Finite Group Databasebeta

← C3×C5×#2643 #14275677

Subgroups — C3×C5×#2643 #14275677

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#401C211yesmaximal, characteristic, complemented
2C3×C5×#400C213yesmaximal, complemented
3C3×C5×#397C213yesmaximal, complemented
4C3×C5×#396C211yesmaximal, characteristic, complemented
5C3×C5×#386C213yesmaximal
6C3×C5×#385C213yesmaximal, complemented
7C2×C3×C5×#95C211yesmaximal, characteristic, complemented
8C5×#2643C311yesmaximal, characteristic, direct product factor, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C23×C3×C4×C5C2213yes—
11C2×C3×C5×C4⋊C4C2213yes—
12C2×C3×C5×C4⋊C4C2213yes—
13C2×C3×C5×C22⋊C4C2213yes—
14C2×C3×C5×C22⋊C4C2213yes—
15C2×C3×C5×C22⋊C4C2213yes—
16C3×C5×#95C2211yescharacteristic
17C3×C5×#95C2213yes—
18C3×C5×#95C2213yes—
19C3×C5×#95C2213yes—
20C3×C5×#95C2213yes—
21C3×C5×#95C2213yes—
22C3×#2643C511yesmaximal, characteristic, direct product factor, Hall
23C5×#401C2×C311yescharacteristic, complemented
24C5×#400C2×C313yescomplemented
25C5×#397C2×C313yescomplemented
26C5×#396C2×C311yescharacteristic, complemented
27C5×#386C2×C313yes—
28C5×#385C2×C313yescomplemented
29C2×C5×#95C2×C311yescharacteristic, complemented
30C24×C3×C5C2311yescharacteristic
31C24×C3×C5C2311yescharacteristic
32C2×C3×C5×D4—26no—
33C22×C3×C4×C5—26no—
34C22×C3×C4×C5—43no—
35C22×C3×C4×C5—43no—
36C22×C3×C4×C5C2313yes—
37C22×C3×C4×C5C2313yes—
38C22×C3×C4×C5C2313yes—
39C22×C3×C4×C5C2313yes—
40C22×C3×C4×C5C2311yescharacteristic
41C3×C5×C4⋊C4—43no—
42C3×C5×C4⋊C4—43no—
43C3×C5×C22⋊C4—26no—
44C3×C5×C22⋊C4—43no—
45C3×C5×C22⋊C4—43no—
46C3×#401C2×C511yescharacteristic, complemented
47C3×#400C2×C513yescomplemented
48C3×#397C2×C513yescomplemented
49C3×#396C2×C511yescharacteristic, complemented
50C3×#386C2×C513yes—
51C3×#385C2×C513yescomplemented
52C2×C3×#95C2×C511yescharacteristic, complemented
53C22×C5×D4C22×C311yescharacteristic
54C23×C4×C5C22×C313yes—
55C2×C5×C4⋊C4C22×C313yes—
56C2×C5×C4⋊C4C22×C313yes—
57C2×C5×C22⋊C4C22×C313yes—
58C2×C5×C22⋊C4C22×C313yes—
59C2×C5×C22⋊C4C22×C313yes—
60C5×#95C22×C311yescharacteristic
61C5×#95C22×C313yes—
62C5×#95C22×C313yes—
63C5×#95C22×C313yes—
64C5×#95C22×C313yes—
65C5×#95C22×C313yes—
66#2643C3×C511yescharacteristic, direct product factor, Sylow
67C23×C3×C5—23no—
68C23×C3×C5—21no—
69C23×C3×C5—23no—
70C23×C3×C5—23no—
71C23×C3×C5—21no—
72C23×C3×C5#4116yes—
73C23×C3×C5C2411yescharacteristic
74C3×C5×D4—44no—
75C2×C3×C4×C5—23no—
76C2×C3×C4×C5—23no—
77C2×C3×C4×C5—23no—
78C2×C3×C4×C5—23no—
79C2×C3×C4×C5—23no—
80C2×C3×C4×C5—23no—
81C2×C3×C4×C5—23no—
82C2×C3×C4×C5—23no—
83C2×C3×C4×C5—23no—
84C2×C3×C4×C5—23no—
85C2×C3×C4×C5—23no—
86C2×C3×C4×C5—23no—
87C2×C3×C4×C5—23no—
88C2×C3×C4×C5—412no—
89C22×C3×D4C22×C511yescharacteristic
90C23×C3×C4C22×C513yes—
91C2×C3×C4⋊C4C22×C513yes—
92C2×C3×C4⋊C4C22×C513yes—
93C2×C3×C22⋊C4C22×C513yes—
94C2×C3×C22⋊C4C22×C513yes—
95C2×C3×C22⋊C4C22×C513yes—
96C3×#95C22×C511yescharacteristic
97C3×#95C22×C513yes—
98C3×#95C22×C513yes—
99C3×#95C22×C513yes—
100C3×#95C22×C513yes—
101C3×#95C22×C513yes—
102C24×C5C23×C311yescharacteristic
103C24×C5C23×C311yescharacteristic
104C2×C5×D4—26no—
105C22×C4×C5—26no—
106C22×C4×C5—43no—
107C22×C4×C5—43no—
108C22×C4×C5C23×C313yes—
109C22×C4×C5C23×C313yes—
110C22×C4×C5C23×C313yes—
111C22×C4×C5C23×C313yes—
112C22×C4×C5C23×C311yescharacteristic
113C5×C4⋊C4—43no—
114C5×C4⋊C4—43no—
115C5×C22⋊C4—26no—
116C5×C22⋊C4—43no—
117C5×C22⋊C4—43no—
118#401C2×C3×C511yescharacteristic, complemented
119#400C2×C3×C513yescomplemented
120#397C2×C3×C513yescomplemented
121#396C2×C3×C511yescharacteristic, complemented
122#386C2×C3×C513yes—
123#385C2×C3×C513yescomplemented
124C2×#95C2×C3×C511yescharacteristic, complemented
125C22×C3×C5—26no—
126C22×C3×C5—26no—
127C22×C3×C5—41no—
128C22×C3×C5—43no—
129C22×C3×C5—43no—
130C22×C3×C5#12614yes—
131C22×C3×C5C2×#4113yes—
132C22×C3×C5H(5,𝔽2)13yes—
133C22×C3×C52−1+411yescharacteristic
134C3×C4×C5—41no—
135C3×C4×C5—43no—
136C3×C4×C5—43no—
137C3×C4×C5—43no—
138C3×C4×C5—43no—
139C24×C3C23×C511yescharacteristic
140C24×C3C23×C511yescharacteristic
141C2×C3×D4—26no—
142C22×C3×C4—26no—
143C22×C3×C4—43no—
144C22×C3×C4—43no—
145C22×C3×C4C23×C511yescharacteristic
146C22×C3×C4C23×C513yes—
147C22×C3×C4C23×C513yes—
148C22×C3×C4C23×C513yes—
149C22×C3×C4C23×C513yes—
150C3×C4⋊C4—43no—
151C3×C4⋊C4—43no—
152C3×C22⋊C4—26no—
153C3×C22⋊C4—43no—
154C3×C22⋊C4—43no—
155C23×C5—23no—
156C23×C5—21no—
157C23×C5—23no—
158C23×C5—23no—
159C23×C5—21no—
160C23×C5C3×#4116yes—
161C23×C5C24×C311yescharacteristic
162C5×D4—44no—
163C2×C4×C5—23no—
164C2×C4×C5—23no—
165C2×C4×C5—23no—
166C2×C4×C5—23no—
167C2×C4×C5—23no—
168C2×C4×C5—23no—
169C2×C4×C5—23no—
170C2×C4×C5—23no—
171C2×C4×C5—23no—
172C2×C4×C5—23no—
173C2×C4×C5—23no—
174C2×C4×C5—23no—
175C2×C4×C5—23no—
176C2×C4×C5—412no—
177C22×D4C22×C3×C511yescharacteristic
178C23×C4C22×C3×C513yes—
179C2×C4⋊C4C22×C3×C513yes—
180C2×C4⋊C4C22×C3×C513yes—
181C2×C22⋊C4C22×C3×C513yes—
182C2×C22⋊C4C22×C3×C513yes—
183C2×C22⋊C4C22×C3×C513yes—
184#95C22×C3×C511yescharacteristic
185#95C22×C3×C513yes—
186#95C22×C3×C513yes—
187#95C22×C3×C513yes—
188#95C22×C3×C513yes—
189#95C22×C3×C513yes—
190C2×C3×C5—24no—
191C2×C3×C5—81no—
192C2×C3×C5C2×#12611yescharacteristic
193C2×C3×C5#53813yes—
194C2×C3×C5#53913yes—
195C23×C3—23no—
196C23×C3—21no—
197C23×C3—23no—
198C23×C3—23no—
199C23×C3—21no—
200C23×C3C5×#4116yes—
201C23×C3C24×C511yescharacteristic
202C3×D4—44no—
203C2×C3×C4—23no—
204C2×C3×C4—23no—
205C2×C3×C4—23no—
206C2×C3×C4—23no—
207C2×C3×C4—23no—
208C2×C3×C4—23no—
209C2×C3×C4—23no—
210C2×C3×C4—23no—
211C2×C3×C4—23no—
212C2×C3×C4—23no—
213C2×C3×C4—23no—
214C2×C3×C4—23no—
215C2×C3×C4—23no—
216C2×C3×C4—412no—
217C22×C5—26no—
218C22×C5—26no—
219C22×C5—41no—
220C22×C5—43no—
221C22×C5—43no—
222C22×C5C3×#12614yes—
223C22×C5C2×C3×#4113yes—
224C22×C5C3×H(5,𝔽2)13yes—
225C22×C5C3×2−1+411yescharacteristic
226C4×C5—41no—
227C4×C5—43no—
228C4×C5—43no—
229C4×C5—43no—
230C4×C5—43no—
231C24C23×C3×C511yescharacteristic
232C24C23×C3×C511yescharacteristic
233C2×D4—26no—
234C22×C4—26no—
235C22×C4—43no—
236C22×C4—43no—
237C22×C4C23×C3×C511yescharacteristic
238C22×C4C23×C3×C513yes—
239C22×C4C23×C3×C513yes—
240C22×C4C23×C3×C513yes—
241C22×C4C23×C3×C513yes—
242C4⋊C4—43no—
243C4⋊C4—43no—
244C22⋊C4—26no—
245C22⋊C4—43no—
246C22⋊C4—43no—
247C3×C5#264311yescharacteristic, direct product factor, Hall
248C22×C3—26no—
249C22×C3—26no—
250C22×C3—41no—
251C22×C3—43no—
252C22×C3—43no—
253C22×C3C5×#12614yes—
254C22×C3C2×C5×#4113yes—
255C22×C3C5×H(5,𝔽2)13yes—
256C22×C3C5×2−1+411yescharacteristic
257C3×C4—41no—
258C3×C4—43no—
259C3×C4—43no—
260C3×C4—43no—
261C3×C4—43no—
262C2×C5—24no—
263C2×C5—81no—
264C2×C5C2×C3×#12611yescharacteristic
265C2×C5C3×#53813yes—
266C2×C5C3×#53913yes—
267C23—23no—
268C23—21no—
269C23—23no—
270C23—23no—
271C23—21no—
272C23C3×C5×#4116yes—
273C23C24×C3×C511yescharacteristic
274D4—44no—
275C2×C4—23no—
276C2×C4—23no—
277C2×C4—23no—
278C2×C4—23no—
279C2×C4—23no—
280C2×C4—23no—
281C2×C4—23no—
282C2×C4—23no—
283C2×C4—23no—
284C2×C4—23no—
285C2×C4—23no—
286C2×C4—23no—
287C2×C4—23no—
288C2×C4—412no—
289C2×C3—24no—
290C2×C3—81no—
291C2×C3C2×C5×#12611yescharacteristic
292C2×C3C5×#53813yes—
293C2×C3C5×#53913yes—
294C5C3×#264311yescharacteristic, direct product factor, Sylow
295C22—26no—
296C22—26no—
297C22—41no—
298C22—43no—
299C22—43no—
300C22C3×C5×#12614yes—
301C22C2×C3×C5×#4113yes—
302C22C3×C5×H(5,𝔽2)13yes—
303C22C3×C5×2−1+411yescharacteristic
304C4—41no—
305C4—43no—
306C4—43no—
307C4—43no—
308C4—43no—
309C3C5×#264311yescharacteristic, direct product factor, Sylow
310C2—24no—
311C2—81no—
312C2C2×C3×C5×#12611yescharacteristic
313C2C3×C5×#53813yes—
314C2C3×C5×#53913yes—
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC22×C3×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C5×#401C2semidirect
2. C3×C5×#400C2semidirect
3. C3×C5×#397C2semidirect
4. C3×C5×#396C2semidirect
6. C3×C5×#385C2semidirect
7. C2×C3×C5×#95C2semidirect
8. C5×#2643C3direct (N × H)
22. C3×#2643C5direct (N × H)
23. C5×#401C2×C3semidirect
24. C5×#400C2×C3semidirect
25. C5×#397C2×C3semidirect
26. C5×#396C2×C3semidirect
28. C5×#385C2×C3semidirect
29. C2×C5×#95C2×C3semidirect
46. C3×#401C2×C5semidirect
47. C3×#400C2×C5semidirect
48. C3×#397C2×C5semidirect
49. C3×#396C2×C5semidirect
51. C3×#385C2×C5semidirect
52. C2×C3×#95C2×C5semidirect
66. #2643C3×C5direct (N × H)
118. #401C2×C3×C5semidirect
119. #400C2×C3×C5semidirect
120. #397C2×C3×C5semidirect
121. #396C2×C3×C5semidirect
123. #385C2×C3×C5semidirect
124. C2×#95C2×C3×C5semidirect
247. C3×C5#2643direct (N × H)
294. C5C3×#2643direct (N × H)
309. C3C5×#2643direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#4012
C3×C5×#4002
C3×C5×#3972
C3×C5×#3962
C3×C5×#3862
C3×C5×#3852
C2×C3×C5×#952
C5×#26433
C3×#26435