Subgroups — C₂×C₃²×C₁₇×C₅⋊D₅ #29506084

Order 15300.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₅⋊D₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₇×C₅⋊D₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₅×C₁₇	—	5	6	no	maximal
6	C₃×C₁₇×C₅⋊D₅	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅²×C₁₇	C₂×C₃	1	4	yes	complemented
8	C₂×C₁₇×C₅⋊D₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₅×C₁₇	D₅	1	6	yes	complemented
10	C₃²×D₅×C₁₇	—	5	12	no	—
11	C₃×C₅²×C₁₇	C₂²×C₃	1	4	yes	complemented
12	C₂×C₃×D₅×C₁₇	—	5	24	no	—
13	C₂×C₃²×C₅⋊D₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₅²×C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented
15	C₁₇×C₅⋊D₅	C₂×C₃²	1	2	yes	direct product factor
16	C₃²×C₅×C₁₇	C₂×D₅	1	6	yes	complemented
17	C₂²×C₃²×C₁₇	—	25	1	no	Hall
18	C₂×C₃×C₅×C₁₇	C₃×D₅	1	24	yes	complemented
19	C₃×D₅×C₁₇	—	5	48	no	—
20	C₂×C₃²×C₅²	C₂×C₁₇	1	1	yes	characteristic, complemented
21	C₃²×C₅⋊D₅	C₂×C₁₇	1	2	yes	direct product factor
22	C₅²×C₁₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
23	C₂×D₅×C₁₇	—	5	6	no	—
24	C₂×C₃²×C₁₇	—	25	2	no	—
25	C₂×C₃²×C₁₇	C₅⋊D₅	1	1	yes	characteristic, direct product factor
26	C₂×C₃×C₅⋊D₅	C₃×C₁₇	1	4	yes	direct product factor
27	C₃×C₅×C₁₇	C₂×C₃×D₅	1	24	yes	complemented
28	C₃²×C₅²	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₃×C₁₇	—	25	4	no	—
30	C₂×C₃²×D₅	—	5	6	no	—
31	C₂×C₅×C₁₇	C₃²×D₅	1	6	yes	complemented
32	D₅×C₁₇	—	5	12	no	—
33	C₃²×C₁₇	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₃×C₅²	C₂×C₃×C₁₇	1	4	yes	complemented
35	C₃×C₅⋊D₅	C₂×C₃×C₁₇	1	8	yes	direct product factor
36	C₂×C₃×C₁₇	—	25	8	no	—
37	C₂×C₃×C₁₇	C₃×C₅⋊D₅	1	4	yes	direct product factor
38	C₂×C₅⋊D₅	C₃²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₃²×C₅	D₅×C₁₇	1	6	yes	complemented
40	C₃²×D₅	—	5	12	no	—
41	C₅×C₁₇	C₂×C₃²×D₅	1	6	yes	complemented
42	C₃×C₅²	C₂²×C₃×C₁₇	1	4	yes	complemented
43	C₂²×C₁₇	—	25	1	no	Hall
44	C₂×C₃×D₅	—	5	24	no	—
45	C₃×C₁₇	C₂×C₃×C₅⋊D₅	1	4	yes	direct product factor
46	C₂×C₅²	C₂×C₃²×C₁₇	1	1	yes	characteristic, complemented
47	C₅⋊D₅	C₂×C₃²×C₁₇	1	2	yes	direct product factor
48	C₃²×C₅	C₂×D₅×C₁₇	1	6	yes	complemented
49	C₂²×C₃²	—	25	1	no	Hall
50	C₂×C₁₇	—	25	2	no	—
51	C₂×C₁₇	C₃²×C₅⋊D₅	1	1	yes	characteristic, direct product factor
52	C₂×C₃×C₅	C₃×D₅×C₁₇	1	24	yes	complemented
53	C₃×D₅	—	5	48	no	—
54	C₅²	C₂²×C₃²×C₁₇	1	1	yes	characteristic, complemented, Sylow
55	C₂×D₅	—	5	6	no	—
56	C₂×C₃²	—	25	2	no	—
57	C₂×C₃²	C₁₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor
58	C₁₇	C₂×C₃²×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
59	C₃×C₅	C₂×C₃×D₅×C₁₇	1	24	yes	complemented
60	C₂²×C₃	—	25	4	no	—
61	C₂×C₅	C₃²×D₅×C₁₇	1	6	yes	complemented
62	D₅	—	5	12	no	—
63	C₃²	C₂×C₁₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	—	25	8	no	—
65	C₂×C₃	C₃×C₁₇×C₅⋊D₅	1	4	yes	direct product factor
66	C₅	C₂×C₃²×D₅×C₁₇	1	6	yes	complemented
67	C₂²	—	25	1	no	Sylow
68	C₃	C₂×C₃×C₁₇×C₅⋊D₅	1	4	yes	direct product factor
69	C₂	—	25	2	no	—
70	C₂	C₃²×C₁₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₇	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₃²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₁₇	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃²×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₇×C₅⋊D₅	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₁₇	C₂	semidirect
3. C₂×C₃×C₁₇×C₅⋊D₅	C₃	direct (N × H)
4. C₃²×C₅²×C₁₇	C₂²	semidirect
6. C₃×C₁₇×C₅⋊D₅	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅²×C₁₇	C₂×C₃	semidirect
8. C₂×C₁₇×C₅⋊D₅	C₃²	direct (N × H)
9. C₂×C₃²×C₅×C₁₇	D₅	semidirect
11. C₃×C₅²×C₁₇	C₂²×C₃	semidirect
13. C₂×C₃²×C₅⋊D₅	C₁₇	direct (N × H)
14. C₂×C₅²×C₁₇	C₂×C₃²	semidirect
15. C₁₇×C₅⋊D₅	C₂×C₃²	direct (N × H)
16. C₃²×C₅×C₁₇	C₂×D₅	semidirect
18. C₂×C₃×C₅×C₁₇	C₃×D₅	semidirect
20. C₂×C₃²×C₅²	C₂×C₁₇	semidirect
21. C₃²×C₅⋊D₅	C₂×C₁₇	direct (N × H)
22. C₅²×C₁₇	C₂²×C₃²	semidirect
25. C₂×C₃²×C₁₇	C₅⋊D₅	direct (N × H)
26. C₂×C₃×C₅⋊D₅	C₃×C₁₇	direct (N × H)
27. C₃×C₅×C₁₇	C₂×C₃×D₅	semidirect
28. C₃²×C₅²	C₂²×C₁₇	semidirect
31. C₂×C₅×C₁₇	C₃²×D₅	semidirect
33. C₃²×C₁₇	C₂×C₅⋊D₅	direct (N × H)
34. C₂×C₃×C₅²	C₂×C₃×C₁₇	semidirect
35. C₃×C₅⋊D₅	C₂×C₃×C₁₇	direct (N × H)
37. C₂×C₃×C₁₇	C₃×C₅⋊D₅	direct (N × H)
38. C₂×C₅⋊D₅	C₃²×C₁₇	direct (N × H)
39. C₂×C₃²×C₅	D₅×C₁₇	semidirect
41. C₅×C₁₇	C₂×C₃²×D₅	semidirect
42. C₃×C₅²	C₂²×C₃×C₁₇	semidirect
45. C₃×C₁₇	C₂×C₃×C₅⋊D₅	direct (N × H)
46. C₂×C₅²	C₂×C₃²×C₁₇	semidirect
47. C₅⋊D₅	C₂×C₃²×C₁₇	direct (N × H)
48. C₃²×C₅	C₂×D₅×C₁₇	semidirect
51. C₂×C₁₇	C₃²×C₅⋊D₅	direct (N × H)
52. C₂×C₃×C₅	C₃×D₅×C₁₇	semidirect
54. C₅²	C₂²×C₃²×C₁₇	semidirect
57. C₂×C₃²	C₁₇×C₅⋊D₅	direct (N × H)
58. C₁₇	C₂×C₃²×C₅⋊D₅	direct (N × H)
59. C₃×C₅	C₂×C₃×D₅×C₁₇	semidirect
61. C₂×C₅	C₃²×D₅×C₁₇	semidirect
63. C₃²	C₂×C₁₇×C₅⋊D₅	direct (N × H)
65. C₂×C₃	C₃×C₁₇×C₅⋊D₅	direct (N × H)
66. C₅	C₂×C₃²×D₅×C₁₇	semidirect
68. C₃	C₂×C₃×C₁₇×C₅⋊D₅	direct (N × H)
70. C₂	C₃²×C₁₇×C₅⋊D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₇×C₅⋊D₅	2
C₂×C₃²×C₅²×C₁₇	2
C₂×C₃×C₁₇×C₅⋊D₅	3
C₂×C₃²×D₅×C₁₇	5
C₂×C₃²×C₅⋊D₅	17

Subgroups — C2×C32×C17×C5⋊D5 #29506084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₁₇×C₅⋊D₅ #29506084