Subgroups — #11926878

Order 1216.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10597392	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597292	C₂	1	1	yes	maximal, characteristic, complemented
5	(C₂×D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#10597275	C₂	1	1	yes	maximal, characteristic, complemented
7	#10597264	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₉	—	2	1	no	—
10	C₂×C₄×D₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	(C₂×D₁₉)⋊C₄	—	2	1	no	—
14	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
16	Dic₁₉⋊C₄	—	2	1	no	—
17	Dic₁₉⋊C₄	—	2	1	no	—
18	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×D₁₉	D₄	1	1	yes	characteristic
20	Q₈×C₁₉	—	2	1	no	—
21	Q₈×C₁₉	—	2	1	no	—
22	C₂×C₄×C₁₉	—	2	1	no	—
23	C₂×C₄×C₁₉	—	2	1	no	—
24	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₉	—	2	1	no	—
26	C₂×Dic₁₉	—	2	1	no	—
27	C₂×Dic₁₉	D₄	1	1	yes	characteristic
28	C₄×D₁₉	—	2	1	no	—
29	C₄×D₁₉	—	2	1	no	—
30	C₄×D₁₉	—	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	C₂×D₁₉	—	2	1	no	—
35	C₂×D₁₉	—	2	1	no	—
36	C₂×D₁₉	Q₁₆	1	2	yes	—
37	C₄×C₁₉	—	4	1	no	—
38	C₄×C₁₉	—	4	1	no	—
39	C₄×C₁₉	#41	1	1	yes	characteristic
40	C₄×C₁₉	#41	1	1	yes	characteristic
41	Dic₁₉	—	2	1	no	—
42	Dic₁₉	—	4	1	no	—
43	Dic₁₉	—	4	1	no	—
44	#484	—	19	1	no	maximal, Sylow
45	C₂×C₁₉	#123	1	1	yes	characteristic
46	C₂×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
47	C₂×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
48	D₁₉	—	2	2	no	—
49	C₂²⋊Q₈	—	19	1	no	—
50	C₂×C₄⋊C₄	—	19	1	no	—
51	#107	—	19	1	no	—
52	#107	—	19	1	no	—
53	#103	—	19	1	no	—
54	#103	D₁₉	1	1	yes	characteristic, complemented
55	C₂²⋊C₈	—	19	1	no	—
56	C₁₉	#484	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	C₂×D₁₉	1	1	yes	characteristic
58	C₂²×C₄	—	19	1	no	—
59	C₂²×C₄	—	38	1	no	—
60	C₂×C₈	—	19	1	no	—
61	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
62	C₄⋊C₄	—	19	1	no	—
63	C₄⋊C₄	—	19	1	no	—
64	C₄⋊C₄	—	38	1	no	—
65	C₄⋊C₄	—	38	1	no	—
66	C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
67	C₂²⋊C₄	—	38	1	no	—
68	C₂³	—	19	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	19	1	no	—
74	C₂×C₄	—	38	1	no	—
75	C₂×C₄	—	38	1	no	—
76	C₂×C₄	—	38	1	no	—
77	C₂×C₄	—	38	1	no	—
78	C₂×C₄	—	76	2	no	—
79	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	38	1	no	—
82	C₂²	—	19	2	no	—
83	C₂²	—	38	1	no	—
84	C₂²	—	38	1	no	—
85	C₂²	D₄×D₁₉	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	38	1	no	—
89	C₄	—	76	1	no	—
90	C₄	—	76	1	no	—
91	C₄	#64541	1	1	yes	characteristic
92	C₄	#64543	1	1	yes	characteristic
93	C₂	—	38	2	no	—
94	C₂	#10597329	1	1	yes	characteristic
95	C₂	#10597360	1	1	yes	characteristic
96	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	C₂²×C₁₉	C₂×D₄
prime radical	C₂²×D₁₉	D₄
hypercenter	#103	D₁₉
hypocenter	C₁₉	#484
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
3. C₁₉×#103	C₂	semidirect
4. #10597292	C₂	semidirect
6. #10597275	C₂	semidirect
7. #10597264	C₂	semidirect
54. #103	D₁₉	semidirect
56. C₁₉	#484	semidirect

Maximal subgroups

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

subgroup	index
#10597392	2
C₄⋊C₄×D₁₉	2
C₁₉×#103	2
#10597292	2
(C₂×D₁₉)⋊C₈	2
#10597275	2
#10597264	2
#484	19