Finite Group Databasebeta

← #14471817

Subgroups — #14471817

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
1C5×#5585C211yesmaximal, characteristic, complemented
2#11752645C211yesmaximal, characteristic, complemented
3C4×#6717C211yesmaximal, characteristic, complemented
4C3×#65310C211yesmaximal, characteristic, complemented
5#11749236C212yesmaximal, complemented
6#11749188C212yesmaximal, complemented
7#11747395C212yesmaximal, complemented
8#11747230C212yesmaximal, complemented
9#11747045C211yesmaximal, characteristic
10#11746901C211yesmaximal, characteristic, complemented
11#11746857C211yesmaximal, characteristic, complemented
12#10615444—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14C2×#6717C2211yescharacteristic
15C4×D60C2211yescharacteristic
16C5×#947C2212yes—
17C5×#894—22no—
18C5×#893C2212yes—
19C5×#875—21no—
20C5×#874C2211yescharacteristic
21C4×C5×D12—21no—
22C4×C5×Dic6C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24#91437—21no—
25#91428C2212yes—
26#91411—22no—
27#91383—21no—
28#91381C2212yes—
29C2×#6654C2212yes—
30#91119C2211yescharacteristic
31#91093C2211yescharacteristic
32#91092C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C3×#3967C2212yes—
35C3×#3939C2212yes—
36C3×C4⋊#168C2211yescharacteristic
37Dic3⋊#168C2212yes—
38#90967C2212yes—
39#90966C2212yes—
40#90966C2212yes—
41Dic3×#168C2212yes—
42#81134—51nomaximal, Hall
43C5×#559—31no—
44#65913—31no—
45#65361—31no—
46#65359—31no—
47#65346—32no—
48#65345—32no—
49C4×#688—31no—
50Q8×#168—31no—
51#65310D311yescharacteristic, complemented
52C4×#686—32no—
53#65298—32no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C5×D12—21no—
58C2×C5×D12—21no—
59C2×C5×D12C2312yes—
60C2×C4×C5×D3—22no—
61C2×C5×Dic6D411yescharacteristic
62C2×C3×Dic10—21no—
63C2×#1200—22no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4C2311yescharacteristic
66C3×C42×C5—21no—
67C3×C42×C5C2311yescharacteristic
68#6717—22no—
69#6714—21no—
70C4⋊Dic15C2311yescharacteristic
71C2×C3⋊#168C2311yescharacteristic
72C2×C3⋊#168C2311yescharacteristic
73C5×(C2×D3)⋊C4—22no—
74C5×(C2×D3)⋊C4—22no—
75C5×(C2×D3)⋊C4—22no—
76C5×C4⋊Dic3D411yescharacteristic
77C5×Dic3⋊C4D412yes—
78C4×C5×Dic3C2312yes—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2312yes—
81C2×C3×#168C2312yes—
82#6669—22no—
83#6668—22no—
84#6667—22no—
85#6654—24no—
86#5730—51no—
87#5585D511yescharacteristic, complemented
88C3×#477—51no—
89#5088—51no—
90C4×#215—51no—
91#4891—52no—
92#4872—52no—
93#4843—51no—
94#4830—51no—
95#4819—52no—
96#4800—52no—
97C5×#127—31no—
98C5×#124—32no—
99C5×#124—61no—
100C5×#123—62no—
101C4×C5×Q8—31no—
102C4×C5×Q8C2×D311yescharacteristic
103C4×C5×D4—32no—
104C4×C5×D4—61no—
105#4092—61no—
106C2×#688—31no—
107C2×#686—32no—
108#4042—62no—
109D5×C4⋊C4—61no—
110C4×D20—31no—
111C4×D20—32no—
112#4016—32no—
113#4015C2×D311yescharacteristic
114#3967—31no—
115#3967C2×D312yes—
116#3964—32no—
117#3964—32no—
118#3964—32no—
119#3941—31no—
120#3940—31no—
121#3939C2×D312yes—
122C4⋊#168—32no—
123C4⋊#168C2×D311yescharacteristic
124C4×#168—31no—
125C4×#168—32no—
126#3361—151noSylow
127C22×D15—21no—
128C22×C5×D3—22no—
129C3×C5×Q8—21no—
130C3×C5×Q8—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—21no—
137D60—21no—
138D60#4112yes—
139C4×D15—42no—
140C2×C5×Dic3C2×D412yes—
141C2×C5×Dic3C2×D412yes—
142C5×D12—22no—
143C5×D12—22no—
144C5×D12—42no—
145C5×D12—81no—
146C4×C5×D3—82no—
147C5×Dic6—22no—
148C2×C3×Dic5—22no—
149C3×Dic10—81no—
150#1200—82no—
151C3⋊#168—21no—
152C3⋊#168—21no—
153C3×#168—22no—
154C3×C4⋊Q8—51no—
155C3×C4×Q8C2×D511yescharacteristic
156#947C2×D512yes—
157#946—102no—
158C2×#215—51no—
159C2×D24—52no—
160#897—101no—
161#894—22no—
162#893—52no—
163#893C2×D512yes—
164D3×C4⋊C4—101no—
165#890—52no—
166#875—21no—
167#874C2×D511yescharacteristic
168C4×D12—21no—
169C4×D12—51no—
170C4×Dic6C2×D511yescharacteristic
171C3×#107—52no—
172C3×C4⋊C8—51no—
173C3×#103—52no—
174#835—51no—
175#821—52no—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#809—52no—
179#809—52no—
180#809—51no—
181#808—51no—
182C4×C3⋊C8—51no—
183C2×C5×Q8—31no—
184C2×C5×Q8C22×D311yescharacteristic
185C2×C5×D4—32no—
186C2×C5×D4—61no—
187C2×C5×D4—61no—
188C22×C4×C5—62no—
189C2×D20—31no—
190C2×C4×D5—61no—
191C2×C4×D5—62no—
192C2×Dic10—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—31no—
195C5×C4⋊C4—32no—
196C5×C4⋊C4C22×D311yescharacteristic
197C5×C22⋊C4—62no—
198C5×C22⋊C4—62no—
199C5×C22⋊C4—62no—
200C42×C5—21no—
201C42×C5—32no—
202C42×C5C22×D311yescharacteristic
203#688—62no—
204#686—64no—
205#685—62no—
206#685—61no—
207C4⋊Dic5—21no—
208C4⋊Dic5—31no—
209C4⋊Dic5C22×D312yes—
210#683—62no—
211#683—62no—
212C2×#168—31no—
213C2×#168—31no—
214C2×#168C22×D312yes—
215#559—31no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—51no—
221#463—152no—
222#459—151no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C2×C5×D3—42no—
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C3×C4×C5—21no—
234C3×C4×C5—41no—
235C3×C4×C5—41no—
236C3×C4×C5#13512yes—
237C3×C4×C5C2×#4111yescharacteristic
238C3×C4×C52−1+411yescharacteristic
239Dic15—41no—
240C3×Dic5—42no—
241C5×Dic3—22no—
242C5×Dic3—22no—
243C2×C3×Q8—101no—
244C2×C3×Q8C22×D511yescharacteristic
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—51no—
248C2×D12C22×D512yes—
249C2×C4×D3—22no—
250C2×C4×D3—101no—
251C2×C4×D3—102no—
252C2×Dic6C22⋊D511yescharacteristic
253C2×C3×C8—52no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—52no—
256C3×C4⋊C4—101no—
257C3×C4⋊C4C22×D511yescharacteristic
258C3×C42—21no—
259C3×C42C22×D511yescharacteristic
260#215—102no—
261(C2×D3)⋊C4—22no—
262(C2×D3)⋊C4—22no—
263(C2×D3)⋊C4—22no—
264(C2×D3)⋊C4—101no—
265(C2×D3)⋊C4—102no—
266C4⋊Dic3—51no—
267C4⋊Dic3—102no—
268C4⋊Dic3C22⋊D511yescharacteristic
269Dic3⋊C4—102no—
270Dic3⋊C4C22⋊D512yes—
271C4×Dic3C22×D512yes—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—51no—
274D24—104no—
275C23×C5—62no—
276C22×D5—61no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×Q8—62no—
280C5×D4—62no—
281C5×D4—62no—
282C5×D4—122no—
283C5×D4—241no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—32no—
287C2×C4×C5—32no—
288C2×C4×C5—242no—
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5C23×D311yescharacteristic
292C2×Dic5—22no—
293C2×Dic5—61no—
294D20—32no—
295D20—61no—
296C4×D5—122no—
297C4×D5—242no—
298Dic10—81no—
299#168—22no—
300#168—61no—
301#168—61no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8—51no—
305#127—31no—
306#125—152no—
307#124—32no—
308#124—61no—
309#123—62no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—31no—
313C4×Q8D3×D511yescharacteristic
314C4×D4—32no—
315C4×D4—61no—
316C4×D4—152no—
317C4×D4—151no—
318C2×C4⋊C4—301no—
319#107—52no—
320#106—151no—
321C4⋊C8—51no—
322C4⋊C8—152no—
323#103—52no—
324#103—151no—
325#102—152no—
326#102—152no—
327#102—152no—
328#102—151no—
329C4×C8—152no—
330C4×C8—151no—
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334D15—42no—
335C5×D3—82no—
336C22×D3—22no—
337C22×D3—101no—
338C3×Q8—21no—
339C3×Q8—21no—
340C3×Q8—401no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—102no—
344C2×C3×C4C2×C22⋊D511yescharacteristic
345C2×C3×C4C2×C22⋊D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—101no—
348C2×Dic3C2×C22⋊D512yes—
349C2×Dic3C2×C22⋊D512yes—
350D12—22no—
351D12—22no—
352D12—42no—
353D12—52no—
354D12—81no—
355D12—101no—
356C4×D3—82no—
357C4×D3—202no—
358C4×D3—402no—
359Dic6—22no—
360C3×C8—102no—
361C3⋊C8—101no—
362C3⋊C8—101no—
363C22×C5—122no—
364C22×C5—122no—
365C22×C5—122no—
366C22×C5C2×D3×D411yescharacteristic
367C2×D5—62no—
368C2×D5—121no—
369C2×D5—121no—
370C4×C5—21no—
371C4×C5—41no—
372C4×C5—41no—
373C4×C5—62no—
374C4×C5—62no—
375C4×C5#91912yes—
376C4×C5#100711yescharacteristic
377C4×C5D3×#4111yescharacteristic
378Dic5—42no—
379Dic5—121no—
380C2×Q8—31no—
381C2×Q8—101no—
382C2×Q8C2×D3×D511yescharacteristic
383C2×D4—32no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4—151no—
387C22×C4—62no—
388C22×C4—302no—
389C22×C4—301no—
390SD16—302no—
391D8—304no—
392C2×C8—52no—
393C2×C8—151no—
394C2×C8—151no—
395C4⋊C4—21no—
396C4⋊C4—31no—
397C4⋊C4—32no—
398C4⋊C4—52no—
399C4⋊C4—101no—
400C4⋊C4—151no—
401C4⋊C4—302no—
402C4⋊C4—302no—
403C4⋊C4C2×D3×D511yescharacteristic
404C22⋊C4—62no—
405C22⋊C4—62no—
406C22⋊C4—62no—
407C22⋊C4—302no—
408C22⋊C4—301no—
409C42—21no—
410C42—32no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3C22×C22⋊D511yescharacteristic
414C2×D3—42no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—102no—
418C2×D3—201no—
419C2×D3—201no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—202no—
424C3×C4#409612yes—
425C3×C4D5×#4111yescharacteristic
426C3×C4#415011yescharacteristic
427Dic3—22no—
428Dic3—22no—
429Dic3—201no—
430C2×C5—242no—
431C2×C5#563311yescharacteristic
432C2×C5C2×#91911yescharacteristic
433C2×C5#577411yescharacteristic
434D5—122no—
435C23—62no—
436C23—301no—
437Q8—21no—
438Q8—21no—
439Q8—62no—
440Q8—401no—
441D4—62no—
442D4—62no—
443D4—122no—
444D4—152no—
445D4—241no—
446D4—301no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—32no—
450C2×C4—32no—
451C2×C4—102no—
452C2×C4—242no—
453C2×C4—301no—
454C2×C4—602no—
455C2×C4—1202no—
456C2×C4D3×C22⋊D511yescharacteristic
457C2×C4D3×C22⋊D511yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—102no—
460C8—301no—
461C8—301no—
462C2×C3C2×#409611yescharacteristic
463C2×C3#6616511yescharacteristic
464C2×C3#6616911yescharacteristic
465D3—82no—
466D3—202no—
467C5#8113411yescharacteristic, complemented, Sylow
468C22—122no—
469C22—122no—
470C22—122no—
471C22—302no—
472C22—601no—
473C22—601no—
474C22C2×D3×C22⋊D511yescharacteristic
475C4—21no—
476C4—41no—
477C4—41no—
478C4—62no—
479C4—62no—
480C4—202no—
481C4—601no—
482C4#9151912yes—
483C4#9200411yescharacteristic
484C4#9201611yescharacteristic
485C3#1061544411yescharacteristic, complemented, Sylow
486C2—242no—
487C2—602no—
488C2#1175454611yescharacteristic
489C2C2×#9151911yescharacteristic
490C2#1175532311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11747045C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5585C2semidirect
2. #11752645C2semidirect
3. C4×#6717C2semidirect
4. C3×#65310C2semidirect
5. #11749236C2semidirect
6. #11749188C2semidirect
7. #11747395C2semidirect
8. #11747230C2semidirect
10. #11746901C2semidirect
11. #11746857C2semidirect
51. #65310D3semidirect
87. #5585D5semidirect
412. C3×C5#3361semidirect
467. C5#81134semidirect
485. C3#10615444semidirect

Maximal subgroups

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

subgroupindex
C5×#55852
#117526452
C4×#67172
C3×#653102
#117492362
#117491882
#117473952
#117472302
#117470452
#117469012
#117468572
#106154443
#811345