Finite Group Databasebeta

← #14429247

Subgroups — #14429247

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×C5×#901C211yesmaximal, characteristic, complemented
2#11754607C211yesmaximal, characteristic
3#11754271C211yesmaximal, characteristic, complemented
4C2×#91313C211yesmaximal, characteristic, complemented
5C2×#91100C211yesmaximal, characteristic, complemented
6C3×#65402C211yesmaximal, characteristic, complemented
7#11748455C211yesmaximal, characteristic, complemented
8#11747948C212yesmaximal, complemented
9#11747947C212yesmaximal, complemented
10#11747911C212yesmaximal, complemented
11#11747908C212yesmaximal, complemented
12#10615539—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×C5×C8C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C5×#901—24no—
20C2×C5×ΓL(1,𝔽25)C2212yes—
21C2×C5×D3×C8C2212yes—
22C3×#4072C2211yescharacteristic
23#91571—22no—
24#91543—22no—
25#91456C2212yes—
26#91449—21no—
27#91376—21no—
28#91373—21no—
29#91369C2212yes—
30#91365C2212yes—
31#91365C2212yes—
32#91359—21no—
33C2×#6662C2212yes—
34#91313—24no—
35C2×#6657C2212yes—
36#91100C2212yes—
37#91100C2212yes—
38C3×#3953C2211yescharacteristic
39C3×#3953C2211yescharacteristic
40C3×#3948C2211yescharacteristic
41C3×#3948C2211yescharacteristic
42#90990C2212yes—
43#90987C2212yes—
44#78841—51nomaximal, Hall
45C2×C5×#131—31no—
46#66167—31no—
47#66159—31no—
48C2×#4055—31no—
49#65426—32no—
50#65423—32no—
51#65410—31no—
52#65405—32no—
53#65403—32no—
54#65402D311yescharacteristic, complemented
55C2×#3948—31no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15—21no—
58C22×Dic15—21no—
59C2×Dic30—22no—
60C2×Dic30—22no—
61C2×Dic30—21no—
62C2×Dic30C2312yes—
63C2×C5×#67D412yes—
64C5×#235—22no—
65C5×#235—22no—
66C2×C5×D12D411yescharacteristic
67C2×C4×C5×D3C2312yes—
68C2×C5×Dic6D411yescharacteristic
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—
76C2×C3×C5×C8—22no—
77C2×C3×C5×C8C2311yescharacteristic
78C2×C3×C5×C8C2311yescharacteristic
79C4⋊Dic15—21no—
80C4⋊Dic15C2312yes—
81C5×#208D414yescomplemented
82C2×C5×C3⋊C8C2312yes—
83C5×ΓL(1,𝔽25)—24no—
84C5×D3×C8—24no—
85C3×C22⋊Dic5—21no—
86C3×C4⋊Dic5C2311yescharacteristic
87C3×C4⋊Dic5C2311yescharacteristic
88C3×C4×Dic5—21no—
89#6669—22no—
90#6668—22no—
91#6668—22no—
92(C2×D3)⋊Dic5—22no—
93(C2×D3)⋊Dic5—22no—
94(C2×D3)⋊Dic5—22no—
95#6665—22no—
96#6662—24no—
97#6657—24no—
98#5833—51no—
99C2×#951—51no—
100C2×#901D511yescharacteristic, complemented
101#5526—51no—
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—
110C2×#709C2×D311yescharacteristic
111C22×Dic10—31no—
112C5×#131—64no—
113C2×C5×M16—31no—
114C2×C5×M16—32no—
115C22×C5×C8—32no—
116C22×C5×C8C2×D311yescharacteristic
117#4092—61no—
118#4090—61no—
119#4085—62no—
120#4084—61no—
121#4082—61no—
122#4081—62no—
123#4076—32no—
124#4072C2×D311yescharacteristic
125C2×C4⋊Dic5—31no—
126#4070—32no—
127#4070—32no—
128#4070—32no—
129#4055—64no—
130C2×Dic20—32no—
131C2×#677—32no—
132#3953C2×D311yescharacteristic
133#3953C2×D311yescharacteristic
134#3950—32no—
135#3949—32no—
136#3948—32no—
137#3948—32no—
138#3948C2×D311yescharacteristic
139#3948C2×D311yescharacteristic
140#3063—151noSylow
141C23×C3×C5C2×D411yescharacteristic
142C22×C5×D3C2×D412yes—
143C22×C3×D5—21no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5#4112yes—
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—22no—
149C2×Dic15—22no—
150C2×Dic15—42no—
151C2×Dic15—81no—
152Dic30—22no—
153Dic30—22no—
154Dic30—42no—
155C5×#67—24no—
156C2×C5×Dic3C2×D412yes—
157C5×D12—22no—
158C4×C5×D3—22no—
159C4×C5×D3—22no—
160C5×Dic6—22no—
161C3×C22⋊D5—42no—
162C2×C3×Dic5—21no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—21no—
165C3×D20—21no—
166C3×D20—21no—
167C3×C4×D5—42no—
168C3×Dic10—21no—
169C3×Dic10—21no—
170#1201—82no—
171C3×C5×C8—21no—
172C3×C5×C8—21no—
173C5×C3⋊C8C2×D414yes—
174C2×C3×#41—51no—
175C2×#235C2×D511yescharacteristic
176C22×Dic6—51no—
177C22×C3×C8C2×D511yescharacteristic
178C3×#117—51no—
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×#208C2×D511yescharacteristic
189#901—24no—
190C2×ΓL(1,𝔽25)C2×D512yes—
191C2×D3×C8C2×D512yes—
192#897—52no—
193#897—52no—
194#886—102no—
195#875—101no—
196#869—101no—
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×D4—32no—
209C2×C5×D4—31no—
210C22×C4×C5—32no—
211C22×C4×C5C22×D311yescharacteristic
212C2×C22⋊D5—21no—
213C2×C22⋊D5—62no—
214C22×Dic5—61no—
215C22×Dic5—61no—
216#709—22no—
217#709—22no—
218C2×D20C22×D311yescharacteristic
219C2×C4×D5—21no—
220C2×Dic10—32no—
221C2×Dic10—62no—
222C2×Dic10—62no—
223C2×Dic10—61no—
224C2×Dic10C22×D311yescharacteristic
225C5×M16—34no—
226C5×M16—64no—
227C2×C5×C8—22no—
228C2×C5×C8—32no—
229C2×C5×C8—64no—
230C2×C5×C8C22×D311yescharacteristic
231C2×C5×C8C22×D311yescharacteristic
232C22⋊Dic5—21no—
233C22⋊Dic5—62no—
234C22⋊Dic5—62no—
235C22⋊Dic5—62no—
236#685—62no—
237C4⋊Dic5—32no—
238C4⋊Dic5—61no—
239C4⋊Dic5C22×D311yescharacteristic
240C4⋊Dic5C22×D311yescharacteristic
241#683—62no—
242#683—62no—
243#683—62no—
244C4×Dic5—21no—
245Dic20—64no—
246#677—64no—
247C2×#137—151no—
248C2×#131—31no—
249#537—151no—
250#536—151no—
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#12112yes—
269C3×C4×C5C22×D411yescharacteristic
270C3×C4×C5C2×#4111yescharacteristic
271Dic15—42no—
272Dic15—42no—
273C3×Dic5—41no—
274C3×Dic5—41no—
275C3×Dic5—41no—
276C5×Dic3—22no—
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×#67D2012yes—
286C22×Dic3—101no—
287C22×Dic3—101no—
288#235—22no—
289#235—22no—
290C2×D12D2011yescharacteristic
291C2×C4×D3C22×D512yes—
292C2×Dic6—52no—
293C2×Dic6—102no—
294C2×Dic6—102no—
295C2×Dic6—101no—
296C2×Dic6D2011yescharacteristic
297C2×C3×C8—22no—
298C2×C3×C8C22×D511yescharacteristic
299C2×C3×C8C22×D511yescharacteristic
300C3×C4⋊C4—51no—
301C3×C4⋊C4—51no—
302C3×C22⋊C4—101no—
303C3×C42—101no—
304#217—102no—
305#216—104no—
306#214—104no—
307(C2×D3)⋊C4—102no—
308(C2×D3)⋊C4—102no—
309(C2×D3)⋊C4—102no—
310C4⋊Dic3—52no—
311C4⋊Dic3—101no—
312C4⋊Dic3—102no—
313C4⋊Dic3—102no—
314Dic3⋊C4—102no—
315#208C22⋊D514yescomplemented
316C2×C3⋊C8C22×D512yes—
317ΓL(1,𝔽25)—24no—
318D3×C8—24no—
319C23×C5—32no—
320C23×C5D3×D411yescharacteristic
321C22×D5—21no—
322C5×Q8—62no—
323C5×D4—64no—
324C5×D4—62no—
325C2×C4×C5—32no—
326C2×C4×C5—62no—
327C2×C4×C5—62no—
328C2×C4×C5#23512yes—
329C2×C4×C5D3×D411yescharacteristic
330C2×C4×C5D3×D412yes—
331C2×C4×C5C23×D311yescharacteristic
332C22⋊D5—42no—
333C22⋊D5—242no—
334C2×Dic5—21no—
335C2×Dic5—21no—
336C2×Dic5—21no—
337C2×Dic5—62no—
338C2×Dic5—62no—
339C2×Dic5—122no—
340C2×Dic5—241no—
341D20—21no—
342D20—21no—
343C4×D5—42no—
344Dic10—21no—
345Dic10—21no—
346Dic10—62no—
347Dic10—62no—
348Dic10—122no—
349C5×C8—21no—
350C5×C8—21no—
351C5×C8—34no—
352C2×#41—31no—
353C2×#41—51no—
354C22×Q8—151no—
355#137—304no—
356C2×Q16—152no—
357C2×SD16—152no—
358#131—64no—
359C2×M16—31no—
360C2×M16—32no—
361C22×C8—32no—
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—51no—
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×D2011yescharacteristic
391C22×D3C2×D2012yes—
392C3×Q8—101no—
393C3×Q8—101no—
394C3×D4—101no—
395C3×D4—101no—
396C3×D4—202no—
397C2×C3×C4—101no—
398C2×C3×C4—101no—
399C2×C3×C4—101no—
400C2×C3×C4—202no—
401C2×C3×C4C2×D2011yescharacteristic
402C2×C3×C4#70912yes—
403C2×C3×C4C2×C22⋊D512yes—
404C2×C3×C4C23×D511yescharacteristic
405#67—24no—
406#67—402no—
407C2×Dic3—102no—
408C2×Dic3—102no—
409C2×Dic3—202no—
410C2×Dic3—401no—
411C2×Dic3C2×D2012yes—
412D12—22no—
413C4×D3—22no—
414C4×D3—22no—
415Dic6—22no—
416Dic6—102no—
417Dic6—102no—
418Dic6—202no—
419C3×C8—21no—
420C3×C8—21no—
421C3⋊C8C2×C22⋊D514yes—
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—62no—
433C4×C5#88412yes—
434C4×C5C2×#23511yescharacteristic
435C4×C5C2×D3×D411yescharacteristic
436Dic5—41no—
437Dic5—41no—
438Dic5—41no—
439Dic5—122no—
440Dic5—122no—
441#41—62no—
442#41—62no—
443#41—102no—
444#41—102no—
445C2×Q8—31no—
446C2×Q8—51no—
447C2×Q8—152no—
448C2×Q8—301no—
449C2×Q8—302no—
450C2×Q8—302no—
451C2×D4—32no—
452C2×D4—31no—
453C2×D4—51no—
454C2×D4—101no—
455C2×D4—302no—
456C22×C4—32no—
457C22×C4—101no—
458C22×C4—301no—
459C22×C4—301no—
460C22×C4C2×D3×D511yescharacteristic
461Q16—304no—
462SD16—304no—
463M16—34no—
464M16—64no—
465C2×C8—22no—
466C2×C8—32no—
467C2×C8—64no—
468C2×C8C2×D3×D511yescharacteristic
469C2×C8C2×D3×D511yescharacteristic
470C4⋊C4—51no—
471C4⋊C4—51no—
472C4⋊C4—152no—
473C4⋊C4—302no—
474C4⋊C4—302no—
475C4⋊C4—302no—
476C4⋊C4—301no—
477C22⋊C4—101no—
478C22⋊C4—302no—
479C22⋊C4—302no—
480C22⋊C4—302no—
481C22⋊C4—302no—
482C42—101no—
483C3×C5#306311yescharacteristic, complemented, Hall
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—201no—
487C22×C3—201no—
488C22×C3—201no—
489C22×C3#407612yes—
490C22×C3C22×D2011yescharacteristic
491C2×D3—22no—
492C2×D3—22no—
493C2×D3—22no—
494C3×C4—201no—
495C3×C4—201no—
496C3×C4—201no—
497C3×C4#407612yes—
498C3×C4C2×#70911yescharacteristic
499C3×C4C22×C22⋊D511yescharacteristic
500Dic3—22no—
501Dic3—202no—
502Dic3—202no—
503C2×C5—22no—
504C2×C5—122no—
505C2×C5C2×#88411yescharacteristic
506C2×C5#577011yescharacteristic
507C2×C5#577111yescharacteristic
508D5—81no—
509C23—32no—
510C23—101no—
511C23D3×D2011yescharacteristic
512Q8—62no—
513Q8—101no—
514Q8—101no—
515Q8—302no—
516Q8—302no—
517Q8—602no—
518D4—64no—
519D4—62no—
520D4—101no—
521D4—101no—
522D4—202no—
523D4—1202no—
524C2×C4—32no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—101no—
528C2×C4—101no—
529C2×C4—101no—
530C2×C4—202no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—602no—
534C2×C4—1201no—
535C2×C4#677112yes—
536C2×C4D3×D2011yescharacteristic
537C2×C4D3×C22⋊D512yes—
538C2×C4C22×D3×D511yescharacteristic
539C8—21no—
540C8—21no—
541C8—34no—
542C2×C3—22no—
543C2×C3—401no—
544C2×C3#6608511yescharacteristic
545C2×C3#6608711yescharacteristic
546C2×C3C2×#407611yescharacteristic
547D3—42no—
548C5#7884111yescharacteristic, complemented, Sylow
549C22—21no—
550C22—21no—
551C22—62no—
552C22—62no—
553C22—62no—
554C22—201no—
555C22—201no—
556C22—201no—
557C22#9145412yes—
558C22C2×D3×D2011yescharacteristic
559C4—62no—
560C4—201no—
561C4—201no—
562C4—201no—
563C4—602no—
564C4—602no—
565C4#9145412yes—
566C4C2×#677111yescharacteristic
567C4C2×D3×C22⋊D511yescharacteristic
568C3#1061553911yescharacteristic, complemented, Sylow
569C2—22no—
570C2—122no—
571C2—401no—
572C2#1175397211yescharacteristic
573C2#1175400311yescharacteristic
574C2C2×#9145411yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11754607C2
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×C5×#901C2semidirect
3. #11754271C2semidirect
4. C2×#91313C2semidirect
5. C2×#91100C2semidirect
6. C3×#65402C2semidirect
7. #11748455C2semidirect
8. #11747948C2semidirect
9. #11747947C2semidirect
10. #11747911C2semidirect
11. #11747908C2semidirect
54. #65402D3semidirect
81. C5×#208D4semidirect
100. C2×#901D5semidirect
315. #208C22⋊D5semidirect
483. C3×C5#3063semidirect
548. C5#78841semidirect
568. C3#10615539semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9012
#117546072
#117542712
C2×#913132
C2×#911002
C3×#654022
#117484552
#117479482
#117479472
#117479112
#117479082
#106155393
#788415