Subgroups — C₂×C₅×C₂²⋊C₉ #67116

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	A₄
commutator, hypocenter	C₂²	C₂×C₅×C₉
Frattini	C₃	C₂×C₅×A₄
Fitting, socle, prime radical	C₂³×C₃×C₅	C₃
cosocle	C₂²×C₃	C₂×C₃×C₅
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₃×C₅

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×C₂²⋊C₉	C₂	direct (N × H)
4. C₂×C₂²⋊C₉	C₅	direct (N × H)
9. C₂³×C₅	C₉	semidirect
10. C₂²⋊C₉	C₂×C₅	direct (N × H)
17. C₂²×C₅	C₂×C₉	semidirect
25. C₂×C₅	C₂²⋊C₉	direct (N × H)
27. C₂³	C₅×C₉	semidirect
31. C₅	C₂×C₂²⋊C₉	direct (N × H)
34. C₂²	C₂×C₅×C₉	semidirect
38. C₂	C₅×C₂²⋊C₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₂²⋊C₉	2
C₂³×C₃×C₅	3
C₂×C₅×C₉	4
C₂×C₂²⋊C₉	5

Subgroups — C2×C5×C22⋊C9 #67116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₂²⋊C₉ #67116