Subgroups — C₂×D₃₅×C₁₀₃ #28385751

Order 14420.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₅×C₁₀₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₇×C₁₀₃	—	5	1	no	maximal, Hall
5	C₂×D₅×C₁₀₃	—	7	1	no	maximal, Hall
6	C₂×C₇×C₁₀₃	D₅	1	1	yes	characteristic, complemented
7	D₇×C₁₀₃	—	5	2	no	—
8	C₂×C₅×C₁₀₃	D₇	1	1	yes	characteristic, complemented
9	D₅×C₁₀₃	—	7	2	no	—
10	C₇×C₁₀₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₁₀₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₁₀₃	—	35	1	no	Hall
13	C₂×C₁₀₃	—	35	2	no	—
14	C₂×C₁₀₃	D₃₅	1	1	yes	characteristic, direct product factor
15	C₂×D₃₅	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₀₃	C₂×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₅×C₇	C₂×C₁₀₃	1	1	yes	characteristic, complemented
18	D₃₅	C₂×C₁₀₃	1	2	yes	direct product factor
19	C₅×C₇	C₂²×C₁₀₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₇	—	5	1	no	Hall
21	C₂×D₅	—	7	1	no	Hall
22	C₂×C₇	D₅×C₁₀₃	1	1	yes	characteristic, complemented
23	D₇	—	5	2	no	—
24	C₂×C₅	D₇×C₁₀₃	1	1	yes	characteristic, complemented
25	D₅	—	7	2	no	—
26	C₇	C₂×D₅×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
27	C₅	C₂×D₇×C₁₀₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	35	1	no	Sylow
29	C₂	—	35	2	no	—
30	C₂	D₃₅×C₁₀₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₀₃	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₀₃	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₁₀₃

Complements

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

N	H ≅ G/N	type
1. D₃₅×C₁₀₃	C₂	direct (N × H)
2. C₂×C₅×C₇×C₁₀₃	C₂	semidirect
3. C₅×C₇×C₁₀₃	C₂²	semidirect
6. C₂×C₇×C₁₀₃	D₅	semidirect
8. C₂×C₅×C₁₀₃	D₇	semidirect
10. C₇×C₁₀₃	C₂×D₅	semidirect
11. C₅×C₁₀₃	C₂×D₇	semidirect
14. C₂×C₁₀₃	D₃₅	direct (N × H)
15. C₂×D₃₅	C₁₀₃	direct (N × H)
16. C₁₀₃	C₂×D₃₅	direct (N × H)
17. C₂×C₅×C₇	C₂×C₁₀₃	semidirect
18. D₃₅	C₂×C₁₀₃	direct (N × H)
19. C₅×C₇	C₂²×C₁₀₃	semidirect
22. C₂×C₇	D₅×C₁₀₃	semidirect
24. C₂×C₅	D₇×C₁₀₃	semidirect
26. C₇	C₂×D₅×C₁₀₃	semidirect
27. C₅	C₂×D₇×C₁₀₃	semidirect
30. C₂	D₃₅×C₁₀₃	direct (N × H)

Maximal subgroups

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

subgroup	index
D₃₅×C₁₀₃	2
C₂×C₅×C₇×C₁₀₃	2
C₂×D₇×C₁₀₃	5
C₂×D₅×C₁₀₃	7
C₂×D₃₅	103

Subgroups — C2×D35×C103 #28385751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃₅×C₁₀₃ #28385751