Finite Group Databasebeta

← C32×D4×Dic5 #13087856

Subgroups — C32×D4×Dic5 #13087856

Order 1440.

564 conjugacy classes of subgroups; only the 306 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 306 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
1C2×C32×C5×D4C211yesmaximal, characteristic
2C22×C32×Dic5C212yesmaximal, complemented
3C32×C22⋊Dic5C212yesmaximal, complemented
4C32×C4⋊Dic5C211yesmaximal, characteristic, complemented
5C32×C4×Dic5C211yesmaximal, characteristic, complemented
6C3×D4×Dic5C314yesmaximal, direct product factor
7C23×C32×C5C2212yes—
8C32×C5×D4C414yescomplemented
9C2×C32×C4×C5C2211yescharacteristic
10C2×C32×Dic5—24no—
11C2×C32×Dic5C2211yescharacteristic
12C2×C32×Dic5C2212yes—
13C2×C32×Dic5C2211yescharacteristic
14C32×C4×D4—51nomaximal, Hall
15C2×C3×C5×D4C2×C314yes—
16C22×C3×Dic5C2×C318yescomplemented
17C3×C22⋊Dic5C2×C318yescomplemented
18C3×C4⋊Dic5C2×C314yescomplemented
19C3×C4×Dic5C2×C314yescomplemented
20C22×C32×C5—22no—
21C22×C32×C5—22no—
22C22×C32×C5C2×C414yescomplemented
23C22×C32×C5C2311yescharacteristic
24C32×C4×C5C2×C412yescomplemented
25C32×Dic5—22no—
26C32×Dic5—21no—
27C32×Dic5D412yesdirect product factor
28D4×Dic5C3211yescharacteristic, direct product factor, Hall
29C2×C32×D4D511yescharacteristic
30C22×C32×C4—52no—
31C32×C4⋊C4—51no—
32C32×C22⋊C4—52no—
33C32×C42—51no—
34C23×C3×C5C22×C318yes—
35C3×C5×D4C3×C4116yescomplemented
36C2×C3×C4×C5C22×C314yes—
37C2×C3×Dic5—216no—
38C2×C3×Dic5C22×C314yes—
39C2×C3×Dic5C22×C318yes—
40C2×C3×Dic5C22×C314yes—
41C3×C4×D4—54no—
42C2×C32×C5—24no—
43C2×C32×C5C22×C411yescharacteristic
44C2×C32×C5C2×D411yescharacteristic
45C2×C32×C5#4111yescharacteristic
46C2×C5×D4C2×C3211yescharacteristic
47C22×Dic5C2×C3212yescomplemented
48C22⋊Dic5C2×C3212yescomplemented
49C4⋊Dic5C2×C3211yescharacteristic, complemented
50C4×Dic5C2×C3211yescharacteristic, complemented
51C23×C32C2×D512yes—
52C32×D4Dic514yesdirect product factor
53C2×C32×C4—51no—
54C2×C32×C4—51no—
55C2×C32×C4—52no—
56C2×C32×C4—104no—
57C2×C32×C4C2×D511yescharacteristic
58C22×C3×C5—28no—
59C22×C3×C5—28no—
60C22×C3×C5C2×C3×C4116yescomplemented
61C22×C3×C5C23×C314yes—
62C3×C4×C5C2×C3×C418yescomplemented
63C3×Dic5—28no—
64C3×Dic5—24no—
65C3×Dic5C3×D418yesdirect product factor
66C2×C3×D4C3×D514yes—
67C22×C3×C4—58no—
68C3×C4⋊C4—54no—
69C3×C22⋊C4—58no—
70C3×C42—54no—
71C32×C5C4×D411yescharacteristic, complemented, Hall
72C23×C5C22×C3212yes—
73C5×D4C32×C414yescomplemented
74C2×C4×C5C22×C3211yescharacteristic
75C2×Dic5—24no—
76C2×Dic5C22×C3211yescharacteristic
77C2×Dic5C22×C3212yes—
78C2×Dic5C22×C3211yescharacteristic
79C22×C32—22no—
80C22×C32—22no—
81C22×C32C2×Dic514yescomplemented
82C22×C32C22×D511yescharacteristic
83C32×C4—52no—
84C32×C4—102no—
85C32×C4—101no—
86C32×C4C2×Dic512yescomplemented
87C4×D4—51noSylow
88C2×C3×C5—216no—
89C2×C3×C5C22×C3×C414yes—
90C2×C3×C5C2×C3×D414yes—
91C2×C3×C5C3×#4114yes—
92C23×C3C2×C3×D518yes—
93C3×D4C3×Dic5116yesdirect product factor
94C2×C3×C4—54no—
95C2×C3×C4—54no—
96C2×C3×C4—58no—
97C2×C3×C4—1016no—
98C2×C3×C4C2×C3×D514yes—
99C22×C5—22no—
100C22×C5—22no—
101C22×C5C2×C32×C414yescomplemented
102C22×C5C23×C3211yescharacteristic
103C4×C5C2×C32×C412yescomplemented
104Dic5—22no—
105Dic5—21no—
106Dic5C32×D412yesdirect product factor
107C2×C32—24no—
108C2×C32D4×D511yescharacteristic
109C2×C32#71111yescharacteristic
110C2×C32C22×Dic511yescharacteristic
111C2×D4C32×D511yescharacteristic
112C22×C4—52no—
113C4⋊C4—51no—
114C22⋊C4—52no—
115C42—51no—
116C3×C5C3×C4×D414yescomplemented
117C22×C3—28no—
118C22×C3—28no—
119C22×C3C2×C3×Dic5116yescomplemented
120C22×C3C22×C3×D514yes—
121C3×C4—58no—
122C3×C4—108no—
123C3×C4—104no—
124C3×C4C2×C3×Dic518yescomplemented
125C2×C5—24no—
126C2×C5C22×C32×C411yescharacteristic
127C2×C5C2×C32×D411yescharacteristic
128C2×C5C32×#4111yescharacteristic
129C32D4×Dic511yescharacteristic, direct product factor, Sylow
130C23C2×C32×D512yes—
131D4C32×Dic514yesdirect product factor
132C2×C4—51no—
133C2×C4—51no—
134C2×C4—52no—
135C2×C4—104no—
136C2×C4C2×C32×D511yescharacteristic
137C2×C3—216no—
138C2×C3C3×D4×D514yes—
139C2×C3C3×#71114yes—
140C2×C3C22×C3×Dic514yes—
141C5C32×C4×D411yescharacteristic, complemented, Sylow
142C22—22no—
143C22—22no—
144C22C2×C32×Dic514yescomplemented
145C22C22×C32×D511yescharacteristic
146C4—52no—
147C4—102no—
148C4—101no—
149C4C2×C32×Dic512yescomplemented
150C3C3×D4×Dic514yesdirect product factor
151C2—24no—
152C2C32×D4×D511yescharacteristic
153C2C32×#71111yescharacteristic
154C2C22×C32×Dic511yescharacteristic
subgroupG/H
centerC22×C32C22×D5
commutatorC2×C5C22×C32×C4
FrattiniC22C22×C32×D5
Fitting, prime radicalC2×C32×C5×D4C2
socleC22×C32×C5C23
cosocleC22×C5C23×C32
hypercenterC2×C32×D4D5
hypocenterC5C32×C4×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C32 ◁ C2×C32×D4

Complements

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

NH ≅ G/Ntype
2. C22×C32×Dic5C2semidirect
3. C32×C22⋊Dic5C2semidirect
4. C32×C4⋊Dic5C2semidirect
5. C32×C4×Dic5C2semidirect
6. C3×D4×Dic5C3direct (N × H)
8. C32×C5×D4C4semidirect
16. C22×C3×Dic5C2×C3semidirect
17. C3×C22⋊Dic5C2×C3semidirect
18. C3×C4⋊Dic5C2×C3semidirect
19. C3×C4×Dic5C2×C3semidirect
22. C22×C32×C5C2×C4semidirect
24. C32×C4×C5C2×C4semidirect
27. C32×Dic5D4direct (N × H)
28. D4×Dic5C32direct (N × H)
35. C3×C5×D4C3×C4semidirect
47. C22×Dic5C2×C32semidirect
48. C22⋊Dic5C2×C32semidirect
49. C4⋊Dic5C2×C32semidirect
50. C4×Dic5C2×C32semidirect
52. C32×D4Dic5direct (N × H)
60. C22×C3×C5C2×C3×C4semidirect
62. C3×C4×C5C2×C3×C4semidirect
65. C3×Dic5C3×D4direct (N × H)
71. C32×C5C4×D4semidirect
73. C5×D4C32×C4semidirect
81. C22×C32C2×Dic5semidirect
86. C32×C4C2×Dic5semidirect
93. C3×D4C3×Dic5direct (N × H)
101. C22×C5C2×C32×C4semidirect
103. C4×C5C2×C32×C4semidirect
106. Dic5C32×D4direct (N × H)
116. C3×C5C3×C4×D4semidirect
119. C22×C3C2×C3×Dic5semidirect
124. C3×C4C2×C3×Dic5semidirect
129. C32D4×Dic5direct (N × H)
131. D4C32×Dic5direct (N × H)
141. C5C32×C4×D4semidirect
144. C22C2×C32×Dic5semidirect
149. C4C2×C32×Dic5semidirect
150. C3C3×D4×Dic5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×D42
C22×C32×Dic52
C32×C22⋊Dic52
C32×C4⋊Dic52
C32×C4×Dic52
C3×D4×Dic53
C32×C4×D45