Subgroups — C₃×#3967 #91037

Order 480.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#168	C₂	1	1	yes	maximal, characteristic
4	#3967	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×Q₈	—	2	1	no	—
6	C₃×C₅×Q₈	C₄	1	2	yes	complemented
7	C₂×C₃×C₄×C₅	—	2	1	no	—
8	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₃×Dic₅	—	2	1	no	—
10	C₃×#168	—	2	1	no	—
11	C₃×#103	—	5	1	no	maximal, Hall
12	C₂×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
13	C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic
14	C₂×#168	C₂×C₃	1	1	yes	characteristic
15	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
16	C₃×C₄×C₅	—	2	2	no	—
17	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
18	C₃×C₄×C₅	D₄	1	1	yes	characteristic
19	C₃×Dic₅	—	4	1	no	—
20	C₂×C₃×Q₈	D₅	1	1	yes	characteristic
21	C₂×C₃×C₈	—	5	1	no	—
22	C₃×C₄⋊C₄	—	5	1	no	—
23	C₅×Q₈	—	2	1	no	—
24	C₅×Q₈	C₃×C₄	1	2	yes	complemented
25	C₂×C₄×C₅	—	2	1	no	—
26	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
27	C₂×Dic₅	—	2	1	no	—
28	#168	—	2	1	no	—
29	#103	—	5	1	no	Sylow
30	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₃×C₅	SD₁₆	1	1	yes	characteristic
32	C₂×C₃×C₅	Q₁₆	1	1	yes	characteristic
33	C₃×Q₈	—	2	1	no	—
34	C₃×Q₈	Dic₅	1	2	yes	complemented
35	C₂×C₃×C₄	—	2	1	no	—
36	C₂×C₃×C₄	—	10	1	no	—
37	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
38	C₃×C₈	—	10	1	no	—
39	C₂²×C₅	C₃×D₄	1	1	yes	characteristic
40	C₄×C₅	—	2	2	no	—
41	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
42	C₄×C₅	C₃×D₄	1	1	yes	characteristic
43	Dic₅	—	4	1	no	—
44	C₂×Q₈	C₃×D₅	1	1	yes	characteristic
45	C₂×C₈	—	5	1	no	—
46	C₄⋊C₄	—	5	1	no	—
47	C₃×C₅	#103	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₃	C₂²⋊D₅	1	1	yes	characteristic
49	C₃×C₄	—	2	2	no	—
50	C₃×C₄	—	20	1	no	—
51	C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
52	C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
53	C₂×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₅	C₃×SD₁₆	1	1	yes	characteristic
55	C₂×C₅	C₃×Q₁₆	1	1	yes	characteristic
56	Q₈	—	2	1	no	—
57	Q₈	C₃×Dic₅	1	2	yes	complemented
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	10	1	no	—
60	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
61	C₈	—	10	1	no	—
62	C₂×C₃	#688	1	1	yes	characteristic
63	C₂×C₃	#689	1	1	yes	characteristic
64	C₂×C₃	C₂²⋊Dic₅	1	1	yes	characteristic
65	C₅	C₃×#103	1	1	yes	characteristic, complemented, Sylow
66	C₂²	C₃×C₂²⋊D₅	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	20	1	no	—
69	C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
70	C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
71	C₃	#3967	1	1	yes	characteristic, direct product factor, Sylow
72	C₂	C₃×#688	1	1	yes	characteristic
73	C₂	C₃×#689	1	1	yes	characteristic
74	C₂	C₃×C₂²⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²⋊D₅
commutator	C₄×C₅	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₅
Fitting	C₂×C₃×C₅×Q₈	C₂
socle, prime radical	C₂²×C₃×C₅	D₄
cosocle	C₂×C₄×C₅	C₂²×C₃
hypercenter	C₂×C₃×Q₈	D₅
hypocenter	C₅	C₃×#103
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×Q₈

Complements

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

N	H ≅ G/N	type
4. #3967	C₃	direct (N × H)
6. C₃×C₅×Q₈	C₄	semidirect
24. C₅×Q₈	C₃×C₄	semidirect
34. C₃×Q₈	Dic₅	semidirect
47. C₃×C₅	#103	semidirect
57. Q₈	C₃×Dic₅	semidirect
65. C₅	C₃×#103	semidirect
71. C₃	#3967	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×Q₈	2
C₃×C₄⋊Dic₅	2
C₂×C₃×#168	2
#3967	3
C₃×#103	5

Subgroups — C3×#3967 #91037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3967 #91037