Finite Group Databasebeta

← #14429249

Subgroups — #14429249

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×C3×#4047C211yesmaximal, characteristic, complemented
2#11754607C211yesmaximal, characteristic
3#11754252C211yesmaximal, characteristic, complemented
4C2×#91322C211yesmaximal, characteristic, complemented
5C2×#91100C211yesmaximal, characteristic, complemented
6C5×#5113C211yesmaximal, characteristic, complemented
7#11748460C211yesmaximal, characteristic, complemented
8#11747940C212yesmaximal, complemented
9#11747939C212yesmaximal, complemented
10#11747895C212yesmaximal, complemented
11#11747892C212yesmaximal, complemented
12#10610572—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×C5×C8C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C5×#926C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C3×#4047—24no—
21C2×C3×#676C2212yes—
22C2×C3×C8×D5C2212yes—
23#91571—22no—
24#91537—22no—
25#91456—21no—
26#91449C2212yes—
27#91389—21no—
28#91369—21no—
29#91364—21no—
30#91360C2212yes—
31#91360C2212yes—
32#91359C2212yes—
33#91322—24no—
34C2×#6663C2212yes—
35C2×#6659C2212yes—
36#91100C2212yes—
37#91100C2212yes—
38C5×#821C2211yescharacteristic
39C5×#821C2211yescharacteristic
40C5×#816C2211yescharacteristic
41C5×#816C2211yescharacteristic
42#90988C2212yes—
43#90985C2212yes—
44#83808—51nomaximal, Hall
45#66167—31no—
46C2×#4097—31no—
47C2×#4047D311yescharacteristic, complemented
48#65860—31no—
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—
58C22×Dic15—21no—
59C2×Dic30—22no—
60C2×Dic30—22no—
61C2×Dic30—21no—
62C2×Dic30C2312yes—
63C2×C5×#67—21no—
64C5×#235—22no—
65C5×#235—22no—
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C2×C3×C22⋊D5D412yes—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20D411yescharacteristic
73C2×C3×C4×D5C2312yes—
74C2×C3×Dic10D411yescharacteristic
75C2×#1201—22no—
76C2×C3×C5×C8—22no—
77C2×C3×C5×C8C2311yescharacteristic
78C2×C3×C5×C8C2311yescharacteristic
79C4⋊Dic15—21no—
80C4⋊Dic15C2312yes—
81C5×#217—21no—
82C5×C4⋊Dic3C2311yescharacteristic
83C5×C4⋊Dic3C2311yescharacteristic
84C4×C5×Dic3—21no—
85C3×#681D414yescomplemented
86C2×C3×#168C2312yes—
87C3×#676—24no—
88C3×C8×D5—24no—
89Dic3⋊Dic5—22no—
90Dic3⋊Dic5—22no—
91#6669—22no—
92(C2×D3)⋊Dic5—22no—
93#6665—22no—
94#6665—22no—
95#6665—22no—
96#6663—24no—
97#6659—24no—
98C2×C3×#131—51no—
99#5833—51no—
100#5825—51no—
101C2×#909—51no—
102#5137—52no—
103#5134—52no—
104#5121—51no—
105#5116—52no—
106#5114—52no—
107#5113D511yescharacteristic, complemented
108C2×#816—51no—
109C2×C5×#41—31no—
110C2×#709C2×D311yescharacteristic
111C22×Dic10—31no—
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⋊Dic5—31no—
122#4070—61no—
123C2×#681C2×D311yescharacteristic
124#4047—24no—
125C2×#676C2×D312yes—
126C2×C8×D5C2×D312yes—
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#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×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—42no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—21no—
159C5×D12—21no—
160C5×D12—21no—
161C4×C5×D3—42no—
162C5×Dic6—21no—
163C5×Dic6—21no—
164C3×C22⋊D5—24no—
165C2×C3×Dic5C2×D412yes—
166C3×D20—22no—
167C3×C4×D5—22no—
168C3×C4×D5—22no—
169C3×Dic10—22no—
170#1201—82no—
171C3×C5×C8—21no—
172C3×C5×C8—21no—
173C3×#168C2×D414yes—
174C2×C3×#41—51no—
175C2×#235C2×D511yescharacteristic
176C22×Dic6—51no—
177C3×#131—104no—
178C2×C3×M16—51no—
179C2×C3×M16—52no—
180C22×C3×C8—52no—
181C22×C3×C8C2×D511yescharacteristic
182#946—101no—
183#944—101no—
184#939—102no—
185#938—101no—
186#936—101no—
187#935—102no—
188#930—52no—
189#926C2×D511yescharacteristic
190C2×C4⋊Dic3—51no—
191#924—52no—
192#924—52no—
193#924—52no—
194#909—104no—
195C2×Dic12—52no—
196C2×#204—52no—
197#821C2×D511yescharacteristic
198#821C2×D511yescharacteristic
199#818—52no—
200#817—52no—
201#816—52no—
202#816—52no—
203#816C2×D511yescharacteristic
204#816C2×D511yescharacteristic
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⋊D5D1212yes—
214C22×Dic5—61no—
215C22×Dic5—61no—
216#709—22no—
217#709—22no—
218C2×D20D1211yescharacteristic
219C2×C4×D5C22×D312yes—
220C2×Dic10—32no—
221C2×Dic10—62no—
222C2×Dic10—62no—
223C2×Dic10—61no—
224C2×Dic10D1211yescharacteristic
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—32no—
239C4⋊Dic5—61no—
240C4⋊Dic5—62no—
241C4⋊Dic5—62no—
242#683—62no—
243#681#6714yescomplemented
244C2×#168C22×D312yes—
245#676—24no—
246C8×D5—24no—
247C2×#137—151no—
248C2×#131—51no—
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—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#12112yes—
269C3×C4×C5C22×D411yescharacteristic
270C3×C4×C5C2×#4111yescharacteristic
271Dic15—42no—
272Dic15—42no—
273C3×Dic5—22no—
274C5×Dic3—41no—
275C5×Dic3—41no—
276C5×Dic3—41no—
277C3×#41—102no—
278C3×#41—102no—
279C2×C3×Q8—51no—
280C2×C3×D4—52no—
281C2×C3×D4—51no—
282C22×C3×C4—52no—
283C22×C3×C4C22×D511yescharacteristic
284C2×#67—21no—
285C2×#67—102no—
286C22×Dic3—101no—
287C22×Dic3—101no—
288#235—22no—
289#235—22no—
290C2×D12C22×D511yescharacteristic
291C2×C4×D3—21no—
292C2×Dic6—52no—
293C2×Dic6—102no—
294C2×Dic6—102no—
295C2×Dic6—101no—
296C2×Dic6C22×D511yescharacteristic
297C3×M16—54no—
298C3×M16—104no—
299C2×C3×C8—22no—
300C2×C3×C8—52no—
301C2×C3×C8—104no—
302C2×C3×C8C22×D511yescharacteristic
303C2×C3×C8C22×D511yescharacteristic
304#217—21no—
305#217—102no—
306#217—102no—
307#217—102no—
308(C2×D3)⋊C4—102no—
309C4⋊Dic3—52no—
310C4⋊Dic3—101no—
311C4⋊Dic3C22×D511yescharacteristic
312C4⋊Dic3C22×D511yescharacteristic
313Dic3⋊C4—102no—
314Dic3⋊C4—102no—
315Dic3⋊C4—102no—
316C4×Dic3—21no—
317Dic12—104no—
318#204—104no—
319C23×C5—61no—
320C23×C5C2×D1211yescharacteristic
321C22×D5C2×D1212yes—
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×C5C2×D1211yescharacteristic
332C2×C4×C5#23512yes—
333C2×C4×C5C2×#6712yes—
334C2×C4×C5C23×D311yescharacteristic
335C22⋊D5—24no—
336C22⋊D5—242no—
337C2×Dic5—62no—
338C2×Dic5—62no—
339C2×Dic5—122no—
340C2×Dic5—241no—
341C2×Dic5C2×D1212yes—
342D20—22no—
343C4×D5—22no—
344C4×D5—22no—
345Dic10—22no—
346Dic10—62no—
347Dic10—62no—
348Dic10—122no—
349C5×C8—21no—
350C5×C8—21no—
351#168C2×#6714yes—
352C2×#41—31no—
353C2×#41—51no—
354C22×Q8—151no—
355#137—304no—
356C2×Q16—152no—
357C2×SD16—152no—
358#131—104no—
359C2×M16—51no—
360C2×M16—52no—
361C22×C8—52no—
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—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×D4—104no—
394C3×D4—102no—
395C2×C3×C4—52no—
396C2×C3×C4—102no—
397C2×C3×C4—102no—
398C2×C3×C4#70912yes—
399C2×C3×C4D4×D511yescharacteristic
400C2×C3×C4D4×D512yes—
401C2×C3×C4C23×D511yescharacteristic
402#67—42no—
403#67—402no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—102no—
408C2×Dic3—102no—
409C2×Dic3—202no—
410C2×Dic3—401no—
411D12—21no—
412D12—21no—
413C4×D3—42no—
414Dic6—21no—
415Dic6—21no—
416Dic6—102no—
417Dic6—102no—
418Dic6—202no—
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#93012yes—
428C22×C5C22×D1211yescharacteristic
429C2×D5—22no—
430C2×D5—22no—
431C2×D5—22no—
432C4×C5—121no—
433C4×C5—121no—
434C4×C5—121no—
435C4×C5#93012yes—
436C4×C5C2×#23511yescharacteristic
437C4×C5C22×#6711yescharacteristic
438Dic5—22no—
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—31no—
452C2×D4—52no—
453C2×D4—51no—
454C2×D4—61no—
455C2×D4—302no—
456C22×C4—52no—
457C22×C4—61no—
458C22×C4—301no—
459C22×C4—301no—
460C22×C4C2×D3×D511yescharacteristic
461Q16—304no—
462SD16—304no—
463M16—54no—
464M16—104no—
465C2×C8—22no—
466C2×C8—52no—
467C2×C8—104no—
468C2×C8C2×D3×D511yescharacteristic
469C2×C8C2×D3×D511yescharacteristic
470C4⋊C4—31no—
471C4⋊C4—31no—
472C4⋊C4—152no—
473C4⋊C4—302no—
474C4⋊C4—302no—
475C4⋊C4—302no—
476C4⋊C4—301no—
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—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—102no—
495C3×C4#403012yes—
496C3×C4C2×#70911yescharacteristic
497C3×C4C2×D4×D511yescharacteristic
498Dic3—41no—
499Dic3—41no—
500Dic3—41no—
501Dic3—202no—
502Dic3—202no—
503C2×C5—22no—
504C2×C5—241no—
505C2×C5#575111yescharacteristic
506C2×C5#575311yescharacteristic
507C2×C5C2×#93011yescharacteristic
508D5—42no—
509C23—52no—
510C23—61no—
511C23D5×D1211yescharacteristic
512Q8—61no—
513Q8—61no—
514Q8—102no—
515Q8—302no—
516Q8—302no—
517Q8—602no—
518D4—61no—
519D4—61no—
520D4—104no—
521D4—102no—
522D4—122no—
523D4—1202no—
524C2×C4—52no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—122no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—602no—
534C2×C4—1201no—
535C2×C4#677112yes—
536C2×C4D5×D1211yescharacteristic
537C2×C4D5×#6712yes—
538C2×C4C22×D3×D511yescharacteristic
539C8—21no—
540C8—21no—
541C8—54no—
542C2×C3—22no—
543C2×C3—202no—
544C2×C3C2×#403011yescharacteristic
545C2×C3#6610411yescharacteristic
546C2×C3#6610511yescharacteristic
547D3—81no—
548C5#8380811yescharacteristic, complemented, Sylow
549C22—21no—
550C22—21no—
551C22—102no—
552C22—102no—
553C22—102no—
554C22—121no—
555C22—121no—
556C22—121no—
557C22#9144812yes—
558C22C2×D5×D1211yescharacteristic
559C4—102no—
560C4—121no—
561C4—121no—
562C4—121no—
563C4—602no—
564C4—602no—
565C4#9144812yes—
566C4C2×#677111yescharacteristic
567C4C2×D5×#6711yescharacteristic
568C3#1061057211yescharacteristic, complemented, Sylow
569C2—22no—
570C2—202no—
571C2—241no—
572C2#1175396211yescharacteristic
573C2#1175398811yescharacteristic
574C2C2×#9144811yescharacteristic
subgroupG/H
centerC22C2×D5×D12
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×C3×#4047C2semidirect
3. #11754252C2semidirect
4. C2×#91322C2semidirect
5. C2×#91100C2semidirect
6. C5×#5113C2semidirect
7. #11748460C2semidirect
8. #11747940C2semidirect
9. #11747939C2semidirect
10. #11747895C2semidirect
11. #11747892C2semidirect
47. C2×#4047D3semidirect
85. C3×#681D4semidirect
107. #5113D5semidirect
243. #681#67semidirect
483. C3×C5#3063semidirect
548. C5#83808semidirect
568. C3#10610572semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40472
#117546072
#117542522
C2×#913222
C2×#911002
C5×#51132
#117484602
#117479402
#117479392
#117478952
#117478922
#106105723
#838085