Subgroups — C₂²×#13133209 #20287968

Order 6784.

1192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133209	C₂	1	24	yes	maximal, direct product factor
2	C₂²×C₄⋊Dic₅₃	C₂	1	2	yes	maximal
3	C₂²×#11719919	C₂	1	4	yes	maximal
4	C₂²×C₄²×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₅₃	C₂²	1	4	yes	—
6	#13133209	C₂²	1	64	yes	direct product factor
7	C₂×C₄⋊Dic₅₃	C₂²	1	24	yes	—
8	C₂×#11719919	C₂²	1	48	yes	—
9	C₂³×C₄×C₅₃	C₂²	1	2	yes	—
10	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₅₃	C₂²	1	12	yes	—
12	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
13	C₂²×C₄×C₅₃	—	2	8	no	—
14	C₂²×C₄×C₅₃	Q₈	1	8	yes	—
15	C₂²×C₄×C₅₃	C₂³	1	12	yes	—
16	C₂²×C₄×C₅₃	C₂³	1	6	yes	—
17	C₂²×Dic₅₃	—	2	16	no	—
18	C₂²×Dic₅₃	C₂³	1	24	yes	—
19	C₄²×C₅₃	C₂³	1	16	yes	—
20	C₄⋊Dic₅₃	C₂³	1	32	yes	—
21	#11719919	C₂³	1	64	yes	—
22	C₂³×C₅₃	C₂×Q₈	1	4	yes	—
23	C₂³×C₅₃	#41	1	8	yes	—
24	C₂³×C₅₃	C₂⁴	1	3	yes	—
25	C₂×C₄×C₅₃	—	2	24	no	—
26	C₂×C₄×C₅₃	C₂×Q₈	1	24	yes	—
27	C₂×C₄×C₅₃	C₂⁴	1	8	yes	—
28	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
29	C₂×Dic₅₃	—	2	48	no	—
30	C₂×Dic₅₃	C₂⁴	1	16	yes	—
31	C₂²×C₅₃	#125	1	16	yes	complemented
32	C₂²×C₅₃	C₂²×Q₈	1	6	yes	—
33	C₂²×C₅₃	C₂×#41	1	12	yes	—
34	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
35	C₄×C₅₃	—	2	8	no	—
36	C₄×C₅₃	C₂²×Q₈	1	8	yes	—
37	Dic₅₃	—	2	16	no	—
38	C₂²×#125	—	53	1	no	maximal, Sylow
39	C₂×C₅₃	C₂×#125	1	12	yes	complemented
40	C₂×C₅₃	C₂³×Q₈	1	1	yes	characteristic
41	C₂×C₅₃	C₂²×#41	1	2	yes	—
42	C₂×#125	—	53	24	no	—
43	C₂²×C₄⋊C₄	—	53	4	no	—
44	C₂²×C₄⋊C₄	—	53	2	no	—
45	C₂²×C₄²	D₅₃	1	1	yes	characteristic
46	C₅₃	C₂²×#125	1	1	yes	characteristic, complemented, Sylow
47	C₂³×C₄	—	53	4	no	—
48	C₂³×C₄	C₂×D₅₃	1	2	yes	—
49	C₂³×C₄	C₂×D₅₃	1	1	yes	characteristic
50	#125	—	53	64	no	—
51	C₂×C₄⋊C₄	—	53	48	no	—
52	C₂×C₄⋊C₄	—	53	24	no	—
53	C₂×C₄²	C₂×D₅₃	1	12	yes	—
54	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
55	C₂²×C₄	—	2	8	no	—
56	C₂²×C₄	—	53	24	no	—
57	C₂²×C₄	—	106	16	no	—
58	C₂²×C₄	Dic₁₀₆	1	8	yes	—
59	C₂²×C₄	C₂²×D₅₃	1	12	yes	—
60	C₂²×C₄	C₂²×D₅₃	1	6	yes	—
61	C₄⋊C₄	—	53	64	no	—
62	C₄⋊C₄	—	53	32	no	—
63	C₄²	C₂²×D₅₃	1	16	yes	—
64	C₂³	C₂×Dic₁₀₆	1	4	yes	—
65	C₂³	#11719945	1	8	yes	—
66	C₂³	C₂³×D₅₃	1	3	yes	—
67	C₂×C₄	—	2	24	no	—
68	C₂×C₄	—	53	16	no	—
69	C₂×C₄	—	106	48	no	—
70	C₂×C₄	C₂×Dic₁₀₆	1	24	yes	—
71	C₂×C₄	C₂³×D₅₃	1	8	yes	—
72	C₂×C₄	C₂³×D₅₃	1	4	yes	—
73	C₂²	#13133209	1	16	yes	direct product factor
74	C₂²	C₂²×Dic₁₀₆	1	6	yes	—
75	C₂²	C₂×#11719945	1	12	yes	—
76	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
77	C₄	—	2	8	no	—
78	C₄	—	106	16	no	—
79	C₄	C₂²×Dic₁₀₆	1	8	yes	—
80	C₂	C₂×#13133209	1	12	yes	direct product factor
81	C₂	C₂³×Dic₁₀₆	1	1	yes	characteristic
82	C₂	C₂²×#11719945	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₅₃
commutator	C₂²×C₅₃	C₂⁵
Frattini	C₂²	C₂⁴×D₅₃
Fitting	C₂²×C₄²×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂³
hypercenter	C₂²×C₄²	D₅₃
hypocenter	C₅₃	C₂²×#125
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×#13133209	C₂	direct (N × H)
6. #13133209	C₂²	direct (N × H)
31. C₂²×C₅₃	#125	semidirect
39. C₂×C₅₃	C₂×#125	semidirect
46. C₅₃	C₂²×#125	semidirect
73. C₂²	#13133209	direct (N × H)
80. C₂	C₂×#13133209	direct (N × H)

Subgroups — C22×#13133209 #20287968

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13133209 #20287968