Subgroups — D₅×C₂²⋊C₉ #67112

Order 360.

40 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	C₂²×C₃×D₅	C₃	1	1	yes	maximal, characteristic
3	C₉×D₅	—	4	1	no	maximal
4	C₂×C₂²⋊C₉	—	5	1	no	maximal, Hall
5	C₂²×C₃×C₅	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×D₅	—	3	1	no	—
7	C₂×C₃×D₅	—	3	1	no	—
8	C₅×C₉	—	4	1	no	Hall
9	C₂²×D₅	C₉	1	1	yes	characteristic, complemented, Hall
10	C₂²⋊C₉	D₅	1	1	yes	characteristic, direct product factor
11	C₂×C₃×C₅	—	3	1	no	—
12	C₃×D₅	—	3	1	no	—
13	C₃×D₅	A₄	1	1	yes	characteristic
14	C₂³×C₃	—	5	1	no	—
15	C₂²×C₅	C₂×C₉	1	1	yes	characteristic, complemented
16	C₂×D₅	—	3	1	no	—
17	C₂×D₅	—	3	1	no	—
18	C₂×C₉	—	20	1	no	—
19	C₃×C₅	C₂×A₄	1	1	yes	characteristic
20	C₂²×C₃	—	15	1	no	—
21	C₂²×C₃	—	15	1	no	—
22	C₂²×C₃	C₃×D₅	1	1	yes	characteristic
23	C₂×C₅	—	3	1	no	—
24	D₅	—	3	1	no	—
25	D₅	C₂²⋊C₉	1	1	yes	characteristic, direct product factor
26	C₉	—	4	1	no	Sylow
27	C₂³	—	5	1	no	Sylow
28	C₂×C₃	—	3	1	no	—
29	C₂×C₃	—	5	1	no	—
30	C₂×C₃	—	15	1	no	—
31	C₅	C₂×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	15	1	no	—
33	C₂²	—	15	1	no	—
34	C₂²	C₉×D₅	1	1	yes	characteristic, complemented
35	C₃	D₅×A₄	1	1	yes	characteristic
36	C₂	—	3	1	no	—
37	C₂	—	5	1	no	—
38	C₂	—	15	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₅×A₄
commutator, hypocenter	C₂²×C₅	C₂×C₉
Fitting, socle, cosocle	C₂²×C₃×C₅	C₂×C₃
prime radical	C₂²×C₃×D₅	C₃
LCS	G ▷ C₂²×C₅
UCS	C₁ ◁ C₃

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.