Finite Group Databasebeta

← #14301595

Subgroups — #14301595

Order 1920.

688 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 156 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×#91836C211yesmaximal, characteristic
2C5×#5812C211yesmaximal, characteristic, complemented
3C2×C3×#3968C211yesmaximal, characteristic, complemented
4#11748396C212yesmaximal
5#11745975C212yesmaximal, complemented
6#10602454—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C22×D60C2211yescharacteristic
9#91836—22no—
10#91836C414yescomplemented
11C2×#6714—22no—
12C2×C4×Dic15C2211yescharacteristic
13C5×Q8×Dic3—24no—
14C5×#926—22no—
15C5×#926C2212yes—
16C2×C3×#681C2212yes—
17C3×#3968—22no—
18#90969—24no—
19#70104—51nomaximal, Hall
20C5×#519—31no—
21C2×#4093—31no—
22C2×#3968D311yescharacteristic, complemented
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—
37#6714—28no—
38C4×Dic15—21no—
39C4×Dic15C2×C412yes—
40C5×#217—22no—
41C5×C4⋊Dic3—24no—
42C5×C4⋊Dic3D414yes—
43C4×C5×Dic3—24no—
44C4×C5×Dic3—22no—
45C3×#681—22no—
46C3×#681—22no—
47C2×C3×#168—22no—
48C2×#947—51no—
49#5812D511yescharacteristic, complemented
50C2×C3×#101—51no—
51#5131—52no—
52#4555—52no—
53C22×C5×Q8C2×D311yescharacteristic
54C22×D20—31no—
55C4×C5×Q8—64no—
56C5×#117—32no—
57C5×#117—62no—
58#4093—34no—
59#4093—62no—
60C2×#685—62no—
61C2×C4×Dic5—31no—
62C2×#681C2×D312yes—
63#3968—22no—
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×C5C22⋊C414yes—
76C2×C3×C4×C5C22×C411yescharacteristic
77C2×C3×C4×C5C2×D412yes—
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4112yes—
80C2×Dic15—22no—
81C2×Dic15—42no—
82D60—24no—
83D60—42no—
84C2×C5×Dic3—24no—
85C3×#168—42no—
86C22×C3×Q8C2×D511yescharacteristic
87C22×D12—51no—
88C2×C3×M16—52no—
89#947—54no—
90#947—102no—
91Q8×Dic3—24no—
92C2×(C2×D3)⋊C4—102no—
93#926—22no—
94#926C2×D512yes—
95C2×C4×Dic3—51no—
96C3×#101—102no—
97#821—104no—
98C23×D5—61no—
99C2×C5×Q8—22no—
100C2×C5×Q8—22no—
101C2×C5×Q8C4×D312yes—
102C2×C5×Q8#6712yes—
103C22×C4×C5D1212yes—
104C22×C4×C5C22×D311yescharacteristic
105C22×Dic5—61no—
106C2×D20—32no—
107C2×D20—62no—
108C2×D20—62no—
109C2×D20—61no—
110C5×C4⋊C4—34no—
111C5×C4⋊C4—64no—
112C5×C22⋊C4—62no—
113C42×C5—64no—
114C42×C5—62no—
115#685—68no—
116C4×Dic5—32no—
117C4×Dic5—61no—
118#681—22no—
119#681—22no—
120C2×#168—22no—
121C2×#124—151no—
122#519—31no—
123#418—152no—
124C2×#101—51no—
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×C5C4×D412yes—
136C3×C4×C5#12112yes—
137Dic15—42no—
138C5×Dic3—44no—
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×M16—102no—
152C3×M16—102no—
153C2×C3×C8—102no—
154#217—22no—
155(C2×D3)⋊C4—108no—
156C4⋊Dic3—24no—
157C4⋊Dic3C22⋊D514yes—
158C4×Dic3—24no—
159C4×Dic3—22no—
160C4×Dic3—52no—
161C4×Dic3—101no—
162C23×C5C2×D1211yescharacteristic
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—64no—
172C2×C4×C5(C2×D3)⋊C414yes—
173C2×C4×C5C2×C4×D311yescharacteristic
174C2×C4×C5D3×D412yes—
175C2×C4×C5#23712yes—
176C2×C4×C5C2×#6711yescharacteristic
177C2×Dic5—62no—
178C2×Dic5—122no—
179D20—64no—
180D20—122no—
181#168—42no—
182C22×Q8D3×D511yescharacteristic
183C22×D4—151no—
184C2×M16—52no—
185#124—154no—
186#124—302no—
187C4×Q8—64no—
188#117—32no—
189#117—62no—
190C2×C22⋊C4—302no—
191C2×C42—151no—
192#102—304no—
193#101—102no—
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#68514yes—
209C2×C3×C4C2×C4×D511yescharacteristic
210C2×C3×C4C2×D2011yescharacteristic
211C2×C3×C4#70912yes—
212C2×C3×C4C2×C22⋊D512yes—
213C2×Dic3—24no—
214C2×Dic3—102no—
215C2×Dic3—202no—
216D12—104no—
217D12—202no—
218C3×C8—202no—
219C22×C5—22no—
220C22×C5#88211yescharacteristic
221C22×C5#88611yescharacteristic
222C22×C5C2×(C2×D3)⋊C411yescharacteristic
223C2×D5—124no—
224C2×D5—122no—
225C2×D5—242no—
226C2×D5—242no—
227C4×C5—24no—
228C4×C5—124no—
229C4×C5#67⋊C412yes—
230C4×C5#93912yes—
231Dic5—122no—
232C24—301no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8#120012yes—
236C2×Q8#120212yes—
237C2×D4—152no—
238C2×D4—302no—
239C2×D4—301no—
240C2×D4—302no—
241C22×C4—301no—
242C22×C4#120312yes—
243C22×C4C2×D3×D511yescharacteristic
244M16—102no—
245M16—102no—
246C2×C8—102no—
247C4⋊C4—34no—
248C4⋊C4—64no—
249C22⋊C4—62no—
250C22⋊C4—308no—
251C42—64no—
252C42—62no—
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×C4C4×C22⋊D512yes—
266C3×C4#407612yes—
267Dic3—44no—
268Dic3—202no—
269C2×C5—21no—
270C2×C5—21no—
271C2×C5#475312yes—
272C2×C5#495811yescharacteristic
273D5—242no—
274C23—302no—
275C23—604no—
276C23—601no—
277C23—601no—
278C23C2×#120311yescharacteristic
279Q8—24no—
280Q8—24no—
281D4—304no—
282D4—602no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—64no—
286C2×C4—302no—
287C2×C4—602no—
288C2×C4#666714yes—
289C2×C4#677912yes—
290C2×C4C2×#120011yescharacteristic
291C2×C4C2×#120211yescharacteristic
292C2×C4D3×C22⋊D512yes—
293C8—202no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3#6550211yescharacteristic
297C2×C3#6553412yes—
298D3—402no—
299C5#7010411yescharacteristic, complemented, Sylow
300C22—22no—
301C22—604no—
302C22—602no—
303C22—1202no—
304C22—1202no—
305C22C2×#666711yescharacteristic
306C22#9154211yescharacteristic
307C22#9157011yescharacteristic
308C4—24no—
309C4—124no—
310C4—602no—
311C4#9155612yes—
312C4#9156912yes—
313C3#1060245411yescharacteristic, complemented, Sylow
314C2—21no—
315C2—21no—
316C2—1202no—
317C2#1174938712yes—
318C2#1174949811yescharacteristic
subgroupG/H
centerC22#91570
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5#120
prime radicalC22×D60C22
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. C5×#5812C2semidirect
3. C2×C3×#3968C2semidirect
5. #11745975C2semidirect
10. #91836C4semidirect
22. C2×#3968D3semidirect
49. #5812D5semidirect
255. C3×C5#1888semidirect
299. C5#70104semidirect
313. C3#10602454semidirect

Maximal subgroups

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

subgroupindex
C2×#918362
C5×#58122
C2×C3×#39682
#117483962
#117459752
#106024543
#701045