Subgroups — C₂×C₃²×C₁₃×C₈₉ #35209702

Order 20826.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₈₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₁₃×C₈₉	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₁₃×C₈₉	C₂×C₃	1	4	yes	direct product factor
4	C₂×C₁₃×C₈₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₃²×C₈₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₈₉	C₂×C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₈₉	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₈₉	C₃×C₁₃	1	4	yes	direct product factor
9	C₃×C₈₉	C₂×C₃×C₁₃	1	4	yes	direct product factor
10	C₂×C₃²×C₁₃	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₈₉	C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃²×C₁₃	C₂×C₈₉	1	1	yes	characteristic, direct product factor, Hall
13	C₈₉	C₂×C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₃×C₁₃	C₃×C₈₉	1	4	yes	direct product factor
15	C₃×C₁₃	C₂×C₃×C₈₉	1	4	yes	direct product factor
16	C₂×C₁₃	C₃²×C₈₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃²	C₁₃×C₈₉	1	1	yes	characteristic, direct product factor, Hall
18	C₁₃	C₂×C₃²×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²	C₂×C₁₃×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₁₃×C₈₉	1	4	yes	direct product factor
21	C₃	C₂×C₃×C₁₃×C₈₉	1	4	yes	direct product factor
22	C₂	C₃²×C₁₃×C₈₉	1	1	yes	characteristic, direct product factor, Sylow

	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. C₃²×C₁₃×C₈₉	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₈₉	C₃	direct (N × H)
3. C₃×C₁₃×C₈₉	C₂×C₃	direct (N × H)
4. C₂×C₁₃×C₈₉	C₃²	direct (N × H)
5. C₂×C₃²×C₈₉	C₁₃	direct (N × H)
6. C₁₃×C₈₉	C₂×C₃²	direct (N × H)
7. C₃²×C₈₉	C₂×C₁₃	direct (N × H)
8. C₂×C₃×C₈₉	C₃×C₁₃	direct (N × H)
9. C₃×C₈₉	C₂×C₃×C₁₃	direct (N × H)
10. C₂×C₃²×C₁₃	C₈₉	direct (N × H)
11. C₂×C₈₉	C₃²×C₁₃	direct (N × H)
12. C₃²×C₁₃	C₂×C₈₉	direct (N × H)
13. C₈₉	C₂×C₃²×C₁₃	direct (N × H)
14. C₂×C₃×C₁₃	C₃×C₈₉	direct (N × H)
15. C₃×C₁₃	C₂×C₃×C₈₉	direct (N × H)
16. C₂×C₁₃	C₃²×C₈₉	direct (N × H)
17. C₂×C₃²	C₁₃×C₈₉	direct (N × H)
18. C₁₃	C₂×C₃²×C₈₉	direct (N × H)
19. C₃²	C₂×C₁₃×C₈₉	direct (N × H)
20. C₂×C₃	C₃×C₁₃×C₈₉	direct (N × H)
21. C₃	C₂×C₃×C₁₃×C₈₉	direct (N × H)
22. C₂	C₃²×C₁₃×C₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×C₈₉	2
C₂×C₃×C₁₃×C₈₉	3
C₂×C₃²×C₈₉	13
C₂×C₃²×C₁₃	89

Subgroups — C2×C32×C13×C89 #35209702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₁₃×C₈₉ #35209702