Finite Group Databasebeta

← C2×#66087⋊C3 #14514145

Subgroups — C2×#66087⋊C3 #14514145

Order 1920.

686 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 87 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×#4150⋊C3C212yesmaximal, complemented
2C2×C5×#131⋊C3C211yesmaximal, characteristic, complemented
3#66087⋊C3C214yesmaximal, direct product factor
4C2×#66087C311yesmaximal, characteristic, complemented, Hall
5C2×C5×#41⋊C3C2211yescharacteristic
6#4150⋊C3—22no—
7#4150⋊C3C2214yescomplemented
8C2×D5×SL(2,𝔽3)—22no—
9C2×C3×D40—41nomaximal
10C5×#131⋊C3C2212yescomplemented
11C2×#578⋊C3—51nomaximal, Hall
12C2×#4150C2×C312yescomplemented
13C2×C5×#131C2×C311yescharacteristic, complemented
14#66087—34no—
15#66087C2×C314yescomplemented
16C2×#4055—32no—
17C22×Dic20—31no—
18C2×#4050—31no—
19C2×C3×D20—42no—
20C5×#41⋊C3D411yescharacteristic
21C5×#41⋊C3C2311yescharacteristic
22C2×C5×SL(2,𝔽3)D411yescharacteristic
23D5×SL(2,𝔽3)—24no—
24C2×C3×C5×C8—41no—
25C3×D40—44no—
26C2×2−1+4⋊C3—52no—
27#578⋊C3—54no—
28C2×#131⋊C3D511yescharacteristic, complemented
29C2×C5×#41C22×C311yescharacteristic
30#4150—22no—
31#4150—34no—
32#4150—62no—
33#4150C22×C314yescomplemented
34C2×Q8×D5—22no—
35C2×#711—62no—
36C2×#709—32no—
37C22×Dic10—32no—
38C5×#131—32no—
39C5×#131C22×C312yescomplemented
40C2×C5×M16—31no—
41C22×C5×C8—31no—
42#4055—38no—
43#4055—38no—
44C2×Dic20—32no—
45C2×Dic20—34no—
46C2×Dic20—31no—
47C2×Dic20—34no—
48#4050—34no—
49#4050—34no—
50C2×D40A411yescharacteristic
51C2×#677—32no—
52C2×#578—51noSylow
53C22×C3×D5—82no—
54C2×C3×C4×C5—41no—
55C3×D20—44no—
56C3×D20—82no—
57C5×SL(2,𝔽3)C2×D411yescharacteristic
58C3×C5×C8—42no—
592−1+4⋊C3—54no—
602−1+4⋊C3—102no—
61C2×#41⋊C3C2×D511yescharacteristic
62C22×SL(2,𝔽3)—102no—
63C2×C3×D8—201no—
64#131⋊C3C2×D512yescomplemented
65C5×#41—31no—
66C5×#41—31no—
67C5×#41C3×D411yescharacteristic
68C5×#41C23×C311yescharacteristic
69C2×C5×Q8C3×D411yescharacteristic
70C2×C5×D4—31no—
71C22×C4×C5—31no—
72C2×C22⋊D5—62no—
73C22×Dic5—62no—
74Q8×D5—24no—
75Q8×D5—64no—
76#711—68no—
77#711—64no—
78#711—64no—
79#709—34no—
80#709—34no—
81#709—62no—
82#709—62no—
83C2×D20C2×A412yes—
84C2×C4×D5—62no—
85C2×Dic10—34no—
86C2×Dic10—32no—
87C2×Dic10—34no—
88C2×Dic10—62no—
89C2×Dic10—62no—
90C2×Dic10—62no—
91C5×M16—32no—
92C5×M16—32no—
93C2×C5×C8—31no—
94C2×C5×C8—32no—
95C2×C5×C8—32no—
96C2×C5×C8C2×A411yescharacteristic
97Dic20—38no—
98Dic20—34no—
99D40C2×A414yes—
100#677—38no—
101C2×2−1+4—52no—
102#578—54no—
103#578—154no—
104C2×#137—152no—
105C2×#135—151no—
106C22×Q16—151no—
107C2×#131C3×D511yescharacteristic, complemented
108C22×C3×C5—41no—
109C2×C3×D5—84no—
110C2×C3×D5—164no—
111C3×C4×C5—41no—
112C3×C4×C5—41no—
113C2×C3×D4—202no—
114#41⋊C3D2011yescharacteristic
115#41⋊C3C22×D511yescharacteristic
116C2×SL(2,𝔽3)—104no—
117C2×SL(2,𝔽3)D2011yescharacteristic
118C3×D8—204no—
119C2×C3×C8—41no—
120C23×C5—31no—
121C22×D5—22no—
122C5×Q8—31no—
123C5×Q8C2×C3×D411yescharacteristic
124C5×D4—31no—
125C5×D4—31no—
126C5×D4—32no—
127C2×C4×C5—31no—
128C2×C4×C5—31no—
129C2×C4×C5—31no—
130C2×C4×C5—31no—
131C2×C4×C5—31no—
132C2×C4×C5C22×A411yescharacteristic
133C22⋊D5—64no—
134C22⋊D5—64no—
135C2×Dic5—64no—
136C2×Dic5—62no—
137C2×Dic5—64no—
138D20—22no—
139D20C22×A414yes—
140C4×D5—64no—
141C4×D5—64no—
142Dic10—34no—
143Dic10—64no—
144Dic10—62no—
145Dic10—64no—
146C5×C8—32no—
147C5×C8C22×A412yes—
1482−1+4—54no—
1492−1+4—102no—
1502−1+4—154no—
1512−1+4—302no—
152C2×#41—152no—
153C2×#41—302no—
154C2×#41C2×C3×D511yescharacteristic
155C22×Q8—102no—
156C22×Q8—152no—
157#137—158no—
158#137—158no—
159#135—154no—
160#135—154no—
161C2×Q16—152no—
162C2×Q16—154no—
163C2×Q16—154no—
164C2×Q16—151no—
165C2×SD16—152no—
166C2×D8—51no—
167#131—32no—
168#131C2×C3×D512yescomplemented
169C2×M16—31no—
170C22×C8—31no—
171C2×C3×C5—41no—
172C2×C3×C5—42no—
173C3×D5—164no—
174C23×C3—402no—
175C3×D4—204no—
176C3×D4—402no—
177C2×C3×C4—41no—
178SL(2,𝔽3)C2×D2011yescharacteristic
179C3×C8—42no—
180C22×C5—31no—
181C22×C5—31no—
182C22×C5—62no—
183C22×C5D4×A411yescharacteristic
184C2×D5—24no—
185C2×D5—44no—
186C4×C5—31no—
187C4×C5—31no—
188C4×C5D4×A411yescharacteristic
189C4×C5C23×A411yescharacteristic
190Dic5—64no—
191#41—31no—
192#41—31no—
193#41—154no—
194#41—154no—
195#41—302no—
196#41—302no—
197#41—308no—
198#41—304no—
199#41—304no—
200#41C3×D2011yescharacteristic
201#41C22×C3×D511yescharacteristic
202C2×Q8—104no—
203C2×Q8—154no—
204C2×Q8—154no—
205C2×Q8—152no—
206C2×Q8—302no—
207C2×Q8—302no—
208C2×Q8—302no—
209C2×Q8—304no—
210C2×Q8C3×D2011yescharacteristic
211C2×D4—31no—
212C2×D4—52no—
213C2×D4—302no—
214C22×C4—31no—
215C22×C4—302no—
216C22×C4—302no—
217Q16—158no—
218Q16—154no—
219SD16—158no—
220D8—54no—
221M16—32no—
222M16—32no—
223C2×C8—31no—
224C2×C8—32no—
225C2×C8—32no—
226C2×C8D5×A411yescharacteristic
227C3×C5—41noHall
228C22×C3—41no—
229C22×C3—404no—
230C22×C3—804no—
231C3×C4—41no—
232C3×C4—41no—
233C2×C5—61no—
234C2×C5—61no—
235C2×C5#578⋊C312yescomplemented
236C2×C5C2×D4×A411yescharacteristic
237D5—44no—
238C23—31no—
239C23—102no—
240Q8—31no—
241Q8—154no—
242Q8—304no—
243Q8—304no—
244Q8—302no—
245Q8C2×C3×D2011yescharacteristic
246D4—31no—
247D4—31no—
248D4—32no—
249D4—54no—
250D4—102no—
251D4—304no—
252D4—304no—
253C2×C4—31no—
254C2×C4—31no—
255C2×C4—31no—
256C2×C4—31no—
257C2×C4—31no—
258C2×C4—304no—
259C2×C4—304no—
260C2×C4—304no—
261C2×C4—302no—
262C2×C4—304no—
263C2×C4C2×D5×A411yescharacteristic
264C8—32no—
265C8C2×D5×A412yes—
266C2×C3—41no—
267C2×C3—42no—
268C2×C3—804no—
269C5C2×#578⋊C311yescharacteristic, complemented, Sylow
270C22—31no—
271C22—31no—
272C22—62no—
273C22—104no—
274C22—204no—
275C22A4×D2011yescharacteristic
276C4—31no—
277C4—31no—
278C4—304no—
279C4A4×D2011yescharacteristic
280C4C22×D5×A411yescharacteristic
281C3—41noSylow
282C2—61no—
283C2—61no—
284C2—204no—
285C2#66087⋊C312yesdirect product factor
286C2C2×A4×D2011yescharacteristic
subgroupG/H
centerC22A4×D20
commutator, cosocleC5×#41C23×C3
FrattiniC4C22×D5×A4
FittingC2×C5×#131C2×C3
socleC22×C5D4×A4
hypercenterC2×C8D5×A4
hypocenterC5×Q8C2×C3×D4
LCSG ▷ C5×#41 ▷ C5×Q8
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×#4150⋊C3C2semidirect
2. C2×C5×#131⋊C3C2semidirect
3. #66087⋊C3C2direct (N × H)
4. C2×#66087C3semidirect
7. #4150⋊C3C22semidirect
10. C5×#131⋊C3C22semidirect
12. C2×#4150C2×C3semidirect
13. C2×C5×#131C2×C3semidirect
15. #66087C2×C3semidirect
28. C2×#131⋊C3D5semidirect
33. #4150C22×C3semidirect
39. C5×#131C22×C3semidirect
64. #131⋊C3C2×D5semidirect
107. C2×#131C3×D5semidirect
168. #131C2×C3×D5semidirect
235. C2×C5#578⋊C3semidirect
269. C5C2×#578⋊C3semidirect
285. C2#66087⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#4150⋊C32
C2×C5×#131⋊C32
#66087⋊C32
C2×#660873
C2×C3×D404
C2×#578⋊C35