Subgroups — C₁₃×(C₃⋊D₃)⋊D₁₉ #22580367

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×D₅₇	C₂	1	2	yes	maximal, complemented
3	D₃×C₁₃×D₁₉	—	3	2	no	maximal
4	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₅₇	D₃	1	2	yes	complemented
6	D₃×C₁₃×C₁₉	—	3	2	no	—
7	D₃×C₁₃×C₁₉	—	6	1	no	—
8	C₃×C₁₃×D₁₉	—	3	2	no	—
9	C₂×C₁₃×D₁₉	—	9	1	no	Hall
10	C₃×C₁₃×C₁₉	—	2	1	no	—
11	C₃×C₁₃×C₁₉	C₂×D₃	1	2	yes	complemented
12	(C₃⋊D₃)⋊D₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₃×C₁₉	—	9	1	no	—
14	C₁₃×D₁₉	—	3	2	no	—
15	D₃²×C₁₃	—	19	1	no	maximal, Hall
16	C₃⋊D₃×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₃×D₅₇	C₂×C₁₃	1	2	yes	complemented
18	C₁₃×C₁₉	D₃²	1	1	yes	characteristic, complemented, Hall
19	C₁₃×C₃⋊D₃	D₁₉	1	1	yes	characteristic, complemented
20	C₃×D₃×C₁₃	—	19	2	no	—
21	D₃×D₁₉	—	3	2	no	—
22	C₃²×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
23	C₂×D₃×C₁₃	—	57	2	no	—
24	C₃²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
25	D₅₇	D₃×C₁₃	1	2	yes	complemented
26	C₃×D₁₉	—	3	2	no	—
27	D₃×C₁₉	—	3	2	no	—
28	D₃×C₁₉	—	6	1	no	—
29	C₂×C₃×C₁₃	—	57	2	no	—
30	D₃×C₁₃	—	3	2	no	—
31	D₃×C₁₃	—	6	1	no	—
32	D₃×C₁₃	—	19	2	no	—
33	C₂×D₁₉	—	9	1	no	Hall
34	C₃×C₁₉	—	2	1	no	—
35	C₃×C₁₉	C₂×D₃×C₁₃	1	2	yes	complemented
36	C₂²×C₁₃	—	171	1	no	Hall
37	C₃×C₁₃	—	2	1	no	—
38	C₃×C₁₃	D₃×D₁₉	1	2	yes	complemented
39	C₂×C₁₉	—	9	1	no	—
40	D₁₉	—	3	2	no	—
41	D₃²	—	19	1	no	Hall
42	C₂×C₁₃	—	9	1	no	—
43	C₂×C₁₃	—	57	2	no	—
44	C₁₉	D₃²×C₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₃⋊D₃	C₁₃×D₁₉	1	1	yes	characteristic, complemented
46	C₃×D₃	—	19	2	no	—
47	C₁₃	(C₃⋊D₃)⋊D₁₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×D₃	—	57	2	no	—
49	C₃²	C₂×C₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	57	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	19	2	no	—
54	C₂²	—	171	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×C₁₃×D₁₉	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	57	2	no	—

	subgroup	G/H
center, hypercenter	C₁₃	(C₃⋊D₃)⋊D₁₉
commutator, hypocenter	C₃²×C₁₉	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃²×C₁₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₃×C₁₉	C₂	semidirect
2. C₃×C₁₃×D₅₇	C₂	semidirect
4. C₃²×C₁₃×C₁₉	C₂²	semidirect
5. C₁₃×D₅₇	D₃	semidirect
11. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
12. (C₃⋊D₃)⋊D₁₉	C₁₃	direct (N × H)
16. C₃⋊D₃×C₁₉	C₂×C₁₃	semidirect
17. C₃×D₅₇	C₂×C₁₃	semidirect
18. C₁₃×C₁₉	D₃²	semidirect
19. C₁₃×C₃⋊D₃	D₁₉	semidirect
22. C₃²×C₁₉	C₂²×C₁₃	semidirect
24. C₃²×C₁₃	C₂×D₁₉	semidirect
25. D₅₇	D₃×C₁₃	semidirect
35. C₃×C₁₉	C₂×D₃×C₁₃	semidirect
38. C₃×C₁₃	D₃×D₁₉	semidirect
44. C₁₉	D₃²×C₁₃	semidirect
45. C₃⋊D₃	C₁₃×D₁₉	semidirect
47. C₁₃	(C₃⋊D₃)⋊D₁₉	direct (N × H)
49. C₃²	C₂×C₁₃×D₁₉	semidirect
56. C₃	D₃×C₁₃×D₁₉	semidirect

Subgroups — C13×(C3⋊D3)⋊D19 #22580367

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×(C₃⋊D₃)⋊D₁₉ #22580367