Subgroups — C₂×C₅×D₅₃₅ #24924164

Order 10700.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅₃₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×D₁₀₇	—	5	1	no	maximal
5	C₂×D₅₃₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅×C₁₀₇	—	2	2	no	—
7	C₂×C₅×C₁₀₇	D₅	1	1	yes	characteristic, complemented
8	C₂×C₅×C₁₀₇	C₂×C₅	1	1	yes	characteristic, complemented
9	D₅₃₅	C₂×C₅	1	2	yes	direct product factor
10	C₅×D₁₀₇	—	5	2	no	—
11	C₅×C₁₀₇	—	2	2	no	—
12	C₅×C₁₀₇	C₂×D₅	1	1	yes	characteristic, complemented
13	C₅×C₁₀₇	C₂²×C₅	1	1	yes	characteristic, complemented
14	C₂×D₁₀₇	—	5	1	no	Hall
15	C₂×C₁₀₇	C₅×D₅	1	1	yes	characteristic, complemented
16	D₁₀₇	—	5	2	no	—
17	C₁₀₇	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅×D₅	—	107	1	no	maximal, Hall
19	C₂×C₅²	D₁₀₇	1	1	yes	characteristic, complemented
20	C₅×D₅	—	107	2	no	—
21	C₅²	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₅	—	535	1	no	—
23	C₂×D₅	—	107	1	no	—
24	C₂×C₅	—	2	2	no	—
25	C₂×C₅	—	535	2	no	—
26	C₂×C₅	C₅×D₁₀₇	1	1	yes	characteristic, complemented
27	C₂×C₅	D₅₃₅	1	1	yes	characteristic, direct product factor
28	D₅	—	107	2	no	—
29	C₅	—	2	2	no	—
30	C₅	C₂×D₅₃₅	1	1	yes	characteristic, direct product factor
31	C₅	C₂×C₅×D₁₀₇	1	1	yes	characteristic, complemented
32	C₂²	—	535	1	no	Sylow
33	C₂	—	535	2	no	—
34	C₂	C₅×D₅₃₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₅₃₅
commutator, cosocle, hypocenter	C₅×C₁₀₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₀₇	C₂
LCS	G ▷ C₅×C₁₀₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₅₃₅	C₂	direct (N × H)
2. C₂×C₅²×C₁₀₇	C₂	semidirect
3. C₅²×C₁₀₇	C₂²	semidirect
5. C₂×D₅₃₅	C₅	direct (N × H)
7. C₂×C₅×C₁₀₇	D₅	semidirect
8. C₂×C₅×C₁₀₇	C₂×C₅	semidirect
9. D₅₃₅	C₂×C₅	direct (N × H)
12. C₅×C₁₀₇	C₂×D₅	semidirect
13. C₅×C₁₀₇	C₂²×C₅	semidirect
15. C₂×C₁₀₇	C₅×D₅	semidirect
17. C₁₀₇	C₂×C₅×D₅	semidirect
19. C₂×C₅²	D₁₀₇	semidirect
21. C₅²	C₂×D₁₀₇	semidirect
26. C₂×C₅	C₅×D₁₀₇	semidirect
27. C₂×C₅	D₅₃₅	direct (N × H)
30. C₅	C₂×D₅₃₅	direct (N × H)
31. C₅	C₂×C₅×D₁₀₇	semidirect
34. C₂	C₅×D₅₃₅	direct (N × H)

Subgroups — C2×C5×D535 #24924164

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×D₅₃₅ #24924164