Subgroups — C₂×#2115×C₁₃₁ #45719220

Order 33536.

1154 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×M₃₂×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#2115×C₁₃₁	C₂	1	8	yes	maximal, direct product factor
4	C₂×#349×C₁₃₁	C₂	1	4	yes	maximal, complemented
5	C₂²×#41×C₁₃₁	C₄	1	1	yes	characteristic
6	C₂×#131×C₁₃₁	—	2	2	no	—
7	C₂×#131×C₁₃₁	—	2	4	no	—
8	C₂×#131×C₁₃₁	—	2	2	no	—
9	C₂×#131×C₁₃₁	C₄	1	4	yes	—
10	C₂×#131×C₁₃₁	C₂²	1	4	yes	—
11	C₂²×M₁₆×C₁₃₁	C₄	1	1	yes	characteristic
12	C₂²×M₁₆×C₁₃₁	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₃₁	C₄	1	2	yes	—
14	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×M₃₂×C₁₃₁	—	2	2	no	—
16	C₂×M₃₂×C₁₃₁	—	2	4	no	—
17	C₂×M₃₂×C₁₃₁	C₂²	1	4	yes	—
18	C₂×M₃₂×C₁₃₁	C₂²	1	8	yes	complemented
19	C₂²×C₁₆×C₁₃₁	—	2	2	no	—
20	#349×C₁₃₁	C₂²	1	16	yes	complemented
21	C₂×#41×C₁₃₁	—	2	2	no	—
22	C₂×#41×C₁₃₁	—	2	2	no	—
23	C₂×#41×C₁₃₁	—	2	2	no	—
24	C₂×#41×C₁₃₁	—	2	2	no	—
25	C₂×#41×C₁₃₁	C₈	1	4	yes	—
26	C₂×#41×C₁₃₁	C₂×C₄	1	4	yes	—
27	C₂²×Q₈×C₁₃₁	C₈	1	1	yes	characteristic
28	C₂²×D₄×C₁₃₁	C₈	1	2	yes	—
29	C₂²×D₄×C₁₃₁	C₈	1	1	yes	characteristic
30	C₂³×C₄×C₁₃₁	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₃₁	C₂×C₄	1	1	yes	characteristic
32	#131×C₁₃₁	—	2	8	no	—
33	#131×C₁₃₁	—	2	8	no	—
34	#131×C₁₃₁	—	2	8	no	—
35	#131×C₁₃₁	—	2	8	no	—
36	C₂×M₁₆×C₁₃₁	—	2	2	no	—
37	C₂×M₁₆×C₁₃₁	—	2	2	no	—
38	C₂×M₁₆×C₁₃₁	—	2	4	no	—
39	C₂×M₁₆×C₁₃₁	—	2	4	no	—
40	C₂×M₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
41	C₂×M₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
42	C₂×M₁₆×C₁₃₁	C₂³	1	4	yes	—
43	C₂²×C₈×C₁₃₁	—	2	4	no	—
44	C₂²×C₈×C₁₃₁	—	2	2	no	—
45	C₂²×C₈×C₁₃₁	—	2	2	no	—
46	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
47	C₂²×C₈×C₁₃₁	C₂×C₄	1	8	yes	—
48	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₁₃₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃₁	D₄	1	2	yes	—
51	C₂²×C₈×C₁₃₁	D₄	1	4	yes	—
52	C₂²×C₈×C₁₃₁	D₄	1	2	yes	—
53	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
55	M₃₂×C₁₃₁	—	2	4	no	—
56	M₃₂×C₁₃₁	—	2	8	no	—
57	M₃₂×C₁₃₁	C₂³	1	8	yes	—
58	C₂×C₁₆×C₁₃₁	—	2	4	no	—
59	C₂×C₁₆×C₁₃₁	—	2	8	no	—
60	C₂⁴×C₁₃₁	C₂×C₈	1	2	yes	—
61	C₂⁴×C₁₃₁	C₂×C₈	1	1	yes	characteristic
62	#41×C₁₃₁	—	2	8	no	—
63	#41×C₁₃₁	—	2	8	no	—
64	#41×C₁₃₁	—	2	8	no	—
65	#41×C₁₃₁	—	2	8	no	—
66	C₂×Q₈×C₁₃₁	—	2	2	no	—
67	C₂×Q₈×C₁₃₁	—	2	2	no	—
68	C₂×Q₈×C₁₃₁	C₂×C₈	1	4	yes	—
69	C₂×D₄×C₁₃₁	—	2	4	no	—
70	C₂×D₄×C₁₃₁	—	2	4	no	—
71	C₂×D₄×C₁₃₁	—	2	2	no	—
72	C₂×D₄×C₁₃₁	—	2	2	no	—
73	C₂×D₄×C₁₃₁	C₂×C₈	1	8	yes	—
74	C₂×D₄×C₁₃₁	C₂×C₈	1	4	yes	—
75	C₂²×C₄×C₁₃₁	—	2	2	no	—
76	C₂²×C₄×C₁₃₁	—	2	2	no	—
77	C₂²×C₄×C₁₃₁	—	2	2	no	—
78	C₂²×C₄×C₁₃₁	—	2	2	no	—
79	C₂²×C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₁₃₁	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₁₃₁	C₂×C₈	1	2	yes	—
82	C₂²×C₄×C₁₃₁	C₂×C₈	1	4	yes	—
83	C₂²×C₄×C₁₃₁	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₃₁	C₂×C₈	1	2	yes	—
85	C₂²×C₄×C₁₃₁	M₁₆	1	2	yes	—
86	C₂²×C₄×C₁₃₁	M₁₆	1	2	yes	—
87	C₂²×C₄×C₁₃₁	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
90	M₁₆×C₁₃₁	—	2	8	no	—
91	M₁₆×C₁₃₁	—	2	8	no	—
92	M₁₆×C₁₃₁	—	2	8	no	—
93	C₂×C₈×C₁₃₁	—	2	2	no	—
94	C₂×C₈×C₁₃₁	—	2	2	no	—
95	C₂×C₈×C₁₃₁	—	2	8	no	—
96	C₂×C₈×C₁₃₁	—	2	8	no	—
97	C₂×C₈×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₃₁	C₂²⋊C₄	1	2	yes	—
99	C₂×C₈×C₁₃₁	C₂²⋊C₄	1	4	yes	—
100	C₂×C₈×C₁₃₁	C₂²⋊C₄	1	4	yes	—
101	C₂×C₈×C₁₃₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₃₁	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
107	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
109	C₂×C₈×C₁₃₁	C₂⁴	1	1	yes	characteristic
110	C₁₆×C₁₃₁	—	2	8	no	—
111	C₂³×C₁₃₁	—	2	2	no	—
112	C₂³×C₁₃₁	—	2	2	no	—
113	C₂³×C₁₃₁	—	4	2	no	—
114	C₂³×C₁₃₁	—	4	4	no	—
115	C₂³×C₁₃₁	C₂²⋊C₈	1	2	yes	—
116	C₂³×C₁₃₁	C₂²⋊C₈	1	2	yes	—
117	C₂³×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
118	C₂³×C₁₃₁	C₂²×C₈	1	4	yes	—
119	C₂³×C₁₃₁	C₂²×C₈	1	2	yes	—
120	Q₈×C₁₃₁	—	2	8	no	—
121	D₄×C₁₃₁	—	2	16	no	—
122	D₄×C₁₃₁	—	2	8	no	—
123	C₂×C₄×C₁₃₁	—	2	2	no	—
124	C₂×C₄×C₁₃₁	—	2	2	no	—
125	C₂×C₄×C₁₃₁	—	2	4	no	—
126	C₂×C₄×C₁₃₁	—	2	4	no	—
127	C₂×C₄×C₁₃₁	—	2	4	no	—
128	C₂×C₄×C₁₃₁	—	2	4	no	—
129	C₂×C₄×C₁₃₁	C₂²⋊C₈	1	2	yes	—
130	C₂×C₄×C₁₃₁	C₂²⋊C₈	1	2	yes	—
131	C₂×C₄×C₁₃₁	C₂²⋊C₈	1	4	yes	—
132	C₂×C₄×C₁₃₁	C₂²⋊C₈	1	4	yes	—
133	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	4	yes	—
136	C₂×C₄×C₁₃₁	C₂²×C₈	1	4	yes	—
137	C₂×C₄×C₁₃₁	C₂²×C₈	1	1	yes	characteristic
138	C₂×C₄×C₁₃₁	C₂²×C₈	1	2	yes	—
139	C₂×C₄×C₁₃₁	C₂×M₁₆	1	1	yes	characteristic
140	C₂×C₄×C₁₃₁	C₂×M₁₆	1	1	yes	characteristic
141	C₂×C₄×C₁₃₁	C₂×M₁₆	1	4	yes	—
142	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
143	C₈×C₁₃₁	—	2	4	no	—
144	C₈×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
145	C₈×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
146	C₈×C₁₃₁	C₂×C₂²⋊C₄	1	2	yes	—
147	C₈×C₁₃₁	C₂²×D₄	1	2	yes	—
148	C₂²×C₁₃₁	—	2	2	no	—
149	C₂²×C₁₃₁	—	2	4	no	—
150	C₂²×C₁₃₁	—	2	4	no	—
151	C₂²×C₁₃₁	—	4	2	no	—
152	C₂²×C₁₃₁	—	4	2	no	—
153	C₂²×C₁₃₁	—	4	4	no	—
154	C₂²×C₁₃₁	—	4	4	no	—
155	C₂²×C₁₃₁	—	4	4	no	—
156	C₂²×C₁₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
157	C₂²×C₁₃₁	C₂×C₂²⋊C₈	1	4	yes	—
158	C₂²×C₁₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
159	C₂²×C₁₃₁	C₂³×C₈	1	1	yes	characteristic
160	C₄×C₁₃₁	—	2	4	no	—
161	C₄×C₁₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
162	C₄×C₁₃₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
163	C₄×C₁₃₁	C₂×C₂²⋊C₈	1	4	yes	—
164	C₄×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
165	C₄×C₁₃₁	C₂²×M₁₆	1	1	yes	characteristic
166	C₂×C₁₃₁	—	2	1	no	—
167	C₂×C₁₃₁	—	2	1	no	—
168	C₂×C₁₃₁	—	2	4	no	—
169	C₂×C₁₃₁	—	4	4	no	—
170	C₂×C₁₃₁	#2115	1	2	yes	direct product factor
171	C₂×C₁₃₁	C₂²×C₂²⋊C₈	1	1	yes	characteristic
172	C₂×#2115	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₁₃₁	C₂×#2115	1	1	yes	characteristic, direct product factor, Sylow
174	C₂²×#131	C₂×C₁₃₁	1	1	yes	characteristic
175	C₂²×M₃₂	C₂×C₁₃₁	1	2	yes	complemented
176	#2115	C₂×C₁₃₁	1	8	yes	direct product factor
177	C₂×#349	C₂×C₁₃₁	1	4	yes	complemented
178	C₂²×#41	C₄×C₁₃₁	1	1	yes	characteristic
179	C₂×#131	—	2	2	no	—
180	C₂×#131	—	2	2	no	—
181	C₂×#131	—	2	4	no	—
182	C₂×#131	C₄×C₁₃₁	1	4	yes	—
183	C₂×#131	C₂²×C₁₃₁	1	4	yes	—
184	C₂²×M₁₆	C₄×C₁₃₁	1	1	yes	characteristic
185	C₂²×M₁₆	C₂²×C₁₃₁	1	2	yes	—
186	C₂³×C₈	C₄×C₁₃₁	1	2	yes	—
187	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
188	C₂×M₃₂	—	2	2	no	—
189	C₂×M₃₂	—	2	4	no	—
190	C₂×M₃₂	C₂²×C₁₃₁	1	4	yes	—
191	C₂×M₃₂	C₂²×C₁₃₁	1	8	yes	complemented
192	C₂²×C₁₆	—	2	2	no	—
193	#349	C₂²×C₁₃₁	1	16	yes	complemented
194	C₂×#41	—	2	2	no	—
195	C₂×#41	—	2	2	no	—
196	C₂×#41	—	2	2	no	—
197	C₂×#41	—	2	2	no	—
198	C₂×#41	C₈×C₁₃₁	1	4	yes	—
199	C₂×#41	C₂×C₄×C₁₃₁	1	4	yes	—
200	C₂²×Q₈	C₈×C₁₃₁	1	1	yes	characteristic
201	C₂²×D₄	C₈×C₁₃₁	1	2	yes	—
202	C₂²×D₄	C₈×C₁₃₁	1	1	yes	characteristic
203	C₂³×C₄	C₂×C₄×C₁₃₁	1	2	yes	—
204	C₂³×C₄	C₂×C₄×C₁₃₁	1	1	yes	characteristic
205	#131	—	2	8	no	—
206	#131	—	2	8	no	—
207	#131	—	2	8	no	—
208	#131	—	2	8	no	—
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	—	2	4	no	—
212	C₂×M₁₆	—	2	4	no	—
213	C₂×M₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
214	C₂×M₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
215	C₂×M₁₆	C₂³×C₁₃₁	1	4	yes	—
216	C₂²×C₈	—	2	4	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₂²×C₈	—	2	2	no	—
219	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
220	C₂²×C₈	C₂×C₄×C₁₃₁	1	8	yes	—
221	C₂²×C₈	C₂×C₄×C₁₃₁	1	1	yes	characteristic
222	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
223	C₂²×C₈	D₄×C₁₃₁	1	2	yes	—
224	C₂²×C₈	D₄×C₁₃₁	1	2	yes	—
225	C₂²×C₈	D₄×C₁₃₁	1	4	yes	—
226	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
228	M₃₂	—	2	4	no	—
229	M₃₂	—	2	8	no	—
230	M₃₂	C₂³×C₁₃₁	1	8	yes	—
231	C₂×C₁₆	—	2	4	no	—
232	C₂×C₁₆	—	2	8	no	—
233	C₂⁴	C₂×C₈×C₁₃₁	1	2	yes	—
234	C₂⁴	C₂×C₈×C₁₃₁	1	1	yes	characteristic
235	#41	—	2	8	no	—
236	#41	—	2	8	no	—
237	#41	—	2	8	no	—
238	#41	—	2	8	no	—
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	—	2	2	no	—
241	C₂×Q₈	C₂×C₈×C₁₃₁	1	4	yes	—
242	C₂×D₄	—	2	4	no	—
243	C₂×D₄	—	2	4	no	—
244	C₂×D₄	—	2	2	no	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	C₂×C₈×C₁₃₁	1	8	yes	—
247	C₂×D₄	C₂×C₈×C₁₃₁	1	4	yes	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
253	C₂²×C₄	C₂²⋊C₄×C₁₃₁	1	2	yes	—
254	C₂²×C₄	C₂×C₈×C₁₃₁	1	2	yes	—
255	C₂²×C₄	C₂×C₈×C₁₃₁	1	4	yes	—
256	C₂²×C₄	C₂×C₈×C₁₃₁	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₈×C₁₃₁	1	2	yes	—
258	C₂²×C₄	M₁₆×C₁₃₁	1	2	yes	—
259	C₂²×C₄	M₁₆×C₁₃₁	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₁₃₁	1	4	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
263	M₁₆	—	2	8	no	—
264	M₁₆	—	2	8	no	—
265	M₁₆	—	2	8	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	8	no	—
269	C₂×C₈	—	2	8	no	—
270	C₂×C₈	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
271	C₂×C₈	C₂²⋊C₄×C₁₃₁	1	2	yes	—
272	C₂×C₈	C₂²⋊C₄×C₁₃₁	1	4	yes	—
273	C₂×C₈	C₂²⋊C₄×C₁₃₁	1	4	yes	—
274	C₂×C₈	C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
275	C₂×C₈	C₂²×C₄×C₁₃₁	1	4	yes	—
276	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
277	C₂×C₈	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
278	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
279	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
280	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
281	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
282	C₂×C₈	C₂⁴×C₁₃₁	1	1	yes	characteristic
283	C₁₆	—	2	8	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	4	2	no	—
287	C₂³	—	4	4	no	—
288	C₂³	C₂²⋊C₈×C₁₃₁	1	2	yes	—
289	C₂³	C₂²⋊C₈×C₁₃₁	1	2	yes	—
290	C₂³	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
291	C₂³	C₂²×C₈×C₁₃₁	1	4	yes	—
292	C₂³	C₂²×C₈×C₁₃₁	1	2	yes	—
293	Q₈	—	2	8	no	—
294	D₄	—	2	16	no	—
295	D₄	—	2	8	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	C₂²⋊C₈×C₁₃₁	1	2	yes	—
303	C₂×C₄	C₂²⋊C₈×C₁₃₁	1	2	yes	—
304	C₂×C₄	C₂²⋊C₈×C₁₃₁	1	4	yes	—
305	C₂×C₄	C₂²⋊C₈×C₁₃₁	1	4	yes	—
306	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
307	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
308	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	4	yes	—
309	C₂×C₄	C₂²×C₈×C₁₃₁	1	4	yes	—
310	C₂×C₄	C₂²×C₈×C₁₃₁	1	1	yes	characteristic
311	C₂×C₄	C₂²×C₈×C₁₃₁	1	2	yes	—
312	C₂×C₄	C₂×M₁₆×C₁₃₁	1	1	yes	characteristic
313	C₂×C₄	C₂×M₁₆×C₁₃₁	1	1	yes	characteristic
314	C₂×C₄	C₂×M₁₆×C₁₃₁	1	4	yes	—
315	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
316	C₈	—	2	4	no	—
317	C₈	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
318	C₈	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
319	C₈	C₂×C₂²⋊C₄×C₁₃₁	1	2	yes	—
320	C₈	C₂²×D₄×C₁₃₁	1	2	yes	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	4	no	—
324	C₂²	—	4	2	no	—
325	C₂²	—	4	2	no	—
326	C₂²	—	4	4	no	—
327	C₂²	—	4	4	no	—
328	C₂²	—	4	4	no	—
329	C₂²	C₂×C₂²⋊C₈×C₁₃₁	1	1	yes	characteristic
330	C₂²	C₂×C₂²⋊C₈×C₁₃₁	1	4	yes	—
331	C₂²	C₂×C₂²⋊C₈×C₁₃₁	1	1	yes	characteristic
332	C₂²	C₂³×C₈×C₁₃₁	1	1	yes	characteristic
333	C₄	—	2	4	no	—
334	C₄	C₂×C₂²⋊C₈×C₁₃₁	1	1	yes	characteristic
335	C₄	C₂×C₂²⋊C₈×C₁₃₁	1	1	yes	characteristic
336	C₄	C₂×C₂²⋊C₈×C₁₃₁	1	4	yes	—
337	C₄	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
338	C₄	C₂²×M₁₆×C₁₃₁	1	1	yes	characteristic
339	C₂	—	2	1	no	—
340	C₂	—	2	1	no	—
341	C₂	—	2	4	no	—
342	C₂	—	4	4	no	—
343	C₂	#2115×C₁₃₁	1	2	yes	direct product factor
344	C₂	C₂²×C₂²⋊C₈×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃₁	C₂²⋊C₄
commutator	C₂²	C₂³×C₈×C₁₃₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂×C₂²⋊C₈
prime radical	C₂²×#41×C₁₃₁	C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₁ ◁ C₂³×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×M₃₂×C₁₃₁	C₂	semidirect
3. #2115×C₁₃₁	C₂	direct (N × H)
4. C₂×#349×C₁₃₁	C₂	semidirect
18. C₂×M₃₂×C₁₃₁	C₂²	semidirect
20. #349×C₁₃₁	C₂²	semidirect
170. C₂×C₁₃₁	#2115	direct (N × H)
172. C₂×#2115	C₁₃₁	direct (N × H)
173. C₁₃₁	C₂×#2115	direct (N × H)
175. C₂²×M₃₂	C₂×C₁₃₁	semidirect
176. #2115	C₂×C₁₃₁	direct (N × H)
177. C₂×#349	C₂×C₁₃₁	semidirect
191. C₂×M₃₂	C₂²×C₁₃₁	semidirect
193. #349	C₂²×C₁₃₁	semidirect
343. C₂	#2115×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×#131×C₁₃₁	2
C₂²×M₃₂×C₁₃₁	2
#2115×C₁₃₁	2
C₂×#349×C₁₃₁	2
C₂×#2115	131

Subgroups — C2×#2115×C131 #45719220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2115×C₁₃₁ #45719220