Finite Group Databasebeta

← #14430776

Subgroups — #14430776

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756280C211yesmaximal, characteristic
2#11756259C211yesmaximal, characteristic, complemented
3C3×C5×#428C211yesmaximal, characteristic, complemented
4#11751232C211yesmaximal, characteristic
5#11751220C211yesmaximal, characteristic, complemented
6#11751099C211yesmaximal, characteristic, complemented
7C2×#91093C211yesmaximal, characteristic
8#11750992C212yesmaximal, complemented
9#11750991C212yesmaximal, complemented
10#11750972C212yesmaximal, complemented
11#11750971C212yesmaximal, complemented
12#10610973—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17#91815C2211yescharacteristic
18#91815C2211yescharacteristic
19#91813—22no—
20C22×C3⋊#168C2211yescharacteristic
21#91782C2212yes—
22#91782C2212yes—
23#91779—21no—
24#91779C2212yescomplemented
25#91777—21no—
26#91777C2212yescomplemented
27C22⋊C4×D15—22no—
28C4×D60—21no—
29C4×D60—21no—
30C3×C5×#107C2212yescomplemented
31C3×C5×#106C2212yescomplemented
32#91105C2212yes—
33#91105C2212yes—
34#91098C2212yescomplemented
35#91098C2212yescomplemented
36#91093C2212yes—
37#91093C2212yes—
38#91092C2211yescharacteristic, complemented
39#91092C2211yescharacteristic, complemented
40#91091C2211yescharacteristic, complemented
41#91091C2211yescharacteristic, complemented
42#79242—51nomaximal, Hall
43#65855—31no—
44#65834—31no—
45C5×#428D311yescharacteristic, complemented
46#65420—31no—
47#65408—31no—
48#65287—31no—
49C2×#3941—31no—
50#65180—32no—
51#65179—32no—
52#65160—32no—
53#65159—32no—
54C23×D15—21no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×D60—21no—
58C2×D60—22no—
59C2×D60Q814yescomplemented
60C2×D60C2312yes—
61C2×C4×D15—22no—
62C2×C4×D15—22no—
63C2×Dic30—22no—
64C3×C5×M16—22no—
65C2×C3×C5×C8C2312yes—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4C2312yes—
68C3×C5×C4⋊C4C2311yescharacteristic
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C22⋊C4—21no—
71C3×C42×C5—21no—
72#6719—21no—
73#6719D412yes—
74#6714—22no—
75#6714—22no—
76C4⋊Dic15—22no—
77C4⋊Dic15D411yescharacteristic
78C4⋊Dic15D411yescharacteristic
79C4⋊Dic15C2311yescharacteristic
80C4⋊Dic15C2311yescharacteristic
81#6712—22no—
82#6712—22no—
83C4×Dic15—21no—
84C4×Dic15C2312yes—
85C2×C3⋊#168—22no—
86C2×C3⋊#168C2311yescharacteristic
87C2×C3⋊#168C2311yescharacteristic
88#5521—51no—
89#5500—51no—
90C3×#428D511yescharacteristic, complemented
91#5131—51no—
92#5119—51no—
93#4998—51no—
94C2×#809—51no—
95#4891—52no—
96#4890—52no—
97#4871—52no—
98#4870—52no—
99C22×D20—31no—
100C2×C5×M16C2×D311yescharacteristic
101C5×#117C2×D311yescharacteristic
102C2×C5×C4⋊C4C2×D311yescharacteristic
103#4072—31no—
104#4072—31no—
105#4070—62no—
106C22×#168—31no—
107#4039—32no—
108#4039—32no—
109#4036—32no—
110#4036—61no—
111#4034—32no—
112#4034—61no—
113D5×C22⋊C4—62no—
114C4×D20—61no—
115C4×D20—61no—
116C5×#107C2×D312yescomplemented
117C5×#106C2×D312yescomplemented
118#3953—32no—
119#3953—32no—
120#3946—32no—
121#3946—32no—
122#3941—32no—
123#3941—32no—
124#3940—31no—
125#3940—31no—
126#3939—31no—
127#3939—31no—
128#3081—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×D15—22no—
131C22×D15—24no—
132C22×D15—81no—
133C22×D15—81no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—81no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×Q812yes—
140C2×C3×C4×C5#4112yes—
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15C2×D412yes—
145C2×Dic15C2×D412yes—
146D60—24no—
147D60—22no—
148D60C2×Q814yes—
149C4×D15—82no—
150C4×D15—82no—
151Dic30—82no—
152C3×C5×C8—22no—
153C3⋊#168—21no—
154C3⋊#168—21no—
155C22×D12—51no—
156C2×C3×M16C2×D511yescharacteristic
157C3×#117C2×D511yescharacteristic
158C2×C3×C4⋊C4C2×D511yescharacteristic
159#926—51no—
160#926—51no—
161#924—102no—
162C22×C3⋊C8—51no—
163#893—52no—
164#893—52no—
165#890—52no—
166#890—101no—
167#888—52no—
168#888—101no—
169D3×C22⋊C4—102no—
170C4×D12—101no—
171C4×D12—101no—
172C3×#107C2×D512yescomplemented
173C3×#106C2×D512yescomplemented
174#821—52no—
175#821—52no—
176Dic3⋊C8—52no—
177Dic3⋊C8—52no—
178#809—52no—
179#809—52no—
180#808—51no—
181#808—51no—
182#807—51no—
183#807—51no—
184C23×D5—61no—
185C22×C4×C5—21no—
186C22×C4×C5C22×D311yescharacteristic
187C2×D20—34no—
188C2×D20—32no—
189C2×D20—62no—
190C2×D20—61no—
191C2×C4×D5—62no—
192C2×C4×D5—62no—
193C2×Dic10—62no—
194C5×M16—22no—
195C2×C5×C8C22×D312yes—
196C5×C4⋊C4—21no—
197C5×C4⋊C4C22×D312yes—
198C5×C4⋊C4C22×D311yescharacteristic
199C5×C4⋊C4C22×D311yescharacteristic
200C5×C22⋊C4—21no—
201C42×C5—21no—
202C22⋊Dic5—32no—
203C22⋊Dic5—61no—
204#685—62no—
205#685—62no—
206C4⋊Dic5—31no—
207C4⋊Dic5—31no—
208C4⋊Dic5—31no—
209C4⋊Dic5—31no—
210C4⋊Dic5—62no—
211#683—62no—
212#683—62no—
213C4×Dic5—32no—
214C4×Dic5—61no—
215C2×#168—31no—
216C2×#168—31no—
217C2×#168—62no—
218#544—151no—
219#518—151no—
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428D1511yescharacteristic, complemented
225#427—151no—
226#424—151no—
227#418—151no—
228C2×#102—151no—
229C22×C3×C5—21no—
230C22×C3×C5—21no—
231C22×C3×C5C22⋊Q812yes—
232C22×C3×C5C22×D411yescharacteristic
233C2×D15—24no—
234C2×D15—42no—
235C2×D15—42no—
236C2×D15—84no—
237C3×C4×C5—42no—
238C3×C4×C5—41no—
239C3×C4×C5—41no—
240C3×C4×C5C22⋊Q812yes—
241C3×C4×C5C22×Q811yescharacteristic
242C3×C4×C5C2×#4111yescharacteristic
243Dic15—22no—
244Dic15—22no—
245Dic15—41no—
246Dic15—41no—
247C23×D3—101no—
248C22×C3×C4—21no—
249C22×C3×C4C22×D511yescharacteristic
250C2×D12—54no—
251C2×D12—52no—
252C2×D12—102no—
253C2×D12—101no—
254C2×C4×D3—102no—
255C2×C4×D3—102no—
256C2×Dic6—102no—
257C3×M16—22no—
258C2×C3×C8C22×D512yes—
259C3×C4⋊C4—21no—
260C3×C4⋊C4C22×D511yescharacteristic
261C3×C4⋊C4C22×D511yescharacteristic
262C3×C4⋊C4C22×D512yes—
263C3×C22⋊C4—21no—
264C3×C42—21no—
265#217—52no—
266#217—101no—
267(C2×D3)⋊C4—102no—
268(C2×D3)⋊C4—102no—
269C4⋊Dic3—51no—
270C4⋊Dic3—51no—
271C4⋊Dic3—51no—
272C4⋊Dic3—51no—
273C4⋊Dic3—102no—
274Dic3⋊C4—102no—
275Dic3⋊C4—102no—
276C4×Dic3—52no—
277C4×Dic3—101no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8—51no—
280C2×C3⋊C8—102no—
281C23×C5D3×D411yescharacteristic
282C22×D5—62no—
283C22×D5—64no—
284C22×D5—241no—
285C22×D5—241no—
286C2×C4×C5—22no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—81no—
290C2×C4×C5#23512yes—
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5D3×Q812yes—
293C2×C4×C5C23×D311yescharacteristic
294C2×Dic5—32no—
295C2×Dic5—32no—
296C2×Dic5—61no—
297C2×Dic5—61no—
298D20—34no—
299D20—64no—
300D20—62no—
301C4×D5—242no—
302C4×D5—242no—
303Dic10—242no—
304C5×C8—22no—
305#168—61no—
306#168—61no—
307C22×D4—151no—
308C2×M16C2×D1511yescharacteristic
309C22×C8—151no—
310C4⋊Q8—152no—
311C4⋊Q8—301no—
312#125—152no—
313#125—301no—
314C22⋊Q8—302no—
315C4×D4—152no—
316C4×D4—152no—
317C4×D4—301no—
318C4×D4—301no—
319#117—151no—
320#117—151no—
321#117C2×D1511yescharacteristic
322C2×C4⋊C4C2×D1511yescharacteristic
323C2×C22⋊C4—302no—
324#107—151no—
325#107—151no—
326#107C2×D1512yescomplemented
327#106—151no—
328#106—151no—
329#106C2×D1512yescomplemented
330C4⋊C8—152no—
331C4⋊C8—152no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102—152no—
336C2×C3×C5—22no—
337C2×C3×C5C2×C22⋊Q811yescharacteristic
338C2×C3×C5#57611yescharacteristic
339C2×C3×C5#57711yescharacteristic
340D15—44no—
341C23×C3D4×D511yescharacteristic
342C22×D3—102no—
343C22×D3—104no—
344C22×D3—401no—
345C22×D3—401no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—81no—
350C2×C3×C4#70912yes—
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4Q8×D512yes—
353C2×C3×C4C23×D511yescharacteristic
354C2×Dic3—52no—
355C2×Dic3—52no—
356C2×Dic3—101no—
357C2×Dic3—101no—
358D12—54no—
359D12—102no—
360D12—104no—
361C4×D3—402no—
362C4×D3—402no—
363Dic6—402no—
364C3×C8—22no—
365C3⋊C8—101no—
366C3⋊C8—101no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5#89612yes—
370C22×C5C2×D3×D411yescharacteristic
371C2×D5—64no—
372C2×D5—122no—
373C2×D5—122no—
374C2×D5—244no—
375C4×C5—42no—
376C4×C5—41no—
377C4×C5—41no—
378C4×C5#89612yes—
379C4×C5C2×#23511yescharacteristic
380C4×C5C2×D3×Q811yescharacteristic
381Dic5—62no—
382Dic5—62no—
383Dic5—121no—
384Dic5—121no—
385C24—301no—
386C2×Q8—302no—
387C2×D4—154no—
388C2×D4—152no—
389C2×D4—302no—
390C2×D4—301no—
391C22×C4—21no—
392C22×C4—302no—
393C22×C4—302no—
394C22×C4C22×D1511yescharacteristic
395M16—22no—
396C2×C8—151no—
397C2×C8—151no—
398C2×C8—302no—
399C2×C8C22×D1512yes—
400C4⋊C4—21no—
401C4⋊C4—151no—
402C4⋊C4—151no—
403C4⋊C4—151no—
404C4⋊C4—151no—
405C4⋊C4—302no—
406C4⋊C4—302no—
407C4⋊C4—302no—
408C4⋊C4C22×D1512yes—
409C4⋊C4C22×D1511yescharacteristic
410C4⋊C4C22×D1511yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—152no—
413C22⋊C4—302no—
414C22⋊C4—302no—
415C22⋊C4—301no—
416C42—21no—
417C42—152no—
418C42—301no—
419C3×C5#308111yescharacteristic, complemented, Hall
420C22×C3—21no—
421C22×C3—21no—
422C22×C3#404212yes—
423C22×C3C2×D4×D511yescharacteristic
424C2×D3—104no—
425C2×D3—202no—
426C2×D3—202no—
427C2×D3—404no—
428C3×C4—42no—
429C3×C4—41no—
430C3×C4—41no—
431C3×C4#404212yes—
432C3×C4C2×#70911yescharacteristic
433C3×C4C2×Q8×D511yescharacteristic
434Dic3—102no—
435Dic3—102no—
436Dic3—201no—
437Dic3—201no—
438C2×C5—22no—
439C2×C5C2×#89611yescharacteristic
440C2×C5#577411yescharacteristic
441C2×C5#577811yescharacteristic
442D5—124no—
443C23—302no—
444C23—304no—
445C23—1201no—
446C23—1201no—
447C23D4×D1511yescharacteristic
448Q8—1202no—
449D4—154no—
450D4—304no—
451D4—302no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—81no—
456C2×C4—152no—
457C2×C4—152no—
458C2×C4—301no—
459C2×C4—301no—
460C2×C4—1202no—
461C2×C4—1202no—
462C2×C4#681712yes—
463C2×C4D4×D1511yescharacteristic
464C2×C4Q8×D1512yes—
465C2×C4C23×D1511yescharacteristic
466C8—22no—
467C8—301no—
468C8—301no—
469C2×C3—22no—
470C2×C3C2×#404211yescharacteristic
471C2×C3#6610811yescharacteristic
472C2×C3#6611211yescharacteristic
473D3—204no—
474C5#7924211yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—304no—
478C22—602no—
479C22—602no—
480C22—1204no—
481C22#9178512yes—
482C22C2×D4×D1511yescharacteristic
483C4—42no—
484C4—41no—
485C4—41no—
486C4—302no—
487C4—302no—
488C4—601no—
489C4—601no—
490C4#9178512yes—
491C4C2×#681711yescharacteristic
492C4C2×Q8×D1511yescharacteristic
493C3#1061097311yescharacteristic, complemented, Sylow
494C2—22no—
495C2—604no—
496C2C2×#9178511yescharacteristic
497C2#1175653311yescharacteristic
498C2#1175653711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#428C2
socleC22×C3×C5C22×D4
prime radicalC22×D60C22
hypercenter#428D15
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #11756259C2semidirect
3. C3×C5×#428C2semidirect
5. #11751220C2semidirect
6. #11751099C2semidirect
8. #11750992C2semidirect
9. #11750991C2semidirect
10. #11750972C2semidirect
11. #11750971C2semidirect
24. #91779C22semidirect
26. #91777C22semidirect
30. C3×C5×#107C22semidirect
31. C3×C5×#106C22semidirect
34. #91098C22semidirect
35. #91098C22semidirect
38. #91092C22semidirect
39. #91092C22semidirect
40. #91091C22semidirect
41. #91091C22semidirect
45. C5×#428D3semidirect
59. C2×D60Q8semidirect
90. C3×#428D5semidirect
116. C5×#107C2×D3semidirect
117. C5×#106C2×D3semidirect
172. C3×#107C2×D5semidirect
173. C3×#106C2×D5semidirect
224. #428D15semidirect
326. #107C2×D15semidirect
329. #106C2×D15semidirect
419. C3×C5#3081semidirect
474. C5#79242semidirect
493. C3#10610973semidirect

Maximal subgroups

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

subgroupindex
#117562802
#117562592
C3×C5×#4282
#117512322
#117512202
#117510992
C2×#910932
#117509922
#117509912
#117509722
#117509712
#106109733
#792425