Subgroups — C₂×Dic₃×C₂₅ #10597042

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	1	yes	maximal, characteristic
2	Dic₃×C₂₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄×C₂₅	—	3	1	no	maximal, Hall
4	C₂×C₃×C₂₅	C₄	1	2	yes	complemented
5	C₂×C₃×C₂₅	C₂²	1	1	yes	characteristic
6	C₂×C₅×Dic₃	C₅	1	1	yes	maximal, characteristic
7	C₂²×C₂₅	D₃	1	1	yes	characteristic
8	C₄×C₂₅	—	3	2	no	—
9	C₃×C₂₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
10	C₂²×C₃×C₅	C₂×C₅	1	1	yes	characteristic
11	C₅×Dic₃	C₂×C₅	1	2	yes	—
12	C₂×C₂₅	Dic₃	1	2	yes	direct product factor
13	C₂×C₂₅	C₂×D₃	1	1	yes	characteristic
14	C₂×C₄×C₅	—	3	1	no	—
15	C₂×C₃×C₅	C₄×C₅	1	2	yes	—
16	C₂×C₃×C₅	C₂²×C₅	1	1	yes	characteristic
17	C₂₅	C₂×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×Dic₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₅	C₅×D₃	1	1	yes	characteristic
20	C₄×C₅	—	3	2	no	—
21	C₃×C₅	C₂×C₄×C₅	1	1	yes	characteristic
22	C₂²×C₃	C₂×C₂₅	1	1	yes	characteristic
23	Dic₃	C₂×C₂₅	1	2	yes	direct product factor
24	C₂×C₅	C₅×Dic₃	1	2	yes	—
25	C₂×C₅	C₂×C₅×D₃	1	1	yes	characteristic
26	C₂×C₄	—	3	1	no	Sylow
27	C₂×C₃	C₄×C₂₅	1	2	yes	complemented
28	C₂×C₃	C₂²×C₂₅	1	1	yes	characteristic
29	C₅	C₂×C₅×Dic₃	1	1	yes	characteristic
30	C₂²	D₃×C₂₅	1	1	yes	characteristic
31	C₄	—	3	2	no	—
32	C₃	C₂×C₄×C₂₅	1	1	yes	characteristic, complemented, Sylow
33	C₂	Dic₃×C₂₅	1	2	yes	direct product factor
34	C₂	C₂×D₃×C₂₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. Dic₃×C₂₅	C₂	direct (N × H)
4. C₂×C₃×C₂₅	C₄	semidirect
9. C₃×C₂₅	C₂×C₄	semidirect
12. C₂×C₂₅	Dic₃	direct (N × H)
17. C₂₅	C₂×Dic₃	direct (N × H)
18. C₂×Dic₃	C₂₅	direct (N × H)
23. Dic₃	C₂×C₂₅	direct (N × H)
27. C₂×C₃	C₄×C₂₅	semidirect
32. C₃	C₂×C₄×C₂₅	semidirect
33. C₂	Dic₃×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
Dic₃×C₂₅	2
C₂×C₄×C₂₅	3
C₂×C₅×Dic₃	5

Subgroups — C2×Dic3×C25 #10597042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₃×C₂₅ #10597042