Subgroups — #30680441

Order 16768.

910 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22554066	C₂	1	2	yes	maximal, complemented
2	#22554061	C₂	1	2	yes	maximal, complemented
3	#22554042	C₂	1	1	yes	maximal, characteristic, complemented
4	#22554040	C₂	1	1	yes	maximal, characteristic, complemented
5	#22554039	C₂	1	1	yes	maximal, characteristic, complemented
6	#22554035	C₂	1	1	yes	maximal, characteristic, complemented
7	#22554034	C₂	1	1	yes	maximal, characteristic, complemented
8	#22554034	C₂	1	2	yes	maximal, complemented
9	#22554034	C₂	1	1	yes	maximal, characteristic, complemented
10	#22554018	C₂	1	1	yes	maximal, characteristic, complemented
11	#22553994	C₂	1	2	yes	maximal, complemented
12	#22553939	C₂	1	2	yes	maximal, complemented
13	#22553936	C₂	1	1	yes	maximal, characteristic
14	#22553934	C₂	1	1	yes	maximal, characteristic
15	#22553925	C₂	1	1	yes	maximal, characteristic, complemented
16	#22553921	C₂	1	2	yes	maximal, complemented
17	#22553921	C₂	1	2	yes	maximal, complemented
18	#22553920	C₂	1	2	yes	maximal, complemented
19	#22553920	C₂	1	1	yes	maximal, characteristic, complemented
20	#22553866	C₂	1	1	yes	maximal, characteristic, complemented
21	#22553866	C₂	1	1	yes	maximal, characteristic, complemented
22	#22553847	C₂	1	1	yes	maximal, characteristic
23	#557×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	#16862246	C₂²	1	1	yes	characteristic
25	#16862245	C₂²	1	1	yes	characteristic
26	#16862245	C₂²	1	1	yes	characteristic
27	#16862245	C₂²	1	2	yes	—
28	#16862245	C₂²	1	1	yes	characteristic
29	#16862245	C₂²	1	2	yes	—
30	#16862244	C₂²	1	1	yes	characteristic
31	#16862244	C₂²	1	1	yes	characteristic
32	#16862244	C₂²	1	1	yes	characteristic
33	#16862244	C₂²	1	2	yes	—
34	#16862244	C₂²	1	2	yes	—
35	#16862241	C₂²	1	2	yes	—
36	#16862241	C₂²	1	2	yes	—
37	#16862241	C₂²	1	2	yes	—
38	#16862241	C₂²	1	2	yes	—
39	#16862241	C₂²	1	2	yes	—
40	#16862241	C₂²	1	2	yes	—
41	#16862241	C₂²	1	2	yes	—
42	#16862241	C₂²	1	2	yes	—
43	#16862241	C₂²	1	2	yes	—
44	#16862240	C₂²	1	2	yes	—
45	#16862240	C₂²	1	2	yes	—
46	#16862240	C₂²	1	2	yes	—
47	#16862240	C₂²	1	2	yes	—
48	#16862238	C₂²	1	2	yes	—
49	#16862238	C₂²	1	2	yes	—
50	#16862237	C₂²	1	2	yes	—
51	#16862237	C₂²	1	1	yes	characteristic
52	#16862237	C₂²	1	2	yes	—
53	#16862236	C₂²	1	1	yes	characteristic
54	#16862236	C₂²	1	1	yes	characteristic
55	#16862236	C₂²	1	2	yes	—
56	#16862236	C₂²	1	2	yes	—
57	#16862236	C₂²	1	2	yes	—
58	#16862236	C₂²	1	2	yes	—
59	#16862236	C₂²	1	2	yes	—
60	#16862236	C₂²	1	2	yes	—
61	#16862235	C₂²	1	1	yes	characteristic
62	#16862235	C₂²	1	2	yes	—
63	#16862234	C₂²	1	2	yes	—
64	#16862234	C₂²	1	1	yes	characteristic
65	#16862234	C₂²	1	1	yes	characteristic
66	#16862231	C₂²	1	2	yes	—
67	#16862231	C₂²	1	2	yes	—
68	#16862231	C₂²	1	2	yes	—
69	#16862226	C₂²	1	1	yes	characteristic
70	#16862226	C₂²	1	1	yes	characteristic
71	#16862226	C₂²	1	1	yes	characteristic
72	#16862226	C₂²	1	2	yes	—
73	#16862224	C₂²	1	1	yes	characteristic
74	#16862224	C₂²	1	1	yes	characteristic
75	#16862224	C₂²	1	2	yes	—
76	#16862224	C₂²	1	2	yes	—
77	#16862224	C₂²	1	2	yes	—
78	#16862224	C₂²	1	2	yes	—
79	#16862224	C₂²	1	2	yes	—
80	#16862224	C₂²	1	2	yes	—
81	#16862222	C₂²	1	1	yes	characteristic
82	#16862222	C₂²	1	1	yes	characteristic
83	#16862222	C₂²	1	2	yes	—
84	#16862222	C₂²	1	2	yes	—
85	#16862221	C₂²	1	1	yes	characteristic
86	C₄×Dic₂₆₂	C₂²	1	2	yes	—
87	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
88	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
89	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
90	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
91	C₄×Dic₂₆₂	C₂²	1	1	yes	characteristic
92	C₄×Dic₂₆₂	C₂²	1	2	yes	—
93	#16862211	C₂²	1	2	yes	—
94	#16862211	C₂²	1	2	yes	—
95	#16862211	C₂²	1	1	yes	characteristic
96	#16862211	C₂²	1	1	yes	characteristic
97	#16862211	C₂²	1	1	yes	characteristic
98	#16862211	C₂²	1	1	yes	characteristic
99	C₄×D₅₂₄	C₂²	1	1	yes	characteristic
100	#16862208	C₂²	1	1	yes	characteristic
101	#16862208	C₂²	1	2	yes	—
102	#16862208	C₂²	1	1	yes	characteristic
103	#16862204	C₂²	1	2	yes	—
104	#16862204	C₂²	1	2	yes	—
105	#16862203	C₂²	1	1	yes	characteristic
106	#16862203	C₂²	1	1	yes	characteristic
107	#16862203	C₂²	1	2	yes	—
108	#16862203	C₂²	1	2	yes	—
109	#16862203	C₂²	1	2	yes	—
110	C₄⋊C₄×D₁₃₁	C₂²	1	2	yes	—
111	C₄²×D₁₃₁	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
113	C₄⋊Q₈×C₁₃₁	C₂²	1	2	yes	—
114	#125×C₁₃₁	C₂²	1	2	yes	—
115	#125×C₁₃₁	C₂²	1	2	yes	—
116	#125×C₁₃₁	C₂²	1	1	yes	characteristic
117	#125×C₁₃₁	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
119	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
121	C₄×Q₈×C₁₃₁	C₂²	1	2	yes	—
122	C₄×Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
123	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
124	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
125	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
126	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₆₂	C₂³	1	2	yes	—
128	C₂×Dic₂₆₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₆₂	C₂³	1	2	yes	—
130	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
131	C₂×D₅₂₄	C₂³	1	2	yes	—
132	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
134	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
136	C₂×C₄×D₁₃₁	C₂³	1	2	yes	—
137	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
140	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
144	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
145	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
146	C₄⋊Dic₁₃₁	C₂³	1	2	yes	—
147	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
148	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
149	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
150	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
151	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
152	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
153	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
154	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
155	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
156	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
157	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
158	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
159	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
160	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
161	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
162	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
163	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
164	Dic₁₃₁⋊C₄	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	1	yes	characteristic
168	Dic₁₃₁⋊C₄	C₂³	1	2	yes	—
169	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
170	Dic₁₃₁⋊C₄	C₂³	1	1	yes	characteristic
171	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
172	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
173	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₃₁)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₃₁)⋊C₄	C₂³	1	2	yes	—
188	C₄×Dic₁₃₁	C₂³	1	2	yes	—
189	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
190	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₃₁	C₂³	1	2	yes	—
193	C₄×Dic₁₃₁	C₂³	1	2	yes	—
194	C₄×Dic₁₃₁	C₂³	1	2	yes	—
195	C₄×Dic₁₃₁	C₂³	1	2	yes	—
196	C₄×Dic₁₃₁	C₂³	1	2	yes	—
197	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₃₁	C₂³	1	1	yes	characteristic
199	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
200	C₂×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
201	C₂×Q₈×C₁₃₁	C₂³	1	2	yes	—
202	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
203	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
204	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
205	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
206	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
207	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
208	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
209	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
210	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
216	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
217	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
218	C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
219	C₄²×C₁₃₁	C₂³	1	2	yes	—
220	C₄²×C₁₃₁	C₂³	1	2	yes	—
221	C₄²×C₁₃₁	C₂³	1	2	yes	—
222	C₂²×D₁₃₁	C₂⁴	1	1	yes	characteristic
223	C₂²×D₁₃₁	C₂⁴	1	2	yes	—
224	Dic₂₆₂	—	2	2	no	—
225	Dic₂₆₂	—	2	2	no	—
226	Dic₂₆₂	—	2	2	no	—
227	Dic₂₆₂	—	2	2	no	—
228	Dic₂₆₂	—	4	1	no	—
229	Dic₂₆₂	—	4	2	no	—
230	Dic₂₆₂	—	4	2	no	—
231	D₅₂₄	—	2	2	no	—
232	D₅₂₄	—	4	2	no	—
233	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
234	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
235	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
236	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
237	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
238	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
239	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
240	C₂×Dic₁₃₁	C₂⁴	1	2	yes	—
241	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₁₃₁	C₂⁴	1	1	yes	characteristic
243	C₄×D₁₃₁	—	2	2	no	—
244	C₄×D₁₃₁	—	2	2	no	—
245	C₄×D₁₃₁	—	2	4	no	—
246	C₄×D₁₃₁	—	4	2	no	—
247	C₄×D₁₃₁	—	4	2	no	—
248	C₄×D₁₃₁	—	4	1	no	—
249	Q₈×C₁₃₁	—	2	2	no	—
250	Q₈×C₁₃₁	—	4	1	no	—
251	Q₈×C₁₃₁	—	4	2	no	—
252	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
258	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₃₁	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
263	C₂²×C₁₃₁	C₂⁵	1	1	yes	characteristic
264	C₂×D₁₃₁	—	2	1	no	—
265	C₂×D₁₃₁	—	2	2	no	—
266	C₂×D₁₃₁	—	2	1	no	—
267	C₂×D₁₃₁	—	2	2	no	—
268	C₂×D₁₃₁	—	2	2	no	—
269	C₂×D₁₃₁	—	2	1	no	—
270	C₄×C₁₃₁	—	2	2	no	—
271	C₄×C₁₃₁	—	2	1	no	—
272	C₄×C₁₃₁	—	2	2	no	—
273	C₄×C₁₃₁	—	2	1	no	—
274	C₄×C₁₃₁	—	2	1	no	—
275	C₄×C₁₃₁	—	2	1	no	—
276	C₄×C₁₃₁	—	2	1	no	—
277	C₄×C₁₃₁	—	2	1	no	—
278	C₄×C₁₃₁	—	2	2	no	—
279	C₄×C₁₃₁	—	2	2	no	—
280	C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
281	Dic₁₃₁	—	2	1	no	—
282	Dic₁₃₁	—	2	1	no	—
283	Dic₁₃₁	—	2	1	no	—
284	Dic₁₃₁	—	2	2	no	—
285	Dic₁₃₁	—	2	2	no	—
286	Dic₁₃₁	—	2	1	no	—
287	Dic₁₃₁	—	2	2	no	—
288	Dic₁₃₁	—	2	1	no	—
289	Dic₁₃₁	—	2	1	no	—
290	Dic₁₃₁	2₋¹⁺⁴	1	2	yes	—
291	C₂×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
292	C₂×C₁₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
293	C₂×C₁₃₁	#585	1	1	yes	characteristic
294	D₁₃₁	—	4	1	no	—
295	D₁₃₁	—	4	2	no	—
296	C₁₃₁	#3555	1	1	yes	characteristic, complemented, Sylow
297	#3555	—	131	1	no	maximal, Sylow
298	#563	—	131	2	no	—
299	#563	—	131	2	no	—
300	Q₈²	—	131	1	no	—
301	#557	—	131	1	no	—
302	#557	—	131	1	no	—
303	#557	D₁₃₁	1	1	yes	characteristic, complemented
304	#556	—	131	2	no	—
305	#556	—	131	1	no	—
306	#556	—	131	1	no	—
307	#556	—	131	1	no	—
308	#554	—	131	1	no	—
309	#552	—	131	2	no	—
310	#544	—	131	2	no	—
311	#542	—	131	1	no	—
312	#542	—	131	1	no	—
313	#541	—	131	2	no	—
314	#541	—	131	2	no	—
315	#541	—	131	1	no	—
316	#541	—	131	1	no	—
317	#541	—	131	2	no	—
318	#533	—	131	1	no	—
319	#533	—	131	1	no	—
320	#529	—	131	1	no	—
321	C₄⋊Q₈	—	131	1	no	—
322	C₄⋊Q₈	—	131	1	no	—
323	C₄⋊Q₈	—	131	1	no	—
324	C₄⋊Q₈	—	131	2	no	—
325	C₄⋊Q₈	—	131	2	no	—
326	C₄⋊Q₈	—	131	1	no	—
327	C₄⋊Q₈	—	131	1	no	—
328	C₄⋊Q₈	—	131	2	no	—
329	C₄⋊Q₈	—	131	1	no	—
330	C₄⋊Q₈	—	131	2	no	—
331	C₄⋊Q₈	—	131	1	no	—
332	C₄⋊Q₈	C₂×D₁₃₁	1	1	yes	characteristic
333	C₄⋊Q₈	C₂×D₁₃₁	1	2	yes	—
334	#126	—	131	2	no	—
335	#126	—	131	2	no	—
336	#126	—	131	2	no	—
337	#126	—	131	2	no	—
338	#126	—	131	2	no	—
339	#126	—	131	2	no	—
340	#126	—	131	2	no	—
341	#126	—	131	2	no	—
342	#126	—	131	2	no	—
343	#126	—	131	2	no	—
344	#126	—	131	2	no	—
345	#126	—	131	2	no	—
346	#126	—	131	2	no	—
347	#125	—	131	1	no	—
348	#125	—	131	1	no	—
349	#125	—	131	2	no	—
350	#125	—	131	2	no	—
351	#125	—	131	2	no	—
352	#125	—	131	2	no	—
353	#125	—	131	2	no	—
354	#125	—	131	2	no	—
355	#125	—	131	2	no	—
356	#125	—	131	2	no	—
357	#125	—	131	1	no	—
358	#125	—	131	2	no	—
359	#125	—	131	2	no	—
360	#125	C₂×D₁₃₁	1	1	yes	characteristic
361	#125	C₂×D₁₃₁	1	2	yes	—
362	#125	C₂×D₁₃₁	1	1	yes	characteristic
363	#125	C₂×D₁₃₁	1	2	yes	—
364	#124	—	131	1	no	—
365	#124	—	131	2	no	—
366	#124	—	131	1	no	—
367	#124	—	131	1	no	—
368	#124	—	131	2	no	—
369	#123	—	131	2	no	—
370	#123	—	131	2	no	—
371	#123	—	131	2	no	—
372	C₂²⋊Q₈	—	131	1	no	—
373	C₂²⋊Q₈	—	131	1	no	—
374	C₂²⋊Q₈	—	131	2	no	—
375	C₂²⋊Q₈	—	131	2	no	—
376	C₂²⋊Q₈	—	131	1	no	—
377	C₂²⋊Q₈	—	131	1	no	—
378	C₂²⋊Q₈	—	131	2	no	—
379	C₂²⋊Q₈	—	131	2	no	—
380	C₂²⋊Q₈	—	131	2	no	—
381	C₂²⋊Q₈	—	131	2	no	—
382	C₂²⋊Q₈	—	131	2	no	—
383	C₂²⋊Q₈	—	131	2	no	—
384	C₂²⋊Q₈	—	131	1	no	—
385	C₂²⋊Q₈	—	131	1	no	—
386	C₂²⋊Q₈	—	131	1	no	—
387	C₂²⋊Q₈	—	131	2	no	—
388	#121	—	131	1	no	—
389	C₄×Q₈	—	131	1	no	—
390	C₄×Q₈	—	131	2	no	—
391	C₄×Q₈	—	131	2	no	—
392	C₄×Q₈	—	131	1	no	—
393	C₄×Q₈	—	131	1	no	—
394	C₄×Q₈	—	131	1	no	—
395	C₄×Q₈	—	131	2	no	—
396	C₄×Q₈	—	131	1	no	—
397	C₄×Q₈	—	131	1	no	—
398	C₄×Q₈	—	131	1	no	—
399	C₄×Q₈	—	131	1	no	—
400	C₄×Q₈	—	131	2	no	—
401	C₄×Q₈	—	131	1	no	—
402	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic
403	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic
404	C₄×Q₈	C₂×D₁₃₁	1	2	yes	—
405	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic
406	C₄×Q₈	C₂×D₁₃₁	1	1	yes	characteristic
407	C₄×D₄	—	131	2	no	—
408	C₄×D₄	—	131	1	no	—
409	C₄×D₄	—	131	1	no	—
410	C₄×D₄	—	131	1	no	—
411	#117	—	131	2	no	—
412	#117	—	131	2	no	—
413	#117	—	131	1	no	—
414	#117	—	131	1	no	—
415	#117	—	131	2	no	—
416	#117	—	131	2	no	—
417	#117	—	131	2	no	—
418	C₂×C₄⋊C₄	—	131	2	no	—
419	C₂×C₄²	—	131	1	no	—
420	C₂×Q₈	—	131	1	no	—
421	C₂×Q₈	—	131	1	no	—
422	C₂×Q₈	—	131	1	no	—
423	C₂×Q₈	—	131	1	no	—
424	C₂×Q₈	—	131	1	no	—
425	C₂×Q₈	—	131	2	no	—
426	C₂×Q₈	—	131	2	no	—
427	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
428	C₂×Q₈	C₂²×D₁₃₁	1	1	yes	characteristic
429	C₂×Q₈	C₂²×D₁₃₁	1	2	yes	—
430	C₂×D₄	—	131	1	no	—
431	C₂×D₄	—	131	2	no	—
432	C₂²×C₄	—	131	1	no	—
433	C₂²×C₄	—	131	1	no	—
434	C₂²×C₄	—	131	2	no	—
435	C₂²×C₄	—	131	1	no	—
436	C₂²×C₄	—	131	2	no	—
437	C₂²×C₄	—	131	2	no	—
438	C₄⋊C₄	—	131	1	no	—
439	C₄⋊C₄	—	131	2	no	—
440	C₄⋊C₄	—	131	1	no	—
441	C₄⋊C₄	—	131	2	no	—
442	C₄⋊C₄	—	131	1	no	—
443	C₄⋊C₄	—	131	1	no	—
444	C₄⋊C₄	—	131	1	no	—
445	C₄⋊C₄	—	131	2	no	—
446	C₄⋊C₄	—	131	1	no	—
447	C₄⋊C₄	—	131	1	no	—
448	C₄⋊C₄	—	131	1	no	—
449	C₄⋊C₄	—	131	1	no	—
450	C₄⋊C₄	—	131	2	no	—
451	C₄⋊C₄	—	131	2	no	—
452	C₄⋊C₄	—	131	2	no	—
453	C₄⋊C₄	—	131	2	no	—
454	C₄⋊C₄	—	131	2	no	—
455	C₄⋊C₄	—	131	2	no	—
456	C₄⋊C₄	—	131	2	no	—
457	C₄⋊C₄	—	131	1	no	—
458	C₄⋊C₄	—	131	2	no	—
459	C₄⋊C₄	—	131	2	no	—
460	C₄⋊C₄	—	131	2	no	—
461	C₄⋊C₄	—	131	2	no	—
462	C₄⋊C₄	—	131	2	no	—
463	C₄⋊C₄	—	131	2	no	—
464	C₄⋊C₄	—	131	2	no	—
465	C₄⋊C₄	—	131	1	no	—
466	C₄⋊C₄	—	131	1	no	—
467	C₄⋊C₄	—	131	2	no	—
468	C₄⋊C₄	—	131	1	no	—
469	C₄⋊C₄	—	131	1	no	—
470	C₄⋊C₄	—	131	2	no	—
471	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
472	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
473	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
474	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
475	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
476	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
477	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
479	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
481	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
482	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
483	C₄⋊C₄	C₂²×D₁₃₁	1	2	yes	—
484	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
485	C₂²⋊C₄	—	131	2	no	—
486	C₂²⋊C₄	—	131	2	no	—
487	C₂²⋊C₄	—	131	1	no	—
488	C₂²⋊C₄	—	131	1	no	—
489	C₂²⋊C₄	—	131	2	no	—
490	C₂²⋊C₄	—	131	2	no	—
491	C₂²⋊C₄	—	131	2	no	—
492	C₂²⋊C₄	—	131	2	no	—
493	C₂²⋊C₄	—	131	1	no	—
494	C₂²⋊C₄	—	131	2	no	—
495	C₂²⋊C₄	—	131	1	no	—
496	C₂²⋊C₄	—	131	2	no	—
497	C₂²⋊C₄	—	131	2	no	—
498	C₂²⋊C₄	—	131	2	no	—
499	C₂²⋊C₄	—	131	2	no	—
500	C₂²⋊C₄	—	131	2	no	—
501	C₂²⋊C₄	—	131	2	no	—
502	C₄²	—	131	1	no	—
503	C₄²	—	131	1	no	—
504	C₄²	—	131	1	no	—
505	C₄²	—	131	2	no	—
506	C₄²	—	131	1	no	—
507	C₄²	—	131	2	no	—
508	C₄²	—	131	1	no	—
509	C₄²	—	131	2	no	—
510	C₄²	—	131	2	no	—
511	C₄²	—	131	2	no	—
512	C₄²	—	131	2	no	—
513	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
514	C₄²	C₂²×D₁₃₁	1	2	yes	—
515	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
516	C₄²	C₂²×D₁₃₁	1	1	yes	characteristic
517	C₄²	C₂²×D₁₃₁	1	2	yes	—
518	C₄²	C₂²×D₁₃₁	1	2	yes	—
519	C₂³	—	131	1	no	—
520	C₂³	—	131	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	262	2	no	—
525	Q₈	—	262	2	no	—
526	Q₈	—	262	2	no	—
527	Q₈	—	262	2	no	—
528	Q₈	—	524	1	no	—
529	Q₈	—	524	2	no	—
530	Q₈	—	524	2	no	—
531	D₄	—	262	2	no	—
532	D₄	—	524	2	no	—
533	C₂×C₄	—	262	2	no	—
534	C₂×C₄	—	262	4	no	—
535	C₂×C₄	—	262	2	no	—
536	C₂×C₄	—	524	2	no	—
537	C₂×C₄	—	524	2	no	—
538	C₂×C₄	—	524	1	no	—
539	C₂×C₄	—	131	1	no	—
540	C₂×C₄	—	131	1	no	—
541	C₂×C₄	—	131	2	no	—
542	C₂×C₄	—	131	2	no	—
543	C₂×C₄	—	131	1	no	—
544	C₂×C₄	—	131	1	no	—
545	C₂×C₄	—	131	1	no	—
546	C₂×C₄	—	131	2	no	—
547	C₂×C₄	—	131	1	no	—
548	C₂×C₄	—	131	1	no	—
549	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
550	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
551	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
552	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
553	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
555	C₂×C₄	C₂³×D₁₃₁	1	2	yes	—
556	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
558	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
559	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
560	C₂²	—	262	1	no	—
561	C₂²	—	262	2	no	—
562	C₂²	—	262	1	no	—
563	C₂²	—	262	2	no	—
564	C₂²	—	262	2	no	—
565	C₂²	—	262	1	no	—
566	C₂²	C₂⁴×D₁₃₁	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	1	no	—
577	C₄	—	262	1	no	—
578	C₄	—	262	1	no	—
579	C₄	—	262	1	no	—
580	C₄	—	262	2	no	—
581	C₄	—	262	2	no	—
582	C₄	—	262	1	no	—
583	C₄	—	262	2	no	—
584	C₄	—	262	1	no	—
585	C₄	—	262	1	no	—
586	C₄	—	131	2	no	—
587	C₄	#16862294	1	2	yes	—
588	C₂	—	524	1	no	—
589	C₂	—	524	2	no	—
590	C₂	2₋¹⁺⁴×D₁₃₁	1	1	yes	characteristic
591	C₂	C₂×#16862294	1	1	yes	characteristic
592	C₂	#22554148	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃₁
commutator, socle, cosocle	C₂²×C₁₃₁	C₂⁵
Fitting	#557×C₁₃₁	C₂
prime radical	#16862221	C₂²
hypercenter	#557	D₁₃₁
hypocenter	C₁₃₁	#3555
LCS	G ▷ C₂²×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ #557

Complements

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

N	H ≅ G/N	type
1. #22554066	C₂	semidirect
2. #22554061	C₂	semidirect
3. #22554042	C₂	semidirect
4. #22554040	C₂	semidirect
5. #22554039	C₂	semidirect
6. #22554035	C₂	semidirect
7. #22554034	C₂	semidirect
8. #22554034	C₂	semidirect
9. #22554034	C₂	semidirect
10. #22554018	C₂	semidirect
11. #22553994	C₂	semidirect
12. #22553939	C₂	semidirect
15. #22553925	C₂	semidirect
16. #22553921	C₂	semidirect
17. #22553921	C₂	semidirect
18. #22553920	C₂	semidirect
19. #22553920	C₂	semidirect
20. #22553866	C₂	semidirect
21. #22553866	C₂	semidirect
23. #557×C₁₃₁	C₂	semidirect
296. C₁₃₁	#3555	semidirect
303. #557	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
#22554061	2
#22554042	2
#22554040	2
#22554039	2
#22554035	2
#22554034	2
#22554018	2
#22553994	2
#22553939	2
#22553936	2
#22553934	2
#22553925	2
#22553921	2
#22553920	2
#22553866	2
#22553847	2
#557×C₁₃₁	2
#3555	131