Finite Group Databasebeta

← #14513686

Subgroups — #14513686

Order 1920.

522 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C42×C5×A4C211yesmaximal, characteristic
2C4⋊(A4⋊Dic5)C212yesmaximal
3#11752130C214yesmaximal
4#10613805—31nomaximal, Hall
5C2×C4×C5×A4C2212yes—
6C2×C4×C5×A4C2211yescharacteristic
7C2×A4⋊Dic5C2214yes—
8#91759—41nomaximal
9#85284—51nomaximal, Hall
10C22×C42×C5D311yescharacteristic
11C2×#4016—31no—
12#65501—32no—
13#65499—34no—
14#65225—31no—
15#65222—34no—
16#65217—32no—
17C22×C5×A4C2311yescharacteristic
18C4×C5×A4—22no—
19C4×C5×A4Q812yes—
20A4⋊Dic5—24no—
21C3×C42×C5—41no—
22C4⋊Dic15—42no—
23#6712—44no—
24C42×A4D511yescharacteristic
25C4⋊SL(2,ℤ/4)—52no—
26SL(2,ℤ/4)⋊C4—54no—
27C23×C4×C5C2×D312yes—
28C23×C4×C5C2×D311yescharacteristic
29C2×C42×C5—31no—
30C2×C42×C5—31no—
31C2×C42×C5—32no—
32C2×C22⋊Dic5—34no—
33C2×C4⋊Dic5—32no—
34C2×C4⋊Dic5—32no—
35C2×#683—34no—
36C2×#683—34no—
37#4016—61no—
38#4016—62no—
39#4016—61no—
40#3963—34no—
41#3963—34no—
42#3963—34no—
43#2851—151noSylow
44C2×C5×A4C2×Q811yescharacteristic
45C2×C5×A4#4112yes—
46C2×C3×C4×C5—41no—
47C2×C3×C4×C5—42no—
48C2×Dic15—44no—
49C2×C4×A4C2×D512yes—
50C2×C4×A4C2×D511yescharacteristic
51C2×SL(2,ℤ/4)—54no—
52#870—201no—
53C24×C5C22×D311yescharacteristic
54C22×C4×C5—22no—
55C22×C4×C5—31no—
56C22×C4×C5—31no—
57C22×C4×C5—32no—
58C22×C4×C5—32no—
59C22×C4×C5—32no—
60C22×C4×C5—62no—
61C22×C4×C5Dic612yes—
62C22×Dic5—34no—
63C22×Dic5—34no—
64C42×C5—32no—
65C42×C5—31no—
66C42×C5—61no—
67C42×C5S411yescharacteristic
68C22⋊Dic5—64no—
69C22⋊Dic5—64no—
70C4⋊Dic5—62no—
71C4⋊Dic5—64no—
72C4⋊Dic5—62no—
73#683—64no—
74#683—68no—
75#683—64no—
76C2×#125—151no—
77C22×C42D1511yescharacteristic
78#389—152no—
79#387—154no—
80#385—154no—
81#382—151no—
82#380—152no—
83C22×C3×C5—41no—
84C5×A4#12511yescharacteristic, complemented
85C3×C4×C5—42no—
86C3×C4×C5—82no—
87Dic15—84no—
88C22×A4C22×D511yescharacteristic
89C4×A4—22no—
90C4×A4Dic1012yes—
91SL(2,ℤ/4)—104no—
92C3×C42—41no—
93C4⋊Dic3—202no—
94Dic3⋊C4—204no—
95C23×C5—31no—
96C23×C5—32no—
97C23×C5—31no—
98C23×C5C2×Dic611yescharacteristic
99C23×C5#23512yes—
100C2×C4×C5—31no—
101C2×C4×C5—32no—
102C2×C4×C5—32no—
103C2×C4×C5—32no—
104C2×C4×C5—34no—
105C2×C4×C5—32no—
106C2×C4×C5—62no—
107C2×C4×C5—62no—
108C2×C4×C5—61no—
109C2×C4×C5—62no—
110C2×C4×C5C2×S412yes—
111C2×C4×C5C2×S411yescharacteristic
112C2×Dic5—64no—
113C2×Dic5—64no—
114C2×Dic5—64no—
115C2×Dic5—64no—
116C2×Dic5—64no—
117C2×Dic5—64no—
118C23×C4C2×D1512yes—
119C23×C4C2×D1511yescharacteristic
120#125—301no—
121#125—302no—
122#125—301no—
123C2×C4⋊C4—152no—
124C2×C4⋊C4—154no—
125C2×C4⋊C4—152no—
126C2×C4⋊C4—154no—
127C2×C22⋊C4—154no—
128C2×C42—31no—
129C2×C42—32no—
130C2×C42—31no—
131#95—154no—
132#95—154no—
133#95—154no—
134C2×C3×C5—41no—
135C2×C3×C5—42no—
136C2×A4C2×Dic1011yescharacteristic
137C2×A4#70912yes—
138C2×C3×C4—41no—
139C2×C3×C4—42no—
140C2×Dic3—204no—
141C22×C5—31no—
142C22×C5—32no—
143C22×C5—31no—
144C22×C5—31no—
145C22×C5—32no—
146C22×C5—32no—
147C22×C5—61no—
148C22×C5#87011yescharacteristic, complemented
149C22×C5C22×S411yescharacteristic
150C4×C5—22no—
151C4×C5—32no—
152C4×C5—62no—
153C4×C5A4⋊Q812yes—
154Dic5—124no—
155Dic5—124no—
156C24C22×D1511yescharacteristic
157C22×C4—22no—
158C22×C4—31no—
159C22×C4—31no—
160C22×C4—32no—
161C22×C4—32no—
162C22×C4—32no—
163C22×C4—62no—
164C22×C4—154no—
165C22×C4—154no—
166C22×C4Dic3012yes—
167C4⋊C4—304no—
168C4⋊C4—302no—
169C4⋊C4—308no—
170C4⋊C4—304no—
171C4⋊C4—304no—
172C4⋊C4—302no—
173C22⋊C4—304no—
174C22⋊C4—304no—
175C42—32no—
176C42—31no—
177C42—61no—
178C42C5⋊S411yescharacteristic
179C3×C5—41noHall
180C22×C3—41no—
181A4#401611yescharacteristic, complemented
182C3×C4—42no—
183C3×C4—82no—
184Dic3—404no—
185C2×C5—32no—
186C2×C5—31no—
187C2×C5—31no—
188C2×C5C2×A4⋊Q811yescharacteristic
189C2×C5#591212yes—
190C23—31no—
191C23—32no—
192C23—31no—
193C23C2×Dic3011yescharacteristic
194C23#681712yes—
195C2×C4—31no—
196C2×C4—32no—
197C2×C4—32no—
198C2×C4—32no—
199C2×C4—34no—
200C2×C4—32no—
201C2×C4—62no—
202C2×C4—62no—
203C2×C4—61no—
204C2×C4—62no—
205C2×C4—304no—
206C2×C4—304no—
207C2×C4—304no—
208C2×C4—304no—
209C2×C4—304no—
210C2×C4—304no—
211C2×C4C2×C5⋊S412yes—
212C2×C4C2×C5⋊S411yescharacteristic
213C2×C3—41no—
214C2×C3—42no—
215C5#8528411yescharacteristic, complemented, Sylow
216C22—31no—
217C22—32no—
218C22—31no—
219C22—31no—
220C22—32no—
221C22—32no—
222C22—61no—
223C22#9175911yescharacteristic, complemented
224C22C22×C5⋊S411yescharacteristic
225C4—22no—
226C4—32no—
227C4—62no—
228C4—604no—
229C4—604no—
230C4#9194812yes—
231C3—41noSylow
232C2—32no—
233C2—31no—
234C2—31no—
235C2C2×#9194811yescharacteristic
236C2#1175689612yes—
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, prime radical, cosocleC22×C5×A4C23
FittingC22×C42×C5D3
socleC24×C5C22×D3
hypercenterC42C5⋊S4
hypocenterC5×A4#125
LCSG ▷ C22×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
84. C5×A4#125semidirect
148. C22×C5#870semidirect
181. A4#4016semidirect
215. C5#85284semidirect
223. C22#91759semidirect

Maximal subgroups

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

subgroupindex
C42×C5×A42
C4⋊(A4⋊Dic5)2
#117521302
#106138053
#917594
#852845