Finite Group Databasebeta

← #14471546

Subgroups — #14471546

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#11752552C211yesmaximal, characteristic
2#11752487C211yesmaximal, characteristic, complemented
3C8×Dic30C211yesmaximal, characteristic, complemented
4C5×#4681C211yesmaximal, characteristic, complemented
5C3×C4×#677C211yesmaximal, characteristic
6#11748036C212yesmaximal, complemented
7#11747881C212yesmaximal, complemented
8#11747749C212yesmaximal
9#11747735C212yesmaximal
10#11747059C211yesmaximal, characteristic
11#11746918C211yesmaximal, characteristic, complemented
12#10613351—31nomaximal, Hall
13C2×D5×Dic6—21no—
14C4×Dic30C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C2×C3×#677C2211yescharacteristic
18C3×C4×D20C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20#91470C2212yes—
21#91434C2212yes—
22#91430—22no—
23#91388—21no—
24#91385C2212yes—
25#91359—21no—
26#91344C2212yes—
27#91336—22no—
28#91333—21no—
29C2×#6655C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#816C2212yes—
35C5×#816C2212yes—
36C3×#3953C2211yescharacteristic
37C3×#3949C2211yescharacteristic
38C3×#3948C2211yescharacteristic
39#90986C2212yes—
40#90972C2212yes—
41#90970C2212yes—
42#79619—51nomaximal, Hall
43#66061—31no—
44#66055—31no—
45C5×#487—31no—
46#65383—31no—
47#65372—31no—
48#65107—32no—
49#65081—32no—
50#65080—32no—
51#65077—32no—
52C4×#677D311yescharacteristic
53C8×Dic10—31no—
54C2×Dic30D411yescharacteristic
55C2×C5×Dic6—21no—
56C2×C5×Dic6C2312yes—
57C2×C3×D20C2311yescharacteristic
58C2×C3×C4×D5—21no—
59C2×C3×Dic10C2311yescharacteristic
60C2×#1204—22no—
61C2×D5×Dic3—22no—
62D5×Dic6—44no—
63C2×C3×C5×C8C2311yescharacteristic
64C2×C3×C5×C8C2311yescharacteristic
65C3×C42×C5C2311yescharacteristic
66C4⋊Dic15D411yescharacteristic
67#6712D412yes—
68C4×Dic15C2312yes—
69C2×C3⋊#168C2312yes—
70C5×C4⋊Dic3—21no—
71C5×C4⋊Dic3—21no—
72C5×C4⋊Dic3—21no—
73C5×C4⋊Dic3C2312yes—
74C3×#685—21no—
75C3×C4⋊Dic5C2311yescharacteristic
76C3×C4⋊Dic5C2311yescharacteristic
77C3×#683—21no—
78C3×C4×Dic5—21no—
79C3×#677—22no—
80Dic3⋊Dic5—22no—
81#6669—22no—
82#6669—22no—
83#6669—22no—
84#6665—22no—
85Dic3×Dic5—22no—
86#6655—24no—
87#5567—51no—
88D4×Dic6—51no—
89C3×C4×SD16—51no—
90#5162—52no—
91#5020—51no—
92#5019—51no—
93#4854—52no—
94#4792—52no—
95#4758—52no—
96#4681D511yescharacteristic, complemented
97C8×Dic6—51no—
98C2×Q8×D5—61no—
99C5×C4⋊Q8—31no—
100C5×C4⋊Q8—31no—
101#4092—61no—
102Q8×Dic5—32no—
103#4090—32no—
104C2×#688—32no—
105C2×#677C2×D311yescharacteristic
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×Dic10C2×D311yescharacteristic
115C5×#103—32no—
116C5×#103—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3967—32no—
119#3953C2×D311yescharacteristic
120#3949C2×D311yescharacteristic
121#3948C2×D311yescharacteristic
122#3946—32no—
123C8×Dic5—32no—
124#3942—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3359—151noSylow
128C22×C3×D5—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—22no—
137C5×Dic6—22no—
138C5×Dic6—22no—
139C5×Dic6—42no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—21no—
143C3×D20—21no—
144C3×D20#4112yes—
145C3×C4×D5—42no—
146C3×Dic10—21no—
147C3×Dic10—21no—
148#1204—44no—
149D5×Dic3—44no—
150C3×C5×C8—21no—
151C3×C5×C8—21no—
152C3⋊#168—22no—
153C22×Dic6—101no—
154C2×C3×SD16—51no—
155C3×C4×Q8—51no—
156C3×C4×D4—51no—
157#944—52no—
158D4×Dic3—52no—
159C2×#214—52no—
160#924—101no—
161#889—102no—
162#888—52no—
163#887—52no—
164#878—102no—
165#870—101no—
166#869C2×D511yescharacteristic
167#869C2×D511yescharacteristic
168C4×Dic6—51no—
169C4×Dic6—101no—
170C3×#106—51no—
171C3×#103—51no—
172C3×#102—51no—
173C3×C4×C8C2×D511yescharacteristic
174#835—52no—
175#816C2×D512yes—
176#816C2×D512yes—
177Dic3⋊C8—52no—
178C8×Dic3—52no—
179#810—52no—
180#808—52no—
181C4⋊(C3⋊C8)—51no—
182C2×C5×Q8—32no—
183C2×C5×Q8—61no—
184Q8×D5—124no—
185C2×D20C22×D311yescharacteristic
186C2×C4×D5—21no—
187C2×C4×D5—62no—
188C2×Dic10—31no—
189C2×Dic10—62no—
190C2×Dic10C22×D311yescharacteristic
191C2×C5×C8C22×D311yescharacteristic
192C2×C5×C8C22×D311yescharacteristic
193C5×C4⋊C4—32no—
194C5×C4⋊C4—61no—
195C5×C4⋊C4—61no—
196C5×C4⋊C4—61no—
197C42×C5C22×D311yescharacteristic
198#688—64no—
199#685—21no—
200#685—62no—
201C4⋊Dic5—31no—
202C4⋊Dic5—62no—
203C4⋊Dic5C22×D311yescharacteristic
204C4⋊Dic5C22×D311yescharacteristic
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—32no—
214#677—22no—
215#557—151no—
216D4×Q8—151no—
217#487—31no—
218#487—152no—
219#475—152no—
220#475—151no—
221#461—152no—
222#461—151no—
223C8×Q8—151no—
224C4×SD16—51no—
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×C5C2×SD1612yes—
232C3×C4×C5C2×#4111yescharacteristic
233C3×C4×C52−1+411yescharacteristic
234Dic15—22no—
235Dic15C2×SD1614yes—
236C3×Dic5—41no—
237C3×Dic5—41no—
238C3×Dic5—41no—
239C5×Dic3—42no—
240C5×Dic3—42no—
241C2×C3×Q8—51no—
242C2×C3×D4—51no—
243C22×C3×C4—101no—
244C22×Dic3—102no—
245C2×Dic6—21no—
246C2×Dic6—51no—
247C2×Dic6—102no—
248C2×Dic6—204no—
249C2×Dic6C22×D512yes—
250C3×SD16—102no—
251C2×C3×C8C22×D511yescharacteristic
252C2×C3×C8C22×D511yescharacteristic
253C3×C4⋊C4—51no—
254C3×C4⋊C4—51no—
255C3×C4⋊C4—101no—
256C3×C22⋊C4—101no—
257C3×C42—101no—
258C3×C42C22×D511yescharacteristic
259#217—102no—
260#214—104no—
261C4⋊Dic3—21no—
262C4⋊Dic3—21no—
263C4⋊Dic3—21no—
264C4⋊Dic3—51no—
265C4⋊Dic3C22×D512yes—
266Dic3⋊C4—52no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269Dic3⋊C4—102no—
270Dic3⋊C4—102no—
271C4×Dic3—52no—
272C4×Dic3—102no—
273C2×C3⋊C8—52no—
274C22×D5—21no—
275C5×Q8—62no—
276C5×Q8—62no—
277C5×Q8—122no—
278C2×C4×C5—62no—
279C2×C4×C5—62no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—21no—
286C2×Dic5—32no—
287C2×Dic5—32no—
288D20—21no—
289D20#23512yes—
290C4×D5—42no—
291C4×D5—124no—
292Dic10—21no—
293Dic10—21no—
294Dic10—34no—
295Dic10—124no—
296C5×C8—21no—
297C5×C8—21no—
298#168—62no—
299C22×Q8—301no—
300C2×SD16—51no—
301C2×SD16—152no—
302C4⋊Q8—31no—
303C4⋊Q8—31no—
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—51no—
315C4×D4—152no—
316#106—51no—
317#106—152no—
318C4⋊C8—152no—
319C4⋊C8—151no—
320#103—32no—
321#103—32no—
322#103—51no—
323#103—152no—
324#103—152no—
325#102—51no—
326C4×C8—152no—
327C4×C8D3×D511yescharacteristic
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331C3×D5—42no—
332C23×C3—101no—
333C3×Q8—101no—
334C3×Q8—101no—
335C3×D4—52no—
336C3×D4—101no—
337C2×C3×C4—101no—
338C2×C3×C4—101no—
339C2×C3×C4—101no—
340C2×C3×C4—202no—
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4C23×D511yescharacteristic
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—52no—
347C2×Dic3—52no—
348C2×Dic3—204no—
349Dic6—22no—
350Dic6—22no—
351Dic6—42no—
352Dic6—54no—
353Dic6—204no—
354C3×C8—21no—
355C3×C8—21no—
356C3⋊C8—102no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—22no—
359C2×D5—41no—
360C2×D5—41no—
361C4×C5—21no—
362C4×C5—122no—
363C4×C5—122no—
364C4×C5D3×SD1612yes—
365C4×C5C2×#23511yescharacteristic
366C4×C5#101011yescharacteristic
367Dic5—34no—
368Dic5—41no—
369Dic5—41no—
370Dic5—41no—
371Dic5—62no—
372C2×Q8—32no—
373C2×Q8—51no—
374C2×Q8—61no—
375C2×Q8—151no—
376C2×Q8—302no—
377C2×Q8—604no—
378C2×D4—51no—
379C22×C4—101no—
380C22×C4—302no—
381SD16—102no—
382SD16—304no—
383C2×C8—152no—
384C2×C8C2×D3×D511yescharacteristic
385C2×C8C2×D3×D511yescharacteristic
386C4⋊C4—32no—
387C4⋊C4—51no—
388C4⋊C4—51no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—61no—
392C4⋊C4—101no—
393C4⋊C4—152no—
394C4⋊C4—151no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—302no—
398C4⋊C4—302no—
399C22⋊C4—101no—
400C22⋊C4—302no—
401C42—101no—
402C42—152no—
403C42—302no—
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—201no—
412C3×C4—201no—
413C3×C4—201no—
414C3×C4D5×SD1612yes—
415C3×C4D5×#4111yescharacteristic
416C3×C4#415011yescharacteristic
417Dic3—42no—
418Dic3—42no—
419Dic3—54no—
420Dic3—102no—
421C2×C5#555211yescharacteristic
422C2×C5C2×D3×SD1611yescharacteristic
423C2×C5#577111yescharacteristic
424D5—42no—
425C23—101no—
426Q8—62no—
427Q8—62no—
428Q8—101no—
429Q8—101no—
430Q8—122no—
431Q8—154no—
432Q8—604no—
433D4—52no—
434D4—101no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—101no—
438C2×C4—101no—
439C2×C4—101no—
440C2×C4—152no—
441C2×C4—152no—
442C2×C4—202no—
443C2×C4—604no—
444C2×C4#677711yescharacteristic
445C2×C4#677711yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—21no—
448C8—21no—
449C8—302no—
450C2×C3—202no—
451C2×C3#6601111yescharacteristic
452C2×C3C2×D5×SD1611yescharacteristic
453C2×C3#6610011yescharacteristic
454C5#7961911yescharacteristic, complemented, Sylow
455C22—102no—
456C22—201no—
457C22—201no—
458C22C2×#677711yescharacteristic
459C4—21no—
460C4—122no—
461C4—122no—
462C4—154no—
463C4—201no—
464C4—201no—
465C4—201no—
466C4—302no—
467C4#9125512yes—
468C4#9200111yescharacteristic
469C4D5×#23511yescharacteristic
470C3#1061335111yescharacteristic, complemented, Sylow
471C2—202no—
472C2#1175255311yescharacteristic
473C2C2×#9125511yescharacteristic
474C2#1175400811yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D20C23
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. C8×Dic30C2semidirect
4. C5×#4681C2semidirect
6. #11748036C2semidirect
7. #11747881C2semidirect
11. #11746918C2semidirect
96. #4681D5semidirect
134. Dic30SD16semidirect
405. C3×C5#3359semidirect
454. C5#79619semidirect
470. C3#10613351semidirect

Maximal subgroups

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

subgroupindex
#117525522
#117524872
C8×Dic302
C5×#46812
C3×C4×#6772
#117480362
#117478812
#117477492
#117477352
#117470592
#117469182
#106133513
#796195