Subgroups — C₃²×D₅×C₅₃ #18012012

Order 4770.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₅×C₅₃	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₅₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₅₃	C₂×C₃	1	4	yes	complemented
5	D₅×C₅₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₅₃	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₅₃	—	5	4	no	—
8	C₅×C₅₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅₃	C₃×D₅	1	4	yes	direct product factor
10	C₂×C₅₃	—	5	1	no	Hall
11	C₃²×D₅	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅₃	C₃²×D₅	1	1	yes	characteristic, direct product factor, Sylow
13	C₃²×C₅	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₅	C₃×C₅₃	1	4	yes	direct product factor
15	C₂×C₃²	—	5	1	no	Hall
16	C₃×C₅	C₂×C₃×C₅₃	1	4	yes	complemented
17	D₅	C₃²×C₅₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃²	D₅×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	—	5	4	no	—
20	C₅	C₂×C₃²×C₅₃	1	1	yes	characteristic, complemented, Sylow
21	C₃	C₃×D₅×C₅₃	1	4	yes	direct product factor
22	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₅₃	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃²×C₅₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₅₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃²×C₅₃

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.