Subgroups — C₂×C₃×D₈×C₁₉ #14269810

Order 1824.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₁₉	C₂	1	2	yes	maximal, complemented
2	C₃×D₈×C₁₉	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₁₉	—	2	2	no	—
6	C₃×D₄×C₁₉	—	2	2	no	—
7	C₃×D₄×C₁₉	C₂²	1	4	yes	complemented
8	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₃×C₈×C₁₉	C₂²	1	2	yes	complemented
10	C₂×D₄×C₁₉	C₂×C₃	1	2	yes	complemented
11	D₈×C₁₉	C₂×C₃	1	4	yes	direct product factor
12	C₂×C₈×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₁₉	—	2	4	no	—
14	C₂²×C₃×C₁₉	—	4	4	no	—
15	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
16	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂³×C₁₉	—	2	2	no	—
19	D₄×C₁₉	—	2	2	no	—
20	D₄×C₁₉	C₂²×C₃	1	4	yes	complemented
21	C₂×C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
22	C₈×C₁₉	C₂²×C₃	1	2	yes	complemented
23	C₂×C₃×C₁₉	—	4	4	no	—
24	C₂×C₃×C₁₉	D₈	1	2	yes	direct product factor
25	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
26	C₂×C₃×D₈	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂²×C₁₉	—	2	4	no	—
28	C₂²×C₁₉	—	4	4	no	—
29	C₂²×C₁₉	C₃×D₄	1	1	yes	characteristic
30	C₄×C₁₉	C₃×D₄	1	1	yes	characteristic
31	C₄×C₁₉	C₂³×C₃	1	1	yes	characteristic
32	C₃×C₁₉	C₂×D₈	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×D₄	C₂×C₁₉	1	2	yes	complemented
34	C₃×D₈	C₂×C₁₉	1	4	yes	direct product factor
35	C₂×C₃×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
36	C₂×C₁₉	—	4	4	no	—
37	C₂×C₁₉	C₃×D₈	1	2	yes	direct product factor
38	C₂×C₁₉	C₂×C₃×D₄	1	1	yes	characteristic
39	C₂×D₈	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂³×C₃	—	2	2	no	—
41	C₃×D₄	—	2	2	no	—
42	C₃×D₄	C₂²×C₁₉	1	4	yes	complemented
43	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
44	C₃×C₈	C₂²×C₁₉	1	2	yes	complemented
45	C₁₉	C₂×C₃×D₈	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×D₄	C₂×C₃×C₁₉	1	2	yes	complemented
47	D₈	C₂×C₃×C₁₉	1	4	yes	direct product factor
48	C₂×C₈	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
49	C₂²×C₃	—	2	4	no	—
50	C₂²×C₃	—	4	4	no	—
51	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
52	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
53	C₃×C₄	C₂³×C₁₉	1	1	yes	characteristic
54	C₂³	—	2	2	no	—
55	D₄	—	2	2	no	—
56	D₄	C₂²×C₃×C₁₉	1	4	yes	complemented
57	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
58	C₈	C₂²×C₃×C₁₉	1	2	yes	complemented
59	C₂×C₃	—	4	4	no	—
60	C₂×C₃	D₈×C₁₉	1	2	yes	direct product factor
61	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
62	C₂²	—	2	4	no	—
63	C₂²	—	4	4	no	—
64	C₂²	C₃×D₄×C₁₉	1	1	yes	characteristic
65	C₄	C₃×D₄×C₁₉	1	1	yes	characteristic
66	C₄	C₂³×C₃×C₁₉	1	1	yes	characteristic
67	C₃	C₂×D₈×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
68	C₂	—	4	4	no	—
69	C₂	C₃×D₈×C₁₉	1	2	yes	direct product factor
70	C₂	C₂×C₃×D₄×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₁₉	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃×C₁₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₁₉ ◁ C₂×C₃×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×C₁₉	C₂	semidirect
2. C₃×D₈×C₁₉	C₂	direct (N × H)
3. C₂×C₃×C₈×C₁₉	C₂	semidirect
4. C₂×D₈×C₁₉	C₃	direct (N × H)
7. C₃×D₄×C₁₉	C₂²	semidirect
9. C₃×C₈×C₁₉	C₂²	semidirect
10. C₂×D₄×C₁₉	C₂×C₃	semidirect
11. D₈×C₁₉	C₂×C₃	direct (N × H)
12. C₂×C₈×C₁₉	C₂×C₃	semidirect
20. D₄×C₁₉	C₂²×C₃	semidirect
22. C₈×C₁₉	C₂²×C₃	semidirect
24. C₂×C₃×C₁₉	D₈	direct (N × H)
26. C₂×C₃×D₈	C₁₉	direct (N × H)
32. C₃×C₁₉	C₂×D₈	direct (N × H)
33. C₂×C₃×D₄	C₂×C₁₉	semidirect
34. C₃×D₈	C₂×C₁₉	direct (N × H)
35. C₂×C₃×C₈	C₂×C₁₉	semidirect
37. C₂×C₁₉	C₃×D₈	direct (N × H)
39. C₂×D₈	C₃×C₁₉	direct (N × H)
42. C₃×D₄	C₂²×C₁₉	semidirect
44. C₃×C₈	C₂²×C₁₉	semidirect
45. C₁₉	C₂×C₃×D₈	direct (N × H)
46. C₂×D₄	C₂×C₃×C₁₉	semidirect
47. D₈	C₂×C₃×C₁₉	direct (N × H)
48. C₂×C₈	C₂×C₃×C₁₉	semidirect
56. D₄	C₂²×C₃×C₁₉	semidirect
58. C₈	C₂²×C₃×C₁₉	semidirect
60. C₂×C₃	D₈×C₁₉	direct (N × H)
67. C₃	C₂×D₈×C₁₉	direct (N × H)
69. C₂	C₃×D₈×C₁₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×D₄×C₁₉	2
C₃×D₈×C₁₉	2
C₂×C₃×C₈×C₁₉	2
C₂×D₈×C₁₉	3
C₂×C₃×D₈	19

Subgroups — C2×C3×D8×C19 #14269810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₈×C₁₉ #14269810