Finite Group Databasebeta

← #14417628

Subgroups — #14417628

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91808C211yesmaximal, characteristic
2#11756333C212yesmaximal, complemented
3C3×C4×C5×Q16C211yesmaximal, characteristic, complemented
4Q16×Dic15C211yesmaximal, characteristic, complemented
5#11751127C212yesmaximal, complemented
6D15×#107C211yesmaximal, characteristic, complemented
7#11750973C211yesmaximal, characteristic, complemented
8#11750918C212yesmaximal, complemented
9#11750904C212yesmaximal, complemented
10C4×D120C211yesmaximal, characteristic, complemented
11#11750790C211yesmaximal, characteristic, complemented
12#10611452—31nomaximal, Hall
13C2×#6821C2212yes—
14C2×C3×C5×Q16C2211yescharacteristic
15C3×C4×C5×Q8C2212yes—
16Q8×Dic15C2212yes—
17C2×#6717C2212yes—
18#91808C418yescomplemented
19C2×D120C2211yescharacteristic
20C2×#6705C2211yescharacteristic
21C2×C8×D15C2211yescharacteristic
22#91782—22no—
23#91782C2212yes—
24C4⋊C4×D15—22no—
25C4⋊C4×D15C2212yes—
26C4×D60—22no—
27C4×D60C2212yes—
28#91761—22no—
29#91761C2211yescharacteristic
30C3×C5×#107C2211yescharacteristic
31C3×C5×#103C2212yes—
32C3×C4×C5×C8C2211yescharacteristic
33#91119C2212yes—
34#91105C2212yes—
35#91102C2211yescharacteristic
36#91099C2211yescharacteristic
37C8×Dic15C2211yescharacteristic
38#91093C2212yes—
39#91091C2212yes—
40#91087C2211yescharacteristic
41#79721—51nomaximal, Hall
42C2×#4065—31no—
43#65908—32no—
44C4×C5×Q16D311yescharacteristic, complemented
45Q16×Dic5—31no—
46#65315—32no—
47D5×#107—31no—
48#65161—31no—
49#65106—32no—
50#65092—32no—
51C4×D40—31no—
52#64978—31no—
53C2×C3×C5×Q8C2312yes—
54#6821—24no—
55#6821C2×C418yescomplemented
56C2×D60—22no—
57C2×D60C2312yes—
58C2×C4×D15—22no—
59C2×C4×D15—22no—
60C2×C4×D15—22no—
61C2×C4×D15—22no—
62C2×C4×D15C2311yescharacteristic
63C3×C5×Q16C2×C414yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65C2×C3×C5×C8C2311yescharacteristic
66C3×C5×C4⋊C4—22no—
67C3×C5×C4⋊C4C2312yes—
68C3×C42×C5—22no—
69C3×C42×C5C2311yescharacteristic
70#6717C2×C418yescomplemented
71#6714—22no—
72#6714—22no—
73#6714D411yescharacteristic
74#6714D411yescharacteristic
75C4⋊Dic15—22no—
76C4⋊Dic15C2312yes—
77#6712—22no—
78#6712D411yescharacteristic
79#6712D411yescharacteristic
80C4×Dic15—22no—
81C4×Dic15C2311yescharacteristic
82C2×C3⋊#168C2311yescharacteristic
83C2×C3⋊#168C2311yescharacteristic
84D120C2×C414yescomplemented
85#6705—22no—
86C8×D15C2×C414yescomplemented
87C2×#919—51no—
88#5574—52no—
89C3×C4×Q16D511yescharacteristic, complemented
90Dic3×Q16—51no—
91#5026—52no—
92D3×#107—51no—
93#4872—51no—
94#4817—52no—
95#4803—52no—
96C4×D24—51no—
97#4689—51no—
98C2×#713—32no—
99C2×C5×Q16C2×D311yescharacteristic
100C4×C5×Q8C2×D312yes—
101Q8×Dic5—32no—
102C2×#688—32no—
103#4065—38no—
104C2×D40—31no—
105C2×#676—31no—
106C2×C8×D5—31no—
107#4039—32no—
108#4039—62no—
109D5×C4⋊C4—32no—
110D5×C4⋊C4—62no—
111C4×D20—32no—
112C4×D20—62no—
113#4018—31no—
114#4018—62no—
115C5×#107C2×D311yescharacteristic
116C5×#103C2×D312yes—
117C4×C5×C8C2×D311yescharacteristic
118#3967—32no—
119#3953—32no—
120#3950—31no—
121#3947—31no—
122C8×Dic5—31no—
123#3941—32no—
124#3939—32no—
125#3935—31no—
126#2951—151noSylow
127C22×D15—22no—
128C22×D15C2×D411yescharacteristic
129C3×C5×Q8—22no—
130C3×C5×Q8C22×C414yes—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137C2×Dic15C2×D411yescharacteristic
138C2×Dic15C2×D411yescharacteristic
139C2×Dic15C2×D411yescharacteristic
140D60—28no—
141D60—22no—
142D60C22×C414yes—
143C4×D15—28no—
144C4×D15—82no—
145C4×D15—82no—
146C4×D15—82no—
147C4×D15C22×C412yes—
148C4×D15#4112yes—
149C3×C5×C8—21no—
150C3×C5×C8C22×C412yes—
151C3⋊#168—21no—
152C3⋊#168C22×C412yes—
153C2×#239—52no—
154C2×C3×Q16C2×D511yescharacteristic
155C3×C4×Q8C2×D512yes—
156Q8×Dic3—52no—
157C2×#215—52no—
158#919—58no—
159C2×D24—51no—
160C2×ΓL(1,𝔽25)—51no—
161C2×D3×C8—51no—
162#893—52no—
163#893—102no—
164D3×C4⋊C4—52no—
165D3×C4⋊C4—102no—
166C4×D12—52no—
167C4×D12—102no—
168#872—51no—
169#872—102no—
170C3×#107C2×D511yescharacteristic
171C3×#103C2×D512yes—
172C3×C4×C8C2×D511yescharacteristic
173#835—52no—
174#821—52no—
175#818—51no—
176#815—51no—
177C8×Dic3—51no—
178#809—52no—
179#807—52no—
180#803—51no—
181C2×C5×Q8C22×D312yes—
182#713—38no—
183#713—64no—
184C2×D20—32no—
185C2×D20—62no—
186C2×C4×D5—31no—
187C2×C4×D5—62no—
188C2×C4×D5—62no—
189C2×C4×D5—62no—
190C2×C4×D5—62no—
191C5×Q16C4×D314yescomplemented
192C2×C5×C8C22×D311yescharacteristic
193C2×C5×C8C22×D311yescharacteristic
194C5×C4⋊C4—22no—
195C5×C4⋊C4C22×D312yes—
196C42×C5—22no—
197C42×C5C22×D311yescharacteristic
198#688—38no—
199#685—31no—
200#685—31no—
201#685—62no—
202#685—62no—
203C4⋊Dic5—32no—
204C4⋊Dic5—62no—
205#683—31no—
206#683—31no—
207#683—62no—
208C4×Dic5—31no—
209C4×Dic5—62no—
210C2×#168—31no—
211C2×#168—31no—
212D40—34no—
213#676—62no—
214C8×D5—34no—
215C2×#135—151no—
216#520—152no—
217#440—152no—
218#440—152no—
219C4×Q16—151no—
220C4×Q16D1511yescharacteristic, complemented
221C4×D8—151no—
222C4×D8—151no—
223C2×#107—151no—
224#417—152no—
225#405—151no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—21no—
228C2×D15—21no—
229C2×D15—24no—
230C2×D15—42no—
231C2×D15—42no—
232C2×D15C4×D412yes—
233C3×C4×C5—24no—
234C3×C4×C5—21no—
235C3×C4×C5—21no—
236C3×C4×C5—42no—
237C3×C4×C5C23×C411yescharacteristic
238C3×C4×C5C2×#4111yescharacteristic
239Dic15—21no—
240Dic15—21no—
241Dic15—42no—
242Dic15C4×D412yes—
243C2×C3×Q8C22×D512yes—
244#239—58no—
245#239—104no—
246C2×D12—52no—
247C2×D12—102no—
248C2×C4×D3—51no—
249C2×C4×D3—102no—
250C2×C4×D3—102no—
251C2×C4×D3—102no—
252C2×C4×D3—102no—
253C3×Q16C4×D514yescomplemented
254C2×C3×C8C22×D511yescharacteristic
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4—22no—
257C3×C4⋊C4C22×D512yes—
258C3×C42—22no—
259C3×C42C22×D511yescharacteristic
260#215—58no—
261(C2×D3)⋊C4—51no—
262(C2×D3)⋊C4—51no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—102no—
265C4⋊Dic3—52no—
266C4⋊Dic3—102no—
267Dic3⋊C4—51no—
268Dic3⋊C4—51no—
269Dic3⋊C4—102no—
270C4×Dic3—51no—
271C4×Dic3—102no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—51no—
274D24—54no—
275ΓL(1,𝔽25)—102no—
276D3×C8—54no—
277C22×D5—31no—
278C22×D5—62no—
279C5×Q8—22no—
280C5×Q8C2×C4×D314yes—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—31no—
287C2×Dic5—31no—
288C2×Dic5—31no—
289C2×Dic5—62no—
290D20—34no—
291D20—68no—
292D20—62no—
293C4×D5—32no—
294C4×D5—32no—
295C4×D5—68no—
296C4×D5—242no—
297C4×D5—242no—
298C4×D5—242no—
299C5×C8—21no—
300C5×C8C2×C4×D312yes—
301#168—32no—
302#168—61no—
303C2×#41—152no—
304#135—158no—
305C2×Q16C2×D1511yescharacteristic
306C2×SD16—152no—
307C2×D8—151no—
308C2×M16—151no—
309C22×C8—151no—
310C4×Q8—152no—
311C4×Q8C2×D1512yes—
312C4×D4—152no—
313C4×D4—152no—
314C4×D4—302no—
315C4×D4—302no—
316#117—151no—
317#117—302no—
318C2×C4⋊C4—152no—
319C2×C4⋊C4—302no—
320#107—151no—
321#107—152no—
322#107C2×D1511yescharacteristic
323#103—152no—
324#103C2×D1512yes—
325#102—152no—
326#102—152no—
327#97—151no—
328#97—151no—
329C4×C8—151no—
330C4×C8C2×D1511yescharacteristic
331C2×C3×C5C2×C4×D411yescharacteristic
332C2×C3×C5#57611yescharacteristic
333C2×C3×C5#57811yescharacteristic
334D15—22no—
335D15—44no—
336C22×D3—51no—
337C22×D3—102no—
338C3×Q8—22no—
339C3×Q8C2×C4×D514yes—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4C23×D511yescharacteristic
345C2×Dic3—51no—
346C2×Dic3—51no—
347C2×Dic3—51no—
348C2×Dic3—102no—
349D12—54no—
350D12—108no—
351D12—102no—
352C4×D3—52no—
353C4×D3—52no—
354C4×D3—108no—
355C4×D3—402no—
356C4×D3—402no—
357C4×D3—402no—
358C3×C8—21no—
359C3×C8C2×C4×D512yes—
360C3⋊C8—52no—
361C3⋊C8—101no—
362C22×C5C2×D3×D411yescharacteristic
363C2×D5—32no—
364C2×D5—61no—
365C2×D5—61no—
366C2×D5—64no—
367C2×D5—122no—
368C2×D5—122no—
369C4×C5—21no—
370C4×C5—21no—
371C4×C5—24no—
372C4×C5—42no—
373C4×C5C22×C4×D311yescharacteristic
374C4×C5D3×#4111yescharacteristic
375Dic5—32no—
376Dic5—61no—
377Dic5—61no—
378Dic5—122no—
379#41—158no—
380#41—304no—
381C2×Q8C22×D1512yes—
382C2×D4—152no—
383C2×D4—302no—
384C22×C4—151no—
385C22×C4—302no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—302no—
389Q16C4×D1514yescomplemented
390SD16—158no—
391D8—154no—
392M16—302no—
393C2×C8—151no—
394C2×C8—154no—
395C2×C8—151no—
396C2×C8C22×D1511yescharacteristic
397C2×C8C22×D1511yescharacteristic
398C4⋊C4—22no—
399C4⋊C4—151no—
400C4⋊C4—151no—
401C4⋊C4—152no—
402C4⋊C4—302no—
403C4⋊C4—302no—
404C4⋊C4C22×D1512yes—
405C22⋊C4—151no—
406C22⋊C4—151no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—22no—
410C42—151no—
411C42—302no—
412C42C22×D1511yescharacteristic
413C3×C5#295111yescharacteristic, complemented, Hall
414C22×C3C2×D4×D511yescharacteristic
415C2×D3—52no—
416C2×D3—101no—
417C2×D3—101no—
418C2×D3—104no—
419C2×D3—202no—
420C2×D3—202no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—24no—
424C3×C4—42no—
425C3×C4C22×C4×D511yescharacteristic
426C3×C4D5×#4111yescharacteristic
427Dic3—52no—
428Dic3—101no—
429Dic3—101no—
430Dic3—202no—
431C2×C5C4×D3×D411yescharacteristic
432C2×C5#576611yescharacteristic
433C2×C5#576911yescharacteristic
434D5—62no—
435D5—124no—
436C23—151no—
437C23—302no—
438Q8—22no—
439Q8C2×C4×D1514yes—
440D4—154no—
441D4—308no—
442D4—302no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—151no—
446C2×C4—152no—
447C2×C4—152no—
448C2×C4—151no—
449C2×C4—151no—
450C2×C4—308no—
451C2×C4—302no—
452C2×C4—1202no—
453C2×C4—1202no—
454C2×C4—1202no—
455C2×C4D4×D1511yescharacteristic
456C2×C4D4×D1511yescharacteristic
457C2×C4C23×D1511yescharacteristic
458C8—21no—
459C8—152no—
460C8—301no—
461C8C2×C4×D1512yes—
462C2×C3C4×D4×D511yescharacteristic
463C2×C3#6610011yescharacteristic
464C2×C3#6610311yescharacteristic
465D3—102no—
466D3—204no—
467C5#7972111yescharacteristic, complemented, Sylow
468C22—152no—
469C22—301no—
470C22—301no—
471C22—304no—
472C22—602no—
473C22—602no—
474C22C2×D4×D1511yescharacteristic
475C4—24no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—152no—
480C4—301no—
481C4—301no—
482C4—602no—
483C4C22×C4×D1511yescharacteristic
484C4#41×D1511yescharacteristic
485C3#1061145211yescharacteristic, complemented, Sylow
486C2—302no—
487C2—604no—
488C2C4×D4×D1511yescharacteristic
489C2#1175652511yescharacteristic
490C2#1175652811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C4×C5×Q16C2
socleC22×C3×C5C22×D4
prime radicalC2×#91808C2
cosocleC2×C3×C4×C5C24
hypercenterC4×Q16D15
hypocenterC3×C5#2951
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #11756333C2semidirect
3. C3×C4×C5×Q16C2semidirect
4. Q16×Dic15C2semidirect
5. #11751127C2semidirect
6. D15×#107C2semidirect
7. #11750973C2semidirect
8. #11750918C2semidirect
9. #11750904C2semidirect
10. C4×D120C2semidirect
11. #11750790C2semidirect
18. #91808C4semidirect
44. C4×C5×Q16D3semidirect
55. #6821C2×C4semidirect
63. C3×C5×Q16C2×C4semidirect
70. #6717C2×C4semidirect
84. D120C2×C4semidirect
86. C8×D15C2×C4semidirect
89. C3×C4×Q16D5semidirect
191. C5×Q16C4×D3semidirect
220. C4×Q16D15semidirect
253. C3×Q16C4×D5semidirect
389. Q16C4×D15semidirect
413. C3×C5#2951semidirect
467. C5#79721semidirect
485. C3#10611452semidirect

Maximal subgroups

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

subgroupindex
C2×#918082
#117563332
C3×C4×C5×Q162
Q16×Dic152
#117511272
D15×#1072
#117509732
#117509182
#117509042
C4×D1202
#117507902
#106114523
#797215