Subgroups — C₃×C₁₉×#101 #14269038

Order 1824.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×M₁₆×C₁₉	C₂	1	2	yes	maximal
3	C₁₉×#101	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×Q₈×C₁₉	—	2	2	no	—
5	C₂×C₃×C₄×C₁₉	C₄	1	2	yes	—
6	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₃×C₈×C₁₉	—	2	2	no	—
8	C₂×Q₈×C₁₉	C₂×C₃	1	1	yes	characteristic
9	M₁₆×C₁₉	C₂×C₃	1	2	yes	—
10	C₂²×C₃×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄×C₁₉	—	2	2	no	—
12	C₃×C₄×C₁₉	D₄	1	2	yes	—
13	Q₈×C₁₉	—	2	2	no	—
14	C₂×C₄×C₁₉	C₃×C₄	1	2	yes	—
15	C₂×C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
16	C₈×C₁₉	—	2	2	no	—
17	C₂×C₃×C₁₉	—	2	1	no	—
18	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₃×#101	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₁₉	C₂×C₃×C₄	1	1	yes	characteristic
21	C₄×C₁₉	—	2	2	no	—
22	C₄×C₁₉	C₃×D₄	1	2	yes	—
23	C₃×C₁₉	#101	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃×Q₈	C₂×C₁₉	1	1	yes	characteristic
25	C₃×M₁₆	C₂×C₁₉	1	2	yes	—
26	C₂×C₁₉	—	2	1	no	—
27	C₂×C₁₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
28	#101	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×Q₈	—	2	2	no	—
30	C₂×C₃×C₄	C₄×C₁₉	1	2	yes	—
31	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
32	C₃×C₈	—	2	2	no	—
33	C₁₉	C₃×#101	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×Q₈	C₂×C₃×C₁₉	1	1	yes	characteristic
35	M₁₆	C₂×C₃×C₁₉	1	2	yes	—
36	C₂²×C₃	C₂×C₄×C₁₉	1	1	yes	characteristic
37	C₃×C₄	—	2	2	no	—
38	C₃×C₄	D₄×C₁₉	1	2	yes	—
39	Q₈	—	2	2	no	—
40	C₂×C₄	C₃×C₄×C₁₉	1	2	yes	—
41	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
42	C₈	—	2	2	no	—
43	C₂×C₃	—	2	1	no	—
44	C₂×C₃	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
45	C₂²	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₃×D₄×C₁₉	1	2	yes	—
48	C₃	C₁₉×#101	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	—	2	1	no	—
50	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	C₂²×C₃×C₁₉	C₂×C₄
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
3. C₁₉×#101	C₃	direct (N × H)
19. C₃×#101	C₁₉	direct (N × H)
23. C₃×C₁₉	#101	direct (N × H)
28. #101	C₃×C₁₉	direct (N × H)
33. C₁₉	C₃×#101	direct (N × H)
48. C₃	C₁₉×#101	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×M₁₆×C₁₉	2
C₁₉×#101	3
C₃×#101	19

Subgroups — C3×C19×#101 #14269038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#101 #14269038