Finite Group Databasebeta

← C3×#65459 #11750067

Subgroups — C3×#65459 #11750067

Order 960.

316 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 90 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×Q8×D5C211yesmaximal, characteristic, complemented
2C2×C3×C5×SD16C211yesmaximal, characteristic, complemented
3C3×#4084C211yesmaximal, characteristic
4C2×C3×#687C211yesmaximal, characteristic, complemented
5C3×#3967C211yesmaximal, characteristic, complemented
6C3×#3952C211yesmaximal, characteristic, complemented
7C3×#3948C211yesmaximal, characteristic, complemented
8#65459C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×D4C2211yescharacteristic
11C2×C3×C22⋊D5—21no—
12C3×Q8×D5—22no—
13C3×Q8×D5—22no—
14C2×C3×C4×D5—21no—
15C2×C3×C4×D5C2211yescharacteristic
16C2×C3×Dic10—21no—
17C2×C3×Dic10C2211yescharacteristic
18C3×C5×SD16—22no—
19C2×C3×C5×C8C2211yescharacteristic
20C3×C22⋊Dic5—21no—
21C3×#687—22no—
22C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×#168C2211yescharacteristic
24C3×#448—51nomaximal, Hall
25C2×Q8×D5C2×C311yescharacteristic, complemented
26C2×C5×SD16C2×C311yescharacteristic, complemented
27#4084C2×C311yescharacteristic
28C2×#687C2×C311yescharacteristic, complemented
29#3967C2×C311yescharacteristic, complemented
30#3952C2×C311yescharacteristic, complemented
31#3948C2×C311yescharacteristic, complemented
32C23×C3×C5—21no—
33C22×C3×D5D411yescharacteristic
34C3×C5×Q8—21no—
35C3×C5×Q8D412yescomplemented
36C3×C5×D4—21no—
37C3×C5×D4—21no—
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5C2311yescharacteristic
40C3×C22⋊D5—42no—
41C2×C3×Dic5—21no—
42C2×C3×Dic5—21no—
43C2×C3×Dic5D411yescharacteristic
44C3×C4×D5—24no—
45C3×C4×D5—21no—
46C3×C4×D5—21no—
47C3×Dic10—24no—
48C3×Dic10—21no—
49C3×Dic10D412yescomplemented
50C3×C5×C8—21no—
51C3×#168—21no—
52C22×C3×Q8—51no—
53C2×C3×SD16—51no—
54C2×C3×SD16D511yescharacteristic, complemented
55C3×#121—51no—
56C3×#103—51no—
57C3×#103—51no—
58C3×C22⋊C8—51no—
59C2×C5×Q8C22×C311yescharacteristic
60C2×C5×D4C22×C311yescharacteristic
61C2×C22⋊D5—21no—
62Q8×D5—22no—
63Q8×D5—22no—
64C2×C4×D5—21no—
65C2×C4×D5C22×C311yescharacteristic
66C2×Dic10—21no—
67C2×Dic10C22×C311yescharacteristic
68C5×SD16—22no—
69C2×C5×C8C22×C311yescharacteristic
70C22⋊Dic5—21no—
71#687—22no—
72C4⋊Dic5C22×C311yescharacteristic
73C2×#168C22×C311yescharacteristic
74#448—51noSylow
75C22×C3×C5—41no—
76C22×C3×C5—41no—
77C22×C3×C5—41no—
78C22×C3×C5C2×D411yescharacteristic
79C2×C3×D5—21no—
80C2×C3×D5—21no—
81C2×C3×D5SD1612yescomplemented
82C3×C4×C5—22no—
83C3×C4×C5C2×D411yescharacteristic
84C3×C4×C5C2×D411yescharacteristic
85C3×Dic5—21no—
86C3×Dic5—22no—
87C3×Dic5—41no—
88C2×C3×Q8—51no—
89C2×C3×Q8—101no—
90C2×C3×Q8—102no—
91C2×C3×Q8—102no—
92C2×C3×Q8C2×D511yescharacteristic
93C2×C3×D4—101no—
94C2×C3×D4C2×D511yescharacteristic
95C22×C3×C4—51no—
96C22×C3×C4—101no—
97C3×SD16—22no—
98C3×SD16—102no—
99C2×C3×C8—51no—
100C2×C3×C8C2×D511yescharacteristic
101C3×C4⋊C4—51no—
102C3×C22⋊C4—101no—
103C23×C5—21no—
104C22×D5C3×D411yescharacteristic
105C5×Q8—21no—
106C5×Q8C3×D412yescomplemented
107C5×D4—21no—
108C5×D4—21no—
109C2×C4×C5—21no—
110C2×C4×C5C23×C311yescharacteristic
111C22⋊D5—42no—
112C2×Dic5—21no—
113C2×Dic5—21no—
114C2×Dic5C3×D411yescharacteristic
115C4×D5—24no—
116C4×D5—21no—
117C4×D5—21no—
118Dic10—24no—
119Dic10—21no—
120Dic10C3×D412yescomplemented
121C5×C8—21no—
122#168—21no—
123C22×Q8—51no—
124C2×SD16—51no—
125C2×SD16C3×D511yescharacteristic, complemented
126#121—51no—
127#103—51no—
128#103—51no—
129C22⋊C8—51no—
130C2×C3×C5—81no—
131C2×C3×C5#12011yescharacteristic
132C2×C3×C5C2×SD1611yescharacteristic
133C2×C3×C5#13711yescharacteristic
134C3×D5—22no—
135C23×C3—21no—
136C23×C3—51no—
137C3×Q8—21no—
138C3×Q8—52no—
139C3×Q8—104no—
140C3×Q8—101no—
141C3×Q8C22⋊D512yescomplemented
142C3×D4—21no—
143C3×D4—21no—
144C3×D4—202no—
145C2×C3×C4—21no—
146C2×C3×C4—51no—
147C2×C3×C4—104no—
148C2×C3×C4—101no—
149C2×C3×C4—101no—
150C2×C3×C4—101no—
151C2×C3×C4—101no—
152C2×C3×C4C22×D511yescharacteristic
153C3×C8—21no—
154C3×C8—101no—
155C22×C5—41no—
156C22×C5—41no—
157C22×C5—41no—
158C22×C5C2×C3×D411yescharacteristic
159C2×D5—21no—
160C2×D5—21no—
161C2×D5C3×SD1612yescomplemented
162C4×C5—22no—
163C4×C5C2×C3×D411yescharacteristic
164C4×C5C2×C3×D411yescharacteristic
165Dic5—21no—
166Dic5—22no—
167Dic5—41no—
168C2×Q8—51no—
169C2×Q8—101no—
170C2×Q8—102no—
171C2×Q8—102no—
172C2×Q8C2×C3×D511yescharacteristic
173C2×D4—101no—
174C2×D4C2×C3×D511yescharacteristic
175C22×C4—51no—
176C22×C4—101no—
177SD16—22no—
178SD16—102no—
179C2×C8—51no—
180C2×C8C2×C3×D511yescharacteristic
181C4⋊C4—51no—
182C22⋊C4—101no—
183C3×C5#44811yescharacteristic, complemented, Hall
184C22×C3—41no—
185C22×C3—41no—
186C22×C3—41no—
187C22×C3—52no—
188C22×C3—101no—
189C22×C3—101no—
190C22×C3D4×D511yescharacteristic
191C3×C4—22no—
192C3×C4—101no—
193C3×C4—102no—
194C3×C4—201no—
195C3×C4D4×D511yescharacteristic
196C3×C4C2×C22⋊D511yescharacteristic
197C2×C5—81no—
198C2×C5C3×#12011yescharacteristic
199C2×C5C2×C3×SD1611yescharacteristic
200C2×C5C3×#13711yescharacteristic
201D5—22no—
202C23—21no—
203C23—51no—
204Q8—21no—
205Q8—52no—
206Q8—104no—
207Q8—101no—
208Q8C3×C22⋊D512yescomplemented
209D4—21no—
210D4—21no—
211D4—202no—
212C2×C4—21no—
213C2×C4—51no—
214C2×C4—104no—
215C2×C4—101no—
216C2×C4—101no—
217C2×C4—101no—
218C2×C4—101no—
219C2×C4C22×C3×D511yescharacteristic
220C8—21no—
221C8—101no—
222C2×C3—81no—
223C2×C3—102no—
224C2×C3D5×SD1611yescharacteristic
225C2×C3#406111yescharacteristic
226C2×C3#408311yescharacteristic
227C5C3×#44811yescharacteristic, complemented, Sylow
228C22—41no—
229C22—41no—
230C22—41no—
231C22—52no—
232C22—101no—
233C22—101no—
234C22C3×D4×D511yescharacteristic
235C4—22no—
236C4—101no—
237C4—102no—
238C4—201no—
239C4C3×D4×D511yescharacteristic
240C4C2×C3×C22⋊D511yescharacteristic
241C3#6545911yescharacteristic, direct product factor, Sylow
242C2—81no—
243C2—102no—
244C2C3×D5×SD1611yescharacteristic
245C2C3×#406111yescharacteristic
246C2C3×#408311yescharacteristic
subgroupG/H
centerC22×C3D4×D5
commutator, cosocleC2×C4×C5C23×C3
FrattiniC2×C4C22×C3×D5
FittingC2×C3×C5×SD16C2
socleC22×C3×C5C2×D4
prime radicalC3×#4084C2
hypercenterC2×C3×SD16D5
hypocenterC5C3×#448
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×D5C2semidirect
2. C2×C3×C5×SD16C2semidirect
4. C2×C3×#687C2semidirect
5. C3×#3967C2semidirect
6. C3×#3952C2semidirect
7. C3×#3948C2semidirect
8. #65459C3direct (N × H)
25. C2×Q8×D5C2×C3semidirect
26. C2×C5×SD16C2×C3semidirect
28. C2×#687C2×C3semidirect
29. #3967C2×C3semidirect
30. #3952C2×C3semidirect
31. #3948C2×C3semidirect
35. C3×C5×Q8D4semidirect
49. C3×Dic10D4semidirect
54. C2×C3×SD16D5semidirect
81. C2×C3×D5SD16semidirect
106. C5×Q8C3×D4semidirect
120. Dic10C3×D4semidirect
125. C2×SD16C3×D5semidirect
141. C3×Q8C22⋊D5semidirect
161. C2×D5C3×SD16semidirect
183. C3×C5#448semidirect
208. Q8C3×C22⋊D5semidirect
227. C5C3×#448semidirect
241. C3#65459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×Q8×D52
C2×C3×C5×SD162
C3×#40842
C2×C3×#6872
C3×#39672
C3×#39522
C3×#39482
#654593
C3×#4485