Finite Group Databasebeta

← C5×D3×#11759818 #44478019

Subgroups — C5×D3×#11759818 #44478019

Order 30420.

192 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C5×D3×#92789C211yesmaximal, characteristic, complemented
2C5×C3⋊#11759818C211yesmaximal, characteristic, complemented
3C3×C5×#11759818C211yesmaximal, characteristic, complemented
4C5×D3×C13×D13C311yesmaximal, characteristic, complemented
5C2×C5×#11759818—31nomaximal
6C3×C5×#92789C2211yescharacteristic, complemented, Hall
7D3×#11759818C511yesmaximal, characteristic, direct product factor, Hall
8C5×C13×D39C2×C311yescharacteristic, complemented
9C5×D3×C132C2×C311yescharacteristic, complemented
10C3×C5×C13×D13C2×C311yescharacteristic, complemented
11C2×C5×#92789—31no—
12C5×#11759818—21no—
13C5×#11759818—31no—
14C5×#11759818D311yescharacteristic, direct product factor
15C2×C5×C13×D13—31noHall
16D3×#92789C2×C511yescharacteristic, complemented
17C3⋊#11759818C2×C511yescharacteristic, complemented
18C3×#11759818C2×C511yescharacteristic, complemented
19C5×#92789—21no—
20C5×#92789C2×D311yescharacteristic, complemented
21C3×C5×C132C22×C311yescharacteristic, complemented
22C2×C5×D3×C13⋊C3—131nomaximal
23C5×D3×D13⋊C3—131nomaximal
24D3×C13×D13C3×C511yescharacteristic, complemented
25C2×#11759818—31no—
26C2×C5×C132—31no—
27C5×C13×D13—31no—
28C5×C13×D13C3×D311yescharacteristic, complemented
29C3×#92789C22×C511yescharacteristic, complemented, Hall
30C2×C3×C5×C13⋊C3—131no—
31C5×C3⋊(D13⋊C3)—131no—
32C5×D3×C13⋊C3—131no—
33C5×D3×C13⋊C3—131no—
34C5×D3×C13⋊C3—131no—
35C3×C5×D13⋊C3—131no—
36C13×D39C2×C3×C511yescharacteristic, complemented
37D3×C132C2×C3×C511yescharacteristic, complemented
38C3×C13×D13C2×C3×C511yescharacteristic, complemented
39C2×#92789—31no—
40#11759818—21no—
41#11759818—31no—
42#11759818C5×D311yescharacteristic, direct product factor
43C5×C132C2×C3×D311yescharacteristic, complemented, Hall
44C2×C5×D3×C13—131no—
45C22×C5×C13⋊C3—391no—
46C5×D3×D13C13⋊C311yescharacteristic, complemented
47C2×C5×D13⋊C3—391no—
48C2×C13×D13—31noHall
49C3×C5×C13⋊C3—131no—
50C3×C5×C13⋊C3—131no—
51C3×C132C22×C3×C511yescharacteristic, complemented
52#92789—21no—
53#92789C2×C5×D311yescharacteristic, complemented
54C2×D3×C13⋊C3—131no—
55D3×D13⋊C3—131no—
56C2×C3×C5×C13—131no—
57C5×D39C2×C13⋊C311yescharacteristic, complemented
58C5×D3×C13—62no—
59C5×D3×C13—131no—
60C5×D3×C13D13⋊C311yescharacteristic, complemented
61C5×D3×C13C2×C13⋊C311yescharacteristic, complemented
62C3×C5×D13C2×C13⋊C311yescharacteristic, complemented
63C2×C5×C13⋊C3—131no—
64C2×C5×C13⋊C3—261no—
65C2×C5×C13⋊C3—391no—
66C2×C5×C13⋊C3—391no—
67C2×C5×C13⋊C3—391no—
68C5×D13⋊C3—131no—
69C5×D13⋊C3—261no—
70C5×D13⋊C3—391no—
71C2×C132—31no—
72C13×D13—31no—
73C13×D13C3×C5×D311yescharacteristic, complemented
74C22×C5×C13—391no—
75C2×C5×D13—31no—
76C2×C3×C13⋊C3—131no—
77C3⋊(D13⋊C3)—131no—
78D3×C13⋊C3—131no—
79D3×C13⋊C3—131no—
80D3×C13⋊C3—131no—
81C3×D13⋊C3—131no—
82C3×C5×C13—62no—
83C3×C5×C13C2×D13⋊C311yescharacteristic, complemented
84C3×C5×C13C22×C13⋊C311yescharacteristic, complemented
85C5×C13⋊C3—131no—
86C5×C13⋊C3—131no—
87C5×C13⋊C3—261no—
88C5×C13⋊C3—261no—
89C2×C3×C5×D3—1691noHall
90C132C2×C3×C5×D311yescharacteristic, complemented, Sylow
91C2×D3×C13—131no—
92C22×C13⋊C3—391no—
93D3×D13C5×C13⋊C311yescharacteristic, complemented
94C2×D13⋊C3—391no—
95C2×C5×C13—31no—
96C2×C5×C13—31no—
97C2×C5×C13—131no—
98C2×C5×C13—182no—
99C2×C5×C13—391no—
100C5×D13—31no—
101C5×D13D3×C13⋊C311yescharacteristic, complemented
102C3×C13⋊C3—131no—
103C3×C13⋊C3—131no—
104C2×C32×C5—1691no—
105C3×C5×D3—1691no—
106C3×C5×D3—1691no—
107C2×C3×C13—131no—
108D39C2×C5×C13⋊C311yescharacteristic, complemented
109C3×D13C2×C5×C13⋊C311yescharacteristic, complemented
110D3×C13—62no—
111D3×C13—131no—
112D3×C13C5×D13⋊C311yescharacteristic, complemented
113D3×C13C2×C5×C13⋊C311yescharacteristic, complemented
114C2×C13⋊C3—131no—
115C2×C13⋊C3—261no—
116C2×C13⋊C3—391no—
117C2×C13⋊C3—391no—
118C2×C13⋊C3—391no—
119D13⋊C3—131no—
120D13⋊C3—261no—
121D13⋊C3—391no—
122C5×C13—62no—
123C5×C13D3×D13⋊C311yescharacteristic, complemented
124C5×C13C2×D3×C13⋊C311yescharacteristic, complemented
125C22×C3×C5—5071no—
126C2×C5×D3—131no—
127C22×C13—391no—
128C2×D13—31no—
129C32×C5—1691noHall
130C3×C13—62no—
131C3×C13C2×C5×D13⋊C311yescharacteristic, complemented
132C3×C13C22×C5×C13⋊C311yescharacteristic, complemented
133C13⋊C3—131no—
134C13⋊C3—131no—
135C13⋊C3—261no—
136C13⋊C3—261no—
137C2×C3×D3—1691noHall
138C2×C3×C5—131no—
139C2×C3×C5—3381no—
140C2×C3×C5—1691no—
141C2×C3×C5—5071no—
142C2×C3×C5—5071no—
143C5×D3—131no—
144C5×D3#1175981811yescharacteristic, direct product factor
145C2×C13—31no—
146C2×C13—31no—
147C2×C13—131no—
148C2×C13—182no—
149C2×C13—391no—
150D13—31no—
151D13C5×D3×C13⋊C311yescharacteristic, complemented
152C22×C5—391noHall
153C2×C32—1691no—
154C3×D3—1691no—
155C3×D3—1691no—
156C3×C5—3381no—
157C3×C5—1691no—
158C3×C5C2×#1175981811yescharacteristic, complemented
159C13—62no—
160C13C5×D3×D13⋊C311yescharacteristic, complemented
161C13C2×C5×D3×C13⋊C311yescharacteristic, complemented
162C22×C3—5071no—
163C2×D3—131no—
164C2×C5—31no—
165C2×C5—131no—
166C2×C5—391no—
167C32—1691noSylow
168C2×C3—131no—
169C2×C3—3381no—
170C2×C3—1691no—
171C2×C3—5071no—
172C2×C3—5071no—
173D3—131no—
174D3C5×#1175981811yescharacteristic, direct product factor
175C5D3×#1175981811yescharacteristic, direct product factor, Sylow
176C22—391noSylow
177C3—3381no—
178C3—1691no—
179C3C2×C5×#1175981811yescharacteristic, complemented
180C2—31no—
181C2—131no—
182C2—391no—
subgroupG/H
center, hypercenterC5D3×#11759818
commutator, cosocle, hypocenterC3×C132C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C132C22×C3
LCSG ▷ C3×C132
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×D3×#92789C2semidirect
2. C5×C3⋊#11759818C2semidirect
3. C3×C5×#11759818C2semidirect
4. C5×D3×C13×D13C3semidirect
6. C3×C5×#92789C22semidirect
7. D3×#11759818C5direct (N × H)
8. C5×C13×D39C2×C3semidirect
9. C5×D3×C132C2×C3semidirect
10. C3×C5×C13×D13C2×C3semidirect
14. C5×#11759818D3direct (N × H)
16. D3×#92789C2×C5semidirect
17. C3⋊#11759818C2×C5semidirect
18. C3×#11759818C2×C5semidirect
20. C5×#92789C2×D3semidirect
21. C3×C5×C132C22×C3semidirect
24. D3×C13×D13C3×C5semidirect
28. C5×C13×D13C3×D3semidirect
29. C3×#92789C22×C5semidirect
36. C13×D39C2×C3×C5semidirect
37. D3×C132C2×C3×C5semidirect
38. C3×C13×D13C2×C3×C5semidirect
42. #11759818C5×D3direct (N × H)
43. C5×C132C2×C3×D3semidirect
46. C5×D3×D13C13⋊C3semidirect
51. C3×C132C22×C3×C5semidirect
53. #92789C2×C5×D3semidirect
57. C5×D39C2×C13⋊C3semidirect
60. C5×D3×C13D13⋊C3semidirect
61. C5×D3×C13C2×C13⋊C3semidirect
62. C3×C5×D13C2×C13⋊C3semidirect
73. C13×D13C3×C5×D3semidirect
83. C3×C5×C13C2×D13⋊C3semidirect
84. C3×C5×C13C22×C13⋊C3semidirect
90. C132C2×C3×C5×D3semidirect
93. D3×D13C5×C13⋊C3semidirect
101. C5×D13D3×C13⋊C3semidirect
108. D39C2×C5×C13⋊C3semidirect
109. C3×D13C2×C5×C13⋊C3semidirect
112. D3×C13C5×D13⋊C3semidirect
113. D3×C13C2×C5×C13⋊C3semidirect
123. C5×C13D3×D13⋊C3semidirect
124. C5×C13C2×D3×C13⋊C3semidirect
131. C3×C13C2×C5×D13⋊C3semidirect
132. C3×C13C22×C5×C13⋊C3semidirect
144. C5×D3#11759818direct (N × H)
151. D13C5×D3×C13⋊C3semidirect
158. C3×C5C2×#11759818semidirect
160. C13C5×D3×D13⋊C3semidirect
161. C13C2×C5×D3×C13⋊C3semidirect
174. D3C5×#11759818direct (N × H)
175. C5D3×#11759818direct (N × H)
179. C3C2×C5×#11759818semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#927892
C5×C3⋊#117598182
C3×C5×#117598182
C5×D3×C13×D133
C2×C5×#117598183
D3×#117598185
C2×C5×D3×C13⋊C313
C5×D3×D13⋊C313