Finite Group Databasebeta

← C3×#65031 #11749639

Subgroups — C3×#65031 #11749639

Order 960.

320 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4144C211yesmaximal, characteristic
2C3×#4081C211yesmaximal, characteristic, complemented
3C3×#4032C212yesmaximal, complemented
4C3×C5×#99C211yesmaximal, characteristic, complemented
5C3×#3938C212yesmaximal, complemented
6#65031C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×D4C2211yescharacteristic
8C2×C3×C22⋊D5—21no—
9C2×C3×C22⋊D5C2212yes—
10C22×C3×Dic5C2211yescharacteristic, complemented
11C3×#711—22no—
12C3×D4×D5—22no—
13C3×#709—21no—
14C3×C5×C22⋊C4C2212yescomplemented
15C3×C22⋊Dic5—21no—
16C3×C22⋊Dic5C2211yescharacteristic, complemented
17C3×#685—22no—
18C3×C4⋊Dic5—22no—
19C3×#683—21no—
20C3×#458—51nomaximal, Hall
21#4144C2×C311yescharacteristic
22#4081C2×C311yescharacteristic, complemented
23#4032C2×C312yescomplemented
24C5×#99C2×C311yescharacteristic, complemented
25#3938C2×C312yescomplemented
26C23×C3×C5D411yescharacteristic
27C23×C3×C5C2311yescharacteristic
28C22×C3×D5—21no—
29C22×C3×D5D412yes—
30C3×C5×D4—22no—
31C2×C3×C4×C5—22no—
32C2×C3×C4×C5D411yescharacteristic
33C3×C22⋊D5—22no—
34C3×C22⋊D5—22no—
35C3×C22⋊D5—22no—
36C2×C3×Dic5—21no—
37C2×C3×Dic5—21no—
38C2×C3×Dic5—21no—
39C2×C3×Dic5—22no—
40C2×C3×Dic5D412yes—
41C3×D20—21no—
42C3×C4×D5—22no—
43C3×Dic10—21no—
44C3×H(5,𝔽2)—51no—
45C3×#123—51no—
46C3×#123—52no—
47C3×#99—52no—
48C3×#99D511yescharacteristic, complemented
49C2×C5×D4C22×C311yescharacteristic
50C2×C22⋊D5—21no—
51C2×C22⋊D5C22×C312yes—
52C22×Dic5C22×C311yescharacteristic, complemented
53#711—22no—
54D4×D5—22no—
55#709—21no—
56C5×C22⋊C4C22×C312yescomplemented
57C22⋊Dic5—21no—
58C22⋊Dic5C22×C311yescharacteristic, complemented
59#685—22no—
60C4⋊Dic5—22no—
61#683—21no—
62#458—51noSylow
63C22×C3×C5—21no—
64C22×C3×C5—41no—
65C22×C3×C5—41no—
66C22×C3×C5C2×D411yescharacteristic
67C22×C3×C5C2×D412yes—
68C2×C3×D5—22no—
69C2×C3×D5—42no—
70C2×C3×D5—81no—
71C3×C4×C5—21no—
72C3×C4×C5—42no—
73C3×Dic5—22no—
74C3×Dic5—41no—
75C3×Dic5—41no—
76C3×#41—102no—
77C3×#41—101no—
78C2×C3×D4—52no—
79C2×C3×D4—102no—
80C2×C3×D4—101no—
81C2×C3×D4C2×D511yescharacteristic
82C22×C3×C4—51no—
83C3×C4⋊C4—102no—
84C3×C4⋊C4—101no—
85C3×C22⋊C4—51no—
86C3×C22⋊C4—102no—
87C3×C22⋊C4—101no—
88C3×C22⋊C4C2×D512yescomplemented
89C23×C5C3×D411yescharacteristic
90C23×C5C23×C311yescharacteristic
91C22×D5—21no—
92C22×D5C3×D412yes—
93C5×D4—22no—
94C2×C4×C5—22no—
95C2×C4×C5C3×D411yescharacteristic
96C22⋊D5—22no—
97C22⋊D5—22no—
98C22⋊D5—22no—
99C2×Dic5—21no—
100C2×Dic5—21no—
101C2×Dic5—21no—
102C2×Dic5—22no—
103C2×Dic5C3×D412yes—
104D20—21no—
105C4×D5—22no—
106Dic10—21no—
107H(5,𝔽2)—51no—
108#123—51no—
109#123—52no—
110#99—52no—
111#99C3×D511yescharacteristic, complemented
112C2×C3×C5—21no—
113C2×C3×C5—22no—
114C2×C3×C5—41no—
115C2×C3×C5#12011yescharacteristic
116C3×D5—42no—
117C23×C3—52no—
118C23×C3—101no—
119C23×C3D2011yescharacteristic
120C23×C3C22×D511yescharacteristic
121C3×Q8—101no—
122C3×D4—22no—
123C3×D4—101no—
124C3×D4—102no—
125C3×D4—102no—
126C3×D4—102no—
127C2×C3×C4—22no—
128C2×C3×C4—52no—
129C2×C3×C4—102no—
130C2×C3×C4—101no—
131C2×C3×C4—101no—
132C2×C3×C4—101no—
133C2×C3×C4—102no—
134C2×C3×C4D2011yescharacteristic
135C22×C5—21no—
136C22×C5—41no—
137C22×C5—41no—
138C22×C5C2×C3×D411yescharacteristic
139C22×C5C2×C3×D412yes—
140C2×D5—22no—
141C2×D5—42no—
142C2×D5—81no—
143C4×C5—21no—
144C4×C5—42no—
145Dic5—22no—
146Dic5—41no—
147Dic5—41no—
148#41—102no—
149#41—101no—
150C2×D4—52no—
151C2×D4—102no—
152C2×D4—101no—
153C2×D4C2×C3×D511yescharacteristic
154C22×C4—51no—
155C4⋊C4—102no—
156C4⋊C4—101no—
157C22⋊C4—51no—
158C22⋊C4—102no—
159C22⋊C4—101no—
160C22⋊C4C2×C3×D512yescomplemented
161C3×C5#45811yescharacteristic, complemented, Hall
162C22×C3—21no—
163C22×C3—41no—
164C22×C3—41no—
165C22×C3—102no—
166C22×C3—202no—
167C22×C3—401no—
168C22×C3C2×D2011yescharacteristic
169C22×C3D4×D512yes—
170C3×C4—21no—
171C3×C4—42no—
172C3×C4—102no—
173C3×C4—201no—
174C3×C4—201no—
175C2×C5—21no—
176C2×C5—22no—
177C2×C5—41no—
178C2×C5C3×#12011yescharacteristic
179D5—42no—
180C23—52no—
181C23—101no—
182C23C3×D2011yescharacteristic
183C23C22×C3×D511yescharacteristic
184Q8—101no—
185D4—22no—
186D4—101no—
187D4—102no—
188D4—102no—
189D4—102no—
190C2×C4—22no—
191C2×C4—52no—
192C2×C4—102no—
193C2×C4—101no—
194C2×C4—101no—
195C2×C4—101no—
196C2×C4—102no—
197C2×C4C3×D2011yescharacteristic
198C2×C3—22no—
199C2×C3—21no—
200C2×C3—41no—
201C2×C3—202no—
202C2×C3#402811yescharacteristic
203C5C3×#45811yescharacteristic, complemented, Sylow
204C22—21no—
205C22—41no—
206C22—41no—
207C22—102no—
208C22—202no—
209C22—401no—
210C22C2×C3×D2011yescharacteristic
211C22C3×D4×D512yes—
212C4—21no—
213C4—42no—
214C4—102no—
215C4—201no—
216C4—201no—
217C3#6503111yescharacteristic, direct product factor, Sylow
218C2—22no—
219C2—21no—
220C2—41no—
221C2—202no—
222C2C3×#402811yescharacteristic
subgroupG/H
centerC2×C3#4028
commutator, cosocleC23×C5C23×C3
FrattiniC23C22×C3×D5
FittingC3×C5×#99C2
socleC2×C3×C5#120
prime radicalC3×#4144C2
hypercenterC3×#99D5
hypocenterC5C3×#458
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×#99

Complements

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

NH ≅ G/Ntype
2. C3×#4081C2semidirect
3. C3×#4032C2semidirect
4. C3×C5×#99C2semidirect
5. C3×#3938C2semidirect
6. #65031C3direct (N × H)
10. C22×C3×Dic5C22semidirect
14. C3×C5×C22⋊C4C22semidirect
16. C3×C22⋊Dic5C22semidirect
22. #4081C2×C3semidirect
23. #4032C2×C3semidirect
24. C5×#99C2×C3semidirect
25. #3938C2×C3semidirect
48. C3×#99D5semidirect
52. C22×Dic5C22×C3semidirect
56. C5×C22⋊C4C22×C3semidirect
58. C22⋊Dic5C22×C3semidirect
88. C3×C22⋊C4C2×D5semidirect
111. #99C3×D5semidirect
160. C22⋊C4C2×C3×D5semidirect
161. C3×C5#458semidirect
203. C5C3×#458semidirect
217. C3#65031direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#41442
C3×#40812
C3×#40322
C3×C5×#992
C3×#39382
#650313
C3×#4585