Finite Group Databasebeta

← C3×C5×#1619 #14274653

Subgroups — C3×C5×#1619 #14274653

Order 1920.

672 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 152 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
1C3×C5×D42C211yesmaximal, characteristic, complemented
2C3×C5×#493C211yesmaximal, characteristic, complemented
3C3×C5×#459C212yesmaximal, complemented
4C3×C5×#331C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C212yesmaximal, complemented
6C5×#1619C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×D4—22no—
8C2×C3×C5×D8—22no—
9C2×C3×C5×D8—22no—
10C3×C5×#127C2211yescharacteristic
11C3×C5×#127C2211yescharacteristic, complemented
12C3×C5×#121—22no—
13C3×C5×#120—22no—
14C3×C4×C5×D4C2212yes—
15C3×C5×C4⋊C8C2212yescomplemented
16C3×C5×#102—22no—
17C3×C4×C5×C8C2211yescharacteristic, complemented
18C3×#1619C511yesmaximal, characteristic, direct product factor, Hall
19C5×D42C2×C311yescharacteristic, complemented
20C5×#493C2×C311yescharacteristic, complemented
21C5×#459C2×C312yescomplemented
22C5×#331C2×C311yescharacteristic, complemented
23C5×D4⋊C8C2×C312yescomplemented
24C24×C3×C5—22no—
25C2×C3×C5×D4—24no—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—21no—
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4—44no—
30C2×C3×C5×D4—44no—
31C2×C3×C5×D4D412yes—
32C2×C3×C5×D4D412yes—
33C22×C3×C4×C5—22no—
34C3×C5×D8—44no—
35C3×C5×D8—44no—
36C2×C3×C5×C8—21no—
37C2×C3×C5×C8—22no—
38C3×C5×C4⋊C4D412yes—
39C3×C5×C22⋊C4—22no—
40C3×C5×C22⋊C4—22no—
41C3×C42×C5C2311yescharacteristic
42C3×D42C2×C511yescharacteristic, complemented
43C3×#493C2×C511yescharacteristic, complemented
44C3×#459C2×C512yescomplemented
45C3×#331C2×C511yescharacteristic, complemented
46C3×D4⋊C8C2×C512yescomplemented
47C22×C5×D4—22no—
48C2×C5×D8—22no—
49C2×C5×D8—22no—
50C5×#127C22×C311yescharacteristic
51C5×#127C22×C311yescharacteristic, complemented
52C5×#121—22no—
53C5×#120—22no—
54C4×C5×D4C22×C312yes—
55C5×C4⋊C8C22×C312yescomplemented
56C5×#102—22no—
57C4×C5×C8C22×C311yescharacteristic, complemented
58#1619C3×C511yescharacteristic, direct product factor, Sylow
59C23×C3×C5—22no—
60C23×C3×C5—22no—
61C23×C3×C5—48no—
62C23×C3×C5—41no—
63C23×C3×C5—82no—
64C3×C5×D4—22no—
65C3×C5×D4—42no—
66C3×C5×D4—42no—
67C3×C5×D4—48no—
68C3×C5×D4—42no—
69C3×C5×D4—42no—
70C3×C5×D4—42no—
71C3×C5×D4—42no—
72C3×C5×D4D814yescomplemented
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5—42no—
75C2×C3×C4×C5—42no—
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5C2×D412yes—
78C3×C5×C8—22no—
79C3×C5×C8—42no—
80C22×C3×D4—22no—
81C2×C3×D8—22no—
82C2×C3×D8—22no—
83C3×#127C22×C511yescharacteristic
84C3×#127C22×C511yescharacteristic, complemented
85C3×#121—22no—
86C3×#120—22no—
87C3×C4×D4C22×C512yes—
88C3×C4⋊C8C22×C512yescomplemented
89C3×#102—22no—
90C3×C4×C8C22×C511yescharacteristic, complemented
91C24×C5—22no—
92C2×C5×D4—24no—
93C2×C5×D4—22no—
94C2×C5×D4—21no—
95C2×C5×D4—22no—
96C2×C5×D4—44no—
97C2×C5×D4—44no—
98C2×C5×D4C3×D412yes—
99C2×C5×D4C3×D412yes—
100C22×C4×C5—22no—
101C5×D8—44no—
102C5×D8—44no—
103C2×C5×C8—21no—
104C2×C5×C8—22no—
105C5×C4⋊C4C3×D412yes—
106C5×C22⋊C4—22no—
107C5×C22⋊C4—22no—
108C42×C5C23×C311yescharacteristic
109D42C2×C3×C511yescharacteristic, complemented
110#493C2×C3×C511yescharacteristic, complemented
111#459C2×C3×C512yescomplemented
112#331C2×C3×C511yescharacteristic, complemented
113D4⋊C8C2×C3×C512yescomplemented
114C22×C3×C5—24no—
115C22×C3×C5—42no—
116C22×C3×C5—42no—
117C22×C3×C5—44no—
118C22×C3×C5—42no—
119C22×C3×C5—88no—
120C22×C3×C5—82no—
121C22×C3×C5—81no—
122C22×C3×C5#12011yescharacteristic
123C3×C4×C5—21no—
124C3×C4×C5—42no—
125C3×C4×C5C2×D812yes—
126C3×C4×C5AGL(1,ℤ/8)12yes—
127C24×C3—22no—
128C2×C3×D4—24no—
129C2×C3×D4—22no—
130C2×C3×D4—22no—
131C2×C3×D4—21no—
132C2×C3×D4—44no—
133C2×C3×D4—44no—
134C2×C3×D4C5×D412yes—
135C2×C3×D4C5×D412yes—
136C22×C3×C4—22no—
137C3×D8—44no—
138C3×D8—44no—
139C2×C3×C8—21no—
140C2×C3×C8—22no—
141C3×C4⋊C4C5×D412yes—
142C3×C22⋊C4—22no—
143C3×C22⋊C4—22no—
144C3×C42C23×C511yescharacteristic
145C23×C5—22no—
146C23×C5—22no—
147C23×C5—48no—
148C23×C5—41no—
149C23×C5—82no—
150C5×D4—22no—
151C5×D4—42no—
152C5×D4—42no—
153C5×D4—48no—
154C5×D4—42no—
155C5×D4—42no—
156C5×D4—42no—
157C5×D4—42no—
158C5×D4C3×D814yescomplemented
159C2×C4×C5—22no—
160C2×C4×C5—42no—
161C2×C4×C5—42no—
162C2×C4×C5C2×C3×D411yescharacteristic
163C2×C4×C5C2×C3×D412yes—
164C5×C8—22no—
165C5×C8—42no—
166C22×D4—22no—
167C2×D8—22no—
168C2×D8—22no—
169#127C22×C3×C511yescharacteristic
170#127C22×C3×C511yescharacteristic, complemented
171#121—22no—
172#120—22no—
173C4×D4C22×C3×C512yes—
174C4⋊C8C22×C3×C512yescomplemented
175#102—22no—
176C4×C8C22×C3×C511yescharacteristic, complemented
177C2×C3×C5—44no—
178C2×C3×C5—82no—
179C2×C3×C5—161no—
180C2×C3×C5#44712yes—
181C2×C3×C5#45311yescharacteristic
182C23×C3—22no—
183C23×C3—22no—
184C23×C3—48no—
185C23×C3—41no—
186C23×C3—82no—
187C3×D4—22no—
188C3×D4—42no—
189C3×D4—42no—
190C3×D4—48no—
191C3×D4—42no—
192C3×D4—42no—
193C3×D4—42no—
194C3×D4—42no—
195C3×D4C5×D814yescomplemented
196C2×C3×C4—22no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4C2×C5×D411yescharacteristic
200C2×C3×C4C2×C5×D412yes—
201C3×C8—22no—
202C3×C8—42no—
203C22×C5—24no—
204C22×C5—42no—
205C22×C5—42no—
206C22×C5—44no—
207C22×C5—42no—
208C22×C5—88no—
209C22×C5—82no—
210C22×C5—81no—
211C22×C5C3×#12011yescharacteristic
212C4×C5—21no—
213C4×C5—42no—
214C4×C5C2×C3×D812yes—
215C4×C5C3×AGL(1,ℤ/8)12yes—
216C24—22no—
217C2×D4—24no—
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—21no—
221C2×D4—44no—
222C2×D4—44no—
223C2×D4C3×C5×D412yes—
224C2×D4C3×C5×D412yes—
225C22×C4—22no—
226D8—44no—
227D8—44no—
228C2×C8—21no—
229C2×C8—22no—
230C4⋊C4C3×C5×D412yes—
231C22⋊C4—22no—
232C22⋊C4—22no—
233C42C23×C3×C511yescharacteristic
234C3×C5#161911yescharacteristic, direct product factor, Hall
235C22×C3—24no—
236C22×C3—42no—
237C22×C3—42no—
238C22×C3—44no—
239C22×C3—42no—
240C22×C3—88no—
241C22×C3—82no—
242C22×C3—81no—
243C22×C3C5×#12011yescharacteristic
244C3×C4—21no—
245C3×C4—42no—
246C3×C4C2×C5×D812yes—
247C3×C4C5×AGL(1,ℤ/8)12yes—
248C2×C5—44no—
249C2×C5—82no—
250C2×C5—161no—
251C2×C5C3×#44712yes—
252C2×C5C3×#45311yescharacteristic
253C23—22no—
254C23—22no—
255C23—48no—
256C23—41no—
257C23—82no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—48no—
262D4—42no—
263D4—42no—
264D4—42no—
265D4—42no—
266D4C3×C5×D814yescomplemented
267C2×C4—22no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4C2×C3×C5×D411yescharacteristic
271C2×C4C2×C3×C5×D412yes—
272C8—22no—
273C8—42no—
274C2×C3—44no—
275C2×C3—82no—
276C2×C3—161no—
277C2×C3C5×#44712yes—
278C2×C3C5×#45311yescharacteristic
279C5C3×#161911yescharacteristic, direct product factor, Sylow
280C22—24no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—44no—
285C22—88no—
286C22—81no—
287C22—82no—
288C22C3×C5×#12011yescharacteristic
289C4—21no—
290C4—42no—
291C4C2×C3×C5×D812yes—
292C4C3×C5×AGL(1,ℤ/8)12yes—
293C3C5×#161911yescharacteristic, direct product factor, Sylow
294C2—44no—
295C2—82no—
296C2—161no—
297C2C3×C5×#44712yes—
298C2C3×C5×#45311yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC42C23×C3×C5
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C5×D42C2semidirect
2. C3×C5×#493C2semidirect
3. C3×C5×#459C2semidirect
4. C3×C5×#331C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C5×#1619C3direct (N × H)
11. C3×C5×#127C22semidirect
15. C3×C5×C4⋊C8C22semidirect
17. C3×C4×C5×C8C22semidirect
18. C3×#1619C5direct (N × H)
19. C5×D42C2×C3semidirect
20. C5×#493C2×C3semidirect
21. C5×#459C2×C3semidirect
22. C5×#331C2×C3semidirect
23. C5×D4⋊C8C2×C3semidirect
42. C3×D42C2×C5semidirect
43. C3×#493C2×C5semidirect
44. C3×#459C2×C5semidirect
45. C3×#331C2×C5semidirect
46. C3×D4⋊C8C2×C5semidirect
51. C5×#127C22×C3semidirect
55. C5×C4⋊C8C22×C3semidirect
57. C4×C5×C8C22×C3semidirect
58. #1619C3×C5direct (N × H)
72. C3×C5×D4D8semidirect
84. C3×#127C22×C5semidirect
88. C3×C4⋊C8C22×C5semidirect
90. C3×C4×C8C22×C5semidirect
109. D42C2×C3×C5semidirect
110. #493C2×C3×C5semidirect
111. #459C2×C3×C5semidirect
112. #331C2×C3×C5semidirect
113. D4⋊C8C2×C3×C5semidirect
158. C5×D4C3×D8semidirect
170. #127C22×C3×C5semidirect
174. C4⋊C8C22×C3×C5semidirect
176. C4×C8C22×C3×C5semidirect
195. C3×D4C5×D8semidirect
234. C3×C5#1619direct (N × H)
266. D4C3×C5×D8semidirect
279. C5C3×#1619direct (N × H)
293. C3C5×#1619direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D422
C3×C5×#4932
C3×C5×#4592
C3×C5×#3312
C3×C5×D4⋊C82
C5×#16193
C3×#16195