Finite Group Databasebeta

← #13085508

Subgroups — #13085508

Order 1440.

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

normal subgroups only

This group has 168 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
1#10624152C211yesmaximal, characteristic
2C4×#4379C211yesmaximal, characteristic, complemented
3C5×#3788C211yesmaximal, characteristic, complemented
4C2×#4379—21no—
5C4⋊(C3⋊D15)C411yescharacteristic, complemented
6C4×C5×C3⋊D3C2211yescharacteristic
7C32×Dic10C411yescharacteristic, complemented
8#67140—21no—
9#67137—21no—
10C5×#622—21no—
11#63785—51nomaximal, Hall
12#6769—62no—
13C2×C3⋊D15—21no—
14C2×C5×C3⋊D3D411yescharacteristic
15#4379—22no—
16C32×C4×C5C2×C411yescharacteristic
17C5×C3⋊Dic3D411yescharacteristic
18C32×Dic5—21no—
19#3957—91nomaximal, Hall
20#3832—51no—
21C4×#157—51no—
22#3788D511yescharacteristic, complemented
23D60—62no—
24C4×C5×D3—62no—
25C3×Dic10—22no—
26#1203—64no—
27#1200—64no—
28C2×C32×C5C22⋊C411yescharacteristic
29C3⋊D15—41no—
30C5×C3⋊D3—21no—
31#709—91no—
32C5×M16—91no—
33C4×Dic5—91no—
34C2×#157—101no—
35C32×Q8—51no—
36C4⋊(C3⋊D3)—51no—
37C4⋊(C3⋊D3)—101no—
38C4×C3⋊D3—101no—
39C4×C3⋊D3C2×D511yescharacteristic
40#622—21no—
41C2×D15—64no—
42C2×C5×D3—62no—
43C3×C4×C5—22no—
44C3×Dic5—24no—
45C5×Dic3—62no—
46#239—302no—
47C32×C5#10411yescharacteristic, complemented, Hall
48C2×C4×C5—91no—
49C22⋊D5—181no—
50C2×Dic5—181no—
51D20—91no—
52C4×D5—181no—
53Dic10#15711yescharacteristic, complemented
54C5×C8—181no—
55C2×C3⋊D3—101no—
56C2×C3⋊D3D2011yescharacteristic
57#157—102no—
58C32×C4—101no—
59C32×C4C4×D511yescharacteristic
60C3⋊Dic3C22⋊D511yescharacteristic
61#104—451noSylow
62C2×C3×C5—22no—
63D15—124no—
64C5×D3—122no—
65C3×Q8—102no—
66D12—302no—
67D12—304no—
68C4×D3—62no—
69C4×D3—304no—
70C22×C5—91no—
71C2×D5—181no—
72C4×C5—91no—
73C4×C5C2×#15711yescharacteristic
74Dic5—21no—
75Dic5—182no—
76C2×C32#68511yescharacteristic
77C3⋊D3—21no—
78C3⋊D3—201no—
79#41—451no—
80M16—91no—
81C42—451no—
82C3×C5—22no—
83C2×D3—62no—
84C2×D3—304no—
85C3×C4—22no—
86C3×C4—104no—
87Dic3—62no—
88C2×C5—181no—
89C2×C5C22⋊#15711yescharacteristic
90D5—361no—
91C32#395711yescharacteristic, complemented, Sylow
92Q8—51no—
93D4—451no—
94D4—901no—
95C2×C4—91no—
96C2×C4—901no—
97C2×C4—901no—
98C8—181no—
99C2×C3—22no—
100D3—122no—
101D3—604no—
102C5#6378511yescharacteristic, complemented, Sylow
103C22—91no—
104C22—901no—
105C4—91no—
106C4—101no—
107C4—902no—
108C4D5×#15711yescharacteristic
109C3—22no—
110C2—181no—
111C2—1801no—
112C2#1062398511yescharacteristic
subgroupG/H
centerC2#10623985
commutator, FittingC32×C4×C5C2×C4
Frattini, hypercenterC4D5×#157
socleC2×C32×C5C22⋊C4
prime radical#10624152C2
cosocleC4×C5×C3⋊D3C22
hypocenterC32×C5#104
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×#4379C2semidirect
3. C5×#3788C2semidirect
5. C4⋊(C3⋊D15)C4semidirect
7. C32×Dic10C4semidirect
22. #3788D5semidirect
47. C32×C5#104semidirect
53. Dic10#157semidirect
91. C32#3957semidirect
102. C5#63785semidirect

Maximal subgroups

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

subgroupindex
#106241522
C4×#43792
C5×#37882
#637855
#39579