Subgroups — C₃×C₄×D₂₅ #10597035

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	C₃×D₂₅	C₄	1	2	yes	direct product factor
7	C₃×C₄×D₅	—	5	1	no	maximal
8	C₂×D₂₅	C₂×C₃	1	1	yes	characteristic
9	C₄×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
10	Dic₂₅	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×C₂₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×D₅	—	5	1	no	—
13	C₃×C₄×C₅	D₅	1	1	yes	characteristic
14	C₃×Dic₅	—	5	1	no	—
15	C₂×C₂₅	C₂²×C₃	1	1	yes	characteristic
16	D₂₅	C₃×C₄	1	2	yes	direct product factor
17	C₄×D₅	—	5	1	no	—
18	C₂×C₃×C₅	C₂×D₅	1	1	yes	characteristic
19	C₃×D₅	—	5	2	no	—
20	C₂₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₄	—	25	1	no	Hall
22	C₂×D₅	—	5	1	no	—
23	C₄×C₅	C₃×D₅	1	1	yes	characteristic
24	Dic₅	—	5	1	no	—
25	C₃×C₅	C₄×D₅	1	1	yes	characteristic
26	C₂²×C₃	—	25	1	no	—
27	C₃×C₄	—	25	1	no	—
28	C₃×C₄	D₂₅	1	1	yes	characteristic, direct product factor
29	C₂×C₅	C₂×C₃×D₅	1	1	yes	characteristic
30	D₅	—	5	2	no	—
31	C₂×C₄	—	25	1	no	Sylow
32	C₂×C₃	—	25	2	no	—
33	C₂×C₃	C₂×D₂₅	1	1	yes	characteristic
34	C₅	C₃×C₄×D₅	1	1	yes	characteristic
35	C₂²	—	25	1	no	—
36	C₄	—	25	1	no	—
37	C₄	C₃×D₂₅	1	1	yes	characteristic, direct product factor
38	C₃	C₄×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
39	C₂	—	25	2	no	—
40	C₂	C₂×C₃×D₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	D₂₅
commutator, hypocenter	C₂₅	C₂×C₃×C₄
Frattini	C₂×C₅	C₂×C₃×D₅
Fitting	C₃×C₄×C₂₅	C₂
socle	C₂×C₃×C₅	C₂×D₅
prime radical	C₂×C₃×D₂₅	C₂
cosocle	C₂×C₂₅	C₂²×C₃
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₂₅	C₂	semidirect
3. C₃×Dic₂₅	C₂	semidirect
4. C₄×D₂₅	C₃	direct (N × H)
6. C₃×D₂₅	C₄	direct (N × H)
9. C₄×C₂₅	C₂×C₃	semidirect
10. Dic₂₅	C₂×C₃	semidirect
11. C₃×C₂₅	C₂×C₄	semidirect
16. D₂₅	C₃×C₄	direct (N × H)
20. C₂₅	C₂×C₃×C₄	semidirect
28. C₃×C₄	D₂₅	direct (N × H)
37. C₄	C₃×D₂₅	direct (N × H)
38. C₃	C₄×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
C₂×C₃×D₂₅	2
C₃×C₄×C₂₅	2
C₃×Dic₂₅	2
C₄×D₂₅	3
C₃×C₄×D₅	5

Subgroups — C3×C4×D25 #10597035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×D₂₅ #10597035