Finite Group Databasebeta

← #14471965

Subgroups — #14471965

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756481C211yesmaximal, characteristic, complemented
2#11752680C211yesmaximal, characteristic
3C5×#5088C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5#11747408C212yesmaximal, complemented
6#11747407C212yesmaximal, complemented
7#11747256C212yesmaximal, complemented
8#11747234C212yesmaximal, complemented
9#11747086C211yesmaximal, characteristic, complemented
10C4×#6657C211yesmaximal, characteristic, complemented
11#11746855C211yesmaximal, characteristic, complemented
12#10613319—31nomaximal, Hall
13C2×#6772—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91833—22no—
16#91777—21no—
17#91777C2212yes—
18#91776—21no—
19#91776C2212yes—
20C4×Dic30C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C5×#874C2211yescharacteristic
23C3×C4×D20C2211yescharacteristic
24#91463C2212yes—
25#91453—22no—
26#91449—21no—
27#91435C2212yes—
28C2×#6659C2212yes—
29C2×#6657C2211yescharacteristic
30C5×#809C2212yes—
31C5×#809C2212yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33C3×#3941C2212yes—
34C3×#3940C2212yes—
35C3×C4⋊#168C2211yescharacteristic
36#90987C2211yescharacteristic
37#90983C2212yes—
38#90974C2211yescharacteristic
39#90967C2212yes—
40#90965C2211yescharacteristic
41#90951C2212yes—
42#81090—51nomaximal, Hall
43#66056—31no—
44#66052—31no—
45C5×#486—31no—
46#65373D311yescharacteristic, complemented
47#65364—31no—
48#65051—32no—
49#65050—32no—
50#65049—32no—
51#65047—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
55C2×Dic30—22no—
56C2×Dic30D411yescharacteristic
57C2×Dic30C2311yescharacteristic
58C2×C5×D12—21no—
59C2×C5×D12—21no—
60C2×C5×D12C2312yes—
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×#1201—22no—
64C2×#1201—22no—
65C2×D3×Dic5—22no—
66#6772—44no—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4C2312yes—
69C3×C42×C5C2311yescharacteristic
70C4⋊Dic15D411yescharacteristic
71C4⋊Dic15C2311yescharacteristic
72#6712—21no—
73#6712—22no—
74#6712—22no—
75#6712D412yes—
76C4×Dic15—21no—
77C4×Dic15—22no—
78C4×Dic15C2312yes—
79C2×C5×C3⋊C8C2311yescharacteristic
80C2×C5×C3⋊C8C2311yescharacteristic
81C3×#685—21no—
82C3×C4⋊Dic5C2311yescharacteristic
83C2×C3×#168C2312yes—
84(C2×D3)⋊Dic5—22no—
85#6659—24no—
86#6657—22no—
87#5722—51no—
88#5553—51no—
89C3×#476—51no—
90#5088D511yescharacteristic, complemented
91C4×#214—51no—
92#4870—52no—
93#4852—52no—
94#4848—51no—
95#4830—51no—
96#4762—52no—
97#4760—52no—
98C2×#711—61no—
99C5×C4⋊Q8C2×D311yescharacteristic
100C5×#127—31no—
101#4090—62no—
102#4086—32no—
103#4085—62no—
104#4084—61no—
105D4×Dic5—32no—
106C2×#687—32no—
107C2×#677—31no—
108#4034—32no—
109#4034—61no—
110#4033—32no—
111#4033—61no—
112C4×D20C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—31no—
115C5×#102—32no—
116C5×#102—32no—
117C4×C5×C8—31no—
118#3964—32no—
119#3953—31no—
120#3949—31no—
121#3948—31no—
122#3946—32no—
123C8×Dic5—32no—
124#3941C2×D312yes—
125#3940C2×D312yes—
126C4⋊#168C2×D311yescharacteristic
127#3362—151noSylow
128C22×C5×D3—22no—
129C22×C3×D5—21no—
130C3×C5×Q8—81no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136C2×Dic15—21no—
137C2×Dic15C2×D412yes—
138C2×Dic15C2×D412yes—
139Dic30—21no—
140Dic30—82no—
141Dic30SD1614yescomplemented
142Dic30#4112yescomplemented
143C5×D12—22no—
144C5×D12—22no—
145C5×D12—42no—
146C5×D12—81no—
147C2×C3×Dic5—21no—
148C3×D20—21no—
149C3×D20—21no—
150C3×C4×D5—42no—
151#1201—44no—
152#1201—82no—
153D3×Dic5—44no—
154C3×#168—22no—
155C5×C3⋊C8—21no—
156C5×C3⋊C8—21no—
157C2×#235—101no—
158C3×C4⋊Q8C2×D511yescharacteristic
159C3×C4×D4—51no—
160#944—102no—
161#940—52no—
162C2×#214—51no—
163#930—101no—
164C2×#204—52no—
165#893—52no—
166#888—52no—
167#888—101no—
168#887—52no—
169#887—101no—
170#884—102no—
171#874C2×D511yescharacteristic
172C4×Dic6—51no—
173C4×Dic6—51no—
174C3×#106—52no—
175C3×C4⋊C8—51no—
176C3×#102—52no—
177#832—51no—
178#821—52no—
179Dic3⋊C8—52no—
180C8×Dic3—52no—
181#810—51no—
182#809C2×D512yes—
183#809C2×D512yes—
184#808—51no—
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×Q8—21no—
187C2×C5×D4—32no—
188C2×C5×D4—61no—
189C2×C5×D4—61no—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192C22×Dic5—62no—
193#711—124no—
194C2×D20C22×D311yescharacteristic
195C2×C4×D5—21no—
196C2×Dic10—31no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C2×C5×C8—31no—
200C2×C5×C8—31no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4C22×D312yes—
203C42×C5C22×D311yescharacteristic
204C22⋊Dic5—62no—
205#687—64no—
206#685—21no—
207C4⋊Dic5—31no—
208C4⋊Dic5—31no—
209C4⋊Dic5C22×D311yescharacteristic
210#683—32no—
211#683—62no—
212#683—62no—
213#683—61no—
214C4×Dic5—32no—
215C4×Dic5—62no—
216C4×Dic5—61no—
217C2×#168C22×D312yes—
218#677—62no—
219Q82—151no—
220#550—151no—
221#486—31no—
222#486—152no—
223#476—51no—
224#476—152no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—151no—
229C4×SD16—152no—
230C22×C3×C5C22×D411yescharacteristic
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C2×C5×D3—42no—
234C2×C3×D5—41no—
235C2×C3×D5—41no—
236C2×C3×D5—41no—
237C3×C4×C5—21no—
238C3×C4×C5—42no—
239C3×C4×C5C2×SD1612yes—
240C3×C4×C5C2×#4111yescharacteristic
241C3×C4×C52−1+411yescharacteristic
242Dic15—22no—
243Dic15—22no—
244Dic15—41no—
245Dic15C2×SD1614yes—
246C3×Dic5—41no—
247C2×C3×Q8—21no—
248C2×C3×D4—51no—
249C22×C3×C4—101no—
250C2×#67—102no—
251C2×#67—102no—
252#235—204no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12C22×D512yes—
256C2×C4×D3—102no—
257C2×Dic6—51no—
258C2×Dic6—51no—
259C2×Dic6—102no—
260C2×C3×C8—52no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—51no—
263C3×C4⋊C4C22×D512yes—
264C3×C22⋊C4—101no—
265C3×C42C22×D511yescharacteristic
266#214—102no—
267(C2×D3)⋊C4—102no—
268C4⋊Dic3—51no—
269C4⋊Dic3—51no—
270Dic3⋊C4—52no—
271Dic3⋊C4—102no—
272Dic3⋊C4—102no—
273Dic3⋊C4—101no—
274C4×Dic3—52no—
275C4×Dic3—102no—
276C4×Dic3—101no—
277C2×C3⋊C8C22×D511yescharacteristic
278C2×C3⋊C8C22×D511yescharacteristic
279#204—104no—
280C23×C5—62no—
281C22×D5—21no—
282C5×Q8—81no—
283C5×D4—62no—
284C5×D4—62no—
285C5×D4—122no—
286C5×D4—241no—
287C2×C4×C5—22no—
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—124no—
292C22⋊D5—242no—
293C2×Dic5—21no—
294C2×Dic5—32no—
295C2×Dic5—32no—
296C2×Dic5—61no—
297C2×Dic5—61no—
298C2×Dic5—124no—
299D20—21no—
300D20—21no—
301C4×D5—42no—
302Dic10—34no—
303Dic10—32no—
304Dic10—61no—
305Dic10—242no—
306C5×C8—61no—
307C5×C8—61no—
308#168—22no—
309C2×#41—301no—
310C2×SD16—151no—
311C2×SD16—152no—
312C4⋊Q8—152no—
313C4⋊Q8—301no—
314C4⋊Q8—302no—
315C4⋊Q8D3×D511yescharacteristic
316#127—31no—
317#127—152no—
318#121—302no—
319#121—301no—
320C4×Q8—151no—
321C4×Q8—152no—
322C4×Q8—151no—
323C4×Q8—301no—
324C4×D4—51no—
325C4×D4—152no—
326#106—52no—
327#106—151no—
328C4⋊C8—51no—
329C4⋊C8—152no—
330#103—151no—
331#102—32no—
332#102—32no—
333#102—52no—
334#102—151no—
335#102—152no—
336C4×C8—31no—
337C4×C8—152no—
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341C3×D5—81no—
342C5×D3—82no—
343C23×C3—101no—
344C22×D3—22no—
345C3×Q8—81no—
346C3×D4—101no—
347C3×D4—101no—
348C2×C3×C4—22no—
349C2×C3×C4—101no—
350C2×C3×C4—202no—
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355#67—402no—
356C2×Dic3—52no—
357C2×Dic3—52no—
358C2×Dic3—101no—
359C2×Dic3—101no—
360D12—22no—
361D12—22no—
362D12—42no—
363D12—81no—
364C4×D3—204no—
365Dic6—54no—
366Dic6—52no—
367Dic6—101no—
368Dic6—402no—
369C3×C8—102no—
370C3⋊C8—21no—
371C3⋊C8—21no—
372C22×C5—122no—
373C22×C5—122no—
374C22×C5—122no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—41no—
377C2×D5—41no—
378C2×D5—41no—
379C4×C5—21no—
380C4×C5—42no—
381C4×C5D3×SD1612yes—
382C4×C5#100711yescharacteristic
383C4×C5D3×#4111yescharacteristic
384Dic5—34no—
385Dic5—41no—
386Dic5—62no—
387Dic5—62no—
388Dic5—121no—
389#41—604no—
390C2×Q8—21no—
391C2×Q8—151no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—32no—
395C2×D4—51no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—302no—
399C2×D4—302no—
400C22×C4—101no—
401C22×C4—302no—
402SD16—302no—
403SD16—304no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8—52no—
407C4⋊C4—21no—
408C4⋊C4—51no—
409C4⋊C4—152no—
410C4⋊C4—151no—
411C4⋊C4—151no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C2×D3×D512yes—
416C22⋊C4—101no—
417C22⋊C4—302no—
418C42—152no—
419C42—302no—
420C42—301no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—201no—
424C22×C3—201no—
425C22×C3—201no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C3×C4—21no—
431C3×C4—42no—
432C3×C4—201no—
433C3×C4D5×SD1612yes—
434C3×C4D5×#4111yescharacteristic
435C3×C4#415011yescharacteristic
436Dic3—54no—
437Dic3—102no—
438Dic3—102no—
439Dic3—201no—
440C2×C5—242no—
441C2×C5#563311yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443C2×C5#577411yescharacteristic
444D5—81no—
445C23—62no—
446C23—101no—
447Q8—81no—
448Q8—154no—
449Q8—152no—
450Q8—301no—
451Q8—1202no—
452D4—62no—
453D4—62no—
454D4—101no—
455D4—101no—
456D4—122no—
457D4—241no—
458D4—604no—
459D4—1202no—
460C2×C4—22no—
461C2×C4—101no—
462C2×C4—152no—
463C2×C4—152no—
464C2×C4—202no—
465C2×C4—301no—
466C2×C4—301no—
467C2×C4—604no—
468C2×C4#679011yescharacteristic
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—61no—
472C8—61no—
473C8—102no—
474C2×C3—401no—
475C2×C3#6601111yescharacteristic
476C2×C3#6609111yescharacteristic
477C2×C3C2×D5×SD1611yescharacteristic
478D3—82no—
479C5#8109011yescharacteristic, complemented, Sylow
480C22—122no—
481C22—122no—
482C22—122no—
483C22—201no—
484C22—201no—
485C22—201no—
486C22C2×#679011yescharacteristic
487C4—21no—
488C4—42no—
489C4—154no—
490C4—201no—
491C4—302no—
492C4—302no—
493C4—601no—
494C4#9150512yes—
495C4#9203011yescharacteristic
496C4#9203411yescharacteristic
497C3#1061331911yescharacteristic, complemented, Sylow
498C2—242no—
499C2—401no—
500C2#1175470411yescharacteristic
501C2C2×#9150511yescharacteristic
502C2#1175523811yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752680C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3362
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. #11756481C2semidirect
3. C5×#5088C2semidirect
4. C3×#65373C2semidirect
5. #11747408C2semidirect
6. #11747407C2semidirect
7. #11747256C2semidirect
8. #11747234C2semidirect
9. #11747086C2semidirect
10. C4×#6657C2semidirect
11. #11746855C2semidirect
46. #65373D3semidirect
90. #5088D5semidirect
141. Dic30SD16semidirect
142. Dic30#41semidirect
422. C3×C5#3362semidirect
479. C5#81090semidirect
497. C3#10613319semidirect

Maximal subgroups

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

subgroupindex
#117564812
#117526802
C5×#50882
C3×#653732
#117474082
#117474072
#117472562
#117472342
#117470862
C4×#66572
#117468552
#106133193
#810905