Subgroups — D₃×(C₁₃⋊C₃)⋊D₁₉ #22580291

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊((C₁₃⋊C₃)⋊D₁₉)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×(C₁₃⋊C₃)⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₂₄₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×(C₁₃⋊C₃)⋊D₁₉	—	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	D₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₂₄₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₁₉×C₁₃⋊C₃	—	3	1	no	—
11	(C₁₃⋊C₃)⋊D₁₉	—	2	1	no	—
12	(C₁₃⋊C₃)⋊D₁₉	—	3	1	no	—
13	(C₁₃⋊C₃)⋊D₁₉	D₃	1	1	yes	characteristic, direct product factor
14	C₂×D₂₄₇	—	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	C₂×C₁₃×C₁₉	—	3	1	no	—
20	D₂₄₇	—	3	1	no	—
21	D₂₄₇	C₃×D₃	1	1	yes	characteristic, complemented
22	D₃×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	C₃⋊(D₁₃⋊C₃)	—	19	1	no	—
28	D₃×C₁₃⋊C₃	D₁₉	1	1	yes	characteristic, complemented
29	C₃×D₁₃⋊C₃	—	19	1	no	—
30	C₂×C₃×D₁₉	—	39	1	no	—
31	D₃×D₁₉	—	13	1	no	—
32	C₃²×C₁₉	—	13	1	no	Hall
33	D₃×D₁₃	—	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	—	13	1	no	—
40	C₃×D₁₉	—	26	1	no	—
41	C₃×D₁₉	—	39	1	no	—
42	D₃×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
43	D₃₉	—	19	1	no	—
44	C₃×D₁₃	—	19	1	no	—
45	D₃×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
46	C₂×C₁₃⋊C₃	—	3	1	no	—
47	D₁₃⋊C₃	—	19	1	no	—
48	D₁₃⋊C₃	—	38	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	—	3	1	no	—
59	D₁₉	—	13	1	no	—
60	D₁₉	—	39	1	no	—
61	C₂×C₃×D₃	—	247	1	no	Hall
62	C₂×C₁₃	—	3	1	no	—
63	D₁₃	—	19	1	no	—
64	D₁₃	—	57	1	no	—
65	C₁₉	D₃×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	—	39	1	no	—
74	C₂×C₃	—	741	1	no	—
75	C₂×C₃	—	494	1	no	—
76	C₂×C₃	—	247	1	no	—
77	C₂×C₃	—	247	1	no	—
78	D₃	—	247	1	no	—
79	D₃	(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, direct product factor
80	C₂²	—	741	1	no	Sylow
81	C₃	—	13	1	no	—
82	C₃	—	26	1	no	—
83	C₃	C₂×(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	741	1	no	—
86	C₂	—	247	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. D₃×C₁₉×C₁₃⋊C₃	C₂	semidirect
2. C₃⋊((C₁₃⋊C₃)⋊D₁₉)	C₂	semidirect
3. C₃×(C₁₃⋊C₃)⋊D₁₉	C₂	semidirect
4. D₃×D₂₄₇	C₃	semidirect
6. C₃×C₁₉×C₁₃⋊C₃	C₂²	semidirect
7. D₇₄₁	C₂×C₃	semidirect
8. D₃×C₁₃×C₁₉	C₂×C₃	semidirect
9. C₃×D₂₄₇	C₂×C₃	semidirect
13. (C₁₃⋊C₃)⋊D₁₉	D₃	direct (N × H)
15. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
17. C₁₉×C₁₃⋊C₃	C₂×D₃	semidirect
21. D₂₄₇	C₃×D₃	semidirect
26. C₁₃×C₁₉	C₂×C₃×D₃	semidirect
28. D₃×C₁₃⋊C₃	D₁₉	semidirect
35. C₃×C₁₃⋊C₃	C₂×D₁₉	semidirect
42. D₃×C₁₉	D₁₃⋊C₃	semidirect
45. D₃×C₁₃	C₃×D₁₉	semidirect
53. C₃×C₁₉	C₂×D₁₃⋊C₃	semidirect
55. C₃×C₁₃	C₂×C₃×D₁₉	semidirect
57. C₁₃⋊C₃	D₃×D₁₉	semidirect
65. C₁₉	D₃×D₁₃⋊C₃	semidirect
69. C₁₃	C₃×D₃×D₁₉	semidirect
79. D₃	(C₁₃⋊C₃)⋊D₁₉	direct (N × H)
83. C₃	C₂×(C₁₃⋊C₃)⋊D₁₉	semidirect

Subgroups — D3×(C13⋊C3)⋊D19 #22580291

Conjugacy classes of subgroups

Complements

Subgroups — D₃×(C₁₃⋊C₃)⋊D₁₉ #22580291