Subgroups — #30680281

Order 16768.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22554057	C₂	1	2	yes	maximal, complemented
2	#22554050	C₂	1	2	yes	maximal, complemented
3	#22554026	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554009	C₂	1	1	yes	maximal, characteristic, complemented
5	#22553997	C₂	1	1	yes	maximal, characteristic, complemented
6	#22553988	C₂	1	2	yes	maximal, complemented
7	#22553980	C₂	1	1	yes	maximal, characteristic, complemented
8	#22553963	C₂	1	1	yes	maximal, characteristic, complemented
9	#22553959	C₂	1	1	yes	maximal, characteristic, complemented
10	#22553956	C₂	1	1	yes	maximal, characteristic, complemented
11	#22553952	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#22553929	C₂	1	1	yes	maximal, characteristic, complemented
14	#22553915	C₂	1	1	yes	maximal, characteristic, complemented
15	#22553912	C₂	1	2	yes	maximal, complemented
16	#22553894	C₂	1	2	yes	maximal, complemented
17	#22553891	C₂	1	1	yes	maximal, characteristic, complemented
18	#22553879	C₂	1	2	yes	maximal, complemented
19	#22553878	C₂	1	1	yes	maximal, characteristic, complemented
20	#22553871	C₂	1	2	yes	maximal, complemented
21	#22553823	C₂	1	1	yes	maximal, characteristic, complemented
22	#22553823	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#121×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523513	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14523513	C₂²	1	2	yes	complemented
26	C₂×#14523513	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14523512	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₁₃₁	C₂²	1	2	yes	—
29	C₂×D₄×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
30	#16862245	C₂²	1	1	yes	characteristic, complemented
31	#16862242	C₂²	1	2	yes	complemented
32	#16862242	C₂²	1	2	yes	complemented
33	#16862242	C₂²	1	1	yes	characteristic, complemented
34	#16862241	C₂²	1	2	yes	complemented
35	#16862239	C₂²	1	2	yes	complemented
36	#16862239	C₂²	1	2	yes	complemented
37	#16862237	C₂²	1	1	yes	characteristic, complemented
38	#16862236	C₂²	1	2	yes	complemented
39	#16862233	C₂²	1	2	yes	complemented
40	#16862233	C₂²	1	2	yes	complemented
41	#16862233	C₂²	1	1	yes	characteristic, complemented
42	#16862232	C₂²	1	2	yes	complemented
43	#16862232	C₂²	1	2	yes	complemented
44	#16862231	C₂²	1	2	yes	complemented
45	#16862230	C₂²	1	2	yes	complemented
46	#16862229	C₂²	1	2	yes	—
47	#16862229	C₂²	1	2	yes	complemented
48	#16862229	C₂²	1	1	yes	characteristic, complemented
49	#16862229	C₂²	1	1	yes	characteristic, complemented
50	#16862229	C₂²	1	2	yes	complemented
51	#16862228	C₂²	1	2	yes	complemented
52	#16862228	C₂²	1	2	yes	complemented
53	#16862227	C₂²	1	2	yes	complemented
54	#16862227	C₂²	1	2	yes	complemented
55	#16862227	C₂²	1	2	yes	complemented
56	#16862226	C₂²	1	1	yes	characteristic, complemented
57	#16862225	C₂²	1	1	yes	characteristic, complemented
58	#16862225	C₂²	1	1	yes	characteristic, complemented
59	#16862225	C₂²	1	1	yes	characteristic, complemented
60	#16862225	C₂²	1	1	yes	characteristic, complemented
61	#16862224	C₂²	1	2	yes	complemented
62	#16862223	C₂²	1	2	yes	complemented
63	#16862223	C₂²	1	2	yes	complemented
64	#16862221	C₂²	1	1	yes	characteristic, complemented
65	#16862220	C₂²	1	1	yes	characteristic
66	#16862220	C₂²	1	1	yes	characteristic
67	#16862220	C₂²	1	1	yes	characteristic, complemented
68	#16862220	C₂²	1	1	yes	characteristic, complemented
69	#16862219	C₂²	1	2	yes	complemented
70	#16862219	C₂²	1	2	yes	complemented
71	#16862218	C₂²	1	2	yes	complemented
72	#16862218	C₂²	1	2	yes	complemented
73	#16862218	C₂²	1	2	yes	complemented
74	#16862218	C₂²	1	2	yes	complemented
75	#16862218	C₂²	1	2	yes	complemented
76	#16862218	C₂²	1	2	yes	complemented
77	#16862217	C₂²	1	1	yes	characteristic, complemented
78	#16862217	C₂²	1	2	yes	complemented
79	#16862217	C₂²	1	2	yes	complemented
80	#16862217	C₂²	1	2	yes	complemented
81	#16862217	C₂²	1	2	yes	complemented
82	#16862217	C₂²	1	1	yes	characteristic, complemented
83	#16862216	C₂²	1	2	yes	complemented
84	#16862215	C₂²	1	1	yes	characteristic
85	#16862215	C₂²	1	2	yes	—
86	#16862215	C₂²	1	2	yes	complemented
87	#16862215	C₂²	1	1	yes	characteristic, complemented
88	#16862215	C₂²	1	2	yes	complemented
89	#16862214	C₂²	1	2	yes	complemented
90	#16862214	C₂²	1	2	yes	complemented
91	#16862214	C₂²	1	2	yes	complemented
92	#16862211	C₂²	1	1	yes	characteristic, complemented
93	D₄×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
94	D₄×Dic₁₃₁	C₂²	1	1	yes	characteristic, complemented
95	#16862208	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₁₃₁	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊D₁₃₁	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₁₃₁	C₂²	1	1	yes	characteristic, complemented
102	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	2	yes	complemented
103	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	2	yes	complemented
104	#16862205	C₂²	1	2	yes	complemented
105	#16862205	C₂²	1	1	yes	characteristic, complemented
106	#16862205	C₂²	1	1	yes	characteristic, complemented
107	#16862204	C₂²	1	1	yes	characteristic, complemented
108	#16862202	C₂²	1	2	yes	complemented
109	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₂²⋊Dic₁₃₁	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₃₁	C₂²	1	2	yes	complemented
112	C₂²×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
113	C₂²×D₄×C₁₃₁	C₂²	1	2	yes	complemented
114	C₂³×C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
115	#121×C₁₃₁	C₂²	1	1	yes	characteristic
116	#121×C₁₃₁	C₂²	1	1	yes	characteristic
117	#121×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
118	#121×C₁₃₁	C₂²	1	2	yes	complemented
119	#121×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
120	#121×C₁₃₁	C₂²	1	2	yes	complemented
121	C₂×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₁₃₁	C₂²	1	2	yes	complemented
123	C₂³×D₁₃₁	C₂³	1	2	yes	—
124	#14523513	—	4	2	no	—
125	#14523513	—	4	4	no	—
126	#14523513	—	4	2	no	—
127	#14523512	—	4	2	no	—
128	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₆₂	C₂³	1	2	yes	—
131	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
132	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
133	C₂×D₅₂₄	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₃₁	—	4	4	no	—
135	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₁₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
150	D₄×D₁₃₁	—	4	2	no	—
151	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
152	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
153	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
157	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
158	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
159	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
162	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
163	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
165	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
166	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
168	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
169	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
170	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
171	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
172	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
190	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₃₁	C₂³	1	2	yes	—
203	C₄×Dic₁₃₁	C₂³	1	2	yes	—
204	C₄×Dic₁₃₁	C₂³	1	2	yes	—
205	C₂⁴×C₁₃₁	C₂³	1	1	yes	characteristic
206	C₂⁴×C₁₃₁	C₂³	1	2	yes	—
207	C₂×D₄×C₁₃₁	—	4	2	no	—
208	C₂×D₄×C₁₃₁	—	4	4	no	—
209	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
212	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
213	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
214	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
215	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
216	C₂²×C₄×C₁₃₁	—	4	2	no	—
217	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₁	C₂³	1	2	yes	—
220	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
221	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
222	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
223	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
224	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
225	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
226	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
229	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
230	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
231	C₂²×D₁₃₁	—	4	2	no	—
232	C₂²×D₁₃₁	—	4	2	no	—
233	C₂²×D₁₃₁	—	4	2	no	—
234	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₃₁	C₂⁴	1	2	yes	—
236	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
237	Dic₂₆₂	—	2	2	no	—
238	Dic₂₆₂	—	4	1	no	—
239	Dic₂₆₂	—	4	2	no	—
240	D₅₂₄	—	2	2	no	—
241	D₅₂₄	—	4	1	no	—
242	D₅₂₄	—	4	2	no	—
243	C₂²⋊D₁₃₁	—	2	2	no	—
244	C₂²⋊D₁₃₁	—	2	4	no	—
245	C₂²⋊D₁₃₁	—	2	2	no	—
246	C₂²⋊D₁₃₁	—	4	2	no	—
247	C₂²⋊D₁₃₁	—	4	2	no	—
248	C₂²⋊D₁₃₁	—	4	2	no	—
249	C₂²⋊D₁₃₁	—	4	1	no	—
250	C₂²⋊D₁₃₁	—	4	2	no	—
251	C₂²⋊D₁₃₁	—	4	2	no	—
252	C₂²⋊D₁₃₁	—	4	1	no	—
253	C₂²⋊D₁₃₁	—	4	2	no	—
254	C₂²⋊D₁₃₁	—	4	2	no	—
255	C₂²⋊D₁₃₁	—	4	1	no	—
256	C₂²⋊D₁₃₁	—	4	1	no	—
257	C₂²⋊D₁₃₁	—	4	2	no	—
258	C₂×Dic₁₃₁	—	4	2	no	—
259	C₂×Dic₁₃₁	—	4	2	no	—
260	C₂×Dic₁₃₁	—	4	2	no	—
261	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
263	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
267	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
268	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
270	C₄×D₁₃₁	—	2	2	no	—
271	C₄×D₁₃₁	—	2	2	no	—
272	C₄×D₁₃₁	—	4	2	no	—
273	C₄×D₁₃₁	—	4	2	no	—
274	C₄×D₁₃₁	—	4	2	no	—
275	C₂³×C₁₃₁	—	2	2	no	—
276	C₂³×C₁₃₁	—	2	4	no	—
277	C₂³×C₁₃₁	—	4	1	no	—
278	C₂³×C₁₃₁	—	4	1	no	—
279	C₂³×C₁₃₁	—	4	2	no	—
280	C₂³×C₁₃₁	—	4	2	no	—
281	C₂³×C₁₃₁	C₂⁴	1	2	yes	—
282	C₂³×C₁₃₁	C₂⁴	1	2	yes	—
283	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
284	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
285	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
286	D₄×C₁₃₁	—	2	2	no	—
287	D₄×C₁₃₁	—	2	2	no	—
288	D₄×C₁₃₁	—	4	2	no	—
289	D₄×C₁₃₁	—	4	2	no	—
290	D₄×C₁₃₁	—	4	2	no	—
291	D₄×C₁₃₁	—	4	2	no	—
292	D₄×C₁₃₁	—	4	2	no	—
293	C₂×C₄×C₁₃₁	—	2	4	no	—
294	C₂×C₄×C₁₃₁	—	2	2	no	—
295	C₂×C₄×C₁₃₁	—	2	2	no	—
296	C₂×C₄×C₁₃₁	—	2	2	no	—
297	C₂×C₄×C₁₃₁	—	4	1	no	—
298	C₂×C₄×C₁₃₁	—	4	1	no	—
299	C₂×C₄×C₁₃₁	—	4	1	no	—
300	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
301	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
302	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
303	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
304	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
305	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
306	C₂²×C₁₃₁	—	2	1	no	—
307	C₂²×C₁₃₁	—	2	1	no	—
308	C₂²×C₁₃₁	—	2	1	no	—
309	C₂²×C₁₃₁	—	2	1	no	—
310	C₂²×C₁₃₁	—	2	2	no	—
311	C₂²×C₁₃₁	—	2	2	no	—
312	C₂²×C₁₃₁	—	2	1	no	—
313	C₂²×C₁₃₁	—	2	1	no	—
314	C₂²×C₁₃₁	—	2	2	no	—
315	C₂²×C₁₃₁	—	2	2	no	—
316	C₂²×C₁₃₁	—	2	2	no	—
317	C₂²×C₁₃₁	—	2	1	no	—
318	C₂²×C₁₃₁	—	2	1	no	—
319	C₂²×C₁₃₁	—	2	2	no	—
320	C₂²×C₁₃₁	—	4	4	no	—
321	C₂²×C₁₃₁	—	8	4	no	—
322	C₂²×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
323	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
324	C₂×D₁₃₁	—	2	1	no	—
325	C₂×D₁₃₁	—	2	1	no	—
326	C₂×D₁₃₁	—	2	1	no	—
327	C₂×D₁₃₁	—	2	2	no	—
328	C₂×D₁₃₁	—	2	2	no	—
329	C₂×D₁₃₁	—	2	1	no	—
330	C₂×D₁₃₁	—	2	1	no	—
331	C₂×D₁₃₁	—	2	2	no	—
332	C₂×D₁₃₁	—	2	1	no	—
333	C₂×D₁₃₁	—	8	4	no	—
334	C₄×C₁₃₁	—	2	1	no	—
335	C₄×C₁₃₁	—	2	1	no	—
336	C₄×C₁₃₁	—	2	1	no	—
337	C₄×C₁₃₁	—	2	2	no	—
338	C₄×C₁₃₁	—	2	2	no	—
339	C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
340	Dic₁₃₁	—	2	1	no	—
341	Dic₁₃₁	—	2	1	no	—
342	Dic₁₃₁	—	2	1	no	—
343	Dic₁₃₁	—	2	2	no	—
344	Dic₁₃₁	—	2	2	no	—
345	Dic₁₃₁	—	2	1	no	—
346	Dic₁₃₁	—	2	1	no	—
347	Dic₁₃₁	—	2	2	no	—
348	Dic₁₃₁	—	2	1	no	—
349	C₂×C₁₃₁	—	2	2	no	—
350	C₂×C₁₃₁	—	4	2	no	—
351	C₂×C₁₃₁	—	4	1	no	—
352	C₂×C₁₃₁	—	4	1	no	—
353	C₂×C₁₃₁	—	4	2	no	—
354	C₂×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
356	C₂×C₁₃₁	#585	1	1	yes	characteristic
357	D₁₃₁	—	4	1	no	—
358	D₁₃₁	—	4	2	no	—
359	D₁₃₁	—	4	1	no	—
360	C₁₃₁	#3542	1	1	yes	characteristic, complemented, Sylow
361	#3542	—	131	1	no	maximal, Sylow
362	#562	—	131	2	no	—
363	#560	—	131	2	no	—
364	#555	—	131	1	no	—
365	#553	—	131	1	no	—
366	#552	—	131	1	no	—
367	#551	—	131	2	no	—
368	#550	—	131	1	no	—
369	#547	—	131	1	no	—
370	#546	—	131	1	no	—
371	#546	—	131	1	no	—
372	#546	—	131	2	no	—
373	D₄²	—	131	1	no	—
374	#542	—	131	1	no	—
375	#540	—	131	2	no	—
376	#540	—	131	1	no	—
377	#538	—	131	2	no	—
378	#537	—	131	1	no	—
379	#535	—	131	2	no	—
380	#535	—	131	1	no	—
381	#534	—	131	2	no	—
382	#525	—	131	1	no	—
383	#525	—	131	1	no	—
384	C₂×#121	D₁₃₁	1	1	yes	characteristic, complemented
385	C₂×#41	—	131	1	no	—
386	C₂×#41	—	131	1	no	—
387	C₂×#41	—	131	1	no	—
388	C₂×#41	—	131	2	no	—
389	C₂²×D₄	—	131	2	no	—
390	C₂²×D₄	—	131	1	no	—
391	C₂²×D₄	C₂×D₁₃₁	1	1	yes	characteristic
392	C₂²×D₄	C₂×D₁₃₁	1	2	yes	complemented
393	C₂³×C₄	C₂×D₁₃₁	1	1	yes	characteristic, complemented
394	C₄⋊Q₈	—	131	1	no	—
395	#127	—	131	2	no	—
396	#127	—	131	2	no	—
397	#127	—	131	1	no	—
398	#126	—	131	2	no	—
399	#126	—	131	2	no	—
400	#126	—	131	2	no	—
401	#125	—	131	2	no	—
402	#125	—	131	1	no	—
403	#124	—	131	2	no	—
404	#124	—	131	2	no	—
405	#124	—	131	1	no	—
406	#124	—	131	2	no	—
407	#124	—	131	2	no	—
408	#123	—	131	2	no	—
409	#123	—	131	2	no	—
410	#123	—	131	2	no	—
411	#123	—	131	1	no	—
412	#123	—	131	1	no	—
413	#123	—	131	2	no	—
414	#123	—	131	2	no	—
415	#123	—	131	2	no	—
416	#123	—	131	2	no	—
417	#123	—	131	2	no	—
418	#123	—	131	2	no	—
419	#123	—	131	2	no	—
420	C₂²⋊Q₈	—	131	1	no	—
421	C₂²⋊Q₈	—	131	1	no	—
422	C₂²⋊Q₈	—	131	1	no	—
423	C₂²⋊Q₈	—	131	1	no	—
424	C₂²⋊Q₈	—	131	2	no	—
425	C₂²⋊Q₈	—	131	1	no	—
426	C₂²⋊Q₈	—	131	2	no	—
427	C₂²⋊Q₈	—	131	2	no	—
428	#121	—	131	2	no	—
429	#121	—	131	2	no	—
430	#121	—	131	1	no	—
431	#121	—	131	2	no	—
432	#121	—	131	2	no	—
433	#121	—	131	1	no	—
434	#121	—	131	2	no	—
435	#121	—	131	2	no	—
436	#121	—	131	2	no	—
437	#121	—	131	2	no	—
438	#121	—	131	2	no	—
439	#121	—	131	2	no	—
440	#121	—	131	1	no	—
441	#121	—	131	1	no	—
442	#121	—	131	1	no	—
443	#121	—	131	1	no	—
444	#121	—	131	1	no	—
445	#121	—	131	2	no	—
446	#121	—	131	2	no	—
447	#121	C₂×D₁₃₁	1	1	yes	characteristic
448	#121	C₂×D₁₃₁	1	1	yes	characteristic
449	#121	C₂×D₁₃₁	1	1	yes	characteristic, complemented
450	#121	C₂×D₁₃₁	1	2	yes	complemented
451	#121	C₂×D₁₃₁	1	1	yes	characteristic, complemented
452	#121	C₂×D₁₃₁	1	2	yes	complemented
453	#120	—	131	1	no	—
454	#120	—	131	2	no	—
455	#120	—	131	2	no	—
456	#120	—	131	1	no	—
457	#120	—	131	2	no	—
458	#120	—	131	2	no	—
459	#120	—	131	2	no	—
460	#120	—	131	2	no	—
461	#120	—	131	2	no	—
462	C₄×Q₈	—	131	1	no	—
463	C₄×D₄	—	131	1	no	—
464	C₄×D₄	—	131	1	no	—
465	C₄×D₄	—	131	2	no	—
466	C₄×D₄	—	131	1	no	—
467	C₄×D₄	—	131	1	no	—
468	C₄×D₄	—	131	2	no	—
469	C₄×D₄	—	131	1	no	—
470	C₄×D₄	—	131	1	no	—
471	C₄×D₄	—	131	1	no	—
472	C₄×D₄	—	131	2	no	—
473	C₄×D₄	—	131	2	no	—
474	#117	—	131	1	no	—
475	#117	—	131	1	no	—
476	#117	—	131	2	no	—
477	#117	—	131	1	no	—
478	#117	—	131	2	no	—
479	C₂×C₄⋊C₄	—	131	1	no	—
480	C₂×C₄⋊C₄	C₂×D₁₃₁	1	1	yes	characteristic, complemented
481	C₂×C₂²⋊C₄	—	131	2	no	—
482	C₂×C₂²⋊C₄	—	131	2	no	—
483	C₂×C₂²⋊C₄	C₂×D₁₃₁	1	2	yes	complemented
484	C₂⁴	—	131	2	no	—
485	C₂⁴	C₂²×D₁₃₁	1	2	yes	—
486	C₂⁴	C₂²×D₁₃₁	1	1	yes	characteristic
487	#41	—	524	2	no	—
488	#41	—	524	4	no	—
489	#41	—	524	2	no	—
490	#41	—	524	2	no	—
491	C₂×Q₈	—	131	1	no	—
492	C₂×Q₈	—	131	1	no	—
493	C₂×Q₈	—	131	2	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	4	4	no	—
496	C₂×D₄	—	524	2	no	—
497	C₂×D₄	—	524	4	no	—
498	C₂×D₄	—	131	1	no	—
499	C₂×D₄	—	131	2	no	—
500	C₂×D₄	—	131	1	no	—
501	C₂×D₄	—	131	1	no	—
502	C₂×D₄	—	131	2	no	—
503	C₂×D₄	—	131	2	no	—
504	C₂×D₄	—	131	2	no	—
505	C₂×D₄	—	131	1	no	—
506	C₂×D₄	—	131	1	no	—
507	C₂×D₄	—	131	2	no	—
508	C₂×D₄	—	131	2	no	—
509	C₂×D₄	—	131	2	no	—
510	C₂×D₄	—	131	2	no	—
511	C₂×D₄	—	131	1	no	—
512	C₂×D₄	—	131	2	no	—
513	C₂×D₄	—	131	1	no	—
514	C₂×D₄	—	131	1	no	—
515	C₂×D₄	—	131	2	no	—
516	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
517	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
518	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
519	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
520	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
521	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
522	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	131	1	no	—
525	C₂²×C₄	—	131	1	no	—
526	C₂²×C₄	—	131	2	no	—
527	C₂²×C₄	—	131	2	no	—
528	C₂²×C₄	—	131	2	no	—
529	C₂²×C₄	—	131	2	no	—
530	C₂²×C₄	—	131	2	no	—
531	C₂²×C₄	—	131	2	no	—
532	C₂²×C₄	C₂²×D₁₃₁	1	2	yes	—
533	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
534	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
535	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
536	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
539	C₄⋊C₄	—	131	2	no	—
540	C₄⋊C₄	—	131	1	no	—
541	C₄⋊C₄	—	131	2	no	—
542	C₄⋊C₄	—	131	1	no	—
543	C₄⋊C₄	—	131	1	no	—
544	C₄⋊C₄	—	131	2	no	—
545	C₄⋊C₄	—	131	2	no	—
546	C₄⋊C₄	—	131	2	no	—
547	C₄⋊C₄	—	131	1	no	—
548	C₄⋊C₄	—	131	2	no	—
549	C₄⋊C₄	—	131	1	no	—
550	C₄⋊C₄	—	131	1	no	—
551	C₄⋊C₄	—	131	2	no	—
552	C₄⋊C₄	—	131	2	no	—
553	C₄⋊C₄	—	131	1	no	—
554	C₄⋊C₄	—	131	1	no	—
555	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
556	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
557	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
558	C₂²⋊C₄	—	131	1	no	—
559	C₂²⋊C₄	—	131	2	no	—
560	C₂²⋊C₄	—	131	2	no	—
561	C₂²⋊C₄	—	131	2	no	—
562	C₂²⋊C₄	—	131	2	no	—
563	C₂²⋊C₄	—	131	1	no	—
564	C₂²⋊C₄	—	131	2	no	—
565	C₂²⋊C₄	—	131	1	no	—
566	C₂²⋊C₄	—	131	2	no	—
567	C₂²⋊C₄	—	131	1	no	—
568	C₂²⋊C₄	—	131	2	no	—
569	C₂²⋊C₄	—	131	1	no	—
570	C₂²⋊C₄	—	131	2	no	—
571	C₂²⋊C₄	—	131	1	no	—
572	C₂²⋊C₄	—	131	2	no	—
573	C₂²⋊C₄	—	131	1	no	—
574	C₂²⋊C₄	—	131	2	no	—
575	C₂²⋊C₄	—	131	2	no	—
576	C₂²⋊C₄	—	131	1	no	—
577	C₂²⋊C₄	—	131	1	no	—
578	C₂²⋊C₄	—	131	2	no	—
579	C₂²⋊C₄	—	131	2	no	—
580	C₂²⋊C₄	—	131	2	no	—
581	C₂²⋊C₄	—	131	2	no	—
582	C₂²⋊C₄	—	131	1	no	—
583	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
584	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
585	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
586	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
587	C₄²	—	131	2	no	—
588	C₄²	—	131	2	no	—
589	C₄²	—	131	1	no	—
590	C₄²	—	131	1	no	—
591	C₄²	—	131	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	4	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	2	no	—
597	C₂³	—	4	2	no	—
598	C₂³	—	524	2	no	—
599	C₂³	—	524	2	no	—
600	C₂³	—	524	2	no	—
601	C₂³	—	131	1	no	—
602	C₂³	—	131	2	no	—
603	C₂³	—	131	1	no	—
604	C₂³	C₂³×D₁₃₁	1	2	yes	—
605	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
606	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
607	C₂³	C₂³×D₁₃₁	1	2	yes	—
608	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
609	Q₈	—	262	2	no	—
610	Q₈	—	524	1	no	—
611	Q₈	—	524	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	2	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	4	2	no	—
617	D₄	—	4	2	no	—
618	D₄	—	4	2	no	—
619	D₄	—	262	2	no	—
620	D₄	—	262	4	no	—
621	D₄	—	262	2	no	—
622	D₄	—	262	2	no	—
623	D₄	—	524	1	no	—
624	D₄	—	524	2	no	—
625	D₄	—	524	2	no	—
626	D₄	—	524	2	no	—
627	D₄	—	524	2	no	—
628	D₄	—	524	1	no	—
629	D₄	—	524	1	no	—
630	D₄	—	524	2	no	—
631	D₄	—	524	2	no	—
632	D₄	—	524	1	no	—
633	D₄	—	524	2	no	—
634	D₄	—	524	2	no	—
635	D₄	—	524	2	no	—
636	D₄	—	524	1	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	262	2	no	—
645	C₂×C₄	—	262	2	no	—
646	C₂×C₄	—	524	2	no	—
647	C₂×C₄	—	524	2	no	—
648	C₂×C₄	—	524	2	no	—
649	C₂×C₄	—	524	2	no	—
650	C₂×C₄	—	524	2	no	—
651	C₂×C₄	—	524	2	no	—
652	C₂×C₄	—	131	1	no	—
653	C₂×C₄	—	131	2	no	—
654	C₂×C₄	—	131	1	no	—
655	C₂×C₄	—	131	1	no	—
656	C₂×C₄	—	131	1	no	—
657	C₂×C₄	—	131	2	no	—
658	C₂×C₄	—	131	2	no	—
659	C₂×C₄	—	131	1	no	—
660	C₂×C₄	—	131	1	no	—
661	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
663	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
666	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	4	4	no	—
682	C₂²	—	262	1	no	—
683	C₂²	—	262	1	no	—
684	C₂²	—	262	1	no	—
685	C₂²	—	262	2	no	—
686	C₂²	—	262	2	no	—
687	C₂²	—	262	1	no	—
688	C₂²	—	262	1	no	—
689	C₂²	—	262	2	no	—
690	C₂²	—	262	1	no	—
691	C₂²	—	8	4	no	—
692	C₂²	—	1048	4	no	—
693	C₂²	#16862291	1	2	yes	—
694	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	262	1	no	—
701	C₄	—	262	1	no	—
702	C₄	—	262	1	no	—
703	C₄	—	262	2	no	—
704	C₄	—	262	1	no	—
705	C₄	—	262	2	no	—
706	C₄	—	262	1	no	—
707	C₄	—	262	2	no	—
708	C₄	—	262	1	no	—
709	C₄	#16862291	1	2	yes	—
710	C₂	—	2	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	4	1	no	—
713	C₂	—	4	2	no	—
714	C₂	—	4	2	no	—
715	C₂	—	524	1	no	—
716	C₂	—	524	2	no	—
717	C₂	—	524	1	no	—
718	C₂	C₂×#16862291	1	1	yes	characteristic
719	C₂	C₂×#16862291	1	1	yes	characteristic
720	C₂	#22554148	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	C₂×#121×C₁₃₁	C₂
hypercenter	C₂×#121	D₁₃₁
hypocenter	C₁₃₁	#3542
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. #22554057	C₂	semidirect
2. #22554050	C₂	semidirect
3. #22554026	C₂	semidirect
4. #22554009	C₂	semidirect
5. #22553997	C₂	semidirect
6. #22553988	C₂	semidirect
7. #22553980	C₂	semidirect
8. #22553963	C₂	semidirect
9. #22553959	C₂	semidirect
10. #22553956	C₂	semidirect
11. #22553952	C₂	semidirect
12. D₄×C₂²⋊D₁₃₁	C₂	semidirect
13. #22553929	C₂	semidirect
14. #22553915	C₂	semidirect
15. #22553912	C₂	semidirect
16. #22553894	C₂	semidirect
17. #22553891	C₂	semidirect
18. #22553879	C₂	semidirect
19. #22553878	C₂	semidirect
20. #22553871	C₂	semidirect
21. #22553823	C₂	semidirect
22. #22553823	C₂	semidirect
23. C₂×#121×C₁₃₁	C₂	semidirect
24. C₂×#14523513	C₂²	semidirect
25. C₂×#14523513	C₂²	semidirect
26. C₂×#14523513	C₂²	semidirect
27. C₂×#14523512	C₂²	semidirect
29. C₂×D₄×D₁₃₁	C₂²	semidirect
30. #16862245	C₂²	semidirect
31. #16862242	C₂²	semidirect
32. #16862242	C₂²	semidirect
33. #16862242	C₂²	semidirect
34. #16862241	C₂²	semidirect
35. #16862239	C₂²	semidirect
36. #16862239	C₂²	semidirect
37. #16862237	C₂²	semidirect
38. #16862236	C₂²	semidirect
39. #16862233	C₂²	semidirect
40. #16862233	C₂²	semidirect
41. #16862233	C₂²	semidirect
42. #16862232	C₂²	semidirect
43. #16862232	C₂²	semidirect
44. #16862231	C₂²	semidirect
45. #16862230	C₂²	semidirect
47. #16862229	C₂²	semidirect
48. #16862229	C₂²	semidirect
49. #16862229	C₂²	semidirect
50. #16862229	C₂²	semidirect
51. #16862228	C₂²	semidirect
52. #16862228	C₂²	semidirect
53. #16862227	C₂²	semidirect
54. #16862227	C₂²	semidirect
55. #16862227	C₂²	semidirect
56. #16862226	C₂²	semidirect
57. #16862225	C₂²	semidirect
58. #16862225	C₂²	semidirect
59. #16862225	C₂²	semidirect
60. #16862225	C₂²	semidirect
61. #16862224	C₂²	semidirect
62. #16862223	C₂²	semidirect
63. #16862223	C₂²	semidirect
64. #16862221	C₂²	semidirect
67. #16862220	C₂²	semidirect
68. #16862220	C₂²	semidirect
69. #16862219	C₂²	semidirect
70. #16862219	C₂²	semidirect
71. #16862218	C₂²	semidirect
72. #16862218	C₂²	semidirect
73. #16862218	C₂²	semidirect
74. #16862218	C₂²	semidirect
75. #16862218	C₂²	semidirect
76. #16862218	C₂²	semidirect
77. #16862217	C₂²	semidirect
78. #16862217	C₂²	semidirect
79. #16862217	C₂²	semidirect
80. #16862217	C₂²	semidirect
81. #16862217	C₂²	semidirect
82. #16862217	C₂²	semidirect
83. #16862216	C₂²	semidirect
86. #16862215	C₂²	semidirect
87. #16862215	C₂²	semidirect
88. #16862215	C₂²	semidirect
89. #16862214	C₂²	semidirect
90. #16862214	C₂²	semidirect
91. #16862214	C₂²	semidirect
92. #16862211	C₂²	semidirect
93. D₄×Dic₁₃₁	C₂²	semidirect
94. D₄×Dic₁₃₁	C₂²	semidirect
95. #16862208	C₂²	semidirect
97. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
98. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
99. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
100. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
101. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
102. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
103. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
104. #16862205	C₂²	semidirect
105. #16862205	C₂²	semidirect
106. #16862205	C₂²	semidirect
107. #16862204	C₂²	semidirect
108. #16862202	C₂²	semidirect
109. C₄⋊C₄×D₁₃₁	C₂²	semidirect
110. C₂×C₂²⋊Dic₁₃₁	C₂²	semidirect
111. C₂²⋊C₄×D₁₃₁	C₂²	semidirect
113. C₂²×D₄×C₁₃₁	C₂²	semidirect
114. C₂³×C₄×C₁₃₁	C₂²	semidirect
117. #121×C₁₃₁	C₂²	semidirect
118. #121×C₁₃₁	C₂²	semidirect
119. #121×C₁₃₁	C₂²	semidirect
120. #121×C₁₃₁	C₂²	semidirect
121. C₂×C₄⋊C₄×C₁₃₁	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₁₃₁	C₂²	semidirect
360. C₁₃₁	#3542	semidirect
384. C₂×#121	D₁₃₁	semidirect
392. C₂²×D₄	C₂×D₁₃₁	semidirect
393. C₂³×C₄	C₂×D₁₃₁	semidirect
449. #121	C₂×D₁₃₁	semidirect
450. #121	C₂×D₁₃₁	semidirect
451. #121	C₂×D₁₃₁	semidirect
452. #121	C₂×D₁₃₁	semidirect
480. C₂×C₄⋊C₄	C₂×D₁₃₁	semidirect
483. C₂×C₂²⋊C₄	C₂×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#22554057	2
#22554050	2
#22554026	2
#22554009	2
#22553997	2
#22553988	2
#22553980	2
#22553963	2
#22553959	2
#22553956	2
#22553952	2
D₄×C₂²⋊D₁₃₁	2
#22553929	2
#22553915	2
#22553912	2
#22553894	2
#22553891	2
#22553879	2
#22553878	2
#22553871	2
#22553823	2
C₂×#121×C₁₃₁	2
#3542	131