Subgroups — #11926893

Order 1216.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10597390	C₂	1	1	yes	maximal, characteristic
2	#10597334	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#103	C₂	1	1	yes	maximal, characteristic
4	#10597292	C₂	1	1	yes	maximal, characteristic
5	#10597273	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
7	#10597267	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₈	—	2	1	no	—
10	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	Dic₁₉⋊C₄	—	2	1	no	—
15	Dic₁₉⋊C₄	—	2	1	no	—
16	Dic₁₉⋊C₄	—	2	1	no	—
17	C₄×Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	Q₈×C₁₉	—	2	1	no	—
20	Q₈×C₁₉	—	2	1	no	—
21	C₂×C₄×C₁₉	—	2	1	no	—
22	C₂×C₄×C₁₉	—	2	1	no	—
23	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×Dic₁₉	—	2	1	no	—
25	C₂×Dic₁₉	—	2	1	no	—
26	C₂×Dic₁₉	D₄	1	1	yes	characteristic
27	C₂×Dic₁₉	D₄	1	1	yes	characteristic
28	Dic₃₈	—	2	1	no	—
29	Dic₃₈	—	2	1	no	—
30	Dic₃₈	—	4	2	no	—
31	C₈×C₁₉	—	2	1	no	—
32	C₁₉⋊C₈	—	2	1	no	—
33	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₄×C₁₉	—	4	1	no	—
35	C₄×C₁₉	—	4	1	no	—
36	C₄×C₁₉	#41	1	1	yes	characteristic
37	C₄×C₁₉	#41	1	1	yes	characteristic
38	Dic₁₉	—	4	1	no	—
39	Dic₁₉	—	4	1	no	—
40	Dic₁₉	SD₁₆	1	2	yes	—
41	Dic₁₉	Q₁₆	1	2	yes	—
42	#487	—	19	1	no	maximal, Sylow
43	C₂×C₁₉	#124	1	1	yes	characteristic
44	C₂×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
45	C₂×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
46	C₄⋊Q₈	—	19	1	no	—
47	C₄⋊Q₈	—	19	1	no	—
48	#103	—	19	1	no	—
49	#103	—	19	1	no	—
50	#103	—	19	1	no	—
51	#103	D₁₉	1	1	yes	characteristic
52	C₄×C₈	—	19	1	no	—
53	C₁₉	#487	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	19	1	no	—
55	C₂×Q₈	—	38	1	no	—
56	C₂×Q₈	C₂×D₁₉	1	1	yes	characteristic
57	C₂×C₈	—	19	1	no	—
58	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
59	C₄⋊C₄	—	19	1	no	—
60	C₄⋊C₄	—	38	1	no	—
61	C₄⋊C₄	—	38	1	no	—
62	C₄⋊C₄	—	38	1	no	—
63	C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
64	C₄²	—	19	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	2	1	no	—
67	Q₈	—	38	1	no	—
68	Q₈	—	38	1	no	—
69	Q₈	—	76	2	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	19	1	no	—
73	C₂×C₄	—	19	1	no	—
74	C₂×C₄	—	38	1	no	—
75	C₂×C₄	—	38	1	no	—
76	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	38	1	no	—
79	C₂²	D₄×D₁₉	1	1	yes	characteristic
80	C₄	—	4	1	no	—
81	C₄	—	4	1	no	—
82	C₄	—	19	2	no	—
83	C₄	—	19	2	no	—
84	C₄	—	76	1	no	—
85	C₄	—	76	1	no	—
86	C₄	#64541	1	1	yes	characteristic
87	C₄	#64543	1	1	yes	characteristic
88	C₂	#10597331	1	1	yes	characteristic
89	C₂	SD₁₆×D₁₉	1	1	yes	characteristic
90	C₂	Q₁₆×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×#103	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₄
hypercenter	#103	D₁₉
hypocenter	C₁₉	#487
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
53. C₁₉	#487	semidirect

Maximal subgroups

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

subgroup	index
#10597390	2
#10597334	2
C₁₉×#103	2
#10597292	2
#10597273	2
C₈×Dic₁₉	2
#10597267	2
#487	19