Subgroups — Dic₃×C₂₅×C₄₃ #27166340

Order 12900.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₅×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₅×C₄₃	—	3	1	no	maximal, Hall
3	C₃×C₂₅×C₄₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×Dic₃×C₄₃	C₅	1	1	yes	maximal, characteristic
5	C₂×C₂₅×C₄₃	D₃	1	1	yes	characteristic
6	C₂×C₃×C₅×C₄₃	C₂×C₅	1	1	yes	characteristic
7	C₂₅×C₄₃	Dic₃	1	1	yes	characteristic, direct product factor, Hall
8	C₄×C₅×C₄₃	—	3	1	no	—
9	C₃×C₅×C₄₃	C₄×C₅	1	1	yes	characteristic
10	Dic₃×C₄₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₄₃	C₅×D₃	1	1	yes	characteristic
12	Dic₃×C₂₅	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₄₃	C₂×C₂₅	1	1	yes	characteristic
14	C₅×C₄₃	C₅×Dic₃	1	1	yes	characteristic
15	C₄×C₄₃	—	3	1	no	Hall
16	C₂×C₃×C₂₅	C₂×C₄₃	1	1	yes	characteristic
17	C₃×C₄₃	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
18	C₄×C₂₅	—	3	1	no	Hall
19	C₂×C₄₃	D₃×C₂₅	1	1	yes	characteristic
20	C₃×C₂₅	C₄×C₄₃	1	1	yes	characteristic, complemented, Hall
21	C₅×Dic₃	C₅×C₄₃	1	1	yes	characteristic
22	C₂×C₂₅	D₃×C₄₃	1	1	yes	characteristic
23	C₄₃	Dic₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃×C₅	C₂×C₅×C₄₃	1	1	yes	characteristic
25	C₂₅	Dic₃×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₄×C₅	—	3	1	no	—
27	C₃×C₅	C₄×C₅×C₄₃	1	1	yes	characteristic
28	Dic₃	C₂₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₅	C₅×D₃×C₄₃	1	1	yes	characteristic
30	C₂×C₃	C₂×C₂₅×C₄₃	1	1	yes	characteristic
31	C₅	C₅×Dic₃×C₄₃	1	1	yes	characteristic
32	C₄	—	3	1	no	Sylow
33	C₃	C₄×C₂₅×C₄₃	1	1	yes	characteristic, complemented, Sylow
34	C₂	D₃×C₂₅×C₄₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₂₅×C₄₃	D₃
commutator, hypocenter	C₃	C₄×C₂₅×C₄₃
Frattini	C₂×C₅	C₅×D₃×C₄₃
Fitting	C₂×C₃×C₂₅×C₄₃	C₂
socle, prime radical	C₂×C₃×C₅×C₄₃	C₂×C₅
cosocle	C₂×C₃×C₅	C₂×C₅×C₄₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₂₅×C₄₃

Complements

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

N	H ≅ G/N	type
3. C₃×C₂₅×C₄₃	C₄	semidirect
7. C₂₅×C₄₃	Dic₃	direct (N × H)
10. Dic₃×C₄₃	C₂₅	direct (N × H)
12. Dic₃×C₂₅	C₄₃	direct (N × H)
17. C₃×C₄₃	C₄×C₂₅	semidirect
20. C₃×C₂₅	C₄×C₄₃	semidirect
23. C₄₃	Dic₃×C₂₅	direct (N × H)
25. C₂₅	Dic₃×C₄₃	direct (N × H)
28. Dic₃	C₂₅×C₄₃	direct (N × H)
33. C₃	C₄×C₂₅×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₂₅×C₄₃	2
C₄×C₂₅×C₄₃	3
C₅×Dic₃×C₄₃	5
Dic₃×C₂₅	43

Subgroups — Dic3×C25×C43 #27166340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×C₂₅×C₄₃ #27166340