Finite Group Databasebeta

← D15⋊#11759816 #44478138

Subgroups — D15⋊#11759816 #44478138

Order 30420.

256 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 35 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
1D15×#92789C211yesmaximal, characteristic, complemented
2C5×C3⋊#11759816C211yesmaximal, characteristic, complemented
3C3×C5⋊#11759816C211yesmaximal, characteristic, complemented
4D15⋊(C13⋊D13)C311yesmaximal, characteristic, complemented
5D5×#11759816—31nomaximal
6C3×C5×#92789C2211yescharacteristic, complemented, Hall
7D3×#11759816—51nomaximal, Hall
8C132×D15C2×C311yescharacteristic, complemented
9C5×C3⋊(C13⋊D13)C2×C311yescharacteristic, complemented
10C3×C5⋊(C13⋊D13)C2×C311yescharacteristic, complemented
11D5×#92789—31no—
12C5⋊#11759816—21no—
13C5⋊#11759816D311yescharacteristic, complemented
14C5×#11759816—31no—
15D5×C13⋊D13—31noHall
16D3×#92789—51no—
17C3⋊#11759816D511yescharacteristic, complemented
18C3×#11759816—51no—
19C5×#92789—21no—
20C5×#92789C2×D311yescharacteristic, complemented
21C3×C5×C132C22×C311yescharacteristic, complemented
22D15⋊(D13⋊C3)—131nomaximal
23D15⋊(D13⋊C3)—131nomaximal
24D3×C13⋊D13—51no—
25C2×#11759816—151no—
26C5⋊(C13⋊D13)C3×D311yescharacteristic, complemented
27D5×C132—31no—
28C5×C13⋊D13—31no—
29C3×#92789C2×D511yescharacteristic, complemented, Hall
30D15×C13⋊C3—261no—
31D15×C13⋊C3—261no—
32C5×C3⋊(D13⋊C3)—131no—
33C5×C3⋊(D13⋊C3)—131no—
34C3×C5⋊(D13⋊C3)—131no—
35C3×C5⋊(D13⋊C3)—131no—
36C3⋊(C13⋊D13)C3×D511yescharacteristic, complemented
37D3×C132—51no—
38C3×C13⋊D13—51no—
39C2×#92789—151no—
40#11759816—31no—
41#11759816—51no—
42#11759816—101no—
43C5×C132C2×C3×D311yescharacteristic, complemented, Hall
44D15⋊D13—131no—
45D15⋊D13—131no—
46D15⋊D13—394no—
47D5×D13⋊C3—391no—
48D5×D13⋊C3—391no—
49C2×C13⋊D13—151noHall
50C3×C5×C13⋊C3—261no—
51C3×C5×C13⋊C3—261no—
52C3×C132C2×C3×D511yescharacteristic, complemented
53#92789—21no—
54#92789D3×D511yescharacteristic, complemented
55D3×D13⋊C3—651no—
56D3×D13⋊C3—651no—
57C13×D15—34no—
58C13×D15D13⋊C311yescharacteristic, complemented
59C13×D15D13⋊C311yescharacteristic, complemented
60C5×D39—131no—
61C5×D39—131no—
62C5×D39—394no—
63C3×D65—131no—
64C3×D65—131no—
65C3×D65—394no—
66C5⋊(D13⋊C3)—131no—
67C5⋊(D13⋊C3)—131no—
68C5⋊(D13⋊C3)—261no—
69C5⋊(D13⋊C3)—261no—
70D5×C13⋊C3—391no—
71D5×C13⋊C3—781no—
72C5×D13⋊C3—391no—
73C5×D13⋊C3—391no—
74C2×C132—151no—
75C13⋊D13—31no—
76C13⋊D13—51no—
77D5×D13—391no—
78D5×D13—391no—
79D5×D13—1174no—
80C3⋊(D13⋊C3)—131no—
81C3⋊(D13⋊C3)—131no—
82D3×C13⋊C3—1301no—
83D3×C13⋊C3—1301no—
84C3×D13⋊C3—651no—
85C3×D13⋊C3—651no—
86C3×C5×C13—34no—
87C3×C5×C13C2×D13⋊C311yescharacteristic, complemented
88C3×C5×C13C2×D13⋊C311yescharacteristic, complemented
89C5×C13⋊C3—131no—
90C5×C13⋊C3—261no—
91C5×C13⋊C3—261no—
92C5×C13⋊C3—521no—
93C3×D3×D5—1691noHall
94C132C3×D3×D511yescharacteristic, complemented, Sylow
95D3×D13—651no—
96D3×D13—651no—
97D3×D13—1954no—
98C2×D13⋊C3—1951no—
99C2×D13⋊C3—1951no—
100D65—131no—
101D65—131no—
102D65—394no—
103C5×D13—391no—
104C5×D13—391no—
105C5×D13—1174no—
106D5×C13—31no—
107D5×C13—31no—
108D5×C13—94no—
109C3×C13⋊C3—261no—
110C3×C13⋊C3—261no—
111C3×D15—3381no—
112C3×C5×D3—1691no—
113C32×D5—1691no—
114D39—131no—
115D39—131no—
116D39—394no—
117C3×D13—651no—
118C3×D13—651no—
119C3×D13—1954no—
120D3×C13—51no—
121D3×C13—51no—
122D3×C13—154no—
123C2×C13⋊C3—3901no—
124C2×C13⋊C3—1951no—
125D13⋊C3—391no—
126D13⋊C3—391no—
127D13⋊C3—651no—
128D13⋊C3—651no—
129D13⋊C3—1301no—
130D13⋊C3—1301no—
131C5×C13—34no—
132C5×C13D3×D13⋊C311yescharacteristic, complemented
133C5×C13D3×D13⋊C311yescharacteristic, complemented
134C2×C3×D5—5071no—
135D3×D5—1691no—
136C2×D13—5854no—
137C2×D13—1951no—
138C2×D13—1951no—
139C32×C5—3381noHall
140C3×C13—34no—
141C3×C13D5×D13⋊C311yescharacteristic, complemented
142C3×C13D5×D13⋊C311yescharacteristic, complemented
143C13⋊C3—131no—
144C13⋊C3—261no—
145C13⋊C3—261no—
146C13⋊C3—521no—
147C2×C3×D3—8451noHall
148C2×C3×C5—5071no—
149D15#1175981611yescharacteristic, complemented
150C3×D5—3381no—
151C3×D5—1691no—
152C3×D5—1691no—
153C3×D5—10141no—
154C5×D3—1691no—
155C2×C13—151no—
156C2×C13—151no—
157C2×C13—454no—
158D13—391no—
159D13—391no—
160D13—651no—
161D13—651no—
162D13—1174no—
163D13—1954no—
164C2×D5—5071noHall
165C2×C32—8451no—
166C3×D3—16901no—
167C3×D3—1691no—
168C3×C5—3381no—
169C3×C5—6761no—
170C3×C5C2×#1175981611yescharacteristic, complemented
171C13—34no—
172C13D15⋊(D13⋊C3)11yescharacteristic, complemented
173C13D15⋊(D13⋊C3)11yescharacteristic, complemented
174C22×C3—25351no—
175C2×D3—8451no—
176C2×C5—5071no—
177D5—31no—
178D5—1691no—
179C32—3381noSylow
180C2×C3—8451no—
181C2×C3—8451no—
182C2×C3—16901no—
183C2×C3—50701no—
184C2×C3—5071no—
185D3—51no—
186D3—1691no—
187C5D3×#1175981611yescharacteristic, complemented, Sylow
188C22—25351noSylow
189C3—3381no—
190C3—6761no—
191C3D5×#1175981611yescharacteristic, complemented
192C2—151no—
193C2—8451no—
194C2—5071no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C132C22×C3
LCSG ▷ C3×C5×C132
UCSC1

Complements

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

NH ≅ G/Ntype
1. D15×#92789C2semidirect
2. C5×C3⋊#11759816C2semidirect
3. C3×C5⋊#11759816C2semidirect
4. D15⋊(C13⋊D13)C3semidirect
6. C3×C5×#92789C22semidirect
8. C132×D15C2×C3semidirect
9. C5×C3⋊(C13⋊D13)C2×C3semidirect
10. C3×C5⋊(C13⋊D13)C2×C3semidirect
13. C5⋊#11759816D3semidirect
17. C3⋊#11759816D5semidirect
20. C5×#92789C2×D3semidirect
21. C3×C5×C132C22×C3semidirect
26. C5⋊(C13⋊D13)C3×D3semidirect
29. C3×#92789C2×D5semidirect
36. C3⋊(C13⋊D13)C3×D5semidirect
43. C5×C132C2×C3×D3semidirect
52. C3×C132C2×C3×D5semidirect
54. #92789D3×D5semidirect
58. C13×D15D13⋊C3semidirect
59. C13×D15D13⋊C3semidirect
87. C3×C5×C13C2×D13⋊C3semidirect
88. C3×C5×C13C2×D13⋊C3semidirect
94. C132C3×D3×D5semidirect
132. C5×C13D3×D13⋊C3semidirect
133. C5×C13D3×D13⋊C3semidirect
141. C3×C13D5×D13⋊C3semidirect
142. C3×C13D5×D13⋊C3semidirect
149. D15#11759816semidirect
170. C3×C5C2×#11759816semidirect
172. C13D15⋊(D13⋊C3)semidirect
173. C13D15⋊(D13⋊C3)semidirect
187. C5D3×#11759816semidirect
191. C3D5×#11759816semidirect

Maximal subgroups

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

subgroupindex
D15×#927892
C5×C3⋊#117598162
C3×C5⋊#117598162
D15⋊(C13⋊D13)3
D5×#117598163
D3×#117598165
D15⋊(D13⋊C3)13