Finite Group Databasebeta

← #14458507

Subgroups — #14458507

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D60C211yesmaximal, characteristic
2#11752654C211yesmaximal, characteristic, complemented
3C5×#5008C211yesmaximal, characteristic, complemented
4C3×C4×#687C211yesmaximal, characteristic, complemented
5#11749064C212yesmaximal, complemented
6#11748957C212yesmaximal, complemented
7#11747357C212yesmaximal, complemented
8#11747203C212yesmaximal, complemented
9#11747064C211yesmaximal, characteristic, complemented
10#11746988C211yesmaximal, characteristic, complemented
11#11746912C211yesmaximal, characteristic, complemented
12#10612806—31nomaximal, Hall
13C2×D4×D15C2212yes—
14C22×D60—21no—
15C3×C4×C5×D4C2211yescharacteristic
16#91819—21no—
17#91784C2212yes—
18#91771—22no—
19#91763C2211yescharacteristic
20C4×D60C2211yescharacteristic
21C5×#869C2211yescharacteristic, complemented
22C2×C3×#687C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic, complemented
24#91437C2212yescomplemented
25#91424—22no—
26#91418—21no—
27#91390C2212yescomplemented
28#91388—21no—
29C2×#6658C2212yescomplemented
30C2×#6648C2212yescomplemented
31C5×#832C2212yes—
32C5×#808C2212yescomplemented
33C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
34C3×#3964C2211yescharacteristic
35C3×#3942C2211yescharacteristic, complemented
36C3×#3940C2211yescharacteristic, complemented
37C3×C4×#168C2211yescharacteristic, complemented
38#90969C2212yescomplemented
39#90969C2212yescomplemented
40#90968C2212yescomplemented
41#90957C2212yescomplemented
42#79676—51nomaximal, Hall
43#66064—31no—
44D4×D20—31no—
45C5×#476—31no—
46#65377—31no—
47C4×#687D311yescharacteristic, complemented
48#65153—32no—
49#65152—32no—
50#65137—31no—
51#65123—31no—
52#65065—32no—
53D5×#102—32no—
54C23×D15—22no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×#1220—22no—
58D4×D15—24no—
59D4×D15—42no—
60C2×D60—22no—
61C2×D60—21no—
62C2×D60—21no—
63C2×D60—44no—
64C2×D60D411yescharacteristic
65C2×D60C2312yes—
66C2×C4×D15C2312yes—
67C2×C5×Dic6—21no—
68C2×C3×Dic10C2311yescharacteristic
69C2×#1200—22no—
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C22⋊C4—21no—
72C3×C42×C5C2311yescharacteristic
73#6714—22no—
74#6714D412yes—
75C4⋊Dic15D411yescharacteristic
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C2×C5×C3⋊C8C2312yes—
79C3×#687—22no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×#683—21no—
82C3×C4×Dic5—21no—
83C2×C3×#168C2311yescharacteristic
84C2×C3×#168C2311yescharacteristic
85Dic3⋊Dic5—22no—
86#6669—22no—
87#6667—22no—
88#6658—42no—
89#6648—42no—
90#5579—51no—
91D4×D12—51no—
92C3×C4×SD16—51no—
93#5169—52no—
94#5027—51no—
95#5008D511yescharacteristic, complemented
96#4863—52no—
97#4807—52no—
98D3×#102—52no—
99#4694—51no—
100C8×D12—51no—
101C2×D4×D5—32no—
102C22×D20—61no—
103C5×C4⋊Q8—31no—
104C4×C5×D4C2×D311yescharacteristic
105#4092—62no—
106C2×#687C2×D311yescharacteristic
107#4076—61no—
108C2×#677—32no—
109C2×C8×D5—32no—
110#4043—32no—
111#4041—32no—
112#4039—61no—
113D5×C4⋊C4—32no—
114#4036—61no—
115#4028—62no—
116#4020—31no—
117C4×D20—31no—
118C4×Dic10C2×D311yescharacteristic, complemented
119C5×#106—32no—
120C5×C4⋊C8—31no—
121C5×#102—32no—
122#3964C2×D311yescharacteristic
123#3953—32no—
124#3952—32no—
125#3942C2×D311yescharacteristic, complemented
126#3941—32no—
127#3941—32no—
128#3940C2×D311yescharacteristic, complemented
129C4×#168C2×D311yescharacteristic, complemented
130#3295—151noSylow
131C23×C3×C5—21no—
132C22×D15—22no—
133C22×D15—44no—
134C22×D15—44no—
135C22×D15—82no—
136C22×D15C2×D412yes—
137C3×C5×D4—21no—
138C3×C5×D4#4112yes—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—42no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144#1220—44no—
145C2×Dic15C2×D412yes—
146D60—22no—
147D60—22no—
148D60—44no—
149D60—42no—
150D60—81no—
151D60SD1614yescomplemented
152C4×D15—22no—
153C4×D15—22no—
154C2×C5×Dic3—22no—
155C5×Dic6—81no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C3×Dic10—21no—
159C3×Dic10—21no—
160#1200—82no—
161C3×#168—21no—
162C3×#168—21no—
163C5×C3⋊C8—22no—
164C2×D3×D4—52no—
165C22×D12—101no—
166C2×C3×SD16—51no—
167C3×C4×Q8—51no—
168C3×C4×D4C2×D511yescharacteristic
169#946—52no—
170C2×#215—52no—
171#930—101no—
172C2×D3×C8—52no—
173#896—102no—
174#895—52no—
175D3×C4⋊C4—52no—
176#882—102no—
177#874—51no—
178C4×D12—51no—
179C4×D12—101no—
180#870—101no—
181#869C2×D511yescharacteristic, complemented
182C3×#106—51no—
183C3×#103—51no—
184C3×#102—51no—
185C3×C4×C8—51no—
186#832C2×D512yes—
187#821—52no—
188#821—52no—
189(C2×D3)⋊C8—52no—
190#809—52no—
191#808C2×D512yescomplemented
192C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
193C23×D5—62no—
194C2×C5×Q8—61no—
195C2×C5×D4C22×D311yescharacteristic
196C22×C4×C5—21no—
197C2×C22⋊D5—62no—
198D4×D5—64no—
199D4×D5—122no—
200C2×D20—31no—
201C2×D20—32no—
202C2×D20—62no—
203C2×D20—61no—
204C2×D20—61no—
205C2×D20—124no—
206C2×C4×D5—32no—
207C2×C4×D5—62no—
208C2×Dic10C22×D311yescharacteristic
209C2×C5×C8—32no—
210C5×C4⋊C4—32no—
211C5×C4⋊C4—61no—
212C5×C4⋊C4C22×D311yescharacteristic
213C5×C22⋊C4—21no—
214C42×C5C22×D311yescharacteristic
215#687—22no—
216#685—32no—
217#685—62no—
218#685—62no—
219C4⋊Dic5—31no—
220C4⋊Dic5—62no—
221C4⋊Dic5C22×D311yescharacteristic
222#683—21no—
223#683—62no—
224C4×Dic5—21no—
225C2×#168C22×D311yescharacteristic
226C2×#168C22×D311yescharacteristic
227#677—122no—
228C8×D5—122no—
229#554—151no—
230D42—151no—
231#486—151no—
232#481—152no—
233#476—31no—
234#465—152no—
235#460—151no—
236#450—152no—
237C4×SD16—51no—
238C8×D4—151no—
239C2×#102—152no—
240C22×C3×C5—22no—
241C22×C3×C5—41no—
242C22×C3×C5—41no—
243C22×C3×C5C22×D411yescharacteristic
244C2×D15—22no—
245C2×D15—22no—
246C2×D15—42no—
247C2×D15—42no—
248C2×D15—42no—
249C2×D15—88no—
250C2×D15C2×SD1614yes—
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5C2×SD1612yes—
254C3×C4×C5C2×#4111yescharacteristic
255C3×C4×C5H(5,𝔽2)11yescharacteristic
256Dic15—22no—
257C3×Dic5—41no—
258C3×Dic5—41no—
259C5×Dic3—42no—
260C23×D3—102no—
261C2×C3×Q8—51no—
262C2×C3×D4C22×D511yescharacteristic
263C22×C3×C4—21no—
264C2×#67—102no—
265D3×D4—104no—
266D3×D4—202no—
267C2×D12—51no—
268C2×D12—52no—
269C2×D12—102no—
270C2×D12—101no—
271C2×D12—101no—
272C2×D12—204no—
273C2×C4×D3—52no—
274C2×C4×D3—102no—
275C2×Dic6—21no—
276C3×SD16—102no—
277C2×C3×C8—51no—
278C2×C3×C8—51no—
279C3×C4⋊C4—51no—
280C3×C4⋊C4—101no—
281C3×C4⋊C4C22×D511yescharacteristic
282C3×C22⋊C4—21no—
283C3×C42—101no—
284C3×C42C22×D511yescharacteristic
285#215—202no—
286(C2×D3)⋊C4—52no—
287(C2×D3)⋊C4—102no—
288(C2×D3)⋊C4—102no—
289C4⋊Dic3—21no—
290C4⋊Dic3—51no—
291C4⋊Dic3C22×D512yes—
292Dic3⋊C4—102no—
293Dic3⋊C4—102no—
294C2×C3⋊C8C22×D512yes—
295D3×C8—202no—
296C23×C5—21no—
297C22×D5—32no—
298C22×D5—62no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—242no—
302C5×Q8—241no—
303C5×D4—21no—
304C5×D4#23512yes—
305C2×C4×C5—21no—
306C2×C4×C5—42no—
307C2×C4×C5—62no—
308C2×C4×C5D3×D411yescharacteristic
309C2×C4×C5D3×D411yescharacteristic
310C2×C4×C5C23×D311yescharacteristic
311C22⋊D5—124no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—32no—
315D20—34no—
316D20—62no—
317D20—62no—
318D20—124no—
319D20—122no—
320D20—241no—
321C4×D5—62no—
322C4×D5—62no—
323C4×D5—242no—
324Dic10—21no—
325Dic10—21no—
326C5×C8—62no—
327#168—21no—
328#168—21no—
329C22×D4—152no—
330C22×D4—301no—
331C2×SD16—51no—
332C2×SD16—152no—
333C22×C8—152no—
334C4⋊Q8—31no—
335#127—151no—
336#125—301no—
337C22⋊Q8—152no—
338C22⋊Q8—302no—
339#121—152no—
340#121—301no—
341#120—302no—
342C4×Q8—51no—
343C4×D4—151no—
344C4×D4—301no—
345C4×D4D3×D511yescharacteristic
346C2×C4⋊C4—152no—
347#106—32no—
348#106—51no—
349C4⋊C8—31no—
350#103—51no—
351#102—32no—
352#102—51no—
353#102—152no—
354#102—152no—
355#102—152no—
356C22⋊C8—152no—
357C4×C8—51no—
358C2×C3×C5—42no—
359C2×C3×C5#54611yescharacteristic
360C2×C3×C5C22×SD1611yescharacteristic
361C2×C3×C5#57611yescharacteristic
362D15—24no—
363D15—82no—
364C23×C3—21no—
365C22×D3—52no—
366C22×D3—102no—
367C22×D3—204no—
368C22×D3—204no—
369C22×D3—402no—
370C3×Q8—101no—
371C3×Q8—101no—
372C3×D4—21no—
373C3×D4#71312yes—
374C2×C3×C4—21no—
375C2×C3×C4—42no—
376C2×C3×C4—101no—
377C2×C3×C4—101no—
378C2×C3×C4D4×D511yescharacteristic
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4C23×D511yescharacteristic
381#67—204no—
382C2×Dic3—22no—
383C2×Dic3—52no—
384D12—54no—
385D12—102no—
386D12—102no—
387D12—204no—
388D12—202no—
389D12—401no—
390C4×D3—102no—
391C4×D3—102no—
392C4×D3—402no—
393Dic6—81no—
394C3×C8—101no—
395C3×C8—101no—
396C3⋊C8—22no—
397C22×C5—22no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5C2×D3×D411yescharacteristic
401C2×D5—34no—
402C2×D5—62no—
403C2×D5—62no—
404C2×D5—122no—
405C2×D5—122no—
406C2×D5—122no—
407C2×D5—248no—
408C4×C5—21no—
409C4×C5—41no—
410C4×C5—122no—
411C4×C5D3×SD1612yes—
412C4×C5C2×#23511yescharacteristic
413C4×C5#100911yescharacteristic
414Dic5—41no—
415Dic5—41no—
416Dic5—62no—
417C24—302no—
418C2×Q8—51no—
419C2×Q8—61no—
420C2×D4—151no—
421C2×D4—152no—
422C2×D4—302no—
423C2×D4—302no—
424C2×D4—304no—
425C2×D4—301no—
426C2×D4—301no—
427C2×D4—604no—
428C2×D4—602no—
429C2×D4C2×D3×D511yescharacteristic
430C22×C4—21no—
431C22×C4—152no—
432C22×C4—302no—
433SD16—102no—
434SD16—602no—
435C2×C8—32no—
436C2×C8—51no—
437C2×C8—51no—
438C2×C8—602no—
439C4⋊C4—32no—
440C4⋊C4—51no—
441C4⋊C4—61no—
442C4⋊C4—101no—
443C4⋊C4—151no—
444C4⋊C4—302no—
445C4⋊C4—302no—
446C4⋊C4C2×D3×D511yescharacteristic
447C22⋊C4—21no—
448C22⋊C4—152no—
449C22⋊C4—302no—
450C22⋊C4—302no—
451C42—101no—
452C42C2×D3×D511yescharacteristic
453C3×C5#329511yescharacteristic, complemented, Hall
454C22×C3—22no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3C2×D4×D511yescharacteristic
458C2×D3—54no—
459C2×D3—102no—
460C2×D3—102no—
461C2×D3—202no—
462C2×D3—202no—
463C2×D3—202no—
464C2×D3—408no—
465C3×C4—21no—
466C3×C4—41no—
467C3×C4—201no—
468C3×C4—201no—
469C3×C4D5×SD1612yes—
470C3×C4C2×#71311yescharacteristic
471C3×C4#414911yescharacteristic
472Dic3—42no—
473Dic3—102no—
474C2×C5—42no—
475C2×C5#555011yescharacteristic
476C2×C5C2×D3×SD1611yescharacteristic
477C2×C5#576911yescharacteristic
478D5—64no—
479D5—242no—
480C23—21no—
481C23—152no—
482C23—302no—
483C23—604no—
484C23—604no—
485C23—1202no—
486Q8—101no—
487Q8—101no—
488Q8—241no—
489D4—21no—
490D4—154no—
491D4—302no—
492D4—302no—
493D4—604no—
494D4—604no—
495D4—602no—
496D4—1201no—
497D4#677312yes—
498C2×C4—21no—
499C2×C4—42no—
500C2×C4—62no—
501C2×C4—101no—
502C2×C4—101no—
503C2×C4—152no—
504C2×C4—302no—
505C2×C4—302no—
506C2×C4—1202no—
507C2×C4#679011yescharacteristic
508C2×C4#679011yescharacteristic
509C2×C4C22×D3×D511yescharacteristic
510C8—62no—
511C8—101no—
512C8—101no—
513C2×C3—42no—
514C2×C3#6596411yescharacteristic
515C2×C3C2×D5×SD1611yescharacteristic
516C2×C3#6610811yescharacteristic
517D3—104no—
518D3—402no—
519C5#7967611yescharacteristic, complemented, Sylow
520C22—22no—
521C22—41no—
522C22—41no—
523C22—154no—
524C22—302no—
525C22—302no—
526C22—602no—
527C22—602no—
528C22—602no—
529C22—1208no—
530C22C2×#679011yescharacteristic
531C4—21no—
532C4—41no—
533C4—122no—
534C4—201no—
535C4—201no—
536C4—302no—
537C4#9148712yes—
538C4C2×#677311yescharacteristic
539C4#9201911yescharacteristic
540C3#1061280611yescharacteristic, complemented, Sylow
541C2—42no—
542C2—304no—
543C2—1202no—
544C2#1175455811yescharacteristic
545C2C2×#9148711yescharacteristic
546C2#1175533211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalD4×D60C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3295
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752654C2semidirect
3. C5×#5008C2semidirect
4. C3×C4×#687C2semidirect
5. #11749064C2semidirect
6. #11748957C2semidirect
7. #11747357C2semidirect
8. #11747203C2semidirect
9. #11747064C2semidirect
10. #11746988C2semidirect
11. #11746912C2semidirect
21. C5×#869C22semidirect
23. C3×C4×Dic10C22semidirect
24. #91437C22semidirect
27. #91390C22semidirect
29. C2×#6658C22semidirect
30. C2×#6648C22semidirect
32. C5×#808C22semidirect
33. C5×C4⋊(C3⋊C8)C22semidirect
35. C3×#3942C22semidirect
36. C3×#3940C22semidirect
37. C3×C4×#168C22semidirect
38. #90969C22semidirect
39. #90969C22semidirect
40. #90968C22semidirect
41. #90957C22semidirect
47. C4×#687D3semidirect
95. #5008D5semidirect
118. C4×Dic10C2×D3semidirect
125. #3942C2×D3semidirect
128. #3940C2×D3semidirect
129. C4×#168C2×D3semidirect
151. D60SD16semidirect
181. #869C2×D5semidirect
191. #808C2×D5semidirect
192. C4⋊(C3⋊C8)C2×D5semidirect
453. C3×C5#3295semidirect
519. C5#79676semidirect
540. C3#10612806semidirect

Maximal subgroups

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

subgroupindex
D4×D602
#117526542
C5×#50082
C3×C4×#6872
#117490642
#117489572
#117473572
#117472032
#117470642
#117469882
#117469122
#106128063
#796765