Subgroups — #14561505

Order 2432.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926601	C₂	1	2	yes	maximal
2	C₂×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₉	C₄	1	2	yes	—
4	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
5	C₁₉×C₄⋊C₈	—	2	2	no	—
6	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
7	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
8	#10597260	C₄	1	4	yes	—
9	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₁₉	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₁₉	—	2	2	no	—
13	C₂×C₈×C₁₉	—	4	2	no	—
14	C₄²×C₁₉	C₂×C₄	1	2	yes	—
15	C₄²×C₁₉	D₄	1	2	yes	—
16	C₂×C₁₉⋊C₈	—	2	4	no	—
17	C₂³×C₁₉	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₉	—	2	2	no	—
19	C₂×C₄×C₁₉	—	2	1	no	—
20	C₂×C₄×C₁₉	—	2	1	no	—
21	C₂×C₄×C₁₉	—	4	1	no	—
22	C₂×C₄×C₁₉	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
26	C₈×C₁₉	—	4	2	no	—
27	C₁₉⋊C₈	—	4	4	no	—
28	#1290	—	19	1	no	maximal, Sylow
29	C₂²×C₁₉	—	2	1	no	—
30	C₂²×C₁₉	—	2	1	no	—
31	C₂²×C₁₉	#95	1	1	yes	characteristic
32	C₂²×C₁₉	#108	1	2	yes	—
33	C₄×C₁₉	—	2	2	no	—
34	C₄×C₁₉	—	2	2	no	—
35	C₄×C₁₉	—	2	1	no	—
36	C₄×C₁₉	#100	1	1	yes	characteristic
37	C₄×C₁₉	#101	1	1	yes	characteristic
38	#432	—	19	2	no	—
39	C₂×C₄⋊C₈	D₁₉	1	1	yes	characteristic
40	C₂×C₁₉	—	2	2	no	—
41	C₂×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
42	C₂×C₁₉	#341	1	1	yes	characteristic
43	C₂×C₁₉	#343	1	1	yes	characteristic
44	C₂²×C₈	Dic₁₉	1	2	yes	—
45	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
46	C₄⋊C₈	—	2	2	no	—
47	C₄⋊C₈	—	38	2	no	—
48	C₂²⋊C₈	—	38	2	no	—
49	#97	—	19	4	no	—
50	C₁₉	#1290	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₄	Dic₃₈	1	1	yes	characteristic
52	C₂²×C₄	D₇₆	1	1	yes	characteristic
53	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
54	C₂×C₈	—	2	2	no	—
55	C₂×C₈	—	4	2	no	—
56	C₂×C₈	—	38	4	no	—
57	C₄²	C₄×D₁₉	1	2	yes	—
58	C₄²	C₂²⋊D₁₉	1	2	yes	—
59	C₂³	C₄⋊Dic₁₉	1	1	yes	characteristic
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	1	no	—
64	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
65	C₂×C₄	Dic₁₉⋊C₄	1	2	yes	—
66	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
67	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
68	C₈	—	4	2	no	—
69	C₈	—	76	4	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	2	1	no	—
72	C₂²	#10597276	1	2	yes	—
73	C₂²	C₁₉⋊#95	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	2	2	no	—
76	C₄	—	2	1	no	—
77	C₄	#10597290	1	1	yes	characteristic
78	C₄	#10597293	1	1	yes	characteristic
79	C₂	—	2	2	no	—
80	C₂	#11926301	1	1	yes	characteristic
81	C₂	#11926309	1	1	yes	characteristic
82	C₂	#11926313	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₄²
Frattini	C₂×C₄²	C₂×D₁₉
Fitting	C₂×C₁₉×C₄⋊C₈	C₂
socle	C₂²×C₁₉	#95
prime radical	C₂³×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂²
hypercenter	C₂×C₄⋊C₈	D₁₉
hypocenter	C₁₉	#1290
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
50. C₁₉	#1290	semidirect

Maximal subgroups

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

subgroup	index
#11926601	2
C₂×C₁₉×C₄⋊C₈	2
#1290	19