Finite Group Databasebeta

← #14417097

Subgroups — #14417097

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754496C211yesmaximal, characteristic, complemented
2#11754488C211yesmaximal, characteristic, complemented
3C2×#91312C211yesmaximal, characteristic
4#11751214C211yesmaximal, characteristic, complemented
5C5×#5101C211yesmaximal, characteristic, complemented
6C2×C3×#3953C211yesmaximal, characteristic, complemented
7#11748453C211yesmaximal, characteristic, complemented
8#11747742C212yesmaximal, complemented
9#11747741C212yesmaximal, complemented
10#11747740C212yesmaximal, complemented
11#11747739C212yesmaximal, complemented
12#10610291—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×C3×C5×C8C2211yescharacteristic
16#91815C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20#91552—22no—
21D5×#217—22no—
22#91437—21no—
23#91434—21no—
24#91434—21no—
25#91428C2212yescomplemented
26Dic3×D20C2212yes—
27Dic3×D20C2212yes—
28#91347—21no—
29#91340C2212yescomplemented
30#91312C418yescomplemented
31C2×#6657C2212yes—
32C2×#6653C2212yes—
33#91105C2211yescharacteristic, complemented
34#91105C2211yescharacteristic, complemented
35#91100C2211yescharacteristic, complemented
36#91100C2211yescharacteristic, complemented
37C5×#815C2212yescomplemented
38C5×C8×Dic3C2212yescomplemented
39C3×#3953C2212yes—
40C3×#3953C2212yes—
41#90990C2212yescomplemented
42#90987C2212yescomplemented
43#78726—51nomaximal, Hall
44C2×#4054—31no—
45#65857—31no—
46#65855—31no—
47C5×#405—31no—
48#65410—31no—
49#65402—31no—
50C2×#3953D311yescharacteristic, complemented
51#65000—32no—
52#64999—32no—
53C4×D40—32no—
54C4×#677—32no—
55C23×C3×D5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58#6817—22no—
59#6817C2×C414yescomplemented
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×Dic30C2311yescharacteristic
63C22×C3×Dic5—21no—
64C2×C3×D20—21no—
65C2×C3×D20—22no—
66C2×C3×D20C2×C414yescomplemented
67C2×C3×D20C2312yes—
68C2×#1200—22no—
69C2×D5×Dic3—22no—
70C2×D5×Dic3—22no—
71C2×C3×C5×C8—22no—
72C2×C3×C5×C8C2311yescharacteristic
73C2×C3×C5×C8C2311yescharacteristic
74#6719—21no—
75C4⋊Dic15C2311yescharacteristic
76C4⋊Dic15C2311yescharacteristic
77C4×Dic15—21no—
78C5×#217D412yes—
79C5×C4⋊Dic3D411yescharacteristic
80C5×C4⋊Dic3D411yescharacteristic
81C4×C5×Dic3C2312yes—
82C5×#208C2×C414yescomplemented
83C2×C5×C3⋊C8C2312yes—
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5C2312yes—
86#6669—22no—
87#6667—22no—
88#6665—22no—
89#6665—22no—
90Dic3×Dic5—22no—
91#6657C2×C418yescomplemented
92#6653C2×C418yescomplemented
93#5798—51no—
94C2×#932—51no—
95#5504—51no—
96C2×C3×#102—51no—
97#5113—51no—
98#5101D511yescharacteristic, complemented
99#4964—51no—
100#4785—52no—
101#4758—52no—
102#4757—52no—
103#4756—52no—
104C2×#709—31no—
105C22×D20C2×D311yescharacteristic
106C2×C5×M16—31no—
107C22×C5×C8C2×D311yescharacteristic
108C5×#117—31no—
109#4072—31no—
110C2×C4⋊Dic5C2×D311yescharacteristic
111#4054—38no—
112C2×D40—32no—
113C2×#677—32no—
114#4039—61no—
115#4039—61no—
116#4038—61no—
117D5×C4⋊C4—61no—
118#4027—62no—
119D5×C22⋊C4—62no—
120C4×D20—32no—
121C4×D20—32no—
122C4×D20—32no—
123C4×Dic10—32no—
124C5×#97—32no—
125C4×C5×C8—32no—
126#3953—31no—
127#3953—31no—
128#3953C2×D312yes—
129#3953C2×D312yes—
130#3950—32no—
131#3949—32no—
132#3948—31no—
133#3948—31no—
134#2946—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C22×C3×D5—22no—
138C22×C3×D5—24no—
139C22×C3×D5—81no—
140C22×C3×D5—81no—
141C2×C3×C4×C5C22×C412yes—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5#4112yes—
144C2×C3×C4×C5C2411yescharacteristic
145#1220—24no—
146C2×Dic15—21no—
147C2×Dic15—21no—
148C2×Dic15—21no—
149D60—21no—
150D60C22×C412yes—
151C4×D15—24no—
152Dic30—21no—
153Dic30C22×C412yes—
154C2×C5×Dic3C2×D412yes—
155C2×C5×Dic3C2×D412yes—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—81no—
158C3×D20—24no—
159C3×D20—22no—
160C3×D20C22×C414yes—
161#1200—82no—
162D5×Dic3—82no—
163D5×Dic3—82no—
164C3×C5×C8—21no—
165C3×C5×C8—21no—
166C5×C3⋊C8C22×C414yes—
167C22×C3×D4—51no—
168C2×#235—51no—
169C22×C3×C8C2×D511yescharacteristic
170C2×C3×C4⋊C4—51no—
171C2×#217—102no—
172D4×Dic3—52no—
173D4×Dic3—52no—
174D4×Dic3—101no—
175D4×Dic3—101no—
176C2×#214—52no—
177#932—58no—
178C2×#213—52no—
179C4×#67—102no—
180#926—51no—
181#926C2×D511yescharacteristic
182C2×#208C2×D511yescharacteristic
183#893—52no—
184#892—101no—
185D3×C4⋊C4—101no—
186#887—52no—
187C3×#102—52no—
188C3×#102—52no—
189#821—51no—
190#821—51no—
191#816—51no—
192#816—51no—
193#815C2×D512yescomplemented
194C8×Dic3C2×D512yescomplemented
195#808—52no—
196#807—52no—
197C23×D5—21no—
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—61no—
200C22×Dic5—21no—
201#709—34no—
202#709—62no—
203C2×D20—21no—
204C2×D20—22no—
205C2×D20—31no—
206C2×D20C4×D314yescomplemented
207C2×D20C22×D312yes—
208C2×C4×D5—61no—
209C2×C4×D5—62no—
210C2×C4×D5—62no—
211C2×C4×D5—62no—
212C2×Dic10—31no—
213C5×M16—34no—
214C2×C5×C8—22no—
215C2×C5×C8—32no—
216C2×C5×C8C22×D311yescharacteristic
217C2×C5×C8C22×D311yescharacteristic
218C5×C4⋊C4—31no—
219C5×C4⋊C4—31no—
220C5×C22⋊C4—32no—
221C42×C5—32no—
222C22⋊Dic5—61no—
223#685—62no—
224#685—62no—
225#685—62no—
226C4⋊Dic5—21no—
227C4⋊Dic5—31no—
228C4⋊Dic5—31no—
229C4⋊Dic5C22×D312yes—
230#683—62no—
231C4×Dic5—62no—
232C4×Dic5—61no—
233D40—38no—
234#677—38no—
235C2×AGL(1,ℤ/8)—151no—
236#520—151no—
237#518—151no—
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428—151no—
243#416—151no—
244C2×#102—51no—
245#405—31no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5C4×D412yes—
249C22×C3×C5C22×D411yescharacteristic
250C2×D15—22no—
251C2×D15—41no—
252C2×D15—41no—
253C2×C3×D5—24no—
254C2×C3×D5—42no—
255C2×C3×D5—42no—
256C2×C3×D5—84no—
257C3×C4×C5C4×D412yes—
258C3×C4×C5C23×C411yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—22no—
261Dic15—41no—
262Dic15—41no—
263C3×Dic5—42no—
264C5×Dic3—22no—
265C5×Dic3—22no—
266C24×C3—101no—
267C2×C3×D4—54no—
268C2×C3×D4—52no—
269C2×C3×D4—101no—
270C2×C3×D4—102no—
271C22×C3×C4—101no—
272C22×C3×C4C22×D511yescharacteristic
273C2×#67—101no—
274C22×Dic3—102no—
275C22×Dic3—102no—
276#235—54no—
277#235—102no—
278C2×D12—51no—
279C2×C4×D3—101no—
280C2×C4×D3—102no—
281C2×Dic6—51no—
282C2×C3×C8—22no—
283C2×C3×C8C22×D511yescharacteristic
284C2×C3×C8C22×D511yescharacteristic
285C3×C4⋊C4—52no—
286C3×C4⋊C4—101no—
287#217—101no—
288#217—102no—
289#217—102no—
290#217D2012yes—
291#214—58no—
292#213—58no—
293(C2×D3)⋊C4—102no—
294C4⋊Dic3—51no—
295C4⋊Dic3—51no—
296C4⋊Dic3D2011yescharacteristic
297C4⋊Dic3D2011yescharacteristic
298Dic3⋊C4—102no—
299C4×Dic3—101no—
300C4×Dic3—102no—
301C4×Dic3C22×D512yes—
302#208C4×D514yescomplemented
303C2×C3⋊C8C22×D512yes—
304C23×C5D3×D411yescharacteristic
305C22×D5—22no—
306C22×D5—24no—
307C22×D5—61no—
308C22×D5—81no—
309C22×D5—81no—
310C2×C4×C5—32no—
311C2×C4×C5—32no—
312C2×C4×C5C2×C4×D312yes—
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5#23712yes—
315C2×C4×C5C23×D311yescharacteristic
316C22⋊D5—64no—
317C2×Dic5—22no—
318C2×Dic5—61no—
319C2×Dic5—61no—
320C2×Dic5—61no—
321C2×Dic5—81no—
322D20—24no—
323D20—22no—
324D20—32no—
325D20—61no—
326D20C2×C4×D314yes—
327C4×D5—64no—
328C4×D5—242no—
329C4×D5—242no—
330C4×D5—242no—
331Dic10—32no—
332Dic10—61no—
333C5×C8—21no—
334C5×C8—21no—
335C5×C8—34no—
336C2×#41—151no—
337C22×D4—51no—
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16—31no—
342C22×C8D3×D511yescharacteristic
343C4×Q8—152no—
344C4×D4—152no—
345C4×D4—152no—
346C4×D4—152no—
347C4×D4—302no—
348C4×D4—301no—
349C4×D4—301no—
350#117—31no—
351#117—151no—
352#117—301no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—301no—
355C2×C22⋊C4—302no—
356#107—152no—
357#106—152no—
358#103—151no—
359#103—151no—
360#102—52no—
361#102—52no—
362#102—151no—
363#102—151no—
364#97—32no—
365C4×C8—32no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5#57611yescharacteristic
369C2×C3×C5#57711yescharacteristic
370D15—42no—
371C3×D5—44no—
372C23×C3—102no—
373C23×C3—104no—
374C23×C3—401no—
375C23×C3—401no—
376C23×C3C2×D2011yescharacteristic
377C22×D3—101no—
378C3×D4—54no—
379C3×D4—102no—
380C3×D4—104no—
381C2×C3×C4—102no—
382C2×C3×C4—401no—
383C2×C3×C4C2×C4×D512yes—
384C2×C3×C4C2×D2011yescharacteristic
385C2×C3×C4#70912yes—
386C2×C3×C4C23×D511yescharacteristic
387#67—104no—
388C2×Dic3—101no—
389C2×Dic3—101no—
390C2×Dic3—101no—
391C2×Dic3—402no—
392C2×Dic3—402no—
393C2×Dic3C2×D2012yes—
394C2×Dic3C2×D2012yes—
395D12—52no—
396D12—101no—
397C4×D3—104no—
398C4×D3—402no—
399Dic6—52no—
400Dic6—101no—
401C3×C8—21no—
402C3×C8—21no—
403C3⋊C8C2×C4×D514yes—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5#67⋊C412yes—
407C22×C5C2×D3×D411yescharacteristic
408C2×D5—24no—
409C2×D5—42no—
410C2×D5—42no—
411C2×D5—62no—
412C2×D5—84no—
413C2×D5—121no—
414C2×D5—121no—
415C4×C5—62no—
416C4×C5—62no—
417C4×C5#67⋊C412yes—
418C4×C5C22×C4×D311yescharacteristic
419C4×C5C2×#23711yescharacteristic
420Dic5—42no—
421Dic5—62no—
422Dic5—121no—
423Dic5—121no—
424C24—101no—
425#41—154no—
426#41—302no—
427C2×Q8—151no—
428C2×D4—54no—
429C2×D4—52no—
430C2×D4—101no—
431C2×D4—102no—
432C2×D4—151no—
433C2×D4—301no—
434C22×C4—101no—
435C22×C4—302no—
436C22×C4—302no—
437C22×C4—302no—
438C22×C4—301no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—158no—
441D8—158no—
442M16—34no—
443C2×C8—22no—
444C2×C8—32no—
445C2×C8C2×D3×D511yescharacteristic
446C2×C8C2×D3×D511yescharacteristic
447C4⋊C4—31no—
448C4⋊C4—31no—
449C4⋊C4—52no—
450C4⋊C4—101no—
451C4⋊C4—151no—
452C4⋊C4—151no—
453C4⋊C4—302no—
454C22⋊C4—32no—
455C22⋊C4—302no—
456C22⋊C4—302no—
457C22⋊C4—302no—
458C22⋊C4—301no—
459C42—32no—
460C42—302no—
461C42—301no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—104no—
466C22×C3—202no—
467C22×C3—202no—
468C22×C3—404no—
469C22×C3C4×D2012yes—
470C22×C3C22×D2011yescharacteristic
471C2×D3—102no—
472C2×D3—201no—
473C2×D3—201no—
474C3×C4—202no—
475C3×C4C4×D2012yes—
476C3×C4C22×C4×D511yescharacteristic
477C3×C4C2×#70911yescharacteristic
478Dic3—22no—
479Dic3—22no—
480Dic3—102no—
481Dic3—201no—
482Dic3—201no—
483C2×C5—22no—
484C2×C5C2×#67⋊C411yescharacteristic
485C2×C5#575711yescharacteristic
486C2×C5#576211yescharacteristic
487D5—44no—
488D5—122no—
489C23—102no—
490C23—104no—
491C23—301no—
492C23—401no—
493C23—401no—
494C23D3×D2011yescharacteristic
495Q8—152no—
496Q8—301no—
497D4—54no—
498D4—104no—
499D4—102no—
500D4—152no—
501D4—304no—
502D4—301no—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—102no—
506C2×C4—301no—
507C2×C4—304no—
508C2×C4—301no—
509C2×C4—301no—
510C2×C4—401no—
511C2×C4—1202no—
512C2×C4—1202no—
513C2×C4—1202no—
514C2×C4C4×D3×D512yes—
515C2×C4D3×D2011yescharacteristic
516C2×C4#677912yes—
517C2×C4C22×D3×D511yescharacteristic
518C8—21no—
519C8—21no—
520C8—34no—
521C2×C3—22no—
522C2×C3—204no—
523C2×C3C2×C4×D2011yescharacteristic
524C2×C3#6608511yescharacteristic
525C2×C3#6608611yescharacteristic
526D3—202no—
527C5#7872611yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—104no—
531C22—202no—
532C22—202no—
533C22—302no—
534C22—404no—
535C22—601no—
536C22—601no—
537C22#9139512yes—
538C22C2×D3×D2011yescharacteristic
539C4—62no—
540C4—62no—
541C4—202no—
542C4—302no—
543C4—601no—
544C4—601no—
545C4#9139512yes—
546C4C2×C4×D3×D511yescharacteristic
547C4C2×#677911yescharacteristic
548C3#1061029111yescharacteristic, complemented, Sylow
549C2—22no—
550C2—204no—
551C2—602no—
552C2#1175397011yescharacteristic
553C2#1175397111yescharacteristic
554C2C2×#9139511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91312C2
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5#2946
LCSG ▷ 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. #11754496C2semidirect
2. #11754488C2semidirect
4. #11751214C2semidirect
5. C5×#5101C2semidirect
6. C2×C3×#3953C2semidirect
7. #11748453C2semidirect
8. #11747742C2semidirect
9. #11747741C2semidirect
10. #11747740C2semidirect
11. #11747739C2semidirect
25. #91428C22semidirect
29. #91340C22semidirect
30. #91312C4semidirect
33. #91105C22semidirect
34. #91105C22semidirect
35. #91100C22semidirect
36. #91100C22semidirect
37. C5×#815C22semidirect
38. C5×C8×Dic3C22semidirect
41. #90990C22semidirect
42. #90987C22semidirect
50. C2×#3953D3semidirect
59. #6817C2×C4semidirect
66. C2×C3×D20C2×C4semidirect
82. C5×#208C2×C4semidirect
91. #6657C2×C4semidirect
92. #6653C2×C4semidirect
98. #5101D5semidirect
193. #815C2×D5semidirect
194. C8×Dic3C2×D5semidirect
206. C2×D20C4×D3semidirect
302. #208C4×D5semidirect
462. C3×C5#2946semidirect
527. C5#78726semidirect
548. C3#10610291semidirect

Maximal subgroups

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

subgroupindex
#117544962
#117544882
C2×#913122
#117512142
C5×#51012
C2×C3×#39532
#117484532
#117477422
#117477412
#117477402
#117477392
#106102913
#787265