Subgroups — C₃×C₁₉×#106 #14269043

Order 1824.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₄×C₁₉	C₂	1	2	yes	maximal
3	C₁₉×#106	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₁₉	—	2	2	no	—
5	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₃×C₈×C₁₉	C₄	1	2	yes	complemented
7	C₂×C₈×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₄⋊C₄×C₁₉	C₂×C₃	1	2	yes	—
9	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
10	C₃×C₄×C₁₉	—	4	2	no	—
11	C₃×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄×C₁₉	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₉	—	2	2	no	—
14	C₂×C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
15	C₈×C₁₉	C₃×C₄	1	2	yes	complemented
16	C₂×C₃×C₁₉	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₃×C₁₉	SD₁₆	1	2	yes	—
18	C₃×#106	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₁₉	C₃×D₄	1	1	yes	characteristic
20	C₄×C₁₉	—	4	2	no	—
21	C₄×C₁₉	C₂×C₃×C₄	1	1	yes	characteristic
22	C₄×C₁₉	C₃×Q₈	1	1	yes	characteristic
23	C₃×C₁₉	#106	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃×C₈	C₂×C₁₉	1	1	yes	characteristic
25	C₃×C₄⋊C₄	C₂×C₁₉	1	2	yes	—
26	C₂×C₁₉	C₃×C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₁₉	C₃×SD₁₆	1	2	yes	—
28	#106	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃×C₄	—	2	2	no	—
30	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
31	C₃×C₈	C₄×C₁₉	1	2	yes	complemented
32	C₁₉	C₃×#106	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₈	C₂×C₃×C₁₉	1	1	yes	characteristic
34	C₄⋊C₄	C₂×C₃×C₁₉	1	2	yes	—
35	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
36	C₃×C₄	—	4	2	no	—
37	C₃×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
38	C₃×C₄	Q₈×C₁₉	1	1	yes	characteristic
39	C₂×C₄	—	2	2	no	—
40	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
41	C₈	C₃×C₄×C₁₉	1	2	yes	complemented
42	C₂×C₃	C₄⋊C₄×C₁₉	1	1	yes	characteristic
43	C₂×C₃	SD₁₆×C₁₉	1	2	yes	—
44	C₂²	C₃×D₄×C₁₉	1	1	yes	characteristic
45	C₄	—	4	2	no	—
46	C₄	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic
47	C₄	C₃×Q₈×C₁₉	1	1	yes	characteristic
48	C₃	C₁₉×#106	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	C₃×C₄⋊C₄×C₁₉	1	1	yes	characteristic
50	C₂	C₃×SD₁₆×C₁₉	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₁₉	D₄
commutator	C₄	C₂×C₃×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂²×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
3. C₁₉×#106	C₃	direct (N × H)
6. C₃×C₈×C₁₉	C₄	semidirect
15. C₈×C₁₉	C₃×C₄	semidirect
18. C₃×#106	C₁₉	direct (N × H)
23. C₃×C₁₉	#106	direct (N × H)
28. #106	C₃×C₁₉	direct (N × H)
31. C₃×C₈	C₄×C₁₉	semidirect
32. C₁₉	C₃×#106	direct (N × H)
41. C₈	C₃×C₄×C₁₉	semidirect
48. C₃	C₁₉×#106	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×C₈×C₁₉	2
C₃×C₄⋊C₄×C₁₉	2
C₁₉×#106	3
C₃×#106	19

Subgroups — C3×C19×#106 #14269043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#106 #14269043