Finite Group Databasebeta

← #44478285

Subgroups — #44478285

Order 30420.

704 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 151 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×C3⋊(C13⋊D13)C211yesmaximal, characteristic, complemented
2C3×C3⋊(C5⋊(C13⋊D13))C211yesmaximal, characteristic, complemented
3C132×C3⋊D15C211yesmaximal, characteristic, complemented
4D15⋊(C13⋊D13)—31nomaximal
5D15×C13⋊D13—31nomaximal
6C32×C5×C132C2211yescharacteristic, complemented, Hall
7(C3⋊D3)⋊(C13⋊D13)—51nomaximal, Hall
8C3⋊(C5⋊(C13⋊D13))D311yescharacteristic, complemented
9C132×D15—31no—
10C132×D15—31no—
11C132×D15—61no—
12C5×C3⋊(C13⋊D13)D311yescharacteristic, complemented
13C3×C5⋊(C13⋊D13)—31no—
14C3×C5×C13⋊D13—31no—
15D5×C13⋊D13—91noHall
16C132×C3⋊D3—51no—
17C3×C3⋊(C13⋊D13)—51no—
18C3×C3⋊(C13⋊D13)D511yescharacteristic, complemented
19C3×C5×C132—21no—
20C3×C5×C132C2×D311yescharacteristic, complemented
21C3×C5×C132C2×D311yescharacteristic, complemented
22D39⋊D15—1314nomaximal
23D3×C13⋊D13—151no—
24D3×C13⋊D13—151no—
25C5⋊(C13⋊D13)—31no—
26D5×C132—91no—
27C5×C13⋊D13—31no—
28C32×C132C2×D511yescharacteristic, complemented, Hall
29C13×C3⋊D15D13114yescomplemented
30C3×D195—1314no—
31C3×C5×D39—1314no—
32C3⋊(C13⋊D13)—51no—
33C3⋊(C13⋊D13)D1511yescharacteristic, complemented
34D3×C132—151no—
35D3×C132—151no—
36D3×C132—301no—
37C3×C13⋊D13—31no—
38C3×C13⋊D13—151no—
39C5×C132D3211yescharacteristic, complemented, Hall
40D15⋊D13—3914no—
41D13×D15—3914no—
42C2×C13⋊D13—451noHall
43C32×C5×C13C2×D13114yescomplemented
44C3×C132—21no—
45C3×C132D3×D511yescharacteristic, complemented
46C3×C132C2×D1511yescharacteristic, complemented
47(C3⋊D3)⋊D13—6514no—
48D195—1314no—
49C13×D15—314no—
50C13×D15—314no—
51C13×D15—614no—
52C5×D39—1314no—
53C3×D65—3914no—
54C3×C5×D13—3914no—
55C2×C132—451no—
56C13⋊D13—31no—
57C13⋊D13—151no—
58D5×D13—11714no—
59C13×C3⋊D3—514no—
60C3×D39—1314no—
61C3×D39—6514no—
62C3×C5×C13—214no—
63C3×C5×C13D3×D13114yescomplemented
64C3×C5×C13D3×D13114yescomplemented
65D3×D15—1691noHall
66C132D3×D1511yescharacteristic, complemented, Sylow
67D3×D13—19514no—
68D3×D13—19514no—
69D65—3914no—
70C5×D13—3914no—
71D5×C13—914no—
72C32×C13D5×D13114yescomplemented
73C3⋊D15C13⋊D1311yescharacteristic, complemented
74C3×D15—1691no—
75C3×C5×D3—1691no—
76D39—1314no—
77D39—6514no—
78C3×D13—3914no—
79C3×D13—19514no—
80D3×C13—1514no—
81D3×C13—1514no—
82D3×C13—3014no—
83C5×C13(C3⋊D3)⋊D13114yescomplemented
84C2×D15—5071no—
85D3×D5—5071no—
86C2×D13—58514no—
87C32×C5C2×C13⋊D1311yescharacteristic, complemented, Hall
88C3×C13—214no—
89C3×C13D13×D15114yescomplemented
90C3×C13D15⋊D13114yescomplemented
91D32—8451noHall
92C2×C3×C5—5071no—
93D15—31no—
94D15—31no—
95D15—61no—
96D15—1691no—
97C3×D5—5071no—
98C5×D3—1691no—
99C2×C13—4514no—
100D13—3914no—
101D13—19514no—
102C2×D5—15211noHall
103C3⋊D3—51no—
104C3×D3—8451no—
105C3×D3—1691no—
106C3×C5—21no—
107C3×C5D3×C13⋊D1311yescharacteristic, complemented
108C3×C5D3×C13⋊D1311yescharacteristic, complemented
109C13D39⋊D15114yescomplemented
110C2×D3—25351no—
111C2×D3—25351no—
112C2×C5—5071no—
113D5—91no—
114D5—5071no—
115C32D5×C13⋊D1311yescharacteristic, complemented, Sylow
116C2×C3—25351no—
117C2×C3—5071no—
118D3—151no—
119D3—151no—
120D3—301no—
121D3—8451no—
122D3—1691no—
123C5(C3⋊D3)⋊(C13⋊D13)11yescharacteristic, complemented, Sylow
124C22—76051noSylow
125C3—21no—
126C3D15×C13⋊D1311yescharacteristic, complemented
127C3D15⋊(C13⋊D13)11yescharacteristic, complemented
128C2—451no—
129C2—25351no—
130C2—5071no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C132C22
LCSG ▷ C32×C5×C132
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C3⋊(C13⋊D13)C2semidirect
2. C3×C3⋊(C5⋊(C13⋊D13))C2semidirect
3. C132×C3⋊D15C2semidirect
6. C32×C5×C132C22semidirect
8. C3⋊(C5⋊(C13⋊D13))D3semidirect
12. C5×C3⋊(C13⋊D13)D3semidirect
18. C3×C3⋊(C13⋊D13)D5semidirect
20. C3×C5×C132C2×D3semidirect
21. C3×C5×C132C2×D3semidirect
28. C32×C132C2×D5semidirect
29. C13×C3⋊D15D13semidirect
33. C3⋊(C13⋊D13)D15semidirect
39. C5×C132D32semidirect
43. C32×C5×C13C2×D13semidirect
45. C3×C132D3×D5semidirect
46. C3×C132C2×D15semidirect
63. C3×C5×C13D3×D13semidirect
64. C3×C5×C13D3×D13semidirect
66. C132D3×D15semidirect
72. C32×C13D5×D13semidirect
73. C3⋊D15C13⋊D13semidirect
83. C5×C13(C3⋊D3)⋊D13semidirect
87. C32×C5C2×C13⋊D13semidirect
89. C3×C13D13×D15semidirect
90. C3×C13D15⋊D13semidirect
107. C3×C5D3×C13⋊D13semidirect
108. C3×C5D3×C13⋊D13semidirect
109. C13D39⋊D15semidirect
115. C32D5×C13⋊D13semidirect
123. C5(C3⋊D3)⋊(C13⋊D13)semidirect
126. C3D15×C13⋊D13semidirect
127. C3D15⋊(C13⋊D13)semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C3⋊(C13⋊D13)2
C3×C3⋊(C5⋊(C13⋊D13))2
C132×C3⋊D152
D15⋊(C13⋊D13)3
D15×C13⋊D133
(C3⋊D3)⋊(C13⋊D13)5
D39⋊D1513