Finite Group Databasebeta

← #14297845

Subgroups — #14297845

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
1#11754455C211yesmaximal, characteristic
2C4×#6712C211yesmaximal, characteristic, complemented
3C2×C5×#805C211yesmaximal, characteristic
4#11748437C211yesmaximal, characteristic, complemented
5C2×#90978C211yesmaximal, characteristic
6C3×#64743C211yesmaximal, characteristic, complemented
7#11745973C211yesmaximal, characteristic, complemented
8#10601148—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11C2×#6712—21no—
12C2×C4×Dic15C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17#67⋊Dic5—21no—
18#67⋊Dic5—21no—
19#91435C411yescharacteristic, complemented
20#91435C411yescharacteristic, complemented
21C4×D3×Dic5—21no—
22#91371—21no—
23#91344C411yescharacteristic, complemented
24#91344C411yescharacteristic, complemented
25#91115—21no—
26C5×#805—22no—
27#90983—21no—
28#90983—21no—
29#90978—22no—
30#68770—51nomaximal, Hall
31#41×Dic5—31no—
32C2×C5×#104—31no—
33C2×#3969—31no—
34#65407—31no—
35C4×#683—31no—
36#64775—31no—
37#64743D311yescharacteristic, complemented
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15—21no—
41C22×Dic15D411yescharacteristic
42C22×Dic15D411yescharacteristic
43C2×C5×#67—21no—
44C5×#235—21no—
45C5×#235—21no—
46C5×#235D412yes—
47C5×#235Q812yes—
48C2×C5×D12C2×C411yescharacteristic
49C2×C4×C5×D3—21no—
50C2×C5×Dic6C2×C411yescharacteristic
51C2×D3×Dic5—21no—
52C2×D3×Dic5—21no—
53C3×C42×C5—21no—
54C3×C42×C5—21no—
55#6712—24no—
56C4×Dic15—21no—
57C4×Dic15—21no—
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15C2×C411yescharacteristic
60C4×Dic15D411yescharacteristic
61C4×Dic15D411yescharacteristic
62C5×#208—21no—
63C5×#208—21no—
64C2×C5×C3⋊C8—21no—
65C3×C22⋊Dic5—21no—
66C3×C4⋊Dic5C2×C411yescharacteristic
67C3×C4⋊Dic5C2×C411yescharacteristic
68C3×C4×Dic5—21no—
69C3×#681—21no—
70C3×#681—21no—
71C2×C3×#168—21no—
72Dic3⋊Dic5—21no—
73Dic3⋊Dic5—21no—
74(C2×D3)⋊Dic5—21no—
75(C2×D3)⋊Dic5—21no—
76Dic3×Dic5—21no—
77Dic3×Dic5—21no—
78#5522—51no—
79C2×#825—51no—
80#5118—51no—
81C4×Dic3⋊C4—51no—
82C2×#805D511yescharacteristic
83C3×#339—51no—
84#4532—51no—
85C2×C5×#41—31no—
86C2×C5×M16—31no—
87C2×C42×C5C2×D311yescharacteristic
88Q8×Dic5—31no—
89Q8×Dic5—31no—
90D4×Dic5—31no—
91D4×Dic5—31no—
92D4×Dic5—61no—
93D4×Dic5—61no—
94#4072—61no—
95#4072C2×D311yescharacteristic
96C2×#683—61no—
97C2×C4×Dic5—31no—
98C2×C4×Dic5—31no—
99C2×C4×Dic5—61no—
100C2×#681C2×D311yescharacteristic
101C5×#104—62no—
102#3969—62no—
103#3963—61no—
104#3946—61no—
105#3946—61no—
106#1806—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×C5×D3—21no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5C22×C411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×Q811yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×C3×C4×C5#4111yescharacteristic
118C2×Dic15—22no—
119C2×Dic15—22no—
120C2×Dic15—41no—
121C2×Dic15—41no—
122C2×Dic15—41no—
123C2×Dic15C22⋊C411yescharacteristic
124C2×Dic15C22⋊C411yescharacteristic
125C2×Dic15C22⋊C411yescharacteristic
126C2×Dic15C22⋊C411yescharacteristic
127C5×#67—22no—
128C5×#67—22no—
129C2×C5×Dic3—21no—
130C5×D12—21no—
131C5×D12C4⋊C412yescomplemented
132C4×C5×D3—22no—
133C4×C5×D3—22no—
134C5×Dic6—21no—
135C5×Dic6C4⋊C412yescomplemented
136C2×C3×Dic5—21no—
137C2×C3×Dic5—21no—
138D3×Dic5—42no—
139D3×Dic5—42no—
140C3×#168—41no—
141C5×C3⋊C8—41no—
142C2×#235C2×D511yescharacteristic
143C2×C3×M16—51no—
144C3×#117—51no—
145C2×C3×C42C2×D511yescharacteristic
146C2×Dic3⋊C4—101no—
147C2×C4×Dic3—51no—
148C2×C4×Dic3—51no—
149C2×#208C2×D511yescharacteristic
150#893—51no—
151#893—51no—
152#887—51no—
153#887—51no—
154#67⋊C4—101no—
155#67⋊C4—101no—
156#872—101no—
157C42×D3—101no—
158C3⋊#95—101no—
159#825—102no—
160Dic3⋊C8—101no—
161Dic3⋊C8—101no—
162#805—22no—
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—21no—
171C22×C4×C5—61no—
172C22×C4×C5C22×D311yescharacteristic
173C22×Dic5—31no—
174C22×Dic5—31no—
175C22×Dic5—61no—
176C22×Dic5—61no—
177C22×Dic5—61no—
178C5×M16—61no—
179C5×M16—61no—
180C2×C5×C8—61no—
181C42×C5—21no—
182C42×C5—21no—
183C22⋊Dic5—21no—
184C22⋊Dic5—61no—
185C22⋊Dic5—61no—
186C4⋊Dic5—61no—
187C4⋊Dic5—61no—
188C4⋊Dic5C4×D311yescharacteristic
189C4⋊Dic5C4×D311yescharacteristic
190#683—64no—
191C4×Dic5—21no—
192C4×Dic5—31no—
193C4×Dic5—31no—
194C4×Dic5—31no—
195C4×Dic5—31no—
196C4×Dic5—61no—
197C4×Dic5—61no—
198C4×Dic5—61no—
199C4×Dic5—61no—
200#681—21no—
201#681—21no—
202C2×#168—21no—
203C4×#41—151no—
204#423—151no—
205C2×#104—31no—
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—42no—
219C3×C4×C5C2×C4⋊C411yescharacteristic
220C3×C4×C5#11711yescharacteristic
221C3×C4×C5#12111yescharacteristic
222C3×C4×C5C22⋊Q811yescharacteristic
223Dic15—21no—
224Dic15—21no—
225Dic15—21no—
226Dic15—42no—
227Dic15#10412yescomplemented
228C3×Dic5—41no—
229C3×Dic5—41no—
230C5×Dic3—22no—
231C22×C3×C4—21no—
232C22×C3×C4C22×D511yescharacteristic
233C2×#67—21no—
234C22×Dic3—51no—
235C22×Dic3—51no—
236C22×Dic3—101no—
237#235—21no—
238#235—21no—
239#235Dic1012yes—
240#235C22⋊D512yes—
241C2×D12C4×D511yescharacteristic
242C2×C4×D3—21no—
243C2×C4×D3—101no—
244C2×C4×D3—101no—
245C2×Dic6C4×D511yescharacteristic
246C3×M16—101no—
247C3×M16—101no—
248C2×C3×C8—101no—
249C3×C4⋊C4—51no—
250C3×C4⋊C4—51no—
251C3×C22⋊C4—101no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42—101no—
255(C2×D3)⋊C4—101no—
256(C2×D3)⋊C4—101no—
257Dic3⋊C4—101no—
258Dic3⋊C4—101no—
259Dic3⋊C4—104no—
260C4×Dic3—51no—
261C4×Dic3—51no—
262C4×Dic3—51no—
263C4×Dic3—51no—
264C4×Dic3—101no—
265C4×Dic3—101no—
266C4×Dic3—101no—
267C4×Dic3—101no—
268#208—21no—
269#208—21no—
270C2×C3⋊C8—21no—
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—22no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—61no—
283C2×C4×C5—62no—
284C2×C4×C5—62no—
285C2×C4×C5C2×C4×D311yescharacteristic
286C2×C4×C5#23511yescharacteristic
287C2×C4×C5#23511yescharacteristic
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5D3×Q811yescharacteristic
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—31no—
294C2×Dic5—31no—
295C2×Dic5—31no—
296C2×Dic5—31no—
297C2×Dic5—62no—
298C2×Dic5—62no—
299C2×Dic5—122no—
300C2×Dic5—122no—
301C2×Dic5—121no—
302C2×Dic5—121no—
303C2×Dic5—121no—
304C5×C8—121no—
305#168—41no—
306C2×#41—31no—
307C2×M16—31no—
308C2×M16—51no—
309C4×Q8—151no—
310C4×Q8—151no—
311C4×D4—151no—
312C4×D4—151no—
313C4×D4—301no—
314C4×D4—301no—
315#117—51no—
316#117—301no—
317C2×C4⋊C4—301no—
318C2×C42—151no—
319C2×C42—151no—
320C2×C42—301no—
321C2×C42D3×D511yescharacteristic
322C4⋊C8—301no—
323C4⋊C8—301no—
324#104—62no—
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×C3D4×D511yescharacteristic
334C22×D3—21no—
335C2×C3×C4—22no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—101no—
339C2×C3×C4—101no—
340C2×C3×C4C2×Dic1011yescharacteristic
341C2×C3×C4C2×C4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4#71111yescharacteristic
344C2×C3×C4#71111yescharacteristic
345C2×C3×C4C2×C22⋊D511yescharacteristic
346#67—22no—
347#67—22no—
348C2×Dic3—21no—
349C2×Dic3—51no—
350C2×Dic3—51no—
351C2×Dic3—51no—
352C2×Dic3—51no—
353C2×Dic3—102no—
354C2×Dic3—102no—
355C2×Dic3—201no—
356C2×Dic3—201no—
357C2×Dic3—201no—
358D12—21no—
359D12#68312yescomplemented
360C4×D3—22no—
361C4×D3—22no—
362C4×D3—202no—
363C4×D3—202no—
364Dic6—21no—
365Dic6#68312yescomplemented
366C3×C8—201no—
367C3⋊C8—41no—
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—42no—
377C4×C5—62no—
378C4×C5#87211yescharacteristic
379C4×C5#88411yescharacteristic
380C4×C5D3×C4⋊C411yescharacteristic
381C4×C5#89611yescharacteristic
382Dic5—32no—
383Dic5—41no—
384Dic5—41no—
385Dic5—61no—
386Dic5—61no—
387Dic5—61no—
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—21no—
397C22×C4—61no—
398C22×C4—151no—
399C22×C4—151no—
400C22×C4—301no—
401C22×C4—301no—
402C22×C4—301no—
403C22×C4C2×D3×D511yescharacteristic
404M16—61no—
405M16—61no—
406M16—101no—
407M16—101no—
408C2×C8—61no—
409C2×C8—101no—
410C4⋊C4—51no—
411C4⋊C4—51no—
412C4⋊C4—304no—
413C4⋊C4—301no—
414C4⋊C4—301no—
415C22⋊C4—101no—
416C22⋊C4—301no—
417C22⋊C4—301no—
418C42—21no—
419C42—21no—
420C42—101no—
421C42—151no—
422C42—151no—
423C42—151no—
424C42—151no—
425C42—301no—
426C42—301no—
427C42—301no—
428C42—301no—
429C3×C5#180611yescharacteristic, complemented, Hall
430C22×C3—21no—
431C22×C3—21no—
432C22×C3#402411yescharacteristic
433C22×C3D5×C22⋊C411yescharacteristic
434C22×C3#408511yescharacteristic
435C2×D3—22no—
436C2×D3—41no—
437C2×D3—41no—
438C3×C4—42no—
439C3×C4—201no—
440C3×C4—201no—
441C3×C4#402311yescharacteristic
442C3×C4#402411yescharacteristic
443C3×C4C2×#68311yescharacteristic
444C3×C4#408511yescharacteristic
445Dic3—22no—
446Dic3—52no—
447Dic3—101no—
448Dic3—101no—
449Dic3—101no—
450Dic3—202no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5—122no—
454C2×C5#466711yescharacteristic
455C2×C5D3×#10411yescharacteristic
456C2×C5#482111yescharacteristic
457C23—61no—
458C23#679011yescharacteristic
459Q8—32no—
460Q8—61no—
461D4—32no—
462D4—62no—
463D4—62no—
464D4—61no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—61no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—101no—
472C2×C4—101no—
473C2×C4—151no—
474C2×C4—151no—
475C2×C4—151no—
476C2×C4—151no—
477C2×C4—302no—
478C2×C4—302no—
479C2×C4—602no—
480C2×C4—602no—
481C2×C4—601no—
482C2×C4—601no—
483C2×C4—601no—
484C2×C4D3×Dic1011yescharacteristic
485C2×C4#677211yescharacteristic
486C2×C4C4×D3×D511yescharacteristic
487C2×C4#677711yescharacteristic
488C2×C4#678211yescharacteristic
489C2×C4D3×C22⋊D511yescharacteristic
490C8—121no—
491C8—201no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3D5×#10411yescharacteristic
495C2×C3#6511011yescharacteristic
496C2×C3#6523111yescharacteristic
497D3—42no—
498C5#6877011yescharacteristic, complemented, Sylow
499C22—21no—
500C22—21no—
501C22—62no—
502C22—121no—
503C22—121no—
504C22#9143211yescharacteristic
505C22#9147311yescharacteristic
506C22#9155811yescharacteristic
507C4—42no—
508C4—62no—
509C4—152no—
510C4—201no—
511C4—201no—
512C4—301no—
513C4—301no—
514C4—301no—
515C4—602no—
516C4#9139811yescharacteristic
517C4D3×#68311yescharacteristic
518C4#9143611yescharacteristic
519C4#9145311yescharacteristic
520C3#1060114811yescharacteristic, complemented, Sylow
521C2—21no—
522C2—21no—
523C2—122no—
524C2#1174711211yescharacteristic
525C2#1174711311yescharacteristic
526C2#1174888711yescharacteristic
subgroupG/H
centerC2×C4#6777
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1806
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#6712C2semidirect
4. #11748437C2semidirect
6. C3×#64743C2semidirect
7. #11745973C2semidirect
19. #91435C4semidirect
20. #91435C4semidirect
23. #91344C4semidirect
24. #91344C4semidirect
37. #64743D3semidirect
131. C5×D12C4⋊C4semidirect
135. C5×Dic6C4⋊C4semidirect
227. Dic15#104semidirect
359. D12#683semidirect
365. Dic6#683semidirect
429. C3×C5#1806semidirect
498. C5#68770semidirect
520. C3#10601148semidirect

Maximal subgroups

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

subgroupindex
#117544552
C4×#67122
C2×C5×#8052
#117484372
C2×#909782
C3×#647432
#117459732
#106011483
#687705