Subgroups — C₅×(C₂²⋊C₉)⋊C₂ #67110

Order 360.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#67	—	3	1	no	maximal
3	C₅×D₉	—	4	1	no	maximal
4	(C₂²⋊C₉)⋊C₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₅	D₃	1	1	yes	characteristic
6	C₂×C₅×D₃	—	3	1	no	—
7	C₅×Dic₃	—	3	1	no	—
8	C₅×C₉	—	4	1	no	Hall
9	C₅×D₄	—	9	1	no	Hall
10	C₂²⋊C₉	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅	—	3	1	no	—
12	C₅×D₃	—	6	1	no	—
13	#67	—	3	1	no	—
14	C₂²×C₅	—	9	1	no	—
15	C₂²×C₅	D₉	1	1	yes	characteristic, complemented
16	C₄×C₅	—	9	1	no	—
17	D₉	—	4	1	no	—
18	C₃×C₅	S₄	1	1	yes	characteristic
19	C₂²×C₃	C₅×D₃	1	1	yes	characteristic
20	C₂×D₃	—	3	1	no	—
21	Dic₃	—	3	1	no	—
22	C₂×C₅	—	3	1	no	—
23	C₂×C₅	—	18	1	no	—
24	C₉	—	4	1	no	Sylow
25	D₄	—	9	1	no	Sylow
26	C₂×C₃	—	3	1	no	—
27	D₃	—	6	1	no	—
28	C₅	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²	—	9	1	no	—
30	C₂²	C₅×D₉	1	1	yes	characteristic, complemented
31	C₄	—	9	1	no	—
32	C₃	C₅×S₄	1	1	yes	characteristic
33	C₂	—	3	1	no	—
34	C₂	—	18	1	no	—

	subgroup	G/H
center, hypercenter	C₅	(C₂²⋊C₉)⋊C₂
commutator, cosocle, hypocenter	C₂²⋊C₉	C₂×C₅
Frattini	C₃	C₅×S₄
Fitting, socle	C₂²×C₃×C₅	D₃
LCS	G ▷ C₂²⋊C₉
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.