Subgroups — C₃×(C₅⋊D₅)⋊D₄₃ #27166451

Order 12900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₂₁₅	C₂	1	2	yes	maximal, complemented
3	(C₅⋊D₅)⋊D₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₅×D₄₃	—	5	2	no	maximal
6	C₄₃×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×D₂₁₅	C₂×C₃	1	2	yes	complemented
8	C₃×D₂₁₅	D₅	1	2	yes	complemented
9	C₃×D₅×C₄₃	—	5	2	no	—
10	C₃×D₅×C₄₃	—	10	2	no	—
11	C₃×C₅×D₄₃	—	5	2	no	—
12	C₅²×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
13	D₅×D₄₃	—	5	2	no	—
14	C₃×C₅×C₄₃	—	2	2	no	—
15	C₃×C₅×C₄₃	C₂×D₅	1	2	yes	complemented
16	C₂×C₃×D₄₃	—	25	1	no	Hall
17	D₂₁₅	C₃×D₅	1	2	yes	complemented
18	C₅×D₄₃	—	5	2	no	—
19	D₅×C₄₃	—	5	2	no	—
20	D₅×C₄₃	—	10	2	no	—
21	C₃×D₅²	—	43	1	no	maximal, Hall
22	C₂×C₃×C₄₃	—	25	1	no	—
23	C₃×D₄₃	—	5	2	no	—
24	C₅×C₄₃	—	2	2	no	—
25	C₅×C₄₃	C₂×C₃×D₅	1	2	yes	complemented
26	C₂×D₄₃	—	25	1	no	Hall
27	C₃×C₅⋊D₅	D₄₃	1	1	yes	characteristic, complemented
28	C₃×C₅×D₅	—	43	2	no	—
29	C₃×C₄₃	D₅²	1	1	yes	characteristic, complemented, Hall
30	D₅²	—	43	1	no	Hall
31	C₂×C₄₃	—	25	1	no	—
32	D₄₃	—	5	2	no	—
33	C₃×C₅²	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×D₅	—	215	2	no	—
35	C₅⋊D₅	C₃×D₄₃	1	1	yes	characteristic, complemented
36	C₅×D₅	—	43	2	no	—
37	C₄₃	C₃×D₅²	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃×C₅	—	215	2	no	—
39	C₃×D₅	—	5	2	no	—
40	C₃×D₅	—	10	2	no	—
41	C₃×D₅	—	43	2	no	—
42	C₅²	C₂×C₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₅	—	215	2	no	—
44	C₃×C₅	—	2	2	no	—
45	C₃×C₅	D₅×D₄₃	1	2	yes	complemented
46	C₂²×C₃	—	1075	1	no	Hall
47	C₂×C₅	—	215	2	no	—
48	D₅	—	5	2	no	—
49	D₅	—	10	2	no	—
50	D₅	—	43	2	no	—
51	C₂×C₃	—	25	1	no	—
52	C₂×C₃	—	215	2	no	—
53	C₅	—	2	2	no	—
54	C₅	C₃×D₅×D₄₃	1	2	yes	complemented
55	C₂²	—	1075	1	no	Sylow
56	C₃	(C₅⋊D₅)⋊D₄₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	—	25	1	no	—
58	C₂	—	215	2	no	—

	subgroup	G/H
center, hypercenter	C₃	(C₅⋊D₅)⋊D₄₃
commutator, cosocle, hypocenter	C₅²×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₄₃	C₂²
LCS	G ▷ C₅²×C₄₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₃×C₅⋊D₅	C₂	semidirect
2. C₃×C₅×D₂₁₅	C₂	semidirect
3. (C₅⋊D₅)⋊D₄₃	C₃	direct (N × H)
4. C₃×C₅²×C₄₃	C₂²	semidirect
6. C₄₃×C₅⋊D₅	C₂×C₃	semidirect
7. C₅×D₂₁₅	C₂×C₃	semidirect
8. C₃×D₂₁₅	D₅	semidirect
12. C₅²×C₄₃	C₂²×C₃	semidirect
15. C₃×C₅×C₄₃	C₂×D₅	semidirect
17. D₂₁₅	C₃×D₅	semidirect
25. C₅×C₄₃	C₂×C₃×D₅	semidirect
27. C₃×C₅⋊D₅	D₄₃	semidirect
29. C₃×C₄₃	D₅²	semidirect
33. C₃×C₅²	C₂×D₄₃	semidirect
35. C₅⋊D₅	C₃×D₄₃	semidirect
37. C₄₃	C₃×D₅²	semidirect
42. C₅²	C₂×C₃×D₄₃	semidirect
45. C₃×C₅	D₅×D₄₃	semidirect
54. C₅	C₃×D₅×D₄₃	semidirect
56. C₃	(C₅⋊D₅)⋊D₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄₃×C₅⋊D₅	2
C₃×C₅×D₂₁₅	2
(C₅⋊D₅)⋊D₄₃	3
C₃×D₅×D₄₃	5
C₃×D₅²	43

Subgroups — C3×(C5⋊D5)⋊D43 #27166451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×(C₅⋊D₅)⋊D₄₃ #27166451