Finite Group Databasebeta

← #14430858

Subgroups — #14430858

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×#5519C211yesmaximal, characteristic, complemented
2C3×#65855C211yesmaximal, characteristic
3#11751100C211yesmaximal, characteristic, complemented
4#11748472C211yesmaximal, characteristic, complemented
5#11748469C211yesmaximal, characteristic, complemented
6#11748366C211yesmaximal, characteristic
7C2×#90964C211yesmaximal, characteristic
8#11746887C212yesmaximal, complemented
9#11746887C212yesmaximal, complemented
10#11746886C212yesmaximal, complemented
11#11746880C212yesmaximal, complemented
12#10615205—31nomaximal, Hall
13C22×C3×D20C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C5×#890—21no—
20C5×#888—21no—
21C5×#878—22no—
22C5×#870C2212yescomplemented
23C5×#869C2212yescomplemented
24C3×#4072C2211yescharacteristic
25C3×#4039—21no—
26C3×#4039—21no—
27C3×D5×C22⋊C4—22no—
28C3×C4×D20C2212yes—
29C3×C4×D20C2212yes—
30C4⋊(C3⋊#168)C2212yescomplemented
31C4⋊(C3⋊#168)C2212yescomplemented
32#90989C2211yescharacteristic, complemented
33#90989C2212yescomplemented
34#90989C2211yescharacteristic, complemented
35#90986C2211yescharacteristic, complemented
36#90986C2212yescomplemented
37#90986C2211yescharacteristic, complemented
38#90964C2212yes—
39#90964C2212yes—
40#90964C2212yes—
41#90964C2212yes—
42#82539—51nomaximal, Hall
43C5×#544—31no—
44#65855D311yescharacteristic
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#65253—31no—
54C23×C3×D5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C5×Dic3—21no—
57C2×C5×Dic6—22no—
58C2×C3×D20—21no—
59C2×C3×D20—22no—
60C2×C3×D20Q814yescomplemented
61C2×C3×D20C2312yes—
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—22no—
64C3×C5×C4⋊C4D411yescharacteristic
65C3×C5×C4⋊C4D411yescharacteristic
66C3×C5×C22⋊C4D412yes—
67C3×C42×C5C2312yes—
68#6710—22no—
69C2×C3⋊#168—22no—
70C2×C3⋊#168C2311yescharacteristic
71C2×C3⋊#168C2312yes—
72C2×C3⋊#168C2311yescharacteristic
73C5×#217—21no—
74C5×C4⋊Dic3—22no—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2312yes—
78C5×C4⋊Dic3C2311yescharacteristic
79C5×Dic3⋊C4—22no—
80C5×Dic3⋊C4—22no—
81C4×C5×Dic3—21no—
82C3×C22⋊Dic5—21no—
83C3×#685—22no—
84C3×#685—22no—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×C4⋊Dic5C2311yescharacteristic
87C3×C4×Dic5—21no—
88C3×#518—51no—
89#5519D511yescharacteristic, complemented
90#5215—51no—
91C2×#832—51no—
92#5009—52no—
93#5009—52no—
94#5008—52no—
95#5007—52no—
96#4999—51no—
97#4998—51no—
98#4995—51no—
99C22×D20C2×D311yescharacteristic
100C5×C4⋊Q8—32no—
101C5×C4⋊Q8—61no—
102C5×#125—32no—
103C5×#125—61no—
104C5×C22⋊Q8—62no—
105C5×#117—31no—
106C5×#117C2×D311yescharacteristic
107C2×C5×C4⋊C4—31no—
108#4072C2×D311yescharacteristic
109C2×#681—31no—
110C22×#168—31no—
111#4039—21no—
112#4039—21no—
113D5×C22⋊C4—22no—
114C4×D20C2×D312yes—
115C4×D20C2×D312yes—
116#3941—32no—
117#3941—32no—
118#3941—32no—
119#3941—32no—
120#3940—31no—
121#3940—31no—
122#3940—32no—
123#3939—31no—
124#3939—31no—
125#3939—32no—
126C4⋊#168—32no—
127C4⋊#168—32no—
128#3081—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×C3×D5—22no—
131C22×C3×D5—24no—
132C22×C3×D5—81no—
133C22×C3×D5—81no—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×Q812yes—
138C2×C3×C4×C5#4112yes—
139C2×C3×C4×C5C2411yescharacteristic
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—81no—
144C5×Dic6—82no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C3×D20—24no—
148C3×D20—22no—
149C3×D20C2×Q814yes—
150C3×C4×D5—82no—
151C3×C4×D5—82no—
152C3⋊#168—21no—
153C3⋊#168—21no—
154C3⋊#168—22no—
155C22×C3×D4—51no—
156C3×C4×D4—52no—
157C3×C4×D4—52no—
158C3×C4×D4—101no—
159C3×C4×D4—101no—
160C3×#117—51no—
161C3×#117C2×D511yescharacteristic
162C2×C3×C22⋊C4—102no—
163#926C2×D511yescharacteristic
164C2×C4⋊Dic3C2×D511yescharacteristic
165C2×#208—51no—
166C22×C3⋊C8—51no—
167#890—21no—
168#888—21no—
169#878—22no—
170#870C2×D512yescomplemented
171#869C2×D512yescomplemented
172#832—52no—
173#832—52no—
174#832—52no—
175#832—52no—
176#808—52no—
177#808—51no—
178#808—51no—
179#807—52no—
180#807—51no—
181#807—51no—
182C4⋊(C3⋊C8)—52no—
183C4⋊(C3⋊C8)—52no—
184C23×D5—21no—
185C2×C5×Q8—62no—
186C22×C4×C5—61no—
187C22×C4×C5C22×D311yescharacteristic
188C2×D20—22no—
189C2×D20—21no—
190C2×D20Dic614yescomplemented
191C2×D20C22×D312yes—
192C2×C4×D5—22no—
193C2×C4×D5—22no—
194C5×C4⋊C4—32no—
195C5×C4⋊C4—31no—
196C5×C4⋊C4—31no—
197C5×C4⋊C4—61no—
198C5×C4⋊C4—62no—
199C5×C4⋊C4—62no—
200C5×C4⋊C4—62no—
201C5×C4⋊C4#6711yescharacteristic
202C5×C4⋊C4#6711yescharacteristic
203C5×C22⋊C4—61no—
204C5×C22⋊C4#6712yes—
205C42×C5—61no—
206C42×C5C22×D312yes—
207C22⋊Dic5—21no—
208#685—22no—
209#685—22no—
210C4⋊Dic5C22×D311yescharacteristic
211C4⋊Dic5C22×D311yescharacteristic
212C4×Dic5—21no—
213#681—62no—
214C2×#168—31no—
215C2×#168—32no—
216C2×#168—31no—
217C2×#168—62no—
218#544—31no—
219#518—51no—
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428—151no—
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×C3×D5—24no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—84no—
237C3×C4×C5—22no—
238C3×C4×C5—22no—
239C3×C4×C5C22⋊Q812yes—
240C3×C4×C5C22×Q811yescharacteristic
241C3×C4×C5C2×#4111yescharacteristic
242C3×Dic5—41no—
243C3×Dic5—41no—
244C5×Dic3—41no—
245C5×Dic3—42no—
246C5×Dic3—41no—
247C24×C3—101no—
248C2×C3×D4—54no—
249C2×C3×D4—52no—
250C2×C3×D4—102no—
251C2×C3×D4—101no—
252C22×C3×C4—102no—
253C22×C3×C4—102no—
254C22×C3×C4C22×D511yescharacteristic
255C22×Dic3—21no—
256C2×Dic6—22no—
257C3×C4⋊C4—51no—
258C3×C4⋊C4—51no—
259C3×C4⋊C4C22⋊D511yescharacteristic
260C3×C4⋊C4C22⋊D511yescharacteristic
261C3×C22⋊C4—101no—
262C3×C22⋊C4—102no—
263C3×C22⋊C4—102no—
264C3×C22⋊C4C22⋊D512yes—
265C3×C42—101no—
266C3×C42C22×D512yes—
267#217—21no—
268C4⋊Dic3—22no—
269C4⋊Dic3—21no—
270C4⋊Dic3C22×D511yescharacteristic
271C4⋊Dic3C22×D512yes—
272C4⋊Dic3C22×D511yescharacteristic
273Dic3⋊C4—22no—
274Dic3⋊C4—22no—
275C4×Dic3—21no—
276#208—102no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—52no—
279C2×C3⋊C8—51no—
280C2×C3⋊C8—102no—
281C23×C5C2×#6711yescharacteristic
282C22×D5—22no—
283C22×D5—24no—
284C22×D5—81no—
285C22×D5—81no—
286C5×Q8—242no—
287C2×C4×C5—61no—
288C2×C4×C5—61no—
289C2×C4×C5—62no—
290C2×C4×C5—241no—
291C2×C4×C5C2×Dic612yes—
292C2×C4×C5#23512yes—
293C2×C4×C5C2×#6712yes—
294C2×C4×C5C2×#6712yes—
295C2×C4×C5C2×#6711yescharacteristic
296C2×C4×C5C23×D311yescharacteristic
297C2×Dic5—21no—
298C2×Dic5—21no—
299D20—24no—
300D20—22no—
301D20C2×Dic614yes—
302C4×D5—82no—
303C4×D5—82no—
304#168—61no—
305#168—61no—
306#168—62no—
307C22×D4—51no—
308C2×M16—151no—
309C22×C8—151no—
310C4⋊Q8—32no—
311C4⋊Q8—61no—
312#125—32no—
313#125—61no—
314C22⋊Q8—62no—
315C4×D4—52no—
316C4×D4—52no—
317C4×D4—101no—
318C4×D4—101no—
319#117—31no—
320#117—51no—
321#117D3×D511yescharacteristic
322C2×C4⋊C4—31no—
323C2×C22⋊C4—102no—
324#107—151no—
325#107—151no—
326#107—152no—
327#106—151no—
328#106—151no—
329#106—152no—
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
340C3×D5—44no—
341C23×C3—102no—
342C23×C3—104no—
343C23×C3—401no—
344C23×C3—401no—
345C23×C3C2×C22⋊D511yescharacteristic
346C3×D4—54no—
347C3×D4—102no—
348C3×D4—104no—
349C2×C3×C4—101no—
350C2×C3×C4—101no—
351C2×C3×C4—402no—
352C2×C3×C4—402no—
353C2×C3×C4Q8×D512yes—
354C2×C3×C4#71312yes—
355C2×C3×C4C2×C22⋊D512yes—
356C2×C3×C4C2×C22⋊D512yes—
357C2×C3×C4C2×C22⋊D511yescharacteristic
358C2×C3×C4C23×D511yescharacteristic
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—81no—
363Dic6—82no—
364C3⋊C8—101no—
365C3⋊C8—101no—
366C3⋊C8—102no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5#92412yes—
370C22×C5C22×#6711yescharacteristic
371C2×D5—24no—
372C2×D5—42no—
373C2×D5—42no—
374C2×D5—84no—
375C4×C5—22no—
376C4×C5—22no—
377C4×C5—122no—
378C4×C5—121no—
379C4×C5—121no—
380C4×C5#92412yes—
381C4×C5C22×Dic611yescharacteristic
382C4×C5C2×#23511yescharacteristic
383Dic5—41no—
384Dic5—41no—
385C24—101no—
386C2×Q8—62no—
387C2×D4—54no—
388C2×D4—52no—
389C2×D4—102no—
390C2×D4—101no—
391C22×C4—61no—
392C22×C4—102no—
393C22×C4—102no—
394C22×C4C2×D3×D511yescharacteristic
395M16—302no—
396C2×C8—151no—
397C2×C8—152no—
398C2×C8—151no—
399C2×C8—302no—
400C4⋊C4—32no—
401C4⋊C4—31no—
402C4⋊C4—31no—
403C4⋊C4—51no—
404C4⋊C4—51no—
405C4⋊C4—61no—
406C4⋊C4—62no—
407C4⋊C4—62no—
408C4⋊C4—62no—
409C4⋊C4#120111yescharacteristic
410C4⋊C4#120111yescharacteristic
411C22⋊C4—61no—
412C22⋊C4—101no—
413C22⋊C4—102no—
414C22⋊C4—102no—
415C22⋊C4#120112yes—
416C42—61no—
417C42—101no—
418C42C2×D3×D512yes—
419C3×C5#308111yescharacteristic, complemented, Hall
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—104no—
423C22×C3—202no—
424C22×C3—202no—
425C22×C3—404no—
426C22×C3#409212yes—
427C22×C3C22×C22⋊D511yescharacteristic
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—201no—
431C3×C4—201no—
432C3×C4#409212yes—
433C3×C4C2×Q8×D511yescharacteristic
434C3×C4C2×#71311yescharacteristic
435Dic3—41no—
436Dic3—42no—
437Dic3—41no—
438C2×C5—22no—
439C2×C5C2×#92411yescharacteristic
440C2×C5#583511yescharacteristic
441C2×C5#583611yescharacteristic
442D5—44no—
443C23—102no—
444C23—104no—
445C23—401no—
446C23—401no—
447C23C2×#120111yescharacteristic
448Q8—242no—
449D4—54no—
450D4—102no—
451D4—104no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—62no—
455C2×C4—101no—
456C2×C4—101no—
457C2×C4—241no—
458C2×C4—402no—
459C2×C4—402no—
460C2×C4D5×Dic612yes—
461C2×C4#677312yes—
462C2×C4C2×#120112yes—
463C2×C4C2×#120112yes—
464C2×C4C2×#120111yescharacteristic
465C2×C4C22×D3×D511yescharacteristic
466C8—301no—
467C8—301no—
468C8—302no—
469C2×C3—22no—
470C2×C3—204no—
471C2×C3C2×#409211yescharacteristic
472C2×C3#6616911yescharacteristic
473C2×C3#6617111yescharacteristic
474C5#8253911yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—104no—
478C22—202no—
479C22—202no—
480C22—404no—
481C22#9135912yes—
482C22C22×#120111yescharacteristic
483C4—22no—
484C4—22no—
485C4—122no—
486C4—121no—
487C4—121no—
488C4—201no—
489C4—201no—
490C4#9135912yes—
491C4C2×D5×Dic611yescharacteristic
492C4C2×#677311yescharacteristic
493C3#1061520511yescharacteristic, complemented, Sylow
494C2—22no—
495C2—204no—
496C2C2×#9135911yescharacteristic
497C2#1175530111yescharacteristic
498C2#1175530311yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D20C22
hypercenter#117D3×D5
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5519C2semidirect
3. #11751100C2semidirect
4. #11748472C2semidirect
5. #11748469C2semidirect
8. #11746887C2semidirect
9. #11746887C2semidirect
10. #11746886C2semidirect
11. #11746880C2semidirect
22. C5×#870C22semidirect
23. C5×#869C22semidirect
30. C4⋊(C3⋊#168)C22semidirect
31. C4⋊(C3⋊#168)C22semidirect
32. #90989C22semidirect
33. #90989C22semidirect
34. #90989C22semidirect
35. #90986C22semidirect
36. #90986C22semidirect
37. #90986C22semidirect
60. C2×C3×D20Q8semidirect
89. #5519D5semidirect
170. #870C2×D5semidirect
171. #869C2×D5semidirect
190. C2×D20Dic6semidirect
419. C3×C5#3081semidirect
474. C5#82539semidirect
493. C3#10615205semidirect

Maximal subgroups

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

subgroupindex
C5×#55192
C3×#658552
#117511002
#117484722
#117484692
#117483662
C2×#909642
#117468872
#117468862
#117468802
#106152053
#825395