Finite Group Databasebeta

← #14471685

Subgroups — #14471685

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752654C211yesmaximal, characteristic, complemented
2#11752486C211yesmaximal, characteristic, complemented
3C4×D120C211yesmaximal, characteristic
4C5×#4681C211yesmaximal, characteristic, complemented
5C3×C8×Dic10C211yesmaximal, characteristic, complemented
6#11747985C212yesmaximal, complemented
7#11747855C212yesmaximal, complemented
8#11747833C212yesmaximal, complemented
9#11747774C212yesmaximal
10#11747087C211yesmaximal, characteristic, complemented
11#11746885C211yesmaximal, characteristic, complemented
12#10613352—31nomaximal, Hall
13C2×D120C2211yescharacteristic
14C4×D60C2211yescharacteristic
15C4×D60C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91437—21no—
20#91424—22no—
21#91418C2212yes—
22#91390—21no—
23#91390—21no—
24#91388C2212yes—
25#91375C2212yes—
26#91347—21no—
27#91337—22no—
28Dic5×Dic6C2212yes—
29C2×#6660C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2211yescharacteristic
32#91105C2211yescharacteristic
33#91102C2211yescharacteristic
34C5×#816C2212yes—
35C5×#816C2212yes—
36C3×#3946C2212yes—
37C3×C8×Dic5C2212yes—
38C3×C4⋊#168C2211yescharacteristic
39#90985C2212yes—
40#90973C2212yes—
41#90969C2212yes—
42#79926—51nomaximal, Hall
43#66066—31no—
44#66064—31no—
45C5×#487—31no—
46#65373—31no—
47#65372—31no—
48#65108—32no—
49#65089—32no—
50#65085—32no—
51#65077—32no—
52C4×D40—31no—
53C8×Dic10D311yescharacteristic, complemented
54C2×D60C2311yescharacteristic
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C4×D15—21no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6C2312yes—
60C2×C3×Dic10D411yescharacteristic
61C2×#1200—22no—
62C2×C3×C5×C8C2311yescharacteristic
63C2×C3×C5×C8C2311yescharacteristic
64C3×C42×C5C2311yescharacteristic
65#6714—21no—
66#6714—21no—
67C4⋊Dic15C2311yescharacteristic
68C4⋊Dic15C2311yescharacteristic
69D120—22no—
70C5×C4⋊Dic3—21no—
71C5×C4⋊Dic3—21no—
72C5×C4⋊Dic3—21no—
73C5×C4⋊Dic3C2312yes—
74C3×C4⋊Dic5D411yescharacteristic
75C3×#683D412yes—
76C3×C4×Dic5C2312yes—
77C2×C3×#168C2312yes—
78Dic3⋊Dic5—22no—
79Dic3⋊Dic5—22no—
80#6669—22no—
81#6667—22no—
82#6667—22no—
83#6667—22no—
84Dic3×Dic5—22no—
85#6660—24no—
86#5584—51no—
87#5579—51no—
88C3×C8×Q8—51no—
89#4844—52no—
90#4842—51no—
91#4841—51no—
92#4829—52no—
93#4697—52no—
94C4×D24—51no—
95C4×#204—52no—
96#4681D511yescharacteristic, complemented
97C5×C4⋊Q8—31no—
98C5×C4⋊Q8—31no—
99#4093—32no—
100#4092—62no—
101Q8×Dic5—32no—
102C2×#688—32no—
103C2×D40—31no—
104#4044—62no—
105#4043—61no—
106#4043—61no—
107#4039—32no—
108#4038—61no—
109D5×C4⋊C4—61no—
110#4036—32no—
111C4×D20—31no—
112C4×D20—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#103—32no—
115C5×#103—32no—
116C4×C5×C8C2×D311yescharacteristic
117#3967—32no—
118#3953—31no—
119#3953—31no—
120#3950—31no—
121#3946C2×D312yes—
122C8×Dic5C2×D312yes—
123#3941—32no—
124#3940—32no—
125C4⋊#168C2×D311yescharacteristic
126#3360—151noSylow
127C22×D15—21no—
128C22×D15—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—21no—
133C2×Dic15—21no—
134D60—21no—
135D60—21no—
136D60—21no—
137D60#4112yes—
138C4×D15—42no—
139C4×D15—42no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C5×Dic6—22no—
143C5×Dic6—22no—
144C5×Dic6—81no—
145C2×C3×Dic5C2×D412yes—
146C2×C3×Dic5C2×D412yes—
147C3×Dic10—22no—
148#1200—82no—
149C3×C5×C8—21no—
150C3×C5×C8—21no—
151C3×#168—22no—
152C3×C4×Q8—51no—
153#946—101no—
154#946—101no—
155C2×D24—51no—
156C2×#204—52no—
157#898—102no—
158#896—102no—
159#892—101no—
160D3×C4⋊C4—101no—
161#875—52no—
162C4×D12—51no—
163C4×D12—51no—
164C4×D12—52no—
165#870—52no—
166#869C2×D511yescharacteristic
167#869C2×D511yescharacteristic
168C4×Dic6—52no—
169C3×C4⋊C8—52no—
170C3×C4⋊C8—51no—
171C3×C4×C8—52no—
172C3×C4×C8C2×D511yescharacteristic
173#821—51no—
174#821—51no—
175#821—52no—
176#818—51no—
177#817—52no—
178#816—52no—
179#816C2×D512yes—
180#816C2×D512yes—
181C2×C5×Q8—32no—
182C2×C5×Q8—61no—
183C2×D20—31no—
184C2×D20—31no—
185C2×C4×D5—61no—
186C2×C4×D5—61no—
187C2×C4×D5—62no—
188C2×Dic10D1211yescharacteristic
189C2×C5×C8C22×D311yescharacteristic
190C2×C5×C8C22×D311yescharacteristic
191C5×C4⋊C4—32no—
192C5×C4⋊C4—61no—
193C5×C4⋊C4—61no—
194C5×C4⋊C4—61no—
195C42×C5C22×D311yescharacteristic
196#688—64no—
197#685—61no—
198#685—61no—
199#685—62no—
200#685—62no—
201#685—62no—
202C4⋊Dic5—31no—
203C4⋊Dic5—31no—
204C4⋊Dic5—62no—
205C4⋊Dic5—62no—
206C4⋊Dic5D1211yescharacteristic
207#683—62no—
208#683D1212yes—
209C4×Dic5—62no—
210C4×Dic5C22×D312yes—
211C2×#168C22×D312yes—
212D40—62no—
213#556—151no—
214#554—151no—
215#488—152no—
216#487—31no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—151no—
221C8×Q8—51no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5C22×D411yescharacteristic
225C2×D15—22no—
226C2×D15—41no—
227C2×D15—41no—
228C2×D15—41no—
229C2×D15—41no—
230C2×D15—41no—
231C3×C4×C5—21no—
232C3×C4×C5#13512yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—41no—
236Dic15—41no—
237C3×Dic5—22no—
238C3×Dic5—22no—
239C5×Dic3—42no—
240C5×Dic3—42no—
241C2×C3×Q8—51no—
242C2×D12—51no—
243C2×D12—51no—
244C2×C4×D3—101no—
245C2×C4×D3—101no—
246C2×C4×D3—102no—
247C2×Dic6—21no—
248C2×Dic6C22×D512yes—
249C2×C3×C8—52no—
250C2×C3×C8C22×D511yescharacteristic
251C2×C3×C8C22×D511yescharacteristic
252C3×C4⋊C4—52no—
253C3×C4⋊C4—51no—
254C3×C42—52no—
255C3×C42C22×D511yescharacteristic
256(C2×D3)⋊C4—102no—
257(C2×D3)⋊C4—102no—
258(C2×D3)⋊C4—102no—
259(C2×D3)⋊C4—101no—
260(C2×D3)⋊C4—101no—
261C4⋊Dic3—21no—
262C4⋊Dic3—21no—
263C4⋊Dic3—21no—
264C4⋊Dic3—51no—
265C4⋊Dic3—51no—
266C4⋊Dic3C22×D512yes—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269Dic3⋊C4—102no—
270C4×Dic3—102no—
271D24—102no—
272#204—104no—
273C22×D5—61no—
274C22×D5—61no—
275C5×Q8—62no—
276C5×Q8—62no—
277C5×Q8—241no—
278C2×C4×C5—62no—
279C2×C4×C5—62no—
280C2×C4×C5C2×D1211yescharacteristic
281C2×C4×C5C2×D1211yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—61no—
284C2×Dic5—61no—
285C2×Dic5C2×D1212yes—
286C2×Dic5C2×D1212yes—
287D20—32no—
288D20—61no—
289D20—61no—
290D20—61no—
291C4×D5—122no—
292C4×D5—122no—
293C4×D5—242no—
294Dic10—22no—
295C5×C8—21no—
296C5×C8—21no—
297#168—22no—
298C2×SD16—152no—
299C2×D8—151no—
300C4⋊Q8—31no—
301C4⋊Q8—31no—
302#126—302no—
303#125—152no—
304#124—152no—
305C22⋊Q8—302no—
306C22⋊Q8—301no—
307C22⋊Q8—301no—
308C4×Q8—51no—
309C4×Q8—152no—
310C4×D4—152no—
311C4×D4—151no—
312C4×D4—151no—
313#117—301no—
314C2×C4⋊C4—301no—
315#107—151no—
316#106—152no—
317C4⋊C8—52no—
318C4⋊C8—51no—
319#103—32no—
320#103—32no—
321#103—152no—
322#102—152no—
323#102—151no—
324#102—151no—
325C4×C8—52no—
326C4×C8D3×D511yescharacteristic
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330D15—42no—
331D15—81no—
332C22×D3—101no—
333C22×D3—101no—
334C3×Q8—102no—
335C2×C3×C4—52no—
336C2×C3×C4—52no—
337C2×C3×C4D4×D511yescharacteristic
338C2×C3×C4D4×D511yescharacteristic
339C2×C3×C4C23×D511yescharacteristic
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—101no—
343C2×Dic3—101no—
344D12—52no—
345D12—101no—
346D12—101no—
347D12—101no—
348C4×D3—202no—
349C4×D3—202no—
350C4×D3—402no—
351Dic6—22no—
352Dic6—22no—
353Dic6—81no—
354C3×C8—21no—
355C3×C8—21no—
356C3×C8—102no—
357C22×C5C22×D1211yescharacteristic
358C2×D5—62no—
359C2×D5—121no—
360C2×D5—121no—
361C2×D5—121no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—21no—
365C4×C5—122no—
366C4×C5—122no—
367C4×C5#90412yes—
368C4×C5#100711yescharacteristic
369C4×C5D3×#4111yescharacteristic
370Dic5—22no—
371Dic5—22no—
372Dic5—121no—
373Dic5—121no—
374C2×Q8—32no—
375C2×Q8—51no—
376C2×Q8—61no—
377C2×D4—151no—
378C2×D4—151no—
379C22×C4—302no—
380C22×C4—301no—
381C22×C4—301no—
382SD16—304no—
383D8—302no—
384C2×C8—52no—
385C2×C8C2×D3×D511yescharacteristic
386C2×C8C2×D3×D511yescharacteristic
387C4⋊C4—32no—
388C4⋊C4—51no—
389C4⋊C4—52no—
390C4⋊C4—61no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C4⋊C4—151no—
394C4⋊C4—151no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—302no—
398C22⋊C4—302no—
399C22⋊C4—302no—
400C22⋊C4—302no—
401C22⋊C4—301no—
402C22⋊C4—301no—
403C42—52no—
404C42—302no—
405C42C2×D3×D511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3C2×D4×D511yescharacteristic
408C2×D3—102no—
409C2×D3—201no—
410C2×D3—201no—
411C2×D3—201no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—21no—
415C3×C4—102no—
416C3×C4—102no—
417C3×C4#406512yes—
418C3×C4D5×#4111yescharacteristic
419C3×C4#415011yescharacteristic
420Dic3—42no—
421Dic3—42no—
422Dic3—201no—
423Dic3—201no—
424C2×C5#557611yescharacteristic
425C2×C5C2×#90411yescharacteristic
426C2×C5#575111yescharacteristic
427D5—122no—
428D5—241no—
429C23—301no—
430C23—301no—
431Q8—62no—
432Q8—62no—
433Q8—102no—
434Q8—241no—
435D4—152no—
436D4—301no—
437D4—301no—
438D4—301no—
439C2×C4—52no—
440C2×C4—52no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—301no—
444C2×C4—301no—
445C2×C4—602no—
446C2×C4—602no—
447C2×C4—1202no—
448C2×C4D5×D1211yescharacteristic
449C2×C4D5×D1211yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—21no—
452C8—21no—
453C8—102no—
454C2×C3#6601111yescharacteristic
455C2×C3#6609611yescharacteristic
456C2×C3C2×#406511yescharacteristic
457D3—202no—
458D3—401no—
459C5#7992611yescharacteristic, complemented, Sylow
460C22—302no—
461C22—601no—
462C22—601no—
463C22—601no—
464C22—601no—
465C22—601no—
466C22C2×D5×D1211yescharacteristic
467C4—21no—
468C4—102no—
469C4—102no—
470C4—122no—
471C4—122no—
472C4—601no—
473C4—601no—
474C4#9127112yes—
475C4#9200411yescharacteristic
476C4#9201611yescharacteristic
477C3#1061335211yescharacteristic, complemented, Sylow
478C2—602no—
479C2—1201no—
480C2#1175253711yescharacteristic
481C2#1175396011yescharacteristic
482C2C2×#9127111yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×D120C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#3360
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. #11752654C2semidirect
2. #11752486C2semidirect
4. C5×#4681C2semidirect
5. C3×C8×Dic10C2semidirect
6. #11747985C2semidirect
7. #11747855C2semidirect
8. #11747833C2semidirect
10. #11747087C2semidirect
11. #11746885C2semidirect
53. C8×Dic10D3semidirect
96. #4681D5semidirect
406. C3×C5#3360semidirect
459. C5#79926semidirect
477. C3#10613352semidirect

Maximal subgroups

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

subgroupindex
#117526542
#117524862
C4×D1202
C5×#46812
C3×C8×Dic102
#117479852
#117478552
#117478332
#117477742
#117470872
#117468852
#106133523
#799265