Finite Group Databasebeta

← #14301575

Subgroups — #14301575

Order 1920.

688 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C3×C5×#519C211yesmaximal, characteristic, complemented
2C2×#91836C211yesmaximal, characteristic
3C2×#91120C211yesmaximal, characteristic, complemented
4#11751102C212yesmaximal
5#11746353C212yesmaximal, complemented
6#10602454—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C22×D60C2211yescharacteristic
9C3×C4×C5×Q8—24no—
10C3×C5×#117—22no—
11C3×C5×#117C2212yes—
12#91836—22no—
13#91836C414yescomplemented
14C2×#6714—22no—
15C2×C4×Dic15C2211yescharacteristic
16C2×#6710C2212yes—
17#91120—22no—
18#91093—24no—
19#71661—51nomaximal, Hall
20C5×#519D311yescharacteristic, complemented
21C2×#4093—31no—
22C2×#3968—31no—
23#65290—32no—
24#64752—32no—
25C23×D15—21no—
26C2×C3×C5×Q8—22no—
27C2×C3×C5×Q8—22no—
28C2×C3×C5×Q8C2×C412yes—
29C2×C3×C5×Q8D412yes—
30C22×C3×C4×C5D412yes—
31C22×C3×C4×C5C2311yescharacteristic
32C22×Dic15—21no—
33C2×D60—22no—
34C2×D60—22no—
35C2×D60—21no—
36C2×D60C2×C412yes—
37C3×C5×C4⋊C4—24no—
38C3×C5×C4⋊C4D414yes—
39C3×C5×C22⋊C4—22no—
40C3×C42×C5—24no—
41C3×C42×C5—22no—
42#6714—28no—
43C4×Dic15—21no—
44C4×Dic15C2×C412yes—
45#6710—22no—
46#6710—22no—
47C2×C3⋊#168—22no—
48C3×#519D511yescharacteristic, complemented
49C2×#947—51no—
50C2×#836—51no—
51#5001—52no—
52#4532—52no—
53C22×C5×Q8C2×D311yescharacteristic
54C22×D20—31no—
55C4×C5×Q8—24no—
56C5×#117—22no—
57C5×#117C2×D312yes—
58#4093—34no—
59#4093—62no—
60C2×#685—62no—
61C2×C4×Dic5—31no—
62C2×#681—32no—
63#3968—62no—
64#3941—64no—
65#1888—151noSylow
66C23×C3×C5C2×D411yescharacteristic
67C22×D15—22no—
68C22×D15—44no—
69C22×D15—41no—
70C22×D15—41no—
71C3×C5×Q8—24no—
72C3×C5×Q8—24no—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5—24no—
76C2×C3×C4×C5C22⋊C414yes—
77C2×C3×C4×C5C22×C411yescharacteristic
78C2×C3×C4×C5C2×D412yes—
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C3×C4×C5#4112yes—
81C2×Dic15—22no—
82C2×Dic15—42no—
83D60—24no—
84D60—42no—
85C3⋊#168—42no—
86C22×C3×Q8C2×D511yescharacteristic
87C22×D12—51no—
88C3×C4×Q8—24no—
89C3×#117—22no—
90C3×#117C2×D512yes—
91#947—54no—
92#947—102no—
93C2×(C2×D3)⋊C4—102no—
94C2×C4×Dic3—51no—
95C2×#208—52no—
96#836—102no—
97#809—104no—
98C23×D5—61no—
99C2×C5×Q8—22no—
100C2×C5×Q8—22no—
101C2×C5×Q8C4×D312yes—
102C2×C5×Q8D1212yes—
103C22×C4×C5#6712yes—
104C22×C4×C5C22×D311yescharacteristic
105C22×Dic5—61no—
106C2×D20—32no—
107C2×D20—62no—
108C2×D20—62no—
109C2×D20—61no—
110C5×C4⋊C4—24no—
111C5×C4⋊C4#6714yes—
112C5×C22⋊C4—22no—
113C42×C5—24no—
114C42×C5—22no—
115#685—68no—
116C4×Dic5—32no—
117C4×Dic5—61no—
118#681—62no—
119#681—62no—
120C2×#168—62no—
121C2×#124—151no—
122#519D1511yescharacteristic, complemented
123#418—152no—
124C2×#101—151no—
125#339—152no—
126C22×C3×C5—22no—
127C22×C3×C5C2×C22⋊C411yescharacteristic
128C22×C3×C5#12011yescharacteristic
129C22×C3×C5#12311yescharacteristic
130C2×D15—44no—
131C2×D15—42no—
132C2×D15—82no—
133C2×D15—82no—
134C3×C4×C5—24no—
135C3×C4×C5—44no—
136C3×C4×C5C4×D412yes—
137C3×C4×C5#12112yes—
138Dic15—42no—
139C23×D3—101no—
140C2×C3×Q8—22no—
141C2×C3×Q8—22no—
142C2×C3×Q8C4×D512yes—
143C2×C3×Q8D2012yes—
144C22×C3×C4C22⋊D512yes—
145C22×C3×C4C22×D511yescharacteristic
146C22×Dic3—101no—
147C2×D12—52no—
148C2×D12—102no—
149C2×D12—102no—
150C2×D12—101no—
151C3×C4⋊C4—24no—
152C3×C4⋊C4C22⋊D514yes—
153C3×C22⋊C4—22no—
154C3×C42—24no—
155C3×C42—22no—
156(C2×D3)⋊C4—108no—
157C4×Dic3—52no—
158C4×Dic3—101no—
159#208—102no—
160#208—102no—
161C2×C3⋊C8—102no—
162C23×C5C2×#6711yescharacteristic
163C22×D5—62no—
164C22×D5—124no—
165C22×D5—121no—
166C22×D5—121no—
167C5×Q8—24no—
168C5×Q8—24no—
169C2×C4×C5—22no—
170C2×C4×C5—22no—
171C2×C4×C5—24no—
172C2×C4×C5(C2×D3)⋊C414yes—
173C2×C4×C5C2×C4×D311yescharacteristic
174C2×C4×C5C2×D1211yescharacteristic
175C2×C4×C5#23512yes—
176C2×C4×C5C2×#6712yes—
177C2×Dic5—62no—
178C2×Dic5—122no—
179D20—64no—
180D20—122no—
181#168—122no—
182C22×Q8C2×D1511yescharacteristic
183C22×D4—151no—
184C2×M16—152no—
185#124—154no—
186#124—302no—
187C4×Q8—24no—
188#117—22no—
189#117C2×D1512yes—
190C2×C22⋊C4—302no—
191C2×C42—151no—
192#102—304no—
193#101—302no—
194C2×C3×C5—21no—
195C2×C3×C5—21no—
196C2×C3×C5#38611yescharacteristic
197C2×C3×C5#45412yes—
198D15—82no—
199C23×C3C2×C22⋊D511yescharacteristic
200C22×D3—102no—
201C22×D3—204no—
202C22×D3—201no—
203C22×D3—201no—
204C3×Q8—24no—
205C3×Q8—24no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—24no—
209C2×C3×C4#68514yes—
210C2×C3×C4C2×C4×D511yescharacteristic
211C2×C3×C4C2×D2011yescharacteristic
212C2×C3×C4#70912yes—
213C2×C3×C4C2×C22⋊D512yes—
214C2×Dic3—102no—
215C2×Dic3—202no—
216D12—104no—
217D12—202no—
218C3⋊C8—202no—
219C22×C5—22no—
220C22×C5C2×(C2×D3)⋊C411yescharacteristic
221C22×C5#92911yescharacteristic
222C22×C5#95311yescharacteristic
223C2×D5—124no—
224C2×D5—122no—
225C2×D5—242no—
226C2×D5—242no—
227C4×C5—24no—
228C4×C5—44no—
229C4×C5C4×#6712yes—
230C4×C5#93012yes—
231Dic5—122no—
232C24—301no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8C4×D1512yes—
236C2×Q8D6012yes—
237C2×D4—152no—
238C2×D4—301no—
239C2×D4—302no—
240C2×D4—302no—
241C22×C4—301no—
242C22×C4#122012yes—
243C22×C4C22×D1511yescharacteristic
244M16—302no—
245M16—302no—
246C2×C8—302no—
247C4⋊C4—24no—
248C4⋊C4#122014yes—
249C22⋊C4—22no—
250C22⋊C4—308no—
251C42—24no—
252C42—22no—
253C42—152no—
254C42—301no—
255C3×C5#188811yescharacteristic, complemented, Hall
256C22×C3—22no—
257C22×C3C2×#68511yescharacteristic
258C22×C3#407511yescharacteristic
259C22×C3#409911yescharacteristic
260C2×D3—204no—
261C2×D3—202no—
262C2×D3—402no—
263C2×D3—402no—
264C3×C4—24no—
265C3×C4—44no—
266C3×C4C4×C22⋊D512yes—
267C3×C4#407612yes—
268Dic3—202no—
269C2×C5—21no—
270C2×C5—21no—
271C2×C5#521311yescharacteristic
272C2×C5#524512yes—
273D5—242no—
274C23—302no—
275C23—604no—
276C23—601no—
277C23—601no—
278C23C2×#122011yescharacteristic
279Q8—24no—
280Q8—24no—
281D4—304no—
282D4—602no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—302no—
287C2×C4—602no—
288C2×C4#671414yes—
289C2×C4C2×C4×D1511yescharacteristic
290C2×C4C2×D6011yescharacteristic
291C2×C4#681712yes—
292C2×C4C2×#122012yes—
293C8—602no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3#6550211yescharacteristic
297C2×C3#6553412yes—
298D3—402no—
299C5#7166111yescharacteristic, complemented, Sylow
300C22—22no—
301C22—604no—
302C22—602no—
303C22—1202no—
304C22—1202no—
305C22C2×#671411yescharacteristic
306C22#9181811yescharacteristic
307C22#9184211yescharacteristic
308C4—24no—
309C4—44no—
310C4—602no—
311C4C4×#122012yes—
312C4#9181912yes—
313C3#1060245411yescharacteristic, complemented, Sylow
314C2—21no—
315C2—21no—
316C2—1202no—
317C2#1175131411yescharacteristic
318C2#1175134612yes—
subgroupG/H
centerC22#91842
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#519C2
socleC22×C3×C5#120
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenter#519D15
hypocenterC3×C5#1888
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C3×C5×#519C2semidirect
3. C2×#91120C2semidirect
5. #11746353C2semidirect
13. #91836C4semidirect
20. C5×#519D3semidirect
48. C3×#519D5semidirect
122. #519D15semidirect
255. C3×C5#1888semidirect
299. C5#71661semidirect
313. C3#10602454semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5192
C2×#918362
C2×#911202
#117511022
#117463532
#106024543
#716615