Subgroups — C₂×C₃⋊D₆₀₉ #20300680

Order 7308.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₆₀₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₆₀₉	—	3	4	no	maximal
4	C₃²×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₂₉	D₃	1	4	yes	complemented
6	D₆₀₉	—	3	8	no	—
7	C₂×C₃⋊D₈₇	—	7	1	no	maximal, Hall
8	C₂×D₂₀₃	—	9	1	no	Hall
9	C₃×C₇×C₂₉	C₂×D₃	1	4	yes	complemented
10	C₂×C₃²×C₂₉	D₇	1	1	yes	characteristic, complemented
11	C₃⋊D₈₇	—	7	2	no	—
12	C₂×C₇×C₂₉	C₃⋊D₃	1	1	yes	characteristic, complemented
13	D₂₀₃	—	9	2	no	—
14	C₂×D₈₇	—	21	4	no	—
15	C₃²×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃⋊D₂₁	—	29	1	no	maximal, Hall
17	C₇×C₂₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₂₉	D₂₁	1	4	yes	complemented
19	D₈₇	—	21	8	no	—
20	C₂×C₃²×C₇	D₂₉	1	1	yes	characteristic, complemented
21	C₃⋊D₂₁	—	29	2	no	—
22	C₂×D₂₉	—	63	1	no	Hall
23	C₃×C₂₉	C₂×D₂₁	1	4	yes	complemented
24	C₂×D₂₁	—	87	4	no	—
25	C₃²×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₂₉	C₃⋊D₂₁	1	1	yes	characteristic, complemented
27	D₂₉	—	63	2	no	—
28	C₂×C₃×C₇	D₈₇	1	4	yes	complemented
29	D₂₁	—	87	8	no	—
30	C₂×C₃⋊D₃	—	203	1	no	Hall
31	C₂₉	C₂×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
32	C₂×D₇	—	261	1	no	Hall
33	C₃×C₇	C₂×D₈₇	1	4	yes	complemented
34	C₂×C₃²	D₂₀₃	1	1	yes	characteristic, complemented
35	C₃⋊D₃	—	203	2	no	—
36	C₂×C₇	C₃⋊D₈₇	1	1	yes	characteristic, complemented
37	D₇	—	261	2	no	—
38	C₂×D₃	—	609	4	no	—
39	C₃²	C₂×D₂₀₃	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×C₃⋊D₈₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₆₀₉	1	4	yes	complemented
42	D₃	—	609	8	no	—
43	C₂²	—	1827	1	no	Sylow
44	C₃	C₂×D₆₀₉	1	4	yes	complemented
45	C₂	—	1827	2	no	—
46	C₂	C₃⋊D₆₀₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₆₀₉
commutator, hypocenter	C₃²×C₇×C₂₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₂₉	C₂
LCS	G ▷ C₃²×C₇×C₂₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₆₀₉	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₂₉	C₂	semidirect
4. C₃²×C₇×C₂₉	C₂²	semidirect
5. C₂×C₃×C₇×C₂₉	D₃	semidirect
9. C₃×C₇×C₂₉	C₂×D₃	semidirect
10. C₂×C₃²×C₂₉	D₇	semidirect
12. C₂×C₇×C₂₉	C₃⋊D₃	semidirect
15. C₃²×C₂₉	C₂×D₇	semidirect
17. C₇×C₂₉	C₂×C₃⋊D₃	semidirect
18. C₂×C₃×C₂₉	D₂₁	semidirect
20. C₂×C₃²×C₇	D₂₉	semidirect
23. C₃×C₂₉	C₂×D₂₁	semidirect
25. C₃²×C₇	C₂×D₂₉	semidirect
26. C₂×C₂₉	C₃⋊D₂₁	semidirect
28. C₂×C₃×C₇	D₈₇	semidirect
31. C₂₉	C₂×C₃⋊D₂₁	semidirect
33. C₃×C₇	C₂×D₈₇	semidirect
34. C₂×C₃²	D₂₀₃	semidirect
36. C₂×C₇	C₃⋊D₈₇	semidirect
39. C₃²	C₂×D₂₀₃	semidirect
40. C₇	C₂×C₃⋊D₈₇	semidirect
41. C₂×C₃	D₆₀₉	semidirect
44. C₃	C₂×D₆₀₉	semidirect
46. C₂	C₃⋊D₆₀₉	direct (N × H)

Subgroups — C2×C3⋊D609 #20300680

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃⋊D₆₀₉ #20300680