Subgroups — #14561739

Order 2432.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597276	C₂	1	2	yes	maximal
2	C₂×C₁₉×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
4	C₂×#64520	—	2	2	no	—
5	C₁₉×M₃₂	—	2	2	no	—
6	C₂×C₁₆×C₁₉	C₄	1	2	yes	—
7	#10597276	—	2	2	no	—
8	#10597276	C₄	1	4	yes	—
9	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
10	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
11	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₁₉	D₄	1	2	yes	—
13	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
14	#64520	—	2	4	no	—
15	#64520	—	4	2	no	—
16	C₂×C₁₉⋊C₈	—	4	2	no	—
17	C₁₆×C₁₉	—	2	2	no	—
18	C₂³×C₁₉	Q₁₆	1	1	yes	characteristic
19	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
22	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
23	C₈×C₁₉	C₄²	1	1	yes	characteristic
24	C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₁₉	C₄⋊C₄	1	2	yes	—
26	C₁₉⋊C₈	—	4	4	no	—
27	#1385	—	19	1	no	maximal, Sylow
28	C₂²×C₁₉	—	4	1	no	—
29	C₂²×C₁₉	#103	1	2	yes	—
30	C₂²×C₁₉	#107	1	1	yes	characteristic
31	C₄×C₁₉	#95	1	1	yes	characteristic
32	C₄×C₁₉	#102	1	2	yes	—
33	C₄×C₁₉	#106	1	1	yes	characteristic
34	C₂×M₃₂	D₁₉	1	1	yes	characteristic
35	C₂×#108	—	19	2	no	—
36	C₂×C₁₉	—	2	2	no	—
37	C₂×C₁₉	—	2	1	no	—
38	C₂×C₁₉	#340	1	1	yes	characteristic
39	C₂×M₁₆	—	38	2	no	—
40	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
41	M₃₂	—	2	2	no	—
42	C₂×C₁₆	Dic₁₉	1	2	yes	—
43	#108	—	19	4	no	—
44	#108	—	38	2	no	—
45	C₁₉	#1385	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	D₇₆	1	1	yes	characteristic
47	M₁₆	—	38	4	no	—
48	M₁₆	—	76	2	no	—
49	C₂×C₈	—	76	2	no	—
50	C₂×C₈	Dic₃₈	1	1	yes	characteristic
51	C₂×C₈	C₄×D₁₉	1	2	yes	—
52	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
53	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
54	C₁₆	—	2	2	no	—
55	C₂³	Dic₇₆	1	1	yes	characteristic
56	C₂×C₄	#64516	1	2	yes	—
57	C₂×C₄	D₁₅₂	1	1	yes	characteristic
58	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
59	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
60	C₈	—	76	4	no	—
61	C₈	C₄×Dic₁₉	1	1	yes	characteristic
62	C₈	Dic₁₉⋊C₄	1	2	yes	—
63	C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
64	C₂²	—	4	1	no	—
65	C₂²	#10597273	1	2	yes	—
66	C₂²	#10597275	1	1	yes	characteristic
67	C₄	#10597274	1	1	yes	characteristic
68	C₄	#10597278	1	2	yes	—
69	C₄	C₁₉⋊#95	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	—	2	1	no	—
72	C₂	#11926307	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10597274
commutator	C₈×C₁₉	C₄²
Frattini	C₂²×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×M₃₂	C₂
socle	C₂×C₁₉	#340
prime radical	C₂³×C₁₉	Q₁₆
cosocle	C₂²×C₈×C₁₉	C₂²
hypercenter	C₂×M₃₂	D₁₉
hypocenter	C₁₉	#1385
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
45. C₁₉	#1385	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597276	2
C₂×C₁₉×M₃₂	2
#1385	19