Subgroups — C₄×D₃×C₂₅ #10597040

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₂₅	—	3	1	no	maximal, Hall
5	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	D₃×C₂₅	C₄	1	2	yes	direct product factor
7	C₄×C₅×D₃	C₅	1	1	yes	maximal, characteristic
8	C₂²×C₂₅	—	3	1	no	—
9	C₄×C₂₅	—	3	1	no	—
10	C₄×C₂₅	D₃	1	1	yes	characteristic, direct product factor
11	C₃×C₂₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×D₃	C₂×C₅	1	1	yes	characteristic
13	C₃×C₄×C₅	C₂×C₅	1	1	yes	characteristic
14	C₅×Dic₃	C₂×C₅	1	1	yes	characteristic
15	C₂×C₂₅	—	3	2	no	—
16	C₂×C₂₅	C₂×D₃	1	1	yes	characteristic
17	C₂×C₄×C₅	—	3	1	no	—
18	C₂×C₃×C₅	C₂²×C₅	1	1	yes	characteristic
19	C₅×D₃	C₄×C₅	1	2	yes	—
20	C₂₅	C₄×D₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₄×D₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂²×C₅	—	3	1	no	—
23	C₄×C₅	—	3	1	no	—
24	C₄×C₅	C₅×D₃	1	1	yes	characteristic
25	C₃×C₅	C₂×C₄×C₅	1	1	yes	characteristic
26	C₂×D₃	C₂×C₂₅	1	1	yes	characteristic
27	C₃×C₄	C₂×C₂₅	1	1	yes	characteristic, complemented
28	Dic₃	C₂×C₂₅	1	1	yes	characteristic, complemented
29	C₂×C₅	—	3	2	no	—
30	C₂×C₅	C₂×C₅×D₃	1	1	yes	characteristic
31	C₂×C₄	—	3	1	no	Sylow
32	C₂×C₃	C₂²×C₂₅	1	1	yes	characteristic
33	D₃	C₄×C₂₅	1	2	yes	direct product factor
34	C₅	C₄×C₅×D₃	1	1	yes	characteristic
35	C₂²	—	3	1	no	—
36	C₄	—	3	1	no	—
37	C₄	D₃×C₂₅	1	1	yes	characteristic, direct product factor
38	C₃	C₂×C₄×C₂₅	1	1	yes	characteristic, complemented, Sylow
39	C₂	—	3	2	no	—
40	C₂	C₂×D₃×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₂₅	D₃
commutator, hypocenter	C₃	C₂×C₄×C₂₅
Frattini	C₂×C₅	C₂×C₅×D₃
Fitting	C₃×C₄×C₂₅	C₂
socle, cosocle	C₂×C₃×C₅	C₂²×C₅
prime radical	C₂×C₅×D₃	C₂×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₄×C₂₅

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₂₅	C₂	semidirect
3. Dic₃×C₂₅	C₂	semidirect
6. D₃×C₂₅	C₄	direct (N × H)
10. C₄×C₂₅	D₃	direct (N × H)
11. C₃×C₂₅	C₂×C₄	semidirect
20. C₂₅	C₄×D₃	direct (N × H)
21. C₄×D₃	C₂₅	direct (N × H)
27. C₃×C₄	C₂×C₂₅	semidirect
28. Dic₃	C₂×C₂₅	semidirect
33. D₃	C₄×C₂₅	direct (N × H)
37. C₄	D₃×C₂₅	direct (N × H)
38. C₃	C₂×C₄×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×C₂₅	2
C₃×C₄×C₂₅	2
Dic₃×C₂₅	2
C₂×C₄×C₂₅	3
C₄×C₅×D₃	5

Subgroups — C4×D3×C25 #10597040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₃×C₂₅ #10597040