Subgroups — C₂×C₅₃×D₁₃⋊C₃ #22551963

Order 8268.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×D₁₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₃⋊C₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₃×C₅₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃⋊C₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₅₃	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₃×C₅₃	C₂×C₃	1	2	yes	complemented
7	C₁₃×C₅₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₃×C₅₃	—	13	1	no	maximal, Hall
9	C₂×C₃×C₅₃	—	13	2	no	—
10	C₂×C₃×C₅₃	—	13	1	no	—
11	C₂²×C₅₃	—	13	1	no	Hall
12	C₃×C₅₃	—	13	1	no	Hall
13	C₂×D₁₃⋊C₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₅₃	—	13	2	no	—
15	C₂×C₅₃	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
16	C₂×C₁₃⋊C₃	C₂×C₅₃	1	1	yes	characteristic, complemented
17	D₁₃⋊C₃	C₂×C₅₃	1	2	yes	direct product factor
18	C₅₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×D₁₃	C₃×C₅₃	1	1	yes	characteristic, complemented, Hall
20	C₁₃⋊C₃	C₂²×C₅₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	C₂×C₃×C₅₃	1	1	yes	characteristic, complemented
22	D₁₃	C₂×C₃×C₅₃	1	2	yes	complemented
23	C₁₃	C₂²×C₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	13	1	no	Hall
25	C₂×C₃	—	13	2	no	—
26	C₂×C₃	—	13	1	no	—
27	C₂²	—	13	1	no	Sylow
28	C₃	—	13	1	no	Sylow
29	C₂	—	13	2	no	—
30	C₂	C₅₃×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅₃	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂²×C₃×C₅₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₅₃	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₅₃×D₁₃⋊C₃	C₂	direct (N × H)
2. C₂×C₁₃⋊C₃×C₅₃	C₂	semidirect
3. C₂×D₁₃×C₅₃	C₃	semidirect
4. C₁₃⋊C₃×C₅₃	C₂²	semidirect
5. C₂×C₁₃×C₅₃	C₂×C₃	semidirect
6. D₁₃×C₅₃	C₂×C₃	semidirect
7. C₁₃×C₅₃	C₂²×C₃	semidirect
13. C₂×D₁₃⋊C₃	C₅₃	direct (N × H)
15. C₂×C₅₃	D₁₃⋊C₃	direct (N × H)
16. C₂×C₁₃⋊C₃	C₂×C₅₃	semidirect
17. D₁₃⋊C₃	C₂×C₅₃	direct (N × H)
18. C₅₃	C₂×D₁₃⋊C₃	direct (N × H)
19. C₂×D₁₃	C₃×C₅₃	semidirect
20. C₁₃⋊C₃	C₂²×C₅₃	semidirect
21. C₂×C₁₃	C₂×C₃×C₅₃	semidirect
22. D₁₃	C₂×C₃×C₅₃	semidirect
23. C₁₃	C₂²×C₃×C₅₃	semidirect
30. C₂	C₅₃×D₁₃⋊C₃	direct (N × H)

Subgroups — C2×C53×D13⋊C3 #22551963

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅₃×D₁₃⋊C₃ #22551963