Finite Group Databasebeta

← C3×C5⋊#1020 #13089613

Subgroups — C3×C5⋊#1020 #13089613

Order 1440.

238 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C22⋊A4C211yesmaximal, characteristic, complemented
2C5⋊#1020C311yesmaximal, characteristic, direct product factor
3C3×#4099—31nomaximal
4C3×C5⋊S4—43nomaximal
5C3×#1020—51nomaximal, Hall
6C24×C3×C5D311yescharacteristic, complemented
7C5×C22⋊A4—21no—
8C5×C22⋊A4C2×C311yescharacteristic, complemented
9C2×C3×C22⋊D5—33no—
10C3×C22⋊Dic5—33no—
11C3×C5×A4—43no—
12C3×C5×A4—81no—
13#4099—31noHall
14C3×C22⋊A4D511yescharacteristic, complemented
15C23×C3×C5—33no—
16C23×C3×C5—61no—
17C22×C3×D5—31no—
18C5⋊S4—43no—
19C3×C22⋊D5—63no—
20C3×C22⋊D5—63no—
21C2×C3×Dic5—33no—
22#1020—51no—
23C3×#120—151no—
24C3×D15—161no—
25C24×C5C3×D311yescharacteristic, complemented
26C2×C22⋊D5—33no—
27C22⋊Dic5—33no—
28C3×S4—203no—
29C22×C3×C5—21no—
30C22×C3×C5—31no—
31C22×C3×C5—33no—
32C22×C3×C5—63no—
33C22×C3×C5S413yescomplemented
34C2×C3×D5—63no—
35C5×A4—43no—
36C5×A4—81no—
37C5×A4—82no—
38C5×A4—83no—
39C3×Dic5—63no—
40C24×C3D1511yescharacteristic, complemented
41C22⋊A4—21no—
42C22⋊A4C3×D511yescharacteristic, complemented
43C2×C3×D4—153no—
44C3×C22⋊C4—153no—
45C32×C5—161noHall
46C23×C5—33no—
47C23×C5—61no—
48C22×D5—31no—
49C22⋊D5—63no—
50C22⋊D5—63no—
51C2×Dic5—33no—
52C3×A4—43no—
53C3×A4—81no—
54#120—151noSylow
55C2×C3×C5—33no—
56C2×C3×C5—61no—
57D15—161no—
58C3×D5—121no—
59C23×C3—33no—
60C23×C3—61no—
61C23×C3—151no—
62S4—203no—
63C3×D4—303no—
64C3×D4—303no—
65C2×C3×C4—153no—
66C22×C5—21no—
67C22×C5—31no—
68C22×C5—33no—
69C22×C5—63no—
70C22×C5C3×S413yescomplemented
71C2×D5—63no—
72Dic5—63no—
73C3×D3—801no—
74C24C3×D1511yescharacteristic, complemented
75C2×D4—153no—
76C22⋊C4—153no—
77C3×C5—161no—
78C3×C5—321no—
79C3×C5#102011yescharacteristic, complemented
80C22×C3—21no—
81C22×C3—31no—
82C22×C3—33no—
83C22×C3—63no—
84C22×C3—303no—
85C22×C3C5⋊S413yescomplemented
86A4—43no—
87A4—81no—
88A4—82no—
89A4—83no—
90C3×C4—303no—
91C2×C5—33no—
92C2×C5—61no—
93D5—121no—
94C32—161noSylow
95C23—33no—
96C23—61no—
97C23—151no—
98D4—303no—
99D4—303no—
100C2×C4—153no—
101C2×C3—33no—
102C2×C3—61no—
103C2×C3—601no—
104D3—801no—
105C5C3×#102011yescharacteristic, complemented, Sylow
106C22—21no—
107C22—31no—
108C22—33no—
109C22—63no—
110C22—303no—
111C22C3×C5⋊S413yescomplemented
112C4—303no—
113C3—161no—
114C3—321no—
115C3C5⋊#102011yescharacteristic, direct product factor
116C2—33no—
117C2—61no—
118C2—601no—
subgroupG/H
center, hypercenterC3C5⋊#1020
commutator, cosocle, hypocenterC5×C22⋊A4C2×C3
FrattiniC1G
Fitting, socleC24×C3×C5D3
LCSG ▷ C5×C22⋊A4
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C5×C22⋊A4C2semidirect
2. C5⋊#1020C3direct (N × H)
6. C24×C3×C5D3semidirect
8. C5×C22⋊A4C2×C3semidirect
14. C3×C22⋊A4D5semidirect
25. C24×C5C3×D3semidirect
33. C22×C3×C5S4semidirect
40. C24×C3D15semidirect
42. C22⋊A4C3×D5semidirect
70. C22×C5C3×S4semidirect
74. C24C3×D15semidirect
79. C3×C5#1020semidirect
85. C22×C3C5⋊S4semidirect
105. C5C3×#1020semidirect
111. C22C3×C5⋊S4semidirect
115. C3C5⋊#1020direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C22⋊A42
C5⋊#10203
C3×#40993
C3×C5⋊S44
C3×#10205