Finite Group Databasebeta

← C3×C31×D15⋊D5 #42124911

Subgroups — C3×C31×D15⋊D5 #42124911

Order 27900.

224 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 60 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×D15×C31C212yesmaximal, complemented
3C31×D15⋊D5C311yesmaximal, characteristic, direct product factor
4C3×D52×C31—31nomaximal
5C32×C52×C31C2211yescharacteristic, complemented, Hall
6C3×D3×D5×C31—52nomaximal
7C5×D15×C31C2×C312yescomplemented
8C3×C31×C5⋊D5—21no—
9C3×C31×C5⋊D5D311yescharacteristic, complemented
10C3×C31×C5⋊D5C2×C311yescharacteristic, complemented
11C3×C5×D5×C31—32no—
12D52×C31—31noHall
13C3×D15×C31D512yescomplemented
14C3×C5×D3×C31—52no—
15C32×D5×C31—52no—
16C32×D5×C31—102no—
17C3×C52×C31—21no—
18C3×C52×C31C2×D311yescharacteristic, complemented
19C3×C52×C31C22×C311yescharacteristic, complemented
20C2×C3×D5×C31—152no—
21D3×D5×C31—52no—
22C31×C5⋊D5C3×D311yescharacteristic, complemented
23C5×D5×C31—32no—
24C32×C5×C31—22no—
25C32×C5×C31C2×D512yescomplemented
26C2×C3×D3×C31—251noHall
27C2×C3×C5×C31—152no—
28D15×C31C3×D512yescomplemented
29C5×D3×C31—52no—
30C3×D5×C31—32no—
31C3×D5×C31—52no—
32C3×D5×C31—52no—
33C3×D5×C31—102no—
34C3×D5×C31—102no—
35C3×D5×C31—102no—
36C3×D5×C31—104no—
37C3×D15⋊D5C3111yesmaximal, characteristic, direct product factor, Hall
38C52×C31C2×C3×D311yescharacteristic, complemented, Hall
39C2×D5×C31—152no—
40C2×C32×C31—251no—
41C3×D3×C31—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×D15C2×C3112yescomplemented
49C32×C5⋊D5C2×C3111yescharacteristic, complemented
50C22×C3×C31—751no—
51C2×D3×C31—251no—
52C2×C5×C31—152no—
53D5×C31—32no—
54D5×C31—52no—
55D5×C31—102no—
56D15⋊D5C3×C3111yescharacteristic, direct product factor
57C3×D52—31no—
58C32×C31D5211yescharacteristic, complemented, Hall
59C32×C52C22×C3111yescharacteristic, complemented, Hall
60C2×C3×C31—152no—
61C2×C3×C31—251no—
62C2×C3×C31—251no—
63C2×C3×C31—501no—
64D3×C31—52no—
65C3×D3×D5—52no—
66C5×C31—22no—
67C5×C31C3×D3×D512yescomplemented
68C5×D15C2×C3×C3112yescomplemented
69C3×C5⋊D5—21no—
70C3×C5⋊D5D3×C3111yescharacteristic, complemented
71C3×C5⋊D5C2×C3×C3111yescharacteristic, complemented
72C3×C5×D5—32no—
73C22×C31—751noHall
74D52—31noHall
75C3×C31—21no—
76C3×C31C3×D5211yescharacteristic, complemented
77C3×C31D15⋊D511yescharacteristic, direct product factor
78C3×D15D5×C3112yescomplemented
79C3×C5×D3—52no—
80C32×D5—52no—
81C32×D5—102no—
82C3×C52—21no—
83C3×C52C2×D3×C3111yescharacteristic, complemented
84C3×C52C22×C3×C3111yescharacteristic, complemented
85C2×C31—152no—
86C2×C31—251no—
87C2×C3×D5—152no—
88D3×D5—52no—
89C5⋊D5C3×D3×C3111yescharacteristic, complemented
90C5×D5—32no—
91C32×C5—22no—
92C32×C5C2×D5×C3112yescomplemented
93C2×C3×D3—251noHall
94C31C3×D15⋊D511yescharacteristic, direct product factor, Sylow
95C2×C3×C5—152no—
96D15C3×D5×C3112yescomplemented
97C3×D5—32no—
98C3×D5—52no—
99C3×D5—52no—
100C3×D5—102no—
101C3×D5—102no—
102C3×D5—102no—
103C3×D5—104no—
104C5×D3—52no—
105C52C2×C3×D3×C3111yescharacteristic, complemented, Sylow
106C2×D5—152no—
107C2×C32—251no—
108C3×D3—52no—
109C3×C5—24no—
110C3×C5—22no—
111C3×C5—22no—
112C3×C5—22no—
113C3×C5D3×D5×C3112yescomplemented
114C3×C5C2×C3×D5×C3112yescomplemented
115C22×C3—751no—
116C2×D3—251no—
117C2×C5—152no—
118D5—32no—
119D5—52no—
120D5—102no—
121C32D52×C3111yescharacteristic, complemented, Sylow
122C2×C3—152no—
123C2×C3—251no—
124C2×C3—251no—
125C2×C3—501no—
126D3—52no—
127C5—22no—
128C5C3×D3×D5×C3112yescomplemented
129C22—751noSylow
130C3—21no—
131C3C3×D52×C3111yescharacteristic, complemented
132C3C31×D15⋊D511yescharacteristic, direct product factor
133C2—152no—
134C2—251no—
subgroupG/H
center, hypercenterC3×C31D15⋊D5
commutator, cosocle, hypocenterC3×C52C22×C3×C31
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C3×C52
UCSC1 ◁ C3×C31

Complements

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

NH ≅ G/Ntype
1. C32×C31×C5⋊D5C2semidirect
2. C3×C5×D15×C31C2semidirect
3. C31×D15⋊D5C3direct (N × H)
5. C32×C52×C31C22semidirect
7. C5×D15×C31C2×C3semidirect
9. C3×C31×C5⋊D5D3semidirect
10. C3×C31×C5⋊D5C2×C3semidirect
13. C3×D15×C31D5semidirect
18. C3×C52×C31C2×D3semidirect
19. C3×C52×C31C22×C3semidirect
22. C31×C5⋊D5C3×D3semidirect
25. C32×C5×C31C2×D5semidirect
28. D15×C31C3×D5semidirect
37. C3×D15⋊D5C31direct (N × H)
38. C52×C31C2×C3×D3semidirect
46. C3×C5×C31D3×D5semidirect
47. C3×C5×C31C2×C3×D5semidirect
48. C3×C5×D15C2×C31semidirect
49. C32×C5⋊D5C2×C31semidirect
56. D15⋊D5C3×C31direct (N × H)
58. C32×C31D52semidirect
59. C32×C52C22×C31semidirect
67. C5×C31C3×D3×D5semidirect
68. C5×D15C2×C3×C31semidirect
70. C3×C5⋊D5D3×C31semidirect
71. C3×C5⋊D5C2×C3×C31semidirect
76. C3×C31C3×D52semidirect
77. C3×C31D15⋊D5direct (N × H)
78. C3×D15D5×C31semidirect
83. C3×C52C2×D3×C31semidirect
84. C3×C52C22×C3×C31semidirect
89. C5⋊D5C3×D3×C31semidirect
92. C32×C5C2×D5×C31semidirect
94. C31C3×D15⋊D5direct (N × H)
96. D15C3×D5×C31semidirect
105. C52C2×C3×D3×C31semidirect
113. C3×C5D3×D5×C31semidirect
114. C3×C5C2×C3×D5×C31semidirect
121. C32D52×C31semidirect
128. C5C3×D3×D5×C31semidirect
131. C3C3×D52×C31semidirect
132. C3C31×D15⋊D5direct (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×D15×C312
C31×D15⋊D53
C3×D52×C313
C3×D3×D5×C315
C3×D15⋊D531