Subgroups — C₃×C₇²×C₅⋊D₅ #20301321

Order 7350.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇²×D₅	—	5	6	no	maximal
4	C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₅⋊D₅	C₇	1	8	yes	maximal, direct product factor
6	C₃×C₅×C₇²	D₅	1	6	yes	complemented
7	C₃×C₅²×C₇	C₂×C₇	1	8	yes	complemented
8	C₇²×D₅	—	5	6	no	—
9	C₇×C₅⋊D₅	C₃×C₇	1	8	yes	direct product factor
10	C₂×C₃×C₇²	—	25	1	no	Hall
11	C₅×C₇²	C₃×D₅	1	6	yes	complemented
12	C₃×C₇×D₅	—	5	48	no	—
13	C₅²×C₇	C₂×C₃×C₇	1	8	yes	complemented
14	C₃×C₅⋊D₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₇²	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅×C₇	C₇×D₅	1	48	yes	complemented
17	C₂×C₇²	—	25	1	no	Hall
18	C₃×C₅²	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
19	C₇×D₅	—	5	48	no	—
20	C₅⋊D₅	C₃×C₇²	1	1	yes	characteristic, direct product factor, Hall
21	C₇²	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₃×C₇	—	25	8	no	—
23	C₅×C₇	C₃×C₇×D₅	1	48	yes	complemented
24	C₃×D₅	—	5	6	no	—
25	C₅²	C₂×C₃×C₇²	1	1	yes	characteristic, complemented, Sylow
26	C₃×C₇	C₇×C₅⋊D₅	1	8	yes	direct product factor
27	C₃×C₅	C₇²×D₅	1	6	yes	complemented
28	C₂×C₇	—	25	8	no	—
29	D₅	—	5	6	no	—
30	C₇	C₃×C₇×C₅⋊D₅	1	8	yes	direct product factor
31	C₂×C₃	—	25	1	no	Hall
32	C₅	C₃×C₇²×D₅	1	6	yes	complemented
33	C₃	C₇²×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇²	C₅⋊D₅
commutator, hypocenter	C₅²	C₂×C₃×C₇²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇²	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₇²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₇²	C₂	semidirect
2. C₇²×C₅⋊D₅	C₃	direct (N × H)
4. C₅²×C₇²	C₂×C₃	semidirect
5. C₃×C₇×C₅⋊D₅	C₇	direct (N × H)
6. C₃×C₅×C₇²	D₅	semidirect
7. C₃×C₅²×C₇	C₂×C₇	semidirect
9. C₇×C₅⋊D₅	C₃×C₇	direct (N × H)
11. C₅×C₇²	C₃×D₅	semidirect
13. C₅²×C₇	C₂×C₃×C₇	semidirect
14. C₃×C₅⋊D₅	C₇²	direct (N × H)
15. C₃×C₇²	C₅⋊D₅	direct (N × H)
16. C₃×C₅×C₇	C₇×D₅	semidirect
18. C₃×C₅²	C₂×C₇²	semidirect
20. C₅⋊D₅	C₃×C₇²	direct (N × H)
21. C₇²	C₃×C₅⋊D₅	direct (N × H)
23. C₅×C₇	C₃×C₇×D₅	semidirect
25. C₅²	C₂×C₃×C₇²	semidirect
26. C₃×C₇	C₇×C₅⋊D₅	direct (N × H)
27. C₃×C₅	C₇²×D₅	semidirect
30. C₇	C₃×C₇×C₅⋊D₅	direct (N × H)
32. C₅	C₃×C₇²×D₅	semidirect
33. C₃	C₇²×C₅⋊D₅	direct (N × H)

Subgroups — C3×C72×C5⋊D5 #20301321

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇²×C₅⋊D₅ #20301321