Finite Group Databasebeta

← C3×C5×#14523128 #44477807

Subgroups — C3×C5×#14523128 #44477807

Order 30420.

576 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 156 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
1C2×C3×C5×#92788C211yesmaximal, characteristic
2C3×C5×#10621725C311yesmaximal, characteristic, complemented
3C5×#14523128C313yesmaximal, direct product factor
4C3×C5×#92788C411yescharacteristic, complemented, Hall
5C3×#14523128C511yesmaximal, characteristic, direct product factor, Hall
6C2×C5×#92788C2×C313yes—
7C2×C3×C5×C132C2×C311yescharacteristic
8C5×#10621725C3211yescharacteristic, complemented, Hall
9C2×C3×#92788C2×C511yescharacteristic
10C5×#92788C3×C413yescomplemented
11C3×C5×C132C3×C411yescharacteristic, complemented
12C3×C5×Dic13⋊C3—131nomaximal
13C3×C5×Dic13⋊C3—131nomaximal
14C3×C5×Dic13⋊C3—1312nomaximal
15C3×#10621725C3×C511yescharacteristic, complemented
16#14523128C3×C513yesdirect product factor
17C2×C5×C132C2×C3211yescharacteristic
18C3×#92788C4×C511yescharacteristic, complemented, Hall
19C2×C3×C5×C13⋊C3—131no—
20C2×C3×C5×C13⋊C3—131no—
21C2×C3×C5×C13⋊C3—1312no—
22C2×C3×C132C2×C3×C511yescharacteristic
23C2×#92788C2×C3×C513yes—
24C5×C132C32×C411yescharacteristic, complemented, Hall
25C3×C5×Dic13—131no—
26C3×C5×Dic13—131no—
27C3×C5×Dic13—3912no—
28C5×Dic13⋊C3—133no—
29C5×Dic13⋊C3—133no—
30C5×Dic13⋊C3—1336no—
31#10621725C32×C511yescharacteristic, complemented, Hall
32C3×C5×C13⋊C3—131no—
33C3×C5×C13⋊C3—131no—
34C3×C5×C13⋊C3—1312no—
35C3×C132C3×C4×C511yescharacteristic, complemented
36#92788C3×C4×C513yescomplemented
37C3×Dic13⋊C3—131no—
38C3×Dic13⋊C3—131no—
39C3×Dic13⋊C3—1312no—
40C2×C3×C5×C13D13⋊C311yescharacteristic
41C2×C3×C5×C13D13⋊C311yescharacteristic
42C2×C3×C5×C13D13⋊C3112yes—
43C2×C5×C13⋊C3—133no—
44C2×C5×C13⋊C3—133no—
45C2×C5×C13⋊C3—1336no—
46C2×C132C2×C32×C511yescharacteristic
47C5×Dic13—131no—
48C5×Dic13—131no—
49C5×Dic13—3912no—
50C2×C3×C13⋊C3—131no—
51C2×C3×C13⋊C3—131no—
52C2×C3×C13⋊C3—1312no—
53C3×C5×C13Dic13⋊C311yescharacteristic, complemented
54C3×C5×C13Dic13⋊C311yescharacteristic, complemented
55C3×C5×C13Dic13⋊C3112yescomplemented
56C5×C13⋊C3—133no—
57C5×C13⋊C3—133no—
58C5×C13⋊C3—1336no—
59C32×C4×C5—1691noHall
60C132C32×C4×C511yescharacteristic, complemented, Sylow
61C3×Dic13—131no—
62C3×Dic13—391no—
63C3×Dic13—3912no—
64Dic13⋊C3—133no—
65Dic13⋊C3—133no—
66Dic13⋊C3—1336no—
67C2×C5×C13C3×D13⋊C311yescharacteristic
68C2×C5×C13C3×D13⋊C311yescharacteristic
69C2×C5×C13C3×D13⋊C3112yes—
70C3×C13⋊C3—131no—
71C3×C13⋊C3—131no—
72C3×C13⋊C3—1312no—
73C2×C32×C5—1691no—
74C2×C3×C13C5×D13⋊C311yescharacteristic
75C2×C3×C13C5×D13⋊C311yescharacteristic
76C2×C3×C13C5×D13⋊C3112yes—
77C2×C13⋊C3—133no—
78C2×C13⋊C3—133no—
79C2×C13⋊C3—1336no—
80C5×C13C3×Dic13⋊C311yescharacteristic, complemented
81C5×C13C3×Dic13⋊C311yescharacteristic, complemented
82C5×C13C3×Dic13⋊C3112yescomplemented
83C3×C4×C5—1693no—
84C3×C4×C5—5071no—
85Dic13—131no—
86Dic13—391no—
87Dic13—3912no—
88C32×C5—1691noHall
89C3×C13C5×Dic13⋊C311yescharacteristic, complemented
90C3×C13C5×Dic13⋊C311yescharacteristic, complemented
91C3×C13C5×Dic13⋊C3112yescomplemented
92C13⋊C3—133no—
93C13⋊C3—133no—
94C13⋊C3—1336no—
95C32×C4—1691noHall
96C2×C3×C5—1693no—
97C2×C3×C5#1175981511yescharacteristic
98C2×C13C3×C5×D13⋊C311yescharacteristic
99C2×C13C3×C5×D13⋊C311yescharacteristic
100C2×C13C3×C5×D13⋊C3112yes—
101C4×C5—5071noHall
102C2×C32—1691no—
103C3×C5—1693no—
104C3×C5#1452312811yescharacteristic, direct product factor
105C13C3×C5×Dic13⋊C311yescharacteristic, complemented
106C13C3×C5×Dic13⋊C311yescharacteristic, complemented
107C13C3×C5×Dic13⋊C3112yescomplemented
108C3×C4—1693no—
109C3×C4—5071no—
110C2×C5C3×#1175981511yescharacteristic
111C32—1691noSylow
112C2×C3—1693no—
113C2×C3C5×#1175981511yescharacteristic
114C5C3×#1452312811yescharacteristic, direct product factor, Sylow
115C4—5071noSylow
116C3—1693no—
117C3C5×#1452312811yescharacteristic, direct product factor
118C2C3×C5×#1175981511yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C5#11759815
commutator, hypocenterC132C32×C4×C5
FrattiniC2C3×C5×#11759815
Fitting, socleC2×C3×C5×C132C2×C3
prime radicalC2×C3×C5×#92788C2
cosocleC2×C132C2×C32×C5
LCSG ▷ C132
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
2. C3×C5×#10621725C3semidirect
3. C5×#14523128C3direct (N × H)
4. C3×C5×#92788C4semidirect
5. C3×#14523128C5direct (N × H)
8. C5×#10621725C32semidirect
10. C5×#92788C3×C4semidirect
11. C3×C5×C132C3×C4semidirect
15. C3×#10621725C3×C5semidirect
16. #14523128C3×C5direct (N × H)
18. C3×#92788C4×C5semidirect
24. C5×C132C32×C4semidirect
31. #10621725C32×C5semidirect
35. C3×C132C3×C4×C5semidirect
36. #92788C3×C4×C5semidirect
53. C3×C5×C13Dic13⋊C3semidirect
54. C3×C5×C13Dic13⋊C3semidirect
55. C3×C5×C13Dic13⋊C3semidirect
60. C132C32×C4×C5semidirect
80. C5×C13C3×Dic13⋊C3semidirect
81. C5×C13C3×Dic13⋊C3semidirect
82. C5×C13C3×Dic13⋊C3semidirect
89. C3×C13C5×Dic13⋊C3semidirect
90. C3×C13C5×Dic13⋊C3semidirect
91. C3×C13C5×Dic13⋊C3semidirect
104. C3×C5#14523128direct (N × H)
105. C13C3×C5×Dic13⋊C3semidirect
106. C13C3×C5×Dic13⋊C3semidirect
107. C13C3×C5×Dic13⋊C3semidirect
114. C5C3×#14523128direct (N × H)
117. C3C5×#14523128direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#927882
C3×C5×#106217253
C5×#145231283
C3×#145231285
C3×C5×Dic13⋊C313