Finite Group Databasebeta

← #44478134

Subgroups — #44478134

Order 30420.

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

normal subgroups only

This group has 192 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
1C3⋊(C5⋊#11759818)C211yesmaximal, characteristic, complemented
2C5×C3⋊#11759818C211yesmaximal, characteristic, complemented
3C3×C5⋊#11759816C211yesmaximal, characteristic, complemented
4D39⋊D65C311yesmaximal, characteristic, complemented
5#11759818⋊D5—31nomaximal
6C3×C5×#92789C2211yescharacteristic, complemented, Hall
7#20258902—51nomaximal, Hall
8C13×D195C2×C311yescharacteristic, complemented
9C5×C13×D39C2×C311yescharacteristic, complemented
10C3×C5⋊(C13⋊D13)C2×C311yescharacteristic, complemented
11C5⋊#11759818—31no—
12C5⋊#11759816—21no—
13C5⋊#11759816D311yescharacteristic, complemented
14C5×#11759818—31no—
15D13×D65—31noHall
16C3⋊#11759818—51no—
17C3⋊#11759818D511yescharacteristic, complemented
18C3×#11759816—51no—
19C5×#92789—21no—
20C5×#92789C2×D311yescharacteristic, complemented
21C3×C5×C132C22×C311yescharacteristic, complemented
22D15⋊(D13⋊C3)—131nomaximal
23D3×C5⋊(D13⋊C3)—131nomaximal
24D39⋊D13—51no—
25#11759818⋊C2—151no—
26C5⋊(C13⋊D13)C3×D311yescharacteristic, complemented
27C13×D65—31no—
28C5×C13×D13—31no—
29C3×#92789C2×D511yescharacteristic, complemented, Hall
30C3⋊(C5⋊(D13⋊C3))—261no—
31D15×C13⋊C3—131no—
32C5×C3⋊(D13⋊C3)—261no—
33C5×D3×C13⋊C3—131no—
34C3×C5⋊(D13⋊C3)—131no—
35C3×C5⋊(D13⋊C3)—131no—
36C13×D39—51no—
37C13×D39C3×D511yescharacteristic, complemented
38C3×C13⋊D13—51no—
39#11759818—31no—
40#11759818—151no—
41#11759816—51no—
42#11759816—101no—
43C5×C132C2×C3×D311yescharacteristic, complemented, Hall
44D15⋊D13—131no—
45D3×D65—131no—
46C2×C5⋊(D13⋊C3)—391no—
47D5×D13⋊C3—391no—
48D132—151noHall
49C3×C5×C13⋊C3—261no—
50C3×C5×C13⋊C3—261no—
51C3×C132C2×C3×D511yescharacteristic, complemented
52#92789—21no—
53#92789D3×D511yescharacteristic, complemented
54D3×D13⋊C3—651no—
55D3×D13⋊C3—651no—
56D195D13⋊C311yescharacteristic, complemented
57C13×D15—131no—
58C5×D39D13⋊C311yescharacteristic, complemented
59C5×D3×C13—131no—
60C3×D65—131no—
61C3×D65—131no—
62C3×D65—782no—
63C2×C5×C13⋊C3—391no—
64C5⋊(D13⋊C3)—131no—
65C5⋊(D13⋊C3)—131no—
66C5⋊(D13⋊C3)—261no—
67C5⋊(D13⋊C3)—261no—
68C5⋊(D13⋊C3)—781no—
69D5×C13⋊C3—391no—
70C5×D13⋊C3—781no—
71C13⋊D13—51no—
72C13×D13—31no—
73C13×D13—151no—
74C2×D65—391no—
75D5×D13—391no—
76C3⋊(D13⋊C3)—261no—
77C3⋊(D13⋊C3)—1301no—
78D3×C13⋊C3—131no—
79D3×C13⋊C3—651no—
80C3×D13⋊C3—651no—
81C3×D13⋊C3—651no—
82C3×C5×C13—62no—
83C3×C5×C13C2×D13⋊C311yescharacteristic, complemented
84C3×C5×C13C2×D13⋊C311yescharacteristic, complemented
85C5×C13⋊C3—261no—
86C5×C13⋊C3—261no—
87C5×C13⋊C3—521no—
88C5×C13⋊C3—521no—
89C3×D3×D5—1691noHall
90C132C3×D3×D511yescharacteristic, complemented, Sylow
91D3×D13—651no—
92D3×D13—651no—
93C2×D13⋊C3—1951no—
94C2×D13⋊C3—1951no—
95C2×C5×C13—391no—
96D65—31no—
97D65—131no—
98D65—131no—
99D65—782no—
100C5×D13—31no—
101D5×C13—391no—
102C3×C13⋊C3—261no—
103C3×C13⋊C3—261no—
104C3×D15—3381no—
105C3×C5×D3—3381no—
106C32×D5—1691no—
107D39—51no—
108D39C5⋊(D13⋊C3)11yescharacteristic, complemented
109C3×D13—651no—
110C3×D13—651no—
111C3×D13—3902no—
112D3×C13—131no—
113D3×C13—651no—
114C2×C13⋊C3—391no—
115C2×C13⋊C3—1951no—
116D13⋊C3—651no—
117D13⋊C3—651no—
118D13⋊C3—781no—
119D13⋊C3—1301no—
120D13⋊C3—1301no—
121D13⋊C3—3901no—
122C5×C13—62no—
123C5×C13D3×D13⋊C311yescharacteristic, complemented
124C5×C13D3×D13⋊C311yescharacteristic, complemented
125C2×C3×D5—5071no—
126D3×D5—1691no—
127C2×D13—1951no—
128C2×D13—1951no—
129C32×C5—6761noHall
130C3×C13—62no—
131C3×C13D5×D13⋊C311yescharacteristic, complemented
132C3×C13C2×C5⋊(D13⋊C3)11yescharacteristic, complemented
133C13⋊C3—261no—
134C13⋊C3—261no—
135C13⋊C3—521no—
136C13⋊C3—521no—
137C2×C3×D3—8451noHall
138C2×C3×C5—10141no—
139D15—131no—
140C3×D5—3381no—
141C3×D5—1691no—
142C3×D5—1691no—
143C3×D5—10141no—
144C5×D3—131no—
145C2×C13—391no—
146C2×C13—1951no—
147D13—31no—
148D13—151no—
149D13—651no—
150D13—651no—
151D13—3902no—
152C2×D5—5071noHall
153C2×C32—8451no—
154C3×D3—3381no—
155C3×D3—16901no—
156C3×C5—6761no—
157C3×C5—6761no—
158C3×C5#11759818⋊C211yescharacteristic, complemented
159C13—62no—
160C13D3×C5⋊(D13⋊C3)11yescharacteristic, complemented
161C13D15⋊(D13⋊C3)11yescharacteristic, complemented
162C22×C3—25351no—
163C2×D3—8451no—
164C2×C5—391no—
165D5—391no—
166D5—1691no—
167C32—6761noSylow
168C2×C3—8451no—
169C2×C3—8451no—
170C2×C3—16901no—
171C2×C3—50701no—
172C2×C3—10141no—
173D3—131no—
174D3—651no—
175C5#2025890211yescharacteristic, complemented, Sylow
176C22—25351noSylow
177C3—6761no—
178C3—6761no—
179C3#11759818⋊D511yescharacteristic, complemented
180C2—391no—
181C2—8451no—
182C2—1951no—
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. C3⋊(C5⋊#11759818)C2semidirect
2. C5×C3⋊#11759818C2semidirect
3. C3×C5⋊#11759816C2semidirect
4. D39⋊D65C3semidirect
6. C3×C5×#92789C22semidirect
8. C13×D195C2×C3semidirect
9. C5×C13×D39C2×C3semidirect
10. C3×C5⋊(C13⋊D13)C2×C3semidirect
13. C5⋊#11759816D3semidirect
17. C3⋊#11759818D5semidirect
20. C5×#92789C2×D3semidirect
21. C3×C5×C132C22×C3semidirect
26. C5⋊(C13⋊D13)C3×D3semidirect
29. C3×#92789C2×D5semidirect
37. C13×D39C3×D5semidirect
43. C5×C132C2×C3×D3semidirect
51. C3×C132C2×C3×D5semidirect
53. #92789D3×D5semidirect
56. D195D13⋊C3semidirect
58. C5×D39D13⋊C3semidirect
83. C3×C5×C13C2×D13⋊C3semidirect
84. C3×C5×C13C2×D13⋊C3semidirect
90. C132C3×D3×D5semidirect
108. D39C5⋊(D13⋊C3)semidirect
123. C5×C13D3×D13⋊C3semidirect
124. C5×C13D3×D13⋊C3semidirect
131. C3×C13D5×D13⋊C3semidirect
132. C3×C13C2×C5⋊(D13⋊C3)semidirect
158. C3×C5#11759818⋊C2semidirect
160. C13D3×C5⋊(D13⋊C3)semidirect
161. C13D15⋊(D13⋊C3)semidirect
175. C5#20258902semidirect
179. C3#11759818⋊D5semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C5⋊#11759818)2
C5×C3⋊#117598182
C3×C5⋊#117598162
D39⋊D653
#11759818⋊D53
#202589025
D15⋊(D13⋊C3)13
D3×C5⋊(D13⋊C3)13