Finite Group Databasebeta

← C3×#22604926 #42124912

Subgroups — C3×#22604926 #42124912

Order 27900.

224 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C32×C31×C5⋊D5C211yesmaximal, characteristic, complemented
2C3×C5×D465C212yesmaximal, complemented
3#22604926C311yesmaximal, characteristic, direct product factor
4C3×(C5⋊D5)⋊D31—31nomaximal
5C32×C52×C31C2211yescharacteristic, complemented, Hall
6C3×D5×D93—52nomaximal
7C5×D465C2×C312yescomplemented
8C3×C31×C5⋊D5—21no—
9C3×C31×C5⋊D5D311yescharacteristic, complemented
10C3×C31×C5⋊D5C2×C311yescharacteristic, complemented
11C3×C5×D155—32no—
12(C5⋊D5)⋊D31—31noHall
13C3×D465D512yescomplemented
14C3×C5×D93—52no—
15C32×D5×C31—52no—
16C32×D5×C31—102no—
17C3×C52×C31—21no—
18C3×C52×C31C2×D311yescharacteristic, complemented
19C3×C52×C31C22×C311yescharacteristic, complemented
20D5×D93—52no—
21C3×D5×D31—152no—
22C31×C5⋊D5C3×D311yescharacteristic, complemented
23C5×D155—32no—
24C32×C5×C31—22no—
25C32×C5×C31C2×D512yescomplemented
26C2×C3×D93—251noHall
27D465C3×D512yescomplemented
28C5×D93—52no—
29C3×D155—32no—
30C3×D5×C31—52no—
31C3×D5×C31—52no—
32C3×D5×C31—102no—
33C3×D5×C31—102no—
34C3×D5×C31—102no—
35C3×D5×C31—104no—
36C3×C5×D31—152no—
37C3×D15⋊D5—311nomaximal, Hall
38C52×C31C2×C3×D311yescharacteristic, complemented, Hall
39D5×D31—152no—
40C2×C32×C31—251no—
41C3×D93—52no—
42C3×C5×C31—24no—
43C3×C5×C31—22no—
44C3×C5×C31—22no—
45C3×C5×C31—22no—
46C3×C5×C31D3×D512yescomplemented
47C3×C5×C31C2×C3×D512yescomplemented
48C3×C5×D15—312no—
49C32×C5⋊D5D3111yescharacteristic, complemented
50C2×D93—251no—
51C2×C3×D31—751no—
52D155—32no—
53C5×D31—152no—
54D5×C31—52no—
55D5×C31—102no—
56D15⋊D5—311no—
57C3×D52—931no—
58C32×C31D5211yescharacteristic, complemented, Hall
59C32×C52C2×D3111yescharacteristic, complemented, Hall
60C2×C3×C31—251no—
61C2×C3×C31—251no—
62C2×C3×C31—501no—
63D93—52no—
64C3×D31—152no—
65C3×D3×D5—1552no—
66C5×C31—22no—
67C5×C31C3×D3×D512yescomplemented
68C5×D15—312no—
69C3×C5⋊D5—21no—
70C3×C5⋊D5C3×D3111yescharacteristic, complemented
71C3×C5⋊D5D9311yescharacteristic, complemented
72C3×C5×D5—932no—
73C2×D31—751noHall
74D52—931noHall
75C3×C31—21no—
76C3×C31C3×D5211yescharacteristic, complemented
77C3×C31D15⋊D511yescharacteristic, complemented
78C3×D15—312no—
79C3×C5×D3—1552no—
80C32×D5—52no—
81C32×D5—102no—
82C3×C52—21no—
83C3×C52C2×C3×D3111yescharacteristic, complemented
84C3×C52C2×D9311yescharacteristic, complemented
85C2×C31—251no—
86D31—152no—
87C2×C3×D5—4652no—
88D3×D5—1552no—
89C5⋊D5C3×D9311yescharacteristic, complemented
90C5×D5—932no—
91C32×C5—22no—
92C32×C5D5×D3112yescomplemented
93C2×C3×D3—7751noHall
94C31C3×D15⋊D511yescharacteristic, complemented, Sylow
95C2×C3×C5—4652no—
96D15—312no—
97C3×D5—52no—
98C3×D5—52no—
99C3×D5—102no—
100C3×D5—102no—
101C3×D5—102no—
102C3×D5—104no—
103C3×D5—932no—
104C5×D3—1552no—
105C52C2×C3×D9311yescharacteristic, complemented, Sylow
106C2×D5—4652no—
107C2×C32—251no—
108C3×D3—1552no—
109C3×C5—24no—
110C3×C5—22no—
111C3×C5—22no—
112C3×C5—22no—
113C3×C5C3×D5×D3112yescomplemented
114C3×C5D5×D9312yescomplemented
115C22×C3—23251no—
116C2×D3—7751no—
117C2×C5—4652no—
118D5—52no—
119D5—102no—
120D5—932no—
121C32(C5⋊D5)⋊D3111yescharacteristic, complemented, Sylow
122C2×C3—251no—
123C2×C3—251no—
124C2×C3—501no—
125C2×C3—4652no—
126D3—1552no—
127C5—22no—
128C5C3×D5×D9312yescomplemented
129C22—23251noSylow
130C3—21no—
131C3C3×(C5⋊D5)⋊D3111yescharacteristic, complemented
132C3#2260492611yescharacteristic, direct product factor
133C2—251no—
134C2—4652no—
subgroupG/H
center, hypercenterC3#22604926
commutator, cosocle, hypocenterC3×C52×C31C22×C3
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C3×C52×C31
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C31×C5⋊D5C2semidirect
2. C3×C5×D465C2semidirect
3. #22604926C3direct (N × H)
5. C32×C52×C31C22semidirect
7. C5×D465C2×C3semidirect
9. C3×C31×C5⋊D5D3semidirect
10. C3×C31×C5⋊D5C2×C3semidirect
13. C3×D465D5semidirect
18. C3×C52×C31C2×D3semidirect
19. C3×C52×C31C22×C3semidirect
22. C31×C5⋊D5C3×D3semidirect
25. C32×C5×C31C2×D5semidirect
27. D465C3×D5semidirect
38. C52×C31C2×C3×D3semidirect
46. C3×C5×C31D3×D5semidirect
47. C3×C5×C31C2×C3×D5semidirect
49. C32×C5⋊D5D31semidirect
58. C32×C31D52semidirect
59. C32×C52C2×D31semidirect
67. C5×C31C3×D3×D5semidirect
70. C3×C5⋊D5C3×D31semidirect
71. C3×C5⋊D5D93semidirect
76. C3×C31C3×D52semidirect
77. C3×C31D15⋊D5semidirect
83. C3×C52C2×C3×D31semidirect
84. C3×C52C2×D93semidirect
89. C5⋊D5C3×D93semidirect
92. C32×C5D5×D31semidirect
94. C31C3×D15⋊D5semidirect
105. C52C2×C3×D93semidirect
113. C3×C5C3×D5×D31semidirect
114. C3×C5D5×D93semidirect
121. C32(C5⋊D5)⋊D31semidirect
128. C5C3×D5×D93semidirect
131. C3C3×(C5⋊D5)⋊D31semidirect
132. C3#22604926direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C31×C5⋊D52
C3×C5×D4652
#226049263
C3×(C5⋊D5)⋊D313
C3×D5×D935
C3×D15⋊D531