Finite Group Databasebeta

← C₂²×C₅²×C₂₆₉ #41001966

Subgroups — C₂²×C₅²×C₂₆₉ #41001966

Order 26900.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₂₆₉	C₂	1	3	yes	maximal, direct product factor
2	C₅²×C₂₆₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₅×C₂₆₉	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅×C₂₆₉	C₂×C₅	1	18	yes	direct product factor
5	C₅×C₂₆₉	C₂²×C₅	1	6	yes	direct product factor
6	C₂²×C₂₆₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₂₆₉	C₂×C₅²	1	3	yes	direct product factor
8	C₂₆₉	C₂²×C₅²	1	1	yes	characteristic, direct product factor, Sylow
9	C₂²×C₅²	C₂₆₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅²	C₂×C₂₆₉	1	3	yes	direct product factor
11	C₅²	C₂²×C₂₆₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₅	C₅×C₂₆₉	1	6	yes	direct product factor
13	C₂×C₅	C₂×C₅×C₂₆₉	1	18	yes	direct product factor
14	C₅	C₂²×C₅×C₂₆₉	1	6	yes	direct product factor
15	C₂²	C₅²×C₂₆₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₅²×C₂₆₉	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₅²×C₂₆₉	C₂	direct (N × H)
2. C₅²×C₂₆₉	C₂²	direct (N × H)
3. C₂²×C₅×C₂₆₉	C₅	direct (N × H)
4. C₂×C₅×C₂₆₉	C₂×C₅	direct (N × H)
5. C₅×C₂₆₉	C₂²×C₅	direct (N × H)
6. C₂²×C₂₆₉	C₅²	direct (N × H)
7. C₂×C₂₆₉	C₂×C₅²	direct (N × H)
8. C₂₆₉	C₂²×C₅²	direct (N × H)
9. C₂²×C₅²	C₂₆₉	direct (N × H)
10. C₂×C₅²	C₂×C₂₆₉	direct (N × H)
11. C₅²	C₂²×C₂₆₉	direct (N × H)
12. C₂²×C₅	C₅×C₂₆₉	direct (N × H)
13. C₂×C₅	C₂×C₅×C₂₆₉	direct (N × H)
14. C₅	C₂²×C₅×C₂₆₉	direct (N × H)
15. C₂²	C₅²×C₂₆₉	direct (N × H)
16. C₂	C₂×C₅²×C₂₆₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅²×C₂₆₉	2
C₂²×C₅×C₂₆₉	5
C₂²×C₅²	269