Finite Group Databasebeta

← D3×#6715 #13087492

Subgroups — D3×#6715 #13087492

Order 1440.

326 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 74 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×D3×D4C211yesmaximal, characteristic, complemented
2D3×D60C211yesmaximal, characteristic, complemented
3#10623909C211yesmaximal, characteristic, complemented
4C3×#6715C211yesmaximal, characteristic, complemented
5#10623800C211yesmaximal, characteristic, complemented
6#10623798C211yesmaximal, characteristic, complemented
7D3×C3⋊#168C211yesmaximal, characteristic, complemented
8C2×#6715—31nomaximal
9D3×#686—31nomaximal
10C22×C3×C5×D3—21no—
11C2×D3×D15—21no—
12C32×C5×D4C2211yescharacteristic, complemented
13C4⋊(C3⋊D15)C2211yescharacteristic, complemented
14C3×D60C2211yescharacteristic, complemented
15C3×C5×#67—21no—
16C3×C5×D12C2211yescharacteristic, complemented
17C3×C4×C5×D3C2211yescharacteristic
18#67151—21no—
19C3⋊(C3⋊#168)C2211yescharacteristic, complemented
20C3×C3⋊#168C2211yescharacteristic, complemented
21D3×#213—51nomaximal, Hall
22C2×C3×C5×D4—31no—
23C2×D60—31no—
24C5×D3×D4D311yescharacteristic, complemented
25D3×D20—31no—
26#6715—31no—
27#6715—31no—
28#6715—31no—
29#6715—31no—
30#6715—61no—
31#6715D311yescharacteristic, direct product factor
32C2×C3⋊#168—31no—
33C3×#686—31no—
34#6654—31no—
35#6652—31no—
36D3×#168—31no—
37C22×C32×C5—21no—
38C2×C3⋊D15—21no—
39C2×C3×D15—21no—
40C2×C3×C5×D3—21no—
41C2×C3×C5×D3—42no—
42C2×C3×C5×D3D411yescharacteristic
43D3×D15—42no—
44C32×C4×C5C2311yescharacteristic
45C3×C5×Dic3D411yescharacteristic
46C2×#686—91noHall
47C3×D3×D4D511yescharacteristic, complemented
48D3×D12—51no—
49#3753—51no—
50C3×#213—51no—
51#3714—51no—
52#3713—51no—
53D3×C3⋊C8—51no—
54C23×C3×C5—61no—
55C22×D15—61no—
56C22×C5×D3—21no—
57C2×D3×D5—61no—
58C3×C5×D4—21no—
59C3×C5×D4—31no—
60C3×C5×D4—61no—
61C3×C5×D4C2×D311yescharacteristic, complemented
62C3×C5×D4C2×D311yescharacteristic, complemented
63C2×C3×C4×C5—31no—
64D60—31no—
65D60—31no—
66D60—61no—
67D60—61no—
68D60C2×D311yescharacteristic, complemented
69C5×#67—21no—
70C5×D12C2×D311yescharacteristic, complemented
71C4×C5×D3C2×D311yescharacteristic
72C3×D20—31no—
73#1202—61no—
74C3⋊#168—31no—
75C3⋊#168—31no—
76C3⋊#168—61no—
77C3⋊#168C2×D311yescharacteristic, complemented
78C3×#168—31no—
79C2×#213—151no—
80D3×D8—151no—
81C2×C32×C5—41no—
82C2×C32×C5C2×D411yescharacteristic
83C3⋊D15—41no—
84C3×D15—41no—
85C3×C5×D3—41no—
86C3×C5×D3D812yescomplemented
87C2×C5×D4—31no—
88C2×D20—91no—
89#686—31no—
90#686—91no—
91#686—91no—
92#686—91no—
93C2×#168—91no—
94C22×C3×D3—21no—
95C2×D32—101no—
96C32×D4C2×D511yescharacteristic, complemented
97C4⋊(C3⋊D3)—51no—
98C3×#67—21no—
99C3×D12—51no—
100C3×D12C2×D511yescharacteristic, complemented
101C3×C4×D3C2×D511yescharacteristic
102#626—101no—
103C3⋊(C3⋊C8)—51no—
104C3×C3⋊C8—51no—
105C22×C3×C5—21no—
106C22×C3×C5—21no—
107C22×C3×C5—31no—
108C22×C3×C5—41no—
109C22×C3×C5—61no—
110C22×C3×C5—122no—
111C2×D15—21no—
112C2×D15—61no—
113C2×D15—61no—
114C2×D15—121no—
115C2×D15—122no—
116C2×C5×D3—21no—
117C2×C5×D3—42no—
118C2×C5×D3#6711yescharacteristic
119C2×C3×D5—61no—
120D3×D5—122no—
121C3×C4×C5—21no—
122C3×C4×C5—31no—
123C3×C4×C5C22×D311yescharacteristic
124C3×C4×C5C22×D311yescharacteristic
125C5×Dic3#6711yescharacteristic
126C2×C3×D4—31no—
127D3×D4—151no—
128D3×D4D1511yescharacteristic, complemented
129C2×D12—151no—
130C3×D8—151no—
131#213—51no—
132#213—151no—
133#213—151no—
134#213—151no—
135#213—151no—
136#213—151no—
137#213—301no—
138C2×C3⋊C8—151no—
139D24—151no—
140D3×C8—151no—
141C32×C5C2×D811yescharacteristic, complemented, Hall
142C23×C5—61no—
143C22×D5—181no—
144C5×D4—31no—
145C5×D4—61no—
146C5×D4D3211yescharacteristic, complemented
147C2×C4×C5—31no—
148D20—31no—
149D20—91no—
150D20—181no—
151#168—31no—
152#168—91no—
153C22×C32—21no—
154C2×C3⋊D3—101no—
155C2×C3×D3—21no—
156C2×C3×D3—42no—
157C2×C3×D3—101no—
158C2×C3×D3C22⋊D511yescharacteristic
159D32—202no—
160C32×C4C22×D511yescharacteristic
161C3×Dic3C22⋊D511yescharacteristic
162C2×D8—451noSylow
163C2×C3×C5—21no—
164C2×C3×C5—32no—
165C2×C3×C5—41no—
166C2×C3×C5—41no—
167C2×C3×C5—81no—
168C2×C3×C5—121no—
169C2×C3×C5D3×D411yescharacteristic
170C2×C3×C5C2×#6711yescharacteristic
171D15—41no—
172D15—121no—
173D15—121no—
174D15—241no—
175C3×D5—121no—
176C5×D3—41no—
177C5×D3#21312yescomplemented
178C23×C3—61no—
179C22×D3—21no—
180C22×D3—301no—
181C22×D3—301no—
182C3×D4—21no—
183C3×D4—31no—
184C3×D4—61no—
185C3×D4—151no—
186C3×D4D3×D511yescharacteristic, complemented
187C3×D4C2×D1511yescharacteristic, complemented
188C2×C3×C4—31no—
189#67—21no—
190#67—301no—
191D12—51no—
192D12—151no—
193D12—151no—
194D12—301no—
195D12—301no—
196D12C2×D1511yescharacteristic, complemented
197C4×D3C2×D1511yescharacteristic
198C3×C8—151no—
199C3⋊C8—51no—
200C3⋊C8—151no—
201C3⋊C8—151no—
202C3⋊C8—301no—
203C22×C5—21no—
204C22×C5—31no—
205C22×C5—61no—
206C22×C5—122no—
207C2×D5—61no—
208C2×D5—181no—
209C2×D5—362no—
210C4×C5—31no—
211C4×C5C2×D3211yescharacteristic
212C2×C32—41no—
213C2×C32C2×C22⋊D511yescharacteristic
214C3⋊D3—201no—
215C3×D3—41no—
216C3×D3—201no—
217C3×D3#68612yescomplemented
218C2×D4—31no—
219C2×D4—451no—
220D8—151no—
221D8—451no—
222D8—451no—
223D8—451no—
224C2×C8—451no—
225C3×C5—21no—
226C3×C5D3×D811yescharacteristic, complemented
227C3×C5C2×#21311yescharacteristic, complemented
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—31no—
231C22×C3—41no—
232C22×C3—61no—
233C22×C3—122no—
234C22×C3—301no—
235C2×D3—21no—
236C2×D3—42no—
237C2×D3—101no—
238C2×D3—301no—
239C2×D3—301no—
240C2×D3—601no—
241C2×D3—602no—
242C2×D3—602no—
243C2×D3#122011yescharacteristic
244C3×C4—21no—
245C3×C4—31no—
246C3×C4C2×D3×D511yescharacteristic
247C3×C4C22×D1511yescharacteristic
248Dic3#122011yescharacteristic
249C2×C5—32no—
250C2×C5—41no—
251C2×C5—121no—
252C2×C5D3×#6711yescharacteristic
253D5—121no—
254D5—361no—
255C32C2×#68611yescharacteristic, complemented, Sylow
256C23—61no—
257C23—901no—
258D4—31no—
259D4—61no—
260D4—151no—
261D4—451no—
262D4—901no—
263D4D3×D1511yescharacteristic, complemented
264C2×C4—31no—
265C8—151no—
266C8—451no—
267C2×C3—21no—
268C2×C3—32no—
269C2×C3—41no—
270C2×C3—41no—
271C2×C3—81no—
272C2×C3—121no—
273C2×C3—601no—
274C2×C3D3×C22⋊D511yescharacteristic
275C2×C3C2×#122011yescharacteristic
276D3—41no—
277D3—201no—
278D3—601no—
279D3—601no—
280D3—1201no—
281D3#671512yesdirect product factor
282C5D3×#21311yescharacteristic, complemented, Sylow
283C22—21no—
284C22—31no—
285C22—61no—
286C22—122no—
287C22—301no—
288C22—901no—
289C22—1802no—
290C4—31no—
291C4C2×D3×D1511yescharacteristic
292C3—21no—
293C3D3×#68611yescharacteristic, complemented
294C3C2×#671511yescharacteristic, complemented
295C2—32no—
296C2—41no—
297C2—121no—
298C2—601no—
299C2—1801no—
300C2D3×#122011yescharacteristic
subgroupG/H
centerC2D3×#1220
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
hypercenterD4D3×D15
hypocenterC32×C5C2×D8
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C3×C5×D3×D4C2semidirect
2. D3×D60C2semidirect
3. #10623909C2semidirect
4. C3×#6715C2semidirect
5. #10623800C2semidirect
6. #10623798C2semidirect
7. D3×C3⋊#168C2semidirect
12. C32×C5×D4C22semidirect
13. C4⋊(C3⋊D15)C22semidirect
14. C3×D60C22semidirect
16. C3×C5×D12C22semidirect
19. C3⋊(C3⋊#168)C22semidirect
20. C3×C3⋊#168C22semidirect
24. C5×D3×D4D3semidirect
31. #6715D3direct (N × H)
47. C3×D3×D4D5semidirect
61. C3×C5×D4C2×D3semidirect
62. C3×C5×D4C2×D3semidirect
68. D60C2×D3semidirect
70. C5×D12C2×D3semidirect
77. C3⋊#168C2×D3semidirect
86. C3×C5×D3D8semidirect
96. C32×D4C2×D5semidirect
100. C3×D12C2×D5semidirect
128. D3×D4D15semidirect
141. C32×C5C2×D8semidirect
146. C5×D4D32semidirect
177. C5×D3#213semidirect
186. C3×D4D3×D5semidirect
187. C3×D4C2×D15semidirect
196. D12C2×D15semidirect
217. C3×D3#686semidirect
226. C3×C5D3×D8semidirect
227. C3×C5C2×#213semidirect
255. C32C2×#686semidirect
263. D4D3×D15semidirect
281. D3#6715direct (N × H)
282. C5D3×#213semidirect
293. C3D3×#686semidirect
294. C3C2×#6715semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×D42
D3×D602
#106239092
C3×#67152
#106238002
#106237982
D3×C3⋊#1682
C2×#67153
D3×#6863
D3×#2135