Subgroups — D₃×(C₁₉⋊C₃)⋊D₁₃ #22580300

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

Subgroups — D3×(C19⋊C3)⋊D13 #22580300

Conjugacy classes of subgroups

Complements

Subgroups — D₃×(C₁₉⋊C₃)⋊D₁₃ #22580300