Finite Group Databasebeta

← #14301193

Subgroups — #14301193

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
1C3×#66156C211yesmaximal, characteristic
2#11754120C211yesmaximal, characteristic, complemented
3#11751337C211yesmaximal, characteristic, complemented
4C5×#5234C211yesmaximal, characteristic, complemented
5#11748365C211yesmaximal, characteristic, complemented
6#11745990C211yesmaximal, characteristic, complemented
7#11745983C211yesmaximal, characteristic, complemented
8#10600805—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C3×#4097—21no—
16C3×#4096—22no—
17C3×#4095—21no—
18C3×#4088C412yescomplemented
19C3×#4078C412yescomplemented
20C2×C3×#681C2211yescharacteristic
21#91284—22no—
22#91283—22no—
23D5×#208—22no—
24#91121—22no—
25C5×#830—22no—
26#90971—21no—
27#90965—21no—
28#72116—51nomaximal, Hall
29#66156D311yescharacteristic
30#66079—31no—
31C5×#408—31no—
32#65525—31no—
33#65402—31no—
34#64776—31no—
35#64772—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×C3×C22⋊D5—21no—
46C3×#709—21no—
47C3×#709—21no—
48C3×#709C2×C412yes—
49C3×#709D412yes—
50C2×C3×D20D411yescharacteristic
51C2×C3×C4×D5—21no—
52C2×C3×Dic10D411yescharacteristic
53#6719—21no—
54C4⋊Dic15—21no—
55C4×Dic15—21no—
56#6710—21no—
57#6710D412yes—
58C2×C3⋊#168—21no—
59C5×#208—21no—
60C5×#208—21no—
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C2×C5×C3⋊C8—21no—
64C2×C5×C3⋊C8D412yes—
65C3×#689—22no—
66C3×#688—22no—
67C3×#687—22no—
68C3×#686—22no—
69C3×#681—21no—
70C3×#681C2×C412yes—
71C2×C3×#168—21no—
72#6649—24no—
73D5×C3⋊C8—24no—
74C3×#575—51no—
75#5819—51no—
76#5236—51no—
77#5234D511yescharacteristic, complemented
78#5233—51no—
79#4559—51no—
80#4558—51no—
81C2×C5×#41C2×D311yescharacteristic
82C2×#709C2×D311yescharacteristic
83C2×C5×M16—31no—
84C22×C5×C8—31no—
85#4097—21no—
86#4096—22no—
87#4095—21no—
88#4088Dic312yescomplemented
89#4078Dic312yescomplemented
90#4072—31no—
91C2×#681—31no—
92C2×#681C2×D311yescharacteristic
93#4053—62no—
94D5×M16—62no—
95#4047—62no—
96C5×C22⋊C8—62no—
97#3969—62no—
98#3953—61no—
99#3948—61no—
100#1881—151noSylow
101C23×C3×C5—21no—
102C23×C3×C5#4111yescharacteristic
103C22×C3×D5—21no—
104C3×C5×Q8—21no—
105C3×C5×Q8—21no—
106C3×C5×D4—21no—
107C3×C5×D4—21no—
108C3×C5×D4—41no—
109C3×C5×D4—41no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—41no—
112C2×C3×C4×C5—41no—
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—22no—
121C3×C22⋊D5—22no—
122C2×C3×Dic5—21no—
123C3×D20—21no—
124C3×D20C22⋊C412yes—
125C3×C4×D5—22no—
126C3×C4×D5—22no—
127C3×Dic10—21no—
128C3×Dic10C22⋊C412yes—
129C3⋊#168—22no—
130C3×#168—22no—
131C5×C3⋊C8—22no—
132C5×C3⋊C8—41no—
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—102no—
142#948—102no—
143#926—51no—
144C2×#208—51no—
145C2×#208—102no—
146C2×#208C2×D511yescharacteristic
147C22×C3⋊C8C2×D511yescharacteristic
148#837—102no—
149#835—101no—
150#832—101no—
151#830—22no—
152C5×#41—21no—
153C5×#41—21no—
154C5×#41—21no—
155C5×#41—21no—
156C2×C5×Q8C2×Dic311yescharacteristic
157C2×C5×D4—21no—
158C2×C5×D4C2×Dic311yescharacteristic
159C22×C4×C5—21no—
160C22×C4×C5C22×D311yescharacteristic
161C2×C22⋊D5—21no—
162#709—21no—
163#709—21no—
164#709C2×Dic312yes—
165#709#6712yes—
166C2×D20#6711yescharacteristic
167C2×C4×D5—21no—
168C2×Dic10#6711yescharacteristic
169C5×M16—61no—
170C5×M16—61no—
171C2×C5×C8—32no—
172C2×C5×C8—61no—
173C2×C5×C8—61no—
174C2×C5×C8—61no—
175C22⋊Dic5—61no—
176#689—22no—
177#688—22no—
178#687—22no—
179#686—22no—
180C4⋊Dic5—61no—
181C4×Dic5—61no—
182#681—21no—
183#681—32no—
184#681—61no—
185#681C2×Dic312yes—
186C2×#168—21no—
187C2×#168—61no—
188#676—64no—
189C8×D5—64no—
190#575—51no—
191#568—151no—
192#421—151no—
193#416—151no—
194#408—31no—
195#344—151no—
196#341—151no—
197C22×C3×C5—41no—
198C22×C3×C5—42no—
199C22×C3×C5—41no—
200C22×C3×C5C4×D411yescharacteristic
201C22×C3×C5#12111yescharacteristic
202C22×C3×C5#12311yescharacteristic
203C2×C3×D5—22no—
204C2×C3×D5—81no—
205C3×C4×C5—41no—
206C3×C4×C5C2×C22⋊C411yescharacteristic
207C3×C4×C5C4×D411yescharacteristic
208C3×C4×C5#12011yescharacteristic
209C3×C4×C5#12111yescharacteristic
210Dic15—81no—
211C3×Dic5—22no—
212C3×#41—21no—
213C3×#41—21no—
214C3×#41—21no—
215C3×#41—21no—
216C3×#41—52no—
217C3×#41—52no—
218C3×#41—101no—
219C3×#41—101no—
220C2×C3×Q8—51no—
221C2×C3×Q8C4×D511yescharacteristic
222C2×C3×D4—21no—
223C2×C3×D4—51no—
224C2×C3×D4—101no—
225C2×C3×D4C4×D511yescharacteristic
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—21no—
240#208—21no—
241#208—52no—
242#208—104no—
243#208—101no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—104no—
248C2×C3⋊C8—101no—
249C2×C3⋊C8C22⋊D512yes—
250C23×C5—21no—
251C23×C5#23711yescharacteristic
252C22×D5—21no—
253C5×Q8—21no—
254C5×Q8—21no—
255C5×D4—21no—
256C5×D4—21no—
257C5×D4—41no—
258C5×D4—41no—
259C2×C4×C5—21no—
260C2×C4×C5—41no—
261C2×C4×C5—41no—
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—22no—
269C22⋊D5—22no—
270C2×Dic5—21no—
271C2×Dic5—121no—
272D20—21no—
273D20#21712yes—
274C4×D5—22no—
275C4×D5—22no—
276Dic10—21no—
277Dic10#21712yes—
278C5×C8—62no—
279C5×C8—121no—
280#168—22no—
281#168—62no—
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—302no—
290#131—302no—
291C2×M16—31no—
292C2×M16—51no—
293C2×M16—151no—
294C2×M16—302no—
295C22×C8—31no—
296#117—151no—
297#104—302no—
298#103—301no—
299#102—301no—
300C22⋊C8—62no—
301C2×C3×C5—21no—
302C2×C3×C5—21no—
303C2×C3×C5—21no—
304C2×C3×C5—81no—
305C2×C3×C5#38611yescharacteristic
306C3×D5—42no—
307C23×C3—21no—
308C23×C3—101no—
309C23×C3#70911yescharacteristic
310C3×Q8—21no—
311C3×Q8—21no—
312C3×Q8—52no—
313C3×Q8—101no—
314C3×D4—21no—
315C3×D4—21no—
316C3×D4—41no—
317C3×D4—41no—
318C3×D4—52no—
319C3×D4—102no—
320C3×D4—102no—
321C3×D4—101no—
322C2×C3×C4—21no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—101no—
326C2×C3×C4—102no—
327C2×C3×C4—102no—
328C2×C3×C4C2×C4×D511yescharacteristic
329C2×C3×C4D4×D511yescharacteristic
330C2×C3×C4D4×D511yescharacteristic
331C2×C3×C4D4×D511yescharacteristic
332C2×C3×C4#71111yescharacteristic
333C2×C3×C4C2×C22⋊D511yescharacteristic
334C2×Dic3—201no—
335C3×C8—102no—
336C3⋊C8—22no—
337C3⋊C8—41no—
338C3⋊C8—102no—
339C22×C5—41no—
340C22×C5—42no—
341C22×C5—41no—
342C22×C5D4×Dic311yescharacteristic
343C22×C5#93511yescharacteristic
344C22×C5#93911yescharacteristic
345C2×D5—22no—
346C2×D5—81no—
347C4×C5—41no—
348C4×C5D4×Dic311yescharacteristic
349C4×C5#93711yescharacteristic
350C4×C5#93911yescharacteristic
351C4×C5C2×#21711yescharacteristic
352Dic5—22no—
353Dic5—241no—
354#41—21no—
355#41—21no—
356#41—21no—
357#41—21no—
358#41—52no—
359#41—52no—
360#41—101no—
361#41—101no—
362C2×Q8—51no—
363C2×Q8D5×Dic311yescharacteristic
364C2×D4—21no—
365C2×D4—51no—
366C2×D4—101no—
367C2×D4D5×Dic311yescharacteristic
368C22×C4—21no—
369C22×C4—101no—
370C22×C4C2×D3×D511yescharacteristic
371Q16—102no—
372SD16—102no—
373SD16—102no—
374D8—102no—
375M16—52no—
376M16—61no—
377M16—61no—
378M16—101no—
379M16—152no—
380M16—304no—
381M16—301no—
382C2×C8—32no—
383C2×C8—61no—
384C2×C8—61no—
385C2×C8—61no—
386C2×C8—101no—
387C2×C8—304no—
388C2×C8—301no—
389C4⋊C4—301no—
390C22⋊C4—301no—
391C42—301no—
392C3×C5#188111yescharacteristic, complemented, Hall
393C22×C3—41no—
394C22×C3—42no—
395C22×C3—41no—
396C22×C3—102no—
397C22×C3—401no—
398C22×C3#402911yescharacteristic
399C22×C3#403011yescharacteristic
400C22×C3C4×C22⋊D511yescharacteristic
401C3×C4—41no—
402C3×C4—102no—
403C3×C4D5×C22⋊C411yescharacteristic
404C3×C4#402711yescharacteristic
405C3×C4#408311yescharacteristic
406C3×C4#408411yescharacteristic
407Dic3—401no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—81no—
412C2×C5#522011yescharacteristic
413D5—42no—
414C23—21no—
415C23—101no—
416C23#677911yescharacteristic
417Q8—21no—
418Q8—21no—
419Q8—52no—
420Q8—101no—
421D4—21no—
422D4—21no—
423D4—41no—
424D4—41no—
425D4—52no—
426D4—102no—
427D4—102no—
428D4—101no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—101no—
433C2×C4—102no—
434C2×C4—102no—
435C2×C4—601no—
436C2×C4C2×D5×Dic311yescharacteristic
437C2×C4#678011yescharacteristic
438C2×C4D5×#6711yescharacteristic
439C2×C4D5×#6711yescharacteristic
440C2×C4D3×C22⋊D511yescharacteristic
441C2×C4#679011yescharacteristic
442C8—62no—
443C8—102no—
444C8—121no—
445C8—302no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—81no—
450C2×C3—202no—
451C2×C3#6524511yescharacteristic
452C5#7211611yescharacteristic, complemented, Sylow
453C22—41no—
454C22—42no—
455C22—41no—
456C22—102no—
457C22—401no—
458C22#9154811yescharacteristic
459C22#9155011yescharacteristic
460C22Dic3×C22⋊D511yescharacteristic
461C4—41no—
462C4—102no—
463C4—1201no—
464C4D5×#21711yescharacteristic
465C4#9154911yescharacteristic
466C4#9155911yescharacteristic
467C4#9157711yescharacteristic
468C3#1060080511yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—81no—
473C2—202no—
474C2#1174951811yescharacteristic
subgroupG/H
centerC4#91577
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
2. #11754120C2semidirect
3. #11751337C2semidirect
4. C5×#5234C2semidirect
5. #11748365C2semidirect
6. #11745990C2semidirect
7. #11745983C2semidirect
18. C3×#4088C4semidirect
19. C3×#4078C4semidirect
77. #5234D5semidirect
88. #4088Dic3semidirect
89. #4078Dic3semidirect
392. C3×C5#1881semidirect
452. C5#72116semidirect
468. C3#10600805semidirect

Maximal subgroups

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

subgroupindex
C3×#661562
#117541202
#117513372
C5×#52342
#117483652
#117459902
#117459832
#106008053
#721165