Finite Group Databasebeta

← #14303008

Subgroups — #14303008

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756563C211yesmaximal, characteristic
2C3×#66132C211yesmaximal, characteristic, complemented
3C2×C5×#834C211yesmaximal, characteristic, complemented
4C2×#90997C212yesmaximal, complemented
5#11746018C212yesmaximal, complemented
6#10600817—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×#1220C2211yescharacteristic
9#91842—21no—
10C2×#6719C2211yescharacteristic
11#91828—22no—
12#91826C412yescomplemented
13#91824C412yescomplemented
14#91818—21no—
15C2×C5×#217C2212yes—
16C2×C3×C22⋊Dic5—21no—
17C2×C3×C22⋊Dic5C2212yes—
18C3×D4×Dic5—24no—
19C3×#4072—21no—
20C5×#834—22no—
21#90997—24no—
22#71656—51nomaximal, Hall
23#66138—31no—
24#66132D311yescharacteristic, complemented
25C2×C5×#99—31no—
26C2×#3938—32no—
27#64746—32no—
28C24×C3×C5D411yescharacteristic
29C24×C3×C5C2311yescharacteristic
30C23×D15C2×C411yescharacteristic, complemented
31C2×C3×C5×D4—22no—
32C2×C3×C5×D4—22no—
33C2×C3×C5×D4C2×C412yes—
34C2×C3×C5×D4D412yes—
35C22×C3×C4×C5D411yescharacteristic
36C2×#1220—22no—
37C2×#1220—21no—
38C2×#1220—21no—
39C2×#1220—22no—
40C2×#1220—22no—
41C22×Dic15—21no—
42C22×Dic15C2×C411yescharacteristic, complemented
43C22×C5×Dic3—22no—
44C22×C3×Dic5—22no—
45C22×C3×Dic5—22no—
46#6719—22no—
47#6719—21no—
48#6719C2×C412yescomplemented
49#6714—22no—
50#6712—22no—
51C5×#217—22no—
52C5×#217—22no—
53C3×C22⋊Dic5—22no—
54C3×C22⋊Dic5—22no—
55C3×C22⋊Dic5D414yescomplemented
56C3×C4⋊Dic5—22no—
57C3×C4×Dic5—22no—
58C3×#518—51no—
59#5804—51no—
60C2×#834D511yescharacteristic, complemented
61C2×#806—52no—
62#4527—52no—
63C22×C5×D4C2×D311yescharacteristic
64C22×C22⋊D5—31no—
65C2×C5×C22⋊C4—32no—
66#4099—61no—
67C2×C22⋊Dic5—21no—
68C2×C22⋊Dic5—31no—
69C2×C22⋊Dic5C2×D312yes—
70#4085—62no—
71#4083—32no—
72#4081—32no—
73D4×Dic5—24no—
74#4075—61no—
75#4072—21no—
76C5×#99—62no—
77#3938—64no—
78#1913—151noSylow
79C23×C3×C5—21no—
80C23×C3×C5—21no—
81C23×C3×C5—81no—
82C23×C3×C5—81no—
83C23×C3×C5C22⋊C412yes—
84C23×C3×C5C22×C411yescharacteristic
85C23×C3×C5C2×D411yescharacteristic
86C23×C3×C5C2×D411yescharacteristic
87C23×C3×C5C2×D412yes—
88C23×C3×C5#4112yes—
89C22×D15—21no—
90C22×D15—22no—
91C22×D15—81no—
92C3×C5×D4—24no—
93C3×C5×D4—24no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22⋊C412yes—
97#1220—41no—
98#1220—42no—
99#1220—41no—
100#1220—82no—
101C2×Dic15—21no—
102C2×Dic15—22no—
103C2×Dic15—22no—
104C2×Dic15—81no—
105C2×C5×Dic3—42no—
106C2×C5×Dic3—82no—
107C2×C3×Dic5—24no—
108C2×C3×Dic5—82no—
109C2×C3×Dic5—82no—
110C22×C3×D4C2×D511yescharacteristic
111C22×#67—51no—
112C3×C4×D4—104no—
113C3×#117—101no—
114C2×C3×C22⋊C4—52no—
115C2×C3×C22⋊C4—101no—
116#953—101no—
117C2×#217—51no—
118C2×#217C2×D512yes—
119#939—102no—
120#937—52no—
121#935—52no—
122#929—101no—
123#834—22no—
124#806—104no—
125C24×C5#6711yescharacteristic
126C24×C5C22×D311yescharacteristic
127C23×D5—31no—
128C2×C5×D4—22no—
129C2×C5×D4—22no—
130C2×C5×D4C4×D312yes—
131C2×C5×D4D1212yes—
132C22×C4×C5—62no—
133C22×C4×C5#6711yescharacteristic
134C2×C22⋊D5—61no—
135C2×C22⋊D5—62no—
136C2×C22⋊D5—61no—
137C2×C22⋊D5—62no—
138C2×C22⋊D5—62no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—31no—
142C22×Dic5—61no—
143C5×C22⋊C4—62no—
144C5×C22⋊C4—62no—
145C22⋊Dic5—22no—
146C22⋊Dic5—22no—
147C22⋊Dic5—32no—
148C22⋊Dic5—62no—
149C22⋊Dic5—61no—
150C22⋊Dic5#6714yescomplemented
151#685—62no—
152C4⋊Dic5—22no—
153#683—62no—
154C4×Dic5—22no—
155#534—151no—
156#518—51no—
157C2×#99—31no—
158C2×#99—152no—
159#342—152no—
160C22×C3×C5—22no—
161C22×C3×C5—42no—
162C22×C3×C5—42no—
163C22×C3×C5—41no—
164C22×C3×C5—41no—
165C22×C3×C5—41no—
166C22×C3×C5—42no—
167C22×C3×C5—42no—
168C22×C3×C5—81no—
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C22×C3×C5C4×D412yes—
171C22×C3×C5#12011yescharacteristic
172C22×C3×C5#12112yes—
173C22×C3×C5#12311yescharacteristic
174C2×D15—42no—
175C2×D15—41no—
176C2×D15—82no—
177C3×C4×C5—22no—
178Dic15—42no—
179Dic15—41no—
180C3×Dic5—44no—
181C5×Dic3—82no—
182C24×C3D2011yescharacteristic
183C24×C3C22×D511yescharacteristic
184C23×D3—51no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4C4×D512yes—
188C2×C3×D4C22⋊D512yes—
189C22×C3×C4—102no—
190C22×C3×C4—102no—
191C22×C3×C4D2011yescharacteristic
192C2×#67—101no—
193C2×#67—102no—
194C2×#67—102no—
195C2×#67—101no—
196C2×#67—102no—
197C22×Dic3—22no—
198C22×Dic3—51no—
199C22×Dic3—101no—
200C3×C4⋊C4—102no—
201C3×C22⋊C4—54no—
202C3×C22⋊C4—102no—
203C3×C22⋊C4—102no—
204C3×C42—102no—
205#217—22no—
206#217—22no—
207#217—52no—
208#217—102no—
209#217—101no—
210(C2×D3)⋊C4—102no—
211Dic3⋊C4—102no—
212C23×C5—21no—
213C23×C5—21no—
214C23×C5—81no—
215C23×C5—81no—
216C23×C5(C2×D3)⋊C412yes—
217C23×C5C2×C4×D311yescharacteristic
218C23×C5C2×D1211yescharacteristic
219C23×C5#23512yes—
220C23×C5C2×#6711yescharacteristic
221C23×C5C2×#6712yes—
222C22×D5—61no—
223C22×D5—62no—
224C22×D5—241no—
225C5×D4—24no—
226C5×D4—24no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—122no—
230C2×C4×C5—242no—
231C2×C4×C5(C2×D3)⋊C412yes—
232C22⋊D5—121no—
233C22⋊D5—122no—
234C22⋊D5—121no—
235C22⋊D5—242no—
236C2×Dic5—24no—
237C2×Dic5—61no—
238C2×Dic5—62no—
239C2×Dic5—62no—
240C2×Dic5—82no—
241C2×Dic5—82no—
242C2×Dic5—241no—
243C22×D4—151no—
244C22×D4D3×D511yescharacteristic
245#123—152no—
246#123—301no—
247#121—302no—
248#120—152no—
249#120—301no—
250C4×D4—104no—
251#117—101no—
252C2×C22⋊C4—32no—
253C2×C22⋊C4—52no—
254C2×C22⋊C4—101no—
255C2×C22⋊C4—151no—
256#99—62no—
257#99—304no—
258C2×C3×C5—22no—
259C2×C3×C5—21no—
260C2×C3×C5—21no—
261C2×C3×C5—22no—
262C2×C3×C5—21no—
263C2×C3×C5—42no—
264C2×C3×C5#38611yescharacteristic
265D15—81no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—81no—
269C23×C3—81no—
270C23×C3#68512yes—
271C23×C3C2×C4×D511yescharacteristic
272C23×C3C2×D2011yescharacteristic
273C23×C3D4×D512yes—
274C23×C3#71112yes—
275C23×C3C2×C22⋊D511yescharacteristic
276C22×D3—101no—
277C22×D3—102no—
278C22×D3—401no—
279C3×D4—24no—
280C3×D4—24no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—104no—
284C2×C3×C4—402no—
285C2×C3×C4—402no—
286C2×C3×C4#68512yes—
287#67—201no—
288#67—201no—
289#67—202no—
290#67—402no—
291C2×Dic3—42no—
292C2×Dic3—82no—
293C2×Dic3—102no—
294C2×Dic3—101no—
295C2×Dic3—102no—
296C2×Dic3—401no—
297C22×C5—22no—
298C22×C5—42no—
299C22×C5—41no—
300C22×C5—42no—
301C22×C5—41no—
302C22×C5—41no—
303C22×C5—42no—
304C22×C5—42no—
305C22×C5—81no—
306C22×C5C2×(C2×D3)⋊C411yescharacteristic
307C22×C5C4×#6712yes—
308C22×C5#92911yescharacteristic
309C22×C5#93012yes—
310C22×C5#95311yescharacteristic
311C2×D5—122no—
312C2×D5—121no—
313C2×D5—242no—
314C4×C5—22no—
315C4×C5—242no—
316Dic5—44no—
317Dic5—122no—
318Dic5—121no—
319C24—151no—
320C24#120211yescharacteristic
321C24C2×D3×D511yescharacteristic
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—302no—
325C2×D4—301no—
326C2×D4—301no—
327C2×D4—302no—
328C2×D4—302no—
329C2×D4#120012yes—
330C2×D4#120312yes—
331C22×C4—62no—
332C22×C4—102no—
333C22×C4—102no—
334C22×C4—151no—
335C22×C4—301no—
336C22×C4#120211yescharacteristic
337C4⋊C4—102no—
338C4⋊C4—302no—
339C22⋊C4—54no—
340C22⋊C4—62no—
341C22⋊C4—62no—
342C22⋊C4—102no—
343C22⋊C4—102no—
344C22⋊C4—152no—
345C22⋊C4—302no—
346C22⋊C4—301no—
347C22⋊C4—302no—
348C42—102no—
349C3×C5#191311yescharacteristic, complemented, Hall
350C22×C3—22no—
351C22×C3—42no—
352C22×C3—41no—
353C22×C3—42no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—81no—
359C22×C3#402712yes—
360C22×C3#402811yescharacteristic
361C22×C3#403211yescharacteristic
362C22×C3C2×#68511yescharacteristic
363C22×C3#408512yes—
364C2×D3—202no—
365C2×D3—201no—
366C2×D3—402no—
367C3×C4—22no—
368C3×C4—204no—
369Dic3—82no—
370Dic3—202no—
371Dic3—201no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5—22no—
375C2×C5—22no—
376C2×C5—21no—
377C2×C5—42no—
378C2×C5#521311yescharacteristic
379D5—241no—
380C23—21no—
381C23—21no—
382C23—81no—
383C23—81no—
384C23—301no—
385C23—302no—
386C23—1201no—
387C23#666712yes—
388C23#678212yes—
389C23C2×#120011yescharacteristic
390C23C2×#120211yescharacteristic
391C23C2×#120311yescharacteristic
392C23D5×#6712yes—
393D4—24no—
394D4—24no—
395D4—601no—
396D4—601no—
397D4—602no—
398D4—1202no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—104no—
402C2×C4—122no—
403C2×C4—242no—
404C2×C4—302no—
405C2×C4—301no—
406C2×C4—302no—
407C2×C4—402no—
408C2×C4—402no—
409C2×C4—1201no—
410C2×C4#666712yes—
411C2×C3—22no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—22no—
415C2×C3—21no—
416C2×C3—42no—
417C2×C3#6524711yescharacteristic
418D3—401no—
419C5#7165611yescharacteristic, complemented, Sylow
420C22—22no—
421C22—42no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—42no—
427C22—42no—
428C22—81no—
429C22—602no—
430C22—601no—
431C22—1202no—
432C22C2×#666711yescharacteristic
433C22#9154611yescharacteristic
434C22#9155212yes—
435C22#9156411yescharacteristic
436C22#9156612yes—
437C4—22no—
438C4—204no—
439C4—242no—
440C4—602no—
441C4—601no—
442C3#1060081711yescharacteristic, complemented, Sylow
443C2—21no—
444C2—22no—
445C2—21no—
446C2—21no—
447C2—22no—
448C2—42no—
449C2—1201no—
450C2#1174949411yescharacteristic
subgroupG/H
centerC2#11749494
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5#386
prime radical#11756563C2
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1913
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C3×#66132C2semidirect
3. C2×C5×#834C2semidirect
4. C2×#90997C2semidirect
5. #11746018C2semidirect
12. #91826C4semidirect
13. #91824C4semidirect
24. #66132D3semidirect
30. C23×D15C2×C4semidirect
42. C22×Dic15C2×C4semidirect
48. #6719C2×C4semidirect
55. C3×C22⋊Dic5D4semidirect
60. C2×#834D5semidirect
150. C22⋊Dic5#67semidirect
349. C3×C5#1913semidirect
419. C5#71656semidirect
442. C3#10600817semidirect

Maximal subgroups

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

subgroupindex
#117565632
C3×#661322
C2×C5×#8342
C2×#909972
#117460182
#106008173
#716565