Finite Group Databasebeta

← #14430881

Subgroups — #14430881

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#11754618C211yesmaximal, characteristic, complemented
2#11754488C211yesmaximal, characteristic
3#11751203C211yesmaximal, characteristic, complemented
4C5×#5106C211yesmaximal, characteristic, complemented
5C2×C3×#3953C211yesmaximal, characteristic
6#11748470C211yesmaximal, characteristic, complemented
7#11748366C211yesmaximal, characteristic
8#11747805C212yesmaximal, complemented
9#11747804C212yesmaximal, complemented
10#11747803C212yesmaximal, complemented
11#11747802C212yesmaximal, complemented
12#10610928—31nomaximal, Hall
13C22×C3×D20C2211yescharacteristic
14C22×C3×C5×C8C2211yescharacteristic
15#91815C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C5×#926C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20#91574—22no—
21D5×#217—22no—
22#91470C2212yescomplemented
23#91469—21no—
24#91434C2212yes—
25#91434C2212yes—
26Dic3×D20—21no—
27Dic3×D20—21no—
28#91384C2212yescomplemented
29#91381—21no—
30#91098C2212yescomplemented
31#91098C2212yescomplemented
32C5×#818C2211yescharacteristic, complemented
33C5×#818C2211yescharacteristic, complemented
34C5×#817C2211yescharacteristic, complemented
35C5×#817C2211yescharacteristic, complemented
36C3×#3953C2212yes—
37C3×#3953C2212yes—
38#90989C2212yescomplemented
39#90986C2212yescomplemented
40#90964C2212yes—
41#90964C2212yes—
42#78731—51nomaximal, Hall
43#65855—31no—
44#65853—31no—
45C5×#427—31no—
46C2×#3953D311yescharacteristic
47#65391—31no—
48#65290—31no—
49#65284—31no—
50#65180—32no—
51#65179—32no—
52#65160—32no—
53#65159—32no—
54C23×C3×D5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×Dic5—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—
64C2×C3×C5×C8—22no—
65C2×C3×C5×C8C2311yescharacteristic
66C2×C3×C5×C8C2311yescharacteristic
67#6719D412yes—
68C4⋊Dic15D411yescharacteristic
69C4⋊Dic15D411yescharacteristic
70C4×Dic15C2312yes—
71#6710—22no—
72C2×C3⋊#168C2312yes—
73C5×#217—21no—
74C5×#217—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2311yescharacteristic
78C5×C4⋊Dic3C2311yescharacteristic
79C4×C5×Dic3—21no—
80C4×C5×Dic3—21no—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5C2312yes—
83Dic3⋊Dic5—22no—
84#6669—22no—
85#6668—22no—
86#6665—22no—
87#6665—22no—
88#5798—51no—
89#5500—51no—
90C2×C3×#102—51no—
91#5215—51no—
92#5106D511yescharacteristic, complemented
93#5102—51no—
94#4964—51no—
95#4766—52no—
96#4763—52no—
97#4761—52no—
98#4759—52no—
99C22×D20C2×D311yescharacteristic
100C22×C5×C8C2×D311yescharacteristic
101C5×#117—31no—
102C5×#117—31no—
103#4072—31no—
104C2×C4⋊Dic5C2×D311yescharacteristic
105C2×#681—31no—
106#4039—32no—
107#4039—32no—
108#4036—32no—
109#4034—32no—
110D5×C22⋊C4—62no—
111#4024—62no—
112C4×D20—61no—
113C4×D20—61no—
114#4016—61no—
115#4015—61no—
116C5×#107—31no—
117C5×#107—31no—
118C5×#106—31no—
119C5×#106—31no—
120#3953C2×D312yes—
121#3953C2×D312yes—
122#3946—32no—
123#3946—32no—
124#3941—32no—
125#3941—32no—
126#3940—32no—
127#3939—32no—
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—21no—
143C2×C5×Dic3—21no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—81no—
146C3×D20—24no—
147C3×D20—22no—
148C3×D20C2×Q814yes—
149#1204—82no—
150D5×Dic3—82no—
151D5×Dic3—82no—
152C3×C5×C8—21no—
153C3×C5×C8—21no—
154C3⋊#168—22no—
155C22×C3×D4—51no—
156C22×C3×C8C2×D511yescharacteristic
157C2×C3×C4⋊C4—51no—
158C2×#217—102no—
159D4×Dic3—52no—
160D4×Dic3—52no—
161D4×Dic3—101no—
162D4×Dic3—101no—
163#926—51no—
164#926C2×D511yescharacteristic
165#926C2×D511yescharacteristic
166#924—102no—
167C2×#208—51no—
168#890—52no—
169#890—101no—
170#888—52no—
171#888—101no—
172C3×#102—52no—
173C3×#102—52no—
174#832—52no—
175#832—52no—
176#818C2×D511yescharacteristic, complemented
177#818C2×D511yescharacteristic, complemented
178#817C2×D511yescharacteristic, complemented
179#817C2×D511yescharacteristic, complemented
180Dic3⋊C8—52no—
181Dic3⋊C8—52no—
182#808—52no—
183#807—52no—
184C23×D5—21no—
185C22×C4×C5C22×D311yescharacteristic
186C22×Dic5—21no—
187C2×D20—21no—
188C2×D20—22no—
189C2×D20Dic614yescomplemented
190C2×D20C22×D312yes—
191C2×C4×D5—62no—
192C2×C4×D5—62no—
193C2×Dic10—62no—
194C2×C5×C8—22no—
195C2×C5×C8C22×D311yescharacteristic
196C2×C5×C8C22×D311yescharacteristic
197C5×C4⋊C4—31no—
198C5×C4⋊C4—31no—
199C5×C4⋊C4—31no—
200C5×C4⋊C4—31no—
201C5×C22⋊C4—61no—
202C5×C22⋊C4—61no—
203C42×C5—61no—
204C42×C5—61no—
205C22⋊Dic5—32no—
206#685—62no—
207#685—62no—
208C4⋊Dic5—21no—
209C4⋊Dic5—31no—
210C4⋊Dic5—31no—
211C4⋊Dic5—62no—
212C4⋊Dic5C22×D312yes—
213#683—62no—
214#683—62no—
215C4×Dic5—32no—
216#681—62no—
217C2×#168—32no—
218#544—151no—
219#518—151no—
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428—151no—
225#427—31no—
226#424—151no—
227#418—151no—
228C2×#102—51no—
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—42no—
243C5×Dic3—41no—
244C5×Dic3—41no—
245C5×Dic3—41no—
246C5×Dic3—41no—
247C24×C3—101no—
248C2×C3×D4—54no—
249C2×C3×D4—52no—
250C2×C3×D4—102no—
251C2×C3×D4—101no—
252C22×C3×C4—101no—
253C22×C3×C4C22×D511yescharacteristic
254C22×Dic3—102no—
255C22×Dic3—102no—
256C2×Dic6—102no—
257C2×C3×C8—22no—
258C2×C3×C8C22×D511yescharacteristic
259C2×C3×C8C22×D511yescharacteristic
260C3×C4⋊C4—52no—
261C3×C4⋊C4—101no—
262#217—21no—
263#217—21no—
264#217—52no—
265#217—102no—
266#217—102no—
267C4⋊Dic3—51no—
268C4⋊Dic3—51no—
269C4⋊Dic3—102no—
270C4⋊Dic3C22×D511yescharacteristic
271C4⋊Dic3C22×D511yescharacteristic
272C4⋊Dic3C22×D511yescharacteristic
273C4⋊Dic3C22×D511yescharacteristic
274Dic3⋊C4—102no—
275Dic3⋊C4—102no—
276C4×Dic3—21no—
277C4×Dic3—21no—
278C4×Dic3—52no—
279#208—102no—
280C2×C3⋊C8—52no—
281C23×C5D3×D411yescharacteristic
282C22×D5—22no—
283C22×D5—24no—
284C22×D5—81no—
285C22×D5—81no—
286C2×C4×C5—61no—
287C2×C4×C5—61no—
288C2×C4×C5—61no—
289C2×C4×C5—61no—
290C2×C4×C5C2×Dic612yes—
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5#23712yes—
293C2×C4×C5C23×D311yescharacteristic
294C2×Dic5—22no—
295C2×Dic5—32no—
296C2×Dic5—32no—
297C2×Dic5—81no—
298D20—24no—
299D20—22no—
300D20C2×Dic614yes—
301C4×D5—242no—
302C4×D5—242no—
303Dic10—242no—
304C5×C8—21no—
305C5×C8—21no—
306#168—62no—
307C22×D4—51no—
308C2×M16—151no—
309C22×C8D3×D511yescharacteristic
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—31no—
321#117—151no—
322C2×C4⋊C4—51no—
323C2×C22⋊C4—302no—
324#107—31no—
325#107—31no—
326#107—152no—
327#106—31no—
328#106—31no—
329#106—152no—
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—102no—
350C2×C3×C4—401no—
351C2×C3×C4#70912yes—
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4Q8×D512yes—
354C2×C3×C4C23×D511yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—52no—
360C2×Dic3—52no—
361C2×Dic3—402no—
362C2×Dic3—402no—
363Dic6—402no—
364C3×C8—21no—
365C3×C8—21no—
366C3⋊C8—102no—
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—121no—
376C4×C5—121no—
377C4×C5—121no—
378C4×C5—121no—
379C4×C5#87812yes—
380C4×C5C22×Dic611yescharacteristic
381C4×C5C2×#23711yescharacteristic
382Dic5—42no—
383Dic5—62no—
384Dic5—62no—
385C24—101no—
386C2×Q8—302no—
387C2×D4—54no—
388C2×D4—52no—
389C2×D4—101no—
390C2×D4—102no—
391C22×C4—101no—
392C22×C4—302no—
393C22×C4—302no—
394C22×C4C2×D3×D511yescharacteristic
395M16—302no—
396C2×C8—22no—
397C2×C8—152no—
398C2×C8C2×D3×D511yescharacteristic
399C2×C8C2×D3×D511yescharacteristic
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—31no—
403C4⋊C4—31no—
404C4⋊C4—52no—
405C4⋊C4—101no—
406C4⋊C4—151no—
407C4⋊C4—151no—
408C4⋊C4—302no—
409C4⋊C4—302no—
410C4⋊C4—302no—
411C22⋊C4—61no—
412C22⋊C4—61no—
413C22⋊C4—152no—
414C22⋊C4—302no—
415C22⋊C4—302no—
416C42—61no—
417C42—61no—
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—202no—
429C3×C4#404212yes—
430C3×C4C2×#70911yescharacteristic
431C3×C4C2×Q8×D511yescharacteristic
432Dic3—41no—
433Dic3—41no—
434Dic3—41no—
435Dic3—41no—
436Dic3—102no—
437Dic3—102no—
438C2×C5—22no—
439C2×C5C2×#87811yescharacteristic
440C2×C5#575711yescharacteristic
441C2×C5#576211yescharacteristic
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—61no—
455C2×C4—61no—
456C2×C4—102no—
457C2×C4—152no—
458C2×C4—152no—
459C2×C4—401no—
460C2×C4—1202no—
461C2×C4—1202no—
462C2×C4D5×Dic612yes—
463C2×C4#677711yescharacteristic
464C2×C4#677912yes—
465C2×C4C22×D3×D511yescharacteristic
466C8—21no—
467C8—21no—
468C8—302no—
469C2×C3—22no—
470C2×C3—204no—
471C2×C3C2×#404211yescharacteristic
472C2×C3#6610311yescharacteristic
473C2×C3#6610411yescharacteristic
474C5#7873111yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—104no—
478C22—202no—
479C22—202no—
480C22—404no—
481C22#9143012yes—
482C22C2×#677711yescharacteristic
483C4—121no—
484C4—121no—
485C4—121no—
486C4—121no—
487C4—202no—
488C4—302no—
489C4—302no—
490C4#9143012yes—
491C4C2×D5×Dic611yescharacteristic
492C4C2×#677911yescharacteristic
493C3#1061092811yescharacteristic, complemented, Sylow
494C2—22no—
495C2—204no—
496C2#1175398011yescharacteristic
497C2#1175398111yescharacteristic
498C2C2×#9143011yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D20C22
hypercenterC22×C8D3×D5
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #11754618C2semidirect
3. #11751203C2semidirect
4. C5×#5106C2semidirect
6. #11748470C2semidirect
8. #11747805C2semidirect
9. #11747804C2semidirect
10. #11747803C2semidirect
11. #11747802C2semidirect
22. #91470C22semidirect
28. #91384C22semidirect
30. #91098C22semidirect
31. #91098C22semidirect
32. C5×#818C22semidirect
33. C5×#818C22semidirect
34. C5×#817C22semidirect
35. C5×#817C22semidirect
38. #90989C22semidirect
39. #90986C22semidirect
59. C2×C3×D20Q8semidirect
92. #5106D5semidirect
176. #818C2×D5semidirect
177. #818C2×D5semidirect
178. #817C2×D5semidirect
179. #817C2×D5semidirect
189. C2×D20Dic6semidirect
419. C3×C5#3081semidirect
474. C5#78731semidirect
493. C3#10610928semidirect

Maximal subgroups

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

subgroupindex
#117546182
#117544882
#117512032
C5×#51062
C2×C3×#39532
#117484702
#117483662
#117478052
#117478042
#117478032
#117478022
#106109283
#787315