Finite Group Databasebeta

← #14301198

Subgroups — #14301198

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#11754145C211yesmaximal, characteristic
2#11754130C211yesmaximal, characteristic, complemented
3#11751214C211yesmaximal, characteristic, complemented
4C5×#5110C211yesmaximal, characteristic, complemented
5#11748424C211yesmaximal, characteristic, complemented
6C3×#64772C211yesmaximal, characteristic, complemented
7#11745990C211yesmaximal, characteristic, complemented
8#10600805—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91322—21no—
17#91321C412yescomplemented
18#91305—21no—
19#91304C412yescomplemented
20#91303—22no—
21#91292—22no—
22#91291—22no—
23#91290—22no—
24#91105—21no—
25#91100—21no—
26C5×(C2×D3)⋊C8—22no—
27#90978—22no—
28#68947—51nomaximal, Hall
29#66156—31no—
30#66079—31no—
31C5×#408—31no—
32#65525—31no—
33#65402—31no—
34#64776—31no—
35#64772D311yescharacteristic, complemented
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
53C2×C3×C5×C8—21no—
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56#6719—21no—
57C4⋊Dic15—21no—
58C4×Dic15—21no—
59C5×#208—21no—
60C5×#208—21no—
61C2×C5×C3⋊C8D412yes—
62C3×#681—21no—
63C3×#681—21no—
64C3×#681C2×C412yes—
65C3×#681D412yes—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68#6663—22no—
69#6660—22no—
70#6659—22no—
71#6654—22no—
72#6651—24no—
73#6648—24no—
74#5748—51no—
75#5745—51no—
76#5139—51no—
77#5113—51no—
78#5110D511yescharacteristic, complemented
79C3×#341—51no—
80#4559—51no—
81C2×C5×#41—31no—
82C2×#709—31no—
83C2×C5×M16—31no—
84C22×C5×C8C2×D311yescharacteristic
85#4097—61no—
86#4096—62no—
87#4095—61no—
88#4088—32no—
89#4078—32no—
90#4072—31no—
91C2×#681C2×D311yescharacteristic
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—
113C2×Dic15—41no—
114D60—21no—
115D60C22⋊C412yes—
116C4×D15—22no—
117C4×D15—22no—
118Dic30—21no—
119Dic30C22⋊C412yes—
120C5×#67—41no—
121C5×#67—41no—
122C2×C5×Dic3—21no—
123C5×D12—21no—
124C5×D12—21no—
125C4×C5×D3—41no—
126C4×C5×D3—41no—
127C5×Dic6—21no—
128C5×Dic6—21no—
129C3×C5×C8—41no—
130C3×#168—22no—
131C3×#168—22no—
132C5×C3⋊C8—22no—
133C2×#235—51no—
134C2×#235C2×D511yescharacteristic
135C2×C3×M16—51no—
136C2×C3×M16—51no—
137C22×C3×C8C2×D511yescharacteristic
138#926—51no—
139C2×#208C2×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#825—102no—
149#821—101no—
150(C2×D3)⋊C8—22no—
151#816—101no—
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—61no—
170C5×M16—61no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8—32no—
175C22⋊Dic5—61no—
176#689—62no—
177#688—62no—
178#687—62no—
179#686—62no—
180C4⋊Dic5—61no—
181C4×Dic5—61no—
182#681—21no—
183#681—21no—
184#681C4×D312yes—
185#681D1212yes—
186C2×#168—21no—
187C2×#168—21no—
188#676—64no—
189C8×D5—64no—
190#575—151no—
191#568—151no—
192#421—151no—
193#416—151no—
194#408—31no—
195#344—151no—
196#341—51no—
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—
210Dic15—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—52no—
230C3×M16—52no—
231C3×M16—101no—
232C3×M16—101no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—101no—
237C2×C3×C8—101no—
238#217—101no—
239C4⋊Dic3—101no—
240C4×Dic3—101no—
241#208—21no—
242#208—21no—
243C2×C3⋊C8C22⋊D512yes—
244Dic12—102no—
245D24—102no—
246#204—102no—
247#204—102no—
248ΓL(1,𝔽25)—104no—
249D3×C8—104no—
250C23×C5—61no—
251C23×C5#23911yescharacteristic
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×C5#23511yescharacteristic
265C2×C4×C5D3×D411yescharacteristic
266C2×C4×C5D3×D411yescharacteristic
267C2×C4×C5D3×D411yescharacteristic
268C22⋊D5—62no—
269C22⋊D5—62no—
270C2×Dic5—61no—
271C2×Dic5—121no—
272D20—32no—
273D20—61no—
274C4×D5—62no—
275C4×D5—62no—
276Dic10—32no—
277Dic10—61no—
278C5×C8—41no—
279C5×C8—62no—
280#168—22no—
281#168—22no—
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—31no—
292C2×M16—51no—
293C2×M16—51no—
294C2×M16—302no—
295C22×C8D3×D511yescharacteristic
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#38611yescharacteristic
305D15—42no—
306C5×D3—81no—
307C23×C3#70911yescharacteristic
308C22×D3—21no—
309C22×D3—101no—
310C2×C3×C4C2×C4×D511yescharacteristic
311C2×C3×C4D4×D511yescharacteristic
312C2×C3×C4D4×D511yescharacteristic
313C2×C3×C4D4×D511yescharacteristic
314C2×C3×C4#71111yescharacteristic
315C2×C3×C4C2×C22⋊D511yescharacteristic
316#67—41no—
317#67—41no—
318#67—102no—
319#67—102no—
320C2×Dic3—21no—
321C2×Dic3—101no—
322C2×Dic3—201no—
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—41no—
336C3×C8—102no—
337C3×C8—102no—
338C3⋊C8—22no—
339C22×C5—41no—
340C22×C5—122no—
341C22×C5—121no—
342C22×C5#89311yescharacteristic
343C22×C5#89411yescharacteristic
344C22×C5#89511yescharacteristic
345C2×D5—62no—
346C2×D5—241no—
347C4×C5—121no—
348C4×C5C4×D1211yescharacteristic
349C4×C5D3×C22⋊C411yescharacteristic
350C4×C5#88211yescharacteristic
351C4×C5#88411yescharacteristic
352Dic5—62no—
353Dic5—241no—
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—52no—
376M16—52no—
377M16—61no—
378M16—61no—
379M16—101no—
380M16—101no—
381M16—304no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—32no—
386C2×C8—101no—
387C2×C8—101no—
388C2×C8—304no—
389C4⋊C4—301no—
390C22⋊C4—301no—
391C42—301no—
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×C4D5×C22⋊C411yescharacteristic
402C3×C4#402711yescharacteristic
403C3×C4#408311yescharacteristic
404C3×C4#408411yescharacteristic
405Dic3—41no—
406Dic3—102no—
407Dic3—401no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—241no—
412C2×C5#466511yescharacteristic
413D5—122no—
414C23—61no—
415C23—301no—
416C23#676911yescharacteristic
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—301no—
433C2×C4—302no—
434C2×C4—302no—
435C2×C4—601no—
436C2×C4C4×D3×D511yescharacteristic
437C2×C4D5×D1211yescharacteristic
438C2×C4#677711yescharacteristic
439C2×C4#678211yescharacteristic
440C2×C4D3×C22⋊D511yescharacteristic
441C2×C4#679011yescharacteristic
442C8—41no—
443C8—62no—
444C8—102no—
445C8—102no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3#6524511yescharacteristic
450D3—81no—
451D3—202no—
452C5#6894711yescharacteristic, complemented, Sylow
453C22—41no—
454C22—122no—
455C22—121no—
456C22—302no—
457C22—1201no—
458C22#9142011yescharacteristic
459C22#9143811yescharacteristic
460C22#9144611yescharacteristic
461C4—121no—
462C4—302no—
463C4—1201no—
464C4#9140511yescharacteristic
465C4#9147311yescharacteristic
466C4#9147511yescharacteristic
467C4#9155711yescharacteristic
468C3#1060080511yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—241no—
473C2—602no—
474C2#1174891911yescharacteristic
subgroupG/H
centerC4#91475
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC2×C3×C5#386
prime radical#11754145C2
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1881
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #11754130C2semidirect
3. #11751214C2semidirect
4. C5×#5110C2semidirect
5. #11748424C2semidirect
6. C3×#64772C2semidirect
7. #11745990C2semidirect
17. #91321C4semidirect
19. #91304C4semidirect
35. #64772D3semidirect
78. #5110D5semidirect
392. C3×C5#1881semidirect
452. C5#68947semidirect
468. C3#10600805semidirect

Maximal subgroups

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

subgroupindex
#117541452
#117541302
#117512142
C5×#51102
#117484242
C3×#647722
#117459902
#106008053
#689475