Finite Group Databasebeta

← #14430860

Subgroups — #14430860

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×#5521C211yesmaximal, characteristic
2C3×#65853C211yesmaximal, characteristic, complemented
3#11751100C211yesmaximal, characteristic, complemented
4#11748470C211yesmaximal, characteristic, complemented
5#11748469C211yesmaximal, characteristic, complemented
6#11748386C211yesmaximal, characteristic
7C2×#90966C211yesmaximal, characteristic
8#11746902C212yesmaximal, complemented
9#11746902C212yesmaximal, complemented
10#11746900C212yesmaximal, complemented
11#11746882C212yesmaximal, complemented
12#10614270—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C5×#893—21no—
19C5×#893—21no—
20C5×D3×C22⋊C4—22no—
21C4×C5×D12C2212yes—
22C4×C5×D12C2212yes—
23C3×#4072C2211yescharacteristic
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C3×#4036—21no—
26C3×#4034—21no—
27C3×#4024—22no—
28C3×#4016C2212yescomplemented
29C3×#4015C2212yescomplemented
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#90966C2212yes—
39#90966C2212yes—
40#90966C2212yes—
41#90966C2212yes—
42#83474—51nomaximal, Hall
43C5×#518—31no—
44#65853D311yescharacteristic, complemented
45#65504—31no—
46C2×#3964—31no—
47#65298—32no—
48#65298—32no—
49#65297—32no—
50#65296—32no—
51#65288—31no—
52#65287—31no—
53#65284—31no—
54C23×C5×D3—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×C5×D12—21no—
57C2×C5×D12—22no—
58C2×C5×D12Q814yescomplemented
59C2×C5×D12C2312yes—
60C2×C4×C5×D3—22no—
61C2×C4×C5×D3—22no—
62C22×C3×Dic5—21no—
63C2×C3×Dic10—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×(C2×D3)⋊C4—22no—
75C5×(C2×D3)⋊C4—22no—
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2311yescharacteristic
78C4×C5×Dic3—21no—
79C3×C22⋊Dic5—21no—
80C3×C4⋊Dic5—22no—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5C2311yescharacteristic
83C3×C4⋊Dic5C2312yes—
84C3×C4⋊Dic5C2311yescharacteristic
85C3×#683—22no—
86C3×#683—22no—
87C3×C4×Dic5—21no—
88C3×#544—51no—
89#5521D511yescharacteristic
90#5087—52no—
91#5084—52no—
92#5066—52no—
93#5066—52no—
94#5001—51no—
95#4999—51no—
96#4998—51no—
97C2×#809—51no—
98#4964—51no—
99C22×C5×D4—31no—
100C4×C5×D4—32no—
101C4×C5×D4—32no—
102C4×C5×D4—61no—
103C4×C5×D4—61no—
104C5×#117—31no—
105C5×#117C2×D311yescharacteristic
106C2×C5×C22⋊C4—62no—
107#4072C2×D311yescharacteristic
108C2×C4⋊Dic5C2×D311yescharacteristic
109C2×#681—31no—
110C22×#168—31no—
111#4036—21no—
112#4034—21no—
113#4024—22no—
114#4016C2×D312yescomplemented
115#4015C2×D312yescomplemented
116#3964—32no—
117#3964—32no—
118#3964—32no—
119#3964—32no—
120#3940—32no—
121#3940—31no—
122#3940—31no—
123#3939—32no—
124#3939—31no—
125#3939—31no—
126C4⋊#168—32no—
127C4⋊#168—32no—
128#3081—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×C5×D3—22no—
131C22×C5×D3—24no—
132C22×C5×D3—81no—
133C22×C5×D3—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—
142C5×D12—24no—
143C5×D12—22no—
144C5×D12C2×Q814yes—
145C4×C5×D3—82no—
146C4×C5×D3—82no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—81no—
151C3×Dic10—82no—
152C3⋊#168—21no—
153C3⋊#168—21no—
154C3⋊#168—22no—
155C22×D12C2×D511yescharacteristic
156C3×C4⋊Q8—52no—
157C3×C4⋊Q8—101no—
158C3×#125—52no—
159C3×#125—101no—
160C3×C22⋊Q8—102no—
161C3×#117—51no—
162C3×#117C2×D511yescharacteristic
163C2×C3×C4⋊C4—51no—
164#926C2×D511yescharacteristic
165C2×#208—51no—
166C22×C3⋊C8—51no—
167#893—21no—
168#893—21no—
169D3×C22⋊C4—22no—
170C4×D12C2×D512yes—
171C4×D12C2×D512yes—
172#809—52no—
173#809—52no—
174#809—52no—
175#809—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—
184C24×C5—61no—
185C2×C5×D4—34no—
186C2×C5×D4—32no—
187C2×C5×D4—62no—
188C2×C5×D4—61no—
189C22×C4×C5—62no—
190C22×C4×C5—62no—
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—21no—
193C2×Dic10—22no—
194C5×C4⋊C4—31no—
195C5×C4⋊C4—31no—
196C5×C4⋊C4#6711yescharacteristic
197C5×C4⋊C4#6711yescharacteristic
198C5×C22⋊C4—61no—
199C5×C22⋊C4—62no—
200C5×C22⋊C4—62no—
201C5×C22⋊C4#6712yes—
202C42×C5—61no—
203C42×C5C22×D312yes—
204C22⋊Dic5—21no—
205C4⋊Dic5—22no—
206C4⋊Dic5—21no—
207C4⋊Dic5C22×D311yescharacteristic
208C4⋊Dic5C22×D312yes—
209C4⋊Dic5C22×D311yescharacteristic
210#683—22no—
211#683—22no—
212C4×Dic5—21no—
213#681—62no—
214C2×#168—31no—
215C2×#168—32no—
216C2×#168—31no—
217C2×#168—62no—
218#544—51no—
219#518—31no—
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×C5×D3—24no—
234C2×C5×D3—42no—
235C2×C5×D3—42no—
236C2×C5×D3—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—42no—
244C3×Dic5—41no—
245C5×Dic3—41no—
246C5×Dic3—41no—
247C23×D3—21no—
248C2×C3×Q8—102no—
249C22×C3×C4—101no—
250C22×C3×C4C22×D511yescharacteristic
251C2×D12—22no—
252C2×D12—21no—
253C2×D12Dic1014yescomplemented
254C2×D12C22×D512yes—
255C2×C4×D3—22no—
256C2×C4×D3—22no—
257C3×C4⋊C4—52no—
258C3×C4⋊C4—51no—
259C3×C4⋊C4—51no—
260C3×C4⋊C4—102no—
261C3×C4⋊C4—102no—
262C3×C4⋊C4—101no—
263C3×C4⋊C4—102no—
264C3×C4⋊C4C22⋊D511yescharacteristic
265C3×C4⋊C4C22⋊D511yescharacteristic
266C3×C22⋊C4—101no—
267C3×C22⋊C4C22⋊D512yes—
268C3×C42—101no—
269C3×C42C22×D512yes—
270#217—21no—
271(C2×D3)⋊C4—22no—
272(C2×D3)⋊C4—22no—
273C4⋊Dic3C22×D511yescharacteristic
274C4⋊Dic3C22×D511yescharacteristic
275C4×Dic3—21no—
276#208—102no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—52no—
279C2×C3⋊C8—51no—
280C2×C3⋊C8—102no—
281C23×C5—62no—
282C23×C5—64no—
283C23×C5—241no—
284C23×C5—241no—
285C23×C5C2×#6711yescharacteristic
286C5×D4—34no—
287C5×D4—64no—
288C5×D4—62no—
289C2×C4×C5—61no—
290C2×C4×C5—61no—
291C2×C4×C5—242no—
292C2×C4×C5—242no—
293C2×C4×C5D3×Q812yes—
294C2×C4×C5#23912yes—
295C2×C4×C5C2×#6712yes—
296C2×C4×C5C2×#6712yes—
297C2×C4×C5C2×#6711yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—22no—
302C2×Dic5—81no—
303Dic10—82no—
304#168—61no—
305#168—61no—
306#168—62no—
307C22×D4—31no—
308C2×M16—151no—
309C22×C8—151no—
310C4⋊Q8—52no—
311C4⋊Q8—101no—
312#125—52no—
313#125—101no—
314C22⋊Q8—102no—
315C4×D4—32no—
316C4×D4—32no—
317C4×D4—61no—
318C4×D4—61no—
319#117—31no—
320#117—51no—
321#117D3×D511yescharacteristic
322C2×C4⋊C4—51no—
323C2×C22⋊C4—62no—
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
340C5×D3—44no—
341C23×C3C2×C22⋊D511yescharacteristic
342C22×D3—22no—
343C22×D3—24no—
344C22×D3—81no—
345C22×D3—81no—
346C3×Q8—402no—
347C2×C3×C4—101no—
348C2×C3×C4—101no—
349C2×C3×C4—102no—
350C2×C3×C4—401no—
351C2×C3×C4C2×Dic1012yes—
352C2×C3×C4#70912yes—
353C2×C3×C4C2×C22⋊D512yes—
354C2×C3×C4C2×C22⋊D512yes—
355C2×C3×C4C2×C22⋊D511yescharacteristic
356C2×C3×C4C23×D511yescharacteristic
357C2×Dic3—21no—
358C2×Dic3—21no—
359D12—22no—
360D12—24no—
361D12C2×Dic1014yes—
362C4×D3—82no—
363C4×D3—82no—
364C3⋊C8—101no—
365C3⋊C8—101no—
366C3⋊C8—102no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5—64no—
370C22×C5—122no—
371C22×C5—122no—
372C22×C5—244no—
373C22×C5#94612yes—
374C22×C5C22×#6711yescharacteristic
375C4×C5—22no—
376C4×C5—22no—
377C4×C5—121no—
378C4×C5—121no—
379C4×C5#94612yes—
380C4×C5C2×D3×Q811yescharacteristic
381C4×C5C2×#23911yescharacteristic
382Dic5—41no—
383Dic5—42no—
384Dic5—41no—
385C24—61no—
386C2×Q8—102no—
387C2×D4—34no—
388C2×D4—32no—
389C2×D4—62no—
390C2×D4—61no—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—101no—
394C22×C4C2×D3×D511yescharacteristic
395M16—302no—
396C2×C8—151no—
397C2×C8—152no—
398C2×C8—151no—
399C2×C8—302no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—52no—
403C4⋊C4—51no—
404C4⋊C4—51no—
405C4⋊C4—101no—
406C4⋊C4—102no—
407C4⋊C4—102no—
408C4⋊C4—102no—
409C4⋊C4#120111yescharacteristic
410C4⋊C4#120111yescharacteristic
411C22⋊C4—61no—
412C22⋊C4—62no—
413C22⋊C4—62no—
414C22⋊C4—101no—
415C22⋊C4#120112yes—
416C42—61no—
417C42—101no—
418C42C2×D3×D512yes—
419C3×C5#308111yescharacteristic, complemented, Hall
420C22×C3—21no—
421C22×C3—21no—
422C22×C3#407012yes—
423C22×C3C22×C22⋊D511yescharacteristic
424C2×D3—24no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—84no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—202no—
431C3×C4—201no—
432C3×C4—201no—
433C3×C4#407012yes—
434C3×C4C22×Dic1011yescharacteristic
435C3×C4C2×#70911yescharacteristic
436Dic3—41no—
437Dic3—41no—
438C2×C5—22no—
439C2×C5—124no—
440C2×C5C2×#94611yescharacteristic
441C2×C5#583511yescharacteristic
442C2×C5#583711yescharacteristic
443C23—62no—
444C23—64no—
445C23—241no—
446C23—241no—
447C23C2×#120111yescharacteristic
448Q8—402no—
449D4—34no—
450D4—62no—
451D4—64no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—101no—
455C2×C4—101no—
456C2×C4—102no—
457C2×C4—242no—
458C2×C4—242no—
459C2×C4—401no—
460C2×C4D3×Dic1012yes—
461C2×C4#676912yes—
462C2×C4C2×#120112yes—
463C2×C4C2×#120112yes—
464C2×C4C2×#120111yescharacteristic
465C2×C4C22×D3×D511yescharacteristic
466C8—301no—
467C8—301no—
468C8—302no—
469C2×C3—22no—
470C2×C3C2×#407011yescharacteristic
471C2×C3#6616911yescharacteristic
472C2×C3#6617011yescharacteristic
473D3—44no—
474C5#8347411yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—64no—
478C22—122no—
479C22—122no—
480C22—244no—
481C22#9136912yes—
482C22C22×#120111yescharacteristic
483C4—22no—
484C4—22no—
485C4—121no—
486C4—121no—
487C4—202no—
488C4—201no—
489C4—201no—
490C4#9136912yes—
491C4C2×D3×Dic1011yescharacteristic
492C4C2×#676911yescharacteristic
493C3#1061427011yescharacteristic, complemented, Sylow
494C2—22no—
495C2—124no—
496C2C2×#9136911yescharacteristic
497C2#1175530111yescharacteristic
498C2#1175530411yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D12C22
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
2. C3×#65853C2semidirect
3. #11751100C2semidirect
4. #11748470C2semidirect
5. #11748469C2semidirect
8. #11746902C2semidirect
9. #11746902C2semidirect
10. #11746900C2semidirect
11. #11746882C2semidirect
28. C3×#4016C22semidirect
29. C3×#4015C22semidirect
30. C4⋊(C3⋊#168)C22semidirect
31. C4⋊(C3⋊#168)C22semidirect
32. #90989C22semidirect
33. #90989C22semidirect
34. #90989C22semidirect
35. #90986C22semidirect
36. #90986C22semidirect
37. #90986C22semidirect
44. #65853D3semidirect
58. C2×C5×D12Q8semidirect
114. #4016C2×D3semidirect
115. #4015C2×D3semidirect
253. C2×D12Dic10semidirect
419. C3×C5#3081semidirect
474. C5#83474semidirect
493. C3#10614270semidirect

Maximal subgroups

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

subgroupindex
C5×#55212
C3×#658532
#117511002
#117484702
#117484692
#117483862
C2×#909662
#117469022
#117469002
#117468822
#106142703
#834745