Finite Group Databasebeta

← #13087501

Subgroups — #13087501

Order 1440.

280 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 60 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
1#10624285C211yesmaximal, characteristic
2#10624198C211yesmaximal, characteristic, complemented
3C3×#6716C211yesmaximal, characteristic, complemented
4C3×C5×#214C211yesmaximal, characteristic, complemented
5#10623809C211yesmaximal, characteristic, complemented
6#10623808C211yesmaximal, characteristic, complemented
7#10623797C211yesmaximal, characteristic, complemented
8#91804—31nomaximal
9#91488—31nomaximal
10C32×C5×D4C2211yescharacteristic
11#67184—21no—
12C2×C3⋊Dic15—21no—
13C4×C3⋊D15C2211yescharacteristic
14#67180C2211yescharacteristic
15C3×Dic30C2211yescharacteristic
16C3×C5×Dic6C2211yescharacteristic
17#67153—21no—
18#67149—21no—
19C3×C3⋊#168C2211yescharacteristic
20C3×C5×C3⋊C8C2211yescharacteristic
21#63931—51nomaximal, Hall
22Q8×D15—31no—
23#6819—31no—
24#6819—31no—
25#6819—61no—
26D15⋊Q8—31no—
27C3×C5×SD16—31no—
28#6718—31no—
29#6716D311yescharacteristic, complemented
30Dic60—31no—
31#6705—31no—
32C5×#214D311yescharacteristic, complemented
33C3×#687—31no—
34#6663—31no—
35#6662—31no—
36#6651—31no—
37C22×C32×C5—21no—
38C2×C3⋊D15D411yescharacteristic
39C32×C4×C5C2311yescharacteristic
40C3⋊Dic15—21no—
41C3⋊Dic15D411yescharacteristic
42C3×Dic15—21no—
43C3×C5×Dic3—21no—
44#4061—91noHall
45#3830—51no—
46#3797—51no—
47C3×#214—51no—
48C3×#214D511yescharacteristic, complemented
49#3719—51no—
50#3719—51no—
51#3712—51no—
52C3×C5×Q8—31no—
53C3×C5×D4—21no—
54C3×C5×D4C2×D311yescharacteristic
55C3×C5×D4C2×D311yescharacteristic
56#1220—61no—
57#1220—61no—
58#1220—62no—
59C2×Dic15—61no—
60C2×Dic15—61no—
61C2×Dic15—62no—
62C4×D15—31no—
63C4×D15—31no—
64C4×D15—61no—
65C4×D15—61no—
66Dic30—31no—
67Dic30—31no—
68Dic30—61no—
69Dic30—61no—
70Dic30C2×D311yescharacteristic
71C5×Dic6C2×D311yescharacteristic
72C3×Dic10—31no—
73#1204—61no—
74#1200—61no—
75C3×C5×C8—31no—
76C3⋊#168C2×D311yescharacteristic
77C3×#168—31no—
78C5×C3⋊C8C2×D311yescharacteristic
79#915—151no—
80#915—151no—
81C2×C32×C5—41no—
82C2×C32×C5C2×D411yescharacteristic
83C3⋊D15—21no—
84Q8×D5—91no—
85#711—91no—
86C5×SD16—31no—
87#689—91no—
88#687—31no—
89Dic20—91no—
90#676—91no—
91C32×D4C2×D511yescharacteristic
92#638—101no—
93C2×C3⋊Dic3—101no—
94C4×C3⋊D3—51no—
95#634—51no—
96C3×Dic6—51no—
97C3×Dic6C2×D511yescharacteristic
98#627—101no—
99#624—101no—
100C3×C3⋊C8—51no—
101C3×C3⋊C8C2×D511yescharacteristic
102C22×C3×C5—22no—
103C22×C3×C5—21no—
104C22×C3×C5—21no—
105C2×D15—31no—
106C2×D15—31no—
107C2×D15—61no—
108C3×C4×C5—21no—
109C3×C4×C5—61no—
110C3×C4×C5C22×D311yescharacteristic
111C3×C4×C5C22×D311yescharacteristic
112Dic15—21no—
113Dic15—31no—
114Dic15—31no—
115Dic15—61no—
116Dic15—62no—
117Dic15—61no—
118Dic15—61no—
119C3×Dic5—61no—
120C5×Dic3—21no—
121D3×Q8—151no—
122D3×Q8—151no—
123#237—151no—
124#237—151no—
125#237—301no—
126C3×SD16—31no—
127C3×SD16—151no—
128#216—151no—
129#216—151no—
130#214—51no—
131#214D1511yescharacteristic, complemented
132Dic12—151no—
133Dic12—151no—
134ΓL(1,𝔽25)—151no—
135ΓL(1,𝔽25)—151no—
136C32×C5#13711yescharacteristic, complemented, Hall
137C5×Q8—31no—
138C5×D4D3211yescharacteristic
139C22⋊D5—181no—
140C2×Dic5—181no—
141C4×D5—91no—
142C4×D5—181no—
143Dic10—31no—
144Dic10—91no—
145Dic10—181no—
146C5×C8—31no—
147#168—31no—
148C22×C32—21no—
149C2×C3⋊D3—51no—
150C32×C4C22×D511yescharacteristic
151C3⋊Dic3—51no—
152C3⋊Dic3—101no—
153C3×Dic3—21no—
154C3×Dic3—101no—
155#137—451noSylow
156C2×C3×C5—21no—
157C2×C3×C5—42no—
158C2×C3×C5—41no—
159C2×C3×C5—41no—
160C2×C3×C5D3×D411yescharacteristic
161C2×C3×C5D3×D411yescharacteristic
162D15—61no—
163D15—61no—
164D15—121no—
165C3×Q8—31no—
166C3×Q8—151no—
167C3×D4—21no—
168C3×D4D3×D511yescharacteristic
169C3×D4C2×D1511yescharacteristic
170#67—301no—
171#67—301no—
172#67—302no—
173C2×Dic3—301no—
174C2×Dic3—301no—
175C2×Dic3—302no—
176C4×D3—151no—
177C4×D3—151no—
178C4×D3—301no—
179C4×D3—301no—
180C4×D3—301no—
181Dic6—51no—
182Dic6—151no—
183Dic6—151no—
184Dic6—301no—
185Dic6—301no—
186Dic6—301no—
187Dic6C2×D1511yescharacteristic
188C3×C8—31no—
189C3×C8—151no—
190C3⋊C8—51no—
191C3⋊C8C2×D1511yescharacteristic
192C22×C5—21no—
193C2×D5—91no—
194C4×C5—61no—
195C4×C5C2×D3211yescharacteristic
196Dic5—61no—
197Dic5—91no—
198Dic5—181no—
199C2×C32—41no—
200C2×C32D4×D511yescharacteristic
201C3⋊D3—101no—
202#41—451no—
203C2×Q8—451no—
204Q16—451no—
205Q16—451no—
206SD16—31no—
207SD16—151no—
208M16—451no—
209C3×C5—21no—
210C3×C5#91511yescharacteristic, complemented
211C3×C5#91511yescharacteristic, complemented
212C22×C3—22no—
213C22×C3—21no—
214C22×C3—21no—
215C2×D3—151no—
216C2×D3—151no—
217C2×D3—301no—
218C3×C4—21no—
219C3×C4—61no—
220C3×C4—301no—
221C3×C4C2×D3×D511yescharacteristic
222C3×C4C22×D1511yescharacteristic
223Dic3—21no—
224Dic3—101no—
225Dic3—151no—
226Dic3—151no—
227Dic3—301no—
228Dic3—302no—
229Dic3—301no—
230Dic3—301no—
231C2×C5—41no—
232C2×C5#381111yescharacteristic
233D5—181no—
234C32#406111yescharacteristic, complemented, Sylow
235Q8—31no—
236Q8—151no—
237Q8—451no—
238Q8—901no—
239D4—901no—
240D4D3×D1511yescharacteristic
241C2×C4—451no—
242C2×C4—901no—
243C2×C4—901no—
244C8—31no—
245C8—151no—
246C2×C3—21no—
247C2×C3—42no—
248C2×C3—41no—
249C2×C3—41no—
250C2×C3#679011yescharacteristic
251C2×C3D4×D1511yescharacteristic
252D3—301no—
253D3—301no—
254D3—601no—
255C5#6393111yescharacteristic, complemented, Sylow
256C22—21no—
257C22—451no—
258C4—61no—
259C4—301no—
260C4—451no—
261C4—901no—
262C4C2×D3×D1511yescharacteristic
263C3—21no—
264C3#9148811yescharacteristic, complemented
265C3#9180411yescharacteristic, complemented
266C2—41no—
267C2—901no—
268C2#1062421811yescharacteristic
subgroupG/H
centerC2#10624218
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
prime radical#10624285C2
hypercenterD4D3×D15
hypocenterC32×C5#137
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. #10623809C2semidirect
6. #10623808C2semidirect
7. #10623797C2semidirect
29. #6716D3semidirect
32. C5×#214D3semidirect
48. C3×#214D5semidirect
131. #214D15semidirect
136. C32×C5#137semidirect
210. C3×C5#915semidirect
211. C3×C5#915semidirect
234. C32#4061semidirect
255. C5#63931semidirect
264. C3#91488semidirect
265. C3#91804semidirect

Maximal subgroups

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

subgroupindex
#106242852
#106241982
C3×#67162
C3×C5×#2142
#106238092
#106238082
#106237972
#918043
#914883
#639315