Subgroups — C₃×C₁₉×#135 #14269813

Order 1824.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×C₁₉	C₂	1	2	yes	maximal, complemented
2	C₃×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×SD₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
4	C₃×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#135	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×Q₈×C₁₉	C₂²	1	2	yes	—
8	C₃×D₄×C₁₉	—	2	2	no	—
9	C₃×D₄×C₁₉	C₂²	1	2	yes	—
10	C₂×C₃×C₄×C₁₉	—	2	2	no	—
11	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	#41×C₁₉	C₂×C₃	1	2	yes	complemented
15	Q₁₆×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
16	SD₁₆×C₁₉	C₂×C₃	1	2	yes	complemented
17	D₈×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂×C₈×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₁₉	—	2	2	no	—
20	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
21	C₃×C₄×C₁₉	—	2	2	no	—
22	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	Q₈×C₁₉	C₂²×C₃	1	2	yes	—
25	D₄×C₁₉	—	2	2	no	—
26	D₄×C₁₉	C₂²×C₃	1	2	yes	—
27	C₂×C₄×C₁₉	—	2	2	no	—
28	C₂×C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
29	C₈×C₁₉	C₂²×C₃	1	1	yes	characteristic
30	C₈×C₁₉	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₃×C₁₉	—	2	1	no	—
32	C₂×C₃×C₁₉	—	4	2	no	—
33	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₃×#135	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂²×C₁₉	—	2	2	no	—
36	C₂²×C₁₉	C₃×D₄	1	1	yes	characteristic
37	C₄×C₁₉	—	2	2	no	—
38	C₄×C₁₉	C₃×D₄	1	1	yes	characteristic
39	C₄×C₁₉	C₂³×C₃	1	1	yes	characteristic
40	C₃×C₁₉	#135	1	1	yes	characteristic, direct product factor, Hall
41	C₃×#41	C₂×C₁₉	1	2	yes	complemented
42	C₃×Q₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
43	C₃×SD₁₆	C₂×C₁₉	1	2	yes	complemented
44	C₃×D₈	C₂×C₁₉	1	1	yes	characteristic, complemented
45	C₂×C₃×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
46	C₂×C₁₉	—	2	1	no	—
47	C₂×C₁₉	—	4	2	no	—
48	C₂×C₁₉	C₂×C₃×D₄	1	1	yes	characteristic
49	#135	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
50	C₃×Q₈	C₂²×C₁₉	1	2	yes	—
51	C₃×D₄	—	2	2	no	—
52	C₃×D₄	C₂²×C₁₉	1	2	yes	—
53	C₂×C₃×C₄	—	2	2	no	—
54	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
55	C₃×C₈	C₂²×C₁₉	1	1	yes	characteristic
56	C₃×C₈	C₂²×C₁₉	1	1	yes	characteristic
57	C₁₉	C₃×#135	1	1	yes	characteristic, direct product factor, Sylow
58	#41	C₂×C₃×C₁₉	1	2	yes	complemented
59	Q₁₆	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
60	SD₁₆	C₂×C₃×C₁₉	1	2	yes	complemented
61	D₈	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
62	C₂×C₈	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
63	C₂²×C₃	—	2	2	no	—
64	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
65	C₃×C₄	—	2	2	no	—
66	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
67	C₃×C₄	C₂³×C₁₉	1	1	yes	characteristic
68	Q₈	C₂²×C₃×C₁₉	1	2	yes	—
69	D₄	—	2	2	no	—
70	D₄	C₂²×C₃×C₁₉	1	2	yes	—
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
73	C₈	C₂²×C₃×C₁₉	1	1	yes	characteristic
74	C₈	C₂²×C₃×C₁₉	1	1	yes	characteristic
75	C₂×C₃	—	2	1	no	—
76	C₂×C₃	—	4	2	no	—
77	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
78	C₂²	—	2	2	no	—
79	C₂²	C₃×D₄×C₁₉	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	C₃×D₄×C₁₉	1	1	yes	characteristic
82	C₄	C₂³×C₃×C₁₉	1	1	yes	characteristic
83	C₃	C₁₉×#135	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	2	1	no	—
85	C₂	—	4	2	no	—
86	C₂	C₂×C₃×D₄×C₁₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃×#41×C₁₉	C₂	semidirect
2. C₃×Q₁₆×C₁₉	C₂	semidirect
3. C₃×SD₁₆×C₁₉	C₂	semidirect
4. C₃×D₈×C₁₉	C₂	semidirect
5. C₂×C₃×C₈×C₁₉	C₂	semidirect
6. C₁₉×#135	C₃	direct (N × H)
14. #41×C₁₉	C₂×C₃	semidirect
15. Q₁₆×C₁₉	C₂×C₃	semidirect
16. SD₁₆×C₁₉	C₂×C₃	semidirect
17. D₈×C₁₉	C₂×C₃	semidirect
18. C₂×C₈×C₁₉	C₂×C₃	semidirect
34. C₃×#135	C₁₉	direct (N × H)
40. C₃×C₁₉	#135	direct (N × H)
41. C₃×#41	C₂×C₁₉	semidirect
42. C₃×Q₁₆	C₂×C₁₉	semidirect
43. C₃×SD₁₆	C₂×C₁₉	semidirect
44. C₃×D₈	C₂×C₁₉	semidirect
45. C₂×C₃×C₈	C₂×C₁₉	semidirect
49. #135	C₃×C₁₉	direct (N × H)
57. C₁₉	C₃×#135	direct (N × H)
58. #41	C₂×C₃×C₁₉	semidirect
59. Q₁₆	C₂×C₃×C₁₉	semidirect
60. SD₁₆	C₂×C₃×C₁₉	semidirect
61. D₈	C₂×C₃×C₁₉	semidirect
62. C₂×C₈	C₂×C₃×C₁₉	semidirect
83. C₃	C₁₉×#135	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#41×C₁₉	2
C₃×Q₁₆×C₁₉	2
C₃×SD₁₆×C₁₉	2
C₃×D₈×C₁₉	2
C₂×C₃×C₈×C₁₉	2
C₁₉×#135	3
C₃×#135	19

Subgroups — C3×C19×#135 #14269813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#135 #14269813