Subgroups — C₃×D₄×C₂₅ #10597050

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₂₅	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₂₅	—	2	2	no	—
5	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	C₃×C₅×D₄	C₅	1	1	yes	maximal, characteristic
7	C₂²×C₂₅	C₂×C₃	1	2	yes	complemented
8	C₄×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×C₂₅	D₄	1	1	yes	characteristic, direct product factor, Hall
10	C₂²×C₃×C₅	C₂×C₅	1	2	yes	—
11	C₃×C₄×C₅	C₂×C₅	1	1	yes	characteristic
12	C₂×C₂₅	—	2	2	no	—
13	C₂×C₂₅	C₂²×C₃	1	1	yes	characteristic
14	C₅×D₄	C₃×C₅	1	1	yes	characteristic
15	C₂×C₃×C₅	—	2	2	no	—
16	C₂×C₃×C₅	C₂²×C₅	1	1	yes	characteristic
17	C₂₅	C₃×D₄	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×D₄	C₂₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₅	C₂×C₃×C₅	1	2	yes	—
20	C₄×C₅	C₂×C₃×C₅	1	1	yes	characteristic
21	C₃×C₅	C₅×D₄	1	1	yes	characteristic
22	C₂²×C₃	C₂×C₂₅	1	2	yes	complemented
23	C₃×C₄	C₂×C₂₅	1	1	yes	characteristic, complemented
24	C₂×C₅	—	2	2	no	—
25	C₂×C₅	C₂²×C₃×C₅	1	1	yes	characteristic
26	D₄	C₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	2	2	no	—
28	C₂×C₃	C₂²×C₂₅	1	1	yes	characteristic
29	C₅	C₃×C₅×D₄	1	1	yes	characteristic
30	C₂²	C₂×C₃×C₂₅	1	2	yes	complemented
31	C₄	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
32	C₃	D₄×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	—	2	2	no	—
34	C₂	C₂²×C₃×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₂₅	C₂²
commutator	C₂	C₂²×C₃×C₂₅
Frattini, cosocle	C₂×C₅	C₂²×C₃×C₅
socle	C₂×C₃×C₅	C₂²×C₅
prime radical	C₃×C₅×D₄	C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₂₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₂₅	C₂	semidirect
2. C₃×C₄×C₂₅	C₂	semidirect
3. D₄×C₂₅	C₃	direct (N × H)
7. C₂²×C₂₅	C₂×C₃	semidirect
8. C₄×C₂₅	C₂×C₃	semidirect
9. C₃×C₂₅	D₄	direct (N × H)
17. C₂₅	C₃×D₄	direct (N × H)
18. C₃×D₄	C₂₅	direct (N × H)
22. C₂²×C₃	C₂×C₂₅	semidirect
23. C₃×C₄	C₂×C₂₅	semidirect
26. D₄	C₃×C₂₅	direct (N × H)
30. C₂²	C₂×C₃×C₂₅	semidirect
31. C₄	C₂×C₃×C₂₅	semidirect
32. C₃	D₄×C₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₂₅	2
C₃×C₄×C₂₅	2
D₄×C₂₅	3
C₃×C₅×D₄	5

Subgroups — C3×D4×C25 #10597050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×C₂₅ #10597050