Finite Group Databasebeta

← C3×#91089 #13085006

Subgroups — C3×#91089 #13085006

Order 1440.

206 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C3×#6817C211yesmaximal, characteristic
2C32×C42×C5C211yesmaximal, characteristic, complemented
3C3×#6710C211yesmaximal, characteristic, complemented
4#91089C311yesmaximal, characteristic, direct product factor
5C3×#3937—31nomaximal
6C2×C32×C4×C5—21no—
7C2×C32×C4×C5C2211yescharacteristic
8C3×#1220—21no—
9C3×D60C411yescharacteristic, complemented
10C3×C4×D15—21no—
11C3×Dic30C411yescharacteristic, complemented
12C3×C3⋊#168—21no—
13C3×#805—51nomaximal, Hall
14#6817C2×C311yescharacteristic
15C3×#709—31no—
16C3×C42×C5—21no—
17C3×C42×C5D311yescharacteristic, complemented
18C3×C42×C5C2×C311yescharacteristic, complemented
19#6710C2×C311yescharacteristic, complemented
20C3×#681—31no—
21C22×C32×C5D411yescharacteristic
22C2×C3×D15—21no—
23C32×C4×C5—22no—
24C32×C4×C5C2×C411yescharacteristic
25C32×C4×C5D411yescharacteristic
26C3×Dic15—21no—
27#3937—31noHall
28C3×#235—51no—
29C32×C42D511yescharacteristic, complemented
30C3×#208—51no—
31C2×C3×C4×C5—22no—
32C2×C3×C4×C5—21no—
33C2×C3×C4×C5—21no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5C2×D311yescharacteristic
36C2×C3×C4×C5C22×C311yescharacteristic
37#1220—21no—
38D60C3×C411yescharacteristic, complemented
39C4×D15—21no—
40Dic30C3×C411yescharacteristic, complemented
41C3×C22⋊D5—61no—
42C3×D20—31no—
43C3×C4×D5—61no—
44C3×Dic10—31no—
45C3⋊#168—21no—
46C3×#168—61no—
47C3×#104—151no—
48#805—51no—
49C2×C32×C5—21no—
50C2×C32×C5C22⋊C411yescharacteristic
51C3×D15—41no—
52#709—31no—
53C42×C5C3×D311yescharacteristic, complemented
54#681—31no—
55C2×C32×C4—21no—
56C2×C32×C4C2×D511yescharacteristic
57C3×#67—101no—
58C3×D12—51no—
59C3×C4×D3—101no—
60C3×Dic6—51no—
61C3×C3⋊C8—101no—
62C22×C3×C5—21no—
63C22×C3×C5#6711yescharacteristic
64C22×C3×C5C3×D411yescharacteristic
65C2×D15—21no—
66C2×C3×D5—61no—
67C3×C4×C5—24no—
68C3×C4×C5—22no—
69C3×C4×C5—22no—
70C3×C4×C5—21no—
71C3×C4×C5—21no—
72C3×C4×C5C4×D311yescharacteristic
73C3×C4×C5D1211yescharacteristic
74C3×C4×C5C2×C3×C411yescharacteristic
75C3×C4×C5C3×D411yescharacteristic
76Dic15—21no—
77C3×Dic5—61no—
78C3×#41—151no—
79#235—51no—
80C3×M16—151no—
81C3×C42—21no—
82C3×C42C3×D511yescharacteristic, complemented
83C3×C42D1511yescharacteristic, complemented
84#208—51no—
85C32×C5#10411yescharacteristic, complemented, Hall
86C2×C4×C5—21no—
87C2×C4×C5C2×C3×D311yescharacteristic
88C22⋊D5—61no—
89D20—31no—
90C4×D5—61no—
91Dic10—31no—
92#168—61no—
93C22×C32C22⋊D511yescharacteristic
94C2×C3×D3—101no—
95C32×C4—22no—
96C32×C4C4×D511yescharacteristic
97C32×C4D2011yescharacteristic
98C3×Dic3—101no—
99#104—151noSylow
100C2×C3×C5—22no—
101C2×C3×C5—21no—
102C2×C3×C5—21no—
103C2×C3×C5—21no—
104C2×C3×C5(C2×D3)⋊C411yescharacteristic
105C2×C3×C5C3×C22⋊C411yescharacteristic
106D15—41no—
107C3×D5—121no—
108C3×Q8—151no—
109C3×D4—151no—
110C3×D4—301no—
111C2×C3×C4—22no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—301no—
116C2×C3×C4C2×C3×D511yescharacteristic
117C2×C3×C4C2×D1511yescharacteristic
118#67—101no—
119D12—51no—
120C4×D3—101no—
121Dic6—51no—
122C3×C8—301no—
123C3⋊C8—101no—
124C22×C5C3×#6711yescharacteristic
125C2×D5—61no—
126C4×C5—22no—
127C4×C5C3×C4×D311yescharacteristic
128C4×C5C3×D1211yescharacteristic
129Dic5—61no—
130C2×C32—21no—
131C2×C32#68511yescharacteristic
132C3×D3—201no—
133#41—151no—
134M16—151no—
135C42C3×D1511yescharacteristic, complemented
136C3×C5—21no—
137C3×C5#80511yescharacteristic, complemented
138C3×C5C3×#10411yescharacteristic, complemented
139C22×C3—21no—
140C22×C3—301no—
141C22×C3C3×C22⋊D511yescharacteristic
142C22×C3#122011yescharacteristic
143C2×D3—101no—
144C3×C4—24no—
145C3×C4—22no—
146C3×C4—22no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—301no—
150C3×C4C3×C4×D511yescharacteristic
151C3×C4C3×D2011yescharacteristic
152C3×C4C4×D1511yescharacteristic
153C3×C4D6011yescharacteristic
154Dic3—101no—
155C2×C5—21no—
156C2×C5C3×(C2×D3)⋊C411yescharacteristic
157D5—121no—
158C32#393711yescharacteristic, complemented, Sylow
159Q8—151no—
160D4—151no—
161D4—301no—
162C2×C4—21no—
163C2×C4—301no—
164C2×C4C2×C3×D1511yescharacteristic
165C8—301no—
166C2×C3—22no—
167C2×C3—21no—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3—601no—
171C2×C3C3×#68511yescharacteristic
172C2×C3#671411yescharacteristic
173D3—201no—
174C5C3×#80511yescharacteristic, complemented, Sylow
175C22—301no—
176C22C3×#122011yescharacteristic
177C4—22no—
178C4—301no—
179C4C3×C4×D1511yescharacteristic
180C4C3×D6011yescharacteristic
181C3—21no—
182C3C3×#393711yescharacteristic, complemented
183C3#9108911yescharacteristic, direct product factor
184C2—21no—
185C2—601no—
186C2C3×#671411yescharacteristic
subgroupG/H
centerC3×C4D60
commutatorC3×C4×C5C2×C3×C4
FrattiniC2×C4C2×C3×D15
FittingC32×C42×C5C2
socleC2×C32×C5C22⋊C4
prime radicalC3×#6817C2
cosocleC2×C3×C4×C5C22×C3
hypercenterC3×C42D15
hypocenterC3×C5C3×#104
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×C42

Complements

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

NH ≅ G/Ntype
2. C32×C42×C5C2semidirect
3. C3×#6710C2semidirect
4. #91089C3direct (N × H)
9. C3×D60C4semidirect
11. C3×Dic30C4semidirect
17. C3×C42×C5D3semidirect
18. C3×C42×C5C2×C3semidirect
19. #6710C2×C3semidirect
29. C32×C42D5semidirect
38. D60C3×C4semidirect
40. Dic30C3×C4semidirect
53. C42×C5C3×D3semidirect
82. C3×C42C3×D5semidirect
83. C3×C42D15semidirect
85. C32×C5#104semidirect
135. C42C3×D15semidirect
137. C3×C5#805semidirect
138. C3×C5C3×#104semidirect
158. C32#3937semidirect
174. C5C3×#805semidirect
182. C3C3×#3937semidirect
183. C3#91089direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#68172
C32×C42×C52
C3×#67102
#910893
C3×#39373
C3×#8055