Subgroups — C₃×C₁₉×#107 #14269044

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×#107	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	D₈	1	1	yes	characteristic
18	C₂×C₃×C₁₉	Q₁₆	1	1	yes	characteristic
19	C₃×#107	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₁₉	C₃×D₄	1	1	yes	characteristic
21	C₄×C₁₉	—	4	2	no	—
22	C₄×C₁₉	C₂×C₃×C₄	1	1	yes	characteristic
23	C₄×C₁₉	C₃×Q₈	1	1	yes	characteristic
24	C₃×C₁₉	#107	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₈	C₂×C₁₉	1	1	yes	characteristic
26	C₃×C₄⋊C₄	C₂×C₁₉	1	2	yes	—
27	C₂×C₁₉	C₃×C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₁₉	C₃×D₈	1	1	yes	characteristic
29	C₂×C₁₉	C₃×Q₁₆	1	1	yes	characteristic
30	#107	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃×C₄	—	2	2	no	—
32	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
33	C₃×C₈	C₄×C₁₉	1	2	yes	complemented
34	C₁₉	C₃×#107	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₈	C₂×C₃×C₁₉	1	1	yes	characteristic
36	C₄⋊C₄	C₂×C₃×C₁₉	1	2	yes	—
37	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
38	C₃×C₄	—	4	2	no	—
39	C₃×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
40	C₃×C₄	Q₈×C₁₉	1	1	yes	characteristic
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
43	C₈	C₃×C₄×C₁₉	1	2	yes	complemented
44	C₂×C₃	C₄⋊C₄×C₁₉	1	1	yes	characteristic
45	C₂×C₃	D₈×C₁₉	1	1	yes	characteristic
46	C₂×C₃	Q₁₆×C₁₉	1	1	yes	characteristic
47	C₂²	C₃×D₄×C₁₉	1	1	yes	characteristic
48	C₄	—	4	2	no	—
49	C₄	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic
50	C₄	C₃×Q₈×C₁₉	1	1	yes	characteristic
51	C₃	C₁₉×#107	1	1	yes	characteristic, direct product factor, Sylow
52	C₂	C₃×C₄⋊C₄×C₁₉	1	1	yes	characteristic
53	C₂	C₃×D₈×C₁₉	1	1	yes	characteristic
54	C₂	C₃×Q₁₆×C₁₉	1	1	yes	characteristic

	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×#107	C₃	direct (N × H)
6. C₃×C₈×C₁₉	C₄	semidirect
15. C₈×C₁₉	C₃×C₄	semidirect
19. C₃×#107	C₁₉	direct (N × H)
24. C₃×C₁₉	#107	direct (N × H)
30. #107	C₃×C₁₉	direct (N × H)
33. C₃×C₈	C₄×C₁₉	semidirect
34. C₁₉	C₃×#107	direct (N × H)
43. C₈	C₃×C₄×C₁₉	semidirect
51. C₃	C₁₉×#107	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×#107	3
C₃×#107	19

Subgroups — C3×C19×#107 #14269044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#107 #14269044