Finite Group Databasebeta

← C2×#10624222 #13089402

Subgroups — C2×#10624222 #13089402

Order 1440.

678 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 175 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
1C2×C4×C5×C3⋊D3C211yesmaximal, characteristic
2C2×C3×Dic30C212yesmaximal, complemented
3C2×#67158C212yesmaximal, complemented
4C2×#67155C212yesmaximal
5#10624222C218yesmaximal, direct product factor
6C2×D3×Dic10—32nomaximal
7C22×C5×C3⋊D3C2211yescharacteristic
8C2×C32×C4×C5C2211yescharacteristic
9C2×C5×C3⋊Dic3C2211yescharacteristic
10C4×C5×C3⋊D3C2214yes—
11C2×C3×Dic15C2214yes—
12C3×Dic30C2218yescomplemented
13#67158C2218yescomplemented
14#67155C2218yes—
15C2×#3797—51nomaximal, Hall
16C2×Dic30D312yescomplemented
17C2×C4×C5×D3—32no—
18C2×C4×C5×D3—61no—
19C2×C3×Dic10—32no—
20C2×#1204—34no—
21C2×D3×Dic5—34no—
22D3×Dic10—316no—
23C22×C32×C5C2311yescharacteristic
24C2×C5×C3⋊D3Q814yescomplemented
25C2×C5×C3⋊D3C2312yes—
26C32×C4×C5C2312yes—
27C5×C3⋊Dic3C2312yes—
28C3×Dic15C2318yes—
29C22×Dic10—91noHall
30C2×C4×C3⋊D3D511yescharacteristic
31C2×C3×Dic6—52no—
32C2×#627—52no—
33C2×#624—52no—
34#3797—58no—
35C22×C5×D3—32no—
36C22×C5×D3—61no—
37C2×C3×C4×C5—21no—
38C2×C3×C4×C5C2×D312yes—
39C2×Dic15C2×D314yes—
40Dic30C2×D318yescomplemented
41C2×C5×Dic3—32no—
42C2×C5×Dic3—61no—
43C4×C5×D3—38no—
44C4×C5×D3—64no—
45C2×C3×Dic5—34no—
46C3×Dic10—38no—
47#1204—316no—
48D3×Dic5—316no—
49C2×D3×Q8—152no—
50C2×C32×C5C2×Q812yescomplemented
51C2×C32×C5C2411yescharacteristic
52C5×C3⋊D3C2×Q814yescomplemented
53C22×C4×C5—91no—
54C22×Dic5—92no—
55C2×Dic10—32no—
56C2×Dic10—98no—
57C2×Dic10—92no—
58C22×C3⋊D3C2×D511yescharacteristic
59C2×C32×C4C2×D511yescharacteristic
60C2×C3⋊Dic3C2×D511yescharacteristic
61C4×C3⋊D3C2×D514yes—
62C2×C3×Dic3—54no—
63C3×Dic6—58no—
64#627—58no—
65#624—58no—
66C22×C3×C5—21no—
67C22×C3×C5C22×D312yes—
68C2×C5×D3—38no—
69C2×C5×D3—34no—
70C2×C5×D3—64no—
71C2×C5×D3—62no—
72C3×C4×C5—22no—
73C3×C4×C5C22×D314yes—
74Dic15C22×D318yes—
75C3×Dic5—38no—
76C5×Dic3—34no—
77C5×Dic3—62no—
78C2×C3×Q8—152no—
79D3×Q8—1516no—
80C2×C4×D3—32no—
81C2×C4×D3—61no—
82C2×C4×D3—154no—
83C2×Dic6—52no—
84C2×Dic6—154no—
85C32×C5C22×Q811yescharacteristic, complemented, Hall
86C23×C5—91no—
87C2×C4×C5—91no—
88C2×C4×C5—94no—
89C2×C4×C5D3211yescharacteristic
90C2×Dic5—34no—
91C2×Dic5—98no—
92Dic10—38no—
93Dic10—98no—
94C22×C32C22×D511yescharacteristic
95C2×C3⋊D3Dic1014yescomplemented
96C2×C3⋊D3C22×D512yes—
97C32×C4C22×D512yes—
98C3⋊Dic3C22×D512yes—
99C3×Dic3—58no—
100C22×Q8—451noSylow
101C2×C3×C5—21no—
102C2×C3×C5—22no—
103C2×C3×C5D3×Q814yescomplemented
104C2×C3×C5C23×D312yes—
105C5×D3—38no—
106C5×D3—64no—
107C22×D3—32no—
108C22×D3—61no—
109C3×Q8—158no—
110C2×C3×C4—21no—
111C2×C3×C4—154no—
112C2×C3×C4D3×D512yes—
113C2×Dic3—32no—
114C2×Dic3—54no—
115C2×Dic3—61no—
116C4×D3—38no—
117C4×D3—64no—
118C4×D3—1516no—
119Dic6—58no—
120Dic6—1516no—
121C22×C5—92no—
122C22×C5—94no—
123C22×C5C2×D3211yescharacteristic
124C4×C5—92no—
125C4×C5C2×D3212yes—
126Dic5—38no—
127C2×C32C2×Dic1012yescomplemented
128C2×C32C23×D511yescharacteristic
129C3⋊D3C2×Dic1014yescomplemented
130C2×Q8—152no—
131C2×Q8—452no—
132C2×Q8—458no—
133C22×C4—91no—
134C22×C4—452no—
135C3×C5—21no—
136C3×C5C2×D3×Q812yescomplemented
137C22×C3—21no—
138C22×C3C2×D3×D512yes—
139C2×D3—38no—
140C2×D3—34no—
141C2×D3—62no—
142C2×D3—64no—
143C3×C4—22no—
144C3×C4—158no—
145C3×C4C2×D3×D514yes—
146Dic3—34no—
147Dic3—58no—
148Dic3—62no—
149C2×C5—94no—
150C2×C5#379712yescomplemented
151C2×C5C22×D3211yescharacteristic
152C32C22×Dic1011yescharacteristic, complemented, Sylow
153C23—91no—
154Q8—158no—
155Q8—458no—
156C2×C4—91no—
157C2×C4—94no—
158C2×C4—154no—
159C2×C4—458no—
160C2×C4(C3⋊D3)⋊D511yescharacteristic
161C2×C3—21no—
162C2×C3—22no—
163C2×C3D3×Dic1014yescomplemented
164C2×C3C22×D3×D512yes—
165D3—38no—
166D3—64no—
167C5C2×#379711yescharacteristic, complemented, Sylow
168C22—92no—
169C22—94no—
170C22C2×(C3⋊D3)⋊D511yescharacteristic
171C4—92no—
172C4—158no—
173C4C2×(C3⋊D3)⋊D512yes—
174C3—21no—
175C3C2×D3×Dic1012yescomplemented
176C2—94no—
177C2#1062422212yesdirect product factor
178C2C22×(C3⋊D3)⋊D511yescharacteristic
subgroupG/H
centerC22C2×(C3⋊D3)⋊D5
commutator, cosocleC2×C32×C5C24
FrattiniC2C22×(C3⋊D3)⋊D5
FittingC2×C32×C4×C5C22
socleC22×C32×C5C23
prime radicalC22×C5×C3⋊D3C22
hypercenterC2×C4(C3⋊D3)⋊D5
hypocenterC32×C5C22×Q8
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×Dic30C2semidirect
3. C2×#67158C2semidirect
5. #10624222C2direct (N × H)
12. C3×Dic30C22semidirect
13. #67158C22semidirect
16. C2×Dic30D3semidirect
24. C2×C5×C3⋊D3Q8semidirect
40. Dic30C2×D3semidirect
50. C2×C32×C5C2×Q8semidirect
52. C5×C3⋊D3C2×Q8semidirect
85. C32×C5C22×Q8semidirect
95. C2×C3⋊D3Dic10semidirect
103. C2×C3×C5D3×Q8semidirect
127. C2×C32C2×Dic10semidirect
129. C3⋊D3C2×Dic10semidirect
136. C3×C5C2×D3×Q8semidirect
150. C2×C5#3797semidirect
152. C32C22×Dic10semidirect
163. C2×C3D3×Dic10semidirect
167. C5C2×#3797semidirect
175. C3C2×D3×Dic10semidirect
177. C2#10624222direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C5×C3⋊D32
C2×C3×Dic302
C2×#671582
C2×#671552
#106242222
C2×D3×Dic103
C2×#37975