Subgroups — C₃×C₁₉×#100 #14269037

Order 1824.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×M₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₁₉×#100	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂³×C₃×C₁₉	C₄	1	2	yes	—
5	C₃×D₄×C₁₉	—	2	2	no	—
6	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₃×C₈×C₁₉	—	2	2	no	—
8	C₂×D₄×C₁₉	C₂×C₃	1	1	yes	characteristic
9	M₁₆×C₁₉	C₂×C₃	1	2	yes	complemented
10	C₂²×C₃×C₁₉	—	2	2	no	—
11	C₂²×C₃×C₁₉	—	4	2	no	—
12	C₂²×C₃×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₃×C₄×C₁₉	D₄	1	2	yes	—
14	C₂³×C₁₉	C₃×C₄	1	2	yes	—
15	D₄×C₁₉	—	2	2	no	—
16	C₂×C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
17	C₈×C₁₉	—	2	2	no	—
18	C₂×C₃×C₁₉	—	2	1	no	—
19	C₂×C₃×C₁₉	—	4	2	no	—
20	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₃×#100	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂²×C₁₉	—	2	2	no	—
23	C₂²×C₁₉	—	4	2	no	—
24	C₂²×C₁₉	C₂×C₃×C₄	1	1	yes	characteristic
25	C₄×C₁₉	C₃×D₄	1	2	yes	—
26	C₃×C₁₉	#100	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃×D₄	C₂×C₁₉	1	1	yes	characteristic
28	C₃×M₁₆	C₂×C₁₉	1	2	yes	complemented
29	C₂×C₁₉	—	2	1	no	—
30	C₂×C₁₉	—	4	2	no	—
31	C₂×C₁₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
32	#100	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₂³×C₃	C₄×C₁₉	1	2	yes	—
34	C₃×D₄	—	2	2	no	—
35	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
36	C₃×C₈	—	2	2	no	—
37	C₁₉	C₃×#100	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×D₄	C₂×C₃×C₁₉	1	1	yes	characteristic
39	M₁₆	C₂×C₃×C₁₉	1	2	yes	complemented
40	C₂²×C₃	—	2	2	no	—
41	C₂²×C₃	—	4	2	no	—
42	C₂²×C₃	C₂×C₄×C₁₉	1	1	yes	characteristic
43	C₃×C₄	D₄×C₁₉	1	2	yes	—
44	C₂³	C₃×C₄×C₁₉	1	2	yes	—
45	D₄	—	2	2	no	—
46	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
47	C₈	—	2	2	no	—
48	C₂×C₃	—	2	1	no	—
49	C₂×C₃	—	4	2	no	—
50	C₂×C₃	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
51	C₂²	—	2	2	no	—
52	C₂²	—	4	2	no	—
53	C₂²	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic
54	C₄	C₃×D₄×C₁₉	1	2	yes	—
55	C₃	C₁₉×#100	1	1	yes	characteristic, direct product factor, Sylow
56	C₂	—	2	1	no	—
57	C₂	—	4	2	no	—
58	C₂	C₃×C₂²⋊C₄×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₁₉	C₂²⋊C₄
commutator	C₂²	C₂×C₃×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂²×C₃×C₁₉
prime radical	C₂×C₃×D₄×C₁₉	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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×M₁₆×C₁₉	C₂	semidirect
3. C₁₉×#100	C₃	direct (N × H)
9. M₁₆×C₁₉	C₂×C₃	semidirect
21. C₃×#100	C₁₉	direct (N × H)
26. C₃×C₁₉	#100	direct (N × H)
28. C₃×M₁₆	C₂×C₁₉	semidirect
32. #100	C₃×C₁₉	direct (N × H)
37. C₁₉	C₃×#100	direct (N × H)
39. M₁₆	C₂×C₃×C₁₉	semidirect
55. C₃	C₁₉×#100	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×D₄×C₁₉	2
C₃×M₁₆×C₁₉	2
C₁₉×#100	3
C₃×#100	19

Subgroups — C3×C19×#100 #14269037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#100 #14269037