Subgroups — C₅×#2070⋊C₃ #14510697

Order 1920.

112 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×#2070	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×Q₈×A₄	—	4	1	no	maximal
4	#2070⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×#430	—	3	1	no	—
6	C₂×C₅×#101	—	3	1	no	—
7	C₅×#338	C₂×C₃	1	1	yes	characteristic
8	C₄×C₅×A₄	—	4	2	no	—
9	C₄×C₅×A₄	—	4	1	no	—
10	#338⋊C₃	C₂×C₅	1	1	yes	characteristic
11	C₂²×C₅×Q₈	A₄	1	1	yes	characteristic
12	C₂×C₅×M₁₆	—	3	1	no	—
13	C₂×C₅×M₁₆	—	3	1	no	—
14	C₅×#108	—	6	2	no	—
15	C₅×#101	—	6	2	no	—
16	#2070	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₅×A₄	—	4	1	no	—
18	C₃×C₅×Q₈	—	16	1	no	—
19	Q₈×A₄	—	4	1	no	—
20	C₂×C₅×Q₈	—	6	1	no	—
21	C₂×C₅×Q₈	—	6	1	no	—
22	C₂²×C₄×C₅	SL(2,𝔽₃)	1	2	yes	—
23	C₂²×C₄×C₅	C₂×A₄	1	1	yes	characteristic
24	C₅×M₁₆	—	3	2	no	—
25	C₅×M₁₆	—	6	1	no	—
26	C₅×M₁₆	—	6	1	no	—
27	C₅×M₁₆	—	6	1	no	—
28	C₂×C₅×C₈	—	6	1	no	—
29	C₂×C₅×C₈	—	6	1	no	—
30	#430	—	3	1	no	—
31	C₂×#101	—	3	1	no	—
32	#338	C₂×C₃×C₅	1	1	yes	characteristic
33	C₅×A₄	—	4	1	no	—
34	C₃×C₄×C₅	—	16	2	no	—
35	C₃×C₄×C₅	—	16	1	no	—
36	C₄×A₄	—	4	2	no	—
37	C₄×A₄	—	4	1	no	—
38	C₂³×C₅	C₂×SL(2,𝔽₃)	1	1	yes	characteristic
39	C₅×Q₈	—	4	1	no	—
40	C₅×Q₈	—	12	1	no	—
41	C₂×C₄×C₅	—	3	1	no	—
42	C₂×C₄×C₅	—	3	1	no	—
43	C₂×C₄×C₅	—	6	2	no	—
44	C₅×C₈	—	6	2	no	—
45	C₅×C₈	—	12	1	no	—
46	C₂²×Q₈	C₅×A₄	1	1	yes	characteristic
47	C₂×M₁₆	—	3	1	no	—
48	C₂×M₁₆	—	3	1	no	—
49	#108	—	6	2	no	—
50	#101	—	6	2	no	—
51	C₂×C₃×C₅	—	16	1	no	—
52	C₂×A₄	—	4	1	no	—
53	C₃×Q₈	—	16	1	no	—
54	C₂²×C₅	—	3	1	no	—
55	C₂²×C₅	—	4	1	no	—
56	C₄×C₅	—	3	1	no	—
57	C₄×C₅	—	4	2	no	—
58	C₄×C₅	#126⋊C₃	1	1	yes	characteristic
59	C₂×Q₈	—	6	1	no	—
60	C₂×Q₈	—	6	1	no	—
61	C₂²×C₄	C₅×SL(2,𝔽₃)	1	2	yes	—
62	C₂²×C₄	C₂×C₅×A₄	1	1	yes	characteristic
63	M₁₆	—	3	2	no	—
64	M₁₆	—	6	1	no	—
65	M₁₆	—	6	1	no	—
66	M₁₆	—	6	1	no	—
67	C₂×C₈	—	6	1	no	—
68	C₂×C₈	—	6	1	no	—
69	C₃×C₅	—	16	1	no	Hall
70	A₄	—	4	1	no	—
71	C₃×C₄	—	16	2	no	—
72	C₃×C₄	—	16	1	no	—
73	C₂×C₅	—	6	1	no	—
74	C₂×C₅	#396⋊C₃	1	1	yes	characteristic
75	C₂³	C₂×C₅×SL(2,𝔽₃)	1	1	yes	characteristic
76	Q₈	—	4	1	no	—
77	Q₈	—	12	1	no	—
78	C₂×C₄	—	3	1	no	—
79	C₂×C₄	—	3	1	no	—
80	C₂×C₄	—	6	2	no	—
81	C₈	—	6	2	no	—
82	C₈	—	12	1	no	—
83	C₂×C₃	—	16	1	no	—
84	C₅	#2070⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
85	C₂²	—	3	1	no	—
86	C₂²	—	4	1	no	—
87	C₄	—	3	1	no	—
88	C₄	—	4	2	no	—
89	C₄	C₅×#126⋊C₃	1	1	yes	characteristic
90	C₃	—	16	1	no	Sylow
91	C₂	—	6	1	no	—
92	C₂	C₅×#396⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	#396⋊C₃
commutator, cosocle, hypocenter	#338	C₂×C₃×C₅
Frattini	C₂²×C₄	C₂×C₅×A₄
Fitting	C₅×#2070	C₃
prime radical	C₅×#338⋊C₃	C₂
hypercenter	C₄×C₅	#126⋊C₃
LCS	G ▷ #338
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#2070	C₃	semidirect
4. #2070⋊C₃	C₅	direct (N × H)
16. #2070	C₃×C₅	semidirect
84. C₅	#2070⋊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×#2070	3
C₅×Q₈×A₄	4
#2070⋊C₃	5

Subgroups — C5×#2070⋊C3 #14510697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#2070⋊C₃ #14510697