Finite Group Databasebeta

← C3×#10605053 #14319709

Subgroups — C3×#10605053 #14319709

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C213yesmaximal
2C2×C3×C5×#95C211yesmaximal, characteristic, complemented
3C3×C4×C22⋊Dic5C213yesmaximal, complemented
4C3×#64955C213yesmaximal, complemented
5C3×D5×#95C211yesmaximal, characteristic, complemented
6C3×#64938C213yesmaximal, complemented
7C3×#64937C211yesmaximal, characteristic, complemented
8#10605053C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×C4×C5C2213yes—
10C22×C3×C22⋊D5C2211yescharacteristic
11C22×C3×C4×D5C2213yes—
12C2×C3×C22⋊Dic5C2213yes—
13C3×C4×C22⋊D5C4124yescomplemented
14C2×C3×#685C2213yes—
15C2×C3×#683C2213yes—
16C2×C3×C4×Dic5C2216yes—
17C2×C3×C4×Dic5C2213yes—
18C3×C5×#95C2211yescharacteristic
19C3×C5×#95C2213yes—
20C3×#3963C2213yes—
21C3×#3963C2213yes—
22C3×#2275—51nomaximal, Hall
23C2×C4×C22⋊D5C2×C313yes—
24C2×C5×#95C2×C311yescharacteristic, complemented
25C4×C22⋊Dic5C2×C313yescomplemented
26#64955C2×C313yescomplemented
27D5×#95C2×C311yescharacteristic, complemented
28#64938C2×C313yescomplemented
29#64937C2×C311yescharacteristic, complemented
30C24×C3×C5C2311yescharacteristic
31C23×C3×D5C2311yescharacteristic
32C22×C3×C4×C5—46no—
33C22×C3×C4×C5C2×C4112yescomplemented
34C22×C3×C4×C5C2313yes—
35C22×C3×C4×C5C2313yes—
36C2×C3×C22⋊D5C2×C4112yes—
37C22×C3×Dic5C2313yes—
38C22×C3×Dic5C2313yes—
39C22×C3×Dic5C2311yescharacteristic
40C2×C3×C4×D5—46no—
41C2×C3×C4×D5C2×C4112yescomplemented
42C3×C22⋊Dic5C2×C4112yescomplemented
43C3×#685C2×C4112yescomplemented
44C3×#683C2×C4112yescomplemented
45C3×C4×Dic5—46no—
46C3×C4×Dic5C2×C4112yescomplemented
47C2×C3×C4×D4—53no—
48C3×C4×C4⋊C4—53no—
49C3×C4×C22⋊C4—53no—
50C3×C4×C22⋊C4—53no—
51C3×#376—51no—
52C2×C3×#95—51no—
53C2×C3×#95D511yescharacteristic, complemented
54C23×C4×C5C22×C313yes—
55C22×C22⋊D5C22×C311yescharacteristic
56C22×C4×D5C22×C313yes—
57C2×C22⋊Dic5C22×C313yes—
58C4×C22⋊D5C3×C4124yescomplemented
59C2×#685C22×C313yes—
60C2×#683C22×C313yes—
61C2×C4×Dic5C22×C316yes—
62C2×C4×Dic5C22×C313yes—
63C5×#95C22×C311yescharacteristic
64C5×#95C22×C313yes—
65#3963C22×C313yes—
66#3963C22×C313yes—
67#2275—51noSylow
68C23×C3×C5—23no—
69C23×C3×C5—21no—
70C23×C3×C5C22×C416yes—
71C23×C3×C5C2411yescharacteristic
72C22×C3×D5—23no—
73C22×C3×D5—21no—
74C22×C3×D5C22×C416yes—
75C2×C3×C4×C5—26no—
76C2×C3×C4×C5—26no—
77C2×C3×C4×C5—412no—
78C2×C3×C4×C5C22×C416yes—
79C2×C3×C4×C5C22×C416yes—
80C3×C22⋊D5C42116yescomplemented
81C2×C3×Dic5—23no—
82C2×C3×Dic5—26no—
83C2×C3×Dic5—23no—
84C2×C3×Dic5C22×C416yes—
85C2×C3×Dic5C22×C416yes—
86C2×C3×Dic5C22×C416yes—
87C3×C4×D5—412no—
88C22×C3×D4—51no—
89C23×C3×C4—53no—
90C23×C3×C4C2×D513yes—
91C3×C4×D4—524no—
92C2×C3×C4⋊C4—53no—
93C2×C3×C22⋊C4—53no—
94C2×C3×C22⋊C4—53no—
95C2×C3×C42—53no—
96C2×C3×C42—56no—
97C3×#95—53no—
98C3×#95—53no—
99C3×#95C2×D511yescharacteristic
100C3×#95C2×D513yes—
101C24×C5C23×C311yescharacteristic
102C23×D5C23×C311yescharacteristic
103C22×C4×C5—46no—
104C22×C4×C5C2×C3×C4112yescomplemented
105C22×C4×C5C23×C313yes—
106C22×C4×C5C23×C313yes—
107C2×C22⋊D5C2×C3×C4112yes—
108C22×Dic5C23×C313yes—
109C22×Dic5C23×C313yes—
110C22×Dic5C23×C311yescharacteristic
111C2×C4×D5—46no—
112C2×C4×D5C2×C3×C4112yescomplemented
113C22⋊Dic5C2×C3×C4112yescomplemented
114#685C2×C3×C4112yescomplemented
115#683C2×C3×C4112yescomplemented
116C4×Dic5—46no—
117C4×Dic5C2×C3×C4112yescomplemented
118C2×C4×D4—53no—
119C4×C4⋊C4—53no—
120C4×C22⋊C4—53no—
121C4×C22⋊C4—53no—
122#376—51no—
123C2×#95—51no—
124C2×#95C3×D511yescharacteristic, complemented
125C22×C3×C5—26no—
126C22×C3×C5—26no—
127C22×C3×C5C2×C4214yes—
128C22×C3×C5C23×C413yes—
129C22×C3×C5H(5,𝔽2)13yes—
130C22×C3×C52−1+411yescharacteristic
131C2×C3×D5—26no—
132C2×C3×D5—26no—
133C2×C3×D5C2×C4214yes—
134C3×C4×C5—26no—
135C3×C4×C5—26no—
136C3×Dic5—26no—
137C3×Dic5—26no—
138C3×Dic5C2×C4214yes—
139C24×C3—51no—
140C24×C3C22×D511yescharacteristic
141C2×C3×D4—512no—
142C22×C3×C4—46no—
143C22×C3×C4—51no—
144C22×C3×C4—53no—
145C22×C3×C4—53no—
146C22×C3×C4—512no—
147C22×C3×C4—206no—
148C22×C3×C4C4×D5112yescomplemented
149C22×C3×C4C22×D513yes—
150C22×C3×C4C22×D513yes—
151C3×C4⋊C4—512no—
152C3×C22⋊C4—512no—
153C3×C22⋊C4—512no—
154C3×C42—512no—
155C3×C42—206no—
156C23×C5—23no—
157C23×C5—21no—
158C23×C5C22×C3×C416yes—
159C23×C5C24×C311yescharacteristic
160C22×D5—23no—
161C22×D5—21no—
162C22×D5C22×C3×C416yes—
163C2×C4×C5—26no—
164C2×C4×C5—26no—
165C2×C4×C5—412no—
166C2×C4×C5C22×C3×C416yes—
167C2×C4×C5C22×C3×C416yes—
168C22⋊D5C3×C42116yescomplemented
169C2×Dic5—23no—
170C2×Dic5—26no—
171C2×Dic5—23no—
172C2×Dic5C22×C3×C416yes—
173C2×Dic5C22×C3×C416yes—
174C2×Dic5C22×C3×C416yes—
175C4×D5—412no—
176C22×D4—51no—
177C23×C4—53no—
178C23×C4C2×C3×D513yes—
179C4×D4—524no—
180C2×C4⋊C4—53no—
181C2×C22⋊C4—53no—
182C2×C22⋊C4—53no—
183C2×C42—53no—
184C2×C42—56no—
185#95—53no—
186#95—53no—
187#95C2×C3×D511yescharacteristic
188#95C2×C3×D513yes—
189C2×C3×C5—24no—
190C2×C3×C5C22×C4211yescharacteristic
191C2×C3×C5#51813yes—
192C2×C3×C5#52013yes—
193C3×D5—24no—
194C23×C3—23no—
195C23×C3—21no—
196C23×C3—56no—
197C23×C3—103no—
198C23×C3—101no—
199C23×C3C2×C4×D516yes—
200C23×C3C23×D511yescharacteristic
201C3×D4—516no—
202C2×C3×C4—26no—
203C2×C3×C4—26no—
204C2×C3×C4—412no—
205C2×C3×C4—56no—
206C2×C3×C4—56no—
207C2×C3×C4—56no—
208C2×C3×C4—103no—
209C2×C3×C4—106no—
210C2×C3×C4—103no—
211C2×C3×C4—2012no—
212C2×C3×C4C2×C4×D516yes—
213C2×C3×C4C2×C4×D516yes—
214C22×C5—26no—
215C22×C5—26no—
216C22×C5C2×C3×C4214yes—
217C22×C5C23×C3×C413yes—
218C22×C5C3×H(5,𝔽2)13yes—
219C22×C5C3×2−1+411yescharacteristic
220C2×D5—26no—
221C2×D5—26no—
222C2×D5C2×C3×C4214yes—
223C4×C5—26no—
224C4×C5—26no—
225Dic5—26no—
226Dic5—26no—
227Dic5C2×C3×C4214yes—
228C24—51no—
229C24C22×C3×D511yescharacteristic
230C2×D4—512no—
231C22×C4—46no—
232C22×C4—51no—
233C22×C4—53no—
234C22×C4—53no—
235C22×C4—512no—
236C22×C4—206no—
237C22×C4C3×C4×D5112yescomplemented
238C22×C4C22×C3×D513yes—
239C22×C4C22×C3×D513yes—
240C4⋊C4—512no—
241C22⋊C4—512no—
242C22⋊C4—512no—
243C42—512no—
244C42—206no—
245C3×C5#227511yescharacteristic, complemented, Hall
246C22×C3—26no—
247C22×C3—26no—
248C22×C3—54no—
249C22×C3—106no—
250C22×C3—106no—
251C22×C3C42×D514yes—
252C22×C3C22×C4×D513yes—
253C22×C3#414413yes—
254C22×C3#414711yescharacteristic
255C3×C4—26no—
256C3×C4—26no—
257C3×C4—54no—
258C3×C4—106no—
259C3×C4—106no—
260C2×C5—24no—
261C2×C5C22×C3×C4211yescharacteristic
262C2×C5C3×#51813yes—
263C2×C5C3×#52013yes—
264D5—24no—
265C23—23no—
266C23—21no—
267C23—56no—
268C23—103no—
269C23—101no—
270C23C2×C3×C4×D516yes—
271C23C23×C3×D511yescharacteristic
272D4—516no—
273C2×C4—26no—
274C2×C4—26no—
275C2×C4—412no—
276C2×C4—56no—
277C2×C4—56no—
278C2×C4—56no—
279C2×C4—103no—
280C2×C4—106no—
281C2×C4—103no—
282C2×C4—2012no—
283C2×C4C2×C3×C4×D516yes—
284C2×C4C2×C3×C4×D516yes—
285C2×C3—24no—
286C2×C3—104no—
287C2×C3C2×C42×D511yescharacteristic
288C2×C3#6582013yes—
289C2×C3#6583813yes—
290C5C3×#227511yescharacteristic, complemented, Sylow
291C22—26no—
292C22—26no—
293C22—54no—
294C22—106no—
295C22—106no—
296C22C3×C42×D514yes—
297C22C22×C3×C4×D513yes—
298C22C3×#414413yes—
299C22C3×#414711yescharacteristic
300C4—26no—
301C4—26no—
302C4—54no—
303C4—106no—
304C4—106no—
305C3#1060505311yescharacteristic, direct product factor, Sylow
306C2—24no—
307C2—104no—
308C2C2×C3×C42×D511yescharacteristic
309C2C3×#6582013yes—
310C2C3×#6583813yes—
subgroupG/H
centerC23×C3C23×D5
commutatorC2×C5C22×C3×C42
FrattiniC23C23×C3×D5
FittingC2×C3×C5×#95C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC2×C3×#95D5
hypocenterC5C3×#2275
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#95C2semidirect
3. C3×C4×C22⋊Dic5C2semidirect
4. C3×#64955C2semidirect
5. C3×D5×#95C2semidirect
6. C3×#64938C2semidirect
7. C3×#64937C2semidirect
8. #10605053C3direct (N × H)
13. C3×C4×C22⋊D5C4semidirect
24. C2×C5×#95C2×C3semidirect
25. C4×C22⋊Dic5C2×C3semidirect
26. #64955C2×C3semidirect
27. D5×#95C2×C3semidirect
28. #64938C2×C3semidirect
29. #64937C2×C3semidirect
33. C22×C3×C4×C5C2×C4semidirect
41. C2×C3×C4×D5C2×C4semidirect
42. C3×C22⋊Dic5C2×C4semidirect
43. C3×#685C2×C4semidirect
44. C3×#683C2×C4semidirect
46. C3×C4×Dic5C2×C4semidirect
53. C2×C3×#95D5semidirect
58. C4×C22⋊D5C3×C4semidirect
80. C3×C22⋊D5C42semidirect
104. C22×C4×C5C2×C3×C4semidirect
112. C2×C4×D5C2×C3×C4semidirect
113. C22⋊Dic5C2×C3×C4semidirect
114. #685C2×C3×C4semidirect
115. #683C2×C3×C4semidirect
117. C4×Dic5C2×C3×C4semidirect
124. C2×#95C3×D5semidirect
148. C22×C3×C4C4×D5semidirect
168. C22⋊D5C3×C42semidirect
237. C22×C4C3×C4×D5semidirect
245. C3×C5#2275semidirect
290. C5C3×#2275semidirect
305. C3#10605053direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C2×C3×C5×#952
C3×C4×C22⋊Dic52
C3×#649552
C3×D5×#952
C3×#649382
C3×#649372
#106050533
C3×#22755