Finite Group Databasebeta

← #14301408

Subgroups — #14301408

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#11756591C211yesmaximal, characteristic
2#11754130C211yesmaximal, characteristic, complemented
3C5×#5236C211yesmaximal, characteristic, complemented
4C3×#65525C211yesmaximal, characteristic, complemented
5#11748626C211yesmaximal, characteristic, complemented
6#11745975C211yesmaximal, characteristic, complemented
7#11745973C211yesmaximal, characteristic, complemented
8#10601210—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11#91836C411yescharacteristic, complemented
12#91833C411yescharacteristic, complemented
13#91829C411yescharacteristic, complemented
14#91828—22no—
15#91825C411yescharacteristic, complemented
16C4×#1220—22no—
17C2×C4×Dic15C2211yescharacteristic
18C5×#926C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C3×#4072C2211yescharacteristic
21C2×C3×#681C2211yescharacteristic
22#91292—22no—
23#91291—22no—
24#91290—22no—
25C5×#837—22no—
26C3×#3969—22no—
27#90997—22no—
28#70417—51nomaximal, Hall
29#66166—31no—
30#66079—31no—
31C5×#421—31no—
32#65525D311yescharacteristic, complemented
33#65295—31no—
34#64775—31no—
35#64752—31no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C2×C3×C5×Q8C2×C411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C2×#1220—22no—
46C2×#1220D412yes—
47C22×Dic15—21no—
48#6817—21no—
49#6817—21no—
50#6817—21no—
51#6817—21no—
52C2×D60C2×C411yescharacteristic
53C2×C4×D15D412yes—
54C2×Dic30C2×C411yescharacteristic
55#6719—22no—
56#6714—22no—
57#6712—22no—
58C4×Dic15—21no—
59C4×Dic15C2×C411yescharacteristic
60C4×Dic15C2×C411yescharacteristic
61C5×#217—21no—
62C5×C4⋊Dic3—21no—
63C4×C5×Dic3—21no—
64C5×#208—21no—
65C5×#208D412yescomplemented
66C2×C5×C3⋊C8—21no—
67C3×C22⋊Dic5—21no—
68C3×C4⋊Dic5—21no—
69C3×C4×Dic5—21no—
70C3×#681—21no—
71C3×#681D412yescomplemented
72C2×C3×#168—21no—
73#6651—24no—
74#6648—24no—
75#5832—51no—
76#5745—51no—
77C3×#421—51no—
78#5236D511yescharacteristic, complemented
79#5006—51no—
80#4555—51no—
81#4532—51no—
82C2×C5×#41C2×D311yescharacteristic
83C2×#709—31no—
84C2×C5×M16—31no—
85C5×#117—31no—
86#4093—31no—
87#4090—31no—
88#4086—31no—
89#4085—62no—
90#4082—31no—
91C4×C22⋊D5—62no—
92#4072C2×D311yescharacteristic
93C2×C4×Dic5—31no—
94C2×#681C2×D311yescharacteristic
95#4053—62no—
96D5×M16—62no—
97#4047—62no—
98C5×#104—62no—
99#3969—22no—
100#3938—62no—
101#1884—151noSylow
102C23×C3×C5—21no—
103C23×C3×C5C2×D411yescharacteristic
104C22×D15C22⋊C412yes—
105C3×C5×Q8—21no—
106C3×C5×Q8—21no—
107C3×C5×D4—21no—
108C3×C5×D4—21no—
109C3×C5×D4—41no—
110C3×C5×D4—41no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120#1220—22no—
121#1220—22no—
122#1220—44no—
123C2×Dic15—21no—
124C2×Dic15—21no—
125C2×Dic15—42no—
126C2×Dic15C22⋊C412yes—
127D60—21no—
128D60—21no—
129C4×D15—22no—
130C4×D15—22no—
131Dic30—21no—
132Dic30—21no—
133C2×C5×Dic3—41no—
134C2×C3×Dic5—41no—
135C3×#168—22no—
136C5×C3⋊C8—22no—
137C2×C3×#41C2×D511yescharacteristic
138C2×#235—51no—
139C2×C3×M16—51no—
140C3×#117—51no—
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×#208C2×D511yescharacteristic
150#907—102no—
151D3×M16—102no—
152#901—102no—
153C3×#104—102no—
154#837—22no—
155#806—102no—
156C5×#41—21no—
157C5×#41—21no—
158C5×#41—21no—
159C5×#41—21no—
160C2×C5×Q8C4×D311yescharacteristic
161C2×C5×D4—21no—
162C2×C5×D4C4×D311yescharacteristic
163C22×C4×C5—21no—
164C22×C4×C5C22×D311yescharacteristic
165C2×C22⋊D5—32no—
166C2×C22⋊D5—62no—
167C22×Dic5—61no—
168#709—61no—
169#709—61no—
170#709—61no—
171#709—61no—
172C2×D20—31no—
173C2×C4×D5—32no—
174C2×Dic10—31no—
175C5×M16—32no—
176C5×M16—61no—
177C2×C5×C8—61no—
178C5×C4⋊C4—61no—
179C5×C22⋊C4—61no—
180C42×C5—61no—
181C22⋊Dic5—21no—
182C22⋊Dic5—62no—
183#685—62no—
184C4⋊Dic5—21no—
185#683—62no—
186C4×Dic5—21no—
187C4×Dic5—31no—
188C4×Dic5—31no—
189C4×Dic5—61no—
190#681—21no—
191#681#6712yescomplemented
192C2×#168—21no—
193#676—64no—
194C8×D5—64no—
195#568—151no—
196#532—151no—
197#421—31no—
198#421—51no—
199#410—151no—
200#339—151no—
201#339—151no—
202C22×C3×C5—41no—
203C22×C3×C5—42no—
204C22×C3×C5—41no—
205C22×C3×C5C2×C22⋊C411yescharacteristic
206C22×C3×C5#12111yescharacteristic
207C22×C3×C5#12111yescharacteristic
208C2×D15—22no—
209C2×D15—42no—
210C3×C4×C5—41no—
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12011yescharacteristic
214C3×C4×C5#12311yescharacteristic
215Dic15—22no—
216Dic15—22no—
217Dic15—41no—
218C3×Dic5—81no—
219C5×Dic3—81no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—21no—
223C3×#41—21no—
224C2×C3×Q8C4×D511yescharacteristic
225C2×C3×D4—21no—
226C2×C3×D4C4×D511yescharacteristic
227C22×C3×C4—21no—
228C22×C3×C4C22×D511yescharacteristic
229C2×#67—52no—
230C2×#67—102no—
231C22×Dic3—101no—
232#235—101no—
233#235—101no—
234#235—101no—
235#235—101no—
236C2×D12—51no—
237C2×C4×D3—52no—
238C2×Dic6—51no—
239C3×M16—52no—
240C3×M16—101no—
241C2×C3×C8—101no—
242C3×C4⋊C4—101no—
243C3×C22⋊C4—101no—
244C3×C42—101no—
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—21no—
255#208C22⋊D512yescomplemented
256C2×C3⋊C8—21no—
257ΓL(1,𝔽25)—104no—
258D3×C8—104no—
259C23×C5—21no—
260C23×C5D3×D411yescharacteristic
261C22×D5—32no—
262C5×Q8—21no—
263C5×Q8—21no—
264C5×D4—21no—
265C5×D4—21no—
266C5×D4—41no—
267C5×D4—41no—
268C2×C4×C5—21no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—121no—
272C2×C4×C5C2×C4×D311yescharacteristic
273C2×C4×C5#23511yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5#23711yescharacteristic
277C2×C4×C5C2×#6711yescharacteristic
278C22⋊D5—62no—
279C22⋊D5—62no—
280C22⋊D5—124no—
281C2×Dic5—32no—
282C2×Dic5—41no—
283C2×Dic5—61no—
284C2×Dic5—61no—
285C2×Dic5—122no—
286D20—61no—
287D20—61no—
288C4×D5—62no—
289C4×D5—62no—
290Dic10—61no—
291Dic10—61no—
292C5×C8—62no—
293#168—22no—
294C2×#41—151no—
295C2×#41D3×D511yescharacteristic
296#131—302no—
297#131—302no—
298C2×M16—31no—
299C2×M16—51no—
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#117—51no—
309C2×C42—151no—
310#104—62no—
311#104—102no—
312#99—302no—
313C2×C3×C5—21no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5—81no—
317C2×C3×C5#38611yescharacteristic
318D15—42no—
319C23×C3—21no—
320C23×C3D4×D511yescharacteristic
321C22×D3—52no—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×D4—21no—
325C3×D4—21no—
326C3×D4—41no—
327C3×D4—41no—
328C2×C3×C4—21no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—201no—
332C2×C3×C4C2×C4×D511yescharacteristic
333C2×C3×C4#70911yescharacteristic
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4#71111yescharacteristic
337C2×C3×C4C2×C22⋊D511yescharacteristic
338#67—102no—
339#67—102no—
340#67—204no—
341C2×Dic3—41no—
342C2×Dic3—52no—
343C2×Dic3—101no—
344C2×Dic3—101no—
345C2×Dic3—202no—
346D12—101no—
347D12—101no—
348C4×D3—102no—
349C4×D3—102no—
350Dic6—101no—
351Dic6—101no—
352C3×C8—102no—
353C3⋊C8—22no—
354C22×C5—41no—
355C22×C5—42no—
356C22×C5—41no—
357C22×C5D3×C22⋊C411yescharacteristic
358C22×C5#88411yescharacteristic
359C22×C5#93811yescharacteristic
360C2×D5—62no—
361C2×D5—122no—
362C4×C5—41no—
363C4×C5—241no—
364C4×C5#67⋊C411yescharacteristic
365C4×C5#88311yescharacteristic
366C4×C5C4×#6711yescharacteristic
367C4×C5#93711yescharacteristic
368Dic5—62no—
369Dic5—62no—
370Dic5—81no—
371Dic5—121no—
372#41—21no—
373#41—21no—
374#41—21no—
375#41—21no—
376#41—301no—
377#41—301no—
378#41—301no—
379#41—301no—
380C2×Q8—151no—
381C2×Q8#120011yescharacteristic
382C2×D4—21no—
383C2×D4—152no—
384C2×D4—151no—
385C2×D4—302no—
386C2×D4#120011yescharacteristic
387C22×C4—21no—
388C22×C4—152no—
389C22×C4—301no—
390C22×C4C2×D3×D511yescharacteristic
391M16—32no—
392M16—52no—
393M16—61no—
394M16—101no—
395M16—304no—
396C2×C8—61no—
397C2×C8—101no—
398C2×C8—304no—
399C4⋊C4—61no—
400C4⋊C4—101no—
401C4⋊C4—302no—
402C22⋊C4—61no—
403C22⋊C4—101no—
404C22⋊C4—302no—
405C22⋊C4—302no—
406C42—61no—
407C42—101no—
408C42—151no—
409C42—151no—
410C42—301no—
411C3×C5#188411yescharacteristic, complemented, Hall
412C22×C3—41no—
413C22×C3—42no—
414C22×C3—41no—
415C22×C3D5×C22⋊C411yescharacteristic
416C22×C3#403011yescharacteristic
417C22×C3#408411yescharacteristic
418C2×D3—102no—
419C2×D3—202no—
420C3×C4—41no—
421C3×C4—401no—
422C3×C4#402711yescharacteristic
423C3×C4#402911yescharacteristic
424C3×C4C4×C22⋊D511yescharacteristic
425C3×C4#408311yescharacteristic
426Dic3—81no—
427Dic3—102no—
428Dic3—102no—
429Dic3—201no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—21no—
433C2×C5—81no—
434C2×C5#495611yescharacteristic
435D5—122no—
436C23—21no—
437C23—152no—
438C23#679011yescharacteristic
439Q8—21no—
440Q8—21no—
441Q8—301no—
442Q8—301no—
443D4—21no—
444D4—21no—
445D4—41no—
446D4—41no—
447D4—302no—
448D4—302no—
449D4—301no—
450D4—301no—
451D4—604no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—121no—
456C2×C4—152no—
457C2×C4—201no—
458C2×C4—301no—
459C2×C4—302no—
460C2×C4—302no—
461C2×C4—301no—
462C2×C4—602no—
463C2×C4#677911yescharacteristic
464C2×C4#678211yescharacteristic
465C2×C4C2×#120011yescharacteristic
466C2×C4D5×#6711yescharacteristic
467C2×C4D3×C22⋊D511yescharacteristic
468C2×C4#679011yescharacteristic
469C8—62no—
470C8—102no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—81no—
475C2×C3#6524511yescharacteristic
476D3—202no—
477C5#7041711yescharacteristic, complemented, Sylow
478C22—41no—
479C22—42no—
480C22—41no—
481C22—302no—
482C22—602no—
483C22#9153311yescharacteristic
484C22#9155711yescharacteristic
485C22#9156111yescharacteristic
486C4—41no—
487C4—241no—
488C4—302no—
489C4—302no—
490C4—401no—
491C4—601no—
492C4#9155211yescharacteristic
493C4#9155611yescharacteristic
494C4#9156211yescharacteristic
495C4#9157711yescharacteristic
496C3#1060121011yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—81no—
501C2—602no—
502C2#1174952011yescharacteristic
subgroupG/H
centerC4#91577
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5#386
prime radical#11756591C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1884
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11754130C2semidirect
3. C5×#5236C2semidirect
4. C3×#65525C2semidirect
5. #11748626C2semidirect
6. #11745975C2semidirect
7. #11745973C2semidirect
11. #91836C4semidirect
12. #91833C4semidirect
13. #91829C4semidirect
15. #91825C4semidirect
32. #65525D3semidirect
65. C5×#208D4semidirect
71. C3×#681D4semidirect
78. #5236D5semidirect
191. #681#67semidirect
255. #208C22⋊D5semidirect
411. C3×C5#1884semidirect
477. C5#70417semidirect
496. C3#10601210semidirect

Maximal subgroups

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

subgroupindex
#117565912
#117541302
C5×#52362
C3×#655252
#117486262
#117459752
#117459732
#106012103
#704175