Finite Group Databasebeta

← #14429241

Subgroups — #14429241

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
1C5×#5526C211yesmaximal, characteristic, complemented
2#11754607C211yesmaximal, characteristic
3C2×#91307C211yesmaximal, characteristic, complemented
4C2×#91286C211yesmaximal, characteristic, complemented
5#11751096C211yesmaximal, characteristic, complemented
6C3×#65291C211yesmaximal, characteristic, complemented
7C2×#90973C211yesmaximal, characteristic, complemented
8#11747354C212yesmaximal, complemented
9#11747353C212yesmaximal, complemented
10#11747323C212yesmaximal, complemented
11#11747321C212yesmaximal, complemented
12#10615131—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C5×#897C2212yes—
20C5×#897C2212yes—
21C5×#886—22no—
22C5×#875—21no—
23C5×#869—21no—
24C22×C3×#168C2211yescharacteristic
25#91571—22no—
26#91456C2212yes—
27#91449—21no—
28#91369C2212yes—
29#91359—21no—
30C2×#6661C2212yes—
31#91307—24no—
32C2×#6655C2212yes—
33C2×#6650C2212yes—
34#91286—24no—
35C2×D3×#168C2212yes—
36#91092C2212yes—
37#91091C2212yes—
38C3×#3942C2211yescharacteristic
39C3×#3942C2211yescharacteristic
40C3×#3941C2211yescharacteristic
41C3×#3941C2211yescharacteristic
42#90973C2212yes—
43#90973C2212yes—
44#78841—51nomaximal, Hall
45C5×#536—31no—
46#66167—31no—
47C2×#4094—31no—
48C2×#4088—31no—
49C2×#3967—31no—
50#65341—32no—
51#65340—32no—
52#65338—32no—
53#65337—32no—
54#65291D311yescharacteristic, complemented
55#65284—31no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15—21no—
58C2×C5×#67D412yes—
59C22×C5×Dic3—21no—
60C5×#235—22no—
61C5×#235—22no—
62C2×C5×D12D411yescharacteristic
63C2×C4×C5×D3C2312yes—
64C2×C5×Dic6—22no—
65C2×C5×Dic6—22no—
66C2×C5×Dic6—21no—
67C2×C5×Dic6D411yescharacteristic
68C2×C5×Dic6C2312yes—
69C2×C3×C22⋊D5—21no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20C2311yescharacteristic
73C2×C3×C4×D5—21no—
74C2×C3×Dic10C2311yescharacteristic
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—
84C5×(C2×D3)⋊C4—22no—
85C5×(C2×D3)⋊C4—22no—
86C5×C4⋊Dic3—22no—
87C5×C4⋊Dic3—22no—
88C2×C3×#168—22no—
89C2×C3×#168C2311yescharacteristic
90C2×C3×#168C2311yescharacteristic
91#6669—22no—
92(C2×D3)⋊Dic5—22no—
93#6665—22no—
94#6661—24no—
95#6655—24no—
96#6650—24no—
97D3×#168—24no—
98#5833—51no—
99C2×#951—51no—
100C2×#901—51no—
101#5526D511yescharacteristic, complemented
102C3×#416—51no—
103C2×#816—51no—
104#4995—51no—
105#4816—52no—
106#4813—52no—
107#4780—52no—
108#4778—52no—
109C2×C5×#41—31no—
110C22×C5×Q8—31no—
111C2×#709C2×D311yescharacteristic
112C5×C4⋊Q8—61no—
113C5×#124—61no—
114C5×#123—62no—
115C5×C22⋊Q8—32no—
116C5×C22⋊Q8—32no—
117C5×#117C2×D311yescharacteristic
118#4094—64no—
119#4092—61no—
120C2×#689—32no—
121#4088—64no—
122C2×#688—32no—
123#4085—62no—
124#4084—61no—
125#4076—32no—
126C2×C4⋊Dic5—31no—
127#4070—32no—
128C2×#681—31no—
129C2×#681—32no—
130C22×#168—32no—
131C22×#168C2×D311yescharacteristic
132#3967—32no—
133#3967—32no—
134#3942C2×D311yescharacteristic
135#3942C2×D311yescharacteristic
136#3941C2×D311yescharacteristic
137#3941C2×D311yescharacteristic
138#3940—32no—
139#3939—32no—
140#3063—151noSylow
141C23×C3×C5C2×D411yescharacteristic
142C22×C5×D3C2×D412yes—
143C22×C3×D5—21no—
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—24no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—42no—
155C2×C5×Dic3C2×D412yes—
156C5×D12—22no—
157C4×C5×D3—22no—
158C4×C5×D3—22no—
159C5×Dic6—22no—
160C5×Dic6—22no—
161C5×Dic6—22no—
162C5×Dic6—42no—
163C3×C22⋊D5—42no—
164C2×C3×Dic5—21no—
165C3×D20—21no—
166C3×D20—21no—
167C3×C4×D5—42no—
168C3×Dic10—21no—
169C3×Dic10—21no—
170#1201—82no—
171C3⋊#168C2×D414yes—
172C3×#168—21no—
173C3×#168—21no—
174C2×C3×#41—51no—
175C2×#235C2×D511yescharacteristic
176C22×Dic6C2×D511yescharacteristic
177C22×C3×C8—51no—
178C3×#117C2×D511yescharacteristic
179#951—104no—
180#946—52no—
181C2×#216—52no—
182#939—102no—
183#938—52no—
184C2×#214—52no—
185#930—101no—
186C2×C4⋊Dic3—51no—
187#924—101no—
188C2×#208—51no—
189#901—104no—
190C2×ΓL(1,𝔽25)—52no—
191C2×D3×C8—52no—
192#897C2×D512yes—
193#897C2×D512yes—
194#886—22no—
195#875—21no—
196#869—21no—
197C3×#103—51no—
198C3×#103—51no—
199C3×#102—51no—
200C3×#102—51no—
201#816—52no—
202#816—52no—
203#808—52no—
204#807—52no—
205C5×#41—62no—
206C5×#41—62no—
207C2×C5×Q8—31no—
208C2×C5×Q8—32no—
209C2×C5×Q8—61no—
210C2×C5×Q8—62no—
211C2×C5×Q8—62no—
212C2×C5×D4—32no—
213C2×C5×D4—31no—
214C22×C4×C5—32no—
215C22×C4×C5—61no—
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—21no—
218C2×C22⋊D5—62no—
219C22×Dic5—61no—
220#709—22no—
221#709—22no—
222C2×D20C22×D311yescharacteristic
223C2×C4×D5—21no—
224C2×Dic10C22×D311yescharacteristic
225C5×C4⋊C4—62no—
226C5×C4⋊C4—62no—
227C5×C4⋊C4C22×D311yescharacteristic
228C5×C4⋊C4C22×D311yescharacteristic
229C5×C22⋊C4—21no—
230C5×C22⋊C4—62no—
231C5×C22⋊C4—62no—
232C42×C5—21no—
233C22⋊Dic5—62no—
234#689—64no—
235#688—64no—
236#685—62no—
237C4⋊Dic5—32no—
238C4⋊Dic5—61no—
239#683—62no—
240#681—34no—
241#681—64no—
242C2×#168—22no—
243C2×#168—32no—
244C2×#168—64no—
245C2×#168C22×D311yescharacteristic
246C2×#168C22×D311yescharacteristic
247C2×#137—151no—
248C2×#131—151no—
249#537—151no—
250#536—31no—
251#470—152no—
252#468—152no—
253#467—152no—
254#465—152no—
255#428—151no—
256#416—51no—
257C2×#103—151no—
258C22×C3×C5—21no—
259C22×C3×C5—21no—
260C22×C3×C5#12112yes—
261C22×C3×C5C22×D411yescharacteristic
262C2×C5×D3—22no—
263C2×C5×D3—22no—
264C2×C5×D3—22no—
265C2×C3×D5—41no—
266C2×C3×D5—41no—
267C2×C3×D5—41no—
268C3×C4×C5—41no—
269C3×C4×C5—41no—
270C3×C4×C5#12112yes—
271C3×C4×C5C22×D411yescharacteristic
272C3×C4×C5C2×#4111yescharacteristic
273Dic15—42no—
274C3×Dic5—41no—
275C5×Dic3—22no—
276C5×Dic3—42no—
277C3×#41—102no—
278C3×#41—102no—
279C2×C3×Q8—51no—
280C2×C3×D4—51no—
281C2×C3×D4—101no—
282C22×C3×C4—101no—
283C22×C3×C4C22×D511yescharacteristic
284C2×#67—102no—
285C2×#67C22⋊D512yes—
286C22×Dic3—21no—
287C22×Dic3—101no—
288#235—22no—
289#235—22no—
290C2×D12C22⋊D511yescharacteristic
291C2×C4×D3C22×D512yes—
292C2×Dic6—22no—
293C2×Dic6—22no—
294C2×Dic6—21no—
295C2×Dic6C22⋊D511yescharacteristic
296C2×Dic6C22×D512yes—
297C2×C3×C8—51no—
298C2×C3×C8—51no—
299C2×C3×C8—102no—
300C3×C4⋊C4C22×D511yescharacteristic
301C3×C4⋊C4C22×D511yescharacteristic
302C3×C22⋊C4—21no—
303C3×C42—21no—
304#217—102no—
305#216—104no—
306#214—104no—
307(C2×D3)⋊C4—22no—
308(C2×D3)⋊C4—22no—
309(C2×D3)⋊C4—102no—
310C4⋊Dic3—22no—
311C4⋊Dic3—22no—
312C4⋊Dic3—52no—
313C4⋊Dic3—101no—
314Dic3⋊C4—102no—
315#208—54no—
316C2×C3⋊C8—52no—
317ΓL(1,𝔽25)—104no—
318D3×C8—104no—
319C23×C5—32no—
320C23×C5D3×D411yescharacteristic
321C22×D5—21no—
322C5×Q8—62no—
323C5×Q8—62no—
324C5×Q8—62no—
325C5×Q8—122no—
326C5×D4—64no—
327C5×D4—62no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—32no—
331C2×C4×C5—62no—
332C2×C4×C5—62no—
333C2×C4×C5—62no—
334C2×C4×C5—122no—
335C2×C4×C5#23512yes—
336C2×C4×C5D3×D412yes—
337C2×C4×C5D3×D411yescharacteristic
338C2×C4×C5C23×D311yescharacteristic
339C22⋊D5—42no—
340C22⋊D5—242no—
341C2×Dic5—21no—
342C2×Dic5—62no—
343C2×Dic5—241no—
344D20—21no—
345D20—21no—
346C4×D5—42no—
347Dic10—21no—
348Dic10—21no—
349#168—21no—
350#168—21no—
351#168—34no—
352C2×#41—31no—
353C2×#41—51no—
354C22×Q8—31no—
355#137—304no—
356C2×Q16—152no—
357C2×SD16—152no—
358#131—304no—
359C2×M16—152no—
360C2×M16—151no—
361C22×C8—51no—
362C22×C8—152no—
363C4⋊Q8—61no—
364#124—61no—
365#123—62no—
366C22⋊Q8—32no—
367C22⋊Q8—32no—
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—51no—
378#103—51no—
379#103—152no—
380#103—152no—
381#102—51no—
382#102—51no—
383C2×C3×C5—22no—
384C2×C3×C5C2×#12111yescharacteristic
385C2×C3×C5#57711yescharacteristic
386C2×C3×C5#57811yescharacteristic
387C3×D5—81no—
388C5×D3—42no—
389C23×C3—101no—
390C23×C3C2×C22⋊D511yescharacteristic
391C22×D3C2×C22⋊D512yes—
392C3×Q8—101no—
393C3×Q8—101no—
394C3×D4—101no—
395C3×D4—101no—
396C3×D4—202no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—101no—
400C2×C3×C4—202no—
401C2×C3×C4D4×D512yes—
402C2×C3×C4#71112yes—
403C2×C3×C4C2×C22⋊D511yescharacteristic
404C2×C3×C4C23×D511yescharacteristic
405#67—24no—
406#67—402no—
407C2×Dic3—22no—
408C2×Dic3—42no—
409C2×Dic3—102no—
410C2×Dic3—401no—
411C2×Dic3C2×C22⋊D512yes—
412D12—22no—
413C4×D3—22no—
414C4×D3—22no—
415Dic6—22no—
416Dic6—22no—
417Dic6—22no—
418Dic6—42no—
419C3×C8—101no—
420C3×C8—101no—
421C3⋊C8—54no—
422C22×C5—21no—
423C22×C5—21no—
424C22×C5—62no—
425C22×C5—62no—
426C22×C5—62no—
427C22×C5#88412yes—
428C22×C5C2×D3×D411yescharacteristic
429C2×D5—41no—
430C2×D5—41no—
431C2×D5—41no—
432C4×C5—41no—
433C4×C5—41no—
434C4×C5—62no—
435C4×C5—122no—
436C4×C5#88412yes—
437C4×C5C2×#23511yescharacteristic
438C4×C5C2×D3×D411yescharacteristic
439Dic5—41no—
440Dic5—122no—
441#41—62no—
442#41—62no—
443#41—102no—
444#41—102no—
445C2×Q8—31no—
446C2×Q8—32no—
447C2×Q8—51no—
448C2×Q8—61no—
449C2×Q8—62no—
450C2×Q8—62no—
451C2×D4—32no—
452C2×D4—31no—
453C2×D4—51no—
454C2×D4—101no—
455C2×D4—302no—
456C22×C4—32no—
457C22×C4—61no—
458C22×C4—101no—
459C22×C4—301no—
460C22×C4C2×D3×D511yescharacteristic
461Q16—304no—
462SD16—304no—
463M16—154no—
464M16—304no—
465C2×C8—51no—
466C2×C8—51no—
467C2×C8—102no—
468C2×C8—152no—
469C2×C8—304no—
470C4⋊C4—62no—
471C4⋊C4—62no—
472C4⋊C4—152no—
473C4⋊C4—302no—
474C4⋊C4—301no—
475C4⋊C4C2×D3×D511yescharacteristic
476C4⋊C4C2×D3×D511yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—62no—
479C22⋊C4—62no—
480C22⋊C4—302no—
481C22⋊C4—302no—
482C42—21no—
483C3×C5#306311yescharacteristic, complemented, Hall
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—201no—
487C22×C3—201no—
488C22×C3—201no—
489C22×C3#408512yes—
490C22×C3C22×C22⋊D511yescharacteristic
491C2×D3—22no—
492C2×D3—22no—
493C2×D3—22no—
494C3×C4—41no—
495C3×C4—41no—
496C3×C4—201no—
497C3×C4#408512yes—
498C3×C4C2×D4×D511yescharacteristic
499C3×C4C2×#71111yescharacteristic
500Dic3—22no—
501Dic3—42no—
502Dic3—202no—
503C2×C5—22no—
504C2×C5—122no—
505C2×C5C2×#88411yescharacteristic
506C2×C5#577011yescharacteristic
507C2×C5#577111yescharacteristic
508D5—81no—
509C23—32no—
510C23—101no—
511C23D3×C22⋊D511yescharacteristic
512Q8—62no—
513Q8—62no—
514Q8—62no—
515Q8—101no—
516Q8—101no—
517Q8—122no—
518D4—64no—
519D4—62no—
520D4—101no—
521D4—101no—
522D4—202no—
523D4—1202no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—32no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—101no—
531C2×C4—122no—
532C2×C4—202no—
533C2×C4—302no—
534C2×C4—1201no—
535C2×C4#677212yes—
536C2×C4#677712yes—
537C2×C4D3×C22⋊D511yescharacteristic
538C2×C4C22×D3×D511yescharacteristic
539C8—101no—
540C8—101no—
541C8—154no—
542C2×C3—22no—
543C2×C3—401no—
544C2×C3C2×#408511yescharacteristic
545C2×C3#6617111yescharacteristic
546C2×C3#6617211yescharacteristic
547D3—42no—
548C5#7884111yescharacteristic, complemented, Sylow
549C22—21no—
550C22—21no—
551C22—62no—
552C22—62no—
553C22—62no—
554C22—201no—
555C22—201no—
556C22—201no—
557C22#9145312yes—
558C22C2×D3×C22⋊D511yescharacteristic
559C4—41no—
560C4—41no—
561C4—62no—
562C4—122no—
563C4—201no—
564C4—602no—
565C4#9145312yes—
566C4C2×#677211yescharacteristic
567C4C2×#677711yescharacteristic
568C3#1061513111yescharacteristic, complemented, Sylow
569C2—22no—
570C2—122no—
571C2—401no—
572C2C2×#9145311yescharacteristic
573C2#1175532611yescharacteristic
574C2#1175534611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
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. C5×#5526C2semidirect
3. C2×#91307C2semidirect
4. C2×#91286C2semidirect
5. #11751096C2semidirect
6. C3×#65291C2semidirect
7. C2×#90973C2semidirect
8. #11747354C2semidirect
9. #11747353C2semidirect
10. #11747323C2semidirect
11. #11747321C2semidirect
54. #65291D3semidirect
82. #6710D4semidirect
101. #5526D5semidirect
483. C3×C5#3063semidirect
548. C5#78841semidirect
568. C3#10615131semidirect

Maximal subgroups

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

subgroupindex
C5×#55262
#117546072
C2×#913072
C2×#912862
#117510962
C3×#652912
C2×#909732
#117473542
#117473532
#117473232
#117473212
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