Finite Group Databasebeta

← A4×C4⋊Dic5 #11752185

Subgroups — A4×C4⋊Dic5 #11752185

Order 960.

226 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 57 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×C4×C5×A4C211yesmaximal, characteristic
2C2×A4×Dic5C212yesmaximal
3C22×C4⋊Dic5C311yesmaximal, characteristic, complemented, Hall
4C22×C5×A4C2211yescharacteristic
5C4×C5×A4C412yescomplemented
6A4×Dic5—22no—
7C3×C4⋊Dic5—41nomaximal
8A4×C4⋊C4—51nomaximal, Hall
9C23×C4×C5C2×C311yescharacteristic
10C23×Dic5C2×C312yes—
11C2×C4⋊Dic5—31no—
12C2×C4⋊Dic5—31no—
13C2×C4⋊Dic5—32no—
14C2×C5×A4C2×C411yescharacteristic
15C2×C5×A4D411yescharacteristic
16C2×C5×A4Q811yescharacteristic
17C2×C3×C4×C5—41no—
18C2×C3×Dic5—42no—
19C2×C4×A4—52no—
20C2×C4×A4D511yescharacteristic
21C24×C5C22×C311yescharacteristic
22C22×C4×C5—31no—
23C22×C4×C5—32no—
24C22×C4×C5—31no—
25C22×C4×C5C3×C412yescomplemented
26C22×Dic5—22no—
27C22×Dic5—32no—
28C22×Dic5—32no—
29C22×Dic5—62no—
30C4⋊Dic5—32no—
31C4⋊Dic5—31no—
32C4⋊Dic5—32no—
33C4⋊Dic5A411yescharacteristic, direct product factor
34C22×C4⋊C4—51noSylow
35C22×C3×C5—41no—
36C5×A4C4⋊C411yescharacteristic, complemented
37C3×C4×C5—42no—
38C3×Dic5—82no—
39C22×A4C2×D511yescharacteristic
40C4×A4—102no—
41C4×A4Dic512yescomplemented
42C3×C4⋊C4—201no—
43C23×C5—31no—
44C23×C5—31no—
45C23×C5—31no—
46C23×C5—31no—
47C23×C5C2×C3×C411yescharacteristic
48C23×C5C3×D411yescharacteristic
49C23×C5C3×Q811yescharacteristic
50C2×C4×C5—32no—
51C2×C4×C5—31no—
52C2×C4×C5—32no—
53C2×C4×C5—32no—
54C2×C4×C5—32no—
55C2×C4×C5C2×A411yescharacteristic
56C2×Dic5—32no—
57C2×Dic5—62no—
58C2×Dic5—62no—
59C2×Dic5—62no—
60C2×Dic5—62no—
61C2×Dic5C2×A412yes—
62C23×C4—52no—
63C23×C4C3×D511yescharacteristic
64C2×C4⋊C4—151no—
65C2×C4⋊C4—152no—
66C2×C4⋊C4—151no—
67C2×C3×C5—41no—
68C2×C3×C5—41no—
69C2×C3×C5—41no—
70C2×A4Dic1011yescharacteristic
71C2×A4D2011yescharacteristic
72C2×A4C2×Dic511yescharacteristic
73C2×C3×C4—41no—
74C2×C3×C4—202no—
75C22×C5—31no—
76C22×C5—31no—
77C22×C5—31no—
78C22×C5—32no—
79C22×C5—31no—
80C22×C5—31no—
81C22×C5—31no—
82C22×C5—31no—
83C22×C5—31no—
84C22×C5—31no—
85C22×C5C3×C4⋊C411yescharacteristic, complemented
86C22×C5C22×A411yescharacteristic
87C4×C5—32no—
88C4×C5C4×A412yescomplemented
89Dic5—22no—
90Dic5—62no—
91C24C2×C3×D511yescharacteristic
92C22×C4—31no—
93C22×C4—31no—
94C22×C4—32no—
95C22×C4—102no—
96C22×C4—152no—
97C22×C4—152no—
98C22×C4—302no—
99C22×C4C3×Dic512yescomplemented
100C4⋊C4—51no—
101C4⋊C4—152no—
102C4⋊C4—152no—
103C4⋊C4—151no—
104C3×C5—41noHall
105C22×C3—41no—
106A4C4⋊Dic511yescharacteristic, direct product factor
107C3×C4—42no—
108C3×C4—402no—
109C2×C5—31no—
110C2×C5—31no—
111C2×C5—31no—
112C2×C5—31no—
113C2×C5C2×C4×A411yescharacteristic
114C2×C5D4×A411yescharacteristic
115C2×C5Q8×A411yescharacteristic
116C23—31no—
117C23—31no—
118C23—31no—
119C23—31no—
120C23C3×Dic1011yescharacteristic
121C23C3×D2011yescharacteristic
122C23C2×C3×Dic511yescharacteristic
123C2×C4—32no—
124C2×C4—31no—
125C2×C4—32no—
126C2×C4—32no—
127C2×C4—32no—
128C2×C4—52no—
129C2×C4—152no—
130C2×C4—302no—
131C2×C4—302no—
132C2×C4—302no—
133C2×C4—302no—
134C2×C4D5×A411yescharacteristic
135C2×C3—41no—
136C2×C3—41no—
137C2×C3—41no—
138C5A4×C4⋊C411yescharacteristic, complemented, Sylow
139C22—31no—
140C22—31no—
141C22—31no—
142C22—32no—
143C22—31no—
144C22—31no—
145C22—31no—
146C22—31no—
147C22—31no—
148C22—31no—
149C22C3×C4⋊Dic511yescharacteristic, complemented
150C22C2×D5×A411yescharacteristic
151C4—32no—
152C4—102no—
153C4—302no—
154C4A4×Dic512yescomplemented
155C3—41noSylow
156C2—31no—
157C2—31no—
158C2—31no—
159C2—31no—
160C2A4×Dic1011yescharacteristic
161C2A4×D2011yescharacteristic
162C2C2×A4×Dic511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×A4
commutatorC23×C5C2×C3×C4
FittingC23×C4×C5C2×C3
socle, cosocleC24×C5C22×C3
prime radicalC22×C5×A4C22
hypercenterC2×C4D5×A4
hypocenterC22×C5C3×C4⋊C4
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic5C3semidirect
5. C4×C5×A4C4semidirect
25. C22×C4×C5C3×C4semidirect
33. C4⋊Dic5A4direct (N × H)
36. C5×A4C4⋊C4semidirect
41. C4×A4Dic5semidirect
85. C22×C5C3×C4⋊C4semidirect
88. C4×C5C4×A4semidirect
99. C22×C4C3×Dic5semidirect
106. A4C4⋊Dic5direct (N × H)
138. C5A4×C4⋊C4semidirect
149. C22C3×C4⋊Dic5semidirect
154. C4A4×Dic5semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×A42
C2×A4×Dic52
C22×C4⋊Dic53
C3×C4⋊Dic54
A4×C4⋊C45