Finite Group Databasebeta

← #14471850

Subgroups — #14471850

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756489C211yesmaximal, characteristic, complemented
2#11752651C211yesmaximal, characteristic, complemented
3C5×#5088C211yesmaximal, characteristic, complemented
4C3×#65380C211yesmaximal, characteristic, complemented
5#11747387C212yesmaximal, complemented
6#11747386C212yesmaximal, complemented
7#11747258C212yesmaximal, complemented
8#11747233C212yesmaximal, complemented
9C4×#6658C211yesmaximal, characteristic, complemented
10#11747045C211yesmaximal, characteristic
11#11746855C211yesmaximal, characteristic, complemented
12#10613316—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14#91835—22no—
15#91786—21no—
16#91782C2212yes—
17C4⋊C4×D15—21no—
18#91779C2212yes—
19C4×D60C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C5×#874C2211yescharacteristic
22C3×C4×Dic10C2211yescharacteristic
23#91435C2212yes—
24#91423—22no—
25Dic5×D12—21no—
26#91373—21no—
27#91370C2212yes—
28C2×#6658C2211yescharacteristic
29C2×#6654C2212yes—
30C5×#809C2212yes—
31C5×#809C2212yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33C3×#3942C2212yes—
34C3×#3939C2212yes—
35C3×C4⋊#168C2211yescharacteristic
36#90987C2211yescharacteristic
37#90983C2212yes—
38#90971C2211yescharacteristic
39#90968C2211yescharacteristic
40#90967C2212yes—
41#90951C2212yes—
42#81134—51nomaximal, Hall
43#66064—31no—
44#66047—31no—
45C5×#486—31no—
46#65380D311yescharacteristic, complemented
47#65361—31no—
48#65076—32no—
49#65057—32no—
50#65052—32no—
51#65045—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C4×D15—22no—
58C2×Dic30D411yescharacteristic
59C2×C5×D12—21no—
60C2×C5×D12—21no—
61C2×C5×D12C2312yes—
62C2×C3×Dic10C2311yescharacteristic
63C2×D3×Dic5—22no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4C2312yes—
66C3×C42×C5C2311yescharacteristic
67#6714—21no—
68#6714—22no—
69C4⋊Dic15—22no—
70C4⋊Dic15D411yescharacteristic
71C4⋊Dic15C2311yescharacteristic
72#6712—22no—
73#6712D412yes—
74C4×Dic15C2312yes—
75C2×C5×C3⋊C8C2311yescharacteristic
76C2×C5×C3⋊C8C2311yescharacteristic
77C3×C4⋊Dic5C2311yescharacteristic
78C3×#683—21no—
79C3×C4×Dic5—21no—
80C2×C3×#168C2312yes—
81(C2×D3)⋊Dic5—22no—
82(C2×D3)⋊Dic5—22no—
83(C2×D3)⋊Dic5—22no—
84#6658—22no—
85#6654—24no—
86#5730—51no—
87#5585—51no—
88C3×#477—51no—
89#5088D511yescharacteristic, complemented
90C4×#215—51no—
91#4891—52no—
92#4872—52no—
93#4843—51no—
94#4830—51no—
95#4819—52no—
96#4800—52no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C5×#127—31no—
99#4092—62no—
100#4082—32no—
101#4082—61no—
102#4081—62no—
103D4×Dic5—32no—
104D4×Dic5—61no—
105C2×#686—32no—
106C2×#677—31no—
107#4043—61no—
108#4039—32no—
109D5×C4⋊C4—61no—
110#4036—32no—
111C4×D20—31no—
112C4×Dic10—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#102—32no—
115C5×#102—32no—
116C4×C5×C8—31no—
117#3964—32no—
118#3953—31no—
119#3949—31no—
120#3948—31no—
121#3946—32no—
122C8×Dic5—32no—
123#3942C2×D312yes—
124#3939C2×D312yes—
125C4⋊#168C2×D311yescharacteristic
126#3361—151noSylow
127C22×D15—21no—
128C22×C5×D3—22no—
129C3×C5×Q8—81no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—21no—
135C2×Dic15C2×D412yes—
136C2×Dic15C2×D412yes—
137D60—21no—
138D60#4112yes—
139C4×D15—42no—
140C4×D15—82no—
141Dic30—22no—
142C5×D12—22no—
143C5×D12—22no—
144C5×D12—42no—
145C5×D12—81no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—21no—
148C3×Dic10—21no—
149C3×Dic10—21no—
150D3×Dic5—82no—
151C3×#168—22no—
152C5×C3⋊C8—21no—
153C5×C3⋊C8—21no—
154C3×C4⋊Q8C2×D511yescharacteristic
155C3×C4×Q8—51no—
156#947—52no—
157#946—102no—
158C2×#215—51no—
159C2×D24—52no—
160#897—101no—
161#894—102no—
162#893—52no—
163#893—52no—
164D3×C4⋊C4—101no—
165#890—52no—
166#875—101no—
167#874C2×D511yescharacteristic
168C4×D12—51no—
169C4×D12—101no—
170C4×Dic6—51no—
171C3×#107—52no—
172C3×C4⋊C8—51no—
173C3×#103—52no—
174#835—51no—
175#821—52no—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#809—51no—
179#809C2×D512yes—
180#809C2×D512yes—
181#808—51no—
182C4×C3⋊C8C2×D511yescharacteristic
183C2×C5×Q8—21no—
184C2×C5×D4—32no—
185C2×C5×D4—61no—
186C2×C5×D4—61no—
187C22×Dic5—62no—
188C2×D20—31no—
189C2×C4×D5—61no—
190C2×C4×D5—62no—
191C2×Dic10—31no—
192C2×Dic10C22×D311yescharacteristic
193C2×C5×C8—31no—
194C2×C5×C8—31no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4C22×D312yes—
197C42×C5C22×D311yescharacteristic
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200C22⋊Dic5—62no—
201#686—64no—
202#685—62no—
203#685—61no—
204C4⋊Dic5—31no—
205C4⋊Dic5—31no—
206C4⋊Dic5—62no—
207C4⋊Dic5C22×D311yescharacteristic
208#683—21no—
209#683—32no—
210#683—62no—
211C4×Dic5—21no—
212C4×Dic5—32no—
213C2×#168C22×D312yes—
214#677—62no—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—31no—
219#478—152no—
220#477—51no—
221#463—152no—
222#459—151no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C2×C5×D3—42no—
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C3×C4×C5—21no—
234C3×C4×C5—42no—
235C3×C4×C5#13512yes—
236C3×C4×C5C2×#4111yescharacteristic
237C3×C4×C52−1+411yescharacteristic
238Dic15—22no—
239Dic15—22no—
240Dic15—41no—
241C3×Dic5—41no—
242C3×Dic5—41no—
243C2×C3×Q8—21no—
244C2×C3×Q8—51no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—51no—
248C2×D12C22×D512yes—
249C2×C4×D3—101no—
250C2×C4×D3—102no—
251C2×C4×D3—102no—
252C2×Dic6—51no—
253C2×C3×C8—52no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—51no—
256C3×C4⋊C4—101no—
257C3×C4⋊C4C22×D512yes—
258C3×C42—101no—
259C3×C42C22×D511yescharacteristic
260#215—102no—
261(C2×D3)⋊C4—102no—
262(C2×D3)⋊C4—102no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—102no—
265(C2×D3)⋊C4—101no—
266C4⋊Dic3—51no—
267C4⋊Dic3—51no—
268C4⋊Dic3—102no—
269Dic3⋊C4—52no—
270Dic3⋊C4—102no—
271C4×Dic3—52no—
272C2×C3⋊C8C22×D511yescharacteristic
273C2×C3⋊C8C22×D511yescharacteristic
274D24—104no—
275C23×C5—62no—
276C22×D5—61no—
277C5×Q8—81no—
278C5×D4—62no—
279C5×D4—62no—
280C5×D4—122no—
281C5×D4—241no—
282C2×C4×C5—22no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—21no—
287C2×Dic5—21no—
288C2×Dic5—32no—
289C2×Dic5—32no—
290C2×Dic5—61no—
291C2×Dic5—242no—
292D20—32no—
293D20—61no—
294C4×D5—122no—
295C4×D5—242no—
296Dic10—21no—
297Dic10—21no—
298Dic10—62no—
299C5×C8—61no—
300C5×C8—61no—
301#168—22no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8D3×D511yescharacteristic
305#127—31no—
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—301no—
311C22⋊Q8—302no—
312C4×Q8—51no—
313C4×Q8—151no—
314C4×D4—152no—
315C4×D4—152no—
316C4×D4—151no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—52no—
320#106—151no—
321C4⋊C8—51no—
322C4⋊C8—152no—
323#103—52no—
324#103—151no—
325#102—32no—
326#102—32no—
327#102—151no—
328#102—152no—
329C4×C8—31no—
330C4×C8—152no—
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334D15—42no—
335C5×D3—82no—
336C22×D3—22no—
337C22×D3—101no—
338C3×Q8—81no—
339C3×Q8—101no—
340C3×Q8—101no—
341C2×C3×C4—22no—
342C2×C3×C4—101no—
343C2×C3×C4—101no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—52no—
348C2×Dic3—52no—
349C2×Dic3—101no—
350D12—22no—
351D12—22no—
352D12—42no—
353D12—52no—
354D12—81no—
355D12—101no—
356C4×D3—202no—
357C4×D3—402no—
358C4×D3—402no—
359Dic6—102no—
360C3×C8—102no—
361C3⋊C8—21no—
362C3⋊C8—21no—
363C22×C5—122no—
364C22×C5—122no—
365C22×C5—122no—
366C22×C5C2×D3×D411yescharacteristic
367C2×D5—62no—
368C2×D5—121no—
369C2×D5—121no—
370C4×C5—21no—
371C4×C5—42no—
372C4×C5#91912yes—
373C4×C5#100711yescharacteristic
374C4×C5D3×#4111yescharacteristic
375Dic5—41no—
376Dic5—41no—
377Dic5—62no—
378Dic5—62no—
379Dic5—121no—
380C2×Q8—21no—
381C2×Q8—51no—
382C2×Q8—151no—
383C2×D4—32no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4—151no—
387C22×C4—302no—
388C22×C4—302no—
389C22×C4—301no—
390SD16—302no—
391D8—304no—
392C2×C8—31no—
393C2×C8—31no—
394C2×C8—52no—
395C4⋊C4—21no—
396C4⋊C4—51no—
397C4⋊C4—101no—
398C4⋊C4—151no—
399C4⋊C4—152no—
400C4⋊C4—151no—
401C4⋊C4—302no—
402C4⋊C4—302no—
403C4⋊C4C2×D3×D512yes—
404C22⋊C4—302no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—301no—
409C42—101no—
410C42—152no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3C2×D4×D511yescharacteristic
414C2×D3—42no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—102no—
418C2×D3—201no—
419C2×D3—201no—
420C3×C4—21no—
421C3×C4—42no—
422C3×C4—201no—
423C3×C4—201no—
424C3×C4#406212yes—
425C3×C4D5×#4111yescharacteristic
426C3×C4#415011yescharacteristic
427Dic3—102no—
428Dic3—102no—
429Dic3—201no—
430C2×C5—242no—
431C2×C5#563311yescharacteristic
432C2×C5C2×#91911yescharacteristic
433C2×C5#577411yescharacteristic
434D5—122no—
435C23—62no—
436C23—301no—
437Q8—81no—
438Q8—101no—
439Q8—101no—
440Q8—302no—
441D4—62no—
442D4—62no—
443D4—122no—
444D4—152no—
445D4—241no—
446D4—301no—
447C2×C4—22no—
448C2×C4—101no—
449C2×C4—101no—
450C2×C4—152no—
451C2×C4—152no—
452C2×C4—301no—
453C2×C4—602no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4#679011yescharacteristic
457C2×C4#679011yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—61no—
460C8—61no—
461C8—102no—
462C2×C3#6601111yescharacteristic
463C2×C3#6609111yescharacteristic
464C2×C3C2×#406211yescharacteristic
465D3—82no—
466D3—202no—
467C5#8113411yescharacteristic, complemented, Sylow
468C22—122no—
469C22—122no—
470C22—122no—
471C22—302no—
472C22—601no—
473C22—601no—
474C22C2×#679011yescharacteristic
475C4—21no—
476C4—42no—
477C4—201no—
478C4—201no—
479C4—302no—
480C4—302no—
481C4—601no—
482C4#9152312yes—
483C4#9203011yescharacteristic
484C4#9203411yescharacteristic
485C3#1061331611yescharacteristic, complemented, Sylow
486C2—242no—
487C2—602no—
488C2#1175470411yescharacteristic
489C2C2×#9152311yescharacteristic
490C2#1175523811yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11747045C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3361
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. #11756489C2semidirect
2. #11752651C2semidirect
3. C5×#5088C2semidirect
4. C3×#65380C2semidirect
5. #11747387C2semidirect
6. #11747386C2semidirect
7. #11747258C2semidirect
8. #11747233C2semidirect
9. C4×#6658C2semidirect
11. #11746855C2semidirect
46. #65380D3semidirect
89. #5088D5semidirect
412. C3×C5#3361semidirect
467. C5#81134semidirect
485. C3#10613316semidirect

Maximal subgroups

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

subgroupindex
#117564892
#117526512
C5×#50882
C3×#653802
#117473872
#117473862
#117472582
#117472332
C4×#66582
#117470452
#117468552
#106133163
#811345