Finite Group Databasebeta

← #41×D45 #13085354

Subgroups — #41×D45 #13085354

Order 1440.

492 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 155 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×C9×#41C211yesmaximal, characteristic, complemented
2#10623713C211yesmaximal, characteristic, complemented
3Q8×D45C211yesmaximal, characteristic, complemented
4#10623711C213yesmaximal, complemented
5D4×D45C213yesmaximal, complemented
6#10623709C213yesmaximal, complemented
7C2×C4×D45C213yesmaximal, complemented
8#41×D15—31nomaximal
9C22×D45C2213yes—
10C5×Q8×C9C2211yescharacteristic, complemented
11C5×D4×C9C2213yescomplemented
12C2×C4×C5×C9C2213yescomplemented
13#67099C2216yescomplemented
14C2×Dic45C2213yescomplemented
15D180C2213yescomplemented
16C4×D45C2211yescharacteristic
17C4×D45C2213yes—
18C4×D45C2213yescomplemented
19C4×D45C2213yescomplemented
20Dic90C2213yescomplemented
21#41×D9—51nomaximal, Hall
22C3×C5×#41D311yescharacteristic
23#6821—31no—
24Q8×D15—31no—
25#6819—33no—
26D4×D15—33no—
27#6817—33no—
28C2×C4×D15—33no—
29C22×C5×C9C2313yes—
30C2×D45—26no—
31C2×D45C2313yes—
32C2×D45C2311yescharacteristic
33C4×C5×C9C2313yes—
34C4×C5×C9C2311yescharacteristic
35Dic45C2313yes—
36Dic45C2311yescharacteristic
37D5×#41—91noHall
38C9×#41D511yescharacteristic, complemented
39#3701—51no—
40Q8×D9—51no—
41#3699—53no—
42D4×D9—53no—
43#3697—53no—
44C2×C4×D9—53no—
45C22×D15—33no—
46C3×C5×Q8C2×D311yescharacteristic
47C3×C5×D4C2×D313yes—
48C2×C3×C4×C5C2×D313yes—
49#1220—36no—
50C2×Dic15—33no—
51D60—33no—
52C4×D15—31no—
53C4×D15—33no—
54C4×D15—33no—
55C4×D15—33no—
56Dic30—33no—
57D3×#41—151no—
58C2×C5×C9—23no—
59C2×C5×C9C2411yescharacteristic
60D45—23no—
61D45#4112yesdirect product factor
62C5×#41D911yescharacteristic, complemented
63#713—91no—
64Q8×D5—91no—
65#711—93no—
66D4×D5—93no—
67#709—93no—
68C2×C4×D5—93no—
69C22×D9—53no—
70Q8×C9C2×D511yescharacteristic, complemented
71D4×C9C2×D513yescomplemented
72C2×C4×C9C2×D513yescomplemented
73#611—56no—
74C2×Dic9—53no—
75D36—53no—
76C4×D9—51no—
77C4×D9—53no—
78C4×D9—53no—
79C4×D9—53no—
80Dic18—53no—
81C22×C3×C5C22×D313yes—
82C2×D15—31no—
83C2×D15—33no—
84C2×D15—66no—
85C3×C4×C5C22×D313yes—
86C3×C4×C5C22×D311yescharacteristic
87Dic15—33no—
88Dic15—31no—
89C3×#41D1511yescharacteristic
90#239—151no—
91D3×Q8—151no—
92#237—153no—
93D3×D4—153no—
94#235—153no—
95C2×C4×D3—153no—
96C5×C9C2×#4111yescharacteristic, complemented, Hall
97C22×D5—93no—
98C5×Q8C2×D911yescharacteristic, complemented
99C5×D4C2×D913yescomplemented
100C2×C4×C5C2×D913yescomplemented
101C22⋊D5—96no—
102C2×Dic5—93no—
103D20—93no—
104C4×D5—91no—
105C4×D5—93no—
106C4×D5—93no—
107C4×D5—93no—
108Dic10—93no—
109C22×C9C22×D513yes—
110C2×D9—51no—
111C2×D9—53no—
112C2×D9—106no—
113C4×C9C22×D513yes—
114C4×C9C22×D511yescharacteristic
115Dic9—53no—
116Dic9—51no—
117C2×#41—451noSylow
118C2×C3×C5—23no—
119C2×C3×C5C23×D311yescharacteristic
120D15—32no—
121D15—63no—
122C22×D3—153no—
123C3×Q8C2×D1511yescharacteristic
124C3×D4C2×D1513yes—
125C2×C3×C4C2×D1513yes—
126#67—156no—
127C2×Dic3—153no—
128D12—153no—
129C4×D3—151no—
130C4×D3—153no—
131C4×D3—153no—
132C4×D3—153no—
133Dic6—153no—
134C22×C5C22×D913yes—
135C2×D5—91no—
136C2×D5—93no—
137C2×D5—186no—
138C4×C5C22×D913yes—
139C4×C5C22×D911yescharacteristic
140Dic5—93no—
141Dic5—91no—
142C2×C9—23no—
143C2×C9C23×D511yescharacteristic
144D9—52no—
145D9—103no—
146#41—451no—
147#41—453no—
148#41—453no—
149#41D4511yescharacteristic, direct product factor
150C2×Q8—451no—
151C2×D4—453no—
152C22×C4—453no—
153C3×C5D3×#4111yescharacteristic
154C22×C3C22×D1513yes—
155C2×D3—151no—
156C2×D3—153no—
157C2×D3—306no—
158C3×C4C22×D1513yes—
159C3×C4C22×D1511yescharacteristic
160Dic3—153no—
161Dic3—151no—
162C2×C5—23no—
163C2×C5C23×D911yescharacteristic
164D5—92no—
165D5—183no—
166C9D5×#4111yescharacteristic, complemented, Sylow
167C23—453no—
168Q8—453no—
169Q8C2×D4511yescharacteristic, complemented
170D4—456no—
171D4—453no—
172D4C2×D4513yescomplemented
173C2×C4—453no—
174C2×C4—453no—
175C2×C4—453no—
176C2×C4—451no—
177C2×C4—453no—
178C2×C4C2×D4513yescomplemented
179C2×C3—23no—
180C2×C3C23×D1511yescharacteristic
181D3—152no—
182D3—303no—
183C5#41×D911yescharacteristic, complemented, Sylow
184C22—451no—
185C22—453no—
186C22—906no—
187C22C22×D4513yes—
188C4—451no—
189C4—453no—
190C4C22×D4513yes—
191C4C22×D4511yescharacteristic
192C3#41×D1511yescharacteristic
193C2—23no—
194C2—452no—
195C2—903no—
196C2C23×D4511yescharacteristic
subgroupG/H
centerC4C22×D45
commutator, cosocleC2×C5×C9C24
FrattiniC2×C3C23×D15
FittingC5×C9×#41C2
socleC2×C3×C5C23×D3
hypercenter#41D45
hypocenterC5×C9C2×#41
LCSG ▷ C2×C5×C9 ▷ C5×C9
UCSC1 ◁ C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C5×C9×#41C2semidirect
2. #10623713C2semidirect
3. Q8×D45C2semidirect
4. #10623711C2semidirect
5. D4×D45C2semidirect
6. #10623709C2semidirect
7. C2×C4×D45C2semidirect
10. C5×Q8×C9C22semidirect
11. C5×D4×C9C22semidirect
12. C2×C4×C5×C9C22semidirect
13. #67099C22semidirect
14. C2×Dic45C22semidirect
15. D180C22semidirect
18. C4×D45C22semidirect
19. C4×D45C22semidirect
20. Dic90C22semidirect
38. C9×#41D5semidirect
61. D45#41direct (N × H)
62. C5×#41D9semidirect
70. Q8×C9C2×D5semidirect
71. D4×C9C2×D5semidirect
72. C2×C4×C9C2×D5semidirect
96. C5×C9C2×#41semidirect
98. C5×Q8C2×D9semidirect
99. C5×D4C2×D9semidirect
100. C2×C4×C5C2×D9semidirect
149. #41D45direct (N × H)
166. C9D5×#41semidirect
169. Q8C2×D45semidirect
172. D4C2×D45semidirect
178. C2×C4C2×D45semidirect
183. C5#41×D9semidirect

Maximal subgroups

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

subgroupindex
C5×C9×#412
#106237132
Q8×D452
#106237112
D4×D452
#106237092
C2×C4×D452
#41×D153
#41×D95