Finite Group Databasebeta

← #14301162

Subgroups — #14301162

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×C5×#575C211yesmaximal, characteristic
2#11756578C211yesmaximal, characteristic, complemented
3#11751337C211yesmaximal, characteristic, complemented
4#11751335C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11746380C211yesmaximal, characteristic, complemented
7#11746379C211yesmaximal, characteristic, complemented
8#10602909—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×C3×C5×#41C2211yescharacteristic
11C3×C5×#137—21no—
12C3×C5×#137C412yescomplemented
13C3×C5×AGL(1,ℤ/8)—21no—
14C3×C5×AGL(1,ℤ/8)C412yescomplemented
15C3×C5×#135—22no—
16C2×C3×C5×M16C2211yescharacteristic
17#91837—22no—
18#91837—22no—
19#91815C2211yescharacteristic
20C2×#6710—22no—
21C2×#6710C2211yescharacteristic
22C2×#6710C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic
24#91121—22no—
25#91119—21no—
26#91116—21no—
27#91114—22no—
28#72116—51nomaximal, Hall
29C5×#575D311yescharacteristic
30#66153—31no—
31#65525—31no—
32#65523—31no—
33#65522—31no—
34#64779—31no—
35#64778—31no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C3×C5×#41—21no—
40C3×C5×#41—21no—
41C3×C5×#41—21no—
42C3×C5×#41C2×C412yes—
43C3×C5×#41D412yes—
44C2×C3×C5×Q8C2×C411yescharacteristic
45C2×C3×C5×Q8D411yescharacteristic
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4C2×C411yescharacteristic
49C2×C3×C5×D4D411yescharacteristic
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5C2311yescharacteristic
53C3×C5×Q16—22no—
54C3×C5×SD16—22no—
55C3×C5×SD16—22no—
56C3×C5×D8—22no—
57C3×C5×M16—21no—
58C3×C5×M16C2×C412yes—
59C2×C3×C5×C8—21no—
60#6719—21no—
61C4⋊Dic15—21no—
62C4×Dic15—21no—
63#6710—24no—
64#6710—21no—
65#6710—21no—
66#6710—21no—
67#6710D412yes—
68C2×C3⋊#168—24no—
69C2×C3⋊#168—21no—
70C2×C3⋊#168—21no—
71C2×C3⋊#168—21no—
72C2×C3⋊#168—21no—
73C2×C3⋊#168D412yes—
74C3×#575D511yescharacteristic
75#5819—51no—
76#5236—51no—
77#5234—51no—
78#5233—51no—
79#4559—51no—
80#4558—51no—
81C2×C5×#41C2×D311yescharacteristic
82C2×C5×#41C2×D311yescharacteristic
83C5×#137—21no—
84C5×#137Dic312yescomplemented
85C5×AGL(1,ℤ/8)—21no—
86C5×AGL(1,ℤ/8)Dic312yescomplemented
87C5×#135—22no—
88C2×C5×M16C2×D311yescharacteristic
89#4094—62no—
90#4094—62no—
91#4072—31no—
92C2×#681—31no—
93C2×#681—31no—
94C2×#681—62no—
95C22×#168—31no—
96#3969—62no—
97#3967—61no—
98#3964—61no—
99C22⋊#168—62no—
100#1881—151noSylow
101C23×C3×C5—21no—
102C23×C3×C5—21no—
103C23×C3×C5#4111yescharacteristic
104C3×C5×Q8—21no—
105C3×C5×Q8—21no—
106C3×C5×Q8—21no—
107C3×C5×Q8C22⋊C412yes—
108C3×C5×D4—22no—
109C3×C5×D4—22no—
110C3×C5×D4—21no—
111C3×C5×D4—21no—
112C3×C5×D4—21no—
113C3×C5×D4—41no—
114C3×C5×D4—41no—
115C3×C5×D4C22⋊C412yes—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—22no—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—21no—
120C2×C3×C4×C5—41no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5C22×C411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×C3×C4×C5C2×D411yescharacteristic
127C2×C3×C4×C5#4111yescharacteristic
128C2×Dic15—41no—
129C3×C5×C8—22no—
130C3⋊#168—22no—
131C3⋊#168—22no—
132C3⋊#168—41no—
133C2×C3×#41C2×D511yescharacteristic
134C2×C3×#41C2×D511yescharacteristic
135C3×#137—21no—
136C3×#137Dic512yescomplemented
137C3×AGL(1,ℤ/8)—21no—
138C3×AGL(1,ℤ/8)Dic512yescomplemented
139C3×#135—22no—
140C2×C3×M16C2×D511yescharacteristic
141#948—102no—
142#948—102no—
143#926—51no—
144C2×#208—51no—
145C2×#208—51no—
146C2×#208—102no—
147C22×C3⋊C8—51no—
148#837—102no—
149#835—101no—
150#832—101no—
151#830—102no—
152C5×#41—21no—
153C5×#41—21no—
154C5×#41—21no—
155C5×#41—21no—
156C5×#41—21no—
157C5×#41—21no—
158C5×#41C2×Dic312yes—
159C5×#41#6712yes—
160C2×C5×Q8C2×Dic311yescharacteristic
161C2×C5×Q8#6711yescharacteristic
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4C2×Dic311yescharacteristic
165C2×C5×D4#6711yescharacteristic
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5C22×D311yescharacteristic
169C5×Q16—22no—
170C5×SD16—22no—
171C5×SD16—22no—
172C5×D8—22no—
173C5×M16—21no—
174C5×M16C2×Dic312yes—
175C2×C5×C8—21no—
176C22⋊Dic5—61no—
177C4⋊Dic5—61no—
178C4×Dic5—61no—
179#681—32no—
180#681—64no—
181#681—61no—
182#681—61no—
183#681—61no—
184C2×#168—32no—
185C2×#168—64no—
186C2×#168—61no—
187C2×#168—61no—
188C2×#168—61no—
189C2×#168—61no—
190#575D1511yescharacteristic
191#568—151no—
192#421—151no—
193#416—151no—
194#408—151no—
195#344—151no—
196#341—151no—
197C22×C3×C5—22no—
198C22×C3×C5—41no—
199C22×C3×C5—42no—
200C22×C3×C5—41no—
201C22×C3×C5—81no—
202C22×C3×C5C4×D411yescharacteristic
203C22×C3×C5#12111yescharacteristic
204C22×C3×C5#12311yescharacteristic
205C3×C4×C5—22no—
206C3×C4×C5—41no—
207C3×C4×C5C2×C22⋊C411yescharacteristic
208C3×C4×C5C4×D411yescharacteristic
209C3×C4×C5#12011yescharacteristic
210C3×C4×C5#12111yescharacteristic
211Dic15—81no—
212C3×#41—21no—
213C3×#41—21no—
214C3×#41—21no—
215C3×#41—21no—
216C3×#41—21no—
217C3×#41—21no—
218C3×#41C2×Dic512yes—
219C3×#41C22⋊D512yes—
220C2×C3×Q8C2×Dic511yescharacteristic
221C2×C3×Q8C22⋊D511yescharacteristic
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4C2×Dic511yescharacteristic
225C2×C3×D4C22⋊D511yescharacteristic
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4C22×D511yescharacteristic
229C3×Q16—22no—
230C3×SD16—22no—
231C3×SD16—22no—
232C3×D8—22no—
233C3×M16—21no—
234C3×M16C2×Dic512yes—
235C2×C3×C8—21no—
236#217—101no—
237C4⋊Dic3—101no—
238C4×Dic3—101no—
239#208—52no—
240#208—104no—
241#208—101no—
242#208—101no—
243#208—101no—
244C2×C3⋊C8—52no—
245C2×C3⋊C8—104no—
246C2×C3⋊C8—101no—
247C2×C3⋊C8—101no—
248C2×C3⋊C8—101no—
249C2×C3⋊C8—101no—
250C23×C5—21no—
251C23×C5—21no—
252C23×C5#23711yescharacteristic
253C5×Q8—21no—
254C5×Q8—21no—
255C5×Q8—21no—
256C5×Q8#21712yes—
257C5×D4—22no—
258C5×D4—22no—
259C5×D4—21no—
260C5×D4—21no—
261C5×D4—21no—
262C5×D4—41no—
263C5×D4—41no—
264C5×D4#21712yes—
265C2×C4×C5—21no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—21no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5D3×D411yescharacteristic
272C2×C4×C5D3×D411yescharacteristic
273C2×C4×C5#23711yescharacteristic
274C2×C4×C5C22×Dic311yescharacteristic
275C2×C4×C5C2×#6711yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C2×Dic5—121no—
278C5×C8—22no—
279#168—62no—
280#168—62no—
281#168—121no—
282C2×#41C2×D1511yescharacteristic
283C2×#41C2×D1511yescharacteristic
284#137—21no—
285#137Dic1512yescomplemented
286AGL(1,ℤ/8)—21no—
287AGL(1,ℤ/8)Dic1512yescomplemented
288#135—22no—
289#131—302no—
290#131—302no—
291C2×M16—151no—
292C2×M16—151no—
293C2×M16—302no—
294C2×M16C2×D1511yescharacteristic
295C22×C8—151no—
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—42no—
305C2×C3×C5—81no—
306C2×C3×C5#38611yescharacteristic
307C23×C3—21no—
308C23×C3—21no—
309C23×C3#71111yescharacteristic
310C3×Q8—21no—
311C3×Q8—21no—
312C3×Q8—21no—
313C3×Q8C22⋊Dic512yes—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—21no—
317C3×D4—21no—
318C3×D4—21no—
319C3×D4—41no—
320C3×D4—41no—
321C3×D4C22⋊Dic512yes—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4D4×D511yescharacteristic
329C2×C3×C4D4×D511yescharacteristic
330C2×C3×C4#71111yescharacteristic
331C2×C3×C4C22×Dic511yescharacteristic
332C2×C3×C4C2×C22⋊D511yescharacteristic
333C2×C3×C4C2×C22⋊D511yescharacteristic
334C2×Dic3—201no—
335C3×C8—22no—
336C3⋊C8—102no—
337C3⋊C8—102no—
338C3⋊C8—201no—
339C22×C5—22no—
340C22×C5—41no—
341C22×C5—42no—
342C22×C5—41no—
343C22×C5—81no—
344C22×C5D4×Dic311yescharacteristic
345C22×C5#93511yescharacteristic
346C22×C5#93911yescharacteristic
347C4×C5—22no—
348C4×C5—41no—
349C4×C5D4×Dic311yescharacteristic
350C4×C5#93711yescharacteristic
351C4×C5#93911yescharacteristic
352C4×C5C2×#21711yescharacteristic
353Dic5—241no—
354#41—21no—
355#41—21no—
356#41—21no—
357#41—21no—
358#41—21no—
359#41—21no—
360#41C2×Dic1512yes—
361#41#122012yes—
362C2×Q8C2×Dic1511yescharacteristic
363C2×Q8#122011yescharacteristic
364C2×D4—21no—
365C2×D4—21no—
366C2×D4C2×Dic1511yescharacteristic
367C2×D4#122011yescharacteristic
368C22×C4—21no—
369C22×C4—21no—
370C22×C4C22×D1511yescharacteristic
371Q16—22no—
372SD16—22no—
373SD16—22no—
374D8—22no—
375M16—21no—
376M16—152no—
377M16—304no—
378M16—301no—
379M16—301no—
380M16—301no—
381M16C2×Dic1512yes—
382C2×C8—21no—
383C2×C8—152no—
384C2×C8—304no—
385C2×C8—301no—
386C2×C8—301no—
387C2×C8—301no—
388C2×C8—301no—
389C4⋊C4—301no—
390C22⋊C4—301no—
391C42—301no—
392C3×C5#188111yescharacteristic, complemented, Hall
393C22×C3—22no—
394C22×C3—41no—
395C22×C3—42no—
396C22×C3—41no—
397C22×C3—81no—
398C22×C3D4×Dic511yescharacteristic
399C22×C3#408111yescharacteristic
400C22×C3#408511yescharacteristic
401C3×C4—22no—
402C3×C4—41no—
403C3×C4D4×Dic511yescharacteristic
404C3×C4#408311yescharacteristic
405C3×C4#408511yescharacteristic
406C3×C4C2×C22⋊Dic511yescharacteristic
407Dic3—401no—
408C2×C5—21no—
409C2×C5—21no—
410C2×C5—21no—
411C2×C5—42no—
412C2×C5—81no—
413C2×C5#522011yescharacteristic
414C23—21no—
415C23—21no—
416C23#681911yescharacteristic
417Q8—21no—
418Q8—21no—
419Q8—21no—
420Q8#671912yes—
421D4—22no—
422D4—22no—
423D4—21no—
424D4—21no—
425D4—21no—
426D4—41no—
427D4—41no—
428D4#671912yes—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—601no—
436C2×C4D4×D1511yescharacteristic
437C2×C4D4×D1511yescharacteristic
438C2×C4#681911yescharacteristic
439C2×C4C22×Dic1511yescharacteristic
440C2×C4C2×#122011yescharacteristic
441C2×C4C2×#122011yescharacteristic
442C8—22no—
443C8—302no—
444C8—302no—
445C8—601no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—42no—
450C2×C3—81no—
451C2×C3#6550911yescharacteristic
452C5#7211611yescharacteristic, complemented, Sylow
453C22—22no—
454C22—41no—
455C22—42no—
456C22—41no—
457C22—81no—
458C22D4×Dic1511yescharacteristic
459C22#9182411yescharacteristic
460C22#9182811yescharacteristic
461C4—22no—
462C4—41no—
463C4—1201no—
464C4D4×Dic1511yescharacteristic
465C4#9182611yescharacteristic
466C4#9182811yescharacteristic
467C4C2×#671911yescharacteristic
468C3#1060290911yescharacteristic, complemented, Sylow
469C2—21no—
470C2—21no—
471C2—21no—
472C2—42no—
473C2—81no—
474C2#1175132111yescharacteristic
subgroupG/H
centerC4#91826
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
Fitting, prime radicalC3×C5×#575C2
socleC2×C3×C5#386
cosocleC22×C3×C4×C5C23
hypercenter#575D15
hypocenterC3×C5#1881
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
2. #11756578C2semidirect
3. #11751337C2semidirect
4. #11751335C2semidirect
5. #11751334C2semidirect
6. #11746380C2semidirect
7. #11746379C2semidirect
12. C3×C5×#137C4semidirect
14. C3×C5×AGL(1,ℤ/8)C4semidirect
84. C5×#137Dic3semidirect
86. C5×AGL(1,ℤ/8)Dic3semidirect
136. C3×#137Dic5semidirect
138. C3×AGL(1,ℤ/8)Dic5semidirect
285. #137Dic15semidirect
287. AGL(1,ℤ/8)Dic15semidirect
392. C3×C5#1881semidirect
452. C5#72116semidirect
468. C3#10602909semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5752
#117565782
#117513372
#117513352
#117513342
#117463802
#117463792
#106029093
#721165