Finite Group Databasebeta

← C3×#91761 #13087969

Subgroups — C3×#91761 #13087969

Order 1440.

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

normal subgroups only

This group has 334 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×C42×C5C211yesmaximal, characteristic, complemented
3C3×#6714C212yesmaximal
4C3×#6712C212yesmaximal, complemented
5C3×C4×Dic15C211yesmaximal, characteristic, complemented
6#91761C311yesmaximal, characteristic, direct product factor
7C3×#4018—31nomaximal
8C22×C3×D15C2211yescharacteristic
9C2×C32×C4×C5C2212yes—
10C2×C32×C4×C5C2211yescharacteristic
11C2×C3×Dic15C2212yes—
12C2×C3×Dic15C2211yescharacteristic
13C3×C4×D15C414yescomplemented
14C3×#872—51nomaximal, Hall
15C2×C4×D15C2×C311yescharacteristic
16C2×C3×C4×D5—31no—
17C3×C42×C5—21no—
18C3×C42×C5D311yescharacteristic, complemented
19C3×C42×C5C2×C311yescharacteristic, complemented
20#6714C2×C312yes—
21#6712C2×C312yescomplemented
22C4×Dic15C2×C311yescharacteristic, complemented
23C3×#685—32no—
24C3×#683—32no—
25C3×C4×Dic5—31no—
26C22×C32×C5C2311yescharacteristic
27C2×C3×D15—22no—
28C2×C3×D15C2×C412yes—
29C32×C4×C5—22no—
30C32×C4×C5C2×C412yes—
31C3×Dic15—22no—
32C3×Dic15C2×C412yes—
33#4018—31noHall
34C2×C3×C4×D3—51no—
35C32×C42D511yescharacteristic, complemented
36C3×(C2×D3)⋊C4—52no—
37C3×Dic3⋊C4—52no—
38C3×C4×Dic3—51no—
39C22×D15C22×C311yescharacteristic
40C22×C3×D5—31no—
41C2×C3×C4×C5—22no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5C2×D312yes—
44C2×C3×C4×C5C2×D311yescharacteristic
45C2×C3×C4×C5C22×C312yes—
46C2×C3×C4×C5C22×C311yescharacteristic
47C2×Dic15C22×C312yes—
48C2×Dic15C22×C311yescharacteristic
49C4×D15C3×C414yescomplemented
50C2×C3×Dic5—31no—
51C2×C3×Dic5—32no—
52C3×C4×D5—34no—
53C3×#117—151no—
54#872—51no—
55C2×C32×C5C22×C411yescharacteristic
56C2×C32×C5#4112yes—
57C3×D15—22no—
58C2×C4×D5—31no—
59C42×C5C3×D311yescharacteristic, complemented
60#685—32no—
61#683—32no—
62C4×Dic5—31no—
63C22×C3×D3—51no—
64C2×C32×C4C2×D512yes—
65C2×C32×C4C2×D511yescharacteristic
66C2×C3×Dic3—51no—
67C2×C3×Dic3—52no—
68C3×C4×D3—54no—
69C22×C3×C5—21no—
70C22×C3×C5C22×D311yescharacteristic
71C22×C3×C5C23×C311yescharacteristic
72C2×D15—22no—
73C2×D15C2×C3×C412yes—
74C2×C3×D5—32no—
75C2×C3×D5—62no—
76C3×C4×C5—24no—
77C3×C4×C5—22no—
78C3×C4×C5—22no—
79C3×C4×C5—22no—
80C3×C4×C5C4×D312yes—
81C3×C4×C5C2×C3×C412yes—
82Dic15—22no—
83Dic15C2×C3×C412yes—
84C3×Dic5—32no—
85C3×Dic5—62no—
86C22×C3×C4—151no—
87C2×C4×D3—51no—
88C3×C4⋊C4—152no—
89C3×C22⋊C4—152no—
90C3×C42—21no—
91C3×C42—151no—
92C3×C42C3×D511yescharacteristic, complemented
93C3×C42D1511yescharacteristic, complemented
94(C2×D3)⋊C4—52no—
95Dic3⋊C4—52no—
96C4×Dic3—51no—
97C32×C5#11711yescharacteristic, complemented, Hall
98C22×D5—31no—
99C2×C4×C5C2×C3×D312yes—
100C2×C4×C5C2×C3×D311yescharacteristic
101C2×Dic5—31no—
102C2×Dic5—32no—
103C4×D5—34no—
104C22×C32C22×D511yescharacteristic
105C2×C3×D3—52no—
106C2×C3×D3—102no—
107C32×C4—22no—
108C32×C4C4×D512yes—
109C3×Dic3—52no—
110C3×Dic3—102no—
111#117—151noSylow
112C2×C3×C5—21no—
113C2×C3×C5—22no—
114C2×C3×C5C2×C4×D311yescharacteristic
115C2×C3×C5#23512yes—
116C2×C3×C5C22×C3×C411yescharacteristic
117C2×C3×C5C3×#4112yes—
118D15—22no—
119C3×D5—62no—
120C23×C3—151no—
121C22×D3—51no—
122C2×C3×C4—22no—
123C2×C3×C4—21no—
124C2×C3×C4—151no—
125C2×C3×C4—154no—
126C2×C3×C4—152no—
127C2×C3×C4C2×C3×D512yes—
128C2×C3×C4C2×C3×D511yescharacteristic
129C2×C3×C4C2×D1512yes—
130C2×C3×C4C2×D1511yescharacteristic
131C2×Dic3—51no—
132C2×Dic3—52no—
133C4×D3—54no—
134C22×C5C22×C3×D311yescharacteristic
135C2×D5—32no—
136C2×D5—62no—
137C4×C5—22no—
138C4×C5C3×C4×D312yes—
139Dic5—32no—
140Dic5—62no—
141C2×C32C2×C4×D511yescharacteristic
142C2×C32#70912yes—
143C3×D3—102no—
144C22×C4—151no—
145C4⋊C4—152no—
146C22⋊C4—152no—
147C42—151no—
148C42C3×D1511yescharacteristic, complemented
149C3×C5—21no—
150C3×C5#87211yescharacteristic, complemented
151C3×C5C3×#11711yescharacteristic, complemented
152C22×C3—21no—
153C22×C3—152no—
154C22×C3—302no—
155C22×C3C22×C3×D511yescharacteristic
156C22×C3C22×D1511yescharacteristic
157C2×D3—52no—
158C2×D3—102no—
159C3×C4—24no—
160C3×C4—22no—
161C3×C4—22no—
162C3×C4—22no—
163C3×C4—152no—
164C3×C4—302no—
165C3×C4C3×C4×D512yes—
166C3×C4C4×D1512yes—
167Dic3—52no—
168Dic3—102no—
169C2×C5C2×C3×C4×D311yescharacteristic
170C2×C5C3×#23512yes—
171D5—62no—
172C32#401811yescharacteristic, complemented, Sylow
173C23—151no—
174C2×C4—151no—
175C2×C4—154no—
176C2×C4—152no—
177C2×C4C2×C3×D1512yes—
178C2×C4C2×C3×D1511yescharacteristic
179C2×C3—21no—
180C2×C3—22no—
181C2×C3—302no—
182C2×C3C2×C3×C4×D511yescharacteristic
183C2×C3C3×#70912yes—
184C2×C3C2×C4×D1511yescharacteristic
185C2×C3#681712yes—
186D3—102no—
187C5C3×#87211yescharacteristic, complemented, Sylow
188C22—152no—
189C22—302no—
190C22C22×C3×D1511yescharacteristic
191C4—22no—
192C4—152no—
193C4—302no—
194C4C3×C4×D1512yes—
195C3—21no—
196C3C3×#401811yescharacteristic, complemented
197C3#9176111yescharacteristic, direct product factor
198C2—302no—
199C2C2×C3×C4×D1511yescharacteristic
200C2C3×#681712yes—
subgroupG/H
centerC2×C3×C4C2×D15
commutatorC2×C3×C5C22×C3×C4
FrattiniC22C22×C3×D15
FittingC32×C42×C5C2
socleC22×C32×C5C23
prime radicalC22×C3×D15C22
cosocleC22×C3×C5C23×C3
hypercenterC3×C42D15
hypocenterC3×C5C3×#117
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42

Complements

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

NH ≅ G/Ntype
2. C32×C42×C5C2semidirect
4. C3×#6712C2semidirect
5. C3×C4×Dic15C2semidirect
6. #91761C3direct (N × H)
13. C3×C4×D15C4semidirect
18. C3×C42×C5D3semidirect
19. C3×C42×C5C2×C3semidirect
21. #6712C2×C3semidirect
22. C4×Dic15C2×C3semidirect
35. C32×C42D5semidirect
49. C4×D15C3×C4semidirect
59. C42×C5C3×D3semidirect
92. C3×C42C3×D5semidirect
93. C3×C42D15semidirect
97. C32×C5#117semidirect
148. C42C3×D15semidirect
150. C3×C5#872semidirect
151. C3×C5C3×#117semidirect
172. C32#4018semidirect
187. C5C3×#872semidirect
196. C3C3×#4018semidirect
197. C3#91761direct (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×C42×C52
C3×#67142
C3×#67122
C3×C4×Dic152
#917613
C3×#40183
C3×#8725