Subgroups — C₂×C₃×C₁₉×(C₅⋊D₅)⋊C₃ #30685833

Order 17100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	(C₅⋊D₅)⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂²×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₉×C₅²⋊C₃	C₂	semidirect
2. C₃×C₁₉×(C₅⋊D₅)⋊C₃	C₂	direct (N × H)
3. C₂×C₃×C₁₉×C₅⋊D₅	C₃	semidirect
4. C₂×C₁₉×(C₅⋊D₅)⋊C₃	C₃	direct (N × H)
5. C₃×C₁₉×C₅²⋊C₃	C₂²	semidirect
6. C₃×C₁₉×C₅⋊D₅	C₂×C₃	semidirect
7. C₂×C₁₉×C₅²⋊C₃	C₂×C₃	semidirect
8. C₁₉×(C₅⋊D₅)⋊C₃	C₂×C₃	direct (N × H)
9. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
10. C₂×C₁₉×C₅⋊D₅	C₃²	semidirect
11. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
12. C₁₉×C₅²⋊C₃	C₂²×C₃	semidirect
14. C₂×C₅²×C₁₉	C₂×C₃²	semidirect
15. C₁₉×C₅⋊D₅	C₂×C₃²	semidirect
16. C₂×C₃×(C₅⋊D₅)⋊C₃	C₁₉	direct (N × H)
20. C₅²×C₁₉	C₂²×C₃²	semidirect
21. C₂×C₃×C₅²⋊C₃	C₂×C₁₉	semidirect
22. C₃×(C₅⋊D₅)⋊C₃	C₂×C₁₉	direct (N × H)
26. C₂×C₃×C₅⋊D₅	C₃×C₁₉	semidirect
27. C₂×(C₅⋊D₅)⋊C₃	C₃×C₁₉	direct (N × H)
31. C₃×C₅²⋊C₃	C₂²×C₁₉	semidirect
35. C₂×C₃×C₅²	C₂×C₃×C₁₉	semidirect
36. C₃×C₅⋊D₅	C₂×C₃×C₁₉	semidirect
37. C₂×C₅²⋊C₃	C₂×C₃×C₁₉	semidirect
38. (C₅⋊D₅)⋊C₃	C₂×C₃×C₁₉	direct (N × H)
42. C₂×C₃×C₁₉	(C₅⋊D₅)⋊C₃	direct (N × H)
43. C₂×C₅⋊D₅	C₃²×C₁₉	semidirect
46. C₃×C₅²	C₂²×C₃×C₁₉	semidirect
47. C₅²⋊C₃	C₂²×C₃×C₁₉	semidirect
50. C₃×C₁₉	C₂×(C₅⋊D₅)⋊C₃	direct (N × H)
51. C₂×C₅²	C₂×C₃²×C₁₉	semidirect
52. C₅⋊D₅	C₂×C₃²×C₁₉	semidirect
54. C₂×C₁₉	C₃×(C₅⋊D₅)⋊C₃	direct (N × H)
58. C₅²	C₂²×C₃²×C₁₉	semidirect
60. C₁₉	C₂×C₃×(C₅⋊D₅)⋊C₃	direct (N × H)
72. C₂×C₃	C₁₉×(C₅⋊D₅)⋊C₃	direct (N × H)
76. C₃	C₂×C₁₉×(C₅⋊D₅)⋊C₃	direct (N × H)
78. C₂	C₃×C₁₉×(C₅⋊D₅)⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₉×C₅²⋊C₃	2
C₃×C₁₉×(C₅⋊D₅)⋊C₃	2
C₂×C₃×C₁₉×C₅⋊D₅	3
C₂×C₁₉×(C₅⋊D₅)⋊C₃	3
C₂×C₃×(C₅⋊D₅)⋊C₃	19
C₂²×C₃²×C₁₉	25

Subgroups — C2×C3×C19×(C5⋊D5)⋊C3 #30685833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₉×(C₅⋊D₅)⋊C₃ #30685833