Finite Group Databasebeta

← C3×#91528 #13086674

Subgroups — C3×#91528 #13086674

Order 1440.

358 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C22×C32×Dic5C211yesmaximal, characteristic
2C3×#6719C211yesmaximal, characteristic
3C3×C5×#217C211yesmaximal, characteristic
4C3×#6668C212yesmaximal, complemented
5C3×Dic3×Dic5C212yesmaximal, complemented
6C3×#4023—31nomaximal
7#91528C311yesmaximal, characteristic, direct product factor
8C23×C32×C5C2211yescharacteristic
9C2×C3×Dic15C2212yes—
10C2×C3×C5×Dic3C2212yes—
11C2×C32×Dic5C414yescomplemented
12C2×C32×Dic5C2211yescharacteristic
13C2×C32×Dic5C2211yescharacteristic
14C3×#926—51nomaximal, Hall
15C22×C3×Dic5—21no—
16C22×C3×Dic5D311yescharacteristic
17C22×C3×Dic5C2×C311yescharacteristic
18C3×C5×C22⋊C4—31no—
19#6719C2×C311yescharacteristic
20C5×#217C2×C311yescharacteristic
21C3×C22⋊Dic5—31no—
22C3×#683—32no—
23C3×C4×Dic5—32no—
24#6668C2×C312yescomplemented
25Dic3×Dic5C2×C312yescomplemented
26C22×C32×C5—22no—
27C22×C32×C5C2×C412yes—
28C22×C32×C5C2311yescharacteristic
29C3×Dic15—22no—
30C3×C5×Dic3—22no—
31C32×Dic5C2×C412yes—
32C32×Dic5C2×C412yes—
33#4023—31noHall
34C22×C32×C4—51no—
35C3×#217—51no—
36C3×#217D511yescharacteristic
37C3×C4⋊Dic3—52no—
38C3×C4×Dic3—52no—
39C23×C3×C5—21no—
40C23×C3×C5C2×D311yescharacteristic
41C23×C3×C5C22×C311yescharacteristic
42C2×C3×C4×C5—32no—
43C2×Dic15C22×C312yes—
44C2×C5×Dic3C22×C312yes—
45C2×C3×Dic5—24no—
46C2×C3×Dic5—21no—
47C2×C3×Dic5—21no—
48C2×C3×Dic5—32no—
49C2×C3×Dic5Dic314yescomplemented
50C2×C3×Dic5C3×C414yescomplemented
51C2×C3×Dic5C2×D311yescharacteristic
52C2×C3×Dic5C2×D311yescharacteristic
53C2×C3×Dic5C22×C311yescharacteristic
54C2×C3×Dic5C22×C311yescharacteristic
55C3×#117—151no—
56#926—51no—
57C2×C32×C5—22no—
58C2×C32×C5C22×C411yescharacteristic
59C2×C32×C5#4112yes—
60C22×Dic5C3×D311yescharacteristic
61C5×C22⋊C4—31no—
62C22⋊Dic5—31no—
63#683—32no—
64C4×Dic5—32no—
65C23×C32C2×D511yescharacteristic
66C2×C32×C4—54no—
67C2×C32×C4—51no—
68C2×C32×C4—51no—
69C2×C3×Dic3—52no—
70C2×C3×Dic3C2×D512yes—
71C22×C3×C5—24no—
72C22×C3×C5—22no—
73C22×C3×C5—22no—
74C22×C3×C5—22no—
75C22×C3×C5—21no—
76C22×C3×C5C2×Dic312yes—
77C22×C3×C5C2×C3×C412yes—
78C22×C3×C5C22×D311yescharacteristic
79C22×C3×C5C23×C311yescharacteristic
80C3×C4×C5—62no—
81Dic15—22no—
82C3×Dic5—22no—
83C3×Dic5—22no—
84C3×Dic5—62no—
85C3×Dic5C2×Dic312yes—
86C3×Dic5C2×Dic312yes—
87C3×Dic5C2×C3×C412yes—
88C3×Dic5C2×C3×C412yes—
89C5×Dic3—22no—
90C22×C3×C4—51no—
91C22×C3×C4—51no—
92C22×C3×C4—101no—
93C3×C4⋊C4—152no—
94C3×C22⋊C4—31no—
95C3×C22⋊C4—151no—
96C3×C42—152no—
97#217—51no—
98#217C3×D511yescharacteristic
99C4⋊Dic3—52no—
100C4×Dic3—52no—
101C32×C5#11711yescharacteristic, complemented, Hall
102C23×C5C2×C3×D311yescharacteristic
103C2×C4×C5—32no—
104C2×Dic5—32no—
105C2×Dic5C3×Dic314yescomplemented
106C2×Dic5C2×C3×D311yescharacteristic
107C2×Dic5C2×C3×D311yescharacteristic
108C22×C32—22no—
109C22×C32C4×D512yes—
110C22×C32C22×D511yescharacteristic
111C32×C4—52no—
112C32×C4—52no—
113C3×Dic3—22no—
114C3×Dic3—102no—
115#117—151noSylow
116C2×C3×C5—24no—
117C2×C3×C5—22no—
118C2×C3×C5—22no—
119C2×C3×C5—22no—
120C2×C3×C5—21no—
121C2×C3×C5#23512yes—
122C2×C3×C5C22×Dic311yescharacteristic
123C2×C3×C5C22×C3×C411yescharacteristic
124C2×C3×C5C3×#4112yes—
125C23×C3—21no—
126C23×C3D3×D511yescharacteristic
127C23×C3C2×C3×D511yescharacteristic
128C2×C3×C4—32no—
129C2×C3×C4—54no—
130C2×C3×C4—54no—
131C2×C3×C4—51no—
132C2×C3×C4—51no—
133C2×C3×C4—51no—
134C2×C3×C4—51no—
135C2×C3×C4—104no—
136C2×C3×C4—101no—
137C2×C3×C4—101no—
138C2×C3×C4—152no—
139C2×Dic3—52no—
140C2×Dic3C2×C3×D512yes—
141C22×C5—22no—
142C22×C5C2×C3×Dic312yes—
143C22×C5C22×C3×D311yescharacteristic
144C4×C5—62no—
145Dic5—62no—
146Dic5C2×C3×Dic312yes—
147Dic5C2×C3×Dic312yes—
148C2×C32—22no—
149C2×C32C2×C4×D511yescharacteristic
150C2×C32#71112yes—
151C22×C4—51no—
152C4⋊C4—152no—
153C22⋊C4—31no—
154C22⋊C4—151no—
155C42—152no—
156C3×C5—21no—
157C3×C5#92611yescharacteristic, complemented
158C3×C5C3×#11711yescharacteristic, complemented
159C22×C3—24no—
160C22×C3—22no—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—21no—
164C22×C3D5×Dic312yes—
165C22×C3C3×C4×D512yes—
166C22×C3C2×D3×D511yescharacteristic
167C22×C3C22×C3×D511yescharacteristic
168C3×C4—52no—
169C3×C4—52no—
170C3×C4—52no—
171C3×C4—52no—
172C3×C4—62no—
173C3×C4—102no—
174C3×C4—102no—
175C3×C4—302no—
176Dic3—22no—
177Dic3—102no—
178C2×C5—22no—
179C2×C5C3×#23512yes—
180C2×C5C22×C3×Dic311yescharacteristic
181C32#402311yescharacteristic, complemented, Sylow
182C23C3×D3×D511yescharacteristic
183C2×C4—32no—
184C2×C4—54no—
185C2×C4—51no—
186C2×C4—51no—
187C2×C4—152no—
188C2×C3—24no—
189C2×C3—22no—
190C2×C3—22no—
191C2×C3—21no—
192C2×C3—22no—
193C2×C3C2×D5×Dic311yescharacteristic
194C2×C3#678212yes—
195C2×C3C2×C3×C4×D511yescharacteristic
196C2×C3C3×#71112yes—
197C5C3×#92611yescharacteristic, complemented, Sylow
198C22—22no—
199C22C3×D5×Dic312yes—
200C22C2×C3×D3×D511yescharacteristic
201C4—52no—
202C4—52no—
203C4—62no—
204C4—302no—
205C3—21no—
206C3#9152811yescharacteristic, direct product factor
207C3C3×#402311yescharacteristic, complemented
208C2—22no—
209C2C2×C3×D5×Dic311yescharacteristic
210C2C3×#678212yes—
subgroupG/H
centerC22×C3C2×D3×D5
commutatorC2×C3×C5C22×C3×C4
FrattiniC22C2×C3×D3×D5
Fitting, prime radicalC23×C32×C5C22
socleC22×C32×C5C23
cosocleC22×C3×C5C23×C3
hypercenterC23×C3D3×D5
hypocenterC3×C5C3×#117
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
4. C3×#6668C2semidirect
5. C3×Dic3×Dic5C2semidirect
7. #91528C3direct (N × H)
11. C2×C32×Dic5C4semidirect
24. #6668C2×C3semidirect
25. Dic3×Dic5C2×C3semidirect
49. C2×C3×Dic5Dic3semidirect
50. C2×C3×Dic5C3×C4semidirect
101. C32×C5#117semidirect
105. C2×Dic5C3×Dic3semidirect
157. C3×C5#926semidirect
158. C3×C5C3×#117semidirect
181. C32#4023semidirect
197. C5C3×#926semidirect
206. C3#91528direct (N × H)
207. C3C3×#4023semidirect

Maximal subgroups

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

subgroupindex
C22×C32×Dic52
C3×#67192
C3×C5×#2172
C3×#66682
C3×Dic3×Dic52
C3×#40233
#915283
C3×#9265