Finite Group Databasebeta

← D5×#830 #11748481

Subgroups — D5×#830 #11748481

Order 960.

404 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 132 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×C3×C4×D5C211yesmaximal, characteristic
2C2×D5×C3⋊C8C212yesmaximal, complemented
3#91114C211yesmaximal, characteristic, complemented
4C5×#830C211yesmaximal, characteristic, complemented
5#90955C212yesmaximal, complemented
6D5×C22⋊C8—31nomaximal, Hall
7C23×C3×D5C411yescharacteristic
8C22×C3×C4×C5C2211yescharacteristic
9C22×C3×Dic5C411yescharacteristic
10C2×C3×C4×D5—24no—
11C2×C3×C4×D5C411yescharacteristic
12C2×C3×C4×D5C411yescharacteristic
13C2×C3×C4×D5C2211yescharacteristic
14C2×C3×C4×D5C2211yescharacteristic
15C2×C3⋊#168C2212yescomplemented
16C2×C5×C3⋊C8C2212yescomplemented
17D5×C3⋊C8—24no—
18C2×#830—51nomaximal, Hall
19C22×C4×D5D311yescharacteristic
20C2×C8×D5—32no—
21C5×C22⋊C8—31no—
22C22⋊#168—31no—
23#3952—32no—
24C23×C3×C5C2×C411yescharacteristic
25C22×C3×D5—22no—
26C22×C3×D5—22no—
27C22×C3×D5C814yescomplemented
28C22×C3×D5C2×C411yescharacteristic
29C22×C3×D5C2×C411yescharacteristic
30C2×C3×C4×C5—22no—
31C2×C3×C4×C5C2×C411yescharacteristic
32C2×C3×C4×C5C2311yescharacteristic
33C2×C3×Dic5—22no—
34C2×C3×Dic5C2×C411yescharacteristic
35C2×C3×Dic5C2×C411yescharacteristic
36C3×C4×D5—22no—
37C3×C4×D5—22no—
38C3×C4×D5—22no—
39C3×C4×D5D414yes—
40C3⋊#168—22no—
41C5×C3⋊C8—22no—
42C23×C3×C4—51no—
43C22×C3⋊C8—52no—
44#830—51no—
45#830—52no—
46#830D511yescharacteristic, direct product factor
47C23×D5Dic311yescharacteristic
48C22×C4×C5C2×D311yescharacteristic
49C22×Dic5Dic311yescharacteristic
50C2×C4×D5—24no—
51C2×C4×D5Dic311yescharacteristic
52C2×C4×D5Dic311yescharacteristic
53C2×C4×D5C2×D311yescharacteristic
54C2×C4×D5C2×D311yescharacteristic
55C2×C5×C8—32no—
56C2×#168—32no—
57C8×D5—64no—
58C2×C22⋊C8—151noSylow
59C22×C3×C5—21no—
60C22×C3×C5—21no—
61C22×C3×C5C2×C812yescomplemented
62C22×C3×C5C22×C411yescharacteristic
63C2×C3×D5—21no—
64C2×C3×D5—21no—
65C2×C3×D5—28no—
66C2×C3×D5C22⋊C412yes—
67C2×C3×D5C2×C812yes—
68C2×C3×D5C2×C812yescomplemented
69C2×C3×D5M1612yes—
70C3×C4×C5—21no—
71C3×C4×C5C2×D412yes—
72C3×Dic5—21no—
73C3×Dic5C22⋊C412yes—
74C24×C3—51no—
75C22×C3×C4—51no—
76C22×C3×C4—51no—
77C22×C3×C4—51no—
78C22×C3×C4—51no—
79C22×C3×C4—51no—
80C22×C3×C4—104no—
81C22×C3×C4C2×D511yescharacteristic
82C2×C3⋊C8—52no—
83C2×C3⋊C8—104no—
84C2×C3⋊C8C2×D512yescomplemented
85C23×C5C2×Dic311yescharacteristic
86C22×D5—22no—
87C22×D5—22no—
88C22×D5C3⋊C814yescomplemented
89C22×D5C2×Dic311yescharacteristic
90C22×D5C2×Dic311yescharacteristic
91C2×C4×C5—22no—
92C2×C4×C5C2×Dic311yescharacteristic
93C2×C4×C5C22×D311yescharacteristic
94C2×Dic5—22no—
95C2×Dic5C2×Dic311yescharacteristic
96C2×Dic5C2×Dic311yescharacteristic
97C4×D5—22no—
98C4×D5—22no—
99C4×D5—22no—
100C4×D5#6714yes—
101C5×C8—62no—
102#168—62no—
103C23×C4—51no—
104C22×C8—152no—
105C22⋊C8—31no—
106C22⋊C8—152no—
107C22⋊C8—151no—
108C2×C3×C5—22no—
109C2×C3×C5C2×C22⋊C411yescharacteristic
110C2×C3×C5C22×C811yescharacteristic
111C2×C3×C5C2×M1611yescharacteristic
112C3×D5—22no—
113C3×D5C22⋊C814yescomplemented
114C23×C3—51no—
115C23×C3—54no—
116C23×C3—51no—
117C23×C3—102no—
118C23×C3—102no—
119C23×C3C4×D511yescharacteristic
120C2×C3×C4—22no—
121C2×C3×C4—51no—
122C2×C3×C4—54no—
123C2×C3×C4—51no—
124C2×C3×C4—102no—
125C2×C3×C4—102no—
126C2×C3×C4—102no—
127C2×C3×C4—102no—
128C2×C3×C4C4×D511yescharacteristic
129C2×C3×C4C22×D511yescharacteristic
130C3⋊C8—22no—
131C3⋊C8—102no—
132C22×C5—21no—
133C22×C5—21no—
134C22×C5C2×C3⋊C812yescomplemented
135C22×C5C22×Dic311yescharacteristic
136C2×D5—21no—
137C2×D5—21no—
138C2×D5—28no—
139C2×D5C2×C3⋊C812yes—
140C2×D5C2×C3⋊C812yescomplemented
141C2×D5#20812yes—
142C2×D5#21712yes—
143C4×C5—21no—
144C4×C5C2×#6712yes—
145Dic5—21no—
146Dic5#21712yes—
147C24—51no—
148C22×C4—51no—
149C22×C4—51no—
150C22×C4—51no—
151C22×C4—51no—
152C22×C4—51no—
153C22×C4—104no—
154C22×C4D3×D511yescharacteristic
155C2×C8—32no—
156C2×C8—152no—
157C2×C8—304no—
158C3×C5C2×C22⋊C811yescharacteristic, complemented, Hall
159C22×C3—21no—
160C22×C3—21no—
161C22×C3—52no—
162C22×C3—52no—
163C22×C3—52no—
164C22×C3—52no—
165C22×C3—108no—
166C22×C3—101no—
167C22×C3—101no—
168C22×C3C8×D512yescomplemented
169C22×C3C2×C4×D511yescharacteristic
170C3×C4—21no—
171C3×C4—52no—
172C3×C4—101no—
173C3×C4D4×D512yes—
174C2×C5—22no—
175C2×C5C22×C3⋊C811yescharacteristic
176C2×C5C2×#20811yescharacteristic
177C2×C5C2×#21711yescharacteristic
178D5—22no—
179D5#83014yesdirect product factor
180C23—51no—
181C23—51no—
182C23—54no—
183C23—102no—
184C23—102no—
185C23D5×Dic311yescharacteristic
186C2×C4—22no—
187C2×C4—51no—
188C2×C4—54no—
189C2×C4—51no—
190C2×C4—102no—
191C2×C4—102no—
192C2×C4—102no—
193C2×C4—102no—
194C2×C4D5×Dic311yescharacteristic
195C2×C4C2×D3×D511yescharacteristic
196C8—62no—
197C8—302no—
198C2×C3—22no—
199C2×C3—54no—
200C2×C3—102no—
201C2×C3D5×C22⋊C411yescharacteristic
202C2×C3C2×C8×D511yescharacteristic
203C2×C3D5×M1611yescharacteristic
204C5C2×#83011yescharacteristic, complemented, Sylow
205C22—21no—
206C22—21no—
207C22—52no—
208C22—52no—
209C22—52no—
210C22—52no—
211C22—108no—
212C22—101no—
213C22—101no—
214C22D5×C3⋊C812yescomplemented
215C22C2×D5×Dic311yescharacteristic
216C4—21no—
217C4—52no—
218C4—101no—
219C4D5×#6712yes—
220C3D5×C22⋊C811yescharacteristic, complemented, Sylow
221C2—22no—
222C2—54no—
223C2—102no—
224C2C2×D5×C3⋊C811yescharacteristic
225C2D5×#20811yescharacteristic
226C2D5×#21711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D3×D5
commutatorC2×C3×C5C22×C8
FittingC22×C3×C4×C5C22
socleC22×C3×C5C22×C4
prime radicalC23×C3×D5C4
cosocleC2×C3×C4×C5C23
hypercenterC22×C4D3×D5
hypocenterC3×C5C2×C22⋊C8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×D5×C3⋊C8C2semidirect
3. #91114C2semidirect
4. C5×#830C2semidirect
5. #90955C2semidirect
15. C2×C3⋊#168C22semidirect
16. C2×C5×C3⋊C8C22semidirect
27. C22×C3×D5C8semidirect
46. #830D5direct (N × H)
61. C22×C3×C5C2×C8semidirect
68. C2×C3×D5C2×C8semidirect
84. C2×C3⋊C8C2×D5semidirect
88. C22×D5C3⋊C8semidirect
113. C3×D5C22⋊C8semidirect
134. C22×C5C2×C3⋊C8semidirect
140. C2×D5C2×C3⋊C8semidirect
158. C3×C5C2×C22⋊C8semidirect
168. C22×C3C8×D5semidirect
179. D5#830direct (N × H)
204. C5C2×#830semidirect
214. C22D5×C3⋊C8semidirect
220. C3D5×C22⋊C8semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×D52
C2×D5×C3⋊C82
#911142
C5×#8302
#909552
D5×C22⋊C83
C2×#8305