Subgroups — C₃⋊D₂₄₄₅ #28412708

Order 14670.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₄₄₅	—	3	4	no	maximal
3	C₃⋊D₄₈₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₆₃	D₃	1	4	yes	complemented
5	D₈₁₅	—	9	1	no	Hall
6	C₃²×C₁₆₃	D₅	1	1	yes	characteristic, complemented, Hall
7	D₄₈₉	—	15	4	no	—
8	C₅×C₁₆₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₆₃	D₁₅	1	4	yes	complemented
10	D₁₆₃	—	45	1	no	Hall
11	C₁₆₃	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
12	C₃⋊D₁₅	—	163	1	no	maximal, Hall
13	C₃²×C₅	D₁₆₃	1	1	yes	characteristic, complemented, Hall
14	D₁₅	—	489	4	no	—
15	C₃⋊D₃	—	815	1	no	Hall
16	C₃×C₅	D₄₈₉	1	4	yes	complemented
17	D₅	—	1467	1	no	Hall
18	C₃²	D₈₁₅	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	2445	4	no	—
20	C₅	C₃⋊D₄₈₉	1	1	yes	characteristic, complemented, Sylow
21	C₃	D₂₄₄₅	1	4	yes	complemented
22	C₂	—	7335	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₁₆₃	C₂
LCS	G ▷ C₃²×C₅×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.