Finite Group Databasebeta

← #14301598

Subgroups — #14301598

Order 1920.

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

normal subgroups only

This group has 688 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
1C2×C5×#947C211yesmaximal, characteristic
2C3×#66146C211yesmaximal, characteristic, complemented
3C2×#91120C211yesmaximal, characteristic, complemented
4#11748386C212yesmaximal
5#11745974C212yesmaximal, complemented
6#10602517—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C22×C5×D12C2211yescharacteristic
9C2×#6710C2212yes—
10C5×#947—22no—
11C5×#947C414yescomplemented
12C2×C5×(C2×D3)⋊C4—22no—
13C2×C4×C5×Dic3C2211yescharacteristic
14C3×Q8×Dic5—24no—
15C3×#4072—22no—
16C3×#4072C2212yes—
17#91120—22no—
18#90966—24no—
19#71661—51nomaximal, Hall
20C2×C5×#124—31no—
21#66146D311yescharacteristic, complemented
22C2×#3968—31no—
23#65504—32no—
24#64743—32no—
25C23×C5×D3—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×C5×Dic3—21no—
33C2×C5×D12—22no—
34C2×C5×D12—22no—
35C2×C5×D12—21no—
36C2×C5×D12C2×C412yes—
37#6710—22no—
38#6710—22no—
39C2×C3⋊#168—22no—
40C5×(C2×D3)⋊C4—28no—
41C4×C5×Dic3—21no—
42C4×C5×Dic3C2×C412yes—
43C3×C22⋊Dic5—22no—
44C3×C4⋊Dic5—24no—
45C3×C4⋊Dic5D414yes—
46C3×C4×Dic5—24no—
47C3×C4×Dic5—22no—
48C3×#519—51no—
49C2×#947D511yescharacteristic
50C2×#836—51no—
51#5001—52no—
52#4532—52no—
53C22×C5×Q8C2×D311yescharacteristic
54C22×C5×D4—31no—
55C5×#124—34no—
56C5×#124—62no—
57C2×C5×C22⋊C4—62no—
58C2×C42×C5—31no—
59Q8×Dic5—24no—
60#4072—22no—
61#4072C2×D312yes—
62C2×#681—32no—
63#3968—62no—
64#3964—64no—
65#1888—151noSylow
66C23×C3×C5C2×D411yescharacteristic
67C22×C5×D3—22no—
68C22×C5×D3—44no—
69C22×C5×D3—41no—
70C22×C5×D3—41no—
71C3×C5×Q8—24no—
72C3×C5×Q8—24no—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5—22no—
75C2×C3×C4×C5C22⋊C414yes—
76C2×C3×C4×C5C22×C411yescharacteristic
77C2×C3×C4×C5C2×D412yes—
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4112yes—
80C2×C5×Dic3—22no—
81C2×C5×Dic3—42no—
82C5×D12—24no—
83C5×D12—42no—
84C2×C3×Dic5—24no—
85C3⋊#168—42no—
86C22×C3×Q8C2×D511yescharacteristic
87C22×D12C2×D511yescharacteristic
88C3×C4×Q8—104no—
89C3×#117—52no—
90C3×#117—102no—
91#947—22no—
92#947Dic514yescomplemented
93C2×(C2×D3)⋊C4—22no—
94C2×C4×Dic3C2×D511yescharacteristic
95C2×#208—52no—
96#836—102no—
97#809—104no—
98C24×C5—61no—
99C2×C5×Q8—22no—
100C2×C5×Q8—22no—
101C2×C5×Q8C4×D312yes—
102C2×C5×Q8D1212yes—
103C2×C5×D4—32no—
104C2×C5×D4—61no—
105C2×C5×D4—62no—
106C2×C5×D4—62no—
107C22×C4×C5—61no—
108C22×C4×C5#6712yes—
109C22×C4×C5C22×D311yescharacteristic
110C5×C22⋊C4—68no—
111C42×C5—32no—
112C42×C5—61no—
113C22⋊Dic5—22no—
114C4⋊Dic5—24no—
115C4⋊Dic5#6714yes—
116C4×Dic5—24no—
117C4×Dic5—22no—
118#681—62no—
119#681—62no—
120C2×#168—62no—
121C2×#124—31no—
122#519—51no—
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×C5×D3—44no—
131C2×C5×D3—42no—
132C2×C5×D3—82no—
133C2×C5×D3—82no—
134C3×C4×C5—24no—
135C3×C4×C5C4×D412yes—
136C3×C4×C5#12112yes—
137C3×Dic5—44no—
138C5×Dic3—42no—
139C23×D3—21no—
140C2×C3×Q8—22no—
141C2×C3×Q8—22no—
142C2×C3×Q8C2×Dic512yes—
143C2×C3×Q8C22⋊D512yes—
144C22×C3×C4C22⋊D512yes—
145C22×C3×C4C22×D511yescharacteristic
146C22×Dic3—21no—
147C2×D12—22no—
148C2×D12—22no—
149C2×D12—21no—
150C2×D12C2×Dic512yes—
151C3×C4⋊C4—54no—
152C3×C4⋊C4—104no—
153C3×C22⋊C4—102no—
154C3×C42—104no—
155C3×C42—102no—
156(C2×D3)⋊C4—28no—
157C4×Dic3—21no—
158C4×Dic3C2×Dic512yes—
159#208—102no—
160#208—102no—
161C2×C3⋊C8—102no—
162C23×C5—62no—
163C23×C5—124no—
164C23×C5—121no—
165C23×C5—121no—
166C23×C5C2×#6711yescharacteristic
167C5×Q8—24no—
168C5×Q8—24no—
169C5×D4—64no—
170C5×D4—122no—
171C2×C4×C5—22no—
172C2×C4×C5—22no—
173C2×C4×C5—62no—
174C2×C4×C5—122no—
175C2×C4×C5(C2×D3)⋊C414yes—
176C2×C4×C5C2×C4×D311yescharacteristic
177C2×C4×C5C2×D1211yescharacteristic
178C2×C4×C5#23512yes—
179C2×C4×C5C2×#6712yes—
180C2×Dic5—24no—
181#168—122no—
182C22×Q8D3×D511yescharacteristic
183C22×D4—31no—
184C2×M16—152no—
185#124—34no—
186#124—62no—
187C4×Q8—104no—
188#117—52no—
189#117—102no—
190C2×C22⋊C4—62no—
191C2×C42—31no—
192#102—304no—
193#101—302no—
194C2×C3×C5—21no—
195C2×C3×C5—21no—
196C2×C3×C5#38611yescharacteristic
197C2×C3×C5#45412yes—
198C5×D3—82no—
199C23×C3C2×C22⋊D511yescharacteristic
200C22×D3—22no—
201C22×D3—44no—
202C22×D3—41no—
203C22×D3—41no—
204C3×Q8—24no—
205C3×Q8—24no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—104no—
209C2×C3×C4C22⋊Dic514yes—
210C2×C3×C4D4×D512yes—
211C2×C3×C4#71112yes—
212C2×C3×C4C22×Dic511yescharacteristic
213C2×C3×C4C2×C22⋊D511yescharacteristic
214C2×Dic3—22no—
215C2×Dic3—42no—
216D12—24no—
217D12—42no—
218C3⋊C8—202no—
219C22×C5—22no—
220C22×C5—124no—
221C22×C5—122no—
222C22×C5—242no—
223C22×C5—242no—
224C22×C5C2×(C2×D3)⋊C411yescharacteristic
225C22×C5#92911yescharacteristic
226C22×C5#95311yescharacteristic
227C4×C5—24no—
228C4×C5—122no—
229C4×C5C4×#6712yes—
230C4×C5#93012yes—
231Dic5—44no—
232C24—61no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8D3×Dic512yes—
236C2×Q8#120312yes—
237C2×D4—32no—
238C2×D4—62no—
239C2×D4—61no—
240C2×D4—62no—
241C22×C4—61no—
242C22×C4#120112yes—
243C22×C4C2×D3×D511yescharacteristic
244M16—302no—
245M16—302no—
246C2×C8—302no—
247C4⋊C4—54no—
248C4⋊C4—104no—
249C22⋊C4—68no—
250C22⋊C4—102no—
251C42—32no—
252C42—61no—
253C42—104no—
254C42—102no—
255C3×C5#188811yescharacteristic, complemented, Hall
256C22×C3—22no—
257C22×C3#408111yescharacteristic
258C22×C3#408311yescharacteristic
259C22×C3C2×C22⋊Dic511yescharacteristic
260C2×D3—44no—
261C2×D3—42no—
262C2×D3—82no—
263C2×D3—82no—
264C3×C4—24no—
265C3×C4—204no—
266C3×C4D4×Dic512yes—
267C3×C4#408512yes—
268Dic3—42no—
269C2×C5—21no—
270C2×C5—21no—
271C2×C5—242no—
272C2×C5#521311yescharacteristic
273C2×C5#524512yes—
274C23—62no—
275C23—124no—
276C23—121no—
277C23—121no—
278C23C2×#120111yescharacteristic
279Q8—24no—
280Q8—24no—
281D4—64no—
282D4—122no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—62no—
286C2×C4—104no—
287C2×C4—122no—
288C2×C4(C2×D3)⋊Dic514yes—
289C2×C4C2×D3×Dic511yescharacteristic
290C2×C4#678212yes—
291C2×C4C2×#120311yescharacteristic
292C2×C4D5×#6712yes—
293C8—602no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3#6535112yes—
297C2×C3#6550911yescharacteristic
298D3—82no—
299C5#7166111yescharacteristic, complemented, Sylow
300C22—22no—
301C22—124no—
302C22—122no—
303C22—242no—
304C22—242no—
305C22C2×(C2×D3)⋊Dic511yescharacteristic
306C22#9153911yescharacteristic
307C22#9156311yescharacteristic
308C4—24no—
309C4—122no—
310C4—204no—
311C4Dic5×#6712yes—
312C4#9156612yes—
313C3#1060251711yescharacteristic, complemented, Sylow
314C2—21no—
315C2—21no—
316C2—242no—
317C2#1174938312yes—
318C2#1174949211yescharacteristic
subgroupG/H
centerC22#91563
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5#120
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenterC22×Q8D3×D5
hypocenterC3×C5#1888
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#66146C2semidirect
3. C2×#91120C2semidirect
5. #11745974C2semidirect
11. C5×#947C4semidirect
21. #66146D3semidirect
92. #947Dic5semidirect
255. C3×C5#1888semidirect
299. C5#71661semidirect
313. C3#10602517semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9472
C3×#661462
C2×#911202
#117483862
#117459742
#106025173
#716615