Finite Group Databasebeta

← #14430893

Subgroups — #14430893

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#11754619C211yesmaximal, characteristic, complemented
2#11754488C211yesmaximal, characteristic
3#11751220C211yesmaximal, characteristic, complemented
4C5×#5121C211yesmaximal, characteristic, complemented
5C3×#65420C211yesmaximal, characteristic
6#11748469C211yesmaximal, characteristic, complemented
7C2×#90964C211yesmaximal, characteristic
8#11747805C212yesmaximal, complemented
9#11747804C212yesmaximal, complemented
10#11747803C212yesmaximal, complemented
11#11747802C212yesmaximal, complemented
12#10610973—31nomaximal, Hall
13C22×C3×D20C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15#91815C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20#91575—22no—
21D5×#217—22no—
22#91470C2212yescomplemented
23#91468—21no—
24#91434C2212yes—
25#91434C2212yes—
26Dic3×D20—21no—
27Dic3×D20—21no—
28#91388—21no—
29#91384C2212yescomplemented
30#91098C2212yescomplemented
31#91098C2212yescomplemented
32C5×#818C2212yescomplemented
33C5×#817C2212yescomplemented
34C3×#3953C2212yes—
35C3×#3953C2212yes—
36#90989C2211yescharacteristic, complemented
37#90989C2211yescharacteristic, complemented
38#90986C2211yescharacteristic, complemented
39#90986C2211yescharacteristic, complemented
40#90964C2212yes—
41#90964C2212yes—
42#78918—51nomaximal, Hall
43#65855—31no—
44#65834—31no—
45C5×#428—31no—
46#65420D311yescharacteristic
47#65408—31no—
48#65287—31no—
49C2×#3941—31no—
50#65180—32no—
51#65179—32no—
52#65160—32no—
53#65159—32no—
54C23×C3×D5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C5×Dic3—21no—
57C2×C3×D20—21no—
58C2×C3×D20—22no—
59C2×C3×D20Q814yescomplemented
60C2×C3×D20C2312yes—
61C2×#1204—22no—
62C2×D5×Dic3—22no—
63C2×D5×Dic3—22no—
64C3×C5×M16—22no—
65C2×C3×C5×C8C2312yes—
66#6719D412yes—
67C4⋊Dic15D411yescharacteristic
68C4⋊Dic15D411yescharacteristic
69C4×Dic15C2312yes—
70C2×C3⋊#168—22no—
71C2×C3⋊#168C2311yescharacteristic
72C2×C3⋊#168C2311yescharacteristic
73C5×#217—21no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2312yes—
78C4×C5×Dic3—21no—
79C3×C22⋊Dic5—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4×Dic5—21no—
83Dic3⋊Dic5—22no—
84#6669—22no—
85#6668—22no—
86#6665—22no—
87#6665—22no—
88#5798—51no—
89#5519—51no—
90C3×#418—51no—
91C2×#832—51no—
92#5121D511yescharacteristic, complemented
93#5119—51no—
94#4998—51no—
95#4766—52no—
96#4763—52no—
97#4761—52no—
98#4759—52no—
99C22×D20C2×D311yescharacteristic
100C2×C5×M16C2×D311yescharacteristic
101C5×#117—31no—
102C2×C5×C4⋊C4—31no—
103#4072—31no—
104#4072C2×D311yescharacteristic
105#4070—62no—
106C22×#168—31no—
107#4039—32no—
108#4039—32no—
109#4036—32no—
110#4036—61no—
111#4034—32no—
112#4034—61no—
113D5×C22⋊C4—62no—
114C4×D20—61no—
115C4×D20—61no—
116C5×#107—32no—
117C5×#106—32no—
118#3953C2×D312yes—
119#3953C2×D312yes—
120#3946—32no—
121#3946—32no—
122#3941—32no—
123#3941—32no—
124#3940—31no—
125#3940—31no—
126#3939—31no—
127#3939—31no—
128#3081—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×C3×D5—22no—
131C22×C3×D5—24no—
132C22×C3×D5—81no—
133C22×C3×D5—81no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×Q812yes—
136C2×C3×C4×C5#4112yes—
137C2×C3×C4×C5C2411yescharacteristic
138C2×Dic15C2×D412yes—
139C2×Dic15C2×D412yes—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—81no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—21no—
146C3×D20—24no—
147C3×D20—22no—
148C3×D20C2×Q814yes—
149#1204—82no—
150D5×Dic3—82no—
151D5×Dic3—82no—
152C3×C5×C8—22no—
153C3⋊#168—21no—
154C3⋊#168—21no—
155C22×C3×D4—51no—
156C2×C3×M16C2×D511yescharacteristic
157C3×#117—51no—
158C2×#217—102no—
159D4×Dic3—52no—
160D4×Dic3—52no—
161D4×Dic3—101no—
162D4×Dic3—101no—
163#926—51no—
164#926C2×D511yescharacteristic
165C2×C4⋊Dic3C2×D511yescharacteristic
166C22×C3⋊C8—51no—
167#890—52no—
168#888—52no—
169#878—102no—
170#870—101no—
171#869—101no—
172C3×#102—52no—
173C3×#102—52no—
174#832—52no—
175#832—52no—
176#818C2×D512yescomplemented
177#817C2×D512yescomplemented
178Dic3⋊C8—52no—
179Dic3⋊C8—52no—
180#808—51no—
181#808—51no—
182#807—51no—
183#807—51no—
184C23×D5—21no—
185C22×C4×C5—61no—
186C22×C4×C5C22×D311yescharacteristic
187C2×D20—21no—
188C2×D20—22no—
189C2×D20Dic614yescomplemented
190C2×D20C22×D312yes—
191C2×C4×D5—62no—
192C2×C4×D5—62no—
193C2×Dic10—62no—
194C5×M16—22no—
195C2×C5×C8C22×D312yes—
196C5×C4⋊C4—32no—
197C5×C4⋊C4—31no—
198C5×C4⋊C4—31no—
199C5×C4⋊C4—61no—
200C5×C22⋊C4—61no—
201C42×C5—61no—
202C22⋊Dic5—21no—
203C22⋊Dic5—32no—
204#685—62no—
205#685—62no—
206C4⋊Dic5—31no—
207C4⋊Dic5—31no—
208C4⋊Dic5—62no—
209C4⋊Dic5C22×D311yescharacteristic
210C4⋊Dic5C22×D311yescharacteristic
211#683—62no—
212#683—62no—
213C4×Dic5—21no—
214C4×Dic5—32no—
215C2×#168—31no—
216C2×#168—31no—
217C2×#168—62no—
218#544—151no—
219#518—151no—
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428—31no—
225#427—151no—
226#424—151no—
227#418—51no—
228C2×#102—151no—
229C22×C3×C5—21no—
230C22×C3×C5—21no—
231C22×C3×C5C22⋊Q812yes—
232C22×C3×C5C22×D411yescharacteristic
233C2×C3×D5—24no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—84no—
237C3×C4×C5C22⋊Q812yes—
238C3×C4×C5C22×Q811yescharacteristic
239C3×C4×C5C2×#4111yescharacteristic
240Dic15—22no—
241Dic15—22no—
242C3×Dic5—41no—
243C3×Dic5—41no—
244C5×Dic3—41no—
245C5×Dic3—42no—
246C5×Dic3—41no—
247C24×C3—101no—
248C2×C3×D4—54no—
249C2×C3×D4—52no—
250C2×C3×D4—102no—
251C2×C3×D4—101no—
252C22×C3×C4C22×D511yescharacteristic
253C22×Dic3—21no—
254C22×Dic3—102no—
255C22×Dic3—102no—
256C2×Dic6—102no—
257C3×M16—22no—
258C2×C3×C8C22×D512yes—
259C3×C4⋊C4—51no—
260C3×C4⋊C4—51no—
261C3×C22⋊C4—101no—
262C3×C42—101no—
263#217—21no—
264#217—52no—
265#217—102no—
266#217—102no—
267C4⋊Dic3—21no—
268C4⋊Dic3—51no—
269C4⋊Dic3—51no—
270C4⋊Dic3—102no—
271C4⋊Dic3C22×D511yescharacteristic
272C4⋊Dic3C22×D511yescharacteristic
273C4⋊Dic3C22×D512yes—
274Dic3⋊C4—102no—
275Dic3⋊C4—102no—
276C4×Dic3—21no—
277C4×Dic3—52no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8—51no—
280C2×C3⋊C8—102no—
281C23×C5D3×D411yescharacteristic
282C22×D5—22no—
283C22×D5—24no—
284C22×D5—81no—
285C22×D5—81no—
286C2×C4×C5—62no—
287C2×C4×C5—61no—
288C2×C4×C5—61no—
289C2×C4×C5—241no—
290C2×C4×C5C2×Dic612yes—
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5#23712yes—
293C2×C4×C5C23×D311yescharacteristic
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—32no—
297C2×Dic5—32no—
298D20—24no—
299D20—22no—
300D20C2×Dic614yes—
301C4×D5—242no—
302C4×D5—242no—
303Dic10—242no—
304C5×C8—22no—
305#168—61no—
306#168—61no—
307C22×D4—51no—
308C2×M16D3×D511yescharacteristic
309C22×C8—151no—
310C4⋊Q8—152no—
311C4⋊Q8—301no—
312#125—152no—
313#125—301no—
314C22⋊Q8—302no—
315C4×D4—152no—
316C4×D4—152no—
317C4×D4—301no—
318C4×D4—301no—
319#117—31no—
320#117—51no—
321#117—151no—
322C2×C4⋊C4—31no—
323C2×C22⋊C4—302no—
324#107—32no—
325#107—151no—
326#107—151no—
327#106—32no—
328#106—151no—
329#106—151no—
330C4⋊C8—152no—
331C4⋊C8—152no—
332#102—52no—
333#102—52no—
334#102—152no—
335#102—152no—
336C2×C3×C5—22no—
337C2×C3×C5C2×C22⋊Q811yescharacteristic
338C2×C3×C5#57611yescharacteristic
339C2×C3×C5#57711yescharacteristic
340C3×D5—44no—
341C23×C3—102no—
342C23×C3—104no—
343C23×C3—401no—
344C23×C3—401no—
345C23×C3D4×D511yescharacteristic
346C3×D4—54no—
347C3×D4—102no—
348C3×D4—104no—
349C2×C3×C4—101no—
350C2×C3×C4—101no—
351C2×C3×C4#70912yes—
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4Q8×D512yes—
354C2×C3×C4C23×D511yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—22no—
358C2×Dic3—52no—
359C2×Dic3—52no—
360C2×Dic3—81no—
361C2×Dic3—402no—
362C2×Dic3—402no—
363Dic6—402no—
364C3×C8—22no—
365C3⋊C8—101no—
366C3⋊C8—101no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5#87812yes—
370C22×C5C2×D3×D411yescharacteristic
371C2×D5—24no—
372C2×D5—42no—
373C2×D5—42no—
374C2×D5—84no—
375C4×C5—122no—
376C4×C5—121no—
377C4×C5—121no—
378C4×C5#87812yes—
379C4×C5C22×Dic611yescharacteristic
380C4×C5C2×#23711yescharacteristic
381Dic5—41no—
382Dic5—41no—
383Dic5—62no—
384Dic5—62no—
385C24—101no—
386C2×Q8—302no—
387C2×D4—54no—
388C2×D4—52no—
389C2×D4—101no—
390C2×D4—102no—
391C22×C4—61no—
392C22×C4—302no—
393C22×C4—302no—
394C22×C4C2×D3×D511yescharacteristic
395M16—22no—
396C2×C8—151no—
397C2×C8—151no—
398C2×C8—302no—
399C2×C8C2×D3×D512yes—
400C4⋊C4—32no—
401C4⋊C4—31no—
402C4⋊C4—31no—
403C4⋊C4—51no—
404C4⋊C4—51no—
405C4⋊C4—61no—
406C4⋊C4—151no—
407C4⋊C4—151no—
408C4⋊C4—302no—
409C4⋊C4—302no—
410C4⋊C4—302no—
411C22⋊C4—61no—
412C22⋊C4—101no—
413C22⋊C4—152no—
414C22⋊C4—302no—
415C22⋊C4—302no—
416C42—61no—
417C42—101no—
418C42—152no—
419C3×C5#308111yescharacteristic, complemented, Hall
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—104no—
423C22×C3—202no—
424C22×C3—202no—
425C22×C3—404no—
426C22×C3#404212yes—
427C22×C3C2×D4×D511yescharacteristic
428C3×C4—201no—
429C3×C4—201no—
430C3×C4#404212yes—
431C3×C4C2×#70911yescharacteristic
432C3×C4C2×Q8×D511yescharacteristic
433Dic3—42no—
434Dic3—41no—
435Dic3—41no—
436Dic3—102no—
437Dic3—102no—
438C2×C5—22no—
439C2×C5C2×#87811yescharacteristic
440C2×C5#577411yescharacteristic
441C2×C5#577511yescharacteristic
442D5—44no—
443C23—102no—
444C23—104no—
445C23—401no—
446C23—401no—
447C23#677711yescharacteristic
448Q8—1202no—
449D4—54no—
450D4—104no—
451D4—102no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—62no—
455C2×C4—101no—
456C2×C4—101no—
457C2×C4—152no—
458C2×C4—152no—
459C2×C4—241no—
460C2×C4—1202no—
461C2×C4—1202no—
462C2×C4D5×Dic612yes—
463C2×C4#677711yescharacteristic
464C2×C4#677912yes—
465C2×C4C22×D3×D511yescharacteristic
466C8—22no—
467C8—301no—
468C8—301no—
469C2×C3—22no—
470C2×C3—204no—
471C2×C3C2×#404211yescharacteristic
472C2×C3#6610811yescharacteristic
473C2×C3#6611211yescharacteristic
474C5#7891811yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—104no—
478C22—202no—
479C22—202no—
480C22—404no—
481C22#9143012yes—
482C22C2×#677711yescharacteristic
483C4—121no—
484C4—122no—
485C4—121no—
486C4—201no—
487C4—201no—
488C4—302no—
489C4—302no—
490C4#9143012yes—
491C4C2×D5×Dic611yescharacteristic
492C4C2×#677911yescharacteristic
493C3#1061097311yescharacteristic, complemented, Sylow
494C2—22no—
495C2—204no—
496C2#1175403711yescharacteristic
497C2#1175403811yescharacteristic
498C2C2×#9143011yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D20C22
hypercenterC2×M16D3×D5
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #11754619C2semidirect
3. #11751220C2semidirect
4. C5×#5121C2semidirect
6. #11748469C2semidirect
8. #11747805C2semidirect
9. #11747804C2semidirect
10. #11747803C2semidirect
11. #11747802C2semidirect
22. #91470C22semidirect
29. #91384C22semidirect
30. #91098C22semidirect
31. #91098C22semidirect
32. C5×#818C22semidirect
33. C5×#817C22semidirect
36. #90989C22semidirect
37. #90989C22semidirect
38. #90986C22semidirect
39. #90986C22semidirect
59. C2×C3×D20Q8semidirect
92. #5121D5semidirect
176. #818C2×D5semidirect
177. #817C2×D5semidirect
189. C2×D20Dic6semidirect
419. C3×C5#3081semidirect
474. C5#78918semidirect
493. C3#10610973semidirect

Maximal subgroups

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

subgroupindex
#117546192
#117544882
#117512202
C5×#51212
C3×#654202
#117484692
C2×#909642
#117478052
#117478042
#117478032
#117478022
#106109733
#789185