Subgroups — C₁₉×#7454 #18013413

Order 4864.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2253	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1422	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1373	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#499	—	2	1	no	—
5	C₁₉×M₆₄	—	2	1	no	—
6	C₁₉×#367	C₄	1	2	yes	—
7	C₁₉×#366	—	2	1	no	—
8	C₁₉×#364	—	2	1	no	—
9	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#125	—	4	1	no	—
11	C₁₉×M₃₂	—	4	1	no	—
12	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
14	C₁₉×#107	—	2	2	no	—
15	C₁₉×#106	—	4	1	no	—
16	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₁₉×C₃₂	—	4	1	no	—
18	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
20	C₄⋊C₄×C₁₉	—	4	2	no	—
21	C₄⋊C₄×C₁₉	—	8	2	no	—
22	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
23	C₁₆×C₁₉	—	2	1	no	—
24	C₁₆×C₁₉	—	8	1	no	—
25	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
26	C₁₆×C₁₉	Q₁₆	1	1	yes	characteristic
27	#7454	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂×C₄×C₁₉	—	2	1	no	—
29	C₂×C₄×C₁₉	—	8	2	no	—
30	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
31	C₈×C₁₉	#101	1	1	yes	characteristic
32	C₈×C₁₉	#103	1	1	yes	characteristic
33	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
34	C₈×C₁₉	Q₃₂	1	1	yes	characteristic
35	#2253	C₂×C₁₉	1	1	yes	characteristic
36	#1422	C₂×C₁₉	1	1	yes	characteristic
37	#1373	C₂×C₁₉	1	1	yes	characteristic
38	C₂²×C₁₉	#361	1	1	yes	characteristic
39	C₄×C₁₉	—	4	1	no	—
40	C₄×C₁₉	—	16	2	no	—
41	C₄×C₁₉	#332	1	1	yes	characteristic
42	C₄×C₁₉	#358	1	1	yes	characteristic
43	#499	—	2	1	no	—
44	M₆₄	—	2	1	no	—
45	#367	C₄×C₁₉	1	2	yes	—
46	#366	—	2	1	no	—
47	#364	—	2	1	no	—
48	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
49	C₂×C₁₉	—	2	1	no	—
50	C₂×C₁₉	#1365	1	1	yes	characteristic
51	#125	—	4	1	no	—
52	M₃₂	—	4	1	no	—
53	C₂×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
54	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
55	#107	—	2	2	no	—
56	#106	—	4	1	no	—
57	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
58	C₃₂	—	4	1	no	—
59	C₁₉	#7454	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
61	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
62	C₄⋊C₄	—	4	2	no	—
63	C₄⋊C₄	—	8	2	no	—
64	C₄²	SD₁₆×C₁₉	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	8	1	no	—
67	C₁₆	SD₁₆×C₁₉	1	1	yes	characteristic
68	C₁₆	Q₁₆×C₁₉	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	8	2	no	—
71	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
72	C₈	C₁₉×#101	1	1	yes	characteristic
73	C₈	C₁₉×#103	1	1	yes	characteristic
74	C₈	C₁₉×SD₃₂	1	1	yes	characteristic
75	C₈	C₁₉×Q₃₂	1	1	yes	characteristic
76	C₂²	C₁₉×#361	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	16	2	no	—
79	C₄	C₁₉×#332	1	1	yes	characteristic
80	C₄	C₁₉×#358	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	C₁₉×#1365	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#1365
commutator	C₂×C₁₆	C₂×C₄×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
prime radical	C₂²×C₁₉	#361
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
27. #7454	C₁₉	direct (N × H)
59. C₁₉	#7454	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2253	2
C₁₉×#1422	2
C₁₉×#1373	2
#7454	19

Subgroups — C19×#7454 #18013413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7454 #18013413