Finite Group Databasebeta

← #14301397

Subgroups — #14301397

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
1C5×#5745C211yesmaximal, characteristic, complemented
2#11754586C211yesmaximal, characteristic
3C3×#65428C211yesmaximal, characteristic, complemented
4#11748625C211yesmaximal, characteristic, complemented
5#11748420C211yesmaximal, characteristic, complemented
6#11746376C211yesmaximal, characteristic, complemented
7#11745973C211yesmaximal, characteristic, complemented
8#10602814—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C5×#907—22no—
16C5×D3×M16—22no—
17C5×#901—22no—
18C3×#4072C2211yescharacteristic
19#91571—22no—
20#91463C411yescharacteristic, complemented
21C4×#1201—22no—
22#91385C411yescharacteristic, complemented
23#91370C411yescharacteristic, complemented
24#91368C411yescharacteristic, complemented
25C3×#3957—22no—
26#90996—22no—
27#90976—22no—
28#70417—51nomaximal, Hall
29C5×#568—31no—
30#66166—31no—
31#65529—31no—
32#65428—31no—
33#65428D311yescharacteristic, complemented
34#64775—31no—
35#64775—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×M16—21no—
56C3×C5×M16D412yescomplemented
57C2×C3×C5×C8—21no—
58#6719—21no—
59C4⋊Dic15—21no—
60C4×Dic15—21no—
61C4×Dic15—21no—
62C4×Dic15C2×C411yescharacteristic
63C4×Dic15C2×C411yescharacteristic
64C5×#208—21no—
65C5×#208D412yescomplemented
66C2×C5×C3⋊C8—21no—
67C5×ΓL(1,𝔽25)—24no—
68C5×D3×C8—24no—
69C3×C22⋊Dic5—21no—
70C3×C4⋊Dic5—21no—
71C3×C4×Dic5—21no—
72#6669—22no—
73(C2×D3)⋊Dic5—22no—
74#6665—22no—
75#5832—51no—
76#5745D511yescharacteristic, complemented
77C3×#421—51no—
78#5236—51no—
79#5006—51no—
80#4555—51no—
81#4532—51no—
82C2×C5×#41—31no—
83C2×#709C2×D311yescharacteristic
84C5×#131—62no—
85C5×#131—62no—
86C2×C5×M16—31no—
87C2×C5×M16—62no—
88C2×C5×M16C2×D311yescharacteristic
89#4093—31no—
90#4090—31no—
91#4086—31no—
92#4085—62no—
93#4082—31no—
94C4×C22⋊D5—62no—
95#4072—31no—
96#4072C2×D311yescharacteristic
97C2×C4×Dic5—31no—
98#3966—62no—
99#3957—22no—
100#3957—62no—
101#1884—151noSylow
102C23×C3×C5C2×D411yescharacteristic
103C22×C5×D3C22⋊C412yes—
104C22×C3×D5—21no—
105C2×C3×C4×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×Dic15—21no—
112C2×Dic15—21no—
113C2×Dic15—42no—
114C2×Dic15—41no—
115C5×#67—22no—
116C5×#67—22no—
117C2×C5×Dic3C22⋊C412yes—
118C5×D12—21no—
119C5×D12—21no—
120C4×C5×D3—22no—
121C4×C5×D3—22no—
122C5×Dic6—21no—
123C5×Dic6—21no—
124C3×C22⋊D5—41no—
125C3×C22⋊D5—41no—
126C2×C3×Dic5—21no—
127C2×C3×Dic5—41no—
128C3×D20—21no—
129C3×D20—21no—
130C3×C4×D5—41no—
131C3×C4×D5—41no—
132C3×Dic10—21no—
133C3×Dic10—21no—
134#1201—44no—
135C3×C5×C8—22no—
136C5×C3⋊C8—22no—
137C2×C3×#41—51no—
138C2×#235C2×D511yescharacteristic
139C2×C3×M16C2×D511yescharacteristic
140C3×#117—51no—
141#947—51no—
142#944—51no—
143#940—51no—
144#939—102no—
145#936—51no—
146C4×#67—102no—
147#926—51no—
148C2×C4×Dic3—51no—
149C2×#208C2×D511yescharacteristic
150#907—22no—
151D3×M16—22no—
152#901—22no—
153C3×#104—102no—
154#837—102no—
155#806—102no—
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×M16—21no—
176C5×M16—32no—
177C5×M16—64no—
178C5×M16—61no—
179C5×M16#6712yescomplemented
180C2×C5×C8—21no—
181C2×C5×C8—64no—
182C2×C5×C8—61no—
183C22⋊Dic5—21no—
184C22⋊Dic5—62no—
185C22⋊Dic5—61no—
186#685—62no—
187C4⋊Dic5—21no—
188C4⋊Dic5—61no—
189#683—62no—
190C4×Dic5—21no—
191C4×Dic5—31no—
192C4×Dic5—31no—
193C4×Dic5—61no—
194C4×Dic5—61no—
195#568—31no—
196#532—151no—
197#421—51no—
198#421—151no—
199#410—151no—
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×C5C4×D411yescharacteristic
211C3×C4×C5C4×D411yescharacteristic
212C3×C4×C5#12011yescharacteristic
213C3×C4×C5#12311yescharacteristic
214Dic15—22no—
215Dic15—41no—
216Dic15—81no—
217C3×Dic5—41no—
218C3×Dic5—81no—
219C5×Dic3—22no—
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×#67D2012yes—
231C22×Dic3—101no—
232#235—21no—
233#235—21no—
234#235—21no—
235#235—21no—
236C2×D12C4×D511yescharacteristic
237C2×C4×D3C22⋊D512yes—
238C2×Dic6C4×D511yescharacteristic
239C3×M16—21no—
240C3×M16C22⋊D512yescomplemented
241C2×C3×C8—21no—
242C3×C4⋊C4—101no—
243C3×C22⋊C4—101no—
244C3×C42—101no—
245#217—102no—
246#217—101no—
247(C2×D3)⋊C4—102no—
248C4⋊Dic3—101no—
249Dic3⋊C4—102no—
250C4×Dic3—51no—
251C4×Dic3—51no—
252C4×Dic3—101no—
253C4×Dic3—101no—
254#208—21no—
255#208C22⋊D512yescomplemented
256C2×C3⋊C8—21no—
257ΓL(1,𝔽25)—24no—
258D3×C8—24no—
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—62no—
270C2×C4×C5—62no—
271C2×C4×C5C2×C4×D311yescharacteristic
272C2×C4×C5#23511yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5#23711yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C22⋊D5—41no—
278C22⋊D5—41no—
279C22⋊D5—124no—
280C2×Dic5—21no—
281C2×Dic5—41no—
282C2×Dic5—61no—
283C2×Dic5—61no—
284C2×Dic5—122no—
285C2×Dic5—121no—
286D20—21no—
287D20—21no—
288C4×D5—41no—
289C4×D5—41no—
290Dic10—21no—
291Dic10—21no—
292C5×C8—22no—
293C5×C8—62no—
294C2×#41—31no—
295C2×#41—51no—
296#131—62no—
297#131—62no—
298C2×M16—31no—
299C2×M16—62no—
300C2×M16D3×D511yescharacteristic
301C4⋊Q8—151no—
302#127—151no—
303#124—151no—
304#124—151no—
305#121—302no—
306C4×D4—302no—
307#117—51no—
308#117—151no—
309C2×C42—151no—
310#104—102no—
311#104—302no—
312#99—302no—
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×D2011yescharacteristic
321C22×D3#68512yes—
322C3×Q8—101no—
323C3×Q8—101no—
324C3×D4—101no—
325C3×D4—101no—
326C3×D4—201no—
327C3×D4—201no—
328C2×C3×C4—101no—
329C2×C3×C4—201no—
330C2×C3×C4—201no—
331C2×C3×C4—201no—
332C2×C3×C4C2×C4×D511yescharacteristic
333C2×C3×C4#70911yescharacteristic
334C2×C3×C4#70911yescharacteristic
335C2×C3×C4C2×C22⋊D511yescharacteristic
336C2×C3×C4C2×C22⋊D511yescharacteristic
337C2×C3×C4C2×C22⋊D511yescharacteristic
338#67—22no—
339#67—22no—
340#67—204no—
341C2×Dic3—101no—
342C2×Dic3—101no—
343C2×Dic3—202no—
344C2×Dic3—201no—
345C2×Dic3#68512yes—
346D12—21no—
347D12—21no—
348C4×D3—22no—
349C4×D3—22no—
350Dic6—21no—
351Dic6—21no—
352C3×C8—22no—
353C3⋊C8—22no—
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#67⋊C411yescharacteristic
364C4×C5#88311yescharacteristic
365C4×C5C4×#6711yescharacteristic
366C4×C5#93711yescharacteristic
367Dic5—41no—
368Dic5—62no—
369Dic5—81no—
370Dic5—121no—
371Dic5—241no—
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—21no—
392M16—32no—
393M16—64no—
394M16—61no—
395M16#120112yescomplemented
396C2×C8—21no—
397C2×C8—64no—
398C2×C8—61no—
399C4⋊C4—101no—
400C4⋊C4—302no—
401C4⋊C4—301no—
402C22⋊C4—101no—
403C22⋊C4—302no—
404C22⋊C4—302no—
405C22⋊C4—301no—
406C42—101no—
407C42—151no—
408C42—151no—
409C42—301no—
410C42—301no—
411C3×C5#188411yescharacteristic, complemented, Hall
412C22×C3—41no—
413C22×C3—202no—
414C22×C3—201no—
415C22×C3C2×#68511yescharacteristic
416C22×C3#407611yescharacteristic
417C22×C3#407611yescharacteristic
418C2×D3—22no—
419C2×D3—42no—
420C3×C4—201no—
421C3×C4—401no—
422C3×C4C4×C22⋊D511yescharacteristic
423C3×C4C4×C22⋊D511yescharacteristic
424C3×C4#407511yescharacteristic
425C3×C4#409911yescharacteristic
426Dic3—22no—
427Dic3—102no—
428Dic3—201no—
429Dic3—401no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—21no—
433C2×C5—122no—
434C2×C5#495611yescharacteristic
435D5—81no—
436C23—32no—
437C23—101no—
438C23D3×D2011yescharacteristic
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—62no—
454C2×C4—62no—
455C2×C4—101no—
456C2×C4—201no—
457C2×C4—201no—
458C2×C4—201no—
459C2×C4—301no—
460C2×C4—301no—
461C2×C4—602no—
462C2×C4—601no—
463C2×C4#676511yescharacteristic
464C2×C4#677111yescharacteristic
465C2×C4C4×D3×D511yescharacteristic
466C2×C4C2×#120111yescharacteristic
467C2×C4D3×C22⋊D511yescharacteristic
468C2×C4D3×C22⋊D511yescharacteristic
469C8—22no—
470C8—62no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—401no—
475C2×C3#6550211yescharacteristic
476D3—42no—
477C5#7041711yescharacteristic, complemented, Sylow
478C22—41no—
479C22—62no—
480C22—122no—
481C22—202no—
482C22—201no—
483C22#9145411yescharacteristic
484C22#9145611yescharacteristic
485C22D3×#68511yescharacteristic
486C4—62no—
487C4—201no—
488C4—302no—
489C4—401no—
490C4—601no—
491C4—1201no—
492C4C4×#120111yescharacteristic
493C4#9144111yescharacteristic
494C4#9145211yescharacteristic
495C4#9156811yescharacteristic
496C3#1060281411yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—122no—
501C2—401no—
502C2#1174891011yescharacteristic
subgroupG/H
centerC4#91568
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754586C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1884
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C5×#5745C2semidirect
3. C3×#65428C2semidirect
4. #11748625C2semidirect
5. #11748420C2semidirect
6. #11746376C2semidirect
7. #11745973C2semidirect
20. #91463C4semidirect
22. #91385C4semidirect
23. #91370C4semidirect
24. #91368C4semidirect
33. #65428D3semidirect
56. C3×C5×M16D4semidirect
65. C5×#208D4semidirect
76. #5745D5semidirect
179. C5×M16#67semidirect
240. C3×M16C22⋊D5semidirect
255. #208C22⋊D5semidirect
395. M16#1201semidirect
411. C3×C5#1884semidirect
477. C5#70417semidirect
496. C3#10602814semidirect

Maximal subgroups

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

subgroupindex
C5×#57452
#117545862
C3×#654282
#117486252
#117484202
#117463762
#117459732
#106028143
#704175