Finite Group Databasebeta

← #13085785

Subgroups — #13085785

Order 1440.

312 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 58 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×#3802C211yesmaximal, characteristic, complemented
2#10624152C211yesmaximal, characteristic, complemented
3#10623820C211yesmaximal, characteristic, complemented
4#10623800C212yesmaximal, complemented
5C3×#6656C212yesmaximal, complemented
6#91496—32nomaximal
7C2×C5×D32—21no—
8C4⋊(C3⋊D15)C2211yescharacteristic, complemented
9C4×C5×C3⋊D3C2211yescharacteristic
10C3×C5×D12C2212yes—
11C32×Dic10C2211yescharacteristic, complemented
12C5×#625—21no—
13#67140—21no—
14#67137—21no—
15C3×C3⋊#168C2212yescomplemented
16#63941—51nomaximal, Hall
17C5×D3×D4—32no—
18#6769—32no—
19#6769—61no—
20#6715—32no—
21C3×#687—32no—
22#6656D312yescomplemented
23#6654—32no—
24#6650—32no—
25C2×C3⋊D15—21no—
26C2×C5×C3⋊D3D411yescharacteristic
27C2×C3×C5×D3—22no—
28C5×D32—42no—
29C32×C4×C5C2311yescharacteristic
30C5×C3⋊Dic3D411yescharacteristic
31C32×Dic5—21no—
32#4078—91noHall
33#3832—51no—
34#3802D511yescharacteristic, complemented
35C3×#215—52no—
36#3714—52no—
37#3712—51no—
38C22×C5×D3—62no—
39C3×C5×D4—32no—
40D60—32no—
41D60—61no—
42C5×#67—62no—
43C5×D12C2×D312yes—
44C4×C5×D3—32no—
45C4×C5×D3—61no—
46C3×Dic10—21no—
47C3×Dic10C2×D312yescomplemented
48#1203—62no—
49#1203—62no—
50#1200—62no—
51#1200—62no—
52C3⋊#168C2×D312yescomplemented
53C3×#168—32no—
54#914—152no—
55C2×C32×C5C2×D411yescharacteristic
56C3⋊D15—41no—
57C5×C3⋊D3—21no—
58C3×C5×D3—42no—
59C2×C5×D4—91no—
60#709—91no—
61#687—32no—
62#686—92no—
63#681—91no—
64C2×D32—21no—
65C32×Q8—51no—
66C4⋊(C3⋊D3)—51no—
67C4⋊(C3⋊D3)—101no—
68C4×C3⋊D3—101no—
69C4×C3⋊D3C2×D511yescharacteristic
70C3×D12C2×D512yes—
71#625—21no—
72C3×C3⋊C8—52no—
73C22×C3×C5—62no—
74C2×D15—62no—
75C2×D15—62no—
76C2×C5×D3—22no—
77C2×C5×D3—32no—
78C2×C5×D3—61no—
79C2×C5×D3—124no—
80C3×C4×C5—21no—
81C3×C4×C5C22×D312yes—
82C3×Dic5—22no—
83C3×Dic5—22no—
84C5×Dic3—32no—
85C5×Dic3—61no—
86#239—152no—
87#239—301no—
88D3×D4—32no—
89C3×SD16—152no—
90#215—52no—
91#213—152no—
92D24—152no—
93ΓL(1,𝔽25)—152no—
94C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
95C23×C5—181no—
96C5×D4—32no—
97C5×D4—181no—
98C2×C4×C5—91no—
99C22⋊D5—181no—
100D20—91no—
101C4×D5—181no—
102Dic10D3211yescharacteristic, complemented
103#168—32no—
104C2×C3⋊D3—101no—
105C2×C3⋊D3C22⋊D511yescharacteristic
106C2×C3×D3—22no—
107D32—42no—
108C32×C4—101no—
109C32×C4C22×D511yescharacteristic
110C3⋊Dic3C22⋊D511yescharacteristic
111AGL(1,ℤ/8)—451noSylow
112C2×C3×C5—21no—
113C2×C3×C5—122no—
114C2×C3×C5D3×D412yes—
115D15—122no—
116D15—122no—
117C5×D3—42no—
118C5×D3—62no—
119C5×D3—121no—
120C22×D3—62no—
121C3×Q8—52no—
122C3×Q8—101no—
123C3×D4—32no—
124#67—62no—
125D12—152no—
126D12—301no—
127D12—302no—
128D12—302no—
129D12D3×D512yes—
130C4×D3—32no—
131C4×D3—61no—
132C4×D3—302no—
133C4×D3—302no—
134C3×C8—152no—
135C3⋊C8—52no—
136C22×C5—62no—
137C22×C5—91no—
138C22×C5—362no—
139C2×D5—181no—
140C4×C5—91no—
141C4×C5C2×D3211yescharacteristic
142Dic5—21no—
143C2×C32C2×C22⋊D511yescharacteristic
144C3⋊D3—21no—
145C3⋊D3—201no—
146C3×D3—42no—
147#41—451no—
148C2×D4—91no—
149SD16—152no—
150D8—452no—
151M16—451no—
152C3×C5—21no—
153C3×C5#91412yescomplemented
154C22×C3—62no—
155C2×D3—22no—
156C2×D3—32no—
157C2×D3—61no—
158C2×D3—124no—
159C2×D3—302no—
160C2×D3—302no—
161C3×C4—21no—
162C3×C4—102no—
163C3×C4—102no—
164C3×C4C2×D3×D512yes—
165Dic3—32no—
166Dic3—61no—
167C2×C5—122no—
168C2×C5—181no—
169C2×C5#381111yescharacteristic
170D5—361no—
171C32#407811yescharacteristic, complemented, Sylow
172C23—181no—
173Q8—51no—
174D4—32no—
175D4—181no—
176D4—451no—
177D4—901no—
178C2×C4—91no—
179C2×C4—901no—
180C8—152no—
181C2×C3—21no—
182C2×C3—122no—
183C2×C3D3×C22⋊D512yes—
184D3—42no—
185D3—62no—
186D3—121no—
187D3—602no—
188D3—602no—
189C5#6394111yescharacteristic, complemented, Sylow
190C22—62no—
191C22—91no—
192C22—362no—
193C22—901no—
194C4—91no—
195C4—101no—
196C4D32×D511yescharacteristic
197C3—21no—
198C3#9149612yescomplemented
199C2—122no—
200C2—181no—
201C2—1801no—
202C2#1062402911yescharacteristic
subgroupG/H
centerC2#10624029
commutator, Fitting, cosocleC32×C4×C5C23
Frattini, hypercenterC4D32×D5
socleC2×C32×C5C2×D4
hypocenterC32×C5AGL(1,ℤ/8)
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C5×#3802C2semidirect
2. #10624152C2semidirect
3. #10623820C2semidirect
4. #10623800C2semidirect
5. C3×#6656C2semidirect
8. C4⋊(C3⋊D15)C22semidirect
11. C32×Dic10C22semidirect
15. C3×C3⋊#168C22semidirect
22. #6656D3semidirect
34. #3802D5semidirect
47. C3×Dic10C2×D3semidirect
52. C3⋊#168C2×D3semidirect
94. C32×C5AGL(1,ℤ/8)semidirect
102. Dic10D32semidirect
153. C3×C5#914semidirect
171. C32#4078semidirect
189. C5#63941semidirect
198. C3#91496semidirect

Maximal subgroups

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

subgroupindex
C5×#38022
#106241522
#106238202
#106238002
C3×#66562
#914963
#639415