Subgroups — C₃×C₁₃⋊C₃×D₈₉ #35209705

Order 20826.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊C₃×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊C₃×D₈₉	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₁₃×D₈₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₈₉	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃⋊C₃×C₈₉	C₂×C₃	1	3	yes	complemented
6	C₁₃×D₈₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃²×D₈₉	—	13	1	no	maximal, Hall
8	C₁₃×C₈₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₈₉	—	13	1	no	Hall
10	C₃×D₈₉	—	13	3	no	—
11	C₃×D₈₉	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
12	C₃×C₈₉	—	13	3	no	—
13	C₃×C₈₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
14	C₂×C₃×C₁₃⋊C₃	—	89	1	no	maximal, Hall
15	D₈₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₃⋊C₃	D₈₉	1	1	yes	characteristic, direct product factor, Hall
17	C₈₉	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₁₃	—	89	1	no	—
19	C₂×C₁₃⋊C₃	—	89	3	no	—
20	C₃×C₁₃	C₃×D₈₉	1	1	yes	characteristic, complemented
21	C₁₃⋊C₃	C₃×D₈₉	1	3	yes	direct product factor
22	C₂×C₁₃	—	89	1	no	Hall
23	C₂×C₃²	—	1157	1	no	Hall
24	C₁₃	C₃²×D₈₉	1	1	yes	characteristic, complemented, Sylow
25	C₃²	—	13	1	no	Sylow
26	C₂×C₃	—	89	1	no	—
27	C₂×C₃	—	1157	3	no	—
28	C₃	—	13	3	no	—
29	C₃	C₁₃⋊C₃×D₈₉	1	1	yes	characteristic, direct product factor
30	C₂	—	89	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₁₃⋊C₃×D₈₉
commutator, cosocle, hypocenter	C₁₃×C₈₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₈₉	C₂×C₃
LCS	G ▷ C₁₃×C₈₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃⋊C₃×C₈₉	C₂	semidirect
2. C₁₃⋊C₃×D₈₉	C₃	direct (N × H)
3. C₃×C₁₃×D₈₉	C₃	semidirect
4. C₃×C₁₃×C₈₉	C₂×C₃	semidirect
5. C₁₃⋊C₃×C₈₉	C₂×C₃	semidirect
6. C₁₃×D₈₉	C₃²	semidirect
8. C₁₃×C₈₉	C₂×C₃²	semidirect
11. C₃×D₈₉	C₁₃⋊C₃	direct (N × H)
13. C₃×C₈₉	C₂×C₁₃⋊C₃	semidirect
15. D₈₉	C₃×C₁₃⋊C₃	direct (N × H)
16. C₃×C₁₃⋊C₃	D₈₉	direct (N × H)
17. C₈₉	C₂×C₃×C₁₃⋊C₃	semidirect
20. C₃×C₁₃	C₃×D₈₉	semidirect
21. C₁₃⋊C₃	C₃×D₈₉	direct (N × H)
24. C₁₃	C₃²×D₈₉	semidirect
29. C₃	C₁₃⋊C₃×D₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₃⋊C₃×C₈₉	2
C₁₃⋊C₃×D₈₉	3
C₃×C₁₃×D₈₉	3
C₃²×D₈₉	13
C₂×C₃×C₁₃⋊C₃	89

Subgroups — C3×C13⋊C3×D89 #35209705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃⋊C₃×D₈₉ #35209705