Finite Group Databasebeta

← #14430782

Subgroups — #14430782

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
1C3×C5×#518C211yesmaximal, characteristic
2#11756278C211yesmaximal, characteristic, complemented
3#11751316C211yesmaximal, characteristic
4C2×#91116C211yesmaximal, characteristic
5#11751110C212yesmaximal, complemented
6#11751110C212yesmaximal, complemented
7#11751109C212yesmaximal, complemented
8#11751108C212yesmaximal, complemented
9#11751100C211yesmaximal, characteristic, complemented
10#11751099C211yesmaximal, characteristic, complemented
11#11751096C211yesmaximal, characteristic, complemented
12#10614270—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C3×C4×C5×D4—21no—
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4C2212yes—
17C3×C4×C5×D4C2212yes—
18C3×C5×#117C2211yescharacteristic
19C3×C5×#117C2211yescharacteristic
20C2×C3×C5×C22⋊C4—22no—
21#91815C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C2×#6710C2211yescharacteristic
24C22×C3⋊#168C2211yescharacteristic
25#91779—21no—
26#91777—21no—
27#91767—22no—
28#91759C2212yescomplemented
29#91758C2212yescomplemented
30#91116C2212yes—
31#91116C2212yes—
32#91116C2212yes—
33#91116C2212yes—
34#91092C2212yescomplemented
35#91092C2211yescharacteristic, complemented
36#91092C2211yescharacteristic, complemented
37#91091C2212yescomplemented
38#91091C2211yescharacteristic, complemented
39#91091C2211yescharacteristic, complemented
40C4⋊(C3⋊#168)C2212yescomplemented
41C4⋊(C3⋊#168)C2212yescomplemented
42#82539—51nomaximal, Hall
43C5×#518D311yescharacteristic
44#65853—31no—
45#65504—31no—
46C2×#3964—31no—
47#65298—32no—
48#65298—32no—
49#65297—32no—
50#65296—32no—
51#65288—31no—
52#65287—31no—
53#65284—31no—
54C24×C3×C5—21no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4Q814yescomplemented
58C2×C3×C5×D4C2312yes—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5C2311yescharacteristic
62C22×Dic15—21no—
63C2×Dic30—22no—
64C3×C5×C4⋊C4D411yescharacteristic
65C3×C5×C4⋊C4D411yescharacteristic
66C3×C5×C4⋊C4C2311yescharacteristic
67C3×C5×C4⋊C4C2311yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C5×C22⋊C4—22no—
70C3×C5×C22⋊C4—22no—
71C3×C5×C22⋊C4D412yes—
72C3×C42×C5—21no—
73C3×C42×C5C2312yes—
74#6719—21no—
75C4⋊Dic15—22no—
76C4⋊Dic15—21no—
77C4⋊Dic15C2311yescharacteristic
78C4⋊Dic15C2312yes—
79C4⋊Dic15C2311yescharacteristic
80#6712—22no—
81#6712—22no—
82C4×Dic15—21no—
83#6710—22no—
84C2×C3⋊#168—22no—
85C2×C3⋊#168C2311yescharacteristic
86C2×C3⋊#168C2311yescharacteristic
87C2×C3⋊#168C2312yes—
88C3×#518D511yescharacteristic
89#5519—51no—
90#5215—51no—
91C2×#832—51no—
92#5009—52no—
93#5009—52no—
94#5008—52no—
95#5007—52no—
96#4999—51no—
97#4998—51no—
98#4995—51no—
99C22×C5×D4C2×D311yescharacteristic
100C4×C5×D4—21no—
101C4×C5×D4—21no—
102C4×C5×D4C2×D312yes—
103C4×C5×D4C2×D312yes—
104C5×#117C2×D311yescharacteristic
105C5×#117C2×D311yescharacteristic
106C2×C5×C22⋊C4—22no—
107#4072—31no—
108C2×C4⋊Dic5—31no—
109C2×#681—31no—
110C22×#168—31no—
111#4036—61no—
112#4034—61no—
113#4024—62no—
114#4016—32no—
115#4015—32no—
116#3964—32no—
117#3964—32no—
118#3964—32no—
119#3964—32no—
120#3940—32no—
121#3940—31no—
122#3940—31no—
123#3939—32no—
124#3939—31no—
125#3939—31no—
126C4⋊#168—32no—
127C4⋊#168—32no—
128#3081—151noSylow
129C23×C3×C5—22no—
130C23×C3×C5—24no—
131C23×C3×C5—81no—
132C23×C3×C5—81no—
133C23×C3×C5C2×D411yescharacteristic
134C3×C5×D4—24no—
135C3×C5×D4—22no—
136C3×C5×D4C2×Q814yes—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—82no—
140C2×C3×C4×C5—82no—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×Q812yes—
145C2×C3×C4×C5#4112yes—
146C2×C3×C4×C5C2411yescharacteristic
147C2×Dic15—21no—
148C2×Dic15—21no—
149C2×Dic15—22no—
150C2×Dic15—81no—
151Dic30—82no—
152C3⋊#168—21no—
153C3⋊#168—21no—
154C3⋊#168—22no—
155C22×C3×D4C2×D511yescharacteristic
156C3×C4×D4—21no—
157C3×C4×D4—21no—
158C3×C4×D4C2×D512yes—
159C3×C4×D4C2×D512yes—
160C3×#117C2×D511yescharacteristic
161C3×#117C2×D511yescharacteristic
162C2×C3×C22⋊C4—22no—
163#926—51no—
164C2×C4⋊Dic3—51no—
165C2×#208—51no—
166C22×C3⋊C8—51no—
167#890—101no—
168#888—101no—
169#878—102no—
170#870—52no—
171#869—52no—
172#832—52no—
173#832—52no—
174#832—52no—
175#832—52no—
176#808—52no—
177#808—51no—
178#808—51no—
179#807—52no—
180#807—51no—
181#807—51no—
182C4⋊(C3⋊C8)—52no—
183C4⋊(C3⋊C8)—52no—
184C24×C5—21no—
185C2×C5×D4—22no—
186C2×C5×D4—21no—
187C2×C5×D4Dic614yescomplemented
188C2×C5×D4C22×D312yes—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—61no—
193C2×Dic10—62no—
194C5×C4⋊C4#6711yescharacteristic
195C5×C4⋊C4#6711yescharacteristic
196C5×C4⋊C4C22×D311yescharacteristic
197C5×C4⋊C4C22×D311yescharacteristic
198C5×C22⋊C4—21no—
199C5×C22⋊C4—22no—
200C5×C22⋊C4—22no—
201C5×C22⋊C4#6712yes—
202C42×C5—21no—
203C42×C5C22×D312yes—
204C22⋊Dic5—61no—
205C4⋊Dic5—31no—
206C4⋊Dic5—32no—
207C4⋊Dic5—31no—
208C4⋊Dic5—62no—
209C4⋊Dic5—61no—
210#683—62no—
211#683—62no—
212C4×Dic5—61no—
213#681—62no—
214C2×#168—31no—
215C2×#168—32no—
216C2×#168—31no—
217C2×#168—62no—
218#544—151no—
219#518D1511yescharacteristic
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428—151no—
225#427—151no—
226#424—151no—
227#418—151no—
228C2×#102—151no—
229C22×C3×C5—21no—
230C22×C3×C5—21no—
231C22×C3×C5—24no—
232C22×C3×C5—42no—
233C22×C3×C5—42no—
234C22×C3×C5—84no—
235C22×C3×C5C22⋊Q812yes—
236C22×C3×C5C22×D411yescharacteristic
237C3×C4×C5—22no—
238C3×C4×C5—22no—
239C3×C4×C5—41no—
240C3×C4×C5—41no—
241C3×C4×C5C22⋊Q812yes—
242C3×C4×C5C22×Q811yescharacteristic
243C3×C4×C5C2×#4111yescharacteristic
244Dic15—41no—
245Dic15—42no—
246Dic15—41no—
247C24×C3—21no—
248C2×C3×D4—22no—
249C2×C3×D4—21no—
250C2×C3×D4Dic1014yescomplemented
251C2×C3×D4C22×D512yes—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4C22×D511yescharacteristic
255C22×Dic3—101no—
256C2×Dic6—102no—
257C3×C4⋊C4C22⋊D511yescharacteristic
258C3×C4⋊C4C22⋊D511yescharacteristic
259C3×C4⋊C4C22×D511yescharacteristic
260C3×C4⋊C4C22×D511yescharacteristic
261C3×C22⋊C4—21no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—22no—
264C3×C22⋊C4C22⋊D512yes—
265C3×C42—21no—
266C3×C42C22×D512yes—
267#217—101no—
268C4⋊Dic3—51no—
269C4⋊Dic3—52no—
270C4⋊Dic3—51no—
271C4⋊Dic3—102no—
272C4⋊Dic3—101no—
273Dic3⋊C4—102no—
274Dic3⋊C4—102no—
275C4×Dic3—101no—
276#208—102no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—52no—
279C2×C3⋊C8—51no—
280C2×C3⋊C8—102no—
281C23×C5—22no—
282C23×C5—24no—
283C23×C5—81no—
284C23×C5—81no—
285C23×C5C2×#6711yescharacteristic
286C5×D4—24no—
287C5×D4—22no—
288C5×D4C2×Dic614yes—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—82no—
292C2×C4×C5—82no—
293C2×C4×C5C2×Dic612yes—
294C2×C4×C5#23512yes—
295C2×C4×C5C2×#6712yes—
296C2×C4×C5C2×#6712yes—
297C2×C4×C5C2×#6711yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C2×Dic5—61no—
300C2×Dic5—61no—
301C2×Dic5—62no—
302C2×Dic5—241no—
303Dic10—242no—
304#168—61no—
305#168—61no—
306#168—62no—
307C22×D4C2×D1511yescharacteristic
308C2×M16—151no—
309C22×C8—151no—
310C4⋊Q8—152no—
311C4⋊Q8—301no—
312#125—152no—
313#125—301no—
314C22⋊Q8—302no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4C2×D1512yes—
318C4×D4C2×D1512yes—
319#117—151no—
320#117C2×D1511yescharacteristic
321#117C2×D1511yescharacteristic
322C2×C4⋊C4—151no—
323C2×C22⋊C4—22no—
324#107—151no—
325#107—151no—
326#107—152no—
327#106—151no—
328#106—151no—
329#106—152no—
330C4⋊C8—152no—
331C4⋊C8—152no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102—152no—
336C2×C3×C5—22no—
337C2×C3×C5—44no—
338C2×C3×C5C2×C22⋊Q811yescharacteristic
339C2×C3×C5#57611yescharacteristic
340C2×C3×C5#57711yescharacteristic
341C23×C3—22no—
342C23×C3—24no—
343C23×C3—81no—
344C23×C3—81no—
345C23×C3C2×C22⋊D511yescharacteristic
346C3×D4—22no—
347C3×D4—24no—
348C3×D4C2×Dic1014yes—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—82no—
352C2×C3×C4—82no—
353C2×C3×C4C2×Dic1012yes—
354C2×C3×C4#70912yes—
355C2×C3×C4C2×C22⋊D512yes—
356C2×C3×C4C2×C22⋊D512yes—
357C2×C3×C4C2×C22⋊D511yescharacteristic
358C2×C3×C4C23×D511yescharacteristic
359C2×Dic3—101no—
360C2×Dic3—101no—
361C2×Dic3—102no—
362C2×Dic3—401no—
363Dic6—402no—
364C3⋊C8—101no—
365C3⋊C8—101no—
366C3⋊C8—102no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5—24no—
370C22×C5—42no—
371C22×C5—42no—
372C22×C5—84no—
373C22×C5#92412yes—
374C22×C5C22×#6711yescharacteristic
375C4×C5—22no—
376C4×C5—22no—
377C4×C5—41no—
378C4×C5—41no—
379C4×C5#92412yes—
380C4×C5C22×Dic611yescharacteristic
381C4×C5C2×#23511yescharacteristic
382Dic5—121no—
383Dic5—122no—
384Dic5—121no—
385C24—21no—
386C2×Q8—302no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4Dic3014yescomplemented
390C2×D4C22×D1512yes—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—301no—
394C22×C4C22×D1511yescharacteristic
395M16—302no—
396C2×C8—151no—
397C2×C8—152no—
398C2×C8—151no—
399C2×C8—302no—
400C4⋊C4—152no—
401C4⋊C4—151no—
402C4⋊C4—151no—
403C4⋊C4—301no—
404C4⋊C4—302no—
405C4⋊C4—302no—
406C4⋊C4—302no—
407C4⋊C4#122011yescharacteristic
408C4⋊C4#122011yescharacteristic
409C4⋊C4C22×D1511yescharacteristic
410C4⋊C4C22×D1511yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—301no—
415C22⋊C4#122012yes—
416C42—21no—
417C42—301no—
418C42C22×D1512yes—
419C3×C5#308111yescharacteristic, complemented, Hall
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—24no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—84no—
426C22×C3#407012yes—
427C22×C3C22×C22⋊D511yescharacteristic
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—41no—
431C3×C4—41no—
432C3×C4#407012yes—
433C3×C4C22×Dic1011yescharacteristic
434C3×C4C2×#70911yescharacteristic
435Dic3—201no—
436Dic3—202no—
437Dic3—201no—
438C2×C5—22no—
439C2×C5—44no—
440C2×C5C2×#92411yescharacteristic
441C2×C5#583511yescharacteristic
442C2×C5#583611yescharacteristic
443C23—22no—
444C23—24no—
445C23—81no—
446C23—81no—
447C23C2×#122011yescharacteristic
448Q8—1202no—
449D4—24no—
450D4—22no—
451D4C2×Dic3014yes—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—301no—
457C2×C4—301no—
458C2×C4—302no—
459C2×C4—1201no—
460C2×C4C2×Dic3012yes—
461C2×C4#681712yes—
462C2×C4C2×#122012yes—
463C2×C4C2×#122012yes—
464C2×C4C2×#122011yescharacteristic
465C2×C4C23×D1511yescharacteristic
466C8—301no—
467C8—301no—
468C8—302no—
469C2×C3—22no—
470C2×C3—44no—
471C2×C3C2×#407011yescharacteristic
472C2×C3#6616911yescharacteristic
473C2×C3#6617011yescharacteristic
474C5#8253911yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—24no—
478C22—42no—
479C22—42no—
480C22—84no—
481C22#9181312yes—
482C22C22×#122011yescharacteristic
483C4—22no—
484C4—22no—
485C4—41no—
486C4—41no—
487C4—602no—
488C4—601no—
489C4—601no—
490C4#9181312yes—
491C4C22×Dic3011yescharacteristic
492C4C2×#681711yescharacteristic
493C3#1061427011yescharacteristic, complemented, Sylow
494C2—22no—
495C2—44no—
496C2C2×#9181311yescharacteristic
497C2#1175659411yescharacteristic
498C2#1175659511yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#518C2
socleC22×C3×C5C22×D4
prime radicalC22×C3×C5×D4C22
hypercenter#518D15
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #11756278C2semidirect
5. #11751110C2semidirect
6. #11751110C2semidirect
7. #11751109C2semidirect
8. #11751108C2semidirect
9. #11751100C2semidirect
10. #11751099C2semidirect
11. #11751096C2semidirect
28. #91759C22semidirect
29. #91758C22semidirect
34. #91092C22semidirect
35. #91092C22semidirect
36. #91092C22semidirect
37. #91091C22semidirect
38. #91091C22semidirect
39. #91091C22semidirect
40. C4⋊(C3⋊#168)C22semidirect
41. C4⋊(C3⋊#168)C22semidirect
57. C2×C3×C5×D4Q8semidirect
187. C2×C5×D4Dic6semidirect
250. C2×C3×D4Dic10semidirect
389. C2×D4Dic30semidirect
419. C3×C5#3081semidirect
474. C5#82539semidirect
493. C3#10614270semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5182
#117562782
#117513162
C2×#911162
#117511102
#117511092
#117511082
#117511002
#117510992
#117510962
#106142703
#825395