Finite Group Databasebeta

← #14309006

Subgroups — #14309006

Order 1920.

580 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 118 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×#5483C211yesmaximal, characteristic
2#11751044C211yesmaximal, characteristic
3#11749473C212yesmaximal
4C3×#64746C211yesmaximal, characteristic
5#11746018C212yesmaximal
6#10602687—31nomaximal, Hall
7C23×Dic15C2211yescharacteristic
8C2×C3×C5×C22⋊C4C2211yescharacteristic
9C2×#6719C2211yescharacteristic
10C2×C5×#217C2212yes—
11C5×#924—22no—
12C5×#878—24no—
13C2×C3×C22⋊Dic5C2212yes—
14#91115—22no—
15#90994—24no—
16#68956—51nomaximal, Hall
17C5×#543—31no—
18#65232—31no—
19#65232—32no—
20#64746—32no—
21#64746D311yescharacteristic
22C24×C3×C5C2311yescharacteristic
23C22×C3×C4×C5D412yes—
24C22×Dic15—22no—
25C22×Dic15—21no—
26C22×Dic15—22no—
27C22×Dic15—21no—
28C22×Dic15—21no—
29C22×Dic15Q812yescomplemented
30C22×C5×Dic3D414yes—
31C2×C5×Dic6—22no—
32C22×C3×Dic5—22no—
33C3×C5×C22⋊C4—22no—
34#6719—22no—
35C5×#217—22no—
36C5×#217—22no—
37C5×C4⋊Dic3—22no—
38C5×Dic3⋊C4—24no—
39C3×C22⋊Dic5—22no—
40C3×C22⋊Dic5—22no—
41#5483D511yescharacteristic
42#4943—51no—
43#4943—52no—
44C3×#342—51no—
45#4527—52no—
46C23×Dic5—31no—
47C5×C22⋊Q8—64no—
48C5×C22⋊Q8—62no—
49C2×C5×C22⋊C4—32no—
50C2×C5×C22⋊C4C2×D311yescharacteristic
51C2×C22⋊Dic5—31no—
52C2×C22⋊Dic5C2×D312yes—
53#3963—64no—
54#3963—62no—
55#2030—151noSylow
56C23×C3×C5—42no—
57C23×C3×C5C2×D411yescharacteristic
58C23×C3×C5C2×D412yes—
59C23×C3×C5C2×Q811yescharacteristic
60C23×C3×C5#4112yes—
61C23×C3×C5#4111yescharacteristic
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×Dic15—24no—
65C2×Dic15—22no—
66C2×Dic15—41no—
67C2×Dic15—41no—
68C2×Dic15—42no—
69C2×Dic15—42no—
70C2×Dic15—41no—
71C2×C5×Dic3—24no—
72C2×C5×Dic3—44no—
73C5×Dic6—82no—
74C2×C3×Dic5—44no—
75C2×C3×Dic5—42no—
76C23×Dic3—51no—
77C2×C3×C22⋊C4—52no—
78C2×C3×C22⋊C4C2×D511yescharacteristic
79C2×#217—51no—
80C2×#217C2×D512yes—
81#924—22no—
82#878—24no—
83C3⋊#95—102no—
84C3⋊#95—104no—
85C24×C5C22×D311yescharacteristic
86C2×C5×Q8—62no—
87C22×C4×C5—34no—
88C22×C4×C5D1212yes—
89C22×Dic5—22no—
90C22×Dic5—32no—
91C22×Dic5—61no—
92C22×Dic5—62no—
93C22×Dic5—62no—
94C22×Dic5—61no—
95C22×Dic5—61no—
96C5×C4⋊C4—64no—
97C5×C4⋊C4—62no—
98C5×C22⋊C4—22no—
99C5×C22⋊C4—62no—
100C5×C22⋊C4—62no—
101C22⋊Dic5—22no—
102C22⋊Dic5—22no—
103C22⋊Dic5—62no—
104#543—31no—
105#381—152no—
106#381—151no—
107#342—51no—
108#342—152no—
109C22×C3×C5—24no—
110C22×C3×C5—22no—
111C22×C3×C5—41no—
112C22×C3×C5—42no—
113C22×C3×C5—41no—
114C22×C3×C5#12011yescharacteristic
115C22×C3×C5C22⋊Q812yes—
116C22×C3×C5C22⋊Q811yescharacteristic
117C22×C3×C5#12411yescharacteristic
118C22×C3×C5#12412yes—
119C3×C4×C5—42no—
120Dic15—42no—
121Dic15—81no—
122C3×Dic5—82no—
123C5×Dic3—44no—
124C24×C3C22×D511yescharacteristic
125C22×C3×C4—102no—
126C22×C3×C4C22⋊D512yes—
127C22×Dic3—52no—
128C22×Dic3—101no—
129C22×Dic3—102no—
130C22×Dic3—101no—
131C22×Dic3—102no—
132C22×Dic3—101no—
133C22×Dic3C22⋊D514yes—
134C2×Dic6—22no—
135C3×C22⋊C4—22no—
136C3×C22⋊C4—102no—
137C3×C22⋊C4—102no—
138#217—22no—
139#217—22no—
140#217—102no—
141C4⋊Dic3—22no—
142Dic3⋊C4—24no—
143C23×C5—42no—
144C23×C5C2×D1211yescharacteristic
145C23×C5#23512yes—
146C23×C5D3×D412yes—
147C23×C5#23711yescharacteristic
148C23×C5D3×Q811yescharacteristic
149C5×Q8—242no—
150C2×C4×C5—22no—
151C2×C4×C5—42no—
152C2×C4×C5—64no—
153C2×C4×C5—124no—
154C2×Dic5—44no—
155C2×Dic5—42no—
156C2×Dic5—64no—
157C2×Dic5—62no—
158C2×Dic5—121no—
159C2×Dic5—121no—
160C2×Dic5—122no—
161C2×Dic5—122no—
162C2×Dic5—121no—
163C23×C4—151no—
164C22⋊Q8—64no—
165C22⋊Q8—62no—
166C2×C22⋊C4—32no—
167C2×C22⋊C4—52no—
168C2×C22⋊C4—151no—
169C2×C22⋊C4D3×D511yescharacteristic
170#95—304no—
171#95—302no—
172C2×C3×C5—22no—
173C2×C3×C5—21no—
174C2×C3×C5—22no—
175C2×C3×C5—21no—
176C2×C3×C5#39311yescharacteristic
177C2×C3×C5#45812yes—
178C23×C3—42no—
179C23×C3Q8×D511yescharacteristic
180C23×C3#71311yescharacteristic
181C23×C3#71312yes—
182C23×C3C2×C22⋊D511yescharacteristic
183C23×C3C2×C22⋊D512yes—
184C2×C3×C4—22no—
185C2×C3×C4—42no—
186C2×C3×C4—204no—
187C2×C3×C4—202no—
188C2×Dic3—24no—
189C2×Dic3—44no—
190C2×Dic3—104no—
191C2×Dic3—102no—
192C2×Dic3—201no—
193C2×Dic3—202no—
194C2×Dic3—201no—
195C2×Dic3—202no—
196C2×Dic3—201no—
197Dic6—82no—
198C22×C5—24no—
199C22×C5—22no—
200C22×C5—42no—
201C22×C5—41no—
202C22×C5—41no—
203C22×C5#87511yescharacteristic
204C22×C5#88211yescharacteristic
205C22×C5#88512yes—
206C22×C5#89612yes—
207C22×C5#89711yescharacteristic
208C4×C5—42no—
209C4×C5—124no—
210Dic5—82no—
211Dic5—122no—
212Dic5—241no—
213C24C2×D3×D511yescharacteristic
214C2×Q8—62no—
215C22×C4—34no—
216C22×C4—102no—
217C22×C4—152no—
218C22×C4—301no—
219C22×C4—302no—
220C22×C4—301no—
221C22×C4—302no—
222C22×C4—301no—
223C22×C4#120312yes—
224C4⋊C4—64no—
225C4⋊C4—62no—
226C22⋊C4—22no—
227C22⋊C4—62no—
228C22⋊C4—62no—
229C22⋊C4—102no—
230C22⋊C4—102no—
231C22⋊C4—302no—
232C3×C5#203011yescharacteristic, complemented, Hall
233C22×C3—24no—
234C22×C3—22no—
235C22×C3—41no—
236C22×C3—41no—
237C22×C3—42no—
238C22×C3#409212yes—
239C22×C3#409211yescharacteristic
240C22×C3#409312yes—
241C22×C3#409311yescharacteristic
242C22×C3#409911yescharacteristic
243C3×C4—42no—
244C3×C4—402no—
245Dic3—44no—
246Dic3—202no—
247Dic3—401no—
248C2×C5—22no—
249C2×C5—21no—
250C2×C5—22no—
251C2×C5—21no—
252C2×C5#467311yescharacteristic
253C2×C5#474212yes—
254C23—42no—
255C23#676611yescharacteristic
256C23D15⋊Q811yescharacteristic
257C23#677312yes—
258C23C2×#120311yescharacteristic
259C23D3×C22⋊D512yes—
260Q8—242no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—64no—
264C2×C4—124no—
265C2×C4—204no—
266C2×C4—202no—
267C2×C4—304no—
268C2×C4—302no—
269C2×C4—602no—
270C2×C4—601no—
271C2×C4—601no—
272C2×C4—602no—
273C2×C4—601no—
274C2×C3—21no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3—21no—
278C2×C3#6552011yescharacteristic
279C2×C3#6553212yes—
280C5#6895611yescharacteristic, complemented, Sylow
281C22—22no—
282C22—24no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22#9137511yescharacteristic
287C22#9138311yescharacteristic
288C22#9142412yes—
289C22#9145512yes—
290C22#9157011yescharacteristic
291C4—42no—
292C4—124no—
293C4—402no—
294C4—602no—
295C4—1201no—
296C3#1060268711yescharacteristic, complemented, Sylow
297C2—22no—
298C2—21no—
299C2—22no—
300C2—21no—
301C2#1174878411yescharacteristic
302C2#1174918412yes—
subgroupG/H
centerC22#91570
commutator, prime radical, cosocleC24×C3×C5C23
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5#120
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2030
LCSG ▷ C24×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
29. C22×Dic15Q8semidirect
232. C3×C5#2030semidirect
280. C5#68956semidirect
296. C3#10602687semidirect

Maximal subgroups

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

subgroupindex
C5×#54832
#117510442
#117494732
C3×#647462
#117460182
#106026873
#689565