Subgroups — C₅⋊D₅×D₂₆₉ #41001982

Order 26900.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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