Finite Group Databasebeta

← #14412775

Subgroups — #14412775

Order 1920.

1452 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1010C211yesmaximal, characteristic
2#11756586C211yesmaximal, characteristic, complemented
3C2×C3×#4094C211yesmaximal, characteristic, complemented
4#11748409C213yesmaximal, complemented
5C2×#90973C213yesmaximal, complemented
6#11748390C213yesmaximal, complemented
7#11748388C213yesmaximal, complemented
8#10615842—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C5×#1010—24no—
11C5×#1010C418yescomplemented
12C2×C5×D3×Q8—21no—
13C2×C5×#237—23no—
14C2×C5×#235C2213yes—
15C22×C5×Dic6C2213yes—
16Q8×Dic15—21no—
17D4×Dic15—23no—
18#91815C2213yes—
19C2×C4⋊Dic15C2213yes—
20C3×#4094—24no—
21C2×C3×#681C2213yes—
22C22×C3×#168C2213yes—
23#90973C2213yes—
24#90973C2213yes—
25#90973C2216yes—
26#90967C2211yescharacteristic
27#90967C2213yes—
28#83806—51nomaximal, Hall
29C2×C5×2−1+4—31no—
30#66161—31no—
31C2×#4094D311yescharacteristic, complemented
32#65522—33no—
33#65521—33no—
34#65514—33no—
35C2×#3967—33no—
36C3×C5×#41C2×C414yes—
37C3×C5×#41D414yes—
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4D413yes—
40C22×C3×C4×C5C2313yes—
41C22×Dic15—23no—
42C2×C5×#67—23no—
43C22×C5×Dic3—23no—
44C5×D3×Q8—28no—
45C5×#237—224no—
46C5×#235—26no—
47C5×#235C2×C4112yescomplemented
48C2×C5×D12C2311yescharacteristic
49C2×C4×C5×D3—23no—
50C2×C5×Dic6—23no—
51C2×C5×Dic6—26no—
52C2×C5×Dic6C2×C4112yescomplemented
53C2×C5×Dic6C2313yes—
54#6719—23no—
55C4⋊Dic15—23no—
56C4⋊Dic15C2313yes—
57C4⋊Dic15C2311yescharacteristic
58C4×Dic15—23no—
59C3×#681—26no—
60C2×C3×#168—26no—
61C2×C3×#168C2311yescharacteristic
62C2×C3×#168C2313yes—
63C2×#1010D511yescharacteristic
64C2×C3×#131—51no—
65#5827—51no—
66#5133—53no—
67#5120—53no—
68#5113—53no—
69C2×#816—53no—
70C5×2−1+4—38no—
71C5×2−1+4—64no—
72C2×C5×#41—33no—
73C2×C5×#41—63no—
74C2×C5×#41C2×D311yescharacteristic
75C22×C5×Q8—33no—
76C22×C5×Q8—61no—
77#4094—24no—
78Q8×Dic5—61no—
79D4×Dic5—63no—
80#4072—33no—
81C2×C4⋊Dic5—33no—
82C2×#681C2×D313yes—
83C22×#168C2×D313yes—
84#3967—33no—
85#3967—36no—
86#3967—33no—
87#3964—33no—
88#3964—31no—
89#2898—151noSylow
90C23×C3×C5C2×D413yes—
91C22×C5×D3—21no—
92C3×C5×Q8C22⋊C414yes—
93C3×C5×D4C22⋊C4112yes—
94C2×C3×C4×C5C22×C416yes—
95C2×C3×C4×C5C2×D413yes—
96C2×C3×C4×C5C2×D416yes—
97C2×C3×C4×C5C2411yescharacteristic
98C2×Dic15—21no—
99C2×Dic15—23no—
100C2×Dic15—83no—
101C5×#67—212no—
102C2×C5×Dic3—212no—
103C2×C5×Dic3—23no—
104C5×D12—21no—
105C5×D12C22×C412yes—
106C4×C5×D3—212no—
107C5×Dic6—212no—
108C5×Dic6—23no—
109C5×Dic6C22×C416yes—
110C3×#168—21no—
111C3×#168—23no—
112C2×C3×#41C2×D511yescharacteristic
113#1010—24no—
114#1010Dic518yescomplemented
115C2×D3×Q8—21no—
116C2×#237—23no—
117C2×#235C2×D513yes—
118C22×Dic6C2×D513yes—
119C3×#131—104no—
120C2×C3×M16—53no—
121C22×C3×C8—53no—
122Q8×Dic3—101no—
123D4×Dic3—103no—
124#926—53no—
125C2×C4⋊Dic3—53no—
126#821—53no—
127#821—51no—
128#816—53no—
129#816—56no—
130#816—53no—
131C5×#41—312no—
132C5×#41—624no—
133C5×#41—66no—
134C5×#41C4×D314yes—
135C5×#41#6714yes—
136C2×C5×Q8—312no—
137C2×C5×Q8—33no—
138C2×C5×Q8—68no—
139C2×C5×Q8—63no—
140C2×C5×Q8—66no—
141C2×C5×Q8D1211yescharacteristic
142C2×C5×D4—31no—
143C2×C5×D4—63no—
144C2×C5×D4D1213yes—
145C22×C4×C5—63no—
146C22×C4×C5—63no—
147C22×C4×C5C22×D313yes—
148C22×Dic5—63no—
149C22⋊Dic5—63no—
150C4⋊Dic5—33no—
151C4⋊Dic5—31no—
152C4⋊Dic5—63no—
153C4×Dic5—63no—
154#681—26no—
155C2×#168—26no—
156C2×#168C22×D311yescharacteristic
157C2×#168C22×D313yes—
158C2×2−1+4—31no—
159C2×#131—51no—
160#520—151no—
161#419—153no—
162#417—153no—
163#416—153no—
164C2×#103—153no—
165C22×C3×C5—23no—
166C22×C3×C5—23no—
167C22×C3×C5C2×C22⋊C416yes—
168C22×C3×C5C22×D411yescharacteristic
169C2×C5×D3—22no—
170C2×C5×D3—41no—
171C2×C5×D3—41no—
172C3×C4×C5C2×C22⋊C416yes—
173C3×C4×C5C23×C411yescharacteristic
174C3×C4×C5C22×D411yescharacteristic
175Dic15—43no—
176Dic15—41no—
177C5×Dic3—26no—
178C3×#41C2×Dic514yes—
179C3×#41C22⋊D514yes—
180C2×C3×Q8C22⋊D511yescharacteristic
181C2×C3×D4C22⋊D513yes—
182C22×C3×C4C22×D513yes—
183C2×#67—23no—
184C22×Dic3—23no—
185C22×Dic3—103no—
186D3×Q8—28no—
187#237—224no—
188#235—26no—
189#235C2×Dic5112yescomplemented
190C2×D12C22×D511yescharacteristic
191C2×C4×D3—23no—
192C2×Dic6—23no—
193C2×Dic6—26no—
194C2×Dic6C2×Dic5112yescomplemented
195C2×Dic6C22×D513yes—
196C3×M16—106no—
197C2×C3×C8—51no—
198C2×C3×C8—53no—
199C2×C3×C8—106no—
200#217—103no—
201C4⋊Dic3—53no—
202C4⋊Dic3—51no—
203C4⋊Dic3—103no—
204C4×Dic3—103no—
205C23×C5—61no—
206C23×C5C2×D1213yes—
207C5×Q8—36no—
208C5×Q8—612no—
209C5×Q8—63no—
210C5×Q8(C2×D3)⋊C414yes—
211C5×D4—32no—
212C5×D4—612no—
213C5×D4—61no—
214C5×D4(C2×D3)⋊C4112yes—
215C2×C4×C5—612no—
216C2×C4×C5—63no—
217C2×C4×C5—612no—
218C2×C4×C5C2×C4×D316yes—
219C2×C4×C5C2×D1213yes—
220C2×C4×C5C2×#6716yes—
221C2×C4×C5C23×D311yescharacteristic
222C2×Dic5—61no—
223C2×Dic5—63no—
224C2×Dic5—243no—
225#168—21no—
226#168—23no—
2272−1+4—38no—
2282−1+4—64no—
229C2×#41—33no—
230C2×#41—63no—
231C2×#41D3×D511yescharacteristic
232C22×Q8—33no—
233C22×Q8—61no—
234#131—104no—
235C2×M16—53no—
236C22×C8—53no—
237C4×Q8—301no—
238C4×D4—303no—
239#117—153no—
240C2×C4⋊C4—153no—
241#103—153no—
242#103—156no—
243#103—153no—
244#102—151no—
245#102—153no—
246C2×C3×C5—26no—
247C2×C3×C5C22×C22⋊C411yescharacteristic
248C2×C3×C5#57711yescharacteristic
249C2×C3×C5#57811yescharacteristic
250C5×D3—42no—
251C23×C3C2×C22⋊D513yes—
252C22×D3—21no—
253C3×Q8C22⋊Dic514yes—
254C3×D4C22⋊Dic5112yes—
255C2×C3×C4C22×Dic516yes—
256C2×C3×C4C2×C22⋊D516yes—
257C2×C3×C4C2×C22⋊D513yes—
258C2×C3×C4C23×D511yescharacteristic
259#67—212no—
260C2×Dic3—212no—
261C2×Dic3—23no—
262C2×Dic3—101no—
263C2×Dic3—103no—
264C2×Dic3—403no—
265D12—21no—
266D12C22×Dic512yes—
267C4×D3—212no—
268Dic6—212no—
269Dic6—23no—
270Dic6C22×Dic516yes—
271C3×C8—101no—
272C3×C8—103no—
273C22×C5—23no—
274C22×C5—23no—
275C22×C5—62no—
276C22×C5—121no—
277C22×C5—121no—
278C22×C5C2×(C2×D3)⋊C416yes—
279C22×C5C22×D1211yescharacteristic
280C4×C5—66no—
281C4×C5C2×(C2×D3)⋊C416yes—
282C4×C5C22×C4×D311yescharacteristic
283C4×C5C22×#6711yescharacteristic
284Dic5—123no—
285Dic5—121no—
286#41—312no—
287#41—624no—
288#41—66no—
289#41D3×Dic514yes—
290#41#120114yes—
291C2×Q8—312no—
292C2×Q8—33no—
293C2×Q8—68no—
294C2×Q8—66no—
295C2×Q8—63no—
296C2×Q8#120311yescharacteristic
297C2×D4—31no—
298C2×D4—63no—
299C2×D4#120313yes—
300C22×C4—63no—
301C22×C4—63no—
302C22×C4—303no—
303C22×C4C2×D3×D513yes—
304M16—106no—
305C2×C8—51no—
306C2×C8—53no—
307C2×C8—106no—
308C4⋊C4—153no—
309C4⋊C4—151no—
310C4⋊C4—303no—
311C22⋊C4—303no—
312C42—303no—
313C3×C5#289811yescharacteristic, complemented, Hall
314C22×C3—23no—
315C22×C3—23no—
316C22×C3C2×C22⋊Dic516yes—
317C22×C3C22×C22⋊D511yescharacteristic
318C2×D3—22no—
319C2×D3—41no—
320C2×D3—41no—
321C3×C4C2×C22⋊Dic516yes—
322C3×C4C23×Dic511yescharacteristic
323C3×C4C22×C22⋊D511yescharacteristic
324Dic3—26no—
325Dic3—203no—
326Dic3—201no—
327C2×C5—26no—
328C2×C5—122no—
329C2×C5#575111yescharacteristic
330C2×C5#575311yescharacteristic
331C2×C5C22×(C2×D3)⋊C411yescharacteristic
332C23—61no—
333C23C2×#120313yes—
334Q8—36no—
335Q8—63no—
336Q8—612no—
337Q8(C2×D3)⋊Dic514yes—
338D4—32no—
339D4—612no—
340D4—61no—
341D4(C2×D3)⋊Dic5112yes—
342C2×C4—63no—
343C2×C4—612no—
344C2×C4—612no—
345C2×C4—301no—
346C2×C4—303no—
347C2×C4—1203no—
348C2×C4C2×D3×Dic516yes—
349C2×C4C2×#120116yes—
350C2×C4C2×#120313yes—
351C2×C4C22×D3×D511yescharacteristic
352C8—101no—
353C8—103no—
354C2×C3—26no—
355C2×C3#6617111yescharacteristic
356C2×C3#6617211yescharacteristic
357C2×C3C22×C22⋊Dic511yescharacteristic
358D3—42no—
359C5#8380611yescharacteristic, complemented, Sylow
360C22—23no—
361C22—23no—
362C22—62no—
363C22—121no—
364C22—121no—
365C22C2×(C2×D3)⋊Dic516yes—
366C22C22×#120311yescharacteristic
367C4—66no—
368C4—601no—
369C4—603no—
370C4C2×(C2×D3)⋊Dic516yes—
371C4C22×D3×Dic511yescharacteristic
372C4C22×#120111yescharacteristic
373C3#1061584211yescharacteristic, complemented, Sylow
374C2—26no—
375C2—122no—
376C2#1175530611yescharacteristic
377C2#1175530811yescharacteristic
378C2C22×(C2×D3)⋊Dic511yescharacteristic
subgroupG/H
centerC22C22×#1203
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#1010C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2898
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11756586C2semidirect
3. C2×C3×#4094C2semidirect
4. #11748409C2semidirect
5. C2×#90973C2semidirect
6. #11748390C2semidirect
7. #11748388C2semidirect
11. C5×#1010C4semidirect
31. C2×#4094D3semidirect
47. C5×#235C2×C4semidirect
52. C2×C5×Dic6C2×C4semidirect
114. #1010Dic5semidirect
189. #235C2×Dic5semidirect
194. C2×Dic6C2×Dic5semidirect
313. C3×C5#2898semidirect
359. C5#83806semidirect
373. C3#10615842semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10102
#117565862
C2×C3×#40942
#117484092
C2×#909732
#117483902
#117483882
#106158423
#838065