Finite Group Databasebeta

← #14460062

Subgroups — #14460062

Order 1920.

772 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
1C3×#65918C211yesmaximal, characteristic, complemented
2#11752493C211yesmaximal, characteristic
3C4×#6717C211yesmaximal, characteristic, complemented
4C5×#5031C211yesmaximal, characteristic, complemented
5#11749406C212yesmaximal, complemented
6#11749366C212yesmaximal, complemented
7#11747501C212yesmaximal, complemented
8#11747342C212yesmaximal, complemented
9#11746996C211yesmaximal, characteristic, complemented
10#11746971C211yesmaximal, characteristic, complemented
11#11746923C211yesmaximal, characteristic, complemented
12#10612223—31nomaximal, Hall
13C2×#6773C2212yes—
14C3×C4×C5×Q8C2211yescharacteristic
15C2×#6717C2211yescharacteristic
16C4×D60C2211yescharacteristic
17C2×C5×#216C2212yes—
18C5×#869C2211yescharacteristic
19C3×#4092C2212yes—
20C3×#4044—22no—
21C3×#4038C2212yes—
22C3×#4021—21no—
23C3×C4×D20C2211yescharacteristic
24C3×#4015C2211yescharacteristic
25C3×C4×Dic10—21no—
26#91465—21no—
27#91437—21no—
28#91359C2212yes—
29#91356—22no—
30C2×D5×C3⋊C8C2212yes—
31#91119C2211yescharacteristic
32#91093C2211yescharacteristic
33#91092C2211yescharacteristic
34C4×C3⋊#168C2211yescharacteristic
35C5×#810C2212yes—
36C5×C4⋊(C3⋊C8)C2211yescharacteristic
37#90990C2212yes—
38#90972C2212yes—
39#90972C2212yes—
40#90968C2212yes—
41#90955C2212yes—
42#83664—51nomaximal, Hall
43#66060—31no—
44#65918D311yescharacteristic, complemented
45C5×#462—31no—
46#65477—32no—
47#65476—32no—
48#65370—31no—
49C4×#688—31no—
50#65135—31no—
51#65123—31no—
52#65103—32no—
53#65093—32no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C5×Dic6C2312yes—
58C2×C3×D20D411yescharacteristic
59C2×C3×C4×D5C2312yes—
60C2×C3×Dic10—21no—
61C2×#1202—22no—
62C2×#1200—22no—
63#6773—24no—
64#6773—42no—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4C2311yescharacteristic
67C3×C42×C5—21no—
68C3×C42×C5C2311yescharacteristic
69#6717—22no—
70#6714—21no—
71C4⋊Dic15C2311yescharacteristic
72C2×C3⋊#168C2311yescharacteristic
73C2×C3⋊#168C2311yescharacteristic
74C5×#216—42no—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3—21no—
77C2×C5×C3⋊C8C2312yes—
78C3×#685—22no—
79C3×#685—22no—
80C3×#685D412yes—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5D411yescharacteristic
83C3×C4⋊Dic5C2312yes—
84C3×#683—22no—
85C3×C4×Dic5—22no—
86#6669—22no—
87#6665—22no—
88D5×C3⋊C8—42no—
89C3×#556—51no—
90#5551—51no—
91#5093—51no—
92#5087—51no—
93#5051—52no—
94#5047—52no—
95#5031D511yescharacteristic, complemented
96C4×#215—51no—
97D4×C3⋊C8—51no—
98#5002—52no—
99#4996—52no—
100C2×#713—32no—
101C2×C5×Q16—32no—
102C5×C4⋊Q8—31no—
103C4×C5×Q8C2×D311yescharacteristic
104#4092—32no—
105#4092C2×D312yes—
106C2×#688—31no—
107C2×C8×D5—32no—
108#4044—22no—
109#4041—61no—
110#4040—62no—
111#4038C2×D312yes—
112D5×C4⋊C4—61no—
113#4021—21no—
114C4×D20—31no—
115C4×D20C2×D311yescharacteristic
116#4015C2×D311yescharacteristic
117C4×Dic10—21no—
118C5×C4⋊C8—31no—
119C5×#103—32no—
120#3967—31no—
121#3967—32no—
122#3967—32no—
123#3953—32no—
124#3952—32no—
125#3950—32no—
126#3941—31no—
127#3940—31no—
128C4×#168—31no—
129#3302—151noSylow
130C22×D15—21no—
131C22×C3×D5C2×D412yes—
132C3×C5×Q8—21no—
133C3×C5×Q8—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—21no—
140D60—21no—
141D60#4112yes—
142C4×D15—42no—
143C2×C5×Dic3—22no—
144C5×Dic6—22no—
145C5×Dic6—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5C2×D412yes—
148C3×D20—22no—
149C3×C4×D5—22no—
150C3×C4×D5—22no—
151C3×Dic10—42no—
152#1202—44no—
153#1200—44no—
154C3⋊#168—21no—
155C3⋊#168—21no—
156C5×C3⋊C8—22no—
157C2×#235—52no—
158C3×C4⋊Q8—51no—
159C3×#126—102no—
160C3×#124—101no—
161C3×C22⋊Q8—52no—
162C3×C4×Q8—101no—
163C3×C4×Q8C2×D511yescharacteristic
164C3×C4×D4—51no—
165C3×#117—52no—
166C2×#216C2×D512yes—
167C2×#215—51no—
168#938—101no—
169#924—52no—
170C22×C3⋊C8—52no—
171D3×C4⋊C4—101no—
172#883—102no—
173C4×D12—51no—
174#869C2×D511yescharacteristic
175#835—51no—
176#830—52no—
177#810—52no—
178#810—52no—
179#810C2×D512yes—
180#809—51no—
181#809—52no—
182#808—51no—
183#807—52no—
184C4⋊(C3⋊C8)C2×D511yescharacteristic
185C4×C3⋊C8—51no—
186C2×C5×Q8—32no—
187C2×C5×Q8C22×D311yescharacteristic
188#713—64no—
189#713—122no—
190C2×D20—31no—
191C2×D20—62no—
192C2×D20#6711yescharacteristic
193C2×C4×D5—61no—
194C2×C4×D5—62no—
195C2×C4×D5C22×D312yes—
196C2×Dic10—21no—
197C5×Q16—122no—
198C2×C5×C8—32no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—61no—
201C5×C4⋊C4—61no—
202C5×C4⋊C4C22×D311yescharacteristic
203C42×C5—21no—
204C42×C5C22×D311yescharacteristic
205#688—62no—
206#685—22no—
207#685—22no—
208#685—62no—
209#685—61no—
210#685#6712yes—
211C4⋊Dic5—21no—
212C4⋊Dic5—31no—
213C4⋊Dic5#6711yescharacteristic
214C4⋊Dic5C22×D312yes—
215#683—22no—
216#683—62no—
217C4×Dic5—22no—
218C2×#168—31no—
219C2×#168—31no—
220C8×D5—122no—
221#556—51no—
222#547—151no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—31no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—151no—
231#416—152no—
232C22×C3×C5C22×D411yescharacteristic
233C2×D15—22no—
234C2×D15—41no—
235C2×D15—41no—
236C2×C3×D5—22no—
237C2×C3×D5—22no—
238C2×C3×D5—22no—
239C3×C4×C5—21no—
240C3×C4×C5—41no—
241C3×C4×C5—41no—
242C3×C4×C5#13512yes—
243C3×C4×C5C2×#4111yescharacteristic
244C3×C4×C5H(5,𝔽2)11yescharacteristic
245Dic15—41no—
246C3×Dic5—22no—
247C3×Dic5—42no—
248C5×Dic3—42no—
249C2×C3×Q8—101no—
250C2×C3×Q8C22×D511yescharacteristic
251C2×C3×D4—51no—
252C22×C3×C4—52no—
253C2×#67—102no—
254#235—104no—
255#235—202no—
256C2×D12—51no—
257C2×C4×D3—102no—
258C2×C4×D3—101no—
259C2×Dic6C22×D512yes—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—51no—
262C3×C4⋊C4—52no—
263C3×C4⋊C4—102no—
264C3×C4⋊C4—101no—
265C3×C4⋊C4C22×D511yescharacteristic
266C3×C22⋊C4—52no—
267C3×C22⋊C4—102no—
268C3×C22⋊C4—102no—
269C3×C42—21no—
270C3×C42—102no—
271C3×C42C22×D511yescharacteristic
272#217—102no—
273#216—42no—
274#215—102no—
275(C2×D3)⋊C4—101no—
276C4⋊Dic3—21no—
277C4⋊Dic3—21no—
278C4⋊Dic3—51no—
279Dic3⋊C4—102no—
280C2×C3⋊C8—51no—
281C2×C3⋊C8—51no—
282C2×C3⋊C8—202no—
283C2×C3⋊C8C22×D512yes—
284C22×D5—61no—
285C22×D5C2×#6712yes—
286C5×Q8—21no—
287C5×Q8—21no—
288C5×Q8—62no—
289C5×Q8—62no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—62no—
293C2×C4×C5C2×#6711yescharacteristic
294C2×C4×C5C2×#6711yescharacteristic
295C2×C4×C5C23×D311yescharacteristic
296C2×Dic5—22no—
297C2×Dic5—61no—
298C2×Dic5C2×#6712yes—
299D20—22no—
300D20—32no—
301D20—61no—
302D20—124no—
303C4×D5—22no—
304C4×D5—22no—
305C4×D5—124no—
306C4×D5—122no—
307Dic10—42no—
308C5×C8—62no—
309#168—61no—
310#168—61no—
311C2×#41—152no—
312C2×Q16—32no—
313C2×SD16—151no—
314C22×C8—152no—
315C4⋊Q8—31no—
316C4⋊Q8—51no—
317#126—102no—
318#124—101no—
319#123—302no—
320C22⋊Q8—52no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—101no—
324C4×Q8D3×D511yescharacteristic
325C4×D4—51no—
326C4×D4—151no—
327#117—52no—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—151no—
331C4⋊C8—31no—
332#103—32no—
333#103—152no—
334#103—152no—
335#103—151no—
336#102—152no—
337#102—151no—
338C22⋊C8—152no—
339C4×C8—151no—
340C2×C3×C5#54611yescharacteristic
341C2×C3×C5C2×#13511yescharacteristic
342C2×C3×C5#57811yescharacteristic
343D15—42no—
344C3×D5—42no—
345C23×C3—52no—
346C22×D3—101no—
347C3×Q8—21no—
348C3×Q8—21no—
349C3×Q8—202no—
350C3×D4—102no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—52no—
354C2×C3×C4—102no—
355C2×C3×C4—102no—
356C2×C3×C4—102no—
357C2×C3×C4D4×D511yescharacteristic
358C2×C3×C4D4×D511yescharacteristic
359C2×C3×C4C23×D511yescharacteristic
360#67—204no—
361C2×Dic3—22no—
362C2×Dic3—101no—
363D12—52no—
364D12—101no—
365C4×D3—204no—
366C4×D3—202no—
367Dic6—22no—
368Dic6—22no—
369C3⋊C8—22no—
370C3⋊C8—101no—
371C3⋊C8—101no—
372C22×C5C22×#6711yescharacteristic
373C2×D5—22no—
374C2×D5—22no—
375C2×D5—22no—
376C2×D5—62no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—41no—
381C4×C5—41no—
382C4×C5—122no—
383C4×C5#95012yes—
384C4×C5D3×#4111yescharacteristic
385C4×C5#100911yescharacteristic
386Dic5—22no—
387Dic5—42no—
388Dic5—121no—
389#41—304no—
390#41—602no—
391C2×Q8—32no—
392C2×Q8—101no—
393C2×Q8C2×D3×D511yescharacteristic
394C2×D4—51no—
395C2×D4—151no—
396C2×D4—302no—
397C22×C4—52no—
398C22×C4—302no—
399C22×C4—301no—
400Q16—122no—
401SD16—302no—
402C2×C8—32no—
403C2×C8—151no—
404C2×C8—151no—
405C2×C8—602no—
406C4⋊C4—21no—
407C4⋊C4—51no—
408C4⋊C4—52no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4—102no—
412C4⋊C4—101no—
413C4⋊C4—151no—
414C4⋊C4—302no—
415C4⋊C4C2×D3×D511yescharacteristic
416C22⋊C4—52no—
417C22⋊C4—102no—
418C22⋊C4—102no—
419C22⋊C4—302no—
420C22⋊C4—301no—
421C42—21no—
422C42—102no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—102no—
426C22×C3—102no—
427C22×C3—102no—
428C22×C3C2×D4×D511yescharacteristic
429C2×D3—102no—
430C2×D3—201no—
431C2×D3—201no—
432C3×C4—21no—
433C3×C4—41no—
434C3×C4—41no—
435C3×C4—102no—
436C3×C4—202no—
437C3×C4#406512yes—
438C3×C4#414411yescharacteristic
439C3×C4D5×#4111yescharacteristic
440Dic3—42no—
441Dic3—201no—
442C2×C5C2×#95011yescharacteristic
443C2×C5#582911yescharacteristic
444C2×C5#583811yescharacteristic
445D5—42no—
446D5—122no—
447C23—52no—
448C23—301no—
449Q8—21no—
450Q8—21no—
451Q8—62no—
452Q8—62no—
453Q8—202no—
454D4—102no—
455D4—152no—
456D4—301no—
457D4—604no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—52no—
461C2×C4—62no—
462C2×C4—102no—
463C2×C4—102no—
464C2×C4—102no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4D5×#6711yescharacteristic
469C2×C4D5×#6711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—62no—
472C8—301no—
473C8—301no—
474C2×C3—202no—
475C2×C3#6594611yescharacteristic
476C2×C3C2×#406511yescharacteristic
477C2×C3#6611311yescharacteristic
478D3—202no—
479C5#8366411yescharacteristic, complemented, Sylow
480C22—102no—
481C22—102no—
482C22—102no—
483C22—302no—
484C22—601no—
485C22—601no—
486C22C2×D5×#6711yescharacteristic
487C4—21no—
488C4—41no—
489C4—41no—
490C4—102no—
491C4—122no—
492C4—202no—
493C4—601no—
494C4#9151612yes—
495C4#9201611yescharacteristic
496C4#9201811yescharacteristic
497C3#1061222311yescharacteristic, complemented, Sylow
498C2—202no—
499C2—602no—
500C2#1175464111yescharacteristic
501C2C2×#9151611yescharacteristic
502C2#1175533611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11752493C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3302
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. C3×#65918C2semidirect
3. C4×#6717C2semidirect
4. C5×#5031C2semidirect
5. #11749406C2semidirect
6. #11749366C2semidirect
7. #11747501C2semidirect
8. #11747342C2semidirect
9. #11746996C2semidirect
10. #11746971C2semidirect
11. #11746923C2semidirect
44. #65918D3semidirect
95. #5031D5semidirect
424. C3×C5#3302semidirect
479. C5#83664semidirect
497. C3#10612223semidirect

Maximal subgroups

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

subgroupindex
C3×#659182
#117524932
C4×#67172
C5×#50312
#117494062
#117493662
#117475012
#117473422
#117469962
#117469712
#117469232
#106122233
#836645