Finite Group Databasebeta

← #11753625

Subgroups — #11753625

Order 960.

456 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 138 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#91782C211yesmaximal, characteristic
2C5×#890C211yesmaximal, characteristic, complemented
3C3×#4036C211yesmaximal, characteristic, complemented
4#91470C211yesmaximal, characteristic, complemented
5C4×#1204C211yesmaximal, characteristic, complemented
6#91437C212yesmaximal, complemented
7#91429C212yesmaximal, complemented
8#91428C211yesmaximal, characteristic
9#91419C212yesmaximal, complemented
10#91418C211yesmaximal, characteristic
11#91377C212yesmaximal, complemented
12#66024—31nomaximal, Hall
13C2×D60C2211yescharacteristic
14C2×C4×D15C2212yes—
15C2×#1204C2211yescharacteristic
16C2×#1204C2212yes—
17C2×#1200C2212yes—
18C2×#1200C2212yes—
19C3×C5×C4⋊C4C2211yescharacteristic
20#6714C2212yes—
21C4×Dic15C2211yescharacteristic
22C5×C4⋊Dic3C2211yescharacteristic
23C5×C4⋊Dic3C2212yes—
24C5×Dic3⋊C4C2212yes—
25C4×C5×Dic3C2211yescharacteristic
26C3×C4⋊Dic5C2211yescharacteristic
27C3×C4⋊Dic5C2212yes—
28C3×#683C2212yes—
29C3×C4×Dic5C2211yescharacteristic
30Dic3⋊Dic5C2211yescharacteristic
31#6669C2211yescharacteristic
32#6669C2212yes—
33#6668C2211yescharacteristic
34#6667C2212yes—
35#6667C2212yes—
36#5690—51nomaximal, Hall
37C5×#125—31no—
38#4043—32no—
39#4042—32no—
40#4042—32no—
41#4039—31no—
42#4039—31no—
43D5×C4⋊C4—32no—
44#4036D311yescharacteristic, complemented
45#4034—31no—
46C4×D20—31no—
47C4×Dic10—31no—
48C22×D15C2312yes—
49C2×C3×C4×C5C2312yes—
50C2×C3×C4×C5C2311yescharacteristic
51C2×Dic15C2311yescharacteristic
52C2×Dic15C2311yescharacteristic
53D60Q814yescomplemented
54C4×D15—24no—
55C2×C5×Dic3C2311yescharacteristic
56C2×C5×Dic3C2312yes—
57C2×C5×Dic3C2311yescharacteristic
58C2×C3×Dic5C2311yescharacteristic
59C2×C3×Dic5C2312yes—
60C2×C3×Dic5C2311yescharacteristic
61#1204—22no—
62#1204—42no—
63#1200—42no—
64#1200—42no—
65C3×#125—51no—
66#897—52no—
67#896—52no—
68#896—52no—
69#893—51no—
70#893—51no—
71D3×C4⋊C4—52no—
72#890D511yescharacteristic, complemented
73#888—51no—
74C4×D12—51no—
75C4×Dic6—51no—
76C2×D20—31no—
77C2×C4×D5—32no—
78C2×C4×D5—32no—
79C2×C4×D5—32no—
80C2×Dic10—31no—
81C2×Dic10—32no—
82C5×C4⋊C4—32no—
83C5×C4⋊C4—31no—
84C5×C4⋊C4—32no—
85C5×C4⋊C4C2×D311yescharacteristic
86C42×C5—31no—
87#685—32no—
88#685—32no—
89#685—32no—
90C4⋊Dic5—31no—
91C4⋊Dic5C2×D311yescharacteristic
92C4⋊Dic5C2×D312yes—
93#683—31no—
94#683—31no—
95#683—32no—
96#683C2×D312yes—
97C4×Dic5—31no—
98C4×Dic5C2×D311yescharacteristic
99#554—151noSylow
100C22×C3×C5C2411yescharacteristic
101C2×D15—22no—
102C2×D15—22no—
103C2×D15C2×Q814yes—
104C3×C4×C5—22no—
105C3×C4×C5C2×Q812yes—
106Dic15—21no—
107Dic15#4112yes—
108C3×Dic5—21no—
109C3×Dic5—21no—
110C3×Dic5—22no—
111C5×Dic3—21no—
112C5×Dic3—21no—
113C5×Dic3—22no—
114C2×D12—51no—
115C2×C4×D3—52no—
116C2×C4×D3—52no—
117C2×C4×D3—52no—
118C2×Dic6—51no—
119C2×Dic6—52no—
120C3×C4⋊C4—52no—
121C3×C4⋊C4—51no—
122C3×C4⋊C4—52no—
123C3×C4⋊C4C2×D511yescharacteristic
124C3×C42—51no—
125(C2×D3)⋊C4—52no—
126(C2×D3)⋊C4—52no—
127(C2×D3)⋊C4—52no—
128C4⋊Dic3—51no—
129C4⋊Dic3C2×D511yescharacteristic
130C4⋊Dic3C2×D512yes—
131Dic3⋊C4—51no—
132Dic3⋊C4—52no—
133Dic3⋊C4—51no—
134Dic3⋊C4C2×D512yes—
135C4×Dic3—51no—
136C4×Dic3C2×D511yescharacteristic
137C22×D5—32no—
138C2×C4×C5—31no—
139C2×C4×C5—32no—
140C2×C4×C5—31no—
141C2×C4×C5C22×D312yes—
142C2×C4×C5C22×D311yescharacteristic
143C2×Dic5—31no—
144C2×Dic5—31no—
145C2×Dic5C22×D311yescharacteristic
146C2×Dic5C22×D311yescharacteristic
147C2×Dic5C22×D312yes—
148D20—34no—
149C4×D5—64no—
150C4×D5—122no—
151C4×D5—122no—
152Dic10—62no—
153Dic10—122no—
154C4⋊Q8—151no—
155#125—31no—
156#125—51no—
157C22⋊Q8—152no—
158C22⋊Q8—152no—
159C22⋊Q8—152no—
160C4×Q8—151no—
161C4×D4—151no—
162C4×D4—151no—
163C4×D4—151no—
164C2×C4⋊C4—152no—
165C2×C3×C5C22×Q811yescharacteristic
166C2×C3×C5C2×#4111yescharacteristic
167C2×C3×C5H(5,𝔽2)11yescharacteristic
168D15—24no—
169C22×D3—52no—
170C2×C3×C4—51no—
171C2×C3×C4—52no—
172C2×C3×C4—51no—
173C2×C3×C4C22×D512yes—
174C2×C3×C4C22×D511yescharacteristic
175C2×Dic3—51no—
176C2×Dic3—51no—
177C2×Dic3C22×D511yescharacteristic
178C2×Dic3C22×D511yescharacteristic
179C2×Dic3C22×D512yes—
180D12—54no—
181C4×D3—104no—
182C4×D3—202no—
183C4×D3—202no—
184Dic6—102no—
185Dic6—202no—
186C22×C5C23×D311yescharacteristic
187C2×D5—34no—
188C2×D5—62no—
189C2×D5—62no—
190C4×C5—22no—
191C4×C5—61no—
192C4×C5—62no—
193C4×C5—61no—
194C4×C5D3×Q812yes—
195Dic5—21no—
196Dic5—22no—
197Dic5—21no—
198Dic5—32no—
199Dic5—61no—
200C2×Q8—151no—
201C2×Q8—152no—
202C2×D4—151no—
203C22×C4—152no—
204C22×C4—152no—
205C22×C4—152no—
206C4⋊C4—32no—
207C4⋊C4—31no—
208C4⋊C4—32no—
209C4⋊C4—52no—
210C4⋊C4—51no—
211C4⋊C4—52no—
212C4⋊C4—151no—
213C4⋊C4—152no—
214C4⋊C4—151no—
215C4⋊C4—151no—
216C4⋊C4D3×D511yescharacteristic
217C22⋊C4—152no—
218C22⋊C4—152no—
219C22⋊C4—152no—
220C42—31no—
221C42—51no—
222C42—151no—
223C3×C5#55411yescharacteristic, complemented, Hall
224C22×C3C23×D511yescharacteristic
225C2×D3—54no—
226C2×D3—102no—
227C2×D3—102no—
228C3×C4—22no—
229C3×C4—101no—
230C3×C4—102no—
231C3×C4—101no—
232C3×C4Q8×D512yes—
233Dic3—21no—
234Dic3—22no—
235Dic3—21no—
236Dic3—52no—
237Dic3—101no—
238C2×C5C2×D3×Q811yescharacteristic
239C2×C5D3×#4111yescharacteristic
240C2×C5#100911yescharacteristic
241D5—64no—
242C23—152no—
243Q8—302no—
244Q8—602no—
245D4—154no—
246C2×C4—31no—
247C2×C4—31no—
248C2×C4—32no—
249C2×C4—51no—
250C2×C4—51no—
251C2×C4—52no—
252C2×C4—151no—
253C2×C4—151no—
254C2×C4—304no—
255C2×C4—602no—
256C2×C4—602no—
257C2×C4C2×D3×D512yes—
258C2×C4C2×D3×D511yescharacteristic
259C2×C3C2×Q8×D511yescharacteristic
260C2×C3D5×#4111yescharacteristic
261C2×C3#414911yescharacteristic
262D3—104no—
263C5#569011yescharacteristic, complemented, Sylow
264C22—154no—
265C22—302no—
266C22—302no—
267C22C22×D3×D511yescharacteristic
268C4—22no—
269C4—61no—
270C4—61no—
271C4—62no—
272C4—101no—
273C4—101no—
274C4—102no—
275C4—152no—
276C4—301no—
277C4D15⋊Q812yes—
278C3#6602411yescharacteristic, complemented, Sylow
279C2—304no—
280C2C2×D15⋊Q811yescharacteristic
281C2#9202411yescharacteristic
282C2#9203511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC2×D60C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#554
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#890C2semidirect
3. C3×#4036C2semidirect
4. #91470C2semidirect
5. C4×#1204C2semidirect
6. #91437C2semidirect
7. #91429C2semidirect
9. #91419C2semidirect
11. #91377C2semidirect
44. #4036D3semidirect
53. D60Q8semidirect
72. #890D5semidirect
223. C3×C5#554semidirect
263. C5#5690semidirect
278. C3#66024semidirect

Maximal subgroups

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

subgroupindex
#917822
C5×#8902
C3×#40362
#914702
C4×#12042
#914372
#914292
#914282
#914192
#914182
#913772
#660243
#56905