Finite Group Databasebeta

← D15×Dic3⋊C4 #13087388

Subgroups — D15×Dic3⋊C4 #13087388

Order 1440.

394 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C2×C3×C4×D15C211yesmaximal, characteristic
2C2×Dic3×D15C211yesmaximal, characteristic
3C2×Dic3×D15C211yesmaximal, characteristic
4#10623906C211yesmaximal, characteristic, complemented
5C3×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
6Dic3⋊Dic15C211yesmaximal, characteristic, complemented
7#10623815C211yesmaximal, characteristic, complemented
8C4⋊C4×D15—31nomaximal
9D5×Dic3⋊C4—31nomaximal
10C22×C3×D15C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C3⋊Dic15C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C3×C4×D15—22no—
16C2×C3×C5×Dic3C2211yescharacteristic
17C2×C3×C5×Dic3C2211yescharacteristic
18Dic3×D15—22no—
19Dic3×D15C414yescomplemented
20D3×Dic3⋊C4—51nomaximal, Hall
21C2×C4×D15—31no—
22C2×C4×D15—31no—
23C2×C4×D15D311yescharacteristic
24C2×C3×C4×D5—31no—
25C2×D5×Dic3—31no—
26C2×D5×Dic3—31no—
27C3×C5×C4⋊C4—31no—
28C4⋊Dic15—31no—
29#6712—31no—
30#6712—31no—
31#6712—31no—
32#6712—61no—
33C5×Dic3⋊C4D311yescharacteristic, complemented
34Dic3⋊Dic5—31no—
35#6669—31no—
36C22×C32×C5C2311yescharacteristic
37C2×C3×D15C2×C412yes—
38C2×C3×D15D412yes—
39C2×C3×D15Q812yes—
40C32×C4×C5—21no—
41C3⋊Dic15—21no—
42C3⋊Dic15C2×C412yescomplemented
43C3×Dic15—21no—
44C3×C5×Dic3—21no—
45C3×C5×Dic3C2×C412yescomplemented
46D5×C4⋊C4—91noHall
47C2×C3×C4×D3—51no—
48C2×D3×Dic3—51no—
49C2×D3×Dic3—51no—
50#3750—51no—
51C3×Dic3⋊C4D511yescharacteristic, complemented
52#3724—51no—
53Dic3⋊Dic3—51no—
54C22×D15C2×D311yescharacteristic
55C22×C3×D5—31no—
56C2×C3×C4×C5—21no—
57C2×C3×C4×C5—31no—
58C2×C3×C4×C5—31no—
59C2×C3×C4×C5C2×D311yescharacteristic
60C2×C3×C4×C5C2×D311yescharacteristic
61C2×Dic15—31no—
62C2×Dic15—31no—
63C2×Dic15—31no—
64C2×Dic15—31no—
65C2×Dic15—61no—
66C2×Dic15—61no—
67C2×Dic15C2×D311yescharacteristic
68C4×D15—22no—
69C4×D15—34no—
70C4×D15—62no—
71C2×C5×Dic3C2×D311yescharacteristic
72C2×C5×Dic3C2×D311yescharacteristic
73C2×C3×Dic5—31no—
74C3×C4×D5—62no—
75D5×Dic3—34no—
76D5×Dic3—62no—
77C2×Dic3⋊C4—151no—
78D3×C4⋊C4—151no—
79C2×C32×C5C22×C411yescharacteristic
80C2×C32×C5C2×D411yescharacteristic
81C2×C32×C5C2×Q811yescharacteristic
82C3×D15C4⋊C414yescomplemented
83C2×C4×D5—31no—
84C2×C4×D5—91no—
85C2×C4×D5—91no—
86C5×C4⋊C4—31no—
87C4⋊Dic5—91no—
88#683—91no—
89#683—91no—
90C22×C3×D3—51no—
91C2×C32×C4C2×D511yescharacteristic
92C2×C3⋊Dic3—51no—
93C2×C3⋊Dic3—51no—
94C2×C3×Dic3—51no—
95C2×C3×Dic3C2×D511yescharacteristic
96C2×C3×Dic3C2×D511yescharacteristic
97C3×C4×D3—102no—
98D3×Dic3—54no—
99D3×Dic3—102no—
100C22×C3×C5—21no—
101C22×C3×C5C22×D311yescharacteristic
102C22×C3×C5C22×D311yescharacteristic
103C2×D15Dic612yes—
104C2×D15C4×D312yes—
105C2×D15#6712yes—
106C2×C3×D5—32no—
107C2×C3×D5—32no—
108C2×C3×D5—32no—
109C3×C4×C5—21no—
110C3×C4×C5—21no—
111C3×C4×C5—32no—
112C3×C4×C5—41no—
113C3×C4×C5—61no—
114Dic15—21no—
115Dic15—32no—
116Dic15—32no—
117Dic15—62no—
118Dic15—61no—
119Dic15—61no—
120Dic15—121no—
121C3×Dic5—61no—
122C5×Dic3—21no—
123C5×Dic3C4×D312yescomplemented
124C22×C3×C4—151no—
125C22×Dic3—151no—
126C22×Dic3—151no—
127C2×C4×D3—51no—
128C2×C4×D3—151no—
129C2×C4×D3—151no—
130C3×C4⋊C4—31no—
131C4⋊Dic3—151no—
132Dic3⋊C4—151no—
133Dic3⋊C4—151no—
134Dic3⋊C4—151no—
135Dic3⋊C4—151no—
136Dic3⋊C4—151no—
137Dic3⋊C4—301no—
138Dic3⋊C4D1511yescharacteristic, direct product factor
139C32×C5C2×C4⋊C411yescharacteristic, complemented, Hall
140C22×D5—31no—
141C2×C4×C5—31no—
142C2×C4×C5—31no—
143C2×C4×C5D3211yescharacteristic
144C2×Dic5—31no—
145C2×Dic5—91no—
146C2×Dic5—91no—
147C4×D5—62no—
148C4×D5—94no—
149C4×D5—182no—
150C22×C32C22×D511yescharacteristic
151C2×C3×D3—52no—
152C2×C3×D3—52no—
153C2×C3×D3—52no—
154C32×C4—21no—
155C3⋊Dic3—52no—
156C3⋊Dic3—101no—
157C3×Dic3—21no—
158C3×Dic3—101no—
159C3×Dic3C4×D512yescomplemented
160C2×C4⋊C4—451noSylow
161C2×C3×C5—21no—
162C2×C3×C5—21no—
163C2×C3×C5—21no—
164C2×C3×C5C2×Dic611yescharacteristic
165C2×C3×C5C2×C4×D311yescharacteristic
166C2×C3×C5C2×C4×D311yescharacteristic
167C2×C3×C5D3×D411yescharacteristic
168C2×C3×C5D3×Q811yescharacteristic
169C2×C3×C5C2×#6711yescharacteristic
170D15Dic3⋊C414yesdirect product factor
171C3×D5—34no—
172C23×C3—151no—
173C22×D3—51no—
174C2×C3×C4—21no—
175C2×C3×C4—31no—
176C2×C3×C4—31no—
177C2×C3×C4—151no—
178C2×C3×C4—302no—
179C2×C3×C4D3×D511yescharacteristic
180C2×C3×C4C2×D1511yescharacteristic
181C2×Dic3—51no—
182C2×Dic3—151no—
183C2×Dic3—151no—
184C2×Dic3—154no—
185C2×Dic3—151no—
186C2×Dic3—151no—
187C2×Dic3—301no—
188C2×Dic3—301no—
189C2×Dic3—302no—
190C2×Dic3C2×D1511yescharacteristic
191C2×Dic3C2×D1511yescharacteristic
192C4×D3—102no—
193C4×D3—154no—
194C4×D3—302no—
195C22×C5C2×D3211yescharacteristic
196C2×D5—32no—
197C2×D5—32no—
198C2×D5—32no—
199C4×C5—21no—
200C4×C5—32no—
201C4×C5—61no—
202Dic5—61no—
203Dic5—92no—
204Dic5—181no—
205C2×C32C2×C4×D511yescharacteristic
206C2×C32D4×D511yescharacteristic
207C2×C32Q8×D511yescharacteristic
208C3×D3—54no—
209C22×C4—151no—
210C22×C4—451no—
211C22×C4—451no—
212C4⋊C4—31no—
213C4⋊C4—451no—
214C4⋊C4—451no—
215C4⋊C4—451no—
216C3×C5—21no—
217C3×C5D3×C4⋊C411yescharacteristic, complemented
218C3×C5C2×Dic3⋊C411yescharacteristic, complemented
219C22×C3—21no—
220C22×C3—152no—
221C22×C3—152no—
222C22×C3—152no—
223C22×C3C2×D3×D511yescharacteristic
224C22×C3C22×D1511yescharacteristic
225C2×D3—52no—
226C2×D3—52no—
227C2×D3—52no—
228C3×C4—21no—
229C3×C4—21no—
230C3×C4—32no—
231C3×C4—41no—
232C3×C4—61no—
233C3×C4—301no—
234Dic3—21no—
235Dic3—101no—
236Dic3—152no—
237Dic3—152no—
238Dic3—302no—
239Dic3—301no—
240Dic3—301no—
241Dic3—601no—
242Dic3C4×D1512yescomplemented
243C2×C5D3×Dic611yescharacteristic
244C2×C5C4×D3211yescharacteristic
245C2×C5D3×#6711yescharacteristic
246D5—34no—
247C32D5×C4⋊C411yescharacteristic, complemented, Sylow
248C23—151no—
249C2×C4—31no—
250C2×C4—31no—
251C2×C4—151no—
252C2×C4—302no—
253C2×C4—454no—
254C2×C4—451no—
255C2×C4—451no—
256C2×C4—902no—
257C2×C4D3×D1511yescharacteristic
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—154no—
262C2×C3D5×Dic611yescharacteristic
263C2×C3C4×D3×D511yescharacteristic
264C2×C3D5×#6711yescharacteristic
265C2×C3C2×C4×D1511yescharacteristic
266C2×C3D4×D1511yescharacteristic
267C2×C3Q8×D1511yescharacteristic
268D3—54no—
269C5D3×Dic3⋊C411yescharacteristic, complemented, Sylow
270C22—152no—
271C22—152no—
272C22—152no—
273C22C2×D3×D1511yescharacteristic
274C4—21no—
275C4—32no—
276C4—61no—
277C4—301no—
278C4—452no—
279C4—901no—
280C3—21no—
281C3D5×Dic3⋊C411yescharacteristic, complemented
282C3C4⋊C4×D1511yescharacteristic, complemented
283C2—154no—
284C2Dic6×D1511yescharacteristic
285C2C4×D3×D1511yescharacteristic
286C2#67×D1511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutatorC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC22×C3×D15C22
hypercenterC2×C4D3×D15
hypocenterC32×C5C2×C4⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #10623906C2semidirect
5. C3×C5×Dic3⋊C4C2semidirect
6. Dic3⋊Dic15C2semidirect
7. #10623815C2semidirect
19. Dic3×D15C4semidirect
33. C5×Dic3⋊C4D3semidirect
42. C3⋊Dic15C2×C4semidirect
45. C3×C5×Dic3C2×C4semidirect
51. C3×Dic3⋊C4D5semidirect
82. C3×D15C4⋊C4semidirect
123. C5×Dic3C4×D3semidirect
138. Dic3⋊C4D15direct (N × H)
139. C32×C5C2×C4⋊C4semidirect
159. C3×Dic3C4×D5semidirect
170. D15Dic3⋊C4direct (N × H)
217. C3×C5D3×C4⋊C4semidirect
218. C3×C5C2×Dic3⋊C4semidirect
242. Dic3C4×D15semidirect
247. C32D5×C4⋊C4semidirect
269. C5D3×Dic3⋊C4semidirect
281. C3D5×Dic3⋊C4semidirect
282. C3C4⋊C4×D15semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D152
C2×Dic3×D152
#106239062
C3×C5×Dic3⋊C42
Dic3⋊Dic152
#106238152
C4⋊C4×D153
D5×Dic3⋊C43
D3×Dic3⋊C45