Finite Group Databasebeta

← #14471914

Subgroups — #14471914

Order 1920.

784 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
1#11756481C211yesmaximal, characteristic, complemented
2#11756312C211yesmaximal, characteristic
3C3×C5×#476C211yesmaximal, characteristic, complemented
4#11751189C211yesmaximal, characteristic, complemented
5C4×#6716C211yesmaximal, characteristic, complemented
6#11750971C212yesmaximal, complemented
7#11750953C212yesmaximal, complemented
8#11750949C211yesmaximal, characteristic, complemented
9#11750931C211yesmaximal, characteristic, complemented
10#11750863C212yesmaximal, complemented
11#11750861C212yesmaximal, complemented
12#10612821—31nomaximal, Hall
13C2×#6817—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16#91833—22no—
17#91829C2212yes—
18C2×#6716C2211yescharacteristic
19#91819—21no—
20C2×#6706C2212yes—
21#91782C2212yes—
22#91777—21no—
23#91777C2212yes—
24#91776—21no—
25#91776C2212yes—
26#91773—22no—
27#91763C2211yescharacteristic
28C4×Dic30C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×#106C2212yes—
31C3×C5×C4⋊C8C2211yescharacteristic
32C3×C5×#102C2212yes—
33#91116C2211yescharacteristic
34#91105C2212yes—
35#91098C2212yes—
36C8×Dic15C2212yes—
37#91094C2211yescharacteristic
38#91093C2212yes—
39#91093C2212yes—
40#91092C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#81090—51nomaximal, Hall
43#66056—31no—
44#65887—31no—
45C5×#476D311yescharacteristic, complemented
46#65377—31no—
47C4×#687—31no—
48#65159—32no—
49#65141—32no—
50#65137—31no—
51#65119—31no—
52#65051—32no—
53#65049—32no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×#1220—22no—
58C2×#1220—22no—
59#6817—44no—
60C2×D60—21no—
61C2×D60—21no—
62C2×D60C2312yes—
63C2×C4×D15—22no—
64C2×Dic30—22no—
65C2×Dic30D411yescharacteristic
66C2×Dic30C2311yescharacteristic
67C2×C3×C5×C8C2312yes—
68C3×C5×C4⋊C4—21no—
69C3×C5×C4⋊C4C2312yes—
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5C2311yescharacteristic
73#6716—22no—
74#6714—22no—
75C4⋊Dic15D411yescharacteristic
76C4⋊Dic15C2311yescharacteristic
77#6712—21no—
78#6712—22no—
79#6712—22no—
80#6712D412yes—
81C4×Dic15—21no—
82C4×Dic15—22no—
83C4×Dic15C2312yes—
84C2×C3⋊#168C2311yescharacteristic
85C2×C3⋊#168C2311yescharacteristic
86#6706—24no—
87#5722—51no—
88#5553—51no—
89C3×#476D511yescharacteristic, complemented
90#5088—51no—
91C4×#214—51no—
92#4870—52no—
93#4852—52no—
94#4848—51no—
95#4830—51no—
96#4762—52no—
97#4760—52no—
98C2×#709—61no—
99C5×C4⋊Q8C2×D311yescharacteristic
100C4×C5×D4C2×D311yescharacteristic
101#4090—62no—
102#4086—32no—
103C2×#687—31no—
104#4076—61no—
105C2×#677—32no—
106#4039—32no—
107#4034—32no—
108#4034—61no—
109#4033—32no—
110#4033—61no—
111#4030—62no—
112#4020—31no—
113C4×Dic10—31no—
114C4×Dic10—31no—
115C5×#106C2×D312yes—
116C5×C4⋊C8C2×D311yescharacteristic
117C5×#102C2×D312yes—
118#3964—31no—
119#3953—32no—
120#3946—32no—
121C8×Dic5—32no—
122#3942—31no—
123#3941—32no—
124#3941—32no—
125#3940—31no—
126C4×#168—31no—
127#3362—151noSylow
128C23×C3×C5—21no—
129C22×D15—22no—
130C3×C5×Q8—81no—
131C3×C5×D4—21no—
132C3×C5×D4—21no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139#1220—44no—
140#1220—82no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15C2×D412yes—
144C2×Dic15C2×D412yes—
145D60—22no—
146D60—22no—
147D60—42no—
148D60—81no—
149C4×D15—44no—
150Dic30—21no—
151Dic30—82no—
152Dic30SD1614yescomplemented
153Dic30#4112yescomplemented
154C3×C5×C8—22no—
155C3⋊#168—21no—
156C3⋊#168—21no—
157C2×#235—101no—
158C3×C4⋊Q8C2×D511yescharacteristic
159C3×C4×D4C2×D511yescharacteristic
160#944—102no—
161#940—52no—
162C2×#214—51no—
163#930—101no—
164C2×#204—52no—
165#893—52no—
166#888—52no—
167#888—101no—
168#887—52no—
169#887—101no—
170#884—102no—
171#874—51no—
172C4×Dic6—51no—
173C4×Dic6—51no—
174C3×#106C2×D512yes—
175C3×C4⋊C8C2×D511yescharacteristic
176C3×#102C2×D512yes—
177#832—51no—
178#821—52no—
179Dic3⋊C8—52no—
180C8×Dic3—52no—
181#810—51no—
182#809—52no—
183#809—52no—
184#808—51no—
185C4×C3⋊C8—51no—
186C2×C5×Q8—21no—
187C2×C5×D4C22×D311yescharacteristic
188C22×C4×C5—21no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191#709—124no—
192C2×D20—32no—
193C2×D20—61no—
194C2×D20—61no—
195C2×C4×D5—62no—
196C2×Dic10—31no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C2×C5×C8C22×D312yes—
200C5×C4⋊C4—21no—
201C5×C4⋊C4C22×D311yescharacteristic
202C5×C4⋊C4C22×D312yes—
203C5×C22⋊C4—21no—
204C42×C5C22×D311yescharacteristic
205#687—62no—
206#685—62no—
207C4⋊Dic5—31no—
208C4⋊Dic5—31no—
209#683—32no—
210#683—62no—
211#683—62no—
212#683—61no—
213C4×Dic5—32no—
214C4×Dic5—62no—
215C4×Dic5—61no—
216C2×#168—31no—
217C2×#168—31no—
218#677—64no—
219Q82—151no—
220#550—151no—
221#486—151no—
222#486—152no—
223#476—152no—
224#476D1511yescharacteristic, complemented
225#460—151no—
226#460—152no—
227C8×Q8—151no—
228C4×SD16—151no—
229C4×SD16—152no—
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5—41no—
233C22×C3×C5C22×D411yescharacteristic
234C2×D15—42no—
235C2×D15—42no—
236C2×D15—42no—
237C3×C4×C5—21no—
238C3×C4×C5—41no—
239C3×C4×C5—42no—
240C3×C4×C5C2×SD1612yes—
241C3×C4×C5C2×#4111yescharacteristic
242C3×C4×C52−1+411yescharacteristic
243Dic15—22no—
244Dic15—22no—
245Dic15—41no—
246Dic15C2×SD1614yes—
247C2×C3×Q8—21no—
248C2×C3×D4C22×D511yescharacteristic
249C22×C3×C4—21no—
250C2×#67—102no—
251C2×#67—102no—
252#235—204no—
253C2×D12—52no—
254C2×D12—101no—
255C2×D12—101no—
256C2×C4×D3—102no—
257C2×Dic6—51no—
258C2×Dic6—51no—
259C2×Dic6—102no—
260C2×C3×C8C22×D512yes—
261C3×C4⋊C4—21no—
262C3×C4⋊C4C22×D511yescharacteristic
263C3×C4⋊C4C22×D512yes—
264C3×C22⋊C4—21no—
265C3×C42C22×D511yescharacteristic
266#214—102no—
267(C2×D3)⋊C4—102no—
268C4⋊Dic3—51no—
269C4⋊Dic3—51no—
270Dic3⋊C4—52no—
271Dic3⋊C4—102no—
272Dic3⋊C4—102no—
273Dic3⋊C4—101no—
274C4×Dic3—52no—
275C4×Dic3—102no—
276C4×Dic3—101no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279#204—104no—
280C23×C5—21no—
281C22×D5—62no—
282C5×Q8—81no—
283C5×D4—21no—
284C5×D4—21no—
285C2×C4×C5—22no—
286C2×C4×C5—21no—
287C2×C4×C5—42no—
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—124no—
292C22⋊D5—242no—
293C2×Dic5—32no—
294C2×Dic5—32no—
295C2×Dic5—61no—
296C2×Dic5—61no—
297D20—62no—
298D20—62no—
299D20—122no—
300D20—241no—
301C4×D5—124no—
302Dic10—34no—
303Dic10—32no—
304Dic10—61no—
305Dic10—242no—
306C5×C8—22no—
307#168—61no—
308#168—61no—
309C2×#41—301no—
310C2×SD16—151no—
311C2×SD16—152no—
312C4⋊Q8—152no—
313C4⋊Q8—301no—
314C4⋊Q8—302no—
315C4⋊Q8C2×D1511yescharacteristic
316#127—152no—
317#127—151no—
318#121—302no—
319#121—301no—
320C4×Q8—151no—
321C4×Q8—152no—
322C4×Q8—151no—
323C4×Q8—301no—
324C4×D4—152no—
325C4×D4C2×D1511yescharacteristic
326#106—151no—
327#106C2×D1512yes—
328C4⋊C8—152no—
329C4⋊C8C2×D1511yescharacteristic
330#103—151no—
331#102—151no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102C2×D1512yes—
336C4×C8—152no—
337C4×C8—151no—
338C2×C3×C5—81no—
339C2×C3×C5#54811yescharacteristic
340C2×C3×C5C22×SD1611yescharacteristic
341C2×C3×C5#57611yescharacteristic
342D15—82no—
343C23×C3—21no—
344C22×D3—102no—
345C3×Q8—81no—
346C3×D4—21no—
347C3×D4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—42no—
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355#67—402no—
356C2×Dic3—52no—
357C2×Dic3—52no—
358C2×Dic3—101no—
359C2×Dic3—101no—
360D12—102no—
361D12—102no—
362D12—202no—
363D12—401no—
364C4×D3—204no—
365Dic6—54no—
366Dic6—52no—
367Dic6—101no—
368Dic6—402no—
369C3×C8—22no—
370C3⋊C8—101no—
371C3⋊C8—101no—
372C22×C5—41no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—122no—
377C2×D5—122no—
378C2×D5—122no—
379C4×C5—21no—
380C4×C5—41no—
381C4×C5—42no—
382C4×C5D3×SD1612yes—
383C4×C5#100711yescharacteristic
384C4×C5D3×#4111yescharacteristic
385Dic5—34no—
386Dic5—62no—
387Dic5—62no—
388Dic5—121no—
389#41—604no—
390C2×Q8—21no—
391C2×Q8—151no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—152no—
395C2×D4—302no—
396C2×D4—302no—
397C2×D4—301no—
398C2×D4—301no—
399C2×D4C22×D1511yescharacteristic
400C22×C4—21no—
401C22×C4—302no—
402SD16—304no—
403SD16—302no—
404C2×C8—151no—
405C2×C8—151no—
406C2×C8C22×D1512yes—
407C4⋊C4—21no—
408C4⋊C4—152no—
409C4⋊C4—151no—
410C4⋊C4—151no—
411C4⋊C4—302no—
412C4⋊C4—302no—
413C4⋊C4—301no—
414C4⋊C4C22×D1512yes—
415C4⋊C4C22×D1511yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—302no—
418C42—152no—
419C42—302no—
420C42—301no—
421C42C22×D1511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—202no—
428C2×D3—202no—
429C2×D3—202no—
430C3×C4—21no—
431C3×C4—41no—
432C3×C4—42no—
433C3×C4D5×SD1612yes—
434C3×C4#414711yescharacteristic
435C3×C4D5×#4111yescharacteristic
436Dic3—54no—
437Dic3—102no—
438Dic3—102no—
439Dic3—201no—
440C2×C5—81no—
441C2×C5#563311yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443C2×C5#577411yescharacteristic
444D5—242no—
445C23—21no—
446C23—302no—
447Q8—81no—
448Q8—154no—
449Q8—152no—
450Q8—301no—
451Q8—1202no—
452D4—21no—
453D4—21no—
454D4—302no—
455D4—302no—
456D4—604no—
457D4—602no—
458D4—1201no—
459D4—1202no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—42no—
463C2×C4—152no—
464C2×C4—152no—
465C2×C4—301no—
466C2×C4—301no—
467C2×C4—604no—
468C2×C4D4×D1511yescharacteristic
469C2×C4D4×D1511yescharacteristic
470C2×C4C23×D1511yescharacteristic
471C8—22no—
472C8—301no—
473C8—301no—
474C2×C3—81no—
475C2×C3#6596711yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477C2×C3#6610811yescharacteristic
478D3—402no—
479C5#8109011yescharacteristic, complemented, Sylow
480C22—41no—
481C22—41no—
482C22—41no—
483C22—602no—
484C22—602no—
485C22—602no—
486C22C2×D4×D1511yescharacteristic
487C4—21no—
488C4—41no—
489C4—42no—
490C4—154no—
491C4—302no—
492C4—302no—
493C4—601no—
494C4SD16×D1512yes—
495C4#9209811yescharacteristic
496C4#41×D1511yescharacteristic
497C3#1061282111yescharacteristic, complemented, Sylow
498C2—81no—
499C2—1202no—
500C2#1175639211yescharacteristic
501C2C2×SD16×D1511yescharacteristic
502C2#1175653311yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#476C2
socleC22×C3×C5C22×D4
prime radical#11756312C2
hypercenter#476D15
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #11756481C2semidirect
3. C3×C5×#476C2semidirect
4. #11751189C2semidirect
5. C4×#6716C2semidirect
6. #11750971C2semidirect
7. #11750953C2semidirect
8. #11750949C2semidirect
9. #11750931C2semidirect
10. #11750863C2semidirect
11. #11750861C2semidirect
45. C5×#476D3semidirect
89. C3×#476D5semidirect
152. Dic30SD16semidirect
153. Dic30#41semidirect
224. #476D15semidirect
422. C3×C5#3362semidirect
479. C5#81090semidirect
497. C3#10612821semidirect

Maximal subgroups

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

subgroupindex
#117564812
#117563122
C3×C5×#4762
#117511892
C4×#67162
#117509712
#117509532
#117509492
#117509312
#117508632
#117508612
#106128213
#810905