Subgroups — C₂×D₂₅×C₄₃⋊C₃ #27166350

Order 12900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₅×C₄₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄₃×D₂₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂₅×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₅×C₄₃⋊C₃	—	5	1	no	maximal
6	C₄₃×D₂₅	C₂×C₃	1	2	yes	complemented
7	C₂×C₂₅×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₅×C₄₃⋊C₃	D₅	1	1	yes	characteristic
9	D₅×C₄₃⋊C₃	—	5	2	no	—
10	C₂₅×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅×C₄₃	—	5	1	no	—
12	C₅×C₄₃⋊C₃	C₂×D₅	1	1	yes	characteristic
13	C₂²×C₄₃⋊C₃	—	25	1	no	Hall
14	C₂×C₅×C₄₃	C₃×D₅	1	1	yes	characteristic
15	D₅×C₄₃	—	5	2	no	—
16	C₂×C₃×D₂₅	—	43	1	no	maximal, Hall
17	C₂×C₄₃⋊C₃	—	25	2	no	—
18	C₂×C₄₃⋊C₃	D₂₅	1	1	yes	characteristic, direct product factor
19	C₅×C₄₃	C₂×C₃×D₅	1	1	yes	characteristic
20	C₂²×C₄₃	—	25	1	no	Hall
21	C₂×C₃×C₂₅	—	43	1	no	—
22	C₃×D₂₅	—	43	2	no	—
23	C₄₃⋊C₃	C₂×D₂₅	1	1	yes	characteristic, direct product factor, Hall
24	C₂×D₂₅	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₄₃	—	25	2	no	—
26	C₂×C₄₃	C₃×D₂₅	1	1	yes	characteristic, complemented
27	C₃×C₂₅	—	43	1	no	Hall
28	C₂×C₃×D₅	—	215	1	no	—
29	C₂×C₂₅	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
30	D₂₅	C₂×C₄₃⋊C₃	1	2	yes	direct product factor
31	C₄₃	C₂×C₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₅	—	43	1	no	—
33	C₃×D₅	—	215	2	no	—
34	C₂₅	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	5	1	no	—
36	C₃×C₅	—	43	1	no	—
37	C₂²×C₃	—	1075	1	no	Hall
38	C₂×C₅	D₅×C₄₃⋊C₃	1	1	yes	characteristic
39	D₅	—	5	2	no	—
40	C₂×C₃	—	43	1	no	—
41	C₂×C₃	—	1075	2	no	—
42	C₅	C₂×D₅×C₄₃⋊C₃	1	1	yes	characteristic
43	C₂²	—	25	1	no	Sylow
44	C₃	—	43	1	no	Sylow
45	C₂	—	25	2	no	—
46	C₂	D₂₅×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₂₅×C₄₃⋊C₃
commutator, cosocle, hypocenter	C₂₅×C₄₃	C₂²×C₃
Frattini	C₅	C₂×D₅×C₄₃⋊C₃
Fitting	C₂×C₂₅×C₄₃	C₂×C₃
socle	C₂×C₅×C₄₃	C₃×D₅
LCS	G ▷ C₂₅×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₅×C₄₃⋊C₃	C₂	semidirect
2. D₂₅×C₄₃⋊C₃	C₂	direct (N × H)
3. C₂×C₄₃×D₂₅	C₃	semidirect
4. C₂₅×C₄₃⋊C₃	C₂²	semidirect
6. C₄₃×D₂₅	C₂×C₃	semidirect
7. C₂×C₂₅×C₄₃	C₂×C₃	semidirect
10. C₂₅×C₄₃	C₂²×C₃	semidirect
18. C₂×C₄₃⋊C₃	D₂₅	direct (N × H)
23. C₄₃⋊C₃	C₂×D₂₅	direct (N × H)
24. C₂×D₂₅	C₄₃⋊C₃	direct (N × H)
26. C₂×C₄₃	C₃×D₂₅	semidirect
29. C₂×C₂₅	C₂×C₄₃⋊C₃	semidirect
30. D₂₅	C₂×C₄₃⋊C₃	direct (N × H)
31. C₄₃	C₂×C₃×D₂₅	semidirect
34. C₂₅	C₂²×C₄₃⋊C₃	semidirect
46. C₂	D₂₅×C₄₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₅×C₄₃⋊C₃	2
D₂₅×C₄₃⋊C₃	2
C₂×C₄₃×D₂₅	3
C₂×D₅×C₄₃⋊C₃	5
C₂×C₃×D₂₅	43

Subgroups — C2×D25×C43⋊C3 #27166350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₂₅×C₄₃⋊C₃ #27166350