Finite Group Databasebeta

← #14301391

Subgroups — #14301391

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754586C211yesmaximal, characteristic
2#11754125C211yesmaximal, characteristic, complemented
3C5×#5006C211yesmaximal, characteristic, complemented
4C3×#65294C211yesmaximal, characteristic, complemented
5#11748421C211yesmaximal, characteristic, complemented
6#11746353C211yesmaximal, characteristic, complemented
7#11745975C211yesmaximal, characteristic, complemented
8#10600838—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91571—22no—
17#91463C411yescharacteristic, complemented
18C4×#1201—22no—
19#91385C411yescharacteristic, complemented
20#91370C411yescharacteristic, complemented
21#91368C411yescharacteristic, complemented
22#91288—22no—
23D3×#681—22no—
24#91286—22no—
25C5×#806—22no—
26C3×#3937—22no—
27#90977—22no—
28#70417—51nomaximal, Hall
29#66166—31no—
30#66153—31no—
31C5×#410—31no—
32#65294—31no—
33#65294D311yescharacteristic, complemented
34#64752—31no—
35#64752—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C2×C5×#67D412yes—
39C5×#235—21no—
40C5×#235—21no—
41C5×#235—21no—
42C5×#235—21no—
43C2×C5×D12C2×C411yescharacteristic
44C2×C4×C5×D3D412yes—
45C2×C5×Dic6C2×C411yescharacteristic
46C2×C3×C22⋊D5—21no—
47C3×#709—21no—
48C3×#709—21no—
49C3×#709—21no—
50C3×#709—21no—
51C2×C3×D20C2×C411yescharacteristic
52C2×C3×C4×D5—21no—
53C2×C3×Dic10C2×C411yescharacteristic
54C2×#1201—22no—
55C3×C5×C4⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C42×C5—21no—
58C4×Dic15—21no—
59C4×Dic15C2×C411yescharacteristic
60C4×Dic15C2×C411yescharacteristic
61#6710—21no—
62#6710D412yescomplemented
63C2×C3⋊#168—21no—
64C5×#217—21no—
65C5×C4⋊Dic3—21no—
66C4×C5×Dic3—21no—
67C3×#681—21no—
68C3×#681D412yescomplemented
69C2×C3×#168—21no—
70#6669—22no—
71(C2×D3)⋊Dic5—22no—
72#6665—22no—
73#6650—24no—
74D3×#168—24no—
75#5832—51no—
76#5745—51no—
77C3×#421—51no—
78#5236—51no—
79#5006D511yescharacteristic, complemented
80#4555—51no—
81#4532—51no—
82C2×C5×#41—31no—
83C2×#709C2×D311yescharacteristic
84C5×#117—31no—
85C5×#117C2×D311yescharacteristic
86#4094—62no—
87#4094—62no—
88#4093—31no—
89#4090—31no—
90#4086—31no—
91#4085—62no—
92#4082—31no—
93C4×C22⋊D5—62no—
94C2×C4×Dic5—31no—
95C2×#681—31no—
96C2×#681—62no—
97C2×#681C2×D311yescharacteristic
98C5×#99—62no—
99#3937—22no—
100#3937—62no—
101#1884—151noSylow
102C23×C3×C5C2×D411yescharacteristic
103C22×C5×D3C22⋊C412yes—
104C22×C3×D5—21no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×Dic15—21no—
113C2×Dic15—21no—
114C2×Dic15—42no—
115C5×#67—22no—
116C5×#67—22no—
117C2×C5×Dic3—41no—
118C2×C5×Dic3C22⋊C412yes—
119C5×D12—21no—
120C5×D12—21no—
121C4×C5×D3—22no—
122C4×C5×D3—22no—
123C5×Dic6—21no—
124C5×Dic6—21no—
125C3×C22⋊D5—41no—
126C3×C22⋊D5—41no—
127C2×C3×Dic5—21no—
128C3×D20—21no—
129C3×D20—21no—
130C3×C4×D5—41no—
131C3×C4×D5—41no—
132C3×Dic10—21no—
133C3×Dic10—21no—
134#1201—44no—
135C3⋊#168—22no—
136C3×#168—22no—
137C2×C3×#41—51no—
138C2×#235C2×D511yescharacteristic
139C2×C3×M16—51no—
140C3×#117C2×D511yescharacteristic
141#947—51no—
142#944—51no—
143#940—51no—
144#939—102no—
145#936—51no—
146C4×#67—102no—
147#926C2×D511yescharacteristic
148C2×C4×Dic3—51no—
149C2×#208—51no—
150#907—102no—
151D3×M16—102no—
152#901—102no—
153C3×#104—102no—
154#837—102no—
155#806—22no—
156C5×#41—61no—
157C5×#41—61no—
158C5×#41—61no—
159C5×#41—61no—
160C2×C5×Q8—31no—
161C2×C5×D4—32no—
162C2×C5×D4—31no—
163C22×C4×C5—32no—
164C22×C4×C5C22×D311yescharacteristic
165C2×C22⋊D5—21no—
166C2×C22⋊D5—62no—
167C22×Dic5—61no—
168#709—21no—
169#709—21no—
170#709—21no—
171#709—21no—
172C2×D20C4×D311yescharacteristic
173C2×C4×D5—21no—
174C2×Dic10C4×D311yescharacteristic
175C5×C4⋊C4—21no—
176C5×C4⋊C4—61no—
177C5×C22⋊C4—21no—
178C5×C22⋊C4—61no—
179C42×C5—21no—
180C42×C5—61no—
181C22⋊Dic5—62no—
182#685—62no—
183#683—62no—
184C4×Dic5—31no—
185C4×Dic5—31no—
186C4×Dic5—61no—
187#681—21no—
188#681—32no—
189#681—64no—
190#681—61no—
191#681#6712yescomplemented
192C2×#168—21no—
193C2×#168—64no—
194C2×#168—61no—
195#568—151no—
196#532—151no—
197#421—51no—
198#421—151no—
199#410—31no—
200#339—151no—
201#339—151no—
202C22×C3×C5—41no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C22×C3×C5#12111yescharacteristic
205C22×C3×C5#12111yescharacteristic
206C2×C5×D3—22no—
207C2×C5×D3—42no—
208C2×C3×D5—42no—
209C2×C3×D5—41no—
210C3×C4×C5—81no—
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12011yescharacteristic
214C3×C4×C5#12311yescharacteristic
215Dic15—22no—
216Dic15—41no—
217C3×Dic5—41no—
218C5×Dic3—22no—
219C5×Dic3—81no—
220C3×#41—101no—
221C3×#41—101no—
222C3×#41—101no—
223C3×#41—101no—
224C2×C3×Q8—51no—
225C2×C3×D4—51no—
226C2×C3×D4—101no—
227C22×C3×C4—101no—
228C22×C3×C4C22×D511yescharacteristic
229C2×#67—102no—
230C2×#67C22⋊D512yes—
231C22×Dic3—101no—
232#235—21no—
233#235—21no—
234#235—21no—
235#235—21no—
236C2×D12C4×D511yescharacteristic
237C2×C4×D3D2012yes—
238C2×Dic6C4×D511yescharacteristic
239C3×M16—52no—
240C3×M16—101no—
241C2×C3×C8—101no—
242C3×C4⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C42—21no—
245#217—21no—
246#217—102no—
247(C2×D3)⋊C4—102no—
248C4⋊Dic3—21no—
249Dic3⋊C4—102no—
250C4×Dic3—21no—
251C4×Dic3—51no—
252C4×Dic3—51no—
253C4×Dic3—101no—
254#208—52no—
255#208—101no—
256C2×C3⋊C8—101no—
257ΓL(1,𝔽25)—104no—
258D3×C8—104no—
259C23×C5—32no—
260C23×C5D3×D411yescharacteristic
261C22×D5—21no—
262C5×Q8—61no—
263C5×Q8—61no—
264C5×D4—62no—
265C5×D4—62no—
266C5×D4—61no—
267C5×D4—61no—
268C2×C4×C5—32no—
269C2×C4×C5—41no—
270C2×C4×C5—62no—
271C2×C4×C5—62no—
272C2×C4×C5—121no—
273C2×C4×C5C2×C4×D311yescharacteristic
274C2×C4×C5#23511yescharacteristic
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5#23711yescharacteristic
278C2×C4×C5C2×#6711yescharacteristic
279C22⋊D5—41no—
280C22⋊D5—41no—
281C22⋊D5—124no—
282C2×Dic5—21no—
283C2×Dic5—61no—
284C2×Dic5—61no—
285C2×Dic5—122no—
286D20—21no—
287D20—21no—
288C4×D5—41no—
289C4×D5—41no—
290Dic10—21no—
291Dic10—21no—
292#168—22no—
293#168—62no—
294C2×#41—31no—
295C2×#41—51no—
296#131—302no—
297#131—302no—
298C2×M16—51no—
299C2×M16—151no—
300C2×M16—302no—
301C4⋊Q8—151no—
302#127—151no—
303#124—151no—
304#124—151no—
305#121—302no—
306C4×D4—302no—
307#117—31no—
308#117D3×D511yescharacteristic
309C2×C42—151no—
310#104—102no—
311#104—302no—
312#99—62no—
313C2×C3×C5—21no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5#38611yescharacteristic
317C3×D5—81no—
318C5×D3—42no—
319C23×C3—101no—
320C23×C3C2×C22⋊D511yescharacteristic
321C22×D3#68512yes—
322C3×Q8—101no—
323C3×Q8—101no—
324C3×D4—101no—
325C3×D4—101no—
326C3×D4—201no—
327C3×D4—201no—
328C2×C3×C4—41no—
329C2×C3×C4—101no—
330C2×C3×C4—201no—
331C2×C3×C4—201no—
332C2×C3×C4C2×C4×D511yescharacteristic
333C2×C3×C4C2×D2011yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4#71111yescharacteristic
337C2×C3×C4#71111yescharacteristic
338#67—22no—
339#67—22no—
340#67—204no—
341C2×Dic3—41no—
342C2×Dic3—101no—
343C2×Dic3—101no—
344C2×Dic3—202no—
345C2×Dic3#68512yes—
346D12—21no—
347D12—21no—
348C4×D3—22no—
349C4×D3—22no—
350Dic6—21no—
351Dic6—21no—
352C3×C8—102no—
353C3⋊C8—102no—
354C22×C5—41no—
355C22×C5—62no—
356C22×C5—122no—
357C22×C5D3×C22⋊C411yescharacteristic
358C22×C5#88411yescharacteristic
359C22×C5#93811yescharacteristic
360C2×D5—42no—
361C2×D5—41no—
362C4×C5—62no—
363C4×C5—81no—
364C4×C5—241no—
365C4×C5#67⋊C411yescharacteristic
366C4×C5#88311yescharacteristic
367C4×C5C4×#6711yescharacteristic
368C4×C5#93711yescharacteristic
369Dic5—41no—
370Dic5—62no—
371Dic5—121no—
372#41—61no—
373#41—61no—
374#41—61no—
375#41—61no—
376#41—101no—
377#41—101no—
378#41—101no—
379#41—101no—
380C2×Q8—31no—
381C2×Q8—51no—
382C2×D4—32no—
383C2×D4—31no—
384C2×D4—51no—
385C2×D4—101no—
386C2×D4—302no—
387C22×C4—32no—
388C22×C4—101no—
389C22×C4—301no—
390C22×C4C2×D3×D511yescharacteristic
391M16—52no—
392M16—101no—
393M16—152no—
394M16—304no—
395M16—301no—
396C2×C8—101no—
397C2×C8—304no—
398C2×C8—301no—
399C4⋊C4—21no—
400C4⋊C4—61no—
401C4⋊C4—302no—
402C22⋊C4—21no—
403C22⋊C4—61no—
404C22⋊C4—302no—
405C22⋊C4—302no—
406C42—21no—
407C42—61no—
408C42—151no—
409C42—151no—
410C42—301no—
411C3×C5#188411yescharacteristic, complemented, Hall
412C22×C3—41no—
413C22×C3—202no—
414C22×C3—201no—
415C22×C3C2×#68511yescharacteristic
416C22×C3#408511yescharacteristic
417C22×C3#408511yescharacteristic
418C2×D3—22no—
419C2×D3—42no—
420C3×C4—81no—
421C3×C4—201no—
422C3×C4#402711yescharacteristic
423C3×C4#402711yescharacteristic
424C3×C4#402811yescharacteristic
425C3×C4#403211yescharacteristic
426Dic3—22no—
427Dic3—81no—
428Dic3—102no—
429Dic3—201no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—21no—
433C2×C5—122no—
434C2×C5#495611yescharacteristic
435D5—81no—
436C23—32no—
437C23—101no—
438C23D3×C22⋊D511yescharacteristic
439Q8—61no—
440Q8—61no—
441Q8—101no—
442Q8—101no—
443D4—62no—
444D4—62no—
445D4—61no—
446D4—61no—
447D4—101no—
448D4—101no—
449D4—201no—
450D4—201no—
451D4—604no—
452C2×C4—32no—
453C2×C4—41no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—101no—
457C2×C4—121no—
458C2×C4—201no—
459C2×C4—201no—
460C2×C4—301no—
461C2×C4—301no—
462C2×C4—602no—
463C2×C4#677211yescharacteristic
464C2×C4C4×D3×D511yescharacteristic
465C2×C4D3×D2011yescharacteristic
466C2×C4#677711yescharacteristic
467C2×C4#678011yescharacteristic
468C2×C4D5×#6711yescharacteristic
469C8—102no—
470C8—302no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—401no—
475C2×C3#6524711yescharacteristic
476D3—42no—
477C5#7041711yescharacteristic, complemented, Sylow
478C22—41no—
479C22—62no—
480C22—122no—
481C22—202no—
482C22—201no—
483C22#9145311yescharacteristic
484C22D3×#68511yescharacteristic
485C22#9156511yescharacteristic
486C4—62no—
487C4—81no—
488C4—201no—
489C4—241no—
490C4—302no—
491C4—601no—
492C4#9144011yescharacteristic
493C4#9144211yescharacteristic
494C4#9145711yescharacteristic
495C4#9147411yescharacteristic
496C3#1060083811yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—122no—
501C2—401no—
502C2#1174891111yescharacteristic
subgroupG/H
centerC4#91474
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radical#11754586C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1884
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11754125C2semidirect
3. C5×#5006C2semidirect
4. C3×#65294C2semidirect
5. #11748421C2semidirect
6. #11746353C2semidirect
7. #11745975C2semidirect
17. #91463C4semidirect
19. #91385C4semidirect
20. #91370C4semidirect
21. #91368C4semidirect
33. #65294D3semidirect
62. #6710D4semidirect
68. C3×#681D4semidirect
79. #5006D5semidirect
191. #681#67semidirect
411. C3×C5#1884semidirect
477. C5#70417semidirect
496. C3#10600838semidirect

Maximal subgroups

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

subgroupindex
#117545862
#117541252
C5×#50062
C3×#652942
#117484212
#117463532
#117459752
#106008383
#704175