Finite Group Databasebeta

← #14416537

Subgroups — #14416537

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic15C211yesmaximal, characteristic, complemented
2C2×#91839C211yesmaximal, characteristic
3#11756281C211yesmaximal, characteristic, complemented
4C3×C5×#416C211yesmaximal, characteristic, complemented
5#11751214C211yesmaximal, characteristic, complemented
6C2×#91099C211yesmaximal, characteristic, complemented
7#11751099C211yesmaximal, characteristic, complemented
8#11750918C212yesmaximal, complemented
9#11750890C212yesmaximal, complemented
10#11750886C212yesmaximal, complemented
11#11750858C212yesmaximal, complemented
12#10610550—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17#91839C418yescomplemented
18Q8×Dic15C2212yes—
19C2×#6718C2211yescharacteristic
20C2×#6717C2211yescharacteristic
21D4×Dic15—22no—
22D4×Dic15C2212yes—
23C2×#6716C2211yescharacteristic
24C2×#6715C2211yescharacteristic
25#91815—21no—
26#91815C2211yescharacteristic
27C2×C4×Dic15—21no—
28C2×C4×Dic15C2211yescharacteristic
29C22×C3⋊#168C2211yescharacteristic
30#91782C2212yes—
31#91776C2212yes—
32#91770—22no—
33#91761—21no—
34C42×D15—21no—
35C3×C5×#103C2212yes—
36C3×C5×#102C2212yes—
37#91105C2212yes—
38#91100C2212yes—
39#91099C2212yes—
40#91099C2212yes—
41#91092C2212yes—
42#91091C2212yes—
43#78819—51nomaximal, Hall
44#41×Dic5—31no—
45C2×#4096—31no—
46#65856—31no—
47C5×#416D311yescharacteristic, complemented
48#65402—31no—
49C2×#3947—31no—
50#65287—31no—
51#65106—32no—
52#65078—32no—
53#65074—32no—
54#65046—32no—
55C3×C5×#41—22no—
56C3×C5×#41C2×C414yescomplemented
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4C2311yescharacteristic
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63C22×Dic15—22no—
64C22×Dic15D412yes—
65#6817—22no—
66#6817C2×C414yescomplemented
67C2×D60C2311yescharacteristic
68C2×C4×D15—21no—
69C2×C4×D15—22no—
70C2×Dic30C2311yescharacteristic
71C2×C3×C5×C8—22no—
72C2×C3×C5×C8C2312yes—
73C3×C5×C4⋊C4C2312yes—
74C3×C5×C22⋊C4—21no—
75C3×C42×C5—21no—
76#6719—21no—
77#6719—22no—
78#6718C2×C414yescomplemented
79#6717C2×C414yescomplemented
80#6716C2×C414yescomplemented
81#6715C2×C414yescomplemented
82#6714—22no—
83C4⋊Dic15—22no—
84C4⋊Dic15C2312yes—
85#6712—22no—
86C4×Dic15—21no—
87C4×Dic15—22no—
88C4×Dic15—22no—
89C4×Dic15D411yescharacteristic
90C4×Dic15D411yescharacteristic
91C4×Dic15C2312yes—
92C2×C3⋊#168C2×C414yescomplemented
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95Dic3×#41—51no—
96C2×#950—51no—
97#5522—51no—
98C3×#416D511yescharacteristic, complemented
99#5113—51no—
100C2×#815—51no—
101#4998—51no—
102#4817—52no—
103#4789—52no—
104#4785—52no—
105#4757—52no—
106C2×C5×#41C2×D311yescharacteristic
107C2×#709—31no—
108C22×C5×C8C2×D311yescharacteristic
109C5×#117C2×D311yescharacteristic
110#4096—38no—
111Q8×Dic5—32no—
112C2×#689—31no—
113C2×#688—31no—
114D4×Dic5—32no—
115D4×Dic5—62no—
116C2×#687—31no—
117C2×#686—31no—
118#4072—31no—
119#4072—61no—
120C2×C4×Dic5—31no—
121C2×C4×Dic5—61no—
122C22×#168—31no—
123#4039—32no—
124#4033—32no—
125#4027—62no—
126#4018—61no—
127C42×D5—61no—
128C5×#103C2×D312yes—
129C5×#102C2×D312yes—
130#3953—32no—
131#3948—32no—
132#3947—32no—
133#3947—32no—
134#3940—32no—
135#3939—32no—
136#2943—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C2×D411yescharacteristic
139C22×D15—21no—
140C3×C5×Q8—21no—
141C3×C5×Q8C22×C412yes—
142C3×C5×D4—24no—
143C3×C5×D4—21no—
144C3×C5×D4C22×C412yes—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—24no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5#4112yes—
151C2×C3×C4×C5C2411yescharacteristic
152#1220—24no—
153C2×Dic15—21no—
154C2×Dic15—22no—
155C2×Dic15—42no—
156C2×Dic15—44no—
157C2×Dic15C2×D412yes—
158C2×Dic15C2×D412yes—
159D60—21no—
160D60C22×C412yes—
161C4×D15—24no—
162C4×D15—44no—
163Dic30—21no—
164Dic30C22×C412yes—
165C3×C5×C8—22no—
166C3⋊#168C22×C412yes—
167C3⋊#168C22×C412yes—
168C2×C3×#41C2×D511yescharacteristic
169C2×#235—51no—
170C22×C3×C8C2×D511yescharacteristic
171C3×#117C2×D511yescharacteristic
172#950—58no—
173Q8×Dic3—52no—
174C2×#216—51no—
175C2×#215—51no—
176D4×Dic3—52no—
177D4×Dic3—102no—
178C2×#214—51no—
179C2×#213—51no—
180#926—51no—
181#926—101no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—101no—
184C22×C3⋊C8—51no—
185#893—52no—
186#887—52no—
187#67⋊C4—102no—
188#872—101no—
189C42×D3—101no—
190C3×#103C2×D512yes—
191C3×#102C2×D512yes—
192#821—52no—
193#816—52no—
194#815—52no—
195#815—52no—
196#808—52no—
197#807—52no—
198C5×#41—22no—
199C5×#41C4×D314yescomplemented
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—61no—
206C22×Dic5—32no—
207C22×Dic5—62no—
208#709—34no—
209#709—62no—
210C2×D20—31no—
211C2×C4×D5—61no—
212C2×C4×D5—62no—
213C2×Dic10—31no—
214C2×C5×C8—22no—
215C2×C5×C8C22×D312yes—
216C5×C4⋊C4C22×D312yes—
217C5×C22⋊C4—21no—
218C42×C5—21no—
219C22⋊Dic5—62no—
220C22⋊Dic5—61no—
221#689—34no—
222#688—34no—
223#687—34no—
224#686—34no—
225#685—62no—
226C4⋊Dic5—32no—
227C4⋊Dic5—62no—
228#683—62no—
229C4×Dic5—31no—
230C4×Dic5—31no—
231C4×Dic5—32no—
232C4×Dic5—62no—
233C4×Dic5—62no—
234C4×Dic5—61no—
235C2×#168—34no—
236C2×#168—31no—
237C2×#168—31no—
238C2×#135—151no—
239C4×#41—151no—
240C4×#41—151no—
241#442—152no—
242#441—152no—
243#440—152no—
244#440—152no—
245#427—151no—
246#416—151no—
247#416D1511yescharacteristic, complemented
248C2×#97—151no—
249C22×C3×C5—22no—
250C22×C3×C5—22no—
251C22×C3×C5—42no—
252C22×C3×C5C4×D412yes—
253C22×C3×C5C22×D411yescharacteristic
254C2×D15—22no—
255C2×D15—42no—
256C3×C4×C5—22no—
257C3×C4×C5—42no—
258C3×C4×C5C4×D412yes—
259C3×C4×C5C23×C411yescharacteristic
260C3×C4×C5C2×#4111yescharacteristic
261Dic15—22no—
262Dic15—22no—
263Dic15—22no—
264Dic15—42no—
265C3×#41—22no—
266C3×#41C4×D514yescomplemented
267C2×C3×Q8C22×D511yescharacteristic
268C2×C3×D4—21no—
269C2×C3×D4C22×D511yescharacteristic
270C22×C3×C4—21no—
271C22×C3×C4C22×D511yescharacteristic
272C2×#67—101no—
273C22×Dic3—52no—
274C22×Dic3—102no—
275#235—54no—
276#235—102no—
277C2×D12—51no—
278C2×C4×D3—101no—
279C2×C4×D3—102no—
280C2×Dic6—51no—
281C2×C3×C8—22no—
282C2×C3×C8C22×D512yes—
283C3×C4⋊C4C22×D512yes—
284C3×C22⋊C4—21no—
285C3×C42—21no—
286#217—102no—
287#217—101no—
288#216—54no—
289#215—54no—
290#214—54no—
291#213—54no—
292(C2×D3)⋊C4—102no—
293C4⋊Dic3—52no—
294C4⋊Dic3—102no—
295Dic3⋊C4—102no—
296C4×Dic3—51no—
297C4×Dic3—51no—
298C4×Dic3—52no—
299C4×Dic3—102no—
300C4×Dic3—102no—
301C4×Dic3—101no—
302C2×C3⋊C8—54no—
303C2×C3⋊C8—51no—
304C2×C3⋊C8—51no—
305C23×C5—21no—
306C23×C5D3×D411yescharacteristic
307C22×D5—61no—
308C5×Q8—21no—
309C5×Q8C2×C4×D312yes—
310C5×D4—24no—
311C5×D4—21no—
312C5×D4C2×C4×D312yes—
313C2×C4×C5—21no—
314C2×C4×C5—24no—
315C2×C4×C5—22no—
316C2×C4×C5C2×C4×D312yes—
317C2×C4×C5D3×D411yescharacteristic
318C2×C4×C5#23712yes—
319C2×C4×C5C23×D311yescharacteristic
320C22⋊D5—64no—
321C2×Dic5—32no—
322C2×Dic5—32no—
323C2×Dic5—61no—
324C2×Dic5—62no—
325C2×Dic5—122no—
326C2×Dic5—124no—
327D20—32no—
328D20—61no—
329C4×D5—64no—
330C4×D5—124no—
331Dic10—32no—
332Dic10—61no—
333C5×C8—22no—
334#168—32no—
335#168—32no—
336C2×#41—151no—
337C2×#41C2×D1511yescharacteristic
338#135—158no—
339C2×Q16—151no—
340C2×SD16—151no—
341C2×SD16—151no—
342C2×D8—151no—
343C22×C8—151no—
344C22×C8C2×D1511yescharacteristic
345C4×Q8—152no—
346C4×Q8—152no—
347C4×D4—152no—
348C4×D4—152no—
349C4×D4—302no—
350C4×D4—302no—
351#117—151no—
352#117—301no—
353#117—301no—
354#117C2×D1511yescharacteristic
355C2×C42—151no—
356C2×C42—301no—
357C2×C42—301no—
358#107—152no—
359#106—152no—
360#103—152no—
361#103C2×D1512yes—
362#102—152no—
363#102C2×D1512yes—
364#97—152no—
365#97—152no—
366C2×C3×C5—22no—
367C2×C3×C5—42no—
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5#57512yes—
370D15—42no—
371C23×C3—21no—
372C23×C3D4×D511yescharacteristic
373C22×D3—101no—
374C3×Q8—21no—
375C3×Q8C2×C4×D512yes—
376C3×D4—24no—
377C3×D4—21no—
378C3×D4C2×C4×D512yes—
379C2×C3×C4—21no—
380C2×C3×C4—24no—
381C2×C3×C4—22no—
382C2×C3×C4C2×C4×D512yes—
383C2×C3×C4D4×D511yescharacteristic
384C2×C3×C4#71112yes—
385C2×C3×C4C23×D511yescharacteristic
386#67—104no—
387C2×Dic3—52no—
388C2×Dic3—52no—
389C2×Dic3—101no—
390C2×Dic3—102no—
391C2×Dic3—202no—
392C2×Dic3—204no—
393D12—52no—
394D12—101no—
395C4×D3—104no—
396C4×D3—204no—
397Dic6—52no—
398Dic6—101no—
399C3×C8—22no—
400C3⋊C8—52no—
401C3⋊C8—52no—
402C22×C5—22no—
403C22×C5—22no—
404C22×C5—42no—
405C22×C5#67⋊C412yes—
406C22×C5C2×D3×D411yescharacteristic
407C2×D5—62no—
408C2×D5—122no—
409C4×C5—22no—
410C4×C5—42no—
411C4×C5#67⋊C412yes—
412C4×C5C22×C4×D311yescharacteristic
413C4×C5C2×#23711yescharacteristic
414Dic5—62no—
415Dic5—62no—
416Dic5—62no—
417Dic5—122no—
418#41—22no—
419#41—154no—
420#41—302no—
421#41C4×D1514yescomplemented
422C2×Q8—151no—
423C2×Q8C22×D1511yescharacteristic
424C2×D4—21no—
425C2×D4—151no—
426C2×D4—301no—
427C2×D4C22×D1511yescharacteristic
428C22×C4—21no—
429C22×C4—152no—
430C22×C4—302no—
431C22×C4—302no—
432C22×C4—301no—
433C22×C4C22×D1511yescharacteristic
434Q16—154no—
435SD16—154no—
436SD16—154no—
437D8—154no—
438C2×C8—22no—
439C2×C8—154no—
440C2×C8—151no—
441C2×C8—151no—
442C2×C8C22×D1512yes—
443C4⋊C4—152no—
444C4⋊C4—302no—
445C4⋊C4—302no—
446C4⋊C4C22×D1512yes—
447C22⋊C4—21no—
448C22⋊C4—302no—
449C22⋊C4—302no—
450C22⋊C4—301no—
451C42—21no—
452C42—151no—
453C42—151no—
454C42—152no—
455C42—302no—
456C42—302no—
457C42—301no—
458C3×C5#294311yescharacteristic, complemented, Hall
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—42no—
462C22×C3#402712yes—
463C22×C3C2×D4×D511yescharacteristic
464C2×D3—102no—
465C2×D3—202no—
466C3×C4—22no—
467C3×C4—42no—
468C3×C4#402712yes—
469C3×C4C22×C4×D511yescharacteristic
470C3×C4C2×#71111yescharacteristic
471Dic3—102no—
472Dic3—102no—
473Dic3—102no—
474Dic3—202no—
475C2×C5—22no—
476C2×C5—42no—
477C2×C5C2×#67⋊C411yescharacteristic
478C2×C5#576812yes—
479D5—122no—
480C23—21no—
481C23—301no—
482C23D4×D1511yescharacteristic
483Q8—21no—
484Q8—152no—
485Q8—301no—
486Q8C2×C4×D1512yes—
487D4—24no—
488D4—21no—
489D4—152no—
490D4—304no—
491D4—301no—
492D4C2×C4×D1512yes—
493C2×C4—21no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—152no—
497C2×C4—152no—
498C2×C4—301no—
499C2×C4—304no—
500C2×C4—302no—
501C2×C4—604no—
502C2×C4—602no—
503C2×C4—604no—
504C2×C4C2×C4×D1512yes—
505C2×C4D4×D1511yescharacteristic
506C2×C4#681912yes—
507C2×C4C23×D1511yescharacteristic
508C8—22no—
509C8—152no—
510C8—152no—
511C2×C3—22no—
512C2×C3—42no—
513C2×C3C2×#402711yescharacteristic
514C2×C3#6610212yes—
515D3—202no—
516C5#7881911yescharacteristic, complemented, Sylow
517C22—22no—
518C22—22no—
519C22—42no—
520C22—302no—
521C22—602no—
522C22#9177012yes—
523C22C2×D4×D1511yescharacteristic
524C4—22no—
525C4—42no—
526C4—302no—
527C4—302no—
528C4—302no—
529C4—602no—
530C4#9177012yes—
531C4C22×C4×D1511yescharacteristic
532C4C2×#681911yescharacteristic
533C3#1061055011yescharacteristic, complemented, Sylow
534C2—22no—
535C2—42no—
536C2—602no—
537C2C2×#9177011yescharacteristic
538C2#1175652712yes—
subgroupG/H
centerC2×C4D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#416C2
socleC22×C3×C5C22×D4
prime radicalC2×#91839C2
cosocleC2×C3×C4×C5C24
hypercenter#416D15
hypocenterC3×C5#2943
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #41×Dic15C2semidirect
3. #11756281C2semidirect
4. C3×C5×#416C2semidirect
5. #11751214C2semidirect
6. C2×#91099C2semidirect
7. #11751099C2semidirect
8. #11750918C2semidirect
9. #11750890C2semidirect
10. #11750886C2semidirect
11. #11750858C2semidirect
17. #91839C4semidirect
47. C5×#416D3semidirect
56. C3×C5×#41C2×C4semidirect
66. #6817C2×C4semidirect
78. #6718C2×C4semidirect
79. #6717C2×C4semidirect
80. #6716C2×C4semidirect
81. #6715C2×C4semidirect
92. C2×C3⋊#168C2×C4semidirect
98. C3×#416D5semidirect
199. C5×#41C4×D3semidirect
247. #416D15semidirect
266. C3×#41C4×D5semidirect
421. #41C4×D15semidirect
458. C3×C5#2943semidirect
516. C5#78819semidirect
533. C3#10610550semidirect

Maximal subgroups

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

subgroupindex
#41×Dic152
C2×#918392
#117562812
C3×C5×#4162
#117512142
C2×#910992
#117510992
#117509182
#117508902
#117508862
#117508582
#106105503
#788195