Finite Group Databasebeta

← #14459942

Subgroups — #14459942

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#11756314C211yesmaximal, characteristic
3C3×C5×#474C211yesmaximal, characteristic, complemented
4#11751194C211yesmaximal, characteristic, complemented
5C4×#6716C211yesmaximal, characteristic, complemented
6#11750989C212yesmaximal, complemented
7#11750988C212yesmaximal, complemented
8#11750950C211yesmaximal, characteristic, complemented
9#11750935C211yesmaximal, characteristic, complemented
10#11750884C212yesmaximal, complemented
11#11750873C212yesmaximal, complemented
12#10612712—31nomaximal, Hall
13C2×#6819C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16#91836—21no—
17Q8×Dic15—21no—
18C2×#6716C2211yescharacteristic
19#91819—21no—
20C2×C4⋊Dic15—21no—
21C2×Dic60C2212yes—
22C2×C8×D15C2212yes—
23#91787—22no—
24#91786C2212yes—
25#91786C2212yes—
26#91781C2212yes—
27#91775—22no—
28C4×D60C2211yescharacteristic
29#91758C2211yescharacteristic
30C4×Dic30C2211yescharacteristic
31C3×C5×#107C2212yes—
32C3×C5×C4⋊C8C2211yescharacteristic
33C3×C5×#102C2212yes—
34#91116C2211yescharacteristic
35#91104C2212yes—
36#91100C2212yes—
37#91094C2212yes—
38#91094C2212yes—
39#91094C2211yescharacteristic
40#91092C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#80981—51nomaximal, Hall
43#66066—31no—
44#65889—31no—
45C5×#474D311yescharacteristic, complemented
46#65382—31no—
47C4×#687—31no—
48#65177—32no—
49#65176—32no—
50#65138—31no—
51#65123—31no—
52#65072—32no—
53#65061—32no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×#1220—22no—
58C22×Dic15—22no—
59#6819—24no—
60#6819—42no—
61C2×D60D411yescharacteristic
62C2×C4×D15C2312yes—
63C2×Dic30C2311yescharacteristic
64C2×Dic30C2312yes—
65C2×C3×C5×C8C2312yes—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4C2312yes—
68C3×C5×C4⋊C4C2311yescharacteristic
69C3×C5×C22⋊C4—21no—
70C3×C42×C5C2311yescharacteristic
71#6716—22no—
72#6714—22no—
73#6714—22no—
74#6714—22no—
75#6714D412yes—
76C4⋊Dic15—21no—
77C4⋊Dic15—21no—
78C4⋊Dic15—22no—
79C4⋊Dic15—22no—
80C4⋊Dic15D411yescharacteristic
81C4⋊Dic15C2311yescharacteristic
82#6712—21no—
83C4×Dic15—21no—
84C4×Dic15—22no—
85C2×C3⋊#168C2311yescharacteristic
86C2×C3⋊#168C2311yescharacteristic
87Dic60—42no—
88C8×D15—42no—
89#5732—51no—
90#5555—51no—
91C3×#474D511yescharacteristic, complemented
92#5093—51no—
93C4×#214—51no—
94#4888—52no—
95#4887—52no—
96#4849—51no—
97#4834—51no—
98#4783—52no—
99#4772—52no—
100C2×#711—32no—
101C5×C4⋊Q8C2×D311yescharacteristic
102C4×C5×D4C2×D311yescharacteristic
103#4093—61no—
104Q8×Dic5—61no—
105C2×#687—31no—
106#4076—61no—
107C2×C4⋊Dic5—61no—
108C2×Dic20—32no—
109C2×C8×D5—32no—
110#4044—62no—
111#4043—32no—
112#4043—32no—
113#4038—32no—
114#4032—62no—
115C4×D20—31no—
116#4015—31no—
117C4×Dic10—31no—
118C5×#107C2×D312yes—
119C5×C4⋊C8C2×D311yescharacteristic
120C5×#102C2×D312yes—
121#3964—31no—
122#3952—32no—
123#3948—32no—
124#3942—31no—
125#3942—32no—
126#3942—32no—
127#3940—31no—
128C4×#168—31no—
129#3302—151noSylow
130C23×C3×C5—21no—
131C22×D15C2×D412yes—
132C3×C5×Q8—42no—
133C3×C5×D4—21no—
134C3×C5×D4#4112yes—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—42no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2411yescharacteristic
141#1220—44no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145C2×Dic15—44no—
146C2×Dic15C2×D412yes—
147D60—22no—
148C4×D15—22no—
149C4×D15—22no—
150Dic30—21no—
151Dic30—22no—
152Dic30—21no—
153Dic30—22no—
154C3×C5×C8—22no—
155C3⋊#168—21no—
156C3⋊#168—21no—
157C2×#237—52no—
158C3×C4⋊Q8C2×D511yescharacteristic
159C3×C4×D4C2×D511yescharacteristic
160#947—101no—
161Q8×Dic3—101no—
162C2×#214—51no—
163#930—101no—
164C2×C4⋊Dic3—101no—
165C2×Dic12—52no—
166C2×D3×C8—52no—
167#898—102no—
168#897—52no—
169#897—52no—
170#892—52no—
171#886—102no—
172C4×D12—51no—
173#869—51no—
174C4×Dic6—51no—
175C3×#107C2×D512yes—
176C3×C4⋊C8C2×D511yescharacteristic
177C3×#102C2×D512yes—
178#832—51no—
179(C2×D3)⋊C8—52no—
180#816—52no—
181#810—51no—
182#810—52no—
183#810—52no—
184#808—51no—
185C4×C3⋊C8—51no—
186C2×C5×Q8—21no—
187C2×C5×D4C22×D311yescharacteristic
188C22×C4×C5—21no—
189C2×C22⋊D5—62no—
190C22×Dic5—62no—
191#711—64no—
192#711—122no—
193C2×D20—31no—
194C2×C4×D5—32no—
195C2×Dic10—32no—
196C2×Dic10—31no—
197C2×C5×C8C22×D312yes—
198C5×C4⋊C4—21no—
199C5×C4⋊C4C22×D311yescharacteristic
200C5×C4⋊C4C22×D312yes—
201C5×C22⋊C4—21no—
202C42×C5C22×D311yescharacteristic
203#687—62no—
204#685—32no—
205#685—62no—
206#685—62no—
207#685—62no—
208C4⋊Dic5—31no—
209C4⋊Dic5—31no—
210C4⋊Dic5—62no—
211C4⋊Dic5—62no—
212C4⋊Dic5—61no—
213C4⋊Dic5—61no—
214#683—61no—
215C4×Dic5—62no—
216C4×Dic5—61no—
217C2×#168—31no—
218C2×#168—31no—
219Dic20—122no—
220C8×D5—122no—
221#556—151no—
222#547—151no—
223#487—151no—
224#485—152no—
225#474D1511yescharacteristic, complemented
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—151no—
231#416—152no—
232C22×C3×C5—22no—
233C22×C3×C5—41no—
234C22×C3×C5—41no—
235C22×C3×C5C22×D411yescharacteristic
236C2×D15—22no—
237C2×D15—22no—
238C2×D15—22no—
239C3×C4×C5—21no—
240C3×C4×C5—41no—
241C3×C4×C5—42no—
242C3×C4×C5#13512yes—
243C3×C4×C5C2×#4111yescharacteristic
244C3×C4×C5H(5,𝔽2)11yescharacteristic
245Dic15—22no—
246Dic15—41no—
247Dic15—42no—
248Dic15—41no—
249C2×C3×Q8—21no—
250C2×C3×D4C22×D511yescharacteristic
251C22×C3×C4—21no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—104no—
255#237—202no—
256C2×D12—51no—
257C2×C4×D3—52no—
258C2×Dic6—52no—
259C2×Dic6—51no—
260C2×C3×C8C22×D512yes—
261C3×C4⋊C4—21no—
262C3×C4⋊C4C22×D511yescharacteristic
263C3×C4⋊C4C22×D512yes—
264C3×C22⋊C4—21no—
265C3×C42C22×D511yescharacteristic
266#214—102no—
267(C2×D3)⋊C4—52no—
268(C2×D3)⋊C4—102no—
269(C2×D3)⋊C4—102no—
270(C2×D3)⋊C4—102no—
271C4⋊Dic3—51no—
272C4⋊Dic3—51no—
273C4⋊Dic3—102no—
274C4⋊Dic3—102no—
275C4⋊Dic3—101no—
276C4⋊Dic3—101no—
277Dic3⋊C4—101no—
278C4×Dic3—102no—
279C4×Dic3—101no—
280C2×C3⋊C8—51no—
281C2×C3⋊C8—51no—
282Dic12—202no—
283D3×C8—202no—
284C23×C5—21no—
285C22×D5—32no—
286C5×Q8—42no—
287C5×D4—21no—
288C5×D4#23912yes—
289C2×C4×C5—22no—
290C2×C4×C5—21no—
291C2×C4×C5—42no—
292C2×C4×C5D3×D411yescharacteristic
293C2×C4×C5D3×D411yescharacteristic
294C2×C4×C5C23×D311yescharacteristic
295C22⋊D5—124no—
296C2×Dic5—32no—
297C2×Dic5—61no—
298C2×Dic5—61no—
299C2×Dic5—62no—
300C2×Dic5—124no—
301D20—62no—
302C4×D5—62no—
303C4×D5—62no—
304Dic10—61no—
305Dic10—62no—
306Dic10—61no—
307Dic10—62no—
308C5×C8—22no—
309#168—61no—
310#168—61no—
311C2×#41—152no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8—152no—
315C4⋊Q8—151no—
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×D4C2×D1511yescharacteristic
327#117—152no—
328C2×C4⋊C4—301no—
329#107C2×D1512yes—
330#106—151no—
331C4⋊C8C2×D1511yescharacteristic
332#103—152no—
333#103—152no—
334#103—151no—
335#103—152no—
336#102—151no—
337#102C2×D1512yes—
338C22⋊C8—152no—
339C4×C8—151no—
340C2×C3×C5—42no—
341C2×C3×C5#54611yescharacteristic
342C2×C3×C5C2×#13511yescharacteristic
343C2×C3×C5#57811yescharacteristic
344D15—42no—
345C23×C3—21no—
346C22×D3—52no—
347C3×Q8—42no—
348C3×D4—21no—
349C3×D4#71312yes—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—42no—
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4C23×D511yescharacteristic
356#67—204no—
357C2×Dic3—52no—
358C2×Dic3—101no—
359C2×Dic3—101no—
360C2×Dic3—102no—
361C2×Dic3—204no—
362D12—102no—
363C4×D3—102no—
364C4×D3—102no—
365Dic6—101no—
366Dic6—102no—
367Dic6—101no—
368Dic6—102no—
369C3×C8—22no—
370C3⋊C8—101no—
371C3⋊C8—101no—
372C22×C5—22no—
373C22×C5—41no—
374C22×C5—41no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—62no—
377C2×D5—62no—
378C2×D5—62no—
379C4×C5—21no—
380C4×C5—41no—
381C4×C5—42no—
382C4×C5#91212yes—
383C4×C5C2×#23911yescharacteristic
384C4×C5#100911yescharacteristic
385Dic5—62no—
386Dic5—121no—
387Dic5—121no—
388Dic5—122no—
389#41—304no—
390#41—602no—
391C2×Q8—21no—
392C2×Q8—152no—
393C2×Q8—151no—
394C2×D4—151no—
395C2×D4—302no—
396C2×D4C22×D1511yescharacteristic
397C22×C4—21no—
398C22×C4—152no—
399C22×C4—302no—
400Q16—602no—
401SD16—302no—
402C2×C8—151no—
403C2×C8—151no—
404C2×C8—602no—
405C2×C8C22×D1512yes—
406C4⋊C4—21no—
407C4⋊C4—151no—
408C4⋊C4—151no—
409C4⋊C4—302no—
410C4⋊C4—302no—
411C4⋊C4—301no—
412C4⋊C4—301no—
413C4⋊C4—301no—
414C4⋊C4C22×D1512yes—
415C4⋊C4C22×D1511yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—152no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4—302no—
421C42—302no—
422C42—301no—
423C42C22×D1511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—22no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3C2×D4×D511yescharacteristic
429C2×D3—102no—
430C2×D3—102no—
431C2×D3—102no—
432C3×C4—21no—
433C3×C4—41no—
434C3×C4—42no—
435C3×C4#405812yes—
436C3×C4C2×#71311yescharacteristic
437C3×C4#414911yescharacteristic
438Dic3—102no—
439Dic3—201no—
440Dic3—201no—
441Dic3—202no—
442C2×C5—42no—
443C2×C5#563011yescharacteristic
444C2×C5C2×#91211yescharacteristic
445C2×C5#577911yescharacteristic
446D5—122no—
447C23—21no—
448C23—152no—
449Q8—42no—
450Q8—301no—
451Q8—302no—
452Q8—301no—
453Q8—302no—
454D4—21no—
455D4—302no—
456D4—604no—
457D4#682112yes—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—42no—
461C2×C4—152no—
462C2×C4—302no—
463C2×C4—302no—
464C2×C4—301no—
465C2×C4—301no—
466C2×C4—302no—
467C2×C4—604no—
468C2×C4D4×D1511yescharacteristic
469C2×C4D4×D1511yescharacteristic
470C2×C4C23×D1511yescharacteristic
471C8—22no—
472C8—301no—
473C8—301no—
474C2×C3—42no—
475C2×C3#6596411yescharacteristic
476C2×C3C2×#405811yescharacteristic
477C2×C3#6611311yescharacteristic
478D3—202no—
479C5#8098111yescharacteristic, complemented, Sylow
480C22—22no—
481C22—41no—
482C22—41no—
483C22—302no—
484C22—302no—
485C22—302no—
486C22C2×D4×D1511yescharacteristic
487C4—21no—
488C4—41no—
489C4—42no—
490C4—302no—
491C4—602no—
492C4—601no—
493C4—601no—
494C4#9180112yes—
495C4C2×#682111yescharacteristic
496C4#9210011yescharacteristic
497C3#1061271211yescharacteristic, complemented, Sylow
498C2—42no—
499C2—602no—
500C2#1175638911yescharacteristic
501C2C2×#9180111yescharacteristic
502C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#474C2
socleC22×C3×C5C22×D4
prime radical#11756314C2
hypercenter#474D15
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11756491C2semidirect
3. C3×C5×#474C2semidirect
4. #11751194C2semidirect
5. C4×#6716C2semidirect
6. #11750989C2semidirect
7. #11750988C2semidirect
8. #11750950C2semidirect
9. #11750935C2semidirect
10. #11750884C2semidirect
11. #11750873C2semidirect
45. C5×#474D3semidirect
91. C3×#474D5semidirect
225. #474D15semidirect
424. C3×C5#3302semidirect
479. C5#80981semidirect
497. C3#10612712semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117563142
C3×C5×#4742
#117511942
C4×#67162
#117509892
#117509882
#117509502
#117509352
#117508842
#117508732
#106127123
#809815