Finite Group Databasebeta

← #14424536

Subgroups — #14424536

Order 1920.

1400 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92101C211yesmaximal, characteristic
2C3×C5×#536C211yesmaximal, characteristic, complemented
3C22×#6718C211yesmaximal, characteristic, complemented
4C2×#91831C211yesmaximal, characteristic, complemented
5#11751335C211yesmaximal, characteristic, complemented
6#11751151C214yesmaximal, complemented
7#11751148C214yesmaximal, complemented
8#11751105C211yesmaximal, characteristic, complemented
9#11751103C211yesmaximal, characteristic, complemented
10#10615142—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C22×C3×C5×Q8C2211yescharacteristic
13#92101—24no—
14#92101—24no—
15C2×Q8×D15—21no—
16C2×#6819—22no—
17C2×#6819—21no—
18C2×#6817C2212yes—
19C2×#6817C2211yescharacteristic
20C22×Dic30C2212yes—
21C22×Dic30C2211yescharacteristic
22C3×C5×C4⋊Q8—21no—
23C3×C5×#124—21no—
24C3×C5×#123—22no—
25C3×C5×C22⋊Q8C2214yes—
26C3×C5×#117C2211yescharacteristic
27C2×#6718—24no—
28C2×#6718C2212yes—
29C2×#6718C2214yes—
30#91831—24no—
31C2×#6717C2212yes—
32C2×#6710C2211yescharacteristic
33C22×C3⋊#168C2211yescharacteristic
34#91114C2214yes—
35#91094C2212yes—
36#91094C2214yes—
37#91093C2212yes—
38#83411—51nomaximal, Hall
39C2×#4150—31no—
40C5×#536D311yescharacteristic, complemented
41C22×#689—31no—
42C2×#4088—31no—
43#65523—31no—
44#65339—34no—
45#65336—34no—
46#65293—31no—
47#65291—31no—
48C3×C5×#41—22no—
49C3×C5×#41—22no—
50C2×C3×C5×Q8—21no—
51C2×C3×C5×Q8—22no—
52C2×C3×C5×Q8—22no—
53C2×C3×C5×Q8D411yescharacteristic
54C2×C3×C5×Q8C2312yes—
55C2×C3×C5×D4D412yes—
56C2×C3×C5×D4D411yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2312yes—
59C22×C3×C4×C5C2311yescharacteristic
60C2×#1220—22no—
61C2×#1220—21no—
62C22×Dic15—22no—
63C22×Dic15—21no—
64Q8×D15—28no—
65#6819—216no—
66#6819—28no—
67#6817—22no—
68#6817—24no—
69#6817—24no—
70#6817D414yes—
71C2×D60C2311yescharacteristic
72C2×C4×D15—22no—
73C2×C4×D15—21no—
74C2×Dic30—22no—
75C2×Dic30—21no—
76C2×Dic30—22no—
77C2×Dic30—24no—
78C2×Dic30—24no—
79C2×Dic30D414yes—
80C2×Dic30C2311yescharacteristic
81C2×Dic30C2312yes—
82C3×C5×C4⋊C4—24no—
83C3×C5×C4⋊C4C2312yes—
84C3×C5×C22⋊C4—21no—
85C3×C5×C22⋊C4—24no—
86C3×C42×C5—21no—
87#6718—24no—
88#6718—28no—
89#6717—24no—
90#6710—22no—
91C2×C3⋊#168—22no—
92C2×C3⋊#168C2312yes—
93C2×C3⋊#168C2312yes—
94C2×#1010—51no—
95C3×#536D511yescharacteristic, complemented
96C22×#216—51no—
97C2×#942—51no—
98#5234—51no—
99#5050—54no—
100#5047—54no—
101#5004—51no—
102#5002—51no—
103C2×C5×#41C2×D311yescharacteristic
104C22×C5×Q8C2×D311yescharacteristic
105#4150—64no—
106#4150—64no—
107C2×Q8×D5—61no—
108C2×#711—62no—
109C2×#711—61no—
110C2×#709—31no—
111C2×#709—32no—
112C22×Dic10—31no—
113C22×Dic10—32no—
114C5×C4⋊Q8—21no—
115C5×#124—21no—
116C5×#123—22no—
117C5×C22⋊Q8C2×D314yes—
118C5×#117C2×D311yescharacteristic
119C2×#689—34no—
120C2×#689—32no—
121C2×#689—64no—
122#4088—64no—
123C2×#688—32no—
124C2×#681—31no—
125C22×#168—31no—
126C22⋊#168—34no—
127#3942—32no—
128#3942—34no—
129#3941—32no—
130#3011—151noSylow
131C23×C3×C5C2×D412yes—
132C23×C3×C5C2×D411yescharacteristic
133C22×D15—21no—
134C3×C5×Q8—22no—
135C3×C5×Q8—22no—
136C3×C5×Q8—22no—
137C3×C5×Q8—42no—
138C3×C5×D4—24no—
139C3×C5×D4—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—42no—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5C2411yescharacteristic
150#1220—28no—
151#1220—24no—
152C2×Dic15—28no—
153C2×Dic15—24no—
154C2×Dic15—21no—
155C2×Dic15—22no—
156D60—21no—
157D60C2×D412yes—
158C4×D15—28no—
159C4×D15—24no—
160Dic30—28no—
161Dic30—24no—
162Dic30—22no—
163Dic30—21no—
164Dic30C2×D412yes—
165Dic30C2×D414yes—
166C3⋊#168—22no—
167C3⋊#168—22no—
168C2×C3×#41C2×D511yescharacteristic
169C22×C3×Q8C2×D511yescharacteristic
170#1010—104no—
171#1010—104no—
172C2×D3×Q8—101no—
173C2×#237—102no—
174C2×#237—101no—
175C2×#235—51no—
176C2×#235—52no—
177C22×Dic6—51no—
178C22×Dic6—52no—
179C3×C4⋊Q8—21no—
180C3×#124—21no—
181C3×#123—22no—
182C3×C22⋊Q8C2×D514yes—
183C3×#117C2×D511yescharacteristic
184C2×#216—52no—
185C2×#216—54no—
186C2×#216—104no—
187#942—104no—
188C2×#215—52no—
189C2×#208—51no—
190C22×C3⋊C8—51no—
191#830—54no—
192#810—52no—
193#810—54no—
194#809—52no—
195C5×#41—22no—
196C5×#41—22no—
197C2×C5×Q8—21no—
198C2×C5×Q8—22no—
199C2×C5×Q8—22no—
200C2×C5×Q8#6711yescharacteristic
201C2×C5×Q8C22×D312yes—
202C2×C5×D4#6712yes—
203C2×C5×D4#6711yescharacteristic
204C22×C4×C5—21no—
205C22×C4×C5C22×D312yes—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—62no—
208C2×C22⋊D5—61no—
209C22×Dic5—62no—
210C22×Dic5—61no—
211Q8×D5—68no—
212#711—616no—
213#711—68no—
214#709—34no—
215#709—64no—
216#709—64no—
217#709—62no—
218C2×D20—31no—
219C2×C4×D5—62no—
220C2×C4×D5—61no—
221C2×Dic10—34no—
222C2×Dic10—32no—
223C2×Dic10—31no—
224C2×Dic10—64no—
225C2×Dic10—64no—
226C2×Dic10—62no—
227C2×Dic10—62no—
228C2×Dic10—61no—
229C5×C4⋊C4—24no—
230C5×C4⋊C4C22×D312yes—
231C5×C22⋊C4—21no—
232C5×C22⋊C4—24no—
233C42×C5—21no—
234#689—64no—
235#689—68no—
236#688—64no—
237#681—62no—
238C2×#168—32no—
239C2×#168—32no—
240C2×#168—62no—
241C2×2−1+4—151no—
242C2×#137—151no—
243C22×Q16—151no—
244#536D1511yescharacteristic, complemented
245#452—154no—
246#451—154no—
247#419—151no—
248#416—151no—
249#408—151no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—24no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×D15—22no—
256C2×D15—42no—
257C3×C4×C5—22no—
258C3×C4×C5—42no—
259C3×C4×C5—42no—
260C3×C4×C5#12012yes—
261C3×C4×C5C22×D411yescharacteristic
262C3×C4×C5C22×D411yescharacteristic
263Dic15—22no—
264Dic15—24no—
265C3×#41—22no—
266C3×#41—22no—
267C2×C3×Q8—21no—
268C2×C3×Q8—22no—
269C2×C3×Q8—22no—
270C2×C3×Q8C22⋊D511yescharacteristic
271C2×C3×Q8C22×D512yes—
272C2×C3×D4C22⋊D512yes—
273C2×C3×D4C22⋊D511yescharacteristic
274C22×C3×C4—21no—
275C22×C3×C4C22×D512yes—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—102no—
278C2×#67—101no—
279C22×Dic3—102no—
280C22×Dic3—101no—
281D3×Q8—108no—
282#237—1016no—
283#237—108no—
284#235—54no—
285#235—104no—
286#235—104no—
287#235—102no—
288C2×D12—51no—
289C2×C4×D3—102no—
290C2×C4×D3—101no—
291C2×Dic6—54no—
292C2×Dic6—52no—
293C2×Dic6—51no—
294C2×Dic6—104no—
295C2×Dic6—104no—
296C2×Dic6—102no—
297C2×Dic6—102no—
298C2×Dic6—101no—
299C3×C4⋊C4—24no—
300C3×C4⋊C4C22×D512yes—
301C3×C22⋊C4—21no—
302C3×C22⋊C4—24no—
303C3×C42—21no—
304#216—104no—
305#216—108no—
306#215—104no—
307#208—102no—
308C2×C3⋊C8—52no—
309C2×C3⋊C8—52no—
310C2×C3⋊C8—102no—
311C23×C5C2×#6712yes—
312C23×C5C2×#6711yescharacteristic
313C22×D5—61no—
314C5×Q8—22no—
315C5×Q8—22no—
316C5×Q8—22no—
317C5×Q8—42no—
318C5×D4—24no—
319C5×D4—22no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—42no—
325C2×C4×C5D3×D412yes—
326C2×C4×C5D3×D412yes—
327C2×C4×C5C2×#6712yes—
328C2×C4×C5C2×#6711yescharacteristic
329C2×C4×C5C23×D311yescharacteristic
330C22⋊D5—68no—
331C22⋊D5—64no—
332C2×Dic5—68no—
333C2×Dic5—64no—
334C2×Dic5—62no—
335C2×Dic5—61no—
336D20—32no—
337D20—61no—
338C4×D5—68no—
339C4×D5—64no—
340Dic10—34no—
341Dic10—32no—
342Dic10—68no—
343Dic10—64no—
344Dic10—61no—
345Dic10—62no—
346#168—62no—
347#168—62no—
3482−1+4—304no—
3492−1+4—304no—
350C2×#41—151no—
351C2×#41—152no—
352C2×#41—302no—
353C2×#41—301no—
354C2×#41C2×D1511yescharacteristic
355C22×Q8—151no—
356C22×Q8—152no—
357C22×Q8—301no—
358C22×Q8C2×D1511yescharacteristic
359#137—304no—
360C2×Q16—154no—
361C2×Q16—152no—
362C2×Q16—304no—
363C2×SD16—152no—
364C2×M16—151no—
365C22×C8—151no—
366C4⋊Q8—21no—
367#124—21no—
368#123—22no—
369C22⋊Q8C2×D1514yes—
370#117C2×D1511yescharacteristic
371#103—152no—
372#103—154no—
373#102—152no—
374C22⋊C8—154no—
375C2×C3×C5—22no—
376C2×C3×C5—42no—
377C2×C3×C5C2×#12011yescharacteristic
378C2×C3×C5#57812yes—
379D15—42no—
380C23×C3C2×C22⋊D512yes—
381C23×C3C2×C22⋊D511yescharacteristic
382C22×D3—101no—
383C3×Q8—22no—
384C3×Q8—22no—
385C3×Q8—22no—
386C3×Q8—42no—
387C3×D4—24no—
388C3×D4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—42no—
394C2×C3×C4D4×D512yes—
395C2×C3×C4D4×D512yes—
396C2×C3×C4C2×C22⋊D512yes—
397C2×C3×C4C2×C22⋊D511yescharacteristic
398C2×C3×C4C23×D511yescharacteristic
399#67—108no—
400#67—104no—
401C2×Dic3—108no—
402C2×Dic3—102no—
403C2×Dic3—101no—
404C2×Dic3—104no—
405D12—52no—
406D12—101no—
407C4×D3—108no—
408C4×D3—104no—
409Dic6—54no—
410Dic6—52no—
411Dic6—108no—
412Dic6—101no—
413Dic6—102no—
414Dic6—104no—
415C3⋊C8—102no—
416C3⋊C8—102no—
417C22×C5—22no—
418C22×C5—22no—
419C22×C5—24no—
420C22×C5#93712yes—
421C22×C5C22×#6711yescharacteristic
422C2×D5—62no—
423C2×D5—122no—
424C4×C5—22no—
425C4×C5—42no—
426C4×C5—42no—
427C4×C5#93712yes—
428C4×C5C2×D3×D411yescharacteristic
429C4×C5C2×D3×D411yescharacteristic
430Dic5—64no—
431Dic5—62no—
432#41—22no—
433#41—22no—
434#41—154no—
435#41—304no—
436#41—304no—
437#41—3016no—
438#41—308no—
439#41—302no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—154no—
444C2×Q8—152no—
445C2×Q8—151no—
446C2×Q8—304no—
447C2×Q8—304no—
448C2×Q8—308no—
449C2×Q8—302no—
450C2×Q8—302no—
451C2×Q8—301no—
452C2×Q8#122011yescharacteristic
453C2×Q8C22×D1512yes—
454C2×D4—151no—
455C2×D4—302no—
456C2×D4—301no—
457C2×D4#122012yes—
458C2×D4#122011yescharacteristic
459C22×C4—21no—
460C22×C4—302no—
461C22×C4—301no—
462C22×C4—302no—
463C22×C4—301no—
464C22×C4C22×D1512yes—
465C22×C4C22×D1511yescharacteristic
466Q16—308no—
467Q16—304no—
468SD16—304no—
469M16—302no—
470C2×C8—152no—
471C2×C8—152no—
472C2×C8—302no—
473C4⋊C4—24no—
474C4⋊C4C22×D1512yes—
475C22⋊C4—21no—
476C22⋊C4—24no—
477C42—21no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—24no—
482C22×C3#408312yes—
483C22×C3C22×C22⋊D511yescharacteristic
484C2×D3—102no—
485C2×D3—202no—
486C3×C4—22no—
487C3×C4—42no—
488C3×C4—42no—
489C3×C4#408312yes—
490C3×C4C2×D4×D511yescharacteristic
491C3×C4C2×D4×D511yescharacteristic
492Dic3—104no—
493Dic3—102no—
494C2×C5—22no—
495C2×C5—42no—
496C2×C5C2×#93711yescharacteristic
497C2×C5#583812yes—
498D5—122no—
499C23—301no—
500C23C2×#122012yes—
501C23C2×#122011yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—22no—
505Q8—42no—
506Q8—154no—
507Q8—152no—
508Q8—308no—
509Q8—304no—
510Q8—302no—
511Q8—301no—
512D4—24no—
513D4—22no—
514D4—152no—
515D4—308no—
516D4—304no—
517D4—301no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—42no—
523C2×C4—308no—
524C2×C4—308no—
525C2×C4—304no—
526C2×C4—302no—
527C2×C4—301no—
528C2×C4—304no—
529C2×C4D4×D1512yes—
530C2×C4D4×D1512yes—
531C2×C4C2×#122012yes—
532C2×C4C2×#122011yescharacteristic
533C2×C4C23×D1511yescharacteristic
534C8—302no—
535C8—302no—
536C2×C3—22no—
537C2×C3—42no—
538C2×C3C2×#408311yescharacteristic
539C2×C3#6617212yes—
540D3—202no—
541C5#8341111yescharacteristic, complemented, Sylow
542C22—22no—
543C22—22no—
544C22—24no—
545C22—302no—
546C22—602no—
547C22#9182612yes—
548C22C22×#122011yescharacteristic
549C4—22no—
550C4—42no—
551C4—42no—
552C4—304no—
553C4—302no—
554C4#9182612yes—
555C4C2×D4×D1511yescharacteristic
556C4C2×D4×D1511yescharacteristic
557C3#1061514211yescharacteristic, complemented, Sylow
558C2—22no—
559C2—42no—
560C2—602no—
561C2C2×#9182611yescharacteristic
562C2#1175659712yes—
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#536C2
socleC22×C3×C5C22×D4
prime radicalC2×#92101C2
hypercenter#536D15
hypocenterC3×C5#3011
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C3×C5×#536C2semidirect
3. C22×#6718C2semidirect
4. C2×#91831C2semidirect
5. #11751335C2semidirect
6. #11751151C2semidirect
7. #11751148C2semidirect
8. #11751105C2semidirect
9. #11751103C2semidirect
40. C5×#536D3semidirect
95. C3×#536D5semidirect
244. #536D15semidirect
478. C3×C5#3011semidirect
541. C5#83411semidirect
557. C3#10615142semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
C3×C5×#5362
C22×#67182
C2×#918312
#117513352
#117511512
#117511482
#117511052
#117511032
#106151423
#834115