Finite Group Databasebeta

← #14301206

Subgroups — #14301206

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×#66082C211yesmaximal, characteristic
2#11754120C211yesmaximal, characteristic, complemented
3#11748420C211yesmaximal, characteristic, complemented
4#11748365C211yesmaximal, characteristic, complemented
5#11748342C211yesmaximal, characteristic, complemented
6#11746380C211yesmaximal, characteristic, complemented
7C5×#4558C211yesmaximal, characteristic, complemented
8#10599740—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C3×#4055—21no—
17C3×#4055C412yescomplemented
18C3×#4054—21no—
19C3×#4054C412yescomplemented
20C3×#4050—22no—
21#91284—22no—
22#91283—22no—
23D5×#208—22no—
24#90976—22no—
25#90971—21no—
26#90965—21no—
27#90955—22no—
28#72116—51nomaximal, Hall
29#66082D311yescharacteristic
30#66079—31no—
31#65428—31no—
32#65402—31no—
33#65399—31no—
34C5×#341—31no—
35#64779—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×C3×C22⋊D5—21no—
38C2×C3×C22⋊D5—21no—
39C3×#709—21no—
40C3×#709—21no—
41C3×#709—21no—
42C3×#709—21no—
43C3×#709—21no—
44C3×#709—21no—
45C3×#709C2×C412yes—
46C3×#709D412yes—
47C2×C3×D20C2×C411yescharacteristic
48C2×C3×D20D411yescharacteristic
49C2×C3×C4×D5—21no—
50C2×C3×C4×D5—21no—
51C2×C3×Dic10C2×C411yescharacteristic
52C2×C3×Dic10D411yescharacteristic
53C3×C5×M16—21no—
54C3×C5×M16C2×C412yes—
55C2×C3×C5×C8—21no—
56#6719—21no—
57C4⋊Dic15—21no—
58C4×Dic15—21no—
59#6710—21no—
60#6710—21no—
61C2×C3⋊#168D412yes—
62C5×#208—21no—
63C5×#208D412yes—
64C2×C5×C3⋊C8—21no—
65C2×C5×C3⋊C8—21no—
66C2×C5×C3⋊C8—21no—
67C2×C5×C3⋊C8—21no—
68C3×Dic20—22no—
69C3×D40—22no—
70C3×#677—22no—
71C3×#677—22no—
72#6649—24no—
73D5×C3⋊C8—24no—
74C3×#575—51no—
75#5819—51no—
76#5236—51no—
77#5234—51no—
78#5233—51no—
79#4559—51no—
80#4558D511yescharacteristic, complemented
81C2×#709C2×D311yescharacteristic
82C2×#709C2×D311yescharacteristic
83C2×C5×M16—31no—
84C2×C5×M16C2×D311yescharacteristic
85C22×C5×C8—31no—
86#4072—31no—
87C2×#681—31no—
88#4055—21no—
89#4055Dic312yescomplemented
90#4054—21no—
91#4054Dic312yescomplemented
92#4053—62no—
93D5×M16—62no—
94#4050—22no—
95#4047—62no—
96#3957—62no—
97#3953—61no—
98#3952—62no—
99#3948—61no—
100#1881—151noSylow
101C23×C3×C5#4111yescharacteristic
102C22×C3×D5—21no—
103C22×C3×D5—21no—
104C2×C3×C4×C5C22×C411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×Dic15—41no—
111C3×C22⋊D5—22no—
112C3×C22⋊D5—22no—
113C3×C22⋊D5—41no—
114C3×C22⋊D5—41no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117C3×D20—21no—
118C3×D20—21no—
119C3×D20—21no—
120C3×D20C22⋊C412yes—
121C3×C4×D5—22no—
122C3×C4×D5—22no—
123C3×C4×D5—41no—
124C3×C4×D5—41no—
125C3×Dic10—21no—
126C3×Dic10—21no—
127C3×Dic10—21no—
128C3×Dic10C22⋊C412yes—
129C3×C5×C8—22no—
130C3⋊#168—22no—
131C5×C3⋊C8—22no—
132C5×C3⋊C8—41no—
133C2×C3×#41—51no—
134C2×C3×#41—51no—
135C3×#137—52no—
136C3×#137—101no—
137C3×AGL(1,ℤ/8)—52no—
138C3×AGL(1,ℤ/8)—101no—
139C3×#135—102no—
140C2×C3×M16C2×D511yescharacteristic
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—102no—
152C22×C4×C5C22×D311yescharacteristic
153C2×C22⋊D5—21no—
154C2×C22⋊D5—21no—
155#709—21no—
156#709—21no—
157#709—21no—
158#709—21no—
159#709—21no—
160#709—21no—
161#709C2×Dic312yes—
162#709#6712yes—
163C2×D20C2×Dic311yescharacteristic
164C2×D20#6711yescharacteristic
165C2×C4×D5—21no—
166C2×C4×D5—21no—
167C2×Dic10C2×Dic311yescharacteristic
168C2×Dic10#6711yescharacteristic
169C5×M16—21no—
170C5×M16—32no—
171C5×M16—61no—
172C5×M16C2×Dic312yes—
173C2×C5×C8—21no—
174C2×C5×C8—61no—
175C2×C5×C8—61no—
176C2×C5×C8—61no—
177C2×C5×C8—61no—
178C22⋊Dic5—61no—
179C4⋊Dic5—61no—
180C4×Dic5—61no—
181#681—61no—
182#681—61no—
183C2×#168—32no—
184Dic20—22no—
185D40—22no—
186#677—22no—
187#677—22no—
188#676—64no—
189C8×D5—64no—
190#575—51no—
191#568—151no—
192#421—151no—
193#416—151no—
194#408—151no—
195#344—151no—
196#341—31no—
197C22×C3×C5—41no—
198C22×C3×C5C4×D411yescharacteristic
199C22×C3×C5#12111yescharacteristic
200C22×C3×C5#12311yescharacteristic
201C2×C3×D5—22no—
202C2×C3×D5—42no—
203C2×C3×D5—41no—
204C2×C3×D5—81no—
205C3×C4×C5C2×C22⋊C411yescharacteristic
206C3×C4×C5C4×D411yescharacteristic
207C3×C4×C5#12011yescharacteristic
208C3×C4×C5#12111yescharacteristic
209Dic15—81no—
210C3×Dic5—22no—
211C3×Dic5—41no—
212C3×#41—52no—
213C3×#41—52no—
214C3×#41—101no—
215C3×#41—101no—
216C3×#41—101no—
217C3×#41—101no—
218C3×#41—101no—
219C3×#41—101no—
220C2×C3×Q8—51no—
221C2×C3×Q8—51no—
222C2×C3×D4—51no—
223C2×C3×D4—51no—
224C2×C3×D4—101no—
225C2×C3×D4—101no—
226C22×C3×C4—101no—
227C22×C3×C4—101no—
228C22×C3×C4C22×D511yescharacteristic
229C3×Q16—102no—
230C3×SD16—102no—
231C3×SD16—102no—
232C3×D8—102no—
233C3×M16—21no—
234C3×M16C4×D512yes—
235C2×C3×C8—21no—
236#217—101no—
237C4⋊Dic3—101no—
238C4×Dic3—101no—
239#208—21no—
240#208—104no—
241#208—101no—
242#208—101no—
243#208D2012yes—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—52no—
249C2×C3⋊C8—104no—
250C23×C5#23711yescharacteristic
251C22×D5—21no—
252C22×D5—21no—
253C2×C4×C5D3×D411yescharacteristic
254C2×C4×C5D3×D411yescharacteristic
255C2×C4×C5#23711yescharacteristic
256C2×C4×C5C22×Dic311yescharacteristic
257C2×C4×C5C2×#6711yescharacteristic
258C2×C4×C5C2×#6711yescharacteristic
259C22⋊D5—22no—
260C22⋊D5—22no—
261C22⋊D5—41no—
262C22⋊D5—41no—
263C2×Dic5—21no—
264C2×Dic5—21no—
265C2×Dic5—121no—
266D20—21no—
267D20—21no—
268D20—21no—
269D20#21712yes—
270C4×D5—22no—
271C4×D5—22no—
272C4×D5—41no—
273C4×D5—41no—
274Dic10—21no—
275Dic10—21no—
276Dic10—21no—
277Dic10#21712yes—
278C5×C8—22no—
279C5×C8—62no—
280C5×C8—121no—
281#168—62no—
282C2×#41—51no—
283C2×#41—51no—
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—151no—
293C2×M16—302no—
294C2×M16D3×D511yescharacteristic
295C22×C8—31no—
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#38611yescharacteristic
305C3×D5—42no—
306C3×D5—81no—
307C23×C3—101no—
308C23×C3—101no—
309C23×C3#71311yescharacteristic
310C3×Q8—52no—
311C3×Q8—101no—
312C3×Q8—101no—
313C3×Q8—101no—
314C3×D4—52no—
315C3×D4—102no—
316C3×D4—102no—
317C3×D4—101no—
318C3×D4—101no—
319C3×D4—101no—
320C3×D4—201no—
321C3×D4—201no—
322C2×C3×C4—101no—
323C2×C3×C4—102no—
324C2×C3×C4—102no—
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×C4D4×D511yescharacteristic
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×Dic3—201no—
335C3×C8—22no—
336C3⋊C8—22no—
337C3⋊C8—41no—
338C3⋊C8—102no—
339C22×C5—41no—
340C22×C5D4×Dic311yescharacteristic
341C22×C5#93511yescharacteristic
342C22×C5#93911yescharacteristic
343C2×D5—22no—
344C2×D5—42no—
345C2×D5—41no—
346C2×D5—81no—
347C4×C5D4×Dic311yescharacteristic
348C4×C5#93711yescharacteristic
349C4×C5#93911yescharacteristic
350C4×C5C2×#21711yescharacteristic
351Dic5—22no—
352Dic5—41no—
353Dic5—241no—
354#41—52no—
355#41—52no—
356#41—101no—
357#41—101no—
358#41—101no—
359#41—101no—
360#41—101no—
361#41—101no—
362C2×Q8—51no—
363C2×Q8—51no—
364C2×D4—51no—
365C2×D4—51no—
366C2×D4—101no—
367C2×D4—101no—
368C22×C4—101no—
369C22×C4—101no—
370C22×C4C2×D3×D511yescharacteristic
371Q16—102no—
372SD16—102no—
373SD16—102no—
374D8—102no—
375M16—21no—
376M16—32no—
377M16—61no—
378M16—304no—
379M16—301no—
380M16—301no—
381M16D5×Dic312yes—
382C2×C8—21no—
383C2×C8—61no—
384C2×C8—61no—
385C2×C8—61no—
386C2×C8—61no—
387C2×C8—152no—
388C2×C8—304no—
389C4⋊C4—301no—
390C22⋊C4—301no—
391C42—301no—
392C3×C5#188111yescharacteristic, complemented, Hall
393C22×C3—41no—
394C22×C3—102no—
395C22×C3—202no—
396C22×C3—201no—
397C22×C3—401no—
398C22×C3#403911yescharacteristic
399C22×C3#404011yescharacteristic
400C22×C3#404111yescharacteristic
401C3×C4—102no—
402C3×C4—201no—
403C3×C4C4×D2011yescharacteristic
404C3×C4D5×C22⋊C411yescharacteristic
405C3×C4#402811yescharacteristic
406C3×C4#403011yescharacteristic
407Dic3—401no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5#522011yescharacteristic
412D5—42no—
413D5—81no—
414C23—101no—
415C23—101no—
416C23#676611yescharacteristic
417Q8—52no—
418Q8—101no—
419Q8—101no—
420Q8—101no—
421D4—52no—
422D4—102no—
423D4—102no—
424D4—101no—
425D4—101no—
426D4—101no—
427D4—201no—
428D4—201no—
429C2×C4—101no—
430C2×C4—102no—
431C2×C4—102no—
432C2×C4—101no—
433C2×C4—201no—
434C2×C4—201no—
435C2×C4—601no—
436C2×C4#676511yescharacteristic
437C2×C4D3×D2011yescharacteristic
438C2×C4#677711yescharacteristic
439C2×C4C2×D5×Dic311yescharacteristic
440C2×C4D5×#6711yescharacteristic
441C2×C4D5×#6711yescharacteristic
442C8—22no—
443C8—62no—
444C8—121no—
445C8—302no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—202no—
450C2×C3—401no—
451C2×C3#6495411yescharacteristic
452C5#7211611yescharacteristic, complemented, Sylow
453C22—41no—
454C22—102no—
455C22—202no—
456C22—201no—
457C22—401no—
458C22#9140711yescharacteristic
459C22#9140911yescharacteristic
460C22#9143411yescharacteristic
461C4—102no—
462C4—201no—
463C4—1201no—
464C4#9140811yescharacteristic
465C4Dic3×D2011yescharacteristic
466C4#9147411yescharacteristic
467C4D5×#21711yescharacteristic
468C3#1059974011yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—202no—
473C2—401no—
474C2#1174889611yescharacteristic
subgroupG/H
centerC4#91474
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC3×#66082C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1881
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
2. #11754120C2semidirect
3. #11748420C2semidirect
4. #11748365C2semidirect
5. #11748342C2semidirect
6. #11746380C2semidirect
7. C5×#4558C2semidirect
17. C3×#4055C4semidirect
19. C3×#4054C4semidirect
80. #4558D5semidirect
89. #4055Dic3semidirect
91. #4054Dic3semidirect
392. C3×C5#1881semidirect
452. C5#72116semidirect
468. C3#10599740semidirect

Maximal subgroups

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

subgroupindex
C3×#660822
#117541202
#117484202
#117483652
#117483422
#117463802
C5×#45582
#105997403
#721165