Finite Group Databasebeta

← #14430785

Subgroups — #14430785

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#11756278C211yesmaximal, characteristic, complemented
3C3×C5×#424C211yesmaximal, characteristic, complemented
4#11751232C211yesmaximal, characteristic
5#11751222C211yesmaximal, characteristic, complemented
6C2×#91105C211yesmaximal, characteristic
7#11751207C211yesmaximal, characteristic, complemented
8#11750948C212yesmaximal, complemented
9#11750948C212yesmaximal, complemented
10#11750947C212yesmaximal, complemented
11#11750943C212yesmaximal, complemented
12#10610821—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17#91815C2211yescharacteristic
18#91815C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20#91782—21no—
21#91782—21no—
22#91779—21no—
23#91777—21no—
24C22⋊C4×D15—22no—
25#91767—22no—
26C4×D60C2212yes—
27C4×D60C2212yes—
28#91759C2212yescomplemented
29#91758C2212yescomplemented
30C3×C5×C4⋊C8C2212yescomplemented
31C3×C5×C4⋊C8C2212yescomplemented
32#91105C2212yes—
33#91105C2212yes—
34#91105C2212yes—
35#91105C2212yes—
36#91102C2211yescharacteristic, complemented
37#91102C2212yescomplemented
38#91102C2211yescharacteristic, complemented
39#91101C2211yescharacteristic, complemented
40#91101C2212yescomplemented
41#91101C2211yescharacteristic, complemented
42#79090—51nomaximal, Hall
43#65855—31no—
44#65853—31no—
45C5×#424D311yescharacteristic, complemented
46#65420—31no—
47#65410—31no—
48C2×#3953—31no—
49#65395—31no—
50#65136—32no—
51#65136—32no—
52#65135—32no—
53#65131—32no—
54C23×D15—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
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×C8—22no—
66C2×C3×C5×C8C2311yescharacteristic
67C2×C3×C5×C8C2311yescharacteristic
68C2×C3×C5×C8C2312yes—
69C3×C5×C4⋊C4D411yescharacteristic
70C3×C5×C4⋊C4D411yescharacteristic
71C3×C5×C22⋊C4D412yes—
72C3×C42×C5C2312yes—
73#6719—21no—
74#6719—21no—
75#6714—22no—
76#6714—22no—
77C4⋊Dic15—22no—
78C4⋊Dic15—21no—
79C4⋊Dic15C2311yescharacteristic
80C4⋊Dic15C2312yes—
81C4⋊Dic15C2311yescharacteristic
82C4⋊Dic15C2311yescharacteristic
83C4⋊Dic15C2311yescharacteristic
84#6712—22no—
85#6712—22no—
86C4×Dic15—21no—
87C4×Dic15—21no—
88#5521—51no—
89#5519—51no—
90C3×#424D511yescharacteristic, complemented
91#5131—51no—
92#5121—51no—
93C2×#821—51no—
94#5106—51no—
95#4847—52no—
96#4847—52no—
97#4846—52no—
98#4842—52no—
99C22×D20—31no—
100C2×C5×M16C2×D311yescharacteristic
101C22×C5×C8C2×D311yescharacteristic
102C5×#117C2×D311yescharacteristic
103#4072—31no—
104#4072—31no—
105C2×C4⋊Dic5—31no—
106#4039—61no—
107#4039—61no—
108#4036—61no—
109#4034—61no—
110D5×C22⋊C4—62no—
111#4024—62no—
112C4×D20—32no—
113C4×D20—32no—
114#4016—32no—
115#4015—32no—
116C5×C4⋊C8C2×D312yescomplemented
117C5×C4⋊C8C2×D312yescomplemented
118#3953—32no—
119#3953—32no—
120#3953—32no—
121#3953—32no—
122#3950—31no—
123#3950—32no—
124#3950—31no—
125#3949—31no—
126#3949—32no—
127#3949—31no—
128#3081—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×D15—22no—
131C22×D15—24no—
132C22×D15—81no—
133C22×D15—81no—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×Q812yes—
138C2×C3×C4×C5#4112yes—
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145C2×Dic15—81no—
146D60—24no—
147D60—22no—
148D60C2×Q814yes—
149C4×D15—82no—
150C4×D15—82no—
151Dic30—82no—
152C3×C5×C8—21no—
153C3×C5×C8—21no—
154C3×C5×C8—22no—
155C22×D12—51no—
156C2×C3×M16C2×D511yescharacteristic
157C22×C3×C8C2×D511yescharacteristic
158C3×#117C2×D511yescharacteristic
159#926—51no—
160#926—51no—
161C2×C4⋊Dic3—51no—
162#893—101no—
163#893—101no—
164#890—101no—
165#888—101no—
166D3×C22⋊C4—102no—
167#878—102no—
168C4×D12—52no—
169C4×D12—52no—
170#870—52no—
171#869—52no—
172C3×C4⋊C8C2×D512yescomplemented
173C3×C4⋊C8C2×D512yescomplemented
174#821—52no—
175#821—52no—
176#821—52no—
177#821—52no—
178#818—52no—
179#818—51no—
180#818—51no—
181#817—52no—
182#817—51no—
183#817—51no—
184C23×D5—61no—
185C22×C4×C5C22×D311yescharacteristic
186C22×Dic5—61no—
187C2×D20—34no—
188C2×D20—32no—
189C2×D20—61no—
190C2×D20—62no—
191C2×C4×D5—62no—
192C2×C4×D5—62no—
193C2×Dic10—62no—
194C5×M16—22no—
195C2×C5×C8—22no—
196C2×C5×C8C22×D311yescharacteristic
197C2×C5×C8C22×D311yescharacteristic
198C2×C5×C8C22×D312yes—
199C5×C4⋊C4D1211yescharacteristic
200C5×C4⋊C4D1211yescharacteristic
201C5×C22⋊C4D1212yes—
202C42×C5C22×D312yes—
203C22⋊Dic5—61no—
204C22⋊Dic5—61no—
205#685—62no—
206#685—62no—
207C4⋊Dic5—31no—
208C4⋊Dic5—31no—
209C4⋊Dic5—31no—
210C4⋊Dic5—32no—
211C4⋊Dic5—31no—
212C4⋊Dic5—62no—
213C4⋊Dic5—61no—
214#683—62no—
215#683—62no—
216C4×Dic5—61no—
217C4×Dic5—61no—
218#544—151no—
219#518—151no—
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428—151no—
225#427—151no—
226#424D1511yescharacteristic, complemented
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—22no—
238C3×C4×C5—22no—
239C3×C4×C5C22⋊Q812yes—
240C3×C4×C5C22×Q811yescharacteristic
241C3×C4×C5C2×#4111yescharacteristic
242Dic15—41no—
243Dic15—42no—
244Dic15—41no—
245Dic15—41no—
246Dic15—41no—
247C23×D3—101no—
248C22×C3×C4C22×D511yescharacteristic
249C22×Dic3—101no—
250C2×D12—54no—
251C2×D12—52no—
252C2×D12—101no—
253C2×D12—102no—
254C2×C4×D3—102no—
255C2×C4×D3—102no—
256C2×Dic6—102no—
257C3×M16—22no—
258C2×C3×C8—22no—
259C2×C3×C8C22×D511yescharacteristic
260C2×C3×C8C22×D512yes—
261C2×C3×C8C22×D511yescharacteristic
262C3×C4⋊C4D2011yescharacteristic
263C3×C4⋊C4D2011yescharacteristic
264C3×C22⋊C4D2012yes—
265C3×C42C22×D512yes—
266#217—101no—
267#217—101no—
268(C2×D3)⋊C4—102no—
269(C2×D3)⋊C4—102no—
270C4⋊Dic3—51no—
271C4⋊Dic3—51no—
272C4⋊Dic3—51no—
273C4⋊Dic3—52no—
274C4⋊Dic3—51no—
275C4⋊Dic3—102no—
276C4⋊Dic3—101no—
277Dic3⋊C4—102no—
278Dic3⋊C4—102no—
279C4×Dic3—101no—
280C4×Dic3—101no—
281C23×C5C2×D1211yescharacteristic
282C22×D5—62no—
283C22×D5—64no—
284C22×D5—241no—
285C22×D5—241no—
286C2×C4×C5C2×D1212yes—
287C2×C4×C5C2×D1212yes—
288C2×C4×C5C2×D1211yescharacteristic
289C2×C4×C5#23712yes—
290C2×C4×C5D3×Q812yes—
291C2×C4×C5C23×D311yescharacteristic
292C2×Dic5—61no—
293C2×Dic5—61no—
294C2×Dic5—61no—
295C2×Dic5—61no—
296C2×Dic5—62no—
297C2×Dic5—241no—
298D20—34no—
299D20—64no—
300D20—62no—
301C4×D5—242no—
302C4×D5—242no—
303Dic10—242no—
304C5×C8—21no—
305C5×C8—21no—
306C5×C8—22no—
307C22×D4—151no—
308C2×M16C2×D1511yescharacteristic
309C22×C8C2×D1511yescharacteristic
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⋊C4—151no—
323C2×C22⋊C4—302no—
324#107—151no—
325#107—151no—
326#107—152no—
327#106—151no—
328#106—151no—
329#106—152no—
330C4⋊C8C2×D1512yescomplemented
331C4⋊C8C2×D1512yescomplemented
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×C3C2×D2011yescharacteristic
342C22×D3—102no—
343C22×D3—104no—
344C22×D3—401no—
345C22×D3—401no—
346C2×C3×C4C2×D2012yes—
347C2×C3×C4C2×D2012yes—
348C2×C3×C4C2×D2011yescharacteristic
349C2×C3×C4#71112yes—
350C2×C3×C4Q8×D512yes—
351C2×C3×C4C23×D511yescharacteristic
352C2×Dic3—101no—
353C2×Dic3—101no—
354C2×Dic3—101no—
355C2×Dic3—101no—
356C2×Dic3—102no—
357C2×Dic3—401no—
358D12—54no—
359D12—102no—
360D12—104no—
361C4×D3—402no—
362C4×D3—402no—
363Dic6—402no—
364C3×C8—21no—
365C3×C8—21no—
366C3×C8—22no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5#89712yes—
370C22×C5C22×D1211yescharacteristic
371C2×D5—64no—
372C2×D5—122no—
373C2×D5—122no—
374C2×D5—244no—
375C4×C5—22no—
376C4×C5—22no—
377C4×C5#89712yes—
378C4×C5C2×#23711yescharacteristic
379C4×C5C2×D3×Q811yescharacteristic
380Dic5—121no—
381Dic5—121no—
382Dic5—121no—
383Dic5—122no—
384Dic5—121no—
385C24—301no—
386C2×Q8—302no—
387C2×D4—154no—
388C2×D4—152no—
389C2×D4—301no—
390C2×D4—302no—
391C22×C4—301no—
392C22×C4—302no—
393C22×C4—302no—
394C22×C4C22×D1511yescharacteristic
395M16—22no—
396C2×C8—22no—
397C2×C8C22×D1511yescharacteristic
398C2×C8C22×D1512yes—
399C2×C8C22×D1511yescharacteristic
400C4⋊C4—152no—
401C4⋊C4—151no—
402C4⋊C4—151no—
403C4⋊C4—151no—
404C4⋊C4—151no—
405C4⋊C4—301no—
406C4⋊C4—302no—
407C4⋊C4—302no—
408C4⋊C4—302no—
409C4⋊C4D6011yescharacteristic
410C4⋊C4D6011yescharacteristic
411C22⋊C4—301no—
412C22⋊C4—301no—
413C22⋊C4—302no—
414C22⋊C4—302no—
415C22⋊C4D6012yes—
416C42—301no—
417C42—301no—
418C42C22×D1512yes—
419C3×C5#308111yescharacteristic, complemented, Hall
420C22×C3—21no—
421C22×C3—21no—
422C22×C3#404312yes—
423C22×C3C22×D2011yescharacteristic
424C2×D3—104no—
425C2×D3—202no—
426C2×D3—202no—
427C2×D3—404no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4#404312yes—
431C3×C4C2×#71111yescharacteristic
432C3×C4C2×Q8×D511yescharacteristic
433Dic3—201no—
434Dic3—201no—
435Dic3—201no—
436Dic3—202no—
437Dic3—201no—
438C2×C5—22no—
439C2×C5C2×#89711yescharacteristic
440C2×C5#575111yescharacteristic
441C2×C5#575211yescharacteristic
442D5—124no—
443C23—302no—
444C23—304no—
445C23—1201no—
446C23—1201no—
447C23C2×D6011yescharacteristic
448Q8—1202no—
449D4—154no—
450D4—304no—
451D4—302no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—301no—
455C2×C4—301no—
456C2×C4—302no—
457C2×C4—1202no—
458C2×C4—1202no—
459C2×C4—1201no—
460C2×C4C2×D6012yes—
461C2×C4C2×D6012yes—
462C2×C4C2×D6011yescharacteristic
463C2×C4#681912yes—
464C2×C4Q8×D1512yes—
465C2×C4C23×D1511yescharacteristic
466C8—21no—
467C8—21no—
468C8—22no—
469C2×C3—22no—
470C2×C3C2×#404311yescharacteristic
471C2×C3#6608511yescharacteristic
472C2×C3#6608611yescharacteristic
473D3—204no—
474C5#7909011yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—304no—
478C22—602no—
479C22—602no—
480C22—1204no—
481C22#9178612yes—
482C22C22×D6011yescharacteristic
483C4—22no—
484C4—22no—
485C4—601no—
486C4—601no—
487C4—601no—
488C4—602no—
489C4—601no—
490C4#9178612yes—
491C4C2×#681911yescharacteristic
492C4C2×Q8×D1511yescharacteristic
493C3#1061082111yescharacteristic, complemented, Sylow
494C2—22no—
495C2—604no—
496C2C2×#9178611yescharacteristic
497C2#1175651011yescharacteristic
498C2#1175651111yescharacteristic
subgroupG/H
centerC22C22×D60
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#424C2
socleC22×C3×C5C22×D4
prime radicalC22×D60C22
hypercenter#424D15
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #11756278C2semidirect
3. C3×C5×#424C2semidirect
5. #11751222C2semidirect
7. #11751207C2semidirect
8. #11750948C2semidirect
9. #11750948C2semidirect
10. #11750947C2semidirect
11. #11750943C2semidirect
28. #91759C22semidirect
29. #91758C22semidirect
30. C3×C5×C4⋊C8C22semidirect
31. C3×C5×C4⋊C8C22semidirect
36. #91102C22semidirect
37. #91102C22semidirect
38. #91102C22semidirect
39. #91101C22semidirect
40. #91101C22semidirect
41. #91101C22semidirect
45. C5×#424D3semidirect
59. C2×D60Q8semidirect
90. C3×#424D5semidirect
116. C5×C4⋊C8C2×D3semidirect
117. C5×C4⋊C8C2×D3semidirect
172. C3×C4⋊C8C2×D5semidirect
173. C3×C4⋊C8C2×D5semidirect
226. #424D15semidirect
330. C4⋊C8C2×D15semidirect
331. C4⋊C8C2×D15semidirect
419. C3×C5#3081semidirect
474. C5#79090semidirect
493. C3#10610821semidirect

Maximal subgroups

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

subgroupindex
#117562802
#117562782
C3×C5×#4242
#117512322
#117512222
C2×#911052
#117512072
#117509482
#117509472
#117509432
#106108213
#790905