Finite Group Databasebeta

← C5×D3×C17×D15 #29506023

Subgroups — C5×D3×C17×D15 #29506023

Order 15300.

212 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 64 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×C17×C3⋊D15C211yesmaximal, characteristic, complemented
2C3×C5×C17×D15C211yesmaximal, characteristic, complemented
3C3×C52×D3×C17C211yesmaximal, characteristic, complemented
4C2×C5×C17×D15—31nomaximal
5C5×D3×D5×C17—31nomaximal
6C32×C52×C17C2211yescharacteristic, complemented, Hall
7D3×C17×D15C511yesmaximal, characteristic, direct product factor
8C5×D32×C17—51nomaximal
9C5×C17×D15—31no—
10C5×C17×D15—31no—
11C5×C17×D15—61no—
12C5×C17×D15D311yescharacteristic, direct product factor
13C52×D3×C17D311yescharacteristic, complemented
14C3×C5×D5×C17—31no—
15C2×C3×C52×C17—31no—
16C2×C5×D5×C17—91noHall
17C17×C3⋊D15C2×C511yescharacteristic, complemented
18C5×C17×C3⋊D3—51no—
19C3×C17×D15C2×C511yescharacteristic, complemented
20C3×C5×D3×C17—22no—
21C3×C5×D3×C17—51no—
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×C17×D15—31no—
28C2×C5×D3×C17—151no—
29C2×C5×D3×C17—151no—
30D3×D5×C17—31no—
31C5×D3×D15C1711yesmaximal, characteristic, direct product factor, Hall
32C2×C52×C17—31no—
33C5×D5×C17—31no—
34C5×D5×C17—91no—
35C32×C5×C17—22no—
36C32×C5×C17C2×D511yescharacteristic, complemented
37C32×C5×C17C22×C511yescharacteristic, complemented
38D32×C17—51noHall
39C2×C3×C5×C17—31no—
40C2×C3×C5×C17—31no—
41C2×C3×C5×C17—62no—
42C2×C3×C5×C17—151no—
43C17×D15—31no—
44C17×D15—31no—
45C17×D15—61no—
46C17×D15C5×D311yescharacteristic, direct product factor
47C5×D3×C17—22no—
48C5×D3×C17—51no—
49C5×D3×C17—151no—
50C5×D3×C17—151no—
51C5×D3×C17—301no—
52C5×D3×C17C5×D311yescharacteristic, complemented
53C5×D3×C17D1511yescharacteristic, direct product factor
54C3×D5×C17—31no—
55C5×C3⋊D15C2×C1711yescharacteristic, complemented
56C3×C5×D15C2×C1711yescharacteristic, complemented
57C3×C52×D3C2×C1711yescharacteristic, complemented
58C52×C17D3211yescharacteristic, complemented, Hall
59C22×C5×C17—451no—
60C2×D5×C17—91no—
61C17×C3⋊D3—51no—
62C3×D3×C17—51no—
63C3×D3×C17C5×D511yescharacteristic, complemented
64C2×C5×D15—31no—
65C5×D3×D5—31no—
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×C52C22×C1711yescharacteristic, complemented, Hall
76C2×D3×C17—151no—
77C2×D3×C17—151no—
78D3×D15C5×C1711yescharacteristic, direct product factor
79C5×D32—51no—
80C2×C5×C17—31no—
81C2×C5×C17—31no—
82C2×C5×C17—62no—
83C2×C5×C17—151no—
84C2×C5×C17—451no—
85D5×C17—31no—
86D5×C17—91no—
87C32×C17C2×C5×D511yescharacteristic, complemented, Hall
88C2×C3×C52—31no—
89C5×D15—31no—
90C5×D15—31no—
91C5×D15—61no—
92C5×D15D3×C1711yescharacteristic, direct product factor
93C52×D3D3×C1711yescharacteristic, complemented
94C3×C5×D5—31no—
95C2×C3×C17—31no—
96C2×C3×C17—151no—
97D3×C17—51no—
98D3×C17—151no—
99D3×C17—151no—
100D3×C17—301no—
101D3×C17C5×D1511yescharacteristic, direct product factor
102C2×C5×D5—91noHall
103C3⋊D15C2×C5×C1711yescharacteristic, complemented
104C5×C3⋊D3—51no—
105C3×D15C2×C5×C1711yescharacteristic, complemented
106C3×C5×D3—22no—
107C3×C5×D3—51no—
108C3×C5×D3D5×C1711yescharacteristic, complemented
109C3×C5×D3C2×C5×C1711yescharacteristic, complemented
110C5×C17—22no—
111C5×C17C5×D3211yescharacteristic, complemented
112C5×C17D3×D1511yescharacteristic, direct product factor
113C3×C52—21no—
114C3×C52C2×D3×C1711yescharacteristic, complemented
115C3×C52C2×D3×C1711yescharacteristic, complemented
116C22×C17—451noHall
117C2×D15—31no—
118C2×C5×D3—151no—
119C2×C5×D3—151no—
120D3×D5—31no—
121C3×C17—21no—
122C3×C17C5×D3×D511yescharacteristic, complemented
123C3×C17C2×C5×D1511yescharacteristic, complemented
124C2×C52—31no—
125C5×D5—31no—
126C5×D5—91no—
127C32×C5—22no—
128C32×C5C2×D5×C1711yescharacteristic, complemented
129C32×C5C22×C5×C1711yescharacteristic, complemented
130D32—51noHall
131C2×C17—31no—
132C2×C17—151no—
133C2×C17—451no—
134C2×C3×C5—31no—
135C2×C3×C5—31no—
136C2×C3×C5—62no—
137C2×C3×C5—151no—
138D15—31no—
139D15—31no—
140D15—61no—
141D15C5×D3×C1711yescharacteristic, direct product factor
142C3×D5—31no—
143C5×D3—22no—
144C5×D3—51no—
145C5×D3—151no—
146C5×D3—151no—
147C5×D3—301no—
148C5×D3C5×D3×C1711yescharacteristic, complemented
149C5×D3C17×D1511yescharacteristic, direct product factor
150C52D32×C1711yescharacteristic, complemented, Sylow
151C22×C5—451no—
152C2×D5—91no—
153C3⋊D3—51no—
154C3×D3—51no—
155C3×D3C5×D5×C1711yescharacteristic, complemented
156C17C5×D3×D1511yescharacteristic, direct product factor, Sylow
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5D3×D5×C1711yescharacteristic, complemented
163C3×C5C2×C5×D3×C1711yescharacteristic, complemented
164C3×C5C2×C5×D3×C1711yescharacteristic, complemented
165C3×C5C2×C17×D1511yescharacteristic, complemented
166C2×D3—151no—
167C2×D3—151no—
168C2×C5—31no—
169C2×C5—31no—
170C2×C5—62no—
171C2×C5—151no—
172C2×C5—451no—
173D5—31no—
174D5—91no—
175C32C2×C5×D5×C1711yescharacteristic, complemented, Sylow
176C2×C3—31no—
177C2×C3—151no—
178D3—51no—
179D3—151no—
180D3—151no—
181D3—301no—
182D3C5×C17×D1511yescharacteristic, direct product factor
183C5—22no—
184C5C5×D32×C1711yescharacteristic, complemented
185C5D3×C17×D1511yescharacteristic, direct product factor
186C22—451noSylow
187C3—21no—
188C3C5×D3×D5×C1711yescharacteristic, complemented
189C3C2×C5×C17×D1511yescharacteristic, complemented
190C2—31no—
191C2—151no—
192C2—451no—
subgroupG/H
center, hypercenterC5×C17D3×D15
commutator, cosocle, hypocenterC32×C5C22×C5×C17
FrattiniC1G
Fitting, socleC32×C52×C17C22
LCSG ▷ C32×C5
UCSC1 ◁ C5×C17

Complements

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

NH ≅ G/Ntype
1. C5×C17×C3⋊D15C2semidirect
2. C3×C5×C17×D15C2semidirect
3. C3×C52×D3×C17C2semidirect
6. C32×C52×C17C22semidirect
7. D3×C17×D15C5direct (N × H)
12. C5×C17×D15D3direct (N × H)
13. C52×D3×C17D3semidirect
17. C17×C3⋊D15C2×C5semidirect
19. C3×C17×D15C2×C5semidirect
22. C3×C5×D3×C17D5semidirect
23. C3×C5×D3×C17C2×C5semidirect
25. C3×C52×C17C2×D3semidirect
26. C3×C52×C17C2×D3semidirect
31. C5×D3×D15C17direct (N × H)
36. C32×C5×C17C2×D5semidirect
37. C32×C5×C17C22×C5semidirect
46. C17×D15C5×D3direct (N × H)
52. C5×D3×C17C5×D3semidirect
53. C5×D3×C17D15direct (N × H)
55. C5×C3⋊D15C2×C17semidirect
56. C3×C5×D15C2×C17semidirect
57. C3×C52×D3C2×C17semidirect
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×C52C22×C17semidirect
78. D3×D15C5×C17direct (N × H)
87. C32×C17C2×C5×D5semidirect
92. C5×D15D3×C17direct (N × H)
93. C52×D3D3×C17semidirect
101. D3×C17C5×D15direct (N × H)
103. C3⋊D15C2×C5×C17semidirect
105. C3×D15C2×C5×C17semidirect
108. C3×C5×D3D5×C17semidirect
109. C3×C5×D3C2×C5×C17semidirect
111. C5×C17C5×D32semidirect
112. C5×C17D3×D15direct (N × H)
114. C3×C52C2×D3×C17semidirect
115. C3×C52C2×D3×C17semidirect
122. C3×C17C5×D3×D5semidirect
123. C3×C17C2×C5×D15semidirect
128. C32×C5C2×D5×C17semidirect
129. C32×C5C22×C5×C17semidirect
141. D15C5×D3×C17direct (N × H)
148. C5×D3C5×D3×C17semidirect
149. C5×D3C17×D15direct (N × H)
150. C52D32×C17semidirect
155. C3×D3C5×D5×C17semidirect
156. C17C5×D3×D15direct (N × H)
162. C3×C5D3×D5×C17semidirect
163. C3×C5C2×C5×D3×C17semidirect
164. C3×C5C2×C5×D3×C17semidirect
165. C3×C5C2×C17×D15semidirect
175. C32C2×C5×D5×C17semidirect
182. D3C5×C17×D15direct (N × H)
184. C5C5×D32×C17semidirect
185. C5D3×C17×D15direct (N × H)
188. C3C5×D3×D5×C17semidirect
189. C3C2×C5×C17×D15semidirect

Maximal subgroups

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

subgroupindex
C5×C17×C3⋊D152
C3×C5×C17×D152
C3×C52×D3×C172
C2×C5×C17×D153
C5×D3×D5×C173
D3×C17×D155
C5×D32×C175
C5×D3×D1517