Finite Group Databasebeta

← C5×D3×D255 #29506024

Subgroups — C5×D3×D255 #29506024

Order 15300.

212 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 56 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×C3⋊D255C211yesmaximal, characteristic, complemented
2C3×C5×D255C211yesmaximal, characteristic, complemented
3C3×C52×D3×C17C211yesmaximal, characteristic, complemented
4C2×C5×D255—31nomaximal
5C5×D3×D85—31nomaximal
6C32×C52×C17C2211yescharacteristic, complemented, Hall
7D3×D255C511yesmaximal, characteristic, direct product factor
8C5×D3×D51—51nomaximal
9C5×D255—31no—
10C5×D255—31no—
11C5×D255—61no—
12C5×D255D311yescharacteristic, direct product factor
13C52×D3×C17D311yescharacteristic, complemented
14C3×C5×D85—31no—
15C2×C3×C52×C17—31no—
16C2×C5×D85—91noHall
17C3⋊D255C2×C511yescharacteristic, complemented
18C5×C3⋊D51—51no—
19C3×D255C2×C511yescharacteristic, complemented
20C3×C5×D51—51no—
21C3×C5×D3×C17—22no—
22C3×C5×D3×C17D511yescharacteristic, complemented
23C3×C5×D3×C17C2×C511yescharacteristic, complemented
24C3×C52×C17—21no—
25C3×C52×C17C2×D311yescharacteristic, complemented
26C3×C52×C17C2×D311yescharacteristic, complemented
27C2×D255—31no—
28C2×C5×D51—151no—
29D3×D85—31no—
30C5×D3×D17—151no—
31C5×D3×D15—171nomaximal, Hall
32C2×C52×C17—31no—
33C5×D85—31no—
34C5×D85—91no—
35C32×C5×C17—22no—
36C32×C5×C17C2×D511yescharacteristic, complemented
37C32×C5×C17C22×C511yescharacteristic, complemented
38D3×D51—51noHall
39C2×C3×C5×C17—31no—
40C2×C3×C5×C17—31no—
41C2×C3×C5×C17—62no—
42D255—31no—
43D255—31no—
44D255—61no—
45D255C5×D311yescharacteristic, direct product factor
46C5×D51—51no—
47C5×D51—151no—
48C5×D51—151no—
49C5×D51—301no—
50C5×D3×C17—22no—
51C5×D3×C17C5×D311yescharacteristic, complemented
52C5×D3×C17D1511yescharacteristic, complemented
53C3×D85—31no—
54C3×C5×D17—151no—
55C5×C3⋊D15—171no—
56C3×C5×D15—171no—
57C3×C52×D3D1711yescharacteristic, complemented
58C52×C17D3211yescharacteristic, complemented, Hall
59C2×D85—91no—
60C2×C5×D17—451no—
61C3⋊D51—51no—
62C3×D51—51no—
63C3×D3×C17C5×D511yescharacteristic, complemented
64C2×C5×D15—511no—
65C5×D3×D5—511no—
66C3×C5×C17—21no—
67C3×C5×C17—21no—
68C3×C5×C17—22no—
69C3×C5×C17—22no—
70C3×C5×C17—42no—
71C3×C5×C17D3×D511yescharacteristic, complemented
72C3×C5×C17C2×C5×D311yescharacteristic, complemented
73C3×C5×C17C2×C5×D311yescharacteristic, complemented
74C3×C5×C17C2×D1511yescharacteristic, complemented
75C32×C52C2×D1711yescharacteristic, complemented, Hall
76C2×D51—151no—
77D3×D17—151no—
78D3×D15—171no—
79C5×D32—851no—
80C2×C5×C17—31no—
81C2×C5×C17—31no—
82C2×C5×C17—62no—
83D85—31no—
84D85—91no—
85C5×D17—151no—
86C5×D17—451no—
87C32×C17C2×C5×D511yescharacteristic, complemented, Hall
88C2×C3×C52—31no—
89C5×D15—171no—
90C5×D15—511no—
91C5×D15—511no—
92C5×D15—1021no—
93C52×D3D5111yescharacteristic, complemented
94C3×C5×D5—511no—
95C2×C3×C17—31no—
96D51—51no—
97D51—151no—
98D51—151no—
99D51—301no—
100C3×D17—151no—
101D3×C17C5×D1511yescharacteristic, complemented
102C2×C5×D5—1531noHall
103C3⋊D15—171no—
104C5×C3⋊D3—851no—
105C3×D15—171no—
106C3×C5×D3—22no—
107C3×C5×D3—851no—
108C3×C5×D3C5×D1711yescharacteristic, complemented
109C3×C5×D3D8511yescharacteristic, complemented
110C5×C17—22no—
111C5×C17C5×D3211yescharacteristic, complemented
112C5×C17D3×D1511yescharacteristic, complemented
113C3×C52—21no—
114C3×C52D3×D1711yescharacteristic, complemented
115C3×C52C2×D5111yescharacteristic, complemented
116C2×D17—451noHall
117C2×D15—511no—
118C2×C5×D3—2551no—
119C2×C5×D3—2551no—
120D3×D5—511no—
121C3×C17—21no—
122C3×C17C5×D3×D511yescharacteristic, complemented
123C3×C17C2×C5×D1511yescharacteristic, complemented
124C2×C52—31no—
125C5×D5—511no—
126C5×D5—1531no—
127C32×C5—22no—
128C32×C5C2×C5×D1711yescharacteristic, complemented
129C32×C5C2×D8511yescharacteristic, complemented
130D32—851noHall
131C2×C17—31no—
132D17—151no—
133D17—451no—
134C2×C3×C5—31no—
135C2×C3×C5—31no—
136C2×C3×C5—62no—
137C2×C3×C5—2551no—
138D15—171no—
139D15—511no—
140D15—511no—
141D15—1021no—
142C3×D5—511no—
143C5×D3—22no—
144C5×D3—851no—
145C5×D3—5101no—
146C5×D3—2551no—
147C5×D3—2551no—
148C5×D3C5×D5111yescharacteristic, complemented
149C5×D3D25511yescharacteristic, direct product factor
150C52D3×D5111yescharacteristic, complemented, Sylow
151C22×C5—7651no—
152C2×D5—1531no—
153C3⋊D3—851no—
154C3×D3—851no—
155C3×D3C5×D8511yescharacteristic, complemented
156C17C5×D3×D1511yescharacteristic, complemented, Sylow
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C5×D3×D1711yescharacteristic, complemented
163C3×C5D3×D8511yescharacteristic, complemented
164C3×C5C2×C5×D5111yescharacteristic, complemented
165C3×C5C2×D25511yescharacteristic, complemented
166C2×D3—2551no—
167C2×D3—2551no—
168C2×C5—31no—
169C2×C5—31no—
170C2×C5—62no—
171C2×C5—7651no—
172C2×C5—2551no—
173D5—511no—
174D5—1531no—
175C32C2×C5×D8511yescharacteristic, complemented, Sylow
176C2×C3—31no—
177C2×C3—2551no—
178D3—851no—
179D3—5101no—
180D3—2551no—
181D3—2551no—
182D3C5×D25511yescharacteristic, direct product factor
183C5—22no—
184C5C5×D3×D5111yescharacteristic, complemented
185C5D3×D25511yescharacteristic, direct product factor
186C22—7651noSylow
187C3—21no—
188C3C5×D3×D8511yescharacteristic, complemented
189C3C2×C5×D25511yescharacteristic, complemented
190C2—31no—
191C2—7651no—
192C2—2551no—
subgroupG/H
center, hypercenterC5D3×D255
commutator, cosocle, hypocenterC32×C5×C17C22×C5
FrattiniC1G
Fitting, socleC32×C52×C17C22
LCSG ▷ C32×C5×C17
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D255C2semidirect
2. C3×C5×D255C2semidirect
3. C3×C52×D3×C17C2semidirect
6. C32×C52×C17C22semidirect
7. D3×D255C5direct (N × H)
12. C5×D255D3direct (N × H)
13. C52×D3×C17D3semidirect
17. C3⋊D255C2×C5semidirect
19. C3×D255C2×C5semidirect
22. C3×C5×D3×C17D5semidirect
23. C3×C5×D3×C17C2×C5semidirect
25. C3×C52×C17C2×D3semidirect
26. C3×C52×C17C2×D3semidirect
36. C32×C5×C17C2×D5semidirect
37. C32×C5×C17C22×C5semidirect
45. D255C5×D3direct (N × H)
51. C5×D3×C17C5×D3semidirect
52. C5×D3×C17D15semidirect
57. C3×C52×D3D17semidirect
58. C52×C17D32semidirect
63. C3×D3×C17C5×D5semidirect
71. C3×C5×C17D3×D5semidirect
72. C3×C5×C17C2×C5×D3semidirect
73. C3×C5×C17C2×C5×D3semidirect
74. C3×C5×C17C2×D15semidirect
75. C32×C52C2×D17semidirect
87. C32×C17C2×C5×D5semidirect
93. C52×D3D51semidirect
101. D3×C17C5×D15semidirect
108. C3×C5×D3C5×D17semidirect
109. C3×C5×D3D85semidirect
111. C5×C17C5×D32semidirect
112. C5×C17D3×D15semidirect
114. C3×C52D3×D17semidirect
115. C3×C52C2×D51semidirect
122. C3×C17C5×D3×D5semidirect
123. C3×C17C2×C5×D15semidirect
128. C32×C5C2×C5×D17semidirect
129. C32×C5C2×D85semidirect
148. C5×D3C5×D51semidirect
149. C5×D3D255direct (N × H)
150. C52D3×D51semidirect
155. C3×D3C5×D85semidirect
156. C17C5×D3×D15semidirect
162. C3×C5C5×D3×D17semidirect
163. C3×C5D3×D85semidirect
164. C3×C5C2×C5×D51semidirect
165. C3×C5C2×D255semidirect
175. C32C2×C5×D85semidirect
182. D3C5×D255direct (N × H)
184. C5C5×D3×D51semidirect
185. C5D3×D255direct (N × H)
188. C3C5×D3×D85semidirect
189. C3C2×C5×D255semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊D2552
C3×C5×D2552
C3×C52×D3×C172
C2×C5×D2553
C5×D3×D853
D3×D2555
C5×D3×D515
C5×D3×D1517