Finite Group Databasebeta

← C3×#91781 #13087990

Subgroups — C3×#91781 #13087990

Order 1440.

330 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 126 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×C3×C4×D15C211yesmaximal, characteristic
2C32×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C3×#6714C212yesmaximal
4C3×C4⋊Dic15C211yesmaximal, characteristic, complemented
5C3×C4×Dic15C212yesmaximal, complemented
6#91781C311yesmaximal, characteristic, direct product factor
7C3×#4038—31nomaximal
8C22×C3×D15C2211yescharacteristic
9C2×C32×C4×C5C2212yes—
10C2×C32×C4×C5C2211yescharacteristic
11C2×C3×Dic15C2212yes—
12C2×C3×Dic15C2211yescharacteristic
13C3×C4×D15C414yescomplemented
14C3×#892—51nomaximal, Hall
15C2×C4×D15C2×C311yescharacteristic
16C2×C3×C4×D5—31no—
17C3×C5×C4⋊C4—21no—
18C3×C5×C4⋊C4D311yescharacteristic, complemented
19C3×C5×C4⋊C4C2×C311yescharacteristic, complemented
20#6714C2×C312yes—
21C4⋊Dic15C2×C311yescharacteristic, complemented
22C4×Dic15C2×C312yescomplemented
23C3×#685—32no—
24C3×C4⋊Dic5—31no—
25C3×C4×Dic5—32no—
26C22×C32×C5C2311yescharacteristic
27C2×C3×D15—21no—
28C2×C3×D15—21no—
29C2×C3×D15C2×C412yes—
30C32×C4×C5—22no—
31C32×C4×C5C2×C412yes—
32C3×Dic15—22no—
33C3×Dic15C2×C412yes—
34#4038—31noHall
35C2×C3×C4×D3—51no—
36C32×C4⋊C4D511yescharacteristic, complemented
37C3×(C2×D3)⋊C4—52no—
38C3×C4⋊Dic3—51no—
39C3×C4×Dic3—52no—
40C22×D15C22×C311yescharacteristic
41C22×C3×D5—31no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—22no—
44C2×C3×C4×C5C2×D312yes—
45C2×C3×C4×C5C2×D311yescharacteristic
46C2×C3×C4×C5C22×C312yes—
47C2×C3×C4×C5C22×C311yescharacteristic
48C2×Dic15C22×C312yes—
49C2×Dic15C22×C311yescharacteristic
50C4×D15C3×C414yescomplemented
51C2×C3×Dic5—31no—
52C2×C3×Dic5—32no—
53C3×C4×D5—34no—
54C3×#117—151no—
55#892—51no—
56C2×C32×C5C22×C411yescharacteristic
57C2×C32×C5#4111yescharacteristic
58C2×C32×C5#4111yescharacteristic
59C3×D15—22no—
60C2×C4×D5—31no—
61C5×C4⋊C4C3×D311yescharacteristic, complemented
62#685—32no—
63C4⋊Dic5—31no—
64C4×Dic5—32no—
65C22×C3×D3—51no—
66C2×C32×C4C2×D512yes—
67C2×C32×C4C2×D511yescharacteristic
68C2×C3×Dic3—51no—
69C2×C3×Dic3—52no—
70C3×C4×D3—54no—
71C22×C3×C5—21no—
72C22×C3×C5C22×D311yescharacteristic
73C22×C3×C5C23×C311yescharacteristic
74C2×D15—21no—
75C2×D15—21no—
76C2×D15C2×C3×C412yes—
77C2×C3×D5—32no—
78C2×C3×D5—61no—
79C2×C3×D5—61no—
80C3×C4×C5—22no—
81C3×C4×C5—22no—
82C3×C4×C5—22no—
83C3×C4×C5—42no—
84C3×C4×C5C4×D312yes—
85C3×C4×C5C2×C3×C412yes—
86Dic15—22no—
87Dic15C2×C3×C412yes—
88C3×Dic5—32no—
89C3×Dic5—62no—
90C22×C3×C4—151no—
91C2×C4×D3—51no—
92C3×C4⋊C4—21no—
93C3×C4⋊C4—151no—
94C3×C4⋊C4C3×D511yescharacteristic, complemented
95C3×C4⋊C4D1511yescharacteristic, complemented
96C3×C22⋊C4—152no—
97C3×C42—152no—
98(C2×D3)⋊C4—52no—
99C4⋊Dic3—51no—
100C4×Dic3—52no—
101C32×C5#11711yescharacteristic, complemented, Hall
102C22×D5—31no—
103C2×C4×C5C2×C3×D312yes—
104C2×C4×C5C2×C3×D311yescharacteristic
105C2×Dic5—31no—
106C2×Dic5—32no—
107C4×D5—34no—
108C22×C32C22×D511yescharacteristic
109C2×C3×D3—52no—
110C2×C3×D3—101no—
111C2×C3×D3—101no—
112C32×C4—22no—
113C32×C4C4×D512yes—
114C3×Dic3—52no—
115C3×Dic3—102no—
116#117—151noSylow
117C2×C3×C5—21no—
118C2×C3×C5—21no—
119C2×C3×C5—21no—
120C2×C3×C5C2×C4×D311yescharacteristic
121C2×C3×C5#23711yescharacteristic
122C2×C3×C5#23911yescharacteristic
123C2×C3×C5C22×C3×C411yescharacteristic
124C2×C3×C5C3×#4111yescharacteristic
125C2×C3×C5C3×#4111yescharacteristic
126D15—22no—
127C3×D5—62no—
128C23×C3—151no—
129C22×D3—51no—
130C2×C3×C4—21no—
131C2×C3×C4—22no—
132C2×C3×C4—151no—
133C2×C3×C4—154no—
134C2×C3×C4—152no—
135C2×C3×C4C2×C3×D512yes—
136C2×C3×C4C2×C3×D511yescharacteristic
137C2×C3×C4C2×D1512yes—
138C2×C3×C4C2×D1511yescharacteristic
139C2×Dic3—51no—
140C2×Dic3—52no—
141C4×D3—54no—
142C22×C5C22×C3×D311yescharacteristic
143C2×D5—32no—
144C2×D5—61no—
145C2×D5—61no—
146C4×C5—22no—
147C4×C5C3×C4×D312yes—
148Dic5—32no—
149Dic5—62no—
150C2×C32C2×C4×D511yescharacteristic
151C2×C32#71111yescharacteristic
152C2×C32#71311yescharacteristic
153C3×D3—102no—
154C22×C4—151no—
155C4⋊C4—151no—
156C4⋊C4C3×D1511yescharacteristic, complemented
157C22⋊C4—152no—
158C42—152no—
159C3×C5—21no—
160C3×C5#89211yescharacteristic, complemented
161C3×C5C3×#11711yescharacteristic, complemented
162C22×C3—21no—
163C22×C3—152no—
164C22×C3—301no—
165C22×C3—301no—
166C22×C3C22×C3×D511yescharacteristic
167C22×C3C22×D1511yescharacteristic
168C2×D3—52no—
169C2×D3—101no—
170C2×D3—101no—
171C3×C4—22no—
172C3×C4—22no—
173C3×C4—22no—
174C3×C4—42no—
175C3×C4—152no—
176C3×C4—302no—
177C3×C4C3×C4×D512yes—
178C3×C4C4×D1512yes—
179Dic3—52no—
180Dic3—102no—
181C2×C5C2×C3×C4×D311yescharacteristic
182C2×C5C3×#23711yescharacteristic
183C2×C5C3×#23911yescharacteristic
184D5—62no—
185C32#403811yescharacteristic, complemented, Sylow
186C23—151no—
187C2×C4—151no—
188C2×C4—154no—
189C2×C4—152no—
190C2×C4C2×C3×D1512yes—
191C2×C4C2×C3×D1511yescharacteristic
192C2×C3—21no—
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—302no—
196C2×C3C2×C3×C4×D511yescharacteristic
197C2×C3C3×#71111yescharacteristic
198C2×C3C3×#71311yescharacteristic
199C2×C3C2×C4×D1511yescharacteristic
200C2×C3#681911yescharacteristic
201C2×C3#682111yescharacteristic
202D3—102no—
203C5C3×#89211yescharacteristic, complemented, Sylow
204C22—152no—
205C22—301no—
206C22—301no—
207C22C22×C3×D1511yescharacteristic
208C4—22no—
209C4—152no—
210C4—302no—
211C4C3×C4×D1512yes—
212C3—21no—
213C3C3×#403811yescharacteristic, complemented
214C3#9178111yescharacteristic, direct product factor
215C2—302no—
216C2C2×C3×C4×D1511yescharacteristic
217C2C3×#681911yescharacteristic
218C2C3×#682111yescharacteristic
subgroupG/H
centerC22×C3C22×D15
commutatorC2×C3×C5C22×C3×C4
FrattiniC22C22×C3×D15
FittingC32×C5×C4⋊C4C2
socleC22×C32×C5C23
prime radicalC22×C3×D15C22
cosocleC22×C3×C5C23×C3
hypercenterC3×C4⋊C4D15
hypocenterC3×C5C3×#117
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C5×C4⋊C4C2semidirect
4. C3×C4⋊Dic15C2semidirect
5. C3×C4×Dic15C2semidirect
6. #91781C3direct (N × H)
13. C3×C4×D15C4semidirect
18. C3×C5×C4⋊C4D3semidirect
19. C3×C5×C4⋊C4C2×C3semidirect
21. C4⋊Dic15C2×C3semidirect
22. C4×Dic15C2×C3semidirect
36. C32×C4⋊C4D5semidirect
50. C4×D15C3×C4semidirect
61. C5×C4⋊C4C3×D3semidirect
94. C3×C4⋊C4C3×D5semidirect
95. C3×C4⋊C4D15semidirect
101. C32×C5#117semidirect
156. C4⋊C4C3×D15semidirect
160. C3×C5#892semidirect
161. C3×C5C3×#117semidirect
185. C32#4038semidirect
203. C5C3×#892semidirect
213. C3C3×#4038semidirect
214. C3#91781direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×D152
C32×C5×C4⋊C42
C3×#67142
C3×C4⋊Dic152
C3×C4×Dic152
#917813
C3×#40383
C3×#8925