Finite Group Databasebeta

← #14302142

Subgroups — #14302142

Order 1920.

780 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×D15C211yesmaximal, characteristic, complemented
2C2×#91784C211yesmaximal, characteristic
3C2×#91107C211yesmaximal, characteristic, complemented
4C2×#91107C211yesmaximal, characteristic, complemented
5#11751227C211yesmaximal, characteristic, complemented
6C3×C5×#343C211yesmaximal, characteristic, complemented
7#11746351C211yesmaximal, characteristic, complemented
8#10599785—31nomaximal, Hall
9C22×D60C412yes—
10C22×D60C2211yescharacteristic
11C22×C4×D15C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C2×#6714C412yes—
16C2×#6710C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18M16×D15—22no—
19M16×D15—22no—
20C2×#6705—21no—
21C2×C8×D15—21no—
22#91784—21no—
23#91784—21no—
24#91784—21no—
25#91784—21no—
26#91107—22no—
27#91107—22no—
28#91104—21no—
29#91104—21no—
30#68992—51nomaximal, Hall
31C2×D5×M16—31no—
32C2×#4041—31no—
33C2×#3955—31no—
34C2×#3955—31no—
35#65415—31no—
36C5×#343D311yescharacteristic, complemented
37#64750—31no—
38C23×D15C2×C411yescharacteristic
39C23×D15C2×C412yes—
40C22×C3×C4×C5C2×C412yes—
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15C2×C411yescharacteristic
43C2×D60—22no—
44C2×D60—22no—
45C2×D60—21no—
46C2×D60—21no—
47C2×D60—21no—
48C2×D60—21no—
49C2×D60—21no—
50C2×D60—21no—
51C2×D60—44no—
52C2×C4×D15—21no—
53C2×C4×D15—21no—
54C2×C4×D15—21no—
55C2×C4×D15—21no—
56C2×C4×D15D411yescharacteristic
57C2×C4×D15D411yescharacteristic
58C2×C4×D15D411yescharacteristic
59C2×C4×D15D411yescharacteristic
60C3×C5×M16—21no—
61C3×C5×M16—21no—
62C3×C5×M16—21no—
63C3×C5×M16D412yescomplemented
64C2×C3×C5×C8—21no—
65C2×C3×C5×C8—21no—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4—21no—
68#6714—22no—
69#6714—22no—
70#6710—21no—
71#6710—21no—
72#6710—21no—
73#6710D412yescomplemented
74C2×C3⋊#168—21no—
75C2×C3⋊#168—21no—
76#6705—24no—
77C8×D15—24no—
78C2×D3×M16—51no—
79C2×#895—51no—
80C2×#823—51no—
81C2×#823—51no—
82#5126—51no—
83C3×#343D511yescharacteristic, complemented
84#4530—51no—
85C22×D20—31no—
86C22×D20—32no—
87C22×C4×D5—31no—
88C2×C5×M16C2×D311yescharacteristic
89C2×C5×M16C2×D311yescharacteristic
90C2×C5×C4⋊C4C2×D311yescharacteristic
91C2×#685—32no—
92C2×#681—31no—
93C2×#681—31no—
94D5×M16—62no—
95D5×M16—62no—
96C2×#676—61no—
97C2×C8×D5—61no—
98#4041—61no—
99#4041—61no—
100#4041—61no—
101#4041—61no—
102#3955—62no—
103#3955—62no—
104#3952—61no—
105#3952—61no—
106#1900—151noSylow
107C23×C3×C5C22×C411yescharacteristic
108C22×D15—21no—
109C22×D15—21no—
110C22×D15—22no—
111C22×D15—22no—
112C22×D15—22no—
113C22×D15—22no—
114C22×D15—41no—
115C22×D15—42no—
116C22×D15—42no—
117C22×D15C22⋊C411yescharacteristic
118C22×D15C22⋊C411yescharacteristic
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—42no—
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5#4111yescharacteristic
126C2×C3×C4×C5#4111yescharacteristic
127C2×Dic15—21no—
128C2×Dic15—21no—
129C2×Dic15C22⋊C411yescharacteristic
130C2×Dic15C22⋊C411yescharacteristic
131D60—44no—
132D60—44no—
133D60—41no—
134D60—41no—
135D60—41no—
136D60—41no—
137C4×D15—21no—
138C4×D15—21no—
139C4×D15—21no—
140C4×D15—21no—
141C4×D15—21no—
142C4×D15—21no—
143C4×D15—21no—
144C4×D15—21no—
145C3×C5×C8—22no—
146C3×C5×C8—41no—
147C3⋊#168—22no—
148C3⋊#168—41no—
149C22×D12—51no—
150C22×D12—52no—
151C22×C4×D3—51no—
152C2×C3×M16C2×D511yescharacteristic
153C2×C3×M16C2×D511yescharacteristic
154C2×C3×C4⋊C4C2×D511yescharacteristic
155C2×(C2×D3)⋊C4—52no—
156C2×#208—51no—
157C2×#208—51no—
158D3×M16—102no—
159D3×M16—102no—
160C2×ΓL(1,𝔽25)—101no—
161C2×D3×C8—101no—
162#895—101no—
163#895—101no—
164#895—101no—
165#895—101no—
166#823—102no—
167#823—102no—
168(C2×D3)⋊C8—101no—
169(C2×D3)⋊C8—101no—
170C23×D5—31no—
171C23×D5—32no—
172C22×C4×C5C4×D312yes—
173C22×C4×C5C22×D311yescharacteristic
174C22×Dic5—31no—
175C2×D20—62no—
176C2×D20—62no—
177C2×D20—61no—
178C2×D20—61no—
179C2×D20—61no—
180C2×D20—61no—
181C2×D20—61no—
182C2×D20—61no—
183C2×D20—124no—
184C2×C4×D5—31no—
185C2×C4×D5—31no—
186C2×C4×D5—31no—
187C2×C4×D5—31no—
188C2×C4×D5—61no—
189C2×C4×D5—61no—
190C2×C4×D5—61no—
191C2×C4×D5—61no—
192C5×M16—21no—
193C5×M16—21no—
194C5×M16—21no—
195C5×M16D1212yescomplemented
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200#685—62no—
201#685—62no—
202#681—32no—
203#681—61no—
204#681—61no—
205#681—61no—
206C2×#168—61no—
207C2×#168—61no—
208#676—64no—
209C8×D5—64no—
210C22×M16—151no—
211C2×#121—151no—
212C2×#100—151no—
213C2×#100—151no—
214#407—151no—
215#343—151no—
216#343D1511yescharacteristic, complemented
217C22×C3×C5—21no—
218C22×C3×C5—21no—
219C22×C3×C5C2×C22⋊C411yescharacteristic
220C22×C3×C5C4×D411yescharacteristic
221C22×C3×C5C4×D411yescharacteristic
222C2×D15—21no—
223C2×D15—21no—
224C2×D15—21no—
225C2×D15—21no—
226C2×D15—21no—
227C2×D15—42no—
228C2×D15—42no—
229C2×D15—42no—
230C2×D15—42no—
231C2×D15—42no—
232C2×D15—82no—
233C2×D15—82no—
234C2×D15#10012yescomplemented
235C3×C4×C5—42no—
236C3×C4×C5#12011yescharacteristic
237C3×C4×C5#12111yescharacteristic
238C3×C4×C5#12111yescharacteristic
239C3×C4×C5#12311yescharacteristic
240Dic15—21no—
241Dic15—21no—
242C23×D3—51no—
243C23×D3—52no—
244C22×C3×C4C4×D512yes—
245C22×C3×C4C22×D511yescharacteristic
246C22×Dic3—51no—
247C2×D12—102no—
248C2×D12—102no—
249C2×D12—101no—
250C2×D12—101no—
251C2×D12—101no—
252C2×D12—101no—
253C2×D12—101no—
254C2×D12—101no—
255C2×D12—204no—
256C2×C4×D3—51no—
257C2×C4×D3—51no—
258C2×C4×D3—51no—
259C2×C4×D3—51no—
260C2×C4×D3—101no—
261C2×C4×D3—101no—
262C2×C4×D3—101no—
263C2×C4×D3—101no—
264C3×M16—21no—
265C3×M16—21no—
266C3×M16—21no—
267C3×M16D2012yescomplemented
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272(C2×D3)⋊C4—102no—
273(C2×D3)⋊C4—102no—
274#208—52no—
275#208—101no—
276#208—101no—
277#208—101no—
278C2×C3⋊C8—101no—
279C2×C3⋊C8—101no—
280ΓL(1,𝔽25)—104no—
281D3×C8—104no—
282C23×C5C2×C4×D311yescharacteristic
283C22×D5—31no—
284C22×D5—31no—
285C22×D5—62no—
286C22×D5—61no—
287C22×D5—61no—
288C22×D5—62no—
289C22×D5—62no—
290C22×D5—62no—
291C22×D5—121no—
292C22×D5—122no—
293C22×D5—122no—
294C2×C4×C5—22no—
295C2×C4×C5—42no—
296C2×C4×C5C2×D1211yescharacteristic
297C2×C4×C5#23511yescharacteristic
298C2×C4×C5D3×D411yescharacteristic
299C2×C4×C5D3×D411yescharacteristic
300C2×C4×C5D3×D411yescharacteristic
301C2×C4×C5#23911yescharacteristic
302C2×Dic5—31no—
303C2×Dic5—31no—
304C2×Dic5—61no—
305C2×Dic5—61no—
306D20—124no—
307D20—124no—
308D20—121no—
309D20—121no—
310D20—121no—
311D20—121no—
312C4×D5—61no—
313C4×D5—61no—
314C4×D5—61no—
315C4×D5—61no—
316C4×D5—61no—
317C4×D5—61no—
318C4×D5—61no—
319C4×D5—61no—
320C5×C8—22no—
321C5×C8—41no—
322#168—62no—
323#168—121no—
324C22×D4—152no—
325C22×D4—151no—
326C23×C4—151no—
327C2×M16—151no—
328C2×M16—151no—
329C2×M16—301no—
330C2×M16—302no—
331C2×M16—302no—
332C2×M16C2×D1511yescharacteristic
333C2×M16C2×D1511yescharacteristic
334C22×C8—301no—
335#121—301no—
336#121—301no—
337#121—301no—
338#121—301no—
339C2×C4⋊C4C2×D1511yescharacteristic
340C2×C22⋊C4—152no—
341#100—302no—
342#100—302no—
343C22⋊C8—301no—
344C22⋊C8—301no—
345C2×C3×C5—21no—
346C2×C3×C5—21no—
347C2×C3×C5#38611yescharacteristic
348C2×C3×C5C2×#10011yescharacteristic
349C2×C3×C5#41311yescharacteristic
350D15—22no—
351D15—41no—
352D15—82no—
353C23×C3C2×C4×D511yescharacteristic
354C22×D3—51no—
355C22×D3—51no—
356C22×D3—102no—
357C22×D3—101no—
358C22×D3—101no—
359C22×D3—102no—
360C22×D3—102no—
361C22×D3—102no—
362C22×D3—201no—
363C22×D3—202no—
364C22×D3—202no—
365C2×C3×C4—22no—
366C2×C3×C4—42no—
367C2×C3×C4C2×D2011yescharacteristic
368C2×C3×C4#70911yescharacteristic
369C2×C3×C4D4×D511yescharacteristic
370C2×C3×C4D4×D511yescharacteristic
371C2×C3×C4D4×D511yescharacteristic
372C2×C3×C4#71311yescharacteristic
373C2×Dic3—51no—
374C2×Dic3—51no—
375C2×Dic3—101no—
376C2×Dic3—101no—
377D12—204no—
378D12—204no—
379D12—201no—
380D12—201no—
381D12—201no—
382D12—201no—
383C4×D3—101no—
384C4×D3—101no—
385C4×D3—101no—
386C4×D3—101no—
387C4×D3—101no—
388C4×D3—101no—
389C4×D3—101no—
390C4×D3—101no—
391C3×C8—22no—
392C3×C8—41no—
393C3⋊C8—102no—
394C3⋊C8—201no—
395C22×C5—21no—
396C22×C5—21no—
397C22×C5C4×D1211yescharacteristic
398C22×C5D3×C22⋊C411yescharacteristic
399C22×C5#89311yescharacteristic
400C2×D5—32no—
401C2×D5—61no—
402C2×D5—61no—
403C2×D5—61no—
404C2×D5—61no—
405C2×D5—61no—
406C2×D5—122no—
407C2×D5—122no—
408C2×D5—122no—
409C2×D5—122no—
410C2×D5—122no—
411C2×D5—242no—
412C2×D5—242no—
413C4×C5—42no—
414C4×C5#88211yescharacteristic
415C4×C5#88411yescharacteristic
416C4×C5#89411yescharacteristic
417C4×C5#89511yescharacteristic
418Dic5—61no—
419Dic5—61no—
420C24—151no—
421C24—152no—
422C2×D4—302no—
423C2×D4—302no—
424C2×D4—301no—
425C2×D4—301no—
426C2×D4—301no—
427C2×D4—301no—
428C2×D4—301no—
429C2×D4—301no—
430C2×D4—604no—
431C22×C4—151no—
432C22×C4—151no—
433C22×C4—151no—
434C22×C4—151no—
435C22×C4—151no—
436C22×C4—301no—
437C22×C4—301no—
438C22×C4—301no—
439C22×C4—301no—
440C22×C4C4×D1512yes—
441C22×C4C22×D1511yescharacteristic
442M16—21no—
443M16—21no—
444M16—21no—
445M16—152no—
446M16—304no—
447M16—301no—
448M16—301no—
449M16—301no—
450M16D6012yescomplemented
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—304no—
454C2×C8—301no—
455C2×C8—301no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C22⋊C4—302no—
459C22⋊C4—302no—
460C3×C5#190011yescharacteristic, complemented, Hall
461C22×C3—21no—
462C22×C3—21no—
463C22×C3C4×D2011yescharacteristic
464C22×C3D5×C22⋊C411yescharacteristic
465C22×C3#403911yescharacteristic
466C2×D3—52no—
467C2×D3—101no—
468C2×D3—101no—
469C2×D3—101no—
470C2×D3—101no—
471C2×D3—101no—
472C2×D3—202no—
473C2×D3—202no—
474C2×D3—202no—
475C2×D3—202no—
476C2×D3—202no—
477C2×D3—402no—
478C2×D3—402no—
479C3×C4—42no—
480C3×C4#402811yescharacteristic
481C3×C4#403011yescharacteristic
482C3×C4#404011yescharacteristic
483C3×C4#404111yescharacteristic
484Dic3—101no—
485Dic3—101no—
486C2×C5—21no—
487C2×C5—21no—
488C2×C5#466511yescharacteristic
489C2×C5D3×#10011yescharacteristic
490C2×C5#475111yescharacteristic
491D5—62no—
492D5—121no—
493D5—242no—
494C23—151no—
495C23—151no—
496C23—302no—
497C23—301no—
498C23—301no—
499C23—302no—
500C23—302no—
501C23—302no—
502C23—601no—
503C23—602no—
504C23—602no—
505C23C2×C4×D1511yescharacteristic
506D4—604no—
507D4—604no—
508D4—601no—
509D4—601no—
510D4—601no—
511D4—601no—
512C2×C4—22no—
513C2×C4—42no—
514C2×C4—151no—
515C2×C4—151no—
516C2×C4—301no—
517C2×C4—301no—
518C2×C4—301no—
519C2×C4—301no—
520C2×C4—301no—
521C2×C4—301no—
522C2×C4—301no—
523C2×C4—301no—
524C2×C4—301no—
525C2×C4—301no—
526C2×C4C2×D6011yescharacteristic
527C2×C4#681711yescharacteristic
528C2×C4D4×D1511yescharacteristic
529C2×C4D4×D1511yescharacteristic
530C2×C4D4×D1511yescharacteristic
531C2×C4#682111yescharacteristic
532C8—22no—
533C8—41no—
534C8—302no—
535C8—601no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3#6495411yescharacteristic
539C2×C3D5×#10011yescharacteristic
540C2×C3#6504011yescharacteristic
541D3—102no—
542D3—201no—
543D3—402no—
544C5#6899211yescharacteristic, complemented, Sylow
545C22—21no—
546C22—21no—
547C22—152no—
548C22—301no—
549C22—301no—
550C22—301no—
551C22—301no—
552C22—301no—
553C22—602no—
554C22—602no—
555C22—602no—
556C22—602no—
557C22—602no—
558C22—1202no—
559C22—1202no—
560C22C4×D6011yescharacteristic
561C22C22⋊C4×D1511yescharacteristic
562C22#9178211yescharacteristic
563C4—42no—
564C4—301no—
565C4—301no—
566C4#9177111yescharacteristic
567C4#9177311yescharacteristic
568C4#9178311yescharacteristic
569C4#9178411yescharacteristic
570C3#1059978511yescharacteristic, complemented, Sylow
571C2—21no—
572C2—21no—
573C2—302no—
574C2—601no—
575C2—1202no—
576C2#1175076611yescharacteristic
577C2D15×#10011yescharacteristic
578C2#1175085211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#343C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91784C2
cosocleC22×C3×C4×C5C23
hypercenter#343D15
hypocenterC3×C5#1900
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×M16×D15C2semidirect
3. C2×#91107C2semidirect
4. C2×#91107C2semidirect
5. #11751227C2semidirect
6. C3×C5×#343C2semidirect
7. #11746351C2semidirect
36. C5×#343D3semidirect
63. C3×C5×M16D4semidirect
73. #6710D4semidirect
83. C3×#343D5semidirect
195. C5×M16D12semidirect
216. #343D15semidirect
234. C2×D15#100semidirect
267. C3×M16D20semidirect
450. M16D60semidirect
460. C3×C5#1900semidirect
544. C5#68992semidirect
570. C3#10599785semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D152
C2×#917842
C2×#911072
#117512272
C3×C5×#3432
#117463512
#105997853
#689925