Finite Group Databasebeta

← #11753499

Subgroups — #11753499

Order 960.

468 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 134 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#91776C211yesmaximal, characteristic, complemented
2C5×#890C211yesmaximal, characteristic, complemented
3C3×#4041C211yesmaximal, characteristic
4#91434C212yesmaximal, complemented
5#91434C211yesmaximal, characteristic, complemented
6#91407C212yesmaximal, complemented
7#91394C212yesmaximal, complemented
8C4×D5×Dic3C211yesmaximal, characteristic, complemented
9#91364C211yesmaximal, characteristic, complemented
10#91361C212yesmaximal, complemented
11#91360C211yesmaximal, characteristic, complemented
12#66025—31nomaximal, Hall
13C2×Dic30C2211yescharacteristic
14C2×C3×D20C2212yes—
15C2×C3×D20C2211yescharacteristic
16C2×C3×C4×D5C2211yescharacteristic
17C2×D5×Dic3C2212yes—
18C2×D5×Dic3C2211yescharacteristic
19C2×D5×Dic3C2211yescharacteristic
20C3×C5×C4⋊C4C2211yescharacteristic
21#6712C2212yes—
22C4×Dic15C2212yes—
23C4×Dic15C2211yescharacteristic
24C5×C4⋊Dic3C2211yescharacteristic
25C5×C4⋊Dic3C2212yes—
26C5×Dic3⋊C4C2212yes—
27C4×C5×Dic3C2211yescharacteristic
28C3×#685C2212yes—
29Dic3⋊Dic5C2212yes—
30#6665C2212yes—
31#6665C2212yes—
32#6665C2212yes—
33#6665C2212yes—
34Dic3×Dic5C2211yescharacteristic
35Dic3×Dic5C2211yescharacteristic
36#5600—51nomaximal, Hall
37C5×#125—31no—
38#4044—32no—
39#4043—31no—
40#4041D311yescharacteristic
41#4040—32no—
42#4039—31no—
43#4039—32no—
44#4038—32no—
45#4033—31no—
46#4021—31no—
47C42×D5—31no—
48C22×C3×D5C2312yes—
49C22×C3×D5C2311yescharacteristic
50C2×C3×C4×C5C2312yes—
51C2×C3×C4×C5C2311yescharacteristic
52C2×Dic15C2311yescharacteristic
53C2×Dic15C2312yes—
54C2×Dic15C2311yescharacteristic
55Dic30—22no—
56C2×C5×Dic3C2311yescharacteristic
57C2×C5×Dic3C2311yescharacteristic
58C2×C5×Dic3C2312yes—
59C2×C3×Dic5C2311yescharacteristic
60C3×D20—24no—
61C3×D20—22no—
62C3×C4×D5—22no—
63D5×Dic3—22no—
64D5×Dic3—22no—
65D5×Dic3—24no—
66C3×#121—51no—
67#936—51no—
68#935—52no—
69D4×Dic3—52no—
70D4×Dic3—51no—
71#924—51no—
72C2×C4×Dic3—51no—
73#890D511yescharacteristic, complemented
74#887—51no—
75#879—52no—
76#877—52no—
77C2×D20C2×D311yescharacteristic
78C2×D20C2×D312yes—
79C2×C4×D5—31no—
80C2×C4×D5—31no—
81C2×C4×D5—32no—
82C2×C4×D5C2×D311yescharacteristic
83C2×Dic10—31no—
84C5×C4⋊C4—32no—
85C5×C4⋊C4—31no—
86C5×C4⋊C4—32no—
87C5×C4⋊C4C2×D311yescharacteristic
88C42×C5—31no—
89#685—32no—
90#685—32no—
91#685—32no—
92#685—32no—
93#685C2×D312yes—
94C4⋊Dic5—32no—
95#683—32no—
96C4×Dic5—31no—
97C4×Dic5—32no—
98C4×Dic5—31no—
99C4×Dic5—31no—
100#529—151noSylow
101C22×C3×C5C2411yescharacteristic
102C2×C3×D5—21no—
103C2×C3×D5—21no—
104C2×C3×D5—22no—
105C2×C3×D5—22no—
106C2×C3×D5—22no—
107C2×C3×D5#4112yes—
108C3×C4×C5—22no—
109C3×C4×C5#4112yes—
110Dic15—21no—
111Dic15—22no—
112Dic15#4112yes—
113C3×Dic5—21no—
114C5×Dic3—21no—
115C5×Dic3—21no—
116C5×Dic3—22no—
117C2×C3×D4—52no—
118C2×C3×D4—51no—
119C22×C3×C4—51no—
120C22×Dic3—52no—
121C22×Dic3—51no—
122C22×Dic3—51no—
123C2×Dic6—51no—
124C3×C4⋊C4C2×D511yescharacteristic
125C3×C22⋊C4—52no—
126#217—52no—
127#217—52no—
128#217—52no—
129#217—52no—
130C4⋊Dic3C2×D512yes—
131C4⋊Dic3C2×D511yescharacteristic
132Dic3⋊C4—52no—
133Dic3⋊C4—52no—
134Dic3⋊C4C2×D512yes—
135C4×Dic3—52no—
136C4×Dic3—51no—
137C4×Dic3—51no—
138C4×Dic3—51no—
139C4×Dic3C2×D511yescharacteristic
140C22×D5C22×D312yes—
141C22×D5C22×D311yescharacteristic
142C2×C4×C5—31no—
143C2×C4×C5—31no—
144C2×C4×C5—32no—
145C2×C4×C5C22×D312yes—
146C2×C4×C5C22×D311yescharacteristic
147C2×Dic5—31no—
148C2×Dic5—31no—
149C2×Dic5—32no—
150C2×Dic5C22×D311yescharacteristic
151D20—24no—
152D20—22no—
153C4×D5—22no—
154C4×D5—62no—
155C4×D5—64no—
156C4×D5—62no—
157Dic10—62no—
158#126—152no—
159#125—31no—
160#124—151no—
161#123—152no—
162C22⋊Q8—151no—
163#121—51no—
164C4×Q8—151no—
165C4×D4—151no—
166C4×D4—152no—
167#117—152no—
168C2×C42—151no—
169C2×C3×C5C2×#4111yescharacteristic
170C2×C3×C5C2×#4111yescharacteristic
171C2×C3×C5C2×#4111yescharacteristic
172C3×D5—22no—
173C3×D5—42no—
174C23×C3—51no—
175C23×C3—52no—
176C3×D4—104no—
177C3×D4—102no—
178C2×C3×C4—51no—
179C2×C3×C4—102no—
180C2×C3×C4C22×D512yes—
181C2×C3×C4C22×D511yescharacteristic
182C2×Dic3—51no—
183C2×Dic3—51no—
184C2×Dic3—52no—
185C2×Dic3—102no—
186C2×Dic3—104no—
187C2×Dic3—102no—
188C2×Dic3C22×D511yescharacteristic
189C2×Dic3C22×D511yescharacteristic
190C2×Dic3C22×D512yes—
191Dic6—102no—
192C22×C5C23×D311yescharacteristic
193C2×D5—21no—
194C2×D5—21no—
195C2×D5—22no—
196C2×D5—22no—
197C2×D5—22no—
198C2×D5#23712yes—
199C4×C5—22no—
200C4×C5—61no—
201C4×C5—61no—
202C4×C5—62no—
203C4×C5#23712yes—
204Dic5—21no—
205Dic5—32no—
206Dic5—62no—
207Dic5—61no—
208C2×Q8—151no—
209C2×D4—52no—
210C2×D4—51no—
211C22×C4—51no—
212C22×C4—151no—
213C22×C4—151no—
214C22×C4—152no—
215C4⋊C4—32no—
216C4⋊C4—31no—
217C4⋊C4—32no—
218C4⋊C4—152no—
219C4⋊C4—152no—
220C4⋊C4D3×D511yescharacteristic
221C22⋊C4—52no—
222C22⋊C4—152no—
223C22⋊C4—152no—
224C22⋊C4—152no—
225C22⋊C4—152no—
226C42—31no—
227C42—151no—
228C42—151no—
229C42—151no—
230C42—152no—
231C3×C5#52911yescharacteristic, complemented, Hall
232C22×C3—52no—
233C22×C3—101no—
234C22×C3—101no—
235C22×C3—102no—
236C22×C3—102no—
237C22×C3—102no—
238C22×C3C23×D511yescharacteristic
239C3×C4—22no—
240C3×C4—101no—
241C3×C4#71312yes—
242Dic3—21no—
243Dic3—21no—
244Dic3—22no—
245Dic3—52no—
246Dic3—102no—
247Dic3—101no—
248C2×C5C2×#23711yescharacteristic
249C2×C5C2×#23711yescharacteristic
250C2×C5D3×#4111yescharacteristic
251D5—22no—
252D5—42no—
253C23—51no—
254C23—52no—
255Q8—302no—
256D4—104no—
257D4—102no—
258C2×C4—31no—
259C2×C4—31no—
260C2×C4—32no—
261C2×C4—51no—
262C2×C4—102no—
263C2×C4—151no—
264C2×C4—151no—
265C2×C4—152no—
266C2×C4—302no—
267C2×C4—304no—
268C2×C4—302no—
269C2×C4C2×D3×D512yes—
270C2×C4C2×D3×D511yescharacteristic
271C2×C3—102no—
272C2×C3—202no—
273C2×C3C2×#71311yescharacteristic
274C2×C3D5×#4111yescharacteristic
275C2×C3D5×#4111yescharacteristic
276C5#560011yescharacteristic, complemented, Sylow
277C22—52no—
278C22—101no—
279C22—101no—
280C22—102no—
281C22—102no—
282C22—102no—
283C22C22×D3×D511yescharacteristic
284C4—22no—
285C4—61no—
286C4—61no—
287C4—62no—
288C4—101no—
289C4—152no—
290C4—302no—
291C4—301no—
292C4#676612yes—
293C3#6602511yescharacteristic, complemented, Sylow
294C2—102no—
295C2—202no—
296C2C2×#676611yescharacteristic
297C2D5×#23711yescharacteristic
298C2#9203411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC3×#4041C2
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#529
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #91776C2semidirect
2. C5×#890C2semidirect
4. #91434C2semidirect
5. #91434C2semidirect
6. #91407C2semidirect
7. #91394C2semidirect
8. C4×D5×Dic3C2semidirect
9. #91364C2semidirect
10. #91361C2semidirect
11. #91360C2semidirect
73. #890D5semidirect
231. C3×C5#529semidirect
276. C5#5600semidirect
293. C3#66025semidirect

Maximal subgroups

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

subgroupindex
#917762
C5×#8902
C3×#40412
#914342
#914072
#913942
C4×D5×Dic32
#913642
#913612
#913602
#660253
#56005