Finite Group Databasebeta

← #14412712

Subgroups — #14412712

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×#92101C211yesmaximal, characteristic
2C2×#91796C211yesmaximal, characteristic, complemented
3#11756263C211yesmaximal, characteristic, complemented
4C3×C5×#417C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11751221C211yesmaximal, characteristic, complemented
7C2×#91094C211yesmaximal, characteristic, complemented
8#11750903C212yesmaximal, complemented
9D15×#103C212yesmaximal, complemented
10#11750873C212yesmaximal, complemented
11#11750872C212yesmaximal, complemented
12#10610614—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14#92101—24no—
15#92101C418yescomplemented
16C2×Q8×D15C2212yes—
17C2×#6819—22no—
18C2×#6819C2212yes—
19C2×#6817—21no—
20C2×#6817C2211yescharacteristic
21C22×Dic30—21no—
22C22×Dic30C2211yescharacteristic
23C2×C3×C5×M16C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C4×#1220—22no—
26#91815C2211yescharacteristic
27C22×C3⋊#168C2211yescharacteristic
28#91796—24no—
29C2×#6705C2212yes—
30C2×C8×D15C2212yes—
31#91782—21no—
32#91781C2212yes—
33C4⋊C4×D15C2212yes—
34#91776—21no—
35C3×C5×#103C2212yes—
36C3×C5×#102C2212yes—
37#91119C2211yescharacteristic
38#91119C2211yescharacteristic
39#91116C2211yescharacteristic
40#91116C2211yescharacteristic
41#91100C2212yes—
42#91100C2212yes—
43#91094C2212yes—
44#91094C2212yes—
45#78883—51nomaximal, Hall
46C2×#4150—31no—
47C2×#4053—31no—
48#65838—31no—
49C5×#417D311yescharacteristic, complemented
50#65522—31no—
51#65409—31no—
52C2×#3942—31no—
53#65091—32no—
54D5×#103—32no—
55#65061—32no—
56#65060—32no—
57C3×C5×#41—22no—
58C3×C5×#41C2×C414yescomplemented
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2311yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×#1220—22no—
66C2×#1220D412yes—
67C22×Dic15—21no—
68C22×Dic15—22no—
69Q8×D15—24no—
70Q8×D15C2×C418yescomplemented
71#6819—216no—
72#6819—24no—
73#6819C2×C418yescomplemented
74#6817—28no—
75#6817C2×C414yes—
76#6817D414yes—
77C2×D60D411yescharacteristic
78C2×C4×D15—22no—
79C2×C4×D15—22no—
80C2×C4×D15C2312yes—
81C2×Dic30—21no—
82C2×Dic30—22no—
83C2×Dic30—22no—
84C2×Dic30—28no—
85C2×Dic30C2×C414yescomplemented
86C2×Dic30D411yescharacteristic
87C2×Dic30C2312yes—
88C3×C5×M16—22no—
89C2×C3×C5×C8C2312yes—
90C3×C5×C4⋊C4—21no—
91C3×C5×C4⋊C4C2312yes—
92#6719—21no—
93#6714—22no—
94C4⋊Dic15C2311yescharacteristic
95C4⋊Dic15C2311yescharacteristic
96#6712—22no—
97C4×Dic15—21no—
98C4×Dic15—22no—
99C2×C3⋊#168—22no—
100C2×C3⋊#168C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102#6705—24no—
103C8×D15—24no—
104C2×#1010—51no—
105C2×#907—51no—
106#5504—51no—
107C3×#417D511yescharacteristic, complemented
108#5233—51no—
109#5120—51no—
110C2×#810—51no—
111#4802—52no—
112D3×#103—52no—
113#4772—52no—
114#4771—52no—
115C2×C5×#41C2×D311yescharacteristic
116#4150—38no—
117#4150—64no—
118C2×Q8×D5—32no—
119C2×#711—32no—
120C2×#711—62no—
121C2×#709—31no—
122C2×#709—61no—
123C22×Dic10—31no—
124C22×Dic10—61no—
125C2×C5×M16C2×D311yescharacteristic
126C2×C5×C4⋊C4C2×D311yescharacteristic
127C4×C22⋊D5—62no—
128#4072—31no—
129C22×#168—31no—
130#4053—64no—
131C2×#676—32no—
132C2×C8×D5—32no—
133#4039—61no—
134#4038—32no—
135D5×C4⋊C4—32no—
136#4033—61no—
137C5×#103C2×D312yes—
138C5×#102C2×D312yes—
139#3967—31no—
140#3967—31no—
141#3964—31no—
142#3964—31no—
143#3948—32no—
144#3948—32no—
145#3942—32no—
146#3942—32no—
147#2898—151noSylow
148C23×C3×C5—21no—
149C23×C3×C5C2×D411yescharacteristic
150C22×D15C2×D412yes—
151C3×C5×Q8—21no—
152C3×C5×Q8C22×C412yes—
153C3×C5×D4—24no—
154C3×C5×D4—21no—
155C3×C5×D4C22×C412yes—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—24no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—81no—
160C2×C3×C4×C5C22×C412yes—
161C2×C3×C4×C5C2×D411yescharacteristic
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2411yescharacteristic
164#1220—28no—
165#1220C22⋊C418yes—
166C2×Dic15—24no—
167C2×Dic15—22no—
168C2×Dic15—28no—
169C2×Dic15—21no—
170C2×Dic15—21no—
171C2×Dic15C2×D412yes—
172D60C22⋊C414yes—
173C4×D15—28no—
174C4×D15—82no—
175C4×D15C22×C414yes—
176C4×D15C2×D414yes—
177Dic30—24no—
178Dic30—22no—
179Dic30—28no—
180Dic30C22⋊C414yes—
181Dic30C22×C414yes—
182C3×C5×C8—22no—
183C3⋊#168—21no—
184C3⋊#168—21no—
185C2×C3×#41C2×D511yescharacteristic
186#1010—58no—
187#1010—104no—
188C2×D3×Q8—52no—
189C2×#237—52no—
190C2×#237—102no—
191C2×#235—51no—
192C2×#235—101no—
193C22×Dic6—51no—
194C22×Dic6—101no—
195C2×C3×M16C2×D511yescharacteristic
196C2×C3×C4⋊C4C2×D511yescharacteristic
197C4×#67—102no—
198#926—51no—
199C22×C3⋊C8—51no—
200#907—104no—
201C2×ΓL(1,𝔽25)—52no—
202C2×D3×C8—52no—
203#893—101no—
204#892—52no—
205D3×C4⋊C4—52no—
206#887—101no—
207C3×#103C2×D512yes—
208C3×#102C2×D512yes—
209#835—51no—
210#835—51no—
211#832—51no—
212#832—51no—
213#816—52no—
214#816—52no—
215#810—52no—
216#810—52no—
217C5×#41—22no—
218C5×#41C4×D314yescomplemented
219C2×C5×Q8C22×D311yescharacteristic
220C2×C5×D4—21no—
221C2×C5×D4C22×D311yescharacteristic
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—32no—
226C2×C22⋊D5—62no—
227C22×Dic5—62no—
228C22×Dic5—61no—
229Q8×D5—38no—
230Q8×D5—64no—
231#711—38no—
232#711—64no—
233#711—616no—
234#709—34no—
235#709—34no—
236#709—68no—
237C2×D20—31no—
238C2×C4×D5—32no—
239C2×C4×D5—62no—
240C2×C4×D5—62no—
241C2×Dic10—31no—
242C2×Dic10—34no—
243C2×Dic10—32no—
244C2×Dic10—68no—
245C2×Dic10—62no—
246C2×Dic10—61no—
247C2×Dic10—62no—
248C5×M16—22no—
249C2×C5×C8C22×D312yes—
250C5×C4⋊C4—21no—
251C5×C4⋊C4C22×D312yes—
252C22⋊Dic5—61no—
253#685—62no—
254C4⋊Dic5—31no—
255C4⋊Dic5—31no—
256#683—62no—
257C4×Dic5—62no—
258C4×Dic5—61no—
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—151no—
268#419—152no—
269#417—152no—
270#417D1511yescharacteristic, complemented
271#416—151no—
272#416—152no—
273C2×#103—151no—
274C2×#103—152no—
275C22×C3×C5—21no—
276C22×C3×C5—21no—
277C22×C3×C5—22no—
278C22×C3×C5—41no—
279C22×C3×C5—41no—
280C22×C3×C5C2×C22⋊C412yes—
281C22×C3×C5C22×D411yescharacteristic
282C2×D15—22no—
283C2×D15—22no—
284C2×D15C2×C22⋊C414yes—
285C3×C4×C5—22no—
286C3×C4×C5—42no—
287C3×C4×C5C2×C22⋊C412yes—
288C3×C4×C5C23×C411yescharacteristic
289C3×C4×C5C22×D411yescharacteristic
290Dic15—24no—
291Dic15—41no—
292Dic15—41no—
293Dic15C2×C22⋊C414yes—
294C3×#41—22no—
295C3×#41C4×D514yescomplemented
296C2×C3×Q8C22×D511yescharacteristic
297C2×C3×D4—21no—
298C2×C3×D4C22×D511yescharacteristic
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—52no—
303C2×#67—102no—
304C22×Dic3—102no—
305C22×Dic3—101no—
306D3×Q8—58no—
307D3×Q8—104no—
308#237—58no—
309#237—104no—
310#237—1016no—
311#235—54no—
312#235—54no—
313#235—108no—
314C2×D12—51no—
315C2×C4×D3—52no—
316C2×C4×D3—102no—
317C2×C4×D3—102no—
318C2×Dic6—51no—
319C2×Dic6—54no—
320C2×Dic6—52no—
321C2×Dic6—108no—
322C2×Dic6—102no—
323C2×Dic6—101no—
324C2×Dic6—102no—
325C3×M16—22no—
326C2×C3×C8C22×D512yes—
327C3×C4⋊C4—21no—
328C3×C4⋊C4C22×D512yes—
329#217—101no—
330(C2×D3)⋊C4—102no—
331C4⋊Dic3—51no—
332C4⋊Dic3—51no—
333Dic3⋊C4—102no—
334C4×Dic3—102no—
335C4×Dic3—101no—
336C2×C3⋊C8—51no—
337C2×C3⋊C8—51no—
338C2×C3⋊C8—102no—
339ΓL(1,𝔽25)—104no—
340D3×C8—104no—
341C23×C5—21no—
342C23×C5D3×D411yescharacteristic
343C22×D5—32no—
344C5×Q8—21no—
345C5×Q8C2×C4×D312yes—
346C5×D4—24no—
347C5×D4—21no—
348C5×D4C2×C4×D312yes—
349C2×C4×C5—21no—
350C2×C4×C5—24no—
351C2×C4×C5—22no—
352C2×C4×C5—81no—
353C2×C4×C5C2×C4×D312yes—
354C2×C4×C5D3×D411yescharacteristic
355C2×C4×C5D3×D412yes—
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—38no—
358C22⋊D5—68no—
359C2×Dic5—32no—
360C2×Dic5—68no—
361C2×Dic5—64no—
362C2×Dic5—62no—
363C2×Dic5—61no—
364C2×Dic5—61no—
365D20—34no—
366C4×D5—34no—
367C4×D5—34no—
368C4×D5—68no—
369C4×D5—242no—
370Dic10—34no—
371Dic10—34no—
372Dic10—68no—
373Dic10—64no—
374Dic10—62no—
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—301no—
383C2×#41—302no—
384C2×#41C2×D1511yescharacteristic
385C22×Q8—152no—
386C22×Q8—151no—
387C22×Q8—301no—
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—151no—
397#117—152no—
398C2×C4⋊C4—152no—
399C2×C4⋊C4C2×D1511yescharacteristic
400#103—151no—
401#103—151no—
402#103—152no—
403#103—152no—
404#103—152no—
405#103—152no—
406#103C2×D1512yes—
407#102—151no—
408#102—151no—
409#102C2×D1512yes—
410C2×C3×C5—22no—
411C2×C3×C5—42no—
412C2×C3×C5C22×C22⋊C411yescharacteristic
413C2×C3×C5#57711yescharacteristic
414C2×C3×C5#57811yescharacteristic
415D15—24no—
416C23×C3—21no—
417C23×C3D4×D511yescharacteristic
418C22×D3—52no—
419C3×Q8—21no—
420C3×Q8C2×C4×D512yes—
421C3×D4—24no—
422C3×D4—21no—
423C3×D4C2×C4×D512yes—
424C2×C3×C4—21no—
425C2×C3×C4—24no—
426C2×C3×C4—22no—
427C2×C3×C4—81no—
428C2×C3×C4C2×C4×D512yes—
429C2×C3×C4D4×D512yes—
430C2×C3×C4D4×D511yescharacteristic
431C2×C3×C4C23×D511yescharacteristic
432#67—58no—
433#67—108no—
434C2×Dic3—52no—
435C2×Dic3—108no—
436C2×Dic3—102no—
437C2×Dic3—104no—
438C2×Dic3—101no—
439C2×Dic3—101no—
440D12—54no—
441C4×D3—54no—
442C4×D3—54no—
443C4×D3—108no—
444C4×D3—402no—
445Dic6—54no—
446Dic6—54no—
447Dic6—108no—
448Dic6—102no—
449Dic6—104no—
450C3×C8—22no—
451C3⋊C8—101no—
452C3⋊C8—101no—
453C22×C5—21no—
454C22×C5—21no—
455C22×C5—22no—
456C22×C5—41no—
457C22×C5—41no—
458C22×C5D3×C22⋊C412yes—
459C22×C5C2×D3×D411yescharacteristic
460C2×D5—34no—
461C2×D5—62no—
462C2×D5—62no—
463C4×C5—22no—
464C4×C5—42no—
465C4×C5D3×C22⋊C412yes—
466C4×C5C22×C4×D311yescharacteristic
467C4×C5C2×D3×D411yescharacteristic
468Dic5—34no—
469Dic5—64no—
470Dic5—121no—
471Dic5—121no—
472#41—22no—
473#41—154no—
474#41—154no—
475#41—158no—
476#41—308no—
477#41—304no—
478#41—3016no—
479#41C4×D1514yescomplemented
480C2×Q8—151no—
481C2×Q8—158no—
482C2×Q8—154no—
483C2×Q8—152no—
484C2×Q8—302no—
485C2×Q8—308no—
486C2×Q8—304no—
487C2×Q8—301no—
488C2×Q8—302no—
489C2×Q8C22×D1511yescharacteristic
490C2×D4—21no—
491C2×D4—152no—
492C2×D4—151no—
493C2×D4—302no—
494C2×D4C22×D1511yescharacteristic
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—152no—
498C22×C4—302no—
499C22×C4—302no—
500C22×C4—302no—
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—21no—
511C4⋊C4—151no—
512C4⋊C4—151no—
513C4⋊C4—302no—
514C4⋊C4C22×D1512yes—
515C22⋊C4—302no—
516C22⋊C4—301no—
517C42—302no—
518C42—301no—
519C3×C5#289811yescharacteristic, complemented, Hall
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—22no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3D5×C22⋊C412yes—
526C22×C3C2×D4×D511yescharacteristic
527C2×D3—54no—
528C2×D3—102no—
529C2×D3—102no—
530C3×C4—22no—
531C3×C4—42no—
532C3×C4D5×C22⋊C412yes—
533C3×C4C22×C4×D511yescharacteristic
534C3×C4C2×D4×D511yescharacteristic
535Dic3—54no—
536Dic3—104no—
537Dic3—201no—
538Dic3—201no—
539C2×C5—22no—
540C2×C5—42no—
541C2×C5C2×D3×C22⋊C411yescharacteristic
542C2×C5#577511yescharacteristic
543C2×C5#577911yescharacteristic
544D5—64no—
545C23—21no—
546C23—152no—
547C23D4×D1511yescharacteristic
548Q8—21no—
549Q8—154no—
550Q8—154no—
551Q8—308no—
552Q8—304no—
553Q8—302no—
554Q8C2×C4×D1512yes—
555D4—24no—
556D4—21no—
557D4—158no—
558D4—154no—
559D4—308no—
560D4C2×C4×D1512yes—
561C2×C4—21no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—81no—
565C2×C4—152no—
566C2×C4—154no—
567C2×C4—154no—
568C2×C4—308no—
569C2×C4—308no—
570C2×C4—304no—
571C2×C4—302no—
572C2×C4—301no—
573C2×C4—301no—
574C2×C4—1202no—
575C2×C4C2×C4×D1512yes—
576C2×C4D4×D1511yescharacteristic
577C2×C4D4×D1512yes—
578C2×C4C23×D1511yescharacteristic
579C8—22no—
580C8—301no—
581C8—301no—
582C2×C3—22no—
583C2×C3—42no—
584C2×C3C2×D5×C22⋊C411yescharacteristic
585C2×C3#6610911yescharacteristic
586C2×C3#6611311yescharacteristic
587D3—104no—
588C5#7888311yescharacteristic, complemented, Sylow
589C22—21no—
590C22—21no—
591C22—22no—
592C22—41no—
593C22—41no—
594C22—154no—
595C22—302no—
596C22—302no—
597C22C22⋊C4×D1512yes—
598C22C2×D4×D1511yescharacteristic
599C4—22no—
600C4—42no—
601C4—154no—
602C4—304no—
603C4—601no—
604C4—601no—
605C4C22⋊C4×D1512yes—
606C4C22×C4×D1511yescharacteristic
607C4C2×D4×D1511yescharacteristic
608C3#1061061411yescharacteristic, complemented, Sylow
609C2—22no—
610C2—42no—
611C2—304no—
612C2C2×C22⋊C4×D1511yescharacteristic
613C2#1175653411yescharacteristic
614C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#417C2
socleC22×C3×C5C22×D4
prime radicalC2×#92101C2
cosocleC2×C3×C4×C5C24
hypercenter#417D15
hypocenterC3×C5#2898
LCSG ▷ 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×#91796C2semidirect
3. #11756263C2semidirect
4. C3×C5×#417C2semidirect
5. #11751334C2semidirect
6. #11751221C2semidirect
7. C2×#91094C2semidirect
8. #11750903C2semidirect
9. D15×#103C2semidirect
10. #11750873C2semidirect
11. #11750872C2semidirect
15. #92101C4semidirect
49. C5×#417D3semidirect
58. C3×C5×#41C2×C4semidirect
70. Q8×D15C2×C4semidirect
73. #6819C2×C4semidirect
85. C2×Dic30C2×C4semidirect
107. C3×#417D5semidirect
218. C5×#41C4×D3semidirect
270. #417D15semidirect
295. C3×#41C4×D5semidirect
479. #41C4×D15semidirect
519. C3×C5#2898semidirect
588. C5#78883semidirect
608. C3#10610614semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
C2×#917962
#117562632
C3×C5×#4172
#117513342
#117512212
C2×#910942
#117509032
D15×#1032
#117508732
#117508722
#106106143
#788835