Finite Group Databasebeta

← D15⋊D435 #39908174

Subgroups — D15⋊D435 #39908174

Order 26100.

212 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 45 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×C29×D15C211yesmaximal, characteristic, complemented
2C3×C3⋊(C5⋊D145)C211yesmaximal, characteristic, complemented
3C5×C3⋊D435C211yesmaximal, characteristic, complemented
4D15⋊D145—31nomaximal
5D5×D435—31nomaximal
6C32×C52×C29C2211yescharacteristic, complemented, Hall
7D15⋊D87—51nomaximal
8D3×D435—51nomaximal
9C3⋊(C5⋊D145)D311yescharacteristic, complemented
10C5×D435—31no—
11C5×D435—31no—
12C5×D435—61no—
13C5×C29×D15D311yescharacteristic, complemented
14C3×C5⋊D145—31no—
15C3×C5×D5×C29—31no—
16D5×D145—91noHall
17C3⋊D435D511yescharacteristic, complemented
18C5×C3⋊D87—51no—
19C3×D435—51no—
20C3×D435—51no—
21C3×D435—102no—
22C3×C29×D15D511yescharacteristic, complemented
23C3×C5×D3×C29—51no—
24C3×C52×C29—21no—
25C3×C52×C29C2×D311yescharacteristic, complemented
26C3×C52×C29C2×D311yescharacteristic, complemented
27C2×D435—151no—
28D15⋊D29—151no—
29D3×D145—151no—
30D5×D87—151no—
31C5⋊D145—31no—
32C5×D145—91no—
33C5×D5×C29—31no—
34C32×C5×C29—22no—
35C32×C5×C29C2×D511yescharacteristic, complemented
36C32×C5×C29C2×D511yescharacteristic, complemented
37D3×D87—251noHall
38D15⋊D15—291nomaximal, Hall
39C2×C3×C5×C29—151no—
40D435—31no—
41D435—31no—
42D435—51no—
43D435—51no—
44D435—61no—
45D435—102no—
46C29×D15D1511yescharacteristic, complemented
47C5×D87—151no—
48C5×D87—151no—
49C5×D87—301no—
50C5×D3×C29—51no—
51C3×D145—151no—
52C3×D145—151no—
53C3×D145—302no—
54C3×D5×C29—31no—
55C52×C29D3211yescharacteristic, complemented, Hall
56C2×D145—451no—
57D5×D29—451no—
58C3⋊D87—51no—
59C3×D87—251no—
60C3×D3×C29—51no—
61C5×C3⋊D15—291no—
62C3×C3⋊(C5⋊D5)—291no—
63C3×C5×D15D2911yescharacteristic, complemented
64C3×C5×C29—22no—
65C3×C5×C29—22no—
66C3×C5×C29—21no—
67C3×C5×C29—21no—
68C3×C5×C29—42no—
69C3×C5×C29D3×D511yescharacteristic, complemented
70C3×C5×C29D3×D511yescharacteristic, complemented
71C3×C5×C29D3×D511yescharacteristic, complemented
72C3×C5×C29C2×D1511yescharacteristic, complemented
73C2×D87—751no—
74D3×D29—751no—
75D15⋊D5—871no—
76D5×D15—871no—
77C2×C5×C29—151no—
78D145—91no—
79D145—151no—
80D145—151no—
81D145—302no—
82C5×D29—451no—
83D5×C29—31no—
84C32×C29D5211yescharacteristic, complemented, Hall
85C32×C52C2×D2911yescharacteristic, complemented, Hall
86(C3⋊D3)⋊D5—1451no—
87D3×D15—1451no—
88C2×C3×C29—151no—
89D87—151no—
90D87—151no—
91D87—251no—
92D87—301no—
93C3×D29—751no—
94D3×C29—51no—
95C3⋊(C5⋊D5)—291no—
96C5×D15—871no—
97C5×D15—871no—
98C5×D15—1741no—
99C5×D15D8711yescharacteristic, complemented
100C3×C5⋊D5—871no—
101C3×C5×D5—31no—
102C5×C29—22no—
103C5×C29D3×D1511yescharacteristic, complemented
104C5×C29(C3⋊D3)⋊D511yescharacteristic, complemented
105C2×D29—2251noHall
106D52—2611noHall
107C3⋊D15—291no—
108C5×C3⋊D3—1451no—
109C3×D15—2902no—
110C3×D15—1451no—
111C3×D15—1451no—
112C3×D15D14511yescharacteristic, complemented
113C3×C5×D3—51no—
114C3×C29—21no—
115C3×C29D5×D1511yescharacteristic, complemented
116C3×C29D15⋊D511yescharacteristic, complemented
117C3×C52—21no—
118C3×C52D3×D2911yescharacteristic, complemented
119C3×C52C2×D8711yescharacteristic, complemented
120C2×D15—4351no—
121D3×D5—4351no—
122D3×D5—4351no—
123D3×D5—4351no—
124C2×C29—151no—
125D29—451no—
126D29—751no—
127C5⋊D5—871no—
128C5×D5—31no—
129C5×D5—2611no—
130C32×C5—22no—
131C32×C5D5×D2911yescharacteristic, complemented
132C32×C5C2×D14511yescharacteristic, complemented
133D32—7251noHall
134C2×C3×C5—151no—
135D15—2902no—
136D15—871no—
137D15—871no—
138D15—1451no—
139D15—1451no—
140D15—1741no—
141D15D43511yescharacteristic, complemented
142C3×D5—31no—
143C3×D5—8702no—
144C3×D5—4351no—
145C3×D5—4351no—
146C5×D3—51no—
147C5×D3—8701no—
148C5×D3—4351no—
149C5×D3—4351no—
150C29D15⋊D1511yescharacteristic, complemented, Sylow
151C52D3×D8711yescharacteristic, complemented, Sylow
152C2×D5—13051no—
153C2×D5—13051no—
154C3⋊D3—1451no—
155C3×D3—51no—
156C3×D3—7251no—
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5D5×D8711yescharacteristic, complemented
163C3×C5D3×D14511yescharacteristic, complemented
164C3×C5D15⋊D2911yescharacteristic, complemented
165C3×C5C2×D43511yescharacteristic, complemented
166C2×D3—21751no—
167C2×D3—21751no—
168C2×C5—151no—
169C2×C5—13051no—
170D5—31no—
171D5—2611no—
172D5—8702no—
173D5—4351no—
174D5—4351no—
175C32D5×D14511yescharacteristic, complemented, Sylow
176C2×C3—151no—
177C2×C3—21751no—
178D3—51no—
179D3—8701no—
180D3—4351no—
181D3—4351no—
182D3—7251no—
183C5—22no—
184C5D3×D43511yescharacteristic, complemented
185C5D15⋊D8711yescharacteristic, complemented
186C22—65251noSylow
187C3—21no—
188C3D5×D43511yescharacteristic, complemented
189C3D15⋊D14511yescharacteristic, complemented
190C2—151no—
191C2—13051no—
192C2—21751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C29C22
LCSG ▷ C32×C52×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C29×D15C2semidirect
2. C3×C3⋊(C5⋊D145)C2semidirect
3. C5×C3⋊D435C2semidirect
6. C32×C52×C29C22semidirect
9. C3⋊(C5⋊D145)D3semidirect
13. C5×C29×D15D3semidirect
17. C3⋊D435D5semidirect
22. C3×C29×D15D5semidirect
25. C3×C52×C29C2×D3semidirect
26. C3×C52×C29C2×D3semidirect
35. C32×C5×C29C2×D5semidirect
36. C32×C5×C29C2×D5semidirect
46. C29×D15D15semidirect
55. C52×C29D32semidirect
63. C3×C5×D15D29semidirect
69. C3×C5×C29D3×D5semidirect
70. C3×C5×C29D3×D5semidirect
71. C3×C5×C29D3×D5semidirect
72. C3×C5×C29C2×D15semidirect
84. C32×C29D52semidirect
85. C32×C52C2×D29semidirect
99. C5×D15D87semidirect
103. C5×C29D3×D15semidirect
104. C5×C29(C3⋊D3)⋊D5semidirect
112. C3×D15D145semidirect
115. C3×C29D5×D15semidirect
116. C3×C29D15⋊D5semidirect
118. C3×C52D3×D29semidirect
119. C3×C52C2×D87semidirect
131. C32×C5D5×D29semidirect
132. C32×C5C2×D145semidirect
141. D15D435semidirect
150. C29D15⋊D15semidirect
151. C52D3×D87semidirect
162. C3×C5D5×D87semidirect
163. C3×C5D3×D145semidirect
164. C3×C5D15⋊D29semidirect
165. C3×C5C2×D435semidirect
175. C32D5×D145semidirect
184. C5D3×D435semidirect
185. C5D15⋊D87semidirect
188. C3D5×D435semidirect
189. C3D15⋊D145semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C29×D152
C3×C3⋊(C5⋊D145)2
C5×C3⋊D4352
D15⋊D1453
D5×D4353
D15⋊D875
D3×D4355
D15⋊D1529