Subgroups — #18069520

Order 4864.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14565434	C₂	1	2	yes	maximal
2	C₁₉×#1452	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₂²⋊(C₁₉⋊C₁₆)	C₄	1	4	yes	—
5	C₄×C₁₉⋊C₁₆	—	2	2	no	—
6	C₁₉×#431	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#322	—	2	2	no	—
9	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
10	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₁₉×C₄⋊C₈	C₈	1	4	yes	—
12	C₁₉×C₂²⋊C₈	—	2	2	no	—
13	C₄×C₈×C₁₉	—	2	2	no	—
14	C₄×C₈×C₁₉	D₄	1	2	yes	—
15	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₄×C₈×C₁₉	Q₈	1	1	yes	characteristic
17	C₂×C₁₉⋊C₁₆	—	2	4	no	—
18	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
20	C₂×C₈×C₁₉	—	2	4	no	—
21	C₂×C₈×C₁₉	—	4	2	no	—
22	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
23	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
24	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₄²×C₁₉	C₄⋊C₄	1	1	yes	characteristic
26	C₄²×C₁₉	C₂×C₈	1	2	yes	—
27	C₁₉⋊C₁₆	—	4	4	no	—
28	#7198	—	19	1	no	maximal, Sylow
29	C₂³×C₁₉	#97	1	1	yes	characteristic
30	C₂×C₄×C₁₉	—	2	2	no	—
31	C₂×C₄×C₁₉	—	2	4	no	—
32	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
35	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
36	C₈×C₁₉	—	2	2	no	—
37	C₈×C₁₉	—	2	2	no	—
38	C₈×C₁₉	—	4	4	no	—
39	#2162	—	19	2	no	—
40	#1452	D₁₉	1	1	yes	characteristic
41	C₂²×C₁₉	—	2	1	no	—
42	C₂²×C₁₉	—	2	2	no	—
43	C₂²×C₁₉	#336	1	1	yes	characteristic
44	C₄×C₁₉	—	2	1	no	—
45	C₄×C₁₉	—	2	2	no	—
46	C₄×C₁₉	#344	1	2	yes	—
47	C₄×C₁₉	#350	1	4	yes	—
48	#431	Dic₁₉	1	2	yes	—
49	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
50	C₄⋊C₁₆	—	38	2	no	—
51	C₂²⋊C₁₆	—	19	4	no	—
52	C₄×C₁₆	—	38	2	no	—
53	#322	—	2	2	no	—
54	C₂×C₁₉	—	4	1	no	—
55	C₂×C₁₉	#1281	1	1	yes	characteristic
56	C₂×C₁₉	#1379	1	2	yes	—
57	C₂²×C₈	C₄×D₁₉	1	2	yes	—
58	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
59	C₂×C₁₆	—	38	4	no	—
60	C₄⋊C₈	C₁₉⋊C₈	1	4	yes	—
61	C₂²⋊C₈	—	2	2	no	—
62	C₄×C₈	—	2	2	no	—
63	C₄×C₈	Dic₃₈	1	1	yes	characteristic
64	C₄×C₈	D₇₆	1	1	yes	characteristic
65	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
66	C₁₉	#7198	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	#64520	1	2	yes	—
68	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
69	C₂×C₈	—	2	4	no	—
70	C₂×C₈	—	4	2	no	—
71	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
72	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
73	C₄²	C₂×C₁₉⋊C₈	1	2	yes	—
74	C₄²	C₄⋊Dic₁₉	1	1	yes	characteristic
75	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
76	C₁₆	—	76	4	no	—
77	C₂³	#10597260	1	1	yes	characteristic
78	C₂×C₄	—	2	2	no	—
79	C₂×C₄	—	2	4	no	—
80	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
81	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
82	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
83	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
84	C₈	—	2	2	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	4	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	2	1	no	—
89	C₂²	#11926299	1	1	yes	characteristic
90	C₄	—	2	2	no	—
91	C₄	—	2	1	no	—
92	C₄	#11926315	1	2	yes	—
93	C₄	#11926328	1	4	yes	—
94	C₂	—	4	1	no	—
95	C₂	#14561480	1	1	yes	characteristic
96	C₂	#14561724	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂²⋊Dic₁₉
commutator	C₂×C₄×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₁₉×#1452	C₂
socle	C₂²×C₁₉	#336
prime radical	C₂³×C₁₉	#97
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	#1452	D₁₉
hypocenter	C₁₉	#7198
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄×C₈ ◁ #1452

Complements

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

N	H ≅ G/N	type
66. C₁₉	#7198	semidirect

Maximal subgroups

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

subgroup	index
#14565434	2
C₁₉×#1452	2
#7198	19