Subgroups — C₁₉×#2255 #14560112

Order 2432.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#500	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#499	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#367	C₂	1	2	yes	maximal
4	C₁₉×#366	C₂	1	2	yes	maximal
5	C₁₉×#346	C₂	1	1	yes	maximal, characteristic
6	C₁₉×C₄⋊Q₈	—	2	1	no	—
7	C₁₉×#125	—	2	1	no	—
8	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#107	—	2	1	no	—
10	C₁₉×#107	C₂²	1	1	yes	characteristic
11	C₁₉×#107	C₂²	1	2	yes	—
12	C₁₉×#107	C₂²	1	1	yes	characteristic
13	C₁₉×#106	—	2	1	no	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₁₉	—	4	1	no	—
16	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₁₉	—	2	1	no	—
19	C₄⋊C₄×C₁₉	—	2	1	no	—
20	C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₄⋊C₄×C₁₉	—	4	1	no	—
22	C₄⋊C₄×C₁₉	—	4	1	no	—
23	C₄⋊C₄×C₁₉	—	4	1	no	—
24	C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₁₆×C₁₉	Q₈	1	4	yes	complemented
26	Q₈×C₁₉	—	8	2	no	—
27	C₂×C₄×C₁₉	—	4	1	no	—
28	C₂×C₄×C₁₉	—	4	1	no	—
29	C₂×C₄×C₁₉	—	4	2	no	—
30	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
31	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
32	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₈×C₁₉	Q₁₆	1	2	yes	—
34	C₈×C₁₉	C₂×Q₈	1	2	yes	—
35	#2255	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
37	C₄×C₁₉	—	2	1	no	—
38	C₄×C₁₉	—	2	1	no	—
39	C₄×C₁₉	—	8	1	no	—
40	C₄×C₁₉	—	8	2	no	—
41	C₄×C₁₉	—	8	1	no	—
42	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
43	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
44	#500	C₂×C₁₉	1	1	yes	characteristic
45	#499	C₂×C₁₉	1	1	yes	characteristic
46	#367	C₂×C₁₉	1	2	yes	—
47	#366	C₂×C₁₉	1	2	yes	—
48	#346	C₂×C₁₉	1	1	yes	characteristic
49	C₂×C₁₉	#500	1	1	yes	characteristic
50	C₂×C₁₉	#509	1	1	yes	characteristic
51	C₂×C₁₉	#510	1	1	yes	characteristic
52	C₄⋊Q₈	—	2	1	no	—
53	#125	—	2	1	no	—
54	C₂×C₁₆	C₂²×C₁₉	1	2	yes	—
55	#107	—	2	1	no	—
56	#107	C₂²×C₁₉	1	1	yes	characteristic
57	#107	C₂²×C₁₉	1	2	yes	—
58	#107	C₂²×C₁₉	1	1	yes	characteristic
59	#106	—	2	1	no	—
60	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
61	C₁₉	#2255	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×Q₈	—	4	1	no	—
63	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
64	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
65	C₄⋊C₄	—	2	1	no	—
66	C₄⋊C₄	—	2	1	no	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	4	1	no	—
69	C₄⋊C₄	—	4	1	no	—
70	C₄⋊C₄	—	4	1	no	—
71	C₄²	D₄×C₁₉	1	1	yes	characteristic
72	C₁₆	Q₈×C₁₉	1	4	yes	complemented
73	Q₈	—	8	2	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
78	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
79	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
80	C₈	Q₁₆×C₁₉	1	2	yes	—
81	C₈	C₂×Q₈×C₁₉	1	2	yes	—
82	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	2	no	—
86	C₄	—	8	1	no	—
87	C₄	—	8	1	no	—
88	C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
89	C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
90	C₂	C₁₉×#500	1	1	yes	characteristic
91	C₂	C₁₉×#509	1	1	yes	characteristic
92	C₂	C₁₉×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
25. C₁₆×C₁₉	Q₈	semidirect
35. #2255	C₁₉	direct (N × H)
61. C₁₉	#2255	direct (N × H)
72. C₁₆	Q₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#500	2
C₁₉×#499	2
C₁₉×#367	2
C₁₉×#366	2
C₁₉×#346	2
#2255	19

Subgroups — C19×#2255 #14560112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2255 #14560112