Finite Group Databasebeta

← #14471932

Subgroups — #14471932

Order 1920.

784 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#11752538C211yesmaximal, characteristic
2#11752473C211yesmaximal, characteristic, complemented
3#11750949C211yesmaximal, characteristic, complemented
4C5×#4842C211yesmaximal, characteristic, complemented
5C3×#65119C211yesmaximal, characteristic, complemented
6#11747995C212yesmaximal, complemented
7#11747843C212yesmaximal, complemented
8#11747762C212yesmaximal, complemented
9#11747760C212yesmaximal, complemented
10C4×#6659C211yesmaximal, characteristic, complemented
11#11746912C211yesmaximal, characteristic, complemented
12#10612821—31nomaximal, Hall
13C2×#6769—21no—
14C2×#6706C2212yes—
15#91763C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C4×C5×D12C2211yescharacteristic
18C5×#869C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20#91470—21no—
21#91468C2212yes—
22#91460—21no—
23#91451C2212yes—
24#91420—22no—
25#91418C2212yes—
26#91333C2212yes—
27#91331—21no—
28#91329—22no—
29C2×#6659C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91105C2212yes—
32C5×#821C2212yes—
33C5×#817C2212yes—
34C3×#3946C2212yes—
35C3×C8×Dic5C2212yes—
36C3×C4×#168C2211yescharacteristic
37#90985C2211yescharacteristic
38#90975C2211yescharacteristic
39#90969C2212yes—
40#90969C2212yes—
41#90967C2211yescharacteristic
42#79932—51nomaximal, Hall
43#66056—31no—
44#65887—31no—
45C5×#476—31no—
46#65377—31no—
47C4×#687—31no—
48#65159—32no—
49#65141—32no—
50#65137—31no—
51#65119D311yescharacteristic, complemented
52#65051—32no—
53#65049—32no—
54C2×D60—21no—
55C2×D60—21no—
56C2×D60C2312yes—
57C2×Dic30C2311yescharacteristic
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C5×Dic6—21no—
61C2×C3×Dic10D411yescharacteristic
62C2×#1204—22no—
63C2×#1203—22no—
64C2×#1203—22no—
65C2×#1200—22no—
66#6769—44no—
67C2×C3×C5×C8C2312yes—
68C3×C42×C5C2311yescharacteristic
69C4⋊Dic15C2311yescharacteristic
70#6712—21no—
71C4×Dic15—21no—
72#6706—24no—
73C5×(C2×D3)⋊C4—21no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C5×C4⋊Dic3C2311yescharacteristic
77C3×C4⋊Dic5D411yescharacteristic
78C3×#683D412yes—
79C3×C4×Dic5C2312yes—
80C2×C3×#168C2311yescharacteristic
81C2×C3×#168C2311yescharacteristic
82#6669—22no—
83#6668—22no—
84#6667—22no—
85Dic3×Dic5—22no—
86#6659—22no—
87#5577—51no—
88Q8×Dic6—51no—
89C3×C8×Q8—51no—
90#4848—51no—
91#4848—52no—
92#4842—52no—
93#4842D511yescharacteristic, complemented
94#4694—51no—
95#4694—52no—
96C4×#204—51no—
97C4×#204—52no—
98C2×#709—61no—
99C5×C4⋊Q8—31no—
100C4×C5×D4—31no—
101#4090—62no—
102#4086—32no—
103C2×#687—31no—
104#4076—61no—
105C2×#677—32no—
106#4039—32no—
107#4034—32no—
108#4034—61no—
109#4033—32no—
110#4033—61no—
111#4030—62no—
112#4020—31no—
113C4×Dic10—31no—
114C4×Dic10C2×D311yescharacteristic
115C5×#106—32no—
116C5×C4⋊C8C2×D311yescharacteristic
117C5×#102—32no—
118#3964—31no—
119#3953—32no—
120#3946C2×D312yes—
121C8×Dic5C2×D312yes—
122#3942—31no—
123#3941—32no—
124#3941—32no—
125#3940—31no—
126C4×#168C2×D311yescharacteristic
127#3362—151noSylow
128C22×D15—22no—
129C22×C5×D3—21no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15—21no—
134C2×Dic15—21no—
135D60—22no—
136D60—22no—
137D60—42no—
138D60—81no—
139Dic30—21no—
140Dic30#4112yescomplemented
141C2×C5×Dic3—22no—
142C2×C5×Dic3—21no—
143C5×D12—21no—
144C5×D12—21no—
145C4×C5×D3—42no—
146C5×Dic6—81no—
147C2×C3×Dic5C2×D412yes—
148C2×C3×Dic5C2×D412yes—
149C3×Dic10SD1614yescomplemented
150#1204—82no—
151#1203—44no—
152#1203—82no—
153#1200—44no—
154C3×C5×C8—22no—
155C3×#168—21no—
156C3×#168—21no—
157C2×#239—101no—
158C3×C4×Q8—51no—
159Q8×Dic3—101no—
160C2×#204—51no—
161C2×#204—52no—
162#895—102no—
163#895—101no—
164#888—101no—
165#888—102no—
166#874—52no—
167#874—51no—
168C4×D12—52no—
169C4×D12C2×D511yescharacteristic
170#869—52no—
171#869C2×D511yescharacteristic
172C4×Dic6—51no—
173C4×Dic6—52no—
174C3×C4⋊C8—52no—
175C3×C4⋊C8C2×D511yescharacteristic
176C3×C4×C8—52no—
177C3×C4×C8—51no—
178#821—51no—
179#821—52no—
180#821—52no—
181#821—52no—
182#821C2×D512yes—
183#817—51no—
184#817C2×D512yes—
185#816—51no—
186C2×C5×Q8—61no—
187C2×C5×D4—31no—
188C22×C4×C5—61no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191#709—124no—
192C2×D20—32no—
193C2×D20—61no—
194C2×D20—61no—
195C2×C4×D5—62no—
196C2×Dic10—31no—
197C2×Dic10—62no—
198C2×Dic10D1211yescharacteristic
199C2×C5×C8C22×D312yes—
200C5×C4⋊C4—31no—
201C5×C4⋊C4—32no—
202C5×C4⋊C4—61no—
203C5×C22⋊C4—61no—
204C42×C5C22×D311yescharacteristic
205#687—62no—
206#685—62no—
207C4⋊Dic5—31no—
208C4⋊Dic5D1211yescharacteristic
209#683—61no—
210#683—62no—
211#683—62no—
212#683D1212yes—
213C4×Dic5—61no—
214C4×Dic5—62no—
215C4×Dic5C22×D312yes—
216C2×#168C22×D311yescharacteristic
217C2×#168C22×D311yescharacteristic
218#677—64no—
219Q82—151no—
220#550—151no—
221#486—152no—
222#486—151no—
223#476—31no—
224#476—152no—
225#460—152no—
226#460—151no—
227C8×Q8—51no—
228C4×SD16—152no—
229C4×SD16—151no—
230C22×C3×C5C22×D411yescharacteristic
231C2×D15—42no—
232C2×D15—42no—
233C2×D15—42no—
234C2×C5×D3—41no—
235C2×C5×D3—41no—
236C2×C5×D3—41no—
237C3×C4×C5—21no—
238C3×C4×C5C2×SD1612yes—
239C3×C4×C5C2×#4111yescharacteristic
240C3×C4×C52−1+411yescharacteristic
241Dic15—22no—
242Dic15—41no—
243C3×Dic5—22no—
244C3×Dic5C2×SD1614yes—
245C5×Dic3—41no—
246C5×Dic3—42no—
247C2×C3×Q8—51no—
248#239—204no—
249C2×D12—52no—
250C2×D12—102no—
251C2×D12—101no—
252C2×D12—102no—
253C2×D12—101no—
254C2×D12C22×D511yescharacteristic
255C2×C4×D3—21no—
256C2×C4×D3—102no—
257C2×Dic6—21no—
258C2×Dic6—51no—
259C2×Dic6—102no—
260C2×C3×C8—51no—
261C2×C3×C8—51no—
262C2×C3×C8C22×D512yes—
263C3×C4⋊C4—52no—
264C3×C4⋊C4—51no—
265C3×C42—52no—
266C3×C42C22×D511yescharacteristic
267(C2×D3)⋊C4—21no—
268(C2×D3)⋊C4—102no—
269C4⋊Dic3—21no—
270C4⋊Dic3—51no—
271C4⋊Dic3—102no—
272C4⋊Dic3C22×D511yescharacteristic
273C4⋊Dic3C22×D512yes—
274Dic3⋊C4—102no—
275Dic3⋊C4—101no—
276C4×Dic3—102no—
277C4×Dic3—101no—
278#204—104no—
279#204—102no—
280C23×C5—61no—
281C22×D5—62no—
282C5×Q8—241no—
283C5×D4—61no—
284C5×D4—61no—
285C2×C4×C5—62no—
286C2×C4×C5—61no—
287C2×C4×C5—122no—
288C2×C4×C5C2×D1211yescharacteristic
289C2×C4×C5C2×D1211yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—124no—
292C22⋊D5—242no—
293C2×Dic5—61no—
294C2×Dic5—61no—
295C2×Dic5C2×D1212yes—
296C2×Dic5C2×D1212yes—
297D20—62no—
298D20—62no—
299D20—122no—
300D20—241no—
301C4×D5—124no—
302Dic10—32no—
303Dic10—61no—
304Dic10—242no—
305Dic10#20414yescomplemented
306C5×C8—22no—
307#168—21no—
308#168—21no—
309C2×#41—301no—
310C2×SD16—151no—
311C2×SD16—152no—
312C4⋊Q8—31no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—152no—
317#127—151no—
318#121—302no—
319#121—301no—
320C4×Q8—51no—
321C4×Q8—152no—
322C4×Q8—151no—
323C4×Q8—301no—
324C4×D4—31no—
325C4×D4—152no—
326#106—32no—
327#106—151no—
328C4⋊C8—52no—
329C4⋊C8D3×D511yescharacteristic
330#103—151no—
331#102—32no—
332#102—152no—
333#102—152no—
334#102—151no—
335#102—152no—
336C4×C8—52no—
337C4×C8—51no—
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341D15—82no—
342C5×D3—81no—
343C22×D3—21no—
344C22×D3—102no—
345C3×Q8—54no—
346C2×C3×C4—52no—
347C2×C3×C4—52no—
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350C2×C3×C4C23×D511yescharacteristic
351C2×Dic3—22no—
352C2×Dic3—21no—
353C2×Dic3—101no—
354C2×Dic3—101no—
355D12—21no—
356D12—21no—
357D12—102no—
358D12—102no—
359D12—204no—
360D12—202no—
361D12—401no—
362D12—402no—
363C4×D3—42no—
364C4×D3—204no—
365Dic6—52no—
366Dic6—81no—
367Dic6—101no—
368Dic6—402no—
369C3×C8—22no—
370C3×C8—101no—
371C3×C8—101no—
372C22×C5—121no—
373C22×C5—121no—
374C22×C5—121no—
375C22×C5C22×D1211yescharacteristic
376C2×D5—122no—
377C2×D5—122no—
378C2×D5—122no—
379C4×C5—21no—
380C4×C5—121no—
381C4×C5—122no—
382C4×C5C2×#20412yes—
383C4×C5#100711yescharacteristic
384C4×C5D3×#4111yescharacteristic
385Dic5—22no—
386Dic5—62no—
387Dic5—121no—
388Dic5C2×#20414yes—
389#41—604no—
390C2×Q8—51no—
391C2×Q8—61no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—31no—
395C2×D4—152no—
396C2×D4—302no—
397C2×D4—302no—
398C2×D4—301no—
399C2×D4—301no—
400C22×C4—61no—
401C22×C4—302no—
402SD16—304no—
403SD16—302no—
404C2×C8—51no—
405C2×C8—51no—
406C2×C8C2×D3×D512yes—
407C4⋊C4—32no—
408C4⋊C4—31no—
409C4⋊C4—52no—
410C4⋊C4—51no—
411C4⋊C4—61no—
412C4⋊C4—151no—
413C4⋊C4—302no—
414C4⋊C4—302no—
415C4⋊C4—301no—
416C22⋊C4—61no—
417C22⋊C4—302no—
418C42—52no—
419C42—302no—
420C42—301no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3C2×D4×D511yescharacteristic
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—41no—
427C2×D3—202no—
428C2×D3—202no—
429C2×D3—202no—
430C3×C4—21no—
431C3×C4—54no—
432C3×C4—102no—
433C3×C4D5×SD1612yes—
434C3×C4#414711yescharacteristic
435C3×C4D5×#4111yescharacteristic
436Dic3—41no—
437Dic3—42no—
438Dic3—102no—
439Dic3—201no—
440C2×C5—241no—
441C2×C5#557611yescharacteristic
442C2×C5C22×#20411yescharacteristic
443C2×C5#575211yescharacteristic
444D5—242no—
445C23—61no—
446C23—302no—
447Q8—54no—
448Q8—152no—
449Q8—241no—
450Q8—301no—
451Q8—1202no—
452D4—61no—
453D4—61no—
454D4—302no—
455D4—302no—
456D4—604no—
457D4—602no—
458D4—1201no—
459D4—1202no—
460C2×C4—52no—
461C2×C4—52no—
462C2×C4—62no—
463C2×C4—61no—
464C2×C4—122no—
465C2×C4—301no—
466C2×C4—301no—
467C2×C4—604no—
468C2×C4D5×D1211yescharacteristic
469C2×C4D5×D1211yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—22no—
472C8—101no—
473C8—101no—
474C2×C3#6596711yescharacteristic
475C2×C3C2×D5×SD1611yescharacteristic
476C2×C3#6610811yescharacteristic
477D3—81no—
478D3—402no—
479C5#7993211yescharacteristic, complemented, Sylow
480C22—121no—
481C22—121no—
482C22—121no—
483C22—602no—
484C22—602no—
485C22—602no—
486C22C2×D5×D1211yescharacteristic
487C4—21no—
488C4—54no—
489C4—102no—
490C4—122no—
491C4—121no—
492C4—302no—
493C4—601no—
494C4D5×#20412yes—
495C4#9202411yescharacteristic
496C4#9202911yescharacteristic
497C3#1061282111yescharacteristic, complemented, Sylow
498C2—241no—
499C2—1202no—
500C2#1175334111yescharacteristic
501C2C2×D5×#20411yescharacteristic
502C2#1175402411yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radical#11752538C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11752473C2semidirect
3. #11750949C2semidirect
4. C5×#4842C2semidirect
5. C3×#65119C2semidirect
6. #11747995C2semidirect
7. #11747843C2semidirect
8. #11747762C2semidirect
9. #11747760C2semidirect
10. C4×#6659C2semidirect
11. #11746912C2semidirect
51. #65119D3semidirect
93. #4842D5semidirect
140. Dic30#41semidirect
149. C3×Dic10SD16semidirect
305. Dic10#204semidirect
422. C3×C5#3362semidirect
479. C5#79932semidirect
497. C3#10612821semidirect

Maximal subgroups

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

subgroupindex
#117525382
#117524732
#117509492
C5×#48422
C3×#651192
#117479952
#117478432
#117477622
#117477602
C4×#66592
#117469122
#106128213
#799325