Finite Group Databasebeta

← #14438651

Subgroups — #14438651

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#11756591C211yesmaximal, characteristic
2C2×#91779C211yesmaximal, characteristic, complemented
3C3×C5×#417C211yesmaximal, characteristic, complemented
4#11751333C211yesmaximal, characteristic, complemented
5#11751234C211yesmaximal, characteristic, complemented
6M16×Dic15C211yesmaximal, characteristic, complemented
7#11751067C211yesmaximal, characteristic, complemented
8#11750901C212yesmaximal, complemented
9#11750898C212yesmaximal, complemented
10#11750869C212yesmaximal, complemented
11#11750865C212yesmaximal, complemented
12#10610610—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17#91836C2211yescharacteristic
18#91833C2211yescharacteristic
19#91829C2211yescharacteristic
20#91828—21no—
21#91828—21no—
22#91825C2211yescharacteristic
23C4×#1220—21no—
24C4×#1220—21no—
25C2×C4⋊Dic15—21no—
26C2×C4⋊Dic15C2211yescharacteristic
27C2×#6712—21no—
28C2×C4×Dic15C2211yescharacteristic
29C2×#6710C2211yescharacteristic
30#91779—21no—
31#91779—21no—
32#91779C2212yes—
33#91779C2212yes—
34C3×C5×#103C2212yes—
35C3×C5×#102C2212yes—
36#91119C2212yes—
37#91116C2212yes—
38#91105C2212yes—
39#91100C2212yes—
40#91099C2212yes—
41C8×Dic15C2212yes—
42#91094C2212yes—
43#91093C2212yes—
44#78879—51nomaximal, Hall
45#66166—31no—
46C2×#4036—31no—
47C5×#417D311yescharacteristic, complemented
48#65521—31no—
49#65422—31no—
50M16×Dic5—31no—
51#65255—31no—
52#65089—32no—
53#65086—32no—
54#65057—32no—
55#65053—32no—
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×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C2×#1220—21no—
65C2×#1220—21no—
66C2×#1220—21no—
67C22×Dic15—21no—
68C22×Dic15D411yescharacteristic
69C22×Dic15D411yescharacteristic
70#6817—22no—
71#6817—22no—
72C2×D60C2311yescharacteristic
73C2×C4×D15—21no—
74C2×Dic30C2311yescharacteristic
75C3×C5×M16—22no—
76C2×C3×C5×C8C2312yes—
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4C2312yes—
79#6719—21no—
80#6719—21no—
81#6714—21no—
82#6714—21no—
83C4⋊Dic15—21no—
84C4⋊Dic15—22no—
85C4⋊Dic15—22no—
86C4⋊Dic15C2312yes—
87#6712—22no—
88#6712—22no—
89#6712—21no—
90#6712—21no—
91C4×Dic15D411yescharacteristic
92C4×Dic15D411yescharacteristic
93C4×Dic15C2311yescharacteristic
94C4×Dic15C2311yescharacteristic
95#6710—22no—
96C2×C3⋊#168C2312yes—
97#5832—51no—
98C2×#890—51no—
99C3×#417D511yescharacteristic, complemented
100#5232—51no—
101#5133—51no—
102Dic3×M16—51no—
103#4966—51no—
104#4800—52no—
105#4797—52no—
106#4768—52no—
107#4764—52no—
108C2×C5×#41C2×D311yescharacteristic
109C2×#709—31no—
110C2×C5×M16C2×D311yescharacteristic
111C2×C5×C4⋊C4C2×D311yescharacteristic
112#4093—31no—
113#4090—31no—
114#4086—31no—
115#4085—61no—
116#4085—61no—
117#4082—31no—
118C4×C22⋊D5—61no—
119C4×C22⋊D5—61no—
120C2×C4⋊Dic5—31no—
121C2×C4⋊Dic5—61no—
122C2×#683—61no—
123C2×C4×Dic5—31no—
124C2×#681—31no—
125#4036—32no—
126#4036—32no—
127#4036—61no—
128#4036—61no—
129C5×#103C2×D312yes—
130C5×#102C2×D312yes—
131#3967—32no—
132#3964—32no—
133#3953—32no—
134#3948—32no—
135#3947—32no—
136C8×Dic5—32no—
137#3942—32no—
138#3941—32no—
139#3142—151noSylow
140C23×C3×C5—21no—
141C23×C3×C5C2×D411yescharacteristic
142C22×D15—21no—
143C3×C5×Q8—21no—
144C3×C5×Q8—21no—
145C3×C5×D4—21no—
146C3×C5×D4—21no—
147C3×C5×D4—42no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—42no—
151C2×C3×C4×C5—42no—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5#4112yes—
154C2×C3×C4×C5#4112yes—
155C2×C3×C4×C5C2411yescharacteristic
156#1220—42no—
157#1220—42no—
158#1220—42no—
159C2×Dic15—22no—
160C2×Dic15—21no—
161C2×Dic15—41no—
162C2×Dic15—41no—
163C2×Dic15—42no—
164C2×Dic15C2×D411yescharacteristic
165C2×Dic15C2×D411yescharacteristic
166C2×Dic15C2×D411yescharacteristic
167C2×Dic15C2×D411yescharacteristic
168D60—21no—
169D60—21no—
170C4×D15—42no—
171Dic30—21no—
172Dic30—21no—
173C3×C5×C8—22no—
174C3⋊#168—22no—
175C2×C3×#41C2×D511yescharacteristic
176C2×#235—51no—
177C2×C3×M16C2×D511yescharacteristic
178C2×C3×C4⋊C4C2×D511yescharacteristic
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×Dic3—51no—
191C2×#208—51no—
192#890—52no—
193#890—52no—
194#890—101no—
195#890—101no—
196C3×#103C2×D512yes—
197C3×#102C2×D512yes—
198#835—52no—
199#832—52no—
200#821—52no—
201#816—52no—
202#815—52no—
203C8×Dic3—52no—
204#810—52no—
205#809—52no—
206C5×#41—22no—
207C5×#41—22no—
208C2×C5×Q8C22×D311yescharacteristic
209C2×C5×D4—21no—
210C2×C5×D4C22×D311yescharacteristic
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5C22×D311yescharacteristic
214C2×C22⋊D5—61no—
215C2×C22⋊D5—61no—
216C2×C22⋊D5—61no—
217C22×Dic5—31no—
218C22×Dic5—31no—
219C22×Dic5—61no—
220#709—62no—
221#709—62no—
222C2×D20—31no—
223C2×C4×D5—61no—
224C2×Dic10—31no—
225C5×M16—22no—
226C2×C5×C8C22×D312yes—
227C5×C4⋊C4—21no—
228C5×C4⋊C4C22×D312yes—
229C22⋊Dic5—61no—
230C22⋊Dic5—61no—
231#685—61no—
232#685—61no—
233C4⋊Dic5—32no—
234C4⋊Dic5—62no—
235C4⋊Dic5—62no—
236C4⋊Dic5—61no—
237#683—62no—
238#683—62no—
239#683—61no—
240#683—61no—
241C4×Dic5—31no—
242C4×Dic5—31no—
243C4×Dic5—31no—
244C4×Dic5—31no—
245#681—62no—
246C2×#168—32no—
247#532—151no—
248C2×#125—151no—
249#491—152no—
250#490—152no—
251#488—152no—
252#488—152no—
253#417—151no—
254#417—151no—
255#417—151no—
256#417D1511yescharacteristic, complemented
257C4×M16—151no—
258C22×C3×C5—21no—
259C22×C3×C5—21no—
260C22×C3×C5—41no—
261C22×C3×C5—41no—
262C22×C3×C5—41no—
263C22×C3×C5#12412yes—
264C22×C3×C5C22×D411yescharacteristic
265C2×D15—41no—
266C2×D15—41no—
267C2×D15—41no—
268C3×C4×C5—41no—
269C3×C4×C5—42no—
270C3×C4×C5#12412yes—
271C3×C4×C5C2×#4111yescharacteristic
272C3×C4×C5C2×#4111yescharacteristic
273Dic15—21no—
274Dic15—21no—
275Dic15—21no—
276Dic15—21no—
277Dic15—41no—
278Dic15—42no—
279C3×#41—22no—
280C3×#41—22no—
281C2×C3×Q8C22×D511yescharacteristic
282C2×C3×D4—21no—
283C2×C3×D4C22×D511yescharacteristic
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4C22×D511yescharacteristic
287C2×#67—101no—
288C2×#67—101no—
289C2×#67—101no—
290C22×Dic3—51no—
291C22×Dic3—51no—
292C22×Dic3—101no—
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—21no—
301C3×C4⋊C4C22×D512yes—
302#217—101no—
303#217—101no—
304(C2×D3)⋊C4—101no—
305(C2×D3)⋊C4—101no—
306C4⋊Dic3—52no—
307C4⋊Dic3—102no—
308C4⋊Dic3—102no—
309C4⋊Dic3—101no—
310Dic3⋊C4—102no—
311Dic3⋊C4—102no—
312Dic3⋊C4—101no—
313Dic3⋊C4—101no—
314C4×Dic3—51no—
315C4×Dic3—51no—
316C4×Dic3—51no—
317C4×Dic3—51no—
318#208—102no—
319C2×C3⋊C8—52no—
320C23×C5—21no—
321C23×C5D3×D411yescharacteristic
322C22×D5—61no—
323C5×Q8—21no—
324C5×Q8—21no—
325C5×D4—21no—
326C5×D4—21no—
327C5×D4—42no—
328C2×C4×C5—22no—
329C2×C4×C5—21no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5#23512yes—
333C2×C4×C5D3×D411yescharacteristic
334C2×C4×C5#23712yes—
335C2×C4×C5C23×D311yescharacteristic
336C22⋊D5—122no—
337C22⋊D5—122no—
338C22⋊D5—122no—
339C2×Dic5—31no—
340C2×Dic5—31no—
341C2×Dic5—31no—
342C2×Dic5—31no—
343C2×Dic5—62no—
344C2×Dic5—61no—
345C2×Dic5—121no—
346C2×Dic5—121no—
347C2×Dic5—122no—
348D20—61no—
349D20—61no—
350C4×D5—122no—
351Dic10—61no—
352Dic10—61no—
353C5×C8—22no—
354#168—62no—
355C2×#41—151no—
356C2×#41C2×D1511yescharacteristic
357C2×M16—151no—
358C2×M16C2×D1511yescharacteristic
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—151no—
372C2×C4⋊C4—301no—
373C2×C4⋊C4—301no—
374C2×C4⋊C4C2×D1511yescharacteristic
375C2×C42—151no—
376#103—152no—
377#103—152no—
378#103—152no—
379#103C2×D1512yes—
380#102—152no—
381#102—152no—
382#102—152no—
383#102C2×D1512yes—
384#97—152no—
385C4×C8—152no—
386C2×C3×C5—22no—
387C2×C3×C5—81no—
388C2×C3×C5C2×#12411yescharacteristic
389C2×C3×C5#57511yescharacteristic
390C2×C3×C5#57511yescharacteristic
391D15—81no—
392C23×C3—21no—
393C23×C3D4×D511yescharacteristic
394C22×D3—101no—
395C3×Q8—21no—
396C3×Q8—21no—
397C3×D4—21no—
398C3×D4—21no—
399C3×D4—42no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4#70912yes—
405C2×C3×C4D4×D511yescharacteristic
406C2×C3×C4#71112yes—
407C2×C3×C4C23×D511yescharacteristic
408#67—202no—
409#67—202no—
410#67—202no—
411C2×Dic3—51no—
412C2×Dic3—51no—
413C2×Dic3—51no—
414C2×Dic3—51no—
415C2×Dic3—102no—
416C2×Dic3—101no—
417C2×Dic3—201no—
418C2×Dic3—201no—
419C2×Dic3—202no—
420D12—101no—
421D12—101no—
422C4×D3—202no—
423Dic6—101no—
424Dic6—101no—
425C3×C8—22no—
426C3⋊C8—102no—
427C22×C5—21no—
428C22×C5—21no—
429C22×C5—41no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5#88512yes—
433C22×C5C2×D3×D411yescharacteristic
434C2×D5—121no—
435C2×D5—121no—
436C2×D5—121no—
437C4×C5—41no—
438C4×C5—42no—
439C4×C5#88512yes—
440C4×C5C2×#23511yescharacteristic
441C4×C5C2×#23711yescharacteristic
442Dic5—61no—
443Dic5—61no—
444Dic5—61no—
445Dic5—61no—
446Dic5—121no—
447Dic5—122no—
448#41—22no—
449#41—22no—
450#41—302no—
451#41—302no—
452C2×Q8—151no—
453C2×Q8C22×D1511yescharacteristic
454C2×D4—21no—
455C2×D4—151no—
456C2×D4—301no—
457C2×D4—301no—
458C2×D4—301no—
459C2×D4C22×D1511yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—151no—
463C22×C4—151no—
464C22×C4—301no—
465C22×C4—301no—
466C22×C4C22×D1511yescharacteristic
467M16—22no—
468M16—302no—
469C2×C8—152no—
470C2×C8C22×D1512yes—
471C4⋊C4—21no—
472C4⋊C4—152no—
473C4⋊C4—302no—
474C4⋊C4—302no—
475C4⋊C4—302no—
476C4⋊C4—302no—
477C4⋊C4—301no—
478C4⋊C4—301no—
479C4⋊C4—301no—
480C4⋊C4C22×D1512yes—
481C22⋊C4—301no—
482C22⋊C4—301no—
483C22⋊C4—301no—
484C22⋊C4—301no—
485C42—151no—
486C42—151no—
487C42—151no—
488C42—151no—
489C3×C5#314211yescharacteristic, complemented, Hall
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3#403112yes—
496C22×C3C2×D4×D511yescharacteristic
497C2×D3—201no—
498C2×D3—201no—
499C2×D3—201no—
500C3×C4—41no—
501C3×C4—42no—
502C3×C4#403112yes—
503C3×C4C2×#70911yescharacteristic
504C3×C4C2×#71111yescharacteristic
505Dic3—101no—
506Dic3—101no—
507Dic3—101no—
508Dic3—101no—
509Dic3—201no—
510Dic3—202no—
511C2×C5—22no—
512C2×C5—81no—
513C2×C5C2×#88511yescharacteristic
514C2×C5#577311yescharacteristic
515C2×C5#577711yescharacteristic
516D5—241no—
517C23—21no—
518C23—301no—
519C23D4×D1511yescharacteristic
520Q8—21no—
521Q8—21no—
522Q8—301no—
523Q8—301no—
524D4—21no—
525D4—21no—
526D4—42no—
527D4—301no—
528D4—301no—
529D4—602no—
530D4—602no—
531D4—602no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—151no—
537C2×C4—151no—
538C2×C4—151no—
539C2×C4—151no—
540C2×C4—301no—
541C2×C4—302no—
542C2×C4—601no—
543C2×C4—601no—
544C2×C4—602no—
545C2×C4—602no—
546C2×C4#681712yes—
547C2×C4D4×D1511yescharacteristic
548C2×C4#681912yes—
549C2×C4C23×D1511yescharacteristic
550C8—22no—
551C8—302no—
552C2×C3—22no—
553C2×C3—81no—
554C2×C3C2×#403111yescharacteristic
555C2×C3#6610711yescharacteristic
556C2×C3#6611111yescharacteristic
557D3—401no—
558C5#7887911yescharacteristic, complemented, Sylow
559C22—21no—
560C22—21no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—601no—
565C22—601no—
566C22—601no—
567C22#9177412yes—
568C22C2×D4×D1511yescharacteristic
569C4—41no—
570C4—42no—
571C4—301no—
572C4—301no—
573C4—301no—
574C4—301no—
575C4—601no—
576C4—602no—
577C4#9177412yes—
578C4C2×#681711yescharacteristic
579C4C2×#681911yescharacteristic
580C3#1061061011yescharacteristic, complemented, Sylow
581C2—22no—
582C2—81no—
583C2—1201no—
584C2C2×#9177411yescharacteristic
585C2#1175653211yescharacteristic
586C2#1175653611yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#417C2
socleC22×C3×C5C22×D4
prime radical#11756591C2
hypercenter#417D15
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#91779C2semidirect
3. C3×C5×#417C2semidirect
4. #11751333C2semidirect
5. #11751234C2semidirect
6. M16×Dic15C2semidirect
7. #11751067C2semidirect
8. #11750901C2semidirect
9. #11750898C2semidirect
10. #11750869C2semidirect
11. #11750865C2semidirect
47. C5×#417D3semidirect
99. C3×#417D5semidirect
256. #417D15semidirect
489. C3×C5#3142semidirect
558. C5#78879semidirect
580. C3#10610610semidirect

Maximal subgroups

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

subgroupindex
#117565912
C2×#917792
C3×C5×#4172
#117513332
#117512342
M16×Dic152
#117510672
#117509012
#117508982
#117508692
#117508652
#106106103
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