Finite Group Databasebeta

← #14459132

Subgroups — #14459132

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#11756486C211yesmaximal, characteristic, complemented
2#11756310C211yesmaximal, characteristic
3C3×C5×#461C211yesmaximal, characteristic, complemented
4#11751272C212yesmaximal, complemented
5#11751271C212yesmaximal, complemented
6#11751180C211yesmaximal, characteristic, complemented
7C4×#6716C211yesmaximal, characteristic, complemented
8#11750952C211yesmaximal, characteristic, complemented
9#11750935C211yesmaximal, characteristic, complemented
10#11750906C212yesmaximal, complemented
11D15×#103C212yesmaximal, complemented
12#10612181—31nomaximal, Hall
13C2×Q8×D15C2212yes—
14C2×#6817—21no—
15C2×C3×C5×SD16C2212yes—
16C3×C5×C4⋊Q8C2211yescharacteristic
17C3×C4×C5×D4C2211yescharacteristic
18#91835C2212yes—
19#91827C2212yes—
20C2×#6716C2211yescharacteristic
21#91813—21no—
22C2×C8×D15C2212yes—
23#91785—22no—
24#91782—21no—
25C4⋊C4×D15C2212yes—
26#91777—21no—
27#91772—22no—
28C4×D60C2211yescharacteristic
29#91758C2211yescharacteristic
30C4×Dic30C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic
32C3×C5×#103C2212yes—
33#91119C2212yes—
34#91119C2212yes—
35#91116C2211yescharacteristic
36#91104C2212yes—
37#91101C2212yes—
38#91100C2212yes—
39#91094C2211yescharacteristic
40#91092C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#80450—51nomaximal, Hall
43#66061—31no—
44#65885—31no—
45C5×#461D311yescharacteristic, complemented
46#65460—32no—
47#65459—32no—
48#65370—31no—
49C4×#687—31no—
50#65140—31no—
51#65123—31no—
52#65094—32no—
53D5×#103—32no—
54C2×C3×C5×Q8C2312yes—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×#1220—22no—
58Q8×D15—24no—
59Q8×D15—42no—
60#6817—44no—
61C2×D60D411yescharacteristic
62C2×C4×D15—22no—
63C2×C4×D15—22no—
64C2×C4×D15C2312yes—
65C2×Dic30—21no—
66C2×Dic30—22no—
67C2×Dic30C2311yescharacteristic
68C3×C5×SD16—42no—
69C2×C3×C5×C8C2312yes—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C5×C22⋊C4—21no—
74C3×C42×C5C2311yescharacteristic
75#6719—22no—
76#6716—22no—
77#6714—22no—
78#6714D412yes—
79C4⋊Dic15—21no—
80C4⋊Dic15D411yescharacteristic
81C4⋊Dic15C2311yescharacteristic
82C4⋊Dic15C2312yes—
83#6712—21no—
84#6712—22no—
85#6712—22no—
86C4×Dic15—21no—
87C2×C3⋊#168C2311yescharacteristic
88C2×C3⋊#168C2311yescharacteristic
89C8×D15—42no—
90#5727—51no—
91#5551—51no—
92C3×#461D511yescharacteristic, complemented
93#5171—52no—
94#5170—52no—
95#5079—51no—
96C4×#214—51no—
97#4851—51no—
98#4834—51no—
99#4805—52no—
100D3×#103—52no—
101C2×Q8×D5—32no—
102C2×#709—61no—
103C2×C5×SD16C2×D312yes—
104C5×C4⋊Q8C2×D311yescharacteristic
105C4×C5×D4C2×D311yescharacteristic
106#4092—32no—
107#4084—32no—
108C2×#687—31no—
109#4070—61no—
110C2×C8×D5—32no—
111#4042—62no—
112#4039—61no—
113D5×C4⋊C4—32no—
114#4034—61no—
115#4029—62no—
116C4×D20—31no—
117#4015—31no—
118C4×Dic10—31no—
119C5×C4⋊C8C2×D311yescharacteristic
120C5×#103C2×D312yes—
121#3967—32no—
122#3967—32no—
123#3964—31no—
124#3952—32no—
125#3949—32no—
126#3948—32no—
127#3942—31no—
128#3940—31no—
129C4×#168—31no—
130#3298—151noSylow
131C23×C3×C5—21no—
132C22×D15C2×D412yes—
133C3×C5×Q8—22no—
134C3×C5×Q8—22no—
135C3×C5×D4—21no—
136C3×C5×D4—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—42no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2411yescharacteristic
143#1220—44no—
144C2×Dic15—21no—
145C2×Dic15—21no—
146C2×Dic15—22no—
147C2×Dic15C2×D412yes—
148D60SD1614yescomplemented
149C4×D15—22no—
150C4×D15—22no—
151C4×D15—44no—
152C4×D15—44no—
153Dic30—21no—
154Dic30—44no—
155Dic30—42no—
156Dic30#4112yescomplemented
157C3×C5×C8—22no—
158C3⋊#168—21no—
159C3⋊#168—21no—
160C2×D3×Q8—52no—
161C2×#235—101no—
162C2×C3×SD16C2×D512yes—
163C3×C4⋊Q8C2×D511yescharacteristic
164C3×C4×D4C2×D511yescharacteristic
165#946—52no—
166#938—52no—
167C2×#214—51no—
168#924—101no—
169C2×D3×C8—52no—
170#896—102no—
171#893—101no—
172D3×C4⋊C4—52no—
173#888—101no—
174#883—102no—
175C4×D12—51no—
176#869—51no—
177C4×Dic6—51no—
178C3×C4⋊C8C2×D511yescharacteristic
179C3×#103C2×D512yes—
180#835—52no—
181#835—52no—
182#832—51no—
183(C2×D3)⋊C8—52no—
184#817—52no—
185#816—52no—
186#810—51no—
187#808—51no—
188C4×C3⋊C8—51no—
189C2×C5×Q8C22×D312yes—
190C2×C5×D4C22×D311yescharacteristic
191C22×C4×C5—21no—
192C2×C22⋊D5—62no—
193Q8×D5—64no—
194Q8×D5—122no—
195#709—124no—
196C2×D20—31no—
197C2×C4×D5—32no—
198C2×C4×D5—62no—
199C2×C4×D5—62no—
200C2×Dic10—31no—
201C2×Dic10—62no—
202C2×Dic10—61no—
203C5×SD16—42no—
204C2×C5×C8C22×D312yes—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4C22×D311yescharacteristic
208C5×C22⋊C4—21no—
209C42×C5C22×D311yescharacteristic
210C22⋊Dic5—62no—
211#687—62no—
212#685—32no—
213#685—62no—
214C4⋊Dic5—31no—
215C4⋊Dic5—31no—
216C4⋊Dic5—32no—
217C4⋊Dic5—61no—
218#683—62no—
219#683—62no—
220#683—61no—
221C4×Dic5—61no—
222C2×#168—31no—
223C2×#168—31no—
224C8×D5—122no—
225D4×Q8—151no—
226#547—151no—
227#487—151no—
228#483—152no—
229#475—151no—
230#465—152no—
231#461D1511yescharacteristic, complemented
232#448—152no—
233C4×SD16—151no—
234C8×D4—151no—
235C2×#103—152no—
236C22×C3×C5—41no—
237C22×C3×C5—41no—
238C22×C3×C5—41no—
239C22×C3×C5C22×D411yescharacteristic
240C2×D15—22no—
241C2×D15—22no—
242C2×D15C2×SD1614yes—
243C3×C4×C5—21no—
244C3×C4×C5—42no—
245C3×C4×C5—41no—
246C3×C4×C5C2×SD1612yes—
247C3×C4×C5C2×#4111yescharacteristic
248C3×C4×C5H(5,𝔽2)11yescharacteristic
249Dic15—22no—
250Dic15—22no—
251Dic15—42no—
252Dic15—41no—
253C2×C3×Q8C22×D512yes—
254C2×C3×D4C22×D511yescharacteristic
255C22×C3×C4—21no—
256C2×#67—102no—
257D3×Q8—104no—
258D3×Q8—202no—
259#235—204no—
260C2×D12—51no—
261C2×C4×D3—52no—
262C2×C4×D3—102no—
263C2×C4×D3—102no—
264C2×Dic6—51no—
265C2×Dic6—102no—
266C2×Dic6—101no—
267C3×SD16—42no—
268C2×C3×C8C22×D512yes—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4C22×D511yescharacteristic
272C3×C22⋊C4—21no—
273C3×C42C22×D511yescharacteristic
274#217—102no—
275#214—102no—
276(C2×D3)⋊C4—52no—
277(C2×D3)⋊C4—102no—
278C4⋊Dic3—51no—
279C4⋊Dic3—51no—
280C4⋊Dic3—52no—
281C4⋊Dic3—101no—
282Dic3⋊C4—102no—
283Dic3⋊C4—102no—
284Dic3⋊C4—101no—
285C4×Dic3—101no—
286C2×C3⋊C8—51no—
287C2×C3⋊C8—51no—
288D3×C8—202no—
289C23×C5—21no—
290C22×D5—32no—
291C5×Q8—22no—
292C5×Q8—22no—
293C5×D4—21no—
294C5×D4—21no—
295C2×C4×C5—21no—
296C2×C4×C5—22no—
297C2×C4×C5—42no—
298C2×C4×C5D3×D411yescharacteristic
299C2×C4×C5D3×D411yescharacteristic
300C2×C4×C5C23×D311yescharacteristic
301C22⋊D5—124no—
302C2×Dic5—32no—
303C2×Dic5—61no—
304C2×Dic5—61no—
305C2×Dic5—62no—
306D20—34no—
307C4×D5—62no—
308C4×D5—62no—
309C4×D5—124no—
310C4×D5—124no—
311Dic10—32no—
312Dic10—61no—
313Dic10—124no—
314Dic10—122no—
315C5×C8—22no—
316#168—61no—
317#168—61no—
318C2×#41—301no—
319C22×Q8—152no—
320C2×SD16—151no—
321C2×SD16C2×D1512yes—
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×Q8—151no—
332C4×D4—151no—
333C4×D4—301no—
334C4×D4C2×D1511yescharacteristic
335C2×C4⋊C4—152no—
336#106—152no—
337#106—151no—
338C4⋊C8C2×D1511yescharacteristic
339#103—152no—
340#103—152no—
341#103—152no—
342#103—151no—
343#103C2×D1512yes—
344#102—151no—
345C22⋊C8—152no—
346C4×C8—151no—
347C2×C3×C5—81no—
348C2×C3×C5#54611yescharacteristic
349C2×C3×C5C22×SD1611yescharacteristic
350C2×C3×C5#57811yescharacteristic
351D15—24no—
352C23×C3—21no—
353C22×D3—52no—
354C3×Q8—22no—
355C3×Q8—22no—
356C3×D4—21no—
357C3×D4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—42no—
361C2×C3×C4D4×D511yescharacteristic
362C2×C3×C4D4×D511yescharacteristic
363C2×C3×C4C23×D511yescharacteristic
364#67—204no—
365C2×Dic3—52no—
366C2×Dic3—101no—
367C2×Dic3—101no—
368C2×Dic3—102no—
369D12—54no—
370C4×D3—102no—
371C4×D3—102no—
372C4×D3—204no—
373C4×D3—204no—
374Dic6—52no—
375Dic6—101no—
376Dic6—204no—
377Dic6—202no—
378C3×C8—22no—
379C3⋊C8—101no—
380C3⋊C8—101no—
381C22×C5—41no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5C2×D3×D411yescharacteristic
385C2×D5—34no—
386C2×D5—62no—
387C2×D5—62no—
388C4×C5—21no—
389C4×C5—41no—
390C4×C5—42no—
391C4×C5D3×SD1612yes—
392C4×C5#100411yescharacteristic
393C4×C5D3×#4111yescharacteristic
394Dic5—62no—
395Dic5—62no—
396Dic5—122no—
397Dic5—121no—
398#41—604no—
399C2×Q8—151no—
400C2×Q8—302no—
401C2×Q8—301no—
402C2×Q8—304no—
403C2×Q8—602no—
404C2×Q8C22×D1512yes—
405C2×D4—151no—
406C2×D4—302no—
407C2×D4C22×D1511yescharacteristic
408C22×C4—21no—
409C22×C4—152no—
410C22×C4—302no—
411C22×C4—302no—
412SD16—42no—
413SD16—302no—
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—152no—
423C4⋊C4—302no—
424C4⋊C4—302no—
425C4⋊C4—301no—
426C4⋊C4—301no—
427C4⋊C4C22×D1511yescharacteristic
428C22⋊C4—21no—
429C22⋊C4—152no—
430C22⋊C4—302no—
431C22⋊C4—302no—
432C42—301no—
433C42C22×D1511yescharacteristic
434C3×C5#329811yescharacteristic, complemented, Hall
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3C2×D4×D511yescharacteristic
439C2×D3—54no—
440C2×D3—102no—
441C2×D3—102no—
442C3×C4—21no—
443C3×C4—41no—
444C3×C4—42no—
445C3×C4D5×SD1612yes—
446C3×C4#414411yescharacteristic
447C3×C4D5×#4111yescharacteristic
448Dic3—102no—
449Dic3—102no—
450Dic3—202no—
451Dic3—201no—
452C2×C5—81no—
453C2×C5#561211yescharacteristic
454C2×C5C2×D3×SD1611yescharacteristic
455C2×C5#577911yescharacteristic
456D5—64no—
457C23—21no—
458C23—152no—
459Q8—22no—
460Q8—22no—
461Q8—152no—
462Q8—301no—
463Q8—604no—
464Q8—602no—
465D4—21no—
466D4—21no—
467D4—154no—
468D4—604no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—42no—
472C2×C4—152no—
473C2×C4—301no—
474C2×C4—302no—
475C2×C4—302no—
476C2×C4—301no—
477C2×C4—302no—
478C2×C4—604no—
479C2×C4—604no—
480C2×C4D4×D1511yescharacteristic
481C2×C4D4×D1511yescharacteristic
482C2×C4C23×D1511yescharacteristic
483C8—22no—
484C8—301no—
485C8—301no—
486C2×C3—81no—
487C2×C3#6594611yescharacteristic
488C2×C3C2×D5×SD1611yescharacteristic
489C2×C3#6611311yescharacteristic
490D3—104no—
491C5#8045011yescharacteristic, complemented, Sylow
492C22—41no—
493C22—41no—
494C22—41no—
495C22—154no—
496C22—302no—
497C22—302no—
498C22C2×D4×D1511yescharacteristic
499C4—21no—
500C4—42no—
501C4—41no—
502C4—302no—
503C4—302no—
504C4—602no—
505C4—601no—
506C4SD16×D1512yes—
507C4#9209511yescharacteristic
508C4#41×D1511yescharacteristic
509C3#1061218111yescharacteristic, complemented, Sylow
510C2—81no—
511C2—304no—
512C2#1175637111yescharacteristic
513C2C2×SD16×D1511yescharacteristic
514C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#461C2
socleC22×C3×C5C22×D4
prime radical#11756310C2
hypercenter#461D15
hypocenterC3×C5#3298
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #11756486C2semidirect
3. C3×C5×#461C2semidirect
4. #11751272C2semidirect
5. #11751271C2semidirect
6. #11751180C2semidirect
7. C4×#6716C2semidirect
8. #11750952C2semidirect
9. #11750935C2semidirect
10. #11750906C2semidirect
11. D15×#103C2semidirect
45. C5×#461D3semidirect
92. C3×#461D5semidirect
148. D60SD16semidirect
156. Dic30#41semidirect
231. #461D15semidirect
434. C3×C5#3298semidirect
491. C5#80450semidirect
509. C3#10612181semidirect

Maximal subgroups

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

subgroupindex
#117564862
#117563102
C3×C5×#4612
#117512722
#117512712
#117511802
C4×#67162
#117509522
#117509352
#117509062
D15×#1032
#106121813
#804505