Subgroups — #14569600

Order 2432.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊#401	C₂	1	2	yes	maximal
2	#11926485	C₂	1	6	yes	maximal
3	#11926450	C₂	1	3	yes	maximal
4	#11926442	C₂	1	3	yes	maximal
5	C₁₉×#376	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₁₉	C₂²	1	3	yes	—
8	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
9	C₂×Dic₁₉⋊C₄	C₂²	1	6	yes	—
10	C₁₉×#95	C₂²	1	3	yes	—
11	C₁₉×#95	C₂²	1	1	yes	characteristic
12	C₁₉⋊#95	C₂²	1	6	yes	—
13	C₁₉⋊#95	C₂²	1	6	yes	—
14	C₁₉⋊#95	C₂²	1	6	yes	—
15	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
16	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₉	C₂³	1	2	yes	—
19	C₂²×Dic₁₉	C₂³	1	6	yes	—
20	C₂×Dic₃₈	—	2	6	no	—
21	C₄²×C₁₉	—	2	6	no	—
22	C₄⋊Dic₁₉	—	2	6	no	—
23	Dic₁₉⋊C₄	—	4	6	no	—
24	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
25	C₂×C₄×C₁₉	—	2	3	no	—
26	C₂×C₄×C₁₉	—	2	3	no	—
27	C₂×C₄×C₁₉	—	2	3	no	—
28	C₂×C₄×C₁₉	—	2	6	no	—
29	C₂×C₄×C₁₉	—	2	3	no	—
30	C₂×C₄×C₁₉	#41	1	6	yes	—
31	C₂×Dic₁₉	—	2	6	no	—
32	C₂×Dic₁₉	—	2	6	no	—
33	C₂×Dic₁₉	—	2	6	no	—
34	C₂×Dic₁₉	—	2	6	no	—
35	Dic₃₈	—	4	4	no	—
36	#2645	—	19	1	no	maximal, Sylow
37	C₂²×C₁₉	C₂×#41	1	3	yes	—
38	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
39	C₂²×C₁₉	2₋¹⁺⁴	1	3	yes	—
40	C₄×C₁₉	—	4	3	no	—
41	C₄×C₁₉	—	4	3	no	—
42	C₄×C₁₉	#126	1	4	yes	—
43	Dic₁₉	—	4	2	no	—
44	Dic₁₉	—	4	6	no	—
45	#401	—	19	2	no	—
46	#400	—	19	6	no	—
47	#391	—	19	3	no	—
48	#389	—	19	3	no	—
49	#376	D₁₉	1	1	yes	characteristic
50	C₂×C₁₉	C₂×#126	1	1	yes	characteristic
51	C₂×C₁₉	#541	1	3	yes	—
52	C₂×C₁₉	#542	1	3	yes	—
53	C₂²×Q₈	—	19	1	no	—
54	C₂×C₄⋊C₄	—	19	3	no	—
55	C₂×C₄⋊C₄	—	19	6	no	—
56	C₂×C₄²	C₂×D₁₉	1	3	yes	—
57	#95	—	19	6	no	—
58	#95	—	19	6	no	—
59	#95	—	19	6	no	—
60	#95	C₂×D₁₉	1	3	yes	—
61	#95	C₂×D₁₉	1	1	yes	characteristic
62	C₁₉	#2645	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₈	—	38	6	no	—
64	C₂²×C₄	—	19	2	no	—
65	C₂²×C₄	—	19	6	no	—
66	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
67	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
68	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
69	C₄⋊C₄	—	38	6	no	—
70	C₄⋊C₄	—	76	6	no	—
71	C₄²	—	2	6	no	—
72	C₂³	C₂³×D₁₉	1	1	yes	characteristic
73	Q₈	—	76	4	no	—
74	C₂×C₄	—	2	3	no	—
75	C₂×C₄	—	2	3	no	—
76	C₂×C₄	—	2	3	no	—
77	C₂×C₄	—	2	6	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	38	6	no	—
80	C₂×C₄	—	38	6	no	—
81	C₂×C₄	—	38	6	no	—
82	C₂×C₄	—	38	6	no	—
83	C₂×C₄	#64541	1	6	yes	—
84	C₂²	C₂×#64541	1	3	yes	—
85	C₂²	#10597435	1	1	yes	characteristic
86	C₂²	#10597436	1	3	yes	—
87	C₄	—	4	3	no	—
88	C₄	—	4	3	no	—
89	C₄	—	76	2	no	—
90	C₄	—	76	6	no	—
91	C₄	#10597322	1	4	yes	—
92	C₂	C₂×#10597322	1	1	yes	characteristic
93	C₂	#11927156	1	3	yes	—
94	C₂	#11927165	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#376	C₂
hypercenter	#376	D₁₉
hypocenter	C₁₉	#2645
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #376

Complements

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

N	H ≅ G/N	type
62. C₁₉	#2645	semidirect

Maximal subgroups

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

subgroup	index
C₁₉⋊#401	2
#11926485	2
#11926450	2
#11926442	2
C₁₉×#376	2
#2645	19