C₂×C₄×C₁₃₁	C₂×#41	1	4	yes	—
272	C₂²×C₁₃₁	—	2	32	no	—
273	C₂²×C₁₃₁	—	2	4	no	—
274	C₂²×C₁₃₁	—	2	4	no	—
275	C₂²×C₁₃₁	—	2	4	no	—
276	C₂²×C₁₃₁	—	2	4	no	—
277	C₂²×C₁₃₁	—	2	4	no	—
278	C₂²×C₁₃₁	—	2	4	no	—
279	C₂²×C₁₃₁	—	2	4	no	—
280	C₂²×C₁₃₁	—	2	4	no	—
281	C₂²×C₁₃₁	—	2	4	no	—
282	C₂²×C₁₃₁	—	4	16	no	—
283	C₂²×C₁₃₁	—	4	2	no	—
284	C₂²×C₁₃₁	—	4	2	no	—
285	C₂²×C₁₃₁	—	4	2	no	—
286	C₂²×C₁₃₁	—	4	2	no	—
287	C₂²×C₁₃₁	C₂×#117	1	4	yes	—
288	C₂²×C₁₃₁	C₂×#117	1	8	yes	complemented
289	C₂²×C₁₃₁	C₂×C₄×D₄	1	4	yes	—
290	C₂²×C₁₃₁	#520	1	4	yes	—
291	C₂²×C₁₃₁	#546	1	4	yes	—
292	C₂²×C₁₃₁	#548	1	4	yes	—
293	C₂²×C₁₃₁	#552	1	4	yes	—
294	C₂²×C₁₃₁	#553	1	4	yes	—
295	C₂²×C₁₃₁	C₂⁴×C₄	1	1	yes	characteristic
296	C₂²×C₁₃₁	C₂³×D₄	1	1	yes	characteristic
297	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
298	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
299	C₂²×C₁₃₁	C₂²×#41	1	1	yes	characteristic
300	C₂²×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
301	C₂²×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
302	C₄×C₁₃₁	—	2	4	no	—
303	C₄×C₁₃₁	—	2	4	no	—
304	C₄×C₁₃₁	—	2	4	no	—
305	C₄×C₁₃₁	—	2	4	no	—
306	C₄×C₁₃₁	—	2	8	no	—
307	C₄×C₁₃₁	—	4	4	no	—
308	C₄×C₁₃₁	—	4	4	no	—
309	C₄×C₁₃₁	—	4	4	no	—
310	C₄×C₁₃₁	C₂×C₄×D₄	1	8	yes	—
311	C₂×C₁₃₁	—	2	8	no	—
312	C₂×C₁₃₁	—	4	4	no	—
313	C₂×C₁₃₁	#2352	1	8	yes	direct product factor
314	C₂×C₁₃₁	C₂²×#117	1	1	yes	characteristic
315	C₂×C₁₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
316	C₂×C₁₃₁	C₂×#520	1	1	yes	characteristic
317	C₂×C₁₃₁	C₂×#546	1	1	yes	characteristic
318	C₂×C₁₃₁	C₂×#548	1	1	yes	characteristic
319	C₂×C₁₃₁	C₂×#552	1	1	yes	characteristic
320	C₂×C₁₃₁	C₂×#553	1	1	yes	characteristic
321	C₂×#2352	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₁₃₁	C₂×#2352	1	1	yes	characteristic, direct product factor, Sylow
323	C₂²×C₄×D₄	C₂×C₁₃₁	1	1	yes	characteristic
324	C₂²×#117	C₂×C₁₃₁	1	1	yes	characteristic, complemented
325	C₂³×C₄⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
326	#2352	C₂×C₁₃₁	1	16	yes	direct product factor
327	C₂×#388	C₂×C₁₃₁	1	2	yes	complemented
328	C₂×#387	C₂×C₁₃₁	1	2	yes	complemented
329	C₂×#386	C₂×C₁₃₁	1	2	yes	—
330	C₂×#382	C₂×C₁₃₁	1	1	yes	characteristic, complemented
331	C₂×#380	C₂×C₁₃₁	1	1	yes	characteristic, complemented
332	C₂×#380	C₂×C₁₃₁	1	1	yes	characteristic, complemented
333	C₂×C₄×C₄⋊C₄	C₂×C₁₃₁	1	1	yes	characteristic, complemented
334	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	1	2	yes	complemented
335	C₂³×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
336	C₂⁴×C₄	C₂²×C₁₃₁	1	2	yes	—
337	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
338	C₂⁴×C₄	C₂²×C₁₃₁	1	1	yes	characteristic
339	C₂×C₄×D₄	C₄×C₁₃₁	1	16	yes	complemented
340	C₂×C₄×D₄	C₂²×C₁₃₁	1	8	yes	—
341	C₂×#117	—	2	8	no	—
342	C₂×#117	C₂²×C₁₃₁	1	8	yes	complemented
343	C₂²×C₄⋊C₄	—	2	8	no	—
344	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
345	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
346	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
347	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
348	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
349	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
350	C₂²×C₄⋊C₄	C₂²×C₁₃₁	1	8	yes	complemented
351	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
352	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
353	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	2	yes	—
354	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂²×C₁₃₁	1	1	yes	characteristic
356	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
357	C₂²×C₄²	C₂²×C₁₃₁	1	2	yes	—
358	C₂²×C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
359	#388	C₂²×C₁₃₁	1	16	yes	complemented
360	#387	C₂²×C₁₃₁	1	16	yes	complemented
361	#386	C₂²×C₁₃₁	1	16	yes	—
362	#382	C₂²×C₁₃₁	1	8	yes	complemented
363	#380	C₂²×C₁₃₁	1	8	yes	complemented
364	#380	C₂²×C₁₃₁	1	8	yes	complemented
365	C₄×C₄⋊C₄	C₂²×C₁₃₁	1	8	yes	complemented
366	C₄×C₂²⋊C₄	C₂²×C₁₃₁	1	16	yes	complemented
367	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
368	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
369	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
370	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
371	C₂×#95	C₂²×C₁₃₁	1	2	yes	—
372	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
373	C₂⁵	C₂³×C₁₃₁	1	1	yes	characteristic
374	C₂²×D₄	—	2	4	no	—
375	C₂²×D₄	—	2	4	no	—
376	C₂²×D₄	C₂×C₄×C₁₃₁	1	8	yes	—
377	C₂²×D₄	C₂³×C₁₃₁	1	4	yes	—
378	C₂³×C₄	—	2	4	no	—
379	C₂³×C₄	—	2	4	no	—
380	C₂³×C₄	—	2	4	no	—
381	C₂³×C₄	—	2	4	no	—
382	C₂³×C₄	—	2	8	no	—
383	C₂³×C₄	—	2	8	no	—
384	C₂³×C₄	—	4	4	no	—
385	C₂³×C₄	C₂×C₄×C₁₃₁	1	8	yes	—
386	C₂³×C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
387	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
388	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
389	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
390	C₂³×C₄	C₂³×C₁₃₁	1	8	yes	—
391	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
396	C₂³×C₄	C₂³×C₁₃₁	1	4	yes	—
397	C₂³×C₄	C₂³×C₁₃₁	1	2	yes	—
398	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
399	C₄×D₄	C₂×C₄×C₁₃₁	1	64	yes	complemented
400	#117	—	2	32	no	—
401	C₂×C₄⋊C₄	—	2	8	no	—
402	C₂×C₄⋊C₄	—	2	4	no	—
403	C₂×C₄⋊C₄	—	2	4	no	—
404	C₂×C₄⋊C₄	—	2	4	no	—
405	C₂×C₄⋊C₄	—	2	32	no	—
406	C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
407	C₂×C₄⋊C₄	D₄×C₁₃₁	1	8	yes	complemented
408	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	8	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	4	yes	—
414	C₂×C₂²⋊C₄	—	2	8	no	—
415	C₂×C₂²⋊C₄	—	2	8	no	—
416	C₂×C₂²⋊C₄	—	4	4	no	—
417	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	—
418	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	1	8	yes	complemented
419	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	8	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃₁	1	4	yes	—
424	C₂×C₄²	—	2	8	no	—
425	C₂×C₄²	—	4	4	no	—
426	C₂×C₄²	C₂×C₄×C₁₃₁	1	8	yes	complemented
427	C₂×C₄²	C₂³×C₁₃₁	1	8	yes	—
428	C₂×C₄²	C₂³×C₁₃₁	1	8	yes	—
429	C₂×C₄²	C₂³×C₁₃₁	1	4	yes	—
430	#95	C₂³×C₁₃₁	1	8	yes	—
431	#95	C₂³×C₁₃₁	1	8	yes	—
432	#95	C₂³×C₁₃₁	1	8	yes	—
433	#95	C₂³×C₁₃₁	1	8	yes	—
434	#95	C₂³×C₁₃₁	1	8	yes	—
435	C₂⁴	—	2	2	no	—
436	C₂⁴	—	2	2	no	—
437	C₂⁴	—	2	2	no	—
438	C₂⁴	—	2	2	no	—
439	C₂⁴	—	2	2	no	—
440	C₂⁴	—	2	2	no	—
441	C₂⁴	—	2	2	no	—
442	C₂⁴	—	2	2	no	—
443	C₂⁴	—	2	2	no	—
444	C₂⁴	—	2	2	no	—
445	C₂⁴	C₂²×C₄×C₁₃₁	1	4	yes	—
446	C₂⁴	C₂²×C₄×C₁₃₁	1	4	yes	—
447	C₂⁴	#41×C₁₃₁	1	4	yes	—
448	C₂⁴	#41×C₁₃₁	1	4	yes	—
449	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
450	C₂⁴	C₂⁴×C₁₃₁	1	2	yes	—
451	C₂⁴	C₂⁴×C₁₃₁	1	1	yes	characteristic
452	C₂×D₄	—	2	32	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	C₂²×C₄×C₁₃₁	1	16	yes	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	32	no	—
467	C₂²×C₄	—	2	32	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	8	no	—
471	C₂²×C₄	—	2	8	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	16	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	16	no	—
483	C₂²×C₄	—	4	8	no	—
484	C₂²×C₄	—	4	32	no	—
485	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
486	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
487	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
488	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
489	C₂²×C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
490	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
491	C₂²×C₄	C₂²×C₄×C₁₃₁	1	16	yes	complemented
492	C₂²×C₄	C₂×D₄×C₁₃₁	1	8	yes	—
493	C₂²×C₄	C₂×D₄×C₁₃₁	1	4	yes	—
494	C₂²×C₄	#41×C₁₃₁	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₁₃₁	1	4	yes	—
503	C₂²×C₄	C₂⁴×C₁₃₁	1	2	yes	—
504	C₄⋊C₄	—	2	16	no	—
505	C₄⋊C₄	—	2	8	no	—
506	C₄⋊C₄	—	2	8	no	—
507	C₄⋊C₄	—	2	8	no	—
508	C₄⋊C₄	C₂²×C₄×C₁₃₁	1	16	yes	complemented
509	C₄⋊C₄	C₂×D₄×C₁₃₁	1	16	yes	complemented
510	C₂²⋊C₄	—	2	16	no	—
511	C₂²⋊C₄	—	2	16	no	—
512	C₂²⋊C₄	—	4	8	no	—
513	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	16	yes	—
514	C₂²⋊C₄	C₂²×C₄×C₁₃₁	1	16	yes	complemented
515	C₄²	—	2	16	no	—
516	C₄²	—	4	8	no	—
517	C₄²	C₂²×C₄×C₁₃₁	1	16	yes	complemented
518	C₂³	—	2	8	no	—
519	C₂³	—	2	8	no	—
520	C₂³	—	2	8	no	—
521	C₂³	—	2	8	no	—
522	C₂³	—	2	8	no	—
523	C₂³	—	2	8	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	8	no	—
529	C₂³	—	2	8	no	—
530	C₂³	—	2	8	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	4	4	no	—
538	C₂³	—	4	4	no	—
539	C₂³	—	4	4	no	—
540	C₂³	—	4	4	no	—
541	C₂³	#117×C₁₃₁	1	16	yes	complemented
542	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
543	C₂³	C₂³×C₄×C₁₃₁	1	4	yes	—
544	C₂³	C₂³×C₄×C₁₃₁	1	2	yes	—
545	C₂³	C₂²×D₄×C₁₃₁	1	2	yes	—
546	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
547	C₂³	C₂×#41×C₁₃₁	1	4	yes	—
548	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
549	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
550	C₂³	C₂×#41×C₁₃₁	1	2	yes	—
551	C₂³	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
552	C₂³	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
553	C₂³	C₂⁵×C₁₃₁	1	1	yes	characteristic
554	D₄	—	2	32	no	—
555	C₂×C₄	—	2	8	no	—
556	C₂×C₄	—	2	8	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	16	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	32	no	—
571	C₂×C₄	—	2	32	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	4	32	no	—
582	C₂×C₄	—	4	8	no	—
583	C₂×C₄	—	4	8	no	—
584	C₂×C₄	—	4	8	no	—
585	C₂×C₄	C₄×D₄×C₁₃₁	1	16	yes	—
586	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
587	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
588	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
589	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
590	C₂×C₄	C₂³×C₄×C₁₃₁	1	4	yes	—
591	C₂×C₄	C₂²×D₄×C₁₃₁	1	8	yes	—
592	C₂×C₄	C₂²×D₄×C₁₃₁	1	4	yes	—
593	C₂×C₄	C₂×#41×C₁₃₁	1	4	yes	—
594	C₂²	—	2	32	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	2	4	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	2	4	no	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	4	16	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	C₂×#117×C₁₃₁	1	4	yes	—
610	C₂²	C₂×#117×C₁₃₁	1	8	yes	complemented
611	C₂²	C₂×C₄×D₄×C₁₃₁	1	4	yes	—
612	C₂²	#520×C₁₃₁	1	4	yes	—
613	C₂²	#546×C₁₃₁	1	4	yes	—
614	C₂²	#548×C₁₃₁	1	4	yes	—
615	C₂²	#552×C₁₃₁	1	4	yes	—
616	C₂²	#553×C₁₃₁	1	4	yes	—
617	C₂²	C₂⁴×C₄×C₁₃₁	1	1	yes	characteristic
618	C₂²	C₂³×D₄×C₁₃₁	1	1	yes	characteristic
619	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
620	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
621	C₂²	C₂²×#41×C₁₃₁	1	1	yes	characteristic
622	C₂²	C₂×H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
623	C₂²	C₂×2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
624	C₄	—	2	4	no	—
625	C₄	—	2	4	no	—
626	C₄	—	2	4	no	—
627	C₄	—	2	4	no	—
628	C₄	—	2	8	no	—
629	C₄	—	4	4	no	—
630	C₄	—	4	4	no	—
631	C₄	—	4	4	no	—
632	C₄	C₂×C₄×D₄×C₁₃₁	1	8	yes	—
633	C₂	—	2	8	no	—
634	C₂	—	4	4	no	—
635	C₂	#2352×C₁₃₁	1	8	yes	direct product factor
636	C₂	C₂²×#117×C₁₃₁	1	1	yes	characteristic
637	C₂	C₂²×C₄×D₄×C₁₃₁	1	1	yes	characteristic
638	C₂	C₂×#520×C₁₃₁	1	1	yes	characteristic
639	C₂	C₂×#546×C₁₃₁	1	1	yes	characteristic
640	C₂	C₂×#548×C₁₃₁	1	1	yes	characteristic
641	C₂	C₂×#552×C₁₃₁	1	1	yes	characteristic
642	C₂	C₂×#553×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃₁
Frattini, cosocle	C₂³	C₂⁵×C₁₃₁
prime radical	C₂³×D₄×C₁₃₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₁₃₁	C₂	semidirect
3. C₂³×C₄⋊C₄×C₁₃₁	C₂	semidirect
4. #2352×C₁₃₁	C₂	direct (N × H)
5. C₂×#388×C₁₃₁	C₂	semidirect
6. C₂×#387×C₁₃₁	C₂	semidirect
8. C₂×#382×C₁₃₁	C₂	semidirect
9. C₂×#380×C₁₃₁	C₂	semidirect
10. C₂×#380×C₁₃₁	C₂	semidirect
11. C₂×C₄×C₄⋊C₄×C₁₃₁	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₁₃₁	C₂	semidirect
17. C₂×C₄×D₄×C₁₃₁	C₄	semidirect
20. C₂×#117×C₁₃₁	C₂²	semidirect
28. C₂²×C₄⋊C₄×C₁₃₁	C₂²	semidirect
37. #388×C₁₃₁	C₂²	semidirect
38. #387×C₁₃₁	C₂²	semidirect
40. #382×C₁₃₁	C₂²	semidirect
41. #380×C₁₃₁	C₂²	semidirect
42. #380×C₁₃₁	C₂²	semidirect
43. C₄×C₄⋊C₄×C₁₃₁	C₂²	semidirect
44. C₄×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
64. C₂³×C₄×C₁₃₁	C₂×C₄	semidirect
77. C₄×D₄×C₁₃₁	C₂×C₄	semidirect
84. C₂×C₄⋊C₄×C₁₃₁	C₂×C₄	semidirect
85. C₂×C₄⋊C₄×C₁₃₁	D₄	semidirect
96. C₂×C₂²⋊C₄×C₁₃₁	C₂×C₄	semidirect
104. C₂×C₄²×C₁₃₁	C₂×C₄	semidirect
169. C₂²×C₄×C₁₃₁	C₂²×C₄	semidirect
186. C₄⋊C₄×C₁₃₁	C₂²×C₄	semidirect
187. C₄⋊C₄×C₁₃₁	C₂×D₄	semidirect
192. C₂²⋊C₄×C₁₃₁	C₂²×C₄	semidirect
195. C₄²×C₁₃₁	C₂²×C₄	semidirect
219. C₂³×C₁₃₁	#117	semidirect
288. C₂²×C₁₃₁	C₂×#117	semidirect
313. C₂×C₁₃₁	#2352	direct (N × H)
321. C₂×#2352	C₁₃₁	direct (N × H)
322. C₁₃₁	C₂×#2352	direct (N × H)
324. C₂²×#117	C₂×C₁₃₁	semidirect
325. C₂³×C₄⋊C₄	C₂×C₁₃₁	semidirect
326. #2352	C₂×C₁₃₁	direct (N × H)
327. C₂×#388	C₂×C₁₃₁	semidirect
328. C₂×#387	C₂×C₁₃₁	semidirect
330. C₂×#382	C₂×C₁₃₁	semidirect
331. C₂×#380	C₂×C₁₃₁	semidirect
332. C₂×#380	C₂×C₁₃₁	semidirect
333. C₂×C₄×C₄⋊C₄	C₂×C₁₃₁	semidirect
334. C₂×C₄×C₂²⋊C₄	C₂×C₁₃₁	semidirect
339. C₂×C₄×D₄	C₄×C₁₃₁	semidirect
342. C₂×#117	C₂²×C₁₃₁	semidirect
350. C₂²×C₄⋊C₄	C₂²×C₁₃₁	semidirect
359. #388	C₂²×C₁₃₁	semidirect
360. #387	C₂²×C₁₃₁	semidirect
362. #382	C₂²×C₁₃₁	semidirect
363. #380	C₂²×C₁₃₁	semidirect
364. #380	C₂²×C₁₃₁	semidirect
365. C₄×C₄⋊C₄	C₂²×C₁₃₁	semidirect
366. C₄×C₂²⋊C₄	C₂²×C₁₃₁	semidirect
386. C₂³×C₄	C₂×C₄×C₁₃₁	semidirect
399. C₄×D₄	C₂×C₄×C₁₃₁	semidirect
406. C₂×C₄⋊C₄	C₂×C₄×C₁₃₁	semidirect
407. C₂×C₄⋊C₄	D₄×C₁₃₁	semidirect
418. C₂×C₂²⋊C₄	C₂×C₄×C₁₃₁	semidirect
426. C₂×C₄²	C₂×C₄×C₁₃₁	semidirect
491. C₂²×C₄	C₂²×C₄×C₁₃₁	semidirect
508. C₄⋊C₄	C₂²×C₄×C₁₃₁	semidirect
509. C₄⋊C₄	C₂×D₄×C₁₃₁	semidirect
514. C₂²⋊C₄	C₂²×C₄×C₁₃₁	semidirect
517. C₄²	C₂²×C₄×C₁₃₁	semidirect
541. C₂³	#117×C₁₃₁	semidirect
610. C₂²	C₂×#117×C₁₃₁	semidirect
635. C₂	#2352×C₁₃₁	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×C₁₃₁	2
C₂²×#117×C₁₃₁	2
C₂³×C₄⋊C₄×C₁₃₁	2
#2352×C₁₃₁	2
C₂×#388×C₁₃₁	2
C₂×#387×C₁₃₁	2
C₂×#386×C₁₃₁	2
C₂×#382×C₁₃₁	2
C₂×#380×C₁₃₁	2
C₂×C₄×C₄⋊C₄×C₁₃₁	2
C₂×C₄×C₂²⋊C₄×C₁₃₁	2
C₂×#2352	131

Subgroups — C2×#2352×C131 #45719999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2352×C₁₃₁ #45719999