Subgroups — C₅⋊D₅×C₁₆₃⋊C₃ #37587361

Order 24450.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₆₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊D₅×C₁₆₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₅×C₁₆₃⋊C₃	—	5	6	no	maximal
4	C₅²×C₁₆₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₆₃⋊C₃	D₅	1	6	yes	complemented
6	D₅×C₁₆₃	—	5	6	no	—
7	C₂×C₁₆₃⋊C₃	—	25	1	no	Hall
8	C₅×C₁₆₃	C₃×D₅	1	6	yes	complemented
9	C₁₆₃⋊C₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₆₃	—	25	1	no	Hall
11	C₁₆₃	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₅⋊D₅	—	163	1	no	maximal, Hall
13	C₃×C₅²	—	163	1	no	Hall
14	C₅⋊D₅	C₁₆₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×D₅	—	815	6	no	—
16	C₅²	C₂×C₁₆₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅	—	163	6	no	—
18	D₅	—	5	6	no	—
19	C₂×C₃	—	4075	1	no	Hall
20	C₅	D₅×C₁₆₃⋊C₃	1	6	yes	complemented
21	C₃	—	163	1	no	Sylow
22	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₁₆₃	C₂×C₃
LCS	G ▷ C₅²×C₁₆₃
UCS	C₁

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.