Finite Group Databasebeta

← #14417819

Subgroups — #14417819

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#912C211yesmaximal, characteristic
2#11754920C212yesmaximal, complemented
3#11751253C211yesmaximal, characteristic, complemented
4C3×#65441C211yesmaximal, characteristic, complemented
5#11749019C212yesmaximal, complemented
6Dic5×#214C212yesmaximal, complemented
7#11748955C212yesmaximal, complemented
8#11747888C211yesmaximal, characteristic, complemented
9#11747856C211yesmaximal, characteristic, complemented
10#11747665C211yesmaximal, characteristic, complemented
11D3×#3949C211yesmaximal, characteristic, complemented
12#10615630—31nomaximal, Hall
13C2×C5×#237C2212yes—
14C2×C3×C5×D8C2211yescharacteristic
15D4×Dic15C2212yes—
16C2×C5×#214C2212yes—
17C5×#912C418yescomplemented
18C2×C5×Dic12C2211yescharacteristic
19C2×C5×D3×C8C2211yescharacteristic
20C3×D4×Dic5C2212yes—
21#67⋊Dic5—22no—
22Dic5×#67—22no—
23C2×Dic3⋊Dic5—22no—
24#91529—22no—
25D3×C4⋊Dic5C2212yes—
26#91371C2211yescharacteristic
27#91344C2212yes—
28Dic5×Dic6C2212yes—
29C2×#6650C2211yescharacteristic
30#91116C2212yes—
31#91101C2211yescharacteristic
32#91099C2211yescharacteristic
33C3×#3964C2212yes—
34C3×#3949C2211yescharacteristic
35C3×#3947C2211yescharacteristic
36#90987C2212yes—
37#90973C2212yes—
38#90972C2212yes—
39#90951C2211yescharacteristic
40Dic5×C3⋊C8C2211yescharacteristic
41#79868—51nomaximal, Hall
42C2×C5×#135—31no—
43#66161—32no—
44#65521—32no—
45#65473—31no—
46#65473—31no—
47SD16×Dic5—32no—
48SD16×Dic5—32no—
49#65441—31no—
50#65441D311yescharacteristic, complemented
51C2×#3949—31no—
52#65390—31no—
53C2×C3×C5×D4C2312yes—
54C22×Dic15—22no—
55C2×C5×#67—22no—
56C22×C5×Dic3—22no—
57C5×#237—24no—
58C5×#237C2×C418yescomplemented
59C2×C4×C5×D3C2311yescharacteristic
60C2×C5×Dic6C2312yes—
61C22×C3×Dic5—22no—
62C2×D3×Dic5—22no—
63C3×C5×D8C2×C414yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65#6719—22no—
66C4⋊Dic15C2312yes—
67C4×Dic15C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C5×#214C2×C418yescomplemented
70C2×C5×C3⋊C8C2311yescharacteristic
71C5×Dic12C2×C414yescomplemented
72C5×D3×C8C2×C414yescomplemented
73C3×C22⋊Dic5—22no—
74C3×C4⋊Dic5C2312yes—
75C3×C4×Dic5C2311yescharacteristic
76C2×C3×#168C2311yescharacteristic
77Dic3⋊Dic5—22no—
78Dic3⋊Dic5—22no—
79Dic3⋊Dic5—22no—
80Dic3⋊Dic5D412yes—
81(C2×D3)⋊Dic5D412yes—
82Dic3×Dic5—22no—
83Dic3×Dic5—22no—
84#6650—22no—
85C2×#912D511yescharacteristic
86#5546—52no—
87C3×#442—51no—
88#5152—51no—
89C4×#214—52no—
90D3×#106—51no—
91#4853—51no—
92#4771—52no—
93#4758—52no—
94#4716—51no—
95#4708—51no—
96C2×C5×#41—32no—
97C5×#135—38no—
98C2×C5×Q16—31no—
99C2×C5×SD16—32no—
100C2×C5×D8C2×D311yescharacteristic
101C22×C5×C8—31no—
102Q8×Dic5—32no—
103Q8×Dic5—32no—
104D4×Dic5—32no—
105D4×Dic5—62no—
106D4×Dic5—62no—
107D4×Dic5C2×D312yes—
108#4072—31no—
109#4072—62no—
110C2×C4⋊Dic5—32no—
111C2×C4⋊Dic5—62no—
112C2×#681—31no—
113#3967—32no—
114#3967—32no—
115#3964—32no—
116#3964C2×D312yes—
117#3949—31no—
118#3949—32no—
119#3949C2×D311yescharacteristic
120#3947—31no—
121#3947C2×D311yescharacteristic
122C8×Dic5—31no—
123C8×Dic5—31no—
124#2952—151noSylow
125C23×C3×C5—22no—
126C22×C5×D3C2×D411yescharacteristic
127C3×C5×D4—22no—
128C3×C5×D4C22×C414yes—
129C2×C3×C4×C5C2411yescharacteristic
130C2×Dic15—22no—
131C2×Dic15—82no—
132C2×Dic15C2×D412yes—
133C5×#67—28no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3—28no—
136C2×C5×Dic3C2×D411yescharacteristic
137C4×C5×D3C22×C412yes—
138C4×C5×D3#4112yes—
139C5×Dic6—22no—
140C5×Dic6C22×C414yes—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—82no—
143C2×C3×Dic5C2×D412yes—
144D3×Dic5—82no—
145C3×C5×C8C22×C412yes—
146C3⋊#168—21no—
147C3×#168—21no—
148C5×C3⋊C8C22×C412yes—
149C2×#237C2×D512yes—
150C2×C3×D8C2×D511yescharacteristic
151C3×C4×D4—52no—
152D4×Dic3—52no—
153C2×#214C2×D512yes—
154C4×#67—102no—
155C2×Dic3⋊C4—102no—
156#912Dic518yescomplemented
157C2×Dic12C2×D511yescharacteristic
158C2×ΓL(1,𝔽25)—51no—
159C2×D3×C8C2×D511yescharacteristic
160D3×C4⋊C4—52no—
161#887—52no—
162#67⋊C4—102no—
163#877—102no—
164#872—51no—
165C4×Dic6—52no—
166C3×#106—51no—
167C3×#102—52no—
168C3×#97—51no—
169#832—52no—
170#817—51no—
171#816—52no—
172#815—51no—
173C8×Dic3—51no—
174#810—52no—
175#808—52no—
176C4×C3⋊C8—51no—
177C5×#41—38no—
178C5×#41—64no—
179C2×C5×Q8—32no—
180C2×C5×D4—62no—
181C2×C5×D4C22×D312yes—
182C22×C4×C5—31no—
183C22×C4×C5—62no—
184C22×Dic5—22no—
185C22×Dic5—62no—
186C22×Dic5—62no—
187C5×Q16—34no—
188C5×SD16—38no—
189C5×D8C4×D314yescomplemented
190C2×C5×C8—31no—
191C2×C5×C8—34no—
192C2×C5×C8C22×D311yescharacteristic
193C22⋊Dic5—22no—
194C22⋊Dic5—32no—
195C22⋊Dic5—62no—
196C4⋊Dic5—32no—
197C4⋊Dic5—32no—
198C4⋊Dic5—62no—
199C4⋊Dic5—62no—
200C4⋊Dic5—62no—
201C4⋊Dic5C22×D312yes—
202C4×Dic5—31no—
203C4×Dic5—62no—
204C4×Dic5—62no—
205C4×Dic5C22×D311yescharacteristic
206#681—62no—
207C2×#168—31no—
208C2×#168C22×D311yescharacteristic
209C2×#135—31no—
210#520—152no—
211#442—51no—
212#442—151no—
213#441—151no—
214#441—151no—
215C4×SD16—152no—
216C4×SD16—152no—
217C2×#106—151no—
218#417—152no—
219#405—151no—
220C22×C3×C5—24no—
221C22×C3×C5—42no—
222C22×C3×C5—42no—
223C22×C3×C5C22×D411yescharacteristic
224C2×C5×D3—22no—
225C2×C5×D3C4×D412yes—
226C3×C4×C5C23×C411yescharacteristic
227C3×C4×C5C2×#4111yescharacteristic
228Dic15—22no—
229Dic15—42no—
230C3×Dic5—22no—
231C3×Dic5—42no—
232C5×Dic3—24no—
233C5×Dic3C4×D412yes—
234C2×C3×D4C22×D512yes—
235C22×C3×C4—102no—
236C2×#67—22no—
237C22×Dic3—22no—
238C22×Dic3—102no—
239#237—24no—
240#237C2×Dic518yescomplemented
241C2×C4×D3—102no—
242C2×C4×D3C22×D511yescharacteristic
243C2×Dic6C22×D512yes—
244C3×D8C2×Dic514yescomplemented
245C2×C3×C8—51no—
246C2×C3×C8C22×D511yescharacteristic
247C3×C4⋊C4—52no—
248C3×C22⋊C4—102no—
249C3×C42—51no—
250#217—102no—
251#214C2×Dic518yescomplemented
252(C2×D3)⋊C4—52no—
253C4⋊Dic3—52no—
254Dic3⋊C4—52no—
255Dic3⋊C4—102no—
256Dic3⋊C4—102no—
257Dic3⋊C4—102no—
258C4×Dic3—51no—
259C4×Dic3—102no—
260C4×Dic3—102no—
261C2×C3⋊C8—51no—
262C2×C3⋊C8C22×D511yescharacteristic
263Dic12C2×Dic514yescomplemented
264ΓL(1,𝔽25)—102no—
265D3×C8C2×Dic514yescomplemented
266C23×C5—22no—
267C23×C5—31no—
268C5×Q8—34no—
269C5×Q8—62no—
270C5×D4—22no—
271C5×D4—68no—
272C5×D4C2×C4×D314yes—
273C2×C4×C5—31no—
274C2×C4×C5—32no—
275C2×C4×C5—32no—
276C2×C4×C5—68no—
277C2×C4×C5—62no—
278C2×C4×C5C23×D311yescharacteristic
279C2×Dic5—22no—
280C2×Dic5—32no—
281C2×Dic5—62no—
282C2×Dic5—82no—
283C2×Dic5—242no—
284C2×Dic5—242no—
285C2×Dic5D3×D412yes—
286C5×C8—32no—
287C5×C8C2×C4×D312yes—
288#168—21no—
289#168—61no—
290C2×#41—32no—
291#135—38no—
292C2×Q16—31no—
293C2×SD16—32no—
294C2×D8D3×D511yescharacteristic
295C2×M16—151no—
296C22×C8—31no—
297C4×Q8—152no—
298C4×Q8—152no—
299C4×D4—52no—
300C4×D4—152no—
301C4×D4—302no—
302C4×D4—302no—
303#117—151no—
304#117—302no—
305C2×C4⋊C4—152no—
306C2×C4⋊C4—302no—
307#106—51no—
308#106—152no—
309#106—151no—
310#103—152no—
311#103—152no—
312#102—52no—
313#102—152no—
314#97—51no—
315#97—151no—
316C4×C8—151no—
317C4×C8—151no—
318C2×C3×C5—44no—
319C2×C3×C5C2×C4×D411yescharacteristic
320C2×C3×C5#57712yes—
321C5×D3—22no—
322C23×C3—22no—
323C22×D3D4×D511yescharacteristic
324C3×D4—22no—
325C3×D4C22×Dic514yes—
326C2×C3×C4—52no—
327C2×C3×C4—102no—
328C2×C3×C4—402no—
329C2×C3×C4C23×D511yescharacteristic
330#67—28no—
331C2×Dic3—22no—
332C2×Dic3—28no—
333C2×Dic3—52no—
334C2×Dic3—102no—
335C2×Dic3—402no—
336C2×Dic3D4×D511yescharacteristic
337C4×D3—402no—
338C4×D3#71112yes—
339C4×D3C22×Dic512yes—
340Dic6—22no—
341Dic6C22×Dic514yes—
342C3×C8—101no—
343C3×C8C22×Dic512yes—
344C3⋊C8—101no—
345C3⋊C8C22×Dic512yes—
346C22×C5—24no—
347C22×C5—32no—
348C22×C5—42no—
349C22×C5—42no—
350C22×C5—62no—
351C22×C5C2×D3×D411yescharacteristic
352C4×C5—32no—
353C4×C5—64no—
354C4×C5C22×C4×D311yescharacteristic
355C4×C5D3×#4111yescharacteristic
356Dic5—22no—
357Dic5—42no—
358Dic5—62no—
359Dic5—122no—
360#41—38no—
361#41—64no—
362C2×Q8—32no—
363C2×D4—62no—
364C2×D4C2×D3×D512yes—
365C22×C4—31no—
366C22×C4—62no—
367C22×C4—102no—
368C22×C4—302no—
369C22×C4—302no—
370Q16—34no—
371SD16—38no—
372D8D3×Dic514yescomplemented
373M16—302no—
374C2×C8—31no—
375C2×C8—34no—
376C2×C8—51no—
377C2×C8—151no—
378C2×C8C2×D3×D511yescharacteristic
379C4⋊C4—52no—
380C4⋊C4—152no—
381C4⋊C4—152no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C22⋊C4—102no—
386C22⋊C4—152no—
387C22⋊C4—302no—
388C42—51no—
389C42—151no—
390C42—302no—
391C42—302no—
392C3×C5#295211yescharacteristic, complemented, Hall
393C22×C3—24no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3C2×D4×D511yescharacteristic
397C2×D3—22no—
398C2×D3D4×Dic512yes—
399C3×C4—102no—
400C3×C4—202no—
401C3×C4C2×#71111yescharacteristic
402C3×C4C23×Dic511yescharacteristic
403Dic3—24no—
404Dic3—102no—
405Dic3—202no—
406Dic3D4×Dic512yes—
407C2×C5—44no—
408C2×C5—62no—
409C2×C5C4×D3×D411yescharacteristic
410C2×C5#577512yes—
411C23—22no—
412C23—31no—
413Q8—34no—
414Q8—62no—
415D4—22no—
416D4—68no—
417D4C2×D3×Dic514yes—
418C2×C4—31no—
419C2×C4—32no—
420C2×C4—32no—
421C2×C4—52no—
422C2×C4—68no—
423C2×C4—62no—
424C2×C4—102no—
425C2×C4—152no—
426C2×C4—302no—
427C2×C4—402no—
428C2×C4—1202no—
429C2×C4—1202no—
430C2×C4C22×D3×D511yescharacteristic
431C8—32no—
432C8—101no—
433C8—301no—
434C8C2×D3×Dic512yes—
435C2×C3—44no—
436C2×C3#6610412yes—
437C2×C3C2×D4×Dic511yescharacteristic
438D3—22no—
439C5#7986811yescharacteristic, complemented, Sylow
440C22—24no—
441C22—32no—
442C22—42no—
443C22—42no—
444C22—62no—
445C22D3×D4×D511yescharacteristic
446C4—32no—
447C4—64no—
448C4—102no—
449C4—202no—
450C4—302no—
451C4—602no—
452C4D3×#71111yescharacteristic
453C4C22×D3×Dic511yescharacteristic
454C3#1061563011yescharacteristic, complemented, Sylow
455C2—44no—
456C2—62no—
457C2#1175406012yes—
458C2D3×D4×Dic511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#912C2
cosocleC2×C3×C4×C5C24
hypercenterC2×D8D3×D5
hypocenterC3×C5#2952
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #11754920C2semidirect
3. #11751253C2semidirect
4. C3×#65441C2semidirect
5. #11749019C2semidirect
6. Dic5×#214C2semidirect
7. #11748955C2semidirect
8. #11747888C2semidirect
9. #11747856C2semidirect
10. #11747665C2semidirect
11. D3×#3949C2semidirect
17. C5×#912C4semidirect
50. #65441D3semidirect
58. C5×#237C2×C4semidirect
63. C3×C5×D8C2×C4semidirect
69. C5×#214C2×C4semidirect
71. C5×Dic12C2×C4semidirect
72. C5×D3×C8C2×C4semidirect
156. #912Dic5semidirect
189. C5×D8C4×D3semidirect
240. #237C2×Dic5semidirect
244. C3×D8C2×Dic5semidirect
251. #214C2×Dic5semidirect
263. Dic12C2×Dic5semidirect
265. D3×C8C2×Dic5semidirect
372. D8D3×Dic5semidirect
392. C3×C5#2952semidirect
439. C5#79868semidirect
454. C3#10615630semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9122
#117549202
#117512532
C3×#654412
#117490192
Dic5×#2142
#117489552
#117478882
#117478562
#117476652
D3×#39492
#106156303
#798685