Finite Group Databasebeta

← #11756418

Subgroups — #11756418

Order 960.

496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C3×C5×#123C211yesmaximal, characteristic, complemented
2#91826C211yesmaximal, characteristic
3#91825C211yesmaximal, characteristic, complemented
4C4×#1220C212yesmaximal, complemented
5#91785C212yesmaximal, complemented
6#91781C212yesmaximal, complemented
7#91772C212yesmaximal, complemented
8C22⋊C4×D15C212yesmaximal, complemented
9#91768C212yesmaximal, complemented
10#65993—31nomaximal, Hall
11C23×D15C2211yescharacteristic
12C2×C3×C5×D4C2211yescharacteristic
13C22×C3×C4×C5C2211yescharacteristic, complemented
14C2×#1220C2212yes—
15C2×C4×D15C2212yes—
16C2×C4×D15C2212yes—
17C2×Dic30C2211yescharacteristic, complemented
18C3×C5×C4⋊C4C2212yescomplemented
19C3×C5×C22⋊C4C2212yes—
20C3×C5×C22⋊C4C2211yescharacteristic, complemented
21#6719C2211yescharacteristic
22#6719C2212yes—
23#6719C2212yescomplemented
24#6714C2212yes—
25#6714C2212yes—
26#6714C2212yes—
27C4⋊Dic15C2212yescomplemented
28#6712C2212yescomplemented
29#6712C2212yescomplemented
30C4×Dic15C2212yescomplemented
31C4×Dic15C2211yescharacteristic, complemented
32#5659—51nomaximal, Hall
33C5×#123D311yescharacteristic, complemented
34#4083—31no—
35#4082—31no—
36C4×C22⋊D5—32no—
37#4042—32no—
38#4038—32no—
39#4029—32no—
40D5×C22⋊C4—32no—
41#4025—32no—
42C23×C3×C5C2311yescharacteristic
43C23×C3×C5C2311yescharacteristic
44C22×D15—24no—
45C22×D15—41no—
46C22×D15C2312yes—
47C3×C5×D4—41no—
48C2×C3×C4×C5—41no—
49C2×C3×C4×C5C2312yes—
50C2×C3×C4×C5C2311yescharacteristic
51C2×C3×C4×C5C2312yes—
52#1220—24no—
53C2×Dic15C2312yes—
54C2×Dic15C2312yes—
55C2×Dic15C2312yes—
56C4×D15—24no—
57C4×D15—42no—
58Dic30—41no—
59C3×#123D511yescharacteristic, complemented
60#937—51no—
61#936—51no—
62C4×#67—52no—
63#896—52no—
64#892—52no—
65#883—52no—
66D3×C22⋊C4—52no—
67#879—52no—
68C23×D5—31no—
69C2×C5×D4C2×D311yescharacteristic
70C22×C4×C5C2×D311yescharacteristic, complemented
71C2×C22⋊D5—32no—
72C2×C4×D5—32no—
73C2×C4×D5—32no—
74C2×Dic10—31no—
75C5×C4⋊C4C2×D312yescomplemented
76C5×C22⋊C4C2×D312yes—
77C5×C22⋊C4C2×D311yescharacteristic, complemented
78C22⋊Dic5—31no—
79C22⋊Dic5—32no—
80C22⋊Dic5—32no—
81#685—32no—
82#685—32no—
83#685—32no—
84C4⋊Dic5—32no—
85#683—32no—
86#683—32no—
87C4×Dic5—32no—
88C4×Dic5—31no—
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—22no—
100C3×C4×C5—21no—
101C3×C4×C5—22no—
102Dic15—22no—
103Dic15—22no—
104Dic15—22no—
105C23×D3—51no—
106C2×C3×D4C2×D511yescharacteristic
107C22×C3×C4C2×D511yescharacteristic, complemented
108C2×#67—52no—
109C2×C4×D3—52no—
110C2×C4×D3—52no—
111C2×Dic6—51no—
112C3×C4⋊C4C2×D512yescomplemented
113C3×C22⋊C4C2×D512yes—
114C3×C22⋊C4C2×D511yescharacteristic, complemented
115#217—51no—
116#217—52no—
117#217—52no—
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×Dic3—51no—
126C23×C5C22×D311yescharacteristic
127C23×C5C22×D311yescharacteristic
128C22×D5—32no—
129C22×D5—64no—
130C22×D5—121no—
131C5×D4—41no—
132C2×C4×C5—41no—
133C2×C4×C5C22×D312yes—
134C2×C4×C5C22×D311yescharacteristic
135C2×C4×C5C22×D312yes—
136C22⋊D5—64no—
137C2×Dic5—32no—
138C2×Dic5—32no—
139C2×Dic5—32no—
140C4×D5—64no—
141C4×D5—122no—
142Dic10—121no—
143#126—152no—
144#124—151no—
145#123—152no—
146#123D1511yescharacteristic, complemented
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—41no—
164C2×C3×C4C22×D512yes—
165C2×C3×C4C22×D511yescharacteristic
166C2×C3×C4C22×D512yes—
167#67—104no—
168C2×Dic3—52no—
169C2×Dic3—52no—
170C2×Dic3—52no—
171C4×D3—104no—
172C4×D3—202no—
173Dic6—201no—
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—22no—
185C4×C5—22no—
186Dic5—62no—
187Dic5—62no—
188Dic5—62no—
189C24—151no—
190C2×Q8—151no—
191C2×D4—152no—
192C2×D4C2×D1511yescharacteristic
193C22×C4—152no—
194C22×C4—152no—
195C22×C4C2×D1511yescharacteristic, complemented
196C4⋊C4—152no—
197C4⋊C4—152no—
198C4⋊C4—152no—
199C4⋊C4C2×D1512yescomplemented
200C22⋊C4—152no—
201C22⋊C4—152no—
202C22⋊C4—151no—
203C22⋊C4—152no—
204C22⋊C4—152no—
205C22⋊C4—152no—
206C22⋊C4C2×D1512yes—
207C22⋊C4C2×D1511yescharacteristic, complemented
208C42—151no—
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—22no—
222C3×C4—22no—
223Dic3—102no—
224Dic3—102no—
225Dic3—102no—
226C2×C5—41no—
227C2×C5—41no—
228C2×C5#100411yescharacteristic
229C2×C5D3×#4112yes—
230D5—64no—
231C23—152no—
232C23—304no—
233C23—601no—
234C23C22×D1511yescharacteristic
235C23C22×D1511yescharacteristic
236Q8—601no—
237D4—41no—
238D4—304no—
239C2×C4—41no—
240C2×C4—152no—
241C2×C4—152no—
242C2×C4—152no—
243C2×C4—304no—
244C2×C4—602no—
245C2×C4C22×D1511yescharacteristic
246C2×C4C22×D1512yes—
247C2×C4C22×D1512yes—
248C2×C3—41no—
249C2×C3—41no—
250C2×C3#414411yescharacteristic
251C2×C3D5×#4112yes—
252D3—104no—
253C5#565911yescharacteristic, complemented, Sylow
254C22—21no—
255C22—21no—
256C22—22no—
257C22—22no—
258C22—154no—
259C22—302no—
260C22—302no—
261C22—604no—
262C22C23×D1511yescharacteristic
263C4—22no—
264C4—21no—
265C4—22no—
266C4—302no—
267C4—302no—
268C4—302no—
269C3#6599311yescharacteristic, complemented, Sylow
270C2—41no—
271C2—41no—
272C2—304no—
273C2#9209511yescharacteristic
274C2#41×D1512yes—
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#123C2
prime radical#91826C2
hypercenter#123D15
hypocenterC3×C5#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C3×C5×#123C2semidirect
3. #91825C2semidirect
4. C4×#1220C2semidirect
5. #91785C2semidirect
6. #91781C2semidirect
7. #91772C2semidirect
8. C22⋊C4×D15C2semidirect
9. #91768C2semidirect
13. C22×C3×C4×C5C22semidirect
17. C2×Dic30C22semidirect
18. C3×C5×C4⋊C4C22semidirect
20. C3×C5×C22⋊C4C22semidirect
23. #6719C22semidirect
27. C4⋊Dic15C22semidirect
28. #6712C22semidirect
29. #6712C22semidirect
30. C4×Dic15C22semidirect
31. C4×Dic15C22semidirect
33. C5×#123D3semidirect
59. C3×#123D5semidirect
70. C22×C4×C5C2×D3semidirect
75. C5×C4⋊C4C2×D3semidirect
77. C5×C22⋊C4C2×D3semidirect
107. C22×C3×C4C2×D5semidirect
112. C3×C4⋊C4C2×D5semidirect
114. C3×C22⋊C4C2×D5semidirect
146. #123D15semidirect
195. C22×C4C2×D15semidirect
199. C4⋊C4C2×D15semidirect
207. C22⋊C4C2×D15semidirect
210. C3×C5#551semidirect
253. C5#5659semidirect
269. C3#65993semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1232
#918262
#918252
C4×#12202
#917852
#917812
#917722
C22⋊C4×D152
#917682
#659933
#56595