Finite Group Databasebeta

← #14417281

Subgroups — #14417281

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
1C5×#5516C211yesmaximal, characteristic, complemented
2#11754509C211yesmaximal, characteristic
3C2×#91307C211yesmaximal, characteristic
4#11751096C211yesmaximal, characteristic, complemented
5C3×#65291C211yesmaximal, characteristic
6C2×#90973C211yesmaximal, characteristic, complemented
7#11748323C211yesmaximal, characteristic, complemented
8#11747267C212yesmaximal, complemented
9#11747266C212yesmaximal, complemented
10#11747222C212yesmaximal, complemented
11#11747221C212yesmaximal, complemented
12#10614278—31nomaximal, Hall
13C22×C5×Dic6C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C3×C5×#117C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C5×#926C2211yescharacteristic
19C5×#887C2212yes—
20C5×#887C2212yes—
21C5×#877—22no—
22C4×C5×Dic6—21no—
23C4×C5×Dic6—21no—
24C22×C3×#168C2211yescharacteristic
25#91559—22no—
26Dic3×D20C2212yes—
27D5×C4⋊Dic3—21no—
28#91358—21no—
29Dic3×Dic10C2212yes—
30C2×#6661C2212yes—
31#91307C418yescomplemented
32C2×#6655C2212yes—
33#91092C2212yes—
34#91091C2212yes—
35C3×#3942C2211yescharacteristic
36C3×#3942C2211yescharacteristic
37C3×#3941C2211yescharacteristic
38C3×#3941C2211yescharacteristic
39#90973C2212yes—
40#90973C2212yes—
41#90953C2212yes—
42Dic3×#168C2212yes—
43#78821—51nomaximal, Hall
44C5×#519—31no—
45C2×#4088—31no—
46#65857—31no—
47C2×#3967—31no—
48#65319—32no—
49C4×#689—32no—
50#65315—32no—
51C4×#688—32no—
52#65291D311yescharacteristic
53#65286—31no—
54#65284—31no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C22×C5×Dic3—21no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6—22no—
60C2×C5×Dic6C2×C414yescomplemented
61C2×C5×Dic6C2312yes—
62C2×C3×C22⋊D5—21no—
63C3×#709—22no—
64C3×#709C2×C414yes—
65C2×C3×D20C2311yescharacteristic
66C2×C3×C4×D5—21no—
67C2×C3×Dic10C2311yescharacteristic
68C2×D5×Dic3—22no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5—21no—
73C4⋊Dic15—21no—
74C4⋊Dic15C2312yes—
75#6710C2×C414yescomplemented
76C2×C3⋊#168C2312yes—
77C5×#217D412yes—
78C5×C4⋊Dic3D411yescharacteristic
79C5×C4⋊Dic3D411yescharacteristic
80C5×Dic3⋊C4—22no—
81C5×Dic3⋊C4—22no—
82C4×C5×Dic3—22no—
83C4×C5×Dic3—22no—
84C4×C5×Dic3C2312yes—
85C2×C3×#168—22no—
86C2×C3×#168C2311yescharacteristic
87C2×C3×#168C2311yescharacteristic
88#6668—22no—
89#6665—22no—
90Dic3×Dic5—22no—
91#6661C2×C418yescomplemented
92#6655C2×C418yescomplemented
93#5827—51no—
94C2×#951—51no—
95#5516D511yescharacteristic, complemented
96C3×#416—51no—
97C2×#816—51no—
98#5101—51no—
99#4995—51no—
100#4790—52no—
101#4789—52no—
102#4758—52no—
103#4757—52no—
104C22×C5×Q8—31no—
105C2×#709C2×D311yescharacteristic
106C4×C5×Q8—32no—
107C4×C5×Q8—32no—
108C4×C5×Q8—61no—
109C4×C5×Q8—61no—
110C5×#117—31no—
111C5×#117—62no—
112C5×#117C2×D311yescharacteristic
113C2×#689—32no—
114#4088—38no—
115C2×#688—32no—
116C2×C4⋊Dic5—31no—
117C2×#681—31no—
118C22×#168C2×D311yescharacteristic
119#4038—61no—
120D5×C4⋊C4—61no—
121#4027—62no—
122C4×D20—32no—
123C4×Dic10—32no—
124#3967—32no—
125#3967—32no—
126#3942C2×D311yescharacteristic
127#3942C2×D311yescharacteristic
128#3941C2×D311yescharacteristic
129#3941C2×D311yescharacteristic
130#3940—32no—
131#3939—32no—
132#3935—32no—
133C4×#168—32no—
134#2947—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×C3×D5—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5#4112yes—
142C2×C3×C4×C5C2411yescharacteristic
143C2×Dic15—22no—
144C2×Dic15—81no—
145C2×C5×Dic3—24no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3C2×D412yes—
148C2×C5×Dic3C2×D412yes—
149C5×Dic6—24no—
150C5×Dic6—22no—
151C5×Dic6C22×C414yes—
152C3×C22⋊D5—24no—
153C2×C3×Dic5—21no—
154C3×D20—21no—
155C3×D20C22×C412yes—
156C3×C4×D5—24no—
157C3×Dic10—21no—
158C3×Dic10C22×C412yes—
159D5×Dic3—82no—
160C3⋊#168C22×C414yes—
161C3×#168—21no—
162C3×#168—21no—
163C2×C3×#41—51no—
164C22×Dic6C2×D511yescharacteristic
165C22×C3×C8—51no—
166C3×#117C2×D511yescharacteristic
167#951—58no—
168Q8×Dic3—52no—
169C2×#216—52no—
170D4×Dic3—52no—
171D4×Dic3—102no—
172C2×#214—52no—
173#926—101no—
174#926C2×D511yescharacteristic
175C2×C4⋊Dic3—51no—
176C2×C4⋊Dic3—101no—
177C2×#208—51no—
178#887C2×D512yes—
179#887C2×D512yes—
180#877—22no—
181C4×Dic6—21no—
182C4×Dic6—21no—
183C3×#103—51no—
184C3×#103—51no—
185C3×#102—51no—
186C3×#102—51no—
187#816—52no—
188#816—52no—
189#815—52no—
190C8×Dic3—52no—
191#808—52no—
192#807—52no—
193C2×C5×Q8—34no—
194C2×C5×Q8—32no—
195C2×C5×Q8—61no—
196C2×C5×Q8—62no—
197C22×C4×C5—61no—
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—21no—
200C22×Dic5—61no—
201#709—22no—
202#709C4×D314yes—
203C2×D20C22×D311yescharacteristic
204C2×C4×D5—21no—
205C2×C4×D5—62no—
206C2×Dic10C22×D311yescharacteristic
207C5×C4⋊C4—31no—
208C5×C4⋊C4—31no—
209C5×C4⋊C4—62no—
210C5×C4⋊C4—62no—
211C5×C4⋊C4C22×D311yescharacteristic
212C5×C4⋊C4C22×D311yescharacteristic
213C5×C22⋊C4—21no—
214C5×C22⋊C4—32no—
215C42×C5—21no—
216C42×C5—32no—
217C42×C5—62no—
218C42×C5—62no—
219#689—38no—
220#688—38no—
221#685—62no—
222C4⋊Dic5—32no—
223C4⋊Dic5—61no—
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—51no—
240C2×#103—151no—
241#405—151no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5C4×D412yes—
245C22×C3×C5C22×D411yescharacteristic
246C2×C3×D5—22no—
247C2×C3×D5—41no—
248C2×C3×D5—41no—
249C3×C4×C5—41no—
250C3×C4×C5—41no—
251C3×C4×C5C4×D412yes—
252C3×C4×C5C23×C411yescharacteristic
253C3×C4×C5C2×#4111yescharacteristic
254Dic15—42no—
255C3×Dic5—22no—
256C5×Dic3—24no—
257C5×Dic3—22no—
258C5×Dic3—22no—
259C3×#41—54no—
260C3×#41—102no—
261C2×C3×Q8—51no—
262C2×C3×D4—51no—
263C2×C3×D4—101no—
264C22×C3×C4—101no—
265C22×C3×C4C22×D511yescharacteristic
266C22×Dic3—21no—
267C22×Dic3—101no—
268C22×Dic3—102no—
269C2×Dic6—22no—
270C2×Dic6—21no—
271C2×Dic6C4×D514yescomplemented
272C2×Dic6C22×D512yes—
273C2×C3×C8—51no—
274C2×C3×C8—51no—
275C2×C3×C8—102no—
276C3×C4⋊C4C22×D511yescharacteristic
277C3×C4⋊C4C22×D511yescharacteristic
278C3×C22⋊C4—21no—
279C3×C42—21no—
280#217—102no—
281#217C22⋊D512yes—
282#216—58no—
283#214—58no—
284C4⋊Dic3—52no—
285C4⋊Dic3—101no—
286C4⋊Dic3—102no—
287C4⋊Dic3C22⋊D511yescharacteristic
288C4⋊Dic3C22⋊D511yescharacteristic
289Dic3⋊C4—22no—
290Dic3⋊C4—22no—
291C4×Dic3—22no—
292C4×Dic3—22no—
293C4×Dic3—102no—
294C4×Dic3C22×D512yes—
295#208—54no—
296C2×C3⋊C8—52no—
297C23×C5D3×D411yescharacteristic
298C22×D5—21no—
299C5×Q8—34no—
300C5×Q8—64no—
301C5×Q8—62no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—32no—
305C2×C4×C5—32no—
306C2×C4×C5—64no—
307C2×C4×C5—62no—
308C2×C4×C5C2×C4×D312yes—
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5#23712yes—
311C2×C4×C5C23×D311yescharacteristic
312C22⋊D5—24no—
313C2×Dic5—21no—
314C2×Dic5—62no—
315C2×Dic5—241no—
316D20—21no—
317D20C2×C4×D312yes—
318C4×D5—24no—
319C4×D5—242no—
320Dic10—21no—
321Dic10C2×C4×D312yes—
322#168—21no—
323#168—21no—
324#168—34no—
325C2×#41—51no—
326C22×Q8—31no—
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—62no—
341#117—301no—
342#117D3×D511yescharacteristic
343C2×C4⋊C4—151no—
344C2×C4⋊C4—301no—
345#107—152no—
346#106—152no—
347#103—51no—
348#103—51no—
349#103—152no—
350#103—152no—
351#102—51no—
352#102—51no—
353#97—152no—
354C4×C8—152no—
355C2×C3×C5—22no—
356C2×C3×C5C2×C4×D411yescharacteristic
357C2×C3×C5#57711yescharacteristic
358C2×C3×C5#57811yescharacteristic
359C3×D5—42no—
360C23×C3—101no—
361C23×C3C2×C22⋊D511yescharacteristic
362C3×Q8—52no—
363C3×Q8—101no—
364C3×D4—52no—
365C3×D4—104no—
366C3×D4—101no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—101no—
370C2×C3×C4—104no—
371C2×C3×C4C2×C4×D512yes—
372C2×C3×C4#70912yes—
373C2×C3×C4C2×C22⋊D511yescharacteristic
374C2×C3×C4C23×D511yescharacteristic
375C2×Dic3—22no—
376C2×Dic3—24no—
377C2×Dic3—102no—
378C2×Dic3—402no—
379C2×Dic3—401no—
380C2×Dic3C2×C22⋊D512yes—
381C2×Dic3C2×C22⋊D512yes—
382Dic6—22no—
383Dic6—24no—
384Dic6C2×C4×D514yes—
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—22no—
393C2×D5—41no—
394C2×D5—41no—
395C4×C5—41no—
396C4×C5—41no—
397C4×C5—64no—
398C4×C5—62no—
399C4×C5—62no—
400C4×C5#67⋊C412yes—
401C4×C5C22×C4×D311yescharacteristic
402C4×C5C2×#23711yescharacteristic
403Dic5—22no—
404Dic5—122no—
405#41—54no—
406#41—102no—
407C2×Q8—34no—
408C2×Q8—32no—
409C2×Q8—51no—
410C2×Q8—62no—
411C2×Q8—61no—
412C2×D4—51no—
413C2×D4—101no—
414C22×C4—61no—
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—62no—
429C4⋊C4—62no—
430C4⋊C4—152no—
431C4⋊C4—302no—
432C4⋊C4—301no—
433C4⋊C4C2×D3×D511yescharacteristic
434C4⋊C4C2×D3×D511yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—32no—
437C22⋊C4—302no—
438C42—21no—
439C42—32no—
440C42—62no—
441C42—62no—
442C42—302no—
443C3×C5#294711yescharacteristic, complemented, Hall
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—102no—
447C22×C3—201no—
448C22×C3—201no—
449C22×C3C4×C22⋊D512yes—
450C22×C3C22×C22⋊D511yescharacteristic
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—102no—
454C3×C4C4×C22⋊D512yes—
455C3×C4C22×C4×D511yescharacteristic
456C3×C4C2×#70911yescharacteristic
457Dic3—24no—
458Dic3—22no—
459Dic3—22no—
460Dic3—202no—
461C2×C5—22no—
462C2×C5C2×#67⋊C411yescharacteristic
463C2×C5#577011yescharacteristic
464C2×C5#577111yescharacteristic
465D5—42no—
466C23—101no—
467C23D3×C22⋊D511yescharacteristic
468Q8—34no—
469Q8—52no—
470Q8—64no—
471Q8—62no—
472Q8—101no—
473D4—52no—
474D4—104no—
475D4—101no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—64no—
481C2×C4—62no—
482C2×C4—101no—
483C2×C4—104no—
484C2×C4—302no—
485C2×C4—1202no—
486C2×C4—1201no—
487C2×C4#676512yes—
488C2×C4C4×D3×D512yes—
489C2×C4D3×C22⋊D511yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—101no—
492C8—101no—
493C8—154no—
494C2×C3—22no—
495C2×C3—202no—
496C2×C3C2×C4×C22⋊D511yescharacteristic
497C2×C3#6617111yescharacteristic
498C2×C3#6617211yescharacteristic
499C5#7882111yescharacteristic, complemented, Sylow
500C22—21no—
501C22—21no—
502C22—102no—
503C22—201no—
504C22—201no—
505C22#9144112yes—
506C22C2×D3×C22⋊D511yescharacteristic
507C4—41no—
508C4—41no—
509C4—64no—
510C4—62no—
511C4—62no—
512C4—102no—
513C4—602no—
514C4#9144112yes—
515C4C2×#676511yescharacteristic
516C4C2×C4×D3×D511yescharacteristic
517C3#1061427811yescharacteristic, complemented, Sylow
518C2—22no—
519C2—202no—
520C2C2×#9144111yescharacteristic
521C2#1175532611yescharacteristic
522C2#1175534611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#709C22
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5516C2semidirect
4. #11751096C2semidirect
6. C2×#90973C2semidirect
7. #11748323C2semidirect
8. #11747267C2semidirect
9. #11747266C2semidirect
10. #11747222C2semidirect
11. #11747221C2semidirect
31. #91307C4semidirect
60. C2×C5×Dic6C2×C4semidirect
75. #6710C2×C4semidirect
91. #6661C2×C4semidirect
92. #6655C2×C4semidirect
95. #5516D5semidirect
271. C2×Dic6C4×D5semidirect
443. C3×C5#2947semidirect
499. C5#78821semidirect
517. C3#10614278semidirect

Maximal subgroups

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

subgroupindex
C5×#55162
#117545092
C2×#913072
#117510962
C3×#652912
C2×#909732
#117483232
#117472672
#117472662
#117472222
#117472212
#106142783
#788215