Subgroups — D₅×D₅₃₅ #24924160

Order 10700.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₅₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₅×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₅₃₅	—	5	1	no	maximal
6	D₅×D₁₀₇	—	5	1	no	maximal
7	C₂×C₅×C₁₀₇	—	5	1	no	—
8	D₅₃₅	—	5	1	no	—
9	D₅₃₅	—	5	1	no	—
10	D₅₃₅	—	10	2	no	—
11	D₅₃₅	D₅	1	1	yes	characteristic, direct product factor
12	C₅×D₁₀₇	—	5	1	no	—
13	D₅×C₁₀₇	D₅	1	1	yes	characteristic, complemented
14	C₅×C₁₀₇	—	2	2	no	—
15	C₅×C₁₀₇	C₂×D₅	1	1	yes	characteristic, complemented
16	C₅×C₁₀₇	C₂×D₅	1	1	yes	characteristic, complemented
17	C₂×D₁₀₇	—	25	1	no	Hall
18	C₂×C₁₀₇	—	5	1	no	—
19	D₁₀₇	—	5	1	no	—
20	D₁₀₇	—	25	1	no	—
21	C₁₀₇	D₅²	1	1	yes	characteristic, complemented, Sylow
22	D₅²	—	107	1	no	maximal, Hall
23	C₅⋊D₅	—	107	1	no	—
24	C₅×D₅	—	107	1	no	—
25	C₅×D₅	D₁₀₇	1	1	yes	characteristic, complemented
26	C₅²	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₅	—	535	1	no	—
28	C₂×D₅	—	535	1	no	—
29	C₂×C₅	—	5	1	no	—
30	C₂×C₅	—	535	1	no	—
31	D₅	—	535	1	no	—
32	D₅	—	535	1	no	—
33	D₅	—	1070	2	no	—
34	D₅	—	107	1	no	—
35	D₅	D₅₃₅	1	1	yes	characteristic, direct product factor
36	C₅	—	2	2	no	—
37	C₅	D₅×D₁₀₇	1	1	yes	characteristic, complemented
38	C₅	C₂×D₅₃₅	1	1	yes	characteristic, complemented
39	C₂²	—	2675	1	no	Sylow
40	C₂	—	5	1	no	—
41	C₂	—	535	1	no	—
42	C₂	—	2675	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₅⋊D₅₃₅	C₂	semidirect
2. C₅×D₅₃₅	C₂	semidirect
3. C₅×D₅×C₁₀₇	C₂	semidirect
4. C₅²×C₁₀₇	C₂²	semidirect
11. D₅₃₅	D₅	direct (N × H)
13. D₅×C₁₀₇	D₅	semidirect
15. C₅×C₁₀₇	C₂×D₅	semidirect
16. C₅×C₁₀₇	C₂×D₅	semidirect
21. C₁₀₇	D₅²	semidirect
25. C₅×D₅	D₁₀₇	semidirect
26. C₅²	C₂×D₁₀₇	semidirect
35. D₅	D₅₃₅	direct (N × H)
37. C₅	D₅×D₁₀₇	semidirect
38. C₅	C₂×D₅₃₅	semidirect

Subgroups — D5×D535 #24924160

Conjugacy classes of subgroups

Complements

Subgroups — D₅×D₅₃₅ #24924160