Subgroups — #30680477

Order 16768.

1160 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22554060	C₂	1	2	yes	maximal, complemented
2	#22554054	C₂	1	2	yes	maximal, complemented
3	#22554047	C₂	1	2	yes	maximal, complemented
4	#22553971	C₂	1	2	yes	maximal, complemented
5	#22553958	C₂	1	2	yes	maximal, complemented
6	#22553954	C₂	1	4	yes	maximal, complemented
7	D₄×D₅₂₄	C₂	1	2	yes	maximal, complemented
8	#22553933	C₂	1	2	yes	maximal, complemented
9	#22553902	C₂	1	2	yes	maximal, complemented
10	#22553901	C₂	1	4	yes	maximal, complemented
11	#22553881	C₂	1	2	yes	maximal, complemented
12	#22553870	C₂	1	2	yes	maximal, complemented
13	#22553862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16862234	C₂	1	1	yes	maximal, characteristic, complemented
15	#529×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14523513	C₂²	1	2	yes	complemented
17	C₂×#14523513	C₂²	1	2	yes	complemented
18	C₂²×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₅₂₄	C₂²	1	1	yes	characteristic
20	C₂²×D₅₂₄	C₂²	1	2	yes	complemented
21	C₂×D₄×D₁₃₁	C₂²	1	4	yes	complemented
22	#16862246	C₂²	1	1	yes	characteristic, complemented
23	#16862243	C₂²	1	2	yes	—
24	#16862243	C₂²	1	1	yes	characteristic, complemented
25	#16862241	C₂²	1	4	yes	complemented
26	#16862235	C₂²	1	4	yes	complemented
27	#16862234	C₂²	1	2	yes	complemented
28	#16862234	C₂²	1	2	yes	complemented
29	#16862234	C₂²	1	2	yes	complemented
30	#16862234	C₂²	1	2	yes	complemented
31	#16862234	C₂²	1	2	yes	complemented
32	#16862234	C₂²	1	2	yes	complemented
33	#16862232	C₂²	1	4	yes	complemented
34	#16862232	C₂²	1	4	yes	complemented
35	#16862231	C₂²	1	4	yes	complemented
36	#16862231	C₂²	1	4	yes	complemented
37	#16862231	C₂²	1	4	yes	complemented
38	#16862228	C₂²	1	4	yes	complemented
39	#16862225	C₂²	1	2	yes	complemented
40	#16862224	C₂²	1	4	yes	complemented
41	#16862224	C₂²	1	4	yes	complemented
42	#16862221	C₂²	1	4	yes	complemented
43	#16862221	C₂²	1	4	yes	complemented
44	#16862221	C₂²	1	4	yes	complemented
45	#16862220	C₂²	1	2	yes	—
46	#16862220	C₂²	1	2	yes	complemented
47	#16862220	C₂²	1	2	yes	complemented
48	#16862219	C₂²	1	4	yes	complemented
49	#16862218	C₂²	1	4	yes	complemented
50	#16862216	C₂²	1	4	yes	complemented
51	#16862216	C₂²	1	4	yes	complemented
52	#16862216	C₂²	1	4	yes	complemented
53	#16862216	C₂²	1	4	yes	complemented
54	#16862214	C₂²	1	4	yes	complemented
55	C₄×Dic₂₆₂	C₂²	1	2	yes	complemented
56	C₄×D₅₂₄	C₂²	1	2	yes	complemented
57	C₄×D₅₂₄	C₂²	1	2	yes	complemented
58	C₄×D₅₂₄	C₂²	1	2	yes	complemented
59	#16862208	C₂²	1	4	yes	complemented
60	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	4	yes	complemented
61	C₂×(C₂×D₁₃₁)⋊C₄	C₂²	1	2	yes	complemented
62	C₂×(C₂×D₁₃₁)⋊C₄	C₂²	1	2	yes	complemented
63	C₂²⋊C₄×D₁₃₁	C₂²	1	4	yes	complemented
64	#126×C₁₃₁	C₂²	1	2	yes	complemented
65	#125×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
66	#124×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
67	#123×C₁₃₁	C₂²	1	2	yes	complemented
68	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
69	#121×C₁₃₁	C₂²	1	1	yes	characteristic
70	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
71	C₄×D₄×C₁₃₁	C₂²	1	2	yes	complemented
72	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
73	#117×C₁₃₁	C₂²	1	2	yes	complemented
74	C₂×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₁₃₁	C₂³	1	2	yes	—
76	C₂³×D₁₃₁	C₂³	1	4	yes	—
77	#14523513	—	4	4	no	—
78	#14523513	—	4	4	no	—
79	C₂×Dic₂₆₂	—	4	2	no	—
80	C₂×Dic₂₆₂	C₂³	1	2	yes	—
81	C₂×Dic₂₆₂	C₂³	1	2	yes	—
82	C₂×Dic₂₆₂	C₂³	1	2	yes	—
83	C₂×D₅₂₄	—	4	2	no	—
84	C₂×D₅₂₄	—	4	4	no	—
85	C₂×D₅₂₄	C₂³	1	2	yes	—
86	C₂×D₅₂₄	C₂³	1	2	yes	—
87	C₂×D₅₂₄	C₂³	1	4	yes	—
88	C₂×D₅₂₄	C₂³	1	2	yes	—
89	C₂×D₅₂₄	C₂³	1	2	yes	—
90	C₂×D₅₂₄	C₂³	1	2	yes	—
91	C₂×D₅₂₄	C₂³	1	4	yes	—
92	C₂×D₅₂₄	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₁₃₁	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₃₁	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₃₁	C₂³	1	4	yes	—
96	D₄×D₁₃₁	—	4	8	no	—
97	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
98	C₂×C₄×D₁₃₁	C₂³	1	4	yes	—
99	C₂×C₄×D₁₃₁	C₂³	1	4	yes	—
100	C₂×C₄×D₁₃₁	C₂³	1	4	yes	—
101	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
102	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
103	Dic₁₃₁⋊C₄	C₂³	1	4	yes	—
104	Dic₁₃₁⋊C₄	C₂³	1	4	yes	—
105	C₂²⋊Dic₁₃₁	C₂³	1	4	yes	—
106	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
107	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
108	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
109	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
110	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
111	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
112	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
113	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
114	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
115	(C₂×D₁₃₁)⋊C₄	C₂³	1	4	yes	—
116	C₄×Dic₁₃₁	C₂³	1	4	yes	—
117	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
118	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
119	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₁₃₁	C₂³	1	2	yes	—
121	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
124	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
125	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
126	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
127	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
128	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
129	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
130	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
131	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
132	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
133	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
134	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
135	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
136	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
137	C₄²×C₁₃₁	C₂³	1	2	yes	—
138	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
139	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
140	C₂²×D₁₃₁	—	2	4	no	—
141	C₂²×D₁₃₁	—	4	4	no	—
142	C₂²×D₁₃₁	—	4	4	no	—
143	C₂²×D₁₃₁	—	4	2	no	—
144	C₂²×D₁₃₁	—	4	4	no	—
145	C₂²×D₁₃₁	—	4	2	no	—
146	C₂²×D₁₃₁	C₂⁴	1	4	yes	—
147	C₂²×D₁₃₁	C₂⁴	1	4	yes	—
148	Dic₂₆₂	—	2	4	no	—
149	Dic₂₆₂	—	4	2	no	—
150	Dic₂₆₂	—	4	2	no	—
151	D₅₂₄	—	2	4	no	—
152	D₅₂₄	—	2	4	no	—
153	D₅₂₄	—	4	4	no	—
154	D₅₂₄	—	4	4	no	—
155	D₅₂₄	—	4	2	no	—
156	D₅₂₄	—	4	2	no	—
157	D₅₂₄	—	4	4	no	—
158	D₅₂₄	—	4	2	no	—
159	C₂²⋊D₁₃₁	—	2	8	no	—
160	C₂²⋊D₁₃₁	—	4	4	no	—
161	C₂²⋊D₁₃₁	—	4	4	no	—
162	C₂×Dic₁₃₁	—	4	2	no	—
163	C₂×Dic₁₃₁	C₂⁴	1	4	yes	—
164	C₂×Dic₁₃₁	C₂⁴	1	4	yes	—
165	C₄×D₁₃₁	—	4	4	no	—
166	C₄×D₁₃₁	—	4	4	no	—
167	C₄×D₁₃₁	—	4	4	no	—
168	C₂³×C₁₃₁	C₂⁴	1	2	yes	—
169	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
170	Q₈×C₁₃₁	—	4	1	no	—
171	D₄×C₁₃₁	—	2	4	no	—
172	D₄×C₁₃₁	—	4	1	no	—
173	C₂×C₄×C₁₃₁	—	2	2	no	—
174	C₂×C₄×C₁₃₁	—	2	2	no	—
175	C₂×C₄×C₁₃₁	—	2	4	no	—
176	C₂×C₄×C₁₃₁	—	4	1	no	—
177	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
183	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
184	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
185	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
186	C₂²×C₁₃₁	—	2	1	no	—
187	C₂²×C₁₃₁	—	2	1	no	—
188	C₂²×C₁₃₁	—	2	2	no	—
189	C₂²×C₁₃₁	—	2	2	no	—
190	C₂²×C₁₃₁	—	2	2	no	—
191	C₂²×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
192	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
193	C₂×D₁₃₁	—	2	4	no	—
194	C₂×D₁₃₁	—	2	4	no	—
195	C₂×D₁₃₁	—	2	4	no	—
196	C₂×D₁₃₁	—	2	4	no	—
197	C₂×D₁₃₁	—	2	4	no	—
198	C₂×D₁₃₁	—	2	4	no	—
199	C₂×D₁₃₁	—	8	4	no	—
200	C₂×D₁₃₁	—	8	8	no	—
201	C₄×C₁₃₁	—	2	1	no	—
202	C₄×C₁₃₁	—	2	2	no	—
203	C₄×C₁₃₁	—	2	1	no	—
204	C₄×C₁₃₁	—	2	1	no	—
205	C₄×C₁₃₁	—	2	2	no	—
206	C₄×C₁₃₁	—	2	1	no	—
207	C₄×C₁₃₁	—	2	1	no	—
208	C₄×C₁₃₁	—	2	2	no	—
209	C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
210	Dic₁₃₁	—	2	4	no	—
211	Dic₁₃₁	—	2	4	no	—
212	C₂×C₁₃₁	—	2	2	no	—
213	C₂×C₁₃₁	—	4	2	no	—
214	C₂×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₁₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₁₃₁	#585	1	1	yes	characteristic
217	D₁₃₁	—	4	4	no	—
218	D₁₃₁	—	4	4	no	—
219	C₁₃₁	#3558	1	1	yes	characteristic, complemented, Sylow
220	#3558	—	131	1	no	maximal, Sylow
221	#562	—	131	2	no	—
222	H(3,𝔽₄)	—	131	2	no	—
223	#559	—	131	2	no	—
224	#548	—	131	2	no	—
225	#546	—	131	4	no	—
226	#546	—	131	2	no	—
227	D₄²	—	131	2	no	—
228	#542	—	131	2	no	—
229	#538	—	131	4	no	—
230	#538	—	131	2	no	—
231	#535	—	131	2	no	—
232	#534	—	131	2	no	—
233	#532	—	131	1	no	—
234	#529	D₁₃₁	1	1	yes	characteristic, complemented
235	C₂×#124	—	131	1	no	—
236	C₂×#41	—	131	2	no	—
237	C₂×#41	—	131	2	no	—
238	C₂²×Q₈	—	131	1	no	—
239	C₂²×D₄	—	131	4	no	—
240	C₂²×D₄	—	131	1	no	—
241	C₂²×D₄	—	131	2	no	—
242	C₄⋊Q₈	—	131	1	no	—
243	#127	—	131	1	no	—
244	#127	—	131	2	no	—
245	#126	—	131	4	no	—
246	#126	C₂×D₁₃₁	1	2	yes	complemented
247	#125	C₂×D₁₃₁	1	1	yes	characteristic, complemented
248	#124	—	131	4	no	—
249	#124	—	131	4	no	—
250	#124	—	131	4	no	—
251	#124	—	131	2	no	—
252	#124	—	131	2	no	—
253	#124	—	131	2	no	—
254	#124	—	131	2	no	—
255	#124	—	131	2	no	—
256	#124	—	131	2	no	—
257	#124	C₂×D₁₃₁	1	1	yes	characteristic, complemented
258	#123	—	131	4	no	—
259	#123	—	131	4	no	—
260	#123	—	131	4	no	—
261	#123	—	131	4	no	—
262	#123	C₂×D₁₃₁	1	2	yes	complemented
263	C₂²⋊Q₈	—	131	2	no	—
264	C₂²⋊Q₈	—	131	4	no	—
265	C₂²⋊Q₈	—	131	4	no	—
266	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
267	#121	—	131	4	no	—
268	#121	—	131	2	no	—
269	#121	—	131	2	no	—
270	#121	—	131	2	no	—
271	#121	—	131	4	no	—
272	#121	—	131	4	no	—
273	#121	—	131	4	no	—
274	#121	—	131	4	no	—
275	#121	C₂×D₁₃₁	1	1	yes	characteristic
276	#120	—	131	4	no	—
277	#120	—	131	4	no	—
278	#120	—	131	4	no	—
279	#120	—	131	4	no	—
280	#120	—	131	4	no	—
281	C₄×Q₈	—	131	2	no	—
282	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
283	C₄×D₄	—	131	4	no	—
284	C₄×D₄	—	131	4	no	—
285	C₄×D₄	—	131	2	no	—
286	C₄×D₄	—	131	2	no	—
287	C₄×D₄	—	131	2	no	—
288	C₄×D₄	C₂×D₁₃₁	1	2	yes	complemented
289	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic, complemented
290	#117	C₂×D₁₃₁	1	2	yes	complemented
291	C₂×C₂²⋊C₄	—	131	2	no	—
292	C₂×C₂²⋊C₄	—	131	2	no	—
293	C₂×C₂²⋊C₄	—	131	4	no	—
294	C₂×C₄²	C₂×D₁₃₁	1	1	yes	characteristic, complemented
295	C₂⁴	—	131	2	no	—
296	C₂⁴	—	131	4	no	—
297	#41	—	524	4	no	—
298	#41	—	524	4	no	—
299	C₂×Q₈	—	524	2	no	—
300	C₂×Q₈	—	131	2	no	—
301	C₂×Q₈	—	131	2	no	—
302	C₂×Q₈	—	131	2	no	—
303	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
304	C₂×D₄	—	524	2	no	—
305	C₂×D₄	—	524	4	no	—
306	C₂×D₄	—	524	8	no	—
307	C₂×D₄	—	131	4	no	—
308	C₂×D₄	—	131	4	no	—
309	C₂×D₄	—	131	4	no	—
310	C₂×D₄	—	131	2	no	—
311	C₂×D₄	—	131	2	no	—
312	C₂×D₄	—	131	4	no	—
313	C₂×D₄	—	131	2	no	—
314	C₂×D₄	—	131	2	no	—
315	C₂×D₄	—	131	2	no	—
316	C₂×D₄	—	131	4	no	—
317	C₂×D₄	—	131	4	no	—
318	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
319	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
320	C₂²×C₄	—	131	2	no	—
321	C₂²×C₄	—	131	4	no	—
322	C₂²×C₄	—	131	4	no	—
323	C₂²×C₄	—	131	4	no	—
324	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₁₃₁	1	2	yes	—
327	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
328	C₄⋊C₄	—	131	4	no	—
329	C₄⋊C₄	—	131	4	no	—
330	C₄⋊C₄	—	131	2	no	—
331	C₄⋊C₄	—	131	2	no	—
332	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
333	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
334	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
335	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
336	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
337	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
338	C₂²⋊C₄	—	131	4	no	—
339	C₂²⋊C₄	—	131	4	no	—
340	C₂²⋊C₄	—	131	4	no	—
341	C₂²⋊C₄	—	131	4	no	—
342	C₂²⋊C₄	—	131	4	no	—
343	C₂²⋊C₄	—	131	4	no	—
344	C₂²⋊C₄	—	131	4	no	—
345	C₂²⋊C₄	—	131	4	no	—
346	C₂²⋊C₄	—	131	4	no	—
347	C₂²⋊C₄	—	131	4	no	—
348	C₂²⋊C₄	—	131	4	no	—
349	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
350	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
351	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
352	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
353	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
354	C₄²	—	131	4	no	—
355	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
356	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
357	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
358	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
359	C₄²	C₂²×D₁₃₁	1	2	yes	—
360	C₂³	—	262	4	no	—
361	C₂³	—	524	2	no	—
362	C₂³	—	524	4	no	—
363	C₂³	—	524	4	no	—
364	C₂³	—	524	2	no	—
365	C₂³	—	524	4	no	—
366	C₂³	—	131	4	no	—
367	C₂³	—	131	4	no	—
368	C₂³	C₂³×D₁₃₁	1	2	yes	—
369	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
370	Q₈	—	4	1	no	—
371	Q₈	—	262	4	no	—
372	Q₈	—	524	2	no	—
373	Q₈	—	524	2	no	—
374	D₄	—	2	4	no	—
375	D₄	—	4	1	no	—
376	D₄	—	262	8	no	—
377	D₄	—	262	4	no	—
378	D₄	—	262	4	no	—
379	D₄	—	524	4	no	—
380	D₄	—	524	2	no	—
381	D₄	—	524	4	no	—
382	D₄	—	524	2	no	—
383	D₄	—	524	2	no	—
384	D₄	—	524	4	no	—
385	D₄	—	524	4	no	—
386	D₄	—	524	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	524	4	no	—
392	C₂×C₄	—	524	4	no	—
393	C₂×C₄	—	524	4	no	—
394	C₂×C₄	—	524	2	no	—
395	C₂×C₄	—	131	4	no	—
396	C₂×C₄	—	131	4	no	—
397	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
398	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
399	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
400	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
404	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
405	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	262	4	no	—
412	C₂²	—	262	4	no	—
413	C₂²	—	262	4	no	—
414	C₂²	—	262	4	no	—
415	C₂²	—	262	4	no	—
416	C₂²	—	262	4	no	—
417	C₂²	—	1048	4	no	—
418	C₂²	—	1048	8	no	—
419	C₂²	#16862292	1	2	yes	—
420	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	2	no	—
429	C₄	—	262	4	no	—
430	C₄	—	262	4	no	—
431	C₄	#16862292	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	4	2	no	—
434	C₂	—	524	4	no	—
435	C₂	—	524	4	no	—
436	C₂	C₂×#16862292	1	1	yes	characteristic
437	C₂	C₂×#16862292	1	1	yes	characteristic
438	C₂	#22554148	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	#529×C₁₃₁	C₂
hypercenter	#529	D₁₃₁
hypocenter	C₁₃₁	#3558
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #22554060	C₂	semidirect
2. #22554054	C₂	semidirect
3. #22554047	C₂	semidirect
4. #22553971	C₂	semidirect
5. #22553958	C₂	semidirect
6. #22553954	C₂	semidirect
7. D₄×D₅₂₄	C₂	semidirect
8. #22553933	C₂	semidirect
9. #22553902	C₂	semidirect
10. #22553901	C₂	semidirect
11. #22553881	C₂	semidirect
12. #22553870	C₂	semidirect
13. #22553862	C₂	semidirect
14. C₂×#16862234	C₂	semidirect
15. #529×C₁₃₁	C₂	semidirect
16. C₂×#14523513	C₂²	semidirect
17. C₂×#14523513	C₂²	semidirect
18. C₂²×Dic₂₆₂	C₂²	semidirect
20. C₂²×D₅₂₄	C₂²	semidirect
21. C₂×D₄×D₁₃₁	C₂²	semidirect
22. #16862246	C₂²	semidirect
24. #16862243	C₂²	semidirect
25. #16862241	C₂²	semidirect
26. #16862235	C₂²	semidirect
27. #16862234	C₂²	semidirect
28. #16862234	C₂²	semidirect
29. #16862234	C₂²	semidirect
30. #16862234	C₂²	semidirect
31. #16862234	C₂²	semidirect
32. #16862234	C₂²	semidirect
33. #16862232	C₂²	semidirect
34. #16862232	C₂²	semidirect
35. #16862231	C₂²	semidirect
36. #16862231	C₂²	semidirect
37. #16862231	C₂²	semidirect
38. #16862228	C₂²	semidirect
39. #16862225	C₂²	semidirect
40. #16862224	C₂²	semidirect
41. #16862224	C₂²	semidirect
42. #16862221	C₂²	semidirect
43. #16862221	C₂²	semidirect
44. #16862221	C₂²	semidirect
46. #16862220	C₂²	semidirect
47. #16862220	C₂²	semidirect
48. #16862219	C₂²	semidirect
49. #16862218	C₂²	semidirect
50. #16862216	C₂²	semidirect
51. #16862216	C₂²	semidirect
52. #16862216	C₂²	semidirect
53. #16862216	C₂²	semidirect
54. #16862214	C₂²	semidirect
55. C₄×Dic₂₆₂	C₂²	semidirect
56. C₄×D₅₂₄	C₂²	semidirect
57. C₄×D₅₂₄	C₂²	semidirect
58. C₄×D₅₂₄	C₂²	semidirect
59. #16862208	C₂²	semidirect
60. (C₂²⋊D₁₃₁)⋊C₄	C₂²	semidirect
61. C₂×(C₂×D₁₃₁)⋊C₄	C₂²	semidirect
62. C₂×(C₂×D₁₃₁)⋊C₄	C₂²	semidirect
63. C₂²⋊C₄×D₁₃₁	C₂²	semidirect
64. #126×C₁₃₁	C₂²	semidirect
65. #125×C₁₃₁	C₂²	semidirect
66. #124×C₁₃₁	C₂²	semidirect
67. #123×C₁₃₁	C₂²	semidirect
68. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
70. C₄×Q₈×C₁₃₁	C₂²	semidirect
71. C₄×D₄×C₁₃₁	C₂²	semidirect
72. C₄×D₄×C₁₃₁	C₂²	semidirect
73. #117×C₁₃₁	C₂²	semidirect
74. C₂×C₄²×C₁₃₁	C₂²	semidirect
219. C₁₃₁	#3558	semidirect
234. #529	D₁₃₁	semidirect
246. #126	C₂×D₁₃₁	semidirect
247. #125	C₂×D₁₃₁	semidirect
257. #124	C₂×D₁₃₁	semidirect
262. #123	C₂×D₁₃₁	semidirect
266. C₂²⋊Q₈	C₂×D₁₃₁	semidirect
282. C₄×Q₈	C₂×D₁₃₁	semidirect
288. C₄×D₄	C₂×D₁₃₁	semidirect
289. C₄×D₄	C₂×D₁₃₁	semidirect
290. #117	C₂×D₁₃₁	semidirect
294. C₂×C₄²	C₂×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#22554060	2
#22554054	2
#22554047	2
#22553971	2
#22553958	2
#22553954	2
D₄×D₅₂₄	2
#22553933	2
#22553902	2
#22553901	2
#22553881	2
#22553870	2
#22553862	2
C₂×#16862234	2
#529×C₁₃₁	2
#3558	131