Subgroups — #30680657

Order 16768.

958 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22554066	C₂	1	1	yes	maximal, characteristic, complemented
2	#22554066	C₂	1	1	yes	maximal, characteristic, complemented
3	#22554062	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554054	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554034	C₂	1	2	yes	maximal, complemented
6	#22554030	C₂	1	2	yes	maximal, complemented
7	#22554029	C₂	1	2	yes	maximal, complemented
8	#22553991	C₂	1	2	yes	maximal, complemented
9	#22553987	C₂	1	2	yes	maximal, complemented
10	#22553986	C₂	1	2	yes	maximal, complemented
11	#22553932	C₂	1	2	yes	maximal, complemented
12	#22553930	C₂	1	2	yes	maximal, complemented
13	#22553927	C₂	1	2	yes	maximal, complemented
14	#22553898	C₂	1	2	yes	maximal, complemented
15	#22553895	C₂	1	2	yes	maximal, complemented
16	#22553894	C₂	1	2	yes	maximal, complemented
17	#22553846	C₂	1	1	yes	maximal, characteristic, complemented
18	#22553846	C₂	1	1	yes	maximal, characteristic, complemented
19	#529×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
20	#16862245	C₂²	1	2	yes	complemented
21	#16862245	C₂²	1	2	yes	complemented
22	#16862244	C₂²	1	2	yes	complemented
23	#16862241	C₂²	1	2	yes	complemented
24	#16862241	C₂²	1	2	yes	complemented
25	#16862241	C₂²	1	2	yes	complemented
26	#16862241	C₂²	1	2	yes	complemented
27	#16862241	C₂²	1	2	yes	complemented
28	#16862240	C₂²	1	2	yes	complemented
29	#16862240	C₂²	1	2	yes	complemented
30	#16862240	C₂²	1	2	yes	complemented
31	#16862239	C₂²	1	2	yes	complemented
32	#16862239	C₂²	1	2	yes	complemented
33	#16862239	C₂²	1	2	yes	complemented
34	#16862239	C₂²	1	2	yes	complemented
35	#16862238	C₂²	1	1	yes	characteristic, complemented
36	#16862238	C₂²	1	1	yes	characteristic, complemented
37	#16862235	C₂²	1	2	yes	—
38	#16862234	C₂²	1	2	yes	—
39	#16862234	C₂²	1	1	yes	characteristic
40	#16862234	C₂²	1	1	yes	characteristic
41	#16862233	C₂²	1	2	yes	complemented
42	#16862232	C₂²	1	2	yes	—
43	#16862232	C₂²	1	2	yes	—
44	#16862232	C₂²	1	2	yes	—
45	#16862232	C₂²	1	2	yes	—
46	#16862232	C₂²	1	2	yes	complemented
47	#16862232	C₂²	1	2	yes	complemented
48	#16862231	C₂²	1	2	yes	—
49	#16862231	C₂²	1	2	yes	—
50	#16862231	C₂²	1	2	yes	—
51	#16862229	C₂²	1	2	yes	—
52	#16862229	C₂²	1	2	yes	complemented
53	#16862229	C₂²	1	2	yes	complemented
54	#16862228	C₂²	1	2	yes	—
55	#16862227	C₂²	1	2	yes	—
56	#16862226	C₂²	1	2	yes	complemented
57	#16862226	C₂²	1	2	yes	complemented
58	#16862225	C₂²	1	1	yes	characteristic, complemented
59	#16862225	C₂²	1	2	yes	complemented
60	#16862225	C₂²	1	1	yes	characteristic, complemented
61	#16862224	C₂²	1	2	yes	complemented
62	#16862224	C₂²	1	2	yes	complemented
63	#16862224	C₂²	1	2	yes	complemented
64	#16862224	C₂²	1	2	yes	complemented
65	#16862223	C₂²	1	2	yes	complemented
66	#16862223	C₂²	1	2	yes	complemented
67	#16862220	C₂²	1	1	yes	characteristic
68	#16862220	C₂²	1	1	yes	characteristic
69	#16862219	C₂²	1	2	yes	—
70	#16862218	C₂²	1	2	yes	—
71	#16862217	C₂²	1	2	yes	—
72	#16862216	C₂²	1	2	yes	—
73	#16862216	C₂²	1	2	yes	—
74	#16862214	C₂²	1	2	yes	—
75	#16862214	C₂²	1	2	yes	complemented
76	C₄×Dic₂₆₂	C₂²	1	2	yes	complemented
77	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
78	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic, complemented
79	#16862211	C₂²	1	2	yes	complemented
80	#16862211	C₂²	1	2	yes	complemented
81	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
82	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
83	#16862208	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₁₃₁	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₁₃₁	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₁₃₁	C₂²	1	2	yes	complemented
87	(C₂²⋊D₁₃₁)⋊C₄	C₂²	1	2	yes	—
88	#16862204	C₂²	1	2	yes	complemented
89	#16862203	C₂²	1	2	yes	complemented
90	#16862203	C₂²	1	2	yes	complemented
91	#16862203	C₂²	1	2	yes	complemented
92	#16862202	C₂²	1	2	yes	complemented
93	C₂×(C₂×D₁₃₁)⋊C₄	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₁₃₁	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₃₁	C₂²	1	2	yes	complemented
96	#126×C₁₃₁	C₂²	1	2	yes	complemented
97	#125×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
98	#124×C₁₃₁	C₂²	1	1	yes	characteristic
99	#123×C₁₃₁	C₂²	1	2	yes	complemented
100	C₂²⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
101	#121×C₁₃₁	C₂²	1	1	yes	characteristic
102	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₁₃₁	C₂²	1	2	yes	complemented
105	#117×C₁₃₁	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₃₁	C₂³	1	2	yes	—
108	C₂×Dic₂₆₂	C₂³	1	2	yes	—
109	C₂×Dic₂₆₂	C₂³	1	2	yes	—
110	C₂×Dic₂₆₂	C₂³	1	2	yes	—
111	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
112	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
113	C₂×D₅₂₄	C₂³	1	2	yes	—
114	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
115	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₁₃₁	C₂³	1	2	yes	—
120	C₂²×Dic₁₃₁	C₂³	1	2	yes	—
121	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
122	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
123	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
124	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
125	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
126	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
127	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
128	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
129	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
131	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
132	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
133	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
134	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
135	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
136	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
137	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
138	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
139	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
140	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
141	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
142	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
143	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
144	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
145	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
146	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
147	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
148	C₂²⋊Dic₁₃₁	C₂³	1	2	yes	—
149	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
150	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
151	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
152	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
153	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
154	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
155	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
156	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
157	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
158	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
165	C₄×Dic₁₃₁	C₂³	1	2	yes	—
166	C₄×Dic₁₃₁	C₂³	1	2	yes	—
167	C₄×Dic₁₃₁	C₂³	1	2	yes	—
168	C₄×Dic₁₃₁	C₂³	1	2	yes	—
169	C₄×Dic₁₃₁	C₂³	1	2	yes	—
170	C₄×Dic₁₃₁	C₂³	1	2	yes	—
171	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
172	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
173	C₂×D₄×C₁₃₁	C₂³	1	2	yes	—
174	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
175	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₁₃₁	C₂³	1	2	yes	—
177	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
179	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
180	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
181	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
183	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₁₃₁	C₂³	1	2	yes	—
189	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
190	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
191	C₄²×C₁₃₁	C₂³	1	2	yes	—
192	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
193	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
194	C₂²×D₁₃₁	—	4	2	no	—
195	C₂²×D₁₃₁	—	4	2	no	—
196	C₂²×D₁₃₁	—	4	2	no	—
197	C₂²×D₁₃₁	C₂⁴	1	2	yes	—
198	C₂²×D₁₃₁	C₂⁴	1	2	yes	—
199	Dic₂₆₂	—	4	2	no	—
200	Dic₂₆₂	—	4	2	no	—
201	Dic₂₆₂	—	4	2	no	—
202	Dic₂₆₂	—	4	1	no	—
203	Dic₂₆₂	—	4	1	no	—
204	D₅₂₄	—	4	1	no	—
205	D₅₂₄	—	4	1	no	—
206	D₅₂₄	—	4	2	no	—
207	C₂²⋊D₁₃₁	—	4	2	no	—
208	C₂²⋊D₁₃₁	—	4	2	no	—
209	C₂²⋊D₁₃₁	—	4	2	no	—
210	C₂²⋊D₁₃₁	—	4	2	no	—
211	C₂×Dic₁₃₁	—	4	2	no	—
212	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
213	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
214	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
215	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
216	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
217	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
218	C₄×D₁₃₁	—	4	2	no	—
219	C₄×D₁₃₁	—	4	2	no	—
220	C₄×D₁₃₁	—	4	2	no	—
221	C₄×D₁₃₁	—	4	2	no	—
222	C₂³×C₁₃₁	C₂⁴	1	2	yes	—
223	C₂³×C₁₃₁	C₂⁴	1	1	yes	characteristic
224	Q₈×C₁₃₁	—	4	1	no	—
225	D₄×C₁₃₁	—	4	1	no	—
226	D₄×C₁₃₁	—	4	2	no	—
227	C₂×C₄×C₁₃₁	—	4	2	no	—
228	C₂×C₄×C₁₃₁	—	4	1	no	—
229	C₂×C₄×C₁₃₁	—	4	1	no	—
230	C₂×C₄×C₁₃₁	—	4	1	no	—
231	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
239	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
240	C₂²×C₁₃₁	—	2	1	no	—
241	C₂²×C₁₃₁	—	2	1	no	—
242	C₂²×C₁₃₁	—	2	1	no	—
243	C₂²×C₁₃₁	—	2	2	no	—
244	C₂²×C₁₃₁	—	2	2	no	—
245	C₂²×C₁₃₁	—	2	2	no	—
246	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
247	C₂×D₁₃₁	—	2	2	no	—
248	C₂×D₁₃₁	—	2	2	no	—
249	C₂×D₁₃₁	—	2	2	no	—
250	C₂×D₁₃₁	—	2	2	no	—
251	C₂×D₁₃₁	—	2	2	no	—
252	C₂×D₁₃₁	—	2	2	no	—
253	C₂×D₁₃₁	—	8	4	no	—
254	C₄×C₁₃₁	—	2	1	no	—
255	C₄×C₁₃₁	—	2	1	no	—
256	C₄×C₁₃₁	—	2	1	no	—
257	C₄×C₁₃₁	—	2	1	no	—
258	C₄×C₁₃₁	—	2	2	no	—
259	C₄×C₁₃₁	—	2	1	no	—
260	C₄×C₁₃₁	—	2	1	no	—
261	C₄×C₁₃₁	—	2	2	no	—
262	C₄×C₁₃₁	—	2	2	no	—
263	Dic₁₃₁	—	2	2	no	—
264	Dic₁₃₁	—	2	2	no	—
265	Dic₁₃₁	—	2	2	no	—
266	Dic₁₃₁	—	2	2	no	—
267	Dic₁₃₁	—	2	2	no	—
268	Dic₁₃₁	—	2	2	no	—
269	C₂×C₁₃₁	—	4	2	no	—
270	C₂×C₁₃₁	—	4	1	no	—
271	C₂×C₁₃₁	#585	1	1	yes	characteristic
272	C₂×C₁₃₁	#585	1	1	yes	characteristic
273	C₂×C₁₃₁	#585	1	1	yes	characteristic
274	D₁₃₁	—	4	2	no	—
275	D₁₃₁	—	4	2	no	—
276	C₁₃₁	#3568	1	1	yes	characteristic, complemented, Sylow
277	#3568	—	131	1	no	maximal, Sylow
278	#563	—	131	1	no	—
279	#563	—	131	1	no	—
280	#563	—	131	1	no	—
281	H(3,𝔽₄)	—	131	1	no	—
282	#556	—	131	2	no	—
283	#556	—	131	2	no	—
284	#556	—	131	2	no	—
285	#551	—	131	2	no	—
286	#551	—	131	2	no	—
287	#551	—	131	2	no	—
288	#542	—	131	2	no	—
289	#542	—	131	2	no	—
290	#542	—	131	2	no	—
291	#538	—	131	2	no	—
292	#538	—	131	2	no	—
293	#538	—	131	2	no	—
294	#529	—	131	1	no	—
295	#529	—	131	1	no	—
296	#529	D₁₃₁	1	1	yes	characteristic, complemented
297	C₄⋊Q₈	—	131	2	no	—
298	C₄⋊Q₈	—	131	2	no	—
299	C₄⋊Q₈	—	131	2	no	—
300	#126	—	131	2	no	—
301	#126	—	131	2	no	—
302	#126	—	131	2	no	—
303	#126	—	131	2	no	—
304	#126	—	131	2	no	—
305	#126	—	131	2	no	—
306	#126	—	131	2	no	—
307	#126	—	131	2	no	—
308	#126	—	131	2	no	—
309	#126	—	131	2	no	—
310	#126	—	131	2	no	—
311	#126	—	131	2	no	—
312	#126	C₂×D₁₃₁	1	2	yes	complemented
313	#125	—	131	1	no	—
314	#125	—	131	1	no	—
315	#125	C₂×D₁₃₁	1	1	yes	characteristic, complemented
316	#124	—	131	2	no	—
317	#124	—	131	2	no	—
318	#124	—	131	2	no	—
319	#124	—	131	2	no	—
320	#124	—	131	2	no	—
321	#124	—	131	2	no	—
322	#124	—	131	2	no	—
323	#124	—	131	2	no	—
324	#124	—	131	1	no	—
325	#124	—	131	1	no	—
326	#124	—	131	2	no	—
327	#124	C₂×D₁₃₁	1	1	yes	characteristic
328	#123	—	131	2	no	—
329	#123	—	131	2	no	—
330	#123	—	131	2	no	—
331	#123	—	131	2	no	—
332	#123	—	131	2	no	—
333	#123	—	131	2	no	—
334	#123	—	131	2	no	—
335	#123	—	131	2	no	—
336	#123	C₂×D₁₃₁	1	2	yes	complemented
337	C₂²⋊Q₈	—	131	1	no	—
338	C₂²⋊Q₈	—	131	1	no	—
339	C₂²⋊Q₈	—	131	2	no	—
340	C₂²⋊Q₈	—	131	2	no	—
341	C₂²⋊Q₈	—	131	2	no	—
342	C₂²⋊Q₈	—	131	2	no	—
343	C₂²⋊Q₈	—	131	2	no	—
344	C₂²⋊Q₈	—	131	2	no	—
345	C₂²⋊Q₈	—	131	2	no	—
346	C₂²⋊Q₈	—	131	2	no	—
347	C₂²⋊Q₈	—	131	2	no	—
348	C₂²⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
349	#121	—	131	2	no	—
350	#121	—	131	2	no	—
351	#121	—	131	1	no	—
352	#121	—	131	1	no	—
353	#121	—	131	2	no	—
354	#121	C₂×D₁₃₁	1	1	yes	characteristic
355	#120	—	131	2	no	—
356	#120	—	131	2	no	—
357	#120	—	131	2	no	—
358	#120	—	131	2	no	—
359	C₄×Q₈	—	131	2	no	—
360	C₄×Q₈	—	131	2	no	—
361	C₄×Q₈	—	131	1	no	—
362	C₄×Q₈	—	131	1	no	—
363	C₄×Q₈	—	131	2	no	—
364	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
365	C₄×D₄	—	131	2	no	—
366	C₄×D₄	—	131	2	no	—
367	C₄×D₄	—	131	2	no	—
368	C₄×D₄	—	131	2	no	—
369	C₄×D₄	—	131	2	no	—
370	C₄×D₄	—	131	1	no	—
371	C₄×D₄	—	131	1	no	—
372	C₄×D₄	C₂×D₁₃₁	1	1	yes	characteristic
373	C₄×D₄	C₂×D₁₃₁	1	2	yes	complemented
374	#117	—	131	2	no	—
375	#117	—	131	2	no	—
376	#117	—	131	2	no	—
377	#117	—	131	2	no	—
378	#117	—	131	2	no	—
379	#117	C₂×D₁₃₁	1	2	yes	complemented
380	C₂×C₂²⋊C₄	—	131	2	no	—
381	C₂×C₂²⋊C₄	—	131	2	no	—
382	C₂×C₂²⋊C₄	—	131	2	no	—
383	C₂×C₄²	C₂×D₁₃₁	1	1	yes	characteristic, complemented
384	C₂⁴	—	131	2	no	—
385	C₂×Q₈	—	131	2	no	—
386	C₂×Q₈	—	131	2	no	—
387	C₂×Q₈	—	131	2	no	—
388	C₂×Q₈	—	131	1	no	—
389	C₂×Q₈	—	131	1	no	—
390	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
391	C₂×D₄	—	131	2	no	—
392	C₂×D₄	—	131	2	no	—
393	C₂×D₄	—	131	2	no	—
394	C₂×D₄	—	131	2	no	—
395	C₂×D₄	—	131	1	no	—
396	C₂×D₄	—	131	1	no	—
397	C₂×D₄	—	131	2	no	—
398	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
399	C₂×D₄	C₂²×D₁₃₁	1	2	yes	—
400	C₂²×C₄	—	131	2	no	—
401	C₂²×C₄	—	131	2	no	—
402	C₂²×C₄	—	131	2	no	—
403	C₂²×C₄	—	131	2	no	—
404	C₂²×C₄	—	131	2	no	—
405	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
406	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
407	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
408	C₂²×C₄	C₂²×D₁₃₁	1	2	yes	—
409	C₄⋊C₄	—	131	2	no	—
410	C₄⋊C₄	—	131	2	no	—
411	C₄⋊C₄	—	131	2	no	—
412	C₄⋊C₄	—	131	2	no	—
413	C₄⋊C₄	—	131	2	no	—
414	C₄⋊C₄	—	131	2	no	—
415	C₄⋊C₄	—	131	2	no	—
416	C₄⋊C₄	—	131	2	no	—
417	C₄⋊C₄	—	131	2	no	—
418	C₄⋊C₄	—	131	2	no	—
419	C₄⋊C₄	—	131	2	no	—
420	C₄⋊C₄	—	131	2	no	—
421	C₄⋊C₄	—	131	2	no	—
422	C₄⋊C₄	—	131	1	no	—
423	C₄⋊C₄	—	131	1	no	—
424	C₄⋊C₄	—	131	1	no	—
425	C₄⋊C₄	—	131	1	no	—
426	C₄⋊C₄	—	131	2	no	—
427	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
428	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
429	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
430	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
431	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
432	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
433	C₂²⋊C₄	—	131	2	no	—
434	C₂²⋊C₄	—	131	2	no	—
435	C₂²⋊C₄	—	131	2	no	—
436	C₂²⋊C₄	—	131	2	no	—
437	C₂²⋊C₄	—	131	2	no	—
438	C₂²⋊C₄	—	131	2	no	—
439	C₂²⋊C₄	—	131	2	no	—
440	C₂²⋊C₄	—	131	2	no	—
441	C₂²⋊C₄	—	131	2	no	—
442	C₂²⋊C₄	—	131	2	no	—
443	C₂²⋊C₄	—	131	2	no	—
444	C₂²⋊C₄	—	131	2	no	—
445	C₂²⋊C₄	—	131	2	no	—
446	C₂²⋊C₄	—	131	2	no	—
447	C₂²⋊C₄	—	131	2	no	—
448	C₂²⋊C₄	—	131	2	no	—
449	C₂²⋊C₄	—	131	2	no	—
450	C₂²⋊C₄	—	131	2	no	—
451	C₂²⋊C₄	—	131	2	no	—
452	C₂²⋊C₄	—	131	2	no	—
453	C₂²⋊C₄	—	131	2	no	—
454	C₂²⋊C₄	—	131	2	no	—
455	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
456	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
457	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
458	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
459	C₂²⋊C₄	C₂²×D₁₃₁	1	2	yes	—
460	C₄²	—	131	2	no	—
461	C₄²	—	131	2	no	—
462	C₄²	—	131	2	no	—
463	C₄²	—	131	2	no	—
464	C₄²	—	131	2	no	—
465	C₄²	—	131	2	no	—
466	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
467	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
468	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
469	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
470	C₄²	C₂²×D₁₃₁	1	2	yes	—
471	C₂³	—	524	2	no	—
472	C₂³	—	524	2	no	—
473	C₂³	—	524	2	no	—
474	C₂³	—	131	2	no	—
475	C₂³	—	131	2	no	—
476	C₂³	C₂³×D₁₃₁	1	2	yes	—
477	C₂³	C₂³×D₁₃₁	1	1	yes	characteristic
478	Q₈	—	4	1	no	—
479	Q₈	—	524	2	no	—
480	Q₈	—	524	1	no	—
481	Q₈	—	524	1	no	—
482	Q₈	—	524	2	no	—
483	Q₈	—	524	2	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	2	no	—
486	D₄	—	524	1	no	—
487	D₄	—	524	1	no	—
488	D₄	—	524	2	no	—
489	D₄	—	524	2	no	—
490	D₄	—	524	2	no	—
491	D₄	—	524	2	no	—
492	D₄	—	524	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	524	2	no	—
498	C₂×C₄	—	524	2	no	—
499	C₂×C₄	—	524	2	no	—
500	C₂×C₄	—	524	2	no	—
501	C₂×C₄	—	524	2	no	—
502	C₂×C₄	—	131	2	no	—
503	C₂×C₄	—	131	2	no	—
504	C₂×C₄	—	131	2	no	—
505	C₂×C₄	—	131	2	no	—
506	C₂×C₄	—	131	2	no	—
507	C₂×C₄	—	131	2	no	—
508	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
509	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
510	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
511	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
512	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
513	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
514	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
515	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
516	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
517	C₂²	—	2	1	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	262	2	no	—
524	C₂²	—	262	2	no	—
525	C₂²	—	262	2	no	—
526	C₂²	—	262	2	no	—
527	C₂²	—	262	2	no	—
528	C₂²	—	262	2	no	—
529	C₂²	—	1048	4	no	—
530	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	262	2	no	—
541	C₄	—	262	2	no	—
542	C₄	—	262	2	no	—
543	C₄	—	262	2	no	—
544	C₄	—	262	2	no	—
545	C₄	—	262	2	no	—
546	C₂	—	4	2	no	—
547	C₂	—	4	1	no	—
548	C₂	—	524	2	no	—
549	C₂	—	524	2	no	—
550	C₂	#22554148	1	1	yes	characteristic
551	C₂	#22554148	1	1	yes	characteristic
552	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	#3568
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. #22554066	C₂	semidirect
2. #22554066	C₂	semidirect
3. #22554062	C₂	semidirect
4. #22554054	C₂	semidirect
5. #22554034	C₂	semidirect
6. #22554030	C₂	semidirect
7. #22554029	C₂	semidirect
8. #22553991	C₂	semidirect
9. #22553987	C₂	semidirect
10. #22553986	C₂	semidirect
11. #22553932	C₂	semidirect
12. #22553930	C₂	semidirect
13. #22553927	C₂	semidirect
14. #22553898	C₂	semidirect
15. #22553895	C₂	semidirect
16. #22553894	C₂	semidirect
17. #22553846	C₂	semidirect
18. #22553846	C₂	semidirect
19. #529×C₁₃₁	C₂	semidirect
20. #16862245	C₂²	semidirect
21. #16862245	C₂²	semidirect
22. #16862244	C₂²	semidirect
23. #16862241	C₂²	semidirect
24. #16862241	C₂²	semidirect
25. #16862241	C₂²	semidirect
26. #16862241	C₂²	semidirect
27. #16862241	C₂²	semidirect
28. #16862240	C₂²	semidirect
29. #16862240	C₂²	semidirect
30. #16862240	C₂²	semidirect
31. #16862239	C₂²	semidirect
32. #16862239	C₂²	semidirect
33. #16862239	C₂²	semidirect
34. #16862239	C₂²	semidirect
35. #16862238	C₂²	semidirect
36. #16862238	C₂²	semidirect
41. #16862233	C₂²	semidirect
46. #16862232	C₂²	semidirect
47. #16862232	C₂²	semidirect
52. #16862229	C₂²	semidirect
53. #16862229	C₂²	semidirect
56. #16862226	C₂²	semidirect
57. #16862226	C₂²	semidirect
58. #16862225	C₂²	semidirect
59. #16862225	C₂²	semidirect
60. #16862225	C₂²	semidirect
61. #16862224	C₂²	semidirect
62. #16862224	C₂²	semidirect
63. #16862224	C₂²	semidirect
64. #16862224	C₂²	semidirect
65. #16862223	C₂²	semidirect
66. #16862223	C₂²	semidirect
75. #16862214	C₂²	semidirect
76. C₄×Dic₂₆₂	C₂²	semidirect
77. C₄×Dic₂₆₂	C₂²	semidirect
78. C₄×Dic₂₆₂	C₂²	semidirect
79. #16862211	C₂²	semidirect
80. #16862211	C₂²	semidirect
85. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
86. C₄×C₂²⋊D₁₃₁	C₂²	semidirect
88. #16862204	C₂²	semidirect
89. #16862203	C₂²	semidirect
90. #16862203	C₂²	semidirect
91. #16862203	C₂²	semidirect
92. #16862202	C₂²	semidirect
93. C₂×(C₂×D₁₃₁)⋊C₄	C₂²	semidirect
94. C₂²⋊C₄×D₁₃₁	C₂²	semidirect
95. C₂²⋊C₄×D₁₃₁	C₂²	semidirect
96. #126×C₁₃₁	C₂²	semidirect
97. #125×C₁₃₁	C₂²	semidirect
99. #123×C₁₃₁	C₂²	semidirect
100. C₂²⋊Q₈×C₁₃₁	C₂²	semidirect
102. C₄×Q₈×C₁₃₁	C₂²	semidirect
104. C₄×D₄×C₁₃₁	C₂²	semidirect
105. #117×C₁₃₁	C₂²	semidirect
106. C₂×C₄²×C₁₃₁	C₂²	semidirect
276. C₁₃₁	#3568	semidirect
296. #529	D₁₃₁	semidirect
312. #126	C₂×D₁₃₁	semidirect
315. #125	C₂×D₁₃₁	semidirect
336. #123	C₂×D₁₃₁	semidirect
348. C₂²⋊Q₈	C₂×D₁₃₁	semidirect
364. C₄×Q₈	C₂×D₁₃₁	semidirect
373. C₄×D₄	C₂×D₁₃₁	semidirect
379. #117	C₂×D₁₃₁	semidirect
383. 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
#22554066	2
#22554062	2
#22554054	2
#22554034	2
#22554030	2
#22554029	2
#22553991	2
#22553987	2
#22553986	2
#22553932	2
#22553930	2
#22553927	2
#22553898	2
#22553895	2
#22553894	2
#22553846	2
#529×C₁₃₁	2
#3568	131