Finite Group Databasebeta

← #14459948

Subgroups — #14459948

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#11756491C211yesmaximal, characteristic, complemented
2#11756485C211yesmaximal, characteristic
3C3×C5×#487C211yesmaximal, characteristic, complemented
4#11751191C211yesmaximal, characteristic, complemented
5#11751188C211yesmaximal, characteristic, complemented
6#11750916C212yesmaximal, complemented
7#11750914C212yesmaximal, complemented
8#11750909C212yesmaximal, complemented
9#11750905C212yesmaximal, complemented
10C4×#6706C211yesmaximal, characteristic, complemented
11C8×D60C211yesmaximal, characteristic, complemented
12#10613345—31nomaximal, Hall
13C2×#6821C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C5×C4⋊Q8C2211yescharacteristic
16#91836—21no—
17#91835C2212yes—
18Q8×Dic15—21no—
19C2×#6718C2212yes—
20C2×#6706C2211yescharacteristic
21C2×C8×D15C2212yes—
22#91787—22no—
23#91786C2212yes—
24#91784—21no—
25#91783—22no—
26#91781C2212yes—
27C4⋊C4×D15—21no—
28C4×D60C2211yescharacteristic
29C4×D60C2211yescharacteristic
30C4×Dic30C2211yescharacteristic
31C3×C5×#103C2212yes—
32C3×C5×#103C2212yes—
33C3×C4×C5×C8C2211yescharacteristic
34#91119C2212yes—
35#91105C2211yescharacteristic
36#91104C2212yes—
37#91101C2211yescharacteristic
38#91100C2211yescharacteristic
39#91093C2212yes—
40#91091C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#81614—51nomaximal, Hall
43#66066—31no—
44#66060—31no—
45C5×#487D311yescharacteristic, complemented
46#65379—31no—
47#65376—31no—
48#65104—32no—
49#65102—32no—
50#65099—32no—
51#65093—32no—
52C4×#677—31no—
53C8×D20—31no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8C2312yes—
56#6821—24no—
57#6821—42no—
58C2×D60—22no—
59C2×D60D411yescharacteristic
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×C4×D15—22no—
63C2×C4×D15C2312yes—
64C2×Dic30C2311yescharacteristic
65C2×C3×C5×C8C2311yescharacteristic
66C2×C3×C5×C8C2311yescharacteristic
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4—21no—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4C2312yes—
71C3×C42×C5C2311yescharacteristic
72#6718—42no—
73#6714—22no—
74#6714—22no—
75#6714—22no—
76#6714—21no—
77#6714D412yes—
78C4⋊Dic15—22no—
79C4⋊Dic15D411yescharacteristic
80C4⋊Dic15C2311yescharacteristic
81C4⋊Dic15C2311yescharacteristic
82#6712—21no—
83#6712—22no—
84C4×Dic15—21no—
85C4×Dic15—22no—
86C2×C3⋊#168C2312yes—
87#6706—22no—
88C8×D15—42no—
89#5732—51no—
90#5726—51no—
91C3×#487D511yescharacteristic, complemented
92#5090—51no—
93#5087—51no—
94#4815—52no—
95#4813—52no—
96#4808—52no—
97#4804—52no—
98C4×#204—51no—
99C8×D12—51no—
100C2×#713—32no—
101C5×C4⋊Q8C2×D311yescharacteristic
102C5×C4⋊Q8C2×D311yescharacteristic
103#4093—61no—
104#4092—32no—
105Q8×Dic5—61no—
106C2×#689—32no—
107C2×#677—31no—
108C2×C8×D5—32no—
109#4044—62no—
110#4043—32no—
111#4041—61no—
112#4040—62no—
113#4038—32no—
114D5×C4⋊C4—61no—
115C4×D20—31no—
116C4×D20—31no—
117C4×Dic10—31no—
118C5×#103C2×D312yes—
119C5×#103C2×D312yes—
120C4×C5×C8C2×D311yescharacteristic
121#3967—32no—
122#3953—31no—
123#3952—32no—
124#3949—31no—
125#3948—31no—
126#3941—32no—
127#3939—32no—
128C4⋊#168—31no—
129#3302—151noSylow
130C22×D15—21no—
131C22×D15C2×D412yes—
132C3×C5×Q8—22no—
133C3×C5×Q8—22no—
134C3×C5×Q8—42no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15C2×D412yes—
144D60—22no—
145D60—21no—
146D60—44no—
147D60#4112yes—
148C4×D15—22no—
149C4×D15—22no—
150C4×D15—44no—
151C4×D15—42no—
152Dic30—21no—
153Dic30—21no—
154C3×C5×C8—21no—
155C3×C5×C8—21no—
156C3⋊#168—22no—
157C2×#239—52no—
158C3×C4⋊Q8C2×D511yescharacteristic
159C3×C4⋊Q8C2×D511yescharacteristic
160#947—101no—
161#946—52no—
162Q8×Dic3—101no—
163C2×#216—52no—
164C2×#204—51no—
165C2×D3×C8—52no—
166#898—102no—
167#897—52no—
168#895—101no—
169#894—102no—
170#892—52no—
171D3×C4⋊C4—101no—
172C4×D12—51no—
173C4×D12—51no—
174C4×Dic6—51no—
175C3×#103C2×D512yes—
176C3×#103C2×D512yes—
177C3×C4×C8C2×D511yescharacteristic
178#835—52no—
179#821—51no—
180(C2×D3)⋊C8—52no—
181#817—51no—
182#816—51no—
183#809—52no—
184#807—52no—
185C4⋊(C3⋊C8)—51no—
186C2×C5×Q8—21no—
187C2×C5×Q8C22×D312yes—
188#713—64no—
189#713—122no—
190C2×D20—31no—
191C2×D20—31no—
192C2×D20—62no—
193C2×C4×D5—32no—
194C2×C4×D5—62no—
195C2×C4×D5—61no—
196C2×Dic10—31no—
197C2×C5×C8C22×D311yescharacteristic
198C2×C5×C8C22×D311yescharacteristic
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4C22×D312yes—
203C42×C5C22×D311yescharacteristic
204#689—122no—
205#685—32no—
206#685—62no—
207#685—62no—
208#685—62no—
209#685—61no—
210C4⋊Dic5—31no—
211C4⋊Dic5—31no—
212C4⋊Dic5—31no—
213C4⋊Dic5—62no—
214#683—62no—
215#683—61no—
216C4×Dic5—62no—
217C4×Dic5—61no—
218C2×#168—32no—
219#677—62no—
220C8×D5—122no—
221#556—151no—
222#547—151no—
223#487D1511yescharacteristic, complemented
224#485—152no—
225#474—151no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—151no—
231#416—152no—
232C22×C3×C5C22×D411yescharacteristic
233C2×D15—22no—
234C2×D15—22no—
235C2×D15—22no—
236C2×D15—22no—
237C2×D15—41no—
238C2×D15—41no—
239C3×C4×C5—21no—
240C3×C4×C5—42no—
241C3×C4×C5—42no—
242C3×C4×C5#13512yes—
243C3×C4×C5C2×#4111yescharacteristic
244C3×C4×C5H(5,𝔽2)11yescharacteristic
245Dic15—22no—
246Dic15—41no—
247Dic15—41no—
248Dic15—41no—
249C2×C3×Q8—21no—
250C2×C3×Q8C22×D512yes—
251#239—104no—
252#239—202no—
253C2×D12—51no—
254C2×D12—51no—
255C2×D12—102no—
256C2×C4×D3—52no—
257C2×C4×D3—102no—
258C2×C4×D3—101no—
259C2×Dic6—51no—
260C2×C3×C8C22×D511yescharacteristic
261C2×C3×C8C22×D511yescharacteristic
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4C22×D512yes—
266C3×C42C22×D511yescharacteristic
267#216—202no—
268(C2×D3)⋊C4—52no—
269(C2×D3)⋊C4—102no—
270(C2×D3)⋊C4—102no—
271(C2×D3)⋊C4—102no—
272(C2×D3)⋊C4—101no—
273C4⋊Dic3—51no—
274C4⋊Dic3—51no—
275C4⋊Dic3—51no—
276C4⋊Dic3—102no—
277Dic3⋊C4—102no—
278Dic3⋊C4—101no—
279C4×Dic3—102no—
280C4×Dic3—101no—
281C2×C3⋊C8—52no—
282#204—102no—
283D3×C8—202no—
284C22×D5—32no—
285C22×D5—61no—
286C5×Q8—22no—
287C5×Q8—22no—
288C5×Q8—42no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5D3×D411yescharacteristic
293C2×C4×C5C23×D311yescharacteristic
294C2×Dic5—32no—
295C2×Dic5—61no—
296C2×Dic5—61no—
297C2×Dic5—61no—
298D20—32no—
299D20—62no—
300D20—61no—
301D20—124no—
302C4×D5—62no—
303C4×D5—62no—
304C4×D5—124no—
305C4×D5—122no—
306Dic10—61no—
307Dic10—61no—
308C5×C8—21no—
309C5×C8—21no—
310#168—62no—
311C2×#41—152no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8—152no—
315C4⋊Q8C2×D1511yescharacteristic
316C4⋊Q8C2×D1511yescharacteristic
317#126—302no—
318#124—301no—
319#123—302no—
320C22⋊Q8—152no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—151no—
324C4×Q8—301no—
325C4×D4—151no—
326C4×D4—151no—
327#117—152no—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—151no—
331C4⋊C8—151no—
332#103—152no—
333#103—151no—
334#103C2×D1512yes—
335#103C2×D1512yes—
336#102—151no—
337#102—152no—
338C22⋊C8—152no—
339C4×C8C2×D1511yescharacteristic
340C2×C3×C5#54611yescharacteristic
341C2×C3×C5C2×#13511yescharacteristic
342C2×C3×C5#57811yescharacteristic
343D15—42no—
344D15—42no—
345C22×D3—52no—
346C22×D3—101no—
347C3×Q8—22no—
348C3×Q8—22no—
349C3×Q8—42no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4C23×D511yescharacteristic
355C2×Dic3—52no—
356C2×Dic3—101no—
357C2×Dic3—101no—
358C2×Dic3—101no—
359D12—52no—
360D12—101no—
361D12—102no—
362D12—204no—
363C4×D3—102no—
364C4×D3—102no—
365C4×D3—204no—
366C4×D3—202no—
367Dic6—101no—
368Dic6—101no—
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—102no—
372C22×C5C2×D3×D411yescharacteristic
373C2×D5—62no—
374C2×D5—62no—
375C2×D5—62no—
376C2×D5—62no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—42no—
381C4×C5—42no—
382C4×C5#91612yes—
383C4×C5D3×#4111yescharacteristic
384C4×C5#100911yescharacteristic
385Dic5—62no—
386Dic5—121no—
387Dic5—121no—
388Dic5—121no—
389#41—304no—
390#41—602no—
391C2×Q8—21no—
392C2×Q8—151no—
393C2×Q8C22×D1512yes—
394C2×D4—151no—
395C2×D4—151no—
396C2×D4—302no—
397C22×C4—152no—
398C22×C4—302no—
399C22×C4—301no—
400Q16—602no—
401SD16—302no—
402C2×C8—152no—
403C2×C8—602no—
404C2×C8C22×D1511yescharacteristic
405C2×C8C22×D1511yescharacteristic
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—151no—
410C4⋊C4—151no—
411C4⋊C4—151no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C22×D1512yes—
416C22⋊C4—152no—
417C22⋊C4—302no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4—301no—
421C42—302no—
422C42—301no—
423C42C22×D1511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3C2×D4×D511yescharacteristic
426C2×D3—102no—
427C2×D3—102no—
428C2×D3—102no—
429C2×D3—102no—
430C2×D3—201no—
431C2×D3—201no—
432C3×C4—21no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4#406212yes—
436C3×C4D5×#4111yescharacteristic
437C3×C4#414911yescharacteristic
438Dic3—102no—
439Dic3—201no—
440Dic3—201no—
441Dic3—201no—
442C2×C5#567611yescharacteristic
443C2×C5C2×#91611yescharacteristic
444C2×C5#576611yescharacteristic
445D5—122no—
446D5—122no—
447C23—152no—
448C23—301no—
449Q8—22no—
450Q8—22no—
451Q8—42no—
452Q8—301no—
453Q8—301no—
454D4—152no—
455D4—302no—
456D4—301no—
457D4—604no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—152no—
461C2×C4—302no—
462C2×C4—302no—
463C2×C4—301no—
464C2×C4—301no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4D4×D1511yescharacteristic
469C2×C4D4×D1511yescharacteristic
470C2×C4C23×D1511yescharacteristic
471C8—21no—
472C8—21no—
473C8—302no—
474C2×C3#6601011yescharacteristic
475C2×C3C2×#406211yescharacteristic
476C2×C3#6610011yescharacteristic
477D3—202no—
478D3—202no—
479C5#8161411yescharacteristic, complemented, Sylow
480C22—302no—
481C22—302no—
482C22—302no—
483C22—302no—
484C22—601no—
485C22—601no—
486C22C2×D4×D1511yescharacteristic
487C4—21no—
488C4—42no—
489C4—42no—
490C4—302no—
491C4—601no—
492C4—601no—
493C4—601no—
494C4#9180512yes—
495C4#41×D1511yescharacteristic
496C4#9210011yescharacteristic
497C3#1061334511yescharacteristic, complemented, Sylow
498C2—602no—
499C2—602no—
500C2#1175643511yescharacteristic
501C2C2×#9180511yescharacteristic
502C2#1175652511yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#487C2
socleC22×C3×C5C22×D4
prime radical#11756485C2
hypercenter#487D15
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #11756491C2semidirect
3. C3×C5×#487C2semidirect
4. #11751191C2semidirect
5. #11751188C2semidirect
6. #11750916C2semidirect
7. #11750914C2semidirect
8. #11750909C2semidirect
9. #11750905C2semidirect
10. C4×#6706C2semidirect
11. C8×D60C2semidirect
45. C5×#487D3semidirect
91. C3×#487D5semidirect
223. #487D15semidirect
424. C3×C5#3302semidirect
479. C5#81614semidirect
497. C3#10613345semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117564852
C3×C5×#4872
#117511912
#117511882
#117509162
#117509142
#117509092
#117509052
C4×#67062
C8×D602
#106133453
#816145