Finite Group Databasebeta

← C3×#65029 #11749637

Subgroups — C3×#65029 #11749637

Order 960.

316 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 102 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×#711C211yesmaximal, characteristic
2C3×#4023C212yesmaximal, complemented
3C3×C5×#99C211yesmaximal, characteristic, complemented
4C3×#3966C211yesmaximal, characteristic, complemented
5C3×#3938C212yesmaximal, complemented
6#65029C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×C5×D4C2211yescharacteristic
8C2×C3×C22⋊D5C411yescharacteristic, complemented
9C2×C3×C22⋊D5C2211yescharacteristic
10C22×C3×Dic5C411yescharacteristic, complemented
11C22×C3×Dic5C2211yescharacteristic
12C3×#711—22no—
13C3×#711—22no—
14C2×C3×C4×D5C411yescharacteristic, complemented
15C2×C3×Dic10C411yescharacteristic, complemented
16C3×C5×C22⋊C4C2212yes—
17C3×C22⋊Dic5C2212yes—
18C3×#683—22no—
19C3×C4×Dic5—22no—
20C3×#410—51nomaximal, Hall
21C2×#711C2×C311yescharacteristic
22#4023C2×C312yescomplemented
23C5×#99C2×C311yescharacteristic, complemented
24#3966C2×C311yescharacteristic, complemented
25#3938C2×C312yescomplemented
26C23×C3×C5C2×C411yescharacteristic
27C23×C3×C5C2311yescharacteristic
28C22×C3×D5C2×C411yescharacteristic
29C3×C5×D4—22no—
30C2×C3×C4×C5—22no—
31C2×C3×C4×C5C2×C411yescharacteristic
32C3×C22⋊D5—22no—
33C3×C22⋊D5—22no—
34C2×C3×Dic5—21no—
35C2×C3×Dic5—21no—
36C2×C3×Dic5—22no—
37C2×C3×Dic5C2×C411yescharacteristic
38C2×C3×Dic5C2×C411yescharacteristic
39C2×C3×Dic5C2×C411yescharacteristic
40C2×C3×Dic5D412yes—
41C2×C3×Dic5D412yes—
42C3×C4×D5—21no—
43C3×C4×D5—21no—
44C3×Dic10—22no—
45C2×C3×#41—51no—
46C3×#117—52no—
47C3×#99—51no—
48C3×#99—52no—
49C3×#99D511yescharacteristic, complemented
50C2×C5×D4C22×C311yescharacteristic
51C2×C22⋊D5C3×C411yescharacteristic, complemented
52C2×C22⋊D5C22×C311yescharacteristic
53C22×Dic5C3×C411yescharacteristic, complemented
54C22×Dic5C22×C311yescharacteristic
55#711—22no—
56#711—22no—
57C2×C4×D5C3×C411yescharacteristic, complemented
58C2×Dic10C3×C411yescharacteristic, complemented
59C5×C22⋊C4C22×C312yes—
60C22⋊Dic5C22×C312yes—
61#683—22no—
62C4×Dic5—22no—
63#410—51noSylow
64C22×C3×C5—21no—
65C22×C3×C5—41no—
66C22×C3×C5—41no—
67C22×C3×C5C22×C411yescharacteristic
68C22×C3×C5C2×D412yes—
69C2×C3×D5—21no—
70C2×C3×D5—41no—
71C3×C4×C5—21no—
72C3×C4×C5—42no—
73C3×Dic5—21no—
74C3×Dic5—42no—
75C3×Dic5C22⋊C412yes—
76C3×Dic5C22⋊C411yescharacteristic
77C3×Dic5C22⋊C411yescharacteristic
78C3×#41—102no—
79C3×#41—102no—
80C2×C3×Q8—51no—
81C2×C3×D4—51no—
82C2×C3×D4—51no—
83C2×C3×D4C2×D511yescharacteristic
84C22×C3×C4—51no—
85C22×C3×C4—51no—
86C22×C3×C4—51no—
87C3×C4⋊C4—102no—
88C3×C22⋊C4—52no—
89C3×C22⋊C4C2×D512yes—
90C3×C42—102no—
91C23×C5C2×C3×C411yescharacteristic
92C23×C5C23×C311yescharacteristic
93C22×D5C2×C3×C411yescharacteristic
94C5×D4—22no—
95C2×C4×C5—22no—
96C2×C4×C5C2×C3×C411yescharacteristic
97C22⋊D5—22no—
98C22⋊D5—22no—
99C2×Dic5—21no—
100C2×Dic5—21no—
101C2×Dic5—22no—
102C2×Dic5C2×C3×C411yescharacteristic
103C2×Dic5C2×C3×C411yescharacteristic
104C2×Dic5C2×C3×C411yescharacteristic
105C2×Dic5C3×D412yes—
106C2×Dic5C3×D412yes—
107C4×D5—21no—
108C4×D5—21no—
109Dic10—22no—
110C2×#41—51no—
111#117—52no—
112#99—51no—
113#99—52no—
114#99C3×D511yescharacteristic, complemented
115C2×C3×C5—22no—
116C2×C3×C5—21no—
117C2×C3×C5—41no—
118C2×C3×C5C2×C22⋊C411yescharacteristic
119C3×D5—41no—
120C23×C3—51no—
121C23×C3C4×D511yescharacteristic
122C23×C3C22×D511yescharacteristic
123C3×Q8—102no—
124C3×D4—22no—
125C3×D4—102no—
126C3×D4—102no—
127C2×C3×C4—22no—
128C2×C3×C4—51no—
129C2×C3×C4—51no—
130C2×C3×C4—52no—
131C2×C3×C4—52no—
132C2×C3×C4—51no—
133C2×C3×C4—101no—
134C2×C3×C4—101no—
135C2×C3×C4—101no—
136C2×C3×C4—101no—
137C2×C3×C4—102no—
138C2×C3×C4C4×D511yescharacteristic
139C22×C5—21no—
140C22×C5—41no—
141C22×C5—41no—
142C22×C5C22×C3×C411yescharacteristic
143C22×C5C2×C3×D412yes—
144C2×D5—21no—
145C2×D5—41no—
146C4×C5—21no—
147C4×C5—42no—
148Dic5—21no—
149Dic5—42no—
150Dic5C3×C22⋊C412yes—
151Dic5C3×C22⋊C411yescharacteristic
152Dic5C3×C22⋊C411yescharacteristic
153#41—102no—
154#41—102no—
155C2×Q8—51no—
156C2×D4—51no—
157C2×D4—51no—
158C2×D4C2×C3×D511yescharacteristic
159C22×C4—51no—
160C22×C4—51no—
161C22×C4—51no—
162C4⋊C4—102no—
163C22⋊C4—52no—
164C22⋊C4C2×C3×D512yes—
165C42—102no—
166C3×C5#41011yescharacteristic, complemented, Hall
167C22×C3—21no—
168C22×C3—41no—
169C22×C3—41no—
170C22×C3—101no—
171C22×C3—201no—
172C22×C3C2×C4×D511yescharacteristic
173C22×C3D4×D512yes—
174C3×C4—21no—
175C3×C4—42no—
176C3×C4—51no—
177C3×C4—51no—
178C3×C4—52no—
179C3×C4—101no—
180C3×C4—202no—
181C2×C5—22no—
182C2×C5—21no—
183C2×C5—41no—
184C2×C5C2×C3×C22⋊C411yescharacteristic
185D5—41no—
186C23—51no—
187C23C3×C4×D511yescharacteristic
188C23C22×C3×D511yescharacteristic
189Q8—102no—
190D4—22no—
191D4—102no—
192D4—102no—
193C2×C4—22no—
194C2×C4—51no—
195C2×C4—51no—
196C2×C4—52no—
197C2×C4—52no—
198C2×C4—51no—
199C2×C4—101no—
200C2×C4—101no—
201C2×C4—101no—
202C2×C4—101no—
203C2×C4—102no—
204C2×C4C3×C4×D511yescharacteristic
205C2×C3—22no—
206C2×C3—21no—
207C2×C3—41no—
208C2×C3—201no—
209C2×C3D5×C22⋊C411yescharacteristic
210C5C3×#41011yescharacteristic, complemented, Sylow
211C22—21no—
212C22—41no—
213C22—41no—
214C22—101no—
215C22—201no—
216C22C2×C3×C4×D511yescharacteristic
217C22C3×D4×D512yes—
218C4—21no—
219C4—42no—
220C4—51no—
221C4—51no—
222C4—52no—
223C4—101no—
224C4—202no—
225C3#6502911yescharacteristic, direct product factor, Sylow
226C2—22no—
227C2—21no—
228C2—41no—
229C2—201no—
230C2C3×D5×C22⋊C411yescharacteristic
subgroupG/H
centerC2×C3D5×C22⋊C4
commutatorC22×C5C22×C3×C4
FrattiniC23C22×C3×D5
FittingC3×C5×#99C2
socleC2×C3×C5C2×C22⋊C4
prime radicalC2×C3×#711C2
cosocleC23×C5C23×C3
hypercenterC3×#99D5
hypocenterC5C3×#410
LCSG ▷ C22×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×#4023C2semidirect
3. C3×C5×#99C2semidirect
4. C3×#3966C2semidirect
5. C3×#3938C2semidirect
6. #65029C3direct (N × H)
8. C2×C3×C22⋊D5C4semidirect
10. C22×C3×Dic5C4semidirect
14. C2×C3×C4×D5C4semidirect
15. C2×C3×Dic10C4semidirect
22. #4023C2×C3semidirect
23. C5×#99C2×C3semidirect
24. #3966C2×C3semidirect
25. #3938C2×C3semidirect
49. C3×#99D5semidirect
51. C2×C22⋊D5C3×C4semidirect
53. C22×Dic5C3×C4semidirect
57. C2×C4×D5C3×C4semidirect
58. C2×Dic10C3×C4semidirect
114. #99C3×D5semidirect
166. C3×C5#410semidirect
210. C5C3×#410semidirect
225. C3#65029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#7112
C3×#40232
C3×C5×#992
C3×#39662
C3×#39382
#650293
C3×#4105