Subgroups — C₂×C₁₃×D₁₃⋊C₉ #20258786

Order 6084.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×D₁₃⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₃×D₁₃	C₃	1	1	yes	maximal, characteristic
4	C₁₃×C₁₃⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃²	C₂×C₃	1	1	yes	characteristic
6	C₃×C₁₃×D₁₃	C₂×C₃	1	2	yes	—
7	C₂×C₁₃×D₁₃	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃²	C₂²×C₃	1	1	yes	characteristic
9	C₂²×C₉×C₁₃	—	13	1	no	maximal
10	C₂×D₁₃⋊C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₁₃²	C₂×C₉	1	1	yes	characteristic, complemented
12	C₁₃×D₁₃	C₂×C₉	1	2	yes	complemented
13	C₂×C₉×C₁₃	—	13	2	no	—
14	C₂×C₉×C₁₃	—	13	1	no	—
15	C₂×C₁₃⋊C₉	C₂×C₁₃	1	1	yes	characteristic, complemented
16	D₁₃⋊C₉	C₂×C₁₃	1	2	yes	direct product factor
17	C₁₃²	C₂²×C₉	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₃×C₁₃	—	13	1	no	—
19	C₂×C₃×D₁₃	C₃×C₁₃	1	1	yes	characteristic
20	C₉×C₁₃	—	13	1	no	—
21	C₁₃⋊C₉	C₂²×C₁₃	1	1	yes	characteristic, complemented
22	C₂×C₃×C₁₃	—	6	2	no	—
23	C₂×C₃×C₁₃	—	13	2	no	—
24	C₂×C₃×C₁₃	D₁₃⋊C₃	1	1	yes	characteristic
25	C₂×C₃×C₁₃	C₂×C₃×C₁₃	1	1	yes	characteristic
26	C₃×D₁₃	C₂×C₃×C₁₃	1	2	yes	—
27	C₂²×C₁₃	—	13	1	no	—
28	C₂×D₁₃	C₉×C₁₃	1	1	yes	characteristic, complemented
29	C₃×C₁₃	—	6	2	no	—
30	C₃×C₁₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic
31	C₃×C₁₃	C₂²×C₃×C₁₃	1	1	yes	characteristic
32	C₂²×C₉	—	13	1	no	Hall
33	C₂×C₁₃	—	6	2	no	—
34	C₂×C₁₃	—	13	2	no	—
35	C₂×C₁₃	D₁₃⋊C₉	1	1	yes	characteristic, direct product factor
36	C₂×C₁₃	C₂×C₉×C₁₃	1	1	yes	characteristic, complemented
37	D₁₃	C₂×C₉×C₁₃	1	2	yes	complemented
38	C₂×C₉	—	13	2	no	—
39	C₂×C₉	—	13	1	no	—
40	C₁₃	—	6	2	no	—
41	C₁₃	C₂×D₁₃⋊C₉	1	1	yes	characteristic, direct product factor
42	C₁₃	C₂²×C₉×C₁₃	1	1	yes	characteristic, complemented
43	C₂²×C₃	—	13	1	no	—
44	C₉	—	13	1	no	Sylow
45	C₂×C₃	—	13	2	no	—
46	C₂×C₃	C₁₃×D₁₃⋊C₃	1	1	yes	characteristic
47	C₂²	—	13	1	no	Sylow
48	C₃	C₂×C₁₃×D₁₃⋊C₃	1	1	yes	characteristic
49	C₂	—	13	2	no	—
50	C₂	C₁₃×D₁₃⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂²×C₉×C₁₃
Frattini	C₃	C₂×C₁₃×D₁₃⋊C₃
Fitting, socle	C₂×C₃×C₁₃²	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×C₁₃⋊C₉	C₂	semidirect
2. C₁₃×D₁₃⋊C₉	C₂	direct (N × H)
4. C₁₃×C₁₃⋊C₉	C₂²	semidirect
7. C₂×C₁₃×D₁₃	C₉	semidirect
10. C₂×D₁₃⋊C₉	C₁₃	direct (N × H)
11. C₂×C₁₃²	C₂×C₉	semidirect
12. C₁₃×D₁₃	C₂×C₉	semidirect
15. C₂×C₁₃⋊C₉	C₂×C₁₃	semidirect
16. D₁₃⋊C₉	C₂×C₁₃	direct (N × H)
17. C₁₃²	C₂²×C₉	semidirect
21. C₁₃⋊C₉	C₂²×C₁₃	semidirect
28. C₂×D₁₃	C₉×C₁₃	semidirect
35. C₂×C₁₃	D₁₃⋊C₉	direct (N × H)
36. C₂×C₁₃	C₂×C₉×C₁₃	semidirect
37. D₁₃	C₂×C₉×C₁₃	semidirect
41. C₁₃	C₂×D₁₃⋊C₉	direct (N × H)
42. C₁₃	C₂²×C₉×C₁₃	semidirect
50. C₂	C₁₃×D₁₃⋊C₉	direct (N × H)

Subgroups — C2×C13×D13⋊C9 #20258786

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₃×D₁₃⋊C₉ #20258786