Finite Group Databasebeta

← #14288253

Subgroups — #14288253

Order 1920.

560 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#11756252C211yesmaximal, characteristic
2#11751054C211yesmaximal, characteristic, complemented
3#11750837C212yesmaximal, complemented
4C3×C5×#323C211yesmaximal, characteristic, complemented
5#11746291C212yesmaximal, complemented
6#10598903—31nomaximal, Hall
7C22×#1220—21no—
8C2×C3×C5×C22⋊C4C2211yescharacteristic
9C2×#6719—21no—
10#91819—21no—
11#91819C2212yes—
12C2×C4⋊Dic15C2211yescharacteristic, complemented
13#91775—22no—
14#91771—22no—
15C3×C5×C22⋊C8C2212yescomplemented
16#91115—21no—
17#91115C2211yescharacteristic, complemented
18#91105—22no—
19#91102—22no—
20#68110—51nomaximal, Hall
21#65827—31no—
22#65242—31no—
23#65025—32no—
24C5×#323D311yescharacteristic, complemented
25#64690—32no—
26C24×C3×C5D411yescharacteristic
27C23×D15—21no—
28C22×C3×C4×C5D411yescharacteristic
29C22×C3×C4×C5C2311yescharacteristic
30C2×#1220—22no—
31C2×#1220—22no—
32C2×#1220—42no—
33C2×#1220—42no—
34C22×Dic15—21no—
35C22×Dic15—21no—
36C22×Dic15—21no—
37C2×D60—21no—
38C2×D60D412yes—
39C2×C3×C5×C8—22no—
40C3×C5×C22⋊C4—22no—
41#6719—42no—
42#6714—22no—
43#6714—22no—
44C4⋊Dic15—21no—
45C4⋊Dic15—22no—
46C4⋊Dic15D412yes—
47#5493—51no—
48#4953—51no—
49#4736—52no—
50C3×#323D511yescharacteristic, complemented
51#4470—52no—
52C22×C22⋊D5—61no—
53C2×C5×C22⋊C4C2×D311yescharacteristic
54C2×C22⋊Dic5—61no—
55#4076—32no—
56#4076—61no—
57C2×C4⋊Dic5—31no—
58#4032—62no—
59#4028—62no—
60C5×C22⋊C8C2×D312yescomplemented
61#3963—31no—
62#3963—61no—
63#3953—62no—
64#3950—62no—
65#1607—151noSylow
66C23×C3×C5—21no—
67C23×C3×C5—21no—
68C23×C3×C5—41no—
69C23×C3×C5—41no—
70C23×C3×C5D812yes—
71C23×C3×C5C2×D411yescharacteristic
72C22×D15—22no—
73C22×D15—42no—
74C22×D15—81no—
75C22×D15—81no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5C2×D412yes—
80#1220—44no—
81#1220—42no—
82#1220—42no—
83C2×Dic15—22no—
84C2×Dic15—42no—
85C2×Dic15—41no—
86C2×Dic15—41no—
87C2×Dic15—41no—
88C2×Dic15—41no—
89C2×Dic15—41no—
90C2×Dic15—41no—
91D60—42no—
92D60—81no—
93C3×C5×C8—42no—
94C22×#67—101no—
95C2×C3×C22⋊C4C2×D511yescharacteristic
96C2×#217—101no—
97#930—52no—
98#930—101no—
99C2×C4⋊Dic3—51no—
100#886—102no—
101#882—102no—
102C3×C22⋊C8C2×D512yescomplemented
103C3⋊#95—51no—
104C3⋊#95—101no—
105#821—102no—
106#818—102no—
107C24×C5D1211yescharacteristic
108C23×D5—61no—
109C22×C4×C5D1211yescharacteristic
110C22×C4×C5C22×D311yescharacteristic
111C2×C22⋊D5—62no—
112C2×C22⋊D5—62no—
113C2×C22⋊D5—122no—
114C2×C22⋊D5—122no—
115C22×Dic5—61no—
116C22×Dic5—61no—
117C22×Dic5—61no—
118C2×D20—32no—
119C2×D20—61no—
120C2×C5×C8—22no—
121C5×C22⋊C4—22no—
122C22⋊Dic5—122no—
123#685—62no—
124#685—62no—
125C4⋊Dic5—32no—
126C4⋊Dic5—61no—
127C4⋊Dic5—62no—
128#534—151no—
129#480—152no—
130#397—151no—
131#327—152no—
132#323D1511yescharacteristic, complemented
133C22×C3×C5—21no—
134C22×C3×C5—21no—
135C22×C3×C5—22no—
136C22×C3×C5—42no—
137C22×C3×C5—41no—
138C22×C3×C5—41no—
139C22×C3×C5—81no—
140C22×C3×C5#12011yescharacteristic
141C22×C3×C5C2×D811yescharacteristic
142C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
143C2×D15—42no—
144C2×D15—42no—
145C2×D15—42no—
146C2×D15—84no—
147C3×C4×C5—22no—
148C3×C4×C5—41no—
149Dic15—42no—
150Dic15—81no—
151Dic15—81no—
152C24×C3D2011yescharacteristic
153C23×D3—101no—
154C22×C3×C4D2011yescharacteristic
155C22×C3×C4C22×D511yescharacteristic
156C2×#67—102no—
157C2×#67—102no—
158C2×#67—202no—
159C2×#67—202no—
160C22×Dic3—101no—
161C22×Dic3—101no—
162C22×Dic3—101no—
163C2×D12—52no—
164C2×D12—101no—
165C2×C3×C8—22no—
166C3×C22⋊C4—22no—
167#217—202no—
168(C2×D3)⋊C4—102no—
169(C2×D3)⋊C4—102no—
170C4⋊Dic3—52no—
171C4⋊Dic3—101no—
172C4⋊Dic3—102no—
173C23×C5—21no—
174C23×C5—21no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5D2412yes—
178C23×C5C2×D1211yescharacteristic
179C22×D5—62no—
180C22×D5—122no—
181C22×D5—241no—
182C22×D5—241no—
183C2×C4×C5—21no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5D3×D412yes—
187C22⋊D5—124no—
188C22⋊D5—122no—
189C22⋊D5—122no—
190C2×Dic5—62no—
191C2×Dic5—122no—
192C2×Dic5—121no—
193C2×Dic5—121no—
194C2×Dic5—121no—
195C2×Dic5—121no—
196C2×Dic5—121no—
197C2×Dic5—121no—
198D20—122no—
199D20—241no—
200C5×C8—42no—
201C22×D4—301no—
202#123—302no—
203#121—152no—
204#121—301no—
205#120—302no—
206C2×C4⋊C4—151no—
207C2×C22⋊C4—301no—
208C2×C22⋊C4C2×D1511yescharacteristic
209#107—302no—
210#102—302no—
211C22⋊C8C2×D1512yescomplemented
212#95—151no—
213#95—301no—
214C2×C3×C5—21no—
215C2×C3×C5—21no—
216C2×C3×C5—42no—
217C2×C3×C5#44711yescharacteristic
218C2×C3×C5#45511yescharacteristic
219C2×C3×C5#45811yescharacteristic
220D15—82no—
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—41no—
224C23×C3—41no—
225C23×C3D4012yes—
226C23×C3C2×D2011yescharacteristic
227C22×D3—102no—
228C22×D3—202no—
229C22×D3—401no—
230C22×D3—401no—
231C2×C3×C4—21no—
232C2×C3×C4—41no—
233C2×C3×C4—41no—
234C2×C3×C4D4×D512yes—
235#67—204no—
236#67—202no—
237#67—202no—
238C2×Dic3—102no—
239C2×Dic3—202no—
240C2×Dic3—201no—
241C2×Dic3—201no—
242C2×Dic3—201no—
243C2×Dic3—201no—
244C2×Dic3—201no—
245C2×Dic3—201no—
246D12—202no—
247D12—401no—
248C3×C8—42no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—22no—
252C22×C5—42no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—81no—
256C22×C5#88211yescharacteristic
257C22×C5C2×D2411yescharacteristic
258C22×C5#90811yescharacteristic
259C2×D5—122no—
260C2×D5—122no—
261C2×D5—122no—
262C2×D5—244no—
263C4×C5—22no—
264C4×C5—41no—
265Dic5—122no—
266Dic5—241no—
267Dic5—241no—
268C24—301no—
269C24D6011yescharacteristic
270C2×D4—152no—
271C2×D4—301no—
272C2×D4—302no—
273C2×D4—302no—
274C2×D4—602no—
275C2×D4—602no—
276C22×C4—301no—
277C22×C4—301no—
278C22×C4—301no—
279C22×C4D6011yescharacteristic
280C22×C4C22×D1511yescharacteristic
281C2×C8—22no—
282C4⋊C4—152no—
283C4⋊C4—301no—
284C4⋊C4—302no—
285C22⋊C4—22no—
286C22⋊C4—302no—
287C22⋊C4—302no—
288C22⋊C4—602no—
289C3×C5#160711yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—22no—
293C22×C3—42no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—81no—
297C22×C3#402811yescharacteristic
298C22×C3C2×D4011yescharacteristic
299C22×C3#405411yescharacteristic
300C2×D3—202no—
301C2×D3—202no—
302C2×D3—202no—
303C2×D3—404no—
304C3×C4—22no—
305C3×C4—41no—
306Dic3—202no—
307Dic3—401no—
308Dic3—401no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5—42no—
312C2×C5#473211yescharacteristic
313C2×C5#474211yescharacteristic
314C2×C5#474611yescharacteristic
315D5—242no—
316C23—21no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23—302no—
321C23—602no—
322C23—1201no—
323C23—1201no—
324C23D12012yes—
325C23C2×D6011yescharacteristic
326D4—602no—
327D4—604no—
328D4—602no—
329D4—602no—
330D4—1201no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—302no—
335C2×C4—602no—
336C2×C4—601no—
337C2×C4—601no—
338C2×C4—601no—
339C2×C4—601no—
340C2×C4—601no—
341C2×C4—601no—
342C2×C4D4×D1512yes—
343C8—42no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—42no—
347C2×C3#6502111yescharacteristic
348C2×C3#6503111yescharacteristic
349C2×C3#6503511yescharacteristic
350D3—402no—
351C5#6811011yescharacteristic, complemented, Sylow
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—602no—
360C22—602no—
361C22—602no—
362C22—1204no—
363C22#9177111yescharacteristic
364C22C2×D12011yescharacteristic
365C22#9179711yescharacteristic
366C4—22no—
367C4—41no—
368C4—602no—
369C4—1201no—
370C4—1201no—
371C3#1059890311yescharacteristic, complemented, Sylow
372C2—21no—
373C2—21no—
374C2—42no—
375C2—1202no—
376C2#1175083311yescharacteristic
377C2#1175084311yescharacteristic
378C2#1175084711yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#323C2
socleC22×C3×C5#120
prime radical#11756252C2
hypercenter#323D15
hypocenterC3×C5#1607
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #11751054C2semidirect
3. #11750837C2semidirect
4. C3×C5×#323C2semidirect
5. #11746291C2semidirect
12. C2×C4⋊Dic15C22semidirect
15. C3×C5×C22⋊C8C22semidirect
17. #91115C22semidirect
24. C5×#323D3semidirect
50. C3×#323D5semidirect
60. C5×C22⋊C8C2×D3semidirect
102. C3×C22⋊C8C2×D5semidirect
132. #323D15semidirect
211. C22⋊C8C2×D15semidirect
289. C3×C5#1607semidirect
351. C5#68110semidirect
371. C3#10598903semidirect

Maximal subgroups

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

subgroupindex
#117562522
#117510542
#117508372
C3×C5×#3232
#117462912
#105989033
#681105