Subgroups — C₄⋊#13133123 #20272911

Order 6784.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133123	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
3	#13133123	—	2	2	no	—
4	C₂×C₁₆×C₅₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₅₃	C₄	1	1	yes	characteristic
7	C₂×C₈×C₅₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₅₃	C₈	1	1	yes	characteristic
10	C₁₆×C₅₃	—	2	1	no	—
11	C₁₆×C₅₃	D₄	1	1	yes	characteristic
12	C₁₆×C₅₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₅₃	C₁₆	1	1	yes	characteristic
14	C₂×C₄×C₅₃	C₁₆	1	1	yes	characteristic
15	C₂×C₄×C₅₃	C₂×C₈	1	1	yes	characteristic
16	C₈×C₅₃	—	2	1	no	—
17	C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₅₃	M₁₆	1	1	yes	characteristic
19	C₂²×C₅₃	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₅₃	—	2	1	no	—
21	C₄×C₅₃	C₃₂	1	2	yes	complemented
22	C₄×C₅₃	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₅₃	M₃₂	1	1	yes	characteristic
24	C₄⋊C₃₂	—	53	1	no	maximal, Sylow
25	C₂×C₅₃	C₄⋊C₁₆	1	1	yes	characteristic
26	C₂×C₅₃	C₂×C₃₂	1	1	yes	characteristic
27	C₂×C₅₃	M₆₄	1	1	yes	characteristic
28	C₂×C₃₂	—	53	2	no	—
29	C₄×C₁₆	D₅₃	1	1	yes	characteristic
30	C₅₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	Dic₅₃	1	1	yes	characteristic
32	C₂×C₁₆	C₂×D₅₃	1	1	yes	characteristic
33	C₄×C₈	Dic₅₃	1	1	yes	characteristic
34	C₃₂	—	106	2	no	—
35	C₂×C₈	#88322	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₅₃	1	1	yes	characteristic
37	C₄²	#88322	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	Dic₁₀₆	1	1	yes	characteristic
40	C₁₆	D₂₁₂	1	1	yes	characteristic
41	C₂×C₄	#11719908	1	1	yes	characteristic
42	C₂×C₄	#11719908	1	1	yes	characteristic
43	C₂×C₄	C₂×#88322	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	#11719917	1	1	yes	characteristic
46	C₈	C₄⋊Dic₅₃	1	1	yes	characteristic
47	C₂²	C₂×#11719908	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	#13133123	1	2	yes	complemented
50	C₄	C₄⋊#88322	1	1	yes	characteristic
51	C₄	#13133157	1	1	yes	characteristic
52	C₂	C₄⋊#11719908	1	1	yes	characteristic
53	C₂	C₂×#13133123	1	1	yes	characteristic
54	C₂	#16810457	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₅₃
commutator	C₂×C₅₃	C₂×C₃₂
Fitting	C₄×C₁₆×C₅₃	C₂
socle	C₂²×C₅₃	C₂×C₁₆
hypercenter	C₄×C₁₆	D₅₃
hypocenter	C₅₃	C₄⋊C₃₂
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
21. C₄×C₅₃	C₃₂	semidirect
30. C₅₃	C₄⋊C₃₂	semidirect
49. C₄	#13133123	semidirect

Subgroups — C4⋊#13133123 #20272911

Conjugacy classes of subgroups

Complements

Subgroups — C₄⋊#13133123 #20272911