Finite Group Databasebeta

← #14438693

Subgroups — #14438693

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754581C211yesmaximal, characteristic
2C2×#91381C211yesmaximal, characteristic, complemented
3#11751234C211yesmaximal, characteristic, complemented
4C5×Dic3×M16C211yesmaximal, characteristic, complemented
5C3×#65422C211yesmaximal, characteristic, complemented
6#11748413C211yesmaximal, characteristic, complemented
7#11748369C211yesmaximal, characteristic, complemented
8#11748008C212yesmaximal, complemented
9#11747990C212yesmaximal, complemented
10#11747988C212yesmaximal, complemented
11#11747970C212yesmaximal, complemented
12#10610260—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×C5×Dic3C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20#91569—21no—
21#91569—21no—
22C2×#6669—21no—
23C2×#6668—21no—
24#91458C2211yescharacteristic
25C4×#1202—21no—
26C4×#1202—21no—
27#91389C2211yescharacteristic
28#91381—21no—
29#91381—21no—
30#91381C2212yes—
31#91381C2212yes—
32#91374C2211yescharacteristic
33#91364C2211yescharacteristic
34#91105C2212yes—
35#91100C2212yes—
36C5×#815C2212yes—
37C5×C8×Dic3C2212yes—
38C3×#3953C2212yes—
39C3×#3948C2212yes—
40#90974C2212yes—
41#90971C2212yes—
42#90968C2212yes—
43#90965C2212yes—
44#78879—51nomaximal, Hall
45#65811—31no—
46C2×#4016—31no—
47C4×C5×M16—31no—
48#65422—31no—
49#65422—31no—
50#65422—31no—
51#65422D311yescharacteristic, complemented
52#65002—32no—
53#64992—32no—
54#64986—32no—
55#64986—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58C22×Dic15—21no—
59#6817—22no—
60#6817—22no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2311yescharacteristic
64C22×C5×Dic3D411yescharacteristic
65C22×C5×Dic3D411yescharacteristic
66C2×C3×C22⋊D5—21no—
67C22×C3×Dic5—21no—
68C3×#709—22no—
69C3×#709—22no—
70C2×C3×D20C2311yescharacteristic
71C2×C3×C4×D5—21no—
72C2×C3×Dic10C2311yescharacteristic
73C2×#1202—21no—
74C2×#1202—21no—
75C3×C5×M16—22no—
76C2×C3×C5×C8C2312yes—
77C4⋊Dic15—21no—
78C4⋊Dic15C2312yes—
79C4×C5×Dic3D411yescharacteristic
80C4×C5×Dic3D411yescharacteristic
81C4×C5×Dic3C2311yescharacteristic
82C4×C5×Dic3C2311yescharacteristic
83C5×#208—22no—
84C2×C5×C3⋊C8C2312yes—
85C3×C4⋊Dic5—21no—
86C3×C4⋊Dic5C2312yes—
87Dic3⋊Dic5—21no—
88Dic3⋊Dic5—21no—
89#6669—22no—
90#6669—22no—
91#6668—22no—
92#6668—22no—
93#6667—21no—
94#6667—21no—
95#6665—21no—
96#6665—21no—
97#5832—51no—
98C2×#890—51no—
99C3×#417—51no—
100#5232—51no—
101#5133—51no—
102Dic3×M16D511yescharacteristic, complemented
103#4966—51no—
104#4800—52no—
105#4797—52no—
106#4768—52no—
107#4764—52no—
108C2×#709—31no—
109C2×#709C2×D311yescharacteristic
110C2×C5×M16—31no—
111C2×C5×M16C2×D311yescharacteristic
112C2×C42×C5—31no—
113#4076—61no—
114#4076—61no—
115C2×C4⋊Dic5—31no—
116C2×C4⋊Dic5C2×D311yescharacteristic
117C2×#683—61no—
118C2×#683—61no—
119#4021—31no—
120#4021—31no—
121#4020—31no—
122C4×D20—61no—
123C4×D20—61no—
124#4016—32no—
125#4016—32no—
126#4016—61no—
127#4016—61no—
128#4015—31no—
129C5×#97—32no—
130C4×C5×C8—32no—
131#3953—32no—
132#3953—32no—
133#3953—32no—
134#3953C2×D312yes—
135#3948—32no—
136#3948—32no—
137#3948—32no—
138#3948C2×D312yes—
139#3142—151noSylow
140C23×C3×C5C2×D411yescharacteristic
141C22×D15—21no—
142C22×C3×D5—21no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5#4112yes—
146C2×C3×C4×C5C2411yescharacteristic
147#1220—42no—
148C2×Dic15—21no—
149C2×Dic15—22no—
150C2×Dic15—42no—
151D60—21no—
152D60—21no—
153C4×D15—42no—
154Dic30—21no—
155Dic30—21no—
156C2×C5×Dic3—41no—
157C2×C5×Dic3—41no—
158C2×C5×Dic3C2×D411yescharacteristic
159C2×C5×Dic3C2×D411yescharacteristic
160C2×C5×Dic3C2×D411yescharacteristic
161C2×C5×Dic3C2×D411yescharacteristic
162C3×C22⋊D5—42no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—42no—
166C3×D20—21no—
167C3×D20—21no—
168C3×C4×D5—42no—
169C3×Dic10—21no—
170C3×Dic10—21no—
171#1202—42no—
172#1202—42no—
173C3×C5×C8—22no—
174C5×C3⋊C8—22no—
175C2×C3×#41—51no—
176C2×#235—51no—
177C2×C3×M16C2×D511yescharacteristic
178C2×C3×C4⋊C4—51no—
179#947—51no—
180#944—51no—
181#940—51no—
182#939—101no—
183#939—101no—
184#936—51no—
185C4×#67—101no—
186C4×#67—101no—
187C2×C4⋊Dic3—51no—
188C2×C4⋊Dic3—101no—
189C2×Dic3⋊C4—101no—
190C2×C4×Dic3C2×D511yescharacteristic
191C2×#208C2×D511yescharacteristic
192#890—52no—
193#890—52no—
194#890—101no—
195#890—101no—
196C3×#103—52no—
197C3×#102—52no—
198#835—52no—
199#832—52no—
200#821—52no—
201#816—52no—
202#815C2×D512yes—
203C8×Dic3C2×D512yes—
204#810—52no—
205#809—52no—
206C22×C4×C5—31no—
207C22×C4×C5—31no—
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—21no—
210C2×C22⋊D5—61no—
211C22×Dic5—21no—
212C22×Dic5—61no—
213#709—22no—
214#709—22no—
215#709—62no—
216#709—62no—
217C2×D20—31no—
218C2×D20—61no—
219C2×D20—61no—
220C2×D20C22×D311yescharacteristic
221C2×C4×D5—21no—
222C2×C4×D5—61no—
223C2×Dic10—31no—
224C2×Dic10C22×D311yescharacteristic
225C5×M16—22no—
226C5×M16—62no—
227C2×C5×C8—32no—
228C2×C5×C8C22×D312yes—
229C42×C5—31no—
230C42×C5—31no—
231C42×C5—31no—
232C42×C5—31no—
233#685—61no—
234#685—61no—
235#685—61no—
236#685—61no—
237C4⋊Dic5—21no—
238C4⋊Dic5—32no—
239C4⋊Dic5—61no—
240C4⋊Dic5—61no—
241C4⋊Dic5—61no—
242C4⋊Dic5C22×D312yes—
243#683—62no—
244#683—62no—
245#683—62no—
246#683—62no—
247#532—151no—
248C2×#125—151no—
249#491—152no—
250#490—152no—
251#488—152no—
252#488—152no—
253#417—51no—
254#417—151no—
255#417—151no—
256#417—151no—
257C4×M16—31no—
258C22×C3×C5—21no—
259C22×C3×C5—21no—
260C22×C3×C5#12412yes—
261C22×C3×C5C22×D411yescharacteristic
262C2×D15—41no—
263C2×D15—41no—
264C2×D15—41no—
265C2×C3×D5—41no—
266C2×C3×D5—41no—
267C2×C3×D5—41no—
268C3×C4×C5#12412yes—
269C3×C4×C5C2×#4111yescharacteristic
270C3×C4×C5C2×#4111yescharacteristic
271Dic15—41no—
272Dic15—42no—
273C3×Dic5—41no—
274C3×Dic5—42no—
275C5×Dic3—21no—
276C5×Dic3—21no—
277C5×Dic3—21no—
278C5×Dic3—21no—
279C3×#41—102no—
280C3×#41—102no—
281C2×C3×Q8—51no—
282C2×C3×D4—51no—
283C2×C3×D4—101no—
284C22×C3×C4—101no—
285C22×C3×C4—101no—
286C22×C3×C4C22×D511yescharacteristic
287C2×#67—101no—
288C2×#67—101no—
289C2×#67—101no—
290C22×Dic3—101no—
291C22×Dic3D2011yescharacteristic
292C22×Dic3D2011yescharacteristic
293#235—102no—
294#235—102no—
295C2×D12—51no—
296C2×C4×D3—101no—
297C2×Dic6—51no—
298C3×M16—22no—
299C2×C3×C8C22×D512yes—
300C3×C4⋊C4—52no—
301C3×C4⋊C4—101no—
302#217—101no—
303#217—101no—
304(C2×D3)⋊C4—101no—
305(C2×D3)⋊C4—101no—
306C4⋊Dic3—52no—
307C4⋊Dic3—101no—
308C4⋊Dic3—102no—
309C4⋊Dic3—102no—
310Dic3⋊C4—102no—
311Dic3⋊C4—102no—
312Dic3⋊C4—101no—
313Dic3⋊C4—101no—
314C4×Dic3D2011yescharacteristic
315C4×Dic3D2011yescharacteristic
316C4×Dic3C22×D511yescharacteristic
317C4×Dic3C22×D511yescharacteristic
318#208—22no—
319C2×C3⋊C8C22×D512yes—
320C23×C5D3×D411yescharacteristic
321C22×D5—21no—
322C22×D5—61no—
323C2×C4×C5—31no—
324C2×C4×C5—31no—
325C2×C4×C5—31no—
326C2×C4×C5—31no—
327C2×C4×C5—121no—
328C2×C4×C5—121no—
329C2×C4×C5#23512yes—
330C2×C4×C5D3×D411yescharacteristic
331C2×C4×C5#23712yes—
332C2×C4×C5C23×D311yescharacteristic
333C22⋊D5—42no—
334C22⋊D5—122no—
335C2×Dic5—22no—
336C2×Dic5—21no—
337C2×Dic5—42no—
338C2×Dic5—62no—
339C2×Dic5—61no—
340C2×Dic5—122no—
341D20—21no—
342D20—21no—
343D20—61no—
344D20—61no—
345D20—122no—
346D20—122no—
347C4×D5—42no—
348C4×D5—122no—
349Dic10—21no—
350Dic10—21no—
351Dic10—61no—
352Dic10—61no—
353C5×C8—22no—
354C5×C8—62no—
355C2×#41—51no—
356C2×#41—151no—
357C2×M16—31no—
358C2×M16D3×D511yescharacteristic
359C4⋊Q8—151no—
360#127—151no—
361#125—152no—
362#125—152no—
363#125—301no—
364#125—301no—
365#124—151no—
366#124—151no—
367#121—301no—
368#121—301no—
369C4×D4—301no—
370C4×D4—301no—
371C2×C4⋊C4—51no—
372C2×C4⋊C4—151no—
373C2×C4⋊C4—301no—
374C2×C4⋊C4—301no—
375C2×C42—31no—
376#103—52no—
377#103—152no—
378#103—152no—
379#103—152no—
380#102—52no—
381#102—152no—
382#102—152no—
383#102—152no—
384#97—32no—
385C4×C8—32no—
386C2×C3×C5—22no—
387C2×C3×C5C2×#12411yescharacteristic
388C2×C3×C5#57511yescharacteristic
389C2×C3×C5#57511yescharacteristic
390D15—81no—
391C3×D5—81no—
392C23×C3—101no—
393C23×C3C2×D2011yescharacteristic
394C22×D3—101no—
395C3×Q8—101no—
396C3×Q8—101no—
397C3×D4—101no—
398C3×D4—101no—
399C3×D4—202no—
400C2×C3×C4—102no—
401C2×C3×C4—101no—
402C2×C3×C4—202no—
403C2×C3×C4—202no—
404C2×C3×C4C2×D2011yescharacteristic
405C2×C3×C4#70912yes—
406C2×C3×C4#70912yes—
407C2×C3×C4C23×D511yescharacteristic
408#67—202no—
409#67—202no—
410#67—202no—
411C2×Dic3—41no—
412C2×Dic3—41no—
413C2×Dic3—102no—
414C2×Dic3—101no—
415C2×Dic3—202no—
416C2×Dic3C2×D2011yescharacteristic
417C2×Dic3C2×D2011yescharacteristic
418C2×Dic3C2×D2011yescharacteristic
419C2×Dic3C2×D2011yescharacteristic
420D12—101no—
421D12—101no—
422C4×D3—202no—
423Dic6—101no—
424Dic6—101no—
425C3×C8—22no—
426C3⋊C8—22no—
427C22×C5—21no—
428C22×C5—21no—
429C22×C5#88512yes—
430C22×C5C2×D3×D411yescharacteristic
431C2×D5—41no—
432C2×D5—41no—
433C2×D5—41no—
434C2×D5—121no—
435C2×D5—121no—
436C2×D5—121no—
437C4×C5—61no—
438C4×C5—61no—
439C4×C5—61no—
440C4×C5—61no—
441C4×C5#88512yes—
442C4×C5C2×#23511yescharacteristic
443C4×C5C2×#23711yescharacteristic
444Dic5—41no—
445Dic5—42no—
446Dic5—121no—
447Dic5—122no—
448#41—102no—
449#41—102no—
450#41—302no—
451#41—302no—
452C2×Q8—51no—
453C2×Q8—151no—
454C2×D4—51no—
455C2×D4—101no—
456C2×D4—151no—
457C2×D4—301no—
458C2×D4—301no—
459C2×D4—301no—
460C22×C4—31no—
461C22×C4—31no—
462C22×C4—101no—
463C22×C4—101no—
464C22×C4—301no—
465C22×C4—301no—
466C22×C4C2×D3×D511yescharacteristic
467M16—22no—
468M16—62no—
469C2×C8—32no—
470C2×C8C2×D3×D512yes—
471C4⋊C4—52no—
472C4⋊C4—101no—
473C4⋊C4—152no—
474C4⋊C4—302no—
475C4⋊C4—302no—
476C4⋊C4—302no—
477C4⋊C4—302no—
478C4⋊C4—301no—
479C4⋊C4—301no—
480C4⋊C4—301no—
481C22⋊C4—301no—
482C22⋊C4—301no—
483C22⋊C4—301no—
484C22⋊C4—301no—
485C42—31no—
486C42—31no—
487C42—31no—
488C42—31no—
489C3×C5#314211yescharacteristic, complemented, Hall
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—201no—
493C22×C3—201no—
494C22×C3—201no—
495C22×C3#402112yes—
496C22×C3C22×D2011yescharacteristic
497C2×D3—201no—
498C2×D3—201no—
499C2×D3—201no—
500C3×C4—201no—
501C3×C4—202no—
502C3×C4#402112yes—
503C3×C4C2×#70911yescharacteristic
504C3×C4C2×#70911yescharacteristic
505Dic3—21no—
506Dic3—21no—
507Dic3—21no—
508Dic3—21no—
509Dic3—201no—
510Dic3—202no—
511C2×C5—22no—
512C2×C5C2×#88511yescharacteristic
513C2×C5#577311yescharacteristic
514C2×C5#577711yescharacteristic
515D5—81no—
516D5—241no—
517C23—101no—
518C23—301no—
519C23D3×D2011yescharacteristic
520Q8—101no—
521Q8—101no—
522Q8—301no—
523Q8—301no—
524D4—101no—
525D4—101no—
526D4—202no—
527D4—301no—
528D4—301no—
529D4—602no—
530D4—602no—
531D4—602no—
532C2×C4—31no—
533C2×C4—31no—
534C2×C4—31no—
535C2×C4—31no—
536C2×C4—101no—
537C2×C4—102no—
538C2×C4—121no—
539C2×C4—121no—
540C2×C4—202no—
541C2×C4—202no—
542C2×C4—301no—
543C2×C4—302no—
544C2×C4—602no—
545C2×C4—602no—
546C2×C4#677112yes—
547C2×C4D3×D2011yescharacteristic
548C2×C4#677912yes—
549C2×C4C22×D3×D511yescharacteristic
550C8—22no—
551C8—62no—
552C2×C3—22no—
553C2×C3—401no—
554C2×C3C2×#402111yescharacteristic
555C2×C3#6608211yescharacteristic
556C2×C3#6608211yescharacteristic
557D3—401no—
558C5#7887911yescharacteristic, complemented, Sylow
559C22—21no—
560C22—21no—
561C22—201no—
562C22—201no—
563C22—201no—
564C22—601no—
565C22—601no—
566C22—601no—
567C22#9135312yes—
568C22C2×D3×D2011yescharacteristic
569C4—61no—
570C4—61no—
571C4—61no—
572C4—61no—
573C4—202no—
574C4—201no—
575C4—602no—
576C4—601no—
577C4#9135312yes—
578C4C2×#677111yescharacteristic
579C4C2×#677911yescharacteristic
580C3#1061026011yescharacteristic, complemented, Sylow
581C2—22no—
582C2—401no—
583C2—1201no—
584C2#1175402811yescharacteristic
585C2#1175402911yescharacteristic
586C2C2×#9135311yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radical#11754581C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#91381C2semidirect
3. #11751234C2semidirect
4. C5×Dic3×M16C2semidirect
5. C3×#65422C2semidirect
6. #11748413C2semidirect
7. #11748369C2semidirect
8. #11748008C2semidirect
9. #11747990C2semidirect
10. #11747988C2semidirect
11. #11747970C2semidirect
51. #65422D3semidirect
102. Dic3×M16D5semidirect
489. C3×C5#3142semidirect
558. C5#78879semidirect
580. C3#10610260semidirect

Maximal subgroups

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

subgroupindex
#117545812
C2×#913812
#117512342
C5×Dic3×M162
C3×#654222
#117484132
#117483692
#117480082
#117479902
#117479882
#117479702
#106102603
#788795