Subgroups — C₅×#5403 #11752074

Order 960.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#984	C₂	1	2	yes	maximal
2	C₅×#131⋊C₃	C₂	1	1	yes	maximal, characteristic
3	C₅×#473	—	3	1	no	maximal, Hall
4	C₅×#41⋊C₃	C₂²	1	1	yes	characteristic
5	C₅×#226	—	2	2	no	—
6	C₅×Dic₁₂	—	4	1	no	maximal
7	#5403	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×#137	—	3	2	no	—
9	C₂×C₅×Q₁₆	—	3	1	no	—
10	C₅×#131	D₃	1	1	yes	characteristic
11	C₅×#108	—	3	1	no	—
12	C₅×#101	—	3	2	no	—
13	C₅×Dic₆	—	4	2	no	—
14	C₅×SL(2,𝔽₃)	D₄	1	1	yes	characteristic
15	C₃×C₅×C₈	—	4	1	no	—
16	#984	C₂×C₅	1	2	yes	—
17	#131⋊C₃	C₂×C₅	1	1	yes	characteristic
18	C₅×#41	C₂×D₃	1	1	yes	characteristic
19	C₂×C₅×Q₈	—	3	2	no	—
20	C₅×Q₁₆	—	6	1	no	—
21	C₅×Q₁₆	—	6	2	no	—
22	C₅×Q₁₆	—	6	1	no	—
23	C₅×SD₁₆	—	6	2	no	—
24	C₅×M₁₆	—	3	1	no	—
25	C₅×M₁₆	—	3	2	no	—
26	C₂×C₅×C₈	—	3	1	no	—
27	#473	—	3	1	no	Sylow
28	C₃×C₄×C₅	—	4	1	no	—
29	C₅×Dic₃	—	8	2	no	—
30	#41⋊C₃	C₂²×C₅	1	1	yes	characteristic
31	#226	—	2	2	no	—
32	Dic₁₂	—	4	1	no	—
33	C₅×Q₈	—	6	2	no	—
34	C₅×Q₈	—	6	2	no	—
35	C₅×Q₈	D₁₂	1	1	yes	characteristic
36	C₅×D₄	—	3	1	no	—
37	C₂×C₄×C₅	—	3	1	no	—
38	C₂×C₄×C₅	—	6	2	no	—
39	C₅×C₈	—	3	1	no	—
40	C₅×C₈	—	6	2	no	—
41	C₅×C₈	S₄	1	1	yes	characteristic
42	#137	—	3	2	no	—
43	C₂×Q₁₆	—	3	1	no	—
44	#131	C₅×D₃	1	1	yes	characteristic
45	#108	—	3	1	no	—
46	#101	—	3	2	no	—
47	C₂×C₃×C₅	—	4	1	no	—
48	Dic₆	—	4	2	no	—
49	SL(2,𝔽₃)	C₅×D₄	1	1	yes	characteristic
50	C₃×C₈	—	4	1	no	—
51	C₂²×C₅	—	3	1	no	—
52	C₄×C₅	—	3	1	no	—
53	C₄×C₅	—	12	2	no	—
54	C₄×C₅	C₂×S₄	1	1	yes	characteristic
55	#41	C₂×C₅×D₃	1	1	yes	characteristic
56	C₂×Q₈	—	3	2	no	—
57	Q₁₆	—	6	1	no	—
58	Q₁₆	—	6	2	no	—
59	Q₁₆	—	6	1	no	—
60	SD₁₆	—	6	2	no	—
61	M₁₆	—	3	1	no	—
62	M₁₆	—	3	2	no	—
63	C₂×C₈	—	3	1	no	—
64	C₃×C₅	—	4	1	no	Hall
65	C₃×C₄	—	4	1	no	—
66	Dic₃	—	8	2	no	—
67	C₂×C₅	—	6	1	no	—
68	C₂×C₅	C₄⋊S₄	1	1	yes	characteristic
69	Q₈	—	6	2	no	—
70	Q₈	—	6	2	no	—
71	Q₈	C₅×D₁₂	1	1	yes	characteristic
72	D₄	—	3	1	no	—
73	C₂×C₄	—	3	1	no	—
74	C₂×C₄	—	6	2	no	—
75	C₈	—	3	1	no	—
76	C₈	—	6	2	no	—
77	C₈	C₅×S₄	1	1	yes	characteristic
78	C₂×C₃	—	4	1	no	—
79	C₅	#5403	1	1	yes	characteristic, direct product factor, Sylow
80	C₂²	—	3	1	no	—
81	C₄	—	3	1	no	—
82	C₄	—	12	2	no	—
83	C₄	C₂×C₅×S₄	1	1	yes	characteristic
84	C₃	—	4	1	no	Sylow
85	C₂	—	6	1	no	—
86	C₂	C₅×C₄⋊S₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	C₄⋊S₄
commutator, cosocle	#41⋊C₃	C₂²×C₅
Frattini	C₄	C₂×C₅×S₄
Fitting	C₅×#131	D₃
prime radical	C₅×#41⋊C₃	C₂²
hypercenter	C₅×C₈	S₄
hypocenter	SL(2,𝔽₃)	C₅×D₄
LCS	G ▷ #41⋊C₃ ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈

Complements

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

N	H ≅ G/N	type
7. #5403	C₅	direct (N × H)
79. C₅	#5403	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×#984	2
C₅×#131⋊C₃	2
C₅×#473	3
C₅×Dic₁₂	4
#5403	5

Subgroups — C5×#5403 #11752074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5403 #11752074