Subgroups — C₅⋊(C₁₃⋊D₂₄₇) #44545779

Order 32110.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊D₂₄₇	—	5	1	no	maximal, Hall
3	C₁₃²×C₁₉	D₅	1	1	yes	characteristic, complemented, Hall
4	D₁₂₃₅	—	13	14	no	maximal
5	C₅⋊(C₁₃⋊D₁₃)	—	19	1	no	maximal, Hall
6	C₅×C₁₃×C₁₉	D₁₃	1	14	yes	complemented
7	C₅×C₁₃²	D₁₉	1	1	yes	characteristic, complemented, Hall
8	D₂₄₇	—	65	14	no	—
9	C₁₃⋊D₁₃	—	95	1	no	Hall
10	C₁₃×C₁₉	D₆₅	1	14	yes	complemented
11	D₉₅	—	169	1	no	Hall
12	C₁₃²	D₉₅	1	1	yes	characteristic, complemented, Sylow
13	D₆₅	—	247	14	no	—
14	C₅×C₁₉	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₃	D₂₄₇	1	14	yes	complemented
16	D₁₉	—	845	1	no	Hall
17	D₁₃	—	1235	14	no	—
18	C₁₉	C₅⋊(C₁₃⋊D₁₃)	1	1	yes	characteristic, complemented, Sylow
19	C₁₃	D₁₂₃₅	1	14	yes	complemented
20	D₅	—	3211	1	no	Hall
21	C₅	C₁₃⋊D₂₄₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	16055	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₃²×C₁₉	C₂
LCS	G ▷ C₅×C₁₃²×C₁₉
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.