Finite Group Databasebeta

← #11752645

Subgroups — #11752645

Order 960.

456 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 144 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
1C4×D60C211yesmaximal, characteristic
2C4×C5×Dic6C211yesmaximal, characteristic, complemented
3C3×#4015C211yesmaximal, characteristic, complemented
4#91437C212yesmaximal, complemented
5#91428C212yesmaximal
6#91411C214yesmaximal, complemented
7#91383C212yesmaximal, complemented
8#91381C212yesmaximal, complemented
9#65913—31nomaximal, Hall
10C2×D60C2211yescharacteristic
11C2×C4×D15C2212yes—
12C2×C5×Dic6C2211yescharacteristic
13C2×C3×Dic10C2212yes—
14C2×#1200C2214yes—
15C3×C42×C5C2211yescharacteristic
16#6714C2212yes—
17C4⋊Dic15C2211yescharacteristic
18C5×C4⋊Dic3C2211yescharacteristic
19C5×Dic3⋊C4C2212yes—
20C4×C5×Dic3C2212yes—
21C3×C4⋊Dic5C2212yes—
22C3×C4⋊Dic5C2212yes—
23#6669C2214yes—
24#6668C2214yes—
25#6667C2214yes—
26#5730—51nomaximal, Hall
27C4×C5×Q8—31no—
28#4092—32no—
29#4042—34no—
30D5×C4⋊C4—32no—
31C4×D20—31no—
32C4×D20—32no—
33#4016—32no—
34#4015D311yescharacteristic, complemented
35C22×D15C2312yes—
36C2×C3×C4×C5C2311yescharacteristic
37C2×C3×C4×C5C2311yescharacteristic
38C2×C3×C4×C5C2311yescharacteristic
39C2×Dic15C2312yes—
40D60Q814yescomplemented
41C4×D15—24no—
42C2×C5×Dic3C2312yes—
43C2×C5×Dic3C2312yes—
44C5×Dic6—22no—
45C2×C3×Dic5C2314yes—
46C3×Dic10—42no—
47#1200—44no—
48C3×C4⋊Q8—51no—
49#946—54no—
50#897—52no—
51#893—52no—
52D3×C4⋊C4—52no—
53#890—52no—
54C4×D12—51no—
55C4×Dic6D511yescharacteristic, complemented
56C2×C5×Q8—31no—
57C2×D20—31no—
58C2×C4×D5—32no—
59C2×C4×D5—34no—
60C2×Dic10C2×D312yes—
61C5×C4⋊C4—32no—
62C5×C4⋊C4—31no—
63C42×C5—32no—
64C42×C5C2×D311yescharacteristic
65#685—32no—
66#685—34no—
67C4⋊Dic5—31no—
68C4⋊Dic5C2×D312yes—
69C4⋊Dic5C2×D312yes—
70#683—34no—
71#683—34no—
72#554—151noSylow
73C22×C3×C5C2411yescharacteristic
74C2×D15—22no—
75C2×D15—22no—
76C2×D15C2×Q814yes—
77C3×C4×C5—21no—
78C3×C4×C5C2×Q812yes—
79C3×C4×C5#4112yes—
80Dic15—22no—
81C3×Dic5—24no—
82C5×Dic3—22no—
83C5×Dic3—22no—
84C2×C3×Q8—52no—
85C2×D12—51no—
86C2×C4×D3—52no—
87C2×C4×D3—54no—
88C2×Dic6C2×D511yescharacteristic
89C3×C4⋊C4—52no—
90C3×C4⋊C4—52no—
91C3×C42C2×D511yescharacteristic
92(C2×D3)⋊C4—52no—
93(C2×D3)⋊C4—54no—
94C4⋊Dic3—51no—
95C4⋊Dic3—54no—
96C4⋊Dic3C2×D511yescharacteristic
97Dic3⋊C4—54no—
98Dic3⋊C4C2×D512yes—
99C4×Dic3C2×D512yes—
100C22×D5—32no—
101C5×Q8—62no—
102C2×C4×C5—32no—
103C2×C4×C5—32no—
104C2×C4×C5C22×D311yescharacteristic
105C2×C4×C5C22×D311yescharacteristic
106C2×C4×C5C22×D311yescharacteristic
107C2×Dic5—32no—
108C2×Dic5C22×D314yes—
109D20—34no—
110C4×D5—64no—
111C4×D5—124no—
112Dic10—42no—
113C4⋊Q8—51no—
114#125—152no—
115C22⋊Q8—154no—
116C22⋊Q8—152no—
117C4×Q8—31no—
118C4×D4—152no—
119C4×D4—151no—
120C2×C4⋊C4—152no—
121C2×C3×C5C22×Q811yescharacteristic
122C2×C3×C5C2×#4111yescharacteristic
123C2×C3×C5H(5,𝔽2)11yescharacteristic
124D15—24no—
125C22×D3—52no—
126C3×Q8—202no—
127C2×C3×C4—54no—
128C2×C3×C4C22×D511yescharacteristic
129C2×C3×C4C22×D511yescharacteristic
130C2×C3×C4C22×D511yescharacteristic
131C2×Dic3—52no—
132C2×Dic3C22×D512yes—
133C2×Dic3C22×D512yes—
134D12—54no—
135C4×D3—104no—
136C4×D3—204no—
137Dic6—22no—
138C22×C5C23×D311yescharacteristic
139C2×D5—34no—
140C2×D5—62no—
141C2×D5—62no—
142C4×C5—21no—
143C4×C5—62no—
144C4×C5—62no—
145C4×C5D3×Q812yes—
146C4×C5#23912yes—
147Dic5—24no—
148Dic5—62no—
149C2×Q8—31no—
150C2×Q8—52no—
151C2×D4—151no—
152C22×C4—154no—
153C22×C4—152no—
154C4⋊C4—31no—
155C4⋊C4—32no—
156C4⋊C4—52no—
157C4⋊C4—52no—
158C4⋊C4—154no—
159C4⋊C4—154no—
160C4⋊C4—151no—
161C22⋊C4—154no—
162C22⋊C4—152no—
163C42—32no—
164C42D3×D511yescharacteristic
165C3×C5#55411yescharacteristic, complemented, Hall
166C22×C3C23×D511yescharacteristic
167C2×D3—54no—
168C2×D3—102no—
169C2×D3—102no—
170C3×C4—21no—
171C3×C4—104no—
172C3×C4#70912yes—
173C3×C4Q8×D512yes—
174Dic3—22no—
175Dic3—22no—
176Dic3—102no—
177C2×C5#100411yescharacteristic
178C2×C5C2×D3×Q811yescharacteristic
179C2×C5C2×#23911yescharacteristic
180D5—64no—
181C23—152no—
182Q8—62no—
183Q8—202no—
184D4—154no—
185C2×C4—32no—
186C2×C4—32no—
187C2×C4—54no—
188C2×C4—152no—
189C2×C4—304no—
190C2×C4—604no—
191C2×C4C2×D3×D511yescharacteristic
192C2×C4C2×D3×D511yescharacteristic
193C2×C4C2×D3×D511yescharacteristic
194C2×C3C2×#70911yescharacteristic
195C2×C3C2×Q8×D511yescharacteristic
196C2×C3#414911yescharacteristic
197D3—104no—
198C5#573011yescharacteristic, complemented, Sylow
199C22—154no—
200C22—302no—
201C22—302no—
202C22C22×D3×D511yescharacteristic
203C4—21no—
204C4—62no—
205C4—62no—
206C4—104no—
207C4—302no—
208C4#676912yes—
209C4D15⋊Q812yes—
210C3#6591311yescharacteristic, complemented, Sylow
211C2—304no—
212C2C2×#676911yescharacteristic
213C2C2×D15⋊Q811yescharacteristic
214C2#9201711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
prime radicalC2×D60C22
hypercenterC42D3×D5
hypocenterC3×C5#554
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×C5×Dic6C2semidirect
3. C3×#4015C2semidirect
4. #91437C2semidirect
6. #91411C2semidirect
7. #91383C2semidirect
8. #91381C2semidirect
34. #4015D3semidirect
40. D60Q8semidirect
55. C4×Dic6D5semidirect
165. C3×C5#554semidirect
198. C5#5730semidirect
210. C3#65913semidirect

Maximal subgroups

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

subgroupindex
C4×D602
C4×C5×Dic62
C3×#40152
#914372
#914282
#914112
#913832
#913812
#659133
#57305