Finite Group Databasebeta

← #14429248

Subgroups — #14429248

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
1C2×#91790C211yesmaximal, characteristic, complemented
2#11754603C211yesmaximal, characteristic
3#11754278C211yesmaximal, characteristic, complemented
4C2×#91309C211yesmaximal, characteristic, complemented
5C5×#5113C211yesmaximal, characteristic, complemented
6C2×C3×#3948C211yesmaximal, characteristic, complemented
7#11748470C211yesmaximal, characteristic, complemented
8#11747955C212yesmaximal, complemented
9#11747954C212yesmaximal, complemented
10#11747929C212yesmaximal, complemented
11#11747928C212yesmaximal, complemented
12#10610572—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C22×C3×Dic10C2211yescharacteristic
16C22×C3×C5×C8C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18#91790—24no—
19C2×#6705C2212yes—
20C2×C8×D15C2212yes—
21C5×#926C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23#91566—22no—
24#91546—22no—
25#91466C2212yes—
26#91460—21no—
27#91390C2212yes—
28#91390C2212yes—
29#91389—21no—
30#91383C2212yes—
31#91374—21no—
32#91365—21no—
33C2×#6661C2212yes—
34#91309—24no—
35C2×#6656C2212yes—
36C5×#821C2211yescharacteristic
37C5×#821C2211yescharacteristic
38C5×#816C2211yescharacteristic
39C5×#816C2211yescharacteristic
40C3×#3948C2212yes—
41C3×#3948C2212yes—
42#90989C2212yes—
43#90986C2212yes—
44#78800—51nomaximal, Hall
45#66167—31no—
46C2×#4097—31no—
47C2×#4047—31no—
48#65860—31no—
49C5×#416—31no—
50C2×#3948D311yescharacteristic, complemented
51#65284—31no—
52#65105—32no—
53#65102—32no—
54#65069—32no—
55#65067—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220D412yes—
58#6817—22no—
59#6817—22no—
60C2×D60D411yescharacteristic
61C2×C4×D15C2312yes—
62C2×Dic30D411yescharacteristic
63C2×C5×#67—21no—
64C5×#235—22no—
65C5×#235—22no—
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C22×C3×Dic5—21no—
70C22×C3×Dic5—21no—
71C2×C3×Dic10—22no—
72C2×C3×Dic10—22no—
73C2×C3×Dic10—21no—
74C2×C3×Dic10C2312yes—
75C2×#1203—22no—
76C2×C3×C5×C8—22no—
77C2×C3×C5×C8C2311yescharacteristic
78C2×C3×C5×C8C2311yescharacteristic
79#6710D414yescomplemented
80C2×C3⋊#168C2312yes—
81#6705—24no—
82C8×D15—24no—
83C5×#217—21no—
84C5×C4⋊Dic3C2311yescharacteristic
85C5×C4⋊Dic3C2311yescharacteristic
86C4×C5×Dic3—21no—
87C3×C4⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89Dic3⋊Dic5—22no—
90Dic3⋊Dic5—22no—
91#6668—22no—
92#6667—22no—
93#6667—22no—
94#6667—22no—
95(C2×D3)⋊Dic5—22no—
96#6661—24no—
97#6656—24no—
98#5816—51no—
99C2×#942—51no—
100C2×#901—51no—
101#5510—51no—
102C2×C3×#103—51no—
103#5113D511yescharacteristic, complemented
104#4964—51no—
105#4816—52no—
106#4813—52no—
107#4812—52no—
108#4807—52no—
109C2×C5×#41—31no—
110C2×#709—31no—
111C22×Dic10C2×D311yescharacteristic
112C22×C5×C8C2×D311yescharacteristic
113C5×#117—31no—
114#4097—64no—
115#4092—32no—
116C2×#689—32no—
117#4085—62no—
118#4084—32no—
119C2×#687—32no—
120#4076—61no—
121C2×C4⋊Dic5C2×D311yescharacteristic
122#4070—61no—
123C2×#681—31no—
124#4047—64no—
125C2×#676—32no—
126C2×C8×D5—32no—
127#4043—32no—
128#4043—32no—
129#4032—62no—
130#4021—61no—
131#4015—61no—
132C5×#103—31no—
133C5×#103—31no—
134C5×#102—31no—
135C5×#102—31no—
136#3948C2×D312yes—
137#3948C2×D312yes—
138#3940—32no—
139#3939—32no—
140#3063—151noSylow
141C23×C3×C5C2×D411yescharacteristic
142C22×D15C2×D412yes—
143C22×C5×D3—21no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5#4112yes—
147C2×C3×C4×C5C2411yescharacteristic
148#1220—24no—
149C2×Dic15C2×D412yes—
150D60—22no—
151C4×D15—22no—
152C4×D15—22no—
153Dic30—22no—
154C5×#67—42no—
155C2×C5×Dic3—21no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—21no—
158C5×D12—21no—
159C5×D12—21no—
160C4×C5×D3—42no—
161C5×Dic6—21no—
162C5×Dic6—21no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—42no—
166C2×C3×Dic5—81no—
167C3×Dic10—22no—
168C3×Dic10—22no—
169C3×Dic10—42no—
170#1203—82no—
171C3×C5×C8—21no—
172C3×C5×C8—21no—
173C3⋊#168C2×D414yes—
174C22×C3×Q8—51no—
175C2×#235—51no—
176C2×#235C2×D511yescharacteristic
177C22×C3×C8C2×D511yescharacteristic
178C2×C3×C4⋊C4—51no—
179#947—101no—
180#946—52no—
181#946—52no—
182#944—101no—
183C2×#216—52no—
184#942—104no—
185C2×#215—52no—
186#930—102no—
187#929—102no—
188#926C2×D511yescharacteristic
189C2×#208—51no—
190#901—104no—
191C2×ΓL(1,𝔽25)—52no—
192C2×D3×C8—52no—
193#897—52no—
194#897—101no—
195#895—52no—
196#895—101no—
197C3×#103—52no—
198C3×#103—52no—
199#821C2×D511yescharacteristic
200#821C2×D511yescharacteristic
201#816C2×D511yescharacteristic
202#816C2×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—32no—
213C2×C22⋊D5—62no—
214C22×Dic5—21no—
215C22×Dic5—21no—
216#709—62no—
217#709—62no—
218C2×D20—31no—
219C2×C4×D5—32no—
220C2×Dic10—22no—
221C2×Dic10—22no—
222C2×Dic10—21no—
223C2×Dic10—31no—
224C2×Dic10C22×D312yes—
225C2×C5×C8—22no—
226C2×C5×C8C22×D311yescharacteristic
227C2×C5×C8C22×D311yescharacteristic
228C5×C4⋊C4—31no—
229C5×C4⋊C4—31no—
230C5×C22⋊C4—61no—
231C42×C5—61no—
232C22⋊Dic5—62no—
233#689—64no—
234#687—64no—
235#685—62no—
236#685—62no—
237#685—62no—
238C4⋊Dic5—21no—
239C4⋊Dic5—62no—
240C4⋊Dic5—62no—
241C4⋊Dic5C22×D312yes—
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—151no—
251#470—152no—
252#468—152no—
253#467—152no—
254#465—152no—
255#428—151no—
256#416—31no—
257C2×#103—51no—
258C22×C3×C5—21no—
259C22×C3×C5—21no—
260C22×C3×C5#12112yes—
261C22×C3×C5C22×D411yescharacteristic
262C2×D15—22no—
263C2×D15—22no—
264C2×D15—22no—
265C2×C5×D3—41no—
266C2×C5×D3—41no—
267C2×C5×D3—41no—
268C3×C4×C5#12112yes—
269C3×C4×C5C22×D411yescharacteristic
270C3×C4×C5C2×#4111yescharacteristic
271Dic15—22no—
272C3×Dic5—42no—
273C3×Dic5—42no—
274C5×Dic3—41no—
275C5×Dic3—41no—
276C5×Dic3—41no—
277C2×C3×Q8—52no—
278C2×C3×Q8—101no—
279C2×C3×Q8—102no—
280C2×C3×Q8—102no—
281C22×C3×C4—101no—
282C22×C3×C4—101no—
283C22×C3×C4C22×D511yescharacteristic
284C2×#67—21no—
285C2×#67—52no—
286#235—22no—
287#235—22no—
288#235—102no—
289#235—102no—
290C2×D12—51no—
291C2×D12—102no—
292C2×D12C22×D511yescharacteristic
293C2×C4×D3—21no—
294C2×C4×D3—52no—
295C2×Dic6—51no—
296C2×Dic6C22×D511yescharacteristic
297C2×C3×C8—22no—
298C2×C3×C8C22×D511yescharacteristic
299C2×C3×C8C22×D511yescharacteristic
300C3×C4⋊C4—52no—
301C3×C4⋊C4—101no—
302#217—21no—
303#216—104no—
304#215—104no—
305(C2×D3)⋊C4—102no—
306(C2×D3)⋊C4—102no—
307(C2×D3)⋊C4—102no—
308(C2×D3)⋊C4—102no—
309C4⋊Dic3—102no—
310C4⋊Dic3C22×D511yescharacteristic
311C4⋊Dic3C22×D511yescharacteristic
312Dic3⋊C4—102no—
313Dic3⋊C4—102no—
314C4×Dic3—21no—
315#208—54no—
316C2×C3⋊C8—52no—
317ΓL(1,𝔽25)—104no—
318D3×C8—104no—
319C23×C5—61no—
320C23×C5D3×D411yescharacteristic
321C22×D5—32no—
322C5×Q8—61no—
323C5×Q8—61no—
324C5×D4—61no—
325C5×D4—61no—
326C5×D4—122no—
327C2×C4×C5—61no—
328C2×C4×C5—61no—
329C2×C4×C5—61no—
330C2×C4×C5—122no—
331C2×C4×C5#23512yes—
332C2×C4×C5D3×D411yescharacteristic
333C2×C4×C5D3×D412yes—
334C2×C4×C5C23×D311yescharacteristic
335C22⋊D5—64no—
336C22⋊D5—242no—
337C2×Dic5—22no—
338C2×Dic5—22no—
339C2×Dic5—32no—
340C2×Dic5—42no—
341C2×Dic5—81no—
342D20—62no—
343C4×D5—62no—
344C4×D5—62no—
345Dic10—22no—
346Dic10—22no—
347Dic10—42no—
348Dic10—62no—
349C5×C8—21no—
350C5×C8—21no—
351#168—34no—
352C2×#41—31no—
353C2×#41—151no—
354C22×Q8—51no—
355#137—304no—
356C2×Q16—152no—
357C2×SD16—152no—
358#131—304no—
359C2×M16—151no—
360C2×M16—152no—
361C22×C8—152no—
362C22×C8D3×D511yescharacteristic
363C4⋊Q8—301no—
364#124—301no—
365#123—302no—
366C22⋊Q8—152no—
367C22⋊Q8—152no—
368C22⋊Q8—152no—
369C22⋊Q8—301no—
370#121—152no—
371#121—301no—
372#121—302no—
373#117—31no—
374C2×C4⋊C4—51no—
375#107—152no—
376#106—152no—
377#103—31no—
378#103—31no—
379#103—52no—
380#103—52no—
381#102—31no—
382#102—31no—
383C2×C3×C5—22no—
384C2×C3×C5C2×#12111yescharacteristic
385C2×C3×C5#57711yescharacteristic
386C2×C3×C5#57811yescharacteristic
387D15—42no—
388C5×D3—81no—
389C23×C3D4×D511yescharacteristic
390C22×D3—21no—
391C22×D3—52no—
392C3×Q8—102no—
393C3×Q8—102no—
394C3×Q8—202no—
395C2×C3×C4—102no—
396C2×C3×C4—102no—
397C2×C3×C4—202no—
398C2×C3×C4—401no—
399C2×C3×C4#70912yes—
400C2×C3×C4D4×D511yescharacteristic
401C2×C3×C4D4×D512yes—
402C2×C3×C4C23×D511yescharacteristic
403#67—42no—
404#67—104no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—21no—
408C2×Dic3—52no—
409D12—21no—
410D12—21no—
411D12—102no—
412D12—402no—
413C4×D3—42no—
414C4×D3—102no—
415C4×D3—102no—
416Dic6—21no—
417Dic6—21no—
418Dic6—102no—
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#88412yes—
428C22×C5C2×D3×D411yescharacteristic
429C2×D5—62no—
430C2×D5—62no—
431C2×D5—62no—
432C4×C5—121no—
433C4×C5—121no—
434C4×C5—121no—
435C4×C5#88412yes—
436C4×C5C2×#23511yescharacteristic
437C4×C5C2×D3×D411yescharacteristic
438Dic5—42no—
439Dic5—42no—
440Dic5—62no—
441#41—62no—
442#41—62no—
443#41—302no—
444#41—302no—
445C2×Q8—31no—
446C2×Q8—52no—
447C2×Q8—101no—
448C2×Q8—102no—
449C2×Q8—102no—
450C2×Q8—151no—
451C2×D4—31no—
452C2×D4—61no—
453C2×D4—152no—
454C2×D4—151no—
455C2×D4—302no—
456C22×C4—61no—
457C22×C4—101no—
458C22×C4—101no—
459C22×C4—152no—
460C22×C4C2×D3×D511yescharacteristic
461Q16—304no—
462SD16—304no—
463M16—154no—
464M16—304no—
465C2×C8—22no—
466C2×C8—152no—
467C2×C8—304no—
468C2×C8C2×D3×D511yescharacteristic
469C2×C8C2×D3×D511yescharacteristic
470C4⋊C4—31no—
471C4⋊C4—31no—
472C4⋊C4—52no—
473C4⋊C4—101no—
474C4⋊C4—302no—
475C4⋊C4—302no—
476C4⋊C4—302no—
477C22⋊C4—61no—
478C22⋊C4—302no—
479C22⋊C4—302no—
480C22⋊C4—302no—
481C22⋊C4—302no—
482C42—61no—
483C3×C5#306311yescharacteristic, complemented, Hall
484C22×C3—21no—
485C22×C3—21no—
486C22×C3#403012yes—
487C22×C3C2×D4×D511yescharacteristic
488C2×D3—41no—
489C2×D3—41no—
490C2×D3—41no—
491C2×D3—102no—
492C2×D3—102no—
493C2×D3—102no—
494C3×C4—202no—
495C3×C4—202no—
496C3×C4#403012yes—
497C3×C4C2×#70911yescharacteristic
498C3×C4C2×D4×D511yescharacteristic
499Dic3—41no—
500Dic3—41no—
501Dic3—41no—
502Dic3—102no—
503C2×C5—22no—
504C2×C5—241no—
505C2×C5C2×#88411yescharacteristic
506C2×C5#576211yescharacteristic
507C2×C5#576611yescharacteristic
508D5—122no—
509C23—61no—
510C23—152no—
511C23#677711yescharacteristic
512Q8—61no—
513Q8—61no—
514Q8—102no—
515Q8—102no—
516Q8—202no—
517Q8—302no—
518D4—61no—
519D4—61no—
520D4—122no—
521D4—304no—
522D4—302no—
523D4—1202no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—122no—
530C2×C4—152no—
531C2×C4—202no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4—401no—
535C2×C4#677112yes—
536C2×C4#677711yescharacteristic
537C2×C4#679012yes—
538C2×C4C22×D3×D511yescharacteristic
539C8—21no—
540C8—21no—
541C8—154no—
542C2×C3—22no—
543C2×C3C2×#403011yescharacteristic
544C2×C3#6610411yescharacteristic
545C2×C3#6610511yescharacteristic
546D3—81no—
547D3—202no—
548C5#7880011yescharacteristic, complemented, Sylow
549C22—21no—
550C22—21no—
551C22—121no—
552C22—121no—
553C22—121no—
554C22—302no—
555C22—302no—
556C22—302no—
557C22#9146112yes—
558C22C2×#677711yescharacteristic
559C4—121no—
560C4—121no—
561C4—121no—
562C4—202no—
563C4—202no—
564C4—302no—
565C4#9146112yes—
566C4C2×#677111yescharacteristic
567C4C2×#679011yescharacteristic
568C3#1061057211yescharacteristic, complemented, Sylow
569C2—22no—
570C2—241no—
571C2—602no—
572C2#1175398011yescharacteristic
573C2#1175401111yescharacteristic
574C2C2×#9146111yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11754603C2
hypercenterC22×C8D3×D5
hypocenterC3×C5#3063
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#91790C2semidirect
3. #11754278C2semidirect
4. C2×#91309C2semidirect
5. C5×#5113C2semidirect
6. C2×C3×#3948C2semidirect
7. #11748470C2semidirect
8. #11747955C2semidirect
9. #11747954C2semidirect
10. #11747929C2semidirect
11. #11747928C2semidirect
50. C2×#3948D3semidirect
79. #6710D4semidirect
103. #5113D5semidirect
483. C3×C5#3063semidirect
548. C5#78800semidirect
568. C3#10610572semidirect

Maximal subgroups

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

subgroupindex
C2×#917902
#117546032
#117542782
C2×#913092
C5×#51132
C2×C3×#39482
#117484702
#117479552
#117479542
#117479292
#117479282
#106105723
#788005