Finite Group Databasebeta

← D15⋊D609 #49141624

Subgroups — D15⋊D609 #49141624

Order 36540.

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

normal subgroups only

This group has 176 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×C7×C29×D15C211yesmaximal, characteristic, complemented
2C3×D3045C211yesmaximal, characteristic, complemented
3C5×C3⋊D609C211yesmaximal, characteristic, complemented
4D15⋊D203—31nomaximal
5D5×D609—31nomaximal
6C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
7D3×D609—51nomaximal, Hall
8D3045D311yescharacteristic, complemented
9C7×C29×D15D311yescharacteristic, complemented
10C5×D609—31no—
11C5×D609—31no—
12C5×D609—61no—
13C3×D1015—31no—
14C3×C7×D5×C29—31no—
15D15⋊D87—71nomaximal, Hall
16D5×D203—91noHall
17C3⋊D609D511yescharacteristic, complemented
18C3×D609—51no—
19C3×D3×C7×C29—51no—
20C3×C5×C7×C29—21no—
21C3×C5×C7×C29C2×D311yescharacteristic, complemented
22C3×C5×C7×C29C2×D311yescharacteristic, complemented
23C5×C3⋊D87—71no—
24C3×D435—71no—
25C3×C29×D15D711yescharacteristic, complemented
26C2×D609—151no—
27D3×D203—151no—
28D1015—31no—
29C7×D5×C29—31no—
30C5×D203—91no—
31C32×C7×C29C2×D511yescharacteristic, complemented, Hall
32D15⋊D29—211no—
33D5×D87—211no—
34C32×C5×C29C2×D711yescharacteristic, complemented, Hall
35D15⋊D21—291nomaximal, Hall
36C2×C3×C7×C29—151no—
37D609—31no—
38D609—31no—
39D609—51no—
40D609—61no—
41D3×C7×C29—51no—
42C3×D203—151no—
43D3×D87—351noHall
44C5×C7×C29D3211yescharacteristic, complemented, Hall
45D435—71no—
46C29×D15D2111yescharacteristic, complemented
47C5×D87—211no—
48C5×D87—211no—
49C5×D87—421no—
50C3×D145—211no—
51C3×D5×C29—31no—
52C2×D203—451noHall
53C5×C3⋊D21—291no—
54C3×D105—291no—
55C3×C7×D15D2911yescharacteristic, complemented
56C3×C7×C29—21no—
57C3×C7×C29D3×D511yescharacteristic, complemented
58C3×C7×C29D3×D511yescharacteristic, complemented
59D5×D29—631noHall
60C3⋊D87—71no—
61C3×D87—351no—
62C3×D3×C29—51no—
63C3×C5×C29—21no—
64C3×C5×C29D3×D711yescharacteristic, complemented
65C3×C5×C29C2×D2111yescharacteristic, complemented
66D15⋊D7—871no—
67D5×D21—871no—
68C2×C7×C29—151no—
69D203—91no—
70D203—151no—
71C2×D87—1051no—
72D3×D29—1051no—
73C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
74D145—211no—
75C5×D29—631no—
76D5×C29—31no—
77C32×C29D5×D711yescharacteristic, complemented, Hall
78D3×D21—1451noHall
79D105—291no—
80C7×D15D8711yescharacteristic, complemented
81C5×D21—871no—
82C5×D21—871no—
83C5×D21—1741no—
84C3×D35—871no—
85C3×C7×D5—31no—
86C7×C29(C3⋊D3)⋊D511yescharacteristic, complemented, Hall
87(C3⋊D3)⋊D5—2031noHall
88C2×C3×C29—151no—
89D87—211no—
90D87—211no—
91D87—351no—
92D87—421no—
93C3×D29—1051no—
94D3×C29—51no—
95C5×C29D3×D2111yescharacteristic, complemented, Hall
96D5×D7—2611noHall
97C3⋊D21—291no—
98C3×D21—1451no—
99C3×D3×C7—51no—
100C2×D29—3151noHall
101C3×C5×C7—21no—
102C3×C5×C7D3×D2911yescharacteristic, complemented
103C3×C5×C7C2×D8711yescharacteristic, complemented
104C5×C3⋊D3—2031no—
105C3×D15—2031no—
106C3×D15D20311yescharacteristic, complemented
107C3×C29—21no—
108C3×C29D5×D2111yescharacteristic, complemented
109C3×C29D15⋊D711yescharacteristic, complemented
110C2×D21—4351no—
111D3×D7—4351no—
112D35—871no—
113C5×D7—2611no—
114C7×D5—31no—
115C32×C7D5×D2911yescharacteristic, complemented, Hall
116D3×D5—6091no—
117D3×D5—6091no—
118C2×C29—151no—
119D29—631no—
120D29—1051no—
121C32×C5C2×D20311yescharacteristic, complemented, Hall
122C2×C3×C7—151no—
123D21—871no—
124D21—871no—
125D21—1451no—
126D21—1741no—
127C3×D7—4351no—
128D3×C7—51no—
129D32—10151noHall
130C5×C7D3×D8711yescharacteristic, complemented, Hall
131D15—2031no—
132D15D60911yescharacteristic, complemented
133C3×D5—31no—
134C3×D5—6091no—
135C5×D3—6091no—
136C5×D3—6091no—
137C5×D3—12181no—
138C29D15⋊D2111yescharacteristic, complemented, Sylow
139C2×D7—13051noHall
140C3×C7—21no—
141C3×C7D5×D8711yescharacteristic, complemented
142C3×C7D15⋊D2911yescharacteristic, complemented
143C2×D5—18271noHall
144C3⋊D3—2031no—
145C3×D3—51no—
146C3×D3—10151no—
147C3×C5—21no—
148C3×C5D3×D20311yescharacteristic, complemented
149C3×C5C2×D60911yescharacteristic, complemented
150C2×C7—151no—
151D7—2611no—
152D7—4351no—
153C2×D3—30451no—
154C2×D3—30451no—
155C2×C5—18271no—
156D5—31no—
157D5—6091no—
158C32D5×D20311yescharacteristic, complemented, Sylow
159C7D15⋊D8711yescharacteristic, complemented, Sylow
160C2×C3—151no—
161C2×C3—30451no—
162D3—51no—
163D3—6091no—
164D3—6091no—
165D3—12181no—
166D3—10151no—
167C5D3×D60911yescharacteristic, complemented, Sylow
168C22—91351noSylow
169C3—21no—
170C3D5×D60911yescharacteristic, complemented
171C3D15⋊D20311yescharacteristic, complemented
172C2—151no—
173C2—18271no—
174C2—30451no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C29C22
LCSG ▷ C32×C5×C7×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×C29×D15C2semidirect
2. C3×D3045C2semidirect
3. C5×C3⋊D609C2semidirect
6. C32×C5×C7×C29C22semidirect
8. D3045D3semidirect
9. C7×C29×D15D3semidirect
17. C3⋊D609D5semidirect
21. C3×C5×C7×C29C2×D3semidirect
22. C3×C5×C7×C29C2×D3semidirect
25. C3×C29×D15D7semidirect
31. C32×C7×C29C2×D5semidirect
34. C32×C5×C29C2×D7semidirect
44. C5×C7×C29D32semidirect
46. C29×D15D21semidirect
55. C3×C7×D15D29semidirect
57. C3×C7×C29D3×D5semidirect
58. C3×C7×C29D3×D5semidirect
64. C3×C5×C29D3×D7semidirect
65. C3×C5×C29C2×D21semidirect
73. C32×C5×C7C2×D29semidirect
77. C32×C29D5×D7semidirect
80. C7×D15D87semidirect
86. C7×C29(C3⋊D3)⋊D5semidirect
95. C5×C29D3×D21semidirect
102. C3×C5×C7D3×D29semidirect
103. C3×C5×C7C2×D87semidirect
106. C3×D15D203semidirect
108. C3×C29D5×D21semidirect
109. C3×C29D15⋊D7semidirect
115. C32×C7D5×D29semidirect
121. C32×C5C2×D203semidirect
130. C5×C7D3×D87semidirect
132. D15D609semidirect
138. C29D15⋊D21semidirect
141. C3×C7D5×D87semidirect
142. C3×C7D15⋊D29semidirect
148. C3×C5D3×D203semidirect
149. C3×C5C2×D609semidirect
158. C32D5×D203semidirect
159. C7D15⋊D87semidirect
167. C5D3×D609semidirect
170. C3D5×D609semidirect
171. C3D15⋊D203semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C29×D152
C3×D30452
C5×C3⋊D6092
D15⋊D2033
D5×D6093
D3×D6095
D15⋊D877
D15⋊D2129