Subgroups — (C₅⋊D₅)⋊D₂₆₉ #41001980

Order 26900.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₃₄₅	C₂	1	2	yes	maximal, complemented
2	C₅⋊D₅×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₂₆₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₅×D₂₆₉	—	5	2	no	maximal
5	D₁₃₄₅	D₅	1	2	yes	complemented
6	C₅×D₂₆₉	—	5	2	no	—
7	D₅×C₂₆₉	—	5	2	no	—
8	D₅×C₂₆₉	—	10	2	no	—
9	C₅×C₂₆₉	—	2	2	no	—
10	C₅×C₂₆₉	C₂×D₅	1	2	yes	complemented
11	C₂×D₂₆₉	—	25	1	no	Hall
12	C₂×C₂₆₉	—	25	1	no	—
13	D₂₆₉	—	5	2	no	—
14	C₂₆₉	D₅²	1	1	yes	characteristic, complemented, Sylow
15	D₅²	—	269	1	no	maximal, Hall
16	C₅⋊D₅	D₂₆₉	1	1	yes	characteristic, complemented
17	C₅×D₅	—	269	2	no	—
18	C₅²	C₂×D₂₆₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×D₅	—	1345	2	no	—
20	C₂×C₅	—	1345	2	no	—
21	D₅	—	5	2	no	—
22	D₅	—	10	2	no	—
23	D₅	—	269	2	no	—
24	C₅	—	2	2	no	—
25	C₅	D₅×D₂₆₉	1	2	yes	complemented
26	C₂²	—	6725	1	no	Sylow
27	C₂	—	25	1	no	—
28	C₂	—	1345	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₂₆₉	C₂²
LCS	G ▷ C₅²×C₂₆₉
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.