Subgroups — C₂²×C₃×C₅×C₇ #88316

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	3	yes	maximal, direct product factor
2	C₂²×C₅×C₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₃×C₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₇	C₂×C₃	1	3	yes	direct product factor
6	C₂²×C₃×C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₇	C₂×C₅	1	3	yes	direct product factor
8	C₅×C₇	C₂²×C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₅	C₂×C₇	1	3	yes	direct product factor
10	C₂²×C₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅	C₂²×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₇	C₂×C₃×C₅	1	3	yes	direct product factor
15	C₂²×C₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₅	C₂×C₃×C₇	1	3	yes	direct product factor
17	C₇	C₂²×C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃	C₂×C₅×C₇	1	3	yes	direct product factor
19	C₅	C₂²×C₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²	C₃×C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₂²×C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₅×C₇	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₇	C₂	direct (N × H)
2. C₂²×C₅×C₇	C₃	direct (N × H)
3. C₃×C₅×C₇	C₂²	direct (N × H)
4. C₂²×C₃×C₇	C₅	direct (N × H)
5. C₂×C₅×C₇	C₂×C₃	direct (N × H)
6. C₂²×C₃×C₅	C₇	direct (N × H)
7. C₂×C₃×C₇	C₂×C₅	direct (N × H)
8. C₅×C₇	C₂²×C₃	direct (N × H)
9. C₂×C₃×C₅	C₂×C₇	direct (N × H)
10. C₂²×C₇	C₃×C₅	direct (N × H)
11. C₃×C₇	C₂²×C₅	direct (N × H)
12. C₂²×C₅	C₃×C₇	direct (N × H)
13. C₃×C₅	C₂²×C₇	direct (N × H)
14. C₂×C₇	C₂×C₃×C₅	direct (N × H)
15. C₂²×C₃	C₅×C₇	direct (N × H)
16. C₂×C₅	C₂×C₃×C₇	direct (N × H)
17. C₇	C₂²×C₃×C₅	direct (N × H)
18. C₂×C₃	C₂×C₅×C₇	direct (N × H)
19. C₅	C₂²×C₃×C₇	direct (N × H)
20. C₂²	C₃×C₅×C₇	direct (N × H)
21. C₃	C₂²×C₅×C₇	direct (N × H)
22. C₂	C₂×C₃×C₅×C₇	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
C₂²×C₅×C₇	3
C₂²×C₃×C₇	5
C₂²×C₃×C₅	7

Subgroups — C22×C3×C5×C7 #88316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₅×C₇ #88316