Finite Group Databasebeta

← C5×D3×#11759817 #44478014

Subgroups — C5×D3×#11759817 #44478014

Order 30420.

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

normal subgroups only

This group has 284 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×#92788C211yesmaximal, characteristic, complemented
2C5×C3⋊#11759817C211yesmaximal, characteristic, complemented
3C3×C5×#11759817C211yesmaximal, characteristic, complemented
4C5×D3×C13×D13C311yesmaximal, characteristic, complemented
5C2×C5×#11759817—31nomaximal
6C3×C5×#92788C2211yescharacteristic, complemented, Hall
7D3×#11759817C511yesmaximal, characteristic, direct product factor, Hall
8C5×C13×D39C2×C311yescharacteristic, complemented
9C5×D3×C132C2×C311yescharacteristic, complemented
10C3×C5×C13×D13C2×C311yescharacteristic, complemented
11C2×C5×#92788—31no—
12C5×#11759817—21no—
13C5×#11759817—31no—
14C5×#11759817D311yescharacteristic, direct product factor
15C2×C5×C13×D13—31noHall
16D3×#92788C2×C511yescharacteristic, complemented
17C3⋊#11759817C2×C511yescharacteristic, complemented
18C3×#11759817C2×C511yescharacteristic, complemented
19C5×#92788—21no—
20C5×#92788C2×D311yescharacteristic, complemented
21C3×C5×C132C22×C311yescharacteristic, complemented
22C2×C5×D3×C13⋊C3—131nomaximal
23C5×D3×D13⋊C3—131nomaximal
24D3×C13×D13C3×C511yescharacteristic, complemented
25C2×#11759817—31no—
26C2×C5×C132—31no—
27C5×C13×D13—31no—
28C5×C13×D13C3×D311yescharacteristic, complemented
29C3×#92788C22×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—
35C5×D3×C13⋊C3—266no—
36C3×C5×D13⋊C3—131no—
37C13×D39C2×C3×C511yescharacteristic, complemented
38D3×C132C2×C3×C511yescharacteristic, complemented
39C3×C13×D13C2×C3×C511yescharacteristic, complemented
40C2×#92788—31no—
41#11759817—21no—
42#11759817—31no—
43#11759817C5×D311yescharacteristic, direct product factor
44C5×C132C2×C3×D311yescharacteristic, complemented, Hall
45C2×C5×D3×C13—131no—
46C22×C5×C13⋊C3—391no—
47C5×D3×D13C13⋊C311yescharacteristic, complemented
48C2×C5×D13⋊C3—391no—
49C2×C13×D13—31noHall
50C3×C5×C13⋊C3—131no—
51C3×C5×C13⋊C3—131no—
52C3×C5×C13⋊C3—266no—
53C3×C132C22×C3×C511yescharacteristic, complemented
54#92788—21no—
55#92788C2×C5×D311yescharacteristic, complemented
56C2×D3×C13⋊C3—131no—
57D3×D13⋊C3—131no—
58C2×C3×C5×C13—131no—
59C5×D39C2×C13⋊C311yescharacteristic, complemented
60C5×D3×C13—26no—
61C5×D3×C13—131no—
62C5×D3×C13D13⋊C311yescharacteristic, complemented
63C5×D3×C13C2×C13⋊C311yescharacteristic, complemented
64C3×C5×D13C2×C13⋊C311yescharacteristic, complemented
65C2×C5×C13⋊C3—131no—
66C2×C5×C13⋊C3—261no—
67C2×C5×C13⋊C3—391no—
68C2×C5×C13⋊C3—391no—
69C2×C5×C13⋊C3—391no—
70C2×C5×C13⋊C3—786no—
71C5×D13⋊C3—131no—
72C5×D13⋊C3—261no—
73C5×D13⋊C3—391no—
74C2×C132—31no—
75C13×D13—31no—
76C13×D13C3×C5×D311yescharacteristic, complemented
77C22×C5×C13—391no—
78C2×C5×D13—31no—
79C2×C3×C13⋊C3—131no—
80C3⋊(D13⋊C3)—131no—
81D3×C13⋊C3—131no—
82D3×C13⋊C3—131no—
83D3×C13⋊C3—131no—
84D3×C13⋊C3—266no—
85C3×D13⋊C3—131no—
86C3×C5×C13—26no—
87C3×C5×C13C2×D13⋊C311yescharacteristic, complemented
88C3×C5×C13C22×C13⋊C311yescharacteristic, complemented
89C5×C13⋊C3—131no—
90C5×C13⋊C3—131no—
91C5×C13⋊C3—261no—
92C5×C13⋊C3—261no—
93C5×C13⋊C3—266no—
94C5×C13⋊C3—526no—
95C2×C3×C5×D3—1691noHall
96C132C2×C3×C5×D311yescharacteristic, complemented, Sylow
97C2×D3×C13—131no—
98C22×C13⋊C3—391no—
99D3×D13C5×C13⋊C311yescharacteristic, complemented
100C2×D13⋊C3—391no—
101C2×C5×C13—31no—
102C2×C5×C13—31no—
103C2×C5×C13—66no—
104C2×C5×C13—131no—
105C2×C5×C13—391no—
106C5×D13—31no—
107C5×D13D3×C13⋊C311yescharacteristic, complemented
108C3×C13⋊C3—131no—
109C3×C13⋊C3—131no—
110C3×C13⋊C3—266no—
111C2×C32×C5—1691no—
112C3×C5×D3—1691no—
113C3×C5×D3—1691no—
114C2×C3×C13—131no—
115D39C2×C5×C13⋊C311yescharacteristic, complemented
116C3×D13C2×C5×C13⋊C311yescharacteristic, complemented
117D3×C13—26no—
118D3×C13—131no—
119D3×C13C5×D13⋊C311yescharacteristic, complemented
120D3×C13C2×C5×C13⋊C311yescharacteristic, complemented
121C2×C13⋊C3—131no—
122C2×C13⋊C3—261no—
123C2×C13⋊C3—391no—
124C2×C13⋊C3—391no—
125C2×C13⋊C3—391no—
126C2×C13⋊C3—786no—
127D13⋊C3—131no—
128D13⋊C3—261no—
129D13⋊C3—391no—
130C5×C13—26no—
131C5×C13D3×D13⋊C311yescharacteristic, complemented
132C5×C13C2×D3×C13⋊C311yescharacteristic, complemented
133C22×C3×C5—5071no—
134C2×C5×D3—131no—
135C22×C13—391no—
136C2×D13—31no—
137C32×C5—1691noHall
138C3×C13—26no—
139C3×C13C2×C5×D13⋊C311yescharacteristic, complemented
140C3×C13C22×C5×C13⋊C311yescharacteristic, complemented
141C13⋊C3—131no—
142C13⋊C3—131no—
143C13⋊C3—261no—
144C13⋊C3—261no—
145C13⋊C3—266no—
146C13⋊C3—526no—
147C2×C3×D3—1691noHall
148C2×C3×C5—131no—
149C2×C3×C5—3381no—
150C2×C3×C5—1691no—
151C2×C3×C5—5071no—
152C2×C3×C5—5071no—
153C5×D3—131no—
154C5×D3#1175981711yescharacteristic, direct product factor
155C2×C13—31no—
156C2×C13—31no—
157C2×C13—66no—
158C2×C13—131no—
159C2×C13—391no—
160D13—31no—
161D13C5×D3×C13⋊C311yescharacteristic, complemented
162C22×C5—391noHall
163C2×C32—1691no—
164C3×D3—1691no—
165C3×D3—1691no—
166C3×C5—3381no—
167C3×C5—1691no—
168C3×C5C2×#1175981711yescharacteristic, complemented
169C13—26no—
170C13C5×D3×D13⋊C311yescharacteristic, complemented
171C13C2×C5×D3×C13⋊C311yescharacteristic, complemented
172C22×C3—5071no—
173C2×D3—131no—
174C2×C5—31no—
175C2×C5—131no—
176C2×C5—391no—
177C32—1691noSylow
178C2×C3—131no—
179C2×C3—3381no—
180C2×C3—1691no—
181C2×C3—5071no—
182C2×C3—5071no—
183D3—131no—
184D3C5×#1175981711yescharacteristic, direct product factor
185C5D3×#1175981711yescharacteristic, direct product factor, Sylow
186C22—391noSylow
187C3—3381no—
188C3—1691no—
189C3C2×C5×#1175981711yescharacteristic, complemented
190C2—31no—
191C2—131no—
192C2—391no—
subgroupG/H
center, hypercenterC5D3×#11759817
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×#92788C2semidirect
2. C5×C3⋊#11759817C2semidirect
3. C3×C5×#11759817C2semidirect
4. C5×D3×C13×D13C3semidirect
6. C3×C5×#92788C22semidirect
7. D3×#11759817C5direct (N × H)
8. C5×C13×D39C2×C3semidirect
9. C5×D3×C132C2×C3semidirect
10. C3×C5×C13×D13C2×C3semidirect
14. C5×#11759817D3direct (N × H)
16. D3×#92788C2×C5semidirect
17. C3⋊#11759817C2×C5semidirect
18. C3×#11759817C2×C5semidirect
20. C5×#92788C2×D3semidirect
21. C3×C5×C132C22×C3semidirect
24. D3×C13×D13C3×C5semidirect
28. C5×C13×D13C3×D3semidirect
29. C3×#92788C22×C5semidirect
37. C13×D39C2×C3×C5semidirect
38. D3×C132C2×C3×C5semidirect
39. C3×C13×D13C2×C3×C5semidirect
43. #11759817C5×D3direct (N × H)
44. C5×C132C2×C3×D3semidirect
47. C5×D3×D13C13⋊C3semidirect
53. C3×C132C22×C3×C5semidirect
55. #92788C2×C5×D3semidirect
59. C5×D39C2×C13⋊C3semidirect
62. C5×D3×C13D13⋊C3semidirect
63. C5×D3×C13C2×C13⋊C3semidirect
64. C3×C5×D13C2×C13⋊C3semidirect
76. C13×D13C3×C5×D3semidirect
87. C3×C5×C13C2×D13⋊C3semidirect
88. C3×C5×C13C22×C13⋊C3semidirect
96. C132C2×C3×C5×D3semidirect
99. D3×D13C5×C13⋊C3semidirect
107. C5×D13D3×C13⋊C3semidirect
115. D39C2×C5×C13⋊C3semidirect
116. C3×D13C2×C5×C13⋊C3semidirect
119. D3×C13C5×D13⋊C3semidirect
120. D3×C13C2×C5×C13⋊C3semidirect
131. C5×C13D3×D13⋊C3semidirect
132. C5×C13C2×D3×C13⋊C3semidirect
139. C3×C13C2×C5×D13⋊C3semidirect
140. C3×C13C22×C5×C13⋊C3semidirect
154. C5×D3#11759817direct (N × H)
161. D13C5×D3×C13⋊C3semidirect
168. C3×C5C2×#11759817semidirect
170. C13C5×D3×D13⋊C3semidirect
171. C13C2×C5×D3×C13⋊C3semidirect
184. D3C5×#11759817direct (N × H)
185. C5D3×#11759817direct (N × H)
189. C3C2×C5×#11759817semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#927882
C5×C3⋊#117598172
C3×C5×#117598172
C5×D3×C13×D133
C2×C5×#117598173
D3×#117598175
C2×C5×D3×C13⋊C313
C5×D3×D13⋊C313