Subgroups — C₃×#4036 #91607

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	C₃×C₄⋊Dic₅	C₂	1	2	yes	maximal
3	C₃×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₃×#683	C₂	1	2	yes	maximal
5	C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
6	#4036	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄×C₅	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×Dic₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×Dic₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×Dic₅	C₂²	1	2	yes	—
12	C₃×#125	—	5	1	no	maximal, Hall
13	C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
14	C₄⋊Dic₅	C₂×C₃	1	2	yes	—
15	C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic
16	#683	C₂×C₃	1	2	yes	—
17	C₄×Dic₅	C₂×C₃	1	1	yes	characteristic
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	C₃×Dic₅	—	2	1	no	—
22	C₃×Dic₅	—	2	1	no	—
23	C₃×Dic₅	—	2	2	no	—
24	C₃×C₄⋊C₄	—	5	2	no	—
25	C₃×C₄⋊C₄	—	5	2	no	—
26	C₃×C₄⋊C₄	—	5	1	no	—
27	C₃×C₄⋊C₄	D₅	1	1	yes	characteristic
28	C₃×C₄²	—	5	1	no	—
29	C₂×C₄×C₅	C₂²×C₃	1	2	yes	—
30	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
31	C₂×Dic₅	C₂²×C₃	1	1	yes	characteristic
32	C₂×Dic₅	C₂²×C₃	1	1	yes	characteristic
33	C₂×Dic₅	C₂²×C₃	1	2	yes	—
34	#125	—	5	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	—	5	1	no	—
39	C₂×C₃×C₄	—	5	1	no	—
40	C₂×C₃×C₄	—	5	2	no	—
41	C₂×C₃×C₄	C₂×D₅	1	2	yes	—
42	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
43	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
44	C₄×C₅	—	2	2	no	—
45	C₄×C₅	C₃×Q₈	1	2	yes	—
46	Dic₅	—	2	1	no	—
47	Dic₅	—	2	1	no	—
48	Dic₅	—	2	2	no	—
49	C₄⋊C₄	—	5	2	no	—
50	C₄⋊C₄	—	5	2	no	—
51	C₄⋊C₄	—	5	1	no	—
52	C₄⋊C₄	C₃×D₅	1	1	yes	characteristic
53	C₄²	—	5	1	no	—
54	C₃×C₅	#125	1	1	yes	characteristic, complemented, Hall
55	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
56	C₃×C₄	—	2	2	no	—
57	C₃×C₄	—	10	1	no	—
58	C₃×C₄	—	10	1	no	—
59	C₃×C₄	—	10	2	no	—
60	C₃×C₄	Dic₁₀	1	2	yes	—
61	C₂×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
62	C₂×C₅	C₃×#41	1	1	yes	characteristic
63	C₂×C₅	C₃×#41	1	1	yes	characteristic
64	C₂×C₄	—	5	1	no	—
65	C₂×C₄	—	5	1	no	—
66	C₂×C₄	—	5	2	no	—
67	C₂×C₄	C₂×C₃×D₅	1	2	yes	—
68	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
69	C₂×C₃	C₂×Dic₁₀	1	1	yes	characteristic
70	C₂×C₃	#711	1	1	yes	characteristic
71	C₂×C₃	#713	1	1	yes	characteristic
72	C₅	C₃×#125	1	1	yes	characteristic, complemented, Sylow
73	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	10	1	no	—
76	C₄	—	10	1	no	—
77	C₄	—	10	2	no	—
78	C₄	C₃×Dic₁₀	1	2	yes	—
79	C₃	#4036	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	C₂×C₃×Dic₁₀	1	1	yes	characteristic
81	C₂	C₃×#711	1	1	yes	characteristic
82	C₂	C₃×#713	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₅
Fitting	C₃×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₃×C₅	C₂³
hypercenter	C₃×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#125
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #4036	C₃	direct (N × H)
54. C₃×C₅	#125	semidirect
72. C₅	C₃×#125	semidirect
79. C₃	#4036	direct (N × H)

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
C₃×C₄⋊Dic₅	2
C₃×#683	2
C₃×C₄×Dic₅	2
#4036	3
C₃×#125	5

Subgroups — C3×#4036 #91607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4036 #91607