Finite Group Databasebeta

← A4×D60 #13089113

Subgroups — A4×D60 #13089113

Order 1440.

276 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 45 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×A4×D15C212yesmaximal, complemented
2C3×C4×C5×A4C211yesmaximal, characteristic, complemented
3C22×D60C311yesmaximal, characteristic, complemented
4A4×D20—31nomaximal
5C2×C3×C5×A4C2211yescharacteristic
6A4×D15—22no—
7C3×D60—41nomaximal
8A4×D12—51nomaximal, Hall
9C23×D15C2×C312yescomplemented
10C2×D5×A4—32no—
11C22×C3×C4×C5C2×C311yescharacteristic, complemented
12C2×D60—31no—
13C2×D60—32no—
14C2×D60—31no—
15C4×C5×A4—21no—
16C4×C5×A4D311yescharacteristic, complemented
17C2×C3×D15—42no—
18C3×C5×A4D411yescharacteristic, complemented
19C32×C4×C5—41no—
20C22×D20—31noHall
21C2×D3×A4—52no—
22C3×C4×A4D511yescharacteristic, complemented
23C23×C3×C5C22×C311yescharacteristic
24C22×D15—22no—
25C22×D15—32no—
26C22×D15—32no—
27C22×D15—62no—
28C2×C5×A4—21no—
29C2×C5×A4C2×D311yescharacteristic
30D5×A4—62no—
31C2×C3×C4×C5—31no—
32C2×C3×C4×C5—31no—
33D60—32no—
34D60—32no—
35D60—31no—
36D60A411yescharacteristic, direct product factor
37C3×D20—121no—
38C22×D12—51no—
39D4×A4—151no—
40C2×C32×C5—41no—
41C3×D15—82no—
42C23×D5—32no—
43C22×C4×C5C3×D311yescharacteristic, complemented
44C2×D20—91no—
45C2×D20—92no—
46C2×D20—91no—
47C2×C3×A4C2×D511yescharacteristic
48D3×A4—102no—
49C3×D12—201no—
50C22×C3×C5—31no—
51C22×C3×C5—31no—
52C22×C3×C5C3×D411yescharacteristic, complemented
53C2×D15—32no—
54C2×D15—62no—
55C2×D15—62no—
56C2×D15—62no—
57C2×D15—62no—
58C2×D15C2×A412yescomplemented
59C2×C3×D5—122no—
60C5×A4—21no—
61C5×A4D1211yescharacteristic, complemented
62C3×C4×C5—31no—
63C3×C4×C5—41no—
64C3×C4×C5—81no—
65C3×C4×C5C2×A411yescharacteristic, complemented
66C23×D3—52no—
67C22×A4—152no—
68C22×C3×C4C3×D511yescharacteristic, complemented
69C2×D12—151no—
70C2×D12—152no—
71C2×D12—151no—
72C4×A4—21no—
73C4×A4D1511yescharacteristic, complemented
74C32×C5—41noHall
75C23×C5C2×C3×D311yescharacteristic
76C22×D5—62no—
77C22×D5—92no—
78C22×D5—92no—
79C22×D5—182no—
80C2×C4×C5—31no—
81C2×C4×C5—31no—
82D20—31no—
83D20—92no—
84D20—92no—
85D20—91no—
86C2×C3×D3—202no—
87C3×A4D2011yescharacteristic, complemented
88C32×C4—41no—
89C22×D4—151noSylow
90C2×C3×C5—31no—
91C2×C3×C5—31no—
92C2×C3×C5—41no—
93C2×C3×C5—81no—
94C2×C3×C5C22×A411yescharacteristic
95D15—22no—
96D15—62no—
97C3×D5—242no—
98C23×C3C2×C3×D511yescharacteristic
99C22×D3—102no—
100C22×D3—152no—
101C22×D3—152no—
102C22×D3—302no—
103C2×A4—21no—
104C2×A4—302no—
105C2×A4C2×D1511yescharacteristic
106C3×D4—601no—
107C2×C3×C4—31no—
108C2×C3×C4—31no—
109D12—51no—
110D12—152no—
111D12—152no—
112D12—151no—
113C22×C5—31no—
114C22×C5—31no—
115C22×C5C3×D1211yescharacteristic, complemented
116C2×D5—32no—
117C2×D5—92no—
118C2×D5—182no—
119C2×D5—182no—
120C2×D5—182no—
121C2×D5—182no—
122C4×C5—31no—
123C4×C5D3×A411yescharacteristic, complemented
124C2×C32—41no—
125C3×D3—402no—
126C24—152no—
127C2×D4—451no—
128C2×D4—451no—
129C2×D4—452no—
130C22×C4C3×D1511yescharacteristic, complemented
131C3×C5—41no—
132C3×C5—81no—
133C3×C5D4×A411yescharacteristic, complemented
134C22×C3—31no—
135C22×C3—31no—
136C22×C3—602no—
137C22×C3C3×D2011yescharacteristic, complemented
138C2×D3—52no—
139C2×D3—152no—
140C2×D3—302no—
141C2×D3—302no—
142C2×D3—302no—
143C2×D3—302no—
144A4—21no—
145A4D6011yescharacteristic, direct product factor
146C3×C4—31no—
147C3×C4—41no—
148C3×C4—81no—
149C3×C4D5×A411yescharacteristic, complemented
150C2×C5—31no—
151C2×C5—31no—
152C2×C5C2×D3×A411yescharacteristic
153D5—62no—
154D5—182no—
155C32—41noSylow
156C23—302no—
157C23—452no—
158C23—452no—
159C23—902no—
160C23C2×C3×D1511yescharacteristic
161D4—151no—
162D4—452no—
163D4—452no—
164D4—451no—
165C2×C4—31no—
166C2×C4—31no—
167C2×C3—31no—
168C2×C3—31no—
169C2×C3—41no—
170C2×C3—81no—
171C2×C3—1202no—
172C2×C3C2×D5×A411yescharacteristic
173D3—102no—
174D3—302no—
175C5A4×D1211yescharacteristic, complemented, Sylow
176C22—31no—
177C22—31no—
178C22—152no—
179C22—452no—
180C22—902no—
181C22—902no—
182C22—902no—
183C22—902no—
184C22C3×D6011yescharacteristic, complemented
185C4—31no—
186C4A4×D1511yescharacteristic, complemented
187C3—41no—
188C3—81no—
189C3A4×D2011yescharacteristic, complemented
190C2—31no—
191C2—31no—
192C2—302no—
193C2—902no—
194C2C2×A4×D1511yescharacteristic
subgroupG/H
center, FrattiniC2C2×A4×D15
commutator, socle, cosocleC23×C3×C5C22×C3
FittingC22×C3×C4×C5C2×C3
hypercenterC4A4×D15
hypocenterC22×C3×C5C3×D4
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×A4×D15C2semidirect
2. C3×C4×C5×A4C2semidirect
3. C22×D60C3semidirect
9. C23×D15C2×C3semidirect
11. C22×C3×C4×C5C2×C3semidirect
16. C4×C5×A4D3semidirect
18. C3×C5×A4D4semidirect
22. C3×C4×A4D5semidirect
36. D60A4direct (N × H)
43. C22×C4×C5C3×D3semidirect
52. C22×C3×C5C3×D4semidirect
58. C2×D15C2×A4semidirect
61. C5×A4D12semidirect
65. C3×C4×C5C2×A4semidirect
68. C22×C3×C4C3×D5semidirect
73. C4×A4D15semidirect
87. C3×A4D20semidirect
115. C22×C5C3×D12semidirect
123. C4×C5D3×A4semidirect
130. C22×C4C3×D15semidirect
133. C3×C5D4×A4semidirect
137. C22×C3C3×D20semidirect
145. A4D60direct (N × H)
149. C3×C4D5×A4semidirect
175. C5A4×D12semidirect
184. C22C3×D60semidirect
186. C4A4×D15semidirect
189. C3A4×D20semidirect

Maximal subgroups

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

subgroupindex
C2×A4×D152
C3×C4×C5×A42
C22×D603
A4×D203
C3×D604
A4×D125