Subgroups — C₃×D₅×D₇ #88299

Order 420.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₇	—	5	1	no	maximal, Hall
7	D₃₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×D₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₇×D₅	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×D₅	—	7	1	no	maximal, Hall
11	C₂×C₃×C₇	—	5	1	no	—
12	C₃×D₇	—	5	1	no	—
13	C₃×D₇	D₅	1	1	yes	characteristic, direct product factor
14	C₅×C₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅	—	7	1	no	—
16	C₃×D₅	—	7	1	no	—
17	C₃×D₅	D₇	1	1	yes	characteristic, direct product factor
18	C₂×D₇	—	5	1	no	Hall
19	C₃×C₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅	—	7	1	no	Hall
21	C₃×C₅	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇	—	5	1	no	—
23	D₇	—	5	1	no	—
24	D₇	C₃×D₅	1	1	yes	characteristic, direct product factor
25	C₂²×C₃	—	35	1	no	Hall
26	C₂×C₅	—	7	1	no	—
27	D₅	—	7	1	no	—
28	D₅	C₃×D₇	1	1	yes	characteristic, direct product factor
29	C₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	5	1	no	—
31	C₂×C₃	—	7	1	no	—
32	C₂×C₃	—	35	1	no	—
33	C₅	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	35	1	no	Sylow
35	C₃	D₅×D₇	1	1	yes	characteristic, direct product factor, Sylow
36	C₂	—	5	1	no	—
37	C₂	—	7	1	no	—
38	C₂	—	35	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×D₇
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇	C₂²
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₃₅	C₂	semidirect
2. C₃×C₇×D₅	C₂	semidirect
3. C₃×C₅×D₇	C₂	semidirect
4. D₅×D₇	C₃	direct (N × H)
5. C₃×C₅×C₇	C₂²	semidirect
7. D₃₅	C₂×C₃	semidirect
8. C₅×D₇	C₂×C₃	semidirect
9. C₇×D₅	C₂×C₃	semidirect
13. C₃×D₇	D₅	direct (N × H)
14. C₅×C₇	C₂²×C₃	semidirect
17. C₃×D₅	D₇	direct (N × H)
19. C₃×C₇	C₂×D₅	semidirect
21. C₃×C₅	C₂×D₇	semidirect
24. D₇	C₃×D₅	direct (N × H)
28. D₅	C₃×D₇	direct (N × H)
29. C₇	C₂×C₃×D₅	semidirect
33. C₅	C₂×C₃×D₇	semidirect
35. C₃	D₅×D₇	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×D₃₅	2
C₃×C₇×D₅	2
C₃×C₅×D₇	2
D₅×D₇	3
C₂×C₃×D₇	5
C₂×C₃×D₅	7

Subgroups — C3×D5×D7 #88299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×D₇ #88299