Finite Group Databasebeta

← C2×#91931 #11756865

Subgroups — C2×#91931 #11756865

Order 960.

596 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 186 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
1C22×#1200C211yesmaximal, characteristic
2C2×#6762C211yesmaximal, characteristic, complemented
3C2×C3×#704C211yesmaximal, characteristic, complemented
4C2×#6740C212yesmaximal, complemented
5#91931C218yesmaximal, direct product factor
6C2×#6738C212yesmaximal, complemented
7C2×D5⋊M16—31nomaximal, Hall
8C23×D15C411yescharacteristic
9C22×C5×Dic3C411yescharacteristic
10C22×C3×Dic5C2211yescharacteristic
11C2×#1200C411yescharacteristic
12C2×#1200C414yes—
13C2×#1200C411yescharacteristic
14C2×#1200C2211yescharacteristic
15C2×#1200C2214yes—
16C2×#1200C2211yescharacteristic
17#6762C2214yescomplemented
18C2×C3⋊#170C2212yescomplemented
19C3×#704C2214yescomplemented
20C2×C3×#170C2212yescomplemented
21#6740C2218yescomplemented
22#6738C2218yescomplemented
23C2×D3×M16—51nomaximal, Hall
24C22×C4×D5—31no—
25C2×#704—31no—
26C2×#704D311yescharacteristic, complemented
27D5⋊M16—38no—
28C2×#700—32no—
29C2×D5⋊C8—32no—
30C23×C3×C5C2×C411yescharacteristic
31C22×D15—24no—
32C22×D15C2×C411yescharacteristic
33C22×D15C2×C414yes—
34C22×D15C2×C411yescharacteristic
35C2×C5×Dic3C2×C414yes—
36C2×C5×Dic3C2×C411yescharacteristic
37C2×C5×Dic3C2×C411yescharacteristic
38C2×C3×Dic5C2×C412yes—
39C2×C3×Dic5C2×C411yescharacteristic
40C2×C3×Dic5C2311yescharacteristic
41C2×C3×Dic5C2312yes—
42#1200C2×C414yes—
43#1200C2×C412yes—
44#1200C2×C412yes—
45#1200C2×C414yes—
46#1200C2312yes—
47#1200C2312yes—
48C3⋊#170C2314yescomplemented
49C3×#170C2314yescomplemented
50C22×C4×D3—51no—
51C2×C3×M16—51no—
52C2×#208—51no—
53D3×M16—58no—
54C2×ΓL(1,𝔽25)—52no—
55C2×D3×C8—52no—
56C23×D5—31no—
57C22×C4×C5—31no—
58C22×Dic5C2×D311yescharacteristic
59C2×C4×D5—31no—
60C2×C4×D5—34no—
61C2×C4×D5—31no—
62C2×C4×D5—31no—
63C2×C4×D5—31no—
64C2×C4×D5—34no—
65#704—34no—
66#704C2×D314yescomplemented
67C2×#170—32no—
68C2×#170C2×D312yescomplemented
69#700—38no—
70D5⋊C8—38no—
71C22×M16—151noSylow
72C22×C3×C5—22no—
73C22×C3×C5C22×C412yes—
74C22×C3×C5C22×C411yescharacteristic
75C2×D15—22no—
76C2×D15—28no—
77C2×D15M1614yescomplemented
78C2×D15C22×C412yes—
79C2×D15C22×C412yes—
80C3×Dic5C22×C411yescharacteristic
81C3×Dic5C22×C412yes—
82C3×Dic5C2411yescharacteristic
83C5×Dic3C22×C412yes—
84C5×Dic3C22×C412yes—
85C23×D3—51no—
86C22×C3×C4—51no—
87C22×Dic3AGL(1,𝔽5)11yescharacteristic
88C2×C4×D3—51no—
89C2×C4×D3—54no—
90C2×C4×D3—51no—
91C2×C4×D3—51no—
92C2×C4×D3—51no—
93C2×C4×D3—54no—
94C3×M16—54no—
95C2×C3×C8—52no—
96#208—54no—
97C2×C3⋊C8—52no—
98ΓL(1,𝔽25)—58no—
99D3×C8—58no—
100C23×C5C4×D311yescharacteristic
101C22×D5—31no—
102C22×D5—34no—
103C22×D5—31no—
104C22×D5—64no—
105C2×C4×C5—34no—
106C2×C4×C5—31no—
107C2×C4×C5—31no—
108C2×Dic5C4×D312yes—
109C2×Dic5C4×D311yescharacteristic
110C2×Dic5C22×D311yescharacteristic
111C2×Dic5C22×D312yes—
112C4×D5—32no—
113C4×D5—34no—
114C4×D5—32no—
115C4×D5—34no—
116C4×D5—32no—
117C4×D5—32no—
118#170—34no—
119#170C22×D314yescomplemented
120C23×C4—151no—
121C2×M16—51no—
122C2×M16—152no—
123C2×M16—158no—
124C2×M16—151no—
125C22×C8—152no—
126C2×C3×C5—22no—
127C2×C3×C5C2×M1612yescomplemented
128C2×C3×C5C23×C411yescharacteristic
129D15—22no—
130D15C2×M1614yescomplemented
131C23×C3C2×AGL(1,𝔽5)11yescharacteristic
132C22×D3—51no—
133C22×D3—54no—
134C22×D3—51no—
135C22×D3—104no—
136C2×C3×C4—52no—
137C2×C3×C4—51no—
138C2×C3×C4—51no—
139C2×C3×C4—52no—
140C2×Dic3C2×AGL(1,𝔽5)14yes—
141C2×Dic3C2×AGL(1,𝔽5)11yescharacteristic
142C2×Dic3C2×AGL(1,𝔽5)11yescharacteristic
143C4×D3—52no—
144C4×D3—54no—
145C4×D3—52no—
146C4×D3—54no—
147C4×D3—52no—
148C4×D3—52no—
149C3×C8—54no—
150C3⋊C8—54no—
151C22×C5—22no—
152C22×C5C2×C4×D312yes—
153C22×C5C2×C4×D311yescharacteristic
154C2×D5—34no—
155C2×D5—32no—
156C2×D5—32no—
157C2×D5—68no—
158C2×D5—62no—
159C4×C5—32no—
160C4×C5—32no—
161Dic5C2×C4×D311yescharacteristic
162Dic5C2×C4×D312yes—
163Dic5C23×D311yescharacteristic
164C24—151no—
165C22×C4—31no—
166C22×C4—51no—
167C22×C4—151no—
168C22×C4—154no—
169C22×C4—151no—
170C22×C4—154no—
171C22×C4—151no—
172C22×C4—151no—
173M16—54no—
174M16—158no—
175M16—154no—
176C2×C8—52no—
177C2×C8—158no—
178C2×C8—152no—
179C3×C5C22×M1611yescharacteristic, complemented, Hall
180C22×C3—22no—
181C22×C3C22×AGL(1,𝔽5)12yes—
182C22×C3C22×AGL(1,𝔽5)11yescharacteristic
183C2×D3—54no—
184C2×D3—52no—
185C2×D3—52no—
186C2×D3—108no—
187C2×D3—102no—
188C3×C4—51no—
189C3×C4—52no—
190C3×C4—51no—
191Dic3C22×AGL(1,𝔽5)12yes—
192Dic3C22×AGL(1,𝔽5)12yes—
193C2×C5—22no—
194C2×C5D3×M1612yescomplemented
195C2×C5C22×C4×D311yescharacteristic
196D5—34no—
197D5—62no—
198C23—151no—
199C23—154no—
200C23—151no—
201C23—304no—
202C23D3×AGL(1,𝔽5)11yescharacteristic
203C2×C4—34no—
204C2×C4—31no—
205C2×C4—31no—
206C2×C4—52no—
207C2×C4—52no—
208C2×C4—51no—
209C2×C4—51no—
210C2×C4—152no—
211C2×C4—152no—
212C2×C4—152no—
213C2×C4—154no—
214C2×C4—154no—
215C2×C4—152no—
216C8—54no—
217C8—154no—
218C2×C3—22no—
219C2×C3D5⋊M1612yescomplemented
220C2×C3C23×AGL(1,𝔽5)11yescharacteristic
221D3—54no—
222D3—102no—
223C5C2×D3×M1611yescharacteristic, complemented, Sylow
224C22—22no—
225C22—154no—
226C22—152no—
227C22—152no—
228C22—308no—
229C22—302no—
230C22C2×D3×AGL(1,𝔽5)12yes—
231C22C2×D3×AGL(1,𝔽5)11yescharacteristic
232C4—32no—
233C4—32no—
234C4—51no—
235C4—52no—
236C4—51no—
237C3C2×D5⋊M1611yescharacteristic, complemented, Sylow
238C2—22no—
239C2—154no—
240C2—302no—
241C2#9193112yesdirect product factor
242C2C22×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C23×C4
FrattiniC2C22×D3×AGL(1,𝔽5)
FittingC23×C3×C5C2×C4
socleC22×C3×C5C22×C4
prime radicalC23×D15C4
cosocleC3×Dic5C24
hypercenterC23D3×AGL(1,𝔽5)
hypocenterC3×C5C22×M16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#6762C2semidirect
3. C2×C3×#704C2semidirect
4. C2×#6740C2semidirect
5. #91931C2direct (N × H)
6. C2×#6738C2semidirect
17. #6762C22semidirect
18. C2×C3⋊#170C22semidirect
19. C3×#704C22semidirect
20. C2×C3×#170C22semidirect
21. #6740C22semidirect
22. #6738C22semidirect
26. C2×#704D3semidirect
48. C3⋊#170C23semidirect
49. C3×#170C23semidirect
66. #704C2×D3semidirect
68. C2×#170C2×D3semidirect
77. C2×D15M16semidirect
119. #170C22×D3semidirect
127. C2×C3×C5C2×M16semidirect
130. D15C2×M16semidirect
179. C3×C5C22×M16semidirect
194. C2×C5D3×M16semidirect
219. C2×C3D5⋊M16semidirect
223. C5C2×D3×M16semidirect
237. C3C2×D5⋊M16semidirect
241. C2#91931direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#12002
C2×#67622
C2×C3×#7042
C2×#67402
#919312
C2×#67382
C2×D5⋊M163
C2×D3×M165