Subgroups — D₅²×C₁₁×C₁₇ #34035259

Order 18700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₅×C₁₁×C₁₇	C₂	1	2	yes	maximal, complemented
3	C₅²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅×C₁₁×C₁₇	—	5	2	no	maximal
5	C₂×C₅×C₁₁×C₁₇	—	5	2	no	—
6	D₅×C₁₁×C₁₇	—	5	2	no	—
7	D₅×C₁₁×C₁₇	—	10	2	no	—
8	D₅×C₁₁×C₁₇	D₅	1	2	yes	direct product factor
9	D₅²×C₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	D₅²×C₁₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₇	—	2	2	no	—
12	C₅×C₁₁×C₁₇	C₂×D₅	1	2	yes	complemented
13	C₁₇×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic, complemented
14	C₅×D₅×C₁₇	C₂×C₁₁	1	2	yes	complemented
15	C₂²×C₁₁×C₁₇	—	25	1	no	Hall
16	C₁₁×C₅⋊D₅	C₂×C₁₇	1	1	yes	characteristic, complemented
17	C₅×D₅×C₁₁	C₂×C₁₇	1	2	yes	complemented
18	C₅²×C₁₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
19	C₂×C₁₁×C₁₇	—	5	2	no	—
20	C₂×C₁₁×C₁₇	—	25	1	no	—
21	C₂×D₅×C₁₇	—	5	2	no	—
22	C₅²×C₁₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
23	C₂×D₅×C₁₁	—	5	2	no	—
24	C₁₁×C₁₇	D₅²	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅×C₁₇	—	5	2	no	—
26	D₅×C₁₇	—	5	2	no	—
27	D₅×C₁₇	—	10	2	no	—
28	D₅×C₁₇	D₅×C₁₁	1	2	yes	direct product factor
29	C₂×C₅×C₁₁	—	5	2	no	—
30	D₅×C₁₁	—	5	2	no	—
31	D₅×C₁₁	—	10	2	no	—
32	D₅×C₁₁	D₅×C₁₇	1	2	yes	direct product factor
33	D₅²	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
34	C₅×C₁₇	—	2	2	no	—
35	C₅×C₁₇	C₂×D₅×C₁₁	1	2	yes	complemented
36	C₂²×C₁₇	—	25	1	no	Hall
37	C₅×C₁₁	—	2	2	no	—
38	C₅×C₁₁	C₂×D₅×C₁₇	1	2	yes	complemented
39	C₅⋊D₅	C₂×C₁₁×C₁₇	1	1	yes	characteristic, complemented
40	C₅×D₅	C₂×C₁₁×C₁₇	1	2	yes	complemented
41	C₂²×C₁₁	—	25	1	no	Hall
42	C₂×C₁₇	—	5	2	no	—
43	C₂×C₁₇	—	25	1	no	—
44	C₅²	C₂²×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₁	—	5	2	no	—
46	C₂×C₁₁	—	25	1	no	—
47	C₂×D₅	—	5	2	no	—
48	C₁₇	D₅²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
49	C₁₁	D₅²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₅	—	5	2	no	—
51	D₅	—	5	2	no	—
52	D₅	—	10	2	no	—
53	D₅	D₅×C₁₁×C₁₇	1	2	yes	direct product factor
54	C₅	—	2	2	no	—
55	C₅	C₂×D₅×C₁₁×C₁₇	1	2	yes	complemented
56	C₂²	—	25	1	no	Sylow
57	C₂	—	5	2	no	—
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₁₇	D₅²
commutator, cosocle, hypocenter	C₅²	C₂²×C₁₁×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₁×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₇×C₅⋊D₅	C₂	semidirect
2. C₅×D₅×C₁₁×C₁₇	C₂	semidirect
3. C₅²×C₁₁×C₁₇	C₂²	semidirect
8. D₅×C₁₁×C₁₇	D₅	direct (N × H)
9. D₅²×C₁₇	C₁₁	direct (N × H)
10. D₅²×C₁₁	C₁₇	direct (N × H)
12. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
13. C₁₇×C₅⋊D₅	C₂×C₁₁	semidirect
14. C₅×D₅×C₁₇	C₂×C₁₁	semidirect
16. C₁₁×C₅⋊D₅	C₂×C₁₇	semidirect
17. C₅×D₅×C₁₁	C₂×C₁₇	semidirect
18. C₅²×C₁₇	C₂²×C₁₁	semidirect
22. C₅²×C₁₁	C₂²×C₁₇	semidirect
24. C₁₁×C₁₇	D₅²	direct (N × H)
28. D₅×C₁₇	D₅×C₁₁	direct (N × H)
32. D₅×C₁₁	D₅×C₁₇	direct (N × H)
33. D₅²	C₁₁×C₁₇	direct (N × H)
35. C₅×C₁₇	C₂×D₅×C₁₁	semidirect
38. C₅×C₁₁	C₂×D₅×C₁₇	semidirect
39. C₅⋊D₅	C₂×C₁₁×C₁₇	semidirect
40. C₅×D₅	C₂×C₁₁×C₁₇	semidirect
44. C₅²	C₂²×C₁₁×C₁₇	semidirect
48. C₁₇	D₅²×C₁₁	direct (N × H)
49. C₁₁	D₅²×C₁₇	direct (N × H)
53. D₅	D₅×C₁₁×C₁₇	direct (N × H)
55. C₅	C₂×D₅×C₁₁×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₇×C₅⋊D₅	2
C₅×D₅×C₁₁×C₁₇	2
C₂×D₅×C₁₁×C₁₇	5
D₅²×C₁₇	11
D₅²×C₁₁	17

Subgroups — D52×C11×C17 #34035259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅²×C₁₁×C₁₇ #34035259