Finite Group Databasebeta

← #14471853

Subgroups — #14471853

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752662C211yesmaximal, characteristic, complemented
2#11752645C211yesmaximal, characteristic, complemented
3#11750944C211yesmaximal, characteristic
4C5×#4830C211yesmaximal, characteristic, complemented
5C3×#65139C211yesmaximal, characteristic, complemented
6#11747988C212yesmaximal, complemented
7#11747801C212yesmaximal, complemented
8#11747798C212yesmaximal, complemented
9#11747793C212yesmaximal, complemented
10C4×#6658C211yesmaximal, characteristic, complemented
11#11746910C211yesmaximal, characteristic, complemented
12#10611658—31nomaximal, Hall
13C2×D120C2212yes—
14#91763C2211yescharacteristic
15C4×D60C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91437—21no—
20#91433—22no—
21#91428C2212yes—
22#91428C2212yes—
23#91418—21no—
24#91411—22no—
25#91383—21no—
26#91381C2212yes—
27#91375—21no—
28#91374C2212yes—
29C2×#6658C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91105C2212yes—
32C5×Dic3⋊C8C2212yes—
33C5×C8×Dic3C2212yes—
34C4×C5×C3⋊C8C2211yescharacteristic
35C3×#3950C2212yes—
36C3×#3948C2212yes—
37#90987C2211yescharacteristic
38#90971C2211yescharacteristic
39#90968C2212yes—
40#90968C2212yes—
41#90968C2211yescharacteristic
42#81134—51nomaximal, Hall
43#65919—31no—
44#65913—31no—
45C5×C8×Q8—31no—
46#65139D311yescharacteristic, complemented
47#65136—32no—
48#65133—32no—
49#65132—31no—
50#64986—32no—
51#64983—31no—
52C4×D40—32no—
53C4×#677—31no—
54C2×D60—21no—
55C2×D60—21no—
56C2×D60C2312yes—
57C2×D60C2311yescharacteristic
58C2×C4×D15—21no—
59C2×C5×Dic6D411yescharacteristic
60C2×C3×Dic10—21no—
61C2×C3×Dic10C2311yescharacteristic
62C2×#1200—22no—
63C2×#1200—22no—
64C2×C3×C5×C8C2312yes—
65C3×C42×C5C2311yescharacteristic
66#6714—21no—
67C4⋊Dic15C2311yescharacteristic
68D120—24no—
69C5×C4⋊Dic3D411yescharacteristic
70C5×Dic3⋊C4D412yes—
71C4×C5×Dic3C2312yes—
72C2×C5×C3⋊C8C2311yescharacteristic
73C2×C5×C3⋊C8C2311yescharacteristic
74C3×C4⋊Dic5—21no—
75C3×C4⋊Dic5C2311yescharacteristic
76C3×C4⋊Dic5C2312yes—
77C3×#683—21no—
78C3×C4×Dic5—21no—
79#6669—22no—
80#6668—22no—
81#6667—22no—
82#6667—22no—
83#6667—22no—
84#6667—22no—
85#6658—22no—
86#5730—51no—
87#5585—51no—
88C3×#477—51no—
89#5088—51no—
90C4×#215—51no—
91#4891—52no—
92#4872—52no—
93#4843—51no—
94#4830D511yescharacteristic, complemented
95#4819—52no—
96#4800—52no—
97C4×C5×Q8—31no—
98#4093—61no—
99#4092—61no—
100C2×D40—32no—
101C2×#677—31no—
102#4042—62no—
103#4040—62no—
104#4039—61no—
105D5×C4⋊C4—61no—
106#4021—32no—
107#4020—31no—
108C4×D20—31no—
109C4×D20—32no—
110C4×D20—32no—
111#4016—32no—
112#4015C2×D311yescharacteristic
113C4×Dic10C2×D311yescharacteristic
114C5×C4⋊C8—32no—
115C5×C4⋊C8C2×D311yescharacteristic
116C4×C5×C8—32no—
117C4×C5×C8—31no—
118#3953—32no—
119#3953—32no—
120#3953—31no—
121#3953—32no—
122#3950C2×D312yes—
123#3949—31no—
124#3948—31no—
125#3948C2×D312yes—
126#3361—151noSylow
127C22×D15—21no—
128C22×D15—22no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—21no—
133D60—22no—
134D60—21no—
135D60—22no—
136D60—42no—
137D60—81no—
138D60#4112yes—
139C4×D15—42no—
140C2×C5×Dic3C2×D412yes—
141C2×C5×Dic3C2×D412yes—
142C5×Dic6—22no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—22no—
146C3×Dic10—21no—
147C3×Dic10—21no—
148C3×Dic10—81no—
149#1200—82no—
150#1200—82no—
151C3×C5×C8—22no—
152C5×C3⋊C8—21no—
153C5×C3⋊C8—21no—
154C3×C4⋊Q8—51no—
155C3×C4×Q8—51no—
156#947—52no—
157#946—102no—
158C2×#215—51no—
159C2×D24—52no—
160#897—101no—
161#894—102no—
162#893—52no—
163#893—52no—
164D3×C4⋊C4—101no—
165#890—52no—
166#875—101no—
167#874—51no—
168C4×D12—51no—
169C4×D12—101no—
170C4×Dic6C2×D511yescharacteristic
171C3×#107—52no—
172C3×C4⋊C8C2×D511yescharacteristic
173C3×#103—52no—
174#835—51no—
175#821—52no—
176Dic3⋊C8C2×D512yes—
177C8×Dic3C2×D512yes—
178#809—51no—
179#809—52no—
180#809—52no—
181#808—51no—
182C4×C3⋊C8C2×D511yescharacteristic
183C2×C5×Q8—31no—
184C2×D20—31no—
185C2×D20—32no—
186C2×D20—61no—
187C2×D20—61no—
188C2×C4×D5—61no—
189C2×C4×D5—62no—
190C2×C4×D5—62no—
191C2×Dic10—21no—
192C2×Dic10C22×D311yescharacteristic
193C2×C5×C8—31no—
194C2×C5×C8—31no—
195C2×C5×C8C22×D312yes—
196C5×C4⋊C4—32no—
197C5×C4⋊C4—31no—
198C42×C5—32no—
199C42×C5C22×D311yescharacteristic
200#685—62no—
201#685—62no—
202#685—62no—
203#685—62no—
204#685—61no—
205C4⋊Dic5—21no—
206C4⋊Dic5—31no—
207C4⋊Dic5C22×D312yes—
208C4⋊Dic5C22×D311yescharacteristic
209#683—21no—
210#683—62no—
211#683—62no—
212C4×Dic5—21no—
213D40—64no—
214#677—62no—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—51no—
221#463—152no—
222#459—151no—
223C8×Q8—31no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C2×D15—42no—
231C2×D15—42no—
232C2×D15—42no—
233C3×C4×C5—21no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—41no—
238C3×Dic5—41no—
239C3×Dic5—41no—
240C3×Dic5—42no—
241C5×Dic3—22no—
242C5×Dic3—22no—
243C2×C3×Q8—51no—
244C2×C3×Q8—101no—
245C2×D12—51no—
246C2×D12—52no—
247C2×D12—101no—
248C2×D12—101no—
249C2×C4×D3—101no—
250C2×C4×D3—102no—
251C2×C4×D3—102no—
252C2×Dic6D2011yescharacteristic
253C2×C3×C8C22×D512yes—
254C3×C4⋊C4—51no—
255C3×C4⋊C4—52no—
256C3×C4⋊C4—101no—
257C3×C4⋊C4—101no—
258C3×C42—101no—
259C3×C42C22×D511yescharacteristic
260#215—102no—
261(C2×D3)⋊C4—101no—
262(C2×D3)⋊C4—102no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—102no—
265(C2×D3)⋊C4—102no—
266C4⋊Dic3—51no—
267C4⋊Dic3—102no—
268C4⋊Dic3D2011yescharacteristic
269Dic3⋊C4—102no—
270Dic3⋊C4D2012yes—
271C4×Dic3C22×D512yes—
272C2×C3⋊C8C22×D511yescharacteristic
273C2×C3⋊C8C22×D511yescharacteristic
274D24—104no—
275C22×D5—61no—
276C22×D5—62no—
277C5×Q8—62no—
278C2×C4×C5—32no—
279C2×C4×C5—32no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—22no—
286C2×Dic5—61no—
287D20—32no—
288D20—61no—
289D20—62no—
290D20—62no—
291D20—122no—
292D20—241no—
293C4×D5—122no—
294C4×D5—242no—
295C4×D5—242no—
296Dic10—21no—
297Dic10—21no—
298Dic10—81no—
299C5×C8—22no—
300C5×C8—61no—
301C5×C8—61no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8—51no—
305#127—151no—
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—31no—
313C4×Q8—51no—
314C4×D4—152no—
315C4×D4—152no—
316C4×D4—151no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—52no—
320#106—151no—
321C4⋊C8—32no—
322C4⋊C8D3×D511yescharacteristic
323#103—52no—
324#103—151no—
325#102—151no—
326#102—152no—
327#102—152no—
328#102—152no—
329C4×C8—32no—
330C4×C8—31no—
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334D15—42no—
335D15—82no—
336C22×D3—101no—
337C22×D3—102no—
338C3×Q8—101no—
339C3×Q8—101no—
340C3×Q8—401no—
341C2×C3×C4—102no—
342C2×C3×C4—101no—
343C2×C3×C4—101no—
344C2×C3×C4C2×D2011yescharacteristic
345C2×C3×C4C2×D2011yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—101no—
348C2×Dic3C2×D2012yes—
349C2×Dic3C2×D2012yes—
350D12—52no—
351D12—101no—
352D12—102no—
353D12—102no—
354D12—202no—
355D12—401no—
356C4×D3—202no—
357C4×D3—402no—
358C4×D3—402no—
359Dic6—22no—
360C3×C8—22no—
361C3⋊C8—21no—
362C3⋊C8—21no—
363C22×C5C2×D3×D411yescharacteristic
364C2×D5—62no—
365C2×D5—121no—
366C2×D5—121no—
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C4×C5—21no—
371C4×C5—62no—
372C4×C5—62no—
373C4×C5#91912yes—
374C4×C5#100711yescharacteristic
375C4×C5D3×#4111yescharacteristic
376Dic5—41no—
377Dic5—42no—
378Dic5—41no—
379Dic5—121no—
380C2×Q8—31no—
381C2×Q8—51no—
382C2×Q8—101no—
383C2×D4—151no—
384C2×D4—152no—
385C2×D4—301no—
386C2×D4—301no—
387C22×C4—302no—
388C22×C4—302no—
389C22×C4—301no—
390SD16—302no—
391D8—304no—
392C2×C8—31no—
393C2×C8—31no—
394C2×C8C2×D3×D512yes—
395C4⋊C4—31no—
396C4⋊C4—32no—
397C4⋊C4—52no—
398C4⋊C4—51no—
399C4⋊C4—101no—
400C4⋊C4—101no—
401C4⋊C4—151no—
402C4⋊C4—302no—
403C4⋊C4—302no—
404C22⋊C4—302no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—301no—
409C42—32no—
410C42—101no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3C22×D2011yescharacteristic
414C2×D3—102no—
415C2×D3—201no—
416C2×D3—201no—
417C2×D3—202no—
418C2×D3—202no—
419C2×D3—202no—
420C3×C4—21no—
421C3×C4—201no—
422C3×C4—202no—
423C3×C4—201no—
424C3×C4#405012yes—
425C3×C4#414711yescharacteristic
426C3×C4D5×#4111yescharacteristic
427Dic3—22no—
428Dic3—22no—
429Dic3—201no—
430C2×C5#563311yescharacteristic
431C2×C5C2×#91911yescharacteristic
432C2×C5#577411yescharacteristic
433D5—122no—
434D5—242no—
435C23—301no—
436C23—302no—
437Q8—62no—
438Q8—101no—
439Q8—101no—
440Q8—401no—
441D4—152no—
442D4—302no—
443D4—301no—
444D4—302no—
445D4—602no—
446D4—1201no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—101no—
450C2×C4—101no—
451C2×C4—102no—
452C2×C4—301no—
453C2×C4—602no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4D3×D2011yescharacteristic
457C2×C4D3×D2011yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—22no—
460C8—61no—
461C8—61no—
462C2×C3#6591011yescharacteristic
463C2×C3C2×#405011yescharacteristic
464C2×C3#6608611yescharacteristic
465D3—202no—
466D3—402no—
467C5#8113411yescharacteristic, complemented, Sylow
468C22—302no—
469C22—601no—
470C22—601no—
471C22—602no—
472C22—602no—
473C22—602no—
474C22C2×D3×D2011yescharacteristic
475C4—21no—
476C4—62no—
477C4—62no—
478C4—201no—
479C4—202no—
480C4—201no—
481C4—601no—
482C4#9127512yes—
483C4#9202411yescharacteristic
484C4#9202911yescharacteristic
485C3#1061165811yescharacteristic, complemented, Sylow
486C2—602no—
487C2—1202no—
488C2#1175334211yescharacteristic
489C2C2×#9127511yescharacteristic
490C2#1175403111yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radical#11750944C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11752662C2semidirect
2. #11752645C2semidirect
4. C5×#4830C2semidirect
5. C3×#65139C2semidirect
6. #11747988C2semidirect
7. #11747801C2semidirect
8. #11747798C2semidirect
9. #11747793C2semidirect
10. C4×#6658C2semidirect
11. #11746910C2semidirect
46. #65139D3semidirect
94. #4830D5semidirect
412. C3×C5#3361semidirect
467. C5#81134semidirect
485. C3#10611658semidirect

Maximal subgroups

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

subgroupindex
#117526622
#117526452
#117509442
C5×#48302
C3×#651392
#117479882
#117478012
#117477982
#117477932
C4×#66582
#117469102
#106116583
#811345