Finite Group Databasebeta

← C2×#91359 #11754239

Subgroups — C2×#91359 #11754239

Order 960.

644 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 208 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×C5×Dic6C211yesmaximal, characteristic, complemented
2C22×C3×C4×D5C211yesmaximal, characteristic
3C2×C4⋊Dic15C211yesmaximal, characteristic, complemented
4C2×#6669C212yesmaximal, complemented
5C2×#6665C212yesmaximal
6#91359C218yesmaximal, direct product factor
7C2×#4092—31nomaximal, Hall
8C23×C3×D5C2211yescharacteristic
9C22×C3×C4×C5C2211yescharacteristic
10C22×Dic15C2212yes—
11C22×C5×Dic3C2212yes—
12C2×C5×Dic6—24no—
13C2×C5×Dic6C2214yescomplemented
14C22×C3×Dic5C2211yescharacteristic
15C2×C3×C4×D5—24no—
16C2×C3×C4×D5C2214yes—
17C4⋊Dic15C2214yescomplemented
18#6669C2218yescomplemented
19#6665C2218yes—
20C2×#924—51nomaximal, Hall
21C22×C5×Q8—31no—
22C22×C4×D5D311yescharacteristic
23#4092—38no—
24C2×#685—32no—
25C2×C4⋊Dic5—31no—
26C2×#683—32no—
27C23×C3×C5C2311yescharacteristic
28C22×C3×D5—22no—
29C22×C3×D5—22no—
30C22×C3×D5Q814yescomplemented
31C22×C3×D5C2312yes—
32C2×C3×C4×C5D414yes—
33C2×C3×C4×C5C2312yes—
34C2×Dic15—24no—
35C2×Dic15C2314yes—
36C2×C5×Dic3—24no—
37C2×C5×Dic3C2314yes—
38C5×Dic6—28no—
39C2×C3×Dic5—22no—
40C2×C3×Dic5C2312yes—
41C3×C4×D5—28no—
42C23×C3×C4—51no—
43C22×Dic6D511yescharacteristic, complemented
44C2×#217—52no—
45C2×C4⋊Dic3—51no—
46#924—58no—
47C2×Dic3⋊C4—52no—
48C23×D5C2×D311yescharacteristic
49C2×C5×Q8—34no—
50C2×C5×Q8—64no—
51C22×C4×C5—32no—
52C22×C4×C5C2×D311yescharacteristic
53C22×Dic5—32no—
54C22×Dic5C2×D311yescharacteristic
55C2×C4×D5—24no—
56C2×C4×D5C2×D314yes—
57#685—38no—
58C4⋊Dic5—34no—
59#683—38no—
60C2×C22⋊Q8—151noSylow
61C22×C3×C5C2×D412yes—
62C22×C3×C5C2×Q812yes—
63C22×C3×C5#4112yes—
64C22×C3×C5C2411yescharacteristic
65C2×C3×D5—28no—
66C2×C3×D5—22no—
67C2×C3×D5—22no—
68C2×C3×D5C2×Q814yescomplemented
69C3×C4×C5C2×D414yes—
70Dic15—24no—
71C3×Dic5—22no—
72C5×Dic3—24no—
73C24×C3—51no—
74C22×C3×C4—51no—
75C22×C3×C4—54no—
76C22×C3×C4—104no—
77C22×C3×C4C2×D511yescharacteristic
78C22×Dic3—52no—
79C22×Dic3C2×D512yes—
80C2×Dic6—24no—
81C2×Dic6C2×D514yescomplemented
82#217—58no—
83C4⋊Dic3—54no—
84Dic3⋊C4—58no—
85C23×C5C22×D311yescharacteristic
86C22×D5—22no—
87C22×D5—22no—
88C22×D5Dic614yescomplemented
89C22×D5C22×D312yes—
90C5×Q8—68no—
91C2×C4×C5—34no—
92C2×C4×C5—64no—
93C2×C4×C5#6714yes—
94C2×C4×C5C22×D312yes—
95C2×Dic5—22no—
96C2×Dic5—34no—
97C2×Dic5—64no—
98C2×Dic5C22×D312yes—
99C4×D5—28no—
100C22×Q8—31no—
101C23×C4—51no—
102C22⋊Q8—158no—
103C2×C4⋊C4—152no—
104C2×C4⋊C4—151no—
105C2×C22⋊C4—152no—
106C2×C3×C5C22⋊Q814yescomplemented
107C2×C3×C5C22×D411yescharacteristic
108C2×C3×C5C22×Q811yescharacteristic
109C2×C3×C5C2×#4111yescharacteristic
110C3×D5—24no—
111C23×C3—54no—
112C23×C3—52no—
113C23×C3—102no—
114C23×C3—102no—
115C23×C3C22×D511yescharacteristic
116C2×C3×C4—52no—
117C2×C3×C4—102no—
118C2×C3×C4—108no—
119C2×C3×C4C22⋊D514yes—
120C2×C3×C4C22×D512yes—
121C2×Dic3—24no—
122C2×Dic3—54no—
123C2×Dic3—104no—
124C2×Dic3C22×D514yes—
125Dic6—28no—
126C22×C5C2×Dic612yes—
127C22×C5#23512yes—
128C22×C5C2×#6712yes—
129C22×C5C23×D311yescharacteristic
130C2×D5—28no—
131C2×D5—22no—
132C2×D5—22no—
133C2×D5C2×Dic614yescomplemented
134C4×C5—64no—
135C4×C5C2×#6714yes—
136Dic5—22no—
137Dic5—64no—
138C24—51no—
139C2×Q8—34no—
140C2×Q8—64no—
141C22×C4—32no—
142C22×C4—51no—
143C22×C4—54no—
144C22×C4—104no—
145C22×C4—152no—
146C22×C4D3×D511yescharacteristic
147C4⋊C4—158no—
148C4⋊C4—154no—
149C22⋊C4—158no—
150C3×C5C2×C22⋊Q811yescharacteristic, complemented, Hall
151C22×C3—54no—
152C22×C3—102no—
153C22×C3—102no—
154C22×C3—108no—
155C22×C3Q8×D512yes—
156C22×C3#71312yes—
157C22×C3C2×C22⋊D512yes—
158C22×C3C23×D511yescharacteristic
159C3×C4—102no—
160C3×C4C2×C22⋊D514yes—
161Dic3—24no—
162Dic3—104no—
163C2×C5#92414yescomplemented
164C2×C5C22×Dic611yescharacteristic
165C2×C5C2×#23511yescharacteristic
166C2×C5C22×#6711yescharacteristic
167D5—24no—
168C23—54no—
169C23—52no—
170C23—102no—
171C23—102no—
172C23C2×D3×D511yescharacteristic
173Q8—68no—
174C2×C4—34no—
175C2×C4—52no—
176C2×C4—64no—
177C2×C4—102no—
178C2×C4—108no—
179C2×C4—154no—
180C2×C4—304no—
181C2×C4#120114yes—
182C2×C4C2×D3×D512yes—
183C2×C3—104no—
184C2×C3#409214yescomplemented
185C2×C3C2×Q8×D511yescharacteristic
186C2×C3C2×#71311yescharacteristic
187C2×C3C22×C22⋊D511yescharacteristic
188C5C2×#92411yescharacteristic, complemented, Sylow
189C22—54no—
190C22—102no—
191C22—102no—
192C22—108no—
193C22D5×Dic612yes—
194C22#677312yes—
195C22C2×#120112yes—
196C22C22×D3×D511yescharacteristic
197C4—64no—
198C4—102no—
199C4—304no—
200C4C2×#120114yes—
201C3C2×#409211yescharacteristic, complemented, Sylow
202C2—104no—
203C2#9135914yesdirect product factor
204C2C2×D5×Dic611yescharacteristic
205C2C2×#677311yescharacteristic
206C2C22×#120111yescharacteristic
subgroupG/H
centerC23C2×D3×D5
commutator, cosocleC22×C3×C5C24
FrattiniC22C22×D3×D5
FittingC22×C3×C4×C5C22
socleC23×C3×C5C23
prime radicalC23×C3×D5C22
hypercenterC22×C4D3×D5
hypocenterC3×C5C2×C22⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×Dic6C2semidirect
3. C2×C4⋊Dic15C2semidirect
4. C2×#6669C2semidirect
6. #91359C2direct (N × H)
13. C2×C5×Dic6C22semidirect
17. C4⋊Dic15C22semidirect
18. #6669C22semidirect
30. C22×C3×D5Q8semidirect
43. C22×Dic6D5semidirect
68. C2×C3×D5C2×Q8semidirect
81. C2×Dic6C2×D5semidirect
88. C22×D5Dic6semidirect
106. C2×C3×C5C22⋊Q8semidirect
133. C2×D5C2×Dic6semidirect
150. C3×C5C2×C22⋊Q8semidirect
163. C2×C5#924semidirect
184. C2×C3#4092semidirect
188. C5C2×#924semidirect
201. C3C2×#4092semidirect
203. C2#91359direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×Dic62
C22×C3×C4×D52
C2×C4⋊Dic152
C2×#66692
C2×#66652
#913592
C2×#40923
C2×#9245