Finite Group Databasebeta

← #14417081

Subgroups — #14417081

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#11756263C211yesmaximal, characteristic, complemented
2#11754488C211yesmaximal, characteristic, complemented
3C2×#91312C211yesmaximal, characteristic
4C5×#4964C211yesmaximal, characteristic, complemented
5C2×C3×#3941C211yesmaximal, characteristic, complemented
6#11748393C211yesmaximal, characteristic, complemented
7#11748324C211yesmaximal, characteristic, complemented
8#11747229C212yesmaximal, complemented
9#11747228C212yesmaximal, complemented
10#11747227C212yesmaximal, complemented
11#11747226C212yesmaximal, complemented
12#10610932—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C4×#1220—22no—
17#91815C2211yescharacteristic
18#91782C2212yescomplemented
19#91781—21no—
20C4⋊C4×D15—21no—
21#91776C2212yescomplemented
22C5×#926C2211yescharacteristic
23C2×C5×#208C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25D5×#217—22no—
26#91434C2212yes—
27#91434C2212yes—
28Dic3×D20—21no—
29Dic3×D20—21no—
30#91312C418yescomplemented
31C2×#6657C2212yes—
32C2×#6653C2212yes—
33C5×#808C2212yescomplemented
34C5×#807C2212yescomplemented
35C3×#3941C2212yes—
36C3×#3941C2212yes—
37#90975C2211yescharacteristic, complemented
38#90975C2211yescharacteristic, complemented
39#90969C2211yescharacteristic, complemented
40#90969C2211yescharacteristic, complemented
41#90954C2212yescomplemented
42#90951C2212yescomplemented
43#78726—51nomaximal, Hall
44C2×#4054—31no—
45#65855—31no—
46#65838—31no—
47C5×#428—31no—
48#65411—31no—
49#65291—31no—
50C2×#3941D311yescharacteristic, complemented
51#65178—32no—
52#65161—32no—
53#65158—32no—
54#65141—32no—
55C23×C3×D5—21no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817C2×C414yescomplemented
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×C4×D15—22no—
64C2×Dic30C2311yescharacteristic
65C2×C3×D20—21no—
66C2×C3×D20—22no—
67C2×C3×D20C2×C414yescomplemented
68C2×C3×D20C2312yes—
69C2×D5×Dic3—22no—
70C2×D5×Dic3—22no—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4C2312yes—
73#6719D412yes—
74#6714—22no—
75C4⋊Dic15D411yescharacteristic
76C4⋊Dic15D411yescharacteristic
77#6712—22no—
78C4×Dic15—22no—
79C4×Dic15C2312yes—
80C5×#217—21no—
81C5×C4⋊Dic3C2311yescharacteristic
82C5×C4⋊Dic3C2311yescharacteristic
83C4×C5×Dic3—21no—
84C5×#208C2×C414yescomplemented
85C2×C5×C3⋊C8C2312yes—
86C2×C3×#168—22no—
87C2×C3×#168C2311yescharacteristic
88C2×C3×#168C2311yescharacteristic
89#6665—22no—
90#6665—22no—
91#6657C2×C418yescomplemented
92#6653C2×C418yescomplemented
93#5798—51no—
94C2×#932—51no—
95#5504—51no—
96C2×C3×#102—51no—
97#5113—51no—
98#5101—51no—
99#4964D511yescharacteristic, complemented
100#4785—52no—
101#4758—52no—
102#4757—52no—
103#4756—52no—
104C2×#709—31no—
105C22×D20C2×D311yescharacteristic
106C2×C5×M16—31no—
107C5×#117—31no—
108C2×C5×C4⋊C4C2×D311yescharacteristic
109C4×C22⋊D5—62no—
110#4072—31no—
111C22×#168C2×D311yescharacteristic
112#4054—38no—
113C2×D40—32no—
114C2×#677—32no—
115#4039—32no—
116#4039—32no—
117#4039—32no—
118#4038—61no—
119D5×C4⋊C4—61no—
120#4033—32no—
121D5×C22⋊C4—62no—
122C4×D20—61no—
123C4×D20—61no—
124C5×#107—32no—
125C5×#106—32no—
126#3947—32no—
127C8×Dic5—32no—
128#3942—31no—
129#3942—31no—
130#3941—31no—
131#3941—31no—
132#3941C2×D312yes—
133#3941C2×D312yes—
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×C5—22no—
142C2×C3×C4×C5—81no—
143C2×C3×C4×C5C22×C412yes—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5#4112yes—
146C2×C3×C4×C5C2411yescharacteristic
147#1220—24no—
148C2×Dic15—21no—
149C2×Dic15C2×D412yes—
150C2×Dic15C2×D412yes—
151D60—21no—
152D60C22×C412yes—
153C4×D15—24no—
154C4×D15—82no—
155Dic30—21no—
156Dic30C22×C412yes—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—21no—
159C3×D20—24no—
160C3×D20—22no—
161C3×D20C22×C414yes—
162D5×Dic3—82no—
163D5×Dic3—82no—
164C3×#168—21no—
165C3×#168—21no—
166C5×C3⋊C8C22×C414yes—
167C22×C3×D4—51no—
168C2×#235—51no—
169C22×C3×C8—51no—
170C2×C3×C4⋊C4C2×D511yescharacteristic
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#815—52no—
194C8×Dic3—52no—
195#808C2×D512yescomplemented
196#807C2×D512yescomplemented
197C23×D5—21no—
198C22×C4×C5—21no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—61no—
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—32no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—31no—
217C5×C4⋊C4—31no—
218C5×C4⋊C4C22×D312yes—
219C5×C22⋊C4—61no—
220C42×C5—61no—
221C22⋊Dic5—32no—
222#685—62no—
223#685—62no—
224#685—62no—
225C4⋊Dic5—31no—
226C4⋊Dic5—31no—
227#683—62no—
228C4×Dic5—32no—
229C4×Dic5—62no—
230C2×#168—22no—
231C2×#168C22×D311yescharacteristic
232C2×#168C22×D311yescharacteristic
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—31no—
243#416—151no—
244C2×#102—51no—
245#405—151no—
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×C5—42no—
258C3×C4×C5C4×D412yes—
259C3×C4×C5C23×C411yescharacteristic
260C3×C4×C5C2×#4111yescharacteristic
261Dic15—22no—
262Dic15—22no—
263Dic15—22no—
264C5×Dic3—41no—
265C5×Dic3—41no—
266C24×C3—101no—
267C2×C3×D4—54no—
268C2×C3×D4—52no—
269C2×C3×D4—101no—
270C2×C3×D4—102no—
271C22×C3×C4—21no—
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—51no—
283C2×C3×C8—51no—
284C2×C3×C8—102no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4C22×D512yes—
287#217—21no—
288#217—52no—
289#217—102no—
290#217—102no—
291#214—58no—
292#213—58no—
293(C2×D3)⋊C4—102no—
294C4⋊Dic3—51no—
295C4⋊Dic3—51no—
296C4⋊Dic3C22×D511yescharacteristic
297C4⋊Dic3C22×D511yescharacteristic
298Dic3⋊C4—102no—
299C4×Dic3—21no—
300C4×Dic3—52no—
301C4×Dic3—102no—
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—22no—
311C2×C4×C5—61no—
312C2×C4×C5—61no—
313C2×C4×C5—81no—
314C2×C4×C5C2×C4×D312yes—
315C2×C4×C5D3×D411yescharacteristic
316C2×C4×C5#23712yes—
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—64no—
319C2×Dic5—32no—
320C2×Dic5—32no—
321C2×Dic5—61no—
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—34no—
334#168—21no—
335#168—21no—
336C2×#41—151no—
337C22×D4—51no—
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16—31no—
342C22×C8—51no—
343C4×Q8—152no—
344C4×D4—152no—
345C4×D4—152no—
346C4×D4—152no—
347C4×D4—301no—
348C4×D4—301no—
349C4×D4—302no—
350#117—31no—
351#117—151no—
352#117—301no—
353C2×C4⋊C4—301no—
354C2×C4⋊C4D3×D511yescharacteristic
355C2×C22⋊C4—302no—
356#107—32no—
357#106—32no—
358#103—151no—
359#103—151no—
360#102—52no—
361#102—52no—
362#102—151no—
363#102—151no—
364#97—152no—
365C4×C8—152no—
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×C3D4×D511yescharacteristic
377C22×D3—101no—
378C3×D4—54no—
379C3×D4—102no—
380C3×D4—104no—
381C2×C3×C4—22no—
382C2×C3×C4—81no—
383C2×C3×C4C2×C4×D512yes—
384C2×C3×C4D4×D511yescharacteristic
385C2×C3×C4#71312yes—
386C2×C3×C4C23×D511yescharacteristic
387#67—104no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—52no—
391C2×Dic3—52no—
392C2×Dic3—101no—
393C2×Dic3—402no—
394C2×Dic3—402no—
395D12—52no—
396D12—101no—
397C4×D3—104no—
398C4×D3—402no—
399Dic6—52no—
400Dic6—101no—
401C3×C8—101no—
402C3×C8—101no—
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—42no—
416C4×C5—121no—
417C4×C5—121no—
418C4×C5#67⋊C412yes—
419C4×C5C22×C4×D311yescharacteristic
420C4×C5C2×#23711yescharacteristic
421Dic5—62no—
422Dic5—62no—
423Dic5—62no—
424C24—101no—
425#41—154no—
426#41—302no—
427C2×Q8—151no—
428C2×D4—54no—
429C2×D4—52no—
430C2×D4—102no—
431C2×D4—101no—
432C2×D4—151no—
433C2×D4—301no—
434C22×C4—21no—
435C22×C4—302no—
436C22×C4—302no—
437C22×C4—302no—
438C22×C4—301no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—158no—
441D8—158no—
442M16—34no—
443C2×C8—32no—
444C2×C8—51no—
445C2×C8—51no—
446C2×C8—102no—
447C4⋊C4—21no—
448C4⋊C4—31no—
449C4⋊C4—31no—
450C4⋊C4—151no—
451C4⋊C4—151no—
452C4⋊C4—302no—
453C4⋊C4C2×D3×D512yes—
454C22⋊C4—61no—
455C22⋊C4—152no—
456C22⋊C4—302no—
457C22⋊C4—302no—
458C22⋊C4—302no—
459C42—61no—
460C42—152no—
461C42—302no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—104no—
466C22×C3—202no—
467C22×C3—202no—
468C22×C3—404no—
469C22×C3#403912yes—
470C22×C3C2×D4×D511yescharacteristic
471C2×D3—102no—
472C2×D3—201no—
473C2×D3—201no—
474C3×C4—42no—
475C3×C4#403912yes—
476C3×C4C22×C4×D511yescharacteristic
477C3×C4C2×#71311yescharacteristic
478Dic3—41no—
479Dic3—41no—
480Dic3—102no—
481Dic3—102no—
482Dic3—102no—
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—
494C23#679011yescharacteristic
495Q8—152no—
496Q8—301no—
497D4—54no—
498D4—104no—
499D4—102no—
500D4—152no—
501D4—304no—
502D4—301no—
503C2×C4—22no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—81no—
507C2×C4—152no—
508C2×C4—152no—
509C2×C4—301no—
510C2×C4—304no—
511C2×C4—1202no—
512C2×C4—1202no—
513C2×C4—1202no—
514C2×C4#676612yes—
515C2×C4C4×D3×D512yes—
516C2×C4#679011yescharacteristic
517C2×C4C22×D3×D511yescharacteristic
518C8—34no—
519C8—101no—
520C8—101no—
521C2×C3—22no—
522C2×C3—204no—
523C2×C3C2×#403911yescharacteristic
524C2×C3#6610811yescharacteristic
525C2×C3#6611211yescharacteristic
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#9139612yes—
538C22C2×#679011yescharacteristic
539C4—42no—
540C4—121no—
541C4—121no—
542C4—302no—
543C4—302no—
544C4—302no—
545C4#9139612yes—
546C4C2×#676611yescharacteristic
547C4C2×C4×D3×D511yescharacteristic
548C3#1061093211yescharacteristic, complemented, Sylow
549C2—22no—
550C2—204no—
551C2—602no—
552C2C2×#9139611yescharacteristic
553C2#1175470311yescharacteristic
554C2#1175509711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91312C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2946
LCSG ▷ 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
1. #11756263C2semidirect
2. #11754488C2semidirect
4. C5×#4964C2semidirect
5. C2×C3×#3941C2semidirect
6. #11748393C2semidirect
7. #11748324C2semidirect
8. #11747229C2semidirect
9. #11747228C2semidirect
10. #11747227C2semidirect
11. #11747226C2semidirect
18. #91782C22semidirect
21. #91776C22semidirect
30. #91312C4semidirect
33. C5×#808C22semidirect
34. C5×#807C22semidirect
37. #90975C22semidirect
38. #90975C22semidirect
39. #90969C22semidirect
40. #90969C22semidirect
41. #90954C22semidirect
42. #90951C22semidirect
50. C2×#3941D3semidirect
60. #6817C2×C4semidirect
67. C2×C3×D20C2×C4semidirect
84. C5×#208C2×C4semidirect
91. #6657C2×C4semidirect
92. #6653C2×C4semidirect
99. #4964D5semidirect
195. #808C2×D5semidirect
196. #807C2×D5semidirect
206. C2×D20C4×D3semidirect
302. #208C4×D5semidirect
462. C3×C5#2946semidirect
527. C5#78726semidirect
548. C3#10610932semidirect

Maximal subgroups

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

subgroupindex
#117562632
#117544882
C2×#913122
C5×#49642
C2×C3×#39412
#117483932
#117483242
#117472292
#117472282
#117472272
#117472262
#106109323
#787265