Finite Group Databasebeta

← #14430887

Subgroups — #14430887

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×#65855C211yesmaximal, characteristic
2#11754620C211yesmaximal, characteristic, complemented
3#11751096C211yesmaximal, characteristic, complemented
4C5×#4998C211yesmaximal, characteristic, complemented
5#11748432C211yesmaximal, characteristic, complemented
6#11748366C211yesmaximal, characteristic
7C2×#90965C211yesmaximal, characteristic
8#11747415C212yesmaximal, complemented
9#11747410C212yesmaximal, complemented
10#11747392C212yesmaximal, complemented
11#11747389C212yesmaximal, complemented
12#10610928—31nomaximal, Hall
13C22×C3×D20C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C22×C5×C3⋊C8C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20C3×#4039C2212yes—
21C3×#4039C2212yes—
22C3×D5×C22⋊C4—22no—
23C3×C4×D20—21no—
24C3×C4×D20—21no—
25#91576—22no—
26#91469—21no—
27#91468C2212yescomplemented
28#91388C2212yescomplemented
29#91381—21no—
30#91092C2212yescomplemented
31#91091C2212yescomplemented
32C5×#808C2211yescharacteristic, complemented
33C5×#808C2211yescharacteristic, complemented
34C5×#807C2211yescharacteristic, complemented
35C5×#807C2211yescharacteristic, complemented
36#90982C2212yescomplemented
37#90982C2212yescomplemented
38#90965C2212yes—
39#90965C2212yes—
40#90964C2212yes—
41#90964C2212yes—
42#82539—51nomaximal, Hall
43#65855D311yescharacteristic
44#65853—31no—
45C5×#427—31no—
46C2×#3953—31no—
47#65391—31no—
48#65290—31no—
49#65284—31no—
50#65180—32no—
51#65179—32no—
52#65160—32no—
53#65159—32no—
54C23×C3×D5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C2×C3×D20—21no—
58C2×C3×D20—22no—
59C2×C3×D20Q814yescomplemented
60C2×C3×D20C2312yes—
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5—22no—
63C2×#1204—22no—
64C3×C5×C4⋊C4C2311yescharacteristic
65C3×C5×C4⋊C4C2311yescharacteristic
66C3×C5×C22⋊C4—21no—
67C3×C42×C5—21no—
68C4⋊Dic15—21no—
69C4⋊Dic15C2312yes—
70#6710—22no—
71C2×C3⋊#168C2312yes—
72C5×#217—21no—
73C5×C4⋊Dic3C2311yescharacteristic
74C5×C4⋊Dic3C2311yescharacteristic
75C4×C5×Dic3—21no—
76C2×C5×C3⋊C8—22no—
77C2×C5×C3⋊C8C2311yescharacteristic
78C2×C5×C3⋊C8C2311yescharacteristic
79C3×C22⋊Dic5D412yes—
80C3×#685—22no—
81C3×#685—22no—
82C3×C4⋊Dic5D411yescharacteristic
83C3×C4⋊Dic5D411yescharacteristic
84C3×C4×Dic5C2312yes—
85Dic3⋊Dic5—22no—
86#6669—22no—
87#6668—22no—
88C3×#518—51no—
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#4998D511yescharacteristic, complemented
98#4995—51no—
99C22×D20C2×D311yescharacteristic
100C22×C5×C8—31no—
101C5×#117—31no—
102C5×#117C2×D311yescharacteristic
103#4072C2×D311yescharacteristic
104C2×C4⋊Dic5—31no—
105C2×#681—31no—
106#4039C2×D312yes—
107#4039C2×D312yes—
108#4036—32no—
109#4034—32no—
110D5×C22⋊C4—22no—
111#4024—62no—
112C4×D20—21no—
113C4×D20—21no—
114#4016—61no—
115#4015—61no—
116C5×#107—31no—
117C5×#107—31no—
118C5×#106—31no—
119C5×#106—31no—
120#3953—32no—
121#3953—32no—
122#3946—32no—
123#3946—32no—
124#3941—32no—
125#3941—32no—
126#3940—32no—
127#3939—32no—
128#3081—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×C3×D5—22no—
131C22×C3×D5—24no—
132C22×C3×D5—81no—
133C22×C3×D5—81no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×Q812yes—
138C2×C3×C4×C5#4112yes—
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—22no—
141C2×Dic15—81no—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—21no—
144C2×C3×Dic5C2×D412yes—
145C2×C3×Dic5C2×D412yes—
146C3×D20—24no—
147C3×D20—22no—
148C3×D20C2×Q814yes—
149C3×C4×D5—82no—
150C3×C4×D5—82no—
151#1204—82no—
152C3⋊#168—22no—
153C5×C3⋊C8—21no—
154C5×C3⋊C8—21no—
155C22×C3×D4—51no—
156C3×C4×D4—52no—
157C3×C4×D4—52no—
158C3×C4×D4—101no—
159C3×C4×D4—101no—
160C3×#117—51no—
161C3×#117C2×D511yescharacteristic
162C2×C3×C22⋊C4—102no—
163#926C2×D511yescharacteristic
164C2×C4⋊Dic3—51no—
165C2×#208—51no—
166C22×C3⋊C8C2×D511yescharacteristic
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#808C2×D511yescharacteristic, complemented
178#808C2×D511yescharacteristic, complemented
179#807—52no—
180#807C2×D511yescharacteristic, complemented
181#807C2×D511yescharacteristic, complemented
182C4⋊(C3⋊C8)—52no—
183C4⋊(C3⋊C8)—52no—
184C23×D5—21no—
185C22×C4×C5C22×D311yescharacteristic
186C22×Dic5—61no—
187C2×D20—22no—
188C2×D20—21no—
189C2×D20Dic614yescomplemented
190C2×D20C22×D312yes—
191C2×C4×D5—22no—
192C2×C4×D5—22no—
193C2×Dic10—62no—
194C2×C5×C8—31no—
195C2×C5×C8—31no—
196C2×C5×C8—62no—
197C5×C4⋊C4—31no—
198C5×C4⋊C4—31no—
199C5×C4⋊C4C22×D311yescharacteristic
200C5×C4⋊C4C22×D311yescharacteristic
201C5×C22⋊C4—21no—
202C5×C22⋊C4—61no—
203C42×C5—21no—
204C42×C5—61no—
205C22⋊Dic5#6712yes—
206#685—22no—
207#685—22no—
208C4⋊Dic5—32no—
209C4⋊Dic5—61no—
210C4⋊Dic5—62no—
211C4⋊Dic5#6711yescharacteristic
212C4⋊Dic5#6711yescharacteristic
213#683—62no—
214#683—62no—
215C4×Dic5C22×D312yes—
216#681—62no—
217C2×#168—32no—
218#544—151no—
219#518—51no—
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428—151no—
225#427—31no—
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×C3×D5—24no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—84no—
237C3×C4×C5—41no—
238C3×C4×C5—41no—
239C3×C4×C5C22⋊Q812yes—
240C3×C4×C5C22×Q811yescharacteristic
241C3×C4×C5C2×#4111yescharacteristic
242Dic15—42no—
243C3×Dic5—22no—
244C3×Dic5—22no—
245C5×Dic3—41no—
246C5×Dic3—41no—
247C24×C3—101no—
248C2×C3×D4—54no—
249C2×C3×D4—52no—
250C2×C3×D4—102no—
251C2×C3×D4—101no—
252C22×C3×C4—102no—
253C22×C3×C4—102no—
254C22×C3×C4C22×D511yescharacteristic
255C22×Dic3—101no—
256C2×Dic6—102no—
257C3×C4⋊C4—51no—
258C3×C4⋊C4—51no—
259C3×C4⋊C4C22×D511yescharacteristic
260C3×C4⋊C4C22×D511yescharacteristic
261C3×C22⋊C4—21no—
262C3×C22⋊C4—52no—
263C3×C22⋊C4—102no—
264C3×C22⋊C4—102no—
265C3×C42—21no—
266C3×C42—52no—
267#217—21no—
268C4⋊Dic3—52no—
269C4⋊Dic3—102no—
270C4⋊Dic3—101no—
271C4⋊Dic3C22×D511yescharacteristic
272C4⋊Dic3C22×D511yescharacteristic
273Dic3⋊C4—102no—
274Dic3⋊C4—102no—
275C4×Dic3—21no—
276#208—102no—
277C2×C3⋊C8—22no—
278C2×C3⋊C8—52no—
279C2×C3⋊C8C22×D511yescharacteristic
280C2×C3⋊C8C22×D511yescharacteristic
281C23×C5C2×#6711yescharacteristic
282C22×D5—22no—
283C22×D5—24no—
284C22×D5—81no—
285C22×D5—81no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—61no—
289C2×C4×C5—61no—
290C2×C4×C5C2×Dic612yes—
291C2×C4×C5#23512yes—
292C2×C4×C5C2×#6711yescharacteristic
293C2×C4×C5C23×D311yescharacteristic
294C2×Dic5—62no—
295C2×Dic5—241no—
296C2×Dic5C2×#6712yes—
297C2×Dic5C2×#6712yes—
298D20—24no—
299D20—22no—
300D20C2×Dic614yes—
301C4×D5—82no—
302C4×D5—82no—
303Dic10—242no—
304C5×C8—61no—
305C5×C8—61no—
306#168—62no—
307C22×D4—51no—
308C2×M16—151no—
309C22×C8—31no—
310C4⋊Q8—152no—
311C4⋊Q8—301no—
312#125—152no—
313#125—301no—
314C22⋊Q8—302no—
315C4×D4—52no—
316C4×D4—52no—
317C4×D4—101no—
318C4×D4—101no—
319#117—31no—
320#117—51no—
321#117D3×D511yescharacteristic
322C2×C4⋊C4—151no—
323C2×C22⋊C4—102no—
324#107—31no—
325#107—31no—
326#107—152no—
327#106—31no—
328#106—31no—
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×C5C2×C22⋊Q811yescharacteristic
338C2×C3×C5#57611yescharacteristic
339C2×C3×C5#57711yescharacteristic
340C3×D5—44no—
341C23×C3—102no—
342C23×C3—104no—
343C23×C3—401no—
344C23×C3—401no—
345C23×C3D4×D511yescharacteristic
346C3×D4—54no—
347C3×D4—102no—
348C3×D4—104no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—52no—
352C2×C3×C4—52no—
353C2×C3×C4—402no—
354C2×C3×C4—402no—
355C2×C3×C4#70912yes—
356C2×C3×C4D4×D511yescharacteristic
357C2×C3×C4Q8×D512yes—
358C2×C3×C4C23×D511yescharacteristic
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—102no—
362C2×Dic3—401no—
363Dic6—402no—
364C3⋊C8—21no—
365C3⋊C8—21no—
366C3⋊C8—102no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5#92412yes—
370C22×C5C22×#6711yescharacteristic
371C2×D5—24no—
372C2×D5—42no—
373C2×D5—42no—
374C2×D5—84no—
375C4×C5—41no—
376C4×C5—41no—
377C4×C5—121no—
378C4×C5—121no—
379C4×C5#92412yes—
380C4×C5C22×Dic611yescharacteristic
381C4×C5C2×#23511yescharacteristic
382Dic5—22no—
383Dic5—22no—
384Dic5—122no—
385C24—101no—
386C2×Q8—302no—
387C2×D4—54no—
388C2×D4—52no—
389C2×D4—102no—
390C2×D4—101no—
391C22×C4—102no—
392C22×C4—102no—
393C22×C4—301no—
394C22×C4C2×D3×D511yescharacteristic
395M16—302no—
396C2×C8—31no—
397C2×C8—31no—
398C2×C8—62no—
399C2×C8—152no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—51no—
403C4⋊C4—51no—
404C4⋊C4—152no—
405C4⋊C4—302no—
406C4⋊C4—302no—
407C4⋊C4—302no—
408C4⋊C4—301no—
409C4⋊C4C2×D3×D511yescharacteristic
410C4⋊C4C2×D3×D511yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—52no—
413C22⋊C4—61no—
414C22⋊C4—102no—
415C22⋊C4—102no—
416C42—21no—
417C42—52no—
418C42—61no—
419C3×C5#308111yescharacteristic, complemented, Hall
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—104no—
423C22×C3—202no—
424C22×C3—202no—
425C22×C3—404no—
426C22×C3#404212yes—
427C22×C3C2×D4×D511yescharacteristic
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—102no—
431C3×C4—102no—
432C3×C4#404212yes—
433C3×C4C2×#70911yescharacteristic
434C3×C4C2×Q8×D511yescharacteristic
435Dic3—41no—
436Dic3—41no—
437Dic3—202no—
438C2×C5—22no—
439C2×C5C2×#92411yescharacteristic
440C2×C5#583511yescharacteristic
441C2×C5#583611yescharacteristic
442D5—44no—
443C23—102no—
444C23—104no—
445C23—401no—
446C23—401no—
447C23D5×#6711yescharacteristic
448Q8—1202no—
449D4—54no—
450D4—102no—
451D4—104no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—52no—
455C2×C4—52no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—302no—
459C2×C4—402no—
460C2×C4—402no—
461C2×C4—1201no—
462C2×C4D5×Dic612yes—
463C2×C4#677112yes—
464C2×C4D5×#6711yescharacteristic
465C2×C4C22×D3×D511yescharacteristic
466C8—61no—
467C8—61no—
468C8—302no—
469C2×C3—22no—
470C2×C3—204no—
471C2×C3C2×#404211yescharacteristic
472C2×C3#6610311yescharacteristic
473C2×C3#6610411yescharacteristic
474C5#8253911yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—104no—
478C22—202no—
479C22—202no—
480C22—404no—
481C22#9134912yes—
482C22C2×D5×#6711yescharacteristic
483C4—41no—
484C4—41no—
485C4—102no—
486C4—102no—
487C4—121no—
488C4—121no—
489C4—602no—
490C4#9134912yes—
491C4C2×D5×Dic611yescharacteristic
492C4C2×#677111yescharacteristic
493C3#1061092811yescharacteristic, complemented, Sylow
494C2—22no—
495C2—204no—
496C2C2×#9134911yescharacteristic
497C2#1175531811yescharacteristic
498C2#1175533711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D20C22
hypercenter#117D3×D5
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11754620C2semidirect
3. #11751096C2semidirect
4. C5×#4998C2semidirect
5. #11748432C2semidirect
8. #11747415C2semidirect
9. #11747410C2semidirect
10. #11747392C2semidirect
11. #11747389C2semidirect
27. #91468C22semidirect
28. #91388C22semidirect
30. #91092C22semidirect
31. #91091C22semidirect
32. C5×#808C22semidirect
33. C5×#808C22semidirect
34. C5×#807C22semidirect
35. C5×#807C22semidirect
36. #90982C22semidirect
37. #90982C22semidirect
59. C2×C3×D20Q8semidirect
97. #4998D5semidirect
177. #808C2×D5semidirect
178. #808C2×D5semidirect
180. #807C2×D5semidirect
181. #807C2×D5semidirect
189. C2×D20Dic6semidirect
419. C3×C5#3081semidirect
474. C5#82539semidirect
493. C3#10610928semidirect

Maximal subgroups

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

subgroupindex
C3×#658552
#117546202
#117510962
C5×#49982
#117484322
#117483662
C2×#909652
#117474152
#117474102
#117473922
#117473892
#106109283
#825395