Finite Group Databasebeta

← #13087500

Subgroups — #13087500

Order 1440.

326 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 62 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
1D4×C3⋊D15C211yesmaximal, characteristic
2#10624198C211yesmaximal, characteristic, complemented
3C3×#6716C211yesmaximal, characteristic, complemented
4C3×C5×#214C211yesmaximal, characteristic, complemented
5#10623806C211yesmaximal, characteristic, complemented
6#10623804C211yesmaximal, characteristic, complemented
7#10623794C211yesmaximal, characteristic, complemented
8SD16×D15—31nomaximal
9#91487—31nomaximal
10C22×C3⋊D15—21no—
11C32×C5×D4C2211yescharacteristic
12#67184—21no—
13C4⋊(C3⋊D15)C2211yescharacteristic
14C4×C3⋊D15C2211yescharacteristic
15C3×Dic30C2211yescharacteristic, complemented
16C3×C5×Dic6C2211yescharacteristic, complemented
17#67153—21no—
18#67149—21no—
19C3×C3⋊#168C2211yescharacteristic, complemented
20C3×C5×C3⋊C8C2211yescharacteristic, complemented
21#63930—51nomaximal, Hall
22Q8×D15—31no—
23D4×D15—31no—
24D4×D15—31no—
25D4×D15—61no—
26D15⋊Q8—31no—
27C3×C5×SD16—31no—
28#6717—31no—
29#6716D311yescharacteristic, complemented
30#6706—31no—
31C8×D15—31no—
32C5×#214D311yescharacteristic, complemented
33C3×#687—31no—
34#6660—31no—
35#6658—31no—
36#6648—31no—
37C22×C32×C5—21no—
38C2×C3⋊D15—21no—
39C2×C3⋊D15—42no—
40C2×C3⋊D15D411yescharacteristic
41C32×C4×C5C2311yescharacteristic
42C3⋊Dic15D411yescharacteristic
43C3×Dic15—21no—
44C3×C5×Dic3—21no—
45D5×SD16—91noHall
46D4×C3⋊D3—51no—
47#3797—51no—
48C3×#214—51no—
49C3×#214D511yescharacteristic, complemented
50#3717—51no—
51#3717—51no—
52#3710—51no—
53C22×D15—61no—
54C22×D15—61no—
55C22×D15—62no—
56C3×C5×Q8—31no—
57C3×C5×D4—21no—
58C3×C5×D4C2×D311yescharacteristic
59C3×C5×D4C2×D311yescharacteristic
60#1220—61no—
61#1220—61no—
62#1220—62no—
63D60—31no—
64D60—31no—
65D60—61no—
66C4×D15—31no—
67C4×D15—31no—
68C4×D15—61no—
69C4×D15—61no—
70Dic30—61no—
71Dic30C2×D311yescharacteristic, complemented
72C5×Dic6C2×D311yescharacteristic, complemented
73C3×Dic10—31no—
74#1204—61no—
75#1200—61no—
76C3×C5×C8—31no—
77C3⋊#168C2×D311yescharacteristic, complemented
78C3×#168—31no—
79C5×C3⋊C8C2×D311yescharacteristic, complemented
80D3×SD16—151no—
81D3×SD16—151no—
82C2×C32×C5—41no—
83C2×C32×C5C2×D411yescharacteristic
84C3⋊D15—41no—
85C3⋊D15SD1612yescomplemented
86Q8×D5—91no—
87D4×D5—91no—
88C5×SD16—31no—
89#688—91no—
90#687—31no—
91#677—91no—
92C8×D5—91no—
93C22×C3⋊D3—101no—
94C32×D4C2×D511yescharacteristic
95#638—101no—
96C4⋊(C3⋊D3)—51no—
97C4×C3⋊D3—51no—
98C3×Dic6—51no—
99C3×Dic6C2×D511yescharacteristic, complemented
100#627—101no—
101#624—101no—
102C3×C3⋊C8—51no—
103C3×C3⋊C8C2×D511yescharacteristic, complemented
104C22×C3×C5—22no—
105C22×C3×C5—21no—
106C22×C3×C5—21no—
107C2×D15—31no—
108C2×D15—31no—
109C2×D15—61no—
110C2×D15—62no—
111C2×D15—61no—
112C2×D15—61no—
113C2×D15—122no—
114C2×D15—122no—
115C2×D15—124no—
116C3×C4×C5—21no—
117C3×C4×C5—61no—
118C3×C4×C5C22×D311yescharacteristic
119C3×C4×C5C22×D311yescharacteristic
120Dic15—21no—
121Dic15—31no—
122Dic15—31no—
123Dic15—61no—
124C3×Dic5—61no—
125C5×Dic3—21no—
126D3×Q8—151no—
127D3×Q8—151no—
128D3×D4—151no—
129D3×D4—151no—
130D3×D4—301no—
131C3×SD16—31no—
132C3×SD16—151no—
133#215—151no—
134#215—151no—
135#214—51no—
136#214D1511yescharacteristic, complemented
137#204—151no—
138#204—151no—
139D3×C8—151no—
140D3×C8—151no—
141C32×C5C2×SD1611yescharacteristic, complemented, Hall
142C22×D5—181no—
143C5×Q8—31no—
144C5×D4D3211yescharacteristic
145C22⋊D5—181no—
146D20—91no—
147C4×D5—91no—
148C4×D5—181no—
149Dic10—31no—
150Dic10—181no—
151C5×C8—31no—
152#168—31no—
153C22×C32—21no—
154C2×C3⋊D3—51no—
155C2×C3⋊D3—101no—
156C2×C3⋊D3—202no—
157C32×C4C22×D511yescharacteristic
158C3⋊Dic3—51no—
159C3×Dic3—21no—
160C3×Dic3—101no—
161C2×SD16—451noSylow
162C2×C3×C5—21no—
163C2×C3×C5—42no—
164C2×C3×C5—41no—
165C2×C3×C5—41no—
166C2×C3×C5D3×D411yescharacteristic
167C2×C3×C5D3×D411yescharacteristic
168D15—32no—
169D15—32no—
170D15—62no—
171D15—122no—
172D15—121no—
173D15—121no—
174C22×D3—301no—
175C22×D3—301no—
176C22×D3—302no—
177C3×Q8—31no—
178C3×Q8—151no—
179C3×D4—21no—
180C3×D4D3×D511yescharacteristic
181C3×D4C2×D1511yescharacteristic
182#67—301no—
183#67—301no—
184#67—302no—
185D12—151no—
186D12—151no—
187D12—301no—
188C4×D3—151no—
189C4×D3—151no—
190C4×D3—301no—
191C4×D3—301no—
192C4×D3—301no—
193Dic6—51no—
194Dic6—301no—
195Dic6—301no—
196Dic6C2×D1511yescharacteristic, complemented
197C3×C8—31no—
198C3×C8—151no—
199C3⋊C8—51no—
200C3⋊C8C2×D1511yescharacteristic, complemented
201C22×C5—21no—
202C2×D5—91no—
203C2×D5—181no—
204C2×D5—362no—
205C4×C5—61no—
206C4×C5C2×D3211yescharacteristic
207Dic5—61no—
208Dic5—91no—
209C2×C32—41no—
210C2×C32D4×D511yescharacteristic
211C3⋊D3—52no—
212C3⋊D3—201no—
213C2×Q8—451no—
214C2×D4—451no—
215SD16—31no—
216SD16—151no—
217SD16—451no—
218SD16—451no—
219C2×C8—451no—
220C3×C5—21no—
221C3×C5D3×SD1611yescharacteristic, complemented
222C3×C5D3×SD1611yescharacteristic, complemented
223C22×C3—22no—
224C22×C3—21no—
225C22×C3—21no—
226C2×D3—151no—
227C2×D3—151no—
228C2×D3—301no—
229C2×D3—302no—
230C2×D3—301no—
231C2×D3—301no—
232C2×D3—602no—
233C2×D3—602no—
234C2×D3—604no—
235C3×C4—21no—
236C3×C4—61no—
237C3×C4—301no—
238C3×C4C2×D3×D511yescharacteristic
239C3×C4C22×D1511yescharacteristic
240Dic3—21no—
241Dic3—101no—
242Dic3—151no—
243Dic3—151no—
244Dic3—301no—
245C2×C5—41no—
246C2×C5#381111yescharacteristic
247D5—92no—
248D5—361no—
249C32D5×SD1611yescharacteristic, complemented, Sylow
250C23—901no—
251Q8—31no—
252Q8—151no—
253Q8—901no—
254D4—451no—
255D4—901no—
256D4D3×D1511yescharacteristic
257C2×C4—451no—
258C2×C4—901no—
259C8—31no—
260C8—151no—
261C2×C3—21no—
262C2×C3—42no—
263C2×C3—41no—
264C2×C3—41no—
265C2×C3#679011yescharacteristic
266C2×C3D4×D1511yescharacteristic
267D3—152no—
268D3—152no—
269D3—302no—
270D3—602no—
271D3—601no—
272D3—601no—
273C5#6393011yescharacteristic, complemented, Sylow
274C22—21no—
275C22—451no—
276C22—901no—
277C22—1802no—
278C4—61no—
279C4—301no—
280C4—451no—
281C4C2×D3×D1511yescharacteristic
282C3—21no—
283C3#9148711yescharacteristic, complemented
284C3SD16×D1511yescharacteristic, complemented
285C2—41no—
286C2—452no—
287C2—1801no—
288C2#1062421811yescharacteristic
subgroupG/H
centerC2#10624218
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
prime radicalD4×C3⋊D15C2
hypercenterD4D3×D15
hypocenterC32×C5C2×SD16
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
2. #10624198C2semidirect
3. C3×#6716C2semidirect
4. C3×C5×#214C2semidirect
5. #10623806C2semidirect
6. #10623804C2semidirect
7. #10623794C2semidirect
15. C3×Dic30C22semidirect
16. C3×C5×Dic6C22semidirect
19. C3×C3⋊#168C22semidirect
20. C3×C5×C3⋊C8C22semidirect
29. #6716D3semidirect
32. C5×#214D3semidirect
49. C3×#214D5semidirect
71. Dic30C2×D3semidirect
72. C5×Dic6C2×D3semidirect
77. C3⋊#168C2×D3semidirect
79. C5×C3⋊C8C2×D3semidirect
85. C3⋊D15SD16semidirect
99. C3×Dic6C2×D5semidirect
103. C3×C3⋊C8C2×D5semidirect
136. #214D15semidirect
141. C32×C5C2×SD16semidirect
196. Dic6C2×D15semidirect
200. C3⋊C8C2×D15semidirect
221. C3×C5D3×SD16semidirect
222. C3×C5D3×SD16semidirect
249. C32D5×SD16semidirect
273. C5#63930semidirect
283. C3#91487semidirect
284. C3SD16×D15semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊D152
#106241982
C3×#67162
C3×C5×#2142
#106238062
#106238042
#106237942
SD16×D153
#914873
#639305