Finite Group Databasebeta

← #14481806

Subgroups — #14481806

Order 1920.

1992 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#544C211yesmaximal, characteristic, complemented
2#11756488C214yesmaximal, complemented
3#11756487C214yesmaximal, complemented
4#11756448C214yesmaximal, complemented
5#11756447C214yesmaximal, complemented
6#11756393C214yesmaximal
7#11756381C214yesmaximal, complemented
8D15×#117C212yesmaximal
9#11756278C212yesmaximal, complemented
10C2×#91781C211yesmaximal, characteristic
11#11756259C211yesmaximal, characteristic, complemented
12#10618482—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C3×C5×C4⋊Q8C2214yescomplemented
15C3×C5×#125C2214yescomplemented
16C3×C5×C22⋊Q8C2214yes—
17C3×C5×#117C2212yes—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19#91835C2218yes—
20Q8×Dic15C2214yescomplemented
21#91833C2214yescomplemented
22C2×#6714C2212yes—
23#91815C2212yes—
24C2×C4⋊Dic15C2211yescharacteristic
25#91813C2214yes—
26C2×C4×Dic15C2212yes—
27#91786C2218yes—
28#91785C2218yes—
29#91785C2218yes—
30#91781C2212yes—
31#91781C2214yes—
32#91781C2214yes—
33#91781C2212yes—
34C4⋊C4×D15C2212yes—
35C4⋊C4×D15C2212yes—
36#91779C2214yescomplemented
37#91779C2214yescomplemented
38#91778C2218yescomplemented
39#91777C2214yescomplemented
40#91777C2214yescomplemented
41#91777C2214yescomplemented
42#91776C2214yescomplemented
43#91776C2218yescomplemented
44C22⋊C4×D15C2214yes—
45#91767C2218yes—
46#91766C2214yes—
47#91761C2214yes—
48C42×D15C2214yes—
49#91759C2214yescomplemented
50#91758C2214yescomplemented
51#86581—51nomaximal, Hall
52C5×#544D311yescharacteristic, complemented
53#66063—34no—
54#66062—34no—
55#66023—34no—
56#66022—34no—
57#65968—34no—
58#65956—34no—
59D5×#117—32no—
60#65853—32no—
61C2×#4038—31no—
62#65834—31no—
63C23×D15C2311yescharacteristic
64C2×C3×C5×Q8C2314yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15C2312yes—
68C22×Dic15C2311yescharacteristic
69C2×C4×D15Q818yescomplemented
70C2×C4×D15C2314yes—
71C2×C4×D15C2314yes—
72C2×C4×D15C2312yes—
73C2×C4×D15C2312yes—
74C2×Dic30C2318yes—
75C2×Dic30C2314yes—
76C3×C5×C4⋊C4C2314yes—
77C3×C5×C4⋊C4C2318yes—
78C3×C5×C4⋊C4C2312yes—
79C3×C5×C4⋊C4C2314yes—
80C3×C5×C4⋊C4C2312yes—
81C3×C5×C22⋊C4C2314yes—
82C3×C42×C5C2314yes—
83#6719C2314yes—
84#6714C2314yes—
85#6714C2314yes—
86#6714C2318yes—
87C4⋊Dic15C2312yes—
88C4⋊Dic15C2314yes—
89C4⋊Dic15C2318yes—
90C4⋊Dic15C2312yes—
91C4⋊Dic15C2314yes—
92#6712C2318yes—
93#6712C2318yes—
94#6712C2314yes—
95#6712C2314yes—
96#6712C2318yes—
97C4×Dic15C2314yes—
98C4×Dic15C2314yes—
99C4×Dic15C2314yes—
100C4×Dic15C2314yes—
101C4×Dic15C2314yes—
102C3×#544D511yescharacteristic, complemented
103#5729—54no—
104#5728—54no—
105#5689—54no—
106#5688—54no—
107#5634—54no—
108#5622—54no—
109D3×#117—52no—
110#5519—52no—
111C2×#892—51no—
112#5500—51no—
113C22×C4×D5—31no—
114C5×C4⋊Q8C2×D314yescomplemented
115C5×#125C2×D314yescomplemented
116C5×C22⋊Q8C2×D314yes—
117C5×#117C2×D312yes—
118C2×C5×C4⋊C4C2×D311yescharacteristic
119#4092—38no—
120Q8×Dic5—34no—
121#4090—34no—
122C2×#685—32no—
123#4072—32no—
124C2×C4⋊Dic5—31no—
125#4070—34no—
126C2×C4×Dic5—32no—
127#4043—38no—
128#4042—38no—
129#4042—38no—
130#4038—32no—
131#4038—34no—
132#4038—34no—
133#4038—32no—
134D5×C4⋊C4—32no—
135D5×C4⋊C4—32no—
136#4036—34no—
137#4036—34no—
138#4035—38no—
139#4034—34no—
140#4034—34no—
141#4034—34no—
142#4033—38no—
143#4033—34no—
144D5×C22⋊C4—34no—
145#4024—38no—
146#4023—34no—
147#4018—34no—
148C42×D5—34no—
149#4016—34no—
150#4015—34no—
151#3458—151noSylow
152C23×C3×C5C2411yescharacteristic
153C22×D15—41no—
154C22×D15—41no—
155C22×D15C2×Q814yes—
156C22×D15C2412yes—
157C3×C5×Q8—44no—
158C2×C3×C4×C5—42no—
159C2×C3×C4×C5C2×Q814yes—
160C2×C3×C4×C5C2414yes—
161C2×C3×C4×C5C2414yes—
162C2×C3×C4×C5C2414yes—
163C2×C3×C4×C5C2412yes—
164C2×Dic15—42no—
165C2×Dic15C2×Q814yes—
166C2×Dic15C2414yes—
167C2×Dic15C2414yes—
168C2×Dic15C2414yes—
169C2×Dic15C2411yescharacteristic
170C2×Dic15C2411yescharacteristic
171C4×D15—44no—
172C4×D15—44no—
173C4×D15C2×Q818yes—
174C4×D15C2×Q818yes—
175Dic30—44no—
176Dic30—48no—
177C22×C4×D3—51no—
178C3×C4⋊Q8C2×D514yescomplemented
179C3×#125C2×D514yescomplemented
180C3×C22⋊Q8C2×D514yes—
181C3×#117C2×D512yes—
182C2×C3×C4⋊C4C2×D511yescharacteristic
183#946—58no—
184Q8×Dic3—54no—
185#944—54no—
186C2×(C2×D3)⋊C4—52no—
187#926—52no—
188C2×C4⋊Dic3—51no—
189#924—54no—
190C2×C4×Dic3—52no—
191#897—58no—
192#896—58no—
193#896—58no—
194#892—52no—
195#892—54no—
196#892—54no—
197#892—52no—
198D3×C4⋊C4—52no—
199D3×C4⋊C4—52no—
200#890—54no—
201#890—54no—
202#889—58no—
203#888—54no—
204#888—54no—
205#888—54no—
206#887—54no—
207#887—58no—
208D3×C22⋊C4—54no—
209#878—58no—
210#877—54no—
211#872—54no—
212C42×D3—54no—
213#870—54no—
214#869—54no—
215C23×D5—31no—
216C2×C5×Q8C22×D314yes—
217C22×C4×C5C22×D312yes—
218C22×C4×C5C22×D311yescharacteristic
219C22×Dic5—31no—
220C22×Dic5—32no—
221C2×C4×D5—38no—
222C2×C4×D5—32no—
223C2×C4×D5—32no—
224C2×C4×D5—34no—
225C2×C4×D5—34no—
226C2×Dic10—38no—
227C2×Dic10—34no—
228C5×C4⋊C4C22×D314yes—
229C5×C4⋊C4C22×D312yes—
230C5×C4⋊C4C22×D312yes—
231C5×C4⋊C4C22×D314yes—
232C5×C4⋊C4C22×D318yes—
233C5×C22⋊C4C22×D314yes—
234C42×C5C22×D314yes—
235C22⋊Dic5—34no—
236#685—34no—
237#685—34no—
238#685—38no—
239C4⋊Dic5—32no—
240C4⋊Dic5—34no—
241C4⋊Dic5—38no—
242C4⋊Dic5—32no—
243C4⋊Dic5—34no—
244#683—38no—
245#683—38no—
246#683—34no—
247#683—34no—
248#683—38no—
249C4×Dic5—34no—
250C4×Dic5—34no—
251C4×Dic5—34no—
252C4×Dic5—34no—
253C4×Dic5—34no—
254#544—154no—
255#544—154no—
256#544—152no—
257#544—151no—
258#544D1511yescharacteristic, complemented
259#543—154no—
260#533—154no—
261#533—154no—
262#533—154no—
263C2×#117—152no—
264C2×#117—151no—
265C22×C3×C5—21no—
266C22×C3×C5—21no—
267C22×C3×C5C22×Q812yes—
268C22×C3×C5C2511yescharacteristic
269C2×D15—22no—
270C2×D15—22no—
271C2×D15—44no—
272C2×D15C22×Q814yes—
273C3×C4×C5—24no—
274C3×C4×C5—24no—
275C3×C4×C5—24no—
276C3×C4×C5C22×Q814yes—
277Dic15—24no—
278Dic15—24no—
279Dic15—24no—
280Dic15C22×Q812yes—
281Dic15C22×Q812yes—
282C23×D3—51no—
283C2×C3×Q8C22×D514yes—
284C22×C3×C4C22×D512yes—
285C22×C3×C4C22×D511yescharacteristic
286C22×Dic3—51no—
287C22×Dic3—52no—
288C2×C4×D3—58no—
289C2×C4×D3—52no—
290C2×C4×D3—52no—
291C2×C4×D3—54no—
292C2×C4×D3—54no—
293C2×Dic6—58no—
294C2×Dic6—54no—
295C3×C4⋊C4C22×D514yes—
296C3×C4⋊C4C22×D518yes—
297C3×C4⋊C4C22×D512yes—
298C3×C4⋊C4C22×D514yes—
299C3×C4⋊C4C22×D512yes—
300C3×C22⋊C4C22×D514yes—
301C3×C42C22×D514yes—
302#217—54no—
303(C2×D3)⋊C4—54no—
304(C2×D3)⋊C4—54no—
305(C2×D3)⋊C4—58no—
306C4⋊Dic3—52no—
307C4⋊Dic3—54no—
308C4⋊Dic3—58no—
309C4⋊Dic3—52no—
310C4⋊Dic3—54no—
311Dic3⋊C4—58no—
312Dic3⋊C4—58no—
313Dic3⋊C4—54no—
314Dic3⋊C4—54no—
315Dic3⋊C4—58no—
316C4×Dic3—54no—
317C4×Dic3—54no—
318C4×Dic3—54no—
319C4×Dic3—54no—
320C4×Dic3—54no—
321C23×C5C23×D311yescharacteristic
322C22×D5—32no—
323C22×D5—34no—
324C22×D5—121no—
325C22×D5—121no—
326C5×Q8—44no—
327C2×C4×C5—42no—
328C2×C4×C5D3×Q814yes—
329C2×C4×C5C23×D314yes—
330C2×C4×C5C23×D314yes—
331C2×C4×C5C23×D314yes—
332C2×C4×C5C23×D312yes—
333C2×Dic5—34no—
334C2×Dic5—31no—
335C2×Dic5—31no—
336C2×Dic5—34no—
337C2×Dic5—34no—
338C2×Dic5—34no—
339C2×Dic5—122no—
340C4×D5—38no—
341C4×D5—38no—
342C4×D5—124no—
343C4×D5—124no—
344Dic10—124no—
345Dic10—128no—
346C23×C4—151no—
347C4⋊Q8—154no—
348C4⋊Q8—154no—
349C4⋊Q8—154no—
350C4⋊Q8—154no—
351C4⋊Q8—154no—
352C4⋊Q8C2×D1514yescomplemented
353#125—158no—
354#125—154no—
355#125—154no—
356#125—154no—
357#125C2×D1514yescomplemented
358C22⋊Q8—158no—
359C22⋊Q8—154no—
360C22⋊Q8—158no—
361C22⋊Q8—158no—
362C22⋊Q8—158no—
363C22⋊Q8—158no—
364C22⋊Q8C2×D1514yes—
365C4×Q8—154no—
366C4×Q8—158no—
367C4×Q8—154no—
368#117—152no—
369#117—152no—
370#117—152no—
371#117—154no—
372#117—154no—
373#117—154no—
374#117—154no—
375#117C2×D1512yes—
376C2×C4⋊C4—151no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4C2×D1511yescharacteristic
380C2×C22⋊C4—152no—
381C2×C22⋊C4—154no—
382C2×C42—152no—
383C2×C42—154no—
384C2×C3×C5—22no—
385C2×C3×C5C23×Q811yescharacteristic
386C2×C3×C5#58511yescharacteristic
387C2×C3×C5#58511yescharacteristic
388D15—24no—
389C23×C3C23×D511yescharacteristic
390C22×D3—52no—
391C22×D3—54no—
392C22×D3—201no—
393C22×D3—201no—
394C3×Q8—44no—
395C2×C3×C4—42no—
396C2×C3×C4Q8×D514yes—
397C2×C3×C4C23×D514yes—
398C2×C3×C4C23×D514yes—
399C2×C3×C4C23×D514yes—
400C2×C3×C4C23×D512yes—
401C2×Dic3—54no—
402C2×Dic3—51no—
403C2×Dic3—51no—
404C2×Dic3—54no—
405C2×Dic3—54no—
406C2×Dic3—54no—
407C2×Dic3—202no—
408C4×D3—58no—
409C4×D3—58no—
410C4×D3—204no—
411C4×D3—204no—
412Dic6—204no—
413Dic6—208no—
414C22×C5—21no—
415C22×C5—21no—
416C22×C5C2×D3×Q812yes—
417C22×C5C24×D311yescharacteristic
418C2×D5—34no—
419C2×D5—62no—
420C2×D5—62no—
421C2×D5—124no—
422C4×C5—24no—
423C4×C5—24no—
424C4×C5—24no—
425C4×C5C2×D3×Q814yes—
426Dic5—32no—
427Dic5—32no—
428Dic5—64no—
429Dic5—64no—
430Dic5—64no—
431C24—151no—
432C2×Q8—154no—
433C2×Q8—158no—
434C2×Q8C22×D1514yes—
435C22×C4—151no—
436C22×C4—158no—
437C22×C4—152no—
438C22×C4—152no—
439C22×C4—152no—
440C22×C4—154no—
441C22×C4—154no—
442C22×C4C22×D1512yes—
443C22×C4C22×D1511yescharacteristic
444C4⋊C4—154no—
445C4⋊C4—154no—
446C4⋊C4—154no—
447C4⋊C4—152no—
448C4⋊C4—152no—
449C4⋊C4—158no—
450C4⋊C4—158no—
451C4⋊C4—158no—
452C4⋊C4—154no—
453C4⋊C4—158no—
454C4⋊C4C22×D1512yes—
455C4⋊C4C22×D1512yes—
456C4⋊C4C22×D1514yes—
457C4⋊C4C22×D1518yes—
458C4⋊C4C22×D1514yes—
459C22⋊C4—154no—
460C22⋊C4—158no—
461C22⋊C4—154no—
462C22⋊C4—154no—
463C22⋊C4C22×D1514yes—
464C42—154no—
465C42—154no—
466C42—154no—
467C42—154no—
468C42—154no—
469C42C22×D1514yes—
470C3×C5#345811yescharacteristic, complemented, Hall
471C22×C3—21no—
472C22×C3—21no—
473C22×C3C2×Q8×D512yes—
474C22×C3C24×D511yescharacteristic
475C2×D3—54no—
476C2×D3—102no—
477C2×D3—102no—
478C2×D3—204no—
479C3×C4—24no—
480C3×C4—24no—
481C3×C4—24no—
482C3×C4C2×Q8×D514yes—
483Dic3—52no—
484Dic3—52no—
485Dic3—104no—
486Dic3—104no—
487Dic3—104no—
488C2×C5—22no—
489C2×C5C22×D3×Q811yescharacteristic
490C2×C5#596611yescharacteristic
491C2×C5#596811yescharacteristic
492D5—64no—
493C23—152no—
494C23—154no—
495C23—601no—
496C23—601no—
497C23C23×D1511yescharacteristic
498Q8—44no—
499Q8—604no—
500Q8—608no—
501C2×C4—42no—
502C2×C4—154no—
503C2×C4—151no—
504C2×C4—151no—
505C2×C4—158no—
506C2×C4—158no—
507C2×C4—154no—
508C2×C4—154no—
509C2×C4—154no—
510C2×C4—604no—
511C2×C4—604no—
512C2×C4—602no—
513C2×C4Q8×D1514yes—
514C2×C4C23×D1514yes—
515C2×C4C23×D1514yes—
516C2×C4C23×D1514yes—
517C2×C4C23×D1512yes—
518C2×C3—22no—
519C2×C3C22×Q8×D511yescharacteristic
520C2×C3#6628511yescharacteristic
521C2×C3#6628711yescharacteristic
522D3—104no—
523C5#8658111yescharacteristic, complemented, Sylow
524C22—21no—
525C22—21no—
526C22—154no—
527C22—302no—
528C22—302no—
529C22—604no—
530C22C2×Q8×D1512yes—
531C22C24×D1511yescharacteristic
532C4—24no—
533C4—24no—
534C4—24no—
535C4—152no—
536C4—152no—
537C4—304no—
538C4—304no—
539C4—304no—
540C4C2×Q8×D1514yes—
541C3#1061848211yescharacteristic, complemented, Sylow
542C2—22no—
543C2—304no—
544C2C22×Q8×D1511yescharacteristic
545C2#1175714811yescharacteristic
546C2#1175715011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D15
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#544C2
prime radicalC23×D15C23
hypercenter#544D15
hypocenterC3×C5#3458
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #544

Complements

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

NH ≅ G/Ntype
1. C3×C5×#544C2semidirect
2. #11756488C2semidirect
3. #11756487C2semidirect
4. #11756448C2semidirect
5. #11756447C2semidirect
7. #11756381C2semidirect
9. #11756278C2semidirect
11. #11756259C2semidirect
14. C3×C5×C4⋊Q8C22semidirect
15. C3×C5×#125C22semidirect
20. Q8×Dic15C22semidirect
21. #91833C22semidirect
36. #91779C22semidirect
37. #91779C22semidirect
38. #91778C22semidirect
39. #91777C22semidirect
40. #91777C22semidirect
41. #91777C22semidirect
42. #91776C22semidirect
43. #91776C22semidirect
49. #91759C22semidirect
50. #91758C22semidirect
52. C5×#544D3semidirect
69. C2×C4×D15Q8semidirect
102. C3×#544D5semidirect
114. C5×C4⋊Q8C2×D3semidirect
115. C5×#125C2×D3semidirect
178. C3×C4⋊Q8C2×D5semidirect
179. C3×#125C2×D5semidirect
258. #544D15semidirect
352. C4⋊Q8C2×D15semidirect
357. #125C2×D15semidirect
470. C3×C5#3458semidirect
523. C5#86581semidirect
541. C3#10618482semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5442
#117564882
#117564872
#117564482
#117564472
#117563932
#117563812
D15×#1172
#117562782
C2×#917812
#117562592
#106184823
#865815