Subgroups — #10603783⋊C₃ #14511593

Order 1920.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(#376⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	#10603783	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	A₄×#170	—	4	1	no	maximal
4	C₅×#95⋊C₃	C₄	1	1	yes	characteristic
5	#1840⋊C₃	—	5	1	no	maximal, Hall
6	#64937	C₂×C₃	1	1	yes	characteristic
7	#64918	—	3	1	no	—
8	#64918	—	3	1	no	—
9	A₄×Dic₅	—	4	1	no	—
10	#376⋊C₃	—	5	1	no	—
11	C₂²×#170	—	3	1	no	—
12	C₂²×#170	A₄	1	1	yes	characteristic
13	C₂×C₄×Dic₅	—	3	1	no	—
14	C₅×#95	C₃×C₄	1	1	yes	characteristic
15	#3963	—	3	1	no	—
16	#1840	—	5	1	no	Sylow
17	C₂×C₅×A₄	—	4	1	no	—
18	C₃×#170	—	16	1	no	—
19	C₈×A₄	—	20	1	no	—
20	#95⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic
21	C₂²×C₄×C₅	—	3	1	no	—
22	C₂²×Dic₅	—	3	1	no	—
23	C₂²×Dic₅	C₂×A₄	1	1	yes	characteristic
24	C₂×#170	—	6	1	no	—
25	C₂×#170	—	6	1	no	—
26	C₂×#170	—	6	2	no	—
27	C₄×Dic₅	—	6	1	no	—
28	C₄×Dic₅	—	6	1	no	—
29	#376	—	5	1	no	—
30	#336	—	15	1	no	—
31	#336	—	15	1	no	—
32	C₅×A₄	—	4	1	no	—
33	C₃×Dic₅	—	16	1	no	—
34	C₄×A₄	—	20	1	no	—
35	C₂³×C₅	C₄×A₄	1	1	yes	characteristic
36	C₂×C₄×C₅	—	6	1	no	—
37	C₂×C₄×C₅	—	6	2	no	—
38	C₂×Dic₅	—	3	1	no	—
39	C₂×Dic₅	—	3	1	no	—
40	C₂×Dic₅	—	6	1	no	—
41	C₂×Dic₅	—	6	1	no	—
42	C₂×Dic₅	—	6	1	no	—
43	#170	—	4	1	no	—
44	#170	—	12	1	no	—
45	C₂²×C₈	—	5	1	no	—
46	C₂²×C₈	—	15	1	no	—
47	C₂×C₄²	—	15	1	no	—
48	#95	—	15	1	no	—
49	#95	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
50	C₂×C₃×C₅	—	16	1	no	—
51	C₂×A₄	—	4	1	no	—
52	C₃×C₈	—	80	1	no	—
53	C₂²×C₅	—	3	1	no	—
54	C₂²×C₅	—	3	1	no	—
55	C₂²×C₅	#131⋊C₃	1	1	yes	characteristic
56	C₄×C₅	—	12	1	no	—
57	Dic₅	—	3	1	no	—
58	Dic₅	—	12	1	no	—
59	Dic₅	#126⋊C₃	1	1	yes	characteristic
60	C₂²×C₄	—	3	1	no	—
61	C₂²×C₄	—	5	1	no	—
62	C₂²×C₄	—	15	1	no	—
63	C₂×C₈	—	30	1	no	—
64	C₂×C₈	—	30	1	no	—
65	C₂×C₈	—	30	2	no	—
66	C₄²	—	30	1	no	—
67	C₄²	—	30	1	no	—
68	C₃×C₅	—	16	1	no	Hall
69	A₄	—	4	1	no	—
70	C₃×C₄	—	80	1	no	—
71	C₂×C₅	—	3	1	no	—
72	C₂×C₅	—	3	1	no	—
73	C₂×C₅	#383⋊C₃	1	1	yes	characteristic
74	C₂³	A₄×AGL(1,𝔽₅)	1	1	yes	characteristic
75	C₂×C₄	—	6	1	no	—
76	C₂×C₄	—	6	2	no	—
77	C₂×C₄	—	15	1	no	—
78	C₂×C₄	—	15	1	no	—
79	C₂×C₄	—	30	1	no	—
80	C₂×C₄	—	30	1	no	—
81	C₂×C₄	—	30	1	no	—
82	C₈	—	20	1	no	—
83	C₈	—	60	1	no	—
84	C₂×C₃	—	16	1	no	—
85	C₅	#1840⋊C₃	1	1	yes	characteristic, complemented, Sylow
86	C₂²	—	3	1	no	—
87	C₂²	—	3	1	no	—
88	C₂²	#4133⋊C₃	1	1	yes	characteristic
89	C₄	—	5	1	no	—
90	C₄	—	12	1	no	—
91	C₄	—	15	1	no	—
92	C₄	—	60	1	no	—
93	C₃	—	16	1	no	Sylow
94	C₂	—	3	1	no	—
95	C₂	—	3	1	no	—
96	C₂	#65690⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	#65690⋊C₃
commutator, Fitting, hypocenter	C₅×#95	C₃×C₄
Frattini	C₂³	A₄×AGL(1,𝔽₅)
socle	C₂³×C₅	C₄×A₄
prime radical	C₅×#95⋊C₃	C₄
cosocle	#64937	C₂×C₃
LCS	G ▷ C₅×#95
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. #10603783	C₃	semidirect
85. C₅	#1840⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊(#376⋊C₃)	2
#10603783	3
A₄×#170	4
#1840⋊C₃	5

Subgroups — #10603783⋊C3 #14511593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10603783⋊C₃ #14511593