Subgroups — C₃×C₁₉×#108 #14269045

Order 1824.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×M₁₆×C₁₉	C₂	1	2	yes	maximal
2	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#108	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
5	C₃×C₈×C₁₉	—	2	2	no	—
6	C₃×C₈×C₁₉	C₄	1	2	yes	—
7	M₁₆×C₁₉	C₂×C₃	1	2	yes	—
8	C₂×C₈×C₁₉	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₃×C₁₉	Q₈	1	1	yes	characteristic
10	C₃×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
12	C₂×C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
13	C₈×C₁₉	—	2	2	no	—
14	C₈×C₁₉	C₃×C₄	1	2	yes	—
15	C₂×C₃×C₁₉	—	2	1	no	—
16	C₂×C₃×C₁₉	C₄⋊C₄	1	1	yes	characteristic
17	C₃×#108	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂²×C₁₉	C₃×Q₈	1	1	yes	characteristic
19	C₄×C₁₉	C₂×C₃×C₄	1	1	yes	characteristic
20	C₄×C₁₉	C₃×D₄	1	1	yes	characteristic
21	C₃×C₁₉	#108	1	1	yes	characteristic, direct product factor, Hall
22	C₃×M₁₆	C₂×C₁₉	1	2	yes	—
23	C₂×C₃×C₈	C₂×C₁₉	1	1	yes	characteristic
24	C₂×C₁₉	—	2	1	no	—
25	C₂×C₁₉	C₃×C₄⋊C₄	1	1	yes	characteristic
26	#108	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
28	C₃×C₈	—	2	2	no	—
29	C₃×C₈	C₄×C₁₉	1	2	yes	—
30	C₁₉	C₃×#108	1	1	yes	characteristic, direct product factor, Sylow
31	M₁₆	C₂×C₃×C₁₉	1	2	yes	—
32	C₂×C₈	C₂×C₃×C₁₉	1	1	yes	characteristic
33	C₂²×C₃	Q₈×C₁₉	1	1	yes	characteristic
34	C₃×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
35	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
36	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
37	C₈	—	2	2	no	—
38	C₈	C₃×C₄×C₁₉	1	2	yes	—
39	C₂×C₃	—	2	1	no	—
40	C₂×C₃	C₄⋊C₄×C₁₉	1	1	yes	characteristic
41	C₂²	C₃×Q₈×C₁₉	1	1	yes	characteristic
42	C₄	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic
43	C₄	C₃×D₄×C₁₉	1	1	yes	characteristic
44	C₃	C₁₉×#108	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	2	1	no	—
46	C₂	C₃×C₄⋊C₄×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₁₉	D₄
commutator	C₄	C₂×C₃×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂²×C₃×C₁₉
socle	C₂×C₃×C₁₉	C₄⋊C₄
prime radical	C₂²×C₃×C₁₉	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₁₉ ◁ C₂×C₃×C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₁₉×#108	C₃	direct (N × H)
17. C₃×#108	C₁₉	direct (N × H)
21. C₃×C₁₉	#108	direct (N × H)
26. #108	C₃×C₁₉	direct (N × H)
30. C₁₉	C₃×#108	direct (N × H)
44. C₃	C₁₉×#108	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×M₁₆×C₁₉	2
C₂×C₃×C₈×C₁₉	2
C₁₉×#108	3
C₃×#108	19

Subgroups — C3×C19×#108 #14269045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#108 #14269045