Finite Group Databasebeta

← C3×D5×#214 #13086631

Subgroups — C3×D5×#214 #13086631

Order 1440.

326 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C32×D4×D5C211yesmaximal, characteristic
2C3×D5×Dic6C211yesmaximal, characteristic, complemented
3C3×#6716C211yesmaximal, characteristic, complemented
4C3×C5×#214C211yesmaximal, characteristic, complemented
5C3×#6657C211yesmaximal, characteristic, complemented
6C3×#6655C211yesmaximal, characteristic, complemented
7C3×D5×C3⋊C8C211yesmaximal, characteristic, complemented
8C3×D5×SD16—31nomaximal
9D5×#214C311yesmaximal, characteristic, direct product factor
10C22×C32×D5—21no—
11C32×C5×D4C2211yescharacteristic
12C3×Dic30C2211yescharacteristic, complemented
13C3×C5×Dic6C2211yescharacteristic, complemented
14C32×C22⋊D5—21no—
15C32×D20C2211yescharacteristic
16C32×C4×D5C2211yescharacteristic
17C3×#1204—21no—
18C3×D5×Dic3—21no—
19C3×C3⋊#168C2211yescharacteristic, complemented
20C3×C5×C3⋊C8C2211yescharacteristic, complemented
21C2×C3×#214—51nomaximal, Hall
22C3×Q8×D5—31no—
23C3×D4×D5—21no—
24C3×D4×D5D311yescharacteristic
25C3×D4×D5C2×C311yescharacteristic
26D5×Dic6C2×C311yescharacteristic, complemented
27C3×C5×SD16—31no—
28#6716C2×C311yescharacteristic, complemented
29C5×#214C2×C311yescharacteristic, complemented
30C3×#688—31no—
31C3×#687—31no—
32C3×#677—31no—
33C3×C8×D5—31no—
34#6657C2×C311yescharacteristic, complemented
35#6655C2×C311yescharacteristic, complemented
36D5×C3⋊C8C2×C311yescharacteristic, complemented
37C22×C32×C5—21no—
38C2×C32×D5—21no—
39C2×C32×D5—42no—
40C2×C32×D5D411yescharacteristic
41C32×C4×C5C2311yescharacteristic
42C3×Dic15—21no—
43C3×C5×Dic3—21no—
44C32×Dic5D411yescharacteristic
45D5×SD16—31noHall
46C2×C32×D4—51no—
47C2×C3×Dic6—51no—
48C3×#214—51no—
49C3×#214—51no—
50C3×#214—51no—
51C3×#214D511yescharacteristic, direct product factor
52C2×C3×C3⋊C8—51no—
53C22×C3×D5—22no—
54C22×C3×D5—21no—
55C22×C3×D5—21no—
56C3×C5×Q8—31no—
57C3×C5×D4—21no—
58C3×C5×D4C2×D311yescharacteristic
59C3×C5×D4C22×C311yescharacteristic
60Dic30C22×C311yescharacteristic, complemented
61C5×Dic6C22×C311yescharacteristic, complemented
62C3×C22⋊D5—22no—
63C3×C22⋊D5—21no—
64C3×C22⋊D5—21no—
65C3×D20—21no—
66C3×D20C2×D311yescharacteristic
67C3×D20C22×C311yescharacteristic
68C3×C4×D5—21no—
69C3×C4×D5—61no—
70C3×C4×D5C2×D311yescharacteristic
71C3×C4×D5C22×C311yescharacteristic
72C3×Dic10—31no—
73C3×Dic10—61no—
74#1204—21no—
75D5×Dic3—21no—
76C3×C5×C8—31no—
77C3⋊#168C22×C311yescharacteristic, complemented
78C3×#168—31no—
79C5×C3⋊C8C22×C311yescharacteristic, complemented
80C2×C3×SD16—151no—
81C2×#214—51no—
82C2×C32×C5—41no—
83C2×C32×C5C2×D411yescharacteristic
84C32×D5—41no—
85C32×D5SD1612yescomplemented
86Q8×D5—31no—
87D4×D5C3×D311yescharacteristic
88C5×SD16—31no—
89#688—31no—
90#687—31no—
91#677—31no—
92C8×D5—31no—
93C23×C32—101no—
94C32×D4—51no—
95C32×D4—101no—
96C32×D4C2×D511yescharacteristic
97C2×C32×C4—51no—
98C2×C3×Dic3—101no—
99C3×Dic6—51no—
100C3×Dic6—101no—
101C3×Dic6C2×D511yescharacteristic, complemented
102C3×C3⋊C8—51no—
103C3×C3⋊C8C2×D511yescharacteristic, complemented
104C22×C3×C5—22no—
105C22×C3×C5—21no—
106C22×C3×C5—21no—
107C2×C3×D5—22no—
108C2×C3×D5—21no—
109C2×C3×D5—21no—
110C2×C3×D5—21no—
111C2×C3×D5—44no—
112C2×C3×D5—42no—
113C2×C3×D5—42no—
114C2×C3×D5#6711yescharacteristic
115C2×C3×D5C3×D411yescharacteristic
116C3×C4×C5—21no—
117C3×C4×C5—61no—
118C3×C4×C5C22×D311yescharacteristic
119C3×C4×C5C23×C311yescharacteristic
120Dic15—21no—
121C3×Dic5—21no—
122C3×Dic5—61no—
123C3×Dic5#6711yescharacteristic
124C3×Dic5C3×D411yescharacteristic
125C5×Dic3—21no—
126C2×C3×Q8—151no—
127C2×C3×D4—51no—
128C2×C3×D4—51no—
129C2×C3×D4—101no—
130C2×Dic6—51no—
131C3×SD16—31no—
132C3×SD16—151no—
133C3×SD16—151no—
134C3×SD16—151no—
135C2×C3×C8—151no—
136#214—51no—
137#214—51no—
138#214—51no—
139#214C3×D511yescharacteristic, direct product factor
140C2×C3⋊C8—51no—
141C32×C5C2×SD1611yescharacteristic, complemented, Hall
142C22×D5—21no—
143C5×Q8—31no—
144C5×D4C2×C3×D311yescharacteristic
145C22⋊D5—21no—
146D20C2×C3×D311yescharacteristic
147C4×D5—61no—
148C4×D5C2×C3×D311yescharacteristic
149Dic10—31no—
150Dic10—61no—
151C5×C8—31no—
152#168—31no—
153C22×C32—21no—
154C22×C32—51no—
155C22×C32—101no—
156C22×C32—202no—
157C32×C4—51no—
158C32×C4C22×D511yescharacteristic
159C3×Dic3—21no—
160C3×Dic3—101no—
161C2×SD16—151noSylow
162C2×C3×C5—21no—
163C2×C3×C5—42no—
164C2×C3×C5—41no—
165C2×C3×C5—41no—
166C2×C3×C5C2×#6711yescharacteristic
167C2×C3×C5C2×C3×D411yescharacteristic
168C3×D5—22no—
169C3×D5—42no—
170C3×D5—41no—
171C3×D5—41no—
172C3×D5#21412yesdirect product factor
173C3×D5C3×SD1612yescomplemented
174C23×C3—101no—
175C23×C3—101no—
176C23×C3—102no—
177C3×Q8—31no—
178C3×Q8—151no—
179C3×Q8—301no—
180C3×D4—21no—
181C3×D4—51no—
182C3×D4—51no—
183C3×D4—101no—
184C3×D4—101no—
185C3×D4—101no—
186C3×D4—102no—
187C3×D4D3×D511yescharacteristic
188C3×D4C2×C3×D511yescharacteristic
189C2×C3×C4—51no—
190C2×C3×C4—51no—
191C2×C3×C4—101no—
192C2×C3×C4—301no—
193C2×Dic3—101no—
194Dic6—51no—
195Dic6—101no—
196Dic6C2×C3×D511yescharacteristic, complemented
197C3×C8—31no—
198C3×C8—151no—
199C3⋊C8—51no—
200C3⋊C8C2×C3×D511yescharacteristic, complemented
201C22×C5—21no—
202C2×D5—21no—
203C2×D5—42no—
204C2×D5C3×#6711yescharacteristic
205C4×C5—61no—
206C4×C5C22×C3×D311yescharacteristic
207Dic5—61no—
208Dic5C3×#6711yescharacteristic
209C2×C32—41no—
210C2×C32—52no—
211C2×C32—201no—
212C2×C32D4×D511yescharacteristic
213C2×Q8—151no—
214C2×D4—51no—
215SD16—31no—
216SD16—151no—
217SD16—151no—
218SD16—151no—
219C2×C8—151no—
220C3×C5—21no—
221C3×C5C2×#21411yescharacteristic, complemented
222C3×C5C2×C3×SD1611yescharacteristic, complemented
223C22×C3—22no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—51no—
227C22×C3—51no—
228C22×C3—101no—
229C22×C3—102no—
230C22×C3—101no—
231C22×C3—101no—
232C22×C3—202no—
233C22×C3—202no—
234C22×C3—204no—
235C3×C4—21no—
236C3×C4—51no—
237C3×C4—51no—
238C3×C4—61no—
239C3×C4—101no—
240C3×C4—301no—
241C3×C4C2×D3×D511yescharacteristic
242C3×C4C22×C3×D511yescharacteristic
243Dic3—21no—
244Dic3—101no—
245C2×C5—41no—
246C2×C5C2×C3×#6711yescharacteristic
247D5—41no—
248D5C3×#21412yesdirect product factor
249C32D5×SD1611yescharacteristic, complemented, Sylow
250C23—101no—
251Q8—31no—
252Q8—151no—
253Q8—301no—
254D4—51no—
255D4—101no—
256D4C3×D3×D511yescharacteristic
257C2×C4—51no—
258C2×C4—301no—
259C8—31no—
260C8—151no—
261C2×C3—21no—
262C2×C3—42no—
263C2×C3—41no—
264C2×C3—41no—
265C2×C3—52no—
266C2×C3—52no—
267C2×C3—102no—
268C2×C3—202no—
269C2×C3—201no—
270C2×C3—201no—
271C2×C3D5×#6711yescharacteristic
272C2×C3C3×D4×D511yescharacteristic
273C5C2×C3×#21411yescharacteristic, complemented, Sylow
274C22—21no—
275C22—51no—
276C22—101no—
277C22—202no—
278C4—51no—
279C4—61no—
280C4—301no—
281C4C2×C3×D3×D511yescharacteristic
282C3—21no—
283C3D5×#21411yescharacteristic, direct product factor
284C3C3×D5×SD1611yescharacteristic, complemented
285C2—41no—
286C2—52no—
287C2—201no—
288C2C3×D5×#6711yescharacteristic
subgroupG/H
centerC2×C3D5×#67
commutator, cosocleC3×C4×C5C23×C3
FrattiniC4C2×C3×D3×D5
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
prime radicalC32×D4×D5C2
hypercenterC3×D4D3×D5
hypocenterC3×C5C2×C3×SD16
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×D5×Dic6C2semidirect
3. C3×#6716C2semidirect
4. C3×C5×#214C2semidirect
5. C3×#6657C2semidirect
6. C3×#6655C2semidirect
7. C3×D5×C3⋊C8C2semidirect
9. D5×#214C3direct (N × H)
12. C3×Dic30C22semidirect
13. C3×C5×Dic6C22semidirect
19. C3×C3⋊#168C22semidirect
20. C3×C5×C3⋊C8C22semidirect
26. D5×Dic6C2×C3semidirect
28. #6716C2×C3semidirect
29. C5×#214C2×C3semidirect
34. #6657C2×C3semidirect
35. #6655C2×C3semidirect
36. D5×C3⋊C8C2×C3semidirect
51. C3×#214D5direct (N × H)
60. Dic30C22×C3semidirect
61. C5×Dic6C22×C3semidirect
77. C3⋊#168C22×C3semidirect
79. C5×C3⋊C8C22×C3semidirect
85. C32×D5SD16semidirect
101. C3×Dic6C2×D5semidirect
103. C3×C3⋊C8C2×D5semidirect
139. #214C3×D5direct (N × H)
141. C32×C5C2×SD16semidirect
172. C3×D5#214direct (N × H)
173. C3×D5C3×SD16semidirect
196. Dic6C2×C3×D5semidirect
200. C3⋊C8C2×C3×D5semidirect
221. C3×C5C2×#214semidirect
222. C3×C5C2×C3×SD16semidirect
248. D5C3×#214direct (N × H)
249. C32D5×SD16semidirect
273. C5C2×C3×#214semidirect
283. C3D5×#214direct (N × H)
284. C3C3×D5×SD16semidirect

Maximal subgroups

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

subgroupindex
C32×D4×D52
C3×D5×Dic62
C3×#67162
C3×C5×#2142
C3×#66572
C3×#66552
C3×D5×C3⋊C82
C3×D5×SD163
D5×#2143
C2×C3×#2145