Finite Group Databasebeta

← #14471541

Subgroups — #14471541

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65901C211yesmaximal, characteristic, complemented
2#11752539C211yesmaximal, characteristic
3C4×#6717C211yesmaximal, characteristic
4C5×#5020C211yesmaximal, characteristic, complemented
5#11749349C212yesmaximal, complemented
6#11749222C212yesmaximal
7#11747411C212yesmaximal, complemented
8#11747225C212yesmaximal
9#11747085C211yesmaximal, characteristic
10#11746924C211yesmaximal, characteristic, complemented
11#11746846C211yesmaximal, characteristic, complemented
12#10612768—31nomaximal, Hall
13C2×D15⋊Q8—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C2×#6717C2211yescharacteristic
16C4×D60C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×#4090C2212yes—
19C3×#4035—22no—
20C3×#4033C2212yes—
21C3×#4016—21no—
22C3×#4015C2211yescharacteristic
23C3×C4×Dic10—21no—
24C3×C4×Dic10C2211yescharacteristic
25#91468C2212yes—
26#91419—22no—
27#91418C2212yes—
28#91383—21no—
29C2×#6658C2212yes—
30#91119C2211yescharacteristic
31#91093C2211yescharacteristic
32#91092C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C5×#835C2212yes—
35C5×#808C2212yes—
36C5×C4⋊(C3⋊C8)C2211yescharacteristic
37#90982C2212yes—
38#90971C2212yes—
39#90970C2212yes—
40#90970C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83688—51nomaximal, Hall
43#66061—31no—
44#65901D311yescharacteristic, complemented
45C5×#475—31no—
46#65382—31no—
47C4×#688—31no—
48#65143—32no—
49#65141—32no—
50#65130—31no—
51#65119—31no—
52#65107—32no—
53#65081—32no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C5×Dic6—21no—
58C2×C3×Dic10D411yescharacteristic
59C2×C3×Dic10C2312yes—
60C2×#1204—22no—
61C2×#1200—22no—
62D15⋊Q8—44no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4C2311yescharacteristic
65C3×C42×C5—21no—
66C3×C42×C5C2311yescharacteristic
67#6717—22no—
68#6714—21no—
69C4⋊Dic15C2311yescharacteristic
70C2×C3⋊#168C2311yescharacteristic
71C2×C3⋊#168C2311yescharacteristic
72C5×C4⋊Dic3—21no—
73C5×C4⋊Dic3C2312yes—
74C2×C5×C3⋊C8C2312yes—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5D411yescharacteristic
78C3×#683—22no—
79C3×#683—22no—
80C3×#683—22no—
81C3×#683D412yes—
82C3×C4×Dic5—22no—
83C3×C4×Dic5C2312yes—
84#6668—22no—
85#6667—22no—
86#6658—24no—
87C3×#557—51no—
88Q8×D12—51no—
89#5083—52no—
90#5083—51no—
91#5079—51no—
92#5079—52no—
93C4×#215—51no—
94C4×#215—52no—
95Q8×C3⋊C8—51no—
96#5020—52no—
97#5020D511yescharacteristic, complemented
98C2×Q8×D5—61no—
99C5×C4⋊Q8—31no—
100C4×C5×Q8C2×D311yescharacteristic
101#4092—61no—
102#4090C2×D312yes—
103C2×#688—31no—
104C2×#677—32no—
105#4042—62no—
106#4039—32no—
107#4035—22no—
108#4034—32no—
109#4033C2×D312yes—
110C4×D20—31no—
111#4016—21no—
112#4015C2×D311yescharacteristic
113C4×Dic10—21no—
114C4×Dic10C2×D311yescharacteristic
115C5×#106—32no—
116C5×C4⋊C8—31no—
117C5×#103—32no—
118#3967—31no—
119#3948—32no—
120#3946—32no—
121C8×Dic5—32no—
122#3942—32no—
123#3942—32no—
124#3941—31no—
125#3940—31no—
126C4×#168—31no—
127#3359—151noSylow
128C22×D15—21no—
129C3×C5×Q8—21no—
130C3×C5×Q8—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—21no—
137D60—21no—
138D60#4112yes—
139C4×D15—42no—
140C2×C5×Dic3—22no—
141C5×Dic6—42no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5C2×D412yes—
144C2×C3×Dic5C2×D412yes—
145C3×Dic10—22no—
146C3×Dic10—22no—
147C3×Dic10SD1614yescomplemented
148#1204—44no—
149#1200—44no—
150C3⋊#168—21no—
151C3⋊#168—21no—
152C5×C3⋊C8—22no—
153C2×D3×Q8—101no—
154C3×C4⋊Q8—52no—
155C3×C4⋊Q8—51no—
156C3×#125—101no—
157C3×#125—102no—
158C3×C4×Q8—51no—
159C3×C4×Q8—52no—
160C3×C4×Q8—101no—
161C3×C4×Q8C2×D511yescharacteristic
162C2×#215—51no—
163C2×#215—52no—
164#897—102no—
165#897—101no—
166C4×D12—51no—
167C4×D12—52no—
168#869—52no—
169#869C2×D511yescharacteristic
170#835—51no—
171#835—52no—
172#835—52no—
173#835—52no—
174#835C2×D512yes—
175#809—51no—
176#808—51no—
177#808C2×D512yes—
178C4⋊(C3⋊C8)—52no—
179C4⋊(C3⋊C8)C2×D511yescharacteristic
180C4×C3⋊C8—51no—
181C4×C3⋊C8—52no—
182C2×C5×Q8—61no—
183C2×C5×Q8C22×D311yescharacteristic
184Q8×D5—124no—
185C2×D20—31no—
186C2×C4×D5—61no—
187C2×C4×D5—62no—
188C2×Dic10—62no—
189C2×Dic10#6711yescharacteristic
190C2×Dic10C22×D312yes—
191C2×C5×C8—32no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—32no—
194C5×C4⋊C4—61no—
195C5×C4⋊C4C22×D311yescharacteristic
196C42×C5—21no—
197C42×C5C22×D311yescharacteristic
198#688—62no—
199#685—61no—
200#685—62no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—31no—
204C4⋊Dic5#6711yescharacteristic
205#683—22no—
206#683—22no—
207#683—22no—
208#683—62no—
209#683#6712yes—
210C4×Dic5—22no—
211C4×Dic5C22×D312yes—
212C2×#168—31no—
213C2×#168—31no—
214#677—64no—
215#557—51no—
216D4×Q8—151no—
217#487—152no—
218#487—151no—
219#475—31no—
220#475—152no—
221#461—152no—
222#461—151no—
223C8×Q8—151no—
224C4×SD16—152no—
225C4×SD16—151no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C3×C4×C5—21no—
231C3×C4×C5—41no—
232C3×C4×C5—41no—
233C3×C4×C5C2×SD1612yes—
234C3×C4×C5C2×#4111yescharacteristic
235C3×C4×C52−1+411yescharacteristic
236Dic15—41no—
237C3×Dic5—22no—
238C3×Dic5—42no—
239C3×Dic5C2×SD1614yes—
240C5×Dic3—42no—
241C2×C3×Q8—51no—
242C2×C3×Q8—52no—
243C2×C3×Q8C22×D511yescharacteristic
244D3×Q8—204no—
245C2×D12—51no—
246C2×C4×D3—102no—
247C2×C4×D3—101no—
248C2×Dic6—21no—
249C2×Dic6—102no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—52no—
252C3×C4⋊C4—51no—
253C3×C4⋊C4—102no—
254C3×C4⋊C4—102no—
255C3×C4⋊C4—102no—
256C3×C4⋊C4—101no—
257C3×C4⋊C4—101no—
258C3×C4⋊C4C22×D511yescharacteristic
259C3×C42—21no—
260C3×C42—52no—
261C3×C42—102no—
262C3×C42C22×D511yescharacteristic
263#215—104no—
264#215—102no—
265(C2×D3)⋊C4—102no—
266(C2×D3)⋊C4—101no—
267C4⋊Dic3—21no—
268C4⋊Dic3—51no—
269C4⋊Dic3—102no—
270C4⋊Dic3C22×D512yes—
271C2×C3⋊C8—51no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8C22×D512yes—
274C22×D5—61no—
275C5×Q8—21no—
276C5×Q8—21no—
277C5×Q8—122no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—62no—
281C2×C4×C5C2×#6711yescharacteristic
282C2×C4×C5C2×#6711yescharacteristic
283C2×C4×C5C23×D311yescharacteristic
284C2×Dic5—22no—
285C2×Dic5—61no—
286C2×Dic5C2×#6712yes—
287C2×Dic5C2×#6712yes—
288D20—32no—
289D20—61no—
290C4×D5—122no—
291C4×D5—124no—
292Dic10—22no—
293Dic10—22no—
294Dic10—124no—
295Dic10#21514yescomplemented
296C5×C8—62no—
297#168—61no—
298#168—61no—
299C22×Q8—301no—
300C2×SD16—152no—
301C2×SD16—151no—
302C4⋊Q8—31no—
303C4⋊Q8—52no—
304C4⋊Q8—51no—
305C4⋊Q8—152no—
306#125—101no—
307#125—102no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—51no—
311C4×Q8—52no—
312C4×Q8—101no—
313C4×Q8D3×D511yescharacteristic
314C4×D4—152no—
315C4×D4—151no—
316#106—32no—
317#106—151no—
318C4⋊C8—31no—
319C4⋊C8—152no—
320#103—32no—
321#103—152no—
322#103—152no—
323#103—152no—
324#103—151no—
325#102—151no—
326C4×C8—152no—
327C4×C8—151no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331D15—42no—
332C22×D3—101no—
333C3×Q8—21no—
334C3×Q8—21no—
335C3×Q8—54no—
336C3×Q8—102no—
337C3×Q8—102no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—52no—
341C2×C3×C4—52no—
342C2×C3×C4—102no—
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4C23×D511yescharacteristic
346C2×Dic3—22no—
347C2×Dic3—101no—
348D12—52no—
349D12—101no—
350C4×D3—204no—
351C4×D3—202no—
352Dic6—42no—
353Dic6—204no—
354C3⋊C8—22no—
355C3⋊C8—101no—
356C3⋊C8—101no—
357C22×C5C22×#6711yescharacteristic
358C2×D5—62no—
359C2×D5—121no—
360C2×D5—121no—
361C4×C5—21no—
362C4×C5—41no—
363C4×C5—41no—
364C4×C5—122no—
365C4×C5C2×#21512yes—
366C4×C5D3×#4111yescharacteristic
367C4×C5#101011yescharacteristic
368Dic5—22no—
369Dic5—42no—
370Dic5—121no—
371Dic5C2×#21514yes—
372C2×Q8—51no—
373C2×Q8—52no—
374C2×Q8—61no—
375C2×Q8—302no—
376C2×Q8—604no—
377C2×Q8C2×D3×D511yescharacteristic
378C2×D4—151no—
379C22×C4—302no—
380C22×C4—301no—
381SD16—304no—
382SD16—302no—
383C2×C8—32no—
384C2×C8—151no—
385C2×C8—151no—
386C4⋊C4—21no—
387C4⋊C4—32no—
388C4⋊C4—52no—
389C4⋊C4—51no—
390C4⋊C4—61no—
391C4⋊C4—102no—
392C4⋊C4—102no—
393C4⋊C4—102no—
394C4⋊C4—101no—
395C4⋊C4—101no—
396C4⋊C4—151no—
397C4⋊C4—302no—
398C4⋊C4C2×D3×D511yescharacteristic
399C22⋊C4—302no—
400C22⋊C4—301no—
401C42—21no—
402C42—52no—
403C42—102no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3C2×D4×D511yescharacteristic
407C2×D3—102no—
408C2×D3—201no—
409C2×D3—201no—
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—54no—
414C3×C4—102no—
415C3×C4—202no—
416C3×C4D5×SD1612yes—
417C3×C4#414711yescharacteristic
418C3×C4D5×#4111yescharacteristic
419Dic3—42no—
420Dic3—201no—
421C2×C5C22×#21511yescharacteristic
422C2×C5#583111yescharacteristic
423C2×C5#583811yescharacteristic
424D5—122no—
425C23—301no—
426Q8—21no—
427Q8—21no—
428Q8—54no—
429Q8—102no—
430Q8—102no—
431Q8—122no—
432Q8—604no—
433D4—152no—
434D4—301no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—52no—
438C2×C4—52no—
439C2×C4—62no—
440C2×C4—102no—
441C2×C4—301no—
442C2×C4—604no—
443C2×C4—602no—
444C2×C4D5×#6711yescharacteristic
445C2×C4D5×#6711yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—62no—
448C8—301no—
449C8—301no—
450C2×C3#6596711yescharacteristic
451C2×C3C2×D5×SD1611yescharacteristic
452C2×C3#6611311yescharacteristic
453D3—202no—
454C5#8368811yescharacteristic, complemented, Sylow
455C22—302no—
456C22—601no—
457C22—601no—
458C22C2×D5×#6711yescharacteristic
459C4—21no—
460C4—41no—
461C4—41no—
462C4—54no—
463C4—102no—
464C4—122no—
465C4—202no—
466C4—601no—
467C4D5×#21512yes—
468C4#9200011yescharacteristic
469C4#9201611yescharacteristic
470C3#1061276811yescharacteristic, complemented, Sylow
471C2—602no—
472C2#1175421511yescharacteristic
473C2C2×D5×#21511yescharacteristic
474C2#1175533611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#65901C2semidirect
4. C5×#5020C2semidirect
5. #11749349C2semidirect
7. #11747411C2semidirect
10. #11746924C2semidirect
11. #11746846C2semidirect
44. #65901D3semidirect
97. #5020D5semidirect
147. C3×Dic10SD16semidirect
295. Dic10#215semidirect
405. C3×C5#3359semidirect
454. C5#83688semidirect
470. C3#10612768semidirect

Maximal subgroups

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

subgroupindex
C3×#659012
#117525392
C4×#67172
C5×#50202
#117493492
#117492222
#117474112
#117472252
#117470852
#117469242
#117468462
#106127683
#836885