Subgroups — C₂×C₇×C₁₃×D₈₉ #44569321

Order 32396.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×D₈₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₃×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₃×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×D₈₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×D₈₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₃×C₈₉	C₂×C₇	1	1	yes	characteristic, complemented
7	C₁₃×D₈₉	C₂×C₇	1	2	yes	direct product factor
8	C₂×C₇×C₈₉	C₂×C₁₃	1	1	yes	characteristic, complemented
9	C₇×D₈₉	C₂×C₁₃	1	2	yes	direct product factor
10	C₁₃×C₈₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₈₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₇×C₁₃	—	89	1	no	maximal, Hall
13	C₂×D₈₉	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₇×C₁₃	—	89	2	no	—
15	C₂×C₇×C₁₃	D₈₉	1	1	yes	characteristic, direct product factor
16	C₂×C₈₉	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
17	D₈₉	C₂×C₇×C₁₃	1	2	yes	direct product factor
18	C₇×C₁₃	C₂×D₈₉	1	1	yes	characteristic, direct product factor, Hall
19	C₈₉	C₂²×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₁₃	—	89	1	no	Hall
21	C₂²×C₇	—	89	1	no	Hall
22	C₂×C₁₃	—	89	2	no	—
23	C₂×C₁₃	C₇×D₈₉	1	1	yes	characteristic, direct product factor
24	C₂×C₇	—	89	2	no	—
25	C₂×C₇	C₁₃×D₈₉	1	1	yes	characteristic, direct product factor
26	C₁₃	C₂×C₇×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂×C₁₃×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	89	1	no	Sylow
29	C₂	—	89	2	no	—
30	C₂	C₇×C₁₃×D₈₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₃	D₈₉
commutator, cosocle, hypocenter	C₈₉	C₂²×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃×C₈₉	C₂
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₂×C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃×D₈₉	C₂	direct (N × H)
2. C₂×C₇×C₁₃×C₈₉	C₂	semidirect
3. C₇×C₁₃×C₈₉	C₂²	semidirect
4. C₂×C₁₃×D₈₉	C₇	direct (N × H)
5. C₂×C₇×D₈₉	C₁₃	direct (N × H)
6. C₂×C₁₃×C₈₉	C₂×C₇	semidirect
7. C₁₃×D₈₉	C₂×C₇	direct (N × H)
8. C₂×C₇×C₈₉	C₂×C₁₃	semidirect
9. C₇×D₈₉	C₂×C₁₃	direct (N × H)
10. C₁₃×C₈₉	C₂²×C₇	semidirect
11. C₇×C₈₉	C₂²×C₁₃	semidirect
13. C₂×D₈₉	C₇×C₁₃	direct (N × H)
15. C₂×C₇×C₁₃	D₈₉	direct (N × H)
16. C₂×C₈₉	C₂×C₇×C₁₃	semidirect
17. D₈₉	C₂×C₇×C₁₃	direct (N × H)
18. C₇×C₁₃	C₂×D₈₉	direct (N × H)
19. C₈₉	C₂²×C₇×C₁₃	semidirect
23. C₂×C₁₃	C₇×D₈₉	direct (N × H)
25. C₂×C₇	C₁₃×D₈₉	direct (N × H)
26. C₁₃	C₂×C₇×D₈₉	direct (N × H)
27. C₇	C₂×C₁₃×D₈₉	direct (N × H)
30. C₂	C₇×C₁₃×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
C₇×C₁₃×D₈₉	2
C₂×C₇×C₁₃×C₈₉	2
C₂×C₁₃×D₈₉	7
C₂×C₇×D₈₉	13
C₂²×C₇×C₁₃	89

Subgroups — C2×C7×C13×D89 #44569321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₁₃×D₈₉ #44569321