Finite Group Databasebeta

← #14437942

Subgroups — #14437942

Order 1920.

976 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 976 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×#127C211yesmaximal, characteristic
2#11752631C211yesmaximal, characteristic, complemented
3C5×#5071C211yesmaximal, characteristic, complemented
4C3×#65360C211yesmaximal, characteristic, complemented
5#11749090C214yesmaximal, complemented
6#11748957C214yesmaximal, complemented
7#11746983C211yesmaximal, characteristic, complemented
8#11746915C211yesmaximal, characteristic, complemented
9#11746911C211yesmaximal, characteristic, complemented
10D5×#490—31nomaximal, Hall
11C2×D4×D15—22no—
12C2×D4×D15C2212yes—
13C3×C5×#127C2211yescharacteristic
14#91829—22no—
15#91829C2212yes—
16#91763C2211yescharacteristic
17C42×D15C2211yescharacteristic
18C5×#870C2211yescharacteristic, complemented
19C3×#4016C2211yescharacteristic, complemented
20#91437C2212yes—
21#91404—22no—
22#91384C2212yescomplemented
23#91382—22no—
24C2×#6648C2212yes—
25C5×#832C2214yescomplemented
26C5×#803C2211yescharacteristic, complemented
27C3×#3964C2214yescomplemented
28C3×#3935C2211yescharacteristic, complemented
29#90969C2214yescomplemented
30#90968C2214yescomplemented
31#90954C2212yescomplemented
32D3×#490—51nomaximal, Hall
33D5×#127—31no—
34D5×#125—31no—
35C5×#490—31no—
36#65360D311yescharacteristic, complemented
37#65356—31no—
38D5×#102—34no—
39#65053—34no—
40#65002—31no—
41D5×#97—31no—
42C23×D15—22no—
43C2×C3×C5×D4—22no—
44C2×C3×C5×D4C2312yes—
45C2×#1220—22no—
46C2×#1220—24no—
47D4×D15—28no—
48D4×D15—48no—
49C2×D60—22no—
50C2×D60C2312yes—
51C2×C4×D15D412yes—
52C2×C4×D15C2311yescharacteristic
53C2×#1200—22no—
54C3×C42×C5C2311yescharacteristic
55C4×Dic15D412yes—
56C4×Dic15C2311yescharacteristic
57C5×C4⋊Dic3C2312yes—
58C5×Dic3⋊C4—22no—
59C2×C5×C3⋊C8C2312yes—
60C3×C4⋊Dic5C2312yes—
61C3×#683—22no—
62C2×C3×#168C2312yes—
63Dic3⋊Dic5—22no—
64#6669—22no—
65#6668—22no—
66#6648—24no—
67D3×#127—51no—
68D3×#125—51no—
69C3×#490—51no—
70#5071D511yescharacteristic, complemented
71#5067—51no—
72D3×#102—54no—
73#4764—54no—
74#4713—51no—
75D3×#97—51no—
76C2×D4×D5—32no—
77C2×D4×D5—62no—
78C5×#127C2×D311yescharacteristic
79C5×#125—31no—
80#4086—32no—
81#4086—62no—
82C2×C8×D5—32no—
83D5×C4⋊C4—32no—
84D5×C4⋊C4—62no—
85#4036—32no—
86#4035—62no—
87#4020—31no—
88C42×D5—31no—
89#4016C2×D311yescharacteristic, complemented
90C5×#102—34no—
91C5×#97—31no—
92#3964C2×D314yescomplemented
93#3953—34no—
94#3947—32no—
95#3941—34no—
96#3935C2×D311yescharacteristic, complemented
97C2×#490—151noSylow
98C23×C3×C5—22no—
99C22×D15—22no—
100C22×D15—44no—
101C22×D15—48no—
102C22×D15C2×D411yescharacteristic
103C3×C5×D4—24no—
104C3×C5×D4—44no—
105C2×C3×C4×C5C2×D412yes—
106C2×C3×C4×C5C2411yescharacteristic
107#1220—48no—
108#1220—44no—
109C2×Dic15C2×D412yes—
110C2×Dic15C2×D411yescharacteristic
111D60—24no—
112D60—44no—
113C4×D15—24no—
114C4×D15#4114yes—
115C2×C5×Dic3—22no—
116C2×C3×Dic5—22no—
117#1200—44no—
118C3×#168—22no—
119C5×C3⋊C8—22no—
120C2×D3×D4—52no—
121C2×D3×D4—102no—
122C3×#127C2×D511yescharacteristic
123C3×#125—51no—
124#940—52no—
125#940—102no—
126C2×D3×C8—52no—
127D3×C4⋊C4—52no—
128D3×C4⋊C4—102no—
129#890—52no—
130#889—102no—
131#874—51no—
132C42×D3—51no—
133#870C2×D511yescharacteristic, complemented
134C3×#102—54no—
135C3×#97—51no—
136#832C2×D514yescomplemented
137#821—54no—
138#815—52no—
139#809—54no—
140#803C2×D511yescharacteristic, complemented
141C23×D5—62no—
142C2×C5×D4—22no—
143C2×C5×D4C22×D312yes—
144C2×C22⋊D5—62no—
145C2×C22⋊D5—64no—
146D4×D5—68no—
147D4×D5—128no—
148C2×D20—32no—
149C2×D20—62no—
150C2×C4×D5—31no—
151C2×C4×D5—32no—
152C2×C4×D5—62no—
153C2×C5×C8—32no—
154C5×C4⋊C4—32no—
155C5×C4⋊C4—62no—
156C42×C5C22×D311yescharacteristic
157C4⋊Dic5—62no—
158C4⋊Dic5C22×D312yes—
159#683—22no—
160#683—62no—
161#683—62no—
162C4×Dic5—32no—
163C4×Dic5—31no—
164C2×#168C22×D312yes—
165C8×D5—64no—
166C2×#127—151no—
167C2×#125—151no—
168#490—31no—
169#490—51no—
170#490—151no—
171#490—151no—
172#490—154no—
173C2×#102—154no—
174C2×#97—151no—
175C22×C3×C5—42no—
176C22×C3×C5—44no—
177C22×C3×C5C22×D411yescharacteristic
178C2×D15—42no—
179C2×D15—44no—
180C2×D15—88no—
181C2×D15#12412yes—
182C2×D15AGL(1,ℤ/8)14yes—
183C3×C4×C5—22no—
184C3×C4×C5C2×#4112yes—
185Dic15—22no—
186Dic15#12412yes—
187C3×Dic5—42no—
188C5×Dic3—42no—
189C23×D3—102no—
190C2×C3×D4—22no—
191C2×C3×D4C22×D512yes—
192C2×#67—104no—
193C2×#67—102no—
194D3×D4—108no—
195D3×D4—208no—
196C2×D12—52no—
197C2×D12—102no—
198C2×C4×D3—51no—
199C2×C4×D3—52no—
200C2×C4×D3—102no—
201C2×C3×C8—52no—
202C3×C4⋊C4—52no—
203C3×C4⋊C4—102no—
204C3×C42C22×D511yescharacteristic
205C4⋊Dic3—102no—
206C4⋊Dic3C22×D512yes—
207Dic3⋊C4—22no—
208Dic3⋊C4—102no—
209Dic3⋊C4—102no—
210C4×Dic3—52no—
211C4×Dic3—51no—
212C2×C3⋊C8C22×D512yes—
213D3×C8—104no—
214C23×C5—22no—
215C22×D5—31no—
216C22×D5—62no—
217C22×D5—124no—
218C22×D5—128no—
219C5×D4—24no—
220C5×D4—44no—
221C2×C4×C5—62no—
222C2×C4×C5D3×D412yes—
223C2×C4×C5C23×D311yescharacteristic
224C22⋊D5—124no—
225C22⋊D5—128no—
226C2×Dic5—22no—
227C2×Dic5—31no—
228C2×Dic5—32no—
229D20—64no—
230D20—124no—
231C4×D5—34no—
232C4×D5—64no—
233C4×D5—124no—
234C5×C8—62no—
235#168—22no—
236C22×D4—152no—
237C22×D4—302no—
238C22×C8—152no—
239#127—152no—
240#127—151no—
241#127—302no—
242#127D3×D511yescharacteristic
243#125—31no—
244#125—51no—
245#125—152no—
246#125—302no—
247C2×C4⋊C4—152no—
248C2×C4⋊C4—302no—
249C2×C42—151no—
250#102—34no—
251#102—54no—
252#102—154no—
253#102—154no—
254#97—31no—
255#97—51no—
256#97—152no—
257C2×C3×C5—82no—
258C2×C3×C5C2×#12411yescharacteristic
259C2×C3×C5C2×AGL(1,ℤ/8)12yes—
260D15—82no—
261D15#49014yescomplemented
262C23×C3—22no—
263C22×D3—51no—
264C22×D3—102no—
265C22×D3—204no—
266C22×D3—208no—
267C3×D4—24no—
268C3×D4—44no—
269C2×C3×C4—102no—
270C2×C3×C4D4×D512yes—
271C2×C3×C4C23×D511yescharacteristic
272#67—204no—
273#67—208no—
274C2×Dic3—22no—
275C2×Dic3—51no—
276C2×Dic3—52no—
277D12—104no—
278D12—204no—
279C4×D3—54no—
280C4×D3—104no—
281C4×D3—204no—
282C3×C8—102no—
283C3⋊C8—22no—
284C22×C5—42no—
285C22×C5—44no—
286C22×C5C2×D3×D411yescharacteristic
287C2×D5—32no—
288C2×D5—34no—
289C2×D5—122no—
290C2×D5—124no—
291C2×D5—248no—
292C4×C5—22no—
293C4×C5—122no—
294C4×C5D3×#4112yes—
295Dic5—32no—
296Dic5—42no—
297Dic5—62no—
298C24—302no—
299C2×D4—22no—
300C2×D4—152no—
301C2×D4—308no—
302C2×D4—304no—
303C2×D4—302no—
304C2×D4—302no—
305C2×D4—608no—
306C2×D4C2×D3×D512yes—
307C22×C4—151no—
308C22×C4—152no—
309C22×C4—302no—
310C2×C8—32no—
311C2×C8—52no—
312C2×C8—304no—
313C4⋊C4—32no—
314C4⋊C4—52no—
315C4⋊C4—62no—
316C4⋊C4—102no—
317C4⋊C4—302no—
318C4⋊C4—302no—
319C4⋊C4—302no—
320C42—152no—
321C42—151no—
322C42C2×D3×D511yescharacteristic
323C3×C5C2×#49011yescharacteristic, complemented, Hall
324C22×C3—44no—
325C22×C3—42no—
326C22×C3C2×D4×D511yescharacteristic
327C2×D3—54no—
328C2×D3—52no—
329C2×D3—204no—
330C2×D3—202no—
331C2×D3—408no—
332C3×C4—22no—
333C3×C4—202no—
334C3×C4D5×#4112yes—
335Dic3—42no—
336Dic3—52no—
337Dic3—102no—
338C2×C5—82no—
339C2×C5D3×#12411yescharacteristic
340C2×C5D3×AGL(1,ℤ/8)12yes—
341D5—34no—
342D5—242no—
343C23—22no—
344C23—151no—
345C23—302no—
346C23—604no—
347C23—608no—
348D4—24no—
349D4—44no—
350D4—304no—
351D4—604no—
352D4—604no—
353D4—608no—
354C2×C4—62no—
355C2×C4—102no—
356C2×C4—151no—
357C2×C4—154no—
358C2×C4—152no—
359C2×C4—304no—
360C2×C4—604no—
361C2×C4#679012yes—
362C2×C4C22×D3×D511yescharacteristic
363C8—62no—
364C8—102no—
365C2×C3—82no—
366C2×C3D5×#12411yescharacteristic
367C2×C3D5×AGL(1,ℤ/8)12yes—
368D3—54no—
369D3—402no—
370C5D3×#49011yescharacteristic, complemented, Sylow
371C22—42no—
372C22—44no—
373C22—152no—
374C22—154no—
375C22—602no—
376C22—604no—
377C22—1208no—
378C22C2×#679011yescharacteristic
379C4—22no—
380C4—122no—
381C4—152no—
382C4—202no—
383C4—302no—
384C4#9202412yes—
385C3D5×#49011yescharacteristic, complemented, Sylow
386C2—82no—
387C2—154no—
388C2—1202no—
389C2#1175470112yes—
390C2#1175483111yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radicalD15×#127C2
hypercenter#127D3×D5
hypocenterC3×C5C2×#490
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11752631C2semidirect
3. C5×#5071C2semidirect
4. C3×#65360C2semidirect
5. #11749090C2semidirect
6. #11748957C2semidirect
7. #11746983C2semidirect
8. #11746915C2semidirect
9. #11746911C2semidirect
18. C5×#870C22semidirect
19. C3×#4016C22semidirect
22. #91384C22semidirect
25. C5×#832C22semidirect
26. C5×#803C22semidirect
27. C3×#3964C22semidirect
28. C3×#3935C22semidirect
29. #90969C22semidirect
30. #90968C22semidirect
31. #90954C22semidirect
36. #65360D3semidirect
70. #5071D5semidirect
89. #4016C2×D3semidirect
92. #3964C2×D3semidirect
96. #3935C2×D3semidirect
133. #870C2×D5semidirect
136. #832C2×D5semidirect
140. #803C2×D5semidirect
261. D15#490semidirect
323. C3×C5C2×#490semidirect
370. C5D3×#490semidirect
385. C3D5×#490semidirect

Maximal subgroups

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

subgroupindex
D15×#1272
#117526312
C5×#50712
C3×#653602
#117490902
#117489572
#117469832
#117469152
#117469112
D5×#4903
D3×#4905