Finite Group Databasebeta

← #14417085

Subgroups — #14417085

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
1C2×#91821C211yesmaximal, characteristic
2C5×#5798C211yesmaximal, characteristic, complemented
3#11754496C211yesmaximal, characteristic, complemented
4C2×C3×#3964C211yesmaximal, characteristic, complemented
5#11749014C212yesmaximal, complemented
6#11749011C212yesmaximal, complemented
7#11748989C212yesmaximal, complemented
8#11748986C212yesmaximal, complemented
9#11748470C211yesmaximal, characteristic, complemented
10#11748393C211yesmaximal, characteristic, complemented
11#11748323C211yesmaximal, characteristic, complemented
12#10614268—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×#6716C2212yes—
16#91821C418yescomplemented
17C2×#6715C2212yes—
18C2×#6710C2211yescharacteristic
19C2×C5×#217—22no—
20C5×D4×Dic3—21no—
21C5×D4×Dic3—21no—
22C5×D4×Dic3C2212yes—
23C5×D4×Dic3C2212yes—
24C5×#926C2211yescharacteristic
25C5×#926C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C22×C3×#168C2211yescharacteristic
28#91552—22no—
29#91437—21no—
30#91428C2212yescomplemented
31#91347—21no—
32#91340C2212yescomplemented
33C3×#3964C2212yes—
34C3×#3964C2212yes—
35#90989C2212yescomplemented
36#90986C2212yescomplemented
37#90975C2211yescharacteristic, complemented
38#90975C2211yescharacteristic, complemented
39#90969C2211yescharacteristic, complemented
40#90969C2211yescharacteristic, complemented
41#90953C2212yescomplemented
42Dic3×#168C2212yescomplemented
43#78726—51nomaximal, Hall
44C5×#518—31no—
45C2×#4078—31no—
46#65857—31no—
47C2×#3964D311yescharacteristic, complemented
48#65307—32no—
49C4×#687—32no—
50#65303—32no—
51C4×#686—32no—
52#65291—31no—
53#65286—31no—
54#65284—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
61C2×#1220—21no—
62#6817—22no—
63#6817C2×C414yescomplemented
64C2×D60C2311yescharacteristic
65C2×C4×D15—21no—
66C2×Dic30C2311yescharacteristic
67C22×C5×Dic3—22no—
68C22×C5×Dic3—22no—
69C22×C3×Dic5—21no—
70C2×#1200—22no—
71#6716C2×C418yescomplemented
72#6715C2×C418yescomplemented
73#6710C2×C414yescomplemented
74C2×C3⋊#168C2312yes—
75C5×#217—21no—
76C5×#217—22no—
77C5×#217—22no—
78C5×#217D412yes—
79C5×C4⋊Dic3D411yescharacteristic
80C5×C4⋊Dic3D411yescharacteristic
81C5×C4⋊Dic3C2311yescharacteristic
82C5×C4⋊Dic3C2311yescharacteristic
83C4×C5×Dic3—21no—
84C4×C5×Dic3C2312yes—
85C3×C4⋊Dic5—21no—
86C3×C4⋊Dic5C2312yes—
87C2×C3×#168—22no—
88C2×C3×#168C2311yescharacteristic
89C2×C3×#168C2311yescharacteristic
90#6669—22no—
91#6667—22no—
92Dic3×Dic5—22no—
93#5798D511yescharacteristic, complemented
94C2×#932—51no—
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—
104C22×C5×D4C2×D311yescharacteristic
105C2×#709—31no—
106C4×C5×D4—32no—
107C4×C5×D4—32no—
108C4×C5×D4—61no—
109C4×C5×D4—61no—
110C5×#117—31no—
111C5×#117—31no—
112C2×C5×C22⋊C4—62no—
113C2×#687—32no—
114#4078—38no—
115C2×#686—32no—
116C2×C4⋊Dic5C2×D311yescharacteristic
117C2×#681—31no—
118C22×#168C2×D311yescharacteristic
119#4038—61no—
120D5×C4⋊C4—61no—
121#4027—62no—
122C4×D20—32no—
123C4×Dic10—32no—
124#3964C2×D312yes—
125#3964C2×D312yes—
126#3942—31no—
127#3942—31no—
128#3941—31no—
129#3941—31no—
130#3940—32no—
131#3939—32no—
132#3935—32no—
133C4×#168—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×D15—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
148#1220—24no—
149C2×Dic15—21no—
150D60—21no—
151D60C22×C412yes—
152C4×D15—24no—
153Dic30—21no—
154Dic30C22×C412yes—
155C2×C5×Dic3—21no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—82no—
158C2×C5×Dic3—82no—
159C2×C5×Dic3C2×D412yes—
160C2×C5×Dic3C2×D412yes—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—81no—
163#1200—82no—
164C3⋊#168C22×C414yes—
165C3×#168—21no—
166C3×#168—21no—
167C22×C3×D4C2×D511yescharacteristic
168C2×#235—51no—
169C22×C3×C8—51no—
170C2×C3×C4⋊C4—51no—
171C2×#217—22no—
172D4×Dic3—21no—
173D4×Dic3—21no—
174D4×Dic3C2×D512yes—
175D4×Dic3C2×D512yes—
176C2×#214—52no—
177#932—58no—
178C2×#213—52no—
179C4×#67—102no—
180#926C2×D511yescharacteristic
181#926C2×D511yescharacteristic
182C2×#208—51no—
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—
198C2×C5×D4—21no—
199C2×C5×D4—22no—
200C2×C5×D4C4×D314yescomplemented
201C2×C5×D4C22×D312yes—
202C22×C4×C5—62no—
203C22×C4×C5—62no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—61no—
206C22×Dic5—21no—
207#709—34no—
208#709—62no—
209C2×D20—31no—
210C2×C4×D5—61no—
211C2×C4×D5—62no—
212C2×Dic10—31no—
213C5×C4⋊C4—31no—
214C5×C4⋊C4—31no—
215C5×C4⋊C4—31no—
216C5×C4⋊C4—31no—
217C5×C22⋊C4—32no—
218C5×C22⋊C4—62no—
219C5×C22⋊C4—62no—
220C5×C22⋊C4—61no—
221C42×C5—32no—
222C42×C5—61no—
223#687—38no—
224#686—38no—
225#685—62no—
226C4⋊Dic5—21no—
227C4⋊Dic5C22×D312yes—
228#683—62no—
229C4×Dic5—62no—
230#681—34no—
231C2×#168—22no—
232C2×#168—32no—
233C2×#168C22×D311yescharacteristic
234C2×#168C22×D311yescharacteristic
235C2×AGL(1,ℤ/8)—151no—
236#520—151no—
237#518—31no—
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×D15—22no—
255C2×D15—41no—
256C2×D15—41no—
257C3×C4×C5C4×D412yes—
258C3×C4×C5C23×C411yescharacteristic
259C3×C4×C5C2×#4111yescharacteristic
260Dic15—22no—
261C3×Dic5—42no—
262C5×Dic3—22no—
263C5×Dic3—22no—
264C5×Dic3—41no—
265C5×Dic3—41no—
266C24×C3—21no—
267C2×C3×D4—22no—
268C2×C3×D4—21no—
269C2×C3×D4C4×D514yescomplemented
270C2×C3×D4C22×D512yes—
271C22×C3×C4—101no—
272C22×C3×C4C22×D511yescharacteristic
273C2×#67—101no—
274C22×Dic3—22no—
275C22×Dic3—22no—
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—52no—
286C3×C4⋊C4—101no—
287#217—21no—
288#217—22no—
289#217—22no—
290#217C22⋊D512yes—
291#214—58no—
292#213—58no—
293(C2×D3)⋊C4—102no—
294C4⋊Dic3C22⋊D511yescharacteristic
295C4⋊Dic3C22⋊D511yescharacteristic
296C4⋊Dic3C22×D511yescharacteristic
297C4⋊Dic3C22×D511yescharacteristic
298Dic3⋊C4—102no—
299C4×Dic3—21no—
300C4×Dic3—102no—
301C4×Dic3C22×D512yes—
302#208—54no—
303C2×C3⋊C8—52no—
304C23×C5—22no—
305C23×C5—24no—
306C23×C5—81no—
307C23×C5—81no—
308C23×C5D3×D411yescharacteristic
309C22×D5—61no—
310C5×D4—24no—
311C5×D4—22no—
312C5×D4C2×C4×D314yes—
313C2×C4×C5—32no—
314C2×C4×C5—32no—
315C2×C4×C5—61no—
316C2×C4×C5—61no—
317C2×C4×C5—242no—
318C2×C4×C5—242no—
319C2×C4×C5C2×C4×D312yes—
320C2×C4×C5D3×D411yescharacteristic
321C2×C4×C5#23712yes—
322C2×C4×C5C23×D311yescharacteristic
323C22⋊D5—64no—
324C2×Dic5—22no—
325C2×Dic5—61no—
326C2×Dic5—81no—
327D20—32no—
328D20—61no—
329C4×D5—64no—
330C4×D5—242no—
331Dic10—32no—
332Dic10—61no—
333#168—21no—
334#168—21no—
335#168—34no—
336C2×#41—151no—
337C22×D4D3×D511yescharacteristic
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16—151no—
342C22×C8—51no—
343C4×Q8—152no—
344C4×D4—32no—
345C4×D4—32no—
346C4×D4—61no—
347C4×D4—61no—
348C4×D4—152no—
349C4×D4—302no—
350#117—31no—
351#117—31no—
352#117—301no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—301no—
355C2×C22⋊C4—62no—
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
371D15—42no—
372C23×C3—22no—
373C23×C3—24no—
374C23×C3—81no—
375C23×C3—81no—
376C23×C3C2×C22⋊D511yescharacteristic
377C22×D3—101no—
378C3×D4—22no—
379C3×D4—24no—
380C3×D4C2×C4×D514yes—
381C2×C3×C4—102no—
382C2×C3×C4—401no—
383C2×C3×C4C2×C4×D512yes—
384C2×C3×C4#70912yes—
385C2×C3×C4C2×C22⋊D511yescharacteristic
386C2×C3×C4C23×D511yescharacteristic
387#67—104no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—82no—
391C2×Dic3—82no—
392C2×Dic3—101no—
393C2×Dic3C2×C22⋊D512yes—
394C2×Dic3C2×C22⋊D512yes—
395D12—52no—
396D12—101no—
397C4×D3—104no—
398C4×D3—402no—
399Dic6—52no—
400Dic6—101no—
401C3×C8—101no—
402C3×C8—101no—
403C3⋊C8—54no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—24no—
407C22×C5—42no—
408C22×C5—42no—
409C22×C5—84no—
410C22×C5#67⋊C412yes—
411C22×C5C2×D3×D411yescharacteristic
412C2×D5—62no—
413C2×D5—121no—
414C2×D5—121no—
415C4×C5—62no—
416C4×C5—62no—
417C4×C5—121no—
418C4×C5—121no—
419C4×C5#67⋊C412yes—
420C4×C5C22×C4×D311yescharacteristic
421C4×C5C2×#23711yescharacteristic
422Dic5—42no—
423Dic5—62no—
424C24—21no—
425#41—154no—
426#41—302no—
427C2×Q8—151no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—151no—
431C2×D4—301no—
432C2×D4#120014yescomplemented
433C2×D4C2×D3×D512yes—
434C22×C4—62no—
435C22×C4—62no—
436C22×C4—101no—
437C22×C4—302no—
438C22×C4—301no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—158no—
441D8—158no—
442M16—154no—
443C2×C8—51no—
444C2×C8—51no—
445C2×C8—102no—
446C2×C8—152no—
447C4⋊C4—31no—
448C4⋊C4—31no—
449C4⋊C4—31no—
450C4⋊C4—31no—
451C4⋊C4—52no—
452C4⋊C4—101no—
453C4⋊C4—302no—
454C22⋊C4—32no—
455C22⋊C4—62no—
456C22⋊C4—62no—
457C22⋊C4—61no—
458C22⋊C4—302no—
459C42—32no—
460C42—61no—
461C42—302no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—24no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—84no—
469C22×C3C4×C22⋊D512yes—
470C22×C3C22×C22⋊D511yescharacteristic
471C2×D3—102no—
472C2×D3—201no—
473C2×D3—201no—
474C3×C4—202no—
475C3×C4C4×C22⋊D512yes—
476C3×C4C22×C4×D511yescharacteristic
477C3×C4C2×#70911yescharacteristic
478Dic3—22no—
479Dic3—22no—
480Dic3—41no—
481Dic3—41no—
482Dic3—102no—
483C2×C5—22no—
484C2×C5—44no—
485C2×C5C2×#67⋊C411yescharacteristic
486C2×C5#575711yescharacteristic
487C2×C5#576211yescharacteristic
488D5—122no—
489C23—22no—
490C23—24no—
491C23—81no—
492C23—81no—
493C23—301no—
494C23D3×C22⋊D511yescharacteristic
495Q8—152no—
496Q8—301no—
497D4—22no—
498D4—24no—
499D4—152no—
500D4—304no—
501D4—301no—
502D4C2×#120014yes—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—102no—
508C2×C4—242no—
509C2×C4—242no—
510C2×C4—301no—
511C2×C4—304no—
512C2×C4—401no—
513C2×C4—1202no—
514C2×C4#677912yes—
515C2×C4C2×#120012yes—
516C2×C4D3×C22⋊D511yescharacteristic
517C2×C4C22×D3×D511yescharacteristic
518C8—101no—
519C8—101no—
520C8—154no—
521C2×C3—22no—
522C2×C3—44no—
523C2×C3C2×C4×C22⋊D511yescharacteristic
524C2×C3#6616911yescharacteristic
525C2×C3#6617011yescharacteristic
526D3—202no—
527C5#7872611yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—24no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22—302no—
535C22—601no—
536C22—601no—
537C22#9155612yes—
538C22C2×D3×C22⋊D511yescharacteristic
539C4—62no—
540C4—62no—
541C4—121no—
542C4—121no—
543C4—202no—
544C4—302no—
545C4#9155612yes—
546C4C2×#677911yescharacteristic
547C4C22×#120011yescharacteristic
548C3#1061426811yescharacteristic, complemented, Sylow
549C2—22no—
550C2—44no—
551C2—602no—
552C2#1175469711yescharacteristic
553C2#1175471111yescharacteristic
554C2C2×#9155611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91821C2
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
2. C5×#5798C2semidirect
3. #11754496C2semidirect
4. C2×C3×#3964C2semidirect
5. #11749014C2semidirect
6. #11749011C2semidirect
7. #11748989C2semidirect
8. #11748986C2semidirect
9. #11748470C2semidirect
10. #11748393C2semidirect
11. #11748323C2semidirect
16. #91821C4semidirect
30. #91428C22semidirect
32. #91340C22semidirect
35. #90989C22semidirect
36. #90986C22semidirect
37. #90975C22semidirect
38. #90975C22semidirect
39. #90969C22semidirect
40. #90969C22semidirect
41. #90953C22semidirect
42. Dic3×#168C22semidirect
47. C2×#3964D3semidirect
58. C2×C3×C5×D4C2×C4semidirect
63. #6817C2×C4semidirect
71. #6716C2×C4semidirect
72. #6715C2×C4semidirect
73. #6710C2×C4semidirect
93. #5798D5semidirect
200. C2×C5×D4C4×D3semidirect
269. C2×C3×D4C4×D5semidirect
432. C2×D4#1200semidirect
462. C3×C5#2946semidirect
527. C5#78726semidirect
548. C3#10614268semidirect

Maximal subgroups

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

subgroupindex
C2×#918212
C5×#57982
#117544962
C2×C3×#39642
#117490142
#117490112
#117489892
#117489862
#117484702
#117483932
#117483232
#106142683
#787265