Finite Group Databasebeta

← #41×C3⋊D15 #13089513

Subgroups — #41×C3⋊D15 #13089513

Order 1440.

984 conjugacy classes of subgroups; only the 257 normal subgroups are shown.

normal subgroups only

This group has 984 conjugacy classes of subgroups — too many to draw. Only its 257 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
1C32×C5×#41C211yesmaximal, characteristic, complemented
2#10624287C211yesmaximal, characteristic, complemented
3Q8×C3⋊D15C211yesmaximal, characteristic, complemented
4#10624285C213yesmaximal, complemented
5D4×C3⋊D15C213yesmaximal, complemented
6#10624283C213yesmaximal, complemented
7C2×C4×C3⋊D15C213yesmaximal, complemented
8#41×D15—34nomaximal
9C22×C3⋊D15C2213yes—
10C32×C5×Q8C2211yescharacteristic, complemented
11C32×C5×D4C2213yescomplemented
12C2×C32×C4×C5C2213yescomplemented
13#67184C2216yescomplemented
14C2×C3⋊Dic15C2213yescomplemented
15C4⋊(C3⋊D15)C2213yescomplemented
16C4×C3⋊D15C2211yescharacteristic
17C4×C3⋊D15C2213yes—
18C4×C3⋊D15C2213yescomplemented
19C4×C3⋊D15C2213yescomplemented
20#67180C2213yescomplemented
21#41×C3⋊D3—51nomaximal, Hall
22C3×C5×#41D314yescomplemented
23#6821—34no—
24Q8×D15—34no—
25#6819—312no—
26D4×D15—312no—
27#6817—312no—
28C2×C4×D15—312no—
29C22×C32×C5C2313yes—
30C2×C3⋊D15—26no—
31C2×C3⋊D15C2313yes—
32C2×C3⋊D15C2311yescharacteristic
33C32×C4×C5C2313yes—
34C32×C4×C5C2311yescharacteristic
35C3⋊Dic15C2313yes—
36C3⋊Dic15C2311yescharacteristic
37D5×#41—91noHall
38C32×#41D511yescharacteristic, complemented
39#3832—51no—
40Q8×C3⋊D3—51no—
41#3830—53no—
42D4×C3⋊D3—53no—
43#3828—53no—
44C2×C4×C3⋊D3—53no—
45C22×D15—312no—
46C3×C5×Q8C2×D314yescomplemented
47C3×C5×D4C2×D3112yescomplemented
48C2×C3×C4×C5C2×D3112yescomplemented
49#1220—324no—
50C2×Dic15—312no—
51D60—312no—
52C4×D15—34no—
53C4×D15—312no—
54C4×D15—312no—
55C4×D15—312no—
56Dic30—312no—
57D3×#41—154no—
58C2×C32×C5—23no—
59C2×C32×C5C2411yescharacteristic
60C3⋊D15—23no—
61C3⋊D15#4112yesdirect product factor
62C5×#41C3⋊D311yescharacteristic, complemented
63#713—91no—
64Q8×D5—91no—
65#711—93no—
66D4×D5—93no—
67#709—93no—
68C2×C4×D5—93no—
69C22×C3⋊D3—53no—
70C32×Q8C2×D511yescharacteristic, complemented
71C32×D4C2×D513yescomplemented
72C2×C32×C4C2×D513yescomplemented
73#638—56no—
74C2×C3⋊Dic3—53no—
75C4⋊(C3⋊D3)—53no—
76C4×C3⋊D3—51no—
77C4×C3⋊D3—53no—
78C4×C3⋊D3—53no—
79C4×C3⋊D3—53no—
80#634—53no—
81C22×C3×C5C22×D3112yes—
82C2×D15—34no—
83C2×D15—312no—
84C2×D15—624no—
85C3×C4×C5C22×D3112yes—
86C3×C4×C5C22×D314yes—
87Dic15—312no—
88Dic15—34no—
89C3×#41D1514yescomplemented
90#239—154no—
91D3×Q8—154no—
92#237—1512no—
93D3×D4—1512no—
94#235—1512no—
95C2×C4×D3—1512no—
96C32×C5C2×#4111yescharacteristic, complemented, Hall
97C22×D5—93no—
98C5×Q8C2×C3⋊D311yescharacteristic, complemented
99C5×D4C2×C3⋊D313yescomplemented
100C2×C4×C5C2×C3⋊D313yescomplemented
101C22⋊D5—96no—
102C2×Dic5—93no—
103D20—93no—
104C4×D5—91no—
105C4×D5—93no—
106C4×D5—93no—
107C4×D5—93no—
108Dic10—93no—
109C22×C32C22×D513yes—
110C2×C3⋊D3—51no—
111C2×C3⋊D3—53no—
112C2×C3⋊D3—106no—
113C32×C4C22×D513yes—
114C32×C4C22×D511yescharacteristic
115C3⋊Dic3—53no—
116C3⋊Dic3—51no—
117C2×#41—451noSylow
118C2×C3×C5—212no—
119C2×C3×C5C23×D314yes—
120D15—38no—
121D15—612no—
122C22×D3—1512no—
123C3×Q8C2×D1514yescomplemented
124C3×D4C2×D15112yescomplemented
125C2×C3×C4C2×D15112yescomplemented
126#67—1524no—
127C2×Dic3—1512no—
128D12—1512no—
129C4×D3—154no—
130C4×D3—1512no—
131C4×D3—1512no—
132C4×D3—1512no—
133Dic6—1512no—
134C22×C5C22×C3⋊D313yes—
135C2×D5—91no—
136C2×D5—93no—
137C2×D5—186no—
138C4×C5C22×C3⋊D313yes—
139C4×C5C22×C3⋊D311yescharacteristic
140Dic5—93no—
141Dic5—91no—
142C2×C32—23no—
143C2×C32C23×D511yescharacteristic
144C3⋊D3—52no—
145C3⋊D3—103no—
146#41—451no—
147#41—453no—
148#41—453no—
149#41C3⋊D1511yescharacteristic, direct product factor
150C2×Q8—451no—
151C2×D4—453no—
152C22×C4—453no—
153C3×C5D3×#4114yescomplemented
154C22×C3C22×D15112yes—
155C2×D3—154no—
156C2×D3—1512no—
157C2×D3—3024no—
158C3×C4C22×D15112yes—
159C3×C4C22×D1514yes—
160Dic3—1512no—
161Dic3—154no—
162C2×C5—23no—
163C2×C5C23×C3⋊D311yescharacteristic
164D5—92no—
165D5—183no—
166C32D5×#4111yescharacteristic, complemented, Sylow
167C23—453no—
168Q8—453no—
169Q8C2×C3⋊D1511yescharacteristic, complemented
170D4—456no—
171D4—453no—
172D4C2×C3⋊D1513yescomplemented
173C2×C4—453no—
174C2×C4—453no—
175C2×C4—453no—
176C2×C4—451no—
177C2×C4—453no—
178C2×C4C2×C3⋊D1513yescomplemented
179C2×C3—212no—
180C2×C3C23×D1514yes—
181D3—158no—
182D3—3012no—
183C5#41×C3⋊D311yescharacteristic, complemented, Sylow
184C22—451no—
185C22—453no—
186C22—906no—
187C22C22×C3⋊D1513yes—
188C4—451no—
189C4—453no—
190C4C22×C3⋊D1513yes—
191C4C22×C3⋊D1511yescharacteristic
192C3#41×D1514yescomplemented
193C2—23no—
194C2—452no—
195C2—903no—
196C2C23×C3⋊D1511yescharacteristic
subgroupG/H
centerC4C22×C3⋊D15
commutator, socle, cosocleC2×C32×C5C24
FrattiniC2C23×C3⋊D15
FittingC32×C5×#41C2
hypercenter#41C3⋊D15
hypocenterC32×C5C2×#41
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C32×C5×#41C2semidirect
2. #10624287C2semidirect
3. Q8×C3⋊D15C2semidirect
4. #10624285C2semidirect
5. D4×C3⋊D15C2semidirect
6. #10624283C2semidirect
7. C2×C4×C3⋊D15C2semidirect
10. C32×C5×Q8C22semidirect
11. C32×C5×D4C22semidirect
12. C2×C32×C4×C5C22semidirect
13. #67184C22semidirect
14. C2×C3⋊Dic15C22semidirect
15. C4⋊(C3⋊D15)C22semidirect
18. C4×C3⋊D15C22semidirect
19. C4×C3⋊D15C22semidirect
20. #67180C22semidirect
22. C3×C5×#41D3semidirect
38. C32×#41D5semidirect
46. C3×C5×Q8C2×D3semidirect
47. C3×C5×D4C2×D3semidirect
48. C2×C3×C4×C5C2×D3semidirect
61. C3⋊D15#41direct (N × H)
62. C5×#41C3⋊D3semidirect
70. C32×Q8C2×D5semidirect
71. C32×D4C2×D5semidirect
72. C2×C32×C4C2×D5semidirect
89. C3×#41D15semidirect
96. C32×C5C2×#41semidirect
98. C5×Q8C2×C3⋊D3semidirect
99. C5×D4C2×C3⋊D3semidirect
100. C2×C4×C5C2×C3⋊D3semidirect
123. C3×Q8C2×D15semidirect
124. C3×D4C2×D15semidirect
125. C2×C3×C4C2×D15semidirect
149. #41C3⋊D15direct (N × H)
153. C3×C5D3×#41semidirect
166. C32D5×#41semidirect
169. Q8C2×C3⋊D15semidirect
172. D4C2×C3⋊D15semidirect
178. C2×C4C2×C3⋊D15semidirect
183. C5#41×C3⋊D3semidirect
192. C3#41×D15semidirect

Maximal subgroups

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

subgroupindex
C32×C5×#412
#106242872
Q8×C3⋊D152
#106242852
D4×C3⋊D152
#106242832
C2×C4×C3⋊D152
#41×D153
#41×C3⋊D35