Finite Group Databasebeta

← #14471962

Subgroups — #14471962

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#11756481C211yesmaximal, characteristic, complemented
2#11752554C211yesmaximal, characteristic
3C5×#5084C211yesmaximal, characteristic, complemented
4C3×#65377C211yesmaximal, characteristic, complemented
5#11747408C212yesmaximal, complemented
6#11747407C212yesmaximal, complemented
7#11747255C212yesmaximal, complemented
8#11747227C212yesmaximal, complemented
9#11747083C211yesmaximal, characteristic, complemented
10C4×#6659C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612821—31nomaximal, Hall
13C2×#6765—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91833—22no—
16#91777—21no—
17#91777C2212yes—
18#91776—21no—
19#91776C2212yes—
20C4×Dic30C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C4×C5×D12C2211yescharacteristic
23C3×#4020C2211yescharacteristic
24#91463C2212yes—
25#91456—21no—
26#91434C2212yes—
27#91408—22no—
28C2×#6659C2211yescharacteristic
29C2×#6657C2212yes—
30C5×#809C2212yes—
31C5×#808C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#3941C2212yes—
34C3×#3941C2212yes—
35C3×C4×#168C2211yescharacteristic
36#90985C2211yescharacteristic
37#90983C2212yes—
38#90975C2211yescharacteristic
39#90967C2211yescharacteristic
40#90965C2212yes—
41#90951C2212yes—
42#81588—51nomaximal, Hall
43#66056—31no—
44#65887—31no—
45C5×#476—31no—
46#65377D311yescharacteristic, complemented
47C4×#687—31no—
48#65159—32no—
49#65141—32no—
50#65137—31no—
51#65119—31no—
52#65051—32no—
53#65049—32no—
54C2×C3×C5×Q8—21no—
55C2×Dic30—22no—
56C2×Dic30D411yescharacteristic
57C2×Dic30C2311yescharacteristic
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C3×D20—21no—
61C2×C3×D20—21no—
62C2×C3×D20C2312yes—
63C2×#1201—22no—
64C2×#1201—22no—
65C2×D5×Dic3—22no—
66#6765—44no—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4C2312yes—
69C3×C42×C5C2311yescharacteristic
70C4⋊Dic15D411yescharacteristic
71C4⋊Dic15C2311yescharacteristic
72#6712—21no—
73#6712—22no—
74#6712—22no—
75#6712D412yes—
76C4×Dic15—21no—
77C4×Dic15—22no—
78C4×Dic15C2312yes—
79C5×(C2×D3)⋊C4—21no—
80C5×C4⋊Dic3C2311yescharacteristic
81C2×C5×C3⋊C8C2312yes—
82C2×C3×#168C2311yescharacteristic
83C2×C3×#168C2311yescharacteristic
84#6665—22no—
85#6659—22no—
86#6657—24no—
87#5722—51no—
88#5718—51no—
89C3×#486—51no—
90#5084D511yescharacteristic, complemented
91#5075—51no—
92#4762—52no—
93#4761—52no—
94#4760—52no—
95#4758—52no—
96C4×#204—51no—
97C8×Dic6—51no—
98C2×#709—61no—
99C5×C4⋊Q8C2×D311yescharacteristic
100C4×C5×D4—31no—
101#4090—62no—
102#4086—32no—
103C2×#687—31no—
104#4076—61no—
105C2×#677—32no—
106#4039—32no—
107#4034—32no—
108#4034—61no—
109#4033—32no—
110#4033—61no—
111#4030—62no—
112#4020C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—31no—
115C5×#106—32no—
116C5×C4⋊C8—31no—
117C5×#102—32no—
118#3964—31no—
119#3953—32no—
120#3946—32no—
121C8×Dic5—32no—
122#3942—31no—
123#3941C2×D312yes—
124#3941C2×D312yes—
125#3940—31no—
126C4×#168C2×D311yescharacteristic
127#3362—151noSylow
128C22×C5×D3—21no—
129C22×C3×D5—22no—
130C3×C5×Q8—81no—
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—82no—
141Dic30SD1614yescomplemented
142Dic30#4112yescomplemented
143C2×C5×Dic3—21no—
144C5×D12—21no—
145C5×D12—21no—
146C4×C5×D3—42no—
147C3×D20—22no—
148C3×D20—22no—
149C3×D20—42no—
150C3×D20—81no—
151#1201—44no—
152#1201—82no—
153D5×Dic3—44no—
154C3×#168—21no—
155C3×#168—21no—
156C5×C3⋊C8—22no—
157C2×#237—101no—
158C3×C4⋊Q8C2×D511yescharacteristic
159C3×#127—51no—
160#944—102no—
161#940—52no—
162#939—102no—
163#938—101no—
164D4×Dic3—52no—
165C2×#214—52no—
166C2×#204—51no—
167#888—52no—
168#888—101no—
169#887—52no—
170#887—101no—
171C4×D12C2×D511yescharacteristic
172C4×Dic6—51no—
173C4×Dic6—51no—
174C3×#102—52no—
175C3×#102—52no—
176C3×C4×C8—51no—
177#832—52no—
178#821—51no—
179#817—51no—
180#816—51no—
181Dic3⋊C8—52no—
182C8×Dic3—52no—
183#809C2×D512yes—
184#808C2×D512yes—
185C4⋊(C3⋊C8)C2×D511yescharacteristic
186C2×C5×Q8—21no—
187C2×C5×D4—31no—
188C22×C4×C5—61no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191#709—124no—
192C2×D20—21no—
193C2×D20—21no—
194C2×D20C22×D312yes—
195C2×C4×D5—62no—
196C2×Dic10—31no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C2×C5×C8—32no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—31no—
202C5×C4⋊C4C22×D312yes—
203C5×C22⋊C4—61no—
204C42×C5C22×D311yescharacteristic
205#687—62no—
206#685—62no—
207C4⋊Dic5—31no—
208C4⋊Dic5—31no—
209#683—32no—
210#683—62no—
211#683—62no—
212#683—61no—
213C4×Dic5—32no—
214C4×Dic5—62no—
215C4×Dic5—61no—
216C2×#168C22×D311yescharacteristic
217C2×#168C22×D311yescharacteristic
218#677—64no—
219Q82—151no—
220#550—151no—
221#486—51no—
222#486—152no—
223#476—31no—
224#476—152no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—151no—
229C4×SD16—152no—
230C22×C3×C5C22×D411yescharacteristic
231C2×C5×D3—41no—
232C2×C5×D3—41no—
233C2×C5×D3—41no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—42no—
237C3×C4×C5—21no—
238C3×C4×C5—42no—
239C3×C4×C5C2×SD1612yes—
240C3×C4×C5C2×#4111yescharacteristic
241C3×C4×C52−1+411yescharacteristic
242Dic15—22no—
243Dic15—22no—
244Dic15—41no—
245Dic15C2×SD1614yes—
246C5×Dic3—41no—
247C2×C3×Q8—21no—
248C2×C3×D4—52no—
249C2×C3×D4—101no—
250C2×C3×D4—101no—
251C2×#67—102no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—204no—
255C2×D12C22×D511yescharacteristic
256C2×C4×D3—21no—
257C2×Dic6—51no—
258C2×Dic6—51no—
259C2×Dic6—102no—
260C2×C3×C8—51no—
261C2×C3×C8—51no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4C22×D512yes—
264C3×C42C22×D511yescharacteristic
265#217—102no—
266#214—104no—
267(C2×D3)⋊C4—21no—
268C4⋊Dic3—51no—
269C4⋊Dic3—51no—
270C4⋊Dic3C22×D511yescharacteristic
271Dic3⋊C4—52no—
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274Dic3⋊C4—101no—
275C4×Dic3—52no—
276C4×Dic3—102no—
277C4×Dic3—101no—
278C2×C3⋊C8C22×D512yes—
279#204—102no—
280C23×C5—61no—
281C22×D5—22no—
282C5×Q8—81no—
283C5×D4—61no—
284C5×D4—61no—
285C2×C4×C5—22no—
286C2×C4×C5—61no—
287C2×C4×C5—122no—
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—124no—
292C22⋊D5—242no—
293C2×Dic5—32no—
294C2×Dic5—32no—
295C2×Dic5—61no—
296C2×Dic5—61no—
297D20—22no—
298D20—22no—
299D20—42no—
300D20—81no—
301C4×D5—124no—
302Dic10—34no—
303Dic10—32no—
304Dic10—61no—
305Dic10—242no—
306C5×C8—62no—
307#168—21no—
308#168—21no—
309C2×#41—301no—
310C2×SD16—152no—
311C2×SD16—151no—
312C4⋊Q8—152no—
313C4⋊Q8—301no—
314C4⋊Q8—302no—
315C4⋊Q8D3×D511yescharacteristic
316#127—51no—
317#127—152no—
318#121—302no—
319#121—301no—
320C4×Q8—151no—
321C4×Q8—152no—
322C4×Q8—151no—
323C4×Q8—301no—
324C4×D4—31no—
325C4×D4—152no—
326#106—32no—
327#106—151no—
328C4⋊C8—31no—
329C4⋊C8—152no—
330#103—151no—
331#102—32no—
332#102—52no—
333#102—52no—
334#102—152no—
335#102—151no—
336C4×C8—51no—
337C4×C8—152no—
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341C3×D5—82no—
342C5×D3—81no—
343C23×C3—102no—
344C22×D3—21no—
345C3×Q8—81no—
346C3×D4—102no—
347C3×D4—102no—
348C3×D4—202no—
349C3×D4—401no—
350C2×C3×C4—22no—
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355#67—402no—
356C2×Dic3—21no—
357C2×Dic3—52no—
358C2×Dic3—52no—
359C2×Dic3—101no—
360C2×Dic3—101no—
361C2×Dic3—204no—
362D12—21no—
363D12—21no—
364C4×D3—42no—
365Dic6—54no—
366Dic6—52no—
367Dic6—101no—
368Dic6—402no—
369C3×C8—101no—
370C3×C8—101no—
371C3⋊C8—22no—
372C22×C5—121no—
373C22×C5—121no—
374C22×C5—121no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—42no—
377C2×D5—42no—
378C2×D5—42no—
379C4×C5—21no—
380C4×C5—42no—
381C4×C5—121no—
382C4×C5D3×SD1612yes—
383C4×C5D3×#4111yescharacteristic
384C4×C5#101011yescharacteristic
385Dic5—34no—
386Dic5—62no—
387Dic5—62no—
388Dic5—121no—
389#41—604no—
390C2×Q8—21no—
391C2×Q8—151no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—31no—
395C2×D4—52no—
396C2×D4—101no—
397C2×D4—101no—
398C2×D4—302no—
399C2×D4—302no—
400C22×C4—61no—
401C22×C4—302no—
402SD16—304no—
403SD16—302no—
404C2×C8—32no—
405C2×C8—51no—
406C2×C8—51no—
407C4⋊C4—21no—
408C4⋊C4—31no—
409C4⋊C4—152no—
410C4⋊C4—151no—
411C4⋊C4—151no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C2×D3×D512yes—
416C22⋊C4—61no—
417C22⋊C4—302no—
418C42—152no—
419C42—302no—
420C42—301no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—202no—
424C22×C3—202no—
425C22×C3—202no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C3×C4—21no—
431C3×C4—42no—
432C3×C4D5×SD1612yes—
433C3×C4#414711yescharacteristic
434C3×C4D5×#4111yescharacteristic
435Dic3—41no—
436Dic3—54no—
437Dic3—102no—
438Dic3—102no—
439Dic3—201no—
440C2×C5—241no—
441C2×C5#567711yescharacteristic
442C2×C5#575711yescharacteristic
443C2×C5C2×D3×SD1611yescharacteristic
444D5—82no—
445C23—61no—
446C23—102no—
447Q8—81no—
448Q8—154no—
449Q8—152no—
450Q8—301no—
451Q8—1202no—
452D4—61no—
453D4—61no—
454D4—102no—
455D4—102no—
456D4—202no—
457D4—401no—
458D4—604no—
459D4—1202no—
460C2×C4—22no—
461C2×C4—61no—
462C2×C4—122no—
463C2×C4—152no—
464C2×C4—152no—
465C2×C4—301no—
466C2×C4—301no—
467C2×C4—604no—
468C2×C4#679011yescharacteristic
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—62no—
472C8—101no—
473C8—101no—
474C2×C3—402no—
475C2×C3#6596711yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477C2×C3#6610811yescharacteristic
478D3—81no—
479C5#8158811yescharacteristic, complemented, Sylow
480C22—121no—
481C22—121no—
482C22—121no—
483C22—202no—
484C22—202no—
485C22—202no—
486C22C2×#679011yescharacteristic
487C4—21no—
488C4—42no—
489C4—121no—
490C4—154no—
491C4—302no—
492C4—302no—
493C4—601no—
494C4#9150512yes—
495C4#9202811yescharacteristic
496C4#9203411yescharacteristic
497C3#1061282111yescharacteristic, complemented, Sylow
498C2—241no—
499C2—402no—
500C2#1175470311yescharacteristic
501C2C2×#9150511yescharacteristic
502C2#1175516611yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752554C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3362
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. #11756481C2semidirect
3. C5×#5084C2semidirect
4. C3×#65377C2semidirect
5. #11747408C2semidirect
6. #11747407C2semidirect
7. #11747255C2semidirect
8. #11747227C2semidirect
9. #11747083C2semidirect
10. C4×#6659C2semidirect
11. #11746851C2semidirect
46. #65377D3semidirect
90. #5084D5semidirect
141. Dic30SD16semidirect
142. Dic30#41semidirect
422. C3×C5#3362semidirect
479. C5#81588semidirect
497. C3#10612821semidirect

Maximal subgroups

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

subgroupindex
#117564812
#117525542
C5×#50842
C3×#653772
#117474082
#117474072
#117472552
#117472272
#117470832
C4×#66592
#117468512
#106128213
#815885