Subgroups — D₂₅×D₂₃₃ #37551921

Order 23300.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₈₂₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₅×D₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₅×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₅×C₂₃₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₂₃₃	—	5	1	no	maximal
6	D₁₁₆₅	—	5	1	no	—
7	C₅×D₂₃₃	D₅	1	1	yes	characteristic
8	D₅×C₂₃₃	—	5	1	no	—
9	C₅×C₂₃₃	C₂×D₅	1	1	yes	characteristic
10	C₂×D₂₃₃	—	25	1	no	Hall
11	C₂×C₂₃₃	—	25	1	no	—
12	D₂₃₃	—	25	1	no	—
13	D₂₃₃	D₂₅	1	1	yes	characteristic, direct product factor
14	C₂₃₃	C₂×D₂₅	1	1	yes	characteristic, complemented, Sylow
15	C₂×D₂₅	—	233	1	no	maximal, Hall
16	C₂×C₂₅	—	233	1	no	—
17	D₂₅	—	233	1	no	—
18	D₂₅	D₂₃₃	1	1	yes	characteristic, direct product factor
19	C₂₅	C₂×D₂₃₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₅	—	1165	1	no	—
21	C₂×C₅	—	233	1	no	—
22	D₅	—	5	1	no	—
23	D₅	—	1165	1	no	—
24	C₅	D₅×D₂₃₃	1	1	yes	characteristic
25	C₂²	—	5825	1	no	Sylow
26	C₂	—	25	1	no	—
27	C₂	—	5825	1	no	—
28	C₂	—	233	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂₅×C₂₃₃	C₂²
Frattini	C₅	D₅×D₂₃₃
socle	C₅×C₂₃₃	C₂×D₅
LCS	G ▷ C₂₅×C₂₃₃
UCS	C₁

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.