Subgroups — C₅×#5398 #11752069

Order 960.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×A₄⋊Q₈	C₂	1	2	yes	maximal
2	C₅×C₈×A₄	C₂	1	1	yes	maximal, characteristic
3	C₅×#467	—	3	1	no	maximal, Hall
4	C₄×C₅×A₄	C₂²	1	1	yes	characteristic
5	C₅×SL(2,ℤ/4)	—	2	2	no	—
6	C₅×Dic₁₂	—	4	1	no	maximal
7	#5398	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×Q₁₆	—	3	1	no	—
9	C₂²×C₅×C₈	D₃	1	1	yes	characteristic
10	C₅×C₂²⋊Q₈	—	3	2	no	—
11	C₅×#107	—	3	1	no	—
12	C₅×#103	—	3	2	no	—
13	C₂×C₅×A₄	D₄	1	1	yes	characteristic
14	C₅×Dic₆	—	4	2	no	—
15	C₃×C₅×C₈	—	4	1	no	—
16	A₄⋊Q₈	C₂×C₅	1	2	yes	—
17	C₈×A₄	C₂×C₅	1	1	yes	characteristic
18	C₂×C₅×Q₈	—	3	2	no	—
19	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
20	C₅×Q₁₆	—	6	1	no	—
21	C₅×Q₁₆	—	6	1	no	—
22	C₂×C₅×C₈	—	3	1	no	—
23	C₂×C₅×C₈	—	3	1	no	—
24	C₅×C₄⋊C₄	—	3	2	no	—
25	C₅×C₄⋊C₄	—	6	2	no	—
26	C₅×C₂²⋊C₄	—	6	2	no	—
27	#467	—	3	1	no	Sylow
28	C₅×A₄	Q₁₆	1	1	yes	characteristic, complemented
29	C₃×C₄×C₅	—	4	1	no	—
30	C₅×Dic₃	—	8	2	no	—
31	C₄×A₄	C₂²×C₅	1	1	yes	characteristic
32	SL(2,ℤ/4)	—	2	2	no	—
33	Dic₁₂	—	4	1	no	—
34	C₂³×C₅	D₁₂	1	1	yes	characteristic
35	C₅×Q₈	—	6	2	no	—
36	C₅×Q₈	—	6	2	no	—
37	C₂×C₄×C₅	—	3	1	no	—
38	C₂×C₄×C₅	—	3	1	no	—
39	C₂×C₄×C₅	—	6	2	no	—
40	C₂×C₄×C₅	—	6	2	no	—
41	C₅×C₈	—	3	1	no	—
42	C₅×C₈	S₄	1	1	yes	characteristic
43	C₂×Q₁₆	—	3	1	no	—
44	C₂²×C₈	C₅×D₃	1	1	yes	characteristic
45	C₂²⋊Q₈	—	3	2	no	—
46	#107	—	3	1	no	—
47	#103	—	3	2	no	—
48	C₂×C₃×C₅	—	4	1	no	—
49	C₂×A₄	C₅×D₄	1	1	yes	characteristic
50	Dic₆	—	4	2	no	—
51	C₃×C₈	—	4	1	no	—
52	C₂²×C₅	—	3	1	no	—
53	C₂²×C₅	—	3	1	no	—
54	C₂²×C₅	Dic₁₂	1	1	yes	characteristic, complemented
55	C₄×C₅	—	3	1	no	—
56	C₄×C₅	—	12	2	no	—
57	C₄×C₅	—	12	2	no	—
58	C₄×C₅	C₂×S₄	1	1	yes	characteristic
59	C₂×Q₈	—	3	2	no	—
60	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic
61	Q₁₆	—	6	1	no	—
62	Q₁₆	—	6	1	no	—
63	C₂×C₈	—	3	1	no	—
64	C₂×C₈	—	3	1	no	—
65	C₄⋊C₄	—	3	2	no	—
66	C₄⋊C₄	—	6	2	no	—
67	C₂²⋊C₄	—	6	2	no	—
68	C₃×C₅	—	4	1	no	Hall
69	A₄	C₅×Q₁₆	1	1	yes	characteristic, complemented
70	C₃×C₄	—	4	1	no	—
71	Dic₃	—	8	2	no	—
72	C₂×C₅	—	3	1	no	—
73	C₂×C₅	—	3	1	no	—
74	C₂×C₅	C₄⋊S₄	1	1	yes	characteristic
75	C₂³	C₅×D₁₂	1	1	yes	characteristic
76	Q₈	—	6	2	no	—
77	Q₈	—	6	2	no	—
78	C₂×C₄	—	3	1	no	—
79	C₂×C₄	—	3	1	no	—
80	C₂×C₄	—	6	2	no	—
81	C₂×C₄	—	6	2	no	—
82	C₈	—	3	1	no	—
83	C₈	C₅×S₄	1	1	yes	characteristic
84	C₂×C₃	—	4	1	no	—
85	C₅	#5398	1	1	yes	characteristic, direct product factor, Sylow
86	C₂²	—	3	1	no	—
87	C₂²	—	3	1	no	—
88	C₂²	C₅×Dic₁₂	1	1	yes	characteristic, complemented
89	C₄	—	3	1	no	—
90	C₄	—	12	2	no	—
91	C₄	—	12	2	no	—
92	C₄	C₂×C₅×S₄	1	1	yes	characteristic
93	C₃	—	4	1	no	Sylow
94	C₂	—	3	1	no	—
95	C₂	—	3	1	no	—
96	C₂	C₅×C₄⋊S₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₄⋊S₄
commutator, cosocle	C₄×A₄	C₂²×C₅
Frattini	C₄	C₂×C₅×S₄
Fitting	C₂²×C₅×C₈	D₃
socle	C₂³×C₅	D₁₂
prime radical	C₂×C₅×A₄	D₄
hypercenter	C₅×C₈	S₄
hypocenter	A₄	C₅×Q₁₆
LCS	G ▷ C₄×A₄ ▷ C₂×A₄ ▷ A₄
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. #5398	C₅	direct (N × H)
28. C₅×A₄	Q₁₆	semidirect
54. C₂²×C₅	Dic₁₂	semidirect
69. A₄	C₅×Q₁₆	semidirect
85. C₅	#5398	direct (N × H)
88. C₂²	C₅×Dic₁₂	semidirect

Maximal subgroups

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

subgroup	index
C₅×A₄⋊Q₈	2
C₅×C₈×A₄	2
C₅×#467	3
C₅×Dic₁₂	4
#5398	5

Subgroups — C5×#5398 #11752069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5398 #11752069