Subgroups — C₅×#890 #91693

Order 480.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₅×C₄⋊Dic₃	C₂	1	2	yes	maximal
3	C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₅×Dic₃⋊C₄	C₂	1	2	yes	maximal
5	C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
6	C₅×#125	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄×C₅	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₅×Dic₃	C₂²	1	1	yes	characteristic
10	C₂×C₅×Dic₃	C₂²	1	1	yes	characteristic
11	C₂×C₅×Dic₃	C₂²	1	2	yes	—
12	#890	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₄⋊C₄	—	3	2	no	—
14	C₅×C₄⋊C₄	—	3	2	no	—
15	C₅×C₄⋊C₄	—	3	1	no	—
16	C₅×C₄⋊C₄	D₃	1	1	yes	characteristic
17	C₄²×C₅	—	3	1	no	—
18	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
19	C₃×C₄×C₅	—	2	2	no	—
20	C₃×C₄×C₅	Q₈	1	2	yes	—
21	C₅×Dic₃	—	2	1	no	—
22	C₅×Dic₃	—	2	1	no	—
23	C₅×Dic₃	—	2	2	no	—
24	C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
25	C₄⋊Dic₃	C₂×C₅	1	2	yes	—
26	C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic
27	Dic₃⋊C₄	C₂×C₅	1	2	yes	—
28	C₄×Dic₃	C₂×C₅	1	1	yes	characteristic
29	C₂×C₄×C₅	—	3	1	no	—
30	C₂×C₄×C₅	—	3	1	no	—
31	C₂×C₄×C₅	—	3	2	no	—
32	C₂×C₄×C₅	C₂×D₃	1	2	yes	—
33	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
34	#125	—	3	1	no	Sylow
35	C₂×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₃×C₅	#41	1	1	yes	characteristic
37	C₂×C₃×C₅	#41	1	1	yes	characteristic
38	C₂×C₃×C₄	C₂²×C₅	1	2	yes	—
39	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
40	C₂×Dic₃	C₂²×C₅	1	1	yes	characteristic
41	C₂×Dic₃	C₂²×C₅	1	1	yes	characteristic
42	C₂×Dic₃	C₂²×C₅	1	2	yes	—
43	C₂²×C₅	C₂²×D₃	1	1	yes	characteristic
44	C₄×C₅	—	2	2	no	—
45	C₄×C₅	—	6	1	no	—
46	C₄×C₅	—	6	1	no	—
47	C₄×C₅	—	6	2	no	—
48	C₄×C₅	Dic₆	1	2	yes	—
49	C₄⋊C₄	—	3	2	no	—
50	C₄⋊C₄	—	3	2	no	—
51	C₄⋊C₄	—	3	1	no	—
52	C₄⋊C₄	C₅×D₃	1	1	yes	characteristic
53	C₄²	—	3	1	no	—
54	C₃×C₅	#125	1	1	yes	characteristic, complemented, Hall
55	C₂²×C₃	C₂³×C₅	1	1	yes	characteristic
56	C₃×C₄	—	2	2	no	—
57	C₃×C₄	C₅×Q₈	1	2	yes	—
58	Dic₃	—	2	1	no	—
59	Dic₃	—	2	1	no	—
60	Dic₃	—	2	2	no	—
61	C₂×C₅	C₂×Dic₆	1	1	yes	characteristic
62	C₂×C₅	#237	1	1	yes	characteristic
63	C₂×C₅	#239	1	1	yes	characteristic
64	C₂×C₄	—	3	1	no	—
65	C₂×C₄	—	3	1	no	—
66	C₂×C₄	—	3	2	no	—
67	C₂×C₄	C₂×C₅×D₃	1	2	yes	—
68	C₂×C₄	C₂×C₅×D₃	1	1	yes	characteristic
69	C₂×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
70	C₂×C₃	C₅×#41	1	1	yes	characteristic
71	C₂×C₃	C₅×#41	1	1	yes	characteristic
72	C₅	#890	1	1	yes	characteristic, direct product factor, Sylow
73	C₂²	C₂²×C₅×D₃	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	6	1	no	—
76	C₄	—	6	1	no	—
77	C₄	—	6	2	no	—
78	C₄	C₅×Dic₆	1	2	yes	—
79	C₃	C₅×#125	1	1	yes	characteristic, complemented, Sylow
80	C₂	C₂×C₅×Dic₆	1	1	yes	characteristic
81	C₂	C₅×#237	1	1	yes	characteristic
82	C₂	C₅×#239	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₅
Frattini	C₂²	C₂²×C₅×D₃
Fitting	C₃×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₃×C₅	C₂³
hypercenter	C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#125
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
12. #890	C₅	direct (N × H)
54. C₃×C₅	#125	semidirect
72. C₅	#890	direct (N × H)
79. C₃	C₅×#125	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₄⋊C₄	2
C₅×C₄⋊Dic₃	2
C₅×Dic₃⋊C₄	2
C₄×C₅×Dic₃	2
C₅×#125	3
#890	5

Subgroups — C5×#890 #91693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#890 #91693