Finite Group Databasebeta

← #14430861

Subgroups — #14430861

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756278C211yesmaximal, characteristic, complemented
2C5×#5521C211yesmaximal, characteristic
3C3×#65288C211yesmaximal, characteristic, complemented
4#11748460C211yesmaximal, characteristic, complemented
5#11748458C211yesmaximal, characteristic, complemented
6#11748389C211yesmaximal, characteristic
7C2×#90967C211yesmaximal, characteristic
8#11746964C212yesmaximal, complemented
9#11746894C212yesmaximal, complemented
10#11746894C212yesmaximal, complemented
11#11746883C212yesmaximal, complemented
12#10614270—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C3×C5×#117C2211yescharacteristic
15#91815C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17#91779—21no—
18#91777—21no—
19#91767—22no—
20#91759C2212yescomplemented
21#91758C2212yescomplemented
22C5×#926C2211yescharacteristic
23C5×#893—21no—
24C5×#893—21no—
25C5×D3×C22⋊C4—22no—
26C4×C5×D12C2212yes—
27C4×C5×D12C2212yes—
28C2×C3×#681C2211yescharacteristic
29C22×C3×#168C2211yescharacteristic
30C3×C4⋊#168C2212yescomplemented
31C3×C4⋊#168C2212yescomplemented
32#90988C2211yescharacteristic, complemented
33#90988C2212yescomplemented
34#90988C2211yescharacteristic, complemented
35#90985C2211yescharacteristic, complemented
36#90985C2212yescomplemented
37#90985C2211yescharacteristic, complemented
38#90967C2212yes—
39#90967C2212yes—
40#90967C2212yes—
41#90967C2212yes—
42#79090—51nomaximal, Hall
43C5×#518—31no—
44#65853—31no—
45#65504—31no—
46C2×#3964—31no—
47#65298—32no—
48#65298—32no—
49#65297—32no—
50#65296—32no—
51#65288D311yescharacteristic, complemented
52#65287—31no—
53#65284—31no—
54C23×C5×D3—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C2×Dic30—22no—
58C2×C5×D12—21no—
59C2×C5×D12—22no—
60C2×C5×D12Q814yescomplemented
61C2×C5×D12C2312yes—
62C2×C4×C5×D3—22no—
63C2×C4×C5×D3—22no—
64C3×C5×C4⋊C4D411yescharacteristic
65C3×C5×C4⋊C4D411yescharacteristic
66C3×C5×C22⋊C4D412yes—
67C3×C42×C5C2312yes—
68#6719—21no—
69C4⋊Dic15—22no—
70C4⋊Dic15—21no—
71C4⋊Dic15C2311yescharacteristic
72C4⋊Dic15C2312yes—
73C4⋊Dic15C2311yescharacteristic
74#6712—22no—
75#6712—22no—
76C4×Dic15—21no—
77C5×#217—21no—
78C5×(C2×D3)⋊C4—22no—
79C5×(C2×D3)⋊C4—22no—
80C5×C4⋊Dic3C2311yescharacteristic
81C5×C4⋊Dic3C2311yescharacteristic
82C4×C5×Dic3—21no—
83C3×#681—22no—
84C2×C3×#168—22no—
85C2×C3×#168C2311yescharacteristic
86C2×C3×#168C2312yes—
87C2×C3×#168C2311yescharacteristic
88#5521D511yescharacteristic
89#5519—51no—
90C3×#424—51no—
91#5131—51no—
92#5121—51no—
93C2×#821—51no—
94#5106—51no—
95#4847—52no—
96#4847—52no—
97#4846—52no—
98#4842—52no—
99C22×C5×D4—31no—
100C4×C5×D4—32no—
101C4×C5×D4—32no—
102C4×C5×D4—61no—
103C4×C5×D4—61no—
104C5×#117—31no—
105C5×#117C2×D311yescharacteristic
106C2×C5×C22⋊C4—62no—
107#4072—31no—
108C2×C4⋊Dic5—31no—
109C2×#681C2×D311yescharacteristic
110C22×#168C2×D311yescharacteristic
111#4036—61no—
112#4034—61no—
113#4024—62no—
114#4016—32no—
115#4015—32no—
116#3964—32no—
117#3964—32no—
118#3964—32no—
119#3964—32no—
120#3940—32no—
121#3940—31no—
122#3940—31no—
123#3939—32no—
124#3939—31no—
125#3939—31no—
126C4⋊#168C2×D312yescomplemented
127C4⋊#168C2×D312yescomplemented
128#3081—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×C5×D3—22no—
131C22×C5×D3—24no—
132C22×C5×D3—81no—
133C22×C5×D3—81no—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×Q812yes—
138C2×C3×C4×C5#4112yes—
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143C2×Dic15—81no—
144Dic30—82no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—21no—
147C5×D12—24no—
148C5×D12—22no—
149C5×D12C2×Q814yes—
150C4×C5×D3—82no—
151C4×C5×D3—82no—
152C3×#168—21no—
153C3×#168—21no—
154C3×#168—22no—
155C22×D12C2×D511yescharacteristic
156C2×C3×M16—51no—
157C22×C3×C8—51no—
158C3×#117C2×D511yescharacteristic
159#926—51no—
160#926C2×D511yescharacteristic
161C2×C4⋊Dic3—51no—
162#893—21no—
163#893—21no—
164#890—101no—
165#888—101no—
166D3×C22⋊C4—22no—
167#878—102no—
168C4×D12C2×D512yes—
169C4×D12C2×D512yes—
170#870—52no—
171#869—52no—
172C3×C4⋊C8—52no—
173C3×C4⋊C8—52no—
174#821—52no—
175#821—52no—
176#821—52no—
177#821—52no—
178#818—52no—
179#818—51no—
180#818—51no—
181#817—52no—
182#817—51no—
183#817—51no—
184C24×C5—61no—
185C2×C5×D4—34no—
186C2×C5×D4—32no—
187C2×C5×D4—61no—
188C2×C5×D4—62no—
189C22×C4×C5—62no—
190C22×C4×C5—62no—
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—61no—
193C2×Dic10—62no—
194C5×C4⋊C4—31no—
195C5×C4⋊C4—31no—
196C5×C4⋊C4D1211yescharacteristic
197C5×C4⋊C4D1211yescharacteristic
198C5×C22⋊C4—61no—
199C5×C22⋊C4—62no—
200C5×C22⋊C4—62no—
201C5×C22⋊C4D1212yes—
202C42×C5—61no—
203C42×C5C22×D312yes—
204C22⋊Dic5—61no—
205C4⋊Dic5—31no—
206C4⋊Dic5—32no—
207C4⋊Dic5—31no—
208C4⋊Dic5—62no—
209C4⋊Dic5—61no—
210#683—62no—
211#683—62no—
212C4×Dic5—61no—
213#681—22no—
214C2×#168—22no—
215C2×#168C22×D311yescharacteristic
216C2×#168C22×D312yes—
217C2×#168C22×D311yescharacteristic
218#544—151no—
219#518—31no—
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428—151no—
225#427—151no—
226#424—51no—
227#418—151no—
228C2×#102—151no—
229C22×C3×C5—21no—
230C22×C3×C5—21no—
231C22×C3×C5C22⋊Q812yes—
232C22×C3×C5C22×D411yescharacteristic
233C2×C5×D3—24no—
234C2×C5×D3—42no—
235C2×C5×D3—42no—
236C2×C5×D3—84no—
237C3×C4×C5—22no—
238C3×C4×C5—22no—
239C3×C4×C5C22⋊Q812yes—
240C3×C4×C5C22×Q811yescharacteristic
241C3×C4×C5C2×#4111yescharacteristic
242Dic15—41no—
243Dic15—42no—
244Dic15—41no—
245C5×Dic3—41no—
246C5×Dic3—41no—
247C23×D3—21no—
248C22×C3×C4C22×D511yescharacteristic
249C22×Dic3—101no—
250C2×D12—22no—
251C2×D12—21no—
252C2×D12Dic1014yescomplemented
253C2×D12C22×D512yes—
254C2×C4×D3—22no—
255C2×C4×D3—22no—
256C2×Dic6—102no—
257C3×M16—102no—
258C2×C3×C8—51no—
259C2×C3×C8—52no—
260C2×C3×C8—51no—
261C2×C3×C8—102no—
262C3×C4⋊C4C22⋊D511yescharacteristic
263C3×C4⋊C4C22⋊D511yescharacteristic
264C3×C22⋊C4C22⋊D512yes—
265C3×C42C22×D512yes—
266#217—21no—
267#217—101no—
268(C2×D3)⋊C4—22no—
269(C2×D3)⋊C4—22no—
270C4⋊Dic3—51no—
271C4⋊Dic3—52no—
272C4⋊Dic3—51no—
273C4⋊Dic3—102no—
274C4⋊Dic3—101no—
275C4⋊Dic3C22×D511yescharacteristic
276C4⋊Dic3C22×D511yescharacteristic
277Dic3⋊C4—102no—
278Dic3⋊C4—102no—
279C4×Dic3—21no—
280C4×Dic3—101no—
281C23×C5—62no—
282C23×C5—64no—
283C23×C5—241no—
284C23×C5—241no—
285C23×C5C2×D1211yescharacteristic
286C5×D4—34no—
287C5×D4—64no—
288C5×D4—62no—
289C2×C4×C5—61no—
290C2×C4×C5—61no—
291C2×C4×C5—242no—
292C2×C4×C5—242no—
293C2×C4×C5C2×D1212yes—
294C2×C4×C5C2×D1212yes—
295C2×C4×C5C2×D1211yescharacteristic
296C2×C4×C5#23712yes—
297C2×C4×C5D3×Q812yes—
298C2×C4×C5C23×D311yescharacteristic
299C2×Dic5—61no—
300C2×Dic5—61no—
301C2×Dic5—62no—
302C2×Dic5—241no—
303Dic10—242no—
304#168—21no—
305#168—21no—
306#168—22no—
307C22×D4—31no—
308C2×M16—51no—
309C22×C8—51no—
310C4⋊Q8—152no—
311C4⋊Q8—301no—
312#125—152no—
313#125—301no—
314C22⋊Q8—302no—
315C4×D4—32no—
316C4×D4—32no—
317C4×D4—61no—
318C4×D4—61no—
319#117—31no—
320#117—151no—
321#117D3×D511yescharacteristic
322C2×C4⋊C4—151no—
323C2×C22⋊C4—62no—
324#107—151no—
325#107—151no—
326#107—152no—
327#106—151no—
328#106—151no—
329#106—152no—
330C4⋊C8—52no—
331C4⋊C8—52no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102—152no—
336C2×C3×C5—22no—
337C2×C3×C5C2×C22⋊Q811yescharacteristic
338C2×C3×C5#57611yescharacteristic
339C2×C3×C5#57711yescharacteristic
340C5×D3—44no—
341C23×C3C2×C22⋊D511yescharacteristic
342C22×D3—22no—
343C22×D3—24no—
344C22×D3—81no—
345C22×D3—81no—
346C2×C3×C4C2×Dic1012yes—
347C2×C3×C4#70912yes—
348C2×C3×C4C2×C22⋊D512yes—
349C2×C3×C4C2×C22⋊D512yes—
350C2×C3×C4C2×C22⋊D511yescharacteristic
351C2×C3×C4C23×D511yescharacteristic
352C2×Dic3—21no—
353C2×Dic3—21no—
354C2×Dic3—101no—
355C2×Dic3—101no—
356C2×Dic3—102no—
357C2×Dic3—401no—
358D12—22no—
359D12—24no—
360D12C2×Dic1014yes—
361C4×D3—82no—
362C4×D3—82no—
363Dic6—402no—
364C3×C8—101no—
365C3×C8—101no—
366C3×C8—102no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5—64no—
370C22×C5—122no—
371C22×C5—122no—
372C22×C5—244no—
373C22×C5#89712yes—
374C22×C5C22×D1211yescharacteristic
375C4×C5—22no—
376C4×C5—22no—
377C4×C5—121no—
378C4×C5—121no—
379C4×C5#89712yes—
380C4×C5C2×#23711yescharacteristic
381C4×C5C2×D3×Q811yescharacteristic
382Dic5—121no—
383Dic5—121no—
384Dic5—122no—
385C24—61no—
386C2×Q8—302no—
387C2×D4—34no—
388C2×D4—32no—
389C2×D4—62no—
390C2×D4—61no—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—301no—
394C22×C4C2×D3×D511yescharacteristic
395M16—102no—
396C2×C8—51no—
397C2×C8—52no—
398C2×C8—51no—
399C2×C8—102no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—152no—
403C4⋊C4—151no—
404C4⋊C4—151no—
405C4⋊C4—301no—
406C4⋊C4—302no—
407C4⋊C4—302no—
408C4⋊C4—302no—
409C4⋊C4#120311yescharacteristic
410C4⋊C4#120311yescharacteristic
411C22⋊C4—61no—
412C22⋊C4—62no—
413C22⋊C4—62no—
414C22⋊C4—301no—
415C22⋊C4#120312yes—
416C42—61no—
417C42—301no—
418C42C2×D3×D512yes—
419C3×C5#308111yescharacteristic, complemented, Hall
420C22×C3—21no—
421C22×C3—21no—
422C22×C3#407012yes—
423C22×C3C22×C22⋊D511yescharacteristic
424C2×D3—24no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—84no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4#407012yes—
431C3×C4C22×Dic1011yescharacteristic
432C3×C4C2×#70911yescharacteristic
433Dic3—41no—
434Dic3—41no—
435Dic3—201no—
436Dic3—202no—
437Dic3—201no—
438C2×C5—22no—
439C2×C5—124no—
440C2×C5C2×#89711yescharacteristic
441C2×C5#575111yescharacteristic
442C2×C5#575211yescharacteristic
443C23—62no—
444C23—64no—
445C23—241no—
446C23—241no—
447C23C2×#120311yescharacteristic
448Q8—1202no—
449D4—34no—
450D4—62no—
451D4—64no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—242no—
455C2×C4—242no—
456C2×C4—301no—
457C2×C4—301no—
458C2×C4—302no—
459C2×C4—1201no—
460C2×C4#676512yes—
461C2×C4D3×Dic1012yes—
462C2×C4C2×#120312yes—
463C2×C4C2×#120312yes—
464C2×C4C2×#120311yescharacteristic
465C2×C4C22×D3×D511yescharacteristic
466C8—101no—
467C8—101no—
468C8—102no—
469C2×C3—22no—
470C2×C3C2×#407011yescharacteristic
471C2×C3#6616911yescharacteristic
472C2×C3#6617011yescharacteristic
473D3—44no—
474C5#7909011yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—64no—
478C22—122no—
479C22—122no—
480C22—244no—
481C22#9136512yes—
482C22C22×#120311yescharacteristic
483C4—22no—
484C4—22no—
485C4—121no—
486C4—121no—
487C4—602no—
488C4—601no—
489C4—601no—
490C4#9136512yes—
491C4C2×#676511yescharacteristic
492C4C2×D3×Dic1011yescharacteristic
493C3#1061427011yescharacteristic, complemented, Sylow
494C2—22no—
495C2—124no—
496C2C2×#9136511yescharacteristic
497C2#1175530511yescharacteristic
498C2#1175530711yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×D12C22
hypercenter#117D3×D5
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756278C2semidirect
3. C3×#65288C2semidirect
4. #11748460C2semidirect
5. #11748458C2semidirect
8. #11746964C2semidirect
9. #11746894C2semidirect
10. #11746894C2semidirect
11. #11746883C2semidirect
20. #91759C22semidirect
21. #91758C22semidirect
30. C3×C4⋊#168C22semidirect
31. C3×C4⋊#168C22semidirect
32. #90988C22semidirect
33. #90988C22semidirect
34. #90988C22semidirect
35. #90985C22semidirect
36. #90985C22semidirect
37. #90985C22semidirect
51. #65288D3semidirect
60. C2×C5×D12Q8semidirect
126. C4⋊#168C2×D3semidirect
127. C4⋊#168C2×D3semidirect
252. C2×D12Dic10semidirect
419. C3×C5#3081semidirect
474. C5#79090semidirect
493. C3#10614270semidirect

Maximal subgroups

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

subgroupindex
#117562782
C5×#55212
C3×#652882
#117484602
#117484582
#117483892
C2×#909672
#117469642
#117468942
#117468832
#106142703
#790905