Subgroups — C₂²×D₅₃⋊C₁₃ #72275889

Order 5512.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅₃⋊C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₅₃⋊C₁₃	C₂	1	6	yes	maximal, direct product factor
3	C₂×C₅₃⋊C₁₃	C₂²	1	3	yes	complemented
4	D₅₃⋊C₁₃	C₂²	1	4	yes	direct product factor
5	C₅₃⋊C₁₃	C₂³	1	1	yes	characteristic, complemented, Hall
6	C₂²×D₅₃	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
7	C₂²×C₅₃	C₂×C₁₃	1	1	yes	characteristic, complemented
8	C₂×D₅₃	C₂×C₁₃	1	6	yes	complemented
9	C₂×C₅₃	C₂²×C₁₃	1	3	yes	complemented
10	D₅₃	C₂²×C₁₃	1	4	yes	complemented
11	C₂³×C₁₃	—	53	1	no	maximal, Hall
12	C₅₃	C₂³×C₁₃	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₁₃	—	53	6	no	—
14	C₂²×C₁₃	—	53	1	no	—
15	C₂×C₁₃	—	53	4	no	—
16	C₂×C₁₃	—	53	3	no	—
17	C₁₃	—	53	1	no	Sylow
18	C₂³	—	53	1	no	Sylow
19	C₂²	—	53	6	no	—
20	C₂²	D₅₃⋊C₁₃	1	1	yes	characteristic, direct product factor
21	C₂	—	53	4	no	—
22	C₂	C₂×D₅₃⋊C₁₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₅₃⋊C₁₃
commutator, cosocle, hypocenter	C₅₃	C₂³×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅₃	C₂×C₁₃
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂²

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.