Subgroups — C₃×#4023 #91594

Order 480.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₂²⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₃×#683	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×Dic₅	C₂	1	2	yes	maximal, complemented
6	#4023	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂×C₃×Dic₅	C₄	1	4	yes	complemented
10	C₂×C₃×Dic₅	C₂²	1	2	yes	—
11	C₂×C₃×Dic₅	C₂²	1	1	yes	characteristic
12	C₂×C₃×Dic₅	C₂²	1	1	yes	characteristic
13	C₃×#117	—	5	1	no	maximal, Hall
14	C₂²×Dic₅	C₂×C₃	1	1	yes	characteristic
15	C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
16	C₂²⋊Dic₅	C₂×C₃	1	1	yes	characteristic
17	#683	C₂×C₃	1	2	yes	complemented
18	C₄×Dic₅	C₂×C₃	1	2	yes	complemented
19	C₂²×C₃×C₅	—	2	2	no	—
20	C₂²×C₃×C₅	C₂×C₄	1	2	yes	—
21	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
22	C₃×C₄×C₅	—	2	2	no	—
23	C₃×Dic₅	—	2	2	no	—
24	C₃×Dic₅	C₂×C₄	1	2	yes	—
25	C₃×Dic₅	C₂×C₄	1	2	yes	—
26	C₂²×C₃×C₄	—	5	1	no	—
27	C₃×C₄⋊C₄	—	5	2	no	—
28	C₃×C₂²⋊C₄	—	5	1	no	—
29	C₃×C₂²⋊C₄	D₅	1	1	yes	characteristic
30	C₃×C₄²	—	5	2	no	—
31	C₂³×C₅	C₂²×C₃	1	1	yes	characteristic
32	C₂×C₄×C₅	C₂²×C₃	1	2	yes	—
33	C₂×Dic₅	C₃×C₄	1	4	yes	complemented
34	C₂×Dic₅	C₂²×C₃	1	2	yes	—
35	C₂×Dic₅	C₂²×C₃	1	1	yes	characteristic
36	C₂×Dic₅	C₂²×C₃	1	1	yes	characteristic
37	#117	—	5	1	no	Sylow
38	C₂×C₃×C₅	—	2	2	no	—
39	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₃×C₅	#41	1	2	yes	—
41	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
42	C₂×C₃×C₄	—	5	4	no	—
43	C₂×C₃×C₄	—	5	1	no	—
44	C₂×C₃×C₄	—	5	1	no	—
45	C₂×C₃×C₄	—	5	2	no	—
46	C₂×C₃×C₄	C₂×D₅	1	2	yes	—
47	C₂²×C₅	—	2	2	no	—
48	C₂²×C₅	C₂×C₃×C₄	1	2	yes	—
49	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
50	C₄×C₅	—	2	2	no	—
51	Dic₅	—	2	2	no	—
52	Dic₅	C₂×C₃×C₄	1	2	yes	—
53	Dic₅	C₂×C₃×C₄	1	2	yes	—
54	C₂²×C₄	—	5	1	no	—
55	C₄⋊C₄	—	5	2	no	—
56	C₂²⋊C₄	—	5	1	no	—
57	C₂²⋊C₄	C₃×D₅	1	1	yes	characteristic
58	C₄²	—	5	2	no	—
59	C₃×C₅	#117	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃	—	2	2	no	—
61	C₂²×C₃	C₄×D₅	1	2	yes	—
62	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
63	C₃×C₄	—	2	2	no	—
64	C₃×C₄	—	5	2	no	—
65	C₃×C₄	—	5	2	no	—
66	C₃×C₄	—	10	2	no	—
67	C₂×C₅	—	2	2	no	—
68	C₂×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
69	C₂×C₅	C₃×#41	1	2	yes	—
70	C₂³	C₂×C₃×D₅	1	1	yes	characteristic
71	C₂×C₄	—	5	4	no	—
72	C₂×C₄	—	5	1	no	—
73	C₂×C₄	—	5	1	no	—
74	C₂×C₄	—	5	2	no	—
75	C₂×C₄	C₂×C₃×D₅	1	2	yes	—
76	C₂×C₃	—	2	2	no	—
77	C₂×C₃	C₂×C₄×D₅	1	1	yes	characteristic
78	C₂×C₃	#711	1	2	yes	—
79	C₅	C₃×#117	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	2	2	no	—
81	C₂²	C₃×C₄×D₅	1	2	yes	—
82	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
83	C₄	—	2	2	no	—
84	C₄	—	5	2	no	—
85	C₄	—	5	2	no	—
86	C₄	—	10	2	no	—
87	C₃	#4023	1	1	yes	characteristic, direct product factor, Sylow
88	C₂	—	2	2	no	—
89	C₂	C₂×C₃×C₄×D₅	1	1	yes	characteristic
90	C₂	C₃×#711	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₅
commutator	C₂×C₅	C₂²×C₃×C₄
Frattini	C₂²	C₂²×C₃×D₅
Fitting	C₃×C₅×C₂²⋊C₄	C₂
socle	C₂²×C₃×C₅	C₂³
prime radical	C₂³×C₃×C₅	C₂²
cosocle	C₂²×C₅	C₂³×C₃
hypercenter	C₃×C₂²⋊C₄	D₅
hypocenter	C₅	C₃×#117
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
4. C₃×#683	C₂	semidirect
5. C₃×C₄×Dic₅	C₂	semidirect
6. #4023	C₃	direct (N × H)
9. C₂×C₃×Dic₅	C₄	semidirect
17. #683	C₂×C₃	semidirect
18. C₄×Dic₅	C₂×C₃	semidirect
33. C₂×Dic₅	C₃×C₄	semidirect
59. C₃×C₅	#117	semidirect
79. C₅	C₃×#117	semidirect
87. C₃	#4023	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×Dic₅	2
C₃×C₅×C₂²⋊C₄	2
C₃×C₂²⋊Dic₅	2
C₃×#683	2
C₃×C₄×Dic₅	2
#4023	3
C₃×#117	5

Subgroups — C3×#4023 #91594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4023 #91594