Finite Group Databasebeta

← #14301594

Subgroups — #14301594

Order 1920.

688 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 160 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
1#11756571C211yesmaximal, characteristic, complemented
2C2×C3×#4093C211yesmaximal, characteristic
3C2×C5×#836C211yesmaximal, characteristic, complemented
4#11748367C212yesmaximal
5#11745978C212yesmaximal, complemented
6#10600897—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic
8C22×C3×D20C2211yescharacteristic
9Q8×Dic15—24no—
10#91815—22no—
11#91815C2212yes—
12C2×C5×#208C2212yes—
13C3×#4093—22no—
14C3×#4093C414yescomplemented
15C2×C3×#685—22no—
16C2×C3×C4×Dic5C2211yescharacteristic
17C5×#836—22no—
18#90965—24no—
19#71724—51nomaximal, Hall
20C2×#4093D311yescharacteristic
21#66146—31no—
22C2×C5×#101—31no—
23#65420—32no—
24#64775—32no—
25C23×C3×D5—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×C3×Dic5—21no—
33C2×C3×D20—22no—
34C2×C3×D20—22no—
35C2×C3×D20—21no—
36C2×C3×D20C2×C412yes—
37#6719—22no—
38C4⋊Dic15—24no—
39C4⋊Dic15D414yes—
40C4×Dic15—24no—
41C4×Dic15—22no—
42C5×#208—22no—
43C5×#208—22no—
44C2×C5×C3⋊C8—22no—
45C3×#685—28no—
46C3×C4×Dic5—21no—
47C3×C4×Dic5C2×C412yes—
48C2×C3×#124—51no—
49#5812—51no—
50C2×#836D511yescharacteristic, complemented
51#5215—52no—
52#4523—52no—
53C22×C5×Q8C2×D311yescharacteristic
54C22×D20C2×D311yescharacteristic
55C2×C5×M16—32no—
56#4093—22no—
57#4093Dic314yescomplemented
58Q8×Dic5—64no—
59C2×#685—22no—
60#4072—32no—
61#4072—62no—
62C2×C4×Dic5C2×D311yescharacteristic
63C5×#101—62no—
64#3953—64no—
65#1888—151noSylow
66C23×C3×C5C2×D411yescharacteristic
67C22×C3×D5—22no—
68C22×C3×D5—44no—
69C22×C3×D5—41no—
70C22×C3×D5—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—24no—
81C2×C3×Dic5—22no—
82C2×C3×Dic5—42no—
83C3×D20—24no—
84C3×D20—42no—
85C5×C3⋊C8—42no—
86C22×C3×Q8C2×D511yescharacteristic
87C22×C3×D4—51no—
88C3×#124—54no—
89C3×#124—102no—
90C2×C3×C22⋊C4—102no—
91C2×C3×C42—51no—
92Q8×Dic3—104no—
93#926—52no—
94#926—102no—
95C2×#208C2×D512yes—
96#836—22no—
97#832—104no—
98C23×D5—21no—
99C2×C5×Q8—22no—
100C2×C5×Q8—22no—
101C2×C5×Q8C2×Dic312yes—
102C2×C5×Q8#6712yes—
103C22×C4×C5#6712yes—
104C22×C4×C5C22×D311yescharacteristic
105C22×Dic5—21no—
106C2×D20—22no—
107C2×D20—22no—
108C2×D20—21no—
109C2×D20C2×Dic312yes—
110C5×M16—62no—
111C5×M16—62no—
112C2×C5×C8—62no—
113C22⋊Dic5—62no—
114#685—28no—
115C4⋊Dic5—34no—
116C4⋊Dic5—64no—
117C4×Dic5—21no—
118C4×Dic5—64no—
119C4×Dic5—62no—
120C4×Dic5C2×Dic312yes—
121C2×#124—51no—
122#519—151no—
123#418—152no—
124C2×#101—31no—
125#339—152no—
126C22×C3×C5—22no—
127C22×C3×C5C2×C22⋊C411yescharacteristic
128C22×C3×C5#12011yescharacteristic
129C22×C3×C5#12311yescharacteristic
130C2×C3×D5—44no—
131C2×C3×D5—42no—
132C2×C3×D5—82no—
133C2×C3×D5—82no—
134C3×C4×C5—24no—
135C3×C4×C5C4×D412yes—
136C3×C4×C5#12112yes—
137Dic15—44no—
138C3×Dic5—42no—
139C24×C3—101no—
140C2×C3×Q8—22no—
141C2×C3×Q8—22no—
142C2×C3×Q8C4×D512yes—
143C2×C3×Q8C22⋊D512yes—
144C2×C3×D4—52no—
145C2×C3×D4—102no—
146C2×C3×D4—102no—
147C2×C3×D4—101no—
148C22×C3×C4—101no—
149C22×C3×C4D2012yes—
150C22×C3×C4C22×D511yescharacteristic
151C3×C22⋊C4—108no—
152C3×C42—52no—
153C3×C42—101no—
154#217—102no—
155C4⋊Dic3—54no—
156C4⋊Dic3—104no—
157C4×Dic3—104no—
158C4×Dic3—102no—
159#208—22no—
160#208—22no—
161C2×C3⋊C8—22no—
162C23×C5C2×#6711yescharacteristic
163C22×D5—22no—
164C22×D5—44no—
165C22×D5—41no—
166C22×D5—41no—
167C5×Q8—24no—
168C5×Q8—24no—
169C2×C4×C5—22no—
170C2×C4×C5—22no—
171C2×C4×C5#21714yes—
172C2×C4×C5D3×D412yes—
173C2×C4×C5#23712yes—
174C2×C4×C5C22×Dic311yescharacteristic
175C2×C4×C5C2×#6711yescharacteristic
176C2×Dic5—22no—
177C2×Dic5—42no—
178C2×Dic5—64no—
179D20—24no—
180D20—42no—
181C5×C8—122no—
182C22×Q8D3×D511yescharacteristic
183C22×D4—51no—
184C2×M16—32no—
185#124—54no—
186#124—102no—
187C4×Q8—304no—
188#117—152no—
189#117—302no—
190C2×C22⋊C4—102no—
191C2×C42—51no—
192#102—304no—
193#101—62no—
194C2×C3×C5—21no—
195C2×C3×C5—21no—
196C2×C3×C5#38611yescharacteristic
197C2×C3×C5#45412yes—
198C3×D5—82no—
199C23×C3—102no—
200C23×C3—204no—
201C23×C3—201no—
202C23×C3—201no—
203C23×C3C2×D2011yescharacteristic
204C3×Q8—24no—
205C3×Q8—24no—
206C3×D4—104no—
207C3×D4—202no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—102no—
211C2×C3×C4—202no—
212C2×C3×C4#68514yes—
213C2×C3×C4C2×C4×D511yescharacteristic
214C2×C3×C4D4×D512yes—
215C2×C3×C4#71112yes—
216C2×C3×C4C2×C22⋊D511yescharacteristic
217C2×Dic3—104no—
218C3⋊C8—42no—
219C22×C5—22no—
220C22×C5#93511yescharacteristic
221C22×C5#93711yescharacteristic
222C22×C5C2×#21711yescharacteristic
223C2×D5—44no—
224C2×D5—42no—
225C2×D5—82no—
226C2×D5—82no—
227C4×C5—24no—
228C4×C5D4×Dic312yes—
229C4×C5#93912yes—
230Dic5—42no—
231Dic5—124no—
232C24—101no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8D5×Dic312yes—
236C2×Q8#120112yes—
237C2×D4—52no—
238C2×D4—102no—
239C2×D4—101no—
240C2×D4—102no—
241C22×C4—101no—
242C22×C4#120212yes—
243C22×C4C2×D3×D511yescharacteristic
244M16—62no—
245M16—62no—
246C2×C8—62no—
247C4⋊C4—154no—
248C4⋊C4—304no—
249C22⋊C4—108no—
250C22⋊C4—302no—
251C42—52no—
252C42—101no—
253C42—304no—
254C42—302no—
255C3×C5#188811yescharacteristic, complemented, Hall
256C22×C3—22no—
257C22×C3—204no—
258C22×C3—202no—
259C22×C3—402no—
260C22×C3—402no—
261C22×C3#402811yescharacteristic
262C22×C3#403211yescharacteristic
263C22×C3C2×#68511yescharacteristic
264C3×C4—24no—
265C3×C4—202no—
266C3×C4#402712yes—
267C3×C4#408512yes—
268Dic3—204no—
269C2×C5—21no—
270C2×C5—21no—
271C2×C5#506212yes—
272C2×C5#522011yescharacteristic
273D5—82no—
274C23—102no—
275C23—204no—
276C23—201no—
277C23—201no—
278C23C2×#120211yescharacteristic
279Q8—24no—
280Q8—24no—
281D4—104no—
282D4—202no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—102no—
286C2×C4—202no—
287C2×C4—304no—
288C2×C4#666514yes—
289C2×C4C2×D5×Dic311yescharacteristic
290C2×C4#678012yes—
291C2×C4C2×#120111yescharacteristic
292C2×C4#679012yes—
293C8—122no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—402no—
297C2×C3#6504212yes—
298C2×C3#6524711yescharacteristic
299C5#7172411yescharacteristic, complemented, Sylow
300C22—22no—
301C22—204no—
302C22—202no—
303C22—402no—
304C22—402no—
305C22C2×#666511yescharacteristic
306C22#9153711yescharacteristic
307C22#9157211yescharacteristic
308C4—24no—
309C4—202no—
310C4—604no—
311C4#9155912yes—
312C4#9157112yes—
313C3#1060089711yescharacteristic, complemented, Sylow
314C2—21no—
315C2—21no—
316C2—402no—
317C2#1174938812yes—
318C2#1174950011yescharacteristic
subgroupG/H
centerC22#91572
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5#120
prime radicalC22×C3×D20C22
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
1. #11756571C2semidirect
3. C2×C5×#836C2semidirect
5. #11745978C2semidirect
14. C3×#4093C4semidirect
50. C2×#836D5semidirect
57. #4093Dic3semidirect
255. C3×C5#1888semidirect
299. C5#71724semidirect
313. C3#10600897semidirect

Maximal subgroups

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

subgroupindex
#117565712
C2×C3×#40932
C2×C5×#8362
#117483672
#117459782
#106008973
#717245