Finite Group Databasebeta

← #11754837

Subgroups — #11754837

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#91824C211yesmaximal, characteristic, complemented
2C5×#936C211yesmaximal, characteristic, complemented
3C3×#4083C211yesmaximal, characteristic
4#91559C212yesmaximal, complemented
5#91548C212yesmaximal, complemented
6D5×#217C212yesmaximal, complemented
7#91530C212yesmaximal, complemented
8#91421C212yesmaximal, complemented
9#91393C212yesmaximal, complemented
10#66013—31nomaximal, Hall
11C23×C3×D5C2211yescharacteristic
12C2×C3×C5×D4C2211yescharacteristic
13C22×Dic15C2211yescharacteristic, complemented
14C2×C5×Dic6C2211yescharacteristic, complemented
15C2×C3×C22⋊D5C2212yes—
16C2×D5×Dic3C2212yes—
17C2×D5×Dic3C2212yes—
18#6719C2212yes—
19#6719C2211yescharacteristic, complemented
20#6712C2212yescomplemented
21C5×#217C2212yes—
22C5×#217C2212yescomplemented
23C4×C5×Dic3C2211yescharacteristic, complemented
24C3×C22⋊Dic5C2211yescharacteristic
25C3×#685C2212yes—
26Dic3⋊Dic5C2212yescomplemented
27#6669C2212yescomplemented
28#6668C2212yescomplemented
29#6665C2212yes—
30#6665C2212yes—
31Dic3×Dic5C2212yescomplemented
32#5587—51nomaximal, Hall
33C5×#124—31no—
34#4092—32no—
35#4083D311yescharacteristic
36#4081—31no—
37#4029—32no—
38#4027—32no—
39D5×C22⋊C4—32no—
40#4025—32no—
41#4018—32no—
42C23×C3×C5C2311yescharacteristic
43C23×C3×C5C2311yescharacteristic
44C22×C3×D5—24no—
45C22×C3×D5—41no—
46C22×C3×D5C2312yes—
47C3×C5×D4—41no—
48C2×C3×C4×C5C2311yescharacteristic
49C2×Dic15—41no—
50C2×Dic15C2312yes—
51C2×Dic15C2312yes—
52C2×C5×Dic3C2312yes—
53C2×C5×Dic3C2312yes—
54C5×Dic6—41no—
55C3×C22⋊D5—24no—
56C2×C3×Dic5C2312yes—
57D5×Dic3—24no—
58D5×Dic3—42no—
59C3×#120—51no—
60C2×#217—52no—
61#936D511yescharacteristic, complemented
62#935—51no—
63#935—52no—
64D4×Dic3—52no—
65#879—52no—
66#878—52no—
67#877—52no—
68C23×D5C2×D311yescharacteristic
69C2×C5×Q8—31no—
70C2×C5×D4C2×D311yescharacteristic
71C2×C22⋊D5C2×D312yes—
72C22×Dic5—31no—
73C2×C4×D5—32no—
74C2×C4×D5—32no—
75C5×C22⋊C4—32no—
76C5×C22⋊C4—32no—
77C42×C5—31no—
78C22⋊Dic5—32no—
79C22⋊Dic5—31no—
80C22⋊Dic5C2×D311yescharacteristic
81#685—32no—
82#685—32no—
83#685C2×D312yes—
84C4⋊Dic5—32no—
85#683—32no—
86#683—32no—
87#683—32no—
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×C3×D5—22no—
96C2×C3×D5—22no—
97C2×C3×D5—44no—
98C2×C3×D5#4114yes—
99C3×C4×C5—21no—
100Dic15—22no—
101Dic15—22no—
102C3×Dic5—22no—
103C5×Dic3—22no—
104C5×Dic3—22no—
105C24×C3—51no—
106C2×C3×D4—52no—
107C2×C3×D4C2×D511yescharacteristic
108C22×Dic3—51no—
109C22×Dic3—52no—
110C22×Dic3—52no—
111C2×Dic6C2×D511yescharacteristic, complemented
112C3×C22⋊C4—51no—
113C3×C22⋊C4—52no—
114#217—52no—
115#217—51no—
116#217—52no—
117#217—52no—
118#217C2×D512yes—
119#217C2×D512yescomplemented
120C4⋊Dic3—52no—
121Dic3⋊C4—52no—
122Dic3⋊C4—52no—
123Dic3⋊C4—52no—
124C4×Dic3—52no—
125C4×Dic3C2×D511yescharacteristic, complemented
126C23×C5C22×D311yescharacteristic
127C23×C5C22×D311yescharacteristic
128C22×D5—24no—
129C22×D5—41no—
130C22×D5C22×D312yes—
131C5×Q8—121no—
132C5×D4—41no—
133C2×C4×C5—32no—
134C2×C4×C5—32no—
135C2×C4×C5C22×D311yescharacteristic
136C22⋊D5—24no—
137C2×Dic5—32no—
138C2×Dic5—32no—
139C2×Dic5—121no—
140C2×Dic5C22×D312yes—
141C4×D5—64no—
142C4×D5—122no—
143#126—152no—
144#124—31no—
145#123—152no—
146#123—151no—
147C22⋊Q8—152no—
148#120—51no—
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
156C3×D5—24no—
157C23×C3—52no—
158C23×C3—104no—
159C23×C3—201no—
160C23×C3C22×D511yescharacteristic
161C23×C3C22×D511yescharacteristic
162C3×D4—41no—
163C3×D4—104no—
164C2×C3×C4—52no—
165C2×C3×C4C22×D511yescharacteristic
166C2×Dic3—52no—
167C2×Dic3—52no—
168C2×Dic3—104no—
169C2×Dic3—202no—
170C2×Dic3—201no—
171C2×Dic3C22×D512yes—
172C2×Dic3C22×D512yes—
173Dic6—41no—
174C22×C5—22no—
175C22×C5—22no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5C23×D311yescharacteristic
179C2×D5—22no—
180C2×D5—22no—
181C2×D5—44no—
182C2×D5#23714yes—
183C4×C5—21no—
184C4×C5—62no—
185C4×C5—62no—
186Dic5—22no—
187Dic5—62no—
188Dic5—62no—
189C24—51no—
190C2×Q8—31no—
191C2×D4—52no—
192C2×D4D3×D511yescharacteristic
193C22×C4—152no—
194C22×C4—152no—
195C22×C4—151no—
196C4⋊C4—152no—
197C4⋊C4—152no—
198C4⋊C4—152no—
199C4⋊C4—152no—
200C22⋊C4—32no—
201C22⋊C4—32no—
202C22⋊C4—51no—
203C22⋊C4—52no—
204C22⋊C4—152no—
205C22⋊C4—152no—
206C22⋊C4—152no—
207C22⋊C4—151no—
208C42—31no—
209C42—152no—
210C3×C5#55111yescharacteristic, complemented, Hall
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—22no—
214C22×C3—22no—
215C22×C3—54no—
216C22×C3—102no—
217C22×C3—102no—
218C22×C3—204no—
219C22×C3C23×D511yescharacteristic
220C3×C4—21no—
221C3×C4—102no—
222Dic3—22no—
223Dic3—22no—
224Dic3—102no—
225Dic3—102no—
226C2×C5—41no—
227C2×C5—41no—
228C2×C5C2×#23712yes—
229C2×C5#100411yescharacteristic
230D5—24no—
231C23—52no—
232C23—104no—
233C23—201no—
234C23C2×D3×D511yescharacteristic
235C23C2×D3×D511yescharacteristic
236Q8—121no—
237D4—41no—
238D4—104no—
239C2×C4—32no—
240C2×C4—32no—
241C2×C4—52no—
242C2×C4—152no—
243C2×C4—152no—
244C2×C4—304no—
245C2×C4—602no—
246C2×C4—601no—
247C2×C4C2×D3×D511yescharacteristic
248C2×C3—41no—
249C2×C3—41no—
250C2×C3—104no—
251C2×C3#414411yescharacteristic
252C2×C3D5×#4112yes—
253C5#558711yescharacteristic, complemented, Sylow
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—54no—
259C22—102no—
260C22—102no—
261C22—204no—
262C22C22×D3×D511yescharacteristic
263C4—21no—
264C4—62no—
265C4—62no—
266C4—102no—
267C4—302no—
268C4—302no—
269C3#6601311yescharacteristic, complemented, Sylow
270C2—41no—
271C2—41no—
272C2—104no—
273C2D5×#23712yes—
274C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
prime radicalC3×#4083C2
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. #91824C2semidirect
2. C5×#936C2semidirect
4. #91559C2semidirect
5. #91548C2semidirect
6. D5×#217C2semidirect
7. #91530C2semidirect
8. #91421C2semidirect
9. #91393C2semidirect
13. C22×Dic15C22semidirect
14. C2×C5×Dic6C22semidirect
19. #6719C22semidirect
20. #6712C22semidirect
22. C5×#217C22semidirect
23. C4×C5×Dic3C22semidirect
26. Dic3⋊Dic5C22semidirect
27. #6669C22semidirect
28. #6668C22semidirect
31. Dic3×Dic5C22semidirect
61. #936D5semidirect
111. C2×Dic6C2×D5semidirect
119. #217C2×D5semidirect
125. C4×Dic3C2×D5semidirect
210. C3×C5#551semidirect
253. C5#5587semidirect
269. C3#66013semidirect

Maximal subgroups

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

subgroupindex
#918242
C5×#9362
C3×#40832
#915592
#915482
D5×#2172
#915302
#914212
#913932
#660133
#55875