Finite Group Databasebeta

← #14297832

Subgroups — #14297832

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#11754444C211yesmaximal, characteristic
2#11751219C211yesmaximal, characteristic, complemented
3C2×C3×#3957C211yesmaximal, characteristic
4C4×#6669C211yesmaximal, characteristic, complemented
5C2×#90977C211yesmaximal, characteristic
6C5×#4555C211yesmaximal, characteristic, complemented
7#11745977C211yesmaximal, characteristic, complemented
8#10599563—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×C4×Dic15C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C4×C5×Dic3C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16#91559—21no—
17#91559—21no—
18C2×#6669—21no—
19#91434C411yescharacteristic, complemented
20#91434C411yescharacteristic, complemented
21C4×D5×Dic3—21no—
22#91357—21no—
23#91331C411yescharacteristic, complemented
24#91331C411yescharacteristic, complemented
25#91098—21no—
26#91098—21no—
27C3×#3957—22no—
28#90994—21no—
29#90977—22no—
30#70355—51nomaximal, Hall
31#65856—31no—
32C2×#3957D311yescharacteristic
33#65407—31no—
34C4×#683—31no—
35C2×#3937—31no—
36C5×#339—31no—
37#64752—31no—
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15D411yescharacteristic
40C22×Dic15D411yescharacteristic
41C22×C5×Dic3—21no—
42C2×C3×C22⋊D5—21no—
43C22×C3×Dic5—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709D412yes—
47C3×#709Q812yes—
48C2×C3×D20C2×C411yescharacteristic
49C2×C3×C4×D5—21no—
50C2×C3×Dic10C2×C411yescharacteristic
51C2×D5×Dic3—21no—
52C2×D5×Dic3—21no—
53C3×C5×M16—21no—
54C3×C5×M16—21no—
55C2×C3×C5×C8—21no—
56C4×Dic15C2×C411yescharacteristic
57C4×Dic15C2×C411yescharacteristic
58C4×Dic15D411yescharacteristic
59C4×Dic15D411yescharacteristic
60#6710—21no—
61#6710—21no—
62C2×C3⋊#168—21no—
63C5×#217—21no—
64C5×C4⋊Dic3C2×C411yescharacteristic
65C5×C4⋊Dic3C2×C411yescharacteristic
66C4×C5×Dic3—21no—
67C4×C5×Dic3—21no—
68C4×C5×Dic3—21no—
69C3×C4×Dic5—21no—
70C3×C4×Dic5—21no—
71#6669—24no—
72#6668—21no—
73#6668—21no—
74#6665—21no—
75#6665—21no—
76Dic3×Dic5—21no—
77Dic3×Dic5—21no—
78Dic3×#41—51no—
79C2×C3×#104—51no—
80C2×#837—51no—
81#5118—51no—
82C4×Dic3⋊C4—51no—
83#4555D511yescharacteristic, complemented
84#4523—51no—
85C2×#709C2×D311yescharacteristic
86C2×C5×M16C2×D311yescharacteristic
87C5×#117—31no—
88C2×C42×C5—31no—
89C2×#683—61no—
90C2×C4×Dic5—31no—
91C2×C4×Dic5C2×D311yescharacteristic
92C2×#681—31no—
93#4039—31no—
94#4039—31no—
95#4033—31no—
96#4033—31no—
97#4027—61no—
98#4027—61no—
99#4018—61no—
100C42×D5—61no—
101#3963—61no—
102#3957—22no—
103#3946—61no—
104#3946—61no—
105#3937—62no—
106#1806—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×C3×D5—21no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×Q811yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×Dic15—22no—
116C2×Dic15—41no—
117C2×Dic15C22⋊C411yescharacteristic
118C2×Dic15C22⋊C411yescharacteristic
119C2×Dic15C22⋊C411yescharacteristic
120C2×Dic15C22⋊C411yescharacteristic
121C2×C5×Dic3—22no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—21no—
124C2×C5×Dic3—41no—
125C2×C5×Dic3—41no—
126C3×C22⋊D5—22no—
127C3×C22⋊D5—22no—
128C2×C3×Dic5—21no—
129C2×C3×Dic5—22no—
130C2×C3×Dic5—41no—
131C2×C3×Dic5—41no—
132C3×D20—21no—
133C3×D20C4⋊C412yescomplemented
134C3×C4×D5—22no—
135C3×C4×D5—22no—
136C3×Dic10—21no—
137C3×Dic10C4⋊C412yescomplemented
138D5×Dic3—42no—
139D5×Dic3—42no—
140C3×C5×C8—41no—
141C3⋊#168—41no—
142C2×C3×#41—51no—
143C2×C3×M16C2×D511yescharacteristic
144C2×C3×C42—51no—
145Q8×Dic3—51no—
146Q8×Dic3—51no—
147D4×Dic3—51no—
148D4×Dic3—51no—
149D4×Dic3—101no—
150D4×Dic3—101no—
151#926—101no—
152#926C2×D511yescharacteristic
153C2×Dic3⋊C4—101no—
154C2×C4×Dic3—51no—
155C2×C4×Dic3—101no—
156C2×C4×Dic3C2×D511yescharacteristic
157C2×#208—51no—
158C3×#104—102no—
159#837—102no—
160C3⋊#95—101no—
161Dic3⋊C8—101no—
162Dic3⋊C8—101no—
163C22×C4×C5—61no—
164C22×C4×C5C22×D311yescharacteristic
165C2×C22⋊D5—21no—
166C22×Dic5—21no—
167C22×Dic5—31no—
168C22×Dic5—31no—
169#709—21no—
170#709—21no—
171#709Dic612yes—
172#709#6712yes—
173C2×D20C4×D311yescharacteristic
174C2×C4×D5—21no—
175C2×C4×D5—61no—
176C2×C4×D5—61no—
177C2×Dic10C4×D311yescharacteristic
178C5×M16—21no—
179C5×M16—21no—
180C2×C5×C8—21no—
181C5×C4⋊C4—31no—
182C5×C4⋊C4—31no—
183C5×C22⋊C4—61no—
184C42×C5—61no—
185C42×C5—61no—
186C42×C5—61no—
187#685—61no—
188#685—61no—
189#683—61no—
190#683—61no—
191#683—64no—
192C4×Dic5—21no—
193C4×Dic5—21no—
194C4×Dic5—31no—
195C4×Dic5—31no—
196C4×Dic5—31no—
197C4×Dic5—31no—
198C4×Dic5—61no—
199C4×Dic5—61no—
200#681—61no—
201#681—61no—
202C2×#168—61no—
203C4×#41—151no—
204#423—151no—
205C2×#104—51no—
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×C5C2×C4⋊C411yescharacteristic
219C3×C4×C5#11711yescharacteristic
220C3×C4×C5#12111yescharacteristic
221C3×C4×C5C22⋊Q811yescharacteristic
222Dic15—21no—
223Dic15—21no—
224Dic15—21no—
225Dic15#10412yescomplemented
226C3×Dic5—22no—
227C3×Dic5—42no—
228C5×Dic3—42no—
229C5×Dic3—41no—
230C5×Dic3—41no—
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—101no—
239C22×C3×C4—101no—
240C22×C3×C4C22×D511yescharacteristic
241C22×Dic3—21no—
242C22×Dic3—51no—
243C22×Dic3—51no—
244C22×Dic3—101no—
245C22×Dic3—101no—
246C3×M16—21no—
247C3×M16—21no—
248C2×C3×C8—21no—
249C3×C42—101no—
250C3×C42—101no—
251#217—21no—
252#217—101no—
253#217—101no—
254C4⋊Dic3—101no—
255C4⋊Dic3—101no—
256C4⋊Dic3C4×D511yescharacteristic
257C4⋊Dic3C4×D511yescharacteristic
258Dic3⋊C4—104no—
259C4×Dic3—21no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3—51no—
263C4×Dic3—51no—
264C4×Dic3—51no—
265C4×Dic3—51no—
266C4×Dic3—101no—
267C4×Dic3—101no—
268#208—101no—
269#208—101no—
270C2×C3⋊C8—101no—
271C23×C5D3×D411yescharacteristic
272C22×D5—21no—
273C2×C4×C5—62no—
274C2×C4×C5—61no—
275C2×C4×C5—61no—
276C2×C4×C5—121no—
277C2×C4×C5—121no—
278C2×C4×C5C2×Dic611yescharacteristic
279C2×C4×C5C2×C4×D311yescharacteristic
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5#23711yescharacteristic
282C2×C4×C5#23711yescharacteristic
283C2×C4×C5C2×#6711yescharacteristic
284C22⋊D5—22no—
285C22⋊D5—22no—
286C2×Dic5—21no—
287C2×Dic5—22no—
288C2×Dic5—31no—
289C2×Dic5—31no—
290C2×Dic5—31no—
291C2×Dic5—31no—
292C2×Dic5—41no—
293C2×Dic5—41no—
294C2×Dic5—62no—
295C2×Dic5—121no—
296D20—21no—
297D20Dic3⋊C412yescomplemented
298C4×D5—22no—
299C4×D5—22no—
300C4×D5—122no—
301C4×D5—122no—
302Dic10—21no—
303Dic10Dic3⋊C412yescomplemented
304C5×C8—41no—
305#168—121no—
306C2×#41—51no—
307C2×M16—151no—
308C2×M16D3×D511yescharacteristic
309C4×Q8—151no—
310C4×Q8—151no—
311C4×D4—151no—
312C4×D4—151no—
313C4×D4—301no—
314C4×D4—301no—
315#117—31no—
316#117—301no—
317C2×C4⋊C4—301no—
318C2×C42—31no—
319C2×C42—51no—
320C2×C42—151no—
321C2×C42—301no—
322C4⋊C8—301no—
323C4⋊C8—301no—
324#104—102no—
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—101no—
342C2×C3×C4—102no—
343C2×C3×C4—102no—
344C2×C3×C4—102no—
345C2×C3×C4—201no—
346C2×C3×C4—201no—
347C2×C3×C4C2×C4×D511yescharacteristic
348C2×C3×C4#70911yescharacteristic
349C2×C3×C4#70911yescharacteristic
350C2×C3×C4D4×D511yescharacteristic
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4Q8×D511yescharacteristic
353C2×Dic3—22no—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—41no—
357C2×Dic3—41no—
358C2×Dic3—51no—
359C2×Dic3—51no—
360C2×Dic3—51no—
361C2×Dic3—51no—
362C2×Dic3—102no—
363C2×Dic3—202no—
364C2×Dic3—202no—
365C2×Dic3—201no—
366C3×C8—41no—
367C3⋊C8—201no—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5#87811yescharacteristic
371C22×C5D3×C22⋊C411yescharacteristic
372C22×C5#93911yescharacteristic
373C2×D5—22no—
374C2×D5—41no—
375C2×D5—41no—
376C4×C5—122no—
377C4×C5—121no—
378C4×C5—121no—
379C4×C5#87711yescharacteristic
380C4×C5#87811yescharacteristic
381C4×C5C2×Dic3⋊C411yescharacteristic
382C4×C5#93911yescharacteristic
383Dic5—22no—
384Dic5—32no—
385Dic5—42no—
386Dic5—61no—
387Dic5—61no—
388Dic5—61no—
389#41—52no—
390#41—52no—
391#41—101no—
392#41—101no—
393C2×Q8—51no—
394C2×D4—51no—
395C2×D4—101no—
396C22×C4—61no—
397C22×C4—101no—
398C22×C4—101no—
399C22×C4—151no—
400C22×C4—151no—
401C22×C4—301no—
402C22×C4—301no—
403C22×C4C2×D3×D511yescharacteristic
404M16—21no—
405M16—21no—
406M16—301no—
407M16—301no—
408C2×C8—21no—
409C2×C8—301no—
410C4⋊C4—31no—
411C4⋊C4—31no—
412C4⋊C4—301no—
413C4⋊C4—301no—
414C4⋊C4—304no—
415C22⋊C4—61no—
416C22⋊C4—301no—
417C22⋊C4—301no—
418C42—61no—
419C42—61no—
420C42—61no—
421C42—101no—
422C42—101no—
423C42—151no—
424C42—151no—
425C42—151no—
426C42—151no—
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—102no—
439C3×C4—202no—
440C3×C4#401811yescharacteristic
441C3×C4#403011yescharacteristic
442C3×C4D5×C4⋊C411yescharacteristic
443C3×C4#404211yescharacteristic
444Dic3—42no—
445Dic3—41no—
446Dic3—41no—
447Dic3—52no—
448Dic3—101no—
449Dic3—101no—
450Dic3—101no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5D3×#10411yescharacteristic
454C2×C5#482111yescharacteristic
455C2×C5#494211yescharacteristic
456D5—42no—
457C23—101no—
458C23#677711yescharacteristic
459Q8—52no—
460Q8—101no—
461D4—52no—
462D4—102no—
463D4—102no—
464D4—101no—
465C2×C4—62no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—101no—
469C2×C4—102no—
470C2×C4—102no—
471C2×C4—102no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—151no—
475C2×C4—151no—
476C2×C4—151no—
477C2×C4—151no—
478C2×C4—201no—
479C2×C4—201no—
480C2×C4—302no—
481C2×C4—602no—
482C2×C4—602no—
483C2×C4—601no—
484C2×C4D5×Dic611yescharacteristic
485C2×C4#676511yescharacteristic
486C2×C4C4×D3×D511yescharacteristic
487C2×C4#677911yescharacteristic
488C2×C4D5×#6711yescharacteristic
489C2×C4#679011yescharacteristic
490C8—41no—
491C8—601no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—202no—
495C2×C3#6495611yescharacteristic
496C2×C3D5×#10411yescharacteristic
497C2×C3#6511011yescharacteristic
498C5#7035511yescharacteristic, complemented, Sylow
499C22—21no—
500C22—21no—
501C22—102no—
502C22—201no—
503C22—201no—
504C22#9140811yescharacteristic
505C22#9143011yescharacteristic
506C22#9147311yescharacteristic
507C4—102no—
508C4—122no—
509C4—121no—
510C4—121no—
511C4—152no—
512C4—202no—
513C4—301no—
514C4—301no—
515C4—301no—
516C4D5×Dic3⋊C411yescharacteristic
517C4#9139311yescharacteristic
518C4#9143111yescharacteristic
519C4#9155011yescharacteristic
520C3#1059956311yescharacteristic, complemented, Sylow
521C2—21no—
522C2—21no—
523C2—202no—
524C2#1174823611yescharacteristic
525C2#1174823711yescharacteristic
526C2#1174888511yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1806
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11751219C2semidirect
4. C4×#6669C2semidirect
6. C5×#4555C2semidirect
7. #11745977C2semidirect
19. #91434C4semidirect
20. #91434C4semidirect
23. #91331C4semidirect
24. #91331C4semidirect
83. #4555D5semidirect
133. C3×D20C4⋊C4semidirect
137. C3×Dic10C4⋊C4semidirect
225. Dic15#104semidirect
297. D20Dic3⋊C4semidirect
303. Dic10Dic3⋊C4semidirect
429. C3×C5#1806semidirect
498. C5#70355semidirect
520. C3#10599563semidirect

Maximal subgroups

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

subgroupindex
#117544442
#117512192
C2×C3×#39572
C4×#66692
C2×#909772
C5×#45552
#117459772
#105995633
#703555