Finite Group Databasebeta

← C2×C5×C22⋊(C42⋊C3) #14511380

Subgroups — C2×C5×C22⋊(C42⋊C3) #14511380

Order 1920.

1080 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 52 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×C22⋊(C42⋊C3)C211yesmaximal, characteristic, direct product factor
2C23×C42×C5C311yesmaximal, characteristic, complemented, Hall
3C2×C5×C22⋊A4—41nomaximal
4C2×C5×C42⋊C3—44nomaximal
5C2×C22⋊(C42⋊C3)C511yesmaximal, characteristic, direct product factor, Hall
6C24×C4×C5—31no—
7C22×C42×C5—31no—
8C22×C42×C5—34no—
9C22×C42×C5—34no—
10C22×C42×C5C2×C311yescharacteristic, complemented
11C5×C22⋊A4—41no—
12C5×C42⋊C3—44no—
13C22⋊(C42⋊C3)C2×C511yescharacteristic, direct product factor
14C25×C5A411yescharacteristic
15C23×C4×C5—36no—
16C23×C4×C5—36no—
17C23×C4×C5—38no—
18C23×C4×C5—38no—
19C23×C4×C5—31no—
20C23×C4×C5—31no—
21C2×C42×C5—312no—
22C2×C42×C5—312no—
23C2×C42×C5—34no—
24C2×C42×C5—34no—
25C2×C42×C5—34no—
26C2×C42×C5A414yescomplemented
27C23×C42C3×C511yescharacteristic, complemented, Sylow
28C2×C5×A4—164no—
29C2×C5×A4—161no—
30C2×C22⋊A4—41no—
31C2×C42⋊C3—44no—
32C24×C5—31no—
33C24×C5—34no—
34C24×C5—34no—
35C24×C5—31no—
36C24×C5C2×A411yescharacteristic
37C22×C4×C5—36no—
38C22×C4×C5—312no—
39C22×C4×C5—36no—
40C22×C4×C5—324no—
41C22×C4×C5—348no—
42C22×C4×C5—324no—
43C22×C4×C5—38no—
44C22×C4×C5—38no—
45C22×C4×C5—34no—
46C42×C5—34no—
47C42×C5—34no—
48C42×C5—312no—
49C42×C5C2×A414yescomplemented
50C24×C4—31no—
51C22×C42—31no—
52C22×C42—34no—
53C22×C42—34no—
54C22×C42C2×C3×C511yescharacteristic, complemented
55C5×A4—164no—
56C5×A4—161no—
57C22⋊A4—41no—
58C42⋊C3—44no—
59C23×C5—36no—
60C23×C5—312no—
61C23×C5—36no—
62C23×C5—312no—
63C23×C5—34no—
64C23×C5—34no—
65C23×C5—34no—
66C23×C5—31no—
67C23×C5—31no—
68C23×C5C42⋊C314yescomplemented
69C23×C5C22⋊A411yescharacteristic
70C2×C4×C5—38no—
71C2×C4×C5—324no—
72C2×C4×C5—348no—
73C2×C4×C5—324no—
74C2×C4×C5—38no—
75C2×C4×C5—34no—
76C2×C4×C5—34no—
77C25C5×A411yescharacteristic
78C23×C4—38no—
79C23×C4—38no—
80C23×C4—36no—
81C23×C4—36no—
82C23×C4—31no—
83C23×C4—31no—
84C2×C42—312no—
85C2×C42—312no—
86C2×C42—34no—
87C2×C42—34no—
88C2×C42—34no—
89C2×C42C5×A414yescomplemented
90C2×C3×C5—641no—
91C2×A4—164no—
92C2×A4—161no—
93C22×C5—31no—
94C22×C5—34no—
95C22×C5—36no—
96C22×C5—36no—
97C22×C5—312no—
98C22×C5—312no—
99C22×C5—34no—
100C22×C5—31no—
101C22×C5—34no—
102C22×C5C2×C42⋊C314yescomplemented
103C22×C5C2×C22⋊A411yescharacteristic
104C4×C5—38no—
105C4×C5—38no—
106C24—31no—
107C24—34no—
108C24—34no—
109C24—31no—
110C24C2×C5×A411yescharacteristic
111C22×C4—36no—
112C22×C4—312no—
113C22×C4—36no—
114C22×C4—324no—
115C22×C4—348no—
116C22×C4—324no—
117C22×C4—38no—
118C22×C4—38no—
119C22×C4—34no—
120C42—34no—
121C42—34no—
122C42—312no—
123C42C2×C5×A414yescomplemented
124C3×C5—641noHall
125A4—164no—
126A4—161no—
127C2×C5—31no—
128C2×C5—31no—
129C2×C5—34no—
130C2×C5—34no—
131C2×C5C22⋊(C42⋊C3)11yescharacteristic, direct product factor
132C23—36no—
133C23—312no—
134C23—36no—
135C23—312no—
136C23—34no—
137C23—34no—
138C23—34no—
139C23—31no—
140C23—31no—
141C23C5×C42⋊C314yescomplemented
142C23C5×C22⋊A411yescharacteristic
143C2×C4—38no—
144C2×C4—324no—
145C2×C4—348no—
146C2×C4—324no—
147C2×C4—38no—
148C2×C4—34no—
149C2×C4—34no—
150C2×C3—641no—
151C5C2×C22⋊(C42⋊C3)11yescharacteristic, direct product factor, Sylow
152C22—31no—
153C22—34no—
154C22—36no—
155C22—36no—
156C22—34no—
157C22—312no—
158C22—312no—
159C22—31no—
160C22—34no—
161C22C2×C5×C42⋊C314yescomplemented
162C22C2×C5×C22⋊A411yescharacteristic
163C4—38no—
164C4—38no—
165C3—641noSylow
166C2—31no—
167C2—34no—
168C2—31no—
169C2—34no—
170C2C5×C22⋊(C42⋊C3)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5C22⋊(C42⋊C3)
commutator, cosocle, hypocenterC22×C42C2×C3×C5
FrattiniC22C2×C5×C22⋊A4
FittingC23×C42×C5C3
socleC25×C5A4
LCSG ▷ C22×C42
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C5×C22⋊(C42⋊C3)C2direct (N × H)
2. C23×C42×C5C3semidirect
5. C2×C22⋊(C42⋊C3)C5direct (N × H)
10. C22×C42×C5C2×C3semidirect
13. C22⋊(C42⋊C3)C2×C5direct (N × H)
26. C2×C42×C5A4semidirect
27. C23×C42C3×C5semidirect
49. C42×C5C2×A4semidirect
54. C22×C42C2×C3×C5semidirect
68. C23×C5C42⋊C3semidirect
89. C2×C42C5×A4semidirect
102. C22×C5C2×C42⋊C3semidirect
123. C42C2×C5×A4semidirect
131. C2×C5C22⋊(C42⋊C3)direct (N × H)
141. C23C5×C42⋊C3semidirect
151. C5C2×C22⋊(C42⋊C3)direct (N × H)
161. C22C2×C5×C42⋊C3semidirect
170. C2C5×C22⋊(C42⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C22⋊(C42⋊C3)2
C23×C42×C53
C2×C5×C22⋊A44
C2×C5×C42⋊C34
C2×C22⋊(C42⋊C3)5