Finite Group Databasebeta

← #14301374

Subgroups — #14301374

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#11756504C211yesmaximal, characteristic, complemented
2#11756236C211yesmaximal, characteristic
3#11751240C211yesmaximal, characteristic, complemented
4#11751107C211yesmaximal, characteristic, complemented
5#11751106C211yesmaximal, characteristic, complemented
6C3×C5×#339C211yesmaximal, characteristic, complemented
7#11746344C211yesmaximal, characteristic, complemented
8#10599570—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14#91819—22no—
15#91815C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17#91796—22no—
18M16×D15—22no—
19#91790—22no—
20#91764C411yescharacteristic, complemented
21#91764C411yescharacteristic, complemented
22#91763C411yescharacteristic, complemented
23C4×D60—22no—
24#91758C411yescharacteristic, complemented
25#91109—22no—
26#91090—22no—
27#91089—22no—
28#68777—51nomaximal, Hall
29#66079—31no—
30#65811—31no—
31#65428—31no—
32#65295—31no—
33#65294—31no—
34C5×#339D311yescharacteristic, complemented
35#64743—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39C2×#1220D412yes—
40#6817—21no—
41#6817—21no—
42#6817—21no—
43#6817—21no—
44#6817—21no—
45#6817—21no—
46#6817—21no—
47#6817—21no—
48C2×D60—22no—
49C2×D60C2×C411yescharacteristic
50C2×D60C2×C411yescharacteristic
51C2×C4×D15—21no—
52C2×C4×D15D412yes—
53C2×Dic30C2×C411yescharacteristic
54C2×Dic30C2×C411yescharacteristic
55C3×C5×M16—21no—
56C3×C5×M16D412yescomplemented
57C2×C3×C5×C8—21no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C42×C5—21no—
61C3×C42×C5—21no—
62C3×C42×C5C2×C411yescharacteristic
63C3×C42×C5C2×C411yescharacteristic
64#6719—21no—
65#6714—22no—
66#6714—22no—
67C4⋊Dic15—22no—
68C4⋊Dic15—21no—
69C4×Dic15—21no—
70#6710—21no—
71#6710D412yescomplemented
72C2×C3⋊#168—21no—
73#6705—24no—
74C8×D15—24no—
75#5745—51no—
76#5477—51no—
77#5139—51no—
78#5006—51no—
79#5005—51no—
80C3×#339D511yescharacteristic, complemented
81#4523—51no—
82C2×#709—31no—
83C2×#709—31no—
84C2×C5×M16C2×D311yescharacteristic
85C5×#117C2×D311yescharacteristic
86C2×C42×C5C2×D311yescharacteristic
87#4076—62no—
88#4072—31no—
89C2×#681—31no—
90#4053—62no—
91D5×M16—62no—
92#4047—62no—
93#4021—31no—
94#4021—31no—
95#4020—31no—
96C4×D20—62no—
97#4015—31no—
98#3957—62no—
99#3938—62no—
100#3937—62no—
101#1884—151noSylow
102C23×C3×C5C2×D411yescharacteristic
103C22×D15—21no—
104C22×D15C22⋊C412yes—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115#1220—22no—
116#1220—22no—
117#1220—41no—
118#1220—41no—
119C2×Dic15—21no—
120C2×Dic15—41no—
121C2×Dic15C22⋊C412yes—
122D60—21no—
123D60—21no—
124D60—21no—
125D60—21no—
126D60—44no—
127C4×D15—22no—
128C4×D15—22no—
129C4×D15—41no—
130C4×D15—41no—
131Dic30—21no—
132Dic30—21no—
133Dic30—21no—
134Dic30—21no—
135C3×C5×C8—22no—
136C3⋊#168—22no—
137C2×#235—51no—
138C2×#235—51no—
139C2×C3×M16C2×D511yescharacteristic
140C3×#117C2×D511yescharacteristic
141C2×C3×C42C2×D511yescharacteristic
142#930—102no—
143#926—51no—
144C2×#208—51no—
145#907—102no—
146D3×M16—102no—
147#901—102no—
148#875—51no—
149#875—51no—
150#874—51no—
151C4×D12—102no—
152#869—51no—
153#825—102no—
154#806—102no—
155#805—102no—
156C22×C4×C5—21no—
157C22×C4×C5C22×D311yescharacteristic
158C2×C22⋊D5—32no—
159C2×C22⋊D5—61no—
160#709—61no—
161#709—61no—
162#709—61no—
163#709—61no—
164#709—61no—
165#709—61no—
166#709—61no—
167#709—61no—
168C2×D20—31no—
169C2×D20—31no—
170C2×D20—62no—
171C2×C4×D5—32no—
172C2×C4×D5—61no—
173C2×Dic10—31no—
174C2×Dic10—31no—
175C5×M16—21no—
176C5×M16D1212yescomplemented
177C2×C5×C8—21no—
178C5×C4⋊C4—21no—
179C5×C22⋊C4—21no—
180C42×C5—21no—
181C42×C5—21no—
182C42×C5C4×D311yescharacteristic
183C42×C5C4×D311yescharacteristic
184C22⋊Dic5—61no—
185#685—62no—
186#685—62no—
187C4⋊Dic5—62no—
188C4⋊Dic5—61no—
189C4×Dic5—61no—
190#681—32no—
191#681—61no—
192C2×#168—61no—
193#676—64no—
194C8×D5—64no—
195#568—151no—
196#532—151no—
197#421—151no—
198#421—151no—
199#410—151no—
200#339—151no—
201#339D1511yescharacteristic, complemented
202C22×C3×C5—41no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C22×C3×C5#12111yescharacteristic
205C22×C3×C5#12111yescharacteristic
206C2×D15—22no—
207C2×D15—42no—
208C2×D15—42no—
209C2×D15—41no—
210C3×C4×C5—22no—
211C3×C4×C5—41no—
212C3×C4×C5—81no—
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5C4×D411yescharacteristic
215C3×C4×C5#12011yescharacteristic
216C3×C4×C5#12311yescharacteristic
217Dic15—22no—
218Dic15—41no—
219Dic15—81no—
220C22×C3×C4—21no—
221C22×C3×C4C22×D511yescharacteristic
222C2×#67—52no—
223C2×#67—101no—
224#235—101no—
225#235—101no—
226#235—101no—
227#235—101no—
228#235—101no—
229#235—101no—
230#235—101no—
231#235—101no—
232C2×D12—51no—
233C2×D12—51no—
234C2×D12—102no—
235C2×C4×D3—52no—
236C2×C4×D3—101no—
237C2×Dic6—51no—
238C2×Dic6—51no—
239C3×M16—21no—
240C3×M16D2012yescomplemented
241C2×C3×C8—21no—
242C3×C4⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C42—21no—
245C3×C42—21no—
246C3×C42C4×D511yescharacteristic
247C3×C42C4×D511yescharacteristic
248#217—101no—
249(C2×D3)⋊C4—102no—
250(C2×D3)⋊C4—102no—
251C4⋊Dic3—102no—
252C4⋊Dic3—101no—
253C4×Dic3—101no—
254#208—52no—
255#208—101no—
256C2×C3⋊C8—101no—
257ΓL(1,𝔽25)—104no—
258D3×C8—104no—
259C23×C5D3×D411yescharacteristic
260C22×D5—32no—
261C22×D5—61no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—42no—
265C2×C4×C5—41no—
266C2×C4×C5C2×C4×D311yescharacteristic
267C2×C4×C5C2×D1211yescharacteristic
268C2×C4×C5#23511yescharacteristic
269C2×C4×C5D3×D411yescharacteristic
270C2×C4×C5D3×D411yescharacteristic
271C2×C4×C5#23911yescharacteristic
272C22⋊D5—62no—
273C22⋊D5—62no—
274C22⋊D5—121no—
275C22⋊D5—121no—
276C2×Dic5—32no—
277C2×Dic5—61no—
278C2×Dic5—121no—
279D20—61no—
280D20—61no—
281D20—61no—
282D20—61no—
283D20—124no—
284C4×D5—62no—
285C4×D5—62no—
286C4×D5—121no—
287C4×D5—121no—
288Dic10—61no—
289Dic10—61no—
290Dic10—61no—
291Dic10—61no—
292C5×C8—22no—
293#168—62no—
294C2×#41—151no—
295C2×#41—151no—
296#131—302no—
297#131—302no—
298C2×M16—151no—
299C2×M16—302no—
300C2×M16C2×D1511yescharacteristic
301C4⋊Q8—151no—
302#127—151no—
303#124—151no—
304#124—151no—
305#121—302no—
306C4×D4—302no—
307#117—151no—
308#117C2×D1511yescharacteristic
309C2×C42C2×D1511yescharacteristic
310#104—302no—
311#104—302no—
312#99—302no—
313C2×C3×C5—21no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5#38611yescharacteristic
317D15—42no—
318D15—81no—
319C23×C3D4×D511yescharacteristic
320C22×D3—52no—
321C22×D3—101no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—42no—
325C2×C3×C4—41no—
326C2×C3×C4C2×C4×D511yescharacteristic
327C2×C3×C4C2×D2011yescharacteristic
328C2×C3×C4#70911yescharacteristic
329C2×C3×C4D4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331C2×C3×C4#71311yescharacteristic
332#67—102no—
333#67—102no—
334#67—201no—
335#67—201no—
336C2×Dic3—52no—
337C2×Dic3—101no—
338C2×Dic3—201no—
339D12—101no—
340D12—101no—
341D12—101no—
342D12—101no—
343D12—204no—
344C4×D3—102no—
345C4×D3—102no—
346C4×D3—201no—
347C4×D3—201no—
348Dic6—101no—
349Dic6—101no—
350Dic6—101no—
351Dic6—101no—
352C3×C8—22no—
353C3⋊C8—102no—
354C22×C5—41no—
355C22×C5D3×C22⋊C411yescharacteristic
356C22×C5#88411yescharacteristic
357C22×C5#89511yescharacteristic
358C2×D5—62no—
359C2×D5—122no—
360C2×D5—122no—
361C2×D5—121no—
362C4×C5—22no—
363C4×C5—41no—
364C4×C5—81no—
365C4×C5C4×D1211yescharacteristic
366C4×C5#88211yescharacteristic
367C4×C5#89311yescharacteristic
368C4×C5#89411yescharacteristic
369Dic5—62no—
370Dic5—121no—
371Dic5—241no—
372#41—301no—
373#41—301no—
374#41—301no—
375#41—301no—
376#41—301no—
377#41—301no—
378#41—301no—
379#41—301no—
380C2×Q8—151no—
381C2×Q8—151no—
382C2×D4—152no—
383C2×D4—151no—
384C2×D4—151no—
385C2×D4—302no—
386C2×D4—301no—
387C22×C4—21no—
388C22×C4—152no—
389C22×C4—301no—
390C22×C4C22×D1511yescharacteristic
391M16—21no—
392M16—152no—
393M16—304no—
394M16—301no—
395M16D6012yescomplemented
396C2×C8—21no—
397C2×C8—304no—
398C2×C8—301no—
399C4⋊C4—21no—
400C4⋊C4—302no—
401C4⋊C4—301no—
402C22⋊C4—21no—
403C22⋊C4—302no—
404C22⋊C4—302no—
405C22⋊C4—301no—
406C42—21no—
407C42—21no—
408C42—301no—
409C42C4×D1511yescharacteristic
410C42C4×D1511yescharacteristic
411C3×C5#188411yescharacteristic, complemented, Hall
412C22×C3—41no—
413C22×C3D5×C22⋊C411yescharacteristic
414C22×C3#403011yescharacteristic
415C22×C3#404111yescharacteristic
416C2×D3—102no—
417C2×D3—202no—
418C2×D3—202no—
419C2×D3—201no—
420C3×C4—22no—
421C3×C4—41no—
422C3×C4—81no—
423C3×C4C4×D2011yescharacteristic
424C3×C4#402811yescharacteristic
425C3×C4#403911yescharacteristic
426C3×C4#404011yescharacteristic
427Dic3—102no—
428Dic3—201no—
429Dic3—401no—
430C2×C5—21no—
431C2×C5—21no—
432C2×C5—21no—
433C2×C5#466511yescharacteristic
434D5—122no—
435D5—241no—
436C23—152no—
437C23—301no—
438C23D4×D1511yescharacteristic
439Q8—301no—
440Q8—301no—
441Q8—301no—
442Q8—301no—
443D4—302no—
444D4—302no—
445D4—301no—
446D4—301no—
447D4—301no—
448D4—301no—
449D4—604no—
450D4—601no—
451D4—601no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—152no—
457C2×C4—302no—
458C2×C4—302no—
459C2×C4—301no—
460C2×C4—601no—
461C2×C4—601no—
462C2×C4—601no—
463C2×C4C2×C4×D1511yescharacteristic
464C2×C4C2×D6011yescharacteristic
465C2×C4#681711yescharacteristic
466C2×C4D4×D1511yescharacteristic
467C2×C4D4×D1511yescharacteristic
468C2×C4#682111yescharacteristic
469C8—22no—
470C8—302no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3#6495411yescharacteristic
475D3—202no—
476D3—401no—
477C5#6877711yescharacteristic, complemented, Sylow
478C22—41no—
479C22—302no—
480C22—602no—
481C22—602no—
482C22—601no—
483C22C22⋊C4×D1511yescharacteristic
484C22#9177311yescharacteristic
485C22#9178411yescharacteristic
486C4—22no—
487C4—41no—
488C4—81no—
489C4—302no—
490C4—601no—
491C4—1201no—
492C4C4×D6011yescharacteristic
493C4#9177111yescharacteristic
494C4#9178211yescharacteristic
495C4#9178311yescharacteristic
496C3#1059957011yescharacteristic, complemented, Sylow
497C2—21no—
498C2—21no—
499C2—21no—
500C2—602no—
501C2—1201no—
502C2#1175076611yescharacteristic
subgroupG/H
centerC4#91771
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#339C2
socleC2×C3×C5#386
prime radical#11756236C2
cosocleC22×C3×C4×C5C23
hypercenter#339D15
hypocenterC3×C5#1884
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #11756504C2semidirect
3. #11751240C2semidirect
4. #11751107C2semidirect
5. #11751106C2semidirect
6. C3×C5×#339C2semidirect
7. #11746344C2semidirect
20. #91764C4semidirect
21. #91764C4semidirect
22. #91763C4semidirect
24. #91758C4semidirect
34. C5×#339D3semidirect
56. C3×C5×M16D4semidirect
71. #6710D4semidirect
80. C3×#339D5semidirect
176. C5×M16D12semidirect
201. #339D15semidirect
240. C3×M16D20semidirect
395. M16D60semidirect
411. C3×C5#1884semidirect
477. C5#68777semidirect
496. C3#10599570semidirect

Maximal subgroups

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

subgroupindex
#117565042
#117562362
#117512402
#117511072
#117511062
C3×C5×#3392
#117463442
#105995703
#687775