Subgroups — C₂×C₅²×D₂₆₉ #41001990

Order 26900.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₅²	D₂₆₉
commutator, cosocle, hypocenter	C₂₆₉	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₂₆₉	C₂
LCS	G ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₅²

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.