Subgroups — #11926741

Order 1216.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×#64526	C₂	1	2	yes	maximal, complemented
3	C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597289	C₂	1	2	yes	maximal, complemented
5	C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₁₉	—	2	1	no	—
7	C₂×D₄×C₁₉	—	2	1	no	—
8	C₂×D₄×C₁₉	C₂²	1	2	yes	—
9	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	#64526	—	2	4	no	—
12	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	Dic₁₉⋊C₄	—	2	1	no	—
14	C₄×Dic₁₉	—	2	1	no	—
15	C₂×C₁₉⋊C₈	C₂²	1	2	yes	—
16	C₂³×C₁₉	—	2	2	no	—
17	D₄×C₁₉	—	2	2	no	—
18	D₄×C₁₉	—	2	2	no	—
19	D₄×C₁₉	—	4	2	no	—
20	D₄×C₁₉	—	4	2	no	—
21	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×Dic₁₉	—	2	1	no	—
25	C₂×Dic₁₉	—	2	1	no	—
26	Dic₃₈	—	2	1	no	—
27	Dic₃₈	D₄	1	2	yes	complemented
28	C₁₉⋊C₈	—	2	2	no	—
29	C₂²×C₁₉	—	4	2	no	—
30	C₂²×C₁₉	—	4	2	no	—
31	C₂²×C₁₉	—	4	2	no	—
32	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₉	—	2	1	no	—
34	C₄×C₁₉	SD₁₆	1	2	yes	complemented
35	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₄×C₁₉	#41	1	1	yes	characteristic
37	Dic₁₉	—	2	2	no	—
38	Dic₁₉	—	4	1	no	—
39	#460	—	19	1	no	maximal, Sylow
40	C₂×C₁₉	—	8	2	no	—
41	C₂×C₁₉	#121	1	1	yes	characteristic
42	C₂×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
43	C₂×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
44	C₂×SD₁₆	—	19	2	no	—
45	#127	D₁₉	1	1	yes	characteristic
46	C₄×Q₈	—	19	1	no	—
47	C₄⋊C₈	—	19	1	no	—
48	#102	—	19	2	no	—
49	C₁₉	#460	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	19	1	no	—
51	C₂×D₄	—	2	1	no	—
52	C₂×D₄	—	2	1	no	—
53	C₂×D₄	C₂×D₁₉	1	2	yes	—
54	SD₁₆	—	38	4	no	—
55	C₂×C₈	—	19	2	no	—
56	C₄⋊C₄	—	19	1	no	—
57	C₄⋊C₄	—	38	1	no	—
58	C₄²	—	38	1	no	—
59	C₄²	C₂×D₁₉	1	1	yes	characteristic
60	C₂³	—	2	2	no	—
61	Q₈	—	19	2	no	—
62	Q₈	—	38	1	no	—
63	D₄	—	2	2	no	—
64	D₄	—	2	2	no	—
65	D₄	—	4	2	no	—
66	D₄	—	4	2	no	—
67	C₂×C₄	—	38	1	no	—
68	C₂×C₄	—	38	1	no	—
69	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
70	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
71	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
72	C₈	—	38	2	no	—
73	C₂²	—	4	2	no	—
74	C₂²	—	4	2	no	—
75	C₂²	—	4	2	no	—
76	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	38	2	no	—
79	C₄	—	76	1	no	—
80	C₄	#64526	1	2	yes	complemented
81	C₄	D₄×D₁₉	1	1	yes	characteristic
82	C₄	#64543	1	1	yes	characteristic
83	C₂	—	8	2	no	—
84	C₂	#10597378	1	1	yes	characteristic
85	C₂	C₂×#64526	1	1	yes	characteristic
86	C₂	#10597384	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting, prime radical	C₁₉×#127	C₂
socle	C₂²×C₁₉	C₂×D₄
hypercenter	#127	D₁₉
hypocenter	C₁₉	#460
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
2. C₂×#64526	C₂	semidirect
3. C₄×Dic₃₈	C₂	semidirect
4. #10597289	C₂	semidirect
5. C₄⋊(C₁₉⋊C₈)	C₂	semidirect
27. Dic₃₈	D₄	semidirect
34. C₄×C₁₉	SD₁₆	semidirect
49. C₁₉	#460	semidirect
80. C₄	#64526	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#127	2
C₂×#64526	2
C₄×Dic₃₈	2
#10597289	2
C₄⋊(C₁₉⋊C₈)	2
#460	19