Finite Group Databasebeta

← #14302160

Subgroups — #14302160

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×#91466C211yesmaximal, characteristic
3C2×C5×#823C211yesmaximal, characteristic, complemented
4C2×#90959C211yesmaximal, characteristic, complemented
5#11748351C211yesmaximal, characteristic, complemented
6C3×#64774C211yesmaximal, characteristic, complemented
7#11745985C211yesmaximal, characteristic, complemented
8#10600874—31nomaximal, Hall
9C22×C4×D15C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C22×#1203C412yes—
12C2×C3×C5×M16C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14M16×D15—22no—
15M16×D15—22no—
16C2×#6705—21no—
17C2×C8×D15—21no—
18C2×C5×#208C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21C2×(C2×D3)⋊Dic5C412yes—
22#91466—21no—
23#91466—21no—
24#91466—21no—
25#91466—21no—
26C5×#823—22no—
27#90959—22no—
28#90957—21no—
29#90957—21no—
30#68992—51nomaximal, Hall
31C2×#4084—31no—
32C2×D5×M16—31no—
33C2×C5×#100—31no—
34C2×#3965—31no—
35#65415—31no—
36#64774—31no—
37#64774D311yescharacteristic, complemented
38C23×D15C2×C411yescharacteristic
39C23×C5×D3C2×C412yes—
40C22×C3×C4×C5C2311yescharacteristic
41C22×Dic15C2×C411yescharacteristic
42C2×C4×D15—21no—
43C2×C4×D15—21no—
44C2×C4×D15—21no—
45C2×C4×D15—21no—
46C2×C4×D15D411yescharacteristic
47C2×C4×D15D411yescharacteristic
48C2×C4×D15D411yescharacteristic
49C2×C4×D15D411yescharacteristic
50C2×C5×D12—21no—
51C2×C5×D12—21no—
52C2×C5×D12—21no—
53C2×C5×D12—21no—
54C2×C5×D12—21no—
55C2×C5×D12—21no—
56C22×C3×Dic5C2×C412yes—
57C2×#1203—22no—
58C2×#1203—22no—
59C2×#1203—44no—
60C3×C5×M16—21no—
61C3×C5×M16D412yescomplemented
62C2×C3×C5×C8—21no—
63#6710—21no—
64#6710D412yescomplemented
65C2×C3⋊#168—21no—
66#6705—24no—
67C8×D15—24no—
68C5×#208—21no—
69C5×#208—21no—
70C2×C5×C3⋊C8—21no—
71C3×C4⋊Dic5—21no—
72C3×C4⋊Dic5—21no—
73C3×#681—21no—
74C3×#681—21no—
75C2×C3×#168—21no—
76(C2×D3)⋊Dic5—22no—
77(C2×D3)⋊Dic5—22no—
78C2×D3×M16—51no—
79C2×#895—51no—
80C2×#823—51no—
81C2×#823D511yescharacteristic, complemented
82#5126—51no—
83C3×#343—51no—
84#4530—51no—
85C22×C5×D4—31no—
86C22×C22⋊D5—32no—
87C22×C4×D5—31no—
88C2×C5×M16—31no—
89C2×C5×M16C2×D311yescharacteristic
90C2×C22⋊Dic5—32no—
91#4084—61no—
92#4084—61no—
93#4084—61no—
94#4084—61no—
95C2×C4⋊Dic5C2×D311yescharacteristic
96C2×#681—31no—
97C2×#681C2×D311yescharacteristic
98D5×M16—62no—
99D5×M16—62no—
100C2×#676—61no—
101C2×C8×D5—61no—
102C5×#100—62no—
103#3965—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—41no—
112C22×D15C22⋊C411yescharacteristic
113C22×D15C22⋊C411yescharacteristic
114C22×C5×D3—22no—
115C22×C5×D3—22no—
116C22×C5×D3—22no—
117C22×C5×D3—42no—
118C22×C5×D3—42no—
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2×D411yescharacteristic
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D411yescharacteristic
123C2×C3×C4×C5#4111yescharacteristic
124C2×C3×C4×C5#4111yescharacteristic
125C2×Dic15—21no—
126C2×Dic15—21no—
127C2×Dic15C22⋊C411yescharacteristic
128C2×Dic15C22⋊C411yescharacteristic
129C4×D15—21no—
130C4×D15—21no—
131C4×D15—21no—
132C4×D15—21no—
133C4×D15—21no—
134C4×D15—21no—
135C4×D15—21no—
136C4×D15—21no—
137C5×D12—41no—
138C5×D12—41no—
139C5×D12—41no—
140C5×D12—41no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—42no—
143#1203—44no—
144#1203—44no—
145C3×C5×C8—22no—
146C3⋊#168—22no—
147C3×#168—41no—
148C5×C3⋊C8—41no—
149C22×D12—52no—
150C22×D12C2×D511yescharacteristic
151C22×C4×D3—51no—
152C2×C3×M16—51no—
153C2×C3×M16C2×D511yescharacteristic
154C2×C3×C4⋊C4—51no—
155C2×(C2×D3)⋊C4—52no—
156C2×#208—51no—
157C2×#208C2×D511yescharacteristic
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—22no—
167#823—102no—
168(C2×D3)⋊C8—101no—
169(C2×D3)⋊C8—101no—
170C24×C5—32no—
171C23×D5—31no—
172C2×C5×D4—61no—
173C2×C5×D4—61no—
174C2×C5×D4—61no—
175C2×C5×D4—61no—
176C2×C5×D4—61no—
177C2×C5×D4—61no—
178C22×C4×C5C22×D311yescharacteristic
179C2×C22⋊D5—62no—
180C2×C22⋊D5—62no—
181C2×C22⋊D5—124no—
182C22×Dic5—31no—
183C22×Dic5C4×D312yes—
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—61no—
194C5×M16—61no—
195C5×M16D1212yescomplemented
196C2×C5×C8—21no—
197C2×C5×C8—61no—
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202#681—21no—
203#681—21no—
204#681—32no—
205#681—61no—
206C2×#168—21no—
207C2×#168—61no—
208#676—64no—
209C8×D5—64no—
210C22×M16—151no—
211C2×#121—151no—
212C2×#100—31no—
213C2×#100—151no—
214#407—151no—
215#343—51no—
216#343—151no—
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#10012yescomplemented
230C2×C5×D3—42no—
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C2×C5×D3—82no—
234C2×C5×D3—82no—
235C3×C4×C5#12011yescharacteristic
236C3×C4×C5#12111yescharacteristic
237C3×C4×C5#12111yescharacteristic
238C3×C4×C5#12311yescharacteristic
239Dic15—21no—
240Dic15—21no—
241C3×Dic5—42no—
242C23×D3—51no—
243C23×D3C4×D512yes—
244C22×C3×C4—52no—
245C22×C3×C4C22×D511yescharacteristic
246C22×Dic3—51no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—102no—
254C2×D12—102no—
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—101no—
266C3×M16—101no—
267C3×M16C22⋊D512yescomplemented
268C2×C3×C8—21no—
269C2×C3×C8—101no—
270C3×C4⋊C4—101no—
271C3×C4⋊C4—101no—
272(C2×D3)⋊C4—102no—
273(C2×D3)⋊C4—102no—
274#208—21no—
275#208—21no—
276#208—52no—
277#208—101no—
278C2×C3⋊C8—21no—
279C2×C3⋊C8—101no—
280ΓL(1,𝔽25)—104no—
281D3×C8—104no—
282C23×C5—62no—
283C23×C5—62no—
284C23×C5—62no—
285C23×C5—122no—
286C23×C5—122no—
287C23×C5C2×C4×D311yescharacteristic
288C22×D5—31no—
289C22×D5—31no—
290C22×D5—62no—
291C22×D5—61no—
292C22×D5—61no—
293C22×D5—121no—
294C5×D4—121no—
295C5×D4—121no—
296C5×D4—121no—
297C5×D4—121no—
298C2×C4×C5C2×D1211yescharacteristic
299C2×C4×C5#23511yescharacteristic
300C2×C4×C5D3×D411yescharacteristic
301C2×C4×C5D3×D411yescharacteristic
302C2×C4×C5D3×D411yescharacteristic
303C2×C4×C5#23911yescharacteristic
304C22⋊D5—124no—
305C22⋊D5—124no—
306C2×Dic5—22no—
307C2×Dic5—31no—
308C2×Dic5—31no—
309C2×Dic5—42no—
310C2×Dic5—61no—
311C2×Dic5—61no—
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—121no—
322#168—41no—
323#168—62no—
324C22×D4—31no—
325C22×D4—152no—
326C23×C4—151no—
327C2×M16—31no—
328C2×M16—51no—
329C2×M16—151no—
330C2×M16—301no—
331C2×M16—302no—
332C2×M16—302no—
333C2×M16D3×D511yescharacteristic
334C22×C8—301no—
335#121—301no—
336#121—301no—
337#121—301no—
338#121—301no—
339C2×C4⋊C4—51no—
340C2×C22⋊C4—152no—
341#100—62no—
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—
352C5×D3—82no—
353C23×C3C2×C4×D511yescharacteristic
354C22×D3—22no—
355C22×D3—22no—
356C22×D3—22no—
357C22×D3—42no—
358C22×D3—42no—
359C22×D3—51no—
360C22×D3—51no—
361C22×D3—102no—
362C22×D3—101no—
363C22×D3—101no—
364C22×D3—201no—
365C2×C3×C4—102no—
366C2×C3×C4—202no—
367C2×C3×C4#70911yescharacteristic
368C2×C3×C4D4×D511yescharacteristic
369C2×C3×C4D4×D511yescharacteristic
370C2×C3×C4D4×D511yescharacteristic
371C2×C3×C4#71111yescharacteristic
372C2×C3×C4C2×C22⋊D511yescharacteristic
373C2×Dic3—51no—
374C2×Dic3—51no—
375C2×Dic3—101no—
376C2×Dic3—101no—
377D12—41no—
378D12—41no—
379D12—41no—
380D12—41no—
381D12—204no—
382D12—204no—
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—201no—
393C3⋊C8—41no—
394C3⋊C8—102no—
395C22×C5—21no—
396C22×C5—21no—
397C22×C5—122no—
398C22×C5—122no—
399C22×C5—122no—
400C22×C5—242no—
401C22×C5—242no—
402C22×C5C4×D1211yescharacteristic
403C22×C5D3×C22⋊C411yescharacteristic
404C22×C5#89311yescharacteristic
405C2×D5—32no—
406C2×D5—61no—
407C2×D5—61no—
408C2×D5—61no—
409C2×D5—61no—
410C2×D5—61no—
411C2×D5—122no—
412C2×D5—122no—
413C4×C5#88211yescharacteristic
414C4×C5#88411yescharacteristic
415C4×C5#89411yescharacteristic
416C4×C5#89511yescharacteristic
417Dic5—42no—
418Dic5—61no—
419Dic5—61no—
420C24—32no—
421C24—151no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—302no—
429C2×D4—302no—
430C2×D4—604no—
431C22×C4—52no—
432C22×C4—151no—
433C22×C4—151no—
434C22×C4—151no—
435C22×C4—151no—
436C22×C4—151no—
437C22×C4—301no—
438C22×C4—301no—
439C22×C4—301no—
440C22×C4—301no—
441C22×C4C2×D3×D511yescharacteristic
442M16—21no—
443M16—61no—
444M16—61no—
445M16—101no—
446M16—101no—
447M16—152no—
448M16—304no—
449M16—301no—
450M16#120312yescomplemented
451C2×C8—21no—
452C2×C8—61no—
453C2×C8—101no—
454C2×C8—304no—
455C2×C8—301no—
456C4⋊C4—101no—
457C4⋊C4—101no—
458C22⋊C4—302no—
459C22⋊C4—302no—
460C3×C5#190011yescharacteristic, complemented, Hall
461C22×C3—21no—
462C22×C3—21no—
463C22×C3D5×C22⋊C411yescharacteristic
464C22×C3#402711yescharacteristic
465C22×C3C4×C22⋊D511yescharacteristic
466C2×D3—42no—
467C2×D3—42no—
468C2×D3—42no—
469C2×D3—52no—
470C2×D3—82no—
471C2×D3—82no—
472C2×D3—101no—
473C2×D3—101no—
474C2×D3—101no—
475C2×D3—101no—
476C2×D3—101no—
477C2×D3—202no—
478C2×D3—202no—
479C3×C4—202no—
480C3×C4#402911yescharacteristic
481C3×C4#403011yescharacteristic
482C3×C4#408311yescharacteristic
483C3×C4#408411yescharacteristic
484Dic3—101no—
485Dic3—101no—
486C2×C5—21no—
487C2×C5—21no—
488C2×C5—242no—
489C2×C5#466511yescharacteristic
490C2×C5D3×#10011yescharacteristic
491C2×C5#475111yescharacteristic
492D5—62no—
493D5—121no—
494C23—62no—
495C23—62no—
496C23—62no—
497C23—122no—
498C23—122no—
499C23—151no—
500C23—151no—
501C23—302no—
502C23—301no—
503C23—301no—
504C23—601no—
505C23C4×D3×D511yescharacteristic
506D4—121no—
507D4—121no—
508D4—121no—
509D4—121no—
510D4—604no—
511D4—604no—
512C2×C4—102no—
513C2×C4—151no—
514C2×C4—151no—
515C2×C4—202no—
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×C4#676811yescharacteristic
527C2×C4#677111yescharacteristic
528C2×C4#677711yescharacteristic
529C2×C4C2×#120311yescharacteristic
530C2×C4#679011yescharacteristic
531C2×C4#679011yescharacteristic
532C8—22no—
533C8—121no—
534C8—201no—
535C8—302no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3D5×#10011yescharacteristic
539C2×C3#6503411yescharacteristic
540C2×C3#6524511yescharacteristic
541D3—82no—
542D3—102no—
543D3—201no—
544C5#6899211yescharacteristic, complemented, Sylow
545C22—21no—
546C22—21no—
547C22—122no—
548C22—122no—
549C22—122no—
550C22—152no—
551C22—242no—
552C22—242no—
553C22—301no—
554C22—301no—
555C22—301no—
556C22—301no—
557C22—301no—
558C22—602no—
559C22—602no—
560C22#9140611yescharacteristic
561C22C4×#120311yescharacteristic
562C22#9147311yescharacteristic
563C4—202no—
564C4—301no—
565C4—301no—
566C4#9135511yescharacteristic
567C4#9146111yescharacteristic
568C4#9146611yescharacteristic
569C4#9157311yescharacteristic
570C3#1060087411yescharacteristic, complemented, Sylow
571C2—21no—
572C2—21no—
573C2—242no—
574C2—302no—
575C2—601no—
576C2#1174822411yescharacteristic
577C2#1174823911yescharacteristic
578C2#1174891811yescharacteristic
subgroupG/H
centerC22#91473
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91466C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1900
LCSG ▷ C23×C3×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
1. C2×M16×D15C2semidirect
3. C2×C5×#823C2semidirect
4. C2×#90959C2semidirect
5. #11748351C2semidirect
6. C3×#64774C2semidirect
7. #11745985C2semidirect
37. #64774D3semidirect
61. C3×C5×M16D4semidirect
64. #6710D4semidirect
81. C2×#823D5semidirect
195. C5×M16D12semidirect
229. C2×D15#100semidirect
267. C3×M16C22⋊D5semidirect
450. M16#1203semidirect
460. C3×C5#1900semidirect
544. C5#68992semidirect
570. C3#10600874semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D152
C2×#914662
C2×C5×#8232
C2×#909592
#117483512
C3×#647742
#117459852
#106008743
#689925