Finite Group Databasebeta

← #14268438

Subgroups — #14268438

Order 1800.

176 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 30 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#11744719C211yesmaximal, characteristic
2C3×C3⋊#1044C211yesmaximal, characteristic, complemented
3C3×C3⋊#1043C211yesmaximal, characteristic, complemented
4#10597183—31nomaximal
5#10597182—31nomaximal
6C5×C3⋊D15C412yescomplemented
7C32×C5⋊D5C2211yescharacteristic
8ΓL(1,𝔽16)⋊D3—52nomaximal
9D15⋊D5—31no—
10D15⋊D5—31no—
11D15⋊D5—61no—
12C3⋊#1044D311yescharacteristic, complemented
13C3⋊#1043D311yescharacteristic, complemented
14C3×#1044—31no—
15C3×#1043—31no—
16C32×C52C2×C411yescharacteristic, complemented, Hall
17D5⋊AGL(1,𝔽5)—91noHall
18D5×C3⋊D3—52no—
19C3×ΓL(1,𝔽16)—52no—
20C3×ΓL(1,𝔽16)—52no—
21C3×ΓL(1,𝔽16)—102no—
22C5×D15—32no—
23C5×D15—32no—
24C5×D15—62no—
25C3×C5⋊D5—21no—
26C3×C5⋊D5C2×D311yescharacteristic
27C3×C5⋊D5C2×D311yescharacteristic
28D3×AGL(1,𝔽5)—152no—
29D3×AGL(1,𝔽5)—152no—
30D52—91no—
31#1044—31no—
32#1043—31no—
33C3⋊D15AGL(1,𝔽5)12yescomplemented
34C5×C3⋊D3—52no—
35C32×D5—52no—
36C32×D5—102no—
37C3×C52—21no—
38C3×C52C4×D311yescharacteristic, complemented
39C3×C52C4×D311yescharacteristic, complemented
40#624—251noHall
41D3×D5—152no—
42D3×D5—152no—
43D3×D5—302no—
44ΓL(1,𝔽16)—52no—
45ΓL(1,𝔽16)—52no—
46ΓL(1,𝔽16)—102no—
47C3×AGL(1,𝔽5)—152no—
48C3×AGL(1,𝔽5)—152no—
49C3×AGL(1,𝔽5)—302no—
50C5⋊D5D3211yescharacteristic
51C5×D5—92no—
52C32×C5—22no—
53C32×C5C2×AGL(1,𝔽5)12yescomplemented
54C2×AGL(1,𝔽5)—452no—
55C2×C3⋊D3—251no—
56C3×Dic3—251no—
57C3×Dic3—251no—
58D15—32no—
59D15—32no—
60D15—62no—
61C3×D5—52no—
62C3×D5—52no—
63C3×D5—102no—
64C3×D5—102no—
65C3×D5—102no—
66C3×D5—202no—
67C5×D3—152no—
68C5×D3—152no—
69C5×D3—302no—
70C52#62411yescharacteristic, complemented, Sylow
71C4×D3—751no—
72C4×D3—751no—
73C2×D5—452no—
74AGL(1,𝔽5)—152no—
75AGL(1,𝔽5)—152no—
76AGL(1,𝔽5)—302no—
77C2×C32—251no—
78C3⋊D3—52no—
79C3×C5—22no—
80C3×C5—22no—
81C3×C5—22no—
82C3×C5—42no—
83C3×C5D3×AGL(1,𝔽5)12yescomplemented
84C3×C5D3×AGL(1,𝔽5)12yescomplemented
85C2×D3—751no—
86C2×D3—751no—
87C2×D3—1501no—
88C3×C4—751no—
89C3×C4—751no—
90Dic3—251no—
91Dic3—251no—
92C2×C5—452no—
93D5—52no—
94D5—92no—
95D5—102no—
96C32D5⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
97C2×C4—2251noSylow
98C2×C3—251no—
99C2×C3—251no—
100C2×C3—501no—
101D3—152no—
102D3—152no—
103D3—302no—
104C5—22no—
105C5ΓL(1,𝔽16)⋊D312yescomplemented
106C22—2251no—
107C4—751no—
108C4—751no—
109C3—21no—
110C3#1059718211yescharacteristic, complemented
111C3#1059718311yescharacteristic, complemented
112C2—251no—
113C2—452no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C52C2×C4
prime radical#11744719C2
cosocleC32×C5⋊D5C22
LCSG ▷ C32×C52
UCSC1

Complements

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

NH ≅ G/Ntype
2. C3×C3⋊#1044C2semidirect
3. C3×C3⋊#1043C2semidirect
6. C5×C3⋊D15C4semidirect
12. C3⋊#1044D3semidirect
13. C3⋊#1043D3semidirect
16. C32×C52C2×C4semidirect
33. C3⋊D15AGL(1,𝔽5)semidirect
38. C3×C52C4×D3semidirect
39. C3×C52C4×D3semidirect
53. C32×C5C2×AGL(1,𝔽5)semidirect
70. C52#624semidirect
83. C3×C5D3×AGL(1,𝔽5)semidirect
84. C3×C5D3×AGL(1,𝔽5)semidirect
96. C32D5⋊AGL(1,𝔽5)semidirect
105. C5ΓL(1,𝔽16)⋊D3semidirect
110. C3#10597182semidirect
111. C3#10597183semidirect

Maximal subgroups

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

subgroupindex
#117447192
C3×C3⋊#10442
C3×C3⋊#10432
#105971833
#105971823
ΓL(1,𝔽16)⋊D35