Finite Group Databasebeta

← #14459933

Subgroups — #14459933

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#556C211yesmaximal, characteristic, complemented
2#11756310C211yesmaximal, characteristic
3#11751194C211yesmaximal, characteristic, complemented
4#11751188C211yesmaximal, characteristic, complemented
5#11751152C212yesmaximal, complemented
6#11751148C212yesmaximal, complemented
7#11751132C211yesmaximal, characteristic, complemented
8C4×#6717C211yesmaximal, characteristic, complemented
9D4×C3⋊#168C211yesmaximal, characteristic, complemented
10#11751103C212yesmaximal, complemented
11#11751097C212yesmaximal, complemented
12#10615395—31nomaximal, Hall
13C2×#6817C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C5×#126—22no—
16C3×C5×#124—21no—
17C3×C5×C22⋊Q8C2212yes—
18C3×C4×C5×Q8—21no—
19C3×C4×C5×Q8C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21C3×C5×#117C2212yes—
22C2×#6718C2212yes—
23C2×#6717C2211yescharacteristic
24#91827—21no—
25#91813C2212yes—
26C22×C3⋊#168C2212yes—
27C4⋊C4×D15—21no—
28#91772—22no—
29C4×D60C2211yescharacteristic
30#91758C2211yescharacteristic
31#91119C2211yescharacteristic
32#91114C2212yes—
33#91094C2212yes—
34#91094C2212yes—
35#91094C2212yes—
36#91093C2212yes—
37#91093C2211yescharacteristic
38#91092C2211yescharacteristic
39#91091C2212yes—
40C4⋊(C3⋊#168)C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#83664—51nomaximal, Hall
43C5×#556D311yescharacteristic, complemented
44#65885—31no—
45#65382—31no—
46#65376—31no—
47#65340—32no—
48#65336—32no—
49#65320—31no—
50C4×#688—31no—
51D4×#168—31no—
52#65291—32no—
53#65285—32no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8C2311yescharacteristic
56C2×C3×C5×D4D411yescharacteristic
57C22×C3×C4×C5C2312yes—
58C2×#1220—22no—
59#6817—24no—
60#6817—42no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×C4×D15—22no—
64C2×Dic30C2312yes—
65C3×C5×C4⋊C4—22no—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4D411yescharacteristic
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2312yes—
71C3×C5×C22⋊C4—22no—
72C3×C5×C22⋊C4—22no—
73C3×C5×C22⋊C4D412yes—
74C3×C42×C5—22no—
75C3×C42×C5—21no—
76C3×C42×C5C2311yescharacteristic
77#6719—22no—
78#6718—42no—
79#6717—22no—
80#6714—21no—
81C4⋊Dic15—21no—
82C4⋊Dic15—21no—
83C4⋊Dic15C2311yescharacteristic
84#6712—22no—
85C2×C3⋊#168—42no—
86C2×C3⋊#168C2311yescharacteristic
87C2×C3⋊#168C2312yes—
88C2×C3⋊#168C2311yescharacteristic
89C3×#556D511yescharacteristic, complemented
90#5551—51no—
91#5093—51no—
92#5087—51no—
93#5051—52no—
94#5047—52no—
95#5031—51no—
96C4×#215—51no—
97D4×C3⋊C8—51no—
98#5002—52no—
99#4996—52no—
100C2×#709—32no—
101C5×C4⋊Q8C2×D311yescharacteristic
102C5×#126—22no—
103C5×#124—21no—
104C5×C22⋊Q8C2×D312yes—
105C4×C5×Q8—21no—
106C4×C5×Q8C2×D311yescharacteristic
107C4×C5×D4C2×D311yescharacteristic
108C5×#117C2×D312yes—
109C2×#689—32no—
110C2×#688—31no—
111#4084—61no—
112#4070—32no—
113C22×#168—32no—
114D5×C4⋊C4—61no—
115#4029—62no—
116C4×D20—31no—
117#4015—31no—
118#3967—31no—
119C22⋊#168—32no—
120#3942—32no—
121#3942—32no—
122#3942—32no—
123#3941—31no—
124#3941—32no—
125#3940—31no—
126#3939—32no—
127C4⋊#168—31no—
128C4×#168—31no—
129#3302—151noSylow
130C23×C3×C5C2×D412yes—
131C22×D15—21no—
132C3×C5×Q8—21no—
133C3×C5×Q8—21no—
134C3×C5×Q8—42no—
135C3×C5×D4—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2411yescharacteristic
145#1220—44no—
146C2×Dic15—21no—
147C2×Dic15—22no—
148D60—21no—
149D60#4112yes—
150C4×D15—44no—
151C4×D15—42no—
152Dic30—22no—
153Dic30—22no—
154C3⋊#168—21no—
155C3⋊#168—21no—
156C3⋊#168—22no—
157C2×#235—52no—
158C3×C4⋊Q8C2×D511yescharacteristic
159C3×#126—22no—
160C3×#124—21no—
161C3×C22⋊Q8C2×D512yes—
162C3×C4×Q8—21no—
163C3×C4×Q8C2×D511yescharacteristic
164C3×C4×D4C2×D511yescharacteristic
165C3×#117C2×D512yes—
166C2×#216—52no—
167C2×#215—51no—
168#938—101no—
169#924—52no—
170C22×C3⋊C8—52no—
171D3×C4⋊C4—101no—
172#883—102no—
173C4×D12—51no—
174#869—51no—
175#835—51no—
176#830—52no—
177#810—52no—
178#810—52no—
179#810—52no—
180#809—51no—
181#809—52no—
182#808—51no—
183#807—52no—
184C4⋊(C3⋊C8)—51no—
185C4×C3⋊C8—51no—
186C2×C5×Q8—21no—
187C2×C5×Q8C22×D311yescharacteristic
188C2×C5×D4#6711yescharacteristic
189C22×C4×C5C22×D312yes—
190C2×C22⋊D5—62no—
191#709—64no—
192#709—122no—
193C2×D20—31no—
194C2×C4×D5—62no—
195C2×C4×D5—61no—
196C2×Dic10—32no—
197C5×C4⋊C4—22no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4#6711yescharacteristic
201C5×C4⋊C4C22×D311yescharacteristic
202C5×C4⋊C4C22×D312yes—
203C5×C22⋊C4—22no—
204C5×C22⋊C4—22no—
205C5×C22⋊C4#6712yes—
206C42×C5—22no—
207C42×C5—21no—
208C42×C5C22×D311yescharacteristic
209C22⋊Dic5—62no—
210#689—122no—
211#688—62no—
212#685—61no—
213C4⋊Dic5—31no—
214C4⋊Dic5—61no—
215C4⋊Dic5—61no—
216#683—62no—
217C2×#168—31no—
218C2×#168—31no—
219C2×#168—32no—
220C2×#168—122no—
221#556D1511yescharacteristic, complemented
222#547—151no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—151no—
231#416—152no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—22no—
235C22×C3×C5C22×D411yescharacteristic
236C2×D15—22no—
237C2×D15—41no—
238C2×D15—41no—
239C3×C4×C5—22no—
240C3×C4×C5—21no—
241C3×C4×C5—41no—
242C3×C4×C5—42no—
243C3×C4×C5—41no—
244C3×C4×C5#13512yes—
245C3×C4×C5C2×#4111yescharacteristic
246C3×C4×C5H(5,𝔽2)11yescharacteristic
247Dic15—42no—
248Dic15—41no—
249C2×C3×Q8—21no—
250C2×C3×Q8C22×D511yescharacteristic
251C2×C3×D4C22⋊D511yescharacteristic
252C22×C3×C4C22×D512yes—
253C2×#67—102no—
254#235—104no—
255#235—202no—
256C2×D12—51no—
257C2×C4×D3—101no—
258C2×C4×D3—102no—
259C2×Dic6—52no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4C22⋊D511yescharacteristic
264C3×C4⋊C4C22×D512yes—
265C3×C4⋊C4C22×D511yescharacteristic
266C3×C22⋊C4—22no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4C22⋊D512yes—
269C3×C42—22no—
270C3×C42—21no—
271C3×C42C22×D511yescharacteristic
272#217—102no—
273#216—202no—
274#215—102no—
275(C2×D3)⋊C4—101no—
276C4⋊Dic3—51no—
277C4⋊Dic3—101no—
278C4⋊Dic3—101no—
279Dic3⋊C4—102no—
280C2×C3⋊C8—51no—
281C2×C3⋊C8—51no—
282C2×C3⋊C8—52no—
283C2×C3⋊C8—202no—
284C23×C5C2×#6712yes—
285C22×D5—61no—
286C5×Q8—21no—
287C5×Q8—21no—
288C5×Q8—42no—
289C5×D4—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—22no—
295C2×C4×C5C2×#6712yes—
296C2×C4×C5C2×#6711yescharacteristic
297C2×C4×C5C2×#6711yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C22⋊D5—124no—
300C2×Dic5—61no—
301C2×Dic5—62no—
302D20—32no—
303D20—61no—
304C4×D5—124no—
305C4×D5—122no—
306Dic10—62no—
307Dic10—62no—
308#168—61no—
309#168—61no—
310#168—62no—
311C2×#41—152no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8—152no—
315C4⋊Q8—151no—
316C4⋊Q8C2×D1511yescharacteristic
317#126—22no—
318#124—21no—
319#123—302no—
320C22⋊Q8—152no—
321C22⋊Q8C2×D1512yes—
322#121—301no—
323C4×Q8—21no—
324C4×Q8C2×D1511yescharacteristic
325C4×D4—151no—
326C4×D4C2×D1511yescharacteristic
327#117C2×D1512yes—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—151no—
331C4⋊C8—151no—
332#103—151no—
333#103—152no—
334#103—152no—
335#103—152no—
336#102—151no—
337#102—152no—
338C22⋊C8—152no—
339C4×C8—151no—
340C2×C3×C5—42no—
341C2×C3×C5#54611yescharacteristic
342C2×C3×C5C2×#13511yescharacteristic
343C2×C3×C5#57811yescharacteristic
344D15—42no—
345C23×C3C2×C22⋊D512yes—
346C22×D3—101no—
347C3×Q8—21no—
348C3×Q8—21no—
349C3×Q8—42no—
350C3×D4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4C2×C22⋊D512yes—
357C2×C3×C4C2×C22⋊D511yescharacteristic
358C2×C3×C4C2×C22⋊D511yescharacteristic
359C2×C3×C4C23×D511yescharacteristic
360#67—204no—
361C2×Dic3—101no—
362C2×Dic3—102no—
363D12—52no—
364D12—101no—
365C4×D3—204no—
366C4×D3—202no—
367Dic6—102no—
368Dic6—102no—
369C3⋊C8—101no—
370C3⋊C8—101no—
371C3⋊C8—102no—
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5C22×#6711yescharacteristic
376C2×D5—62no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—22no—
380C4×C5—21no—
381C4×C5—42no—
382C4×C5—41no—
383C4×C5—41no—
384C4×C5#95012yes—
385C4×C5D3×#4111yescharacteristic
386C4×C5#100911yescharacteristic
387Dic5—121no—
388Dic5—122no—
389#41—304no—
390#41—602no—
391C2×Q8—21no—
392C2×Q8—152no—
393C2×Q8C22×D1511yescharacteristic
394C2×D4—151no—
395C2×D4—302no—
396C2×D4#122011yescharacteristic
397C22×C4—301no—
398C22×C4—302no—
399C22×C4C22×D1512yes—
400Q16—602no—
401SD16—302no—
402C2×C8—151no—
403C2×C8—151no—
404C2×C8—152no—
405C2×C8—602no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—151no—
410C4⋊C4—301no—
411C4⋊C4—302no—
412C4⋊C4—301no—
413C4⋊C4#122011yescharacteristic
414C4⋊C4C22×D1511yescharacteristic
415C4⋊C4C22×D1512yes—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—302no—
419C22⋊C4—301no—
420C22⋊C4#122012yes—
421C42—22no—
422C42—21no—
423C42C22×D1511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3C22×C22⋊D511yescharacteristic
429C2×D3—102no—
430C2×D3—201no—
431C2×D3—201no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—42no—
435C3×C4—41no—
436C3×C4—41no—
437C3×C4#409612yes—
438C3×C4D5×#4111yescharacteristic
439C3×C4#414911yescharacteristic
440Dic3—201no—
441Dic3—202no—
442C2×C5—42no—
443C2×C5C2×#95011yescharacteristic
444C2×C5#582911yescharacteristic
445C2×C5#583811yescharacteristic
446D5—122no—
447C23—301no—
448C23C2×#122012yes—
449Q8—21no—
450Q8—21no—
451Q8—42no—
452Q8—302no—
453Q8—302no—
454D4—22no—
455D4—152no—
456D4—301no—
457D4—604no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—301no—
464C2×C4—302no—
465C2×C4—604no—
466C2×C4—602no—
467C2×C4C2×#122012yes—
468C2×C4C2×#122011yescharacteristic
469C2×C4C2×#122011yescharacteristic
470C2×C4C23×D1511yescharacteristic
471C8—301no—
472C8—301no—
473C8—302no—
474C2×C3—42no—
475C2×C3C2×#409611yescharacteristic
476C2×C3#6616311yescharacteristic
477C2×C3#6617211yescharacteristic
478D3—202no—
479C5#8366411yescharacteristic, complemented, Sylow
480C22—22no—
481C22—22no—
482C22—22no—
483C22—302no—
484C22—601no—
485C22—601no—
486C22C22×#122011yescharacteristic
487C4—22no—
488C4—21no—
489C4—42no—
490C4—41no—
491C4—41no—
492C4—601no—
493C4—602no—
494C4#9183912yes—
495C4#41×D1511yescharacteristic
496C4#9210011yescharacteristic
497C3#1061539511yescharacteristic, complemented, Sylow
498C2—42no—
499C2—602no—
500C2C2×#9183911yescharacteristic
501C2#1175658811yescharacteristic
502C2#1175659711yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#556C2
socleC22×C3×C5C22×D4
prime radical#11756310C2
hypercenter#556D15
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C3×C5×#556C2semidirect
3. #11751194C2semidirect
4. #11751188C2semidirect
5. #11751152C2semidirect
6. #11751148C2semidirect
7. #11751132C2semidirect
8. C4×#6717C2semidirect
9. D4×C3⋊#168C2semidirect
10. #11751103C2semidirect
11. #11751097C2semidirect
43. C5×#556D3semidirect
89. C3×#556D5semidirect
221. #556D15semidirect
424. C3×C5#3302semidirect
479. C5#83664semidirect
497. C3#10615395semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5562
#117563102
#117511942
#117511882
#117511522
#117511482
#117511322
C4×#67172
D4×C3⋊#1682
#117511032
#117510972
#106153953
#836645