Finite Group Databasebeta

← #14417087

Subgroups — #14417087

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#11756557C211yesmaximal, characteristic, complemented
2C2×C5×#932C211yesmaximal, characteristic
3#11754492C211yesmaximal, characteristic, complemented
4C2×C3×#3964C211yesmaximal, characteristic, complemented
5#11749020C212yesmaximal, complemented
6#11749019C212yesmaximal, complemented
7#11748996C212yesmaximal, complemented
8#11748994C212yesmaximal, complemented
9#11748453C211yesmaximal, characteristic, complemented
10#11748388C211yesmaximal, characteristic, complemented
11#11748324C211yesmaximal, characteristic, complemented
12#10615661—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×#6719—22no—
16D4×Dic15—21no—
17D4×Dic15—21no—
18D4×Dic15C2212yes—
19D4×Dic15C2212yes—
20#91815C2211yescharacteristic
21#91815C2211yescharacteristic
22C2×C5×#214C2212yes—
23C5×#932C418yescomplemented
24C2×C5×#213C2212yes—
25C2×C5×#208C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C22×C3×#168C2211yescharacteristic
28Dic5×#67—22no—
29#91435C2212yescomplemented
30D3×C4⋊Dic5—21no—
31#91344C2212yescomplemented
32#91338—21no—
33C3×#3964C2212yes—
34C3×#3964C2212yes—
35#90990C2212yescomplemented
36#90987C2212yescomplemented
37#90973C2211yescharacteristic, complemented
38#90973C2211yescharacteristic, complemented
39#90967C2211yescharacteristic, complemented
40#90967C2211yescharacteristic, complemented
41#90954C2212yescomplemented
42#90951C2212yescomplemented
43#78726—51nomaximal, Hall
44C2×C5×AGL(1,ℤ/8)—31no—
45#66161—31no—
46#66132—31no—
47#65522—31no—
48C2×#3964D311yescharacteristic, complemented
49#65453—32no—
50SD16×Dic5—32no—
51#65441—32no—
52D8×Dic5—32no—
53#65411—31no—
54#65410—31no—
55C24×C3×C5—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4C2×C414yescomplemented
59C2×C3×C5×D4C2312yes—
60C22×C3×C4×C5C2311yescharacteristic
61C22×Dic15—22no—
62C22×Dic15—22no—
63C2×C5×#67—21no—
64C5×#235—22no—
65C5×#235C2×C414yescomplemented
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C22×C3×Dic5—21no—
70C2×D3×Dic5—22no—
71#6719—21no—
72#6719—22no—
73#6719—22no—
74#6719D412yes—
75C4⋊Dic15D411yescharacteristic
76C4⋊Dic15D411yescharacteristic
77C4⋊Dic15C2311yescharacteristic
78C4⋊Dic15C2311yescharacteristic
79C4×Dic15—21no—
80C4×Dic15C2312yes—
81C5×#214C2×C418yescomplemented
82C5×#213C2×C418yescomplemented
83C5×#208C2×C414yescomplemented
84C2×C5×C3⋊C8C2312yes—
85C3×C4⋊Dic5—21no—
86C3×C4⋊Dic5C2312yes—
87C2×C3×#168—22no—
88C2×C3×#168C2311yescharacteristic
89C2×C3×#168C2311yescharacteristic
90Dic3⋊Dic5—22no—
91(C2×D3)⋊Dic5—22no—
92Dic3×Dic5—22no—
93#5798—51no—
94C2×#932D511yescharacteristic
95#5504—51no—
96C2×C3×#102—51no—
97#5113—51no—
98#5101—51no—
99#4964—51no—
100#4785—52no—
101#4758—52no—
102#4757—52no—
103#4756—52no—
104C2×C5×#41—31no—
105C22×C5×D4C2×D311yescharacteristic
106C5×AGL(1,ℤ/8)—38no—
107C2×C5×SD16—32no—
108C2×C5×D8—32no—
109C2×C5×M16—31no—
110C2×C22⋊Dic5—62no—
111Q8×Dic5—32no—
112D4×Dic5—32no—
113D4×Dic5—32no—
114D4×Dic5—32no—
115D4×Dic5—61no—
116D4×Dic5—61no—
117D4×Dic5—62no—
118#4072—31no—
119#4072—31no—
120#4072—61no—
121C2×C4⋊Dic5—61no—
122C2×C4⋊Dic5C2×D311yescharacteristic
123C22×#168C2×D311yescharacteristic
124#3967—31no—
125#3967—31no—
126#3964—31no—
127#3964—31no—
128#3964C2×D312yes—
129#3964C2×D312yes—
130#3950—32no—
131#3949—32no—
132#3947—32no—
133C8×Dic5—32no—
134#2946—151noSylow
135C23×C3×C5—22no—
136C23×C3×C5—24no—
137C23×C3×C5—81no—
138C23×C3×C5—81no—
139C23×C3×C5C2×D411yescharacteristic
140C22×C5×D3—21no—
141C3×C5×D4—24no—
142C3×C5×D4—22no—
143C3×C5×D4C22×C414yes—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5#4112yes—
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—21no—
149C2×Dic15—21no—
150C2×Dic15—82no—
151C2×Dic15—82no—
152C2×Dic15C2×D412yes—
153C2×Dic15C2×D412yes—
154C5×#67—24no—
155C2×C5×Dic3—21no—
156C5×D12—21no—
157C5×D12C22×C412yes—
158C4×C5×D3—24no—
159C5×Dic6—21no—
160C5×Dic6C22×C412yes—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—81no—
163D3×Dic5—82no—
164C3×#168—21no—
165C3×#168—21no—
166C5×C3⋊C8C22×C414yes—
167C22×C3×D4C2×D511yescharacteristic
168C2×#235C2×D511yescharacteristic
169C22×C3×C8—51no—
170C2×C3×C4⋊C4—51no—
171C2×#217—102no—
172D4×Dic3—52no—
173D4×Dic3—52no—
174D4×Dic3—101no—
175D4×Dic3—101no—
176C2×#214C2×D512yes—
177#932Dic518yescomplemented
178C2×#213C2×D512yes—
179C4×#67—102no—
180#926—51no—
181#926—51no—
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#808—52no—
196#807—52no—
197C24×C5—21no—
198C5×#41—34no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—21no—
202C2×C5×D4—22no—
203C2×C5×D4—31no—
204C2×C5×D4—61no—
205C2×C5×D4C4×D314yescomplemented
206C2×C5×D4C22×D312yes—
207C22×C4×C5—61no—
208C22×C4×C5C22×D311yescharacteristic
209C22×Dic5—21no—
210C22×Dic5—62no—
211C22×Dic5—62no—
212C22×Dic5—62no—
213C5×SD16—38no—
214C5×D8—38no—
215C5×M16—34no—
216C2×C5×C8—32no—
217C22⋊Dic5—32no—
218C22⋊Dic5—62no—
219C22⋊Dic5—62no—
220C22⋊Dic5—62no—
221C22⋊Dic5—61no—
222C4⋊Dic5—21no—
223C4⋊Dic5—31no—
224C4⋊Dic5—31no—
225C4⋊Dic5—31no—
226C4⋊Dic5—31no—
227C4⋊Dic5—62no—
228C4⋊Dic5C22×D312yes—
229C4×Dic5—32no—
230C4×Dic5—62no—
231C4×Dic5—61no—
232C2×#168—22no—
233C2×#168C22×D311yescharacteristic
234C2×#168C22×D311yescharacteristic
235C2×AGL(1,ℤ/8)—31no—
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—151no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5—24no—
249C22×C3×C5—42no—
250C22×C3×C5—42no—
251C22×C3×C5—84no—
252C22×C3×C5C4×D412yes—
253C22×C3×C5C22×D411yescharacteristic
254C2×C5×D3—22no—
255C2×C5×D3—41no—
256C2×C5×D3—41no—
257C3×C4×C5C4×D412yes—
258C3×C4×C5C23×C411yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—22no—
261Dic15—22no—
262Dic15—41no—
263Dic15—41no—
264C3×Dic5—42no—
265C5×Dic3—22no—
266C24×C3—21no—
267C2×C3×D4—21no—
268C2×C3×D4—22no—
269C2×C3×D4C2×Dic514yescomplemented
270C2×C3×D4C22×D512yes—
271C22×C3×C4—101no—
272C22×C3×C4C22×D511yescharacteristic
273C2×#67—21no—
274C22×Dic3—102no—
275C22×Dic3—102no—
276#235—22no—
277#235C2×Dic514yescomplemented
278C2×D12C22×D511yescharacteristic
279C2×C4×D3—21no—
280C2×C4×D3—102no—
281C2×Dic6C22×D511yescharacteristic
282C2×C3×C8—51no—
283C2×C3×C8—51no—
284C2×C3×C8—102no—
285C3×C4⋊C4—52no—
286C3×C4⋊C4—101no—
287#217—52no—
288#217—102no—
289#217—102no—
290#217—101no—
291#214C2×Dic518yescomplemented
292#213C2×Dic518yescomplemented
293(C2×D3)⋊C4—102no—
294C4⋊Dic3—51no—
295C4⋊Dic3—51no—
296C4⋊Dic3—51no—
297C4⋊Dic3—51no—
298Dic3⋊C4—102no—
299C4×Dic3—52no—
300C4×Dic3—102no—
301C4×Dic3—101no—
302#208C2×Dic514yescomplemented
303C2×C3⋊C8C22×D512yes—
304C23×C5—22no—
305C23×C5—24no—
306C23×C5—61no—
307C23×C5—81no—
308C23×C5—81no—
309C23×C5D3×D411yescharacteristic
310C5×Q8—32no—
311C5×Q8—61no—
312C5×D4—24no—
313C5×D4—22no—
314C5×D4—32no—
315C5×D4—64no—
316C5×D4—61no—
317C5×D4C2×C4×D314yes—
318C2×C4×C5—61no—
319C2×C4×C5—64no—
320C2×C4×C5C2×C4×D312yes—
321C2×C4×C5D3×D411yescharacteristic
322C2×C4×C5#23712yes—
323C2×C4×C5C23×D311yescharacteristic
324C2×Dic5—22no—
325C2×Dic5—32no—
326C2×Dic5—32no—
327C2×Dic5—61no—
328C2×Dic5—61no—
329C2×Dic5—81no—
330C2×Dic5—242no—
331C2×Dic5—242no—
332C2×Dic5—242no—
333C5×C8—34no—
334#168—21no—
335#168—21no—
336C2×#41—31no—
337C22×D4D3×D511yescharacteristic
338AGL(1,ℤ/8)—38no—
339C2×SD16—32no—
340C2×D8—32no—
341C2×M16—31no—
342C22×C8—51no—
343C4×Q8—152no—
344C4×D4—152no—
345C4×D4—152no—
346C4×D4—152no—
347C4×D4—302no—
348C4×D4—301no—
349C4×D4—301no—
350#117—151no—
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—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5—44no—
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5#57611yescharacteristic
370C2×C3×C5#57711yescharacteristic
371C5×D3—42no—
372C23×C3—22no—
373C23×C3—24no—
374C23×C3—81no—
375C23×C3—81no—
376C23×C3D4×D511yescharacteristic
377C22×D3—21no—
378C3×D4—22no—
379C3×D4—24no—
380C3×D4C22×Dic514yes—
381C2×C3×C4—102no—
382C2×C3×C4—401no—
383C2×C3×C4D4×D511yescharacteristic
384C2×C3×C4#71112yes—
385C2×C3×C4C22×Dic512yes—
386C2×C3×C4C23×D511yescharacteristic
387#67—24no—
388C2×Dic3—21no—
389C2×Dic3—52no—
390C2×Dic3—52no—
391C2×Dic3—101no—
392C2×Dic3—101no—
393C2×Dic3—402no—
394C2×Dic3—402no—
395D12—21no—
396D12C22×Dic512yes—
397C4×D3—24no—
398C4×D3—402no—
399Dic6—21no—
400Dic6C22×Dic512yes—
401C3×C8—101no—
402C3×C8—101no—
403C3⋊C8C22×Dic514yes—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—24no—
407C22×C5—42no—
408C22×C5—42no—
409C22×C5—62no—
410C22×C5—84no—
411C22×C5—121no—
412C22×C5—121no—
413C22×C5#67⋊C412yes—
414C22×C5C2×D3×D411yescharacteristic
415C4×C5—62no—
416C4×C5#67⋊C412yes—
417C4×C5C22×C4×D311yescharacteristic
418C4×C5C2×#23711yescharacteristic
419Dic5—42no—
420Dic5—62no—
421Dic5—62no—
422Dic5—121no—
423Dic5—121no—
424C24—21no—
425#41—34no—
426#41—62no—
427C2×Q8—31no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—31no—
431C2×D4—61no—
432C2×D4D3×Dic514yescomplemented
433C2×D4C2×D3×D512yes—
434C22×C4—61no—
435C22×C4—101no—
436C22×C4—302no—
437C22×C4—302no—
438C22×C4—302no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—38no—
441D8—38no—
442M16—34no—
443C2×C8—32no—
444C2×C8—51no—
445C2×C8—51no—
446C2×C8—102no—
447C4⋊C4—52no—
448C4⋊C4—101no—
449C4⋊C4—151no—
450C4⋊C4—151no—
451C4⋊C4—151no—
452C4⋊C4—151no—
453C4⋊C4—302no—
454C22⋊C4—152no—
455C22⋊C4—302no—
456C22⋊C4—302no—
457C22⋊C4—302no—
458C22⋊C4—301no—
459C42—152no—
460C42—302no—
461C42—301no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—24no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—84no—
469C22×C3D4×Dic512yes—
470C22×C3C2×D4×D511yescharacteristic
471C2×D3—22no—
472C2×D3—41no—
473C2×D3—41no—
474C3×C4—202no—
475C3×C4D4×Dic512yes—
476C3×C4C2×#71111yescharacteristic
477C3×C4C23×Dic511yescharacteristic
478Dic3—22no—
479Dic3—102no—
480Dic3—102no—
481Dic3—201no—
482Dic3—201no—
483C2×C5—22no—
484C2×C5—44no—
485C2×C5—122no—
486C2×C5C2×#67⋊C411yescharacteristic
487C2×C5#575711yescharacteristic
488C2×C5#576211yescharacteristic
489C23—22no—
490C23—24no—
491C23—61no—
492C23—81no—
493C23—81no—
494C23#679011yescharacteristic
495Q8—32no—
496Q8—61no—
497D4—22no—
498D4—24no—
499D4—32no—
500D4—64no—
501D4—61no—
502D4C2×D3×Dic514yes—
503C2×C4—61no—
504C2×C4—64no—
505C2×C4—102no—
506C2×C4—152no—
507C2×C4—152no—
508C2×C4—301no—
509C2×C4—301no—
510C2×C4—401no—
511C2×C4—1202no—
512C2×C4—1202no—
513C2×C4—1202no—
514C2×C4#678012yes—
515C2×C4C2×D3×Dic512yes—
516C2×C4#679011yescharacteristic
517C2×C4C22×D3×D511yescharacteristic
518C8—34no—
519C8—101no—
520C8—101no—
521C2×C3—22no—
522C2×C3—44no—
523C2×C3#6610811yescharacteristic
524C2×C3#6610911yescharacteristic
525C2×C3C2×D4×Dic511yescharacteristic
526D3—42no—
527C5#7872611yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—24no—
531C22—42no—
532C22—42no—
533C22—62no—
534C22—84no—
535C22—121no—
536C22—121no—
537C22#67⋊Dic512yes—
538C22C2×#679011yescharacteristic
539C4—62no—
540C4—202no—
541C4—302no—
542C4—302no—
543C4—601no—
544C4—601no—
545C4#67⋊Dic512yes—
546C4C2×#678011yescharacteristic
547C4C22×D3×Dic511yescharacteristic
548C3#1061566111yescharacteristic, complemented, Sylow
549C2—22no—
550C2—44no—
551C2—122no—
552C2#1175470311yescharacteristic
553C2#1175472811yescharacteristic
554C2C2×#67⋊Dic511yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#932C2
cosocleC2×C3×C4×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #11756557C2semidirect
3. #11754492C2semidirect
4. C2×C3×#3964C2semidirect
5. #11749020C2semidirect
6. #11749019C2semidirect
7. #11748996C2semidirect
8. #11748994C2semidirect
9. #11748453C2semidirect
10. #11748388C2semidirect
11. #11748324C2semidirect
23. C5×#932C4semidirect
29. #91435C22semidirect
31. #91344C22semidirect
35. #90990C22semidirect
36. #90987C22semidirect
37. #90973C22semidirect
38. #90973C22semidirect
39. #90967C22semidirect
40. #90967C22semidirect
41. #90954C22semidirect
42. #90951C22semidirect
48. C2×#3964D3semidirect
58. C2×C3×C5×D4C2×C4semidirect
65. C5×#235C2×C4semidirect
81. C5×#214C2×C4semidirect
82. C5×#213C2×C4semidirect
83. C5×#208C2×C4semidirect
177. #932Dic5semidirect
205. C2×C5×D4C4×D3semidirect
269. C2×C3×D4C2×Dic5semidirect
277. #235C2×Dic5semidirect
291. #214C2×Dic5semidirect
292. #213C2×Dic5semidirect
302. #208C2×Dic5semidirect
432. C2×D4D3×Dic5semidirect
462. C3×C5#2946semidirect
527. C5#78726semidirect
548. C3#10615661semidirect

Maximal subgroups

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

subgroupindex
#117565572
C2×C5×#9322
#117544922
C2×C3×#39642
#117490202
#117490192
#117489962
#117489942
#117484532
#117483882
#117483242
#106156613
#787265