Finite Group Databasebeta

← #14439641

Subgroups — #14439641

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#536C211yesmaximal, characteristic, complemented
2C2×#91840C211yesmaximal, characteristic, complemented
3C2×#91839C211yesmaximal, characteristic
4C22×#6718C211yesmaximal, characteristic, complemented
5C2×#91831C211yesmaximal, characteristic, complemented
6#11756285C211yesmaximal, characteristic, complemented
7#11751193C212yesmaximal, complemented
8#11751187C212yesmaximal, complemented
9#11751161C212yesmaximal, complemented
10#11751160C212yesmaximal, complemented
11#11751098C211yesmaximal, characteristic, complemented
12#10615134—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C3×C5×Q8C2211yescharacteristic
15C2×#6817C2211yescharacteristic
16C22×Dic30C2211yescharacteristic
17C3×C5×C4⋊Q8C2212yes—
18C3×C5×#124C2212yes—
19C3×C5×#123—22no—
20C3×C5×C22⋊Q8—22no—
21C3×C5×#117C2211yescharacteristic
22#91840—24no—
23#91839—24no—
24C2×#6718—24no—
25C2×#6718C2212yes—
26C2×#6718C2212yes—
27C2×#6718C2212yes—
28C2×#6718C2212yes—
29C2×#6718C2211yescharacteristic
30#91831—24no—
31C2×#6717C2211yescharacteristic
32C2×#6717C2212yes—
33C2×#6716C2211yescharacteristic
34C2×#6716C2212yes—
35C2×#6715C2211yescharacteristic
36C2×#6710C2211yescharacteristic
37C22×C3⋊#168C2211yescharacteristic
38#91786—22no—
39#91775—22no—
40#91764C2212yes—
41#91758C2212yes—
42#91087C2212yes—
43C4×C3⋊#168C2212yes—
44#83403—51nomaximal, Hall
45C5×#536D311yescharacteristic, complemented
46C2×#4097—31no—
47C2×#4096—31no—
48C22×#689—31no—
49C2×#4088—31no—
50#65860—31no—
51#65381—32no—
52#65375—32no—
53#65349—32no—
54#65348—32no—
55#65286—31no—
56C3×C5×#41—22no—
57C3×C5×#41—22no—
58C2×C3×C5×Q8—21no—
59C2×C3×C5×Q8—22no—
60C2×C3×C5×Q8—22no—
61C2×C3×C5×Q8C2312yes—
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4—21no—
64C2×C3×C5×D4C2311yescharacteristic
65C22×C3×C4×C5—21no—
66C22×C3×C4×C5—21no—
67C22×C3×C4×C5C2311yescharacteristic
68C2×#1220—21no—
69C22×Dic15—21no—
70#6817—22no—
71#6817—22no—
72C2×D60C2311yescharacteristic
73C2×C4×D15—21no—
74C2×Dic30—22no—
75C2×Dic30—22no—
76C2×Dic30—21no—
77C2×Dic30C2311yescharacteristic
78C2×Dic30C2312yes—
79C3×C5×C4⋊C4—24no—
80C3×C5×C4⋊C4D412yes—
81C3×C5×C22⋊C4—24no—
82C3×C5×C22⋊C4D412yes—
83C3×C42×C5C2312yes—
84#6718—24no—
85#6718—24no—
86#6718—24no—
87#6718—22no—
88#6718—24no—
89#6717—24no—
90#6717—22no—
91#6716—22no—
92#6716—24no—
93#6715—22no—
94#6714—24no—
95C4⋊Dic15—24no—
96#6710D414yes—
97C2×C3⋊#168D414yes—
98C2×C3⋊#168C2311yescharacteristic
99C2×C3⋊#168C2311yescharacteristic
100C2×C3⋊#168C2312yes—
101C3×#536D511yescharacteristic, complemented
102C2×#951—51no—
103C2×#950—51no—
104C22×#216—51no—
105C2×#942—51no—
106#5526—51no—
107#5092—52no—
108#5086—52no—
109#5060—52no—
110#5059—52no—
111#4997—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×Q8C2×D311yescharacteristic
114C2×#709—31no—
115C22×Dic10—31no—
116C5×C4⋊Q8C2×D312yes—
117C5×#124C2×D312yes—
118C5×#123—22no—
119C5×C22⋊Q8—22no—
120C5×#117C2×D311yescharacteristic
121#4097—64no—
122#4096—64no—
123C2×#689—32no—
124C2×#689—32no—
125C2×#689—32no—
126C2×#689—32no—
127C2×#689—31no—
128C2×#689—64no—
129#4088—64no—
130C2×#688—32no—
131C2×#688—31no—
132C2×#687—32no—
133C2×#687—31no—
134C2×#686—31no—
135C2×#681—31no—
136C22×#168—31no—
137#4043—62no—
138#4032—62no—
139#4021—32no—
140#4015—32no—
141#3935—32no—
142C4×#168—32no—
143#3156—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—21no—
147C3×C5×Q8—22no—
148C3×C5×Q8—21no—
149C3×C5×Q8—22no—
150C3×C5×Q8—21no—
151C3×C5×Q8—42no—
152C3×C5×D4—21no—
153C3×C5×D4—21no—
154C3×C5×D4—42no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—42no—
158C2×C3×C4×C5—42no—
159C2×C3×C4×C5C2×D414yes—
160C2×C3×C4×C5C2×D411yescharacteristic
161C2×C3×C4×C5C2×D412yes—
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2411yescharacteristic
164#1220—42no—
165C2×Dic15—21no—
166C2×Dic15—22no—
167C2×Dic15—42no—
168D60—21no—
169D60—21no—
170C4×D15—42no—
171Dic30—22no—
172Dic30—21no—
173Dic30—22no—
174Dic30—21no—
175Dic30—42no—
176C3⋊#168C2×D412yes—
177C3⋊#168C2×D412yes—
178C3⋊#168C2×D414yes—
179C2×C3×#41C2×D511yescharacteristic
180C22×C3×Q8C2×D511yescharacteristic
181C2×#235—51no—
182C22×Dic6—51no—
183C3×C4⋊Q8C2×D512yes—
184C3×#124C2×D512yes—
185C3×#123—22no—
186C3×C22⋊Q8—22no—
187C3×#117C2×D511yescharacteristic
188#951—104no—
189#950—104no—
190C2×#216—52no—
191C2×#216—52no—
192C2×#216—52no—
193C2×#216—51no—
194C2×#216—52no—
195C2×#216—104no—
196#942—104no—
197C2×#215—52no—
198C2×#215—51no—
199C2×#214—51no—
200C2×#214—52no—
201C2×#213—51no—
202C2×#208—51no—
203C22×C3⋊C8—51no—
204#897—102no—
205#886—102no—
206#875—52no—
207#869—52no—
208#803—52no—
209C4×C3⋊C8—52no—
210C5×#41—22no—
211C5×#41—22no—
212C2×C5×Q8—21no—
213C2×C5×Q8—22no—
214C2×C5×Q8—22no—
215C2×C5×Q8C22×D312yes—
216C2×C5×Q8C22×D311yescharacteristic
217C2×C5×D4—21no—
218C2×C5×D4C22×D311yescharacteristic
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5C22×D311yescharacteristic
222C2×C22⋊D5—61no—
223C22×Dic5—61no—
224#709—62no—
225#709—62no—
226C2×D20—31no—
227C2×C4×D5—61no—
228C2×Dic10—32no—
229C2×Dic10—31no—
230C2×Dic10—62no—
231C2×Dic10—62no—
232C2×Dic10—61no—
233C5×C4⋊C4—24no—
234C5×C4⋊C4#6712yes—
235C5×C22⋊C4—24no—
236C5×C22⋊C4#6712yes—
237C42×C5C22×D312yes—
238#689—62no—
239#689—64no—
240#689—64no—
241#689—64no—
242#689—64no—
243#688—62no—
244#688—64no—
245#687—62no—
246#687—64no—
247#686—62no—
248#685—64no—
249C4⋊Dic5—64no—
250#681—34no—
251C2×#168—34no—
252C2×#168—31no—
253C2×#168—32no—
254C2×#168—31no—
255C2×#137—151no—
256C2×#137—151no—
257C2×#135—151no—
258C22×Q16—151no—
259#536—151no—
260#536D1511yescharacteristic, complemented
261#497—152no—
262#497—152no—
263#495—152no—
264#494—152no—
265#405—151no—
266C22×C3×C5—22no—
267C22×C3×C5—41no—
268C22×C3×C5—42no—
269C22×C3×C5#12712yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×D15—41no—
272C2×D15—42no—
273C3×C4×C5—24no—
274C3×C4×C5—41no—
275C3×C4×C5—42no—
276C3×C4×C5#12712yes—
277C3×C4×C5C22×D411yescharacteristic
278C3×C4×C5C22×D411yescharacteristic
279Dic15—42no—
280Dic15—41no—
281C3×#41—22no—
282C3×#41—22no—
283C2×C3×Q8—21no—
284C2×C3×Q8—22no—
285C2×C3×Q8—22no—
286C2×C3×Q8C22×D512yes—
287C2×C3×Q8C22×D511yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4C22×D511yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4C22×D511yescharacteristic
293C2×#67—101no—
294C22×Dic3—101no—
295#235—102no—
296#235—102no—
297C2×D12—51no—
298C2×C4×D3—101no—
299C2×Dic6—51no—
300C2×Dic6—52no—
301C2×Dic6—102no—
302C2×Dic6—102no—
303C2×Dic6—101no—
304C3×C4⋊C4—24no—
305C3×C4⋊C4C22⋊D512yes—
306C3×C22⋊C4—24no—
307C3×C22⋊C4C22⋊D512yes—
308C3×C42C22×D512yes—
309#216—104no—
310#216—104no—
311#216—104no—
312#216—102no—
313#216—104no—
314#215—104no—
315#215—102no—
316#214—102no—
317#214—104no—
318#213—102no—
319(C2×D3)⋊C4—104no—
320C4⋊Dic3—104no—
321#208—54no—
322C2×C3⋊C8—54no—
323C2×C3⋊C8—51no—
324C2×C3⋊C8—52no—
325C2×C3⋊C8—51no—
326C23×C5—21no—
327C23×C5C2×#6711yescharacteristic
328C22×D5—61no—
329C5×Q8—22no—
330C5×Q8—21no—
331C5×Q8—22no—
332C5×Q8—21no—
333C5×Q8—42no—
334C5×D4—21no—
335C5×D4—21no—
336C5×D4—42no—
337C2×C4×C5—22no—
338C2×C4×C5—21no—
339C2×C4×C5—42no—
340C2×C4×C5—42no—
341C2×C4×C5D3×D412yes—
342C2×C4×C5D3×D412yes—
343C2×C4×C5C2×#6714yes—
344C2×C4×C5C2×#6711yescharacteristic
345C2×C4×C5C23×D311yescharacteristic
346C22⋊D5—122no—
347C2×Dic5—61no—
348C2×Dic5—62no—
349C2×Dic5—122no—
350D20—61no—
351D20—61no—
352C4×D5—122no—
353Dic10—62no—
354Dic10—61no—
355Dic10—62no—
356Dic10—61no—
357Dic10—122no—
358#168—32no—
359#168—32no—
360#168—34no—
361C2×#41—151no—
362C2×#41C2×D1511yescharacteristic
363C22×Q8—151no—
364C22×Q8C2×D1511yescharacteristic
365#137—304no—
366#137—304no—
367#135—304no—
368C2×Q16—152no—
369C2×Q16—152no—
370C2×Q16—151no—
371C2×Q16—152no—
372C2×Q16—152no—
373C2×Q16—304no—
374C2×SD16—151no—
375C2×SD16—152no—
376C2×SD16—151no—
377C2×SD16—152no—
378C2×D8—151no—
379C2×M16—151no—
380C22×C8—151no—
381C4⋊Q8—152no—
382C4⋊Q8C2×D1512yes—
383#124—152no—
384#124C2×D1512yes—
385#123—22no—
386#123—302no—
387C22⋊Q8—22no—
388C22⋊Q8—302no—
389#117C2×D1511yescharacteristic
390#97—152no—
391C4×C8—152no—
392C2×C3×C5—22no—
393C2×C3×C5—81no—
394C2×C3×C5C2×#12711yescharacteristic
395C2×C3×C5#57812yes—
396D15—81no—
397C23×C3—21no—
398C23×C3C2×C22⋊D511yescharacteristic
399C22×D3—101no—
400C3×Q8—22no—
401C3×Q8—21no—
402C3×Q8—22no—
403C3×Q8—21no—
404C3×Q8—42no—
405C3×D4—21no—
406C3×D4—21no—
407C3×D4—42no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4D4×D512yes—
413C2×C3×C4D4×D512yes—
414C2×C3×C4C2×C22⋊D514yes—
415C2×C3×C4C2×C22⋊D511yescharacteristic
416C2×C3×C4C23×D511yescharacteristic
417#67—202no—
418C2×Dic3—101no—
419C2×Dic3—102no—
420C2×Dic3—202no—
421D12—101no—
422D12—101no—
423C4×D3—202no—
424Dic6—102no—
425Dic6—101no—
426Dic6—102no—
427Dic6—101no—
428Dic6—202no—
429C3⋊C8—52no—
430C3⋊C8—52no—
431C3⋊C8—54no—
432C22×C5—22no—
433C22×C5—41no—
434C22×C5—42no—
435C22×C5#94012yes—
436C22×C5C22×#6711yescharacteristic
437C2×D5—121no—
438C2×D5—122no—
439C4×C5—24no—
440C4×C5—41no—
441C4×C5—42no—
442C4×C5#94012yes—
443C4×C5C2×D3×D411yescharacteristic
444C4×C5C2×D3×D411yescharacteristic
445Dic5—122no—
446Dic5—121no—
447#41—22no—
448#41—22no—
449#41—302no—
450#41—302no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—152no—
455C2×Q8—151no—
456C2×Q8—301no—
457C2×Q8—302no—
458C2×Q8—302no—
459C2×Q8C22×D1512yes—
460C2×Q8C22×D1511yescharacteristic
461C2×D4—21no—
462C2×D4—151no—
463C2×D4—301no—
464C2×D4C22×D1511yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—301no—
468C22×C4—301no—
469C22×C4C22×D1511yescharacteristic
470Q16—304no—
471Q16—304no—
472Q16—302no—
473Q16—304no—
474Q16—304no—
475SD16—302no—
476SD16—304no—
477SD16—302no—
478SD16—304no—
479D8—302no—
480M16—154no—
481C2×C8—154no—
482C2×C8—151no—
483C2×C8—152no—
484C2×C8—151no—
485C4⋊C4—24no—
486C4⋊C4—304no—
487C4⋊C4#122012yes—
488C22⋊C4—24no—
489C22⋊C4—304no—
490C22⋊C4#122012yes—
491C42C22×D1512yes—
492C3×C5#315611yescharacteristic, complemented, Hall
493C22×C3—22no—
494C22×C3—41no—
495C22×C3—42no—
496C22×C3#408612yes—
497C22×C3C22×C22⋊D511yescharacteristic
498C2×D3—201no—
499C2×D3—202no—
500C3×C4—24no—
501C3×C4—41no—
502C3×C4—42no—
503C3×C4#408612yes—
504C3×C4C2×D4×D511yescharacteristic
505C3×C4C2×D4×D511yescharacteristic
506Dic3—202no—
507Dic3—201no—
508C2×C5—22no—
509C2×C5—81no—
510C2×C5C2×#94011yescharacteristic
511C2×C5#583812yes—
512D5—241no—
513C23—21no—
514C23—301no—
515C23C2×#122011yescharacteristic
516Q8—22no—
517Q8—21no—
518Q8—22no—
519Q8—21no—
520Q8—42no—
521Q8—302no—
522Q8—301no—
523Q8—302no—
524Q8—301no—
525Q8—602no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—301no—
530D4—301no—
531D4—602no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—302no—
537C2×C4—301no—
538C2×C4—602no—
539C2×C4—602no—
540C2×C4D4×D1512yes—
541C2×C4D4×D1512yes—
542C2×C4C2×#122014yes—
543C2×C4C2×#122011yescharacteristic
544C2×C4C23×D1511yescharacteristic
545C8—152no—
546C8—152no—
547C8—154no—
548C2×C3—22no—
549C2×C3—81no—
550C2×C3C2×#408611yescharacteristic
551C2×C3#6617212yes—
552D3—401no—
553C5#8340311yescharacteristic, complemented, Sylow
554C22—22no—
555C22—41no—
556C22—42no—
557C22—601no—
558C22—602no—
559C22#9182912yes—
560C22C22×#122011yescharacteristic
561C4—24no—
562C4—41no—
563C4—42no—
564C4—601no—
565C4—602no—
566C4#9182912yes—
567C4C2×D4×D1511yescharacteristic
568C4C2×D4×D1511yescharacteristic
569C3#1061513411yescharacteristic, complemented, Sylow
570C2—22no—
571C2—81no—
572C2—1201no—
573C2C2×#9182911yescharacteristic
574C2#1175659712yes—
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#536C2
socleC22×C3×C5C22×D4
prime radicalC2×#91839C2
hypercenter#536D15
hypocenterC3×C5#3156
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C3×C5×#536C2semidirect
2. C2×#91840C2semidirect
4. C22×#6718C2semidirect
5. C2×#91831C2semidirect
6. #11756285C2semidirect
7. #11751193C2semidirect
8. #11751187C2semidirect
9. #11751161C2semidirect
10. #11751160C2semidirect
11. #11751098C2semidirect
45. C5×#536D3semidirect
101. C3×#536D5semidirect
260. #536D15semidirect
492. C3×C5#3156semidirect
553. C5#83403semidirect
569. C3#10615134semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5362
C2×#918402
C2×#918392
C22×#67182
C2×#918312
#117562852
#117511932
#117511872
#117511612
#117511602
#117510982
#106151343
#834035