Finite Group Databasebeta

← #14439691

Subgroups — #14439691

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
1#11756575C211yesmaximal, characteristic, complemented
2C2×C5×#942C211yesmaximal, characteristic, complemented
3C22×C3×#689C211yesmaximal, characteristic, complemented
4#11754255C211yesmaximal, characteristic, complemented
5C2×#91315C211yesmaximal, characteristic, complemented
6C2×#91303C211yesmaximal, characteristic
7#11749356C212yesmaximal, complemented
8#11749355C212yesmaximal, complemented
9#11749322C212yesmaximal, complemented
10#11749321C212yesmaximal, complemented
11#11748324C211yesmaximal, characteristic, complemented
12#10615706—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17#91836C2212yes—
18#91835—22no—
19#91833C2212yes—
20#91818—22no—
21#91815C2211yescharacteristic
22C2×C5×#216C2212yes—
23C5×#942—24no—
24C2×C5×#215C2212yes—
25C2×C5×#208C2211yescharacteristic
26C2×C3×#689—24no—
27C2×C3×#689C2212yes—
28C2×C3×#689C2212yes—
29C22×C3×#168C2211yescharacteristic
30#91539—22no—
31#91385C2212yes—
32#91370C2212yes—
33#91369—22no—
34C2×#6663C2211yescharacteristic
35C2×#6662C2212yes—
36C2×#6660C2211yescharacteristic
37C2×#6659C2211yescharacteristic
38#91315—24no—
39C2×#6658C2212yes—
40#91303—24no—
41C2×#6654C2211yescharacteristic
42#90954C2212yes—
43#90951C2212yes—
44#83881—51nomaximal, Hall
45C2×C5×#137—31no—
46#66159—31no—
47C2×#4096—31no—
48#66150—31no—
49C22×#689D311yescharacteristic, complemented
50C2×#4055—31no—
51#65479—32no—
52#65470—32no—
53#65457—32no—
54#65456—32no—
55#65411—31no—
56C2×C3×C5×Q8—21no—
57C2×C3×C5×Q8—22no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8C2312yes—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63#6817—22no—
64#6817—22no—
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
68C2×C5×#67—21no—
69C5×#235—22no—
70C5×#235—22no—
71C2×C5×D12C2311yescharacteristic
72C2×C4×C5×D3—21no—
73C2×C5×Dic6C2311yescharacteristic
74C22×C3×Dic5—21no—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—21no—
78C2×C3×Dic10C2312yes—
79#6719D412yes—
80#6714—24no—
81C4⋊Dic15D412yes—
82#6712—24no—
83C4×Dic15C2312yes—
84C5×#216—24no—
85C5×#215—24no—
86C5×#208D414yes—
87C2×C5×C3⋊C8C2312yes—
88C3×#689—24no—
89C3×#689—24no—
90C2×C3×#168D414yes—
91C2×C3×#168C2311yescharacteristic
92C2×C3×#168C2311yescharacteristic
93#6669—24no—
94(C2×D3)⋊Dic5—24no—
95#6663—22no—
96#6662—24no—
97#6660—22no—
98#6659—22no—
99#6658—24no—
100#6654—22no—
101C22×C3×Q16—51no—
102#5816—51no—
103#5816—51no—
104C2×#942—51no—
105C2×#942D511yescharacteristic, complemented
106C2×#904—51no—
107#5191—52no—
108#5190—52no—
109#5190—52no—
110#5183—52no—
111#5101—51no—
112C2×C5×#41—31no—
113C22×C5×Q8C2×D311yescharacteristic
114C2×#709—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16—31no—
120#4096—64no—
121#4093—32no—
122#4092—62no—
123#4090—32no—
124#4090—32no—
125C2×#689—24no—
126C2×#689—31no—
127C2×#689C2×D312yes—
128C2×#689C2×D312yes—
129C2×#688—31no—
130#4082—32no—
131#4081—62no—
132C2×#687—31no—
133C2×#686—31no—
134#4075—62no—
135#4072—31no—
136#4070—62no—
137C22×#168C2×D311yescharacteristic
138#4055—64no—
139C2×Dic20—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3156—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C5×D3—21no—
147C3×C5×Q8—22no—
148C3×C5×Q8—22no—
149C3×C5×Q8—42no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—42no—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5C2411yescharacteristic
156#1220—42no—
157C2×Dic15—21no—
158C2×Dic15C2×D414yes—
159D60—21no—
160D60—21no—
161C4×D15—42no—
162Dic30—21no—
163Dic30—21no—
164C5×#67—42no—
165C2×C5×Dic3—21no—
166C5×D12—21no—
167C5×D12—21no—
168C4×C5×D3—42no—
169C5×Dic6—21no—
170C5×Dic6—21no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—42no—
173C3×Dic10—22no—
174C3×Dic10—22no—
175C3×Dic10—42no—
176C3×#168C2×D412yes—
177C3×#168C2×D412yes—
178C5×C3⋊C8C2×D414yes—
179C22×C3×Q8—51no—
180C22×C3×Q8C2×D511yescharacteristic
181C2×#235—51no—
182C2×#235C2×D511yescharacteristic
183C2×C3×Q16—52no—
184C2×C3×Q16—52no—
185C2×C3×Q16—104no—
186C22×C3×C8—51no—
187#947—52no—
188#947—52no—
189#946—102no—
190#946—102no—
191#944—52no—
192#944—52no—
193C2×#216—52no—
194C2×#216C2×D512yes—
195#942—24no—
196#942—104no—
197C2×#215—52no—
198C2×#215C2×D512yes—
199#929—102no—
200#929—102no—
201#926—51no—
202C2×#208C2×D511yescharacteristic
203C2×Dic12—51no—
204#904—104no—
205C2×D24—51no—
206C2×#204—51no—
207C2×#204—51no—
208#815—52no—
209C8×Dic3—52no—
210C5×#41—62no—
211C5×#41—62no—
212C2×C5×Q8—21no—
213C2×C5×Q8—22no—
214C2×C5×Q8—22no—
215C2×C5×Q8—31no—
216C2×C5×Q8C22×D312yes—
217C2×C5×D4—31no—
218C2×C5×D4—61no—
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×Q16—64no—
234C5×SD16—64no—
235C5×M16—34no—
236C2×C5×C8—32no—
237C22⋊Dic5—32no—
238C22⋊Dic5—64no—
239#689—24no—
240#689—24no—
241#689—62no—
242#688—62no—
243#687—62no—
244#686—62no—
245#685—64no—
246C4⋊Dic5—32no—
247#683—64no—
248#683—64no—
249C4×Dic5—32no—
250C2×#168#6714yes—
251C2×#168C22×D311yescharacteristic
252C2×#168C22×D311yescharacteristic
253Dic20—64no—
254#677—64no—
255C2×#137—31no—
256C2×#137—151no—
257C2×#135—151no—
258C22×Q16—51no—
259#536—151no—
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#12712yes—
268C22×C3×C5C22×D411yescharacteristic
269C2×D15—41no—
270C2×D15—42no—
271C2×C5×D3—41no—
272C2×C5×D3—42no—
273C3×C4×C5—42no—
274C3×C4×C5#12712yes—
275C3×C4×C5C22×D411yescharacteristic
276C3×C4×C5C22×D411yescharacteristic
277Dic15—24no—
278Dic15—41no—
279C3×Dic5—42no—
280C5×Dic3—41no—
281C2×C3×Q8—21no—
282C2×C3×Q8—22no—
283C2×C3×Q8—22no—
284C2×C3×Q8—52no—
285C2×C3×Q8—101no—
286C2×C3×Q8—102no—
287C2×C3×Q8—102no—
288C2×C3×Q8C22×D512yes—
289C22×C3×C4—21no—
290C22×C3×C4—101no—
291C22×C3×C4C22×D511yescharacteristic
292C2×#67—21no—
293C2×#67—101no—
294#235—22no—
295#235—22no—
296#235—102no—
297#235—102no—
298C2×D12—51no—
299C2×D12C22×D511yescharacteristic
300C2×C4×D3—21no—
301C2×C4×D3—101no—
302C2×Dic6—51no—
303C2×Dic6C22×D511yescharacteristic
304C3×Q16—104no—
305C3×Q16—104no—
306C2×C3×C8—54no—
307C2×C3×C8—51no—
308C2×C3×C8—51no—
309#217—52no—
310#216—24no—
311#216—104no—
312#215—24no—
313#215—104no—
314(C2×D3)⋊C4—104no—
315(C2×D3)⋊C4—104no—
316C4⋊Dic3—52no—
317Dic3⋊C4—104no—
318Dic3⋊C4—104no—
319C4×Dic3—52no—
320#208C22⋊D514yes—
321C2×C3⋊C8C22×D512yes—
322Dic12—102no—
323D24—102no—
324#204—102no—
325#204—102no—
326C23×C5—61no—
327C23×C5D3×D411yescharacteristic
328C22×D5—61no—
329C5×Q8—22no—
330C5×Q8—22no—
331C5×Q8—42no—
332C5×Q8—61no—
333C5×Q8—61no—
334C5×D4—61no—
335C5×D4—61no—
336C5×D4—122no—
337C2×C4×C5—22no—
338C2×C4×C5—42no—
339C2×C4×C5—61no—
340C2×C4×C5—122no—
341C2×C4×C5D3×D412yes—
342C2×C4×C5D3×D411yescharacteristic
343C2×C4×C5C2×#6712yes—
344C2×C4×C5C23×D311yescharacteristic
345C22⋊D5—122no—
346C2×Dic5—22no—
347C2×Dic5—34no—
348C2×Dic5—42no—
349C2×Dic5—61no—
350D20—61no—
351D20—61no—
352C4×D5—122no—
353Dic10—22no—
354Dic10—22no—
355Dic10—42no—
356Dic10—61no—
357Dic10—61no—
358C5×C8—34no—
359#168C2×#6712yes—
360#168C2×#6712yes—
361C2×#41—31no—
362C2×#41—151no—
363C22×Q8—51no—
364C22×Q8D3×D511yescharacteristic
365#137—64no—
366#137—304no—
367#135—304no—
368C2×Q16—32no—
369C2×Q16—52no—
370C2×Q16—52no—
371C2×Q16—104no—
372C2×Q16—152no—
373C2×Q16—151no—
374C2×SD16—32no—
375C2×SD16—152no—
376C2×SD16—151no—
377C2×SD16—151no—
378C2×D8—151no—
379C2×M16—31no—
380C22×C8—51no—
381C4⋊Q8—152no—
382C4⋊Q8—152no—
383#124—152no—
384#124—152no—
385#123—302no—
386#123—302no—
387C22⋊Q8—302no—
388C22⋊Q8—302no—
389#117—151no—
390#97—152no—
391C4×C8—152no—
392C2×C3×C5—22no—
393C2×C3×C5C2×#12711yescharacteristic
394C2×C3×C5#57812yes—
395D15—81no—
396C5×D3—81no—
397C23×C3D4×D511yescharacteristic
398C22×D3—21no—
399C22×D3—101no—
400C3×Q8—22no—
401C3×Q8—22no—
402C3×Q8—42no—
403C3×Q8—102no—
404C3×Q8—102no—
405C3×Q8—202no—
406C2×C3×C4—22no—
407C2×C3×C4—42no—
408C2×C3×C4—102no—
409C2×C3×C4—202no—
410C2×C3×C4D4×D512yes—
411C2×C3×C4D4×D511yescharacteristic
412C2×C3×C4C2×C22⋊D512yes—
413C2×C3×C4C23×D511yescharacteristic
414#67—42no—
415#67—202no—
416C2×Dic3—21no—
417C2×Dic3—54no—
418C2×Dic3—101no—
419D12—21no—
420D12—21no—
421D12—101no—
422D12—101no—
423C4×D3—42no—
424C4×D3—202no—
425Dic6—21no—
426Dic6—21no—
427Dic6—101no—
428Dic6—101no—
429C3×C8—52no—
430C3×C8—52no—
431C3⋊C8C2×C22⋊D514yes—
432C22×C5—22no—
433C22×C5—122no—
434C22×C5—121no—
435C22×C5#94012yes—
436C22×C5C2×D3×D411yescharacteristic
437C2×D5—122no—
438C2×D5—121no—
439C4×C5—42no—
440C4×C5—121no—
441C4×C5#94012yes—
442C4×C5C2×D3×D411yescharacteristic
443C4×C5C22×#6711yescharacteristic
444Dic5—42no—
445Dic5—64no—
446Dic5—121no—
447#41—62no—
448#41—62no—
449#41—302no—
450#41—302no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—31no—
455C2×Q8—52no—
456C2×Q8—101no—
457C2×Q8—102no—
458C2×Q8—102no—
459C2×Q8—151no—
460C2×Q8C2×D3×D512yes—
461C2×D4—31no—
462C2×D4—61no—
463C2×D4—151no—
464C2×D4—301no—
465C22×C4—21no—
466C22×C4—61no—
467C22×C4—101no—
468C22×C4—301no—
469C22×C4C2×D3×D511yescharacteristic
470Q16—64no—
471Q16—104no—
472Q16—104no—
473Q16—304no—
474Q16—302no—
475SD16—64no—
476SD16—304no—
477SD16—302no—
478SD16—302no—
479D8—302no—
480M16—34no—
481C2×C8—32no—
482C2×C8—54no—
483C2×C8—51no—
484C2×C8—51no—
485C4⋊C4—152no—
486C4⋊C4—304no—
487C4⋊C4—304no—
488C22⋊C4—152no—
489C22⋊C4—304no—
490C22⋊C4—304no—
491C42—152no—
492C3×C5#315611yescharacteristic, complemented, Hall
493C22×C3—22no—
494C22×C3#408612yes—
495C22×C3C2×D4×D511yescharacteristic
496C2×D3—42no—
497C2×D3—41no—
498C2×D3—202no—
499C2×D3—201no—
500C3×C4—42no—
501C3×C4—202no—
502C3×C4#408612yes—
503C3×C4C2×D4×D511yescharacteristic
504C3×C4C22×C22⋊D511yescharacteristic
505Dic3—41no—
506Dic3—104no—
507Dic3—201no—
508C2×C5—22no—
509C2×C5—241no—
510C2×C5#576612yes—
511C2×C5C2×#94011yescharacteristic
512D5—241no—
513C23—61no—
514C23—301no—
515C23#679011yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—42no—
519Q8—61no—
520Q8—61no—
521Q8—102no—
522Q8—102no—
523Q8—202no—
524Q8—301no—
525Q8—301no—
526D4—61no—
527D4—61no—
528D4—122no—
529D4—301no—
530D4—301no—
531D4—602no—
532C2×C4—22no—
533C2×C4—42no—
534C2×C4—61no—
535C2×C4—102no—
536C2×C4—122no—
537C2×C4—154no—
538C2×C4—202no—
539C2×C4—301no—
540C2×C4—602no—
541C2×C4D5×#6712yes—
542C2×C4D3×C22⋊D512yes—
543C2×C4#679011yescharacteristic
544C2×C4C22×D3×D511yescharacteristic
545C8—34no—
546C8—52no—
547C8—52no—
548C2×C3—22no—
549C2×C3#6611312yes—
550C2×C3C2×#408611yescharacteristic
551D3—81no—
552D3—401no—
553C5#8388111yescharacteristic, complemented, Sylow
554C22—22no—
555C22—122no—
556C22—121no—
557C22—602no—
558C22—601no—
559C22#9156712yes—
560C22C2×#679011yescharacteristic
561C4—42no—
562C4—121no—
563C4—202no—
564C4—304no—
565C4—601no—
566C4#9156712yes—
567C4C2×D5×#6711yescharacteristic
568C4C2×D3×C22⋊D511yescharacteristic
569C3#1061570611yescharacteristic, complemented, Sylow
570C2—22no—
571C2—241no—
572C2—1201no—
573C2#1175512212yes—
574C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91303C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3156
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #11756575C2semidirect
2. C2×C5×#942C2semidirect
3. C22×C3×#689C2semidirect
4. #11754255C2semidirect
5. C2×#91315C2semidirect
7. #11749356C2semidirect
8. #11749355C2semidirect
9. #11749322C2semidirect
10. #11749321C2semidirect
11. #11748324C2semidirect
49. C22×#689D3semidirect
105. C2×#942D5semidirect
492. C3×C5#3156semidirect
553. C5#83881semidirect
569. C3#10615706semidirect

Maximal subgroups

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

subgroupindex
#117565752
C2×C5×#9422
C22×C3×#6892
#117542552
C2×#913152
C2×#913032
#117493562
#117493552
#117493222
#117493212
#117483242
#106157063
#838815