Subgroups — C₂×C₁₉×D₂₅₅ #34084403

Order 19380.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₂₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×D₈₅	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×D₅₁	—	5	1	no	maximal, Hall
6	C₁₉×D₈₅	—	3	2	no	—
7	C₂×C₅×C₁₇×C₁₉	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₇×C₁₉	D₅	1	1	yes	characteristic, complemented
9	C₁₉×D₅₁	—	5	2	no	—
10	C₅×C₁₇×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₉×D₁₇	—	15	1	no	Hall
12	C₂×C₁₉×D₁₅	—	17	1	no	maximal, Hall
13	C₂×D₂₅₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×C₁₇×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₇×C₁₉	D₁₅	1	1	yes	characteristic, complemented
16	C₁₉×D₁₇	—	15	2	no	—
17	C₂×C₃×C₅×C₁₉	D₁₇	1	1	yes	characteristic, complemented
18	C₁₉×D₁₅	—	17	2	no	—
19	C₂×C₃×C₅×C₁₇	C₂×C₁₉	1	1	yes	characteristic, complemented
20	D₂₅₅	C₂×C₁₉	1	2	yes	direct product factor
21	C₂×D₅×C₁₉	—	51	1	no	Hall
22	C₂×D₈₅	—	3	1	no	Hall
23	C₁₇×C₁₉	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₅×C₁₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃×C₁₉	—	85	1	no	Hall
27	C₂×D₅₁	—	5	1	no	Hall
28	C₂×C₅×C₁₉	D₅₁	1	1	yes	characteristic, complemented
29	D₅×C₁₉	—	51	2	no	—
30	C₂×C₅×C₁₇	D₃×C₁₉	1	1	yes	characteristic, complemented
31	D₈₅	—	3	2	no	—
32	C₂×C₃×C₁₉	D₈₅	1	1	yes	characteristic, complemented
33	D₃×C₁₉	—	85	2	no	—
34	C₂×C₃×C₁₇	D₅×C₁₉	1	1	yes	characteristic, complemented
35	D₅₁	—	5	2	no	—
36	C₅×C₁₉	C₂×D₅₁	1	1	yes	characteristic, complemented, Hall
37	C₅×C₁₇	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
38	C₂²×C₁₉	—	255	1	no	Hall
39	C₂×D₁₇	—	15	1	no	Hall
40	C₂×D₁₅	—	17	1	no	Hall
41	C₃×C₁₉	C₂×D₈₅	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₇	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
43	C₂×C₁₉	—	255	2	no	—
44	C₂×C₁₉	D₂₅₅	1	1	yes	characteristic, direct product factor
45	C₂×C₁₇	C₁₉×D₁₅	1	1	yes	characteristic, complemented
46	D₁₇	—	15	2	no	—
47	C₂×C₃×C₅	C₁₉×D₁₇	1	1	yes	characteristic, complemented
48	D₁₅	—	17	2	no	—
49	C₂×D₅	—	51	1	no	Hall
50	C₁₉	C₂×D₂₅₅	1	1	yes	characteristic, direct product factor, Sylow
51	C₁₇	C₂×C₁₉×D₁₅	1	1	yes	characteristic, complemented, Sylow
52	C₃×C₅	C₂×C₁₉×D₁₇	1	1	yes	characteristic, complemented, Hall
53	C₂×D₃	—	85	1	no	Hall
54	C₂×C₅	C₁₉×D₅₁	1	1	yes	characteristic, complemented
55	D₅	—	51	2	no	—
56	C₂×C₃	C₁₉×D₈₅	1	1	yes	characteristic, complemented
57	D₃	—	85	2	no	—
58	C₅	C₂×C₁₉×D₅₁	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	255	1	no	Sylow
60	C₃	C₂×C₁₉×D₈₅	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	255	2	no	—
62	C₂	C₁₉×D₂₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₂₅₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₇	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₇×C₁₉	C₂
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₂₅₅	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₇×C₁₉	C₂	semidirect
4. C₃×C₅×C₁₇×C₁₉	C₂²	semidirect
7. C₂×C₅×C₁₇×C₁₉	D₃	semidirect
8. C₂×C₃×C₁₇×C₁₉	D₅	semidirect
10. C₅×C₁₇×C₁₉	C₂×D₃	semidirect
13. C₂×D₂₅₅	C₁₉	direct (N × H)
14. C₃×C₁₇×C₁₉	C₂×D₅	semidirect
15. C₂×C₁₇×C₁₉	D₁₅	semidirect
17. C₂×C₃×C₅×C₁₉	D₁₇	semidirect
19. C₂×C₃×C₅×C₁₇	C₂×C₁₉	semidirect
20. D₂₅₅	C₂×C₁₉	direct (N × H)
23. C₁₇×C₁₉	C₂×D₁₅	semidirect
24. C₃×C₅×C₁₉	C₂×D₁₇	semidirect
25. C₃×C₅×C₁₇	C₂²×C₁₉	semidirect
28. C₂×C₅×C₁₉	D₅₁	semidirect
30. C₂×C₅×C₁₇	D₃×C₁₉	semidirect
32. C₂×C₃×C₁₉	D₈₅	semidirect
34. C₂×C₃×C₁₇	D₅×C₁₉	semidirect
36. C₅×C₁₉	C₂×D₅₁	semidirect
37. C₅×C₁₇	C₂×D₃×C₁₉	semidirect
41. C₃×C₁₉	C₂×D₈₅	semidirect
42. C₃×C₁₇	C₂×D₅×C₁₉	semidirect
44. C₂×C₁₉	D₂₅₅	direct (N × H)
45. C₂×C₁₇	C₁₉×D₁₅	semidirect
47. C₂×C₃×C₅	C₁₉×D₁₇	semidirect
50. C₁₉	C₂×D₂₅₅	direct (N × H)
51. C₁₇	C₂×C₁₉×D₁₅	semidirect
52. C₃×C₅	C₂×C₁₉×D₁₇	semidirect
54. C₂×C₅	C₁₉×D₅₁	semidirect
56. C₂×C₃	C₁₉×D₈₅	semidirect
58. C₅	C₂×C₁₉×D₅₁	semidirect
60. C₃	C₂×C₁₉×D₈₅	semidirect
62. C₂	C₁₉×D₂₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×D₂₅₅	2
C₂×C₃×C₅×C₁₇×C₁₉	2
C₂×C₁₉×D₈₅	3
C₂×C₁₉×D₅₁	5
C₂×C₁₉×D₁₅	17
C₂×D₂₅₅	19

Subgroups — C2×C19×D255 #34084403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×D₂₅₅ #34084403