Finite Group Databasebeta

← #14430853

Subgroups — #14430853

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5500C211yesmaximal, characteristic, complemented
2#11754515C211yesmaximal, characteristic
3C2×#91093C211yesmaximal, characteristic
4C3×#65253C211yesmaximal, characteristic, complemented
5#11748469C211yesmaximal, characteristic, complemented
6#11748441C211yesmaximal, characteristic, complemented
7#11748396C211yesmaximal, characteristic
8#11747252C212yesmaximal, complemented
9#11747250C212yesmaximal, complemented
10#11747248C212yesmaximal, complemented
11#11747246C212yesmaximal, complemented
12#10615205—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15C22×C3⋊#168C2211yescharacteristic
16C5×#926C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C5×#924—22no—
19C5×#890—21no—
20C5×#890C2212yescomplemented
21C5×#888—21no—
22C5×#888C2212yescomplemented
23C3×#4072C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25#91561—22no—
26#91428C2212yes—
27#91428C2212yes—
28#91418—21no—
29#91418—21no—
30#91093C2212yes—
31#91093C2212yes—
32C3×#3940C2212yescomplemented
33C3×#3939C2212yescomplemented
34#90989C2211yescharacteristic, complemented
35#90989C2211yescharacteristic, complemented
36#90986C2211yescharacteristic, complemented
37#90986C2211yescharacteristic, complemented
38Dic3⋊#168C2212yescomplemented
39Dic3⋊#168C2212yescomplemented
40#90969C2212yes—
41#90969C2212yes—
42#79242—51nomaximal, Hall
43C5×#544—31no—
44#65855—31no—
45#65376—32no—
46#65373—32no—
47#65355—32no—
48#65355—32no—
49#65290—31no—
50#65288—31no—
51#65287—31no—
52C2×#3941—31no—
53#65253D311yescharacteristic, complemented
54C23×D15—21no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×D60—21no—
58C2×D60—22no—
59C2×D60Q814yescomplemented
60C2×D60C2312yes—
61C2×C5×Dic6—22no—
62C2×#1200—22no—
63C2×#1200—22no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4C2312yes—
66C2×C3⋊#168—22no—
67C2×C3⋊#168C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C5×#217—21no—
70C5×#217D412yes—
71C5×C4⋊Dic3—22no—
72C5×C4⋊Dic3D411yescharacteristic
73C5×C4⋊Dic3D411yescharacteristic
74C5×C4⋊Dic3C2311yescharacteristic
75C5×C4⋊Dic3C2311yescharacteristic
76C5×Dic3⋊C4—22no—
77C5×Dic3⋊C4—22no—
78C4×C5×Dic3—21no—
79C4×C5×Dic3C2312yes—
80C3×C22⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2311yescharacteristic
83C3×C4×Dic5—21no—
84C3×#681—22no—
85C2×C3×#168C2312yes—
86#6667—22no—
87#6667—22no—
88#5521—51no—
89#5500D511yescharacteristic, complemented
90C3×#428—51no—
91#5131—51no—
92#5119—51no—
93#4998—51no—
94C2×#809—51no—
95#4891—52no—
96#4890—52no—
97#4871—52no—
98#4870—52no—
99C22×D20—31no—
100C5×C4⋊Q8—32no—
101C5×C4⋊Q8—61no—
102C5×#125—32no—
103C5×#125—61no—
104C5×C22⋊Q8—62no—
105C5×#117—31no—
106C5×#117—31no—
107C2×C5×C4⋊C4C2×D311yescharacteristic
108#4072C2×D311yescharacteristic
109C2×#681C2×D311yescharacteristic
110C22×#168—31no—
111#4039—61no—
112#4039—61no—
113D5×C22⋊C4—62no—
114C4×D20—32no—
115C4×D20—32no—
116#3941—32no—
117#3941—32no—
118#3941—32no—
119#3941—32no—
120#3940—31no—
121#3940—31no—
122#3940C2×D312yescomplemented
123#3939—31no—
124#3939—31no—
125#3939C2×D312yescomplemented
126C4⋊#168—32no—
127C4⋊#168—32no—
128#3081—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×D15—22no—
131C22×D15—24no—
132C22×D15—81no—
133C22×D15—81no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—81no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×Q812yes—
138C2×C3×C4×C5#4112yes—
139C2×C3×C4×C5C2411yescharacteristic
140D60—24no—
141D60—22no—
142D60C2×Q814yes—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3C2×D412yes—
146C2×C5×Dic3C2×D412yes—
147C5×Dic6—82no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—21no—
150#1200—82no—
151#1200—82no—
152C3⋊#168—21no—
153C3⋊#168—21no—
154C3×#168—22no—
155C22×D12—51no—
156C2×C3×M16—51no—
157C3×#117—51no—
158C2×C3×C4⋊C4C2×D511yescharacteristic
159#926C2×D511yescharacteristic
160#926C2×D511yescharacteristic
161#924—22no—
162C22×C3⋊C8—51no—
163#893—52no—
164#893—52no—
165#890—21no—
166#890C2×D512yescomplemented
167#888—21no—
168#888C2×D512yescomplemented
169D3×C22⋊C4—102no—
170C4×D12—101no—
171C4×D12—101no—
172C3×#107—52no—
173C3×#106—52no—
174#821—52no—
175#821—52no—
176Dic3⋊C8—52no—
177Dic3⋊C8—52no—
178#809—52no—
179#809—52no—
180#808—51no—
181#808—51no—
182#807—51no—
183#807—51no—
184C23×D5—61no—
185C2×C5×Q8—62no—
186C22×C4×C5—21no—
187C22×C4×C5C22×D311yescharacteristic
188C2×D20—34no—
189C2×D20—32no—
190C2×D20—62no—
191C2×D20—61no—
192C2×C4×D5—62no—
193C2×C4×D5—62no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—31no—
196C5×C4⋊C4—31no—
197C5×C4⋊C4—31no—
198C5×C4⋊C4—31no—
199C5×C4⋊C4—62no—
200C5×C4⋊C4—62no—
201C5×C4⋊C4—62no—
202C5×C4⋊C4C22×D312yes—
203C5×C22⋊C4—32no—
204C5×C22⋊C4—61no—
205C42×C5—32no—
206C42×C5—61no—
207C22⋊Dic5—21no—
208#685—62no—
209#685—62no—
210C4⋊Dic5C22×D311yescharacteristic
211C4⋊Dic5C22×D311yescharacteristic
212C4×Dic5—21no—
213#681—22no—
214C2×#168—31no—
215C2×#168—31no—
216C2×#168—62no—
217C2×#168C22×D312yes—
218#544—31no—
219#518—151no—
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428—51no—
225#427—151no—
226#424—151no—
227#418—151no—
228C2×#102—151no—
229C22×C3×C5—21no—
230C22×C3×C5—21no—
231C22×C3×C5C22⋊Q812yes—
232C22×C3×C5C22×D411yescharacteristic
233C2×D15—24no—
234C2×D15—42no—
235C2×D15—42no—
236C2×D15—84no—
237C3×C4×C5—42no—
238C3×C4×C5C22⋊Q812yes—
239C3×C4×C5C22×Q811yescharacteristic
240C3×C4×C5C2×#4111yescharacteristic
241C3×Dic5—41no—
242C3×Dic5—41no—
243C5×Dic3—22no—
244C5×Dic3—22no—
245C5×Dic3—41no—
246C5×Dic3—41no—
247C23×D3—101no—
248C22×C3×C4—21no—
249C22×C3×C4C22×D511yescharacteristic
250C2×D12—54no—
251C2×D12—52no—
252C2×D12—102no—
253C2×D12—101no—
254C2×C4×D3—102no—
255C2×C4×D3—102no—
256C2×Dic6—22no—
257C3×M16—102no—
258C2×C3×C8—52no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—51no—
261C3×C4⋊C4—51no—
262C3×C4⋊C4C22×D512yes—
263C3×C22⋊C4—101no—
264C3×C42—101no—
265#217—21no—
266#217C22⋊D512yes—
267(C2×D3)⋊C4—102no—
268(C2×D3)⋊C4—102no—
269C4⋊Dic3—22no—
270C4⋊Dic3C22⋊D511yescharacteristic
271C4⋊Dic3C22⋊D511yescharacteristic
272C4⋊Dic3C22×D511yescharacteristic
273C4⋊Dic3C22×D511yescharacteristic
274Dic3⋊C4—22no—
275Dic3⋊C4—22no—
276C4×Dic3—21no—
277C4×Dic3C22×D512yes—
278C2×C3⋊C8—51no—
279C2×C3⋊C8—51no—
280C2×C3⋊C8—102no—
281C23×C5D3×D411yescharacteristic
282C22×D5—62no—
283C22×D5—64no—
284C22×D5—241no—
285C22×D5—241no—
286C5×Q8—242no—
287C2×C4×C5—22no—
288C2×C4×C5—32no—
289C2×C4×C5—32no—
290C2×C4×C5—61no—
291C2×C4×C5—61no—
292C2×C4×C5—81no—
293C2×C4×C5#23512yes—
294C2×C4×C5D3×D411yescharacteristic
295C2×C4×C5D3×Q812yes—
296C2×C4×C5C23×D311yescharacteristic
297C2×Dic5—21no—
298C2×Dic5—21no—
299D20—34no—
300D20—64no—
301D20—62no—
302C4×D5—242no—
303C4×D5—242no—
304#168—22no—
305#168—61no—
306#168—61no—
307C22×D4—151no—
308C2×M16—51no—
309C22×C8—151no—
310C4⋊Q8—32no—
311C4⋊Q8—61no—
312#125—32no—
313#125—61no—
314C22⋊Q8—62no—
315C4×D4—152no—
316C4×D4—152no—
317C4×D4—301no—
318C4×D4—301no—
319#117—31no—
320#117—31no—
321#117—51no—
322C2×C4⋊C4D3×D511yescharacteristic
323C2×C22⋊C4—302no—
324#107—52no—
325#107—151no—
326#107—151no—
327#106—52no—
328#106—151no—
329#106—151no—
330C4⋊C8—152no—
331C4⋊C8—152no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102—152no—
336C2×C3×C5—22no—
337C2×C3×C5C2×C22⋊Q811yescharacteristic
338C2×C3×C5#57611yescharacteristic
339C2×C3×C5#57711yescharacteristic
340D15—44no—
341C23×C3C2×C22⋊D511yescharacteristic
342C22×D3—102no—
343C22×D3—104no—
344C22×D3—401no—
345C22×D3—401no—
346C2×C3×C4—22no—
347C2×C3×C4—81no—
348C2×C3×C4—101no—
349C2×C3×C4—101no—
350C2×C3×C4Q8×D512yes—
351C2×C3×C4#71312yes—
352C2×C3×C4C2×C22⋊D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3C2×C22⋊D512yes—
357C2×Dic3C2×C22⋊D512yes—
358D12—54no—
359D12—102no—
360D12—104no—
361C4×D3—402no—
362C4×D3—402no—
363Dic6—82no—
364C3×C8—102no—
365C3⋊C8—101no—
366C3⋊C8—101no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5#89612yes—
370C22×C5C2×D3×D411yescharacteristic
371C2×D5—64no—
372C2×D5—122no—
373C2×D5—122no—
374C2×D5—244no—
375C4×C5—42no—
376C4×C5—62no—
377C4×C5—62no—
378C4×C5—121no—
379C4×C5—121no—
380C4×C5#89612yes—
381C4×C5C2×#23511yescharacteristic
382C4×C5C2×D3×Q811yescharacteristic
383Dic5—41no—
384Dic5—41no—
385C24—301no—
386C2×Q8—62no—
387C2×D4—154no—
388C2×D4—152no—
389C2×D4—302no—
390C2×D4—301no—
391C22×C4—21no—
392C22×C4—302no—
393C22×C4—302no—
394C22×C4C2×D3×D511yescharacteristic
395M16—102no—
396C2×C8—52no—
397C2×C8—151no—
398C2×C8—151no—
399C2×C8—302no—
400C4⋊C4—21no—
401C4⋊C4—31no—
402C4⋊C4—31no—
403C4⋊C4—31no—
404C4⋊C4—31no—
405C4⋊C4—51no—
406C4⋊C4—51no—
407C4⋊C4—62no—
408C4⋊C4—62no—
409C4⋊C4—62no—
410C4⋊C4C2×D3×D512yes—
411C22⋊C4—32no—
412C22⋊C4—61no—
413C22⋊C4—101no—
414C22⋊C4—302no—
415C22⋊C4—302no—
416C42—32no—
417C42—61no—
418C42—101no—
419C3×C5#308111yescharacteristic, complemented, Hall
420C22×C3—21no—
421C22×C3—21no—
422C22×C3#409212yes—
423C22×C3C22×C22⋊D511yescharacteristic
424C2×D3—104no—
425C2×D3—202no—
426C2×D3—202no—
427C2×D3—404no—
428C3×C4—42no—
429C3×C4—201no—
430C3×C4—201no—
431C3×C4#409212yes—
432C3×C4C2×Q8×D511yescharacteristic
433C3×C4C2×#71311yescharacteristic
434Dic3—22no—
435Dic3—22no—
436Dic3—41no—
437Dic3—41no—
438C2×C5—22no—
439C2×C5C2×#89611yescharacteristic
440C2×C5#577411yescharacteristic
441C2×C5#577811yescharacteristic
442D5—124no—
443C23—302no—
444C23—304no—
445C23—1201no—
446C23—1201no—
447C23D3×C22⋊D511yescharacteristic
448Q8—242no—
449D4—154no—
450D4—304no—
451D4—302no—
452C2×C4—22no—
453C2×C4—32no—
454C2×C4—32no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—81no—
458C2×C4—101no—
459C2×C4—101no—
460C2×C4—1202no—
461C2×C4—1202no—
462C2×C4D15⋊Q812yes—
463C2×C4#677312yes—
464C2×C4D3×C22⋊D511yescharacteristic
465C2×C4C22×D3×D511yescharacteristic
466C8—102no—
467C8—301no—
468C8—301no—
469C2×C3—22no—
470C2×C3C2×#409211yescharacteristic
471C2×C3#6616911yescharacteristic
472C2×C3#6617111yescharacteristic
473D3—204no—
474C5#7924211yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—304no—
478C22—602no—
479C22—602no—
480C22—1204no—
481C22#9142412yes—
482C22C2×D3×C22⋊D511yescharacteristic
483C4—42no—
484C4—62no—
485C4—62no—
486C4—121no—
487C4—121no—
488C4—201no—
489C4—201no—
490C4#9142412yes—
491C4C2×D15⋊Q811yescharacteristic
492C4C2×#677311yescharacteristic
493C3#1061520511yescharacteristic, complemented, Sylow
494C2—22no—
495C2—604no—
496C2C2×#9142411yescharacteristic
497C2#1175469811yescharacteristic
498C2#1175509211yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC22×D60C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C5×#5500C2semidirect
4. C3×#65253C2semidirect
5. #11748469C2semidirect
6. #11748441C2semidirect
8. #11747252C2semidirect
9. #11747250C2semidirect
10. #11747248C2semidirect
11. #11747246C2semidirect
20. C5×#890C22semidirect
22. C5×#888C22semidirect
32. C3×#3940C22semidirect
33. C3×#3939C22semidirect
34. #90989C22semidirect
35. #90989C22semidirect
36. #90986C22semidirect
37. #90986C22semidirect
38. Dic3⋊#168C22semidirect
39. Dic3⋊#168C22semidirect
53. #65253D3semidirect
59. C2×D60Q8semidirect
89. #5500D5semidirect
122. #3940C2×D3semidirect
125. #3939C2×D3semidirect
166. #890C2×D5semidirect
168. #888C2×D5semidirect
419. C3×C5#3081semidirect
474. C5#79242semidirect
493. C3#10615205semidirect

Maximal subgroups

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

subgroupindex
C5×#55002
#117545152
C2×#910932
C3×#652532
#117484692
#117484412
#117483962
#117472522
#117472502
#117472482
#117472462
#106152053
#792425