Subgroups — C₅×C₃⋊D₃×C₅₃ #18012018

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	C₅×D₃×C₅₃	—	3	4	no	maximal
3	C₃⋊D₃×C₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₅₃	D₃	1	4	yes	complemented
5	C₂×C₅×C₅₃	—	9	1	no	Hall
6	C₃²×C₅₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₃×C₅₃	—	3	4	no	—
8	C₅×C₅₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₅₃	C₅×D₃	1	4	yes	complemented
10	C₂×C₅₃	—	9	1	no	Hall
11	C₅×C₃⋊D₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅₃	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₃²×C₅	C₂×C₅₃	1	1	yes	characteristic, complemented, Hall
14	C₅×D₃	—	3	4	no	—
15	C₃⋊D₃	C₅×C₅₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅	D₃×C₅₃	1	4	yes	complemented
17	C₂×C₅	—	9	1	no	Hall
18	C₃²	C₂×C₅×C₅₃	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	3	4	no	—
20	C₅	C₃⋊D₃×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₅×D₃×C₅₃	1	4	yes	complemented
22	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₅₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₅×C₅₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₅₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×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.