Subgroups — C₃×D₃×C₅⋊D₅ #11744713

Order 900.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅⋊D₅	—	3	1	no	maximal
5	D₃×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₅²	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₃×D₅	—	5	6	no	maximal
8	C₂×C₃×C₅²	—	3	1	no	—
9	C₃⋊(C₅⋊D₅)	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅²×D₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×C₅⋊D₅	—	2	1	no	—
12	C₃×C₅⋊D₅	—	3	1	no	—
13	C₃×C₅⋊D₅	D₃	1	1	yes	characteristic, direct product factor
14	C₃×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×C₅⋊D₅	—	3	1	no	Hall
16	C₃×D₁₅	—	5	6	no	—
17	C₃×C₅×D₃	D₅	1	6	yes	complemented
18	C₃²×D₅	—	5	6	no	—
19	C₃×C₅²	—	2	1	no	—
20	C₃×C₅²	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅²	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂×C₃×D₅	—	15	6	no	—
23	D₃×D₅	—	5	6	no	—
24	C₂×C₅²	—	3	1	no	—
25	C₅⋊D₅	—	3	1	no	—
26	C₅⋊D₅	C₃×D₃	1	1	yes	characteristic, direct product factor
27	C₃²×C₅	C₂×D₅	1	6	yes	complemented
28	C₂×C₃×D₃	—	25	1	no	Hall
29	C₂×C₃×C₅	—	3	6	no	—
30	D₁₅	—	5	6	no	—
31	C₃×D₅	—	5	6	no	—
32	C₃×D₅	—	5	6	no	—
33	C₃×D₅	—	10	6	no	—
34	C₃×D₅	—	15	6	no	—
35	C₅×D₃	C₃×D₅	1	6	yes	complemented
36	C₅²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₅	—	15	6	no	—
38	C₂×C₃²	—	25	1	no	—
39	C₃×D₃	—	25	1	no	—
40	C₃×D₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor
41	C₃×C₅	—	2	6	no	—
42	C₃×C₅	D₃×D₅	1	6	yes	complemented
43	C₃×C₅	C₂×C₃×D₅	1	6	yes	complemented
44	C₂²×C₃	—	75	1	no	—
45	C₂×D₃	—	25	1	no	—
46	C₂×C₅	—	3	6	no	—
47	D₅	—	5	6	no	—
48	D₅	—	15	6	no	—
49	C₃²	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	3	1	no	—
51	C₂×C₃	—	25	1	no	—
52	C₂×C₃	—	25	1	no	—
53	C₂×C₃	—	50	1	no	—
54	C₂×C₃	—	75	1	no	—
55	D₃	—	25	1	no	—
56	D₃	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor
57	C₅	C₃×D₃×D₅	1	6	yes	complemented
58	C₂²	—	75	1	no	Sylow
59	C₃	—	2	1	no	—
60	C₃	D₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor
61	C₃	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
62	C₂	—	3	1	no	—
63	C₂	—	25	1	no	—
64	C₂	—	75	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃×C₅⋊D₅
commutator, cosocle, hypocenter	C₃×C₅²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅²	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₃⋊(C₅⋊D₅)	C₂	semidirect
2. C₃×C₅²×D₃	C₂	semidirect
3. C₃²×C₅⋊D₅	C₂	semidirect
5. D₃×C₅⋊D₅	C₃	direct (N × H)
6. C₃²×C₅²	C₂²	semidirect
9. C₃⋊(C₅⋊D₅)	C₂×C₃	semidirect
10. C₅²×D₃	C₂×C₃	semidirect
13. C₃×C₅⋊D₅	D₃	direct (N × H)
14. C₃×C₅⋊D₅	C₂×C₃	semidirect
17. C₃×C₅×D₃	D₅	semidirect
20. C₃×C₅²	C₂×D₃	semidirect
21. C₃×C₅²	C₂²×C₃	semidirect
26. C₅⋊D₅	C₃×D₃	direct (N × H)
27. C₃²×C₅	C₂×D₅	semidirect
35. C₅×D₃	C₃×D₅	semidirect
36. C₅²	C₂×C₃×D₃	semidirect
40. C₃×D₃	C₅⋊D₅	direct (N × H)
42. C₃×C₅	D₃×D₅	semidirect
43. C₃×C₅	C₂×C₃×D₅	semidirect
49. C₃²	C₂×C₅⋊D₅	semidirect
56. D₃	C₃×C₅⋊D₅	direct (N × H)
57. C₅	C₃×D₃×D₅	semidirect
60. C₃	D₃×C₅⋊D₅	direct (N × H)
61. C₃	C₂×C₃×C₅⋊D₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃⋊(C₅⋊D₅)	2
C₃×C₅²×D₃	2
C₃²×C₅⋊D₅	2
C₂×C₃×C₅⋊D₅	3
D₃×C₅⋊D₅	3
C₃×D₃×D₅	5

Subgroups — C3×D3×C5⋊D5 #11744713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₅⋊D₅ #11744713