Subgroups — C₁₉×#12522 #18018481

Order 4864.

238 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2254	C₂	1	2	yes	maximal
2	C₁₉×#2252	C₂	1	2	yes	maximal
3	C₁₉×#1710	C₂	1	2	yes	maximal
4	C₈×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#500	C₂²	1	4	yes	—
6	C₁₉×#487	—	2	4	no	—
7	C₁₉×#367	—	2	4	no	—
8	C₁₉×#366	—	2	4	no	—
9	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₈²×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×C₄⋊Q₈	—	2	4	no	—
13	C₂×C₁₆×C₁₉	D₄	1	2	yes	—
14	C₂×C₁₆×C₁₉	D₄	1	2	yes	—
15	C₁₉×#107	—	2	4	no	—
16	C₁₉×#107	—	2	4	no	—
17	C₁₉×#103	—	4	8	no	—
18	C₄×C₈×C₁₉	D₄	1	2	yes	—
19	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×Q₈×C₁₉	—	4	4	no	—
21	C₂×C₈×C₁₉	D₈	1	4	yes	—
22	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
24	C₄⋊C₄×C₁₉	—	4	4	no	—
25	C₄⋊C₄×C₁₉	—	4	4	no	—
26	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
27	C₁₆×C₁₉	Q₁₆	1	4	yes	—
28	C₁₆×C₁₉	Q₁₆	1	4	yes	—
29	#12522	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	Q₈×C₁₉	—	8	8	no	—
31	C₂×C₄×C₁₉	—	8	4	no	—
32	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
34	C₈×C₁₉	—	2	4	no	—
35	C₈×C₁₉	C₂×Q₁₆	1	2	yes	—
36	C₈×C₁₉	C₂×Q₁₆	1	2	yes	—
37	#2254	C₂×C₁₉	1	2	yes	—
38	#2252	C₂×C₁₉	1	2	yes	—
39	#1710	C₂×C₁₉	1	2	yes	—
40	C₈×C₁₆	C₂×C₁₉	1	1	yes	characteristic
41	C₂²×C₁₉	#493	1	1	yes	characteristic
42	C₄×C₁₉	—	16	4	no	—
43	C₄×C₁₉	#494	1	1	yes	characteristic
44	C₄×C₁₉	#494	1	1	yes	characteristic
45	C₄×C₁₉	#508	1	4	yes	—
46	#500	C₂²×C₁₉	1	4	yes	—
47	#487	—	2	4	no	—
48	#367	—	2	4	no	—
49	#366	—	2	4	no	—
50	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
51	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
52	C₈²	C₂²×C₁₉	1	1	yes	characteristic
53	C₂×C₁₉	#1713	1	1	yes	characteristic
54	C₂×C₁₉	#2249	1	2	yes	—
55	C₄⋊Q₈	—	2	4	no	—
56	C₂×C₁₆	D₄×C₁₉	1	2	yes	—
57	C₂×C₁₆	D₄×C₁₉	1	2	yes	—
58	#107	—	2	4	no	—
59	#107	—	2	4	no	—
60	#103	—	4	8	no	—
61	C₄×C₈	D₄×C₁₉	1	2	yes	—
62	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
63	C₁₉	#12522	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×Q₈	—	4	4	no	—
65	C₂×C₈	D₈×C₁₉	1	4	yes	—
66	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
67	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
68	C₄⋊C₄	—	4	4	no	—
69	C₄⋊C₄	—	4	4	no	—
70	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
71	C₁₆	Q₁₆×C₁₉	1	4	yes	—
72	C₁₆	Q₁₆×C₁₉	1	4	yes	—
73	Q₈	—	8	8	no	—
74	C₂×C₄	—	8	4	no	—
75	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
76	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
77	C₈	—	2	4	no	—
78	C₈	C₂×Q₁₆×C₁₉	1	2	yes	—
79	C₈	C₂×Q₁₆×C₁₉	1	2	yes	—
80	C₂²	C₁₉×#493	1	1	yes	characteristic
81	C₄	—	16	4	no	—
82	C₄	C₁₉×#494	1	1	yes	characteristic
83	C₄	C₁₉×#494	1	1	yes	characteristic
84	C₄	C₁₉×#508	1	4	yes	—
85	C₂	C₁₉×#1713	1	1	yes	characteristic
86	C₂	C₁₉×#2249	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
29. #12522	C₁₉	direct (N × H)
63. C₁₉	#12522	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×#2254	2
C₁₉×#2252	2
C₁₉×#1710	2
C₈×C₁₆×C₁₉	2
#12522	19

Subgroups — C19×#12522 #18018481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12522 #18018481