Subgroups — C₃×C₅×#103 #91130

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	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#103	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	—	2	1	no	—
9	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₅×C₈	—	2	1	no	—
11	C₃×#103	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
13	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic
14	C₅×C₄⋊C₄	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	—	4	1	no	—
18	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
19	C₃×C₄×C₅	D₄	1	1	yes	characteristic
20	C₂×C₃×Q₈	C₂×C₅	1	1	yes	characteristic
21	C₂×C₃×C₈	C₂×C₅	1	1	yes	characteristic
22	C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
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	—	2	1	no	—
27	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
28	C₅×C₈	—	2	1	no	—
29	#103	C₃×C₅	1	1	yes	characteristic, direct product factor, 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	C₄×C₅	1	2	yes	complemented
35	C₂×C₃×C₄	—	2	1	no	—
36	C₂×C₃×C₄	—	2	1	no	—
37	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
38	C₃×C₈	—	2	1	no	—
39	C₂²×C₅	C₃×D₄	1	1	yes	characteristic
40	C₄×C₅	—	2	2	no	—
41	C₄×C₅	—	4	1	no	—
42	C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
43	C₄×C₅	C₃×D₄	1	1	yes	characteristic
44	C₂×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
45	C₂×C₈	C₂×C₃×C₅	1	1	yes	characteristic
46	C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
47	C₃×C₅	#103	1	1	yes	characteristic, direct product factor, Hall
48	C₂²×C₃	C₅×D₄	1	1	yes	characteristic
49	C₃×C₄	—	2	2	no	—
50	C₃×C₄	—	4	1	no	—
51	C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
52	C₃×C₄	C₅×D₄	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×C₄×C₅	1	2	yes	complemented
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₂×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₃	C₅×SD₁₆	1	1	yes	characteristic
64	C₂×C₃	C₅×Q₁₆	1	1	yes	characteristic
65	C₅	C₃×#103	1	1	yes	characteristic, direct product factor, Sylow
66	C₂²	C₃×C₅×D₄	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	4	1	no	—
69	C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
70	C₄	C₃×C₅×D₄	1	1	yes	characteristic
71	C₃	C₅×#103	1	1	yes	characteristic, direct product factor, Sylow
72	C₂	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
73	C₂	C₃×C₅×SD₁₆	1	1	yes	characteristic
74	C₂	C₃×C₅×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃×C₅	D₄
commutator	C₄	C₂×C₃×C₄×C₅
Frattini, cosocle	C₂×C₄	C₂²×C₃×C₅
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#103	C₃	direct (N × H)
6. C₃×C₅×Q₈	C₄	semidirect
11. C₃×#103	C₅	direct (N × H)
24. C₅×Q₈	C₃×C₄	semidirect
29. #103	C₃×C₅	direct (N × H)
34. C₃×Q₈	C₄×C₅	semidirect
47. C₃×C₅	#103	direct (N × H)
57. Q₈	C₃×C₄×C₅	semidirect
65. C₅	C₃×#103	direct (N × H)
71. C₃	C₅×#103	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
C₂×C₃×C₅×C₈	2
C₃×C₅×C₄⋊C₄	2
C₅×#103	3
C₃×#103	5

Subgroups — C3×C5×#103 #91130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#103 #91130