Finite Group Databasebeta

← #14458217

Subgroups — #14458217

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11753983C212yesmaximal, complemented
2#11753961C212yesmaximal, complemented
3#11750801C211yesmaximal, characteristic, complemented
4C5×#4695C211yesmaximal, characteristic, complemented
5C3×#64989C211yesmaximal, characteristic, complemented
6#11748090C212yesmaximal, complemented
7#11748081C212yesmaximal, complemented
8#11747116C214yesmaximal, complemented
9#10613522—31nomaximal, Hall
10#92018C2214yescomplemented
11#91793C2211yescharacteristic
12#91790C2212yescomplemented
13C2×C5×D24C2212yescomplemented
14C2×C5×D24C2212yescomplemented
15C5×#874C2212yescomplemented
16C3×#4050C2211yescharacteristic
17C3×#4047C2212yescomplemented
18#91304C2214yescomplemented
19#91299C2214yescomplemented
20#91279—22no—
21#91270—22no—
22#91257—24no—
23#91256—22no—
24#91250—24no—
25D5×D24—22no—
26C3×C4×C5×C8C2211yescharacteristic, complemented
27#91103C2211yescharacteristic, complemented
28#91089C2212yescomplemented
29C3×#3951C2211yescharacteristic, complemented
30C3×#3937C2212yescomplemented
31#90959C2214yescomplemented
32#79894—51nomaximal, Hall
33#66091—32no—
34#66091—32no—
35C5×#493—31no—
36#65449—32no—
37#65449—32no—
38#65366—34no—
39#64989—31no—
40#64989D311yescharacteristic, complemented
41#6817C2312yes—
42C2×C5×D12—42no—
43C2×C5×D12C2314yes—
44C3×#709C2312yes—
45D3×C22⋊D5—44no—
46#6777—24no—
47D5×D12—24no—
48#6772—24no—
49#6768—24no—
50C2×C3×C5×C8C2311yescharacteristic
51C2×C3×C5×C8C2311yescharacteristic
52C3×C42×C5C2311yescharacteristic
53#6710C2312yes—
54Dic60D411yescharacteristic, complemented
55D120D411yescharacteristic, complemented
56#6706D412yescomplemented
57#6705—22no—
58C8×D15—22no—
59C5×D24—22no—
60C5×D24—22no—
61C5×D24—22no—
62C5×D24—22no—
63C3×#681C2312yes—
64C3×Dic20D411yescharacteristic, complemented
65C3×D40D411yescharacteristic, complemented
66C3×#677D412yescomplemented
67C3×#676—22no—
68C3×C8×D5—22no—
69#6659—24no—
70#6656—24no—
71#6654—24no—
72#6652—24no—
73#5769—52no—
74#5752—52no—
75C3×#443—51no—
76#5142—52no—
77#4897—52no—
78#4822—54no—
79#4700—51no—
80#4695D511yescharacteristic, complemented
81#4144—34no—
82C2×C5×D8—32no—
83C2×C5×D8—32no—
84C5×#127—32no—
85#4078—34no—
86#4078—34no—
87#4058—62no—
88#4058—62no—
89#4057—64no—
90#4057—64no—
91D5×D8—62no—
92D5×D8—62no—
93#4050—31no—
94#4050C2×D311yescharacteristic
95#4047—32no—
96#4047C2×D312yescomplemented
97C4×C5×C8C2×D311yescharacteristic, complemented
98#3965—34no—
99#3951—31no—
100#3951C2×D311yescharacteristic, complemented
101#3937—32no—
102#3937C2×D312yescomplemented
103#3292—151noSylow
104C22×C5×D3—24no—
105C2×D3×D5—44no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5C2411yescharacteristic
108#1220—22no—
109D60C2×D412yes—
110C4×D15—22no—
111Dic30C2×D412yes—
112C5×D12—24no—
113C5×D12—24no—
114C5×D12—84no—
115C3×C22⋊D5—22no—
116C3×D20C2×D412yes—
117C3×C4×D5—22no—
118C3×Dic10C2×D412yes—
119#1203—44no—
120#1201—44no—
121D3×Dic5—44no—
122C3×C5×C8C2×D411yescharacteristic
123C3×C5×C8C2×D411yescharacteristic
124C3×C5×C8C2×D411yescharacteristic
125C3×C5×C8C2×D411yescharacteristic
126C3⋊#168—22no—
127C3×#168—22no—
128#1009—54no—
129C3×#135—51no—
130C3×#131—52no—
131#949—54no—
132#919—102no—
133#914—104no—
134D3×D8—102no—
135#908—54no—
136#908—104no—
137#904—51no—
138#904—102no—
139C2×D24—102no—
140C2×D24C2×D512yescomplemented
141C2×D24C2×D512yescomplemented
142#901—52no—
143#874C2×D512yescomplemented
144C3×#108—51no—
145C3×#104—52no—
146C3×C4×C8C2×D511yescharacteristic, complemented
147#823—54no—
148#819—51no—
149#805—52no—
150C2×C5×D4—34no—
151C2×C5×D4—122no—
152C2×C22⋊D5—124no—
153#711—64no—
154#711—64no—
155D4×D5—64no—
156D4×D5—64no—
157#709—32no—
158#709C22×D312yes—
159C5×D8—62no—
160C5×D8—62no—
161C5×D8—62no—
162C5×D8—62no—
163C2×C5×C8C22×D311yescharacteristic
164C2×C5×C8C22×D311yescharacteristic
165C42×C5C22×D311yescharacteristic
166#687—64no—
167#687—64no—
168#686—64no—
169#686—64no—
170#681—32no—
171#681C22×D312yes—
172Dic20—31no—
173Dic20D1211yescharacteristic, complemented
174D40—31no—
175D40D1211yescharacteristic, complemented
176#677—32no—
177#677D1212yescomplemented
178#676—22no—
179#676—62no—
180C8×D5—22no—
181C8×D5—62no—
182#576—152no—
183#576—152no—
184#493—31no—
185#472—152no—
186#472—152no—
187#453—154no—
188#443—51no—
189#443—151no—
190C22×C3×C5H(5,𝔽2)11yescharacteristic
191C2×D15—22no—
192C2×C5×D3—44no—
193C2×C5×D3—84no—
194C2×C3×D5—22no—
195D3×D5—164no—
196C3×C4×C5—22no—
197C3×C4×C5C22×D411yescharacteristic
198C3×C4×C5C22×D411yescharacteristic
199Dic15—22no—
200C3×Dic5—22no—
201C3×#41—52no—
202#239—104no—
203D3×D4—104no—
204D3×D4—204no—
205#235—52no—
206#235—104no—
207C2×D12—42no—
208C2×D12—104no—
209C2×D12C22×D514yes—
210C3×Q16—51no—
211C3×SD16—52no—
212C3×D8—51no—
213C3×M16—52no—
214C3×M16—102no—
215C2×C3×C8—102no—
216C2×C3×C8C22×D511yescharacteristic
217C2×C3×C8C22×D511yescharacteristic
218C3×C42C22×D511yescharacteristic
219#215—104no—
220#213—104no—
221#208—52no—
222Dic12—51no—
223D24—22no—
224D24—22no—
225D24—22no—
226D24—22no—
227D24—51no—
228D24—104no—
229#204—52no—
230#204—104no—
231ΓL(1,𝔽25)—102no—
232D3×C8—102no—
233C23×C5—64no—
234C22×D5—124no—
235C5×D4—64no—
236C5×D4—64no—
237C5×D4—244no—
238C2×C4×C5—21no—
239C2×C4×C5C23×D311yescharacteristic
240C22⋊D5—22no—
241C22⋊D5—62no—
242C22⋊D5—124no—
243C22⋊D5—124no—
244C2×Dic5—124no—
245D20—32no—
246D20C2×D1212yes—
247C4×D5—22no—
248C4×D5—62no—
249Dic10—32no—
250Dic10C2×D1212yes—
251C5×C8C2×D1211yescharacteristic
252C5×C8C2×D1211yescharacteristic
253C5×C8D3×D411yescharacteristic
254C5×C8D3×D411yescharacteristic
255#168—22no—
256#168—62no—
257H(5,𝔽2)—154no—
258AGL(1,ℤ/8)—154no—
259AGL(1,ℤ/8)—154no—
260AGL(1,ℤ/8)—304no—
261AGL(1,ℤ/8)—304no—
262#135—51no—
263#135—151no—
264#135—302no—
265#135—302no—
266C2×D8—32no—
267C2×D8—32no—
268C2×D8—302no—
269C2×D8—302no—
270#131—52no—
271#131—152no—
272#127—32no—
273#108—51no—
274#108—151no—
275#104—52no—
276#104—152no—
277#100—154no—
278C4×C8D3×D511yescharacteristic, complemented
279C2×C3×C5—21no—
280C2×C3×C5D4211yescharacteristic
281D15—42no—
282C3×D5—42no—
283C5×D3—84no—
284C22×D3—24no—
285C22×D3—204no—
286C3×Q8—52no—
287C3×D4—52no—
288C3×D4—102no—
289C2×C3×C4—21no—
290C2×C3×C4—102no—
291C2×C3×C4C23×D511yescharacteristic
292#67—102no—
293#67—204no—
294D12—24no—
295D12—24no—
296D12—52no—
297D12—84no—
298D12—204no—
299C4×D3—102no—
300C4×D3—204no—
301Dic6—52no—
302C3×C8—102no—
303C3×C8D4×D511yescharacteristic
304C3×C8D4×D511yescharacteristic
305C3×C8D4×D511yescharacteristic
306C3×C8D4×D511yescharacteristic
307C3⋊C8—102no—
308C22×C5—124no—
309C22×C5—244no—
310C22×C5#100911yescharacteristic
311C2×D5—22no—
312C2×D5—62no—
313C2×D5—484no—
314C4×C5—22no—
315C4×C5C22×D1211yescharacteristic
316C4×C5C2×D3×D411yescharacteristic
317Dic5—22no—
318Dic5—62no—
319#41—52no—
320#41—152no—
321#41—304no—
322#41—304no—
323C2×D4—34no—
324C2×D4—122no—
325C2×D4—304no—
326C2×D4—304no—
327C2×D4—604no—
328Q16—51no—
329Q16—151no—
330SD16—52no—
331SD16—152no—
332SD16—304no—
333SD16—304no—
334D8—51no—
335D8—62no—
336D8—62no—
337D8—62no—
338D8—62no—
339D8—151no—
340D8—304no—
341D8—304no—
342M16—52no—
343M16—102no—
344M16—152no—
345M16—302no—
346C2×C8—102no—
347C2×C8—302no—
348C2×C8C2×D3×D511yescharacteristic
349C2×C8C2×D3×D511yescharacteristic
350C42C2×D3×D511yescharacteristic
351C3×C5#329211yescharacteristic, complemented, Hall
352C22×C3—102no—
353C22×C3#414411yescharacteristic
354C2×D3—44no—
355C2×D3—84no—
356C2×D3—102no—
357C2×D3—804no—
358C3×C4—22no—
359C3×C4—102no—
360C3×C4C2×D4×D511yescharacteristic
361C3×C4C2×D4×D511yescharacteristic
362Dic3—102no—
363C2×C5—21no—
364C2×C5—244no—
365C2×C5D4×D1211yescharacteristic
366D5—42no—
367D5—122no—
368C23—64no—
369C23—604no—
370Q8—52no—
371Q8—152no—
372D4—52no—
373D4—64no—
374D4—64no—
375D4—102no—
376D4—152no—
377D4—244no—
378D4—302no—
379D4—604no—
380D4—604no—
381C2×C4—21no—
382C2×C4—102no—
383C2×C4—302no—
384C2×C4—604no—
385C2×C4C22×D3×D511yescharacteristic
386C8—102no—
387C8—302no—
388C8D5×D1211yescharacteristic
389C8D5×D1211yescharacteristic
390C8#677711yescharacteristic
391C8#677711yescharacteristic
392C2×C3—21no—
393C2×C3—202no—
394C2×C3#6605111yescharacteristic
395D3—84no—
396D3—202no—
397C5#7989411yescharacteristic, complemented, Sylow
398C22—102no—
399C22—124no—
400C22—244no—
401C22—302no—
402C22—2404no—
403C22#9201811yescharacteristic
404C4—22no—
405C4—102no—
406C4—302no—
407C4C2×D5×D1211yescharacteristic
408C4C2×#677711yescharacteristic
409C3#1061352211yescharacteristic, complemented, Sylow
410C2—21no—
411C2—202no—
412C2—244no—
413C2—602no—
414C2#1175273711yescharacteristic
subgroupG/H
centerC2#11752737
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC2×C3×C5D42
hypercenterC4×C8D3×D5
hypocenterC3×C5#3292
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11753983C2semidirect
2. #11753961C2semidirect
3. #11750801C2semidirect
4. C5×#4695C2semidirect
5. C3×#64989C2semidirect
6. #11748090C2semidirect
7. #11748081C2semidirect
8. #11747116C2semidirect
10. #92018C22semidirect
12. #91790C22semidirect
13. C2×C5×D24C22semidirect
14. C2×C5×D24C22semidirect
15. C5×#874C22semidirect
17. C3×#4047C22semidirect
18. #91304C22semidirect
19. #91299C22semidirect
26. C3×C4×C5×C8C22semidirect
27. #91103C22semidirect
28. #91089C22semidirect
29. C3×#3951C22semidirect
30. C3×#3937C22semidirect
31. #90959C22semidirect
40. #64989D3semidirect
54. Dic60D4semidirect
55. D120D4semidirect
56. #6706D4semidirect
64. C3×Dic20D4semidirect
65. C3×D40D4semidirect
66. C3×#677D4semidirect
80. #4695D5semidirect
96. #4047C2×D3semidirect
97. C4×C5×C8C2×D3semidirect
100. #3951C2×D3semidirect
102. #3937C2×D3semidirect
140. C2×D24C2×D5semidirect
141. C2×D24C2×D5semidirect
143. #874C2×D5semidirect
146. C3×C4×C8C2×D5semidirect
173. Dic20D12semidirect
175. D40D12semidirect
177. #677D12semidirect
278. C4×C8D3×D5semidirect
351. C3×C5#3292semidirect
397. C5#79894semidirect
409. C3#10613522semidirect

Maximal subgroups

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

subgroupindex
#117539832
#117539612
#117508012
C5×#46952
C3×#649892
#117480902
#117480812
#117471162
#106135223
#798945