Finite Group Databasebeta

← #14417091

Subgroups — #14417091

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
1C5×#5521C211yesmaximal, characteristic, complemented
2C3×#65857C211yesmaximal, characteristic, complemented
3C2×#91299C211yesmaximal, characteristic
4#11751098C211yesmaximal, characteristic, complemented
5#11748470C211yesmaximal, characteristic, complemented
6C2×#90966C211yesmaximal, characteristic, complemented
7#11748364C211yesmaximal, characteristic, complemented
8#11747050C212yesmaximal, complemented
9C4×#6656C212yesmaximal, complemented
10#11747021C212yesmaximal, complemented
11C4×#6652C212yesmaximal, complemented
12#10614268—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C22×C3⋊#168C2211yescharacteristic
18C5×#926C2211yescharacteristic
19C5×#893—21no—
20C5×#893—21no—
21C5×D3×C22⋊C4—22no—
22C4×C5×D12C2212yes—
23C4×C5×D12C2212yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C3×#4038—21no—
26C3×D5×C4⋊C4—21no—
27C3×#4027—22no—
28C3×C4×D20C2212yescomplemented
29C3×C4×Dic10C2212yescomplemented
30C2×#6656C2212yes—
31#91299C418yescomplemented
32C2×#6652C2212yes—
33#91087C2212yescomplemented
34C4×C3⋊#168C2212yescomplemented
35#90989C2212yescomplemented
36#90986C2212yescomplemented
37#90970C2211yescharacteristic, complemented
38#90970C2211yescharacteristic, complemented
39#90966C2212yes—
40#90966C2212yes—
41#90964C2211yescharacteristic, complemented
42#90964C2211yescharacteristic, complemented
43#82564—51nomaximal, Hall
44C5×#518—31no—
45C2×#4078—31no—
46#65857D311yescharacteristic, complemented
47C2×#3964—31no—
48#65307—32no—
49C4×#687—32no—
50#65303—32no—
51C4×#686—32no—
52#65291—31no—
53#65286—31no—
54#65284—31no—
55C23×C5×D3—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×C5×D12—21no—
58C2×C5×D12—22no—
59C2×C5×D12C2×C414yescomplemented
60C2×C5×D12C2312yes—
61C2×C4×C5×D3—22no—
62C2×C4×C5×D3—22no—
63C2×C3×C22⋊D5—21no—
64C22×C3×Dic5—21no—
65C3×#709—22no—
66C3×#709C2×C414yescomplemented
67C2×C3×D20C2311yescharacteristic
68C2×C3×C4×D5—21no—
69C2×C3×C4×D5—22no—
70C2×C3×Dic10C2311yescharacteristic
71C3×C5×C4⋊C4D411yescharacteristic
72C3×C5×C4⋊C4D411yescharacteristic
73C3×C5×C22⋊C4D412yes—
74C3×C42×C5C2312yes—
75#6710C2×C414yescomplemented
76C2×C3⋊#168—22no—
77C2×C3⋊#168C2311yescharacteristic
78C2×C3⋊#168C2311yescharacteristic
79C2×C3⋊#168C2312yes—
80C5×#217—21no—
81C5×(C2×D3)⋊C4—22no—
82C5×(C2×D3)⋊C4—22no—
83C5×C4⋊Dic3C2311yescharacteristic
84C5×C4⋊Dic3C2311yescharacteristic
85C4×C5×Dic3—21no—
86C3×#685—22no—
87C3×C4⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89C3×#683—22no—
90C3×C4×Dic5—22no—
91#6656C2×C418yescomplemented
92#6652C2×C418yescomplemented
93C3×#520—51no—
94C2×#949—51no—
95#5521D511yescharacteristic, complemented
96#5233—51no—
97#5026—52no—
98C4×#215—52no—
99#5014—52no—
100C4×#213—52no—
101#4997—51no—
102C2×#809—51no—
103#4964—51no—
104C22×C5×D4—31no—
105C2×#709C2×D311yescharacteristic
106C4×C5×D4—32no—
107C4×C5×D4—32no—
108C4×C5×D4—61no—
109C4×C5×D4—61no—
110C5×#117—31no—
111C5×#117C2×D311yescharacteristic
112C2×C5×C22⋊C4—62no—
113C2×#687—32no—
114#4078—38no—
115C2×#686—32no—
116C2×C4⋊Dic5C2×D311yescharacteristic
117C2×#681—31no—
118C22×#168—31no—
119#4038—21no—
120D5×C4⋊C4—21no—
121#4027—22no—
122C4×D20C2×D312yescomplemented
123C4×Dic10C2×D312yescomplemented
124#3964—32no—
125#3964—32no—
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×C5C2×D411yescharacteristic
136C22×C5×D3—22no—
137C22×C5×D3—24no—
138C22×C5×D3—81no—
139C22×C5×D3—81no—
140C22×C3×D5—21no—
141C2×C3×C4×C5C22×C412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5#4112yes—
146C2×C3×C4×C5C2411yescharacteristic
147C2×C5×Dic3—21no—
148C2×C5×Dic3—21no—
149C5×D12—24no—
150C5×D12—22no—
151C5×D12C22×C414yes—
152C4×C5×D3—82no—
153C4×C5×D3—82no—
154C3×C22⋊D5—24no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—81no—
158C3×D20—21no—
159C3×D20C22×C412yes—
160C3×C4×D5—24no—
161C3×C4×D5—82no—
162C3×Dic10—21no—
163C3×Dic10C22×C412yes—
164C3⋊#168—21no—
165C3⋊#168—21no—
166C3⋊#168C22×C414yes—
167C2×C3×#41—51no—
168C22×D12C2×D511yescharacteristic
169C3×C4×Q8—52no—
170C3×C4×D4—52no—
171C3×C4×D4—102no—
172C3×#117—101no—
173C3×#117C2×D511yescharacteristic
174C2×C3×C4⋊C4—51no—
175C2×C3×C4⋊C4—101no—
176#949—58no—
177C2×#215—52no—
178C2×#213—52no—
179#926C2×D511yescharacteristic
180C2×#208—51no—
181C22×C3⋊C8—51no—
182#893—21no—
183#893—21no—
184D3×C22⋊C4—22no—
185C4×D12C2×D512yes—
186C4×D12C2×D512yes—
187#835—51no—
188#835—51no—
189#832—51no—
190#832—51no—
191#809—52no—
192#809—52no—
193#808—52no—
194#807—52no—
195#803—52no—
196C4×C3⋊C8—52no—
197C24×C5—61no—
198C2×C5×D4—34no—
199C2×C5×D4—32no—
200C2×C5×D4—62no—
201C2×C5×D4—61no—
202C22×C4×C5—62no—
203C22×C4×C5—62no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—21no—
206C22×Dic5—21no—
207#709—22no—
208#709C4×D314yescomplemented
209C2×D20C22×D311yescharacteristic
210C2×C4×D5—21no—
211C2×C4×D5—22no—
212C2×Dic10C22×D311yescharacteristic
213C5×C4⋊C4—31no—
214C5×C4⋊C4—31no—
215C5×C4⋊C4#6711yescharacteristic
216C5×C4⋊C4#6711yescharacteristic
217C5×C22⋊C4—61no—
218C5×C22⋊C4—62no—
219C5×C22⋊C4—62no—
220C5×C22⋊C4#6712yes—
221C42×C5—61no—
222C42×C5C22×D312yes—
223#687—38no—
224#686—38no—
225#685—22no—
226C4⋊Dic5—21no—
227C4⋊Dic5C22×D312yes—
228#683—22no—
229C4×Dic5—22no—
230#681—34no—
231C2×#168—32no—
232C2×#168—31no—
233C2×#168—31no—
234C2×#168—62no—
235C2×AGL(1,ℤ/8)—151no—
236#520—51no—
237#518—31no—
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428—151no—
243#416—151no—
244C2×#102—151no—
245#405—151no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5C4×D412yes—
249C22×C3×C5C22×D411yescharacteristic
250C2×C5×D3—24no—
251C2×C5×D3—42no—
252C2×C5×D3—42no—
253C2×C5×D3—84no—
254C2×C3×D5—22no—
255C2×C3×D5—41no—
256C2×C3×D5—41no—
257C3×C4×C5—22no—
258C3×C4×C5—22no—
259C3×C4×C5C4×D412yes—
260C3×C4×C5C23×C411yescharacteristic
261C3×C4×C5C2×#4111yescharacteristic
262C3×Dic5—22no—
263C3×Dic5—42no—
264C5×Dic3—41no—
265C5×Dic3—41no—
266C23×D3—21no—
267C3×#41—54no—
268C3×#41—102no—
269C2×C3×Q8—51no—
270C2×C3×D4—51no—
271C2×C3×D4—101no—
272C22×C3×C4—101no—
273C22×C3×C4—101no—
274C22×C3×C4—102no—
275C22×C3×C4C22×D511yescharacteristic
276C2×D12—22no—
277C2×D12—21no—
278C2×D12C4×D514yescomplemented
279C2×D12C22×D512yes—
280C2×C4×D3—22no—
281C2×C4×D3—22no—
282C3×C4⋊C4—52no—
283C3×C4⋊C4—102no—
284C3×C4⋊C4—101no—
285C3×C4⋊C4C22⋊D511yescharacteristic
286C3×C4⋊C4C22⋊D511yescharacteristic
287C3×C22⋊C4—102no—
288C3×C22⋊C4C22⋊D512yes—
289C3×C42—102no—
290C3×C42C22×D512yes—
291#217—21no—
292#215—58no—
293#213—58no—
294(C2×D3)⋊C4—22no—
295(C2×D3)⋊C4—22no—
296C4⋊Dic3C22×D511yescharacteristic
297C4⋊Dic3C22×D511yescharacteristic
298C4×Dic3—21no—
299#208—54no—
300C2×C3⋊C8—52no—
301C2×C3⋊C8—51no—
302C2×C3⋊C8—51no—
303C2×C3⋊C8—102no—
304C23×C5—62no—
305C23×C5—64no—
306C23×C5—241no—
307C23×C5—241no—
308C23×C5C2×#6711yescharacteristic
309C22×D5—21no—
310C5×D4—34no—
311C5×D4—64no—
312C5×D4—62no—
313C2×C4×C5—61no—
314C2×C4×C5—61no—
315C2×C4×C5—242no—
316C2×C4×C5—242no—
317C2×C4×C5C2×C4×D312yes—
318C2×C4×C5#23512yes—
319C2×C4×C5C2×#6712yes—
320C2×C4×C5C2×#6712yes—
321C2×C4×C5C2×#6711yescharacteristic
322C2×C4×C5C23×D311yescharacteristic
323C22⋊D5—24no—
324C2×Dic5—21no—
325C2×Dic5—22no—
326C2×Dic5—81no—
327D20—21no—
328D20C2×C4×D312yes—
329C4×D5—24no—
330C4×D5—82no—
331Dic10—21no—
332Dic10C2×C4×D312yes—
333#168—34no—
334#168—61no—
335#168—61no—
336C2×#41—51no—
337C22×D4—31no—
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16—151no—
342C22×C8—151no—
343C4×Q8—52no—
344C4×D4—32no—
345C4×D4—32no—
346C4×D4—52no—
347C4×D4—61no—
348C4×D4—61no—
349C4×D4—102no—
350#117—31no—
351#117—101no—
352#117D3×D511yescharacteristic
353C2×C4⋊C4—51no—
354C2×C4⋊C4—101no—
355C2×C22⋊C4—62no—
356#107—152no—
357#106—152no—
358#103—151no—
359#103—151no—
360#102—151no—
361#102—151no—
362#102—152no—
363#102—152no—
364#97—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5#57611yescharacteristic
369C2×C3×C5#57711yescharacteristic
370C3×D5—42no—
371C5×D3—44no—
372C23×C3—101no—
373C23×C3C2×C22⋊D511yescharacteristic
374C22×D3—22no—
375C22×D3—24no—
376C22×D3—81no—
377C22×D3—81no—
378C3×Q8—52no—
379C3×Q8—101no—
380C3×D4—52no—
381C3×D4—104no—
382C3×D4—101no—
383C2×C3×C4—101no—
384C2×C3×C4—104no—
385C2×C3×C4—102no—
386C2×C3×C4—402no—
387C2×C3×C4—401no—
388C2×C3×C4C2×C4×D512yes—
389C2×C3×C4#70912yes—
390C2×C3×C4C2×C22⋊D512yes—
391C2×C3×C4C2×C22⋊D512yes—
392C2×C3×C4C2×C22⋊D511yescharacteristic
393C2×C3×C4C23×D511yescharacteristic
394C2×Dic3—21no—
395C2×Dic3—21no—
396D12—22no—
397D12—24no—
398D12C2×C4×D514yes—
399C4×D3—82no—
400C4×D3—82no—
401C3⋊C8—54no—
402C3⋊C8—101no—
403C3⋊C8—101no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—64no—
407C22×C5—122no—
408C22×C5—122no—
409C22×C5—244no—
410C22×C5C4×#6712yes—
411C22×C5C22×#6711yescharacteristic
412C2×D5—22no—
413C2×D5—41no—
414C2×D5—41no—
415C4×C5—22no—
416C4×C5—22no—
417C4×C5—121no—
418C4×C5—121no—
419C4×C5C4×#6712yes—
420C4×C5C22×C4×D311yescharacteristic
421C4×C5C2×#23511yescharacteristic
422Dic5—22no—
423Dic5—42no—
424C24—61no—
425#41—54no—
426#41—102no—
427C2×Q8—51no—
428C2×D4—34no—
429C2×D4—32no—
430C2×D4—51no—
431C2×D4—62no—
432C2×D4—61no—
433C2×D4—101no—
434C22×C4—62no—
435C22×C4—62no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4—102no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—158no—
441D8—158no—
442M16—154no—
443C2×C8—152no—
444C2×C8—151no—
445C2×C8—151no—
446C2×C8—302no—
447C4⋊C4—31no—
448C4⋊C4—31no—
449C4⋊C4—52no—
450C4⋊C4—101no—
451C4⋊C4—102no—
452C4⋊C4#120111yescharacteristic
453C4⋊C4#120111yescharacteristic
454C22⋊C4—61no—
455C22⋊C4—62no—
456C22⋊C4—62no—
457C22⋊C4—102no—
458C22⋊C4#120112yes—
459C42—61no—
460C42—102no—
461C42C2×D3×D512yes—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—102no—
466C22×C3—201no—
467C22×C3—201no—
468C22×C3C4×C22⋊D512yes—
469C22×C3C22×C22⋊D511yescharacteristic
470C2×D3—24no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—84no—
474C3×C4—22no—
475C3×C4—22no—
476C3×C4—102no—
477C3×C4—202no—
478C3×C4C4×C22⋊D512yes—
479C3×C4C22×C4×D511yescharacteristic
480C3×C4C2×#70911yescharacteristic
481Dic3—41no—
482Dic3—41no—
483C2×C5—22no—
484C2×C5—124no—
485C2×C5C2×C4×#6711yescharacteristic
486C2×C5#583511yescharacteristic
487C2×C5#583711yescharacteristic
488D5—42no—
489C23—62no—
490C23—64no—
491C23—101no—
492C23—241no—
493C23—241no—
494C23C2×#120111yescharacteristic
495Q8—52no—
496Q8—101no—
497D4—34no—
498D4—52no—
499D4—64no—
500D4—62no—
501D4—104no—
502D4—101no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—101no—
506C2×C4—104no—
507C2×C4—102no—
508C2×C4—242no—
509C2×C4—242no—
510C2×C4—402no—
511C2×C4—401no—
512C2×C4#677112yes—
513C2×C4C4×D3×D512yes—
514C2×C4C2×#120112yes—
515C2×C4C2×#120112yes—
516C2×C4C2×#120111yescharacteristic
517C2×C4C22×D3×D511yescharacteristic
518C8—154no—
519C8—301no—
520C8—301no—
521C2×C3—22no—
522C2×C3—202no—
523C2×C3C2×C4×C22⋊D511yescharacteristic
524C2×C3#6616911yescharacteristic
525C2×C3#6617011yescharacteristic
526D3—44no—
527C5#8256411yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—64no—
531C22—102no—
532C22—122no—
533C22—122no—
534C22—201no—
535C22—201no—
536C22—244no—
537C22C4×#120112yes—
538C22C22×#120111yescharacteristic
539C4—22no—
540C4—22no—
541C4—102no—
542C4—121no—
543C4—121no—
544C4—202no—
545C4C4×#120112yes—
546C4C2×#677111yescharacteristic
547C4C2×C4×D3×D511yescharacteristic
548C3#1061426811yescharacteristic, complemented, Sylow
549C2—22no—
550C2—124no—
551C2—202no—
552C2C2×C4×#120111yescharacteristic
553C2#1175530111yescharacteristic
554C2#1175530411yescharacteristic
subgroupG/H
centerC22C22×#1201
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#91299C2
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5521C2semidirect
2. C3×#65857C2semidirect
4. #11751098C2semidirect
5. #11748470C2semidirect
6. C2×#90966C2semidirect
7. #11748364C2semidirect
8. #11747050C2semidirect
9. C4×#6656C2semidirect
10. #11747021C2semidirect
11. C4×#6652C2semidirect
28. C3×C4×D20C22semidirect
29. C3×C4×Dic10C22semidirect
31. #91299C4semidirect
33. #91087C22semidirect
34. C4×C3⋊#168C22semidirect
35. #90989C22semidirect
36. #90986C22semidirect
37. #90970C22semidirect
38. #90970C22semidirect
41. #90964C22semidirect
42. #90964C22semidirect
46. #65857D3semidirect
59. C2×C5×D12C2×C4semidirect
66. C3×#709C2×C4semidirect
75. #6710C2×C4semidirect
91. #6656C2×C4semidirect
92. #6652C2×C4semidirect
95. #5521D5semidirect
122. C4×D20C2×D3semidirect
123. C4×Dic10C2×D3semidirect
208. #709C4×D3semidirect
278. C2×D12C4×D5semidirect
462. C3×C5#2946semidirect
527. C5#82564semidirect
548. C3#10614268semidirect

Maximal subgroups

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

subgroupindex
C5×#55212
C3×#658572
C2×#912992
#117510982
#117484702
C2×#909662
#117483642
#117470502
C4×#66562
#117470212
C4×#66522
#106142683
#825645