Finite Group Databasebeta

← #42124935

Subgroups — #42124935

Order 27900.

224 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 43 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×D465C212yesmaximal, complemented
2C31×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
3D155⋊D15—32nomaximal
4C32×C52×C31C2211yescharacteristic, complemented, Hall
5D93⋊D15—52nomaximal
6C31×C3⋊(C5⋊D5)—32no—
7C31×C3⋊(C5⋊D5)—61no—
8C5×D465D312yescomplemented
9C3×C5×D155—32no—
10(C5⋊D5)⋊D31—91noHall
11C31×C3⋊D15—52no—
12C31×C3⋊D15—102no—
13C3×D465D512yescomplemented
14C3×C5×D93—52no—
15C3×C52×C31—21no—
16C3×C52×C31C2×D312yescomplemented
17D15⋊D31—152no—
18D15×D31—152no—
19C31×C5⋊D5—91no—
20C5×D155—32no—
21C32×C5×C31—22no—
22C32×C5×C31C2×D512yescomplemented
23(C3⋊D3)⋊D31—251noHall
24D465D1512yescomplemented
25D15×C31—152no—
26D15×C31—152no—
27D15×C31—304no—
28D15×C31—302no—
29D15×C31—304no—
30C5×D93—52no—
31C3×D155—32no—
32C3×C5×D31—152no—
33D152—311nomaximal, Hall
34C52×C31D3211yescharacteristic, complemented, Hall
35D5×D31—452no—
36C3⋊D3×C31—251no—
37C3×D93—52no—
38C3×C5×C31—24no—
39C3×C5×C31—22no—
40C3×C5×C31—24no—
41C3×C5×C31D3×D512yescomplemented
42C3×C5×C31C2×D1512yescomplemented
43C3⋊(C3⋊(C5⋊D5))D3111yescharacteristic, complemented
44C3×C5×D15—312no—
45D3×D31—752no—
46D155—32no—
47C5×D31—152no—
48D5×C31—452no—
49D5×C31—902no—
50D5×D15—932no—
51C32×C31D5211yescharacteristic, complemented, Hall
52C32×C52C2×D3111yescharacteristic, complemented, Hall
53D93—52no—
54C3×D31—152no—
55D3×C31—752no—
56D3×C31—1501no—
57D3×D15—1552no—
58C5×C31—22no—
59C5×C31D3×D1512yescomplemented
60C3⋊(C5⋊D5)—32no—
61C3⋊(C5⋊D5)—61no—
62C5×D15—312no—
63C3×C5×D5—932no—
64C2×D31—2251noHall
65D52—2791noHall
66C3×C31—21no—
67C3×C31D5×D1512yescomplemented
68C3⋊D15—52no—
69C3⋊D15—102no—
70C3×D15—312no—
71C3×C5×D3—1552no—
72C3×C52—21no—
73C3×C52D3×D3112yescomplemented
74C2×C31—2251no—
75D31—152no—
76C2×D15—4652no—
77D3×D5—4652no—
78C5⋊D5—91no—
79C5×D5—932no—
80C32×C5—22no—
81C32×C5D5×D3112yescomplemented
82D32—7751noHall
83C31D15211yescharacteristic, complemented, Sylow
84C2×C3×C5—4652no—
85D15—152no—
86D15—152no—
87D15—304no—
88D15—302no—
89D15—304no—
90D15—312no—
91C3×D5—932no—
92C5×D3—1552no—
93C52(C3⋊D3)⋊D3111yescharacteristic, complemented, Sylow
94C2×D5—13952no—
95C3⋊D3—251no—
96C3×D3—1552no—
97C3×C5—24no—
98C3×C5—22no—
99C3×C5—24no—
100C3×C5D15×D3112yescomplemented
101C3×C5D15⋊D3112yescomplemented
102C2×D3—23252no—
103C2×C5—4652no—
104D5—452no—
105D5—902no—
106D5—932no—
107C32(C5⋊D5)⋊D3111yescharacteristic, complemented, Sylow
108C2×C3—4652no—
109D3—752no—
110D3—1501no—
111D3—1552no—
112C5—22no—
113C5D93⋊D1512yescomplemented
114C22—69751noSylow
115C3—21no—
116C3D155⋊D1512yescomplemented
117C2—4652no—
118C2—2251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C31C22
LCSG ▷ C32×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×D465C2semidirect
2. C31×C3⋊(C3⋊(C5⋊D5))C2semidirect
4. C32×C52×C31C22semidirect
8. C5×D465D3semidirect
13. C3×D465D5semidirect
16. C3×C52×C31C2×D3semidirect
22. C32×C5×C31C2×D5semidirect
24. D465D15semidirect
34. C52×C31D32semidirect
41. C3×C5×C31D3×D5semidirect
42. C3×C5×C31C2×D15semidirect
43. C3⋊(C3⋊(C5⋊D5))D31semidirect
51. C32×C31D52semidirect
52. C32×C52C2×D31semidirect
59. C5×C31D3×D15semidirect
67. C3×C31D5×D15semidirect
73. C3×C52D3×D31semidirect
81. C32×C5D5×D31semidirect
83. C31D152semidirect
93. C52(C3⋊D3)⋊D31semidirect
100. C3×C5D15×D31semidirect
101. C3×C5D15⋊D31semidirect
107. C32(C5⋊D5)⋊D31semidirect
113. C5D93⋊D15semidirect
116. C3D155⋊D15semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D4652
C31×C3⋊(C3⋊(C5⋊D5))2
D155⋊D153
D93⋊D155
D15231