Finite Group Databasebeta

← D15×#208 #13087346

Subgroups — D15×#208 #13087346

Order 1440.

292 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×C3×C4×D15C211yesmaximal, characteristic
2#10623904C211yesmaximal, characteristic, complemented
3C3×C5×#208C211yesmaximal, characteristic, complemented
4#10623795C212yesmaximal, complemented
5C3⋊C8×D15C212yesmaximal, complemented
6M16×D15—31nomaximal
7D5×#208—31nomaximal
8C22×C3×D15C411yescharacteristic
9C2×C32×C4×C5C2211yescharacteristic
10C2×C3×Dic15C411yescharacteristic
11C3×C4×D15C411yescharacteristic
12C3×C4×D15C411yescharacteristic
13C3×C4×D15C2211yescharacteristic
14C3×C4×D15C2211yescharacteristic
15C3⋊(C3⋊#168)C2212yescomplemented
16C3×C5×C3⋊C8C2212yescomplemented
17D3×#208—51nomaximal, Hall
18C2×C4×D15D311yescharacteristic
19C2×C3×C4×D5—31no—
20C3×C5×M16—31no—
21#6710—31no—
22#6710—31no—
23#6710—61no—
24#6705—32no—
25C8×D15—32no—
26C5×#208D311yescharacteristic, complemented
27#6649—32no—
28D5×C3⋊C8—32no—
29C22×C32×C5C2×C411yescharacteristic
30C2×C3×D15—22no—
31C2×C3×D15C2×C411yescharacteristic
32C2×C3×D15C2×C411yescharacteristic
33C32×C4×C5C2×C411yescharacteristic
34C32×C4×C5C2311yescharacteristic
35C3×Dic15C2×C411yescharacteristic
36C3×Dic15C2×C411yescharacteristic
37D5×M16—91noHall
38C2×C3×C4×D3—51no—
39#3748—51no—
40C3×#208D511yescharacteristic, complemented
41#3711—52no—
42D3×C3⋊C8—52no—
43C22×D15Dic311yescharacteristic
44C22×C3×D5—31no—
45C2×C3×C4×C5—21no—
46C2×C3×C4×C5C2×D311yescharacteristic
47C2×C3×C4×C5C2×D311yescharacteristic
48C2×Dic15Dic311yescharacteristic
49C4×D15Dic311yescharacteristic
50C4×D15Dic311yescharacteristic
51C4×D15C2×D311yescharacteristic
52C4×D15C2×D311yescharacteristic
53C2×C3×Dic5—31no—
54C3×C4×D5—31no—
55C3×C4×D5—31no—
56C3×C4×D5—31no—
57C3×C4×D5—31no—
58C3×C5×C8—32no—
59C3⋊#168—32no—
60C3⋊#168—32no—
61C3⋊#168—62no—
62C5×C3⋊C8C2×D312yescomplemented
63C2×#208—151no—
64D3×M16—151no—
65C2×C32×C5—21no—
66C2×C32×C5C22×C411yescharacteristic
67C3×D15—21no—
68C3×D15M1612yescomplemented
69C2×C4×D5—31no—
70C5×M16—31no—
71#681—91no—
72#676—92no—
73C8×D5—92no—
74C22×C3×D3—51no—
75C2×C32×C4C2×D511yescharacteristic
76C2×C3×Dic3—51no—
77C3×C4×D3—51no—
78C3×C4×D3—51no—
79C3×C4×D3—51no—
80C3×C4×D3—51no—
81C3⋊(C3⋊C8)—52no—
82C3×C3⋊C8C2×D512yescomplemented
83C22×C3×C5—21no—
84C22×C3×C5C4×D311yescharacteristic
85C22×C3×C5C2×Dic311yescharacteristic
86C2×D15—22no—
87C2×D15C2×Dic311yescharacteristic
88C2×D15C2×Dic311yescharacteristic
89C2×C3×D5—31no—
90C2×C3×D5—31no—
91C2×C3×D5—62no—
92C3×C4×C5—21no—
93C3×C4×C5—21no—
94C3×C4×C5C4×D311yescharacteristic
95C3×C4×C5C2×Dic311yescharacteristic
96C3×C4×C5C22×D311yescharacteristic
97C3×C4×C5C22×D311yescharacteristic
98Dic15C2×Dic311yescharacteristic
99Dic15C2×Dic311yescharacteristic
100C3×Dic5—31no—
101C3×Dic5—31no—
102C22×C3×C4—151no—
103C2×C4×D3—51no—
104C3×M16—31no—
105#208—151no—
106#208—151no—
107#208—152no—
108#208—301no—
109#208D1511yescharacteristic, direct product factor
110C2×C3⋊C8—152no—
111ΓL(1,𝔽25)—152no—
112D3×C8—152no—
113C32×C5C2×M1611yescharacteristic, complemented, Hall
114C22×D5—31no—
115C2×C4×C5D3211yescharacteristic
116C2×Dic5—31no—
117C4×D5—31no—
118C4×D5—31no—
119C4×D5—31no—
120C4×D5—31no—
121C5×C8—32no—
122#168—92no—
123C22×C32C4×D511yescharacteristic
124C2×C3×D3—51no—
125C2×C3×D3—51no—
126C2×C3×D3—102no—
127C32×C4C4×D511yescharacteristic
128C32×C4C22×D511yescharacteristic
129C3×Dic3—51no—
130C3×Dic3—51no—
131C2×M16—451noSylow
132C2×C3×C5—21no—
133C2×C3×C5—21no—
134C2×C3×C5—21no—
135C2×C3×C5—41no—
136C2×C3×C5C2×C4×D311yescharacteristic
137C2×C3×C5C22×Dic311yescharacteristic
138D15—21no—
139D15#20812yesdirect product factor
140C3×D5—32no—
141C3×D5—61no—
142C23×C3—151no—
143C22×D3—51no—
144C2×C3×C4—21no—
145C2×C3×C4—151no—
146C2×C3×C4—151no—
147C2×C3×C4—151no—
148C2×C3×C4—151no—
149C2×C3×C4—151no—
150C2×C3×C4D3×D511yescharacteristic
151C2×C3×C4C2×D1511yescharacteristic
152C2×Dic3—51no—
153C4×D3—51no—
154C4×D3—51no—
155C4×D3—51no—
156C4×D3—51no—
157C3×C8—32no—
158C3⋊C8—152no—
159C3⋊C8—152no—
160C3⋊C8—302no—
161C3⋊C8C2×D1512yescomplemented
162C22×C5D3×Dic311yescharacteristic
163C2×D5—31no—
164C2×D5—31no—
165C2×D5—62no—
166C4×C5D3×Dic311yescharacteristic
167C4×C5C2×D3211yescharacteristic
168Dic5—31no—
169Dic5—31no—
170C2×C32—21no—
171C2×C32C2×C4×D511yescharacteristic
172C3×D3—52no—
173C3×D3—101no—
174C22×C4—151no—
175M16—31no—
176M16—452no—
177M16—451no—
178C2×C8—452no—
179C3×C5—21no—
180C3×C5D3×M1611yescharacteristic, complemented
181C3×C5C2×#20811yescharacteristic, complemented
182C22×C3—21no—
183C22×C3—151no—
184C22×C3—151no—
185C22×C3—302no—
186C22×C3D5×Dic311yescharacteristic
187C22×C3C4×D1511yescharacteristic
188C2×D3—51no—
189C2×D3—51no—
190C2×D3—102no—
191C3×C4—21no—
192C3×C4—21no—
193C3×C4—151no—
194C3×C4—151no—
195C3×C4D5×Dic311yescharacteristic
196C3×C4C4×D1511yescharacteristic
197C3×C4C2×D3×D511yescharacteristic
198C3×C4C22×D1511yescharacteristic
199Dic3—51no—
200Dic3—51no—
201C2×C5—21no—
202C2×C5C2×D3×Dic311yescharacteristic
203D5—32no—
204D5—61no—
205C32D5×M1611yescharacteristic, complemented, Sylow
206C23—151no—
207C2×C4—151no—
208C2×C4—151no—
209C2×C4—151no—
210C2×C4—151no—
211C2×C4—151no—
212C2×C4D3×D1511yescharacteristic
213C8—32no—
214C8—452no—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—41no—
219C2×C3—152no—
220C2×C3—301no—
221C2×C3C2×D5×Dic311yescharacteristic
222C2×C3C2×C4×D1511yescharacteristic
223D3—52no—
224D3—101no—
225C5D3×#20811yescharacteristic, complemented, Sylow
226C22—151no—
227C22—151no—
228C22—302no—
229C22Dic3×D1511yescharacteristic
230C4—151no—
231C4—151no—
232C4Dic3×D1511yescharacteristic
233C4C2×D3×D1511yescharacteristic
234C3—21no—
235C3D5×#20811yescharacteristic, complemented
236C3M16×D1511yescharacteristic, complemented
237C2—21no—
238C2—152no—
239C2—301no—
240C2C2×Dic3×D1511yescharacteristic
subgroupG/H
center, FrattiniC4C2×D3×D15
commutator, socleC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
prime radicalC22×C3×D15C4
cosocleC32×C4×C5C23
hypercenterC2×C4D3×D15
hypocenterC32×C5C2×M16
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #10623904C2semidirect
3. C3×C5×#208C2semidirect
4. #10623795C2semidirect
5. C3⋊C8×D15C2semidirect
15. C3⋊(C3⋊#168)C22semidirect
16. C3×C5×C3⋊C8C22semidirect
26. C5×#208D3semidirect
40. C3×#208D5semidirect
62. C5×C3⋊C8C2×D3semidirect
68. C3×D15M16semidirect
82. C3×C3⋊C8C2×D5semidirect
109. #208D15direct (N × H)
113. C32×C5C2×M16semidirect
139. D15#208direct (N × H)
161. C3⋊C8C2×D15semidirect
180. C3×C5D3×M16semidirect
181. C3×C5C2×#208semidirect
205. C32D5×M16semidirect
225. C5D3×#208semidirect
235. C3D5×#208semidirect
236. C3M16×D15semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D152
#106239042
C3×C5×#2082
#106237952
C3⋊C8×D152
M16×D153
D5×#2083
D3×#2085