Finite Group Databasebeta

← #14413307

Subgroups — #14413307

Order 1920.

1024 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×#117C211yesmaximal, characteristic
2#11754461C211yesmaximal, characteristic
3C22×#6648C211yesmaximal, characteristic
4C5×#4998C211yesmaximal, characteristic, complemented
5C3×#65287C211yesmaximal, characteristic, complemented
6#11748458C211yesmaximal, characteristic, complemented
7#11748451C211yesmaximal, characteristic, complemented
8#11747441C212yesmaximal, complemented
9#11747440C212yesmaximal, complemented
10#11747439C212yesmaximal, complemented
11#11747438C212yesmaximal, complemented
12D5×#427—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15#91815C2211yescharacteristic
16#91781C2212yes—
17C4⋊C4×D15C2212yes—
18C22⋊C4×D15—21no—
19#91766—21no—
20#91761—21no—
21C42×D15—21no—
22C5×#926C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4072C2211yescharacteristic
25C22×C3×#168C2211yescharacteristic
26#91561—21no—
27#91532—21no—
28#91437C2212yes—
29C4×#1200—21no—
30#91386—21no—
31#91347C2212yes—
32C2×#6648C418yescomplemented
33C2×#6648C2211yescharacteristic
34C2×#6648C2211yescharacteristic
35C2×#6648C2211yescharacteristic
36C2×#6648C2211yescharacteristic
37C5×#808C2212yescomplemented
38C5×#807C2212yescomplemented
39C3×#3940C2212yescomplemented
40C3×#3939C2212yescomplemented
41#90990C2212yescomplemented
42#90988C2212yescomplemented
43#90987C2212yescomplemented
44#90985C2212yescomplemented
45D3×#427—51nomaximal, Hall
46C22×C8×D5—31no—
47D5×#117—31no—
48D5×#117—31no—
49C5×#427—31no—
50#65395—31no—
51#65287—31no—
52#65287D311yescharacteristic, complemented
53#65169—32no—
54D5×#107—32no—
55#65149—32no—
56D5×#106—32no—
57C23×D15D411yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15D411yescharacteristic
60C2×C4×D15—22no—
61C2×C4×D15C2×C414yes—
62C2×C4×D15D411yescharacteristic
63C2×C4×D15D411yescharacteristic
64C2×C4×D15Q814yes—
65C2×C4×D15C2311yescharacteristic
66C2×C4×D15C2311yescharacteristic
67C2×#1200—22no—
68C3×C5×C4⋊C4C2312yes—
69C3×C5×C22⋊C4—21no—
70C3×C42×C5—21no—
71#6719—21no—
72#6714—22no—
73C4⋊Dic15C2312yes—
74#6712—22no—
75C4×Dic15—21no—
76C4×Dic15—22no—
77C5×#217—21no—
78C5×C4⋊Dic3C2312yes—
79C4×C5×Dic3—21no—
80C2×C5×C3⋊C8C2×C414yescomplemented
81C2×C5×C3⋊C8C2311yescharacteristic
82C2×C5×C3⋊C8C2311yescharacteristic
83C3×C22⋊Dic5—21no—
84C3×C4⋊Dic5C2312yes—
85C3×C4×Dic5—21no—
86C2×C3×#168C2×C414yescomplemented
87C2×C3×#168C2311yescharacteristic
88C2×C3×#168C2311yescharacteristic
89#6669—22no—
90#6667—22no—
91Dic3×Dic5—22no—
92#6648C2×C414yes—
93#6648C2×C414yes—
94#6648C2×C414yescomplemented
95#6648C2×C414yescomplemented
96C22×D3×C8—51no—
97D3×#117—51no—
98D3×#117—51no—
99C3×#427—51no—
100#5106—51no—
101#4998—51no—
102#4998D511yescharacteristic, complemented
103#4880—52no—
104D3×#107—52no—
105#4860—52no—
106D3×#106—52no—
107C22×C4×D5—31no—
108C22×C5×C8—31no—
109C5×#117—31no—
110C5×#117C2×D311yescharacteristic
111#4072—31no—
112#4072C2×D311yescharacteristic
113C22×#168C2×D311yescharacteristic
114C2×C8×D5—38no—
115C2×C8×D5—31no—
116C2×C8×D5—31no—
117C2×C8×D5—31no—
118C2×C8×D5—31no—
119#4038—32no—
120#4038—32no—
121D5×C4⋊C4—32no—
122D5×C4⋊C4—32no—
123D5×C22⋊C4—61no—
124D5×C22⋊C4—61no—
125#4023—61no—
126#4023—61no—
127#4018—61no—
128#4018—61no—
129C42×D5—61no—
130C42×D5—61no—
131C5×#107—32no—
132C5×#106—32no—
133#3950—32no—
134#3949—32no—
135#3940—32no—
136#3940C2×D312yescomplemented
137#3939—32no—
138#3939C2×D312yescomplemented
139C2×#427—151noSylow
140C23×C3×C5C2×D411yescharacteristic
141C22×D15—24no—
142C22×D15C4⋊C414yes—
143C22×D15C2×D411yescharacteristic
144C22×D15C2×D411yescharacteristic
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5C22×C412yes—
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×Q812yes—
149C2×C3×C4×C5C2411yescharacteristic
150C2×Dic15—22no—
151C2×Dic15C4⋊C414yes—
152C2×Dic15C2×D411yescharacteristic
153C2×Dic15C2×D411yescharacteristic
154C4×D15—44no—
155C4×D15C4⋊C414yes—
156C4×D15C4⋊C414yes—
157C4×D15C22×C412yes—
158C4×D15C22×C412yes—
159C4×D15C2×Q812yes—
160C4×D15C2×Q812yes—
161C2×C5×Dic3—22no—
162C2×C3×Dic5—22no—
163#1200—44no—
164C3×#168C22×C412yes—
165C3×#168C22×C412yes—
166C5×C3⋊C8C22×C412yes—
167C5×C3⋊C8C22×C412yes—
168C22×C4×D3—51no—
169C22×C3×C8—51no—
170C3×#117—51no—
171C3×#117C2×D511yescharacteristic
172#926—51no—
173#926C2×D511yescharacteristic
174C22×C3⋊C8C2×D511yescharacteristic
175C2×D3×C8—58no—
176C2×D3×C8—51no—
177C2×D3×C8—51no—
178C2×D3×C8—51no—
179C2×D3×C8—51no—
180#892—52no—
181#892—52no—
182D3×C4⋊C4—52no—
183D3×C4⋊C4—52no—
184D3×C22⋊C4—101no—
185D3×C22⋊C4—101no—
186#877—101no—
187#877—101no—
188#872—101no—
189#872—101no—
190C42×D3—101no—
191C42×D3—101no—
192C3×#107—52no—
193C3×#106—52no—
194#818—52no—
195#817—52no—
196#808—52no—
197#808C2×D512yescomplemented
198#807—52no—
199#807C2×D512yescomplemented
200C23×D5—31no—
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—31no—
203C2×C4×D5—34no—
204C2×C4×D5—31no—
205C2×C4×D5—31no—
206C2×C4×D5—34no—
207C2×C4×D5—31no—
208C2×C4×D5—31no—
209C2×C4×D5—62no—
210C2×C4×D5—62no—
211C2×C5×C8—34no—
212C2×C5×C8—31no—
213C2×C5×C8—31no—
214C5×C4⋊C4—32no—
215C5×C4⋊C4C22×D312yes—
216C5×C22⋊C4—21no—
217C5×C22⋊C4—61no—
218C42×C5—21no—
219C42×C5—61no—
220C22⋊Dic5—21no—
221C22⋊Dic5—61no—
222#685—62no—
223#685—62no—
224C4⋊Dic5—32no—
225C4⋊Dic5C22×D312yes—
226#683—62no—
227#683—62no—
228C4×Dic5—21no—
229C4×Dic5—62no—
230C4×Dic5—62no—
231C4×Dic5—61no—
232C2×#168C4×D314yescomplemented
233C2×#168C22×D311yescharacteristic
234C2×#168C22×D311yescharacteristic
235C8×D5—34no—
236C8×D5—34no—
237C8×D5—34no—
238C8×D5—34no—
239C23×C8—151no—
240C2×#117—151no—
241C2×#117—151no—
242#427—31no—
243#427—51no—
244#427—152no—
245#427—152no—
246#427—151no—
247#427—151no—
248C2×#107—152no—
249C2×#106—152no—
250C22×C3×C5—22no—
251C22×C3×C5C2×C4⋊C412yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×D15—22no—
254C2×D15—28no—
255C2×D15C2×C4⋊C412yes—
256C2×D15C2×C4⋊C412yes—
257C2×D15#13514yes—
258C3×C4×C5—42no—
259C3×C4×C5C2×C4⋊C412yes—
260C3×C4×C5C23×C411yescharacteristic
261C3×C4×C5C22×Q811yescharacteristic
262Dic15—42no—
263Dic15C2×C4⋊C412yes—
264Dic15C2×C4⋊C412yes—
265C3×Dic5—42no—
266C5×Dic3—42no—
267C23×D3—51no—
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—51no—
270C2×C4×D3—54no—
271C2×C4×D3—51no—
272C2×C4×D3—51no—
273C2×C4×D3—54no—
274C2×C4×D3—51no—
275C2×C4×D3—51no—
276C2×C4×D3—102no—
277C2×C4×D3—102no—
278C2×C3×C8—54no—
279C2×C3×C8—51no—
280C2×C3×C8—51no—
281C3×C4⋊C4—52no—
282C3×C4⋊C4C22×D512yes—
283C3×C22⋊C4—21no—
284C3×C22⋊C4—101no—
285C3×C42—21no—
286C3×C42—101no—
287#217—21no—
288#217—101no—
289(C2×D3)⋊C4—102no—
290(C2×D3)⋊C4—102no—
291C4⋊Dic3—52no—
292C4⋊Dic3C22×D512yes—
293Dic3⋊C4—102no—
294Dic3⋊C4—102no—
295C4×Dic3—21no—
296C4×Dic3—102no—
297C4×Dic3—102no—
298C4×Dic3—101no—
299C2×C3⋊C8C4×D514yescomplemented
300C2×C3⋊C8C22×D511yescharacteristic
301C2×C3⋊C8C22×D511yescharacteristic
302D3×C8—54no—
303D3×C8—54no—
304D3×C8—54no—
305D3×C8—54no—
306C23×C5D3×D411yescharacteristic
307C22×D5—31no—
308C22×D5—34no—
309C22×D5—31no—
310C22×D5—64no—
311C2×C4×C5—22no—
312C2×C4×C5—62no—
313C2×C4×C5C2×C4×D312yes—
314C2×C4×C5D3×D411yescharacteristic
315C2×C4×C5D3×Q812yes—
316C2×C4×C5C23×D311yescharacteristic
317C2×Dic5—22no—
318C2×Dic5—34no—
319C2×Dic5—31no—
320C2×Dic5—31no—
321C2×Dic5—62no—
322C4×D5—34no—
323C4×D5—34no—
324C4×D5—32no—
325C4×D5—32no—
326C4×D5—32no—
327C4×D5—32no—
328C4×D5—124no—
329C4×D5—124no—
330C5×C8—32no—
331C5×C8—32no—
332#168C2×C4×D312yes—
333#168C2×C4×D312yes—
334C23×C4—151no—
335C22×C8—31no—
336C22×C8—51no—
337C22×C8—151no—
338C22×C8—151no—
339C22×C8—151no—
340C22×C8—151no—
341C22×C8—158no—
342#117—31no—
343#117—51no—
344#117—152no—
345#117—151no—
346#117—152no—
347#117—301no—
348#117—301no—
349#117—301no—
350#117—301no—
351#117D3×D511yescharacteristic
352C2×C4⋊C4—152no—
353C2×C4⋊C4—152no—
354C2×C22⋊C4—301no—
355C2×C22⋊C4—301no—
356C2×C42—301no—
357C2×C42—301no—
358#107—32no—
359#107—52no—
360#107—152no—
361#107—152no—
362#106—32no—
363#106—52no—
364#106—152no—
365#106—152no—
366C2×C3×C5—22no—
367C2×C3×C5C22×C4⋊C411yescharacteristic
368C2×C3×C5C2×#13512yes—
369D15—22no—
370D15#42714yescomplemented
371C23×C3D4×D511yescharacteristic
372C22×D3—51no—
373C22×D3—51no—
374C22×D3—54no—
375C22×D3—104no—
376C2×C3×C4—22no—
377C2×C3×C4—102no—
378C2×C3×C4C2×C4×D512yes—
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4Q8×D512yes—
381C2×C3×C4C23×D511yescharacteristic
382C2×Dic3—22no—
383C2×Dic3—51no—
384C2×Dic3—51no—
385C2×Dic3—54no—
386C2×Dic3—102no—
387C4×D3—52no—
388C4×D3—52no—
389C4×D3—52no—
390C4×D3—52no—
391C4×D3—54no—
392C4×D3—54no—
393C4×D3—204no—
394C4×D3—204no—
395C3×C8—52no—
396C3×C8—52no—
397C3⋊C8C2×C4×D512yes—
398C3⋊C8C2×C4×D512yes—
399C22×C5—22no—
400C22×C5D3×C4⋊C412yes—
401C22×C5C2×D3×D411yescharacteristic
402C2×D5—32no—
403C2×D5—34no—
404C2×D5—32no—
405C2×D5—68no—
406C2×D5—62no—
407C4×C5—42no—
408C4×C5—122no—
409C4×C5D3×C4⋊C412yes—
410C4×C5C22×C4×D311yescharacteristic
411C4×C5C2×D3×Q811yescharacteristic
412Dic5—32no—
413Dic5—32no—
414Dic5—42no—
415Dic5—122no—
416C24—151no—
417C22×C4—151no—
418C22×C4—154no—
419C22×C4—154no—
420C22×C4—151no—
421C22×C4—151no—
422C22×C4—151no—
423C22×C4—151no—
424C22×C4—302no—
425C22×C4—302no—
426C22×C4C2×D3×D511yescharacteristic
427C2×C8—34no—
428C2×C8—31no—
429C2×C8—31no—
430C2×C8—54no—
431C2×C8—51no—
432C2×C8—51no—
433C2×C8—154no—
434C2×C8—154no—
435C2×C8—154no—
436C2×C8—154no—
437C4⋊C4—32no—
438C4⋊C4—52no—
439C4⋊C4—152no—
440C4⋊C4—302no—
441C4⋊C4—302no—
442C4⋊C4C2×D3×D512yes—
443C22⋊C4—21no—
444C22⋊C4—61no—
445C22⋊C4—101no—
446C22⋊C4—302no—
447C22⋊C4—302no—
448C22⋊C4—301no—
449C42—21no—
450C42—61no—
451C42—101no—
452C42—302no—
453C42—302no—
454C42—301no—
455C3×C5C2×#42711yescharacteristic, complemented, Hall
456C22×C3—22no—
457C22×C3D5×C4⋊C412yes—
458C22×C3C2×D4×D511yescharacteristic
459C2×D3—52no—
460C2×D3—54no—
461C2×D3—52no—
462C2×D3—108no—
463C2×D3—102no—
464C3×C4—42no—
465C3×C4—202no—
466C3×C4D5×C4⋊C412yes—
467C3×C4C22×C4×D511yescharacteristic
468C3×C4C2×Q8×D511yescharacteristic
469Dic3—42no—
470Dic3—52no—
471Dic3—52no—
472Dic3—202no—
473C2×C5—22no—
474C2×C5C2×D3×C4⋊C411yescharacteristic
475C2×C5D3×#13512yes—
476D5—34no—
477D5—62no—
478C23—151no—
479C23—154no—
480C23—151no—
481C23—304no—
482C23#679011yescharacteristic
483C2×C4—22no—
484C2×C4—62no—
485C2×C4—102no—
486C2×C4—154no—
487C2×C4—151no—
488C2×C4—151no—
489C2×C4—154no—
490C2×C4—154no—
491C2×C4—152no—
492C2×C4—152no—
493C2×C4—152no—
494C2×C4—152no—
495C2×C4—302no—
496C2×C4—604no—
497C2×C4—604no—
498C2×C4D15⋊Q812yes—
499C2×C4C4×D3×D512yes—
500C2×C4#679011yescharacteristic
501C2×C4C22×D3×D511yescharacteristic
502C8—32no—
503C8—32no—
504C8—52no—
505C8—52no—
506C2×C3—22no—
507C2×C3C2×D5×C4⋊C411yescharacteristic
508C2×C3D5×#13512yes—
509D3—54no—
510D3—102no—
511C5D3×#42711yescharacteristic, complemented, Sylow
512C22—22no—
513C22—152no—
514C22—154no—
515C22—152no—
516C22—308no—
517C22—302no—
518C22#9140412yes—
519C22C2×#679011yescharacteristic
520C4—42no—
521C4—122no—
522C4—152no—
523C4—152no—
524C4—202no—
525C4—602no—
526C4#9140412yes—
527C4C2×D15⋊Q811yescharacteristic
528C4C2×C4×D3×D511yescharacteristic
529C3D5×#42711yescharacteristic, complemented, Sylow
530C2—22no—
531C2—154no—
532C2—302no—
533C2C2×#9140411yescharacteristic
534C2#1175532812yes—
subgroupG/H
centerC2×C4#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC23×D15D4
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5C2×#427
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. C5×#4998C2semidirect
5. C3×#65287C2semidirect
6. #11748458C2semidirect
7. #11748451C2semidirect
8. #11747441C2semidirect
9. #11747440C2semidirect
10. #11747439C2semidirect
11. #11747438C2semidirect
32. C2×#6648C4semidirect
37. C5×#808C22semidirect
38. C5×#807C22semidirect
39. C3×#3940C22semidirect
40. C3×#3939C22semidirect
41. #90990C22semidirect
42. #90988C22semidirect
43. #90987C22semidirect
44. #90985C22semidirect
52. #65287D3semidirect
80. C2×C5×C3⋊C8C2×C4semidirect
86. C2×C3×#168C2×C4semidirect
94. #6648C2×C4semidirect
95. #6648C2×C4semidirect
102. #4998D5semidirect
136. #3940C2×D3semidirect
138. #3939C2×D3semidirect
197. #808C2×D5semidirect
199. #807C2×D5semidirect
232. C2×#168C4×D3semidirect
299. C2×C3⋊C8C4×D5semidirect
370. D15#427semidirect
455. C3×C5C2×#427semidirect
511. C5D3×#427semidirect
529. C3D5×#427semidirect

Maximal subgroups

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

subgroupindex
D15×#1172
#117544612
C22×#66482
C5×#49982
C3×#652872
#117484582
#117484512
#117474412
#117474402
#117474392
#117474382
D5×#4273
D3×#4275