Finite Group Databasebeta

← #14282989

Subgroups — #14282989

Order 1920.

668 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5606C211yesmaximal, characteristic
2D3×#3963C211yesmaximal, characteristic, complemented
3#11748505C211yesmaximal, characteristic, complemented
4#11746358C211yesmaximal, characteristic, complemented
5C3×#64757C211yesmaximal, characteristic, complemented
6#11745963C211yesmaximal, characteristic, complemented
7#11745962C211yesmaximal, characteristic, complemented
8#10602501—31nomaximal, Hall
9C2×C5×#237C411yescharacteristic, complemented
10C22×C4×C5×D3C2211yescharacteristic
11C22×D3×Dic5—21no—
12C3×C5×#121C2211yescharacteristic
13C5×#938C411yescharacteristic, complemented
14C5×#937—21no—
15C5×D4×Dic3—21no—
16C5×#924C2211yescharacteristic
17C5×#897C411yescharacteristic, complemented
18C5×#892C411yescharacteristic, complemented
19C5×#883—21no—
20C5×#67⋊C4—21no—
21C2×#6650—21no—
22#91115C2211yescharacteristic
23#91114C2211yescharacteristic
24C3×#3963C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90994—21no—
27(C2×D3)⋊#168—21no—
28#68302—51nomaximal, Hall
29C5×#525—31no—
30C2×#3963—31no—
31#65496—31no—
32#64758—31no—
33#64758—31no—
34#64757—31no—
35#64757D311yescharacteristic, complemented
36C23×C5×D3D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2×C411yescharacteristic, complemented
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15—21no—
41C2×C5×#67—21no—
42C2×C5×#67—21no—
43C22×C5×Dic3—21no—
44C22×C5×Dic3D411yescharacteristic
45C5×#237—42no—
46C2×C4×C5×D3—42no—
47C2×C4×C5×D3C2×C411yescharacteristic
48C2×C4×C5×D3C2×C411yescharacteristic
49C2×C4×C5×D3D411yescharacteristic
50C2×C4×C5×D3D411yescharacteristic
51C2×C5×Dic6C2×C411yescharacteristic, complemented
52C22×C3×Dic5—21no—
53C2×D3×Dic5—24no—
54C2×D3×Dic5—42no—
55C2×D3×Dic5—42no—
56C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
57C3×C5×C22⋊C4—21no—
58C2×C3⋊#168—21no—
59C5×#217—21no—
60C5×#217—21no—
61C5×(C2×D3)⋊C4—21no—
62C5×(C2×D3)⋊C4—21no—
63C5×C4⋊Dic3—21no—
64C5×C4⋊Dic3C2×C411yescharacteristic, complemented
65C5×Dic3⋊C4—21no—
66C4×C5×Dic3—21no—
67C2×C3×#168—21no—
68#6650—42no—
69#5606D511yescharacteristic
70#4726—51no—
71D3×#95—51no—
72C3×#327—51no—
73#4537—51no—
74#4467—51no—
75#4452—51no—
76C2×C5×#41—31no—
77C23×C4×C5—31no—
78C23×Dic5—61no—
79C5×#123—61no—
80C5×C22⋊Q8—31no—
81C5×C22⋊Q8—31no—
82C5×#121—31no—
83C5×#121C2×D311yescharacteristic
84C5×#120—61no—
85C4×C5×D4—61no—
86C4×C5×D4—61no—
87C5×#117—31no—
88C2×#681—61no—
89#3963—31no—
90#3963—61no—
91#3963C2×D311yescharacteristic
92C22⋊#168—31no—
93C22⋊#168—61no—
94C22⋊#168C2×D311yescharacteristic
95#1504—151noSylow
96C23×C3×C5—21no—
97C23×C3×C5C2×D411yescharacteristic
98C22×C5×D3—21no—
99C22×C5×D3—21no—
100C22×C5×D3—22no—
101C22×C5×D3—22no—
102C22×C5×D3C22⋊C411yescharacteristic
103C22×C5×D3C22⋊C411yescharacteristic
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C3×C5×D4—41no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×Dic15—22no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114C5×#67—42no—
115C5×#67—42no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—21no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3—42no—
120C2×C5×Dic3C22⋊C411yescharacteristic
121C2×C5×Dic3C22⋊C411yescharacteristic
122C4×C5×D3—22no—
123C4×C5×D3—22no—
124C4×C5×D3—41no—
125C4×C5×D3—41no—
126C5×Dic6—41no—
127C2×C3×Dic5—22no—
128C2×C3×Dic5—41no—
129C2×C3×Dic5—41no—
130D3×Dic5—48no—
131C3⋊#168—41no—
132C3×#168—41no—
133C2×#237Dic511yescharacteristic, complemented
134C22×C4×D3—101no—
135C22×C4×D3C2×D511yescharacteristic
136C3×#121C2×D511yescharacteristic
137#938Dic511yescharacteristic, complemented
138#937—21no—
139D4×Dic3—21no—
140#924C2×D511yescharacteristic
141C2×ΓL(1,𝔽25)—101no—
142#897Dic511yescharacteristic, complemented
143#892Dic511yescharacteristic, complemented
144#883—21no—
145#67⋊C4—21no—
146C3×C22⋊C8—51no—
147C3×#95—51no—
148C3⋊#95—51no—
149C3⋊#95—101no—
150#830—51no—
151(C2×D3)⋊C8—101no—
152C24×C5—31no—
153C5×#41—122no—
154C2×C5×Q8—31no—
155C2×C5×D4—21no—
156C2×C5×D4—61no—
157C2×C5×D4—61no—
158C2×C5×D4C4×D311yescharacteristic, complemented
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5—61no—
165C22×C4×C5—122no—
166C22×C4×C5C22×D311yescharacteristic
167C22×Dic5—21no—
168C22×Dic5—64no—
169C22×Dic5—61no—
170C22×Dic5—122no—
171C22×Dic5—122no—
172C5×C4⋊C4—31no—
173C5×C4⋊C4—61no—
174C5×C4⋊C4—61no—
175C5×C4⋊C4C4×D311yescharacteristic, complemented
176C5×C22⋊C4—21no—
177C5×C22⋊C4—61no—
178C5×C22⋊C4—61no—
179C5×C22⋊C4—61no—
180C5×C22⋊C4—61no—
181C42×C5—61no—
182#681—122no—
183C2×#168—21no—
184C2×#168—61no—
185#525—31no—
186#407—151no—
187C2×#95—151no—
188#328—151no—
189#328—151no—
190#327—51no—
191#327—151no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5—41no—
195C22×C3×C5—41no—
196C22×C3×C5—41no—
197C22×C3×C5C2×C22⋊C411yescharacteristic
198C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
199C22×C3×C5#13711yescharacteristic
200C2×C5×D3—24no—
201C2×C5×D3—24no—
202C2×C5×D3—21no—
203C2×C5×D3—21no—
204C2×C5×D3—21no—
205C2×C5×D3—21no—
206C2×C5×D3#9912yes—
207C2×C5×D3#10412yes—
208C3×C4×C5—21no—
209C3×C4×C5—21no—
210C3×C4×C5—41no—
211Dic15—42no—
212C3×Dic5—42no—
213C5×Dic3—21no—
214C5×Dic3—21no—
215C5×Dic3—41no—
216C5×Dic3—41no—
217C23×D3C22⋊D511yescharacteristic
218C2×C3×D4—21no—
219C2×C3×D4C2×Dic511yescharacteristic, complemented
220C22×C3×C4—101no—
221C22×C3×C4C22×D511yescharacteristic
222C2×#67—21no—
223C2×#67—21no—
224C22×Dic3—21no—
225C22×Dic3—101no—
226C22×Dic3C22⋊D511yescharacteristic
227#237—42no—
228C2×C4×D3—42no—
229C2×C4×D3—104no—
230C2×C4×D3—202no—
231C2×C4×D3—202no—
232C2×C4×D3C2×Dic511yescharacteristic
233C2×C4×D3C2×Dic511yescharacteristic
234C2×C4×D3C22⋊D511yescharacteristic
235C2×C4×D3C22⋊D511yescharacteristic
236C2×Dic6C2×Dic511yescharacteristic, complemented
237C2×C3×C8—101no—
238C3×C4⋊C4C2×Dic511yescharacteristic, complemented
239C3×C22⋊C4—21no—
240#217—21no—
241#217—21no—
242(C2×D3)⋊C4—21no—
243(C2×D3)⋊C4—21no—
244C4⋊Dic3—21no—
245C4⋊Dic3C2×Dic511yescharacteristic, complemented
246Dic3⋊C4—21no—
247C4×Dic3—21no—
248C2×C3⋊C8—101no—
249ΓL(1,𝔽25)—202no—
250C23×C5—21no—
251C23×C5—31no—
252C23×C5—31no—
253C23×C5—62no—
254C23×C5—62no—
255C23×C5—61no—
256C23×C5—61no—
257C23×C5D3×D411yescharacteristic
258C5×Q8—121no—
259C5×D4—41no—
260C5×D4—41no—
261C5×D4—41no—
262C5×D4—122no—
263C5×D4—122no—
264C2×C4×C5—21no—
265C2×C4×C5—31no—
266C2×C4×C5—31no—
267C2×C4×C5—41no—
268C2×C4×C5—62no—
269C2×C4×C5—62no—
270C2×C4×C5—61no—
271C2×C4×C5—61no—
272C2×C4×C5—121no—
273C2×C4×C5—121no—
274C2×C4×C5—121no—
275C2×C4×C5—122no—
276C2×C4×C5C2×C4×D311yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×Dic5—22no—
279C2×Dic5—41no—
280C2×Dic5—41no—
281C2×Dic5—62no—
282C2×Dic5—128no—
283C2×Dic5—121no—
284C2×Dic5—121no—
285#168—41no—
286#168—121no—
287C2×#41—31no—
288C23×C4—31no—
289C23×C4—301no—
290C2×M16—301no—
291#123—61no—
292C22⋊Q8—31no—
293C22⋊Q8—31no—
294#121—31no—
295#121D3×D511yescharacteristic
296#120—61no—
297C4×D4—61no—
298C4×D4—61no—
299#117—31no—
300C22⋊C8—51no—
301C22⋊C8—151no—
302C22⋊C8—301no—
303#95—51no—
304#95—151no—
305#95—301no—
306C2×C3×C5—21no—
307C2×C3×C5—21no—
308C2×C3×C5—81no—
309C2×C3×C5C2×#9911yescharacteristic
310C2×C3×C5#41711yescharacteristic
311C2×C3×C5C2×#10411yescharacteristic
312C5×D3—22no—
313C5×D3—22no—
314C23×C3—21no—
315C23×C3C2×C22⋊D511yescharacteristic
316C22×D3—21no—
317C22×D3—21no—
318C22×D3—22no—
319C22×D3—22no—
320C22×D3C22⋊Dic511yescharacteristic
321C22×D3C22⋊Dic511yescharacteristic
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—41no—
325C2×C3×C4—21no—
326C2×C3×C4—41no—
327C2×C3×C4—102no—
328C2×C3×C4—201no—
329C2×C3×C4—201no—
330C2×C3×C4C22×Dic511yescharacteristic
331C2×C3×C4C2×C22⋊D511yescharacteristic
332#67—42no—
333#67—42no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—41no—
337C2×Dic3—42no—
338C2×Dic3—102no—
339C2×Dic3—201no—
340C2×Dic3—201no—
341C2×Dic3C22⋊Dic511yescharacteristic
342C2×Dic3C22⋊Dic511yescharacteristic
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—41no—
346C4×D3—41no—
347C4×D3—208no—
348Dic6—41no—
349C3×C8—201no—
350C3⋊C8—201no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—32no—
354C22×C5—32no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—41no—
358C22×C5—64no—
359C22×C5—64no—
360C22×C5—61no—
361C22×C5—61no—
362C22×C5—61no—
363C22×C5—61no—
364C22×C5D3×C22⋊C411yescharacteristic
365C22×C5#91111yescharacteristic
366C22×C5#91511yescharacteristic
367C4×C5—21no—
368C4×C5—21no—
369C4×C5—41no—
370C4×C5—61no—
371C4×C5—61no—
372C4×C5—121no—
373C4×C5—121no—
374Dic5—42no—
375Dic5—122no—
376C24—31no—
377#41—122no—
378C2×Q8—31no—
379C2×D4—21no—
380C2×D4—61no—
381C2×D4—61no—
382C2×D4D3×Dic511yescharacteristic, complemented
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—61no—
389C22×C4—101no—
390C22×C4—122no—
391C22×C4—304no—
392C22×C4—301no—
393C22×C4—602no—
394C22×C4—602no—
395C22×C4C2×D3×D511yescharacteristic
396M16—602no—
397C2×C8—101no—
398C2×C8—301no—
399C4⋊C4—31no—
400C4⋊C4—61no—
401C4⋊C4—61no—
402C4⋊C4D3×Dic511yescharacteristic, complemented
403C22⋊C4—21no—
404C22⋊C4—61no—
405C22⋊C4—61no—
406C22⋊C4—61no—
407C22⋊C4—61no—
408C42—61no—
409C3×C5#150411yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3#409511yescharacteristic
416C22×C3#409711yescharacteristic
417C22×C3C2×C22⋊Dic511yescharacteristic
418C2×D3—24no—
419C2×D3—24no—
420C2×D3—21no—
421C2×D3—21no—
422C2×D3—21no—
423C2×D3—21no—
424C2×D3#396612yes—
425C2×D3#396912yes—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—41no—
429C3×C4—202no—
430Dic3—21no—
431Dic3—21no—
432Dic3—41no—
433Dic3—41no—
434Dic3—202no—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—62no—
438C2×C5—62no—
439C2×C5—81no—
440C2×C5D3×#9911yescharacteristic
441C2×C5#477111yescharacteristic
442C2×C5D3×#10411yescharacteristic
443C23—21no—
444C23—31no—
445C23—31no—
446C23—62no—
447C23—62no—
448C23—61no—
449C23—61no—
450C23D3×C22⋊D511yescharacteristic
451Q8—121no—
452D4—41no—
453D4—41no—
454D4—41no—
455D4—122no—
456D4—122no—
457C2×C4—21no—
458C2×C4—31no—
459C2×C4—31no—
460C2×C4—41no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—102no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—122no—
470C2×C4—201no—
471C2×C4—201no—
472C2×C4—302no—
473C2×C4—608no—
474C2×C4—601no—
475C2×C4—601no—
476C2×C4C2×D3×Dic511yescharacteristic
477C2×C4D3×C22⋊D511yescharacteristic
478C8—201no—
479C8—601no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—81no—
483C2×C3C2×#396611yescharacteristic
484C2×C3#6552111yescharacteristic
485C2×C3C2×#396911yescharacteristic
486D3—22no—
487D3—22no—
488C5#6830211yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—32no—
492C22—32no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—64no—
497C22—64no—
498C22—61no—
499C22—61no—
500C22—61no—
501C22—61no—
502C22#9148011yescharacteristic
503C22#9148611yescharacteristic
504C22D3×C22⋊Dic511yescharacteristic
505C4—21no—
506C4—21no—
507C4—41no—
508C4—61no—
509C4—61no—
510C4—121no—
511C4—121no—
512C4—202no—
513C4—602no—
514C3#1060250111yescharacteristic, complemented, Sylow
515C2—21no—
516C2—21no—
517C2—62no—
518C2—62no—
519C2—81no—
520C2#1174895511yescharacteristic
521C2D3×#396611yescharacteristic
522C2D3×#396911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5606C2
cosocleC22×C3×C4×C5C23
hypercenter#121D3×D5
hypocenterC3×C5#1504
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. D3×#3963C2semidirect
3. #11748505C2semidirect
4. #11746358C2semidirect
5. C3×#64757C2semidirect
6. #11745963C2semidirect
7. #11745962C2semidirect
9. C2×C5×#237C4semidirect
13. C5×#938C4semidirect
17. C5×#897C4semidirect
18. C5×#892C4semidirect
35. #64757D3semidirect
38. C2×C3×C5×D4C2×C4semidirect
51. C2×C5×Dic6C2×C4semidirect
56. C3×C5×C4⋊C4C2×C4semidirect
64. C5×C4⋊Dic3C2×C4semidirect
133. C2×#237Dic5semidirect
137. #938Dic5semidirect
142. #897Dic5semidirect
143. #892Dic5semidirect
158. C2×C5×D4C4×D3semidirect
175. C5×C4⋊C4C4×D3semidirect
219. C2×C3×D4C2×Dic5semidirect
236. C2×Dic6C2×Dic5semidirect
238. C3×C4⋊C4C2×Dic5semidirect
245. C4⋊Dic3C2×Dic5semidirect
382. C2×D4D3×Dic5semidirect
402. C4⋊C4D3×Dic5semidirect
409. C3×C5#1504semidirect
488. C5#68302semidirect
514. C3#10602501semidirect

Maximal subgroups

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

subgroupindex
C5×#56062
D3×#39632
#117485052
#117463582
C3×#647572
#117459632
#117459622
#106025013
#683025