Subgroups — (#14578514⋊C₂)⋊C₅ #37567261

Order 24390.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578514⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(D₂₇₁⋊C₃)⋊C₅	C₃	1	1	yes	maximal, characteristic
3	#14578514⋊C₂	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	(C₂₇₁⋊C₃)⋊C₅	C₂×C₃	1	1	yes	characteristic
5	D₂₇₁⋊C₅	C₉	1	1	yes	characteristic, complemented, Hall
6	#14578514	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₂₇₁⋊C₃	C₃×C₅	1	1	yes	characteristic
8	C₂₇₁⋊C₅	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₂₇₁⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic
10	D₂₇₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂₇₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅×C₉	—	271	1	no	maximal, Hall
13	C₅×C₉	—	271	1	no	Hall
14	C₂×C₃×C₅	—	271	1	no	—
15	C₂×C₉	—	271	1	no	Hall
16	C₃×C₅	—	271	1	no	—
17	C₂×C₅	—	2439	1	no	Hall
18	C₉	—	271	1	no	Sylow
19	C₂×C₃	—	271	1	no	—
20	C₅	—	2439	1	no	Sylow
21	C₃	—	271	1	no	—
22	C₂	—	2439	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂₇₁	C₂×C₅×C₉
prime radical	(D₂₇₁⋊C₃)⋊C₅	C₃
cosocle	C₂₇₁⋊C₃	C₂×C₃×C₅
LCS	G ▷ C₂₇₁
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.