Finite Group Databasebeta

← #11752620

Subgroups — #11752620

Order 960.

468 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 132 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
1C42×D15C211yesmaximal, characteristic, complemented
2C5×#870C211yesmaximal, characteristic, complemented
3C3×#4021C211yesmaximal, characteristic, complemented
4#91465C211yesmaximal, characteristic
5#91434C211yesmaximal, characteristic, complemented
6#91396C212yesmaximal, complemented
7#91394C212yesmaximal, complemented
8#91390C211yesmaximal, characteristic, complemented
9#91366C212yesmaximal, complemented
10#91354C212yesmaximal, complemented
11#91331C211yesmaximal, characteristic, complemented
12#66025—31nomaximal, Hall
13C2×C4×D15C2211yescharacteristic
14C2×C4×D15C2211yescharacteristic
15C2×C4×D15C2211yescharacteristic
16C2×C3×D20C2211yescharacteristic
17C2×C3×Dic10C2211yescharacteristic
18C2×#1202C2212yes—
19C2×D5×Dic3C2212yes—
20C3×C42×C5C2211yescharacteristic
21C4×Dic15C2211yescharacteristic
22C4×Dic15C2211yescharacteristic
23C4×Dic15C2211yescharacteristic
24C5×C4⋊Dic3C2211yescharacteristic
25C5×C4⋊Dic3C2211yescharacteristic
26C5×Dic3⋊C4C2212yes—
27C5×Dic3⋊C4C2212yes—
28C3×#685C2212yes—
29C3×#685C2212yes—
30Dic3⋊Dic5C2212yes—
31#6668C2212yes—
32#6667C2212yes—
33#6665C2212yes—
34#6665C2212yes—
35Dic3×Dic5C2212yes—
36#5680—51nomaximal, Hall
37C5×#125—31no—
38#4044—32no—
39#4043—31no—
40#4041—31no—
41#4040—32no—
42#4039—31no—
43#4039—32no—
44#4038—32no—
45#4033—31no—
46#4021D311yescharacteristic, complemented
47C42×D5—31no—
48C22×D15C2311yescharacteristic
49C22×C3×D5C2312yes—
50C2×C3×C4×C5C2311yescharacteristic
51C2×C3×C4×C5C2311yescharacteristic
52C2×C3×C4×C5C2311yescharacteristic
53C2×Dic15C2311yescharacteristic
54C2×Dic15C2311yescharacteristic
55C2×Dic15C2311yescharacteristic
56C4×D15—22no—
57C4×D15—22no—
58C4×D15—22no—
59C2×C5×Dic3C2312yes—
60C2×C5×Dic3C2312yes—
61C2×C3×Dic5C2312yes—
62C3×D20—22no—
63C3×Dic10—22no—
64#1202—24no—
65D5×Dic3—24no—
66C3×#124—51no—
67#946—51no—
68Q8×Dic3—51no—
69#938—51no—
70D4×Dic3—51no—
71#883—52no—
72#67⋊C4—52no—
73#879—52no—
74#877—52no—
75C42×D3—51no—
76#870D511yescharacteristic, complemented
77C2×D20—32no—
78C2×D20C2×D311yescharacteristic
79C2×C4×D5—32no—
80C2×C4×D5—31no—
81C2×C4×D5—31no—
82C2×C4×D5—31no—
83C2×Dic10C2×D311yescharacteristic
84C5×C4⋊C4—32no—
85C5×C4⋊C4—32no—
86C5×C4⋊C4—31no—
87C5×C4⋊C4—31no—
88C42×C5C2×D311yescharacteristic
89#685—32no—
90#685—32no—
91#685—32no—
92#685C2×D312yes—
93#685C2×D312yes—
94C4⋊Dic5—32no—
95#683—32no—
96C4×Dic5—31no—
97C4×Dic5—31no—
98C4×Dic5—31no—
99C4×Dic5—32no—
100#529—151noSylow
101C22×C3×C5C2411yescharacteristic
102C2×D15—21no—
103C2×D15—21no—
104C2×D15#4112yes—
105C2×C3×D5—22no—
106C2×C3×D5—22no—
107C2×C3×D5—22no—
108C3×C4×C5—21no—
109C3×C4×C5—21no—
110C3×C4×C5#4112yes—
111Dic15—21no—
112Dic15—21no—
113Dic15#4112yes—
114C3×Dic5—22no—
115C5×Dic3—22no—
116C5×Dic3—22no—
117C2×C3×Q8—51no—
118C2×C3×D4—51no—
119C2×#67—52no—
120C22×Dic3—52no—
121C2×C4×D3—51no—
122C2×C4×D3—51no—
123C2×C4×D3—51no—
124C3×C22⋊C4—52no—
125C3×C22⋊C4—52no—
126C3×C42C2×D511yescharacteristic
127#217—52no—
128#217—52no—
129(C2×D3)⋊C4—52no—
130C4⋊Dic3—52no—
131C4⋊Dic3C2×D511yescharacteristic
132C4⋊Dic3C2×D511yescharacteristic
133Dic3⋊C4—52no—
134Dic3⋊C4C2×D512yes—
135Dic3⋊C4C2×D512yes—
136C4×Dic3—51no—
137C4×Dic3—51no—
138C4×Dic3—51no—
139C4×Dic3—52no—
140C22×D5—31no—
141C22×D5C22×D312yes—
142C2×C4×C5—32no—
143C2×C4×C5—32no—
144C2×C4×C5C22×D311yescharacteristic
145C2×C4×C5C22×D311yescharacteristic
146C2×C4×C5C22×D311yescharacteristic
147C2×Dic5—31no—
148C2×Dic5—31no—
149C2×Dic5—31no—
150C2×Dic5C22×D312yes—
151D20—22no—
152D20—64no—
153C4×D5—62no—
154C4×D5—64no—
155C4×D5—62no—
156C4×D5—62no—
157Dic10—22no—
158#126—152no—
159#125—31no—
160#124—51no—
161#123—152no—
162C22⋊Q8—151no—
163#121—151no—
164C4×Q8—151no—
165C4×D4—152no—
166C4×D4—151no—
167#117—152no—
168C2×C42—151no—
169C2×C3×C5C2×#4111yescharacteristic
170C2×C3×C5C2×#4111yescharacteristic
171C2×C3×C5C2×#4111yescharacteristic
172D15—22no—
173C3×D5—42no—
174C23×C3—52no—
175C22×D3—51no—
176C3×Q8—102no—
177C3×D4—102no—
178C2×C3×C4—52no—
179C2×C3×C4C22×D511yescharacteristic
180C2×C3×C4C22×D511yescharacteristic
181C2×C3×C4C22×D511yescharacteristic
182#67—104no—
183C2×Dic3—51no—
184C2×Dic3—51no—
185C2×Dic3—51no—
186C2×Dic3—104no—
187C2×Dic3C22×D512yes—
188C2×Dic3C22×D512yes—
189C4×D3—102no—
190C4×D3—102no—
191C4×D3—102no—
192C22×C5C23×D311yescharacteristic
193C2×D5—22no—
194C2×D5—22no—
195C2×D5—22no—
196C2×D5—32no—
197C2×D5—61no—
198C2×D5—61no—
199C4×C5—21no—
200C4×C5—21no—
201C4×C5—62no—
202C4×C5—62no—
203C4×C5#23712yes—
204Dic5—22no—
205Dic5—32no—
206Dic5—61no—
207Dic5—61no—
208C2×Q8—51no—
209C2×D4—51no—
210C2×D4—152no—
211C22×C4—152no—
212C22×C4—151no—
213C22×C4—151no—
214C22×C4—151no—
215C4⋊C4—32no—
216C4⋊C4—31no—
217C4⋊C4—32no—
218C4⋊C4—31no—
219C4⋊C4—152no—
220C4⋊C4—152no—
221C22⋊C4—52no—
222C22⋊C4—52no—
223C22⋊C4—152no—
224C22⋊C4—152no—
225C22⋊C4—152no—
226C42—152no—
227C42—151no—
228C42—151no—
229C42—151no—
230C42D3×D511yescharacteristic
231C3×C5#52911yescharacteristic, complemented, Hall
232C22×C3—102no—
233C22×C3—102no—
234C22×C3—102no—
235C22×C3C23×D511yescharacteristic
236C2×D3—52no—
237C2×D3—101no—
238C2×D3—101no—
239C3×C4—21no—
240C3×C4—21no—
241C3×C4—102no—
242C3×C4#71312yes—
243Dic3—22no—
244Dic3—22no—
245Dic3—52no—
246Dic3—101no—
247Dic3—101no—
248C2×C5C2×#23711yescharacteristic
249C2×C5D3×#4111yescharacteristic
250C2×C5D3×#4111yescharacteristic
251D5—42no—
252D5—62no—
253C23—52no—
254C23—151no—
255Q8—102no—
256D4—102no—
257D4—304no—
258C2×C4—32no—
259C2×C4—32no—
260C2×C4—52no—
261C2×C4—151no—
262C2×C4—151no—
263C2×C4—151no—
264C2×C4—302no—
265C2×C4—302no—
266C2×C4—304no—
267C2×C4—302no—
268C2×C4C2×D3×D511yescharacteristic
269C2×C4C2×D3×D511yescharacteristic
270C2×C4C2×D3×D511yescharacteristic
271C2×C3—202no—
272C2×C3C2×#71311yescharacteristic
273C2×C3D5×#4111yescharacteristic
274C2×C3D5×#4111yescharacteristic
275D3—102no—
276C5#568011yescharacteristic, complemented, Sylow
277C22—102no—
278C22—102no—
279C22—102no—
280C22—152no—
281C22—301no—
282C22—301no—
283C22C22×D3×D511yescharacteristic
284C4—21no—
285C4—21no—
286C4—62no—
287C4—62no—
288C4—102no—
289C4—152no—
290C4—301no—
291C4—301no—
292C4#676612yes—
293C3#6602511yescharacteristic, complemented, Sylow
294C2—202no—
295C2—302no—
296C2C2×#676611yescharacteristic
297C2#9201611yescharacteristic
298C2#9201611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
prime radical#91465C2
hypercenterC42D3×D5
hypocenterC3×C5#529
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C42×D15C2semidirect
2. C5×#870C2semidirect
3. C3×#4021C2semidirect
5. #91434C2semidirect
6. #91396C2semidirect
7. #91394C2semidirect
8. #91390C2semidirect
9. #91366C2semidirect
10. #91354C2semidirect
11. #91331C2semidirect
46. #4021D3semidirect
76. #870D5semidirect
231. C3×C5#529semidirect
276. C5#5680semidirect
293. C3#66025semidirect

Maximal subgroups

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

subgroupindex
C42×D152
C5×#8702
C3×#40212
#914652
#914342
#913962
#913942
#913902
#913662
#913542
#913312
#660253
#56805