Subgroups — D₅²×C₂₆₉ #41001978

Order 26900.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂₆₉	D₅²
commutator, cosocle, hypocenter	C₅²	C₂²×C₂₆₉
Frattini	C₁	G
Fitting, socle	C₅²×C₂₆₉	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂₆₉

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.