Subgroups — C₂×C₃⋊((C₁₃⋊C₃)⋊D₁₉) #22580337

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂	C₃⋊((C₁₃⋊C₃)⋊D₁₉)
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×C₁₉×C₁₃⋊C₃	C₂	semidirect
2. C₃⋊((C₁₃⋊C₃)⋊D₁₉)	C₂	direct (N × H)
3. C₂×D₇₄₁	C₃	semidirect
5. C₃×C₁₉×C₁₃⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₃×C₁₉	C₂×C₃	semidirect
7. D₇₄₁	C₂×C₃	semidirect
9. C₂×C₁₉×C₁₃⋊C₃	D₃	semidirect
12. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
14. C₁₉×C₁₃⋊C₃	C₂×D₃	semidirect
16. C₂×C₁₃×C₁₉	C₃×D₃	semidirect
21. C₁₃×C₁₉	C₂×C₃×D₃	semidirect
22. C₂×C₃×C₁₃⋊C₃	D₁₉	semidirect
29. C₃×C₁₃⋊C₃	C₂×D₁₉	semidirect
32. C₂×C₃×C₁₉	D₁₃⋊C₃	semidirect
35. C₂×C₃×C₁₃	C₃×D₁₉	semidirect
38. C₂×C₁₃⋊C₃	D₅₇	semidirect
43. C₃×C₁₉	C₂×D₁₃⋊C₃	semidirect
45. C₃×C₁₃	C₂×C₃×D₁₉	semidirect
47. C₁₃⋊C₃	C₂×D₅₇	semidirect
48. C₂×C₁₉	C₃⋊(D₁₃⋊C₃)	semidirect
51. C₂×C₁₃	C₃×D₅₇	semidirect
53. C₁₉	C₂×C₃⋊(D₁₃⋊C₃)	semidirect
56. C₁₃	C₂×C₃×D₅₇	semidirect
63. C₂×C₃	(C₁₃⋊C₃)⋊D₁₉	semidirect
68. C₃	C₂×(C₁₃⋊C₃)⋊D₁₉	semidirect
70. C₂	C₃⋊((C₁₃⋊C₃)⋊D₁₉)	direct (N × H)

Subgroups — C2×C3⋊((C13⋊C3)⋊D19) #22580337

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃⋊((C₁₃⋊C₃)⋊D₁₉) #22580337