Finite Group Databasebeta

← #14439705

Subgroups — #14439705

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
1C2×#91839C211yesmaximal, characteristic
2C5×#5825C211yesmaximal, characteristic, complemented
3C2×C3×#4097C211yesmaximal, characteristic, complemented
4#11754278C211yesmaximal, characteristic, complemented
5C2×#91321C211yesmaximal, characteristic, complemented
6C22×#6661C211yesmaximal, characteristic, complemented
7#11749357C212yesmaximal, complemented
8#11749324C212yesmaximal, complemented
9#11749110C212yesmaximal, complemented
10#11749078C212yesmaximal, complemented
11#11748327C211yesmaximal, characteristic, complemented
12#10615134—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17#91839—24no—
18C2×#6718C2211yescharacteristic
19C2×#6717C2211yescharacteristic
20C2×#6716C2211yescharacteristic
21C2×#6715C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic
23C5×#944C2212yes—
24C5×#936C2212yes—
25C5×#935—22no—
26C5×#926C2211yescharacteristic
27C5×#924—22no—
28C3×#4097—24no—
29C2×C3×#689C2212yes—
30C2×C3×#687C2212yes—
31C2×C3×#681C2211yescharacteristic
32#91546—22no—
33#91390—22no—
34#91389C2212yes—
35#91374C2212yes—
36#91321—24no—
37C2×#6663C2212yes—
38C2×#6661—24no—
39C2×#6661C2212yes—
40C2×#6661C2212yes—
41C2×#6660C2212yes—
42#90953C2212yes—
43Dic3×#168C2212yes—
44#83975—51nomaximal, Hall
45C5×#536—31no—
46C2×#4097D311yescharacteristic, complemented
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×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64#6817—22no—
65#6817—22no—
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C22×C5×Dic3—21no—
70C2×C5×Dic6—22no—
71C2×C5×Dic6—22no—
72C2×C5×Dic6—21no—
73C2×C5×Dic6C2312yes—
74C22×C3×Dic5—21no—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—21no—
78C2×C3×Dic10C2312yes—
79#6718—22no—
80#6717—22no—
81#6716—22no—
82#6715—22no—
83C2×C3⋊#168D414yes—
84C2×C3⋊#168C2311yescharacteristic
85C2×C3⋊#168C2311yescharacteristic
86C5×#217—24no—
87C5×#217D412yes—
88C5×C4⋊Dic3D412yes—
89C5×Dic3⋊C4—24no—
90C4×C5×Dic3C2312yes—
91C3×#689—24no—
92C3×#687—24no—
93C3×#681D414yes—
94C2×C3×#168C2312yes—
95Dic3⋊Dic5—24no—
96#6667—24no—
97#6663—24no—
98#6661—24no—
99#6661—24no—
100#6660—24no—
101C2×C3×#137—51no—
102#5825D511yescharacteristic, complemented
103C2×#950—51no—
104#5816—51no—
105C22×#216—51no—
106C2×#909—51no—
107#5190—52no—
108#5183—52no—
109#5168—52no—
110#5167—52no—
111#5122—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×Q8—31no—
114C2×#709—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×C4⋊Q8—32no—
117C5×#124—32no—
118C5×#123—62no—
119C5×C22⋊Q8—62no—
120C5×#117—31no—
121#4097—24no—
122#4096—64no—
123C2×#689—31no—
124C2×#689—32no—
125C2×#689—32no—
126C2×#689—32no—
127C2×#689—64no—
128C2×#689C2×D312yes—
129#4088—64no—
130C2×#688—31no—
131C2×#688—32no—
132C2×#687—31no—
133C2×#687C2×D312yes—
134C2×#686—31no—
135C2×#681C2×D311yescharacteristic
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—21no—
148C3×C5×Q8—21no—
149C3×C5×D4—21no—
150C3×C5×D4—21no—
151C3×C5×D4—42no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—42no—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2×D412yes—
157C2×C3×C4×C5C2411yescharacteristic
158#1220—42no—
159C2×Dic15—21no—
160D60—21no—
161D60—21no—
162C4×D15—42no—
163Dic30—21no—
164Dic30—21no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—42no—
167C2×C5×Dic3C2×D414yes—
168C5×Dic6—22no—
169C5×Dic6—22no—
170C5×Dic6—42no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—42no—
173C3×Dic10—22no—
174C3×Dic10—22no—
175C3×Dic10—42no—
176C3⋊#168C2×D412yes—
177C3⋊#168C2×D412yes—
178C3×#168C2×D414yes—
179C2×C3×#41C2×D511yescharacteristic
180C22×C3×Q8—51no—
181C2×#235—51no—
182C22×Dic6C2×D511yescharacteristic
183C3×#137—104no—
184C2×C3×Q16—52no—
185C2×C3×SD16—52no—
186C2×C3×M16—51no—
187#950—104no—
188#947—52no—
189#946—102no—
190#944—52no—
191#944C2×D512yes—
192C2×#216—51no—
193C2×#216—52no—
194C2×#216—52no—
195C2×#216—104no—
196C2×#215—51no—
197#936C2×D512yes—
198#935—22no—
199C2×#214—51no—
200C2×#213—51no—
201#929—102no—
202#926C2×D511yescharacteristic
203#924—22no—
204C22×C3⋊C8—51no—
205#909—104no—
206C2×Dic12—52no—
207C2×#204—52no—
208#815—52no—
209C8×Dic3—52no—
210C5×#41—22no—
211C5×#41—22no—
212C2×C5×Q8—32no—
213C2×C5×Q8—61no—
214C2×C5×Q8—62no—
215C2×C5×Q8—62no—
216C2×C5×Q8C22×D311yescharacteristic
217C2×C5×D4—21no—
218C2×C5×D4C22×D311yescharacteristic
219C22×C4×C5—21no—
220C22×C4×C5—61no—
221C22×C4×C5C22×D311yescharacteristic
222C2×C22⋊D5—61no—
223C22×Dic5—21no—
224#709—62no—
225#709—62no—
226C2×D20—31no—
227C2×C4×D5—61no—
228C2×Dic10—22no—
229C2×Dic10—22no—
230C2×Dic10—21no—
231C2×Dic10—31no—
232C2×Dic10C22×D312yes—
233C5×C4⋊C4—32no—
234C5×C4⋊C4—64no—
235C5×C22⋊C4—32no—
236C5×C22⋊C4—64no—
237C42×C5—32no—
238#689—24no—
239#689—64no—
240#689—64no—
241#689—62no—
242#689—64no—
243#688—62no—
244#688—64no—
245#687—24no—
246#687—62no—
247#686—62no—
248#685—64no—
249C4⋊Dic5—64no—
250#681#6714yes—
251C2×#168—34no—
252C2×#168—31no—
253C2×#168—31no—
254C2×#168C22×D312yes—
255C2×#137—51no—
256C2×#137—151no—
257C2×#135—151no—
258C22×Q16—151no—
259#536—31no—
260#536—151no—
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—41no—
274C3×C4×C5#12712yes—
275C3×C4×C5C22×D411yescharacteristic
276C3×C4×C5C22×D411yescharacteristic
277Dic15—41no—
278C3×Dic5—42no—
279C5×Dic3—24no—
280C5×Dic3—42no—
281C3×#41—22no—
282C3×#41—22no—
283C2×C3×Q8—52no—
284C2×C3×Q8—101no—
285C2×C3×Q8—102no—
286C2×C3×Q8—102no—
287C2×C3×Q8C22×D511yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4C22×D511yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4—101no—
292C22×C3×C4C22×D511yescharacteristic
293C2×#67—101no—
294C22×Dic3—21no—
295#235—102no—
296#235—102no—
297C2×D12—51no—
298C2×C4×D3—101no—
299C2×Dic6—22no—
300C2×Dic6—22no—
301C2×Dic6—21no—
302C2×Dic6—51no—
303C2×Dic6C22×D512yes—
304C3×Q16—104no—
305C3×SD16—104no—
306C3×M16—54no—
307C2×C3×C8—52no—
308#217—24no—
309#217C22⋊D512yes—
310#216—104no—
311#216—104no—
312#216—102no—
313#215—102no—
314#214—102no—
315#213—102no—
316(C2×D3)⋊C4—104no—
317C4⋊Dic3C22⋊D512yes—
318Dic3⋊C4—24no—
319Dic3⋊C4—104no—
320C4×Dic3C22×D512yes—
321C2×C3⋊C8—54no—
322C2×C3⋊C8—51no—
323C2×C3⋊C8—51no—
324Dic12—104no—
325#204—104no—
326C23×C5—21no—
327C23×C5D3×D411yescharacteristic
328C22×D5—61no—
329C5×Q8—21no—
330C5×Q8—21no—
331C5×Q8—62no—
332C5×Q8—62no—
333C5×Q8—122no—
334C5×D4—21no—
335C5×D4—21no—
336C5×D4—42no—
337C2×C4×C5—21no—
338C2×C4×C5—34no—
339C2×C4×C5—42no—
340C2×C4×C5—62no—
341C2×C4×C5—122no—
342C2×C4×C5D3×D411yescharacteristic
343C2×C4×C5D3×D412yes—
344C2×C4×C5C2×#6712yes—
345C2×C4×C5C23×D311yescharacteristic
346C22⋊D5—122no—
347C2×Dic5—22no—
348C2×Dic5—42no—
349C2×Dic5—61no—
350D20—61no—
351D20—61no—
352C4×D5—122no—
353Dic10—22no—
354Dic10—22no—
355Dic10—42no—
356Dic10—61no—
357Dic10—61no—
358#168—32no—
359#168—32no—
360#168C2×#6714yes—
361C2×#41—151no—
362C2×#41D3×D511yescharacteristic
363C22×Q8—31no—
364C22×Q8—51no—
365#137—104no—
366#137—304no—
367#135—304no—
368C2×Q16—52no—
369C2×Q16—152no—
370C2×Q16—152no—
371C2×Q16—152no—
372C2×Q16—151no—
373C2×Q16—304no—
374C2×SD16—52no—
375C2×SD16—152no—
376C2×SD16—151no—
377C2×SD16—151no—
378C2×D8—151no—
379C2×M16—51no—
380C22×C8—151no—
381C4⋊Q8—32no—
382C4⋊Q8—152no—
383#124—32no—
384#124—152no—
385#123—62no—
386#123—302no—
387C22⋊Q8—62no—
388C22⋊Q8—302no—
389#117—31no—
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—21no—
401C3×Q8—21no—
402C3×Q8—102no—
403C3×Q8—102no—
404C3×Q8—202no—
405C3×D4—21no—
406C3×D4—21no—
407C3×D4—42no—
408C2×C3×C4—21no—
409C2×C3×C4—42no—
410C2×C3×C4—102no—
411C2×C3×C4—202no—
412C2×C3×C4D4×D512yes—
413C2×C3×C4D4×D512yes—
414C2×C3×C4C2×C22⋊D511yescharacteristic
415C2×C3×C4C23×D511yescharacteristic
416#67—202no—
417C2×Dic3—22no—
418C2×Dic3—42no—
419C2×Dic3—101no—
420C2×Dic3C2×C22⋊D514yes—
421D12—101no—
422D12—101no—
423C4×D3—202no—
424Dic6—22no—
425Dic6—22no—
426Dic6—42no—
427Dic6—101no—
428Dic6—101no—
429C3×C8—54no—
430C3⋊C8—52no—
431C3⋊C8—52no—
432C22×C5—22no—
433C22×C5—42no—
434C22×C5—41no—
435C22×C5#94012yes—
436C22×C5C2×D3×D411yescharacteristic
437C2×D5—122no—
438C2×D5—121no—
439C4×C5—41no—
440C4×C5—64no—
441C4×C5—122no—
442C4×C5#94012yes—
443C4×C5C2×D3×D411yescharacteristic
444C4×C5C22×#6711yescharacteristic
445Dic5—42no—
446Dic5—121no—
447#41—22no—
448#41—22no—
449#41—302no—
450#41—302no—
451C2×Q8—32no—
452C2×Q8—52no—
453C2×Q8—61no—
454C2×Q8—62no—
455C2×Q8—62no—
456C2×Q8—101no—
457C2×Q8—102no—
458C2×Q8—102no—
459C2×Q8—151no—
460C2×Q8C2×D3×D511yescharacteristic
461C2×D4—21no—
462C2×D4—151no—
463C2×D4—301no—
464C2×D4C2×D3×D511yescharacteristic
465C22×C4—21no—
466C22×C4—61no—
467C22×C4—101no—
468C22×C4—301no—
469C22×C4C2×D3×D511yescharacteristic
470Q16—104no—
471Q16—304no—
472Q16—302no—
473Q16—304no—
474Q16—304no—
475SD16—104no—
476SD16—304no—
477SD16—302no—
478SD16—302no—
479D8—302no—
480M16—54no—
481C2×C8—52no—
482C2×C8—154no—
483C2×C8—151no—
484C2×C8—151no—
485C4⋊C4—32no—
486C4⋊C4—64no—
487C4⋊C4—304no—
488C22⋊C4—32no—
489C22⋊C4—64no—
490C22⋊C4—304no—
491C42—32no—
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—41no—
501C3×C4—202no—
502C3×C4#408612yes—
503C3×C4C2×D4×D511yescharacteristic
504C3×C4C2×D4×D511yescharacteristic
505Dic3—24no—
506Dic3—42no—
507Dic3—201no—
508C2×C5—22no—
509C2×C5—81no—
510C2×C5#577912yes—
511C2×C5C2×#94011yescharacteristic
512D5—241no—
513C23—21no—
514C23—301no—
515C23D3×C22⋊D511yescharacteristic
516Q8—21no—
517Q8—21no—
518Q8—62no—
519Q8—62no—
520Q8—102no—
521Q8—102no—
522Q8—122no—
523Q8—202no—
524Q8—301no—
525Q8—301no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—301no—
530D4—301no—
531D4—602no—
532C2×C4—21no—
533C2×C4—34no—
534C2×C4—42no—
535C2×C4—62no—
536C2×C4—102no—
537C2×C4—122no—
538C2×C4—202no—
539C2×C4—301no—
540C2×C4—602no—
541C2×C4D5×#6712yes—
542C2×C4D3×C22⋊D511yescharacteristic
543C2×C4#679012yes—
544C2×C4C22×D3×D511yescharacteristic
545C8—54no—
546C8—152no—
547C8—152no—
548C2×C3—22no—
549C2×C3—81no—
550C2×C3C2×#408611yescharacteristic
551C2×C3#6617212yes—
552D3—401no—
553C5#8397511yescharacteristic, complemented, Sylow
554C22—22no—
555C22—42no—
556C22—41no—
557C22—602no—
558C22—601no—
559C22#9156712yes—
560C22C2×D3×C22⋊D511yescharacteristic
561C4—41no—
562C4—64no—
563C4—122no—
564C4—202no—
565C4—601no—
566C4#9156712yes—
567C4C2×D5×#6711yescharacteristic
568C4C2×#679011yescharacteristic
569C3#1061513411yescharacteristic, complemented, Sylow
570C2—22no—
571C2—81no—
572C2—1201no—
573C2#1175534112yes—
574C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×#91839C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3156
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C5×#5825C2semidirect
3. C2×C3×#4097C2semidirect
4. #11754278C2semidirect
5. C2×#91321C2semidirect
6. C22×#6661C2semidirect
7. #11749357C2semidirect
8. #11749324C2semidirect
9. #11749110C2semidirect
10. #11749078C2semidirect
11. #11748327C2semidirect
46. C2×#4097D3semidirect
102. #5825D5semidirect
492. C3×C5#3156semidirect
553. C5#83975semidirect
569. C3#10615134semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C5×#58252
C2×C3×#40972
#117542782
C2×#913212
C22×#66612
#117493572
#117493242
#117491102
#117490782
#117483272
#106151343
#839755