Subgroups — C₂×C₃×Q₁₆×C₁₉ #14269812

Order 1824.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₉	C₂	1	2	yes	maximal
2	C₃×Q₁₆×C₁₉	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×Q₈×C₁₉	—	2	2	no	—
6	C₃×Q₈×C₁₉	C₂²	1	4	yes	—
7	C₂×C₃×C₄×C₁₉	—	2	2	no	—
8	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₃×C₈×C₁₉	C₂²	1	2	yes	—
10	C₂×Q₈×C₁₉	C₂×C₃	1	2	yes	—
11	Q₁₆×C₁₉	C₂×C₃	1	4	yes	direct product factor
12	C₂×C₈×C₁₉	C₂×C₃	1	1	yes	characteristic
13	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
14	C₃×C₄×C₁₉	—	2	4	no	—
15	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	Q₈×C₁₉	—	2	2	no	—
18	Q₈×C₁₉	C₂²×C₃	1	4	yes	—
19	C₂×C₄×C₁₉	—	2	2	no	—
20	C₂×C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
21	C₈×C₁₉	C₂²×C₃	1	2	yes	—
22	C₂×C₃×C₁₉	Q₁₆	1	2	yes	direct product factor
23	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
24	C₂×C₃×Q₁₆	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₁₉	C₃×D₄	1	1	yes	characteristic
26	C₄×C₁₉	—	2	4	no	—
27	C₄×C₁₉	C₃×D₄	1	1	yes	characteristic
28	C₄×C₁₉	C₂³×C₃	1	1	yes	characteristic
29	C₃×C₁₉	C₂×Q₁₆	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×Q₈	C₂×C₁₉	1	2	yes	—
31	C₃×Q₁₆	C₂×C₁₉	1	4	yes	direct product factor
32	C₂×C₃×C₈	C₂×C₁₉	1	1	yes	characteristic
33	C₂×C₁₉	C₃×Q₁₆	1	2	yes	direct product factor
34	C₂×C₁₉	C₂×C₃×D₄	1	1	yes	characteristic
35	C₂×Q₁₆	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×Q₈	—	2	2	no	—
37	C₃×Q₈	C₂²×C₁₉	1	4	yes	—
38	C₂×C₃×C₄	—	2	2	no	—
39	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
40	C₃×C₈	C₂²×C₁₉	1	2	yes	—
41	C₁₉	C₂×C₃×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×Q₈	C₂×C₃×C₁₉	1	2	yes	—
43	Q₁₆	C₂×C₃×C₁₉	1	4	yes	direct product factor
44	C₂×C₈	C₂×C₃×C₁₉	1	1	yes	characteristic
45	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
46	C₃×C₄	—	2	4	no	—
47	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
48	C₃×C₄	C₂³×C₁₉	1	1	yes	characteristic
49	Q₈	—	2	2	no	—
50	Q₈	C₂²×C₃×C₁₉	1	4	yes	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
53	C₈	C₂²×C₃×C₁₉	1	2	yes	—
54	C₂×C₃	Q₁₆×C₁₉	1	2	yes	direct product factor
55	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
56	C₂²	C₃×D₄×C₁₉	1	1	yes	characteristic
57	C₄	—	2	4	no	—
58	C₄	C₃×D₄×C₁₉	1	1	yes	characteristic
59	C₄	C₂³×C₃×C₁₉	1	1	yes	characteristic
60	C₃	C₂×Q₁₆×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	C₃×Q₁₆×C₁₉	1	2	yes	direct product factor
62	C₂	C₂×C₃×D₄×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	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
2. C₃×Q₁₆×C₁₉	C₂	direct (N × H)
4. C₂×Q₁₆×C₁₉	C₃	direct (N × H)
11. Q₁₆×C₁₉	C₂×C₃	direct (N × H)
22. C₂×C₃×C₁₉	Q₁₆	direct (N × H)
24. C₂×C₃×Q₁₆	C₁₉	direct (N × H)
29. C₃×C₁₉	C₂×Q₁₆	direct (N × H)
31. C₃×Q₁₆	C₂×C₁₉	direct (N × H)
33. C₂×C₁₉	C₃×Q₁₆	direct (N × H)
35. C₂×Q₁₆	C₃×C₁₉	direct (N × H)
41. C₁₉	C₂×C₃×Q₁₆	direct (N × H)
43. Q₁₆	C₂×C₃×C₁₉	direct (N × H)
54. C₂×C₃	Q₁₆×C₁₉	direct (N × H)
60. C₃	C₂×Q₁₆×C₁₉	direct (N × H)
61. C₂	C₃×Q₁₆×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
C₃×Q₁₆×C₁₉	2
C₂×C₃×C₈×C₁₉	2
C₂×Q₁₆×C₁₉	3
C₂×C₃×Q₁₆	19

Subgroups — C2×C3×Q16×C19 #14269812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×Q₁₆×C₁₉ #14269812