Finite Group Databasebeta

← #14471531

Subgroups — #14471531

Order 1920.

740 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#11752558C211yesmaximal, characteristic
2#11752487C211yesmaximal, characteristic, complemented
3#11750931C211yesmaximal, characteristic, complemented
4C5×#4841C211yesmaximal, characteristic
5C3×#65140C211yesmaximal, characteristic, complemented
6#11748036C212yesmaximal, complemented
7#11747881C212yesmaximal, complemented
8#11747807C212yesmaximal
9#11747786C212yesmaximal
10C4×#6656C211yesmaximal, characteristic
11#11746923C211yesmaximal, characteristic, complemented
12#10612145—31nomaximal, Hall
13C2×D3×Dic10—21no—
14C4×Dic30C2211yescharacteristic
15C2×C5×#204C2212yes—
16C4×C5×D12C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20#91470C2212yes—
21#91436—22no—
22#91435C2212yes—
23#91388—21no—
24#91385C2212yes—
25#91369—21no—
26#91344C2212yes—
27#91336—22no—
28#91333—21no—
29C2×#6656C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4×C3⋊#168C2211yescharacteristic
34C5×#816C2212yes—
35C3×#3949C2212yes—
36C3×#3948C2212yes—
37#90986C2211yescharacteristic
38#90972C2212yes—
39#90972C2212yes—
40#90970C2211yescharacteristic
41#90966C2211yescharacteristic
42#81037—51nomaximal, Hall
43#66055—31no—
44D4×Dic10—31no—
45C5×#461—31no—
46#65451—32no—
47SD16×Dic5—32no—
48#65370—31no—
49C4×#687—31no—
50#65140D311yescharacteristic, complemented
51#65119—31no—
52#65081—32no—
53#65080—32no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12C2311yescharacteristic
56C2×C4×C5×D3—21no—
57C2×C5×Dic6C2312yes—
58C2×C3×Dic10—21no—
59C2×C3×Dic10C2311yescharacteristic
60C2×#1204—22no—
61C2×D3×Dic5—22no—
62D3×Dic10—44no—
63C2×C3×C5×C8C2312yes—
64C3×C42×C5C2311yescharacteristic
65C4⋊Dic15D411yescharacteristic
66#6712D412yes—
67C4×Dic15C2312yes—
68C2×C3⋊#168C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C5×(C2×D3)⋊C4—21no—
71C5×C4⋊Dic3—21no—
72C5×C4⋊Dic3—21no—
73C5×C4⋊Dic3C2311yescharacteristic
74C5×#204—24no—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5C2312yes—
77C3×C4⋊Dic5C2311yescharacteristic
78C3×#683—21no—
79C3×C4×Dic5—21no—
80Dic3⋊Dic5—22no—
81#6669—22no—
82#6669—22no—
83#6669—22no—
84(C2×D3)⋊Dic5—22no—
85Dic3×Dic5—22no—
86#6656—22no—
87#5727—51no—
88#5567—51no—
89C3×#475—51no—
90#5093—51no—
91C4×#215—51no—
92#4854—52no—
93#4852—52no—
94#4841D511yescharacteristic
95#4830—51no—
96#4818—52no—
97#4792—52no—
98C22×Dic10—61no—
99C2×C5×SD16—32no—
100C5×C4⋊Q8—31no—
101C4×C5×D4—31no—
102Q8×Dic5—32no—
103#4090—32no—
104D4×Dic5—32no—
105C2×#687—31no—
106#4070—61no—
107#4036—61no—
108#4035—62no—
109#4034—32no—
110#4033—61no—
111#4024—62no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10C2×D311yescharacteristic
115C5×C4⋊C8C2×D311yescharacteristic
116C5×#103—32no—
117#3967—32no—
118#3967—32no—
119#3964—31no—
120#3949C2×D312yes—
121#3948C2×D312yes—
122#3946—32no—
123C8×Dic5—32no—
124#3942—31no—
125#3940—31no—
126C4×#168—31no—
127#3359—151noSylow
128C22×C5×D3—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15C2×D412yes—
133C2×Dic15C2×D412yes—
134Dic30SD1614yescomplemented
135C2×C5×Dic3—22no—
136C2×C5×Dic3—21no—
137C5×D12—21no—
138C5×D12#4112yes—
139C4×C5×D3—42no—
140C5×Dic6—22no—
141C5×Dic6—22no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—21no—
145C3×Dic10—21no—
146C3×Dic10—21no—
147C3×Dic10—42no—
148#1204—44no—
149D3×Dic5—44no—
150C3×C5×C8—22no—
151C3⋊#168—21no—
152C3⋊#168—21no—
153C2×D3×Q8—101no—
154C3×C4⋊Q8—51no—
155C3×C4×Q8—51no—
156#946—101no—
157#944—52no—
158C2×#215—51no—
159C2×#204C2×D512yes—
160#896—102no—
161#893—52no—
162#889—102no—
163#888—52no—
164#887—52no—
165C4×D12C2×D511yescharacteristic
166#870—101no—
167#869C2×D511yescharacteristic
168C4×Dic6—51no—
169C4×Dic6—101no—
170C3×#106—52no—
171C3×C4⋊C8C2×D511yescharacteristic
172C3×#103—52no—
173#835—51no—
174#816C2×D512yes—
175Dic3⋊C8—52no—
176C8×Dic3—52no—
177#810—52no—
178#810—52no—
179#809—51no—
180#808—51no—
181C4×C3⋊C8—51no—
182C2×C5×Q8—32no—
183C2×C5×D4—31no—
184C22×C4×C5—61no—
185C22×Dic5—62no—
186C2×Dic10—21no—
187C2×Dic10—31no—
188C2×Dic10—62no—
189C2×Dic10—124no—
190C2×Dic10C22×D311yescharacteristic
191C5×SD16—64no—
192C2×C5×C8C22×D312yes—
193C5×C4⋊C4—31no—
194C5×C4⋊C4—61no—
195C5×C4⋊C4—61no—
196C5×C22⋊C4—61no—
197C42×C5C22×D311yescharacteristic
198C22⋊Dic5—62no—
199#687—62no—
200C4⋊Dic5—21no—
201C4⋊Dic5—31no—
202C4⋊Dic5—62no—
203C4⋊Dic5C22×D311yescharacteristic
204C4⋊Dic5C22×D312yes—
205#683—21no—
206#683—32no—
207#683—62no—
208#683—62no—
209#683—62no—
210C4×Dic5—21no—
211C4×Dic5—32no—
212C4×Dic5—62no—
213C2×#168—31no—
214C2×#168—31no—
215#557—151no—
216D4×Q8—151no—
217#487—152no—
218#487—151no—
219#475—51no—
220#475—152no—
221#461—31no—
222#461—152no—
223C8×Q8—151no—
224C4×SD16—152no—
225C4×SD16—151no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C5×D3—22no—
228C2×C5×D3—41no—
229C2×C5×D3—41no—
230C3×C4×C5—21no—
231C3×C4×C5C2×SD1612yes—
232C3×C4×C5C2×#4111yescharacteristic
233C3×C4×C52−1+411yescharacteristic
234Dic15—22no—
235Dic15C2×SD1614yes—
236C3×Dic5—41no—
237C3×Dic5—42no—
238C3×Dic5—41no—
239C5×Dic3—42no—
240C5×Dic3—41no—
241C2×C3×Q8—51no—
242C2×C3×Q8—101no—
243D3×Q8—204no—
244C2×D12C22×D511yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—102no—
247C2×Dic6—51no—
248C2×Dic6—102no—
249C2×Dic6C22×D512yes—
250C2×C3×C8C22×D512yes—
251C3×C4⋊C4—51no—
252C3×C4⋊C4—52no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4—101no—
255C3×C42—101no—
256C3×C42C22×D511yescharacteristic
257#215—102no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—102no—
260C4⋊Dic3—21no—
261C4⋊Dic3—21no—
262C4⋊Dic3—51no—
263C4⋊Dic3C22×D511yescharacteristic
264Dic3⋊C4—52no—
265Dic3⋊C4—102no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269C4×Dic3—52no—
270C4×Dic3—102no—
271C2×C3⋊C8—51no—
272C2×C3⋊C8—51no—
273#204—24no—
274C23×C5—61no—
275C5×Q8—62no—
276C5×Q8—62no—
277C5×D4—32no—
278C5×D4—61no—
279C2×C4×C5—62no—
280C2×C4×C5—61no—
281C2×C4×C5—122no—
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5C23×D311yescharacteristic
285C2×Dic5—21no—
286C2×Dic5—21no—
287C2×Dic5—22no—
288C2×Dic5—32no—
289C2×Dic5—32no—
290C2×Dic5—124no—
291Dic10—21no—
292Dic10—21no—
293Dic10—34no—
294Dic10—42no—
295Dic10—124no—
296C5×C8—22no—
297#168—61no—
298#168—61no—
299C22×Q8—301no—
300C2×SD16—32no—
301C2×SD16—151no—
302C4⋊Q8—31no—
303C4⋊Q8—51no—
304C4⋊Q8—152no—
305C4⋊Q8—152no—
306#125—301no—
307#125—302no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—51no—
311C4×Q8—151no—
312C4×Q8—152no—
313C4×Q8—301no—
314C4×D4—31no—
315C4×D4—152no—
316#106—52no—
317#106—151no—
318C4⋊C8—152no—
319C4⋊C8D3×D511yescharacteristic
320#103—32no—
321#103—52no—
322#103—151no—
323#103—152no—
324#103—152no—
325#102—151no—
326C4×C8—152no—
327C4×C8—151no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331C5×D3—42no—
332C22×D3—21no—
333C3×Q8—101no—
334C3×Q8—101no—
335C3×Q8—202no—
336C2×C3×C4—101no—
337C2×C3×C4—101no—
338C2×C3×C4—102no—
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4C23×D511yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—21no—
344C2×Dic3—52no—
345C2×Dic3—52no—
346D12—21no—
347D12#71112yes—
348C4×D3—42no—
349C4×D3—204no—
350Dic6—22no—
351Dic6—22no—
352Dic6—54no—
353Dic6—204no—
354C3×C8—22no—
355C3⋊C8—101no—
356C3⋊C8—101no—
357C22×C5—62no—
358C22×C5—121no—
359C22×C5—121no—
360C22×C5C2×D3×D411yescharacteristic
361C4×C5—21no—
362C4×C5—122no—
363C4×C5—121no—
364C4×C5D3×SD1612yes—
365C4×C5#100711yescharacteristic
366C4×C5D3×#4111yescharacteristic
367Dic5—34no—
368Dic5—41no—
369Dic5—42no—
370Dic5—41no—
371Dic5—62no—
372C2×Q8—32no—
373C2×Q8—51no—
374C2×Q8—101no—
375C2×Q8—151no—
376C2×Q8—302no—
377C2×Q8—604no—
378C2×D4—31no—
379C22×C4—61no—
380C22×C4—302no—
381SD16—64no—
382SD16—302no—
383C2×C8—151no—
384C2×C8—151no—
385C2×C8C2×D3×D512yes—
386C4⋊C4—31no—
387C4⋊C4—51no—
388C4⋊C4—52no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—101no—
392C4⋊C4—101no—
393C4⋊C4—152no—
394C4⋊C4—151no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—302no—
398C4⋊C4—302no—
399C22⋊C4—61no—
400C22⋊C4—302no—
401C42—101no—
402C42—152no—
403C42—302no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3C2×D4×D511yescharacteristic
407C2×D3—22no—
408C2×D3—41no—
409C2×D3—41no—
410C3×C4—21no—
411C3×C4—202no—
412C3×C4—201no—
413C3×C4—201no—
414C3×C4D5×SD1612yes—
415C3×C4C2×#71111yescharacteristic
416C3×C4#415011yescharacteristic
417Dic3—41no—
418Dic3—42no—
419Dic3—54no—
420Dic3—102no—
421C2×C5—122no—
422C2×C5#563311yescharacteristic
423C2×C5C2×D3×SD1611yescharacteristic
424C2×C5#577911yescharacteristic
425C23—61no—
426Q8—62no—
427Q8—62no—
428Q8—101no—
429Q8—101no—
430Q8—154no—
431Q8—202no—
432Q8—604no—
433D4—32no—
434D4—61no—
435C2×C4—62no—
436C2×C4—61no—
437C2×C4—101no—
438C2×C4—101no—
439C2×C4—102no—
440C2×C4—122no—
441C2×C4—152no—
442C2×C4—152no—
443C2×C4—604no—
444C2×C4#677711yescharacteristic
445C2×C4#677711yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—22no—
448C8—301no—
449C8—301no—
450C2×C3#6593211yescharacteristic
451C2×C3C2×D5×SD1611yescharacteristic
452C2×C3#6611311yescharacteristic
453D3—42no—
454C5#8103711yescharacteristic, complemented, Sylow
455C22—62no—
456C22—121no—
457C22—121no—
458C22C2×#677711yescharacteristic
459C4—21no—
460C4—122no—
461C4—121no—
462C4—154no—
463C4—201no—
464C4—201no—
465C4—202no—
466C4—302no—
467C4#9125512yes—
468C4D3×#71111yescharacteristic
469C4#9203011yescharacteristic
470C3#1061214511yescharacteristic, complemented, Sylow
471C2—122no—
472C2#1175370311yescharacteristic
473C2C2×#9125511yescharacteristic
474C2#1175404311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×D12C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11752487C2semidirect
3. #11750931C2semidirect
5. C3×#65140C2semidirect
6. #11748036C2semidirect
7. #11747881C2semidirect
11. #11746923C2semidirect
50. #65140D3semidirect
134. Dic30SD16semidirect
405. C3×C5#3359semidirect
454. C5#81037semidirect
470. C3#10612145semidirect

Maximal subgroups

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

subgroupindex
#117525582
#117524872
#117509312
C5×#48412
C3×#651402
#117480362
#117478812
#117478072
#117477862
C4×#66562
#117469232
#106121453
#810375