Subgroups — D₁₉×C₃⋊(D₁₃⋊C₃) #22580280

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊((C₁₃⋊C₃)⋊D₁₉)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×C₃⋊(D₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₃₉	C₃	1	1	yes	maximal, characteristic, complemented
5	D₁₉×D₁₃⋊C₃	—	3	1	no	maximal
6	C₃×C₁₉×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₇₄₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₉×D₃₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×C₁₃×D₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	(C₁₃⋊C₃)⋊D₁₉	—	3	1	no	—
11	C₁₉×D₁₃⋊C₃	—	3	1	no	—
12	D₁₉×C₁₃⋊C₃	—	2	1	no	—
13	D₁₉×C₁₃⋊C₃	D₃	1	1	yes	characteristic, complemented
14	D₁₃×D₁₉	—	3	1	no	Hall
15	C₃×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₁₉×C₁₃⋊C₃	—	2	1	no	—
17	C₁₉×C₁₃⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×D₃×D₁₉	—	13	1	no	maximal, Hall
19	D₂₄₇	—	3	1	no	—
20	C₁₃×D₁₉	C₃×D₃	1	1	yes	characteristic, complemented
21	C₁₉×D₁₃	—	3	1	no	—
22	C₂×C₃⋊(D₁₃⋊C₃)	—	19	1	no	maximal, Hall
23	C₃×D₅₇	—	13	1	no	—
24	C₃×D₃×C₁₉	—	13	1	no	—
25	C₃²×D₁₉	—	13	1	no	—
26	C₁₃×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₁₃⋊C₃	—	19	1	no	—
28	C₃⋊(D₁₃⋊C₃)	—	19	1	no	—
29	C₃⋊(D₁₃⋊C₃)	D₁₉	1	1	yes	characteristic, direct product factor
30	C₂×C₃×D₁₉	—	39	1	no	—
31	D₃×D₁₉	—	13	1	no	—
32	C₃²×C₁₉	—	13	1	no	Hall
33	C₂×D₃₉	—	19	1	no	—
34	C₂×D₁₃⋊C₃	—	57	1	no	—
35	C₃×C₁₃⋊C₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₁₉	—	39	1	no	—
37	D₅₇	—	13	1	no	—
38	C₃×D₁₉	—	13	1	no	—
39	C₃×D₁₉	—	26	1	no	—
40	C₃×D₁₉	—	39	1	no	—
41	C₃×D₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
42	D₃×C₁₉	—	13	1	no	—
43	C₂×C₃×C₁₃	—	19	1	no	—
44	D₃₉	—	19	1	no	—
45	D₃₉	C₃×D₁₉	1	1	yes	characteristic, complemented
46	C₂×C₁₃⋊C₃	—	19	1	no	—
47	C₂×C₁₃⋊C₃	—	38	1	no	—
48	D₁₃⋊C₃	—	3	1	no	—
49	D₁₃⋊C₃	—	57	1	no	—
50	C₂×D₁₉	—	39	1	no	Hall
51	C₃×C₁₉	—	13	1	no	—
52	C₃×C₁₉	—	26	1	no	—
53	C₃×C₁₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
54	C₂×D₁₃	—	57	1	no	Hall
55	C₃×C₁₃	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
56	C₁₃⋊C₃	—	2	1	no	—
57	C₁₃⋊C₃	D₃×D₁₉	1	1	yes	characteristic, complemented
58	C₂×C₁₉	—	39	1	no	—
59	D₁₉	—	39	1	no	—
60	D₁₉	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
61	C₂×C₃×D₃	—	247	1	no	Hall
62	C₂×C₁₃	—	19	1	no	—
63	D₁₃	—	3	1	no	—
64	D₁₃	—	57	1	no	—
65	C₁₉	C₂×C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃²	—	247	1	no	—
67	C₃×D₃	—	13	1	no	—
68	C₃×D₃	—	247	1	no	—
69	C₁₃	C₃×D₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	741	1	no	—
71	C₂×D₃	—	247	1	no	—
72	C₃²	—	13	1	no	Sylow
73	C₂×C₃	—	19	1	no	—
74	C₂×C₃	—	39	1	no	—
75	C₂×C₃	—	741	1	no	—
76	C₂×C₃	—	494	1	no	—
77	C₂×C₃	—	247	1	no	—
78	D₃	—	13	1	no	—
79	D₃	—	247	1	no	—
80	C₂²	—	741	1	no	Sylow
81	C₃	—	13	1	no	—
82	C₃	—	26	1	no	—
83	C₃	D₁₉×D₁₃⋊C₃	1	1	yes	characteristic, complemented
84	C₂	—	19	1	no	—
85	C₂	—	39	1	no	—
86	C₂	—	741	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₃×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊((C₁₃⋊C₃)⋊D₁₉)	C₂	semidirect
2. C₁₉×C₃⋊(D₁₃⋊C₃)	C₂	semidirect
3. C₃×D₁₉×C₁₃⋊C₃	C₂	semidirect
4. D₁₉×D₃₉	C₃	semidirect
6. C₃×C₁₉×C₁₃⋊C₃	C₂²	semidirect
7. D₇₄₁	C₂×C₃	semidirect
8. C₁₉×D₃₉	C₂×C₃	semidirect
9. C₃×C₁₃×D₁₉	C₂×C₃	semidirect
13. D₁₉×C₁₃⋊C₃	D₃	semidirect
15. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
17. C₁₉×C₁₃⋊C₃	C₂×D₃	semidirect
20. C₁₃×D₁₉	C₃×D₃	semidirect
26. C₁₃×C₁₉	C₂×C₃×D₃	semidirect
29. C₃⋊(D₁₃⋊C₃)	D₁₉	direct (N × H)
35. C₃×C₁₃⋊C₃	C₂×D₁₉	semidirect
41. C₃×D₁₉	D₁₃⋊C₃	semidirect
45. D₃₉	C₃×D₁₉	semidirect
53. C₃×C₁₉	C₂×D₁₃⋊C₃	semidirect
55. C₃×C₁₃	C₂×C₃×D₁₉	semidirect
57. C₁₃⋊C₃	D₃×D₁₉	semidirect
60. D₁₉	C₃⋊(D₁₃⋊C₃)	direct (N × H)
65. C₁₉	C₂×C₃⋊(D₁₃⋊C₃)	semidirect
69. C₁₃	C₃×D₃×D₁₉	semidirect
83. C₃	D₁₉×D₁₃⋊C₃	semidirect

Subgroups — D19×C3⋊(D13⋊C3) #22580280

Conjugacy classes of subgroups

Complements

Subgroups — D₁₉×C₃⋊(D₁₃⋊C₃) #22580280