Subgroups — C₂×C₃×SD₁₆×C₁₉ #14269811

Order 1824.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₃×SD₁₆×C₁₉	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×SD₁₆×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₁₉	—	2	1	no	—
7	C₃×Q₈×C₁₉	—	2	1	no	—
8	C₃×Q₈×C₁₉	C₂²	1	2	yes	complemented
9	C₃×D₄×C₁₉	—	2	1	no	—
10	C₃×D₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₃×C₄×C₁₉	—	2	1	no	—
12	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₃×C₈×C₁₉	C₂²	1	2	yes	complemented
14	C₂×Q₈×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×D₄×C₁₉	C₂×C₃	1	1	yes	characteristic
16	SD₁₆×C₁₉	C₂×C₃	1	4	yes	direct product factor
17	C₂×C₈×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₁₉	—	2	2	no	—
19	C₂²×C₃×C₁₉	—	4	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	C₂³×C₁₉	—	2	1	no	—
25	Q₈×C₁₉	—	2	1	no	—
26	Q₈×C₁₉	C₂²×C₃	1	2	yes	complemented
27	D₄×C₁₉	—	2	1	no	—
28	D₄×C₁₉	C₂²×C₃	1	2	yes	—
29	C₂×C₄×C₁₉	—	2	1	no	—
30	C₂×C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
31	C₈×C₁₉	C₂²×C₃	1	2	yes	complemented
32	C₂×C₃×C₁₉	—	4	2	no	—
33	C₂×C₃×C₁₉	SD₁₆	1	2	yes	direct product factor
34	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₃×SD₁₆	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂²×C₁₉	—	2	2	no	—
37	C₂²×C₁₉	—	4	2	no	—
38	C₂²×C₁₉	C₃×D₄	1	1	yes	characteristic
39	C₄×C₁₉	—	2	2	no	—
40	C₄×C₁₉	C₃×D₄	1	1	yes	characteristic
41	C₄×C₁₉	C₂³×C₃	1	1	yes	characteristic
42	C₃×C₁₉	C₂×SD₁₆	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₃×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
44	C₂×C₃×D₄	C₂×C₁₉	1	1	yes	characteristic
45	C₃×SD₁₆	C₂×C₁₉	1	4	yes	direct product factor
46	C₂×C₃×C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
47	C₂×C₁₉	—	4	2	no	—
48	C₂×C₁₉	C₃×SD₁₆	1	2	yes	direct product factor
49	C₂×C₁₉	C₂×C₃×D₄	1	1	yes	characteristic
50	C₂×SD₁₆	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₂³×C₃	—	2	1	no	—
52	C₃×Q₈	—	2	1	no	—
53	C₃×Q₈	C₂²×C₁₉	1	2	yes	complemented
54	C₃×D₄	—	2	1	no	—
55	C₃×D₄	C₂²×C₁₉	1	2	yes	—
56	C₂×C₃×C₄	—	2	1	no	—
57	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
58	C₃×C₈	C₂²×C₁₉	1	2	yes	complemented
59	C₁₉	C₂×C₃×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×Q₈	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
61	C₂×D₄	C₂×C₃×C₁₉	1	1	yes	characteristic
62	SD₁₆	C₂×C₃×C₁₉	1	4	yes	direct product factor
63	C₂×C₈	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
64	C₂²×C₃	—	2	2	no	—
65	C₂²×C₃	—	4	2	no	—
66	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
67	C₃×C₄	—	2	2	no	—
68	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
69	C₃×C₄	C₂³×C₁₉	1	1	yes	characteristic
70	C₂³	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	C₂²×C₃×C₁₉	1	2	yes	complemented
73	D₄	—	2	1	no	—
74	D₄	C₂²×C₃×C₁₉	1	2	yes	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
77	C₈	C₂²×C₃×C₁₉	1	2	yes	complemented
78	C₂×C₃	—	4	2	no	—
79	C₂×C₃	SD₁₆×C₁₉	1	2	yes	direct product factor
80	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
81	C₂²	—	2	2	no	—
82	C₂²	—	4	2	no	—
83	C₂²	C₃×D₄×C₁₉	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	C₃×D₄×C₁₉	1	1	yes	characteristic
86	C₄	C₂³×C₃×C₁₉	1	1	yes	characteristic
87	C₃	C₂×SD₁₆×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
88	C₂	—	4	2	no	—
89	C₂	C₃×SD₁₆×C₁₉	1	2	yes	direct product factor
90	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
prime radical	C₂×C₃×D₄×C₁₉	C₂
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×Q₈×C₁₉	C₂	semidirect
3. C₃×SD₁₆×C₁₉	C₂	direct (N × H)
4. C₂×C₃×C₈×C₁₉	C₂	semidirect
5. C₂×SD₁₆×C₁₉	C₃	direct (N × H)
8. C₃×Q₈×C₁₉	C₂²	semidirect
13. C₃×C₈×C₁₉	C₂²	semidirect
14. C₂×Q₈×C₁₉	C₂×C₃	semidirect
16. SD₁₆×C₁₉	C₂×C₃	direct (N × H)
17. C₂×C₈×C₁₉	C₂×C₃	semidirect
26. Q₈×C₁₉	C₂²×C₃	semidirect
31. C₈×C₁₉	C₂²×C₃	semidirect
33. C₂×C₃×C₁₉	SD₁₆	direct (N × H)
35. C₂×C₃×SD₁₆	C₁₉	direct (N × H)
42. C₃×C₁₉	C₂×SD₁₆	direct (N × H)
43. C₂×C₃×Q₈	C₂×C₁₉	semidirect
45. C₃×SD₁₆	C₂×C₁₉	direct (N × H)
46. C₂×C₃×C₈	C₂×C₁₉	semidirect
48. C₂×C₁₉	C₃×SD₁₆	direct (N × H)
50. C₂×SD₁₆	C₃×C₁₉	direct (N × H)
53. C₃×Q₈	C₂²×C₁₉	semidirect
58. C₃×C₈	C₂²×C₁₉	semidirect
59. C₁₉	C₂×C₃×SD₁₆	direct (N × H)
60. C₂×Q₈	C₂×C₃×C₁₉	semidirect
62. SD₁₆	C₂×C₃×C₁₉	direct (N × H)
63. C₂×C₈	C₂×C₃×C₁₉	semidirect
72. Q₈	C₂²×C₃×C₁₉	semidirect
77. C₈	C₂²×C₃×C₁₉	semidirect
79. C₂×C₃	SD₁₆×C₁₉	direct (N × H)
87. C₃	C₂×SD₁₆×C₁₉	direct (N × H)
89. C₂	C₃×SD₁₆×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×Q₈×C₁₉	2
C₂×C₃×D₄×C₁₉	2
C₃×SD₁₆×C₁₉	2
C₂×C₃×C₈×C₁₉	2
C₂×SD₁₆×C₁₉	3
C₂×C₃×SD₁₆	19

Subgroups — C2×C3×SD16×C19 #14269811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×SD₁₆×C₁₉ #14269811