Finite Group Databasebeta

← #14301204

Subgroups — #14301204

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
1#11756504C211yesmaximal, characteristic, complemented
2#11754145C211yesmaximal, characteristic
3C5×#5129C211yesmaximal, characteristic, complemented
4#11748425C211yesmaximal, characteristic, complemented
5#11748411C211yesmaximal, characteristic, complemented
6C3×#64776C211yesmaximal, characteristic, complemented
7#11745983C211yesmaximal, characteristic, complemented
8#10600805—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13#91796—22no—
14M16×D15—22no—
15#91790—22no—
16C22×C5×C3⋊C8C2211yescharacteristic
17C3×#4072C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91322—21no—
20#91321C412yescomplemented
21#91305—21no—
22#91304C412yescomplemented
23#91303—22no—
24C5×(C2×D3)⋊C8—22no—
25#90979—22no—
26#90974—21no—
27#90968—21no—
28#69035—51nomaximal, Hall
29#66156—31no—
30#66079—31no—
31C5×#408—31no—
32#65525—31no—
33#65402—31no—
34#64776D311yescharacteristic, complemented
35#64772—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220—21no—
38#6817—21no—
39#6817—21no—
40#6817C2×C412yes—
41#6817D412yes—
42C2×D60D411yescharacteristic
43C2×C4×D15—21no—
44C2×Dic30D411yescharacteristic
45C2×C5×#67—21no—
46C5×#235—21no—
47C5×#235—21no—
48C5×#235—21no—
49C5×#235—21no—
50C2×C5×D12C2×C411yescharacteristic
51C2×C4×C5×D3—21no—
52C2×C5×Dic6C2×C411yescharacteristic
53C3×C5×M16—21no—
54C3×C5×M16—21no—
55C2×C3×C5×C8D412yes—
56#6710—21no—
57#6710D412yes—
58C2×C3⋊#168—21no—
59#6705—24no—
60C8×D15—24no—
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C2×C5×C3⋊C8—21no—
64C3×C22⋊Dic5—21no—
65C3×C4⋊Dic5—21no—
66C3×C4×Dic5—21no—
67C3×#681—21no—
68C3×#681C2×C412yes—
69C2×C3×#168—21no—
70#6663—22no—
71#6660—22no—
72#6659—22no—
73#6654—22no—
74#5748—51no—
75#5745—51no—
76#5129D511yescharacteristic, complemented
77#5005—51no—
78#5002—51no—
79C3×#344—51no—
80#4558—51no—
81C2×C5×#41—31no—
82C2×#709—31no—
83C2×C5×M16C2×D311yescharacteristic
84C22×C5×C8—31no—
85#4097—61no—
86#4096—62no—
87#4095—61no—
88#4088—32no—
89#4078—32no—
90#4072C2×D311yescharacteristic
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#4111yescharacteristic
102C22×D15—21no—
103C22×C5×D3—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
110#1220—22no—
111#1220—22no—
112C2×Dic15—21no—
113D60—21no—
114D60C22⋊C412yes—
115C4×D15—22no—
116C4×D15—22no—
117Dic30—21no—
118Dic30C22⋊C412yes—
119C5×#67—41no—
120C5×#67—41no—
121C2×C5×Dic3—21no—
122C5×D12—21no—
123C5×D12—21no—
124C4×C5×D3—41no—
125C4×C5×D3—41no—
126C5×Dic6—21no—
127C5×Dic6—21no—
128C2×C3×Dic5—41no—
129C3×C5×C8—22no—
130C3⋊#168—22no—
131C3×#168—22no—
132C5×C3⋊C8—41no—
133C2×#235—51no—
134C2×#235C2×D511yescharacteristic
135C2×C3×M16—51no—
136C2×C3×M16C2×D511yescharacteristic
137C3×#117—51no—
138C2×#208—51no—
139C22×C3⋊C8C2×D511yescharacteristic
140#909—52no—
141#909—101no—
142#908—52no—
143#908—101no—
144#907—102no—
145D3×M16—102no—
146#904—102no—
147#901—102no—
148(C2×D3)⋊C8—22no—
149#810—101no—
150#809—101no—
151#805—102no—
152C5×#41—61no—
153C5×#41—61no—
154C5×#41—61no—
155C5×#41—61no—
156C2×C5×Q8—31no—
157C2×C5×D4—31no—
158C2×C5×D4—61no—
159C22×C4×C5—61no—
160C22×C4×C5C22×D311yescharacteristic
161C2×C22⋊D5—61no—
162#709—32no—
163#709—32no—
164#709—61no—
165#709—61no—
166C2×D20—31no—
167C2×C4×D5—61no—
168C2×Dic10—31no—
169C5×M16—21no—
170C5×M16—21no—
171C2×C5×C8—61no—
172C2×C5×C8—61no—
173C2×C5×C8—61no—
174C2×C5×C8D1212yes—
175C22⋊Dic5—21no—
176#689—62no—
177#688—62no—
178#687—62no—
179#686—62no—
180C4⋊Dic5—21no—
181C4×Dic5—21no—
182#681—21no—
183#681—32no—
184#681—61no—
185#681C4×D312yes—
186C2×#168—21no—
187C2×#168—61no—
188#676—64no—
189C8×D5—64no—
190#575—151no—
191#568—151no—
192#421—151no—
193#416—151no—
194#408—31no—
195#344—51no—
196#341—151no—
197C22×C3×C5—41no—
198C22×C3×C5C4×D411yescharacteristic
199C22×C3×C5#12111yescharacteristic
200C22×C3×C5#12311yescharacteristic
201C2×D15—22no—
202C2×D15—81no—
203C2×C5×D3—42no—
204C2×C5×D3—41no—
205C3×C4×C5C2×C22⋊C411yescharacteristic
206C3×C4×C5C4×D411yescharacteristic
207C3×C4×C5#12011yescharacteristic
208C3×C4×C5#12111yescharacteristic
209Dic15—22no—
210C3×Dic5—81no—
211C5×Dic3—41no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—21no—
214C2×#67—101no—
215#235—21no—
216#235—21no—
217#235—21no—
218#235—21no—
219#235—52no—
220#235—52no—
221#235—101no—
222#235—101no—
223C2×D12—51no—
224C2×D12C4×D511yescharacteristic
225C2×C4×D3—21no—
226C2×C4×D3—101no—
227C2×Dic6—51no—
228C2×Dic6C4×D511yescharacteristic
229C3×M16—21no—
230C3×M16—21no—
231C3×M16—52no—
232C3×M16—101no—
233C2×C3×C8—101no—
234C2×C3×C8C22⋊D512yes—
235C3×C4⋊C4—101no—
236C3×C22⋊C4—101no—
237C3×C42—101no—
238#208—52no—
239#208—101no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—101no—
244Dic12—102no—
245D24—102no—
246#204—102no—
247#204—102no—
248ΓL(1,𝔽25)—104no—
249D3×C8—104no—
250C23×C5—61no—
251C23×C5#23511yescharacteristic
252C22×D5—61no—
253C5×Q8—61no—
254C5×Q8—61no—
255C5×D4—61no—
256C5×D4—61no—
257C5×D4—121no—
258C5×D4—121no—
259C2×C4×C5—61no—
260C2×C4×C5—121no—
261C2×C4×C5—121no—
262C2×C4×C5C2×C4×D311yescharacteristic
263C2×C4×C5C2×D1211yescharacteristic
264C2×C4×C5D3×D411yescharacteristic
265C2×C4×C5D3×D411yescharacteristic
266C2×C4×C5D3×D411yescharacteristic
267C2×C4×C5#23911yescharacteristic
268C22⋊D5—62no—
269C22⋊D5—62no—
270C2×Dic5—41no—
271C2×Dic5—61no—
272D20—32no—
273D20—61no—
274C4×D5—62no—
275C4×D5—62no—
276Dic10—32no—
277Dic10—61no—
278C5×C8—22no—
279C5×C8—121no—
280#168—22no—
281#168—62no—
282C2×#41—31no—
283C2×#41—151no—
284#137—152no—
285#137—301no—
286AGL(1,ℤ/8)—152no—
287AGL(1,ℤ/8)—301no—
288#135—302no—
289#131—302no—
290#131—302no—
291C2×M16—51no—
292C2×M16—151no—
293C2×M16—302no—
294C2×M16D3×D511yescharacteristic
295C22×C8—31no—
296#117—51no—
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#38611yescharacteristic
305D15—42no—
306C5×D3—81no—
307C23×C3#70911yescharacteristic
308C22×D3—21no—
309C22×D3—101no—
310C2×C3×C4—201no—
311C2×C3×C4C2×C4×D511yescharacteristic
312C2×C3×C4D4×D511yescharacteristic
313C2×C3×C4D4×D511yescharacteristic
314C2×C3×C4D4×D511yescharacteristic
315C2×C3×C4#71111yescharacteristic
316C2×C3×C4C2×C22⋊D511yescharacteristic
317#67—41no—
318#67—41no—
319#67—102no—
320#67—102no—
321C2×Dic3—21no—
322C2×Dic3—101no—
323D12—21no—
324D12—21no—
325D12—52no—
326D12—101no—
327C4×D3—41no—
328C4×D3—41no—
329C4×D3—102no—
330C4×D3—102no—
331Dic6—21no—
332Dic6—21no—
333Dic6—52no—
334Dic6—101no—
335C3×C8—22no—
336C3×C8—102no—
337C3⋊C8—41no—
338C3⋊C8—102no—
339C22×C5—41no—
340C22×C5—122no—
341C22×C5—121no—
342C22×C5C4×D1211yescharacteristic
343C22×C5#88411yescharacteristic
344C22×C5#89411yescharacteristic
345C2×D5—62no—
346C2×D5—241no—
347C4×C5—121no—
348C4×C5D3×C22⋊C411yescharacteristic
349C4×C5#88211yescharacteristic
350C4×C5#89311yescharacteristic
351C4×C5#89511yescharacteristic
352Dic5—62no—
353Dic5—81no—
354#41—61no—
355#41—61no—
356#41—61no—
357#41—61no—
358#41—152no—
359#41—152no—
360#41—301no—
361#41—301no—
362C2×Q8—31no—
363C2×Q8—151no—
364C2×D4—31no—
365C2×D4—61no—
366C2×D4—151no—
367C2×D4—301no—
368C22×C4—61no—
369C22×C4—301no—
370C22×C4C2×D3×D511yescharacteristic
371Q16—302no—
372SD16—302no—
373SD16—302no—
374D8—302no—
375M16—21no—
376M16—21no—
377M16—52no—
378M16—101no—
379M16—152no—
380M16—304no—
381M16—301no—
382C2×C8—61no—
383C2×C8—61no—
384C2×C8—61no—
385C2×C8—101no—
386C2×C8—304no—
387C2×C8—301no—
388C2×C8#120312yes—
389C4⋊C4—101no—
390C22⋊C4—101no—
391C42—101no—
392C3×C5#188111yescharacteristic, complemented, Hall
393C22×C3—41no—
394C22×C3#402911yescharacteristic
395C22×C3#403011yescharacteristic
396C22×C3C4×C22⋊D511yescharacteristic
397C2×D3—42no—
398C2×D3—41no—
399C2×D3—102no—
400C2×D3—401no—
401C3×C4—401no—
402C3×C4D5×C22⋊C411yescharacteristic
403C3×C4#402711yescharacteristic
404C3×C4#408311yescharacteristic
405C3×C4#408411yescharacteristic
406Dic3—41no—
407Dic3—102no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—241no—
412C2×C5#466511yescharacteristic
413D5—122no—
414C23—61no—
415C23—301no—
416C23#677111yescharacteristic
417Q8—61no—
418Q8—61no—
419Q8—152no—
420Q8—301no—
421D4—61no—
422D4—61no—
423D4—121no—
424D4—121no—
425D4—152no—
426D4—302no—
427D4—302no—
428D4—301no—
429C2×C4—61no—
430C2×C4—121no—
431C2×C4—121no—
432C2×C4—201no—
433C2×C4—301no—
434C2×C4—302no—
435C2×C4—302no—
436C2×C4#676811yescharacteristic
437C2×C4C4×D3×D511yescharacteristic
438C2×C4#677711yescharacteristic
439C2×C4C2×#120311yescharacteristic
440C2×C4#679011yescharacteristic
441C2×C4#679011yescharacteristic
442C8—22no—
443C8—102no—
444C8—121no—
445C8—302no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3#6524511yescharacteristic
450D3—81no—
451D3—202no—
452C5#6903511yescharacteristic, complemented, Sylow
453C22—41no—
454C22—122no—
455C22—121no—
456C22—302no—
457C22—1201no—
458C22#9135511yescharacteristic
459C22C4×#120311yescharacteristic
460C22#9146111yescharacteristic
461C4—121no—
462C4—302no—
463C4—401no—
464C4#9140611yescharacteristic
465C4#9146611yescharacteristic
466C4#9147311yescharacteristic
467C4#9157311yescharacteristic
468C3#1060080511yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—241no—
473C2—602no—
474C2#1174891811yescharacteristic
subgroupG/H
centerC4#91573
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754145C2
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
1. #11756504C2semidirect
3. C5×#5129C2semidirect
4. #11748425C2semidirect
5. #11748411C2semidirect
6. C3×#64776C2semidirect
7. #11745983C2semidirect
20. #91321C4semidirect
22. #91304C4semidirect
34. #64776D3semidirect
76. #5129D5semidirect
392. C3×C5#1881semidirect
452. C5#69035semidirect
468. C3#10600805semidirect

Maximal subgroups

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

subgroupindex
#117565042
#117541452
C5×#51292
#117484252
#117484112
C3×#647762
#117459832
#106008053
#690355