Finite Group Databasebeta

← #14472161

Subgroups — #14472161

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752487C211yesmaximal, characteristic, complemented
2#11752486C211yesmaximal, characteristic
3C4×#6706C211yesmaximal, characteristic
4C5×#4681C211yesmaximal, characteristic, complemented
5C3×C8×Dic10C211yesmaximal, characteristic, complemented
6#11747985C212yesmaximal
7#11747860C212yesmaximal, complemented
8#11747857C212yesmaximal
9#11747834C212yesmaximal, complemented
10#11747105C211yesmaximal, characteristic, complemented
11#11746966C211yesmaximal, characteristic
12#10613356—31nomaximal, Hall
13C2×#6706C2211yescharacteristic
14C4×D60C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91390—21no—
20#91388C2212yes—
21#91385—21no—
22#91375C2212yes—
23#91347—21no—
24#91344—21no—
25#91337—22no—
26#91336—22no—
27#91333C2212yes—
28Dic5×Dic6C2212yes—
29C2×#6663C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2211yescharacteristic
32#91101C2211yescharacteristic
33#91100C2211yescharacteristic
34C5×#816C2212yes—
35C5×#816C2212yes—
36C3×#3946C2212yes—
37C3×C8×Dic5C2212yes—
38C3×C4⋊#168C2211yescharacteristic
39#90988C2212yes—
40#90973C2212yes—
41#90969C2212yes—
42#79934—51nomaximal, Hall
43#66066—31no—
44#66055—31no—
45C5×#487—31no—
46#65379—31no—
47#65376—31no—
48#65089—32no—
49#65088—32no—
50#65087—32no—
51#65079—32no—
52C4×#677—31no—
53C8×Dic10D311yescharacteristic, complemented
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30C2311yescharacteristic
57C2×C5×Dic6—21no—
58C2×C5×Dic6C2312yes—
59C2×C3×Dic10D411yescharacteristic
60C2×C3×C5×C8C2311yescharacteristic
61C2×C3×C5×C8C2311yescharacteristic
62C3×C42×C5C2311yescharacteristic
63#6714—21no—
64C4⋊Dic15C2311yescharacteristic
65C4⋊Dic15C2311yescharacteristic
66#6712—21no—
67C4×Dic15—21no—
68#6706—22no—
69C5×C4⋊Dic3—21no—
70C5×C4⋊Dic3—21no—
71C5×C4⋊Dic3—21no—
72C5×C4⋊Dic3C2312yes—
73C3×C4⋊Dic5D411yescharacteristic
74C3×#683D412yes—
75C3×C4×Dic5C2312yes—
76C2×C3×#168C2312yes—
77Dic3⋊Dic5—22no—
78Dic3⋊Dic5—22no—
79#6669—22no—
80#6669—22no—
81#6667—22no—
82#6667—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6663—24no—
86#5584—51no—
87#5567—51no—
88C3×C8×Q8—51no—
89#4849—51no—
90#4846—51no—
91#4845—52no—
92#4829—52no—
93C4×Dic12—52no—
94#4697—52no—
95C4×#204—51no—
96#4681D511yescharacteristic, complemented
97C5×C4⋊Q8—31no—
98C5×C4⋊Q8—31no—
99#4093—32no—
100Q8×Dic5—32no—
101Q8×Dic5—61no—
102#4090—61no—
103C2×#689—32no—
104C2×#677—31no—
105#4044—62no—
106#4043—61no—
107#4038—61no—
108#4036—32no—
109#4035—62no—
110#4033—32no—
111C4×D20—31no—
112C4×Dic10—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#103—32no—
115C5×#103—32no—
116C4×C5×C8C2×D311yescharacteristic
117#3967—32no—
118#3953—31no—
119#3949—31no—
120#3948—31no—
121#3946C2×D312yes—
122C8×Dic5C2×D312yes—
123#3941—32no—
124#3939—32no—
125C4⋊#168C2×D311yescharacteristic
126#3364—151noSylow
127C22×D15—21no—
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—21no—
132C2×Dic15—21no—
133C2×Dic15—21no—
134D60—21no—
135D60—21no—
136C4×D15—42no—
137Dic30—21no—
138Dic30#4112yes—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C5×Dic6—22no—
142C5×Dic6—22no—
143C5×Dic6—42no—
144C2×C3×Dic5C2×D412yes—
145C2×C3×Dic5C2×D412yes—
146C3×Dic10—22no—
147C3×C5×C8—21no—
148C3×C5×C8—21no—
149C3×#168—22no—
150C3×C4×Q8—51no—
151#946—101no—
152#944—101no—
153C2×Dic12—52no—
154C2×#204—51no—
155#898—102no—
156#892—101no—
157#889—102no—
158#887—101no—
159#875—52no—
160C4×D12—51no—
161#870—52no—
162#869C2×D511yescharacteristic
163#869C2×D511yescharacteristic
164C4×Dic6—52no—
165C4×Dic6—51no—
166C4×Dic6—52no—
167C3×C4⋊C8—52no—
168C3×C4⋊C8—51no—
169C3×C4×C8—52no—
170C3×C4×C8C2×D511yescharacteristic
171#821—51no—
172#821—52no—
173#818—52no—
174#817—51no—
175#816—52no—
176#816—51no—
177#816C2×D512yes—
178#816C2×D512yes—
179C2×C5×Q8—32no—
180C2×C5×Q8—61no—
181C2×D20—31no—
182C2×C4×D5—61no—
183C2×Dic10—31no—
184C2×Dic10D1211yescharacteristic
185C2×C5×C8C22×D311yescharacteristic
186C2×C5×C8C22×D311yescharacteristic
187C5×C4⋊C4—32no—
188C5×C4⋊C4—61no—
189C5×C4⋊C4—61no—
190C5×C4⋊C4—61no—
191C42×C5C22×D311yescharacteristic
192#689—64no—
193#685—61no—
194#685—62no—
195#685—62no—
196C4⋊Dic5—31no—
197C4⋊Dic5—31no—
198C4⋊Dic5—62no—
199C4⋊Dic5—62no—
200C4⋊Dic5D1211yescharacteristic
201#683—61no—
202#683—62no—
203#683—62no—
204#683D1212yes—
205C4×Dic5—61no—
206C4×Dic5—62no—
207C4×Dic5—62no—
208C4×Dic5C22×D312yes—
209C2×#168C22×D312yes—
210#677—62no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—31no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—151no—
219C8×Q8—51no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×D15—41no—
224C2×D15—41no—
225C2×D15—41no—
226C3×C4×C5—21no—
227C3×C4×C5#13512yes—
228C3×C4×C5C2×#4111yescharacteristic
229C3×C4×C52−1+411yescharacteristic
230Dic15—22no—
231Dic15—41no—
232Dic15—41no—
233C3×Dic5—22no—
234C3×Dic5—22no—
235C5×Dic3—42no—
236C5×Dic3—42no—
237C2×C3×Q8—51no—
238C2×D12—51no—
239C2×C4×D3—101no—
240C2×Dic6—21no—
241C2×Dic6—51no—
242C2×Dic6C22×D512yes—
243C2×C3×C8—52no—
244C2×C3×C8C22×D511yescharacteristic
245C2×C3×C8C22×D511yescharacteristic
246C3×C4⋊C4—52no—
247C3×C4⋊C4—51no—
248C3×C42—52no—
249C3×C42C22×D511yescharacteristic
250(C2×D3)⋊C4—102no—
251(C2×D3)⋊C4—102no—
252(C2×D3)⋊C4—101no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255C4⋊Dic3—21no—
256C4⋊Dic3—51no—
257C4⋊Dic3—51no—
258C4⋊Dic3C22×D512yes—
259Dic3⋊C4—102no—
260Dic3⋊C4—102no—
261Dic3⋊C4—102no—
262Dic3⋊C4—102no—
263Dic3⋊C4—101no—
264C4×Dic3—102no—
265C4×Dic3—102no—
266C4×Dic3—101no—
267Dic12—104no—
268#204—102no—
269C22×D5—61no—
270C5×Q8—62no—
271C5×Q8—62no—
272C5×Q8—122no—
273C2×C4×C5—62no—
274C2×C4×C5—62no—
275C2×C4×C5C2×D1211yescharacteristic
276C2×C4×C5C2×D1211yescharacteristic
277C2×C4×C5C23×D311yescharacteristic
278C2×Dic5—61no—
279C2×Dic5—61no—
280C2×Dic5—61no—
281C2×Dic5C2×D1212yes—
282C2×Dic5C2×D1212yes—
283D20—61no—
284D20—61no—
285C4×D5—122no—
286Dic10—22no—
287Dic10—32no—
288Dic10—61no—
289C5×C8—21no—
290C5×C8—21no—
291#168—22no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—31no—
295C4⋊Q8—31no—
296C4⋊Q8—301no—
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—51no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—151no—
306C4×Q8—301no—
307C4×D4—151no—
308#117—301no—
309#107—152no—
310#106—151no—
311C4⋊C8—52no—
312C4⋊C8—51no—
313#103—32no—
314#103—32no—
315#103—152no—
316#103—151no—
317#102—152no—
318#102—151no—
319C4×C8—52no—
320C4×C8D3×D511yescharacteristic
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324D15—81no—
325C22×D3—101no—
326C3×Q8—102no—
327C2×C3×C4—52no—
328C2×C3×C4—52no—
329C2×C3×C4D4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331C2×C3×C4C23×D511yescharacteristic
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—101no—
335C2×Dic3—101no—
336C2×Dic3—101no—
337D12—101no—
338D12—101no—
339C4×D3—202no—
340Dic6—22no—
341Dic6—22no—
342Dic6—42no—
343Dic6—52no—
344Dic6—101no—
345C3×C8—21no—
346C3×C8—21no—
347C3×C8—102no—
348C22×C5C22×D1211yescharacteristic
349C2×D5—121no—
350C2×D5—121no—
351C2×D5—121no—
352C4×C5—21no—
353C4×C5—122no—
354C4×C5—122no—
355C4×C5#90412yes—
356C4×C5#100711yescharacteristic
357C4×C5D3×#4111yescharacteristic
358Dic5—22no—
359Dic5—22no—
360Dic5—62no—
361Dic5—121no—
362Dic5—121no—
363C2×Q8—32no—
364C2×Q8—51no—
365C2×Q8—61no—
366C2×Q8—151no—
367C2×D4—151no—
368C22×C4—301no—
369Q16—304no—
370SD16—302no—
371C2×C8—52no—
372C2×C8C2×D3×D511yescharacteristic
373C2×C8C2×D3×D511yescharacteristic
374C4⋊C4—32no—
375C4⋊C4—51no—
376C4⋊C4—52no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—151no—
381C4⋊C4—151no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—302no—
386C4⋊C4—301no—
387C22⋊C4—302no—
388C22⋊C4—302no—
389C22⋊C4—301no—
390C42—52no—
391C42—302no—
392C42—302no—
393C42—301no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C2×D4×D511yescharacteristic
397C2×D3—201no—
398C2×D3—201no—
399C2×D3—201no—
400C3×C4—21no—
401C3×C4—102no—
402C3×C4—102no—
403C3×C4#406212yes—
404C3×C4D5×#4111yescharacteristic
405C3×C4#415011yescharacteristic
406Dic3—42no—
407Dic3—42no—
408Dic3—102no—
409Dic3—201no—
410Dic3—201no—
411C2×C5#557611yescharacteristic
412C2×C5C2×#90411yescharacteristic
413C2×C5#575311yescharacteristic
414D5—241no—
415C23—301no—
416Q8—62no—
417Q8—62no—
418Q8—102no—
419Q8—122no—
420Q8—152no—
421Q8—301no—
422D4—301no—
423D4—301no—
424C2×C4—52no—
425C2×C4—52no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—301no—
429C2×C4—301no—
430C2×C4—301no—
431C2×C4—602no—
432C2×C4D5×D1211yescharacteristic
433C2×C4D5×D1211yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—21no—
436C8—21no—
437C8—102no—
438C2×C3#6601111yescharacteristic
439C2×C3C2×#406211yescharacteristic
440C2×C3#6610011yescharacteristic
441D3—401no—
442C5#7993411yescharacteristic, complemented, Sylow
443C22—601no—
444C22—601no—
445C22—601no—
446C22C2×D5×D1211yescharacteristic
447C4—21no—
448C4—102no—
449C4—102no—
450C4—122no—
451C4—122no—
452C4—302no—
453C4—601no—
454C4—601no—
455C4#9126912yes—
456C4#9200411yescharacteristic
457C4#9201611yescharacteristic
458C3#1061335611yescharacteristic, complemented, Sylow
459C2—1201no—
460C2#1175253711yescharacteristic
461C2#1175398711yescharacteristic
462C2C2×#9126911yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenterC4×C8D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11752487C2semidirect
4. C5×#4681C2semidirect
5. C3×C8×Dic10C2semidirect
7. #11747860C2semidirect
9. #11747834C2semidirect
10. #11747105C2semidirect
53. C8×Dic10D3semidirect
96. #4681D5semidirect
395. C3×C5#3364semidirect
442. C5#79934semidirect
458. C3#10613356semidirect

Maximal subgroups

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

subgroupindex
#117524872
#117524862
C4×#67062
C5×#46812
C3×C8×Dic102
#117479852
#117478602
#117478572
#117478342
#117471052
#117469662
#106133563
#799345