Finite Group Databasebeta

← #14413535

Subgroups — #14413535

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×C5×#907C211yesmaximal, characteristic
2#11754513C211yesmaximal, characteristic
3#11754492C211yesmaximal, characteristic
4#11751222C211yesmaximal, characteristic, complemented
5C3×#65410C211yesmaximal, characteristic, complemented
6C2×#90990C211yesmaximal, characteristic, complemented
7#11748451C211yesmaximal, characteristic, complemented
8#11747679C212yesmaximal, complemented
9#11747630C212yesmaximal, complemented
10#11747628C212yesmaximal, complemented
11D3×#3950C212yesmaximal, complemented
12#10615516—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15#91815C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C22×C5×C3⋊C8C2211yescharacteristic
18C5×#907C418yescomplemented
19C2×C5×ΓL(1,𝔽25)C2212yes—
20C2×C5×D3×C8C2212yes—
21C3×#4072C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23#67⋊Dic5—22no—
24Dic5×#67—22no—
25#91435—21no—
26D3×C4⋊Dic5C2212yes—
27D3×C4⋊Dic5C2212yes—
28Dic5×D12—21no—
29#91344—21no—
30#91338C2212yes—
31#91338C2212yes—
32Dic5×Dic6—21no—
33#91102C2212yes—
34#91101C2212yes—
35C3×#3950C2212yes—
36C3×#3949C2212yes—
37#90990C2211yescharacteristic
38#90990C2212yes—
39#90990C2212yes—
40#90990C2211yescharacteristic
41#90987C2211yescharacteristic
42#90987C2211yescharacteristic
43#79210—51nomaximal, Hall
44C2×C5×#131—31no—
45#66161—31no—
46#66161—31no—
47#65410—32no—
48#65410—32no—
49#65410—31no—
50#65410D311yescharacteristic, complemented
51#65395—31no—
52#65395—32no—
53C2×#3950—31no—
54C2×#3950—32no—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—21no—
57C2×C5×#67D412yes—
58C5×#235C2×C414yes—
59C5×#235Q814yes—
60C2×C5×D12D411yescharacteristic
61C2×C4×C5×D3C2312yes—
62C2×C5×Dic6D411yescharacteristic
63C22×C3×Dic5—21no—
64C2×D3×Dic5—22no—
65C2×D3×Dic5—22no—
66C3×C5×M16C2×C414yescomplemented
67C2×C3×C5×C8C2312yes—
68#6719—21no—
69C4⋊Dic15—21no—
70C4⋊Dic15C2311yescharacteristic
71C4⋊Dic15C2312yes—
72C4⋊Dic15C2311yescharacteristic
73C4×Dic15—21no—
74C2×C5×C3⋊C8C2×C414yescomplemented
75C2×C5×C3⋊C8C2311yescharacteristic
76C2×C5×C3⋊C8C2311yescharacteristic
77C5×ΓL(1,𝔽25)C2×C418yescomplemented
78C5×D3×C8C2×C418yescomplemented
79C3×C22⋊Dic5—21no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2312yes—
83C3×C4⋊Dic5C2311yescharacteristic
84C3×C4×Dic5—21no—
85Dic3⋊Dic5—22no—
86Dic3⋊Dic5—22no—
87(C2×D3)⋊Dic5—22no—
88(C2×D3)⋊Dic5—22no—
89Dic3×Dic5—22no—
90Dic3×Dic5—22no—
91C2×#907D511yescharacteristic
92#5523—51no—
93#5504—51no—
94C3×#428—51no—
95#5121—51no—
96#4998—51no—
97C2×#807—51no—
98#4881—52no—
99D3×#107—52no—
100#4861—52no—
101#4860—52no—
102C2×C5×#41—31no—
103C5×#131—38no—
104C2×C5×M16—32no—
105C2×C5×M16C2×D311yescharacteristic
106C22×C5×C8—31no—
107C22×C5×C8—32no—
108Q8×Dic5—61no—
109Q8×Dic5—61no—
110D4×Dic5—61no—
111D4×Dic5—61no—
112D4×Dic5—62no—
113D4×Dic5—62no—
114#4072—31no—
115#4072—32no—
116#4072—32no—
117#4072C2×D311yescharacteristic
118C2×C4⋊Dic5—31no—
119C2×C4⋊Dic5—32no—
120C2×C4⋊Dic5—32no—
121C2×C4⋊Dic5C2×D311yescharacteristic
122#3950—32no—
123#3950—31no—
124#3950—32no—
125#3950—32no—
126#3950—31no—
127#3950C2×D312yes—
128#3949—32no—
129#3949—31no—
130#3949—31no—
131#3949C2×D312yes—
132#2913—151noSylow
133C23×C3×C5C2×D411yescharacteristic
134C22×C5×D3C2×D412yes—
135C2×C3×C4×C5C22×C412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×Q812yes—
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—21no—
140C2×Dic15—22no—
141C2×Dic15—21no—
142C2×Dic15—81no—
143C5×#67C4⋊C418yes—
144C2×C5×Dic3C2×D412yes—
145C5×D12C4⋊C414yes—
146C4×C5×D3C22×C414yes—
147C4×C5×D3C2×Q814yes—
148C5×Dic6C4⋊C414yes—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—81no—
153D3×Dic5—82no—
154D3×Dic5—82no—
155C3×C5×C8C22×C414yes—
156C5×C3⋊C8C22×C412yes—
157C5×C3⋊C8C22×C412yes—
158C2×#235C2×D511yescharacteristic
159C2×C3×M16C2×D511yescharacteristic
160C3×#117—51no—
161C2×C3×C4⋊C4—51no—
162C4×#67—102no—
163#926—51no—
164C2×C4⋊Dic3—51no—
165C22×C3⋊C8C2×D511yescharacteristic
166#907Dic518yescomplemented
167C2×ΓL(1,𝔽25)C2×D512yes—
168C2×D3×C8C2×D512yes—
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#818—52no—
181#817—52no—
182#808—51no—
183#808—51no—
184#807—51no—
185#807—52no—
186#807—52no—
187#807—51no—
188C5×#41—34no—
189C5×#41—34no—
190C2×C5×Q8—31no—
191C2×C5×D4—32no—
192C2×C5×D4—31no—
193C22×C4×C5—32no—
194C22×C4×C5C22×D311yescharacteristic
195C22×Dic5—21no—
196C22×Dic5—62no—
197C22×Dic5—62no—
198C22×Dic5—61no—
199C5×M16—38no—
200C5×M16C4×D314yescomplemented
201C2×C5×C8—34no—
202C2×C5×C8—31no—
203C2×C5×C8—31no—
204C2×C5×C8—38no—
205C2×C5×C8C22×D312yes—
206C22⋊Dic5—21no—
207C22⋊Dic5—62no—
208C22⋊Dic5—62no—
209C22⋊Dic5—61no—
210C4⋊Dic5—21no—
211C4⋊Dic5—31no—
212C4⋊Dic5—31no—
213C4⋊Dic5—32no—
214C4⋊Dic5—62no—
215C4⋊Dic5—62no—
216C4⋊Dic5—61no—
217C4⋊Dic5C22×D311yescharacteristic
218C4⋊Dic5C22×D311yescharacteristic
219C4⋊Dic5C22×D312yes—
220C4×Dic5—21no—
221C4×Dic5—62no—
222C4×Dic5—62no—
223C4×Dic5—61no—
224C2×#131—31no—
225#520—151no—
226#520—151no—
227#428—51no—
228#428—152no—
229#428—152no—
230#428—151no—
231#427—152no—
232#427—151no—
233C2×#107—152no—
234C2×#107—151no—
235C22×C3×C5—21no—
236C22×C3×C5—21no—
237C22×C3×C5C2×C4⋊C412yes—
238C22×C3×C5C22×D411yescharacteristic
239C2×C5×D3—22no—
240C2×C5×D3—22no—
241C2×C5×D3C2×C4⋊C414yes—
242C3×C4×C5C2×C4⋊C412yes—
243C3×C4×C5C23×C411yescharacteristic
244C3×C4×C5C22×Q811yescharacteristic
245Dic15—41no—
246Dic15—42no—
247Dic15—41no—
248C3×Dic5—41no—
249C3×Dic5—42no—
250C3×Dic5—41no—
251C5×Dic3C2×C4⋊C414yes—
252C22×C3×C4—101no—
253C22×C3×C4C22×D511yescharacteristic
254C2×#67D2012yes—
255C22×Dic3—101no—
256#235Dic1014yes—
257#235C2×Dic514yes—
258C2×D12D2011yescharacteristic
259C2×C4×D3—102no—
260C2×C4×D3—102no—
261C2×C4×D3C22×D512yes—
262C2×Dic6D2011yescharacteristic
263C3×M16C2×Dic514yescomplemented
264C2×C3×C8C22×D512yes—
265C3×C4⋊C4—52no—
266C3×C4⋊C4—51no—
267C3×C4⋊C4—51no—
268C3×C4⋊C4—101no—
269C3×C22⋊C4—101no—
270C3×C42—101no—
271#217—101no—
272(C2×D3)⋊C4—102no—
273(C2×D3)⋊C4—102no—
274C4⋊Dic3—52no—
275C4⋊Dic3—51no—
276C4⋊Dic3—51no—
277C4⋊Dic3—101no—
278Dic3⋊C4—102no—
279Dic3⋊C4—102no—
280C4×Dic3—101no—
281C4×Dic3—102no—
282C4×Dic3—102no—
283C2×C3⋊C8C2×Dic514yescomplemented
284C2×C3⋊C8C22×D511yescharacteristic
285C2×C3⋊C8C22×D511yescharacteristic
286ΓL(1,𝔽25)C2×Dic518yescomplemented
287D3×C8C2×Dic518yescomplemented
288C23×C5—32no—
289C23×C5D3×D411yescharacteristic
290C5×Q8—34no—
291C5×D4—38no—
292C5×D4—34no—
293C2×C4×C5—32no—
294C2×C4×C5—34no—
295C2×C4×C5—34no—
296C2×C4×C5C2×C4×D312yes—
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5D3×Q812yes—
299C2×C4×C5C23×D311yescharacteristic
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—22no—
303C2×Dic5—61no—
304C2×Dic5—62no—
305C2×Dic5—61no—
306C2×Dic5—81no—
307C2×Dic5—242no—
308C2×Dic5—242no—
309C2×Dic5—241no—
310C5×C8—32no—
311C5×C8—32no—
312C5×C8C2×C4×D314yes—
313C2×#41—31no—
314#131—38no—
315C2×M16—32no—
316C2×M16D3×D511yescharacteristic
317C22×C8—31no—
318C22×C8—32no—
319C4×Q8—301no—
320C4×Q8—301no—
321C4×D4—301no—
322C4×D4—302no—
323C4×D4—301no—
324C4×D4—302no—
325#117—51no—
326#117—152no—
327#117—152no—
328#117—151no—
329C2×C4⋊C4—51no—
330C2×C4⋊C4—152no—
331C2×C4⋊C4—152no—
332C2×C4⋊C4—151no—
333#107—52no—
334#107—152no—
335#107—151no—
336#107—152no—
337#107—151no—
338#107—152no—
339#106—52no—
340#106—151no—
341#106—151no—
342#106—152no—
343C2×C3×C5—22no—
344C2×C3×C5C22×C4⋊C411yescharacteristic
345C2×C3×C5#57611yescharacteristic
346C2×C3×C5#57811yescharacteristic
347C5×D3—24no—
348C23×C3C2×D2011yescharacteristic
349C22×D3C2×D2012yes—
350C2×C3×C4—101no—
351C2×C3×C4—102no—
352C2×C3×C4—101no—
353C2×C3×C4—401no—
354C2×C3×C4C2×Dic1012yes—
355C2×C3×C4C2×D2011yescharacteristic
356C2×C3×C4C22×Dic512yes—
357C2×C3×C4C23×D511yescharacteristic
358#67C4⋊Dic518yes—
359C2×Dic3—101no—
360C2×Dic3—101no—
361C2×Dic3—102no—
362C2×Dic3—401no—
363C2×Dic3C2×D2012yes—
364D12C4⋊Dic514yes—
365C4×D3—402no—
366C4×D3—402no—
367C4×D3C2×Dic1014yes—
368C4×D3C22×Dic514yes—
369Dic6C4⋊Dic514yes—
370C3×C8C22×Dic514yes—
371C3⋊C8C22×Dic512yes—
372C3⋊C8C22×Dic512yes—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—34no—
376C22×C5—62no—
377C22×C5—62no—
378C22×C5D3×C4⋊C412yes—
379C22×C5C2×D3×D411yescharacteristic
380C4×C5—34no—
381C4×C5D3×C4⋊C412yes—
382C4×C5C22×C4×D311yescharacteristic
383C4×C5C2×D3×Q811yescharacteristic
384Dic5—42no—
385Dic5—41no—
386Dic5—41no—
387Dic5—121no—
388Dic5—122no—
389Dic5—121no—
390#41—34no—
391#41—34no—
392C2×Q8—31no—
393C2×D4—32no—
394C2×D4—31no—
395C22×C4—32no—
396C22×C4—101no—
397C22×C4—302no—
398C22×C4—302no—
399C22×C4—301no—
400C22×C4C2×D3×D511yescharacteristic
401M16—38no—
402M16D3×Dic514yescomplemented
403C2×C8—34no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8—38no—
407C2×C8C2×D3×D512yes—
408C4⋊C4—51no—
409C4⋊C4—52no—
410C4⋊C4—51no—
411C4⋊C4—101no—
412C4⋊C4—151no—
413C4⋊C4—151no—
414C4⋊C4—152no—
415C4⋊C4—302no—
416C4⋊C4—302no—
417C4⋊C4—301no—
418C22⋊C4—101no—
419C22⋊C4—302no—
420C22⋊C4—302no—
421C22⋊C4—301no—
422C42—101no—
423C42—302no—
424C42—302no—
425C42—301no—
426C3×C5#291311yescharacteristic, complemented, Hall
427C22×C3—21no—
428C22×C3—21no—
429C22×C3C2×C4⋊Dic512yes—
430C22×C3C22×D2011yescharacteristic
431C2×D3—22no—
432C2×D3—22no—
433C2×D3C2×C4⋊Dic514yes—
434C3×C4—201no—
435C3×C4—202no—
436C3×C4—201no—
437C3×C4C2×C4⋊Dic512yes—
438C3×C4C22×Dic1011yescharacteristic
439C3×C4C23×Dic511yescharacteristic
440Dic3—201no—
441Dic3—202no—
442Dic3—201no—
443Dic3C2×C4⋊Dic514yes—
444C2×C5—22no—
445C2×C5—64no—
446C2×C5C2×D3×C4⋊C411yescharacteristic
447C2×C5#577411yescharacteristic
448C2×C5#577911yescharacteristic
449C23—32no—
450C23D3×D2011yescharacteristic
451Q8—34no—
452D4—38no—
453D4—34no—
454C2×C4—32no—
455C2×C4—34no—
456C2×C4—34no—
457C2×C4—101no—
458C2×C4—101no—
459C2×C4—102no—
460C2×C4—301no—
461C2×C4—302no—
462C2×C4—301no—
463C2×C4—401no—
464C2×C4—1202no—
465C2×C4—1202no—
466C2×C4—1201no—
467C2×C4D3×Dic1012yes—
468C2×C4D3×D2011yescharacteristic
469C2×C4C2×D3×Dic512yes—
470C2×C4C22×D3×D511yescharacteristic
471C8—32no—
472C8—32no—
473C8C2×D3×Dic514yes—
474C2×C3—22no—
475C2×C3#6608611yescharacteristic
476C2×C3#6608711yescharacteristic
477C2×C3C22×C4⋊Dic511yescharacteristic
478D3—24no—
479C5#7921011yescharacteristic, complemented, Sylow
480C22—21no—
481C22—21no—
482C22—34no—
483C22—62no—
484C22—62no—
485C22D3×C4⋊Dic512yes—
486C22C2×D3×D2011yescharacteristic
487C4—34no—
488C4—202no—
489C4—201no—
490C4—201no—
491C4—601no—
492C4—602no—
493C4—601no—
494C4D3×C4⋊Dic512yes—
495C4C2×D3×Dic1011yescharacteristic
496C4C22×D3×Dic511yescharacteristic
497C3#1061551611yescharacteristic, complemented, Sylow
498C2—22no—
499C2—64no—
500C2#1175403111yescharacteristic
501C2#1175404211yescharacteristic
502C2C2×D3×C4⋊Dic511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2913
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. #11751222C2semidirect
5. C3×#65410C2semidirect
6. C2×#90990C2semidirect
7. #11748451C2semidirect
8. #11747679C2semidirect
9. #11747630C2semidirect
10. #11747628C2semidirect
11. D3×#3950C2semidirect
18. C5×#907C4semidirect
50. #65410D3semidirect
66. C3×C5×M16C2×C4semidirect
74. C2×C5×C3⋊C8C2×C4semidirect
77. C5×ΓL(1,𝔽25)C2×C4semidirect
78. C5×D3×C8C2×C4semidirect
166. #907Dic5semidirect
200. C5×M16C4×D3semidirect
263. C3×M16C2×Dic5semidirect
283. C2×C3⋊C8C2×Dic5semidirect
286. ΓL(1,𝔽25)C2×Dic5semidirect
287. D3×C8C2×Dic5semidirect
402. M16D3×Dic5semidirect
426. C3×C5#2913semidirect
479. C5#79210semidirect
497. C3#10615516semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9072
#117545132
#117544922
#117512222
C3×#654102
C2×#909902
#117484512
#117476792
#117476302
#117476282
D3×#39502
#106155163
#792105