Finite Group Databasebeta

← #11754863

Subgroups — #11754863

Order 960.

472 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 128 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#91824C211yesmaximal, characteristic, complemented
2C5×#935C211yesmaximal, characteristic, complemented
3C3×#4086C211yesmaximal, characteristic
4#91559C212yesmaximal, complemented
5Dic3×C22⋊D5C212yesmaximal, complemented
6#91534C212yesmaximal, complemented
7#91534C212yesmaximal, complemented
8#91407C212yesmaximal, complemented
9#91323C212yesmaximal, complemented
10#65998—31nomaximal, Hall
11C2×C3×C5×D4C2211yescharacteristic
12C22×Dic15C2211yescharacteristic
13C22×C5×Dic3C2211yescharacteristic
14C2×C3×C22⋊D5C2212yes—
15C2×C3×C22⋊D5C2212yes—
16C2×C3×D20C2211yescharacteristic
17C2×#1204C2212yes—
18C2×D5×Dic3C2212yes—
19#6719C2211yescharacteristic
20#6719C2212yes—
21#6712C2212yes—
22C5×#217C2211yescharacteristic
23C5×#217C2212yes—
24C5×Dic3⋊C4C2212yes—
25C3×C4×Dic5C2211yescharacteristic
26#6668C2212yes—
27#6665C2212yes—
28#6665C2212yes—
29#6665C2212yes—
30Dic3×Dic5C2212yes—
31Dic3×Dic5C2212yes—
32#5713—51nomaximal, Hall
33C5×#123—31no—
34#4086D311yescharacteristic
35#4081—31no—
36C4×C22⋊D5—32no—
37#4040—32no—
38#4033—32no—
39#4031—32no—
40#4031—32no—
41#4027—32no—
42C23×C3×C5C2311yescharacteristic
43C23×C3×C5C2311yescharacteristic
44C22×C3×D5C2312yes—
45C3×C5×D4—41no—
46C2×C3×C4×C5C2311yescharacteristic
47C2×Dic15—41no—
48C2×Dic15C2312yes—
49C2×Dic15C2312yes—
50C2×C5×Dic3—41no—
51C2×C5×Dic3C2312yes—
52C2×C5×Dic3C2312yes—
53C3×C22⋊D5—24no—
54C3×C22⋊D5—24no—
55C2×C3×Dic5C2312yes—
56C3×D20—41no—
57#1204—24no—
58D5×Dic3—42no—
59C3×#127—51no—
60#936—52no—
61#936—52no—
62#935—51no—
63#935—52no—
64#935D511yescharacteristic, complemented
65D4×Dic3—52no—
66D4×Dic3—52no—
67C4×Dic6—52no—
68C2×C5×D4C2×D311yescharacteristic
69C22×C4×C5—31no—
70C2×C22⋊D5C2×D312yes—
71C2×C22⋊D5C2×D312yes—
72C22×Dic5—31no—
73C2×D20C2×D311yescharacteristic
74C2×C4×D5—32no—
75C2×Dic10—32no—
76C5×C4⋊C4—32no—
77C5×C22⋊C4—32no—
78C5×C22⋊C4—31no—
79C22⋊Dic5—31no—
80C22⋊Dic5—32no—
81#685—32no—
82#685—32no—
83#685—32no—
84#683—32no—
85#683—32no—
86C4×Dic5—32no—
87C4×Dic5—32no—
88C4×Dic5C2×D311yescharacteristic
89#559—151noSylow
90C22×C3×C5—22no—
91C22×C3×C5—22no—
92C22×C3×C5—21no—
93C22×C3×C5—21no—
94C22×C3×C5C2411yescharacteristic
95C2×C3×D5—22no—
96C2×C3×D5—22no—
97C2×C3×D5—22no—
98C3×C4×C5—21no—
99Dic15—22no—
100Dic15—22no—
101C3×Dic5#4114yes—
102C5×Dic3—22no—
103C5×Dic3—22no—
104C2×C3×D4—52no—
105C2×C3×D4—52no—
106C2×C3×D4—51no—
107C2×C3×D4C2×D511yescharacteristic
108C22×Dic3—51no—
109C22×Dic3—52no—
110C22×Dic3C2×D511yescharacteristic
111C2×Dic6—52no—
112C3×C42—51no—
113#217—52no—
114#217—51no—
115#217—52no—
116#217—52no—
117#217—52no—
118#217C2×D512yes—
119#217C2×D511yescharacteristic
120C4⋊Dic3—52no—
121Dic3⋊C4—52no—
122Dic3⋊C4C2×D512yes—
123C4×Dic3—52no—
124C4×Dic3—52no—
125C23×C5C22×D311yescharacteristic
126C23×C5C22×D311yescharacteristic
127C22×D5C22×D312yes—
128C5×D4—41no—
129C2×C4×C5—32no—
130C2×C4×C5—32no—
131C2×C4×C5—121no—
132C2×C4×C5C22×D311yescharacteristic
133C22⋊D5—24no—
134C22⋊D5—24no—
135C2×Dic5—32no—
136C2×Dic5—32no—
137C2×Dic5—121no—
138C2×Dic5C22×D312yes—
139D20—41no—
140C4×D5—122no—
141Dic10—64no—
142#127—51no—
143#124—152no—
144#124—152no—
145#123—31no—
146#123—152no—
147#123—151no—
148C4×Q8—152no—
149C4×D4—152no—
150C4×D4—152no—
151C2×C3×C5—41no—
152C2×C3×C5—41no—
153C2×C3×C5C2×#4112yes—
154C2×C3×C5H(5,𝔽2)11yescharacteristic
155C3×D5—42no—
156C23×C3—52no—
157C23×C3C22×D511yescharacteristic
158C23×C3C22×D511yescharacteristic
159C3×D4—41no—
160C3×D4—104no—
161C3×D4—104no—
162C3×D4—201no—
163C2×C3×C4—52no—
164C2×C3×C4C22×D511yescharacteristic
165C2×Dic3—41no—
166C2×Dic3—52no—
167C2×Dic3—52no—
168C2×Dic3—202no—
169C2×Dic3—201no—
170C2×Dic3C22×D512yes—
171C2×Dic3C22×D512yes—
172Dic6—104no—
173C22×C5—22no—
174C22×C5—22no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5C23×D311yescharacteristic
178C2×D5—22no—
179C2×D5—22no—
180C2×D5—22no—
181C4×C5—21no—
182C4×C5—62no—
183C4×C5—62no—
184Dic5—62no—
185Dic5—62no—
186Dic5#23714yes—
187C2×Q8—152no—
188C2×D4—52no—
189C2×D4—52no—
190C2×D4—51no—
191C2×D4D3×D511yescharacteristic
192C22×C4—31no—
193C22×C4—152no—
194C22×C4—151no—
195C4⋊C4—32no—
196C4⋊C4—152no—
197C4⋊C4—152no—
198C22⋊C4—32no—
199C22⋊C4—31no—
200C22⋊C4—152no—
201C22⋊C4—152no—
202C22⋊C4—152no—
203C22⋊C4—152no—
204C22⋊C4—151no—
205C42—51no—
206C42—152no—
207C42—152no—
208C3×C5#55911yescharacteristic, complemented, Hall
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—22no—
212C22×C3—22no—
213C22×C3—102no—
214C22×C3—102no—
215C22×C3—102no—
216C22×C3C23×D511yescharacteristic
217C3×C4—21no—
218C3×C4—54no—
219Dic3—22no—
220Dic3—22no—
221Dic3—102no—
222Dic3—102no—
223C2×C5—41no—
224C2×C5—41no—
225C2×C5C2×#23712yes—
226C2×C5#100411yescharacteristic
227D5—42no—
228C23—52no—
229C23C2×D3×D511yescharacteristic
230C23C2×D3×D511yescharacteristic
231Q8—304no—
232D4—41no—
233D4—104no—
234D4—104no—
235D4—201no—
236C2×C4—32no—
237C2×C4—32no—
238C2×C4—52no—
239C2×C4—121no—
240C2×C4—152no—
241C2×C4—152no—
242C2×C4—602no—
243C2×C4—601no—
244C2×C4C2×D3×D511yescharacteristic
245C2×C3—41no—
246C2×C3—41no—
247C2×C3—202no—
248C2×C3#414411yescharacteristic
249C2×C3D5×#4112yes—
250C5#571311yescharacteristic, complemented, Sylow
251C22—22no—
252C22—22no—
253C22—21no—
254C22—21no—
255C22—102no—
256C22—102no—
257C22—102no—
258C22C22×D3×D511yescharacteristic
259C4—21no—
260C4—54no—
261C4—62no—
262C4—62no—
263C4—302no—
264C4—302no—
265C3#6599811yescharacteristic, complemented, Sylow
266C2—41no—
267C2—41no—
268C2—202no—
269C2D5×#23712yes—
270C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
prime radicalC3×#4086C2
hypercenterC2×D4D3×D5
hypocenterC3×C5#559
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #91824C2semidirect
2. C5×#935C2semidirect
4. #91559C2semidirect
5. Dic3×C22⋊D5C2semidirect
6. #91534C2semidirect
7. #91534C2semidirect
8. #91407C2semidirect
9. #91323C2semidirect
64. #935D5semidirect
208. C3×C5#559semidirect
250. C5#5713semidirect
265. C3#65998semidirect

Maximal subgroups

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

subgroupindex
#918242
C5×#9352
C3×#40862
#915592
Dic3×C22⋊D52
#915342
#914072
#913232
#659983
#57135