Subgroups — C₂×C₃×C₄₃×D₂₅ #27166366

Order 12900.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₄₃×D₂₅	C₂	direct (N × H)
2. C₂×C₃×C₂₅×C₄₃	C₂	semidirect
3. C₂×C₄₃×D₂₅	C₃	direct (N × H)
4. C₃×C₂₅×C₄₃	C₂²	semidirect
6. C₄₃×D₂₅	C₂×C₃	direct (N × H)
7. C₂×C₂₅×C₄₃	C₂×C₃	semidirect
10. C₂₅×C₄₃	C₂²×C₃	semidirect
16. C₂×C₃×D₂₅	C₄₃	direct (N × H)
18. C₂×C₃×C₄₃	D₂₅	direct (N × H)
21. C₂×C₃×C₂₅	C₂×C₄₃	semidirect
22. C₃×D₂₅	C₂×C₄₃	direct (N × H)
23. C₃×C₄₃	C₂×D₂₅	direct (N × H)
24. C₂×D₂₅	C₃×C₄₃	direct (N × H)
26. C₂×C₄₃	C₃×D₂₅	direct (N × H)
27. C₃×C₂₅	C₂²×C₄₃	semidirect
29. C₂×C₂₅	C₂×C₃×C₄₃	semidirect
30. D₂₅	C₂×C₃×C₄₃	direct (N × H)
31. C₄₃	C₂×C₃×D₂₅	direct (N × H)
34. C₂₅	C₂²×C₃×C₄₃	semidirect
41. C₂×C₃	C₄₃×D₂₅	direct (N × H)
44. C₃	C₂×C₄₃×D₂₅	direct (N × H)
46. C₂	C₃×C₄₃×D₂₅	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×D₂₅	2
C₂×C₃×C₂₅×C₄₃	2
C₂×C₄₃×D₂₅	3
C₂×C₃×D₅×C₄₃	5
C₂×C₃×D₂₅	43

Subgroups — C2×C3×C43×D25 #27166366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄₃×D₂₅ #27166366