Finite Group Databasebeta

← #14297713

Subgroups — #14297713

Order 1920.

616 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#887C211yesmaximal, characteristic
2#11751860C211yesmaximal, characteristic
3D5⋊(Dic3⋊C8)C211yesmaximal, characteristic
4C2×#91154C211yesmaximal, characteristic
5C2×#91153C211yesmaximal, characteristic
6#11746745C211yesmaximal, characteristic
7C3×#64874C211yesmaximal, characteristic
8#10604451—31nomaximal, Hall
9C2×D5×Dic6C2211yescharacteristic
10C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
11C2×D5⋊(C3⋊C8)C2211yescharacteristic
12C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
13C2×C3×D5⋊C8C2211yescharacteristic
14C2×Dic3⋊AGL(1,𝔽5)—21no—
15C2×Dic3⋊AGL(1,𝔽5)—21no—
16#91776C411yescharacteristic, complemented
17C5×#887C411yescharacteristic, complemented
18C3×D5×C4⋊C4C2211yescharacteristic
19D5×Dic3⋊C4—21no—
20C4×D5×Dic3—21no—
21C4×D5×Dic3C2211yescharacteristic
22#91344C411yescharacteristic, complemented
23#91340C411yescharacteristic, complemented
24#91325—21no—
25#91324—21no—
26#91177—21no—
27Dic3⋊#170—21no—
28#91154—22no—
29#91153—22no—
30#68904—51nomaximal, Hall
31C4×Q8×D5—31no—
32C2×#4009—31no—
33C2×#4009—31no—
34#65688—31no—
35D5⋊(C4⋊C8)—31no—
36#64874—31no—
37#64874D311yescharacteristic
38C22×ΓL(1,𝔽16)—21no—
39C22×C3×AGL(1,𝔽5)—21no—
40C2×Dic30C2×C411yescharacteristic
41C2×C5×Dic6C2×C411yescharacteristic
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5C2311yescharacteristic
44C2×#1204—21no—
45C2×D5×Dic3—21no—
46C2×D5×Dic3D411yescharacteristic
47C2×D5×Dic3D411yescharacteristic
48D5×Dic6—21no—
49D5×Dic6—21no—
50D5×Dic6D412yes—
51D5×Dic6Q812yes—
52C2×C3⋊#170—21no—
53C4⋊ΓL(1,𝔽16)—21no—
54C4⋊ΓL(1,𝔽16)—21no—
55D5⋊(C3⋊C8)—21no—
56D5⋊(C3⋊C8)—21no—
57C2×C3×#170—21no—
58C3×C4⋊AGL(1,𝔽5)—21no—
59C3×C4⋊AGL(1,𝔽5)—21no—
60C3×D5⋊C8—21no—
61C3×D5⋊C8—21no—
62Dic3⋊AGL(1,𝔽5)—42no—
63Dic3⋊AGL(1,𝔽5)—42no—
64C3×C5×C4⋊C4C2×C411yescharacteristic
65#6712—21no—
66C4×Dic15—21no—
67C4×Dic15C2×C411yescharacteristic
68C5×Dic3⋊C4—21no—
69C4×C5×Dic3—21no—
70C4×C5×Dic3C2×C411yescharacteristic
71C3×C4⋊Dic5C2×C411yescharacteristic
72C3×#683—21no—
73Dic3⋊Dic5—21no—
74#6669—21no—
75Dic3×Dic5—21no—
76Dic3×Dic5—21no—
77Dic3×Dic5D411yescharacteristic
78Dic3×Dic5D411yescharacteristic
79C2×#887—51no—
80C2×#816—51no—
81C2×Dic3⋊C8—51no—
82#4975—51no—
83C2×#810—51no—
84C3×#340—51no—
85#4529—51no—
86C2×Q8×D5—31no—
87C2×C4⋊AGL(1,𝔽5)—31no—
88C2×C4⋊AGL(1,𝔽5)—61no—
89C2×C4⋊AGL(1,𝔽5)—61no—
90C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
91C2×D5⋊C8—31no—
92C2×D5⋊C8C2×D311yescharacteristic
93C4×C5×Q8—31no—
94Q8×Dic5—31no—
95D5×C4⋊C4—61no—
96D5×C4⋊C4C2×D311yescharacteristic
97#4033—31no—
98#4033—61no—
99C42×D5—31no—
100C42×D5—61no—
101C4×Dic10—31no—
102C4×Dic10—61no—
103#4009—62no—
104#4009—62no—
105#4004—61no—
106C4⋊#170—61no—
107#1803—151noSylow
108C22×C3×D5C2×D411yescharacteristic
109C2×ΓL(1,𝔽16)—41no—
110C2×ΓL(1,𝔽16)—41no—
111C2×ΓL(1,𝔽16)—41no—
112C2×C3×AGL(1,𝔽5)—41no—
113C2×C3×AGL(1,𝔽5)—41no—
114C2×C3×AGL(1,𝔽5)—41no—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5C22×C411yescharacteristic
117C2×Dic15—21no—
118C2×Dic15C22⋊C411yescharacteristic
119C2×Dic15C22⋊C411yescharacteristic
120Dic30—21no—
121Dic30C4⋊C412yescomplemented
122C2×C5×Dic3—21no—
123C2×C5×Dic3C22⋊C411yescharacteristic
124C2×C5×Dic3C22⋊C411yescharacteristic
125C5×Dic6—21no—
126C5×Dic6C4⋊C412yescomplemented
127C2×C3×Dic5—21no—
128C2×C3×Dic5C2×D411yescharacteristic
129C3×C4×D5—41no—
130C3×C4×D5—41no—
131C3×C4×D5C2×D411yescharacteristic
132C3×C4×D5C2×Q811yescharacteristic
133C3×C4×D5#4111yescharacteristic
134C3×C4×D5#4111yescharacteristic
135#1204—22no—
136#1204—22no—
137D5×Dic3—22no—
138D5×Dic3—22no—
139D5×Dic3—21no—
140D5×Dic3—21no—
141D5×Dic3SD1612yes—
142D5×Dic3Q1612yes—
143C3⋊#170—41no—
144C3×#170—41no—
145C22×Dic6—51no—
146C22×C3×C8—51no—
147C2×C3×C4⋊C4—51no—
148C2×C3×C4⋊C4—51no—
149C2×C4⋊Dic3—51no—
150C2×Dic3⋊C4—101no—
151C2×Dic3⋊C4—101no—
152C2×Dic3⋊C4—101no—
153C2×C4×Dic3—51no—
154C2×C4×Dic3—101no—
155C22×C3⋊C8—51no—
156#887—51no—
157#887—51no—
158#887—51no—
159#887—101no—
160#887—101no—
161#887AGL(1,𝔽5)11yescharacteristic, complemented
162#816—102no—
163Dic3⋊C8—101no—
164Dic3⋊C8—101no—
165#810—102no—
166C22×AGL(1,𝔽5)—21no—
167C22×AGL(1,𝔽5)—61no—
168C2×C5×Q8—31no—
169Q8×D5—32no—
170Q8×D5—32no—
171Q8×D5—61no—
172Q8×D5—61no—
173C2×C4×D5—21no—
174C2×C4×D5—31no—
175C2×C4×D5—31no—
176C2×C4×D5—61no—
177C2×C4×D5C22×D311yescharacteristic
178C2×Dic10—31no—
179C2×Dic10—61no—
180C2×#170—21no—
181C2×#170—61no—
182C4⋊AGL(1,𝔽5)—21no—
183C4⋊AGL(1,𝔽5)—21no—
184C4⋊AGL(1,𝔽5)—61no—
185C4⋊AGL(1,𝔽5)—61no—
186C4⋊AGL(1,𝔽5)—122no—
187C4⋊AGL(1,𝔽5)—122no—
188D5⋊C8—21no—
189D5⋊C8—21no—
190D5⋊C8—61no—
191D5⋊C8—61no—
192C5×C4⋊C4—61no—
193C5×C4⋊C4C4×D311yescharacteristic
194C42×C5—31no—
195C42×C5—61no—
196C4⋊Dic5—61no—
197C4⋊Dic5C4×D311yescharacteristic
198#683—21no—
199#683—61no—
200#683—61no—
201C4×Dic5—31no—
202C4×Dic5—31no—
203C4×Dic5—31no—
204C4×Dic5—61no—
205C4×Dic5—61no—
206C4×Dic5—61no—
207C2×C4×Q8—151no—
208C2×C4⋊C8—151no—
209C2×#103—151no—
210C2×#103—151no—
211#384—151no—
212#340—51no—
213#340—151no—
214C22×C3×C5C2×C22⋊C411yescharacteristic
215C2×C3×D5#12111yescharacteristic
216C2×C3×D5C22⋊Q811yescharacteristic
217C2×C3×D5C2×SD1611yescharacteristic
218C2×C3×D5C2×Q1611yescharacteristic
219C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
220C2×C3×D5#13711yescharacteristic
221ΓL(1,𝔽16)—81no—
222C3×AGL(1,𝔽5)—81no—
223C3×C4×C5—41no—
224C3×C4×C5C2×C4⋊C411yescharacteristic
225C3×C4×C5#11711yescharacteristic
226Dic15—22no—
227Dic15—21no—
228Dic15#10312yescomplemented
229C3×Dic5—41no—
230C3×Dic5#12111yescharacteristic
231C3×Dic5C22⋊Q811yescharacteristic
232C5×Dic3—22no—
233C5×Dic3—21no—
234C5×Dic3#10312yescomplemented
235C22×C3×C4—51no—
236C22×C3×C4—101no—
237C22×C3×C4—101no—
238C22×Dic3—51no—
239C22×Dic3—51no—
240C22×Dic3—101no—
241C22×Dic3—101no—
242C2×Dic6—51no—
243C2×Dic6—52no—
244C2×Dic6—52no—
245C2×Dic6—101no—
246C2×Dic6—101no—
247C2×Dic6—101no—
248C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
249C2×C3×C8—101no—
250C2×C3×C8—101no—
251C2×C3×C8—101no—
252C3×C4⋊C4—51no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4—101no—
255C3×C4⋊C4—101no—
256C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
257C4⋊Dic3—101no—
258C4⋊Dic3—101no—
259Dic3⋊C4—21no—
260Dic3⋊C4—101no—
261Dic3⋊C4—101no—
262Dic3⋊C4—101no—
263Dic3⋊C4—202no—
264Dic3⋊C4—202no—
265C4×Dic3—21no—
266C4×Dic3—51no—
267C4×Dic3—51no—
268C4×Dic3—51no—
269C4×Dic3—101no—
270C4×Dic3—101no—
271C4×Dic3—101no—
272C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
273C2×C3⋊C8—101no—
274C2×C3⋊C8—101no—
275C2×C3⋊C8—101no—
276C22×D5D3×D411yescharacteristic
277C2×AGL(1,𝔽5)—41no—
278C2×AGL(1,𝔽5)—41no—
279C2×AGL(1,𝔽5)—41no—
280C2×AGL(1,𝔽5)—121no—
281C2×AGL(1,𝔽5)—121no—
282C2×AGL(1,𝔽5)—121no—
283C5×Q8—32no—
284C5×Q8—61no—
285C2×C4×C5—21no—
286C2×C4×C5—31no—
287C2×C4×C5—31no—
288C2×C4×C5—61no—
289C2×C4×C5C2×C4×D311yescharacteristic
290C2×Dic5—21no—
291C2×Dic5—31no—
292C2×Dic5—31no—
293C2×Dic5—61no—
294C2×Dic5D3×D411yescharacteristic
295C4×D5—32no—
296C4×D5—32no—
297C4×D5—41no—
298C4×D5—41no—
299C4×D5—62no—
300C4×D5—62no—
301C4×D5—61no—
302C4×D5—61no—
303C4×D5#23511yescharacteristic
304C4×D5#23511yescharacteristic
305C4×D5D3×D411yescharacteristic
306C4×D5D3×Q811yescharacteristic
307Dic10—32no—
308Dic10—61no—
309Dic10—62no—
310Dic10—62no—
311#170—41no—
312#170—121no—
313C22×Q8—151no—
314C22×C8—51no—
315C22×C8—151no—
316C4×Q8—31no—
317C4×Q8—151no—
318C4×Q8—151no—
319C4×Q8—151no—
320C4×Q8—301no—
321C4×Q8—301no—
322C2×C4⋊C4—51no—
323C2×C4⋊C4—51no—
324C2×C4⋊C4—151no—
325C2×C4⋊C4—301no—
326C2×C4⋊C4—301no—
327C2×C4⋊C4—301no—
328C2×C42—151no—
329C2×C42—301no—
330C4⋊C8—301no—
331C4⋊C8—301no—
332#103—302no—
333#103—302no—
334C2×C3×C5#38011yescharacteristic
335C2×C3×C5C2×#10311yescharacteristic
336C2×C3×C5#41711yescharacteristic
337C3×D5#46011yescharacteristic
338C3×D5#46211yescharacteristic
339C3×D5#47511yescharacteristic
340C3×D5#47711yescharacteristic
341C23×C3—51no—
342C2×C3×C4—21no—
343C2×C3×C4—51no—
344C2×C3×C4—51no—
345C2×C3×C4—51no—
346C2×C3×C4—51no—
347C2×C3×C4—51no—
348C2×C3×C4—101no—
349C2×C3×C4—201no—
350C2×C3×C4—201no—
351C2×C3×C4—201no—
352C2×C3×C4—201no—
353C2×C3×C4—201no—
354C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—51no—
357C2×Dic3—52no—
358C2×Dic3—52no—
359C2×Dic3—51no—
360C2×Dic3—101no—
361C2×Dic3—102no—
362C2×Dic3—102no—
363C2×Dic3—101no—
364C2×Dic3—101no—
365C2×Dic3—201no—
366C2×Dic3—201no—
367C2×Dic3—201no—
368C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
369C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
370Dic6—21no—
371Dic6—52no—
372Dic6—102no—
373Dic6—102no—
374Dic6—101no—
375Dic6C4⋊AGL(1,𝔽5)12yescomplemented
376C3×C8—201no—
377C3⋊C8—201no—
378C22×C5D3×C22⋊C411yescharacteristic
379C2×D5#88411yescharacteristic
380C2×D5#89611yescharacteristic
381C2×D5#91111yescharacteristic
382C2×D5D3×SD1611yescharacteristic
383C2×D5#91511yescharacteristic
384C2×D5D3×Q1611yescharacteristic
385AGL(1,𝔽5)—81no—
386AGL(1,𝔽5)—241no—
387C4×C5—32no—
388C4×C5—41no—
389C4×C5—62no—
390C4×C5—61no—
391C4×C5#87211yescharacteristic
392C4×C5D3×C4⋊C411yescharacteristic
393Dic5—32no—
394Dic5—41no—
395Dic5—62no—
396Dic5—61no—
397Dic5#88411yescharacteristic
398Dic5#89611yescharacteristic
399C2×Q8—31no—
400C2×Q8—152no—
401C2×Q8—152no—
402C2×Q8—151no—
403C2×Q8—301no—
404C2×Q8—301no—
405C2×Q8—301no—
406C22×C4—51no—
407C22×C4—101no—
408C22×C4—101no—
409C22×C4—151no—
410C22×C4—151no—
411C22×C4—301no—
412C22×C4—301no—
413C2×C8—101no—
414C2×C8—101no—
415C2×C8—101no—
416C2×C8—301no—
417C2×C8—301no—
418C2×C8—301no—
419C4⋊C4—51no—
420C4⋊C4—61no—
421C4⋊C4—101no—
422C4⋊C4—101no—
423C4⋊C4—101no—
424C4⋊C4—301no—
425C4⋊C4—301no—
426C4⋊C4—301no—
427C4⋊C4—301no—
428C4⋊C4—301no—
429C4⋊C4—602no—
430C4⋊C4—602no—
431C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
432C42—31no—
433C42—61no—
434C42—151no—
435C42—151no—
436C42—151no—
437C42—301no—
438C42—301no—
439C42—301no—
440C3×C5#180311yescharacteristic, complemented, Hall
441C22×C3—51no—
442C22×C3—51no—
443C22×C3—51no—
444C22×C3—51no—
445C22×C3—51no—
446C22×C3—51no—
447C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
448C3×C4—41no—
449C3×C4—51no—
450C3×C4—51no—
451C3×C4—201no—
452C3×C4—401no—
453C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
454C3×C4#413011yescharacteristic
455Dic3—21no—
456Dic3—22no—
457Dic3—52no—
458Dic3—101no—
459Dic3—102no—
460Dic3—401no—
461Dic3#400912yescomplemented
462C2×C5#466711yescharacteristic
463C2×C5#477111yescharacteristic
464C2×C5D3×#10311yescharacteristic
465D5#476211yescharacteristic
466D5#479511yescharacteristic
467D5#485411yescharacteristic
468D5#487511yescharacteristic
469C23—51no—
470Q8—32no—
471Q8—61no—
472Q8—152no—
473Q8—302no—
474Q8—302no—
475Q8—301no—
476C2×C4—21no—
477C2×C4—31no—
478C2×C4—31no—
479C2×C4—51no—
480C2×C4—51no—
481C2×C4—51no—
482C2×C4—51no—
483C2×C4—51no—
484C2×C4—61no—
485C2×C4—101no—
486C2×C4—152no—
487C2×C4—152no—
488C2×C4—151no—
489C2×C4—151no—
490C2×C4—201no—
491C2×C4—201no—
492C2×C4—201no—
493C2×C4—201no—
494C2×C4—201no—
495C2×C4—301no—
496C2×C4—301no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—301no—
500C2×C4—601no—
501C2×C4—601no—
502C2×C4—601no—
503C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
504C8—201no—
505C8—601no—
506C2×C3—51no—
507C2×C3—51no—
508C2×C3—51no—
509C2×C3—51no—
510C2×C3#6576511yescharacteristic
511C2×C3C2×#400911yescharacteristic
512C2×C3#6579311yescharacteristic
513C5#6890411yescharacteristic, complemented, Sylow
514C22—51no—
515C22—51no—
516C22—51no—
517C22—51no—
518C22—51no—
519C22—51no—
520C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
521C4—32no—
522C4—41no—
523C4—51no—
524C4—51no—
525C4—61no—
526C4—62no—
527C4—152no—
528C4—201no—
529C4—301no—
530C4—302no—
531C4—401no—
532C4—1201no—
533C4#9190911yescharacteristic
534C4D3×C4⋊AGL(1,𝔽5)11yescharacteristic
535C3#1060445111yescharacteristic, complemented, Sylow
536C2—51no—
537C2—51no—
538C2—51no—
539C2—51no—
540C2#1175185411yescharacteristic
541C2#1175193711yescharacteristic
542C2D3×#400911yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1803
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #91776C4semidirect
17. C5×#887C4semidirect
22. #91344C4semidirect
23. #91340C4semidirect
121. Dic30C4⋊C4semidirect
126. C5×Dic6C4⋊C4semidirect
161. #887AGL(1,𝔽5)semidirect
228. Dic15#103semidirect
234. C5×Dic3#103semidirect
375. Dic6C4⋊AGL(1,𝔽5)semidirect
440. C3×C5#1803semidirect
461. Dic3#4009semidirect
513. C5#68904semidirect
535. C3#10604451semidirect

Maximal subgroups

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

subgroupindex
D5×#8872
#117518602
D5⋊(Dic3⋊C8)2
C2×#911542
C2×#911532
#117467452
C3×#648742
#106044513
#689045