Finite Group Databasebeta

← #14297850

Subgroups — #14297850

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5522C211yesmaximal, characteristic
2C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
3#11748440C211yesmaximal, characteristic, complemented
4C2×#90979C211yesmaximal, characteristic
5C2×#90978C211yesmaximal, characteristic
6#11746353C211yesmaximal, characteristic, complemented
7C3×#64752C211yesmaximal, characteristic, complemented
8#10602439—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C5×#893C411yescharacteristic, complemented
15C5×#893C411yescharacteristic, complemented
16C5×#887C411yescharacteristic, complemented
17C5×#887C411yescharacteristic, complemented
18C5×#67⋊C4—21no—
19C5×#67⋊C4—21no—
20C5×#872—21no—
21C42×C5×D3—21no—
22C2×C3×C4×Dic5C2211yescharacteristic
23C2×C3×#681C2211yescharacteristic
24C2×Dic3⋊Dic5—21no—
25#90994—21no—
26Dic3⋊#168—21no—
27Dic3⋊#168—21no—
28#90979—22no—
29#90978—22no—
30#68770—51nomaximal, Hall
31C4×C5×#41—31no—
32C2×#3969—31no—
33C2×#3969—31no—
34C4×C4⋊Dic5—31no—
35#65213—31no—
36#64752—31no—
37#64752D311yescharacteristic, complemented
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C2×C5×#67—21no—
41C22×C5×Dic3D411yescharacteristic
42C22×C5×Dic3D411yescharacteristic
43C5×#235—21no—
44C5×#235—21no—
45C5×#235D412yes—
46C5×#235Q812yes—
47C2×C5×D12C2×C411yescharacteristic
48C2×C4×C5×D3—21no—
49C2×C4×C5×D3—21no—
50C2×C4×C5×D3—21no—
51C2×C5×Dic6C2×C411yescharacteristic
52C22×C3×Dic5—21no—
53C3×C5×C4⋊C4C2×C411yescharacteristic
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56C3×C42×C5—21no—
57C4×Dic15—21no—
58C4×Dic15—21no—
59#6710—21no—
60#6710—21no—
61C2×C3⋊#168—21no—
62C5×(C2×D3)⋊C4—21no—
63C5×(C2×D3)⋊C4—21no—
64C5×Dic3⋊C4—21no—
65C5×Dic3⋊C4—21no—
66C4×C5×Dic3—21no—
67C4×C5×Dic3—21no—
68C4×C5×Dic3C2×C411yescharacteristic
69C4×C5×Dic3C2×C411yescharacteristic
70C4×C5×Dic3D411yescharacteristic
71C4×C5×Dic3D411yescharacteristic
72C3×C4×Dic5—21no—
73C3×C4×Dic5—21no—
74C3×#681—21no—
75C3×#681—21no—
76C2×C3×#168—21no—
77Dic3⋊Dic5—24no—
78#5522D511yescharacteristic
79C2×#825—51no—
80#5118—51no—
81C4×Dic3⋊C4—51no—
82C2×#805—51no—
83C3×#339—51no—
84#4532—51no—
85C2×C5×#41—31no—
86C4×C5×Q8—31no—
87C4×C5×Q8—31no—
88C4×C5×D4—31no—
89C4×C5×D4—31no—
90C4×C5×D4—61no—
91C4×C5×D4—61no—
92C5×#117—61no—
93C5×#117C2×D311yescharacteristic
94C2×C42×C5—31no—
95C2×C42×C5—61no—
96C2×C4⋊Dic5—61no—
97C2×C4×Dic5—31no—
98C2×C4×Dic5C2×D311yescharacteristic
99C2×#681—31no—
100C2×#681C2×D311yescharacteristic
101#3969—62no—
102#3969—62no—
103#3963—61no—
104C4⋊#168—61no—
105C4⋊#168—61no—
106#1806—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×C5×D3—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×Q811yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×Dic15—22no—
118C2×Dic15—41no—
119C2×Dic15—41no—
120C5×#67—22no—
121C5×#67—22no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—22no—
124C2×C5×Dic3—41no—
125C2×C5×Dic3C22⋊C411yescharacteristic
126C2×C5×Dic3C22⋊C411yescharacteristic
127C2×C5×Dic3C22⋊C411yescharacteristic
128C2×C5×Dic3C22⋊C411yescharacteristic
129C5×D12—21no—
130C5×D12C4⋊C412yescomplemented
131C4×C5×D3—22no—
132C4×C5×D3—22no—
133C4×C5×D3—42no—
134C4×C5×D3—42no—
135C5×Dic6—21no—
136C5×Dic6C4⋊C412yescomplemented
137C2×C3×Dic5—22no—
138C2×C3×Dic5—41no—
139C2×C3×Dic5—41no—
140C3⋊#168—41no—
141C3×#168—41no—
142C2×#235C2×D511yescharacteristic
143C2×C3×M16—51no—
144C3×#117C2×D511yescharacteristic
145C2×C3×C42—51no—
146C2×Dic3⋊C4—101no—
147C2×C4×Dic3—51no—
148C2×C4×Dic3C2×D511yescharacteristic
149C2×#208—51no—
150#893Dic511yescharacteristic, complemented
151#893Dic511yescharacteristic, complemented
152#887Dic511yescharacteristic, complemented
153#887Dic511yescharacteristic, complemented
154#67⋊C4—21no—
155#67⋊C4—21no—
156#872—21no—
157C42×D3—21no—
158C3⋊#95—101no—
159#825—102no—
160Dic3⋊C8—101no—
161Dic3⋊C8—101no—
162#805—102no—
163C5×#41—32no—
164C5×#41—32no—
165C5×#41—61no—
166C5×#41—61no—
167C2×C5×Q8—31no—
168C2×C5×D4—31no—
169C2×C5×D4—61no—
170C22×C4×C5—31no—
171C22×C4×C5—31no—
172C22×C4×C5—61no—
173C22×C4×C5—61no—
174C22×C4×C5—61no—
175C22×C4×C5C22×D311yescharacteristic
176C22×Dic5—21no—
177C22×Dic5—61no—
178C5×C4⋊C4—61no—
179C5×C4⋊C4—61no—
180C5×C4⋊C4C4×D311yescharacteristic
181C5×C4⋊C4C4×D311yescharacteristic
182C5×C22⋊C4—21no—
183C5×C22⋊C4—61no—
184C5×C22⋊C4—61no—
185C42×C5—21no—
186C42×C5—31no—
187C42×C5—31no—
188C42×C5—31no—
189C42×C5—31no—
190C42×C5—61no—
191C42×C5—61no—
192C4⋊Dic5—64no—
193C4×Dic5—21no—
194C4×Dic5—21no—
195C4×Dic5—61no—
196C4×Dic5—61no—
197#681—21no—
198#681—21no—
199#681—61no—
200#681—61no—
201C2×#168—21no—
202C2×#168—61no—
203C4×#41—31no—
204#423—151no—
205C2×#104—151no—
206C2×#104—151no—
207C4×C4⋊C4—151no—
208#339—51no—
209#339—151no—
210C22×C3×C5—21no—
211C22×C3×C5—21no—
212C22×C3×C5C2×C22⋊C411yescharacteristic
213C22×C3×C5#12111yescharacteristic
214C22×C3×C5C22⋊Q811yescharacteristic
215C2×C5×D3—22no—
216C2×C5×D3—41no—
217C2×C5×D3—41no—
218C3×C4×C5—41no—
219C3×C4×C5—41no—
220C3×C4×C5C2×C4⋊C411yescharacteristic
221C3×C4×C5#11711yescharacteristic
222C3×C4×C5#12111yescharacteristic
223C3×C4×C5C22⋊Q811yescharacteristic
224Dic15—42no—
225C3×Dic5—42no—
226C5×Dic3—22no—
227C5×Dic3—21no—
228C5×Dic3—21no—
229C5×Dic3—21no—
230C5×Dic3#10412yescomplemented
231C22×C3×C4—101no—
232C22×C3×C4C22×D511yescharacteristic
233C2×#67—21no—
234C22×Dic3—101no—
235C22×Dic3C22⋊D511yescharacteristic
236C22×Dic3C22⋊D511yescharacteristic
237#235—21no—
238#235—21no—
239#235Dic1012yes—
240#235D2012yes—
241C2×D12C2×Dic511yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×Dic6C2×Dic511yescharacteristic
246C3×M16—101no—
247C3×M16—101no—
248C2×C3×C8—101no—
249C3×C4⋊C4C2×Dic511yescharacteristic
250C3×C4⋊C4C2×Dic511yescharacteristic
251C3×C22⋊C4—21no—
252C3×C42—21no—
253C3×C42—101no—
254C3×C42—101no—
255(C2×D3)⋊C4—21no—
256(C2×D3)⋊C4—21no—
257Dic3⋊C4—21no—
258Dic3⋊C4—21no—
259Dic3⋊C4—104no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3—101no—
263C4×Dic3—101no—
264C4×Dic3C2×Dic511yescharacteristic
265C4×Dic3C2×Dic511yescharacteristic
266C4×Dic3C22⋊D511yescharacteristic
267C4×Dic3C22⋊D511yescharacteristic
268#208—101no—
269#208—101no—
270C2×C3⋊C8—101no—
271C23×C5—61no—
272C23×C5D3×D411yescharacteristic
273C5×Q8—32no—
274C5×Q8—61no—
275C5×D4—32no—
276C5×D4—62no—
277C5×D4—62no—
278C5×D4—61no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—31no—
282C2×C4×C5—31no—
283C2×C4×C5—31no—
284C2×C4×C5—31no—
285C2×C4×C5—62no—
286C2×C4×C5—61no—
287C2×C4×C5—62no—
288C2×C4×C5—62no—
289C2×C4×C5—122no—
290C2×C4×C5—122no—
291C2×C4×C5—121no—
292C2×C4×C5C2×C4×D311yescharacteristic
293C2×C4×C5#23511yescharacteristic
294C2×C4×C5#23511yescharacteristic
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5D3×Q811yescharacteristic
298C2×Dic5—22no—
299C2×Dic5—41no—
300C2×Dic5—41no—
301C2×Dic5—62no—
302C2×Dic5—121no—
303C2×Dic5—121no—
304#168—41no—
305#168—121no—
306C2×#41—31no—
307C2×M16—51no—
308C2×M16—151no—
309C4×Q8—31no—
310C4×Q8—31no—
311C4×D4—31no—
312C4×D4—31no—
313C4×D4—61no—
314C4×D4—61no—
315#117—61no—
316#117D3×D511yescharacteristic
317C2×C4⋊C4—301no—
318C2×C42—31no—
319C2×C42—51no—
320C2×C42—61no—
321C2×C42—151no—
322C4⋊C8—301no—
323C4⋊C8—301no—
324#104—302no—
325#104—302no—
326#95—301no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5#38011yescharacteristic
330C2×C3×C5C2×#10411yescharacteristic
331C2×C3×C5#42111yescharacteristic
332C5×D3—42no—
333C23×C3C2×C22⋊D511yescharacteristic
334C22×D3—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—102no—
338C2×C3×C4—201no—
339C2×C3×C4—201no—
340C2×C3×C4C2×Dic1011yescharacteristic
341C2×C3×C4C2×D2011yescharacteristic
342C2×C3×C4#70911yescharacteristic
343C2×C3×C4#70911yescharacteristic
344C2×C3×C4C22×Dic511yescharacteristic
345C2×C3×C4C2×C22⋊D511yescharacteristic
346#67—22no—
347#67—22no—
348C2×Dic3—21no—
349C2×Dic3—22no—
350C2×Dic3—41no—
351C2×Dic3—102no—
352C2×Dic3—201no—
353C2×Dic3—201no—
354C2×Dic3C22⋊Dic511yescharacteristic
355C2×Dic3C22⋊Dic511yescharacteristic
356C2×Dic3C22⋊Dic511yescharacteristic
357C2×Dic3C22⋊Dic511yescharacteristic
358D12—21no—
359D12C4⋊Dic512yescomplemented
360C4×D3—22no—
361C4×D3—22no—
362C4×D3—42no—
363C4×D3—42no—
364Dic6—21no—
365Dic6C4⋊Dic512yescomplemented
366C3×C8—201no—
367C3⋊C8—201no—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5—62no—
371C22×C5—121no—
372C22×C5—121no—
373C22×C5D3×C22⋊C411yescharacteristic
374C22×C5#88411yescharacteristic
375C22×C5#89611yescharacteristic
376C4×C5—32no—
377C4×C5—41no—
378C4×C5—41no—
379C4×C5—62no—
380C4×C5—61no—
381C4×C5—61no—
382C4×C5—61no—
383C4×C5#87211yescharacteristic
384C4×C5#88411yescharacteristic
385C4×C5D3×C4⋊C411yescharacteristic
386C4×C5#89611yescharacteristic
387Dic5—42no—
388Dic5—122no—
389#41—32no—
390#41—32no—
391#41—61no—
392#41—61no—
393C2×Q8—31no—
394C2×D4—31no—
395C2×D4—61no—
396C22×C4—31no—
397C22×C4—31no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—101no—
402C22×C4—301no—
403C22×C4C2×D3×D511yescharacteristic
404M16—101no—
405M16—101no—
406M16—301no—
407M16—301no—
408C2×C8—101no—
409C2×C8—301no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—304no—
413C4⋊C4D3×Dic511yescharacteristic
414C4⋊C4D3×Dic511yescharacteristic
415C22⋊C4—21no—
416C22⋊C4—61no—
417C22⋊C4—61no—
418C42—21no—
419C42—31no—
420C42—31no—
421C42—31no—
422C42—31no—
423C42—61no—
424C42—61no—
425C42—101no—
426C42—101no—
427C42—301no—
428C42—301no—
429C3×C5#180611yescharacteristic, complemented, Hall
430C22×C3—21no—
431C22×C3—21no—
432C22×C3#407011yescharacteristic
433C22×C3#407611yescharacteristic
434C22×C3C2×C22⋊Dic511yescharacteristic
435C2×D3—22no—
436C2×D3—41no—
437C2×D3—41no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—202no—
441C3×C4#407011yescharacteristic
442C3×C4C2×C4⋊Dic511yescharacteristic
443C3×C4#407211yescharacteristic
444C3×C4#407611yescharacteristic
445Dic3—22no—
446Dic3—21no—
447Dic3—21no—
448Dic3—21no—
449Dic3—202no—
450Dic3#396912yescomplemented
451C2×C5—21no—
452C2×C5—21no—
453C2×C5—122no—
454C2×C5#466711yescharacteristic
455C2×C5D3×#10411yescharacteristic
456C2×C5#482111yescharacteristic
457C23—61no—
458C23D3×C22⋊D511yescharacteristic
459Q8—32no—
460Q8—61no—
461D4—32no—
462D4—62no—
463D4—62no—
464D4—61no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—31no—
470C2×C4—31no—
471C2×C4—62no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—102no—
476C2×C4—122no—
477C2×C4—122no—
478C2×C4—121no—
479C2×C4—201no—
480C2×C4—201no—
481C2×C4—302no—
482C2×C4—601no—
483C2×C4—601no—
484C2×C4D3×Dic1011yescharacteristic
485C2×C4#677111yescharacteristic
486C2×C4#677111yescharacteristic
487C2×C4D3×D2011yescharacteristic
488C2×C4C2×D3×Dic511yescharacteristic
489C2×C4D3×C22⋊D511yescharacteristic
490C8—201no—
491C8—601no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3#6550111yescharacteristic
495C2×C3C2×#396911yescharacteristic
496C2×C3#6552511yescharacteristic
497D3—42no—
498C5#6877011yescharacteristic, complemented, Sylow
499C22—21no—
500C22—21no—
501C22—62no—
502C22—121no—
503C22—121no—
504C22#9135211yescharacteristic
505C22#9145411yescharacteristic
506C22D3×C22⋊Dic511yescharacteristic
507C4—32no—
508C4—41no—
509C4—41no—
510C4—61no—
511C4—61no—
512C4—61no—
513C4—62no—
514C4—202no—
515C4—602no—
516C4#9135211yescharacteristic
517C4#9137111yescharacteristic
518C4D3×C4⋊Dic511yescharacteristic
519C4#9145411yescharacteristic
520C3#1060243911yescharacteristic, complemented, Sylow
521C2—21no—
522C2—21no—
523C2—122no—
524C2#1174878211yescharacteristic
525C2D3×#396911yescharacteristic
526C2#1174942911yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1806
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C4×Dic3⋊Dic5C2semidirect
3. #11748440C2semidirect
6. #11746353C2semidirect
7. C3×#64752C2semidirect
14. C5×#893C4semidirect
15. C5×#893C4semidirect
16. C5×#887C4semidirect
17. C5×#887C4semidirect
37. #64752D3semidirect
130. C5×D12C4⋊C4semidirect
136. C5×Dic6C4⋊C4semidirect
150. #893Dic5semidirect
151. #893Dic5semidirect
152. #887Dic5semidirect
153. #887Dic5semidirect
230. C5×Dic3#104semidirect
359. D12C4⋊Dic5semidirect
365. Dic6C4⋊Dic5semidirect
429. C3×C5#1806semidirect
450. Dic3#3969semidirect
498. C5#68770semidirect
520. C3#10602439semidirect

Maximal subgroups

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

subgroupindex
C5×#55222
C4×Dic3⋊Dic52
#117484402
C2×#909792
C2×#909782
#117463532
C3×#647522
#106024393
#687705