Finite Group Databasebeta

← #14301185

Subgroups — #14301185

Order 1920.

620 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5819C211yesmaximal, characteristic, complemented
2C3×#66156C211yesmaximal, characteristic
3#11751334C211yesmaximal, characteristic, complemented
4#11748420C211yesmaximal, characteristic, complemented
5#11748343C211yesmaximal, characteristic, complemented
6#11745990C211yesmaximal, characteristic, complemented
7#11745982C211yesmaximal, characteristic, complemented
8#10602813—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11#91815C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C5×#948—22no—
14C5×#948—22no—
15C2×C5×#208—22no—
16C2×C5×#208C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C3×#4097C412yescomplemented
19C3×#4096—22no—
20C3×#4095C412yescomplemented
21C3×#4088—21no—
22C3×#4078—21no—
23C2×C3×#681C2211yescharacteristic
24#91119—21no—
25#91116—21no—
26#90976—22no—
27#90955—22no—
28#72116—51nomaximal, Hall
29C5×#568—31no—
30#66156D311yescharacteristic
31#65522—31no—
32#65428—31no—
33#65418—31no—
34#64778—31no—
35#64776—31no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41C2×C412yes—
39C3×C5×#41D412yes—
40C2×C3×C5×Q8D411yescharacteristic
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4D411yescharacteristic
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2311yescharacteristic
45C2×C3×C22⋊D5—21no—
46C3×#709—21no—
47C3×#709—21no—
48C3×#709—21no—
49C3×#709—21no—
50C2×C3×D20C2×C411yescharacteristic
51C2×C3×C4×D5—21no—
52C2×C3×Dic10C2×C411yescharacteristic
53#6719—21no—
54C4⋊Dic15—21no—
55C4×Dic15—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C5×#208—24no—
60C5×#208—21no—
61C5×#208—21no—
62C5×#208—21no—
63C5×#208D412yes—
64C2×C5×C3⋊C8—24no—
65C2×C5×C3⋊C8—21no—
66C2×C5×C3⋊C8D412yes—
67C3×#689—22no—
68C3×#688—22no—
69C3×#687—22no—
70C3×#686—22no—
71C3×#681—21no—
72C3×#681C2×C412yes—
73C2×C3×#168—21no—
74C3×#575—51no—
75#5819D511yescharacteristic, complemented
76#5236—51no—
77#5234—51no—
78#5233—51no—
79#4559—51no—
80#4558—51no—
81C2×C5×#41C2×D311yescharacteristic
82C2×#709C2×D311yescharacteristic
83C5×#131—62no—
84C5×#131—62no—
85C2×C5×M16—31no—
86C2×C5×M16—31no—
87C2×C5×M16—62no—
88#4097Dic312yescomplemented
89#4096—22no—
90#4095Dic312yescomplemented
91#4088—21no—
92#4078—21no—
93#4072—31no—
94C2×#681C2×D311yescharacteristic
95C22×#168—31no—
96#3967—61no—
97#3964—61no—
98#3957—62no—
99#3952—62no—
100#1881—151noSylow
101C23×C3×C5—21no—
102C23×C3×C5#4111yescharacteristic
103C22×C3×D5—21no—
104C3×C5×Q8—21no—
105C3×C5×Q8C22⋊C412yes—
106C3×C5×D4—22no—
107C3×C5×D4—22no—
108C3×C5×D4—21no—
109C3×C5×D4C22⋊C412yes—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5C22×C411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×Dic15—41no—
120C3×C22⋊D5—41no—
121C3×C22⋊D5—41no—
122C2×C3×Dic5—21no—
123C3×D20—21no—
124C3×D20—21no—
125C3×C4×D5—41no—
126C3×C4×D5—41no—
127C3×Dic10—21no—
128C3×Dic10—21no—
129C3⋊#168—41no—
130C3×#168—22no—
131C5×C3⋊C8—22no—
132C5×C3⋊C8—22no—
133C2×C3×#41—51no—
134C2×C3×#41C2×D511yescharacteristic
135C3×#137—52no—
136C3×#137—101no—
137C3×AGL(1,ℤ/8)—52no—
138C3×AGL(1,ℤ/8)—101no—
139C3×#135—102no—
140C2×C3×M16—51no—
141#948—22no—
142#948—22no—
143#926—51no—
144C2×#208—22no—
145C2×#208C2×D511yescharacteristic
146C2×#208C2×D511yescharacteristic
147C22×C3⋊C8—51no—
148#837—102no—
149#835—101no—
150#832—101no—
151#830—102no—
152C5×#41—21no—
153C5×#41—21no—
154C5×#41C2×Dic312yes—
155C5×#41#6712yes—
156C2×C5×Q8#6711yescharacteristic
157C2×C5×D4—21no—
158C2×C5×D4#6711yescharacteristic
159C22×C4×C5—21no—
160C22×C4×C5C22×D311yescharacteristic
161C2×C22⋊D5—21no—
162#709—21no—
163#709—21no—
164#709—21no—
165#709—21no—
166C2×D20C2×Dic311yescharacteristic
167C2×C4×D5—21no—
168C2×Dic10C2×Dic311yescharacteristic
169C5×M16—32no—
170C5×M16—64no—
171C5×M16—61no—
172C5×M16—61no—
173C5×M16—61no—
174C2×C5×C8—32no—
175C2×C5×C8—64no—
176C2×C5×C8—61no—
177C22⋊Dic5—61no—
178#689—22no—
179#688—22no—
180#687—22no—
181#686—22no—
182C4⋊Dic5—61no—
183C4×Dic5—61no—
184#681—21no—
185#681C2×Dic312yes—
186C2×#168—21no—
187C2×#168—61no—
188C2×#168—61no—
189C2×#168—61no—
190#575—51no—
191#568—31no—
192#421—151no—
193#416—151no—
194#408—151no—
195#344—151no—
196#341—151no—
197C22×C3×C5—22no—
198C22×C3×C5—41no—
199C22×C3×C5—81no—
200C22×C3×C5C4×D411yescharacteristic
201C22×C3×C5#12111yescharacteristic
202C22×C3×C5#12311yescharacteristic
203C2×C3×D5—42no—
204C2×C3×D5—41no—
205C3×C4×C5—22no—
206C3×C4×C5C2×C22⋊C411yescharacteristic
207C3×C4×C5C4×D411yescharacteristic
208C3×C4×C5#12011yescharacteristic
209C3×C4×C5#12111yescharacteristic
210Dic15—81no—
211C3×Dic5—41no—
212C3×#41—21no—
213C3×#41—21no—
214C3×#41—101no—
215C3×#41—101no—
216C3×#41—101no—
217C3×#41—101no—
218C3×#41C4×D512yes—
219C3×#41C22⋊D512yes—
220C2×C3×Q8—51no—
221C2×C3×Q8D2011yescharacteristic
222C2×C3×D4—21no—
223C2×C3×D4—51no—
224C2×C3×D4—101no—
225C2×C3×D4D2011yescharacteristic
226C22×C3×C4—21no—
227C22×C3×C4—101no—
228C22×C3×C4C22×D511yescharacteristic
229C3×Q16—102no—
230C3×SD16—102no—
231C3×SD16—102no—
232C3×D8—102no—
233C3×M16—52no—
234C3×M16—101no—
235C2×C3×C8—101no—
236#217—101no—
237C4⋊Dic3—101no—
238C4×Dic3—101no—
239#208—24no—
240#208—21no—
241#208—21no—
242#208—21no—
243#208C22⋊D512yes—
244C2×C3⋊C8—24no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—101no—
247C2×C3⋊C8—101no—
248C2×C3⋊C8—101no—
249C2×C3⋊C8C22⋊D512yes—
250C23×C5—21no—
251C23×C5#23711yescharacteristic
252C22×D5—21no—
253C5×Q8—21no—
254C5×Q8#21712yes—
255C5×D4—22no—
256C5×D4—22no—
257C5×D4—21no—
258C5×D4#21712yes—
259C2×C4×C5—21no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5D3×D411yescharacteristic
263C2×C4×C5D3×D411yescharacteristic
264C2×C4×C5#23711yescharacteristic
265C2×C4×C5C22×Dic311yescharacteristic
266C2×C4×C5C2×#6711yescharacteristic
267C2×C4×C5C2×#6711yescharacteristic
268C22⋊D5—41no—
269C22⋊D5—41no—
270C2×Dic5—21no—
271C2×Dic5—121no—
272D20—21no—
273D20—21no—
274C4×D5—41no—
275C4×D5—41no—
276Dic10—21no—
277Dic10—21no—
278C5×C8—62no—
279C5×C8—62no—
280#168—22no—
281#168—121no—
282C2×#41—51no—
283C2×#41D3×D511yescharacteristic
284#137—52no—
285#137—101no—
286AGL(1,ℤ/8)—52no—
287AGL(1,ℤ/8)—101no—
288#135—102no—
289#131—62no—
290#131—62no—
291C2×M16—31no—
292C2×M16—31no—
293C2×M16—51no—
294C2×M16—62no—
295C22×C8—151no—
296#117—151no—
297#104—302no—
298#103—301no—
299#102—301no—
300C22⋊C8—302no—
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5—21no—
304C2×C3×C5—42no—
305C2×C3×C5#38611yescharacteristic
306C3×D5—81no—
307C23×C3—21no—
308C23×C3—101no—
309C23×C3#70911yescharacteristic
310C3×Q8—21no—
311C3×Q8—101no—
312C3×Q8—101no—
313C3×Q8#68512yes—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—21no—
317C3×D4—101no—
318C3×D4—101no—
319C3×D4—201no—
320C3×D4—201no—
321C3×D4#68512yes—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—101no—
326C2×C3×C4—201no—
327C2×C3×C4—201no—
328C2×C3×C4C2×C4×D511yescharacteristic
329C2×C3×C4C2×D2011yescharacteristic
330C2×C3×C4#70911yescharacteristic
331C2×C3×C4C2×C22⋊D511yescharacteristic
332C2×C3×C4C2×C22⋊D511yescharacteristic
333C2×C3×C4C2×C22⋊D511yescharacteristic
334C2×Dic3—201no—
335C3×C8—102no—
336C3⋊C8—22no—
337C3⋊C8—22no—
338C3⋊C8—201no—
339C22×C5—22no—
340C22×C5—41no—
341C22×C5—81no—
342C22×C5D4×Dic311yescharacteristic
343C22×C5#93511yescharacteristic
344C22×C5#93911yescharacteristic
345C2×D5—42no—
346C2×D5—41no—
347C4×C5—22no—
348C4×C5D4×Dic311yescharacteristic
349C4×C5#93711yescharacteristic
350C4×C5#93911yescharacteristic
351C4×C5C2×#21711yescharacteristic
352Dic5—41no—
353Dic5—241no—
354#41—21no—
355#41—21no—
356#41—101no—
357#41—101no—
358#41—101no—
359#41—101no—
360#41D5×Dic312yes—
361#41#120112yes—
362C2×Q8—51no—
363C2×Q8#120211yescharacteristic
364C2×D4—21no—
365C2×D4—51no—
366C2×D4—101no—
367C2×D4#120211yescharacteristic
368C22×C4—21no—
369C22×C4—101no—
370C22×C4C2×D3×D511yescharacteristic
371Q16—102no—
372SD16—102no—
373SD16—102no—
374D8—102no—
375M16—32no—
376M16—52no—
377M16—64no—
378M16—61no—
379M16—61no—
380M16—61no—
381M16—101no—
382C2×C8—32no—
383C2×C8—64no—
384C2×C8—61no—
385C2×C8—101no—
386C2×C8—301no—
387C2×C8—301no—
388C2×C8—301no—
389C4⋊C4—301no—
390C22⋊C4—301no—
391C42—301no—
392C3×C5#188111yescharacteristic, complemented, Hall
393C22×C3—22no—
394C22×C3—41no—
395C22×C3—81no—
396C22×C3—202no—
397C22×C3—201no—
398C22×C3C4×C22⋊D511yescharacteristic
399C22×C3#407511yescharacteristic
400C22×C3#407611yescharacteristic
401C3×C4—22no—
402C3×C4—201no—
403C3×C4C2×#68511yescharacteristic
404C3×C4C4×C22⋊D511yescharacteristic
405C3×C4#407611yescharacteristic
406C3×C4#409911yescharacteristic
407Dic3—401no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—42no—
412C2×C5#522011yescharacteristic
413D5—81no—
414C23—21no—
415C23—101no—
416C23#677911yescharacteristic
417Q8—21no—
418Q8—101no—
419Q8—101no—
420Q8#666512yes—
421D4—22no—
422D4—22no—
423D4—21no—
424D4—101no—
425D4—101no—
426D4—201no—
427D4—201no—
428D4#666512yes—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—101no—
433C2×C4—201no—
434C2×C4—201no—
435C2×C4—601no—
436C2×C4C2×D5×Dic311yescharacteristic
437C2×C4#677911yescharacteristic
438C2×C4C2×#120111yescharacteristic
439C2×C4C2×#120211yescharacteristic
440C2×C4D3×C22⋊D511yescharacteristic
441C2×C4D3×C22⋊D511yescharacteristic
442C8—62no—
443C8—62no—
444C8—102no—
445C8—601no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—42no—
450C2×C3—401no—
451C2×C3#6550211yescharacteristic
452C5#7211611yescharacteristic, complemented, Sylow
453C22—22no—
454C22—41no—
455C22—81no—
456C22—202no—
457C22—201no—
458C22#9153611yescharacteristic
459C22Dic3×C22⋊D511yescharacteristic
460C22#9156911yescharacteristic
461C4—22no—
462C4—201no—
463C4—1201no—
464C4C2×#666511yescharacteristic
465C4Dic3×C22⋊D511yescharacteristic
466C4#9156811yescharacteristic
467C4#9156911yescharacteristic
468C3#1060281311yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—42no—
473C2—401no—
474C2#1174949511yescharacteristic
subgroupG/H
centerC4#91568
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5#386
prime radicalC3×#66156C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1881
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
1. C5×#5819C2semidirect
3. #11751334C2semidirect
4. #11748420C2semidirect
5. #11748343C2semidirect
6. #11745990C2semidirect
7. #11745982C2semidirect
18. C3×#4097C4semidirect
20. C3×#4095C4semidirect
75. #5819D5semidirect
88. #4097Dic3semidirect
90. #4095Dic3semidirect
392. C3×C5#1881semidirect
452. C5#72116semidirect
468. C3#10602813semidirect

Maximal subgroups

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

subgroupindex
C5×#58192
C3×#661562
#117513342
#117484202
#117483432
#117459902
#117459822
#106028133
#721165