Subgroups — C₁₃×D₇×D₈₉ #44569310

Order 32396.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₆₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₇×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₃×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₃×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×D₈₉	—	7	1	no	maximal, Hall
6	D₇×D₈₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃×C₈₉	—	7	1	no	—
8	C₁₃×D₈₉	—	7	1	no	—
9	C₁₃×D₈₉	D₇	1	1	yes	characteristic, direct product factor
10	D₆₂₃	C₂×C₁₃	1	1	yes	characteristic, complemented
11	C₇×D₈₉	C₂×C₁₃	1	1	yes	characteristic, complemented
12	D₇×C₈₉	C₂×C₁₃	1	1	yes	characteristic, complemented
13	C₁₃×C₈₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₈₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₃×D₇	—	89	1	no	maximal, Hall
16	C₂×D₈₉	—	7	1	no	Hall
17	C₂×C₇×C₁₃	—	89	1	no	—
18	C₁₃×D₇	—	89	1	no	—
19	C₁₃×D₇	D₈₉	1	1	yes	characteristic, direct product factor
20	C₂×C₈₉	—	7	1	no	—
21	D₈₉	—	7	1	no	—
22	D₈₉	C₁₃×D₇	1	1	yes	characteristic, direct product factor
23	C₇×C₁₃	C₂×D₈₉	1	1	yes	characteristic, complemented, Hall
24	C₈₉	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
25	C₂²×C₁₃	—	623	1	no	Hall
26	C₂×D₇	—	89	1	no	Hall
27	C₂×C₁₃	—	7	1	no	—
28	C₂×C₁₃	—	89	1	no	—
29	C₂×C₁₃	—	623	1	no	—
30	C₂×C₇	—	89	1	no	—
31	D₇	—	89	1	no	—
32	D₇	C₁₃×D₈₉	1	1	yes	characteristic, direct product factor
33	C₁₃	D₇×D₈₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₇	C₂×C₁₃×D₈₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	623	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	89	1	no	—
38	C₂	—	623	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₇×D₈₉
commutator, cosocle, hypocenter	C₇×C₈₉	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₈₉	C₂²
LCS	G ▷ C₇×C₈₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₆₂₃	C₂	semidirect
2. C₁₃×D₇×C₈₉	C₂	semidirect
3. C₇×C₁₃×D₈₉	C₂	semidirect
4. C₇×C₁₃×C₈₉	C₂²	semidirect
6. D₇×D₈₉	C₁₃	direct (N × H)
9. C₁₃×D₈₉	D₇	direct (N × H)
10. D₆₂₃	C₂×C₁₃	semidirect
11. C₇×D₈₉	C₂×C₁₃	semidirect
12. D₇×C₈₉	C₂×C₁₃	semidirect
13. C₁₃×C₈₉	C₂×D₇	semidirect
14. C₇×C₈₉	C₂²×C₁₃	semidirect
19. C₁₃×D₇	D₈₉	direct (N × H)
22. D₈₉	C₁₃×D₇	direct (N × H)
23. C₇×C₁₃	C₂×D₈₉	semidirect
24. C₈₉	C₂×C₁₃×D₇	semidirect
32. D₇	C₁₃×D₈₉	direct (N × H)
33. C₁₃	D₇×D₈₉	direct (N × H)
34. C₇	C₂×C₁₃×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×D₆₂₃	2
C₁₃×D₇×C₈₉	2
C₇×C₁₃×D₈₉	2
C₂×C₁₃×D₈₉	7
D₇×D₈₉	13
C₂×C₁₃×D₇	89

Subgroups — C13×D7×D89 #44569310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₇×D₈₉ #44569310