Finite Group Databasebeta

← #14301209

Subgroups — #14301209

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×#5748C211yesmaximal, characteristic
2#11754125C211yesmaximal, characteristic, complemented
3#11748425C211yesmaximal, characteristic, complemented
4#11748382C211yesmaximal, characteristic, complemented
5#11748347C211yesmaximal, characteristic, complemented
6#11746379C211yesmaximal, characteristic, complemented
7C3×#64779C211yesmaximal, characteristic, complemented
8#10602909—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C5×#909—21no—
15C5×#909C412yescomplemented
16C5×#908—21no—
17C5×#908C412yescomplemented
18C5×#904—22no—
19C3×#4072C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91288—22no—
22D3×#681—22no—
23#91286—22no—
24#90979—22no—
25#90972—21no—
26#90966—21no—
27(C2×D3)⋊#168—22no—
28#69035—51nomaximal, Hall
29C5×#575—31no—
30#66153—31no—
31#65525—31no—
32#65523—31no—
33#65522—31no—
34#64779D311yescharacteristic, complemented
35#64778—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×C5×#67—21no—
38C2×C5×#67—21no—
39C5×#235—21no—
40C5×#235—21no—
41C5×#235—21no—
42C5×#235—21no—
43C5×#235—21no—
44C5×#235—21no—
45C5×#235C2×C412yes—
46C5×#235D412yes—
47C2×C5×D12C2×C411yescharacteristic
48C2×C5×D12D411yescharacteristic
49C2×C4×C5×D3—21no—
50C2×C4×C5×D3—21no—
51C2×C5×Dic6C2×C411yescharacteristic
52C2×C5×Dic6D411yescharacteristic
53C3×C5×M16—21no—
54C3×C5×M16C2×C412yes—
55C2×C3×C5×C8—21no—
56#6710—21no—
57#6710D412yes—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61C2×C3⋊#168—21no—
62C5×Dic12—22no—
63C5×D24—22no—
64C5×#204—22no—
65C5×#204—22no—
66C3×C22⋊Dic5—21no—
67C3×C4⋊Dic5—21no—
68C3×C4×Dic5—21no—
69C3×#681—21no—
70C3×#681—21no—
71C2×C3×#168D412yes—
72#6650—24no—
73D3×#168—24no—
74#5748D511yescharacteristic
75#5745—51no—
76#5129—51no—
77#5005—51no—
78#5002—51no—
79C3×#344—51no—
80#4558—51no—
81C2×C5×#41—31no—
82C2×C5×#41—31no—
83C5×#137—32no—
84C5×#137—61no—
85C5×AGL(1,ℤ/8)—32no—
86C5×AGL(1,ℤ/8)—61no—
87C5×#135—62no—
88C2×C5×M16C2×D311yescharacteristic
89#4094—62no—
90#4094—62no—
91#4072C2×D311yescharacteristic
92C2×#681—31no—
93C2×#681—62no—
94C2×#681C2×D311yescharacteristic
95C22×#168—31no—
96#3969—62no—
97#3967—61no—
98#3964—61no—
99C22⋊#168—62no—
100#1881—151noSylow
101C23×C3×C5#4111yescharacteristic
102C22×C5×D3—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
110C5×#67—22no—
111C5×#67—22no—
112C5×#67—41no—
113C5×#67—41no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C5×D12—21no—
117C5×D12—21no—
118C5×D12—21no—
119C5×D12C22⋊C412yes—
120C4×C5×D3—22no—
121C4×C5×D3—22no—
122C4×C5×D3—41no—
123C4×C5×D3—41no—
124C5×Dic6—21no—
125C5×Dic6—21no—
126C5×Dic6—21no—
127C5×Dic6C22⋊C412yes—
128C2×C3×Dic5—41no—
129C3×C5×C8—22no—
130C3⋊#168—22no—
131C3⋊#168—41no—
132C3×#168—22no—
133C2×#235C2×D511yescharacteristic
134C2×#235C2×D511yescharacteristic
135C2×C3×M16—51no—
136C2×C3×M16C2×D511yescharacteristic
137C3×#117—51no—
138C2×#208—51no—
139C22×C3⋊C8—51no—
140#909—21no—
141#909Dic512yescomplemented
142#908—21no—
143#908Dic512yescomplemented
144#907—102no—
145D3×M16—102no—
146#904—22no—
147#901—102no—
148(C2×D3)⋊C8—102no—
149#810—101no—
150#809—101no—
151#805—102no—
152C5×#41—32no—
153C5×#41—32no—
154C5×#41—61no—
155C5×#41—61no—
156C5×#41—61no—
157C5×#41—61no—
158C5×#41—61no—
159C5×#41—61no—
160C2×C5×Q8—31no—
161C2×C5×Q8—31no—
162C2×C5×D4—31no—
163C2×C5×D4—31no—
164C2×C5×D4—61no—
165C2×C5×D4—61no—
166C22×C4×C5—61no—
167C22×C4×C5—61no—
168C22×C4×C5C22×D311yescharacteristic
169C5×Q16—62no—
170C5×SD16—62no—
171C5×SD16—62no—
172C5×D8—62no—
173C5×M16—21no—
174C5×M16C4×D312yes—
175C2×C5×C8—21no—
176C22⋊Dic5—21no—
177C4⋊Dic5—21no—
178C4×Dic5—21no—
179#681—21no—
180#681—21no—
181#681—32no—
182#681—64no—
183#681—61no—
184C2×#168—64no—
185C2×#168—61no—
186C2×#168—61no—
187C2×#168—61no—
188C2×#168—61no—
189C2×#168D1212yes—
190#575—31no—
191#568—151no—
192#421—151no—
193#416—151no—
194#408—151no—
195#344—51no—
196#341—151no—
197C22×C3×C5—41no—
198C22×C3×C5C4×D411yescharacteristic
199C22×C3×C5#12111yescharacteristic
200C22×C3×C5#12311yescharacteristic
201C2×C5×D3—22no—
202C2×C5×D3—42no—
203C2×C5×D3—41no—
204C2×C5×D3—81no—
205C3×C4×C5C2×C22⋊C411yescharacteristic
206C3×C4×C5C4×D411yescharacteristic
207C3×C4×C5#12011yescharacteristic
208C3×C4×C5#12111yescharacteristic
209C3×Dic5—81no—
210C5×Dic3—22no—
211C5×Dic3—41no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—21no—
214C2×#67—21no—
215#235—21no—
216#235—21no—
217#235—21no—
218#235—21no—
219#235—21no—
220#235—21no—
221#235C2×Dic512yes—
222#235C22⋊D512yes—
223C2×D12C2×Dic511yescharacteristic
224C2×D12C22⋊D511yescharacteristic
225C2×C4×D3—21no—
226C2×C4×D3—21no—
227C2×Dic6C2×Dic511yescharacteristic
228C2×Dic6C22⋊D511yescharacteristic
229C3×M16—21no—
230C3×M16—101no—
231C3×M16—101no—
232C3×M16C2×Dic512yes—
233C2×C3×C8—21no—
234C2×C3×C8—52no—
235C3×C4⋊C4—101no—
236C3×C22⋊C4—101no—
237C3×C42—101no—
238#208—52no—
239#208—101no—
240C2×C3⋊C8—101no—
241C2×C3⋊C8—101no—
242C2×C3⋊C8—101no—
243C2×C3⋊C8—101no—
244Dic12—22no—
245D24—22no—
246#204—22no—
247#204—22no—
248ΓL(1,𝔽25)—104no—
249D3×C8—104no—
250C23×C5—61no—
251C23×C5—61no—
252C23×C5#23511yescharacteristic
253C5×Q8—32no—
254C5×Q8—61no—
255C5×Q8—61no—
256C5×Q8—61no—
257C5×D4—32no—
258C5×D4—62no—
259C5×D4—62no—
260C5×D4—61no—
261C5×D4—61no—
262C5×D4—61no—
263C5×D4—121no—
264C5×D4—121no—
265C2×C4×C5—61no—
266C2×C4×C5—62no—
267C2×C4×C5—62no—
268C2×C4×C5—61no—
269C2×C4×C5—121no—
270C2×C4×C5—121no—
271C2×C4×C5C2×C4×D311yescharacteristic
272C2×C4×C5C2×D1211yescharacteristic
273C2×C4×C5D3×D411yescharacteristic
274C2×C4×C5D3×D411yescharacteristic
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5#23911yescharacteristic
277C2×Dic5—41no—
278C5×C8—22no—
279#168—22no—
280#168—62no—
281#168—121no—
282C2×#41—31no—
283C2×#41—31no—
284#137—32no—
285#137—61no—
286AGL(1,ℤ/8)—32no—
287AGL(1,ℤ/8)—61no—
288#135—62no—
289#131—302no—
290#131—302no—
291C2×M16—51no—
292C2×M16—151no—
293C2×M16—302no—
294C2×M16D3×D511yescharacteristic
295C22×C8—151no—
296#117—51no—
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
305C5×D3—42no—
306C5×D3—81no—
307C23×C3#71111yescharacteristic
308C22×D3—21no—
309C22×D3—21no—
310C2×C3×C4—201no—
311C2×C3×C4D4×D511yescharacteristic
312C2×C3×C4D4×D511yescharacteristic
313C2×C3×C4#71111yescharacteristic
314C2×C3×C4C22×Dic511yescharacteristic
315C2×C3×C4C2×C22⋊D511yescharacteristic
316C2×C3×C4C2×C22⋊D511yescharacteristic
317#67—22no—
318#67—22no—
319#67—41no—
320#67—41no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323D12—21no—
324D12—21no—
325D12—21no—
326D12C22⋊Dic512yes—
327C4×D3—22no—
328C4×D3—22no—
329C4×D3—41no—
330C4×D3—41no—
331Dic6—21no—
332Dic6—21no—
333Dic6—21no—
334Dic6C22⋊Dic512yes—
335C3×C8—22no—
336C3×C8—102no—
337C3⋊C8—102no—
338C3⋊C8—201no—
339C22×C5—41no—
340C22×C5—62no—
341C22×C5—122no—
342C22×C5—121no—
343C22×C5—241no—
344C22×C5C4×D1211yescharacteristic
345C22×C5#88411yescharacteristic
346C22×C5#89411yescharacteristic
347C4×C5—62no—
348C4×C5—121no—
349C4×C5D3×C22⋊C411yescharacteristic
350C4×C5#88211yescharacteristic
351C4×C5#89311yescharacteristic
352C4×C5#89511yescharacteristic
353Dic5—81no—
354#41—32no—
355#41—32no—
356#41—61no—
357#41—61no—
358#41—61no—
359#41—61no—
360#41—61no—
361#41—61no—
362C2×Q8—31no—
363C2×Q8—31no—
364C2×D4—31no—
365C2×D4—31no—
366C2×D4—61no—
367C2×D4—61no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4C2×D3×D511yescharacteristic
371Q16—62no—
372SD16—62no—
373SD16—62no—
374D8—62no—
375M16—21no—
376M16—101no—
377M16—101no—
378M16—152no—
379M16—304no—
380M16—301no—
381M16D3×Dic512yes—
382C2×C8—21no—
383C2×C8—52no—
384C2×C8—304no—
385C2×C8—301no—
386C2×C8—301no—
387C2×C8—301no—
388C2×C8—301no—
389C4⋊C4—101no—
390C22⋊C4—101no—
391C42—101no—
392C3×C5#188111yescharacteristic, complemented, Hall
393C22×C3—41no—
394C22×C3D4×Dic511yescharacteristic
395C22×C3#408111yescharacteristic
396C22×C3#408511yescharacteristic
397C2×D3—22no—
398C2×D3—42no—
399C2×D3—41no—
400C2×D3—81no—
401C3×C4—401no—
402C3×C4D4×Dic511yescharacteristic
403C3×C4#408311yescharacteristic
404C3×C4#408511yescharacteristic
405C3×C4C2×C22⋊Dic511yescharacteristic
406Dic3—22no—
407Dic3—41no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—122no—
412C2×C5—241no—
413C2×C5#466511yescharacteristic
414C23—61no—
415C23—61no—
416C23#677211yescharacteristic
417Q8—32no—
418Q8—61no—
419Q8—61no—
420Q8—61no—
421D4—32no—
422D4—62no—
423D4—62no—
424D4—61no—
425D4—61no—
426D4—61no—
427D4—121no—
428D4—121no—
429C2×C4—61no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—61no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—201no—
436C2×C4#676811yescharacteristic
437C2×C4D5×D1211yescharacteristic
438C2×C4#677711yescharacteristic
439C2×C4C2×D3×Dic511yescharacteristic
440C2×C4D3×C22⋊D511yescharacteristic
441C2×C4D3×C22⋊D511yescharacteristic
442C8—22no—
443C8—102no—
444C8—302no—
445C8—601no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3#6550911yescharacteristic
450D3—42no—
451D3—81no—
452C5#6903511yescharacteristic, complemented, Sylow
453C22—41no—
454C22—62no—
455C22—122no—
456C22—121no—
457C22—241no—
458C22Dic5×D1211yescharacteristic
459C22#9142311yescharacteristic
460C22#9145311yescharacteristic
461C4—62no—
462C4—121no—
463C4—401no—
464C4#9141611yescharacteristic
465C4#9143511yescharacteristic
466C4#9147511yescharacteristic
467C4D3×C22⋊Dic511yescharacteristic
468C3#1060290911yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—122no—
473C2—241no—
474C2#1174890111yescharacteristic
subgroupG/H
centerC4#91475
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC5×#5748C2
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. #11754125C2semidirect
3. #11748425C2semidirect
4. #11748382C2semidirect
5. #11748347C2semidirect
6. #11746379C2semidirect
7. C3×#64779C2semidirect
15. C5×#909C4semidirect
17. C5×#908C4semidirect
34. #64779D3semidirect
141. #909Dic5semidirect
143. #908Dic5semidirect
392. C3×C5#1881semidirect
452. C5#69035semidirect
468. C3#10602909semidirect

Maximal subgroups

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

subgroupindex
C5×#57482
#117541252
#117484252
#117483822
#117483472
#117463792
C3×#647792
#106029093
#690355