Finite Group Databasebeta

← #11754877

Subgroups — #11754877

Order 960.

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

normal subgroups only

This group has 496 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#91825C211yesmaximal, characteristic, complemented
2C5×#937C211yesmaximal, characteristic
3C3×#4081C211yesmaximal, characteristic, complemented
4#91555C212yesmaximal, complemented
5D3×C22⋊Dic5C212yesmaximal, complemented
6Dic5×#67C212yesmaximal, complemented
7#91530C212yesmaximal, complemented
8#91432C212yesmaximal, complemented
9#91400C212yesmaximal, complemented
10#65921—31nomaximal, Hall
11C23×C5×D3C2211yescharacteristic
12C2×C3×C5×D4C2211yescharacteristic
13C2×Dic30C2211yescharacteristic, complemented
14C2×C5×#67C2212yes—
15C22×C3×Dic5C2211yescharacteristic, complemented
16C2×D3×Dic5C2212yes—
17C2×D3×Dic5C2212yes—
18#6719C2212yes—
19#6719C2212yescomplemented
20C4×Dic15C2211yescharacteristic, complemented
21C5×#217C2211yescharacteristic
22C5×(C2×D3)⋊C4C2212yes—
23C3×C22⋊Dic5C2212yes—
24C3×C22⋊Dic5C2211yescharacteristic, complemented
25C3×#683C2212yescomplemented
26Dic3⋊Dic5C2212yescomplemented
27#6669C2212yescomplemented
28#6668C2212yescomplemented
29(C2×D3)⋊Dic5C2212yes—
30(C2×D3)⋊Dic5C2212yes—
31Dic3×Dic5C2212yescomplemented
32#5659—51nomaximal, Hall
33C5×#120—31no—
34C2×C22⋊Dic5—32no—
35#4082—31no—
36#4081—32no—
37#4081D311yescharacteristic, complemented
38D4×Dic5—32no—
39#4025—32no—
40#4024—32no—
41#4023—32no—
42C23×C3×C5C2311yescharacteristic
43C23×C3×C5C2311yescharacteristic
44C22×C5×D3—24no—
45C22×C5×D3—41no—
46C22×C5×D3C2312yes—
47C3×C5×D4—41no—
48C2×C3×C4×C5C2311yescharacteristic
49C2×Dic15C2312yes—
50C2×Dic15C2312yes—
51Dic30—41no—
52C5×#67—24no—
53C2×C5×Dic3C2312yes—
54C2×C3×Dic5—41no—
55C2×C3×Dic5C2312yes—
56C2×C3×Dic5C2312yes—
57D3×Dic5—24no—
58D3×Dic5—42no—
59C3×#123—51no—
60#937D511yescharacteristic
61#936—51no—
62C4×#67—52no—
63#896—52no—
64#892—52no—
65#883—52no—
66D3×C22⋊C4—52no—
67#879—52no—
68C24×C5—31no—
69C2×C5×D4—32no—
70C2×C5×D4C2×D311yescharacteristic
71C22×Dic5—32no—
72C22×Dic5—32no—
73C22×Dic5C2×D311yescharacteristic, complemented
74C2×Dic10—31no—
75C5×C22⋊C4—31no—
76C5×C22⋊C4—32no—
77C22⋊Dic5—32no—
78C22⋊Dic5—32no—
79C22⋊Dic5—32no—
80C22⋊Dic5—32no—
81C22⋊Dic5C2×D312yes—
82C22⋊Dic5C2×D311yescharacteristic, complemented
83C4⋊Dic5—32no—
84#683—32no—
85#683—32no—
86#683C2×D312yescomplemented
87C4×Dic5—31no—
88C4×Dic5—32no—
89#551—151noSylow
90C22×C3×C5—22no—
91C22×C3×C5—22no—
92C22×C3×C5—21no—
93C22×C3×C5—21no—
94C22×C3×C5C2411yescharacteristic
95C2×C5×D3—22no—
96C2×C5×D3—22no—
97C2×C5×D3—44no—
98C2×C5×D3#4114yes—
99C3×C4×C5—21no—
100Dic15—22no—
101Dic15—22no—
102C3×Dic5—22no—
103C3×Dic5—22no—
104C5×Dic3—22no—
105C23×D3C2×D511yescharacteristic
106C2×C3×D4C2×D511yescharacteristic
107C22×C3×C4—51no—
108C2×#67C2×D512yes—
109C2×C4×D3—52no—
110C2×C4×D3—52no—
111C2×Dic6—51no—
112C3×C4⋊C4—52no—
113C3×C22⋊C4—52no—
114C3×C22⋊C4—51no—
115#217—52no—
116#217—52no—
117#217C2×D511yescharacteristic
118(C2×D3)⋊C4—52no—
119(C2×D3)⋊C4—52no—
120(C2×D3)⋊C4C2×D512yes—
121C4⋊Dic3—52no—
122Dic3⋊C4—52no—
123Dic3⋊C4—52no—
124C4×Dic3—51no—
125C4×Dic3—52no—
126C23×C5—32no—
127C23×C5—64no—
128C23×C5—121no—
129C23×C5C22×D311yescharacteristic
130C23×C5C22×D311yescharacteristic
131C5×D4—41no—
132C5×D4—64no—
133C2×C4×C5—32no—
134C2×C4×C5C22×D311yescharacteristic
135C2×Dic5—32no—
136C2×Dic5—32no—
137C2×Dic5—41no—
138C2×Dic5—64no—
139C2×Dic5—122no—
140C2×Dic5C22×D312yes—
141C2×Dic5C22×D312yes—
142Dic10—121no—
143#126—152no—
144#124—151no—
145#123—51no—
146#123—152no—
147C22⋊Q8—152no—
148#120—31no—
149C4×D4—152no—
150#117—152no—
151C2×C22⋊C4—152no—
152C2×C3×C5—41no—
153C2×C3×C5—41no—
154C2×C3×C5C2×#4112yes—
155C2×C3×C5H(5,𝔽2)11yescharacteristic
156C5×D3—24no—
157C23×C3C22×D511yescharacteristic
158C23×C3C22×D511yescharacteristic
159C22×D3—24no—
160C22×D3—41no—
161C22×D3C22×D512yes—
162C3×D4—41no—
163C2×C3×C4—52no—
164C2×C3×C4—52no—
165C2×C3×C4—201no—
166C2×C3×C4C22×D511yescharacteristic
167#67—24no—
168C2×Dic3—52no—
169C2×Dic3—52no—
170C2×Dic3C22×D512yes—
171C4×D3—104no—
172C4×D3—202no—
173Dic6—201no—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5—22no—
177C22×C5—22no—
178C22×C5—34no—
179C22×C5—62no—
180C22×C5—62no—
181C22×C5—124no—
182C22×C5C23×D311yescharacteristic
183C4×C5—21no—
184C4×C5—62no—
185Dic5—22no—
186Dic5—22no—
187Dic5—62no—
188Dic5—62no—
189C24—31no—
190C2×Q8—151no—
191C2×D4—32no—
192C2×D4D3×D511yescharacteristic
193C22×C4—51no—
194C22×C4—152no—
195C22×C4—152no—
196C4⋊C4—52no—
197C4⋊C4—152no—
198C4⋊C4—152no—
199C4⋊C4—152no—
200C22⋊C4—31no—
201C22⋊C4—32no—
202C22⋊C4—52no—
203C22⋊C4—51no—
204C22⋊C4—152no—
205C22⋊C4—152no—
206C22⋊C4—152no—
207C22⋊C4—152no—
208C42—152no—
209C42—151no—
210C3×C5#55111yescharacteristic, complemented, Hall
211C22×C3—22no—
212C22×C3—22no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3C23×D511yescharacteristic
216C2×D3—22no—
217C2×D3—22no—
218C2×D3—44no—
219C2×D3#71114yes—
220C3×C4—21no—
221C3×C4—102no—
222C3×C4—102no—
223Dic3—22no—
224Dic3—102no—
225Dic3—102no—
226C2×C5—41no—
227C2×C5—41no—
228C2×C5—64no—
229C2×C5#100411yescharacteristic
230C2×C5D3×#4112yes—
231C23—32no—
232C23—64no—
233C23—121no—
234C23C2×D3×D511yescharacteristic
235C23C2×D3×D511yescharacteristic
236Q8—601no—
237D4—41no—
238D4—64no—
239C2×C4—32no—
240C2×C4—52no—
241C2×C4—52no—
242C2×C4—152no—
243C2×C4—152no—
244C2×C4—201no—
245C2×C4—304no—
246C2×C4—602no—
247C2×C4C2×D3×D511yescharacteristic
248C2×C3—41no—
249C2×C3—41no—
250C2×C3C2×#71112yes—
251C2×C3#414411yescharacteristic
252D3—24no—
253C5#565911yescharacteristic, complemented, Sylow
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—34no—
259C22—62no—
260C22—62no—
261C22—124no—
262C22C22×D3×D511yescharacteristic
263C4—21no—
264C4—62no—
265C4—102no—
266C4—102no—
267C4—302no—
268C4—302no—
269C3#6592111yescharacteristic, complemented, Sylow
270C2—41no—
271C2—41no—
272C2—64no—
273C2D3×#71112yes—
274C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
prime radicalC5×#937C2
hypercenterC2×D4D3×D5
hypocenterC3×C5#551
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. #91825C2semidirect
3. C3×#4081C2semidirect
4. #91555C2semidirect
5. D3×C22⋊Dic5C2semidirect
6. Dic5×#67C2semidirect
7. #91530C2semidirect
8. #91432C2semidirect
9. #91400C2semidirect
13. C2×Dic30C22semidirect
15. C22×C3×Dic5C22semidirect
19. #6719C22semidirect
20. C4×Dic15C22semidirect
24. C3×C22⋊Dic5C22semidirect
25. C3×#683C22semidirect
26. Dic3⋊Dic5C22semidirect
27. #6669C22semidirect
28. #6668C22semidirect
31. Dic3×Dic5C22semidirect
37. #4081D3semidirect
73. C22×Dic5C2×D3semidirect
82. C22⋊Dic5C2×D3semidirect
86. #683C2×D3semidirect
210. C3×C5#551semidirect
253. C5#5659semidirect
269. C3#65921semidirect

Maximal subgroups

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

subgroupindex
#918252
C5×#9372
C3×#40812
#915552
D3×C22⋊Dic52
Dic5×#672
#915302
#914322
#914002
#659213
#56595