Finite Group Databasebeta

← #14413479

Subgroups — #14413479

Order 1920.

952 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
1C2×#91796C211yesmaximal, characteristic
2#11754506C211yesmaximal, characteristic
3#11754496C211yesmaximal, characteristic
4C5×#5121C211yesmaximal, characteristic, complemented
5C3×#65410C211yesmaximal, characteristic, complemented
6#11748469C211yesmaximal, characteristic, complemented
7C2×#90986C211yesmaximal, characteristic, complemented
8#11747690C212yesmaximal, complemented
9#11747640C212yesmaximal, complemented
10#11747638C212yesmaximal, complemented
11#11747632C212yesmaximal, complemented
12#10610940—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15C22×C3⋊#168C2211yescharacteristic
16#91796C418yescomplemented
17C2×#6705C2212yes—
18C2×C8×D15C2212yes—
19C5×#926C2211yescharacteristic
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C3×#4072C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23#91556—22no—
24#91552—22no—
25#91437C2212yes—
26#91437C2212yes—
27#91428—21no—
28#91418—21no—
29#91347C2212yes—
30#91347C2212yes—
31#91340—21no—
32#91333—21no—
33C5×#818C2212yes—
34C5×#817C2212yes—
35C3×#3950C2212yes—
36C3×#3949C2212yes—
37#90989C2211yescharacteristic
38#90989C2211yescharacteristic
39#90986C2211yescharacteristic
40#90986C2212yes—
41#90986C2212yes—
42#90986C2211yescharacteristic
43#79209—51nomaximal, Hall
44C2×#4053—31no—
45#65857—31no—
46#65838—31no—
47C5×#428—31no—
48#65410D311yescharacteristic, complemented
49#65287—31no—
50C2×#3940—31no—
51#65170—32no—
52#65169—32no—
53#65150—32no—
54D5×#106—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220D412yes—
57#6817C2×C414yes—
58#6817Q814yes—
59C2×D60D411yescharacteristic
60C2×C4×D15C2312yes—
61C2×Dic30D411yescharacteristic
62C22×C5×Dic3—21no—
63C22×C3×Dic5—21no—
64C2×#1200—22no—
65C2×#1200—22no—
66C3×C5×M16C2×C414yescomplemented
67C2×C3×C5×C8C2312yes—
68C2×C3⋊#168C2×C414yescomplemented
69C2×C3⋊#168C2311yescharacteristic
70C2×C3⋊#168C2311yescharacteristic
71#6705C2×C418yescomplemented
72C8×D15C2×C418yescomplemented
73C5×#217—21no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×C4⋊Dic3C2312yes—
77C5×C4⋊Dic3C2311yescharacteristic
78C4×C5×Dic3—21no—
79C3×C22⋊Dic5—21no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2312yes—
83C3×C4⋊Dic5C2311yescharacteristic
84C3×C4×Dic5—21no—
85#6669—22no—
86#6669—22no—
87#6667—22no—
88#6667—22no—
89Dic3×Dic5—22no—
90Dic3×Dic5—22no—
91C2×#907—51no—
92#5523—51no—
93#5504—51no—
94C3×#428—51no—
95#5121D511yescharacteristic, complemented
96#4998—51no—
97C2×#808—51no—
98#4881—52no—
99#4880—52no—
100#4861—52no—
101D3×#106—52no—
102C2×#709—31no—
103C2×C5×M16C2×D311yescharacteristic
104C5×#117—31no—
105C2×C5×C4⋊C4—31no—
106C4×C22⋊D5—62no—
107#4072C2×D311yescharacteristic
108C2×C4⋊Dic5C2×D311yescharacteristic
109C22×#168—31no—
110#4053—38no—
111C2×#676—32no—
112C2×C8×D5—32no—
113#4039—61no—
114#4038—32no—
115#4038—32no—
116D5×C4⋊C4—32no—
117D5×C4⋊C4—32no—
118#4033—61no—
119#4027—62no—
120C4×D20—61no—
121C4×Dic10—61no—
122C5×#107—32no—
123C5×#106—32no—
124#3950C2×D312yes—
125#3949C2×D312yes—
126#3940—31no—
127#3940—31no—
128#3940—32no—
129#3940—32no—
130#3939—31no—
131#3939—31no—
132#2912—151noSylow
133C23×C3×C5C2×D411yescharacteristic
134C22×D15C2×D412yes—
135C2×C3×C4×C5C22×C412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×Q812yes—
138C2×C3×C4×C5C2411yescharacteristic
139#1220C4⋊C418yes—
140C2×Dic15C2×D412yes—
141D60C4⋊C414yes—
142C4×D15C22×C414yes—
143C4×D15C2×Q814yes—
144Dic30C4⋊C414yes—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—81no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—81no—
153#1200—82no—
154#1200—82no—
155C3×C5×C8C22×C414yes—
156C3⋊#168C22×C412yes—
157C3⋊#168C22×C412yes—
158C2×#235—51no—
159C2×C3×M16C2×D511yescharacteristic
160C3×#117—51no—
161C2×C3×C4⋊C4—51no—
162C4×#67—102no—
163#926C2×D511yescharacteristic
164C2×C4⋊Dic3C2×D511yescharacteristic
165C22×C3⋊C8—51no—
166#907—58no—
167C2×ΓL(1,𝔽25)—52no—
168C2×D3×C8—52no—
169#893—101no—
170#892—52no—
171#892—52no—
172D3×C4⋊C4—52no—
173D3×C4⋊C4—52no—
174#887—101no—
175#67⋊C4—102no—
176C4×D12—101no—
177C4×Dic6—101no—
178C3×#107—52no—
179C3×#106—52no—
180#818C2×D512yes—
181#817C2×D512yes—
182#808—51no—
183#808—52no—
184#808—52no—
185#808—51no—
186#807—51no—
187#807—51no—
188C22×C4×C5—61no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—32no—
191C22×Dic5—21no—
192#709—34no—
193#709—34no—
194C2×D20—31no—
195C2×C4×D5—32no—
196C2×C4×D5—62no—
197C2×C4×D5—62no—
198C2×Dic10—31no—
199C5×M16C4×D314yescomplemented
200C2×C5×C8C22×D312yes—
201C5×C4⋊C4—32no—
202C5×C4⋊C4—31no—
203C5×C4⋊C4—31no—
204C5×C4⋊C4—61no—
205C5×C22⋊C4—61no—
206C42×C5—61no—
207C22⋊Dic5—21no—
208#685—62no—
209#685—62no—
210C4⋊Dic5—21no—
211C4⋊Dic5C22×D311yescharacteristic
212C4⋊Dic5C22×D311yescharacteristic
213C4⋊Dic5C22×D312yes—
214#683—62no—
215#683—62no—
216C4×Dic5—21no—
217C4×Dic5—62no—
218C4×Dic5—62no—
219C2×#168—34no—
220C2×#168—31no—
221C2×#168—31no—
222#676—38no—
223C8×D5—38no—
224C2×#131—151no—
225#520—151no—
226#520—151no—
227#428—31no—
228#428—51no—
229#428—152no—
230#428—152no—
231#427—152no—
232#427—151no—
233C2×#106—152no—
234C2×#106—151no—
235C22×C3×C5—21no—
236C22×C3×C5—21no—
237C22×C3×C5C2×C4⋊C412yes—
238C22×C3×C5C22×D411yescharacteristic
239C2×D15—22no—
240C2×D15—22no—
241C2×D15C2×C4⋊C414yes—
242C3×C4×C5C2×C4⋊C412yes—
243C3×C4×C5C23×C411yescharacteristic
244C3×C4×C5C22×Q811yescharacteristic
245Dic15C2×C4⋊C414yes—
246C3×Dic5—41no—
247C3×Dic5—42no—
248C3×Dic5—41no—
249C5×Dic3—41no—
250C5×Dic3—42no—
251C5×Dic3—41no—
252C22×C3×C4—101no—
253C22×C3×C4C22×D511yescharacteristic
254C2×#67—52no—
255C22×Dic3—21no—
256#235—54no—
257#235—54no—
258C2×D12—51no—
259C2×C4×D3—52no—
260C2×C4×D3—102no—
261C2×C4×D3—102no—
262C2×Dic6—51no—
263C3×M16C4×D514yescomplemented
264C2×C3×C8C22×D512yes—
265C3×C4⋊C4—51no—
266C3×C4⋊C4—51no—
267C3×C4⋊C4—52no—
268C3×C4⋊C4—101no—
269C3×C22⋊C4—101no—
270C3×C42—101no—
271#217—21no—
272(C2×D3)⋊C4—102no—
273(C2×D3)⋊C4—102no—
274C4⋊Dic3—21no—
275C4⋊Dic3C22×D511yescharacteristic
276C4⋊Dic3C22×D511yescharacteristic
277C4⋊Dic3C22×D512yes—
278Dic3⋊C4—102no—
279Dic3⋊C4—102no—
280C4×Dic3—21no—
281C4×Dic3—102no—
282C4×Dic3—102no—
283C2×C3⋊C8—54no—
284C2×C3⋊C8—51no—
285C2×C3⋊C8—51no—
286ΓL(1,𝔽25)—58no—
287D3×C8—58no—
288C23×C5D3×D411yescharacteristic
289C22×D5—32no—
290C2×C4×C5—61no—
291C2×C4×C5—62no—
292C2×C4×C5—61no—
293C2×C4×C5—241no—
294C2×C4×C5C2×C4×D312yes—
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5D3×Q812yes—
297C2×C4×C5C23×D311yescharacteristic
298C22⋊D5—38no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—22no—
302C2×Dic5—32no—
303C2×Dic5—81no—
304D20—34no—
305C4×D5—34no—
306C4×D5—34no—
307C4×D5—242no—
308C4×D5—242no—
309Dic10—34no—
310C5×C8C2×C4×D314yes—
311#168—32no—
312#168—32no—
313C2×#41—151no—
314#131—158no—
315C2×M16—152no—
316C2×M16D3×D511yescharacteristic
317C22×C8—151no—
318C22×C8—152no—
319C4×Q8—301no—
320C4×Q8—301no—
321C4×D4—301no—
322C4×D4—301no—
323C4×D4—302no—
324C4×D4—302no—
325#117—31no—
326#117—51no—
327#117—152no—
328#117—152no—
329C2×C4⋊C4—31no—
330C2×C4⋊C4—51no—
331C2×C4⋊C4—152no—
332C2×C4⋊C4—152no—
333#107—32no—
334#107—52no—
335#107—151no—
336#107—151no—
337#106—32no—
338#106—52no—
339#106—151no—
340#106—152no—
341#106—152no—
342#106—151no—
343C2×C3×C5—22no—
344C2×C3×C5C22×C4⋊C411yescharacteristic
345C2×C3×C5#57711yescharacteristic
346C2×C3×C5#57711yescharacteristic
347D15—24no—
348C23×C3D4×D511yescharacteristic
349C22×D3—52no—
350C2×C3×C4—101no—
351C2×C3×C4—102no—
352C2×C3×C4—101no—
353C2×C3×C4—401no—
354C2×C3×C4C2×C4×D512yes—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4Q8×D512yes—
357C2×C3×C4C23×D511yescharacteristic
358#67—58no—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—52no—
363C2×Dic3—81no—
364D12—54no—
365C4×D3—54no—
366C4×D3—54no—
367C4×D3—402no—
368C4×D3—402no—
369Dic6—54no—
370C3×C8C2×C4×D514yes—
371C3⋊C8—52no—
372C3⋊C8—52no—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5D3×C4⋊C412yes—
376C22×C5C2×D3×D411yescharacteristic
377C2×D5—34no—
378C2×D5—62no—
379C2×D5—62no—
380C4×C5—121no—
381C4×C5—122no—
382C4×C5—121no—
383C4×C5D3×C4⋊C412yes—
384C4×C5C22×C4×D311yescharacteristic
385C4×C5C2×D3×Q811yescharacteristic
386Dic5—34no—
387Dic5—42no—
388Dic5—41no—
389Dic5—41no—
390#41—154no—
391#41—154no—
392C2×Q8—151no—
393C2×D4—152no—
394C2×D4—151no—
395C22×C4—61no—
396C22×C4—101no—
397C22×C4—152no—
398C22×C4—302no—
399C22×C4—302no—
400C22×C4C2×D3×D511yescharacteristic
401M16—158no—
402M16#120014yescomplemented
403C2×C8—154no—
404C2×C8—151no—
405C2×C8—151no—
406C2×C8—158no—
407C2×C8C2×D3×D512yes—
408C4⋊C4—31no—
409C4⋊C4—32no—
410C4⋊C4—31no—
411C4⋊C4—51no—
412C4⋊C4—52no—
413C4⋊C4—51no—
414C4⋊C4—61no—
415C4⋊C4—101no—
416C4⋊C4—302no—
417C4⋊C4—302no—
418C22⋊C4—61no—
419C22⋊C4—101no—
420C22⋊C4—302no—
421C22⋊C4—302no—
422C42—61no—
423C42—101no—
424C42—302no—
425C42—302no—
426C3×C5#291211yescharacteristic, complemented, Hall
427C22×C3—21no—
428C22×C3—21no—
429C22×C3D5×C4⋊C412yes—
430C22×C3C2×D4×D511yescharacteristic
431C2×D3—54no—
432C2×D3—102no—
433C2×D3—102no—
434C3×C4—201no—
435C3×C4—202no—
436C3×C4—201no—
437C3×C4D5×C4⋊C412yes—
438C3×C4C22×C4×D511yescharacteristic
439C3×C4C2×Q8×D511yescharacteristic
440Dic3—42no—
441Dic3—41no—
442Dic3—41no—
443Dic3—54no—
444C2×C5—22no—
445C2×C5C2×D3×C4⋊C411yescharacteristic
446C2×C5#577511yescharacteristic
447C2×C5#577811yescharacteristic
448D5—64no—
449C23—152no—
450C23#677711yescharacteristic
451Q8—154no—
452D4—158no—
453D4—154no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—62no—
457C2×C4—101no—
458C2×C4—101no—
459C2×C4—102no—
460C2×C4—152no—
461C2×C4—154no—
462C2×C4—154no—
463C2×C4—241no—
464C2×C4—401no—
465C2×C4—1202no—
466C2×C4—1202no—
467C2×C4D15⋊Q812yes—
468C2×C4#677711yescharacteristic
469C2×C4C2×#120012yes—
470C2×C4C22×D3×D511yescharacteristic
471C8—152no—
472C8—152no—
473C8C2×#120014yes—
474C2×C3—22no—
475C2×C3C2×D5×C4⋊C411yescharacteristic
476C2×C3#6610911yescharacteristic
477C2×C3#6611211yescharacteristic
478D3—104no—
479C5#7920911yescharacteristic, complemented, Sylow
480C22—21no—
481C22—21no—
482C22—154no—
483C22—302no—
484C22—302no—
485C22#9143712yes—
486C22C2×#677711yescharacteristic
487C4—121no—
488C4—122no—
489C4—121no—
490C4—154no—
491C4—202no—
492C4—201no—
493C4—201no—
494C4#9143712yes—
495C4C2×D15⋊Q811yescharacteristic
496C4C22×#120011yescharacteristic
497C3#1061094011yescharacteristic, complemented, Sylow
498C2—22no—
499C2—304no—
500C2#1175403711yescharacteristic
501C2#1175403911yescharacteristic
502C2C2×#9143711yescharacteristic
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2912
LCSG ▷ 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
4. C5×#5121C2semidirect
5. C3×#65410C2semidirect
6. #11748469C2semidirect
7. C2×#90986C2semidirect
8. #11747690C2semidirect
9. #11747640C2semidirect
10. #11747638C2semidirect
11. #11747632C2semidirect
16. #91796C4semidirect
48. #65410D3semidirect
66. C3×C5×M16C2×C4semidirect
68. C2×C3⋊#168C2×C4semidirect
71. #6705C2×C4semidirect
72. C8×D15C2×C4semidirect
95. #5121D5semidirect
199. C5×M16C4×D3semidirect
263. C3×M16C4×D5semidirect
402. M16#1200semidirect
426. C3×C5#2912semidirect
479. C5#79209semidirect
497. C3#10610940semidirect

Maximal subgroups

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

subgroupindex
C2×#917962
#117545062
#117544962
C5×#51212
C3×#654102
#117484692
C2×#909862
#117476902
#117476402
#117476382
#117476322
#106109403
#792095