Finite Group Databasebeta

← #14298383

Subgroups — #14298383

Order 1920.

632 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 129 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×C3×D5×C4⋊C4C211yesmaximal, characteristic
2#11752414C212yesmaximal
3#11746790C214yesmaximal, complemented
4#10604337—31nomaximal, Hall
5C22×C3×C4×D5C412yes—
6C22×C3×C4×D5C2211yescharacteristic
7C2×#6762C2214yes—
8C2×C3×C5×C4⋊C4C411yescharacteristic
9C2×C3×C4⋊Dic5C411yescharacteristic
10C2×C3×#683C2212yes—
11C3×D5×C4⋊C4—22no—
12C3×D5×C4⋊C4—22no—
13#91232—22no—
14#91232—22no—
15#71562—51nomaximal, Hall
16C2×D5×C4⋊C4D311yescharacteristic
17#65755—32no—
18#64919—34no—
19C23×C3×D5C2×C411yescharacteristic
20C22×C3×C4×C5C2×C411yescharacteristic
21C22×C3×C4×C5C2×C412yes—
22C22×C3×Dic5C2×C412yes—
23C22×C3×Dic5C2311yescharacteristic
24C2×C3×C4×D5—24no—
25C2×C3×C4×D5—22no—
26C2×C3×C4×D5—22no—
27C2×C3×C4×D5—44no—
28C2×C3×C4×D5D412yes—
29C2×C3×C4×D5D412yes—
30#6762—28no—
31C2×C3⋊#170—24no—
32C3×C5×C4⋊C4—22no—
33C3×C4⋊Dic5—22no—
34C3×#683—24no—
35C22×C3×C4⋊C4—51no—
36#5207—52no—
37#4530—54no—
38C22×C4×D5Dic312yes—
39C22×C4×D5C2×D311yescharacteristic
40C2×#704—34no—
41C2×C5×C4⋊C4Dic311yescharacteristic
42C2×C4⋊Dic5Dic311yescharacteristic
43C2×#683C2×D312yes—
44D5×C4⋊C4—22no—
45D5×C4⋊C4—22no—
46#4003—62no—
47#4003—62no—
48#1821—151noSylow
49C23×C3×C5C22×C411yescharacteristic
50C22×C3×D5—22no—
51C22×C3×D5—22no—
52C22×C3×D5—22no—
53C22×C3×D5C22⋊C411yescharacteristic
54C22×C3×D5C22⋊C411yescharacteristic
55C2×C3×C4×C5—22no—
56C2×C3×C4×C5—22no—
57C2×C3×C4×C5—42no—
58C2×C3×C4×C5C22⋊C412yes—
59C2×C3×Dic5—22no—
60C2×C3×Dic5—42no—
61C2×C3×Dic5C2×D412yes—
62C2×C3×Dic5#4114yes—
63C3×C4×D5—24no—
64C3×C4×D5—24no—
65C3×C4×D5—44no—
66C3×C4×D5—44no—
67C3⋊#170—44no—
68C23×C3×C4—51no—
69C23×C3×C4—52no—
70C2×C3×C4⋊C4—52no—
71C2×C3×C4⋊C4—51no—
72C2×C3×C4⋊C4—102no—
73C2×C3×C4⋊C4—102no—
74C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
75C2×#208—54no—
76#830—102no—
77#830—102no—
78C23×D5C2×Dic311yescharacteristic
79C22×C4×C5C2×Dic312yes—
80C22×C4×C5C2×Dic311yescharacteristic
81C22×Dic5C2×Dic312yes—
82C22×Dic5C22×D311yescharacteristic
83C2×C4×D5—24no—
84C2×C4×D5—22no—
85C2×C4×D5—22no—
86C2×C4×D5—44no—
87C2×C4×D5#6712yes—
88C2×C4×D5#6712yes—
89#704—68no—
90C2×#170—64no—
91C5×C4⋊C4—22no—
92C4⋊Dic5—22no—
93#683—24no—
94C22×C4⋊C4—51no—
95#407—152no—
96#343—154no—
97C22×C3×C5—21no—
98C22×C3×C5—21no—
99C22×C3×C5C2×C22⋊C411yescharacteristic
100C22×C3×C5#11712yes—
101C2×C3×D5—28no—
102C2×C3×D5—21no—
103C2×C3×D5—21no—
104C2×C3×D5—21no—
105C2×C3×D5—21no—
106C2×C3×D5#10012yes—
107C2×C3×D5#10112yes—
108C3×C4×C5—22no—
109C3×C4×C5—42no—
110C3×Dic5—42no—
111C3×Dic5#12314yes—
112C24×C3—51no—
113C22×C3×C4—51no—
114C22×C3×C4—52no—
115C22×C3×C4—52no—
116C22×C3×C4—52no—
117C22×C3×C4—104no—
118C22×C3×C4—102no—
119C22×C3×C4—102no—
120C22×C3×C4—204no—
121C22×C3×C4C2×AGL(1,𝔽5)12yes—
122C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
123C3×C4⋊C4—22no—
124C3×C4⋊C4—104no—
125C3×C4⋊C4—102no—
126#208—108no—
127C2×C3⋊C8—104no—
128C23×C5C22×Dic311yescharacteristic
129C22×D5—22no—
130C22×D5—22no—
131C22×D5—22no—
132C22×D5#21711yescharacteristic
133C22×D5#21711yescharacteristic
134C2×C4×C5—22no—
135C2×C4×C5—22no—
136C2×C4×C5—42no—
137C2×C4×C5#21712yes—
138C2×Dic5—22no—
139C2×Dic5—42no—
140C2×Dic5#23514yes—
141C2×Dic5C2×#6712yes—
142C4×D5—24no—
143C4×D5—24no—
144C4×D5—44no—
145C4×D5—44no—
146#170—124no—
147C23×C4—51no—
148C23×C4—52no—
149C2×M16—154no—
150C2×C4⋊C4—52no—
151C2×C4⋊C4—51no—
152C2×C4⋊C4—102no—
153C2×C4⋊C4—102no—
154C2×C4⋊C4ΓL(1,𝔽16)11yescharacteristic
155C22⋊C8—302no—
156C22⋊C8—302no—
157C2×C3×C5—22no—
158C2×C3×C5#38111yescharacteristic
159C2×C3×C5C2×#10011yescharacteristic
160C2×C3×C5C2×#10111yescharacteristic
161C3×D5—22no—
162C3×D5—22no—
163C23×C3—51no—
164C23×C3—51no—
165C23×C3—102no—
166C23×C3—102no—
167C23×C3—102no—
168C23×C3C22×AGL(1,𝔽5)11yescharacteristic
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—42no—
172C2×C3×C4—54no—
173C2×C3×C4—52no—
174C2×C3×C4—104no—
175C2×C3×C4—104no—
176C2×C3×C4—102no—
177C2×C3×C4—204no—
178C2×C3×C4—204no—
179C2×C3×C4—202no—
180C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
181C3⋊C8—204no—
182C22×C5—21no—
183C22×C5—21no—
184C22×C5#92612yes—
185C22×C5C2×#21711yescharacteristic
186C2×D5—28no—
187C2×D5—21no—
188C2×D5—21no—
189C2×D5—21no—
190C2×D5—21no—
191C2×D5#83312yes—
192C2×D5#83612yes—
193C4×C5—22no—
194C4×C5—42no—
195Dic5—42no—
196Dic5#92914yes—
197C24—51no—
198C22×C4—51no—
199C22×C4—52no—
200C22×C4—52no—
201C22×C4—52no—
202C22×C4—104no—
203C22×C4—102no—
204C22×C4—102no—
205C22×C4—204no—
206C22×C4C2×ΓL(1,𝔽16)12yes—
207C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
208M16—308no—
209C2×C8—304no—
210C4⋊C4—22no—
211C4⋊C4—104no—
212C4⋊C4—102no—
213C3×C5#182111yescharacteristic, complemented, Hall
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—52no—
217C22×C3—52no—
218C22×C3—108no—
219C22×C3—101no—
220C22×C3—101no—
221C22×C3—101no—
222C22×C3—101no—
223C22×C3#413012yes—
224C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
225C3×C4—22no—
226C3×C4—42no—
227C3×C4—54no—
228C3×C4—202no—
229C2×C5—22no—
230C2×C5#521111yescharacteristic
231C2×C5C2×#83311yescharacteristic
232C2×C5C2×#83611yescharacteristic
233D5—22no—
234D5—22no—
235C23—51no—
236C23—51no—
237C23—102no—
238C23—102no—
239C23—102no—
240C23C22×ΓL(1,𝔽16)11yescharacteristic
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—54no—
245C2×C4—52no—
246C2×C4—104no—
247C2×C4—104no—
248C2×C4—102no—
249C2×C4—204no—
250C2×C4—204no—
251C2×C4—202no—
252C2×C4#676312yes—
253C8—604no—
254C2×C3—22no—
255C2×C3—102no—
256C2×C3—102no—
257C2×C3#6576411yescharacteristic
258C2×C3D5⋊#10011yescharacteristic
259C2×C3D5⋊#10111yescharacteristic
260C5#7156211yescharacteristic, complemented, Sylow
261C22—21no—
262C22—21no—
263C22—52no—
264C22—52no—
265C22—108no—
266C22—101no—
267C22—101no—
268C22—101no—
269C22—101no—
270C22#9198912yes—
271C22C2×#676311yescharacteristic
272C4—22no—
273C4—42no—
274C4—54no—
275C4—202no—
276C3#1060433711yescharacteristic, complemented, Sylow
277C2—22no—
278C2—102no—
279C2—102no—
280C2#1175242311yescharacteristic
281C2D5⋊#83311yescharacteristic
282C2D5⋊#83611yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×Dic5C23
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1821
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #11746790C2semidirect
213. C3×C5#1821semidirect
260. C5#71562semidirect
276. C3#10604337semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C4⋊C42
#117524142
#117467902
#106043373
#715625