Finite Group Databasebeta

← C3×#91775 #13087983

Subgroups — C3×#91775 #13087983

Order 1440.

346 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 110 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×#1220C211yesmaximal, characteristic
2C22×C3×Dic15C211yesmaximal, characteristic, complemented
3C32×C5×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×#6714C212yesmaximal, complemented
5C3×C4⋊Dic15C212yesmaximal, complemented
6#91775C311yesmaximal, characteristic, direct product factor
7C3×#4032—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C3×D15C2211yescharacteristic
10C2×C32×C4×C5C2212yes—
11C3×#1220—22no—
12C2×C3×Dic15—22no—
13C2×C3×Dic15C2212yes—
14C2×C3×Dic15C2211yescharacteristic
15C3×#886—51nomaximal, Hall
16C2×#1220C2×C311yescharacteristic
17C22×Dic15C2×C311yescharacteristic, complemented
18C2×C3×C22⋊D5—31no—
19C22×C3×Dic5—31no—
20C3×C5×C22⋊C4—21no—
21C3×C5×C22⋊C4D311yescharacteristic, complemented
22C3×C5×C22⋊C4C2×C311yescharacteristic, complemented
23#6714C2×C312yescomplemented
24C4⋊Dic15C2×C312yescomplemented
25C3×#685—32no—
26C3×C4⋊Dic5—32no—
27C22×C32×C5—22no—
28C22×C32×C5D412yes—
29C22×C32×C5C2311yescharacteristic
30C2×C3×D15—21no—
31C2×C3×D15—22no—
32C32×C4×C5—22no—
33C3×Dic15—22no—
34C3×Dic15—21no—
35#4032—31noHall
36C2×C3×#67—51no—
37C22×C3×Dic3—51no—
38C32×C22⋊C4D511yescharacteristic, complemented
39C3×(C2×D3)⋊C4—52no—
40C3×C4⋊Dic3—52no—
41C23×C3×C5—21no—
42C23×C3×C5C2×D311yescharacteristic
43C23×C3×C5C22×C311yescharacteristic
44C22×D15C22×C311yescharacteristic
45C22×C3×D5—31no—
46C2×C3×C4×C5—22no—
47C2×C3×C4×C5C2×D312yes—
48C2×C3×C4×C5C22×C312yes—
49#1220—22no—
50C2×Dic15—22no—
51C2×Dic15C22×C311yescharacteristic
52C2×Dic15C22×C312yes—
53C3×C22⋊D5—62no—
54C2×C3×Dic5—31no—
55C2×C3×Dic5—32no—
56C2×C3×Dic5—62no—
57C3×#123—151no—
58#886—51no—
59C2×C32×C5—22no—
60C2×C32×C5C2×D411yescharacteristic
61C2×C32×C5#4112yes—
62C3×D15—41no—
63C2×C22⋊D5—31no—
64C22×Dic5—31no—
65C5×C22⋊C4C3×D311yescharacteristic, complemented
66#685—32no—
67C4⋊Dic5—32no—
68C23×C32C2×D511yescharacteristic
69C22×C3×D3—51no—
70C2×C32×C4C2×D512yes—
71C3×#67—102no—
72C2×C3×Dic3—51no—
73C2×C3×Dic3—52no—
74C2×C3×Dic3—102no—
75C22×C3×C5—22no—
76C22×C3×C5—22no—
77C22×C3×C5—22no—
78C22×C3×C5—21no—
79C22×C3×C5—42no—
80C22×C3×C5D1212yes—
81C22×C3×C5C3×D412yes—
82C22×C3×C5C22×D311yescharacteristic
83C22×C3×C5C23×C311yescharacteristic
84C2×D15—21no—
85C2×D15—22no—
86C2×C3×D5—61no—
87C2×C3×D5—62no—
88C3×C4×C5—22no—
89C3×C4×C5—22no—
90C3×C4×C5—42no—
91Dic15—22no—
92Dic15—21no—
93C3×Dic5—62no—
94C3×Dic5—61no—
95C2×C3×D4—151no—
96C22×C3×C4—151no—
97C2×#67—51no—
98C22×Dic3—51no—
99C3×C4⋊C4—152no—
100C3×C22⋊C4—21no—
101C3×C22⋊C4—152no—
102C3×C22⋊C4C3×D511yescharacteristic, complemented
103C3×C22⋊C4D1511yescharacteristic, complemented
104(C2×D3)⋊C4—52no—
105C4⋊Dic3—52no—
106C32×C5#12311yescharacteristic, complemented, Hall
107C23×C5C2×C3×D311yescharacteristic
108C22×D5—31no—
109C2×C4×C5C2×C3×D312yes—
110C22⋊D5—62no—
111C2×Dic5—31no—
112C2×Dic5—32no—
113C2×Dic5—62no—
114C22×C32—22no—
115C22×C32D2012yes—
116C22×C32C22×D511yescharacteristic
117C2×C3×D3—101no—
118C2×C3×D3—102no—
119C32×C4—22no—
120C3×Dic3—102no—
121C3×Dic3—101no—
122#123—151noSylow
123C2×C3×C5—22no—
124C2×C3×C5—22no—
125C2×C3×C5—21no—
126C2×C3×C5—22no—
127C2×C3×C5—42no—
128C2×C3×C5C2×D1211yescharacteristic
129C2×C3×C5#23712yes—
130C2×C3×C5C2×C3×D411yescharacteristic
131C2×C3×C5C3×#4112yes—
132D15—41no—
133C3×D5—121no—
134C23×C3—21no—
135C23×C3—151no—
136C23×C3C2×C3×D511yescharacteristic
137C23×C3C2×D1511yescharacteristic
138C22×D3—51no—
139C3×D4—302no—
140C2×C3×C4—22no—
141C2×C3×C4—152no—
142C2×C3×C4—151no—
143C2×C3×C4—302no—
144C2×C3×C4C2×C3×D512yes—
145C2×C3×C4C2×D1512yes—
146#67—102no—
147C2×Dic3—51no—
148C2×Dic3—52no—
149C2×Dic3—102no—
150C22×C5—22no—
151C22×C5C3×D1212yes—
152C22×C5C22×C3×D311yescharacteristic
153C2×D5—61no—
154C2×D5—62no—
155C4×C5—22no—
156Dic5—62no—
157Dic5—61no—
158C2×C32—22no—
159C2×C32C2×D2011yescharacteristic
160C2×C32#71112yes—
161C3×D3—201no—
162C2×D4—151no—
163C22×C4—151no—
164C4⋊C4—152no—
165C22⋊C4—152no—
166C22⋊C4C3×D1511yescharacteristic, complemented
167C3×C5—21no—
168C3×C5#88611yescharacteristic, complemented
169C3×C5C3×#12311yescharacteristic, complemented
170C22×C3—22no—
171C22×C3—22no—
172C22×C3—22no—
173C22×C3—21no—
174C22×C3—42no—
175C22×C3—301no—
176C22×C3—302no—
177C22×C3C3×D2012yes—
178C22×C3D6012yes—
179C22×C3C22×C3×D511yescharacteristic
180C22×C3C22×D1511yescharacteristic
181C2×D3—101no—
182C2×D3—102no—
183C3×C4—22no—
184C3×C4—22no—
185C3×C4—42no—
186C3×C4—302no—
187C3×C4—301no—
188Dic3—102no—
189Dic3—101no—
190C2×C5—22no—
191C2×C5C2×C3×D1211yescharacteristic
192C2×C5C3×#23712yes—
193D5—121no—
194C32#403211yescharacteristic, complemented, Sylow
195C23—151no—
196C23C2×C3×D1511yescharacteristic
197D4—302no—
198C2×C4—152no—
199C2×C4—151no—
200C2×C4—302no—
201C2×C4C2×C3×D1512yes—
202C2×C3—22no—
203C2×C3—22no—
204C2×C3—21no—
205C2×C3—22no—
206C2×C3—42no—
207C2×C3—601no—
208C2×C3C2×C3×D2011yescharacteristic
209C2×C3C3×#71112yes—
210C2×C3C2×D6011yescharacteristic
211C2×C3#681912yes—
212D3—201no—
213C5C3×#88611yescharacteristic, complemented, Sylow
214C22—22no—
215C22—301no—
216C22—302no—
217C22C3×D6012yes—
218C22C22×C3×D1511yescharacteristic
219C4—22no—
220C4—302no—
221C4—301no—
222C3—21no—
223C3C3×#403211yescharacteristic, complemented
224C3#9177511yescharacteristic, direct product factor
225C2—22no—
226C2—601no—
227C2C2×C3×D6011yescharacteristic
228C2C3×#681912yes—
subgroupG/H
centerC22×C3C22×D15
commutator, cosocleC22×C3×C5C23×C3
FrattiniC22C22×C3×D15
FittingC32×C5×C22⋊C4C2
socleC22×C32×C5C23
prime radicalC2×C3×#1220C2
hypercenterC3×C22⋊C4D15
hypocenterC3×C5C3×#123
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic15C2semidirect
3. C32×C5×C22⋊C4C2semidirect
4. C3×#6714C2semidirect
5. C3×C4⋊Dic15C2semidirect
6. #91775C3direct (N × H)
17. C22×Dic15C2×C3semidirect
21. C3×C5×C22⋊C4D3semidirect
22. C3×C5×C22⋊C4C2×C3semidirect
23. #6714C2×C3semidirect
24. C4⋊Dic15C2×C3semidirect
38. C32×C22⋊C4D5semidirect
65. C5×C22⋊C4C3×D3semidirect
102. C3×C22⋊C4C3×D5semidirect
103. C3×C22⋊C4D15semidirect
106. C32×C5#123semidirect
166. C22⋊C4C3×D15semidirect
168. C3×C5#886semidirect
169. C3×C5C3×#123semidirect
194. C32#4032semidirect
213. C5C3×#886semidirect
223. C3C3×#4032semidirect
224. C3#91775direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#12202
C22×C3×Dic152
C32×C5×C22⋊C42
C3×#67142
C3×C4⋊Dic152
#917753
C3×#40323
C3×#8865