Finite Group Databasebeta

← C3×#92034 #13089238

Subgroups — C3×#92034 #13089238

Order 1440.

696 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D15C211yesmaximal, characteristic, complemented
2C3×C5×#239C211yesmaximal, characteristic, complemented
3C32×#713C211yesmaximal, characteristic, complemented
4C3×#6777C213yesmaximal, complemented
5C3×C4×D3×D5C213yesmaximal, complemented
6C3×#6772C213yesmaximal, complemented
7C3×#6765C213yesmaximal, complemented
8C3×D5×#41—31nomaximal
9#92034C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×D5C2213yes—
11C32×C5×Q8C2211yescharacteristic, complemented
12C3×C4×D15C2213yes—
13C3×Dic30C2213yescomplemented
14C3×C5×D12C2213yescomplemented
15C3×C4×C5×D3C2213yescomplemented
16C32×D20C2213yescomplemented
17C32×C4×D5C2213yescomplemented
18C3×#1201C2216yescomplemented
19C3×#1200C2211yescharacteristic
20C3×D3×Dic5C2213yescomplemented
21C3×D5×Dic3C2213yescomplemented
22C3×D3×#41—51nomaximal, Hall
23C3×C5×#41—31no—
24Q8×D15C2×C311yescharacteristic, complemented
25C5×#239C2×C311yescharacteristic, complemented
26C3×#713—21no—
27C3×#713D311yescharacteristic, complemented
28C3×#713C2×C311yescharacteristic, complemented
29C3×Q8×D5—31no—
30C3×#711—33no—
31C3×D4×D5—33no—
32C3×#709—33no—
33C2×C3×C4×D5—33no—
34#6777C2×C313yescomplemented
35C4×D3×D5C2×C313yescomplemented
36#6772C2×C313yescomplemented
37#6765C2×C313yescomplemented
38C2×C3×D15C2311yescharacteristic
39C2×C3×C5×D3C2313yes—
40C2×C32×D5C2313yes—
41C3×D3×D5—26no—
42C32×C4×C5C2313yes—
43C3×Dic15C2313yes—
44C3×C5×Dic3C2311yescharacteristic
45C32×Dic5C2311yescharacteristic
46D5×#41—31noHall
47C32×#41—51no—
48C3×#239D511yescharacteristic, complemented
49C3×D3×Q8—51no—
50C3×#237—53no—
51C3×D3×D4—53no—
52C3×#235—53no—
53C2×C3×C4×D3—53no—
54C22×C3×D5—33no—
55C2×D3×D5C22×C313yes—
56C3×C5×Q8—21no—
57C3×C5×Q8C2×D311yescharacteristic, complemented
58C3×C5×Q8C22×C311yescharacteristic, complemented
59C3×C5×D4—33no—
60C2×C3×C4×C5—33no—
61C4×D15C22×C313yes—
62Dic30C22×C313yescomplemented
63C5×D12C22×C313yescomplemented
64C4×C5×D3C22×C313yescomplemented
65C3×C22⋊D5—36no—
66C2×C3×Dic5—33no—
67C3×D20—23no—
68C3×D20C2×D313yescomplemented
69C3×D20C22×C313yescomplemented
70C3×C4×D5—23no—
71C3×C4×D5—33no—
72C3×C4×D5—33no—
73C3×C4×D5—31no—
74C3×C4×D5C2×D313yescomplemented
75C3×C4×D5C22×C313yescomplemented
76C3×Dic10—33no—
77#1201C22×C316yescomplemented
78#1200C22×C311yescharacteristic
79D3×Dic5C22×C313yescomplemented
80D5×Dic3C22×C313yescomplemented
81C2×C3×#41—151no—
82D3×#41—51no—
83C2×C32×C5C2411yescharacteristic
84C3×D15#4112yescomplemented
85C3×C5×D3—23no—
86C32×D5—23no—
87C5×#41—31no—
88#713C3×D311yescharacteristic, complemented
89Q8×D5—31no—
90#711—33no—
91D4×D5—33no—
92#709—33no—
93C2×C4×D5—33no—
94C22×C3×D3—53no—
95C32×Q8C2×D511yescharacteristic, complemented
96C32×D4—53no—
97C2×C32×C4—53no—
98C3×#67—56no—
99C2×C3×Dic3—53no—
100C3×D12C2×D513yescomplemented
101C3×C4×D3—53no—
102C3×C4×D3—53no—
103C3×C4×D3—51no—
104C3×C4×D3C2×D513yescomplemented
105C3×Dic6—53no—
106C22×C3×C5—33no—
107C2×D15C23×C311yescharacteristic
108C2×C5×D3C23×C313yes—
109C2×C3×D5—23no—
110C2×C3×D5—31no—
111C2×C3×D5—66no—
112C2×C3×D5C22×D313yes—
113C2×C3×D5C23×C313yes—
114D3×D5—26no—
115C3×C4×C5—23no—
116C3×C4×C5—31no—
117C3×C4×C5C22×D313yes—
118C3×C4×C5C23×C313yes—
119Dic15C23×C313yes—
120C3×Dic5—21no—
121C3×Dic5—33no—
122C3×Dic5C22×D311yescharacteristic
123C3×Dic5C23×C311yescharacteristic
124C5×Dic3C23×C311yescharacteristic
125C3×#41—31no—
126C3×#41—51no—
127C3×#41—51no—
128C3×#41—101no—
129C3×#41—153no—
130C3×#41—153no—
131C2×C3×Q8—151no—
132C2×C3×D4—153no—
133C22×C3×C4—153no—
134#239C3×D511yescharacteristic, complemented
135D3×Q8—51no—
136#237—53no—
137D3×D4—53no—
138#235—53no—
139C2×C4×D3—53no—
140C32×C5C2×#4111yescharacteristic, complemented, Hall
141C22×D5—33no—
142C5×Q8C2×C3×D311yescharacteristic, complemented
143C5×D4—33no—
144C2×C4×C5—33no—
145C22⋊D5—36no—
146C2×Dic5—33no—
147D20C2×C3×D313yescomplemented
148C4×D5—33no—
149C4×D5—33no—
150C4×D5—31no—
151C4×D5C2×C3×D313yescomplemented
152Dic10—33no—
153C22×C32—53no—
154C2×C3×D3—51no—
155C2×C3×D3—106no—
156C2×C3×D3C22×D513yes—
157C32×C4—51no—
158C32×C4C22×D513yes—
159C3×Dic3—53no—
160C3×Dic3C22×D511yescharacteristic
161C2×#41—151noSylow
162C2×C3×C5—21no—
163C2×C3×C5—63no—
164C2×C3×C5C23×D311yescharacteristic
165C2×C3×C5C24×C311yescharacteristic
166D15C3×#4112yescomplemented
167C3×D5—23no—
168C3×D5—23no—
169C3×D5—32no—
170C3×D5—43no—
171C5×D3—23no—
172C23×C3—153no—
173C22×D3—53no—
174C3×Q8—21no—
175C3×Q8—153no—
176C3×Q8D3×D511yescharacteristic, complemented
177C3×Q8C2×C3×D511yescharacteristic, complemented
178C3×D4—33no—
179C3×D4—53no—
180C3×D4—53no—
181C3×D4—103no—
182C3×D4—156no—
183C2×C3×C4—33no—
184C2×C3×C4—53no—
185C2×C3×C4—53no—
186C2×C3×C4—103no—
187C2×C3×C4—151no—
188C2×C3×C4—153no—
189C2×C3×C4—153no—
190C2×C3×C4—153no—
191#67—56no—
192C2×Dic3—53no—
193D12C2×C3×D513yescomplemented
194C4×D3—53no—
195C4×D3—53no—
196C4×D3—51no—
197C4×D3C2×C3×D513yescomplemented
198Dic6—53no—
199C22×C5—33no—
200C2×D5—31no—
201C2×D5—66no—
202C2×D5C22×C3×D313yes—
203C4×C5—31no—
204C4×C5C22×C3×D313yes—
205Dic5—33no—
206Dic5C22×C3×D311yescharacteristic
207C2×C32—103no—
208C2×C32C23×D511yescharacteristic
209C3×D3—23no—
210C3×D3—52no—
211#41—31no—
212#41—51no—
213#41—153no—
214#41—153no—
215C2×Q8—151no—
216C2×D4—153no—
217C22×C4—153no—
218C3×C5—21no—
219C3×C5D3×#4111yescharacteristic, complemented
220C3×C5C2×C3×#4111yescharacteristic, complemented
221C22×C3—33no—
222C22×C3—53no—
223C22×C3—53no—
224C22×C3—103no—
225C22×C3—151no—
226C22×C3—306no—
227C2×D3—51no—
228C2×D3—106no—
229C2×D3C22×C3×D513yes—
230C3×C4—23no—
231C3×C4—31no—
232C3×C4—51no—
233C3×C4—51no—
234C3×C4—101no—
235C3×C4—153no—
236C3×C4C2×D3×D513yes—
237C3×C4C22×C3×D513yes—
238Dic3—53no—
239Dic3C22×C3×D511yescharacteristic
240C2×C5—63no—
241C2×C5C23×C3×D311yescharacteristic
242D5—23no—
243D5—32no—
244C32D5×#4111yescharacteristic, complemented, Sylow
245C23—153no—
246Q8—153no—
247Q8C3×D3×D511yescharacteristic, complemented
248D4—33no—
249D4—53no—
250D4—156no—
251C2×C4—33no—
252C2×C4—53no—
253C2×C4—151no—
254C2×C4—153no—
255C2×C4—153no—
256C2×C4—153no—
257C2×C3—21no—
258C2×C3—63no—
259C2×C3—103no—
260C2×C3—103no—
261C2×C3—152no—
262C2×C3—203no—
263C2×C3C22×D3×D511yescharacteristic
264C2×C3C23×C3×D511yescharacteristic
265D3—23no—
266D3—52no—
267C5C3×D3×#4111yescharacteristic, complemented, Sylow
268C22—33no—
269C22—53no—
270C22—151no—
271C22—306no—
272C4—31no—
273C4—51no—
274C4—153no—
275C4C2×C3×D3×D513yes—
276C3—21no—
277C3#9203411yescharacteristic, direct product factor
278C3C3×D5×#4111yescharacteristic, complemented
279C2—63no—
280C2—103no—
281C2—152no—
282C2C22×C3×D3×D511yescharacteristic
subgroupG/H
centerC2×C3C22×D3×D5
commutator, cosocleC2×C3×C5C24×C3
FrattiniC2C22×C3×D3×D5
FittingC32×C5×Q8C22
socleC2×C32×C5C24
hypercenterC3×Q8D3×D5
hypocenterC3×C5C2×C3×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C3×Q8

Complements

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

NH ≅ G/Ntype
1. C3×Q8×D15C2semidirect
2. C3×C5×#239C2semidirect
3. C32×#713C2semidirect
4. C3×#6777C2semidirect
5. C3×C4×D3×D5C2semidirect
6. C3×#6772C2semidirect
7. C3×#6765C2semidirect
9. #92034C3direct (N × H)
11. C32×C5×Q8C22semidirect
13. C3×Dic30C22semidirect
14. C3×C5×D12C22semidirect
15. C3×C4×C5×D3C22semidirect
16. C32×D20C22semidirect
17. C32×C4×D5C22semidirect
18. C3×#1201C22semidirect
20. C3×D3×Dic5C22semidirect
21. C3×D5×Dic3C22semidirect
24. Q8×D15C2×C3semidirect
25. C5×#239C2×C3semidirect
27. C3×#713D3semidirect
28. C3×#713C2×C3semidirect
34. #6777C2×C3semidirect
35. C4×D3×D5C2×C3semidirect
36. #6772C2×C3semidirect
37. #6765C2×C3semidirect
48. C3×#239D5semidirect
57. C3×C5×Q8C2×D3semidirect
58. C3×C5×Q8C22×C3semidirect
62. Dic30C22×C3semidirect
63. C5×D12C22×C3semidirect
64. C4×C5×D3C22×C3semidirect
68. C3×D20C2×D3semidirect
69. C3×D20C22×C3semidirect
74. C3×C4×D5C2×D3semidirect
75. C3×C4×D5C22×C3semidirect
77. #1201C22×C3semidirect
79. D3×Dic5C22×C3semidirect
80. D5×Dic3C22×C3semidirect
84. C3×D15#41semidirect
88. #713C3×D3semidirect
95. C32×Q8C2×D5semidirect
100. C3×D12C2×D5semidirect
104. C3×C4×D3C2×D5semidirect
134. #239C3×D5semidirect
140. C32×C5C2×#41semidirect
142. C5×Q8C2×C3×D3semidirect
147. D20C2×C3×D3semidirect
151. C4×D5C2×C3×D3semidirect
166. D15C3×#41semidirect
176. C3×Q8D3×D5semidirect
177. C3×Q8C2×C3×D5semidirect
193. D12C2×C3×D5semidirect
197. C4×D3C2×C3×D5semidirect
219. C3×C5D3×#41semidirect
220. C3×C5C2×C3×#41semidirect
244. C32D5×#41semidirect
247. Q8C3×D3×D5semidirect
267. C5C3×D3×#41semidirect
277. C3#92034direct (N × H)
278. C3C3×D5×#41semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D152
C3×C5×#2392
C32×#7132
C3×#67772
C3×C4×D3×D52
C3×#67722
C3×#67652
C3×D5×#413
#920343
C3×D3×#415