Finite Group Databasebeta

← #14297848

Subgroups — #14297848

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
1C3×#65856C211yesmaximal, characteristic
2C4×#6668C211yesmaximal, characteristic, complemented
3#11748431C211yesmaximal, characteristic, complemented
4C2×#90977C211yesmaximal, characteristic
5C2×#90976C211yesmaximal, characteristic
6#11746353C211yesmaximal, characteristic, complemented
7C5×#4532C211yesmaximal, characteristic, complemented
8#10599563—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16C3×#4039C411yescharacteristic, complemented
17C3×#4039C411yescharacteristic, complemented
18C3×#4033C411yescharacteristic, complemented
19C3×#4033C411yescharacteristic, complemented
20C3×#4027—21no—
21C3×#4027—21no—
22C3×#4018—21no—
23C3×C42×D5—21no—
24C2×#6668—21no—
25#90994—21no—
26#90982—21no—
27#90982—21no—
28#90977—22no—
29#90976—22no—
30#71646—51nomaximal, Hall
31#65856D311yescharacteristic
32C2×#3957—31no—
33#65407—31no—
34C4×#683—31no—
35C2×#3937—31no—
36C5×#339—31no—
37#64752—31no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×C5×Dic3—21no—
41C2×C3×C22⋊D5—21no—
42C22×C3×Dic5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C3×#709—21no—
45C3×#709—21no—
46C3×#709D412yes—
47C3×#709Q812yes—
48C2×C3×D20C2×C411yescharacteristic
49C2×C3×C4×D5—21no—
50C2×C3×C4×D5—21no—
51C2×C3×C4×D5—21no—
52C2×C3×Dic10C2×C411yescharacteristic
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—
62C4×C5×Dic3—21no—
63C4×C5×Dic3—21no—
64C5×#208—21no—
65C5×#208—21no—
66C2×C5×C3⋊C8—21no—
67C3×#685—21no—
68C3×#685—21no—
69C3×#683—21no—
70C3×#683—21no—
71C3×C4×Dic5—21no—
72C3×C4×Dic5—21no—
73C3×C4×Dic5C2×C411yescharacteristic
74C3×C4×Dic5C2×C411yescharacteristic
75C3×C4×Dic5D411yescharacteristic
76C3×C4×Dic5D411yescharacteristic
77#6668—24no—
78C3×C4×#41—51no—
79C2×#837—51no—
80C2×#837—51no—
81C4×C4⋊Dic3—51no—
82#4924—51no—
83#4532—51no—
84#4532D511yescharacteristic, complemented
85C2×#709C2×D311yescharacteristic
86C2×C5×M16—31no—
87C5×#117C2×D311yescharacteristic
88C2×C42×C5—31no—
89C2×#683—61no—
90C2×C4×Dic5—31no—
91C2×C4×Dic5C2×D311yescharacteristic
92C2×#681—31no—
93#4039Dic311yescharacteristic, complemented
94#4039Dic311yescharacteristic, complemented
95#4033Dic311yescharacteristic, complemented
96#4033Dic311yescharacteristic, complemented
97#4027—21no—
98#4027—21no—
99#4018—21no—
100C42×D5—21no—
101#3963—61no—
102#3957—62no—
103#3946—61no—
104#3946—61no—
105#3937—62no—
106#1806—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×C3×D5—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—
120C2×C5×Dic3—22no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3—41no—
123C3×C22⋊D5—22no—
124C3×C22⋊D5—22no—
125C2×C3×Dic5—21no—
126C2×C3×Dic5—22no—
127C2×C3×Dic5—41no—
128C2×C3×Dic5C22⋊C411yescharacteristic
129C2×C3×Dic5C22⋊C411yescharacteristic
130C2×C3×Dic5C22⋊C411yescharacteristic
131C2×C3×Dic5C22⋊C411yescharacteristic
132C3×D20—21no—
133C3×D20C4⋊C412yescomplemented
134C3×C4×D5—22no—
135C3×C4×D5—22no—
136C3×C4×D5—42no—
137C3×C4×D5—42no—
138C3×Dic10—21no—
139C3×Dic10C4⋊C412yescomplemented
140C3⋊#168—41no—
141C5×C3⋊C8—41no—
142C2×C3×#41—51no—
143C3×C4×Q8—51no—
144C3×C4×Q8—51no—
145C3×C4×D4—51no—
146C3×C4×D4—51no—
147C3×C4×D4—101no—
148C3×C4×D4—101no—
149C3×#117—101no—
150C3×#117C2×D511yescharacteristic
151C2×C3×C42—51no—
152C2×C3×C42—101no—
153C2×C4⋊Dic3—101no—
154C2×C4×Dic3—51no—
155C2×C4×Dic3C2×D511yescharacteristic
156C2×#208—51no—
157C2×#208C2×D511yescharacteristic
158#837—102no—
159#837—102no—
160C3⋊#95—101no—
161C4⋊(C3⋊C8)—101no—
162C4⋊(C3⋊C8)—101no—
163C22×C4×C5—61no—
164C22×C4×C5C22×D311yescharacteristic
165C2×C22⋊D5—21no—
166C22×Dic5—61no—
167C22×Dic5#6711yescharacteristic
168C22×Dic5#6711yescharacteristic
169#709—21no—
170#709—21no—
171#709Dic612yes—
172#709D1212yes—
173C2×D20C2×Dic311yescharacteristic
174C2×C4×D5—21no—
175C2×C4×D5—21no—
176C2×C4×D5—21no—
177C2×Dic10C2×Dic311yescharacteristic
178C5×M16—61no—
179C5×M16—61no—
180C2×C5×C8—61no—
181C5×C4⋊C4C2×Dic311yescharacteristic
182C5×C4⋊C4C2×Dic311yescharacteristic
183C5×C22⋊C4—21no—
184C42×C5—21no—
185C42×C5—61no—
186C42×C5—61no—
187#685—21no—
188#685—21no—
189#683—21no—
190#683—21no—
191#683—64no—
192C4×Dic5—21no—
193C4×Dic5—21no—
194C4×Dic5—61no—
195C4×Dic5—61no—
196C4×Dic5C2×Dic311yescharacteristic
197C4×Dic5C2×Dic311yescharacteristic
198C4×Dic5#6711yescharacteristic
199C4×Dic5#6711yescharacteristic
200#681—61no—
201#681—61no—
202C2×#168—61no—
203C4×#41—51no—
204#423—151no—
205C2×#104—151no—
206C2×#104—151no—
207C4×C4⋊C4—151no—
208#339—31no—
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×C3×D5—22no—
216C2×C3×D5—41no—
217C2×C3×D5—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—22no—
226C3×Dic5—21no—
227C3×Dic5—21no—
228C3×Dic5—21no—
229C3×Dic5#10412yescomplemented
230C5×Dic3—42no—
231C3×#41—52no—
232C3×#41—52no—
233C3×#41—101no—
234C3×#41—101no—
235C2×C3×Q8—51no—
236C2×C3×D4—51no—
237C2×C3×D4—101no—
238C22×C3×C4—51no—
239C22×C3×C4—51no—
240C22×C3×C4—101no—
241C22×C3×C4—101no—
242C22×C3×C4—101no—
243C22×C3×C4C22×D511yescharacteristic
244C22×Dic3—21no—
245C22×Dic3—101no—
246C3×C4⋊C4—101no—
247C3×C4⋊C4—101no—
248C3×C4⋊C4C4×D511yescharacteristic
249C3×C4⋊C4C4×D511yescharacteristic
250C3×C22⋊C4—21no—
251C3×C22⋊C4—101no—
252C3×C22⋊C4—101no—
253C3×C42—21no—
254C3×C42—51no—
255C3×C42—51no—
256C3×C42—51no—
257C3×C42—51no—
258C3×C42—101no—
259C3×C42—101no—
260C4⋊Dic3—104no—
261C4×Dic3—21no—
262C4×Dic3—21no—
263C4×Dic3—101no—
264C4×Dic3—101no—
265#208—21no—
266#208—21no—
267#208—101no—
268#208—101no—
269C2×C3⋊C8—21no—
270C2×C3⋊C8—101no—
271C23×C5C2×#6711yescharacteristic
272C22×D5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—62no—
276C2×C4×C5—121no—
277C2×C4×C5—121no—
278C2×C4×C5C2×Dic611yescharacteristic
279C2×C4×C5C2×D1211yescharacteristic
280C2×C4×C5#23511yescharacteristic
281C2×C4×C5#23511yescharacteristic
282C2×C4×C5C22×Dic311yescharacteristic
283C2×C4×C5C2×#6711yescharacteristic
284C22⋊D5—22no—
285C22⋊D5—22no—
286C2×Dic5—21no—
287C2×Dic5—22no—
288C2×Dic5—41no—
289C2×Dic5—62no—
290C2×Dic5—121no—
291C2×Dic5—121no—
292C2×Dic5#21711yescharacteristic
293C2×Dic5#21711yescharacteristic
294C2×Dic5#21711yescharacteristic
295C2×Dic5#21711yescharacteristic
296D20—21no—
297D20C4⋊Dic312yescomplemented
298C4×D5—22no—
299C4×D5—22no—
300C4×D5—42no—
301C4×D5—42no—
302Dic10—21no—
303Dic10C4⋊Dic312yescomplemented
304C5×C8—121no—
305#168—121no—
306C2×#41—51no—
307C2×M16—31no—
308C2×M16—151no—
309C4×Q8—51no—
310C4×Q8—51no—
311C4×D4—51no—
312C4×D4—51no—
313C4×D4—101no—
314C4×D4—101no—
315#117—101no—
316#117D3×D511yescharacteristic
317C2×C4⋊C4—301no—
318C2×C42—31no—
319C2×C42—51no—
320C2×C42—101no—
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
332C3×D5—42no—
333C23×C3—101no—
334C23×C3D4×D511yescharacteristic
335C3×Q8—52no—
336C3×Q8—101no—
337C3×D4—52no—
338C3×D4—102no—
339C3×D4—102no—
340C3×D4—101no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—51no—
344C2×C3×C4—51no—
345C2×C3×C4—51no—
346C2×C3×C4—51no—
347C2×C3×C4—102no—
348C2×C3×C4—101no—
349C2×C3×C4—102no—
350C2×C3×C4—102no—
351C2×C3×C4—202no—
352C2×C3×C4—202no—
353C2×C3×C4—201no—
354C2×C3×C4C2×C4×D511yescharacteristic
355C2×C3×C4#70911yescharacteristic
356C2×C3×C4#70911yescharacteristic
357C2×C3×C4D4×D511yescharacteristic
358C2×C3×C4D4×D511yescharacteristic
359C2×C3×C4Q8×D511yescharacteristic
360C2×Dic3—22no—
361C2×Dic3—41no—
362C2×Dic3—41no—
363C2×Dic3—102no—
364C2×Dic3—201no—
365C2×Dic3—201no—
366C3⋊C8—41no—
367C3⋊C8—201no—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5#92411yescharacteristic
371C22×C5#93011yescharacteristic
372C22×C5C2×#21711yescharacteristic
373C2×D5—22no—
374C2×D5—41no—
375C2×D5—41no—
376C4×C5—41no—
377C4×C5—41no—
378C4×C5—122no—
379C4×C5#92411yescharacteristic
380C4×C5C2×C4⋊Dic311yescharacteristic
381C4×C5#92611yescharacteristic
382C4×C5#93011yescharacteristic
383Dic5—22no—
384Dic5—21no—
385Dic5—21no—
386Dic5—21no—
387Dic5—122no—
388Dic5#83712yescomplemented
389#41—52no—
390#41—52no—
391#41—101no—
392#41—101no—
393C2×Q8—51no—
394C2×D4—51no—
395C2×D4—101no—
396C22×C4—51no—
397C22×C4—51no—
398C22×C4—61no—
399C22×C4—101no—
400C22×C4—101no—
401C22×C4—101no—
402C22×C4—301no—
403C22×C4C2×D3×D511yescharacteristic
404M16—61no—
405M16—61no—
406M16—301no—
407M16—301no—
408C2×C8—61no—
409C2×C8—301no—
410C4⋊C4—101no—
411C4⋊C4—101no—
412C4⋊C4—304no—
413C4⋊C4D5×Dic311yescharacteristic
414C4⋊C4D5×Dic311yescharacteristic
415C22⋊C4—21no—
416C22⋊C4—101no—
417C22⋊C4—101no—
418C42—21no—
419C42—51no—
420C42—51no—
421C42—51no—
422C42—51no—
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—102no—
433C22×C3—201no—
434C22×C3—201no—
435C22×C3D5×C22⋊C411yescharacteristic
436C22×C3#403011yescharacteristic
437C22×C3#404211yescharacteristic
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—52no—
441C3×C4—101no—
442C3×C4—101no—
443C3×C4—101no—
444C3×C4—102no—
445C3×C4#401811yescharacteristic
446C3×C4#403011yescharacteristic
447C3×C4D5×C4⋊C411yescharacteristic
448C3×C4#404211yescharacteristic
449Dic3—42no—
450Dic3—202no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5#521211yescharacteristic
454C2×C5C2×#83711yescharacteristic
455C2×C5#523611yescharacteristic
456D5—42no—
457C23—101no—
458C23D5×#6711yescharacteristic
459Q8—52no—
460Q8—101no—
461D4—52no—
462D4—102no—
463D4—102no—
464D4—101no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—51no—
468C2×C4—51no—
469C2×C4—51no—
470C2×C4—51no—
471C2×C4—62no—
472C2×C4—102no—
473C2×C4—101no—
474C2×C4—102no—
475C2×C4—102no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—202no—
479C2×C4—202no—
480C2×C4—201no—
481C2×C4—302no—
482C2×C4—601no—
483C2×C4—601no—
484C2×C4D5×Dic611yescharacteristic
485C2×C4#677111yescharacteristic
486C2×C4#677111yescharacteristic
487C2×C4D5×D1211yescharacteristic
488C2×C4C2×D5×Dic311yescharacteristic
489C2×C4D5×#6711yescharacteristic
490C8—121no—
491C8—601no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—202no—
495C2×C3#6495611yescharacteristic
496C2×C3D5×#10411yescharacteristic
497C2×C3#6511011yescharacteristic
498C5#7164611yescharacteristic, complemented, Sylow
499C22—21no—
500C22—21no—
501C22—102no—
502C22—201no—
503C22—201no—
504C22#9134911yescharacteristic
505C22#9144811yescharacteristic
506C22D5×#21711yescharacteristic
507C4—41no—
508C4—41no—
509C4—52no—
510C4—101no—
511C4—101no—
512C4—101no—
513C4—102no—
514C4—122no—
515C4—602no—
516C4#9134911yescharacteristic
517C4#9135711yescharacteristic
518C4D5×C4⋊Dic311yescharacteristic
519C4#9144811yescharacteristic
520C3#1059956311yescharacteristic, complemented, Sylow
521C2—21no—
522C2—21no—
523C2—202no—
524C2#1174873811yescharacteristic
525C2D5×#83711yescharacteristic
526C2#1174942711yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#709C22
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×#6668C2semidirect
3. #11748431C2semidirect
6. #11746353C2semidirect
7. C5×#4532C2semidirect
16. C3×#4039C4semidirect
17. C3×#4039C4semidirect
18. C3×#4033C4semidirect
19. C3×#4033C4semidirect
84. #4532D5semidirect
93. #4039Dic3semidirect
94. #4039Dic3semidirect
95. #4033Dic3semidirect
96. #4033Dic3semidirect
133. C3×D20C4⋊C4semidirect
139. C3×Dic10C4⋊C4semidirect
229. C3×Dic5#104semidirect
297. D20C4⋊Dic3semidirect
303. Dic10C4⋊Dic3semidirect
388. Dic5#837semidirect
429. C3×C5#1806semidirect
498. C5#71646semidirect
520. C3#10599563semidirect

Maximal subgroups

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

subgroupindex
C3×#658562
C4×#66682
#117484312
C2×#909772
C2×#909762
#117463532
C5×#45322
#105995633
#716465