Finite Group Databasebeta

← #11751323

Subgroups — #11751323

Order 960.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C22×C3×C5×D4C211yesmaximal, characteristic
2C2×#6719C212yesmaximal, complemented
3C2×#6719C212yesmaximal, complemented
4C2×#6712C211yesmaximal, characteristic, complemented
5#91115C211yesmaximal, characteristic, complemented
6#65511—31nomaximal, Hall
7C24×C3×C5C2212yes—
8C2×C3×C5×D4—24no—
9C2×C3×C5×D4—22no—
10C22×C3×C4×C5C2211yescharacteristic
11C22×Dic15C2211yescharacteristic
12C22×Dic15C2212yes—
13C22×Dic15C2211yescharacteristic
14#6719—24no—
15#6719—24no—
16#6712—22no—
17#5222—51nomaximal, Hall
18C22×C5×D4D311yescharacteristic
19C2×C22⋊Dic5—32no—
20C2×C22⋊Dic5—32no—
21C2×#683—31no—
22#3963—31no—
23C23×C3×C5—22no—
24C23×C3×C5—22no—
25C23×C3×C5—22no—
26C23×C3×C5—22no—
27C23×C3×C5—22no—
28C23×C3×C5—22no—
29C23×C3×C5D414yes—
30C23×C3×C5C2311yescharacteristic
31C3×C5×D4—28no—
32C2×C3×C4×C5—22no—
33C2×C3×C4×C5D412yes—
34C2×Dic15—21no—
35C2×Dic15—21no—
36C2×Dic15—21no—
37C2×Dic15—22no—
38C2×Dic15—22no—
39C2×Dic15—22no—
40C2×Dic15—22no—
41C2×Dic15D412yescomplemented
42C22×C3×D4D511yescharacteristic
43C2×#217—52no—
44C2×#217—52no—
45C2×Dic3⋊C4—51no—
46C3⋊#95—51no—
47C24×C5C2×D312yes—
48C2×C5×D4—24no—
49C2×C5×D4—22no—
50C22×C4×C5C2×D311yescharacteristic
51C22×Dic5—31no—
52C22×Dic5—32no—
53C22×Dic5—31no—
54C22⋊Dic5—64no—
55C22⋊Dic5—64no—
56#683—62no—
57#394—151noSylow
58C22×C3×C5—24no—
59C22×C3×C5—24no—
60C22×C3×C5—24no—
61C22×C3×C5—42no—
62C22×C3×C5—42no—
63C22×C3×C5—42no—
64C22×C3×C5—42no—
65C22×C3×C5C2×D411yescharacteristic
66C22×C3×C5C2×D412yes—
67C22×C3×C5C2×D411yescharacteristic
68C22×C3×C5#4111yescharacteristic
69C22×C3×C5#4112yes—
70C3×C4×C5—22no—
71Dic15—22no—
72Dic15—41no—
73Dic15—42no—
74C24×C3C2×D512yes—
75C2×C3×D4—24no—
76C2×C3×D4—22no—
77C22×C3×C4C2×D511yescharacteristic
78C22×Dic3—51no—
79C22×Dic3—52no—
80C22×Dic3—51no—
81#217—104no—
82#217—104no—
83Dic3⋊C4—102no—
84C23×C5—22no—
85C23×C5—22no—
86C23×C5—22no—
87C23×C5—22no—
88C23×C5—22no—
89C23×C5—22no—
90C23×C5#6714yes—
91C23×C5C22×D311yescharacteristic
92C5×D4—28no—
93C2×C4×C5—22no—
94C2×C4×C5#6712yes—
95C2×Dic5—32no—
96C2×Dic5—61no—
97C2×Dic5—61no—
98C2×Dic5—62no—
99C2×Dic5—62no—
100C2×Dic5—61no—
101C2×Dic5—62no—
102C2×Dic5—62no—
103C22×D4D1511yescharacteristic
104C2×C4⋊C4—151no—
105C2×C22⋊C4—152no—
106C2×C22⋊C4—152no—
107#95—151no—
108C2×C3×C5—44no—
109C2×C3×C5#12011yescharacteristic
110C2×C3×C5#12111yescharacteristic
111C2×C3×C5#12112yes—
112C2×C3×C5#12312yes—
113C2×C3×C5#12411yescharacteristic
114C23×C3—22no—
115C23×C3—22no—
116C23×C3—22no—
117C23×C3—22no—
118C23×C3—22no—
119C23×C3—22no—
120C23×C3C22⋊D514yes—
121C23×C3C22×D511yescharacteristic
122C3×D4—28no—
123C2×C3×C4—22no—
124C2×C3×C4C22⋊D512yes—
125C2×Dic3—52no—
126C2×Dic3—101no—
127C2×Dic3—101no—
128C2×Dic3—102no—
129C2×Dic3—102no—
130C2×Dic3—101no—
131C2×Dic3—102no—
132C2×Dic3—102no—
133C22×C5—24no—
134C22×C5—24no—
135C22×C5—24no—
136C22×C5—42no—
137C22×C5—42no—
138C22×C5—42no—
139C22×C5—42no—
140C22×C5D3×D411yescharacteristic
141C22×C5#23711yescharacteristic
142C22×C5#23712yes—
143C22×C5C2×#6712yes—
144C22×C5C2×#6711yescharacteristic
145C4×C5—22no—
146Dic5—62no—
147Dic5—122no—
148Dic5—121no—
149C24C2×D1512yes—
150C2×D4—24no—
151C2×D4—22no—
152C22×C4—151no—
153C22×C4—152no—
154C22×C4—151no—
155C22×C4C2×D1511yescharacteristic
156C4⋊C4—302no—
157C22⋊C4—304no—
158C22⋊C4—304no—
159C3×C5#39411yescharacteristic, complemented, Hall
160C22×C3—24no—
161C22×C3—24no—
162C22×C3—24no—
163C22×C3—42no—
164C22×C3—42no—
165C22×C3—42no—
166C22×C3—42no—
167C22×C3D4×D511yescharacteristic
168C22×C3#71111yescharacteristic
169C22×C3#71112yes—
170C22×C3C2×C22⋊D512yes—
171C22×C3C2×C22⋊D511yescharacteristic
172C3×C4—22no—
173Dic3—102no—
174Dic3—201no—
175Dic3—202no—
176C2×C5—44no—
177C2×C5#93512yes—
178C2×C5#93611yescharacteristic
179C2×C5#93811yescharacteristic
180C2×C5#93912yes—
181C2×C5#95311yescharacteristic
182C23—22no—
183C23—22no—
184C23—22no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23#122014yes—
189C23C22×D1511yescharacteristic
190D4—28no—
191C2×C4—22no—
192C2×C4—152no—
193C2×C4—301no—
194C2×C4—301no—
195C2×C4—302no—
196C2×C4—302no—
197C2×C4—302no—
198C2×C4—302no—
199C2×C4—301no—
200C2×C4#122012yes—
201C2×C3—44no—
202C2×C3#408112yes—
203C2×C3#408211yescharacteristic
204C2×C3#408411yescharacteristic
205C2×C3#408512yes—
206C2×C3#409911yescharacteristic
207C5#522211yescharacteristic, complemented, Sylow
208C22—24no—
209C22—24no—
210C22—24no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22D4×D1511yescharacteristic
216C22#681911yescharacteristic
217C22#681912yes—
218C22C2×#122012yes—
219C22C2×#122011yescharacteristic
220C4—22no—
221C4—302no—
222C4—602no—
223C4—601no—
224C3#6551111yescharacteristic, complemented, Sylow
225C2—44no—
226C2#9182412yes—
227C2#9182511yescharacteristic
228C2#9182711yescharacteristic
229C2#9182812yes—
230C2#9184211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D15
commutator, socle, cosocleC23×C3×C5C23
Fitting, prime radicalC22×C3×C5×D4C2
hypercenterC22×D4D15
hypocenterC3×C5#394
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#6719C2semidirect
3. C2×#6719C2semidirect
4. C2×#6712C2semidirect
5. #91115C2semidirect
41. C2×Dic15D4semidirect
159. C3×C5#394semidirect
207. C5#5222semidirect
224. C3#65511semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×D42
C2×#67192
C2×#67122
#911152
#655113
#52225