Finite Group Databasebeta

← #14459114

Subgroups — #14459114

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756485C211yesmaximal, characteristic
2Q8×D60C211yesmaximal, characteristic, complemented
3C3×C5×#475C211yesmaximal, characteristic, complemented
4#11751194C211yesmaximal, characteristic, complemented
5C4×#6717C211yesmaximal, characteristic, complemented
6#11750965C212yesmaximal, complemented
7#11750963C212yesmaximal, complemented
8#11750942C211yesmaximal, characteristic, complemented
9#11750935C211yesmaximal, characteristic, complemented
10#11750907C212yesmaximal, complemented
11D15×#103C212yesmaximal, complemented
12#10612753—31nomaximal, Hall
13C2×#6821—21no—
14C2×Q8×D15C2212yes—
15C3×C5×C4⋊Q8C2211yescharacteristic
16C3×C4×C5×Q8C2211yescharacteristic
17#91835—21no—
18C2×#6717C2211yescharacteristic
19C2×#6706C2212yes—
20C2×C8×D15C2212yes—
21#91786—22no—
22#91786C2212yes—
23#91784C2212yes—
24#91783—22no—
25C4⋊C4×D15C2212yes—
26C4×D60—21no—
27C4×D60C2211yescharacteristic
28C4×D60C2211yescharacteristic
29#91758—21no—
30#91758C2211yescharacteristic
31C3×C5×#106C2212yes—
32C3×C5×C4⋊C8C2211yescharacteristic
33C3×C5×#103C2212yes—
34#91119C2211yescharacteristic
35#91104C2212yes—
36#91100C2212yes—
37#91094C2212yes—
38#91094C2212yes—
39#91093C2211yescharacteristic
40#91092C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#81022—51nomaximal, Hall
43#66060—31no—
44Q8×D20—31no—
45C5×#475D311yescharacteristic, complemented
46#65382—31no—
47C4×#688—31no—
48#65153—32no—
49#65151—32no—
50#65130—31no—
51#65123—31no—
52#65095—32no—
53D5×#103—32no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8C2311yescharacteristic
56#6821—44no—
57Q8×D15—24no—
58Q8×D15—42no—
59C2×D60—22no—
60C2×D60D411yescharacteristic
61C2×D60C2311yescharacteristic
62C2×C4×D15—22no—
63C2×C4×D15—22no—
64C2×C4×D15—21no—
65C2×C4×D15C2312yes—
66C2×Dic30—22no—
67C2×Dic30C2312yes—
68C2×C3×C5×C8C2312yes—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C42×C5—21no—
74C3×C42×C5C2311yescharacteristic
75#6717—22no—
76#6714—22no—
77#6714—21no—
78#6714—22no—
79#6714D412yes—
80C4⋊Dic15—21no—
81C4⋊Dic15—21no—
82C4⋊Dic15—22no—
83C4⋊Dic15D411yescharacteristic
84C4⋊Dic15C2311yescharacteristic
85#6712—22no—
86C2×C3⋊#168C2311yescharacteristic
87C2×C3⋊#168C2311yescharacteristic
88#6706—42no—
89C8×D15—42no—
90#5726—51no—
91Q8×D12—51no—
92C3×#475D511yescharacteristic, complemented
93#5093—51no—
94C4×#215—51no—
95#4864—52no—
96#4862—52no—
97#4841—51no—
98#4834—51no—
99#4806—52no—
100D3×#103—52no—
101C2×#713—61no—
102C2×Q8×D5—32no—
103C5×C4⋊Q8C2×D311yescharacteristic
104C4×C5×Q8C2×D311yescharacteristic
105#4092—61no—
106C2×#688—31no—
107C2×#677—32no—
108C2×C8×D5—32no—
109#4043—32no—
110#4043—62no—
111#4041—32no—
112#4040—62no—
113D5×C4⋊C4—32no—
114C4×D20—31no—
115C4×D20—31no—
116C4×D20—61no—
117#4015—31no—
118#4015—61no—
119C5×#106C2×D312yes—
120C5×C4⋊C8C2×D311yescharacteristic
121C5×#103C2×D312yes—
122#3967—31no—
123#3952—32no—
124#3948—32no—
125#3942—32no—
126#3942—32no—
127#3941—31no—
128#3940—31no—
129C4×#168—31no—
130#3298—151noSylow
131C22×D15—21no—
132C22×D15C2×D412yes—
133C3×C5×Q8—21no—
134C3×C5×Q8—42no—
135C3×C5×Q8#4112yescomplemented
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143C2×Dic15—22no—
144C2×Dic15C2×D412yes—
145D60—21no—
146D60—21no—
147D60—44no—
148D60SD1614yescomplemented
149C4×D15—22no—
150C4×D15—22no—
151C4×D15—44no—
152C4×D15—44no—
153C4×D15—42no—
154Dic30—22no—
155Dic30—22no—
156Dic30—44no—
157C3×C5×C8—22no—
158C3⋊#168—21no—
159C3⋊#168—21no—
160C2×#239—101no—
161C2×D3×Q8—52no—
162C3×C4⋊Q8C2×D511yescharacteristic
163C3×C4×Q8C2×D511yescharacteristic
164#946—101no—
165C2×#215—51no—
166C2×#204—52no—
167C2×D3×C8—52no—
168#897—52no—
169#897—102no—
170#895—52no—
171#894—102no—
172D3×C4⋊C4—52no—
173C4×D12—51no—
174C4×D12—51no—
175C4×D12—101no—
176#869—51no—
177#869—101no—
178C3×#106C2×D512yes—
179C3×C4⋊C8C2×D511yescharacteristic
180C3×#103C2×D512yes—
181#835—51no—
182(C2×D3)⋊C8—52no—
183#816—52no—
184#810—52no—
185#810—52no—
186#809—51no—
187#808—51no—
188C4×C3⋊C8—51no—
189C2×C5×Q8—21no—
190C2×C5×Q8C22×D311yescharacteristic
191#713—124no—
192Q8×D5—64no—
193Q8×D5—122no—
194C2×D20—31no—
195C2×D20—31no—
196C2×D20—62no—
197C2×C4×D5—32no—
198C2×C4×D5—62no—
199C2×C4×D5—62no—
200C2×C4×D5—61no—
201C2×Dic10—32no—
202C2×Dic10—62no—
203C2×C5×C8C22×D312yes—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4C22×D311yescharacteristic
207C5×C4⋊C4C22×D312yes—
208C42×C5—21no—
209C42×C5C22×D311yescharacteristic
210#688—62no—
211#685—32no—
212#685—62no—
213#685—62no—
214#685—61no—
215C4⋊Dic5—31no—
216C4⋊Dic5—31no—
217C4⋊Dic5—62no—
218C4⋊Dic5—61no—
219C4⋊Dic5—61no—
220#683—62no—
221C2×#168—31no—
222C2×#168—31no—
223#677—122no—
224C8×D5—122no—
225D4×Q8—151no—
226#547—151no—
227#487—151no—
228#483—152no—
229#475D1511yescharacteristic, complemented
230#465—152no—
231#461—151no—
232#448—152no—
233C4×SD16—151no—
234C8×D4—151no—
235C2×#103—152no—
236C22×C3×C5C22×D411yescharacteristic
237C2×D15—22no—
238C2×D15—22no—
239C2×D15—41no—
240C2×D15—41no—
241C2×D15—41no—
242C2×D15C2×SD1614yes—
243C3×C4×C5—22no—
244C3×C4×C5—21no—
245C3×C4×C5—42no—
246C3×C4×C5—41no—
247C3×C4×C5C2×SD1612yes—
248C3×C4×C5C2×#4111yescharacteristic
249C3×C4×C5H(5,𝔽2)11yescharacteristic
250Dic15—22no—
251Dic15—42no—
252Dic15—41no—
253C2×C3×Q8—21no—
254C2×C3×Q8C22×D511yescharacteristic
255#239—204no—
256D3×Q8—104no—
257D3×Q8—202no—
258C2×D12—51no—
259C2×D12—51no—
260C2×D12—102no—
261C2×C4×D3—52no—
262C2×C4×D3—102no—
263C2×C4×D3—102no—
264C2×C4×D3—101no—
265C2×Dic6—52no—
266C2×Dic6—102no—
267C2×C3×C8C22×D512yes—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4C22×D511yescharacteristic
271C3×C4⋊C4C22×D512yes—
272C3×C42—21no—
273C3×C42C22×D511yescharacteristic
274#215—102no—
275(C2×D3)⋊C4—52no—
276(C2×D3)⋊C4—102no—
277(C2×D3)⋊C4—102no—
278(C2×D3)⋊C4—101no—
279C4⋊Dic3—51no—
280C4⋊Dic3—51no—
281C4⋊Dic3—102no—
282C4⋊Dic3—101no—
283C4⋊Dic3—101no—
284Dic3⋊C4—102no—
285C2×C3⋊C8—51no—
286C2×C3⋊C8—51no—
287#204—202no—
288D3×C8—202no—
289C22×D5—32no—
290C22×D5—61no—
291C5×Q8—21no—
292C5×Q8—42no—
293C5×Q8#23912yescomplemented
294C2×C4×C5—21no—
295C2×C4×C5—22no—
296C2×C4×C5—21no—
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5D3×D411yescharacteristic
299C2×C4×C5C23×D311yescharacteristic
300C2×Dic5—32no—
301C2×Dic5—61no—
302C2×Dic5—62no—
303D20—34no—
304D20—61no—
305D20—61no—
306D20—124no—
307C4×D5—62no—
308C4×D5—62no—
309C4×D5—124no—
310C4×D5—124no—
311C4×D5—122no—
312Dic10—62no—
313Dic10—62no—
314Dic10—124no—
315C5×C8—22no—
316#168—61no—
317#168—61no—
318C2×#41—301no—
319C22×Q8—152no—
320C2×SD16—151no—
321C2×SD16—152no—
322C22×C8—152no—
323C4⋊Q8—151no—
324C4⋊Q8—301no—
325C4⋊Q8C2×D1511yescharacteristic
326#123—302no—
327C22⋊Q8—152no—
328C22⋊Q8—302no—
329C22⋊Q8—301no—
330#121—152no—
331C4×Q8C2×D1511yescharacteristic
332C4×D4—151no—
333C4×D4—151no—
334C4×D4—301no—
335C2×C4⋊C4—152no—
336#106—151no—
337#106C2×D1512yes—
338C4⋊C8C2×D1511yescharacteristic
339#103—151no—
340#103—152no—
341#103—152no—
342#103—152no—
343#103C2×D1512yes—
344#102—151no—
345C22⋊C8—152no—
346C4×C8—151no—
347C2×C3×C5#54611yescharacteristic
348C2×C3×C5C22×SD1611yescharacteristic
349C2×C3×C5#57811yescharacteristic
350D15—24no—
351D15—81no—
352C22×D3—52no—
353C22×D3—101no—
354C3×Q8—21no—
355C3×Q8—42no—
356C3×Q8#71312yescomplemented
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4D4×D511yescharacteristic
361C2×C3×C4D4×D511yescharacteristic
362C2×C3×C4C23×D511yescharacteristic
363C2×Dic3—52no—
364C2×Dic3—101no—
365C2×Dic3—102no—
366D12—54no—
367D12—101no—
368D12—101no—
369D12—204no—
370C4×D3—102no—
371C4×D3—102no—
372C4×D3—204no—
373C4×D3—204no—
374C4×D3—202no—
375Dic6—102no—
376Dic6—102no—
377Dic6—204no—
378C3×C8—22no—
379C3⋊C8—101no—
380C3⋊C8—101no—
381C22×C5C2×D3×D411yescharacteristic
382C2×D5—34no—
383C2×D5—62no—
384C2×D5—62no—
385C2×D5—121no—
386C2×D5—121no—
387C2×D5—121no—
388C4×C5—21no—
389C4×C5—22no—
390C4×C5—42no—
391C4×C5—41no—
392C4×C5D3×SD1612yes—
393C4×C5C2×#23911yescharacteristic
394C4×C5#100911yescharacteristic
395Dic5—62no—
396Dic5—121no—
397Dic5—122no—
398#41—604no—
399C2×Q8—21no—
400C2×Q8—152no—
401C2×Q8—302no—
402C2×Q8—304no—
403C2×Q8—602no—
404C2×Q8C22×D1511yescharacteristic
405C2×D4—151no—
406C2×D4—151no—
407C2×D4—302no—
408C22×C4—152no—
409C22×C4—302no—
410C22×C4—302no—
411C22×C4—301no—
412SD16—302no—
413SD16—602no—
414C2×C8—151no—
415C2×C8—151no—
416C2×C8—602no—
417C2×C8C22×D1512yes—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—151no—
421C4⋊C4—151no—
422C4⋊C4—302no—
423C4⋊C4—302no—
424C4⋊C4—301no—
425C4⋊C4—301no—
426C4⋊C4C22×D1511yescharacteristic
427C4⋊C4C22×D1512yes—
428C22⋊C4—152no—
429C22⋊C4—302no—
430C22⋊C4—302no—
431C22⋊C4—301no—
432C42—21no—
433C42C22×D1511yescharacteristic
434C3×C5#329811yescharacteristic, complemented, Hall
435C22×C3C2×D4×D511yescharacteristic
436C2×D3—54no—
437C2×D3—102no—
438C2×D3—102no—
439C2×D3—201no—
440C2×D3—201no—
441C2×D3—201no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—42no—
445C3×C4—41no—
446C3×C4D5×SD1612yes—
447C3×C4C2×#71311yescharacteristic
448C3×C4#414911yescharacteristic
449Dic3—102no—
450Dic3—201no—
451Dic3—202no—
452C2×C5#563011yescharacteristic
453C2×C5C2×D3×SD1611yescharacteristic
454C2×C5#577911yescharacteristic
455D5—64no—
456D5—241no—
457C23—152no—
458C23—301no—
459Q8—21no—
460Q8—42no—
461Q8—302no—
462Q8—302no—
463Q8—604no—
464Q8#682112yescomplemented
465D4—154no—
466D4—301no—
467D4—301no—
468D4—604no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—152no—
473C2×C4—302no—
474C2×C4—302no—
475C2×C4—301no—
476C2×C4—302no—
477C2×C4—604no—
478C2×C4—604no—
479C2×C4—602no—
480C2×C4D4×D1511yescharacteristic
481C2×C4D4×D1511yescharacteristic
482C2×C4C23×D1511yescharacteristic
483C8—22no—
484C8—301no—
485C8—301no—
486C2×C3#6596411yescharacteristic
487C2×C3C2×D5×SD1611yescharacteristic
488C2×C3#6611311yescharacteristic
489D3—104no—
490D3—401no—
491C5#8102211yescharacteristic, complemented, Sylow
492C22—154no—
493C22—302no—
494C22—302no—
495C22—601no—
496C22—601no—
497C22—601no—
498C22C2×D4×D1511yescharacteristic
499C4—22no—
500C4—21no—
501C4—42no—
502C4—41no—
503C4—302no—
504C4—602no—
505C4—601no—
506C4SD16×D1512yes—
507C4C2×#682111yescharacteristic
508C4#9210011yescharacteristic
509C3#1061275311yescharacteristic, complemented, Sylow
510C2—304no—
511C2—1201no—
512C2#1175638911yescharacteristic
513C2C2×SD16×D1511yescharacteristic
514C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#475C2
socleC22×C3×C5C22×D4
prime radical#11756485C2
hypercenter#475D15
hypocenterC3×C5#3298
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. Q8×D60C2semidirect
3. C3×C5×#475C2semidirect
4. #11751194C2semidirect
5. C4×#6717C2semidirect
6. #11750965C2semidirect
7. #11750963C2semidirect
8. #11750942C2semidirect
9. #11750935C2semidirect
10. #11750907C2semidirect
11. D15×#103C2semidirect
45. C5×#475D3semidirect
92. C3×#475D5semidirect
135. C3×C5×Q8#41semidirect
148. D60SD16semidirect
229. #475D15semidirect
293. C5×Q8#239semidirect
356. C3×Q8#713semidirect
434. C3×C5#3298semidirect
464. Q8#6821semidirect
491. C5#81022semidirect
509. C3#10612753semidirect

Maximal subgroups

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

subgroupindex
#117564852
Q8×D602
C3×C5×#4752
#117511942
C4×#67172
#117509652
#117509632
#117509422
#117509352
#117509072
D15×#1032
#106127533
#810225