Finite Group Databasebeta

← #14471528

Subgroups — #14471528

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#11756480C211yesmaximal, characteristic, complemented
2#11752552C211yesmaximal, characteristic
3C5×#5079C211yesmaximal, characteristic, complemented
4C3×#65372C211yesmaximal, characteristic
5#11749361C212yesmaximal, complemented
6#11749239C212yesmaximal
7#11749229C212yesmaximal
8#11749189C212yesmaximal, complemented
9C4×#6657C211yesmaximal, characteristic
10#11746946C211yesmaximal, characteristic, complemented
11#11746855C211yesmaximal, characteristic, complemented
12#10613351—31nomaximal, Hall
13C2×D5×Dic6—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15Q8×Dic15C2212yes—
16#91833C2212yes—
17#91779—21no—
18#91778—22no—
19#91776—21no—
20C4×Dic30C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C5×#869C2211yescharacteristic
23C2×C3×#688C2212yes—
24C3×C4×D20C2211yescharacteristic
25#91470C2212yes—
26#91434C2212yes—
27#91430—22no—
28#91359—21no—
29C2×#6657C2211yescharacteristic
30C5×#835C2212yes—
31C5×#835C2212yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33C3×#3967C2212yes—
34C3×C4⋊#168C2211yescharacteristic
35#90987C2211yescharacteristic
36#90985C2212yes—
37#90983C2212yes—
38#90975C2212yes—
39#90974C2211yescharacteristic
40#90965C2211yescharacteristic
41#90951C2212yes—
42#80414—51nomaximal, Hall
43#66061—31no—
44#66055—31no—
45C5×#487—31no—
46#65383—31no—
47#65372D311yescharacteristic
48#65107—32no—
49#65081—32no—
50#65080—32no—
51#65077—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8C2312yes—
55C2×Dic30D411yescharacteristic
56C2×Dic30C2311yescharacteristic
57C2×C5×Dic6—21no—
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C2×#1204—22no—
61C2×D5×Dic3—22no—
62D5×Dic6—44no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4—21no—
65C3×C42×C5C2311yescharacteristic
66C4⋊Dic15—22no—
67C4⋊Dic15D411yescharacteristic
68C4⋊Dic15C2311yescharacteristic
69#6712—21no—
70#6712—22no—
71#6712—22no—
72#6712D412yes—
73C4×Dic15—21no—
74C4×Dic15—22no—
75C4×Dic15C2312yes—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C2×C5×C3⋊C8C2311yescharacteristic
79C2×C5×C3⋊C8C2311yescharacteristic
80C3×#688—24no—
81C3×#685—21no—
82C3×C4⋊Dic5C2311yescharacteristic
83C2×C3×#168C2312yes—
84#6669—22no—
85#6665—22no—
86#6657—22no—
87#5721—51no—
88D4×Dic6—51no—
89C3×#461—51no—
90#5162—52no—
91Dic3×SD16—52no—
92#5079D511yescharacteristic, complemented
93C4×#214—51no—
94#4851—51no—
95#4830—51no—
96#4792—52no—
97#4791—52no—
98C2×Q8×D5—61no—
99C5×C4⋊Q8—31no—
100C5×C4⋊Q8C2×D311yescharacteristic
101#4092—61no—
102Q8×Dic5—32no—
103#4090—32no—
104C2×#688C2×D312yes—
105C2×#677—31no—
106#4042—62no—
107#4039—32no—
108#4036—61no—
109#4035—62no—
110#4034—32no—
111#4033—61no—
112C4×D20C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—31no—
115C5×#103—32no—
116C5×#103—32no—
117C4×C5×C8—31no—
118#3967C2×D312yes—
119#3953—31no—
120#3949—31no—
121#3948—31no—
122#3946—32no—
123C8×Dic5—32no—
124#3942—32no—
125#3940—32no—
126C4⋊#168C2×D311yescharacteristic
127#3359—151noSylow
128C22×C3×D5—21no—
129C3×C5×Q8—22no—
130C3×C5×Q8—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136C2×Dic15—21no—
137C2×Dic15C2×D412yes—
138C2×Dic15C2×D412yes—
139Dic30—21no—
140Dic30—21no—
141Dic30SD1614yescomplemented
142C2×C5×Dic3—22no—
143C5×Dic6—42no—
144C2×C3×Dic5—21no—
145C3×D20—21no—
146C3×D20#4112yes—
147C3×C4×D5—42no—
148#1204—44no—
149D5×Dic3—44no—
150C3×#168—22no—
151C5×C3⋊C8—21no—
152C5×C3⋊C8—21no—
153C22×Dic6—101no—
154C2×C3×SD16—52no—
155C3×C4⋊Q8C2×D511yescharacteristic
156C3×C4×D4—51no—
157Q8×Dic3—52no—
158#944—52no—
159D4×Dic3—52no—
160C2×#214—51no—
161#924—101no—
162#890—101no—
163#889—102no—
164#888—52no—
165#887—101no—
166#878—102no—
167#869C2×D511yescharacteristic
168C4×Dic6—51no—
169C4×Dic6—51no—
170C3×C4⋊C8—51no—
171C3×#103—52no—
172#835C2×D512yes—
173#835C2×D512yes—
174#832—51no—
175#817—52no—
176#816—52no—
177Dic3⋊C8—52no—
178C8×Dic3—52no—
179#810—51no—
180#808—51no—
181C4×C3⋊C8C2×D511yescharacteristic
182C2×C5×Q8—61no—
183C2×C5×Q8C22×D312yes—
184Q8×D5—124no—
185C2×D20C22×D311yescharacteristic
186C2×C4×D5—21no—
187C2×C4×D5—62no—
188C2×Dic10—31no—
189C2×Dic10—31no—
190C2×Dic10—62no—
191C2×C5×C8—31no—
192C2×C5×C8—31no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—32no—
196C5×C4⋊C4—61no—
197C42×C5C22×D311yescharacteristic
198#688—24no—
199#685—21no—
200#685—62no—
201C4⋊Dic5—31no—
202C4⋊Dic5—31no—
203C4⋊Dic5—62no—
204C4⋊Dic5C22×D311yescharacteristic
205#683—32no—
206#683—62no—
207#683—62no—
208#683—62no—
209#683—61no—
210C4×Dic5—32no—
211C4×Dic5—62no—
212C4×Dic5—61no—
213C2×#168C22×D312yes—
214#677—62no—
215#557—151no—
216D4×Q8—151no—
217#487—31no—
218#487—152no—
219#475—152no—
220#475—151no—
221#461—51no—
222#461—152no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×SD16—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C3×D5—22no—
228C2×C3×D5—41no—
229C2×C3×D5—41no—
230C3×C4×C5—21no—
231C3×C4×C5—42no—
232C3×C4×C5C2×SD1612yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—22no—
236Dic15—41no—
237Dic15—41no—
238Dic15C2×SD1614yes—
239C3×Dic5—41no—
240C5×Dic3—42no—
241C2×C3×Q8C22×D512yes—
242C2×C3×D4—51no—
243C22×C3×C4—101no—
244C22×Dic3—102no—
245C2×Dic6—21no—
246C2×Dic6—51no—
247C2×Dic6—51no—
248C2×Dic6—102no—
249C2×Dic6—204no—
250C3×SD16—104no—
251C2×C3×C8—52no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—51no—
255C3×C22⋊C4—101no—
256C3×C42C22×D511yescharacteristic
257#217—102no—
258#214—102no—
259C4⋊Dic3—21no—
260C4⋊Dic3—51no—
261C4⋊Dic3—51no—
262C4⋊Dic3—102no—
263C4⋊Dic3C22×D512yes—
264Dic3⋊C4—52no—
265Dic3⋊C4—102no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—101no—
269C4×Dic3—52no—
270C4×Dic3—102no—
271C4×Dic3—101no—
272C2×C3⋊C8C22×D511yescharacteristic
273C2×C3⋊C8C22×D511yescharacteristic
274C22×D5—21no—
275C5×Q8—22no—
276C5×Q8—22no—
277C5×Q8—122no—
278C2×C4×C5—22no—
279C2×C4×C5—62no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—21no—
284C2×Dic5—32no—
285C2×Dic5—32no—
286C2×Dic5—61no—
287C2×Dic5—61no—
288D20—21no—
289D20#23712yes—
290C4×D5—42no—
291C4×D5—124no—
292Dic10—34no—
293Dic10—61no—
294Dic10—61no—
295Dic10—124no—
296C5×C8—61no—
297C5×C8—61no—
298#168—22no—
299C22×Q8—301no—
300C2×SD16—52no—
301C2×SD16—151no—
302C4⋊Q8—31no—
303C4⋊Q8—152no—
304C4⋊Q8—152no—
305C4⋊Q8D3×D511yescharacteristic
306#125—302no—
307#125—301no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—151no—
311C4×Q8—152no—
312C4×Q8—151no—
313C4×Q8—301no—
314C4×D4—51no—
315C4×D4—152no—
316#106—152no—
317#106—151no—
318C4⋊C8—51no—
319C4⋊C8—152no—
320#103—32no—
321#103—32no—
322#103—52no—
323#103—152no—
324#103—151no—
325#102—151no—
326C4×C8—31no—
327C4×C8—152no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331C3×D5—42no—
332C23×C3—101no—
333C3×Q8—22no—
334C3×Q8—22no—
335C3×D4—52no—
336C3×D4—101no—
337C2×C3×C4—22no—
338C2×C3×C4—101no—
339C2×C3×C4—202no—
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4C23×D511yescharacteristic
343C2×Dic3—22no—
344C2×Dic3—52no—
345C2×Dic3—52no—
346C2×Dic3—101no—
347C2×Dic3—101no—
348C2×Dic3—204no—
349Dic6—42no—
350Dic6—54no—
351Dic6—101no—
352Dic6—101no—
353Dic6—204no—
354C3×C8—102no—
355C3⋊C8—21no—
356C3⋊C8—21no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—22no—
359C2×D5—41no—
360C2×D5—41no—
361C4×C5—21no—
362C4×C5—42no—
363C4×C5—122no—
364C4×C5D3×SD1612yes—
365C4×C5C2×#23711yescharacteristic
366C4×C5#101011yescharacteristic
367Dic5—34no—
368Dic5—41no—
369Dic5—62no—
370Dic5—121no—
371Dic5—121no—
372C2×Q8—61no—
373C2×Q8—151no—
374C2×Q8—151no—
375C2×Q8—302no—
376C2×Q8—604no—
377C2×Q8C2×D3×D512yes—
378C2×D4—51no—
379C22×C4—101no—
380C22×C4—302no—
381SD16—104no—
382SD16—302no—
383C2×C8—31no—
384C2×C8—31no—
385C2×C8—52no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—32no—
389C4⋊C4—51no—
390C4⋊C4—61no—
391C4⋊C4—152no—
392C4⋊C4—151no—
393C4⋊C4—151no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—302no—
398C4⋊C4—301no—
399C22⋊C4—101no—
400C22⋊C4—302no—
401C42—152no—
402C42—302no—
403C42—301no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3—102no—
407C22×C3—201no—
408C22×C3—201no—
409C22×C3C2×D4×D511yescharacteristic
410C3×C4—21no—
411C3×C4—42no—
412C3×C4—201no—
413C3×C4D5×SD1612yes—
414C3×C4D5×#4111yescharacteristic
415C3×C4#415011yescharacteristic
416Dic3—42no—
417Dic3—54no—
418Dic3—102no—
419Dic3—201no—
420Dic3—201no—
421C2×C5#559811yescharacteristic
422C2×C5C2×D3×SD1611yescharacteristic
423C2×C5#577911yescharacteristic
424D5—42no—
425C23—101no—
426Q8—22no—
427Q8—22no—
428Q8—122no—
429Q8—154no—
430Q8—301no—
431Q8—301no—
432Q8—604no—
433D4—52no—
434D4—101no—
435C2×C4—22no—
436C2×C4—62no—
437C2×C4—101no—
438C2×C4—152no—
439C2×C4—152no—
440C2×C4—202no—
441C2×C4—301no—
442C2×C4—301no—
443C2×C4—604no—
444C2×C4#679011yescharacteristic
445C2×C4#679011yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—61no—
448C8—61no—
449C8—102no—
450C2×C3—202no—
451C2×C3#6601111yescharacteristic
452C2×C3C2×D5×SD1611yescharacteristic
453C2×C3#6610011yescharacteristic
454C5#8041411yescharacteristic, complemented, Sylow
455C22—102no—
456C22—201no—
457C22—201no—
458C22C2×#679011yescharacteristic
459C4—21no—
460C4—42no—
461C4—122no—
462C4—154no—
463C4—201no—
464C4—302no—
465C4—601no—
466C4—601no—
467C4#9150512yes—
468C4#9202011yescharacteristic
469C4D5×#23711yescharacteristic
470C3#1061335111yescharacteristic, complemented, Sylow
471C2—202no—
472C2#1175481611yescharacteristic
473C2C2×#9150511yescharacteristic
474C2#1175511911yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D20C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11756480C2semidirect
3. C5×#5079C2semidirect
5. #11749361C2semidirect
8. #11749189C2semidirect
10. #11746946C2semidirect
11. #11746855C2semidirect
92. #5079D5semidirect
141. Dic30SD16semidirect
405. C3×C5#3359semidirect
454. C5#80414semidirect
470. C3#10613351semidirect

Maximal subgroups

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

subgroupindex
#117564802
#117525522
C5×#50792
C3×#653722
#117493612
#117492392
#117492292
#117491892
C4×#66572
#117469462
#117468552
#106133513
#804145