Finite Group Databasebeta

← #14471943

Subgroups — #14471943

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752680C211yesmaximal, characteristic
2#11752473C211yesmaximal, characteristic, complemented
3C8×Dic30C211yesmaximal, characteristic, complemented
4C5×#4694C211yesmaximal, characteristic, complemented
5C3×C4×#677C211yesmaximal, characteristic, complemented
6#11748011C212yesmaximal, complemented
7#11747993C212yesmaximal, complemented
8#11747808C212yesmaximal, complemented
9#11747737C212yesmaximal, complemented
10#11747060C211yesmaximal, characteristic, complemented
11#11746880C211yesmaximal, characteristic, complemented
12#10613319—31nomaximal, Hall
13C2×#6772—21no—
14C4×Dic30C2211yescharacteristic
15C5×#874C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C2×C3×#677C2211yescharacteristic
18C3×C4×D20C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20#91470C2212yes—
21#91468—21no—
22#91463C2212yes—
23#91453—22no—
24#91449—21no—
25#91435C2212yes—
26#91333—21no—
27#91331C2212yes—
28#91329—22no—
29C2×#6656C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#821C2212yes—
35C5×#821C2212yes—
36C3×#3953C2211yescharacteristic
37C3×#3949C2211yescharacteristic
38C3×#3948C2211yescharacteristic
39#90986C2212yes—
40#90966C2212yes—
41#90964C2212yes—
42#79622—51nomaximal, Hall
43#66056—31no—
44#66052—31no—
45C5×#486—31no—
46#65373—31no—
47#65364—31no—
48#65051—32no—
49#65050—32no—
50#65049—32no—
51#65047—32no—
52C4×#677D311yescharacteristic, complemented
53C8×Dic10—31no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12—21no—
56C2×C5×D12—21no—
57C2×C5×D12C2312yes—
58C2×C5×Dic6—21no—
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×Dic10C2311yescharacteristic
62C2×#1204—22no—
63C2×#1201—22no—
64C2×#1201—22no—
65C2×D3×Dic5—22no—
66#6772—44no—
67C2×C3×C5×C8C2311yescharacteristic
68C2×C3×C5×C8C2311yescharacteristic
69C3×C42×C5C2311yescharacteristic
70C4⋊Dic15D411yescharacteristic
71#6712D412yes—
72C4×Dic15C2312yes—
73C2×C3⋊#168C2312yes—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C3×#685—21no—
77C3×C4⋊Dic5C2311yescharacteristic
78C3×C4⋊Dic5C2311yescharacteristic
79C3×#683—21no—
80C3×C4×Dic5—21no—
81C3×#677—22no—
82#6669—22no—
83#6668—22no—
84(C2×D3)⋊Dic5—22no—
85Dic3×Dic5—22no—
86#6656—24no—
87Q8×Dic6—51no—
88#5553—51no—
89C3×C4×SD16—51no—
90#5163—52no—
91#5027—51no—
92#5008—51no—
93#4870—52no—
94#4788—52no—
95#4760—52no—
96#4694D511yescharacteristic, complemented
97C8×Dic6—51no—
98C2×#711—61no—
99C5×C4⋊Q8—31no—
100C5×#127—31no—
101#4090—62no—
102#4086—32no—
103#4085—62no—
104#4084—61no—
105D4×Dic5—32no—
106C2×#687—32no—
107C2×#677C2×D311yescharacteristic
108#4034—32no—
109#4034—61no—
110#4033—32no—
111#4033—61no—
112C4×D20C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10C2×D311yescharacteristic
115C5×#102—32no—
116C5×#102—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3964—32no—
119#3953C2×D311yescharacteristic
120#3949C2×D311yescharacteristic
121#3948C2×D311yescharacteristic
122#3946—32no—
123C8×Dic5—32no—
124#3941—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3362—151noSylow
128C22×C5×D3—22no—
129C22×C3×D5—21no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15C2×D412yes—
134C2×Dic15C2×D412yes—
135Dic30SD1614yescomplemented
136C2×C5×Dic3—22no—
137C5×D12—22no—
138C5×D12—22no—
139C5×D12—42no—
140C5×D12—81no—
141C5×Dic6—81no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C3×D20—21no—
146C3×D20—21no—
147C3×C4×D5—42no—
148C3×Dic10—21no—
149C3×Dic10#4112yescomplemented
150#1204—82no—
151#1201—44no—
152#1201—82no—
153D3×Dic5—44no—
154C3×C5×C8—21no—
155C3×C5×C8—21no—
156C3⋊#168—22no—
157C2×#235—101no—
158C2×C3×SD16—51no—
159C3×C4×Q8—51no—
160C3×C4×D4—51no—
161Q8×Dic3—52no—
162C2×#215—52no—
163#940—52no—
164#930—101no—
165#893—52no—
166#888—52no—
167#888—102no—
168#884—102no—
169#874C2×D511yescharacteristic
170#869—101no—
171#869C2×D511yescharacteristic
172C4×Dic6—51no—
173C4×Dic6—101no—
174C3×#106—51no—
175C3×#103—51no—
176C3×#102—51no—
177C3×C4×C8C2×D511yescharacteristic
178#832—52no—
179#821C2×D512yes—
180#821C2×D512yes—
181Dic3⋊C8—52no—
182C8×Dic3—52no—
183#809—52no—
184#808—52no—
185C4⋊(C3⋊C8)—51no—
186C2×C5×Q8—61no—
187C2×C5×D4—32no—
188C2×C5×D4—61no—
189C2×C5×D4—61no—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192C22×Dic5—62no—
193#711—124no—
194C2×D20C22×D311yescharacteristic
195C2×C4×D5—21no—
196C2×Dic10—31no—
197C2×Dic10—62no—
198C2×Dic10C22×D311yescharacteristic
199C2×C5×C8C22×D311yescharacteristic
200C2×C5×C8C22×D311yescharacteristic
201C5×C4⋊C4—32no—
202C5×C4⋊C4—61no—
203C42×C5C22×D311yescharacteristic
204C22⋊Dic5—62no—
205#687—64no—
206#685—21no—
207C4⋊Dic5—31no—
208C4⋊Dic5C22×D311yescharacteristic
209C4⋊Dic5C22×D311yescharacteristic
210#683—21no—
211#683—32no—
212#683—62no—
213#683—62no—
214C4×Dic5—21no—
215C4×Dic5—32no—
216C4×Dic5—62no—
217C2×#168—32no—
218#677—22no—
219Q82—151no—
220#550—151no—
221#486—31no—
222#486—152no—
223#476—152no—
224#476—151no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—51no—
229C4×SD16—152no—
230C22×C3×C5C22×D411yescharacteristic
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C2×C5×D3—42no—
234C2×C3×D5—41no—
235C2×C3×D5—41no—
236C2×C3×D5—41no—
237C3×C4×C5—21no—
238C3×C4×C5C2×SD1612yes—
239C3×C4×C5C2×#4111yescharacteristic
240C3×C4×C52−1+411yescharacteristic
241Dic15—22no—
242Dic15C2×SD1614yes—
243C3×Dic5—22no—
244C3×Dic5—41no—
245C3×Dic5—41no—
246C5×Dic3—42no—
247C2×C3×Q8—51no—
248C2×C3×D4—51no—
249C22×C3×C4—101no—
250C2×#67—102no—
251C2×#67—102no—
252#235—204no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12C22×D512yes—
256C2×C4×D3—102no—
257C2×Dic6—21no—
258C2×Dic6—51no—
259C2×Dic6—102no—
260C3×SD16—102no—
261C2×C3×C8C22×D511yescharacteristic
262C2×C3×C8C22×D511yescharacteristic
263C3×C4⋊C4—51no—
264C3×C4⋊C4—51no—
265C3×C4⋊C4—101no—
266C3×C22⋊C4—101no—
267C3×C42—101no—
268C3×C42C22×D511yescharacteristic
269#215—104no—
270(C2×D3)⋊C4—102no—
271C4⋊Dic3—21no—
272C4⋊Dic3—51no—
273C4⋊Dic3—102no—
274C4⋊Dic3C22×D512yes—
275Dic3⋊C4—52no—
276Dic3⋊C4—102no—
277C4×Dic3—52no—
278C4×Dic3—102no—
279C2×C3⋊C8—52no—
280C23×C5—62no—
281C22×D5—21no—
282C5×Q8—241no—
283C5×D4—62no—
284C5×D4—62no—
285C5×D4—122no—
286C5×D4—241no—
287C2×C4×C5—62no—
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—124no—
292C22⋊D5—242no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—32no—
297C2×Dic5—32no—
298C2×Dic5—124no—
299D20—21no—
300D20—21no—
301C4×D5—42no—
302Dic10—21no—
303Dic10—34no—
304Dic10—242no—
305Dic10#23512yescomplemented
306C5×C8—21no—
307C5×C8—21no—
308#168—62no—
309C2×#41—301no—
310C2×SD16—51no—
311C2×SD16—152no—
312C4⋊Q8—31no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—31no—
317#127—152no—
318#121—302no—
319#121—301no—
320C4×Q8—51no—
321C4×Q8—151no—
322C4×Q8—152no—
323C4×Q8—301no—
324C4×D4—51no—
325C4×D4—152no—
326#106—51no—
327#106—152no—
328C4⋊C8—152no—
329C4⋊C8—151no—
330#103—51no—
331#102—32no—
332#102—32no—
333#102—51no—
334#102—152no—
335#102—152no—
336C4×C8—152no—
337C4×C8D3×D511yescharacteristic
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341C3×D5—81no—
342C5×D3—82no—
343C23×C3—101no—
344C22×D3—22no—
345C3×Q8—52no—
346C3×Q8—101no—
347C3×D4—101no—
348C3×D4—101no—
349C2×C3×C4—101no—
350C2×C3×C4—101no—
351C2×C3×C4—101no—
352C2×C3×C4—202no—
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4C23×D511yescharacteristic
356#67—204no—
357#67—402no—
358C2×Dic3—22no—
359C2×Dic3—52no—
360C2×Dic3—52no—
361D12—22no—
362D12—22no—
363D12—42no—
364D12—81no—
365C4×D3—204no—
366Dic6—54no—
367Dic6—81no—
368Dic6—402no—
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—102no—
372C22×C5—122no—
373C22×C5—122no—
374C22×C5—122no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—41no—
377C2×D5—41no—
378C2×D5—41no—
379C4×C5—21no—
380C4×C5—122no—
381C4×C5D3×SD1612yes—
382C4×C5C2×#23511yescharacteristic
383C4×C5#101011yescharacteristic
384Dic5—22no—
385Dic5—34no—
386Dic5—41no—
387Dic5—41no—
388Dic5—62no—
389#41—604no—
390C2×Q8—51no—
391C2×Q8—61no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—32no—
395C2×D4—51no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—302no—
399C2×D4—302no—
400C22×C4—101no—
401C22×C4—302no—
402SD16—102no—
403SD16—304no—
404C2×C8—152no—
405C2×C8C2×D3×D511yescharacteristic
406C2×C8C2×D3×D511yescharacteristic
407C4⋊C4—32no—
408C4⋊C4—51no—
409C4⋊C4—51no—
410C4⋊C4—61no—
411C4⋊C4—101no—
412C4⋊C4—152no—
413C4⋊C4—151no—
414C4⋊C4—302no—
415C4⋊C4—302no—
416C22⋊C4—101no—
417C22⋊C4—302no—
418C42—101no—
419C42—152no—
420C42—302no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—201no—
424C22×C3—201no—
425C22×C3—201no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C3×C4—21no—
431C3×C4—102no—
432C3×C4—201no—
433C3×C4—201no—
434C3×C4D5×SD1612yes—
435C3×C4D5×#4111yescharacteristic
436C3×C4#415011yescharacteristic
437Dic3—42no—
438Dic3—54no—
439Dic3—102no—
440C2×C5—242no—
441C2×C5#555211yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443C2×C5#576911yescharacteristic
444D5—81no—
445C23—62no—
446C23—101no—
447Q8—52no—
448Q8—101no—
449Q8—154no—
450Q8—241no—
451Q8—1202no—
452D4—62no—
453D4—62no—
454D4—101no—
455D4—101no—
456D4—122no—
457D4—241no—
458D4—604no—
459D4—1202no—
460C2×C4—62no—
461C2×C4—101no—
462C2×C4—101no—
463C2×C4—101no—
464C2×C4—152no—
465C2×C4—152no—
466C2×C4—202no—
467C2×C4—604no—
468C2×C4#677711yescharacteristic
469C2×C4#677711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—21no—
472C8—21no—
473C8—302no—
474C2×C3—401no—
475C2×C3#6601111yescharacteristic
476C2×C3#6609111yescharacteristic
477C2×C3C2×D5×SD1611yescharacteristic
478D3—82no—
479C5#7962211yescharacteristic, complemented, Sylow
480C22—122no—
481C22—122no—
482C22—122no—
483C22—201no—
484C22—201no—
485C22—201no—
486C22C2×#677711yescharacteristic
487C4—21no—
488C4—102no—
489C4—122no—
490C4—154no—
491C4—201no—
492C4—201no—
493C4—302no—
494C4#9125512yes—
495C4#9200111yescharacteristic
496C4D5×#23511yescharacteristic
497C3#1061331911yescharacteristic, complemented, Sylow
498C2—242no—
499C2—401no—
500C2#1175255311yescharacteristic
501C2C2×#9125511yescharacteristic
502C2#1175398311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11752680C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#3362
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. #11752473C2semidirect
3. C8×Dic30C2semidirect
4. C5×#4694C2semidirect
5. C3×C4×#677C2semidirect
6. #11748011C2semidirect
7. #11747993C2semidirect
8. #11747808C2semidirect
9. #11747737C2semidirect
10. #11747060C2semidirect
11. #11746880C2semidirect
52. C4×#677D3semidirect
96. #4694D5semidirect
135. Dic30SD16semidirect
149. C3×Dic10#41semidirect
305. Dic10#235semidirect
422. C3×C5#3362semidirect
479. C5#79622semidirect
497. C3#10613319semidirect

Maximal subgroups

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

subgroupindex
#117526802
#117524732
C8×Dic302
C5×#46942
C3×C4×#6772
#117480112
#117479932
#117478082
#117477372
#117470602
#117468802
#106133193
#796225