Subgroups — #14269710

Order 1824.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11744889	C₂	1	2	yes	maximal
4	#11744887	C₂	1	2	yes	maximal, complemented
5	C₄×Dic₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#10597318	—	3	1	no	maximal, Hall
7	C₂²×D₅₇	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₅₇	C₂²	1	2	yes	—
11	C₂×Dic₅₇	C₂²	1	1	yes	characteristic
12	C₄×D₅₇	C₄	1	4	yes	complemented
13	C₂×C₄×D₁₉	—	3	1	no	—
14	C₄²×C₁₉	D₃	1	1	yes	characteristic, complemented
15	(C₂×D₁₉)⋊C₄	—	3	2	no	—
16	Dic₁₉⋊C₄	—	3	2	no	—
17	C₄×Dic₁₉	—	3	1	no	—
18	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×D₅₇	—	2	2	no	—
20	C₂×D₅₇	C₂×C₄	1	2	yes	—
21	C₃×C₄×C₁₉	—	2	2	no	—
22	C₃×C₄×C₁₉	C₂×C₄	1	2	yes	—
23	Dic₅₇	—	2	2	no	—
24	Dic₅₇	C₂×C₄	1	2	yes	—
25	C₂²×D₁₉	—	3	1	no	—
26	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	—
27	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
28	C₂×Dic₁₉	—	3	1	no	—
29	C₂×Dic₁₉	—	3	2	no	—
30	C₄×D₁₉	—	3	4	no	—
31	C₂×C₃×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₃×C₁₉	#41	1	2	yes	—
33	D₅₇	—	2	2	no	—
34	#872	—	19	1	no	maximal, Hall
35	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
36	C₂×D₁₉	—	3	2	no	—
37	C₂×D₁₉	—	6	2	no	—
38	C₄×C₁₉	—	2	2	no	—
39	C₄×C₁₉	C₄×D₃	1	2	yes	—
40	Dic₁₉	—	3	2	no	—
41	Dic₁₉	—	6	2	no	—
42	C₃×C₁₉	#117	1	1	yes	characteristic, complemented, Hall
43	C₂×C₄×D₃	—	19	1	no	—
44	C₃×C₄²	D₁₉	1	1	yes	characteristic, complemented
45	(C₂×D₃)⋊C₄	—	19	2	no	—
46	Dic₃⋊C₄	—	19	2	no	—
47	C₄×Dic₃	—	19	1	no	—
48	C₂×C₁₉	C₂×C₄×D₃	1	1	yes	characteristic
49	C₂×C₁₉	#235	1	2	yes	—
50	D₁₉	—	6	2	no	—
51	#117	—	57	1	no	Sylow
52	C₂²×D₃	—	19	1	no	—
53	C₂×C₃×C₄	C₂×D₁₉	1	2	yes	—
54	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
55	C₂×Dic₃	—	19	1	no	—
56	C₂×Dic₃	—	19	2	no	—
57	C₄×D₃	—	19	4	no	—
58	C₁₉	#872	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₄	—	57	1	no	—
60	C₄⋊C₄	—	57	2	no	—
61	C₂²⋊C₄	—	57	2	no	—
62	C₄²	—	57	1	no	—
63	C₄²	D₅₇	1	1	yes	characteristic, complemented
64	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
65	C₂×D₃	—	19	2	no	—
66	C₂×D₃	—	38	2	no	—
67	C₃×C₄	—	2	2	no	—
68	C₃×C₄	C₄×D₁₉	1	2	yes	—
69	Dic₃	—	19	2	no	—
70	Dic₃	—	38	2	no	—
71	C₂³	—	57	1	no	—
72	C₂×C₄	—	57	1	no	—
73	C₂×C₄	—	57	4	no	—
74	C₂×C₄	—	57	2	no	—
75	C₂×C₄	C₂×D₅₇	1	2	yes	—
76	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
77	C₂×C₃	C₂×C₄×D₁₉	1	1	yes	characteristic
78	C₂×C₃	#64541	1	2	yes	—
79	D₃	—	38	2	no	—
80	C₂²	—	57	2	no	—
81	C₂²	—	114	2	no	—
82	C₂²	C₂²×D₅₇	1	1	yes	characteristic
83	C₄	—	2	2	no	—
84	C₄	—	57	2	no	—
85	C₄	—	114	2	no	—
86	C₄	C₄×D₅₇	1	2	yes	—
87	C₃	#10597318	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	114	2	no	—
89	C₂	C₂×C₄×D₅₇	1	1	yes	characteristic
90	C₂	#11744985	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₅₇
commutator	C₂×C₃×C₁₉	C₂²×C₄
Frattini	C₂²	C₂²×D₅₇
Fitting	C₃×C₄²×C₁₉	C₂
socle, cosocle	C₂²×C₃×C₁₉	C₂³
prime radical	C₂²×D₅₇	C₂²
hypercenter	C₄²	D₅₇
hypocenter	C₃×C₁₉	#117
LCS	G ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₃×C₄²×C₁₉	C₂	semidirect
4. #11744887	C₂	semidirect
5. C₄×Dic₅₇	C₂	semidirect
12. C₄×D₅₇	C₄	semidirect
14. C₄²×C₁₉	D₃	semidirect
42. C₃×C₁₉	#117	semidirect
44. C₃×C₄²	D₁₉	semidirect
58. C₁₉	#872	semidirect
63. C₄²	D₅₇	semidirect
87. C₃	#10597318	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₅₇	2
C₃×C₄²×C₁₉	2
#11744889	2
#11744887	2
C₄×Dic₅₇	2
#10597318	3
#872	19