Subgroups — #18070416

Order 4864.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₀₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₀₄	—	2	1	no	—
5	D₆₀₈	—	2	1	no	—
6	D₆₀₈	C₄	1	2	yes	complemented
7	C₁₉⋊C₆₄	—	2	1	no	—
8	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
9	C₁₉×#366	—	2	1	no	—
10	C₂×D₁₅₂	—	4	1	no	—
11	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
12	C₁₉×#107	—	4	1	no	—
13	D₃₀₄	—	2	2	no	—
14	D₃₀₄	—	4	1	no	—
15	C₁₉×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₉×C₃₂	D₄	1	1	yes	characteristic
17	C₂×D₇₆	—	8	1	no	—
18	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
19	C₄⋊C₄×C₁₉	—	8	1	no	—
20	D₁₅₂	—	4	2	no	—
21	D₁₅₂	—	8	1	no	—
22	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
24	#7537	—	19	1	no	maximal, Sylow
25	C₂²×D₁₉	—	16	1	no	—
26	C₂×C₄×C₁₉	—	16	1	no	—
27	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
28	D₇₆	—	8	2	no	—
29	D₇₆	—	16	1	no	—
30	C₈×C₁₉	#102	1	1	yes	characteristic
31	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
32	C₂×D₃₂	—	19	1	no	—
33	C₂×C₆₄	—	19	1	no	—
34	#1423	D₁₉	1	1	yes	characteristic, complemented
35	C₂²×C₁₉	D₃₂	1	1	yes	characteristic
36	C₂×D₁₉	—	16	2	no	—
37	C₂×D₁₉	—	32	1	no	—
38	C₂×D₁₉	—	32	1	no	—
39	C₄×C₁₉	—	32	1	no	—
40	C₄×C₁₉	#357	1	1	yes	characteristic
41	C₄×C₁₉	SD₆₄	1	1	yes	characteristic
42	C₂×D₁₆	—	38	1	no	—
43	D₃₂	—	19	2	no	—
44	D₃₂	—	38	1	no	—
45	C₂×C₃₂	C₂×D₁₉	1	1	yes	characteristic
46	#366	—	2	1	no	—
47	C₆₄	—	38	1	no	—
48	C₂×C₁₉	#1415	1	1	yes	characteristic
49	C₂×C₁₉	D₆₄	1	1	yes	characteristic
50	C₂×C₁₉	SD₁₂₈	1	1	yes	characteristic
51	D₁₉	—	32	2	no	—
52	C₂×D₈	—	76	1	no	—
53	D₁₆	—	38	2	no	—
54	D₁₆	—	76	1	no	—
55	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
56	#107	—	4	1	no	—
57	C₃₂	C₄×D₁₉	1	1	yes	characteristic
58	C₃₂	D₇₆	1	1	yes	characteristic
59	C₁₉	#7537	1	1	yes	characteristic, complemented, Sylow
60	C₂×D₄	—	152	1	no	—
61	D₈	—	76	2	no	—
62	D₈	—	152	1	no	—
63	C₂×C₈	#64525	1	1	yes	characteristic
64	C₄⋊C₄	—	8	1	no	—
65	C₁₆	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
66	C₁₆	#64527	1	1	yes	characteristic
67	C₂³	—	304	1	no	—
68	D₄	—	304	1	no	—
69	D₄	—	152	2	no	—
70	C₂×C₄	—	16	1	no	—
71	C₂×C₄	#10597283	1	1	yes	characteristic
72	C₈	#10597266	1	1	yes	characteristic
73	C₈	#10597285	1	1	yes	characteristic
74	C₂²	—	304	2	no	—
75	C₂²	—	608	1	no	—
76	C₂²	—	608	1	no	—
77	C₂²	#11926379	1	1	yes	characteristic
78	C₄	—	32	1	no	—
79	C₄	#11926344	1	1	yes	characteristic
80	C₄	#11926381	1	1	yes	characteristic
81	C₂	—	608	2	no	—
82	C₂	#14561812	1	1	yes	characteristic
83	C₂	#14561847	1	1	yes	characteristic
84	C₂	#14561849	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926379
commutator	C₁₉×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₉
Fitting	C₁₉×#1423	C₂
socle	C₂²×C₁₉	D₃₂
prime radical	C₂×D₆₀₈	C₂
cosocle	C₂×C₁₉×C₃₂	C₂²
hypercenter	#1423	D₁₉
hypocenter	C₁₉	#7537
LCS	G ▷ C₁₉×C₃₂ ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1423

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉⋊C₆₄	C₂	semidirect
3. C₁₉×#1423	C₂	semidirect
6. D₆₀₈	C₄	semidirect
34. #1423	D₁₉	semidirect
59. C₁₉	#7537	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₆₀₈	2
C₂×C₁₉⋊C₆₄	2
C₁₉×#1423	2
#7537	19