Finite Group Databasebeta

← #14471922

Subgroups — #14471922

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#11756477C211yesmaximal, characteristic
2#11752472C211yesmaximal, characteristic, complemented
3C5×#5075C211yesmaximal, characteristic, complemented
4C3×#65359C211yesmaximal, characteristic, complemented
5#11749116C212yesmaximal, complemented
6#11749019C212yesmaximal, complemented
7#11749016C212yesmaximal, complemented
8#11748943C212yesmaximal, complemented
9C4×#6660C211yesmaximal, characteristic, complemented
10#11746942C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612100—31nomaximal, Hall
13C2×#6819—21no—
14C3×C5×#127C2211yescharacteristic
15#91829C2212yes—
16#91828—22no—
17#91827—21no—
18D4×Dic15C2212yes—
19C4×D60C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C2×C5×#214C2212yes—
22C4×C5×Dic6C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24#91470C2212yes—
25#91469—21no—
26#91344C2212yes—
27#91340—21no—
28#91327—22no—
29C2×#6660C2211yescharacteristic
30C5×#832C2212yes—
31C5×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×#3964C2212yes—
33C3×#3964C2212yes—
34C3×C4×#168C2211yescharacteristic
35#90987C2212yes—
36#90985C2211yescharacteristic
37#90983C2212yes—
38#90973C2211yescharacteristic
39#90969C2211yescharacteristic
40#90968C2212yes—
41#90951C2212yes—
42#81588—51nomaximal, Hall
43#66052—31no—
44Q8×Dic10—31no—
45C5×#460—31no—
46#65452—32no—
47SD16×Dic5—32no—
48#65359D311yescharacteristic, complemented
49C4×#688—31no—
50#65131—31no—
51#65119—31no—
52#65050—32no—
53#65049—32no—
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4C2312yes—
57C2×#1220—22no—
58C2×#1220—22no—
59C22×Dic15—22no—
60#6819—44no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30D411yescharacteristic
64C2×C5×Dic6C2311yescharacteristic
65C2×C3×Dic10—21no—
66C2×#1204—22no—
67C3×C42×C5C2311yescharacteristic
68#6719—22no—
69#6714—21no—
70C4⋊Dic15D411yescharacteristic
71C4⋊Dic15C2311yescharacteristic
72#6712D412yes—
73C4×Dic15C2312yes—
74C5×#214—24no—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×Dic3⋊C4—21no—
77C4×C5×Dic3—21no—
78C2×C5×C3⋊C8C2312yes—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2312yes—
81C2×C3×#168C2311yescharacteristic
82C2×C3×#168C2311yescharacteristic
83Dic3⋊Dic5—22no—
84#6669—22no—
85Dic3×Dic5—22no—
86#6660—22no—
87#5722—51no—
88#5718—51no—
89C3×#486—51no—
90#5084—51no—
91#5075D511yescharacteristic, complemented
92#4762—52no—
93#4761—52no—
94#4760—52no—
95#4758—52no—
96C4×#204—51no—
97C8×Dic6—51no—
98C2×#711—61no—
99C2×C5×SD16—32no—
100C5×#127C2×D311yescharacteristic
101C4×C5×Q8—31no—
102Q8×Dic5—32no—
103C2×#688—31no—
104#4086—32no—
105#4085—62no—
106#4084—61no—
107D4×Dic5—32no—
108#4034—32no—
109#4034—62no—
110C4×D20—31no—
111#4015—61no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×C4⋊C8—31no—
116C5×#102—32no—
117#3967—31no—
118#3964C2×D312yes—
119#3964C2×D312yes—
120#3953—32no—
121#3949—32no—
122#3946—32no—
123C8×Dic5—32no—
124#3941—31no—
125#3940—31no—
126C4×#168C2×D311yescharacteristic
127#3362—151noSylow
128C23×C3×C5—22no—
129C22×D15—21no—
130C3×C5×D4—22no—
131C3×C5×D4—22no—
132C3×C5×D4—42no—
133C3×C5×D4—81no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137#1220—44no—
138#1220—82no—
139C2×Dic15—21no—
140C2×Dic15—44no—
141C2×Dic15C2×D412yes—
142C2×Dic15C2×D412yes—
143D60—21no—
144D60—21no—
145C4×D15—42no—
146Dic30SD1614yescomplemented
147C2×C5×Dic3—21no—
148C2×C5×Dic3—21no—
149C5×Dic6—21no—
150C5×Dic6#4112yescomplemented
151C2×C3×Dic5—22no—
152C3×Dic10—81no—
153#1204—82no—
154C3×#168—21no—
155C3×#168—21no—
156C5×C3⋊C8—22no—
157C2×#237—101no—
158C3×C4⋊Q8—51no—
159C3×#127C2×D511yescharacteristic
160#944—102no—
161#940—52no—
162#939—102no—
163#938—101no—
164D4×Dic3—52no—
165C2×#214C2×D512yes—
166C2×#204—51no—
167#888—52no—
168#888—101no—
169#887—52no—
170#887—101no—
171C4×D12—51no—
172C4×Dic6—51no—
173C4×Dic6C2×D511yescharacteristic
174C3×#102—52no—
175C3×#102—52no—
176C3×C4×C8—51no—
177#832C2×D512yes—
178#821—51no—
179#817—51no—
180#816—51no—
181Dic3⋊C8—52no—
182C8×Dic3—52no—
183#809—52no—
184#808—52no—
185C4⋊(C3⋊C8)C2×D511yescharacteristic
186C2×C5×Q8—31no—
187C2×C5×D4—21no—
188C2×C5×D4—21no—
189C2×C5×D4C22×D312yes—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192C22×Dic5—62no—
193#711—124no—
194C2×D20—31no—
195C2×C4×D5—61no—
196C2×Dic10—21no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C5×SD16—64no—
200C2×C5×C8—32no—
201C5×C4⋊C4—31no—
202C5×C4⋊C4—61no—
203C42×C5—61no—
204C42×C5C22×D311yescharacteristic
205C22⋊Dic5—62no—
206#688—62no—
207#685—61no—
208C4⋊Dic5—21no—
209C4⋊Dic5—31no—
210C4⋊Dic5—31no—
211C4⋊Dic5—62no—
212C4⋊Dic5C22×D312yes—
213#683—32no—
214#683—62no—
215C4×Dic5—32no—
216C4×Dic5—62no—
217C2×#168C22×D311yescharacteristic
218C2×#168C22×D311yescharacteristic
219Q82—151no—
220#550—151no—
221#486—51no—
222#486—152no—
223#476—152no—
224#476—151no—
225#460—31no—
226#460—152no—
227C8×Q8—151no—
228C4×SD16—151no—
229C4×SD16—152no—
230C22×C3×C5—42no—
231C22×C3×C5—42no—
232C22×C3×C5—42no—
233C22×C3×C5C22×D411yescharacteristic
234C2×D15—41no—
235C2×D15—41no—
236C2×D15—41no—
237C3×C4×C5—21no—
238C3×C4×C5C2×SD1612yes—
239C3×C4×C5C2×#4111yescharacteristic
240C3×C4×C52−1+411yescharacteristic
241Dic15—22no—
242Dic15—41no—
243Dic15C2×SD1614yes—
244C3×Dic5—42no—
245C5×Dic3—22no—
246C5×Dic3—41no—
247C2×C3×Q8—101no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4C22×D512yes—
251C2×#67—102no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—204no—
255C2×D12—51no—
256C2×C4×D3—101no—
257C2×Dic6—51no—
258C2×Dic6—102no—
259C2×Dic6C22×D511yescharacteristic
260C2×C3×C8—51no—
261C2×C3×C8—51no—
262C3×C4⋊C4—52no—
263C3×C4⋊C4—101no—
264C3×C42C22×D511yescharacteristic
265#217—102no—
266#214—24no—
267(C2×D3)⋊C4—101no—
268C4⋊Dic3—51no—
269C4⋊Dic3—51no—
270C4⋊Dic3C22×D511yescharacteristic
271Dic3⋊C4—21no—
272Dic3⋊C4—52no—
273Dic3⋊C4—102no—
274Dic3⋊C4—102no—
275C4×Dic3—21no—
276C4×Dic3—52no—
277C4×Dic3—102no—
278C2×C3⋊C8C22×D512yes—
279#204—102no—
280C23×C5—22no—
281C22×D5—61no—
282C5×Q8—32no—
283C5×Q8—61no—
284C5×D4—22no—
285C5×D4—22no—
286C5×D4—42no—
287C5×D4—81no—
288C2×C4×C5—61no—
289C2×C4×C5—61no—
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C22⋊D5—242no—
295C2×Dic5—22no—
296C2×Dic5—32no—
297C2×Dic5—32no—
298C2×Dic5—61no—
299C2×Dic5—124no—
300D20—61no—
301D20—61no—
302C4×D5—122no—
303Dic10—34no—
304Dic10—81no—
305Dic10—242no—
306C5×C8—62no—
307#168—21no—
308#168—21no—
309C2×#41—301no—
310C2×SD16—32no—
311C2×SD16—151no—
312C4⋊Q8—51no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—152no—
317#127D3×D511yescharacteristic
318#121—301no—
319#121—302no—
320C4×Q8—31no—
321C4×Q8—151no—
322C4×Q8—152no—
323C4×Q8—301no—
324C4×D4—152no—
325C4×D4—151no—
326#106—151no—
327#106—152no—
328C4⋊C8—31no—
329C4⋊C8—152no—
330#103—151no—
331#102—32no—
332#102—52no—
333#102—52no—
334#102—151no—
335#102—152no—
336C4×C8—51no—
337C4×C8—152no—
338C2×C3×C5—82no—
339C2×C3×C5#54811yescharacteristic
340C2×C3×C5C22×SD1611yescharacteristic
341C2×C3×C5#57611yescharacteristic
342D15—81no—
343C23×C3—22no—
344C22×D3—101no—
345C3×Q8—401no—
346C3×D4—22no—
347C3×D4—22no—
348C3×D4—42no—
349C3×D4—81no—
350C2×C3×C4—102no—
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355#67—402no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—52no—
359C2×Dic3—52no—
360C2×Dic3—101no—
361C2×Dic3—204no—
362D12—101no—
363D12—101no—
364C4×D3—202no—
365Dic6—21no—
366Dic6—54no—
367Dic6—402no—
368Dic6#71112yescomplemented
369C3×C8—101no—
370C3×C8—101no—
371C3⋊C8—22no—
372C22×C5—42no—
373C22×C5—42no—
374C22×C5—42no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—121no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—62no—
381C4×C5—121no—
382C4×C5D3×SD1612yes—
383C4×C5D3×#4111yescharacteristic
384C4×C5#101011yescharacteristic
385Dic5—34no—
386Dic5—42no—
387Dic5—62no—
388Dic5—121no—
389#41—604no—
390C2×Q8—31no—
391C2×Q8—101no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—151no—
397C2×D4—302no—
398C2×D4—302no—
399C2×D4C2×D3×D512yes—
400C22×C4—302no—
401C22×C4—301no—
402SD16—64no—
403SD16—302no—
404C2×C8—32no—
405C2×C8—51no—
406C2×C8—51no—
407C4⋊C4—31no—
408C4⋊C4—52no—
409C4⋊C4—61no—
410C4⋊C4—101no—
411C4⋊C4—152no—
412C4⋊C4—151no—
413C4⋊C4—151no—
414C4⋊C4—302no—
415C4⋊C4—302no—
416C22⋊C4—302no—
417C22⋊C4—301no—
418C42—61no—
419C42—152no—
420C42—302no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—201no—
428C2×D3—201no—
429C2×D3—201no—
430C3×C4—21no—
431C3×C4—202no—
432C3×C4D5×SD1612yes—
433C3×C4C2×#71111yescharacteristic
434C3×C4#415011yescharacteristic
435Dic3—22no—
436Dic3—41no—
437Dic3—54no—
438Dic3—102no—
439Dic3—201no—
440C2×C5—82no—
441C2×C5#567711yescharacteristic
442C2×C5#575711yescharacteristic
443C2×C5C2×D3×SD1611yescharacteristic
444D5—241no—
445C23—22no—
446C23—301no—
447Q8—32no—
448Q8—61no—
449Q8—154no—
450Q8—401no—
451Q8—1202no—
452D4—22no—
453D4—22no—
454D4—42no—
455D4—81no—
456D4—301no—
457D4—301no—
458D4—604no—
459D4—1202no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—102no—
463C2×C4—152no—
464C2×C4—152no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4#679011yescharacteristic
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—62no—
472C8—101no—
473C8—101no—
474C2×C3—82no—
475C2×C3#6593211yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477C2×C3#6610811yescharacteristic
478D3—401no—
479C5#8158811yescharacteristic, complemented, Sylow
480C22—42no—
481C22—42no—
482C22—42no—
483C22—601no—
484C22—601no—
485C22—601no—
486C22C2×#679011yescharacteristic
487C4—21no—
488C4—62no—
489C4—121no—
490C4—154no—
491C4—202no—
492C4—302no—
493C4—601no—
494C4#9148712yes—
495C4#9202011yescharacteristic
496C4D3×#71111yescharacteristic
497C3#1061210011yescharacteristic, complemented, Sylow
498C2—82no—
499C2—1201no—
500C2#1175470311yescharacteristic
501C2C2×#9148711yescharacteristic
502C2#1175482711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radical#11756477C2
hypercenter#127D3×D5
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11752472C2semidirect
3. C5×#5075C2semidirect
4. C3×#65359C2semidirect
5. #11749116C2semidirect
6. #11749019C2semidirect
7. #11749016C2semidirect
8. #11748943C2semidirect
9. C4×#6660C2semidirect
10. #11746942C2semidirect
11. #11746851C2semidirect
48. #65359D3semidirect
91. #5075D5semidirect
146. Dic30SD16semidirect
150. C5×Dic6#41semidirect
368. Dic6#711semidirect
422. C3×C5#3362semidirect
479. C5#81588semidirect
497. C3#10612100semidirect

Maximal subgroups

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

subgroupindex
#117564772
#117524722
C5×#50752
C3×#653592
#117491162
#117490192
#117490162
#117489432
C4×#66602
#117469422
#117468512
#106121003
#815885