Subgroups — C₂×C₃⋊(C₃⋊Dic₁₅) #11762136

Order 1080.

448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊Dic₁₅)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊Dic₁₅	—	3	13	no	maximal
4	C₂×C₃³×C₅	C₄	1	2	yes	complemented
5	C₂×C₃³×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊(C₃⋊Dic₃)	—	5	1	no	maximal, Hall
7	C₂²×C₃²×C₅	D₃	1	13	yes	—
8	C₃⋊Dic₁₅	—	3	26	no	—
9	C₃³×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂×Dic₁₅	—	9	13	no	—
11	C₂²×C₃³	D₅	1	1	yes	characteristic
12	C₃⋊(C₃⋊Dic₃)	—	5	2	no	—
13	C₂×C₃²×C₅	Dic₃	1	26	yes	complemented
14	C₂×C₃²×C₅	C₂×D₃	1	13	yes	—
15	C₂×C₃⋊Dic₃	—	15	13	no	—
16	C₂²×C₃×C₅	C₃⋊D₃	1	13	yes	—
17	Dic₁₅	—	9	26	no	—
18	C₂×C₃³	Dic₅	1	2	yes	complemented
19	C₂×C₃³	C₂×D₅	1	1	yes	characteristic
20	C₃²×C₅	C₂×Dic₃	1	13	yes	complemented
21	C₂×Dic₅	—	27	1	no	Hall
22	C₂²×C₃²	D₁₅	1	13	yes	—
23	C₃⋊Dic₃	—	15	26	no	—
24	C₂×C₃×C₅	C₃⋊Dic₃	1	26	yes	complemented
25	C₂×C₃×C₅	C₂×C₃⋊D₃	1	13	yes	—
26	C₃³	C₂×Dic₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×Dic₃	—	45	13	no	—
28	C₂²×C₅	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
29	Dic₅	—	27	2	no	—
30	C₂×C₃²	Dic₁₅	1	26	yes	complemented
31	C₂×C₃²	C₂×D₁₅	1	13	yes	—
32	C₃×C₅	C₂×C₃⋊Dic₃	1	13	yes	complemented
33	C₂²×C₃	C₃⋊D₁₅	1	13	yes	—
34	Dic₃	—	45	26	no	—
35	C₂×C₅	C₃⋊(C₃⋊Dic₃)	1	2	yes	complemented
36	C₂×C₅	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
37	C₃²	C₂×Dic₁₅	1	13	yes	complemented
38	C₂×C₄	—	135	1	no	Sylow
39	C₂×C₃	C₃⋊Dic₁₅	1	26	yes	complemented
40	C₂×C₃	C₂×C₃⋊D₁₅	1	13	yes	—
41	C₅	C₂×C₃⋊(C₃⋊Dic₃)	1	1	yes	characteristic, complemented, Sylow
42	C₂²	C₃⋊(C₃⋊D₁₅)	1	1	yes	characteristic
43	C₄	—	135	2	no	—
44	C₃	C₂×C₃⋊Dic₁₅	1	13	yes	complemented
45	C₂	C₃⋊(C₃⋊Dic₁₅)	1	2	yes	direct product factor
46	C₂	C₂×C₃⋊(C₃⋊D₁₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊(C₃⋊D₁₅)
commutator, hypocenter	C₃³×C₅	C₂×C₄
Frattini	C₂	C₂×C₃⋊(C₃⋊D₁₅)
Fitting, socle, prime radical	C₂²×C₃³×C₅	C₂
cosocle	C₂×C₃³×C₅	C₂²
LCS	G ▷ C₃³×C₅
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₃⋊Dic₁₅)	C₂	direct (N × H)
4. C₂×C₃³×C₅	C₄	semidirect
9. C₃³×C₅	C₂×C₄	semidirect
13. C₂×C₃²×C₅	Dic₃	semidirect
18. C₂×C₃³	Dic₅	semidirect
20. C₃²×C₅	C₂×Dic₃	semidirect
24. C₂×C₃×C₅	C₃⋊Dic₃	semidirect
26. C₃³	C₂×Dic₅	semidirect
30. C₂×C₃²	Dic₁₅	semidirect
32. C₃×C₅	C₂×C₃⋊Dic₃	semidirect
35. C₂×C₅	C₃⋊(C₃⋊Dic₃)	semidirect
37. C₃²	C₂×Dic₁₅	semidirect
39. C₂×C₃	C₃⋊Dic₁₅	semidirect
41. C₅	C₂×C₃⋊(C₃⋊Dic₃)	semidirect
44. C₃	C₂×C₃⋊Dic₁₅	semidirect
45. C₂	C₃⋊(C₃⋊Dic₁₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃³×C₅	2
C₃⋊(C₃⋊Dic₁₅)	2
C₂×C₃⋊Dic₁₅	3
C₂×C₃⋊(C₃⋊Dic₃)	5

Subgroups — C2×C3⋊(C3⋊Dic15) #11762136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(C₃⋊Dic₁₅) #11762136