Subgroups — D₃×C₇×D₅ #88302

Order 420.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×D₅	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₃×C₇	—	5	1	no	maximal, Hall
7	C₂×C₅×C₇	—	3	1	no	—
8	C₇×D₅	—	3	1	no	—
9	C₇×D₅	D₃	1	1	yes	characteristic, direct product factor
10	D₃×D₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₇	—	5	1	no	—
12	D₃×C₇	—	5	1	no	—
13	D₃×C₇	D₅	1	1	yes	characteristic, direct product factor
14	C₅×C₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	D₁₅	C₂×C₇	1	1	yes	characteristic, complemented
16	C₃×D₅	C₂×C₇	1	1	yes	characteristic, complemented
17	C₅×D₃	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂²×C₇	—	15	1	no	Hall
19	C₃×C₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅	—	3	1	no	Hall
21	C₃×C₅	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇	—	3	1	no	—
23	C₂×C₇	—	5	1	no	—
24	C₂×C₇	—	15	1	no	—
25	C₂×D₃	—	5	1	no	Hall
26	C₂×C₅	—	3	1	no	—
27	D₅	—	3	1	no	—
28	D₅	D₃×C₇	1	1	yes	characteristic, direct product factor
29	C₇	D₃×D₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	—	5	1	no	—
31	D₃	—	5	1	no	—
32	D₃	C₇×D₅	1	1	yes	characteristic, direct product factor
33	C₅	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	15	1	no	Sylow
35	C₃	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	5	1	no	—
38	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₅	C₂	semidirect
2. C₅×D₃×C₇	C₂	semidirect
3. C₃×C₇×D₅	C₂	semidirect
5. C₃×C₅×C₇	C₂²	semidirect
9. C₇×D₅	D₃	direct (N × H)
10. D₃×D₅	C₇	direct (N × H)
13. D₃×C₇	D₅	direct (N × H)
14. C₅×C₇	C₂×D₃	semidirect
15. D₁₅	C₂×C₇	semidirect
16. C₃×D₅	C₂×C₇	semidirect
17. C₅×D₃	C₂×C₇	semidirect
19. C₃×C₇	C₂×D₅	semidirect
21. C₃×C₅	C₂²×C₇	semidirect
28. D₅	D₃×C₇	direct (N × H)
29. C₇	D₃×D₅	direct (N × H)
32. D₃	C₇×D₅	direct (N × H)
33. C₅	C₂×D₃×C₇	semidirect
35. C₃	C₂×C₇×D₅	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₁₅	2
C₅×D₃×C₇	2
C₃×C₇×D₅	2
C₂×C₇×D₅	3
C₂×D₃×C₇	5
D₃×D₅	7

Subgroups — D3×C7×D5 #88302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×D₅ #88302