Subgroups — #20289929

Order 6784.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811641	C₂	1	2	yes	maximal
2	#88324⋊C₈	C₂	1	4	yes	maximal, complemented
3	C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#13133284	C₄	1	4	yes	—
5	#13133274	C₄	1	4	yes	—
6	C₄×#88324	C₂²	1	4	yes	—
7	C₂×C₈×D₅₃	C₄	1	2	yes	—
8	C₄²×D₅₃	C₂²	1	1	yes	characteristic
9	C₄×#88322	C₄	1	1	yes	characteristic
10	C₈×Dic₅₃	C₂²	1	2	yes	—
11	C₄×C₈×C₅₃	C₄	1	1	yes	characteristic
12	C₂×C₄×D₅₃	C₂×C₄	1	2	yes	—
13	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
14	C₂×#88324	C₂×C₄	1	8	yes	—
15	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
16	C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₅₃	C₂×C₄	1	2	yes	—
18	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
19	C₂×#88322	C₂×C₄	1	2	yes	—
20	C₈×D₅₃	—	2	4	no	—
21	C₂²×D₅₃	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₅₃	C₄²	1	2	yes	—
23	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×Dic₅₃	C₄²	1	1	yes	characteristic
25	C₂×Dic₅₃	C₂²×C₄	1	2	yes	—
26	C₄×D₅₃	—	2	4	no	—
27	C₄×D₅₃	M₁₆	1	4	yes	—
28	#88324	—	2	8	no	—
29	C₈×C₅₃	—	2	2	no	—
30	#88322	—	2	2	no	—
31	C₂²×C₅₃	C₂×C₄²	1	1	yes	characteristic
32	C₂×D₅₃	—	2	2	no	—
33	C₂×D₅₃	#97	1	2	yes	—
34	C₄×C₅₃	—	2	2	no	—
35	C₄×C₅₃	C₂×M₁₆	1	2	yes	—
36	Dic₅₃	#97	1	2	yes	—
37	Dic₅₃	#131	1	4	yes	—
38	#1452	—	53	1	no	maximal, Sylow
39	C₂×C₅₃	C₂×#97	1	1	yes	characteristic
40	C₂×C₅₃	#405	1	2	yes	—
41	D₅₃	—	2	2	no	—
42	#431	—	53	2	no	—
43	C₂×C₄×C₈	—	53	1	no	—
44	#322	—	53	4	no	—
45	C₅₃	#1452	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₈	—	53	2	no	—
47	C₂×C₄²	—	53	1	no	—
48	C₄⋊C₈	—	53	4	no	—
49	C₂²⋊C₈	—	53	4	no	—
50	C₄×C₈	—	53	4	no	—
51	C₄×C₈	—	53	2	no	—
52	C₄×C₈	—	53	1	no	—
53	C₄×C₈	#6157	1	1	yes	characteristic
54	C₂²×C₄	—	53	1	no	—
55	C₂²×C₄	—	53	2	no	—
56	C₂×C₈	—	53	8	no	—
57	C₂×C₈	—	53	2	no	—
58	C₂×C₈	—	106	4	no	—
59	C₂×C₈	C₂×#6157	1	2	yes	—
60	C₄²	—	53	2	no	—
61	C₄²	—	53	1	no	—
62	C₄²	C₂×#6157	1	1	yes	characteristic
63	C₂³	—	53	1	no	—
64	C₂×C₄	—	53	1	no	—
65	C₂×C₄	—	53	2	no	—
66	C₂×C₄	—	53	4	no	—
67	C₂×C₄	—	106	4	no	—
68	C₂×C₄	C₄×#6157	1	2	yes	—
69	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	106	8	no	—
72	C₈	—	106	2	no	—
73	C₂²	—	53	2	no	—
74	C₂²	—	106	2	no	—
75	C₂²	C₂×C₄×#6157	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	53	2	no	—
78	C₄	—	53	4	no	—
79	C₄	D₅₃⋊M₁₆	1	2	yes	—
80	C₂	—	106	2	no	—
81	C₂	#16811582	1	1	yes	characteristic
82	C₂	#16811586	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6157
commutator, socle	C₂²×C₅₃	C₂×C₄²
Fitting	C₄×C₈×C₅₃	C₄
hypercenter	C₄×C₈	#6157
hypocenter	C₅₃	#1452
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #88324⋊C₈	C₂	semidirect
45. C₅₃	#1452	semidirect