Finite Group Databasebeta

← #11752003

Subgroups — #11752003

Order 960.

380 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 86 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
4#91171C214yesmaximal, complemented
5#65755—31nomaximal, Hall
6C23×D15C411yescharacteristic
7C22×C5×Dic3C411yescharacteristic
8C22×C3×Dic5C2211yescharacteristic
9C2×#1200—22no—
10C2×#1200—22no—
11C2×#1200C412yes—
12C2×#1200C2212yes—
13#6762—22no—
14C2×C3⋊#170C2212yescomplemented
15C3×#704—22no—
16C2×C3×#170C2212yescomplemented
17#5126—51nomaximal, Hall
18C22×C4×D5—31no—
19C2×#704—31no—
20C2×#704D311yescharacteristic, complemented
21#4003—34no—
22C23×C3×C5C2×C411yescharacteristic
23C22×D15—22no—
24C22×D15—24no—
25C22×D15C2×C412yes—
26C2×C5×Dic3—22no—
27C2×C5×Dic3C2×C412yes—
28C2×C3×Dic5C2×C411yescharacteristic
29C2×C3×Dic5D412yes—
30C2×C3×Dic5D412yes—
31C2×C3×Dic5C2311yescharacteristic
32#1200—24no—
33#1200—22no—
34#1200—22no—
35C3⋊#170—22no—
36C3×#170—22no—
37C22×C4×D3—51no—
38C2×C3×M16—51no—
39C2×#208—51no—
40(C2×D3)⋊C8—54no—
41C23×D5—31no—
42C22×C4×C5—31no—
43C22×Dic5C2×D311yescharacteristic
44C2×C4×D5—32no—
45C2×C4×D5—32no—
46C2×C4×D5—62no—
47C2×C4×D5—62no—
48#704—22no—
49#704—62no—
50C2×#170—32no—
51C2×#170C2×D312yescomplemented
52#407—151noSylow
53C22×C3×C5—22no—
54C22×C3×C5C22⋊C412yes—
55C22×C3×C5C22×C411yescharacteristic
56C2×D15—28no—
57C2×D15—22no—
58C2×D15—22no—
59C2×D15M1614yescomplemented
60C3×Dic5C22⋊C412yes—
61C3×Dic5C2×D411yescharacteristic
62C3×Dic5C2×D411yescharacteristic
63C5×Dic3—22no—
64C23×D3—51no—
65C22×C3×C4—51no—
66C22×Dic3AGL(1,𝔽5)11yescharacteristic
67C2×C4×D3—52no—
68C2×C4×D3—52no—
69C2×C4×D3—102no—
70C2×C4×D3—102no—
71C3×M16—102no—
72C2×C3×C8—52no—
73#208—102no—
74C2×C3⋊C8—52no—
75C23×C5C4×D311yescharacteristic
76C22×D5—32no—
77C22×D5—64no—
78C22×D5—62no—
79C2×C4×C5—32no—
80C2×C4×C5—62no—
81C2×Dic5C4×D311yescharacteristic
82C2×Dic5D1212yes—
83C2×Dic5#6712yes—
84C2×Dic5C22×D311yescharacteristic
85C4×D5—64no—
86C4×D5—62no—
87C4×D5—62no—
88#170—22no—
89#170—62no—
90C23×C4—151no—
91C2×M16—51no—
92C2×M16—151no—
93C22⋊C8—154no—
94C2×C3×C5—22no—
95C2×C3×C5C2×C22⋊C411yescharacteristic
96C2×C3×C5C2×M1612yes—
97D15—24no—
98C23×C3C2×AGL(1,𝔽5)11yescharacteristic
99C22×D3—52no—
100C22×D3—104no—
101C22×D3—102no—
102C2×C3×C4—52no—
103C2×C3×C4—52no—
104C2×C3×C4—51no—
105C2×C3×C4—51no—
106C2×Dic3—22no—
107C2×Dic3C2×AGL(1,𝔽5)12yes—
108C4×D3—104no—
109C4×D3—102no—
110C4×D3—102no—
111C3×C8—102no—
112C3⋊C8—102no—
113C22×C5—22no—
114C22×C5(C2×D3)⋊C412yes—
115C22×C5C2×C4×D311yescharacteristic
116C2×D5—34no—
117C2×D5—68no—
118C2×D5—62no—
119C2×D5—62no—
120C4×C5—62no—
121Dic5(C2×D3)⋊C412yes—
122Dic5C2×D1211yescharacteristic
123Dic5C2×#6711yescharacteristic
124C24—151no—
125C22×C4—31no—
126C22×C4—51no—
127C22×C4—152no—
128C22×C4—152no—
129C22×C4—302no—
130C22×C4—302no—
131M16—102no—
132M16—302no—
133C2×C8—52no—
134C2×C8—152no—
135C3×C5#40711yescharacteristic, complemented, Hall
136C22×C3—22no—
137C22×C3C22⋊AGL(1,𝔽5)12yes—
138C22×C3C22×AGL(1,𝔽5)11yescharacteristic
139C2×D3—54no—
140C2×D3—108no—
141C2×D3—102no—
142C2×D3—102no—
143C3×C4—52no—
144C3×C4—51no—
145C3×C4—51no—
146Dic3—22no—
147C2×C5—22no—
148C2×C5D3×M1612yes—
149C2×C5C2×(C2×D3)⋊C411yescharacteristic
150D5—64no—
151C23—152no—
152C23—304no—
153C23—302no—
154C23D3×AGL(1,𝔽5)11yescharacteristic
155C2×C4—32no—
156C2×C4—52no—
157C2×C4—52no—
158C2×C4—51no—
159C2×C4—51no—
160C2×C4—62no—
161C2×C4—302no—
162C2×C4—302no—
163C2×C4—304no—
164C8—102no—
165C8—302no—
166C2×C3—22no—
167C2×C3D5⋊M1612yes—
168C2×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
169D3—104no—
170C5#512611yescharacteristic, complemented, Sylow
171C22—22no—
172C22—154no—
173C22—308no—
174C22—302no—
175C22—302no—
176C22(C2×D3)⋊AGL(1,𝔽5)12yes—
177C22C2×D3×AGL(1,𝔽5)11yescharacteristic
178C4—51no—
179C4—51no—
180C4—52no—
181C4—62no—
182C3#6575511yescharacteristic, complemented, Sylow
183C2—22no—
184C2—304no—
185C2C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
186C2#9193112yes—
subgroupG/H
center, FrattiniC22C2×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C22×C4
FittingC23×C3×C5C2×C4
prime radicalC23×D15C4
cosocleC2×C3×Dic5C23
hypercenterC23D3×AGL(1,𝔽5)
hypocenterC3×C5#407
LCSG ▷ C22×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. #91171C2semidirect
14. C2×C3⋊#170C22semidirect
16. C2×C3×#170C22semidirect
20. C2×#704D3semidirect
51. C2×#170C2×D3semidirect
59. C2×D15M16semidirect
135. C3×C5#407semidirect
170. C5#5126semidirect
182. C3#65755semidirect

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
#911712
#657553
#51265