Finite Group Databasebeta

← #14429254

Subgroups — #14429254

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
1#11756269C211yesmaximal, characteristic
2#11754270C211yesmaximal, characteristic, complemented
3C2×#91321C211yesmaximal, characteristic, complemented
4C2×#91291C211yesmaximal, characteristic, complemented
5C2×C5×#810C211yesmaximal, characteristic, complemented
6C3×#65253C211yesmaximal, characteristic, complemented
7#11748411C211yesmaximal, characteristic, complemented
8#11747451C212yesmaximal, complemented
9#11747450C212yesmaximal, complemented
10#11747347C212yesmaximal, complemented
11#11747346C212yesmaximal, complemented
12#10610531—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17#91819—22no—
18#91786—21no—
19#91786C2212yes—
20#91784—21no—
21#91784C2212yes—
22C22×C5×C3⋊C8C2211yescharacteristic
23C3×#4072C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25#91542—22no—
26#91383C2212yes—
27#91383C2212yes—
28#91376—21no—
29#91375—21no—
30#91321—24no—
31C2×#6663C2212yes—
32C2×#6660C2212yes—
33C2×#6651C2212yes—
34#91291—24no—
35C2×#6648C2212yes—
36C5×#810C2212yes—
37C5×#810C2212yes—
38C3×#3940C2212yes—
39C3×#3939C2212yes—
40#90974C2211yescharacteristic
41#90974C2211yescharacteristic
42#90968C2211yescharacteristic
43#90968C2211yescharacteristic
44#79214—51nomaximal, Hall
45#66150—31no—
46C2×#4088—31no—
47C2×#4047—31no—
48#65844—31no—
49C2×C5×#103—31no—
50#65402—31no—
51#65253D311yescharacteristic, complemented
52#65105—32no—
53#65102—32no—
54#65101—32no—
55#65096—32no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59C2×#1220D412yes—
60#6817—22no—
61#6817—22no—
62#6817—22no—
63#6817—22no—
64C2×D60—22no—
65C2×D60D411yescharacteristic
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×C4×D15C2312yes—
69C2×Dic30D411yescharacteristic
70C2×Dic30C2311yescharacteristic
71C22×C5×Dic3—21no—
72C2×C5×Dic6—22no—
73C2×C5×Dic6—22no—
74C2×C5×Dic6—21no—
75C2×C5×Dic6C2312yes—
76C3×C5×C4⋊C4—21no—
77C3×C5×C4⋊C4C2312yes—
78#6714—22no—
79#6714—22no—
80C4⋊Dic15—22no—
81C2×C5×C3⋊C8—22no—
82C2×C5×C3⋊C8C2311yescharacteristic
83C2×C5×C3⋊C8C2311yescharacteristic
84C3×C22⋊Dic5—21no—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×C4⋊Dic5C2311yescharacteristic
87C3×C4×Dic5—21no—
88C3×#681D414yescomplemented
89C2×C3×#168C2312yes—
90#6668—22no—
91#6668—22no—
92#6667—22no—
93#6667—22no—
94#6663—24no—
95#6660—24no—
96#6651—24no—
97#6648—24no—
98C2×#909—51no—
99C2×#907—51no—
100#5526—51no—
101#5510—51no—
102C3×#428—51no—
103#5002—51no—
104C2×#810D511yescharacteristic, complemented
105#4887—52no—
106#4886—52no—
107#4867—52no—
108#4864—52no—
109C22×C5×Q8—31no—
110C2×#709—31no—
111C2×#709—31no—
112C22×C5×C8—31no—
113C2×C5×C4⋊C4C2×D311yescharacteristic
114#4093—61no—
115#4092—32no—
116#4092—32no—
117#4090—61no—
118C2×#689—32no—
119#4088—64no—
120C2×#688—32no—
121#4076—62no—
122#4075—62no—
123#4072C2×D311yescharacteristic
124C2×#681C2×D311yescharacteristic
125#4047—64no—
126C2×#676—32no—
127C2×C8×D5—32no—
128#4043—32no—
129#4043—61no—
130#4041—32no—
131#4041—61no—
132C5×#103—32no—
133C5×#103—32no—
134#3953—31no—
135#3953—31no—
136#3948—31no—
137#3948—31no—
138#3940C2×D312yes—
139#3939C2×D312yes—
140#3063—151noSylow
141C23×C3×C5C2×D411yescharacteristic
142C22×D15—21no—
143C22×D15C2×D412yes—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—81no—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5#4112yes—
149C2×C3×C4×C5C2411yescharacteristic
150#1220—24no—
151#1220—42no—
152C2×Dic15—21no—
153C2×Dic15C2×D412yes—
154D60—22no—
155D60—21no—
156D60—21no—
157D60—82no—
158C4×D15—22no—
159C4×D15—22no—
160C4×D15—42no—
161Dic30—22no—
162Dic30—21no—
163Dic30—21no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—42no—
166C5×Dic6—22no—
167C5×Dic6—22no—
168C5×Dic6—42no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—21no—
171C3×#168C2×D414yes—
172C5×C3⋊C8—21no—
173C5×C3⋊C8—21no—
174C2×#235—51no—
175C2×#235—51no—
176C22×Dic6C2×D511yescharacteristic
177C2×C3×M16—51no—
178C3×#117—51no—
179C2×C3×C4⋊C4C2×D511yescharacteristic
180#930—102no—
181C22×C3⋊C8C2×D511yescharacteristic
182#909—104no—
183#907—104no—
184C2×Dic12—52no—
185C2×#204—52no—
186C2×ΓL(1,𝔽25)—52no—
187C2×D3×C8—52no—
188#897—52no—
189#897—52no—
190#897—52no—
191#897—101no—
192#895—52no—
193#895—101no—
194#886—102no—
195#875—101no—
196#869—101no—
197C3×#107—52no—
198C3×#106—52no—
199#810—51no—
200#810—51no—
201#810C2×D512yes—
202#810C2×D512yes—
203#809—51no—
204#809—51no—
205C2×C5×Q8—32no—
206C2×C5×Q8—61no—
207C2×C5×Q8—62no—
208C2×C5×Q8—62no—
209C22×C4×C5—21no—
210C22×C4×C5—61no—
211C22×C4×C5C22×D311yescharacteristic
212C2×C22⋊D5—32no—
213C2×C22⋊D5—61no—
214#709—62no—
215#709—62no—
216#709—62no—
217#709—62no—
218C2×D20—31no—
219C2×D20—31no—
220C2×D20—62no—
221C2×C4×D5—32no—
222C2×C4×D5—61no—
223C2×Dic10—31no—
224C2×Dic10—31no—
225C2×C5×C8—31no—
226C2×C5×C8—31no—
227C2×C5×C8—62no—
228C5×C4⋊C4—21no—
229C5×C4⋊C4C22×D312yes—
230C22⋊Dic5—21no—
231#689—64no—
232#688—64no—
233#685—62no—
234#685—62no—
235#685—62no—
236#685—62no—
237C4⋊Dic5—62no—
238C4⋊Dic5C22×D311yescharacteristic
239C4⋊Dic5C22×D311yescharacteristic
240#683—62no—
241#683—62no—
242C4×Dic5—21no—
243#681D1214yescomplemented
244C2×#168C22×D312yes—
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—51no—
256#416—151no—
257C2×#103—31no—
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×D15—41no—
266C2×D15—41no—
267C2×D15—41no—
268C3×C4×C5—42no—
269C3×C4×C5#12112yes—
270C3×C4×C5C22×D411yescharacteristic
271C3×C4×C5C2×#4111yescharacteristic
272Dic15—22no—
273Dic15—41no—
274C3×Dic5—41no—
275C3×Dic5—41no—
276C5×Dic3—42no—
277C22×C3×C4—21no—
278C22×C3×C4C22×D511yescharacteristic
279C2×#67—52no—
280C2×#67—101no—
281C22×Dic3—21no—
282#235—102no—
283#235—102no—
284#235—102no—
285#235—102no—
286C2×D12—51no—
287C2×D12—51no—
288C2×D12—102no—
289C2×C4×D3—52no—
290C2×C4×D3—101no—
291C2×Dic6—22no—
292C2×Dic6—22no—
293C2×Dic6—21no—
294C2×Dic6—51no—
295C2×Dic6—51no—
296C2×Dic6C22×D512yes—
297C3×M16—54no—
298C2×C3×C8—52no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—51no—
301C3×C4⋊C4—51no—
302C3×C4⋊C4C22×D512yes—
303C3×C22⋊C4—101no—
304C3×C42—101no—
305(C2×D3)⋊C4—102no—
306(C2×D3)⋊C4—102no—
307(C2×D3)⋊C4—102no—
308(C2×D3)⋊C4—102no—
309C4⋊Dic3—102no—
310C4⋊Dic3—102no—
311C4⋊Dic3—102no—
312C2×C3⋊C8—22no—
313C2×C3⋊C8C22×D511yescharacteristic
314C2×C3⋊C8C22×D511yescharacteristic
315Dic12—104no—
316#204—104no—
317ΓL(1,𝔽25)—104no—
318D3×C8—104no—
319C23×C5D3×D411yescharacteristic
320C22×D5—32no—
321C22×D5—61no—
322C5×Q8—62no—
323C5×Q8—62no—
324C5×Q8—122no—
325C2×C4×C5—22no—
326C2×C4×C5—62no—
327C2×C4×C5—81no—
328C2×C4×C5—122no—
329C2×C4×C5C2×D1212yes—
330C2×C4×C5D3×D411yescharacteristic
331C2×C4×C5#23912yes—
332C2×C4×C5C23×D311yescharacteristic
333C22⋊D5—64no—
334C22⋊D5—122no—
335C2×Dic5—21no—
336C2×Dic5—21no—
337C2×Dic5—32no—
338C2×Dic5—61no—
339D20—62no—
340D20—61no—
341D20—61no—
342D20—242no—
343C4×D5—62no—
344C4×D5—62no—
345C4×D5—122no—
346Dic10—62no—
347Dic10—61no—
348Dic10—61no—
349C5×C8—61no—
350C5×C8—61no—
351#168C2×D1214yes—
352C2×#41—151no—
353C2×#41—151no—
354C22×Q8—31no—
355#137—304no—
356C2×Q16—152no—
357C2×SD16—152no—
358#131—304no—
359C2×M16—51no—
360C2×M16—152no—
361C22×C8—31no—
362C22×C8—152no—
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⋊C4D3×D511yescharacteristic
375#107—52no—
376#106—52no—
377#103—32no—
378#103—32no—
379#103—151no—
380#103—151no—
381#102—151no—
382#102—151no—
383C2×C3×C5—22no—
384C2×C3×C5C2×#12111yescharacteristic
385C2×C3×C5#57711yescharacteristic
386C2×C3×C5#57811yescharacteristic
387D15—42no—
388D15—81no—
389C23×C3D4×D511yescharacteristic
390C22×D3—52no—
391C22×D3—101no—
392C2×C3×C4—22no—
393C2×C3×C4—81no—
394C2×C3×C4—101no—
395C2×C3×C4—101no—
396C2×C3×C4#70912yes—
397C2×C3×C4D4×D512yes—
398C2×C3×C4D4×D511yescharacteristic
399C2×C3×C4C23×D511yescharacteristic
400#67—104no—
401#67—202no—
402C2×Dic3—22no—
403C2×Dic3—42no—
404C2×Dic3—52no—
405C2×Dic3—101no—
406D12—101no—
407D12—101no—
408D12—102no—
409D12—402no—
410C4×D3—102no—
411C4×D3—102no—
412C4×D3—202no—
413Dic6—22no—
414Dic6—22no—
415Dic6—42no—
416Dic6—102no—
417Dic6—101no—
418Dic6—101no—
419C3×C8—54no—
420C3⋊C8—21no—
421C3⋊C8—21no—
422C22×C5—21no—
423C22×C5—21no—
424C22×C5#89512yes—
425C22×C5C2×D3×D411yescharacteristic
426C2×D5—62no—
427C2×D5—62no—
428C2×D5—62no—
429C2×D5—121no—
430C2×D5—121no—
431C2×D5—121no—
432C4×C5—42no—
433C4×C5—122no—
434C4×C5#89512yes—
435C4×C5C22×D1211yescharacteristic
436C4×C5C2×#23911yescharacteristic
437Dic5—41no—
438Dic5—41no—
439Dic5—62no—
440Dic5—121no—
441#41—302no—
442#41—302no—
443#41—302no—
444#41—302no—
445C2×Q8—32no—
446C2×Q8—61no—
447C2×Q8—62no—
448C2×Q8—62no—
449C2×Q8—151no—
450C2×Q8—151no—
451C2×D4—152no—
452C2×D4—151no—
453C2×D4—151no—
454C2×D4—302no—
455C2×D4—301no—
456C22×C4—21no—
457C22×C4—61no—
458C22×C4—152no—
459C22×C4—301no—
460C22×C4C2×D3×D511yescharacteristic
461Q16—304no—
462SD16—304no—
463M16—54no—
464M16—304no—
465C2×C8—31no—
466C2×C8—31no—
467C2×C8—52no—
468C2×C8—62no—
469C2×C8—304no—
470C4⋊C4—21no—
471C4⋊C4—51no—
472C4⋊C4—51no—
473C4⋊C4—302no—
474C4⋊C4—302no—
475C4⋊C4—302no—
476C4⋊C4C2×D3×D512yes—
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#403012yes—
487C22×C3C2×D4×D511yescharacteristic
488C2×D3—102no—
489C2×D3—102no—
490C2×D3—102no—
491C2×D3—201no—
492C2×D3—201no—
493C2×D3—201no—
494C3×C4—42no—
495C3×C4—201no—
496C3×C4—201no—
497C3×C4#403012yes—
498C3×C4C2×#70911yescharacteristic
499C3×C4C2×D4×D511yescharacteristic
500Dic3—42no—
501Dic3—102no—
502Dic3—201no—
503C2×C5—22no—
504C2×C5C2×#89511yescharacteristic
505C2×C5#577511yescharacteristic
506C2×C5#577911yescharacteristic
507D5—122no—
508D5—241no—
509C23—152no—
510C23—301no—
511C23#679011yescharacteristic
512Q8—62no—
513Q8—62no—
514Q8—122no—
515Q8—302no—
516Q8—301no—
517Q8—301no—
518D4—304no—
519D4—302no—
520D4—301no—
521D4—301no—
522D4—602no—
523D4—1202no—
524C2×C4—22no—
525C2×C4—62no—
526C2×C4—81no—
527C2×C4—101no—
528C2×C4—101no—
529C2×C4—122no—
530C2×C4—152no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—301no—
534C2×C4—602no—
535C2×C4#676912yes—
536C2×C4D5×D1212yes—
537C2×C4#679011yescharacteristic
538C2×C4C22×D3×D511yescharacteristic
539C8—54no—
540C8—61no—
541C8—61no—
542C2×C3—22no—
543C2×C3C2×#403011yescharacteristic
544C2×C3#6609611yescharacteristic
545C2×C3#6610011yescharacteristic
546D3—202no—
547D3—401no—
548C5#7921411yescharacteristic, complemented, Sylow
549C22—21no—
550C22—21no—
551C22—302no—
552C22—302no—
553C22—302no—
554C22—601no—
555C22—601no—
556C22—601no—
557C22#9142012yes—
558C22C2×#679011yescharacteristic
559C4—42no—
560C4—122no—
561C4—201no—
562C4—201no—
563C4—302no—
564C4—601no—
565C4#9142012yes—
566C4C2×#676911yescharacteristic
567C4C2×D5×D1211yescharacteristic
568C3#1061053111yescharacteristic, complemented, Sylow
569C2—22no—
570C2—602no—
571C2—1201no—
572C2C2×#9142011yescharacteristic
573C2#1175472511yescharacteristic
574C2#1175511911yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radical#11756269C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3063
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11754270C2semidirect
3. C2×#91321C2semidirect
4. C2×#91291C2semidirect
5. C2×C5×#810C2semidirect
6. C3×#65253C2semidirect
7. #11748411C2semidirect
8. #11747451C2semidirect
9. #11747450C2semidirect
10. #11747347C2semidirect
11. #11747346C2semidirect
51. #65253D3semidirect
88. C3×#681D4semidirect
104. C2×#810D5semidirect
243. #681D12semidirect
483. C3×C5#3063semidirect
548. C5#79214semidirect
568. C3#10610531semidirect

Maximal subgroups

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

subgroupindex
#117562692
#117542702
C2×#913212
C2×#912912
C2×C5×#8102
C3×#652532
#117484112
#117474512
#117474502
#117473472
#117473462
#106105313
#792145