Subgroups — C₂×C₃×C₇×D₅ #88310

Order 420.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×D₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₃×C₇	—	5	1	no	maximal, Hall
6	C₂×C₅×C₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×D₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇	—	5	2	no	—
10	C₂×C₃×C₇	D₅	1	1	yes	characteristic, direct product factor
11	C₅×C₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅	C₂×C₇	1	1	yes	characteristic, complemented
13	C₃×D₅	C₂×C₇	1	2	yes	direct product factor
14	C₂²×C₇	—	5	1	no	Hall
15	C₃×C₇	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂×D₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₅	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇	—	5	2	no	—
19	C₂×C₇	C₃×D₅	1	1	yes	characteristic, direct product factor
20	C₂²×C₃	—	5	1	no	Hall
21	C₂×C₅	C₂×C₃×C₇	1	1	yes	characteristic, complemented
22	D₅	C₂×C₃×C₇	1	2	yes	direct product factor
23	C₇	C₂×C₃×D₅	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₃	—	5	2	no	—
25	C₂×C₃	C₇×D₅	1	1	yes	characteristic, direct product factor
26	C₅	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	5	1	no	Sylow
28	C₃	C₂×C₇×D₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	5	2	no	—
30	C₂	C₃×C₇×D₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₇	C₂	semidirect
2. C₃×C₇×D₅	C₂	direct (N × H)
3. C₂×C₇×D₅	C₃	direct (N × H)
4. C₃×C₅×C₇	C₂²	semidirect
6. C₂×C₅×C₇	C₂×C₃	semidirect
7. C₇×D₅	C₂×C₃	direct (N × H)
8. C₂×C₃×D₅	C₇	direct (N × H)
10. C₂×C₃×C₇	D₅	direct (N × H)
11. C₅×C₇	C₂²×C₃	semidirect
12. C₂×C₃×C₅	C₂×C₇	semidirect
13. C₃×D₅	C₂×C₇	direct (N × H)
15. C₃×C₇	C₂×D₅	direct (N × H)
16. C₂×D₅	C₃×C₇	direct (N × H)
17. C₃×C₅	C₂²×C₇	semidirect
19. C₂×C₇	C₃×D₅	direct (N × H)
21. C₂×C₅	C₂×C₃×C₇	semidirect
22. D₅	C₂×C₃×C₇	direct (N × H)
23. C₇	C₂×C₃×D₅	direct (N × H)
25. C₂×C₃	C₇×D₅	direct (N × H)
26. C₅	C₂²×C₃×C₇	semidirect
28. C₃	C₂×C₇×D₅	direct (N × H)
30. C₂	C₃×C₇×D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₇	2
C₃×C₇×D₅	2
C₂×C₇×D₅	3
C₂²×C₃×C₇	5
C₂×C₃×D₅	7

Subgroups — C2×C3×C7×D5 #88310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×D₅ #88310