Finite Group Databasebeta

← #14460010

Subgroups — #14460010

Order 1920.

772 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#11756310C211yesmaximal, characteristic
2C5×#5542C211yesmaximal, characteristic, complemented
3C3×D4×#168C211yesmaximal, characteristic, complemented
4#11748566C212yesmaximal, complemented
5#11748557C212yesmaximal, complemented
6#11748463C212yesmaximal, complemented
7#11748393C212yesmaximal, complemented
8#11747101C211yesmaximal, characteristic, complemented
9C4×#6660C211yesmaximal, characteristic, complemented
10#11746966C211yesmaximal, characteristic, complemented
11#11746930C211yesmaximal, characteristic, complemented
12#10615395—31nomaximal, Hall
13C2×#6817C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15#91827—21no—
16#91813C2212yes—
17C4⋊C4×D15—21no—
18#91772—22no—
19C4×D60C2211yescharacteristic
20#91758C2211yescharacteristic
21C5×#936—21no—
22C5×#926C2212yes—
23C5×#924C2212yes—
24C5×#887—21no—
25C5×#879—22no—
26C5×#869C2211yescharacteristic
27C4×C5×Dic6C2211yescharacteristic
28C22×C3×#168C2212yes—
29C2×#6663C2212yes—
30C2×#6660C2211yescharacteristic
31C3×C22⋊#168C2212yes—
32C3×C4⋊#168C2211yescharacteristic
33C3×C4×#168C2211yescharacteristic
34#90988C2212yes—
35#90985C2211yescharacteristic
36#90975C2212yes—
37#90975C2212yes—
38#90975C2212yes—
39#90973C2211yescharacteristic
40#90969C2211yescharacteristic
41#90969C2212yes—
42#79442—51nomaximal, Hall
43C5×#556—31no—
44#65885—31no—
45#65382—31no—
46#65376—31no—
47#65340—32no—
48#65336—32no—
49#65320—31no—
50C4×#688—31no—
51D4×#168D311yescharacteristic, complemented
52#65291—32no—
53#65285—32no—
54C2×C3×C5×D4D411yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×#1220—22no—
57#6817—24no—
58#6817—42no—
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×C4×D15—22no—
62C2×Dic30C2312yes—
63C2×C5×Dic6—21no—
64C2×C5×Dic6C2311yescharacteristic
65C3×C5×C4⋊C4D411yescharacteristic
66C3×C5×C22⋊C4D412yes—
67C3×C42×C5C2311yescharacteristic
68#6719—22no—
69#6714—21no—
70C4⋊Dic15—21no—
71C4⋊Dic15—21no—
72C4⋊Dic15C2311yescharacteristic
73#6712—22no—
74C5×#217—22no—
75C5×#217—22no—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2311yescharacteristic
78C5×C4⋊Dic3C2312yes—
79C5×Dic3⋊C4—21no—
80C5×Dic3⋊C4—22no—
81C4×C5×Dic3—21no—
82C4×C5×Dic3—22no—
83C2×C3×#168—42no—
84C2×C3×#168C2311yescharacteristic
85C2×C3×#168C2312yes—
86C2×C3×#168C2311yescharacteristic
87#6663—42no—
88#6660—22no—
89#5551—51no—
90#5542D511yescharacteristic, complemented
91C3×C8×D4—51no—
92#5116—52no—
93#5113—52no—
94#4849—51no—
95#4846—51no—
96#4733—52no—
97#4723—52no—
98C4×#204—51no—
99#4681—51no—
100C2×#709—32no—
101C5×C4⋊Q8—31no—
102C5×#126—62no—
103C5×#124—61no—
104C5×C22⋊Q8—32no—
105C4×C5×Q8—31no—
106C4×C5×Q8—61no—
107C4×C5×D4C2×D311yescharacteristic
108C5×#117—32no—
109C2×#689—32no—
110C2×#688—31no—
111#4084—61no—
112#4070—32no—
113C22×#168C2×D312yes—
114D5×C4⋊C4—61no—
115#4029—62no—
116C4×D20—31no—
117#4015—31no—
118#3967—31no—
119C22⋊#168C2×D312yes—
120#3942—32no—
121#3942—32no—
122#3942—32no—
123#3941—31no—
124#3941—32no—
125#3940—31no—
126#3939—32no—
127C4⋊#168C2×D311yescharacteristic
128C4×#168C2×D311yescharacteristic
129#3302—151noSylow
130C23×C3×C5C2×D412yes—
131C22×D15—21no—
132C3×C5×D4—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139#1220—44no—
140C2×Dic15—21no—
141C2×Dic15—22no—
142D60—21no—
143D60#4112yes—
144C4×D15—44no—
145C4×D15—42no—
146Dic30—22no—
147Dic30—22no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—22no—
151C5×Dic6—21no—
152C5×Dic6—21no—
153C5×Dic6—42no—
154C3×#168—21no—
155C3×#168—22no—
156C3×#168—21no—
157C2×#235—52no—
158C22×C3×C8—52no—
159C3×C4×D4C2×D511yescharacteristic
160#938—101no—
161#936—21no—
162#926C2×D512yes—
163#924—52no—
164#924C2×D512yes—
165C2×Dic12—52no—
166C2×#204—51no—
167D3×C4⋊C4—101no—
168#887—21no—
169#883—102no—
170#879—22no—
171C4×D12—51no—
172#869—51no—
173#869C2×D511yescharacteristic
174C4×Dic6C2×D511yescharacteristic
175C3×C4⋊C8—51no—
176C3×C22⋊C8—52no—
177C3×C4×C8—51no—
178#821—51no—
179#821—52no—
180#818—52no—
181#817—51no—
182#816—51no—
183#816—52no—
184#816—52no—
185#816—52no—
186C2×C5×Q8—31no—
187C2×C5×Q8—61no—
188C2×C5×D4D1211yescharacteristic
189C22×C4×C5C22×D312yes—
190C2×C22⋊D5—62no—
191#709—64no—
192#709—122no—
193C2×D20—31no—
194C2×C4×D5—62no—
195C2×C4×D5—61no—
196C2×Dic10—32no—
197C5×C4⋊C4—31no—
198C5×C4⋊C4—32no—
199C5×C4⋊C4—61no—
200C5×C4⋊C4—62no—
201C5×C4⋊C4—61no—
202C5×C4⋊C4D1211yescharacteristic
203C5×C22⋊C4—62no—
204C5×C22⋊C4—62no—
205C5×C22⋊C4D1212yes—
206C42×C5—62no—
207C42×C5—61no—
208C42×C5C22×D311yescharacteristic
209C22⋊Dic5—62no—
210#689—122no—
211#688—62no—
212#685—61no—
213C4⋊Dic5—31no—
214C4⋊Dic5—61no—
215C4⋊Dic5—61no—
216#683—62no—
217C2×#168—42no—
218C2×#168C22×D311yescharacteristic
219C2×#168C22×D311yescharacteristic
220C2×#168C22×D312yes—
221#556—31no—
222#547—151no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—51no—
231#416—152no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—22no—
235C22×C3×C5C22×D411yescharacteristic
236C2×D15—22no—
237C2×D15—41no—
238C2×D15—41no—
239C3×C4×C5—22no—
240C3×C4×C5—21no—
241C3×C4×C5#13512yes—
242C3×C4×C5C2×#4111yescharacteristic
243C3×C4×C5H(5,𝔽2)11yescharacteristic
244Dic15—42no—
245Dic15—41no—
246C5×Dic3—41no—
247C5×Dic3—42no—
248C5×Dic3—41no—
249C2×C3×D4C22⋊D511yescharacteristic
250C22×C3×C4C22×D512yes—
251C2×#67—102no—
252#235—104no—
253#235—202no—
254C2×D12—51no—
255C2×C4×D3—101no—
256C2×C4×D3—102no—
257C2×Dic6—21no—
258C2×Dic6—52no—
259C2×Dic6C22×D511yescharacteristic
260C2×C3×C8—51no—
261C2×C3×C8—51no—
262C2×C3×C8—52no—
263C2×C3×C8—202no—
264C3×C4⋊C4C22⋊D511yescharacteristic
265C3×C22⋊C4C22⋊D512yes—
266C3×C42C22×D511yescharacteristic
267#217—22no—
268#217—22no—
269#217—102no—
270(C2×D3)⋊C4—101no—
271C4⋊Dic3—21no—
272C4⋊Dic3—51no—
273C4⋊Dic3—101no—
274C4⋊Dic3—101no—
275C4⋊Dic3C22×D511yescharacteristic
276C4⋊Dic3C22×D512yes—
277Dic3⋊C4—21no—
278Dic3⋊C4—22no—
279Dic3⋊C4—102no—
280C4×Dic3—21no—
281C4×Dic3—22no—
282Dic12—202no—
283#204—102no—
284C23×C5C2×D1212yes—
285C22×D5—61no—
286C5×Q8—61no—
287C5×Q8—61no—
288C5×Q8—122no—
289C5×D4—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—61no—
293C2×C4×C5—62no—
294C2×C4×C5—61no—
295C2×C4×C5C2×D1212yes—
296C2×C4×C5C2×D1211yescharacteristic
297C2×C4×C5C2×D1211yescharacteristic
298C2×C4×C5C23×D311yescharacteristic
299C22⋊D5—124no—
300C2×Dic5—61no—
301C2×Dic5—62no—
302D20—32no—
303D20—61no—
304C4×D5—124no—
305C4×D5—122no—
306Dic10—62no—
307Dic10—62no—
308#168—21no—
309#168—22no—
310#168—21no—
311C2×#41—152no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8—52no—
315C4⋊Q8—31no—
316C4⋊Q8—151no—
317#126—62no—
318#124—61no—
319#123—302no—
320C22⋊Q8—32no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—31no—
324C4×Q8—61no—
325C4×D4—151no—
326C4×D4D3×D511yescharacteristic
327#117—32no—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—151no—
331C4⋊C8—51no—
332#103—152no—
333#103—152no—
334#103—152no—
335#103—151no—
336#102—151no—
337#102—152no—
338C22⋊C8—52no—
339C4×C8—51no—
340C2×C3×C5—42no—
341C2×C3×C5#54611yescharacteristic
342C2×C3×C5C2×#13511yescharacteristic
343C2×C3×C5#57811yescharacteristic
344D15—42no—
345C23×C3C2×C22⋊D512yes—
346C22×D3—101no—
347C3×D4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4C2×C22⋊D512yes—
351C2×C3×C4C2×C22⋊D511yescharacteristic
352C2×C3×C4C2×C22⋊D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—22no—
358C2×Dic3—101no—
359C2×Dic3—102no—
360D12—52no—
361D12—101no—
362C4×D3—204no—
363C4×D3—202no—
364Dic6—21no—
365Dic6—21no—
366Dic6—42no—
367Dic6—102no—
368Dic6—102no—
369C3×C8—101no—
370C3×C8—102no—
371C3×C8—101no—
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5C22×D1211yescharacteristic
376C2×D5—62no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—22no—
381C4×C5—122no—
382C4×C5—121no—
383C4×C5—121no—
384C4×C5#90412yes—
385C4×C5#100411yescharacteristic
386C4×C5D3×#4111yescharacteristic
387Dic5—121no—
388Dic5—122no—
389#41—304no—
390#41—602no—
391C2×Q8—31no—
392C2×Q8—61no—
393C2×Q8—152no—
394C2×D4—151no—
395C2×D4—302no—
396C2×D4#120311yescharacteristic
397C22×C4—301no—
398C22×C4—302no—
399C22×C4C2×D3×D512yes—
400Q16—602no—
401SD16—302no—
402C2×C8—51no—
403C2×C8—51no—
404C2×C8—52no—
405C2×C8—202no—
406C4⋊C4—31no—
407C4⋊C4—32no—
408C4⋊C4—61no—
409C4⋊C4—62no—
410C4⋊C4—61no—
411C4⋊C4—151no—
412C4⋊C4—301no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4#120311yescharacteristic
416C22⋊C4—62no—
417C22⋊C4—62no—
418C22⋊C4—302no—
419C22⋊C4—301no—
420C22⋊C4#120312yes—
421C42—62no—
422C42—61no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3C22×C22⋊D511yescharacteristic
429C2×D3—102no—
430C2×D3—201no—
431C2×D3—201no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4#409612yes—
435C3×C4D5×#4111yescharacteristic
436C3×C4#414911yescharacteristic
437Dic3—42no—
438Dic3—41no—
439Dic3—41no—
440Dic3—201no—
441Dic3—202no—
442C2×C5—42no—
443C2×C5#555411yescharacteristic
444C2×C5C2×#90411yescharacteristic
445C2×C5#575311yescharacteristic
446D5—122no—
447C23—301no—
448C23C2×#120312yes—
449Q8—61no—
450Q8—61no—
451Q8—122no—
452Q8—302no—
453Q8—302no—
454D4—22no—
455D4—152no—
456D4—301no—
457D4—604no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—61no—
461C2×C4—62no—
462C2×C4—61no—
463C2×C4—301no—
464C2×C4—302no—
465C2×C4—604no—
466C2×C4—602no—
467C2×C4C2×#120312yes—
468C2×C4C2×#120311yescharacteristic
469C2×C4C2×#120311yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—101no—
472C8—101no—
473C8—102no—
474C2×C3—42no—
475C2×C3C2×#409611yescharacteristic
476C2×C3#6616311yescharacteristic
477C2×C3#6617211yescharacteristic
478D3—202no—
479C5#7944211yescharacteristic, complemented, Sylow
480C22—22no—
481C22—22no—
482C22—22no—
483C22—302no—
484C22—601no—
485C22—601no—
486C22C22×#120311yescharacteristic
487C4—21no—
488C4—22no—
489C4—121no—
490C4—122no—
491C4—121no—
492C4—601no—
493C4—602no—
494C4#9130312yes—
495C4#9202411yescharacteristic
496C4#9202611yescharacteristic
497C3#1061539511yescharacteristic, complemented, Sylow
498C2—42no—
499C2—602no—
500C2C2×#9130311yescharacteristic
501C2#1175498211yescharacteristic
502C2#1175530611yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radical#11756310C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C5×#5542C2semidirect
3. C3×D4×#168C2semidirect
4. #11748566C2semidirect
5. #11748557C2semidirect
6. #11748463C2semidirect
7. #11748393C2semidirect
8. #11747101C2semidirect
9. C4×#6660C2semidirect
10. #11746966C2semidirect
11. #11746930C2semidirect
51. D4×#168D3semidirect
90. #5542D5semidirect
424. C3×C5#3302semidirect
479. C5#79442semidirect
497. C3#10615395semidirect

Maximal subgroups

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

subgroupindex
#117563102
C5×#55422
C3×D4×#1682
#117485662
#117485572
#117484632
#117483932
#117471012
C4×#66602
#117469662
#117469302
#106153953
#794425