Finite Group Databasebeta

← #14417256

Subgroups — #14417256

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91831C211yesmaximal, characteristic
2C5×#5812C211yesmaximal, characteristic, complemented
3#11754496C211yesmaximal, characteristic
4C2×C3×#3967C211yesmaximal, characteristic, complemented
5#11749260C212yesmaximal, complemented
6#11749257C212yesmaximal, complemented
7#11749235C212yesmaximal, complemented
8#11749232C212yesmaximal, complemented
9#11748470C211yesmaximal, characteristic, complemented
10#11748393C211yesmaximal, characteristic
11#11748323C211yesmaximal, characteristic, complemented
12#10614278—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×#6718C2212yes—
16#91831C418yescomplemented
17C2×#6717C2212yes—
18C2×#6710C2211yescharacteristic
19C5×Q8×Dic3—21no—
20C5×Q8×Dic3—21no—
21C5×Q8×Dic3C2212yes—
22C5×Q8×Dic3C2212yes—
23C5×#926—22no—
24C5×#926C2211yescharacteristic
25C5×#926C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C22×C3×#168C2211yescharacteristic
28#91552—22no—
29#91437—21no—
30#91428C2212yes—
31#91347—21no—
32#91340C2212yes—
33C3×#3967C2212yes—
34C3×#3967C2212yes—
35#90989C2212yes—
36#90986C2212yes—
37#90975C2211yescharacteristic
38#90975C2211yescharacteristic
39#90969C2211yescharacteristic
40#90969C2211yescharacteristic
41#90953C2212yes—
42Dic3×#168C2212yes—
43#78774—51nomaximal, Hall
44C5×#519—31no—
45C2×#4088—31no—
46#65857—31no—
47C2×#3967D311yescharacteristic, complemented
48#65319—32no—
49C4×#689—32no—
50#65315—32no—
51C4×#688—32no—
52#65291—31no—
53#65286—31no—
54#65284—31no—
55C2×C3×C5×Q8—21no—
56C2×C3×C5×Q8—22no—
57C2×C3×C5×Q8C2×C414yescomplemented
58C2×C3×C5×Q8C2312yes—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5C2311yescharacteristic
61C2×#1220—21no—
62#6817—22no—
63#6817C2×C414yes—
64C2×D60C2311yescharacteristic
65C2×C4×D15—21no—
66C2×Dic30C2311yescharacteristic
67C22×C3×Dic5—21no—
68C2×#1200—22no—
69#6718C2×C418yescomplemented
70#6717C2×C418yescomplemented
71#6710C2×C414yescomplemented
72C2×C3⋊#168C2312yes—
73C5×#217—21no—
74C5×#217D412yes—
75C5×C4⋊Dic3—22no—
76C5×C4⋊Dic3—22no—
77C5×C4⋊Dic3D411yescharacteristic
78C5×C4⋊Dic3D411yescharacteristic
79C5×C4⋊Dic3C2311yescharacteristic
80C5×C4⋊Dic3C2311yescharacteristic
81C4×C5×Dic3—21no—
82C4×C5×Dic3—22no—
83C4×C5×Dic3—22no—
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#5812D511yescharacteristic, complemented
94C2×#942—51no—
95#5504—51no—
96C2×C3×#103—51no—
97#5113—51no—
98#5101—51no—
99#4964—51no—
100#4817—52no—
101#4790—52no—
102#4789—52no—
103#4788—52no—
104C22×C5×Q8C2×D311yescharacteristic
105C2×#709—31no—
106C4×C5×Q8—32no—
107C4×C5×Q8—32no—
108C4×C5×Q8—61no—
109C4×C5×Q8—61no—
110C5×#117—31no—
111C5×#117—31no—
112C5×#117—62no—
113C2×#689—32no—
114#4088—38no—
115C2×#688—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#3967C2×D312yes—
125#3967C2×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#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C3×C5×Q8—24no—
138C3×C5×Q8—22no—
139C3×C5×Q8C22×C414yes—
140C2×C3×C4×C5—24no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C22×C412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5#4112yes—
145C2×C3×C4×C5C2411yescharacteristic
146#1220—24no—
147C2×Dic15—21no—
148D60—21no—
149D60C22×C412yes—
150C4×D15—24no—
151Dic30—21no—
152Dic30C22×C412yes—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—21no—
155C2×C5×Dic3C2×D412yes—
156C2×C5×Dic3C2×D412yes—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—81no—
159#1200—82no—
160C3⋊#168C22×C414yes—
161C3×#168—21no—
162C3×#168—21no—
163C22×C3×Q8C2×D511yescharacteristic
164C2×#235—51no—
165C22×C3×C8—51no—
166C2×C3×C4⋊C4—51no—
167Q8×Dic3—21no—
168Q8×Dic3—21no—
169Q8×Dic3C2×D512yes—
170Q8×Dic3C2×D512yes—
171C2×#216—52no—
172#942—58no—
173C2×#215—52no—
174C4×#67—102no—
175#926—22no—
176#926C2×D511yescharacteristic
177#926C2×D511yescharacteristic
178C2×#208—51no—
179#893—52no—
180#892—101no—
181D3×C4⋊C4—101no—
182#887—52no—
183C3×#103—52no—
184C3×#103—52no—
185#821—51no—
186#821—51no—
187#816—51no—
188#816—51no—
189#815—52no—
190C8×Dic3—52no—
191#808—52no—
192#807—52no—
193C2×C5×Q8—21no—
194C2×C5×Q8—22no—
195C2×C5×Q8C4×D314yescomplemented
196C2×C5×Q8C22×D312yes—
197C22×C4×C5—21no—
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—61no—
200C22×Dic5—21no—
201#709—34no—
202#709—62no—
203C2×D20—31no—
204C2×C4×D5—61no—
205C2×C4×D5—62no—
206C2×Dic10—31no—
207C5×C4⋊C4—31no—
208C5×C4⋊C4—31no—
209C5×C4⋊C4—31no—
210C5×C4⋊C4—31no—
211C5×C4⋊C4—62no—
212C5×C4⋊C4—62no—
213C5×C22⋊C4—32no—
214C5×C22⋊C4—61no—
215C42×C5—32no—
216C42×C5—62no—
217C42×C5—62no—
218C42×C5—61no—
219#689—38no—
220#688—38no—
221#685—62no—
222C4⋊Dic5—21no—
223C4⋊Dic5C22×D312yes—
224#683—62no—
225C4×Dic5—62no—
226#681—34no—
227C2×#168—22no—
228C2×#168—32no—
229C2×#168C22×D311yescharacteristic
230C2×#168C22×D311yescharacteristic
231C2×#137—151no—
232#520—151no—
233#519—31no—
234#441—152no—
235#440—152no—
236C4×Q16—152no—
237C4×SD16—152no—
238#428—151no—
239#416—151no—
240C2×#103—51no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×D15—22no—
247C2×D15—41no—
248C2×D15—41no—
249C3×C4×C5—24no—
250C3×C4×C5C4×D412yes—
251C3×C4×C5C23×C411yescharacteristic
252C3×C4×C5C2×#4111yescharacteristic
253Dic15—22no—
254C3×Dic5—42no—
255C5×Dic3—22no—
256C5×Dic3—22no—
257C5×Dic3—41no—
258C5×Dic3—41no—
259C2×C3×Q8—22no—
260C2×C3×Q8—21no—
261C2×C3×Q8C4×D514yescomplemented
262C2×C3×Q8C22×D512yes—
263C22×C3×C4—21no—
264C22×C3×C4—101no—
265C22×C3×C4C22×D511yescharacteristic
266C2×#67—101no—
267#235—54no—
268#235—102no—
269C2×D12—51no—
270C2×C4×D3—101no—
271C2×C4×D3—102no—
272C2×Dic6—51no—
273C2×C3×C8—51no—
274C2×C3×C8—51no—
275C2×C3×C8—102no—
276C3×C4⋊C4—52no—
277C3×C4⋊C4—101no—
278#217—21no—
279#217C22⋊D512yes—
280#216—58no—
281#215—58no—
282(C2×D3)⋊C4—102no—
283C4⋊Dic3—22no—
284C4⋊Dic3—22no—
285C4⋊Dic3C22⋊D511yescharacteristic
286C4⋊Dic3C22⋊D511yescharacteristic
287C4⋊Dic3C22×D511yescharacteristic
288C4⋊Dic3C22×D511yescharacteristic
289Dic3⋊C4—102no—
290C4×Dic3—21no—
291C4×Dic3—22no—
292C4×Dic3—22no—
293C4×Dic3—102no—
294C4×Dic3C22×D512yes—
295#208—54no—
296C2×C3⋊C8—52no—
297C23×C5D3×D411yescharacteristic
298C22×D5—61no—
299C5×Q8—24no—
300C5×Q8—22no—
301C5×Q8C2×C4×D314yes—
302C2×C4×C5—24no—
303C2×C4×C5—22no—
304C2×C4×C5—32no—
305C2×C4×C5—32no—
306C2×C4×C5—61no—
307C2×C4×C5—61no—
308C2×C4×C5C2×C4×D312yes—
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5#23712yes—
311C2×C4×C5C23×D311yescharacteristic
312C22⋊D5—64no—
313C2×Dic5—22no—
314C2×Dic5—61no—
315C2×Dic5—81no—
316D20—32no—
317D20—61no—
318C4×D5—64no—
319C4×D5—242no—
320Dic10—32no—
321Dic10—61no—
322#168—21no—
323#168—21no—
324#168—34no—
325C2×#41—151no—
326C22×Q8D3×D511yescharacteristic
327#137—158no—
328C2×Q16—152no—
329C2×SD16—152no—
330C2×M16—151no—
331C22×C8—51no—
332C4×Q8—32no—
333C4×Q8—32no—
334C4×Q8—61no—
335C4×Q8—61no—
336C4×Q8—152no—
337C4×D4—152no—
338C4×D4—302no—
339#117—31no—
340#117—31no—
341#117—62no—
342#117—301no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—301no—
345#107—152no—
346#106—152no—
347#103—52no—
348#103—52no—
349#103—151no—
350#103—151no—
351#102—151no—
352#102—151no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359D15—42no—
360C23×C3C2×C22⋊D511yescharacteristic
361C22×D3—101no—
362C3×Q8—22no—
363C3×Q8—24no—
364C3×Q8C2×C4×D514yes—
365C2×C3×C4—22no—
366C2×C3×C4—24no—
367C2×C3×C4—102no—
368C2×C3×C4—401no—
369C2×C3×C4C2×C4×D512yes—
370C2×C3×C4#70912yes—
371C2×C3×C4C2×C22⋊D511yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373#67—104no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—101no—
377C2×Dic3C2×C22⋊D512yes—
378C2×Dic3C2×C22⋊D512yes—
379D12—52no—
380D12—101no—
381C4×D3—104no—
382C4×D3—402no—
383Dic6—52no—
384Dic6—101no—
385C3×C8—101no—
386C3×C8—101no—
387C3⋊C8—54no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5#67⋊C412yes—
391C22×C5C2×D3×D411yescharacteristic
392C2×D5—62no—
393C2×D5—121no—
394C2×D5—121no—
395C4×C5—24no—
396C4×C5—62no—
397C4×C5—62no—
398C4×C5—121no—
399C4×C5—121no—
400C4×C5#67⋊C412yes—
401C4×C5C22×C4×D311yescharacteristic
402C4×C5C2×#23711yescharacteristic
403Dic5—42no—
404Dic5—62no—
405#41—154no—
406#41—302no—
407C2×Q8—22no—
408C2×Q8—21no—
409C2×Q8—151no—
410C2×Q8#120014yescomplemented
411C2×Q8C2×D3×D512yes—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—21no—
415C22×C4—101no—
416C22×C4—302no—
417C22×C4—301no—
418C22×C4C2×D3×D511yescharacteristic
419Q16—158no—
420SD16—158no—
421M16—154no—
422C2×C8—51no—
423C2×C8—51no—
424C2×C8—102no—
425C2×C8—152no—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—31no—
429C4⋊C4—31no—
430C4⋊C4—52no—
431C4⋊C4—62no—
432C4⋊C4—62no—
433C4⋊C4—101no—
434C4⋊C4—302no—
435C22⋊C4—32no—
436C22⋊C4—61no—
437C22⋊C4—302no—
438C42—32no—
439C42—62no—
440C42—62no—
441C42—61no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3C4×C22⋊D512yes—
447C22×C3C22×C22⋊D511yescharacteristic
448C2×D3—102no—
449C2×D3—201no—
450C2×D3—201no—
451C3×C4—24no—
452C3×C4—202no—
453C3×C4C4×C22⋊D512yes—
454C3×C4C22×C4×D511yescharacteristic
455C3×C4C2×#70911yescharacteristic
456Dic3—22no—
457Dic3—22no—
458Dic3—41no—
459Dic3—41no—
460Dic3—102no—
461C2×C5—22no—
462C2×C5C2×#67⋊C411yescharacteristic
463C2×C5#576211yescharacteristic
464C2×C5#576611yescharacteristic
465D5—122no—
466C23—301no—
467C23D3×C22⋊D511yescharacteristic
468Q8—22no—
469Q8—24no—
470Q8—152no—
471Q8—301no—
472Q8C2×#120014yes—
473D4—152no—
474D4—304no—
475D4—301no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—102no—
483C2×C4—301no—
484C2×C4—304no—
485C2×C4—401no—
486C2×C4—1202no—
487C2×C4#677912yes—
488C2×C4C2×#120012yes—
489C2×C4D3×C22⋊D511yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—101no—
492C8—101no—
493C8—154no—
494C2×C3—22no—
495C2×C3C2×C4×C22⋊D511yescharacteristic
496C2×C3#6617111yescharacteristic
497C2×C3#6617211yescharacteristic
498D3—202no—
499C5#7877411yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—302no—
503C22—601no—
504C22—601no—
505C22#9155612yes—
506C22C2×D3×C22⋊D511yescharacteristic
507C4—24no—
508C4—62no—
509C4—62no—
510C4—121no—
511C4—121no—
512C4—202no—
513C4—302no—
514C4#9155612yes—
515C4C2×#677911yescharacteristic
516C4C22×#120011yescharacteristic
517C3#1061427811yescharacteristic, complemented, Sylow
518C2—22no—
519C2—602no—
520C2#1175509111yescharacteristic
521C2#1175510511yescharacteristic
522C2C2×#9155611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenterC22×Q8D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5812C2semidirect
4. C2×C3×#3967C2semidirect
5. #11749260C2semidirect
6. #11749257C2semidirect
7. #11749235C2semidirect
8. #11749232C2semidirect
9. #11748470C2semidirect
11. #11748323C2semidirect
16. #91831C4semidirect
47. C2×#3967D3semidirect
57. C2×C3×C5×Q8C2×C4semidirect
69. #6718C2×C4semidirect
70. #6717C2×C4semidirect
71. #6710C2×C4semidirect
93. #5812D5semidirect
195. C2×C5×Q8C4×D3semidirect
261. C2×C3×Q8C4×D5semidirect
410. C2×Q8#1200semidirect
443. C3×C5#2947semidirect
499. C5#78774semidirect
517. C3#10614278semidirect

Maximal subgroups

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

subgroupindex
C2×#918312
C5×#58122
#117544962
C2×C3×#39672
#117492602
#117492572
#117492352
#117492322
#117484702
#117483932
#117483232
#106142783
#787745