Subgroups — C₂²×C₃×D₂₅ #10597060

Order 600.

96 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, complemented
2	C₂×C₃×D₂₅	C₂	1	6	yes	maximal, direct product factor
3	C₂²×D₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₂₅	C₂²	1	3	yes	complemented
5	C₃×D₂₅	C₂²	1	4	yes	direct product factor
6	C₂²×C₃×D₅	—	5	1	no	maximal
7	C₂²×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×D₂₅	C₂×C₃	1	6	yes	direct product factor
9	C₃×C₂₅	C₂³	1	1	yes	characteristic, complemented, Hall
10	C₂²×C₃×C₅	D₅	1	1	yes	characteristic
11	C₂×C₃×D₅	—	5	6	no	—
12	C₂×C₂₅	C₂²×C₃	1	3	yes	complemented
13	D₂₅	C₂²×C₃	1	4	yes	direct product factor
14	C₂²×D₅	—	5	1	no	—
15	C₂×C₃×C₅	C₂×D₅	1	3	yes	—
16	C₃×D₅	—	5	4	no	—
17	C₂₅	C₂³×C₃	1	1	yes	characteristic, complemented, Sylow
18	C₂³×C₃	—	25	1	no	Hall
19	C₂²×C₅	C₃×D₅	1	1	yes	characteristic
20	C₂×D₅	—	5	6	no	—
21	C₃×C₅	C₂²×D₅	1	1	yes	characteristic
22	C₂²×C₃	—	25	6	no	—
23	C₂²×C₃	D₂₅	1	1	yes	characteristic, direct product factor
24	C₂×C₅	C₂×C₃×D₅	1	3	yes	—
25	D₅	—	5	4	no	—
26	C₂³	—	25	1	no	Sylow
27	C₂×C₃	—	25	4	no	—
28	C₂×C₃	C₂×D₂₅	1	3	yes	direct product factor
29	C₅	C₂²×C₃×D₅	1	1	yes	characteristic
30	C₂²	—	25	6	no	—
31	C₂²	C₃×D₂₅	1	1	yes	characteristic, direct product factor
32	C₃	C₂²×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	—	25	4	no	—
34	C₂	C₂×C₃×D₂₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂³×C₃
Frattini	C₅	C₂²×C₃×D₅
Fitting	C₂²×C₃×C₂₅	C₂
socle	C₂²×C₃×C₅	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂²×C₃

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

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