Subgroups — C₂×C₁₃×D₆₈₉ #49089331

Order 35828.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₆₈₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₃²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃²×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×D₅₃	—	13	1	no	maximal
5	C₂×D₆₈₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₁₃×C₅₃	—	2	6	no	—
7	C₂×C₁₃×C₅₃	D₁₃	1	1	yes	characteristic, complemented
8	C₂×C₁₃×C₅₃	C₂×C₁₃	1	1	yes	characteristic, complemented
9	D₆₈₉	C₂×C₁₃	1	2	yes	direct product factor
10	C₁₃×D₅₃	—	13	2	no	—
11	C₁₃×C₅₃	—	2	6	no	—
12	C₁₃×C₅₃	C₂×D₁₃	1	1	yes	characteristic, complemented
13	C₁₃×C₅₃	C₂²×C₁₃	1	1	yes	characteristic, complemented
14	C₂×C₁₃×D₁₃	—	53	1	no	maximal, Hall
15	C₂×C₁₃²	D₅₃	1	1	yes	characteristic, complemented
16	C₁₃×D₁₃	—	53	2	no	—
17	C₂×D₅₃	—	13	1	no	Hall
18	C₁₃²	C₂×D₅₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅₃	C₁₃×D₁₃	1	1	yes	characteristic, complemented
20	D₅₃	—	13	2	no	—
21	C₅₃	C₂×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₁₃	—	689	1	no	—
23	C₂×D₁₃	—	53	1	no	—
24	C₂×C₁₃	—	2	6	no	—
25	C₂×C₁₃	—	689	2	no	—
26	C₂×C₁₃	C₁₃×D₅₃	1	1	yes	characteristic, complemented
27	C₂×C₁₃	D₆₈₉	1	1	yes	characteristic, direct product factor
28	D₁₃	—	53	2	no	—
29	C₁₃	—	2	6	no	—
30	C₁₃	C₂×D₆₈₉	1	1	yes	characteristic, direct product factor
31	C₁₃	C₂×C₁₃×D₅₃	1	1	yes	characteristic, complemented
32	C₂²	—	689	1	no	Sylow
33	C₂	—	689	2	no	—
34	C₂	C₁₃×D₆₈₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₆₈₉
commutator, cosocle, hypocenter	C₁₃×C₅₃	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃²×C₅₃	C₂
LCS	G ▷ C₁₃×C₅₃
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₆₈₉	C₂	direct (N × H)
2. C₂×C₁₃²×C₅₃	C₂	semidirect
3. C₁₃²×C₅₃	C₂²	semidirect
5. C₂×D₆₈₉	C₁₃	direct (N × H)
7. C₂×C₁₃×C₅₃	D₁₃	semidirect
8. C₂×C₁₃×C₅₃	C₂×C₁₃	semidirect
9. D₆₈₉	C₂×C₁₃	direct (N × H)
12. C₁₃×C₅₃	C₂×D₁₃	semidirect
13. C₁₃×C₅₃	C₂²×C₁₃	semidirect
15. C₂×C₁₃²	D₅₃	semidirect
18. C₁₃²	C₂×D₅₃	semidirect
19. C₂×C₅₃	C₁₃×D₁₃	semidirect
21. C₅₃	C₂×C₁₃×D₁₃	semidirect
26. C₂×C₁₃	C₁₃×D₅₃	semidirect
27. C₂×C₁₃	D₆₈₉	direct (N × H)
30. C₁₃	C₂×D₆₈₉	direct (N × H)
31. C₁₃	C₂×C₁₃×D₅₃	semidirect
34. C₂	C₁₃×D₆₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×D₆₈₉	2
C₂×C₁₃²×C₅₃	2
C₂×C₁₃×D₅₃	13
C₂×D₆₈₉	13
C₂×C₁₃×D₁₃	53

Subgroups — C2×C13×D689 #49089331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₆₈₉ #49089331