Subgroups — C₃×C₁₉×#103 #14269040

Order 1824.

84 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	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#103	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×Q₈×C₁₉	—	2	1	no	—
6	C₃×Q₈×C₁₉	C₄	1	2	yes	complemented
7	C₂×C₃×C₄×C₁₉	—	2	1	no	—
8	C₂×C₃×C₄×C₁₉	—	2	1	no	—
9	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₃×C₈×C₁₉	—	2	1	no	—
11	C₂×Q₈×C₁₉	C₂×C₃	1	1	yes	characteristic
12	C₂×C₈×C₁₉	C₂×C₃	1	1	yes	characteristic
13	C₄⋊C₄×C₁₉	C₂×C₃	1	1	yes	characteristic
14	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
15	C₃×C₄×C₁₉	—	2	2	no	—
16	C₃×C₄×C₁₉	—	4	1	no	—
17	C₃×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
19	Q₈×C₁₉	—	2	1	no	—
20	Q₈×C₁₉	C₃×C₄	1	2	yes	complemented
21	C₂×C₄×C₁₉	—	2	1	no	—
22	C₂×C₄×C₁₉	—	2	1	no	—
23	C₂×C₄×C₁₉	C₂²×C₃	1	1	yes	characteristic
24	C₈×C₁₉	—	2	1	no	—
25	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₃×C₁₉	SD₁₆	1	1	yes	characteristic
27	C₂×C₃×C₁₉	Q₁₆	1	1	yes	characteristic
28	C₃×#103	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂²×C₁₉	C₃×D₄	1	1	yes	characteristic
30	C₄×C₁₉	—	2	2	no	—
31	C₄×C₁₉	—	4	1	no	—
32	C₄×C₁₉	C₂×C₃×C₄	1	1	yes	characteristic
33	C₄×C₁₉	C₃×D₄	1	1	yes	characteristic
34	C₃×C₁₉	#103	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₃×Q₈	C₂×C₁₉	1	1	yes	characteristic
36	C₂×C₃×C₈	C₂×C₁₉	1	1	yes	characteristic
37	C₃×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
38	C₂×C₁₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₁₉	C₃×SD₁₆	1	1	yes	characteristic
40	C₂×C₁₉	C₃×Q₁₆	1	1	yes	characteristic
41	#103	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₃×Q₈	—	2	1	no	—
43	C₃×Q₈	C₄×C₁₉	1	2	yes	complemented
44	C₂×C₃×C₄	—	2	1	no	—
45	C₂×C₃×C₄	—	2	1	no	—
46	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
47	C₃×C₈	—	2	1	no	—
48	C₁₉	C₃×#103	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×Q₈	C₂×C₃×C₁₉	1	1	yes	characteristic
50	C₂×C₈	C₂×C₃×C₁₉	1	1	yes	characteristic
51	C₄⋊C₄	C₂×C₃×C₁₉	1	1	yes	characteristic
52	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
53	C₃×C₄	—	2	2	no	—
54	C₃×C₄	—	4	1	no	—
55	C₃×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
56	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
57	Q₈	—	2	1	no	—
58	Q₈	C₃×C₄×C₁₉	1	2	yes	complemented
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	C₂²×C₃×C₁₉	1	1	yes	characteristic
62	C₈	—	2	1	no	—
63	C₂×C₃	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
64	C₂×C₃	SD₁₆×C₁₉	1	1	yes	characteristic
65	C₂×C₃	Q₁₆×C₁₉	1	1	yes	characteristic
66	C₂²	C₃×D₄×C₁₉	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	4	1	no	—
69	C₄	C₂×C₃×C₄×C₁₉	1	1	yes	characteristic
70	C₄	C₃×D₄×C₁₉	1	1	yes	characteristic
71	C₃	C₁₉×#103	1	1	yes	characteristic, direct product factor, Sylow
72	C₂	C₃×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
73	C₂	C₃×SD₁₆×C₁₉	1	1	yes	characteristic
74	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
4. C₁₉×#103	C₃	direct (N × H)
6. C₃×Q₈×C₁₉	C₄	semidirect
20. Q₈×C₁₉	C₃×C₄	semidirect
28. C₃×#103	C₁₉	direct (N × H)
34. C₃×C₁₉	#103	direct (N × H)
41. #103	C₃×C₁₉	direct (N × H)
43. C₃×Q₈	C₄×C₁₉	semidirect
48. C₁₉	C₃×#103	direct (N × H)
58. Q₈	C₃×C₄×C₁₉	semidirect
71. C₃	C₁₉×#103	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
C₂×C₃×C₈×C₁₉	2
C₃×C₄⋊C₄×C₁₉	2
C₁₉×#103	3
C₃×#103	19

Subgroups — C3×C19×#103 #14269040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×#103 #14269040