Finite Group Databasebeta

← #14412715

Subgroups — #14412715

Order 1920.

1452 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92098C211yesmaximal, characteristic
2C2×#91796C211yesmaximal, characteristic, complemented
3#11756282C211yesmaximal, characteristic, complemented
4C3×C5×#419C211yesmaximal, characteristic, complemented
5C2×#91119C211yesmaximal, characteristic, complemented
6#11751234C211yesmaximal, characteristic, complemented
7#11751103C211yesmaximal, characteristic, complemented
8#11750905C212yesmaximal, complemented
9#11750904C212yesmaximal, complemented
10#11750903C212yesmaximal, complemented
11D15×#103C212yesmaximal, complemented
12#10610688—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14#92098—24no—
15#92098C418yescomplemented
16C2×#6821—21no—
17C2×#6821C2212yes—
18C2×Q8×D15—21no—
19C2×Q8×D15C2212yes—
20C2×#6817—22no—
21C2×#6817C2211yescharacteristic
22C2×#6817C2211yescharacteristic
23C2×C3×C5×M16C2211yescharacteristic
24C3×C5×#117C2211yescharacteristic
25C2×C4⋊Dic15C2211yescharacteristic
26C22×C3⋊#168C2211yescharacteristic
27#91796—24no—
28C2×#6705C2212yes—
29C2×C8×D15C2212yes—
30#91781C2212yes—
31C4⋊C4×D15C2212yes—
32#91770—22no—
33C4×D60—21no—
34C4×Dic30—21no—
35C3×C5×#103C2212yes—
36C3×C5×#103C2212yes—
37#91119C2212yes—
38#91119C2212yes—
39#91105C2212yes—
40#91100C2212yes—
41#91094C2211yescharacteristic
42#91094C2211yescharacteristic
43#91093C2211yescharacteristic
44#91093C2211yescharacteristic
45#78957—51nomaximal, Hall
46C2×#4147—31no—
47C2×#4053—31no—
48#65857—31no—
49C5×#419D311yescharacteristic, complemented
50C2×#3967—31no—
51#65422—31no—
52#65291—31no—
53#65093—32no—
54#65092—32no—
55#65091—32no—
56D5×#103—32no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8C2×C414yescomplemented
60C2×C3×C5×Q8C2312yes—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64C2×#1220D412yes—
65C22×Dic15—21no—
66#6821—28no—
67#6821—24no—
68#6821C2×C418yescomplemented
69Q8×D15—24no—
70Q8×D15—28no—
71Q8×D15C2×C418yescomplemented
72#6817—22no—
73#6817—216no—
74#6817C2×C414yes—
75#6817C2×C414yescomplemented
76#6817D414yes—
77C2×D60—22no—
78C2×D60D411yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—22no—
81C2×C4×D15—21no—
82C2×C4×D15—22no—
83C2×C4×D15—22no—
84C2×C4×D15C2312yes—
85C2×Dic30—22no—
86C2×Dic30D411yescharacteristic
87C2×Dic30C2311yescharacteristic
88C3×C5×M16—22no—
89C2×C3×C5×C8C2312yes—
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C5×C4⋊C4C2311yescharacteristic
92C3×C5×C22⋊C4—21no—
93C3×C42×C5—21no—
94#6714—22no—
95C4⋊Dic15—21no—
96C4⋊Dic15C2312yes—
97#6712—22no—
98C4×Dic15—22no—
99C2×C3⋊#168—22no—
100C2×C3⋊#168C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102#6705—24no—
103C8×D15—24no—
104C2×#1007—51no—
105C2×#907—51no—
106#5523—51no—
107C3×#419D511yescharacteristic, complemented
108C2×#835—51no—
109#5133—51no—
110#5002—51no—
111#4804—52no—
112#4803—52no—
113#4802—52no—
114D3×#103—52no—
115C22×C5×Q8C2×D311yescharacteristic
116#4147—38no—
117#4147—64no—
118C2×#713—32no—
119C2×#713—61no—
120C2×Q8×D5—32no—
121C2×Q8×D5—61no—
122C2×#709—31no—
123C2×#709—31no—
124C2×#709—62no—
125C2×C5×M16C2×D311yescharacteristic
126C5×#117C2×D311yescharacteristic
127C2×C4⋊Dic5—31no—
128C22×#168—31no—
129#4053—64no—
130C2×#676—32no—
131C2×C8×D5—32no—
132#4038—32no—
133D5×C4⋊C4—32no—
134#4027—62no—
135C4×D20—61no—
136C4×Dic10—61no—
137C5×#103C2×D312yes—
138C5×#103C2×D312yes—
139#3967—32no—
140#3967—32no—
141#3953—32no—
142#3948—32no—
143#3942—31no—
144#3942—31no—
145#3941—31no—
146#3941—31no—
147#2898—151noSylow
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—21no—
150C22×D15C2×D412yes—
151C3×C5×Q8—24no—
152C3×C5×Q8—22no—
153C3×C5×Q8C22×C414yes—
154C2×C3×C4×C5—24no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—21no—
158C2×C3×C4×C5C22×C412yes—
159C2×C3×C4×C5C2×D411yescharacteristic
160C2×C3×C4×C5C2×D412yes—
161C2×C3×C4×C5C2411yescharacteristic
162#1220—24no—
163#1220C22⋊C418yes—
164C2×Dic15—21no—
165C2×Dic15—22no—
166C2×Dic15—81no—
167C2×Dic15C2×D412yes—
168D60—28no—
169D60—21no—
170D60C22⋊C414yes—
171D60C22×C412yes—
172C4×D15—28no—
173C4×D15—24no—
174C4×D15—28no—
175C4×D15—82no—
176C4×D15C22×C414yes—
177C4×D15C2×D414yes—
178Dic30—21no—
179Dic30—28no—
180Dic30C22⋊C414yes—
181Dic30C22×C412yes—
182C3×C5×C8—22no—
183C3⋊#168—21no—
184C3⋊#168—21no—
185C22×C3×Q8C2×D511yescharacteristic
186#1007—58no—
187#1007—104no—
188C2×#239—52no—
189C2×#239—101no—
190C2×D3×Q8—52no—
191C2×D3×Q8—101no—
192C2×#235—51no—
193C2×#235—51no—
194C2×#235—102no—
195C2×C3×M16C2×D511yescharacteristic
196C3×#117C2×D511yescharacteristic
197C2×C4⋊Dic3—51no—
198C22×C3⋊C8—51no—
199#907—104no—
200C2×ΓL(1,𝔽25)—52no—
201C2×D3×C8—52no—
202#892—52no—
203D3×C4⋊C4—52no—
204#67⋊C4—102no—
205C4×D12—101no—
206C4×Dic6—101no—
207C3×#103C2×D512yes—
208C3×#103C2×D512yes—
209#835—52no—
210#835—52no—
211#821—52no—
212#816—52no—
213#810—51no—
214#810—51no—
215#809—51no—
216#809—51no—
217C2×C5×Q8—21no—
218C2×C5×Q8—22no—
219C2×C5×Q8C4×D314yescomplemented
220C2×C5×Q8C22×D312yes—
221C22×C4×C5—21no—
222C22×C4×C5C22×D311yescharacteristic
223C2×C22⋊D5—32no—
224C2×C22⋊D5—61no—
225C22×Dic5—61no—
226#713—38no—
227#713—64no—
228#713—68no—
229Q8×D5—38no—
230Q8×D5—68no—
231Q8×D5—64no—
232#709—34no—
233#709—34no—
234#709—34no—
235#709—616no—
236#709—62no—
237C2×D20—31no—
238C2×D20—31no—
239C2×D20—62no—
240C2×C4×D5—32no—
241C2×C4×D5—62no—
242C2×C4×D5—62no—
243C2×C4×D5—61no—
244C2×C4×D5—62no—
245C2×Dic10—31no—
246C2×Dic10—31no—
247C2×Dic10—62no—
248C5×M16—22no—
249C2×C5×C8C22×D312yes—
250C5×C4⋊C4C22×D311yescharacteristic
251C5×C4⋊C4C22×D311yescharacteristic
252C5×C22⋊C4—21no—
253C42×C5—21no—
254#685—62no—
255C4⋊Dic5—32no—
256C4⋊Dic5—61no—
257#683—62no—
258C4×Dic5—62no—
259C2×#168—31no—
260C2×#168—31no—
261C2×#168—62no—
262#676—64no—
263C8×D5—64no—
264C2×2−1+4—151no—
265C2×#131—151no—
266#520—151no—
267#419—152no—
268#419D1511yescharacteristic, complemented
269#417—151no—
270#417—152no—
271#416—151no—
272#416—152no—
273C2×#103—151no—
274C2×#103—152no—
275C22×C3×C5—21no—
276C22×C3×C5—21no—
277C22×C3×C5C2×C22⋊C412yes—
278C22×C3×C5C22×D411yescharacteristic
279C2×D15—22no—
280C2×D15—22no—
281C2×D15—22no—
282C2×D15—41no—
283C2×D15—41no—
284C2×D15C2×C22⋊C414yes—
285C3×C4×C5—24no—
286C3×C4×C5—41no—
287C3×C4×C5—41no—
288C3×C4×C5C2×C22⋊C412yes—
289C3×C4×C5C23×C411yescharacteristic
290C3×C4×C5C22×D411yescharacteristic
291Dic15—22no—
292Dic15—42no—
293Dic15C2×C22⋊C414yes—
294C2×C3×Q8—21no—
295C2×C3×Q8—22no—
296C2×C3×Q8C4×D514yescomplemented
297C2×C3×Q8C22×D512yes—
298C22×C3×C4—21no—
299C22×C3×C4C22×D511yescharacteristic
300C2×#67—52no—
301C2×#67—101no—
302C22×Dic3—101no—
303#239—58no—
304#239—104no—
305#239—108no—
306D3×Q8—58no—
307D3×Q8—108no—
308D3×Q8—104no—
309#235—54no—
310#235—54no—
311#235—54no—
312#235—1016no—
313#235—102no—
314C2×D12—51no—
315C2×D12—51no—
316C2×D12—102no—
317C2×C4×D3—52no—
318C2×C4×D3—102no—
319C2×C4×D3—102no—
320C2×C4×D3—101no—
321C2×C4×D3—102no—
322C2×Dic6—51no—
323C2×Dic6—51no—
324C2×Dic6—102no—
325C3×M16—22no—
326C2×C3×C8C22×D512yes—
327C3×C4⋊C4C22×D511yescharacteristic
328C3×C4⋊C4C22×D511yescharacteristic
329C3×C22⋊C4—21no—
330C3×C42—21no—
331(C2×D3)⋊C4—102no—
332C4⋊Dic3—52no—
333C4⋊Dic3—101no—
334Dic3⋊C4—102no—
335C4×Dic3—102no—
336C2×C3⋊C8—51no—
337C2×C3⋊C8—51no—
338C2×C3⋊C8—102no—
339ΓL(1,𝔽25)—104no—
340D3×C8—104no—
341C23×C5D3×D411yescharacteristic
342C22×D5—32no—
343C22×D5—61no—
344C5×Q8—24no—
345C5×Q8—22no—
346C5×Q8C2×C4×D314yes—
347C2×C4×C5—24no—
348C2×C4×C5—22no—
349C2×C4×C5—21no—
350C2×C4×C5—21no—
351C2×C4×C5C2×C4×D312yes—
352C2×C4×C5D3×D411yescharacteristic
353C2×C4×C5D3×D412yes—
354C2×C4×C5C23×D311yescharacteristic
355C22⋊D5—38no—
356C22⋊D5—64no—
357C2×Dic5—32no—
358C2×Dic5—61no—
359C2×Dic5—62no—
360C2×Dic5—241no—
361D20—34no—
362D20—32no—
363D20—68no—
364D20—61no—
365C4×D5—34no—
366C4×D5—34no—
367C4×D5—68no—
368C4×D5—68no—
369C4×D5—64no—
370C4×D5—242no—
371Dic10—34no—
372Dic10—32no—
373Dic10—68no—
374Dic10—61no—
375C5×C8—22no—
376#168—61no—
377#168—61no—
3782−1+4—158no—
3792−1+4—304no—
380C2×#41—151no—
381C2×#41—152no—
382C2×#41—151no—
383C2×#41—302no—
384C2×#41—301no—
385C22×Q8—152no—
386C22×Q8—301no—
387C22×Q8C2×D1511yescharacteristic
388#131—304no—
389C2×M16—152no—
390C2×M16C2×D1511yescharacteristic
391C22×C8—151no—
392C22×C8—152no—
393C4×Q8—301no—
394C4×D4—301no—
395C4×D4—302no—
396#117—152no—
397#117C2×D1511yescharacteristic
398C2×C4⋊C4—151no—
399C2×C4⋊C4—152no—
400#103—152no—
401#103—152no—
402#103—152no—
403#103—151no—
404#103—151no—
405#103C2×D1512yes—
406#103C2×D1512yes—
407#102—152no—
408#102—151no—
409#102—151no—
410C2×C3×C5—22no—
411C2×C3×C5C22×C22⋊C411yescharacteristic
412C2×C3×C5#57711yescharacteristic
413C2×C3×C5#57811yescharacteristic
414D15—24no—
415D15—42no—
416C23×C3D4×D511yescharacteristic
417C22×D3—52no—
418C22×D3—101no—
419C3×Q8—22no—
420C3×Q8—24no—
421C3×Q8C2×C4×D514yes—
422C2×C3×C4—22no—
423C2×C3×C4—24no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4C2×C4×D512yes—
427C2×C3×C4D4×D512yes—
428C2×C3×C4D4×D511yescharacteristic
429C2×C3×C4C23×D511yescharacteristic
430#67—58no—
431#67—104no—
432C2×Dic3—52no—
433C2×Dic3—101no—
434C2×Dic3—102no—
435C2×Dic3—401no—
436D12—52no—
437D12—54no—
438D12—108no—
439D12—101no—
440C4×D3—54no—
441C4×D3—54no—
442C4×D3—108no—
443C4×D3—108no—
444C4×D3—104no—
445C4×D3—402no—
446Dic6—54no—
447Dic6—52no—
448Dic6—108no—
449Dic6—101no—
450C3×C8—22no—
451C3⋊C8—101no—
452C3⋊C8—101no—
453C22×C5—21no—
454C22×C5—21no—
455C22×C5D3×C22⋊C412yes—
456C22×C5C2×D3×D411yescharacteristic
457C2×D5—34no—
458C2×D5—62no—
459C2×D5—62no—
460C2×D5—62no—
461C2×D5—121no—
462C2×D5—121no—
463C4×C5—24no—
464C4×C5—41no—
465C4×C5—41no—
466C4×C5D3×C22⋊C412yes—
467C4×C5C22×C4×D311yescharacteristic
468C4×C5C2×D3×D411yescharacteristic
469Dic5—34no—
470Dic5—62no—
471Dic5—122no—
472#41—154no—
473#41—154no—
474#41—158no—
475#41—154no—
476#41—3016no—
477#41—304no—
478#41—308no—
479#41—302no—
480C2×Q8—21no—
481C2×Q8—22no—
482C2×Q8—151no—
483C2×Q8—158no—
484C2×Q8—151no—
485C2×Q8—302no—
486C2×Q8—304no—
487C2×Q8—308no—
488C2×Q8C4×D1514yescomplemented
489C2×Q8C22×D1512yes—
490C2×D4—152no—
491C2×D4—151no—
492C2×D4—151no—
493C2×D4—302no—
494C2×D4—301no—
495C22×C4—21no—
496C22×C4—152no—
497C22×C4—302no—
498C22×C4—302no—
499C22×C4—302no—
500C22×C4—301no—
501C22×C4—301no—
502C22×C4C22×D1511yescharacteristic
503M16—22no—
504M16—304no—
505C2×C8—151no—
506C2×C8—151no—
507C2×C8—304no—
508C2×C8—302no—
509C2×C8C22×D1512yes—
510C4⋊C4—152no—
511C4⋊C4—302no—
512C4⋊C4—301no—
513C4⋊C4C22×D1511yescharacteristic
514C4⋊C4C22×D1511yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—302no—
517C42—21no—
518C42—302no—
519C3×C5#289811yescharacteristic, complemented, Hall
520C22×C3—21no—
521C22×C3—21no—
522C22×C3D5×C22⋊C412yes—
523C22×C3C2×D4×D511yescharacteristic
524C2×D3—54no—
525C2×D3—102no—
526C2×D3—102no—
527C2×D3—102no—
528C2×D3—201no—
529C2×D3—201no—
530C3×C4—24no—
531C3×C4—41no—
532C3×C4—41no—
533C3×C4D5×C22⋊C412yes—
534C3×C4C22×C4×D511yescharacteristic
535C3×C4C2×D4×D511yescharacteristic
536Dic3—54no—
537Dic3—102no—
538Dic3—202no—
539C2×C5—22no—
540C2×C5C2×D3×C22⋊C411yescharacteristic
541C2×C5#577811yescharacteristic
542C2×C5#577911yescharacteristic
543D5—64no—
544D5—122no—
545C23—152no—
546C23—301no—
547C23D4×D1511yescharacteristic
548Q8—24no—
549Q8—22no—
550Q8—154no—
551Q8—152no—
552Q8—308no—
553Q8—301no—
554Q8C2×C4×D1514yes—
555D4—158no—
556D4—154no—
557D4—152no—
558D4—308no—
559D4—304no—
560D4—301no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—152no—
566C2×C4—154no—
567C2×C4—154no—
568C2×C4—308no—
569C2×C4—308no—
570C2×C4—301no—
571C2×C4—304no—
572C2×C4—302no—
573C2×C4—1202no—
574C2×C4—1201no—
575C2×C4C2×C4×D1512yes—
576C2×C4D4×D1511yescharacteristic
577C2×C4D4×D1512yes—
578C2×C4C23×D1511yescharacteristic
579C8—22no—
580C8—301no—
581C8—301no—
582C2×C3—22no—
583C2×C3C2×D5×C22⋊C411yescharacteristic
584C2×C3#6611211yescharacteristic
585C2×C3#6611311yescharacteristic
586D3—104no—
587D3—202no—
588C5#7895711yescharacteristic, complemented, Sylow
589C22—21no—
590C22—21no—
591C22—154no—
592C22—302no—
593C22—302no—
594C22—302no—
595C22—601no—
596C22—601no—
597C22C22⋊C4×D1512yes—
598C22C2×D4×D1511yescharacteristic
599C4—24no—
600C4—41no—
601C4—41no—
602C4—154no—
603C4—302no—
604C4—602no—
605C4C22⋊C4×D1512yes—
606C4C22×C4×D1511yescharacteristic
607C4C2×D4×D1511yescharacteristic
608C3#1061068811yescharacteristic, complemented, Sylow
609C2—22no—
610C2—304no—
611C2—602no—
612C2C2×C22⋊C4×D1511yescharacteristic
613C2#1175653711yescharacteristic
614C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#419C2
socleC22×C3×C5C22×D4
prime radicalC2×#92098C2
cosocleC2×C3×C4×C5C24
hypercenter#419D15
hypocenterC3×C5#2898
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C2×#91796C2semidirect
3. #11756282C2semidirect
4. C3×C5×#419C2semidirect
5. C2×#91119C2semidirect
6. #11751234C2semidirect
7. #11751103C2semidirect
8. #11750905C2semidirect
9. #11750904C2semidirect
10. #11750903C2semidirect
11. D15×#103C2semidirect
15. #92098C4semidirect
49. C5×#419D3semidirect
59. C2×C3×C5×Q8C2×C4semidirect
68. #6821C2×C4semidirect
71. Q8×D15C2×C4semidirect
75. #6817C2×C4semidirect
107. C3×#419D5semidirect
219. C2×C5×Q8C4×D3semidirect
268. #419D15semidirect
296. C2×C3×Q8C4×D5semidirect
488. C2×Q8C4×D15semidirect
519. C3×C5#2898semidirect
588. C5#78957semidirect
608. C3#10610688semidirect

Maximal subgroups

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

subgroupindex
C2×#920982
C2×#917962
#117562822
C3×C5×#4192
C2×#911192
#117512342
#117511032
#117509052
#117509042
#117509032
D15×#1032
#106106883
#789575