Subgroups — C₅×C₁₃⋊D₂₄₇ #44545773

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	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃²×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₂₄₇	—	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	—	13	14	no	—
9	C₁₃⋊D₁₃	—	19	1	no	Hall
10	C₁₃×C₁₉	C₅×D₁₃	1	14	yes	complemented
11	C₅×D₁₉	—	169	1	no	Hall
12	C₁₃²	C₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
13	C₅×D₁₃	—	247	14	no	—
14	C₅×C₁₉	C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₃	D₂₄₇	1	14	yes	complemented
16	D₁₉	—	169	1	no	Hall
17	D₁₃	—	247	14	no	—
18	C₁₉	C₅×C₁₃⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
19	C₁₃	C₅×D₂₄₇	1	14	yes	complemented
20	C₂×C₅	—	3211	1	no	Hall
21	C₅	C₁₃⋊D₂₄₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	3211	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₁₃⋊D₂₄₇
commutator, cosocle, hypocenter	C₁₃²×C₁₉	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃²×C₁₉	C₂
LCS	G ▷ C₁₃²×C₁₉
UCS	C₁ ◁ C₅

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.