Subgroups — #18070349

Order 4864.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926377	C₂	1	1	yes	maximal, characteristic
2	#14561846	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₆×D₁₉	C₄	1	1	yes	characteristic
5	#11926377	—	2	1	no	—
6	#11926377	—	2	1	no	—
7	C₂×C₁₉⋊C₃₂	C₄	1	1	yes	characteristic
8	C₁₉⋊C₆₄	—	2	1	no	—
9	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
10	C₁₉×C₆₄	—	2	1	no	—
11	C₂×C₈×D₁₉	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	C₈	1	1	yes	characteristic
14	C₁₆×D₁₉	—	2	1	no	—
15	C₁₆×D₁₉	—	2	1	no	—
16	C₁₉×C₃₂	D₄	1	1	yes	characteristic
17	C₁₉×C₃₂	D₄	1	1	yes	characteristic
18	C₁₉⋊C₃₂	—	2	1	no	—
19	C₂×C₄×D₁₉	C₁₆	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
21	C₂×C₁₉⋊C₈	C₁₆	1	1	yes	characteristic
22	C₈×D₁₉	—	2	1	no	—
23	C₈×D₁₉	—	2	1	no	—
24	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
26	C₁₉⋊C₁₆	—	2	1	no	—
27	#7513	—	19	1	no	maximal, Sylow
28	C₂²×D₁₉	C₃₂	1	1	yes	characteristic
29	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
30	C₂×Dic₁₉	C₃₂	1	1	yes	characteristic
31	C₄×D₁₉	—	2	1	no	—
32	C₄×D₁₉	—	2	1	no	—
33	C₈×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
34	C₈×C₁₉	M₃₂	1	1	yes	characteristic
35	C₁₉⋊C₈	—	2	1	no	—
36	C₂×M₆₄	—	19	1	no	—
37	M₁₂₈	—	19	1	no	—
38	M₁₂₈	D₁₉	1	1	yes	characteristic, complemented
39	C₂²×C₁₉	C₂×C₃₂	1	1	yes	characteristic
40	C₂×D₁₉	—	2	1	no	—
41	C₂×D₁₉	—	4	1	no	—
42	C₄×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
43	C₄×C₁₉	M₆₄	1	1	yes	characteristic
44	Dic₁₉	—	2	1	no	—
45	C₂²×C₁₆	—	19	1	no	—
46	M₆₄	—	38	1	no	—
47	M₆₄	—	38	1	no	—
48	C₂×C₃₂	—	19	1	no	—
49	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
50	C₆₄	—	2	1	no	—
51	C₆₄	—	38	1	no	—
52	C₂×C₁₉	—	2	1	no	—
53	C₂×C₁₉	C₂²⋊C₃₂	1	1	yes	characteristic
54	D₁₉	—	4	1	no	—
55	C₂²×C₈	—	19	1	no	—
56	C₂×C₁₆	—	19	1	no	—
57	C₂×C₁₆	—	38	1	no	—
58	C₂×C₁₆	—	38	1	no	—
59	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
60	C₃₂	—	38	1	no	—
61	C₃₂	D₇₆	1	1	yes	characteristic
62	C₃₂	C₂²⋊D₁₉	1	1	yes	characteristic
63	C₁₉	#7513	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₄	—	19	1	no	—
65	C₂×C₈	—	19	1	no	—
66	C₂×C₈	—	38	1	no	—
67	C₂×C₈	—	38	1	no	—
68	C₂×C₈	C₈×D₁₉	1	1	yes	characteristic
69	C₁₆	—	38	1	no	—
70	C₁₆	#64515	1	1	yes	characteristic
71	C₁₆	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
72	C₂³	—	19	1	no	—
73	C₂×C₄	—	19	1	no	—
74	C₂×C₄	—	38	1	no	—
75	C₂×C₄	—	38	1	no	—
76	C₂×C₄	C₁₆×D₁₉	1	1	yes	characteristic
77	C₈	—	38	1	no	—
78	C₈	#10597255	1	1	yes	characteristic
79	C₈	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
80	C₂²	—	38	1	no	—
81	C₂²	—	76	1	no	—
82	C₂²	C₃₂×D₁₉	1	1	yes	characteristic
83	C₄	—	38	1	no	—
84	C₄	(C₂×D₁₉)⋊C₁₆	1	1	yes	characteristic
85	C₄	#11926377	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	76	1	no	—
88	C₂	(C₂×D₁₉)⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	(C₂×D₁₉)⋊C₄
commutator	C₂²×C₁₉	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₁₉×M₁₂₈	C₂
socle	C₂×C₁₉	C₂²⋊C₃₂
prime radical	C₂²×D₁₉	C₃₂
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	M₁₂₈	D₁₉
hypocenter	C₁₉	#7513
LCS	G ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
2. #14561846	C₂	semidirect
3. C₁₉×M₁₂₈	C₂	semidirect
38. M₁₂₈	D₁₉	semidirect
63. C₁₉	#7513	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926377	2
#14561846	2
C₁₉×M₁₂₈	2
#7513	19