Subgroups — C₂×C₃⋊((C₁₉⋊C₃)⋊D₁₃) #22580344

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂	C₃⋊((C₁₉⋊C₃)⋊D₁₃)
commutator, hypocenter	C₃×C₁₃×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₃×C₁₉⋊C₃	C₂	semidirect
2. C₃⋊((C₁₉⋊C₃)⋊D₁₃)	C₂	direct (N × H)
3. C₂×D₇₄₁	C₃	semidirect
5. C₃×C₁₃×C₁₉⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₃×C₁₉	C₂×C₃	semidirect
7. D₇₄₁	C₂×C₃	semidirect
9. C₂×C₁₃×C₁₉⋊C₃	D₃	semidirect
12. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
14. C₁₃×C₁₉⋊C₃	C₂×D₃	semidirect
16. C₂×C₁₃×C₁₉	C₃×D₃	semidirect
19. C₂×C₃×C₁₉⋊C₃	D₁₃	semidirect
21. C₁₃×C₁₉	C₂×C₃×D₃	semidirect
26. C₃×C₁₉⋊C₃	C₂×D₁₃	semidirect
30. C₂×C₃×C₁₉	C₃×D₁₃	semidirect
33. C₂×C₁₉⋊C₃	D₃₉	semidirect
37. C₂×C₃×C₁₃	D₁₉⋊C₃	semidirect
41. C₃×C₁₉	C₂×C₃×D₁₃	semidirect
43. C₁₉⋊C₃	C₂×D₃₉	semidirect
47. C₃×C₁₃	C₂×D₁₉⋊C₃	semidirect
48. C₂×C₁₉	C₃×D₃₉	semidirect
51. C₂×C₁₃	C₃⋊(D₁₉⋊C₃)	semidirect
53. C₁₉	C₂×C₃×D₃₉	semidirect
56. C₁₃	C₂×C₃⋊(D₁₉⋊C₃)	semidirect
63. C₂×C₃	(C₁₉⋊C₃)⋊D₁₃	semidirect
68. C₃	C₂×(C₁₉⋊C₃)⋊D₁₃	semidirect
70. C₂	C₃⋊((C₁₉⋊C₃)⋊D₁₃)	direct (N × H)

Subgroups — C2×C3⋊((C19⋊C3)⋊D13) #22580344

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃⋊((C₁₉⋊C₃)⋊D₁₃) #22580344