Finite Group Databasebeta

← #14460272

Subgroups — #14460272

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756312C211yesmaximal, characteristic
2#11756301C211yesmaximal, characteristic, complemented
3C3×C5×C8×D4C211yesmaximal, characteristic, complemented
4#11751215C212yesmaximal, complemented
5#11751214C212yesmaximal, complemented
6#11750952C211yesmaximal, characteristic, complemented
7#11750949C211yesmaximal, characteristic, complemented
8#11750838C212yesmaximal, complemented
9#11750834C212yesmaximal, complemented
10C4×Dic60C211yesmaximal, characteristic, complemented
11#11750795C211yesmaximal, characteristic, complemented
12#10611182—31nomaximal, Hall
13C2×#6817C2212yes—
14C22×C3×C5×C8C2212yes—
15C3×C4×C5×D4C2211yescharacteristic
16#91829—21no—
17#91825—21no—
18#91819C2212yes—
19#91815C2212yes—
20#91813C2212yes—
21C2×Dic60C2211yescharacteristic
22C2×#6706C2212yes—
23#91782—21no—
24#91776—21no—
25#91773—22no—
26#91768—22no—
27#91763C2211yescharacteristic
28#91758C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C4×Dic30C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic
32C3×C5×C22⋊C8C2212yes—
33C3×C4×C5×C8C2211yescharacteristic
34#91105C2212yes—
35#91105C2212yes—
36#91105C2212yes—
37#91102C2211yescharacteristic
38#91101C2212yes—
39#91100C2212yes—
40#91100C2211yescharacteristic
41#91100C2211yescharacteristic
42#79451—51nomaximal, Hall
43#65887—31no—
44#65876—31no—
45C5×C8×D4D311yescharacteristic, complemented
46#65403—32no—
47#65402—32no—
48#65140—31no—
49#65137—31no—
50#65026—32no—
51#65022—32no—
52C4×Dic20—31no—
53#64983—31no—
54C2×C3×C5×D4D411yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×#1220—22no—
57C2×#1220—22no—
58#6817—24no—
59#6817—42no—
60C2×D60—21no—
61C2×D60—21no—
62C2×D60C2312yes—
63C2×C4×D15—22no—
64C2×Dic30—21no—
65C2×Dic30C2311yescharacteristic
66C2×Dic30C2311yescharacteristic
67C2×C3×C5×C8—42no—
68C2×C3×C5×C8C2312yes—
69C2×C3×C5×C8C2311yescharacteristic
70C2×C3×C5×C8C2311yescharacteristic
71C3×C5×C4⋊C4D411yescharacteristic
72C3×C5×C22⋊C4D412yes—
73C3×C42×C5C2311yescharacteristic
74#6719—22no—
75#6719—22no—
76#6714—22no—
77C4⋊Dic15—21no—
78C4⋊Dic15C2311yescharacteristic
79C4⋊Dic15C2311yescharacteristic
80C4⋊Dic15C2312yes—
81#6712—21no—
82#6712—21no—
83#6712—22no—
84C4×Dic15—21no—
85C4×Dic15—21no—
86C4×Dic15—22no—
87Dic60—22no—
88#6706—42no—
89#5553—51no—
90#5542—51no—
91C3×C8×D4D511yescharacteristic, complemented
92#5114—52no—
93#5113—52no—
94#4851—51no—
95#4848—51no—
96#4737—52no—
97#4733—52no—
98C4×Dic12—51no—
99#4694—51no—
100C2×#709—32no—
101C22×C5×C8C2×D312yes—
102C4×C5×D4C2×D311yescharacteristic
103#4086—61no—
104#4082—61no—
105#4076—32no—
106#4072—32no—
107#4070—32no—
108C2×Dic20—31no—
109C2×#677—32no—
110#4039—61no—
111#4033—61no—
112#4030—62no—
113#4025—62no—
114#4020—31no—
115#4015—31no—
116C4×Dic10—31no—
117C4×Dic10—31no—
118C5×C4⋊C8C2×D311yescharacteristic
119C5×C22⋊C8C2×D312yes—
120C4×C5×C8C2×D311yescharacteristic
121#3953—32no—
122#3953—32no—
123#3953—32no—
124#3950—31no—
125#3949—32no—
126#3948—32no—
127#3948—31no—
128#3948—31no—
129#3304—151noSylow
130C23×C3×C5C2×D412yes—
131C22×D15—22no—
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—
140#1220—82no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145C2×Dic15—21no—
146D60—22no—
147D60—22no—
148D60—42no—
149D60—81no—
150C4×D15—44no—
151Dic30—21no—
152Dic30—21no—
153Dic30—21no—
154Dic30—42no—
155Dic30#4112yes—
156C3×C5×C8—21no—
157C3×C5×C8—22no—
158C3×C5×C8—21no—
159C2×#235—52no—
160C22×C3×C8C2×D512yes—
161C3×C4×D4C2×D511yescharacteristic
162#940—101no—
163#936—101no—
164#930—52no—
165#926—52no—
166#924—52no—
167C2×Dic12—51no—
168C2×#204—52no—
169#893—101no—
170#887—101no—
171#884—102no—
172#879—102no—
173#874—51no—
174#869—51no—
175C4×Dic6—51no—
176C4×Dic6—51no—
177C3×C4⋊C8C2×D511yescharacteristic
178C3×C22⋊C8C2×D512yes—
179C3×C4×C8C2×D511yescharacteristic
180#821—52no—
181#821—52no—
182#821—52no—
183#818—51no—
184#817—52no—
185#816—51no—
186#816—51no—
187#816—52no—
188C2×C5×D4D1211yescharacteristic
189C22×C4×C5C22×D312yes—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192#709—64no—
193#709—122no—
194C2×D20—32no—
195C2×D20—61no—
196C2×D20—61no—
197C2×C4×D5—62no—
198C2×Dic10—31no—
199C2×Dic10—31no—
200C2×Dic10—61no—
201C2×C5×C8—42no—
202C2×C5×C8C22×D311yescharacteristic
203C2×C5×C8C22×D312yes—
204C2×C5×C8C22×D311yescharacteristic
205C5×C4⋊C4D1211yescharacteristic
206C5×C22⋊C4D1212yes—
207C42×C5C22×D311yescharacteristic
208C22⋊Dic5—62no—
209C22⋊Dic5—62no—
210#685—62no—
211C4⋊Dic5—31no—
212C4⋊Dic5—32no—
213C4⋊Dic5—31no—
214C4⋊Dic5—61no—
215#683—61no—
216#683—61no—
217#683—62no—
218C4×Dic5—61no—
219C4×Dic5—61no—
220C4×Dic5—62no—
221Dic20—62no—
222#677—122no—
223#556—151no—
224#550—151no—
225#486—151no—
226#482—152no—
227#475—151no—
228#465—152no—
229#460—151no—
230#452—152no—
231C4×Q16—151no—
232C8×D4D1511yescharacteristic, complemented
233#416—152no—
234C22×C3×C5—22no—
235C22×C3×C5—22no—
236C22×C3×C5—22no—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—42no—
239C2×D15—42no—
240C2×D15—42no—
241C3×C4×C5—22no—
242C3×C4×C5—21no—
243C3×C4×C5#13512yes—
244C3×C4×C5C2×#4111yescharacteristic
245C3×C4×C5H(5,𝔽2)11yescharacteristic
246Dic15—22no—
247Dic15—41no—
248Dic15—42no—
249Dic15—41no—
250Dic15—41no—
251C2×C3×D4D2011yescharacteristic
252C22×C3×C4C22×D512yes—
253C2×#67—102no—
254C2×#67—102no—
255#235—104no—
256#235—202no—
257C2×D12—52no—
258C2×D12—101no—
259C2×D12—101no—
260C2×C4×D3—102no—
261C2×Dic6—51no—
262C2×Dic6—51no—
263C2×Dic6—101no—
264C2×C3×C8—42no—
265C2×C3×C8C22×D511yescharacteristic
266C2×C3×C8C22×D512yes—
267C2×C3×C8C22×D511yescharacteristic
268C3×C4⋊C4D2011yescharacteristic
269C3×C22⋊C4D2012yes—
270C3×C42C22×D511yescharacteristic
271#217—102no—
272#217—102no—
273(C2×D3)⋊C4—102no—
274C4⋊Dic3—51no—
275C4⋊Dic3—52no—
276C4⋊Dic3—51no—
277C4⋊Dic3—101no—
278Dic3⋊C4—101no—
279Dic3⋊C4—101no—
280Dic3⋊C4—102no—
281C4×Dic3—101no—
282C4×Dic3—101no—
283C4×Dic3—102no—
284Dic12—102no—
285#204—202no—
286C23×C5C2×D1212yes—
287C22×D5—62no—
288C5×D4—22no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5C2×D1212yes—
292C2×C4×C5C2×D1211yescharacteristic
293C2×C4×C5C2×D1211yescharacteristic
294C2×C4×C5C23×D311yescharacteristic
295C22⋊D5—124no—
296C22⋊D5—242no—
297C2×Dic5—61no—
298C2×Dic5—61no—
299C2×Dic5—61no—
300C2×Dic5—62no—
301C2×Dic5—61no—
302D20—62no—
303D20—62no—
304D20—122no—
305D20—241no—
306C4×D5—124no—
307Dic10—32no—
308Dic10—61no—
309Dic10—61no—
310Dic10—61no—
311Dic10—122no—
312C5×C8—22no—
313C5×C8—21no—
314C5×C8—21no—
315C2×#41—152no—
316C2×Q16—151no—
317C2×SD16—152no—
318C22×C8C2×D1512yes—
319C4⋊Q8—151no—
320#127—151no—
321#127—301no—
322#126—302no—
323#124—301no—
324C22⋊Q8—152no—
325#121—152no—
326#121—302no—
327C4×Q8—151no—
328C4×Q8—151no—
329C4×Q8—301no—
330C4×D4—301no—
331C4×D4C2×D1511yescharacteristic
332#117—152no—
333#107—151no—
334#106—152no—
335C4⋊C8C2×D1511yescharacteristic
336#103—151no—
337#103—152no—
338#103—151no—
339#102—152no—
340#102—152no—
341#102—152no—
342C22⋊C8C2×D1512yes—
343C4×C8C2×D1511yescharacteristic
344C2×C3×C5—42no—
345C2×C3×C5#54611yescharacteristic
346C2×C3×C5C2×#13511yescharacteristic
347C2×C3×C5#57711yescharacteristic
348D15—82no—
349C23×C3C2×D2012yes—
350C22×D3—102no—
351C3×D4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4C2×D2012yes—
355C2×C3×C4C2×D2011yescharacteristic
356C2×C3×C4C2×D2011yescharacteristic
357C2×C3×C4C23×D511yescharacteristic
358#67—204no—
359#67—402no—
360C2×Dic3—101no—
361C2×Dic3—101no—
362C2×Dic3—101no—
363C2×Dic3—102no—
364C2×Dic3—101no—
365D12—102no—
366D12—102no—
367D12—202no—
368D12—401no—
369C4×D3—204no—
370Dic6—52no—
371Dic6—101no—
372Dic6—101no—
373Dic6—101no—
374Dic6—202no—
375C3×C8—22no—
376C3×C8—21no—
377C3×C8—21no—
378C22×C5—22no—
379C22×C5—22no—
380C22×C5—22no—
381C22×C5C22×D1211yescharacteristic
382C2×D5—122no—
383C2×D5—122no—
384C2×D5—122no—
385C4×C5—21no—
386C4×C5—22no—
387C4×C5#90412yes—
388C4×C5#100411yescharacteristic
389C4×C5D3×#4111yescharacteristic
390Dic5—62no—
391Dic5—122no—
392Dic5—121no—
393Dic5—121no—
394Dic5—121no—
395#41—304no—
396#41—602no—
397C2×Q8—151no—
398C2×Q8—151no—
399C2×Q8—301no—
400C2×D4—152no—
401C2×D4—302no—
402C2×D4—302no—
403C2×D4—301no—
404C2×D4—301no—
405C2×D4D6011yescharacteristic
406C22×C4—302no—
407C22×C4C22×D1512yes—
408Q16—302no—
409SD16—602no—
410C2×C8—42no—
411C2×C8C22×D1511yescharacteristic
412C2×C8C22×D1511yescharacteristic
413C2×C8C22×D1512yes—
414C4⋊C4—152no—
415C4⋊C4—151no—
416C4⋊C4—151no—
417C4⋊C4—301no—
418C4⋊C4—301no—
419C4⋊C4—302no—
420C4⋊C4—301no—
421C4⋊C4D6011yescharacteristic
422C22⋊C4—302no—
423C22⋊C4—302no—
424C22⋊C4—302no—
425C22⋊C4D6012yes—
426C42—302no—
427C42—301no—
428C42—301no—
429C42C22×D1511yescharacteristic
430C3×C5#330411yescharacteristic, complemented, Hall
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3C22×D2011yescharacteristic
435C2×D3—202no—
436C2×D3—202no—
437C2×D3—202no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4#405012yes—
441C3×C4#414411yescharacteristic
442C3×C4D5×#4111yescharacteristic
443Dic3—102no—
444Dic3—202no—
445Dic3—201no—
446Dic3—201no—
447Dic3—201no—
448C2×C5—42no—
449C2×C5#555411yescharacteristic
450C2×C5C2×#90411yescharacteristic
451C2×C5#575111yescharacteristic
452D5—242no—
453C23—302no—
454C23C2×D6012yes—
455Q8—152no—
456Q8—301no—
457Q8—301no—
458Q8—301no—
459Q8—602no—
460D4—22no—
461D4—302no—
462D4—302no—
463D4—604no—
464D4—602no—
465D4—1201no—
466D4—1202no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—301no—
470C2×C4—301no—
471C2×C4—302no—
472C2×C4—301no—
473C2×C4—301no—
474C2×C4—604no—
475C2×C4C2×D6012yes—
476C2×C4C2×D6011yescharacteristic
477C2×C4C2×D6011yescharacteristic
478C2×C4C23×D1511yescharacteristic
479C8—21no—
480C8—22no—
481C8—21no—
482C2×C3—42no—
483C2×C3#6588811yescharacteristic
484C2×C3C2×#405011yescharacteristic
485C2×C3#6608511yescharacteristic
486D3—402no—
487C5#7945111yescharacteristic, complemented, Sylow
488C22—22no—
489C22—22no—
490C22—22no—
491C22—602no—
492C22—602no—
493C22—602no—
494C22C22×D6011yescharacteristic
495C4—22no—
496C4—21no—
497C4—302no—
498C4—601no—
499C4—602no—
500C4—601no—
501C4—601no—
502C4#9179312yes—
503C4#9209511yescharacteristic
504C4#41×D1511yescharacteristic
505C3#1061118211yescharacteristic, complemented, Sylow
506C2—42no—
507C2—1202no—
508C2#1175631311yescharacteristic
509C2C2×#9179311yescharacteristic
510C2#1175651011yescharacteristic
subgroupG/H
centerC22C22×D60
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×C8×D4C2
socleC22×C3×C5C22×D4
prime radical#11756312C2
hypercenterC8×D4D15
hypocenterC3×C5#3304
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #11756301C2semidirect
3. C3×C5×C8×D4C2semidirect
4. #11751215C2semidirect
5. #11751214C2semidirect
6. #11750952C2semidirect
7. #11750949C2semidirect
8. #11750838C2semidirect
9. #11750834C2semidirect
10. C4×Dic60C2semidirect
11. #11750795C2semidirect
45. C5×C8×D4D3semidirect
91. C3×C8×D4D5semidirect
232. C8×D4D15semidirect
430. C3×C5#3304semidirect
487. C5#79451semidirect
505. C3#10611182semidirect

Maximal subgroups

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

subgroupindex
#117563122
#117563012
C3×C5×C8×D42
#117512152
#117512142
#117509522
#117509492
#117508382
#117508342
C4×Dic602
#117507952
#106111823
#794515