Finite Group Databasebeta

← #11754898

Subgroups — #11754898

Order 960.

496 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 124 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#91826C211yesmaximal, characteristic
2C5×#936C211yesmaximal, characteristic, complemented
3C3×#4081C211yesmaximal, characteristic, complemented
4#91562C212yesmaximal, complemented
5#91561C212yesmaximal, complemented
6#91552C212yesmaximal, complemented
7#91531C212yesmaximal, complemented
8#91424C212yesmaximal, complemented
9#91403C212yesmaximal, complemented
10#66013—31nomaximal, Hall
11C23×D15C2211yescharacteristic
12C2×C3×C5×D4C2211yescharacteristic
13C2×#1220C2212yes—
14C2×C5×Dic6C2211yescharacteristic, complemented
15C22×C3×Dic5C2211yescharacteristic, complemented
16C2×#1200C2212yes—
17C2×#1200C2212yes—
18#6719C2211yescharacteristic
19#6714C2212yes—
20C5×#217C2212yes—
21C5×#217C2212yescomplemented
22C4×C5×Dic3C2211yescharacteristic, complemented
23C3×C22⋊Dic5C2212yes—
24C3×C22⋊Dic5C2211yescharacteristic, complemented
25C3×#683C2212yescomplemented
26Dic3⋊Dic5C2212yescomplemented
27#6669C2212yescomplemented
28#6668C2212yescomplemented
29#6667C2212yes—
30#6667C2212yes—
31Dic3×Dic5C2212yescomplemented
32#5659—51nomaximal, Hall
33C5×#124—31no—
34#4092—32no—
35#4083—31no—
36#4081D311yescharacteristic, complemented
37#4029—32no—
38#4027—32no—
39D5×C22⋊C4—32no—
40#4025—32no—
41#4018—32no—
42C23×C3×C5C2311yescharacteristic
43C23×C3×C5C2311yescharacteristic
44C22×D15—24no—
45C22×D15—41no—
46C22×D15C2312yes—
47C3×C5×D4—41no—
48C2×C3×C4×C5C2311yescharacteristic
49#1220—24no—
50C2×Dic15C2312yes—
51C2×C5×Dic3C2312yes—
52C2×C5×Dic3C2312yes—
53C5×Dic6—41no—
54C2×C3×Dic5—41no—
55C2×C3×Dic5C2312yes—
56C2×C3×Dic5C2312yes—
57#1200—24no—
58#1200—42no—
59C3×#123—51no—
60#937—51no—
61#936D511yescharacteristic, complemented
62C4×#67—52no—
63#896—52no—
64#892—52no—
65#883—52no—
66D3×C22⋊C4—52no—
67#879—52no—
68C23×D5—31no—
69C2×C5×Q8—31no—
70C2×C5×D4C2×D311yescharacteristic
71C2×C22⋊D5—32no—
72C22×Dic5C2×D311yescharacteristic, complemented
73C2×C4×D5—32no—
74C2×C4×D5—32no—
75C5×C22⋊C4—32no—
76C5×C22⋊C4—32no—
77C42×C5—31no—
78C22⋊Dic5—31no—
79C22⋊Dic5C2×D312yes—
80C22⋊Dic5C2×D311yescharacteristic, complemented
81#685—32no—
82#685—32no—
83#685—32no—
84C4⋊Dic5—32no—
85#683—32no—
86#683—32no—
87#683C2×D312yescomplemented
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×D15—22no—
96C2×D15—22no—
97C2×D15—44no—
98C2×D15#4114yes—
99C3×C4×C5—21no—
100Dic15—22no—
101C3×Dic5—22no—
102C3×Dic5—22no—
103C5×Dic3—22no—
104C5×Dic3—22no—
105C23×D3—51no—
106C2×C3×D4C2×D511yescharacteristic
107C22×C3×C4—51no—
108C2×#67—52no—
109C2×C4×D3—52no—
110C2×C4×D3—52no—
111C2×Dic6C2×D511yescharacteristic, complemented
112C3×C4⋊C4—52no—
113C3×C22⋊C4—52no—
114C3×C22⋊C4—51no—
115#217—51no—
116#217C2×D512yes—
117#217C2×D512yescomplemented
118(C2×D3)⋊C4—52no—
119(C2×D3)⋊C4—52no—
120(C2×D3)⋊C4—52no—
121C4⋊Dic3—52no—
122Dic3⋊C4—52no—
123Dic3⋊C4—52no—
124C4×Dic3—52no—
125C4×Dic3C2×D511yescharacteristic, complemented
126C23×C5C22×D311yescharacteristic
127C23×C5C22×D311yescharacteristic
128C22×D5—32no—
129C22×D5—64no—
130C22×D5—121no—
131C5×Q8—121no—
132C5×D4—41no—
133C2×C4×C5—32no—
134C2×C4×C5—32no—
135C2×C4×C5C22×D311yescharacteristic
136C22⋊D5—64no—
137C2×Dic5—32no—
138C2×Dic5—41no—
139C2×Dic5C22×D312yes—
140C2×Dic5C22×D312yes—
141C4×D5—64no—
142C4×D5—122no—
143#126—152no—
144#124—31no—
145#123—51no—
146#123—152no—
147C22⋊Q8—152no—
148#120—151no—
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
156D15—24no—
157C23×C3C22×D511yescharacteristic
158C23×C3C22×D511yescharacteristic
159C22×D3—52no—
160C22×D3—104no—
161C22×D3—201no—
162C3×D4—41no—
163C2×C3×C4—52no—
164C2×C3×C4—52no—
165C2×C3×C4—201no—
166C2×C3×C4C22×D511yescharacteristic
167#67—104no—
168C2×Dic3—52no—
169C2×Dic3C22×D512yes—
170C2×Dic3C22×D512yes—
171C4×D3—104no—
172C4×D3—202no—
173Dic6—41no—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5—22no—
177C22×C5—22no—
178C22×C5C23×D311yescharacteristic
179C2×D5—34no—
180C2×D5—62no—
181C2×D5—62no—
182C2×D5—124no—
183C4×C5—21no—
184C4×C5—62no—
185C4×C5—62no—
186Dic5—22no—
187Dic5—22no—
188Dic5—62no—
189C24—151no—
190C2×Q8—31no—
191C2×D4—152no—
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—32no—
201C22⋊C4—32no—
202C22⋊C4—52no—
203C22⋊C4—51no—
204C22⋊C4—152no—
205C22⋊C4—152no—
206C22⋊C4—151no—
207C22⋊C4—152no—
208C42—31no—
209C42—152no—
210C3×C5#55111yescharacteristic, complemented, Hall
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—22no—
214C22×C3—22no—
215C22×C3C23×D511yescharacteristic
216C2×D3—54no—
217C2×D3—102no—
218C2×D3—102no—
219C2×D3—204no—
220C3×C4—21no—
221C3×C4—102no—
222C3×C4—102no—
223Dic3—22no—
224Dic3—22no—
225Dic3—102no—
226C2×C5—41no—
227C2×C5—41no—
228C2×C5#100411yescharacteristic
229C2×C5D3×#4112yes—
230D5—64no—
231C23—152no—
232C23—304no—
233C23—601no—
234C23C2×D3×D511yescharacteristic
235C23C2×D3×D511yescharacteristic
236Q8—121no—
237D4—41no—
238D4—304no—
239C2×C4—32no—
240C2×C4—32no—
241C2×C4—52no—
242C2×C4—52no—
243C2×C4—152no—
244C2×C4—201no—
245C2×C4—304no—
246C2×C4—602no—
247C2×C4C2×D3×D511yescharacteristic
248C2×C3—41no—
249C2×C3—41no—
250C2×C3#414411yescharacteristic
251C2×C3D5×#4112yes—
252D3—104no—
253C5#565911yescharacteristic, complemented, Sylow
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—154no—
259C22—302no—
260C22—302no—
261C22—604no—
262C22C22×D3×D511yescharacteristic
263C4—21no—
264C4—62no—
265C4—62no—
266C4—102no—
267C4—102no—
268C4—302no—
269C3#6601311yescharacteristic, complemented, Sylow
270C2—41no—
271C2—41no—
272C2—304no—
273C2#9202412yes—
274C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
prime radical#91826C2
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
2. C5×#936C2semidirect
3. C3×#4081C2semidirect
4. #91562C2semidirect
5. #91561C2semidirect
6. #91552C2semidirect
7. #91531C2semidirect
8. #91424C2semidirect
9. #91403C2semidirect
14. C2×C5×Dic6C22semidirect
15. C22×C3×Dic5C22semidirect
21. C5×#217C22semidirect
22. C4×C5×Dic3C22semidirect
24. C3×C22⋊Dic5C22semidirect
25. C3×#683C22semidirect
26. Dic3⋊Dic5C22semidirect
27. #6669C22semidirect
28. #6668C22semidirect
31. Dic3×Dic5C22semidirect
36. #4081D3semidirect
61. #936D5semidirect
72. C22×Dic5C2×D3semidirect
80. C22⋊Dic5C2×D3semidirect
87. #683C2×D3semidirect
111. C2×Dic6C2×D5semidirect
117. #217C2×D5semidirect
125. C4×Dic3C2×D5semidirect
210. C3×C5#551semidirect
253. C5#5659semidirect
269. C3#66013semidirect

Maximal subgroups

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

subgroupindex
#918262
C5×#9362
C3×#40812
#915622
#915612
#915522
#915312
#914242
#914032
#660133
#56595