Finite Group Databasebeta

← #14429243

Subgroups — #14429243

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65860C211yesmaximal, characteristic, complemented
2#11754607C211yesmaximal, characteristic
3C2×#91309C211yesmaximal, characteristic, complemented
4C2×#91283C211yesmaximal, characteristic, complemented
5#11751096C211yesmaximal, characteristic, complemented
6C5×#5002C211yesmaximal, characteristic, complemented
7C2×#90971C211yesmaximal, characteristic, complemented
8#11747343C212yesmaximal, complemented
9#11747341C212yesmaximal, complemented
10#11747311C212yesmaximal, complemented
11#11747309C212yesmaximal, complemented
12#10610572—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C22×C3×Dic10C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C22×C5×C3⋊C8C2211yescharacteristic
20C3×#4043C2212yes—
21C3×#4043C2212yes—
22C3×#4032—22no—
23C3×#4021—21no—
24C3×#4015—21no—
25#91571—22no—
26#91456—21no—
27#91449C2212yes—
28#91369—21no—
29#91359C2212yes—
30C2×#6661C2212yes—
31#91309—24no—
32C2×#6656C2212yes—
33C2×#6649C2212yes—
34#91283—24no—
35C2×D5×C3⋊C8C2212yes—
36#91092C2212yes—
37#91091C2212yes—
38C5×#810C2211yescharacteristic
39C5×#810C2211yescharacteristic
40C5×#809C2211yescharacteristic
41C5×#809C2211yescharacteristic
42#90971C2212yes—
43#90971C2212yes—
44#83400—51nomaximal, Hall
45#66167—31no—
46C2×#4097—31no—
47C2×#4047—31no—
48#65860D311yescharacteristic, complemented
49C5×#416—31no—
50C2×#3948—31no—
51#65284—31no—
52#65105—32no—
53#65102—32no—
54#65069—32no—
55#65067—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15—21no—
58C2×C5×#67—21no—
59C5×#235—22no—
60C5×#235—22no—
61C2×C5×D12C2311yescharacteristic
62C2×C4×C5×D3—21no—
63C2×C5×Dic6C2311yescharacteristic
64C2×C3×C22⋊D5D412yes—
65C22×C3×Dic5—21no—
66C3×#709—22no—
67C3×#709—22no—
68C2×C3×D20D411yescharacteristic
69C2×C3×C4×D5C2312yes—
70C2×C3×Dic10—22no—
71C2×C3×Dic10—22no—
72C2×C3×Dic10—21no—
73C2×C3×Dic10D411yescharacteristic
74C2×C3×Dic10C2312yes—
75C2×#1201—22no—
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C4⋊C4C2311yescharacteristic
78C3×C5×C22⋊C4—21no—
79C3×C42×C5—21no—
80C4⋊Dic15—21no—
81C4⋊Dic15C2312yes—
82#6710D414yescomplemented
83C2×C3⋊#168C2312yes—
84C2×C5×C3⋊C8—22no—
85C2×C5×C3⋊C8C2311yescharacteristic
86C2×C5×C3⋊C8C2311yescharacteristic
87C3×#685—22no—
88C3×#685—22no—
89C3×C4⋊Dic5—22no—
90C3×C4⋊Dic5—22no—
91#6669—22no—
92(C2×D3)⋊Dic5—22no—
93#6665—22no—
94#6661—24no—
95#6656—24no—
96#6649—24no—
97D5×C3⋊C8—24no—
98C3×#536—51no—
99#5833—51no—
100C2×#948—51no—
101C2×#942—51no—
102C2×#835—51no—
103#5052—52no—
104#5051—52no—
105#5049—52no—
106#5048—52no—
107#5002D511yescharacteristic, complemented
108#4995—51no—
109C2×C5×#41—31no—
110C2×#709C2×D311yescharacteristic
111C22×Dic10C2×D311yescharacteristic
112C22×C5×C8—31no—
113C5×#117C2×D311yescharacteristic
114#4097—64no—
115#4092—32no—
116C2×#689—32no—
117#4085—62no—
118#4084—32no—
119C2×#687—32no—
120#4076—61no—
121C2×C4⋊Dic5—31no—
122#4070—61no—
123C2×#681—31no—
124#4047—64no—
125C2×#676—32no—
126C2×C8×D5—32no—
127#4043C2×D312yes—
128#4043C2×D312yes—
129#4032—22no—
130#4021—21no—
131#4015—21no—
132C5×#103—31no—
133C5×#103—31no—
134C5×#102—31no—
135C5×#102—31no—
136#3948—32no—
137#3948—32no—
138#3940—32no—
139#3939—32no—
140#3063—151noSylow
141C23×C3×C5C2×D411yescharacteristic
142C22×C5×D3—21no—
143C22×C3×D5C2×D412yes—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5#4112yes—
149C2×C3×C4×C5C2411yescharacteristic
150C2×Dic15—22no—
151C2×Dic15—81no—
152C5×#67—42no—
153C2×C5×Dic3—21no—
154C5×D12—21no—
155C5×D12—21no—
156C4×C5×D3—42no—
157C5×Dic6—21no—
158C5×Dic6—21no—
159C3×C22⋊D5—24no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—42no—
162C2×C3×Dic5C2×D412yes—
163C3×D20—22no—
164C3×C4×D5—22no—
165C3×C4×D5—22no—
166C3×Dic10—22no—
167C3×Dic10—22no—
168C3×Dic10—22no—
169C3×Dic10—42no—
170#1201—82no—
171C3⋊#168C2×D414yes—
172C5×C3⋊C8—21no—
173C5×C3⋊C8—21no—
174C2×C3×#41—51no—
175C22×C3×Q8—51no—
176C2×#235C2×D511yescharacteristic
177C3×C4⋊Q8—101no—
178C3×#124—101no—
179C3×#123—102no—
180C3×C22⋊Q8—52no—
181C3×C22⋊Q8—52no—
182C3×#117C2×D511yescharacteristic
183#948—104no—
184#946—101no—
185C2×#216—52no—
186#942—104no—
187C2×#215—52no—
188#939—102no—
189#938—101no—
190#930—52no—
191C2×C4⋊Dic3—51no—
192#924—52no—
193C2×#208—51no—
194C2×#208—52no—
195C22×C3⋊C8—52no—
196C22×C3⋊C8C2×D511yescharacteristic
197#835—52no—
198#835—52no—
199#810C2×D511yescharacteristic
200#810C2×D511yescharacteristic
201#809C2×D511yescharacteristic
202#809C2×D511yescharacteristic
203#808—52no—
204#807—52no—
205C5×#41—62no—
206C5×#41—62no—
207C2×C5×Q8—31no—
208C2×C5×D4—31no—
209C2×C5×D4—61no—
210C22×C4×C5—61no—
211C22×C4×C5C22×D311yescharacteristic
212C2×C22⋊D5—62no—
213C2×C22⋊D5#6712yes—
214C22×Dic5—21no—
215C22×Dic5—61no—
216#709—22no—
217#709—22no—
218C2×D20#6711yescharacteristic
219C2×C4×D5C22×D312yes—
220C2×Dic10—22no—
221C2×Dic10—22no—
222C2×Dic10—21no—
223C2×Dic10#6711yescharacteristic
224C2×Dic10C22×D312yes—
225C2×C5×C8—31no—
226C2×C5×C8—31no—
227C2×C5×C8—62no—
228C5×C4⋊C4C22×D311yescharacteristic
229C5×C4⋊C4C22×D311yescharacteristic
230C5×C22⋊C4—21no—
231C42×C5—21no—
232C22⋊Dic5—62no—
233#689—64no—
234#687—64no—
235#685—22no—
236#685—22no—
237#685—62no—
238C4⋊Dic5—22no—
239C4⋊Dic5—22no—
240C4⋊Dic5—32no—
241C4⋊Dic5—61no—
242#683—62no—
243#681—34no—
244C2×#168—32no—
245#676—64no—
246C8×D5—64no—
247C2×#137—151no—
248C2×#131—151no—
249#537—151no—
250#536—51no—
251#470—152no—
252#468—152no—
253#467—152no—
254#465—152no—
255#428—151no—
256#416—31no—
257C2×#103—151no—
258C22×C3×C5—21no—
259C22×C3×C5—21no—
260C22×C3×C5#12112yes—
261C22×C3×C5C22×D411yescharacteristic
262C2×C5×D3—41no—
263C2×C5×D3—41no—
264C2×C5×D3—41no—
265C2×C3×D5—22no—
266C2×C3×D5—22no—
267C2×C3×D5—22no—
268C3×C4×C5—41no—
269C3×C4×C5—41no—
270C3×C4×C5#12112yes—
271C3×C4×C5C22×D411yescharacteristic
272C3×C4×C5C2×#4111yescharacteristic
273Dic15—42no—
274C3×Dic5—22no—
275C3×Dic5—42no—
276C5×Dic3—41no—
277C3×#41—102no—
278C3×#41—102no—
279C2×C3×Q8—51no—
280C2×C3×Q8—52no—
281C2×C3×Q8—101no—
282C2×C3×Q8—102no—
283C2×C3×Q8—102no—
284C2×C3×D4—52no—
285C2×C3×D4—51no—
286C22×C3×C4—52no—
287C22×C3×C4—101no—
288C22×C3×C4C22×D511yescharacteristic
289C2×#67—21no—
290C2×#67—102no—
291C22×Dic3—101no—
292#235—22no—
293#235—22no—
294C2×D12C22×D511yescharacteristic
295C2×C4×D3—21no—
296C2×Dic6C22×D511yescharacteristic
297C3×C4⋊C4—102no—
298C3×C4⋊C4—102no—
299C3×C4⋊C4C22×D511yescharacteristic
300C3×C4⋊C4C22×D511yescharacteristic
301C3×C22⋊C4—21no—
302C3×C22⋊C4—102no—
303C3×C22⋊C4—102no—
304C3×C42—21no—
305#217—102no—
306#216—104no—
307#215—104no—
308(C2×D3)⋊C4—102no—
309C4⋊Dic3—52no—
310C4⋊Dic3—101no—
311Dic3⋊C4—102no—
312#208—54no—
313#208—104no—
314C2×C3⋊C8—22no—
315C2×C3⋊C8—52no—
316C2×C3⋊C8—104no—
317C2×C3⋊C8C22×D511yescharacteristic
318C2×C3⋊C8C22×D511yescharacteristic
319C23×C5—61no—
320C23×C5C2×#6711yescharacteristic
321C22×D5C2×#6712yes—
322C5×Q8—61no—
323C5×Q8—61no—
324C5×D4—61no—
325C5×D4—61no—
326C5×D4—122no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—61no—
330C2×C4×C5—122no—
331C2×C4×C5D3×D412yes—
332C2×C4×C5#23712yes—
333C2×C4×C5C2×#6711yescharacteristic
334C2×C4×C5C23×D311yescharacteristic
335C22⋊D5—24no—
336C22⋊D5—242no—
337C2×Dic5—22no—
338C2×Dic5—42no—
339C2×Dic5—62no—
340C2×Dic5—241no—
341C2×Dic5C2×#6712yes—
342D20—22no—
343C4×D5—22no—
344C4×D5—22no—
345Dic10—22no—
346Dic10—22no—
347Dic10—22no—
348Dic10—42no—
349C5×C8—61no—
350C5×C8—61no—
351#168—34no—
352C2×#41—31no—
353C2×#41—51no—
354C22×Q8—51no—
355#137—304no—
356C2×Q16—152no—
357C2×SD16—152no—
358#131—304no—
359C2×M16—152no—
360C2×M16—151no—
361C22×C8—31no—
362C22×C8—152no—
363C4⋊Q8—101no—
364#124—101no—
365#123—102no—
366C22⋊Q8—52no—
367C22⋊Q8—52no—
368C22⋊Q8—152no—
369C22⋊Q8—301no—
370#121—152no—
371#121—301no—
372#121—302no—
373#117D3×D511yescharacteristic
374C2×C4⋊C4—151no—
375#107—152no—
376#106—152no—
377#103—31no—
378#103—31no—
379#103—152no—
380#103—152no—
381#102—31no—
382#102—31no—
383C2×C3×C5—22no—
384C2×C3×C5C2×#12111yescharacteristic
385C2×C3×C5#57711yescharacteristic
386C2×C3×C5#57811yescharacteristic
387C3×D5—42no—
388C5×D3—81no—
389C23×C3—52no—
390C23×C3D4×D511yescharacteristic
391C22×D3—21no—
392C3×Q8—102no—
393C3×Q8—102no—
394C3×Q8—102no—
395C3×Q8—202no—
396C3×D4—104no—
397C3×D4—102no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—52no—
401C2×C3×C4—102no—
402C2×C3×C4—102no—
403C2×C3×C4—102no—
404C2×C3×C4—202no—
405C2×C3×C4#70912yes—
406C2×C3×C4D4×D512yes—
407C2×C3×C4D4×D511yescharacteristic
408C2×C3×C4C23×D511yescharacteristic
409#67—42no—
410#67—402no—
411C2×Dic3—21no—
412C2×Dic3—102no—
413C2×Dic3—401no—
414D12—21no—
415D12—21no—
416C4×D3—42no—
417Dic6—21no—
418Dic6—21no—
419C3⋊C8—21no—
420C3⋊C8—21no—
421C3⋊C8—54no—
422C22×C5—21no—
423C22×C5—21no—
424C22×C5—121no—
425C22×C5—121no—
426C22×C5—121no—
427C22×C5#93912yes—
428C22×C5C22×#6711yescharacteristic
429C2×D5—22no—
430C2×D5—22no—
431C2×D5—22no—
432C4×C5—41no—
433C4×C5—41no—
434C4×C5—121no—
435C4×C5#93912yes—
436C4×C5C2×D3×D411yescharacteristic
437C4×C5C2×#23711yescharacteristic
438Dic5—22no—
439Dic5—42no—
440Dic5—122no—
441#41—62no—
442#41—62no—
443#41—102no—
444#41—102no—
445C2×Q8—31no—
446C2×Q8—51no—
447C2×Q8—52no—
448C2×Q8—101no—
449C2×Q8—102no—
450C2×Q8—102no—
451C2×D4—31no—
452C2×D4—52no—
453C2×D4—51no—
454C2×D4—61no—
455C2×D4—302no—
456C22×C4—52no—
457C22×C4—61no—
458C22×C4—101no—
459C22×C4—301no—
460C22×C4C2×D3×D511yescharacteristic
461Q16—304no—
462SD16—304no—
463M16—154no—
464M16—304no—
465C2×C8—31no—
466C2×C8—31no—
467C2×C8—62no—
468C2×C8—152no—
469C2×C8—304no—
470C4⋊C4—102no—
471C4⋊C4—102no—
472C4⋊C4—152no—
473C4⋊C4—302no—
474C4⋊C4—301no—
475C4⋊C4C2×D3×D511yescharacteristic
476C4⋊C4C2×D3×D511yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—102no—
479C22⋊C4—102no—
480C22⋊C4—302no—
481C22⋊C4—302no—
482C42—21no—
483C3×C5#306311yescharacteristic, complemented, Hall
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—102no—
487C22×C3—102no—
488C22×C3—102no—
489C22×C3#403012yes—
490C22×C3C2×D4×D511yescharacteristic
491C2×D3—41no—
492C2×D3—41no—
493C2×D3—41no—
494C3×C4—41no—
495C3×C4—41no—
496C3×C4—102no—
497C3×C4—202no—
498C3×C4#403012yes—
499C3×C4C2×#70911yescharacteristic
500C3×C4C2×D4×D511yescharacteristic
501Dic3—41no—
502Dic3—202no—
503C2×C5—22no—
504C2×C5—241no—
505C2×C5C2×#93911yescharacteristic
506C2×C5#583711yescharacteristic
507C2×C5#583811yescharacteristic
508D5—42no—
509C23—52no—
510C23—61no—
511C23D5×#6711yescharacteristic
512Q8—61no—
513Q8—61no—
514Q8—102no—
515Q8—102no—
516Q8—102no—
517Q8—202no—
518D4—61no—
519D4—61no—
520D4—104no—
521D4—102no—
522D4—122no—
523D4—1202no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—52no—
527C2×C4—61no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—122no—
532C2×C4—202no—
533C2×C4—302no—
534C2×C4—1201no—
535C2×C4#676512yes—
536C2×C4#677712yes—
537C2×C4D5×#6711yescharacteristic
538C2×C4C22×D3×D511yescharacteristic
539C8—61no—
540C8—61no—
541C8—154no—
542C2×C3—22no—
543C2×C3—202no—
544C2×C3C2×#403011yescharacteristic
545C2×C3#6610411yescharacteristic
546C2×C3#6610511yescharacteristic
547D3—81no—
548C5#8340011yescharacteristic, complemented, Sylow
549C22—21no—
550C22—21no—
551C22—102no—
552C22—102no—
553C22—102no—
554C22—121no—
555C22—121no—
556C22—121no—
557C22#9140812yes—
558C22C2×D5×#6711yescharacteristic
559C4—41no—
560C4—41no—
561C4—102no—
562C4—121no—
563C4—202no—
564C4—602no—
565C4#9140812yes—
566C4C2×#676511yescharacteristic
567C4C2×#677711yescharacteristic
568C3#1061057211yescharacteristic, complemented, Sylow
569C2—22no—
570C2—202no—
571C2—241no—
572C2C2×#9140811yescharacteristic
573C2#1175531911yescharacteristic
574C2#1175533811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radical#11754607C2
hypercenter#117D3×D5
hypocenterC3×C5#3063
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#65860C2semidirect
3. C2×#91309C2semidirect
4. C2×#91283C2semidirect
5. #11751096C2semidirect
6. C5×#5002C2semidirect
7. C2×#90971C2semidirect
8. #11747343C2semidirect
9. #11747341C2semidirect
10. #11747311C2semidirect
11. #11747309C2semidirect
48. #65860D3semidirect
82. #6710D4semidirect
107. #5002D5semidirect
483. C3×C5#3063semidirect
548. C5#83400semidirect
568. C3#10610572semidirect

Maximal subgroups

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

subgroupindex
C3×#658602
#117546072
C2×#913092
C2×#912832
#117510962
C5×#50022
C2×#909712
#117473432
#117473412
#117473112
#117473092
#106105723
#834005