Subgroups — C₅×#1747⋊C₃ #14510682

Order 1920.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#338⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×#1747	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₈×A₄	—	4	1	no	maximal
4	#1747⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×#405	—	3	1	no	—
6	C₅×#338	C₂×C₃	1	1	yes	characteristic
7	C₅×H(3,ℤ/4)	—	3	1	no	—
8	C₄×C₅×A₄	—	4	1	no	—
9	#338⋊C₃	C₂×C₅	1	1	yes	characteristic
10	C₂×C₅×M₁₆	—	3	1	no	—
11	C₂²×C₅×C₈	A₄	1	1	yes	characteristic
12	C₅×#117	—	3	1	no	—
13	C₅×#97	—	3	2	no	—
14	C₄×C₅×C₈	—	3	2	no	—
15	#1747	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅×A₄	—	4	1	no	—
17	C₃×C₅×C₈	—	16	1	no	—
18	C₈×A₄	—	4	1	no	—
19	C₂²×C₄×C₅	C₂×A₄	1	1	yes	characteristic
20	C₅×M₁₆	—	6	2	no	—
21	C₂×C₅×C₈	—	3	1	no	—
22	C₂×C₅×C₈	—	3	1	no	—
23	C₂×C₅×C₈	—	3	2	no	—
24	C₅×C₄⋊C₄	—	6	1	no	—
25	C₅×C₂²⋊C₄	—	6	1	no	—
26	C₄²×C₅	—	3	2	no	—
27	#405	—	3	1	no	—
28	#338	C₂×C₃×C₅	1	1	yes	characteristic
29	H(3,ℤ/4)	—	3	1	no	—
30	C₅×A₄	—	4	1	no	—
31	C₃×C₄×C₅	—	16	1	no	—
32	C₄×A₄	—	4	1	no	—
33	C₂³×C₅	#41⋊C₃	1	1	yes	characteristic
34	C₂×C₄×C₅	—	3	1	no	—
35	C₂×C₄×C₅	—	3	1	no	—
36	C₂×C₄×C₅	—	6	2	no	—
37	C₅×C₈	—	3	1	no	—
38	C₅×C₈	—	6	2	no	—
39	C₅×C₈	C₄²⋊C₃	1	1	yes	characteristic
40	C₂×M₁₆	—	3	1	no	—
41	C₂²×C₈	C₅×A₄	1	1	yes	characteristic
42	#117	—	3	1	no	—
43	#97	—	3	2	no	—
44	C₄×C₈	—	3	2	no	—
45	C₂×C₃×C₅	—	16	1	no	—
46	C₂×A₄	—	4	1	no	—
47	C₃×C₈	—	16	1	no	—
48	C₂²×C₅	—	3	1	no	—
49	C₂²×C₅	—	4	1	no	—
50	C₄×C₅	—	3	1	no	—
51	C₄×C₅	—	12	2	no	—
52	C₄×C₅	C₂×C₄²⋊C₃	1	1	yes	characteristic
53	C₂²×C₄	C₂×C₅×A₄	1	1	yes	characteristic
54	M₁₆	—	6	2	no	—
55	C₂×C₈	—	3	1	no	—
56	C₂×C₈	—	3	1	no	—
57	C₂×C₈	—	3	2	no	—
58	C₄⋊C₄	—	6	1	no	—
59	C₂²⋊C₄	—	6	1	no	—
60	C₄²	—	3	2	no	—
61	C₃×C₅	—	16	1	no	Hall
62	A₄	—	4	1	no	—
63	C₃×C₄	—	16	1	no	—
64	C₂×C₅	—	6	1	no	—
65	C₂×C₅	#376⋊C₃	1	1	yes	characteristic
66	C₂³	C₅×#41⋊C₃	1	1	yes	characteristic
67	C₂×C₄	—	3	1	no	—
68	C₂×C₄	—	3	1	no	—
69	C₂×C₄	—	6	2	no	—
70	C₈	—	3	1	no	—
71	C₈	—	6	2	no	—
72	C₈	C₅×C₄²⋊C₃	1	1	yes	characteristic
73	C₂×C₃	—	16	1	no	—
74	C₅	#1747⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²	—	3	1	no	—
76	C₂²	—	4	1	no	—
77	C₄	—	3	1	no	—
78	C₄	—	12	2	no	—
79	C₄	C₂×C₅×C₄²⋊C₃	1	1	yes	characteristic
80	C₃	—	16	1	no	Sylow
81	C₂	—	6	1	no	—
82	C₂	C₅×#376⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₅×C₈	C₄²⋊C₃
commutator, cosocle, hypocenter	#338	C₂×C₃×C₅
Frattini	C₂²×C₄	C₂×C₅×A₄
Fitting	C₅×#1747	C₃
socle	C₂×C₅	#376⋊C₃
prime radical	C₅×#338⋊C₃	C₂
LCS	G ▷ #338
UCS	C₁ ◁ C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₅×#1747	C₃	semidirect
4. #1747⋊C₃	C₅	direct (N × H)
15. #1747	C₃×C₅	semidirect
74. C₅	#1747⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#338⋊C₃	2
C₅×#1747	3
C₅×C₈×A₄	4
#1747⋊C₃	5

Subgroups — C5×#1747⋊C3 #14510682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#1747⋊C₃ #14510682