Subgroups — C₂×C₃²×C₁₉×C₅⋊D₅ #30685978

Order 17100.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×C₅⋊D₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₉×C₅⋊D₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₅×C₁₉	—	5	6	no	maximal
6	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	4	yes	complemented
8	C₂×C₁₉×C₅⋊D₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₅×C₁₉	D₅	1	6	yes	complemented
10	C₃²×D₅×C₁₉	—	5	12	no	—
11	C₃×C₅²×C₁₉	C₂²×C₃	1	4	yes	complemented
12	C₂×C₃×D₅×C₁₉	—	5	24	no	—
13	C₂×C₅²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
14	C₁₉×C₅⋊D₅	C₂×C₃²	1	2	yes	direct product factor
15	C₂×C₃²×C₅⋊D₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃²×C₅×C₁₉	C₂×D₅	1	6	yes	complemented
17	C₂²×C₃²×C₁₉	—	25	1	no	Hall
18	C₂×C₃×C₅×C₁₉	C₃×D₅	1	24	yes	complemented
19	C₃×D₅×C₁₉	—	5	48	no	—
20	C₅²×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃²×C₅²	C₂×C₁₉	1	1	yes	characteristic, complemented
22	C₃²×C₅⋊D₅	C₂×C₁₉	1	2	yes	direct product factor
23	C₂×D₅×C₁₉	—	5	6	no	—
24	C₂×C₃²×C₁₉	—	25	2	no	—
25	C₂×C₃²×C₁₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor
26	C₂×C₃×C₅⋊D₅	C₃×C₁₉	1	4	yes	direct product factor
27	C₃×C₅×C₁₉	C₂×C₃×D₅	1	24	yes	complemented
28	C₂²×C₃×C₁₉	—	25	4	no	—
29	C₃²×C₅²	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₁₉	C₃²×D₅	1	6	yes	complemented
31	D₅×C₁₉	—	5	12	no	—
32	C₂×C₃²×D₅	—	5	6	no	—
33	C₃²×C₁₉	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₃×C₅²	C₂×C₃×C₁₉	1	4	yes	complemented
35	C₃×C₅⋊D₅	C₂×C₃×C₁₉	1	8	yes	direct product factor
36	C₂×C₃×C₁₉	—	25	8	no	—
37	C₂×C₃×C₁₉	C₃×C₅⋊D₅	1	4	yes	direct product factor
38	C₂×C₅⋊D₅	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
39	C₅×C₁₉	C₂×C₃²×D₅	1	6	yes	complemented
40	C₂×C₃²×C₅	D₅×C₁₉	1	6	yes	complemented
41	C₃²×D₅	—	5	12	no	—
42	C₂²×C₁₉	—	25	1	no	Hall
43	C₃×C₅²	C₂²×C₃×C₁₉	1	4	yes	complemented
44	C₂×C₃×D₅	—	5	24	no	—
45	C₃×C₁₉	C₂×C₃×C₅⋊D₅	1	4	yes	direct product factor
46	C₂×C₅²	C₂×C₃²×C₁₉	1	1	yes	characteristic, complemented
47	C₅⋊D₅	C₂×C₃²×C₁₉	1	2	yes	direct product factor
48	C₃²×C₅	C₂×D₅×C₁₉	1	6	yes	complemented
49	C₂×C₁₉	—	25	2	no	—
50	C₂×C₁₉	C₃²×C₅⋊D₅	1	1	yes	characteristic, direct product factor
51	C₂²×C₃²	—	25	1	no	Hall
52	C₂×C₃×C₅	C₃×D₅×C₁₉	1	24	yes	complemented
53	C₃×D₅	—	5	48	no	—
54	C₅²	C₂²×C₃²×C₁₉	1	1	yes	characteristic, complemented, Sylow
55	C₂×D₅	—	5	6	no	—
56	C₁₉	C₂×C₃²×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃²	—	25	2	no	—
58	C₂×C₃²	C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor
59	C₃×C₅	C₂×C₃×D₅×C₁₉	1	24	yes	complemented
60	C₂²×C₃	—	25	4	no	—
61	C₂×C₅	C₃²×D₅×C₁₉	1	6	yes	complemented
62	D₅	—	5	12	no	—
63	C₃²	C₂×C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	—	25	8	no	—
65	C₂×C₃	C₃×C₁₉×C₅⋊D₅	1	4	yes	direct product factor
66	C₅	C₂×C₃²×D₅×C₁₉	1	6	yes	complemented
67	C₂²	—	25	1	no	Sylow
68	C₃	C₂×C₃×C₁₉×C₅⋊D₅	1	4	yes	direct product factor
69	C₂	—	25	2	no	—
70	C₂	C₃²×C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃²×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₉×C₅⋊D₅	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₁₉	C₂	semidirect
3. C₂×C₃×C₁₉×C₅⋊D₅	C₃	direct (N × H)
4. C₃²×C₅²×C₁₉	C₂²	semidirect
6. C₃×C₁₉×C₅⋊D₅	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
8. C₂×C₁₉×C₅⋊D₅	C₃²	direct (N × H)
9. C₂×C₃²×C₅×C₁₉	D₅	semidirect
11. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
13. C₂×C₅²×C₁₉	C₂×C₃²	semidirect
14. C₁₉×C₅⋊D₅	C₂×C₃²	direct (N × H)
15. C₂×C₃²×C₅⋊D₅	C₁₉	direct (N × H)
16. C₃²×C₅×C₁₉	C₂×D₅	semidirect
18. C₂×C₃×C₅×C₁₉	C₃×D₅	semidirect
20. C₅²×C₁₉	C₂²×C₃²	semidirect
21. C₂×C₃²×C₅²	C₂×C₁₉	semidirect
22. C₃²×C₅⋊D₅	C₂×C₁₉	direct (N × H)
25. C₂×C₃²×C₁₉	C₅⋊D₅	direct (N × H)
26. C₂×C₃×C₅⋊D₅	C₃×C₁₉	direct (N × H)
27. C₃×C₅×C₁₉	C₂×C₃×D₅	semidirect
29. C₃²×C₅²	C₂²×C₁₉	semidirect
30. C₂×C₅×C₁₉	C₃²×D₅	semidirect
33. C₃²×C₁₉	C₂×C₅⋊D₅	direct (N × H)
34. C₂×C₃×C₅²	C₂×C₃×C₁₉	semidirect
35. C₃×C₅⋊D₅	C₂×C₃×C₁₉	direct (N × H)
37. C₂×C₃×C₁₉	C₃×C₅⋊D₅	direct (N × H)
38. C₂×C₅⋊D₅	C₃²×C₁₉	direct (N × H)
39. C₅×C₁₉	C₂×C₃²×D₅	semidirect
40. C₂×C₃²×C₅	D₅×C₁₉	semidirect
43. C₃×C₅²	C₂²×C₃×C₁₉	semidirect
45. C₃×C₁₉	C₂×C₃×C₅⋊D₅	direct (N × H)
46. C₂×C₅²	C₂×C₃²×C₁₉	semidirect
47. C₅⋊D₅	C₂×C₃²×C₁₉	direct (N × H)
48. C₃²×C₅	C₂×D₅×C₁₉	semidirect
50. C₂×C₁₉	C₃²×C₅⋊D₅	direct (N × H)
52. C₂×C₃×C₅	C₃×D₅×C₁₉	semidirect
54. C₅²	C₂²×C₃²×C₁₉	semidirect
56. C₁₉	C₂×C₃²×C₅⋊D₅	direct (N × H)
58. C₂×C₃²	C₁₉×C₅⋊D₅	direct (N × H)
59. C₃×C₅	C₂×C₃×D₅×C₁₉	semidirect
61. C₂×C₅	C₃²×D₅×C₁₉	semidirect
63. C₃²	C₂×C₁₉×C₅⋊D₅	direct (N × H)
65. C₂×C₃	C₃×C₁₉×C₅⋊D₅	direct (N × H)
66. C₅	C₂×C₃²×D₅×C₁₉	semidirect
68. C₃	C₂×C₃×C₁₉×C₅⋊D₅	direct (N × H)
70. C₂	C₃²×C₁₉×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×C₁₉×C₅⋊D₅	2
C₂×C₃²×C₅²×C₁₉	2
C₂×C₃×C₁₉×C₅⋊D₅	3
C₂×C₃²×D₅×C₁₉	5
C₂×C₃²×C₅⋊D₅	19

Subgroups — C2×C32×C19×C5⋊D5 #30685978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₁₉×C₅⋊D₅ #30685978