Finite Group Databasebeta

← #13087729

Subgroups — #13087729

Order 1440.

312 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C5×#3830C211yesmaximal, characteristic, complemented
2#10624227C211yesmaximal, characteristic, complemented
3C3×#6715C212yesmaximal, complemented
4#10623823C212yesmaximal, complemented
5#10623820C211yesmaximal, characteristic, complemented
6#91480—32nomaximal
7C2×(C3⋊D3)⋊D5—21no—
8C32×C5×D4C2211yescharacteristic, complemented
9C5×#638—21no—
10C2×C5×C3⋊Dic3—21no—
11C4×C5×C3⋊D3C2211yescharacteristic
12C5×#634C2211yescharacteristic, complemented
13C3×D60C2212yes—
14#67157—21no—
15C3×C3⋊#168C2212yescomplemented
16#63927—51nomaximal, Hall
17C5×#237—32no—
18C5×#237—61no—
19D3×D20—32no—
20#6715D312yescomplemented
21C3×#686—32no—
22#6660—32no—
23#6655—32no—
24#6650—32no—
25C22×C32×C5—21no—
26C2×C5×C3⋊D3D411yescharacteristic
27C2×C3×D15—22no—
28(C3⋊D3)⋊D5—42no—
29C32×C4×C5C2311yescharacteristic
30C5×C3⋊Dic3—21no—
31C5×C3⋊Dic3D411yescharacteristic
32#4095—91noHall
33#3830D511yescharacteristic, complemented
34#3802—51no—
35C3×#213—52no—
36#3716—52no—
37#3712—51no—
38C2×D3×D5—62no—
39C3×C5×D4—21no—
40C3×C5×D4C2×D312yescomplemented
41D60C2×D312yes—
42C5×#67—62no—
43C5×#67—62no—
44C2×C5×Dic3—62no—
45C2×C5×Dic3—62no—
46C4×C5×D3—32no—
47C4×C5×D3—61no—
48C5×Dic6—32no—
49C5×Dic6—61no—
50C3×D20—32no—
51#1202—62no—
52C3⋊#168C2×D312yescomplemented
53C3×#168—32no—
54#911—152no—
55C2×C32×C5—41no—
56C2×C32×C5C2×D411yescharacteristic
57C5×C3⋊D3—21no—
58C3×D15—42no—
59C5×#41—91no—
60C2×D20—91no—
61#688—92no—
62#686—32no—
63#681—91no—
64C2×D32—101no—
65C32×D4C2×D511yescharacteristic, complemented
66#638—21no—
67C2×C3⋊Dic3—21no—
68C4×C3⋊D3C2×D511yescharacteristic
69#634C2×D511yescharacteristic, complemented
70C3×D12—52no—
71#625—101no—
72C3×C3⋊C8—52no—
73C22×C3×C5—22no—
74C22×C3×C5—22no—
75C2×D15—22no—
76C2×C5×D3—32no—
77C2×C5×D3—61no—
78C2×C3×D5—62no—
79D3×D5—124no—
80C3×C4×C5—21no—
81C3×C4×C5C22×D312yes—
82C5×Dic3—32no—
83C5×Dic3—61no—
84C5×Dic3—62no—
85C5×Dic3—62no—
86#237—32no—
87#237—61no—
88D3×D4—152no—
89C3×D8—152no—
90#214—152no—
91#213—52no—
92#204—152no—
93ΓL(1,𝔽25)—152no—
94C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
95C22×D5—181no—
96C5×Q8—91no—
97C5×D4—181no—
98C5×D4D3211yescharacteristic, complemented
99C2×C4×C5—91no—
100C2×C4×C5—181no—
101D20—32no—
102D20—181no—
103#168—32no—
104C22×C32—21no—
105C2×C3⋊D3C22⋊D511yescharacteristic
106C2×C3×D3—102no—
107D32—202no—
108C32×C4C22×D511yescharacteristic
109C3⋊Dic3—21no—
110C3⋊Dic3C22⋊D511yescharacteristic
111AGL(1,ℤ/8)—451noSylow
112C2×C3×C5—21no—
113C2×C3×C5—42no—
114C2×C3×C5—42no—
115C2×C3×C5D3×D412yes—
116D15—42no—
117C3×D5—122no—
118C5×D3—62no—
119C5×D3—121no—
120C22×D3—302no—
121C3×D4—21no—
122C3×D4—152no—
123C3×D4D3×D512yescomplemented
124#67—62no—
125#67—62no—
126#67—302no—
127C2×Dic3—62no—
128C2×Dic3—62no—
129D12—52no—
130C4×D3—32no—
131C4×D3—61no—
132Dic6—32no—
133Dic6—61no—
134C3×C8—152no—
135C3⋊C8—52no—
136C22×C5—21no—
137C22×C5—91no—
138C2×D5—62no—
139C2×D5—362no—
140C4×C5—91no—
141C4×C5—181no—
142C4×C5C2×D3211yescharacteristic
143C2×C32—41no—
144C2×C32C2×C22⋊D511yescharacteristic
145C3⋊D3—21no—
146C3×D3—202no—
147#41—91no—
148C2×D4—451no—
149SD16—452no—
150D8—152no—
151M16—451no—
152C3×C5—21no—
153C3×C5#91112yescomplemented
154C22×C3—22no—
155C22×C3—22no—
156C22×C3—302no—
157C2×D3—32no—
158C2×D3—61no—
159C2×D3—102no—
160C2×D3—604no—
161C3×C4—21no—
162C3×C4C2×D3×D512yes—
163Dic3—32no—
164Dic3—61no—
165Dic3—62no—
166Dic3—62no—
167C2×C5—41no—
168C2×C5—181no—
169C2×C5#381111yescharacteristic
170D5—122no—
171C32#409511yescharacteristic, complemented, Sylow
172C23—901no—
173Q8—91no—
174D4—152no—
175D4—181no—
176D4—901no—
177D4(C3⋊D3)⋊D511yescharacteristic, complemented
178C2×C4—91no—
179C2×C4—181no—
180C8—152no—
181C2×C3—21no—
182C2×C3—42no—
183C2×C3—42no—
184C2×C3—602no—
185C2×C3D3×C22⋊D512yes—
186D3—62no—
187D3—121no—
188D3—202no—
189C5#6392711yescharacteristic, complemented, Sylow
190C22—21no—
191C22—91no—
192C22—302no—
193C22—1802no—
194C4—91no—
195C4—181no—
196C4C2×(C3⋊D3)⋊D511yescharacteristic
197C3—21no—
198C3#9148012yescomplemented
199C2—41no—
200C2—181no—
201C2—602no—
202C2#1062423611yescharacteristic
subgroupG/H
centerC2#10624236
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×(C3⋊D3)⋊D5
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
hypercenterD4(C3⋊D3)⋊D5
hypocenterC32×C5AGL(1,ℤ/8)
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C5×#3830C2semidirect
2. #10624227C2semidirect
3. C3×#6715C2semidirect
4. #10623823C2semidirect
5. #10623820C2semidirect
8. C32×C5×D4C22semidirect
12. C5×#634C22semidirect
15. C3×C3⋊#168C22semidirect
20. #6715D3semidirect
33. #3830D5semidirect
40. C3×C5×D4C2×D3semidirect
52. C3⋊#168C2×D3semidirect
65. C32×D4C2×D5semidirect
69. #634C2×D5semidirect
94. C32×C5AGL(1,ℤ/8)semidirect
98. C5×D4D32semidirect
123. C3×D4D3×D5semidirect
153. C3×C5#911semidirect
171. C32#4095semidirect
177. D4(C3⋊D3)⋊D5semidirect
189. C5#63927semidirect
198. C3#91480semidirect

Maximal subgroups

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

subgroupindex
C5×#38302
#106242272
C3×#67152
#106238232
#106238202
#914803
#639275