Subgroups — D₅×C₁₇×D₅₅ #34035262

Order 18700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₅⋊D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₇×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₅×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×D₅₅	—	5	1	no	maximal
6	D₅×C₁₇×D₁₁	—	5	1	no	maximal
7	C₂×C₅×C₁₁×C₁₇	—	5	1	no	—
8	C₁₇×D₅₅	—	5	1	no	—
9	C₁₇×D₅₅	—	5	1	no	—
10	C₁₇×D₅₅	—	10	2	no	—
11	C₁₇×D₅₅	D₅	1	1	yes	characteristic, direct product factor
12	D₅×C₁₁×C₁₇	D₅	1	1	yes	characteristic, complemented
13	C₅×C₁₇×D₁₁	—	5	1	no	—
14	D₅²×C₁₇	—	11	1	no	maximal, Hall
15	D₅×D₅₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₅×C₁₁×C₁₇	—	2	2	no	—
17	C₅×C₁₁×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
18	C₅×C₁₁×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
19	C₁₇×C₅⋊D₅	—	11	1	no	—
20	C₅×D₅×C₁₇	—	11	1	no	—
21	C₅×D₅×C₁₇	D₁₁	1	1	yes	characteristic, complemented
22	C₂×C₁₇×D₁₁	—	25	1	no	Hall
23	C₅⋊D₅₅	C₂×C₁₇	1	1	yes	characteristic, complemented
24	C₅×D₅₅	C₂×C₁₇	1	1	yes	characteristic, complemented
25	C₅×D₅×C₁₁	C₂×C₁₇	1	1	yes	characteristic, complemented
26	C₅²×C₁₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₁₁×C₁₇	—	5	1	no	—
28	C₁₇×D₁₁	—	5	1	no	—
29	C₁₇×D₁₁	—	25	1	no	—
30	C₂×D₅×C₁₇	—	55	1	no	—
31	C₂×D₅×C₁₇	—	55	1	no	—
32	C₅²×C₁₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
33	C₂×D₅₅	—	5	1	no	—
34	D₅×D₁₁	—	5	1	no	—
35	C₁₁×C₁₇	D₅²	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₁₇	—	5	1	no	—
37	C₂×C₅×C₁₇	—	55	1	no	—
38	D₅×C₁₇	—	11	1	no	—
39	D₅×C₁₇	—	55	1	no	—
40	D₅×C₁₇	—	55	1	no	—
41	D₅×C₁₇	—	110	2	no	—
42	D₅×C₁₇	D₅₅	1	1	yes	characteristic, direct product factor
43	C₂×C₅×C₁₁	—	5	1	no	—
44	D₅₅	—	5	1	no	—
45	D₅₅	—	5	1	no	—
46	D₅₅	—	10	2	no	—
47	D₅₅	D₅×C₁₇	1	1	yes	characteristic, direct product factor
48	C₅×D₁₁	—	5	1	no	—
49	D₅×C₁₁	D₅×C₁₇	1	1	yes	characteristic, complemented
50	D₅²	—	11	1	no	Hall
51	C₅×C₁₇	—	2	2	no	—
52	C₅×C₁₇	D₅×D₁₁	1	1	yes	characteristic, complemented
53	C₅×C₁₇	C₂×D₅₅	1	1	yes	characteristic, complemented
54	C₂²×C₁₇	—	275	1	no	Hall
55	C₅×C₁₁	—	2	2	no	—
56	C₅×C₁₁	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented
57	C₅×C₁₁	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented
58	C₅⋊D₅	—	11	1	no	—
59	C₅×D₅	—	11	1	no	—
60	C₅×D₅	C₁₇×D₁₁	1	1	yes	characteristic, complemented
61	C₂×D₁₁	—	25	1	no	Hall
62	C₂×C₁₇	—	5	1	no	—
63	C₂×C₁₇	—	275	1	no	—
64	C₂×C₁₇	—	55	1	no	—
65	C₅²	C₂×C₁₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₁₁	—	5	1	no	—
67	D₁₁	—	5	1	no	—
68	D₁₁	—	25	1	no	—
69	C₂×D₅	—	55	1	no	—
70	C₂×D₅	—	55	1	no	—
71	C₁₇	D₅×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
72	C₁₁	D₅²×C₁₇	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	—	5	1	no	—
74	C₂×C₅	—	55	1	no	—
75	D₅	—	11	1	no	—
76	D₅	—	55	1	no	—
77	D₅	—	55	1	no	—
78	D₅	—	110	2	no	—
79	D₅	C₁₇×D₅₅	1	1	yes	characteristic, direct product factor
80	C₅	—	2	2	no	—
81	C₅	D₅×C₁₇×D₁₁	1	1	yes	characteristic, complemented
82	C₅	C₂×C₁₇×D₅₅	1	1	yes	characteristic, complemented
83	C₂²	—	275	1	no	Sylow
84	C₂	—	5	1	no	—
85	C₂	—	275	1	no	—
86	C₂	—	55	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	D₅×D₅₅
commutator, cosocle, hypocenter	C₅²×C₁₁	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	C₂²
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₅⋊D₅₅	C₂	semidirect
2. C₅×C₁₇×D₅₅	C₂	semidirect
3. C₅×D₅×C₁₁×C₁₇	C₂	semidirect
4. C₅²×C₁₁×C₁₇	C₂²	semidirect
11. C₁₇×D₅₅	D₅	direct (N × H)
12. D₅×C₁₁×C₁₇	D₅	semidirect
15. D₅×D₅₅	C₁₇	direct (N × H)
17. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
18. C₅×C₁₁×C₁₇	C₂×D₅	semidirect
21. C₅×D₅×C₁₇	D₁₁	semidirect
23. C₅⋊D₅₅	C₂×C₁₇	semidirect
24. C₅×D₅₅	C₂×C₁₇	semidirect
25. C₅×D₅×C₁₁	C₂×C₁₇	semidirect
26. C₅²×C₁₇	C₂×D₁₁	semidirect
32. C₅²×C₁₁	C₂²×C₁₇	semidirect
35. C₁₁×C₁₇	D₅²	semidirect
42. D₅×C₁₇	D₅₅	direct (N × H)
47. D₅₅	D₅×C₁₇	direct (N × H)
49. D₅×C₁₁	D₅×C₁₇	semidirect
52. C₅×C₁₇	D₅×D₁₁	semidirect
53. C₅×C₁₇	C₂×D₅₅	semidirect
56. C₅×C₁₁	C₂×D₅×C₁₇	semidirect
57. C₅×C₁₁	C₂×D₅×C₁₇	semidirect
60. C₅×D₅	C₁₇×D₁₁	semidirect
65. C₅²	C₂×C₁₇×D₁₁	semidirect
71. C₁₇	D₅×D₅₅	direct (N × H)
72. C₁₁	D₅²×C₁₇	semidirect
79. D₅	C₁₇×D₅₅	direct (N × H)
81. C₅	D₅×C₁₇×D₁₁	semidirect
82. C₅	C₂×C₁₇×D₅₅	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₅⋊D₅₅	2
C₅×C₁₇×D₅₅	2
C₅×D₅×C₁₁×C₁₇	2
C₂×C₁₇×D₅₅	5
D₅×C₁₇×D₁₁	5
D₅²×C₁₇	11
D₅×D₅₅	17

Subgroups — D5×C17×D55 #34035262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₇×D₅₅ #34035262