Subgroups — C₃×C₇×D₅₀₅ #35234582

Order 21210.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅₀₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×D₁₀₁	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₀₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×D₅₀₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇×C₁₀₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₀₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×D₁₀₁	—	5	1	no	Hall
9	D₅₀₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₇×C₁₀₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
11	C₃×D₁₀₁	—	5	1	no	Hall
12	C₅×C₁₀₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₀₁	C₇×D₅	1	1	yes	characteristic, complemented, Hall
14	C₃×C₇×D₅	—	101	1	no	maximal, Hall
15	D₁₀₁	—	5	1	no	Hall
16	C₃×C₅×C₇	D₁₀₁	1	1	yes	characteristic, complemented, Hall
17	C₁₀₁	C₃×C₇×D₅	1	1	yes	characteristic, complemented, Sylow
18	C₇×D₅	—	101	1	no	Hall
19	C₂×C₃×C₇	—	505	1	no	Hall
20	C₅×C₇	C₃×D₁₀₁	1	1	yes	characteristic, complemented, Hall
21	C₃×D₅	—	101	1	no	Hall
22	C₃×C₇	D₅₀₅	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅	C₇×D₁₀₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇	—	505	1	no	Hall
25	D₅	—	101	1	no	Hall
26	C₇	C₃×D₅₀₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	505	1	no	Hall
28	C₅	C₃×C₇×D₁₀₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₇×D₅₀₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	505	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₅₀₅
commutator, cosocle, hypocenter	C₅×C₁₀₁	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₀₁	C₂
LCS	G ▷ C₅×C₁₀₁
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₀₁	C₂	semidirect
2. C₇×D₅₀₅	C₃	direct (N × H)
4. C₅×C₇×C₁₀₁	C₂×C₃	semidirect
5. C₃×D₅₀₅	C₇	direct (N × H)
6. C₃×C₇×C₁₀₁	D₅	semidirect
7. C₃×C₅×C₁₀₁	C₂×C₇	semidirect
9. D₅₀₅	C₃×C₇	direct (N × H)
10. C₇×C₁₀₁	C₃×D₅	semidirect
12. C₅×C₁₀₁	C₂×C₃×C₇	semidirect
13. C₃×C₁₀₁	C₇×D₅	semidirect
16. C₃×C₅×C₇	D₁₀₁	semidirect
17. C₁₀₁	C₃×C₇×D₅	semidirect
20. C₅×C₇	C₃×D₁₀₁	semidirect
22. C₃×C₇	D₅₀₅	direct (N × H)
23. C₃×C₅	C₇×D₁₀₁	semidirect
26. C₇	C₃×D₅₀₅	direct (N × H)
28. C₅	C₃×C₇×D₁₀₁	semidirect
29. C₃	C₇×D₅₀₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×C₁₀₁	2
C₇×D₅₀₅	3
C₃×C₇×D₁₀₁	5
C₃×D₅₀₅	7
C₃×C₇×D₅	101

Subgroups — C3×C7×D505 #35234582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₅₀₅ #35234582