Finite Group Databasebeta

← #13086183

Subgroups — #13086183

Order 1440.

266 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 70 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#10623829C211yesmaximal, characteristic
2#10623811C211yesmaximal, characteristic
3Dic3×Dic15C211yesmaximal, characteristic, complemented
4C5×#3724C211yesmaximal, characteristic, complemented
5#10623773C211yesmaximal, characteristic, complemented
6C3×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
7C3×#6667C211yesmaximal, characteristic
8#91366—31nomaximal
9#91345—31nomaximal
10C22×C3×D15C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C5×C3⋊Dic3C2211yescharacteristic
13C2×C3×Dic15C2211yescharacteristic
14C2×C3×C5×Dic3C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17#63861—51nomaximal, Hall
18#6714—31no—
19C4×Dic15—31no—
20C5×Dic3⋊C4—31no—
21C5×Dic3⋊C4—31no—
22C3×#685—31no—
23C3×C4⋊Dic5—31no—
24Dic3⋊Dic5D311yescharacteristic, complemented
25#6668—31no—
26#6668—31no—
27#6668—61no—
28#6667—31no—
29#6667D311yescharacteristic
30#6665—31no—
31#6665—31no—
32Dic3×Dic5—31no—
33C22×C32×C5C2311yescharacteristic
34C2×C3×D15—21no—
35C2×C3×D15—21no—
36C2×C3×D15—21no—
37C3⋊Dic15—21no—
38C5×C3⋊Dic3—21no—
39C3×Dic15—21no—
40C3×C5×Dic3—21no—
41C3×C5×Dic3—21no—
42C32×Dic5—21no—
43#4044—91noHall
44C4⋊(C3⋊Dic3)—51no—
45C3×(C2×D3)⋊C4—51no—
46C3×Dic3⋊C4—51no—
47#3724D511yescharacteristic, complemented
48(C2×D3)⋊Dic3—51no—
49(C2×D3)⋊Dic3—51no—
50Dic32—51no—
51C22×D15C2×D311yescharacteristic
52C22×C3×D5—31no—
53C2×C3×C4×C5—31no—
54C2×C3×C4×C5—31no—
55C2×Dic15—31no—
56C2×Dic15—31no—
57C2×Dic15—61no—
58C2×Dic15C2×D311yescharacteristic
59C2×C5×Dic3—31no—
60C2×C5×Dic3—31no—
61C2×C5×Dic3—61no—
62C2×C5×Dic3C2×D311yescharacteristic
63C2×C5×Dic3C2×D311yescharacteristic
64C2×C3×Dic5—21no—
65C2×C3×Dic5—31no—
66C2×C3×Dic5C2×D311yescharacteristic
67C2×C3×Dic5C2×D311yescharacteristic
68#898—151no—
69#879—151no—
70C2×C32×C5#4111yescharacteristic
71C2×C32×C5#4111yescharacteristic
72C2×C32×C5#4111yescharacteristic
73C3×D15—41no—
74C5×C4⋊C4—91no—
75#685—31no—
76#685—91no—
77#685—91no—
78C4⋊Dic5—31no—
79#683—91no—
80C4×Dic5—91no—
81C22×C3×D3—51no—
82C2×C32×C4—51no—
83C2×C3⋊Dic3—51no—
84C2×C3⋊Dic3C2×D511yescharacteristic
85C2×C3×Dic3—51no—
86C2×C3×Dic3C2×D511yescharacteristic
87C2×C3×Dic3C2×D511yescharacteristic
88C22×C3×C5—21no—
89C22×C3×C5C22×D311yescharacteristic
90C22×C3×C5C22×D311yescharacteristic
91C2×D15—21no—
92C2×D15—21no—
93C2×D15—21no—
94C2×C3×D5—61no—
95C2×C3×D5—61no—
96C2×C3×D5—61no—
97C3×C4×C5—61no—
98C3×C4×C5—61no—
99Dic15—21no—
100Dic15—61no—
101Dic15—61no—
102Dic15—121no—
103C3×Dic5—22no—
104C3×Dic5—21no—
105C3×Dic5—21no—
106C3×Dic5—61no—
107C5×Dic3—21no—
108C5×Dic3—21no—
109C5×Dic3—61no—
110C5×Dic3—61no—
111C5×Dic3—121no—
112C3×C4⋊C4—151no—
113C3×C22⋊C4—151no—
114#217—151no—
115#217—151no—
116(C2×D3)⋊C4—51no—
117(C2×D3)⋊C4—151no—
118(C2×D3)⋊C4—151no—
119C4⋊Dic3—151no—
120C4⋊Dic3—151no—
121C4⋊Dic3—301no—
122Dic3⋊C4—31no—
123Dic3⋊C4—31no—
124Dic3⋊C4—51no—
125C4×Dic3—151no—
126C4×Dic3—151no—
127C32×C5#12611yescharacteristic, complemented, Hall
128C22×D5—31no—
129C2×C4×C5—31no—
130C2×C4×C5—31no—
131C2×C4×C5—91no—
132C2×Dic5—31no—
133C2×Dic5—91no—
134C2×Dic5D3211yescharacteristic
135C22×C32C22×D511yescharacteristic
136C2×C3×D3—101no—
137C2×C3×D3—101no—
138C2×C3×D3—101no—
139C32×C4—101no—
140C3⋊Dic3—21no—
141C3⋊Dic3—101no—
142C3×Dic3—21no—
143C3×Dic3—21no—
144C3×Dic3—101no—
145#126—451noSylow
146C2×C3×C5—21no—
147C2×C3×C5—21no—
148C2×C3×C5—21no—
149C2×C3×C5#23511yescharacteristic
150C2×C3×C5#23511yescharacteristic
151C2×C3×C5#23711yescharacteristic
152C2×C3×C5#23711yescharacteristic
153C2×C3×C5#23711yescharacteristic
154C2×C3×C5#23911yescharacteristic
155D15—41no—
156C3×D5—121no—
157C23×C3—151no—
158C22×D3—51no—
159C2×C3×C4—31no—
160C2×C3×C4—31no—
161C2×C3×C4—51no—
162C2×C3×C4—51no—
163C2×C3×C4—101no—
164C2×C3×C4—151no—
165C2×Dic3—31no—
166C2×Dic3—31no—
167C2×Dic3—51no—
168C2×Dic3—61no—
169C2×Dic3—151no—
170C2×Dic3—151no—
171C2×Dic3—301no—
172C2×Dic3D3×D511yescharacteristic
173C2×Dic3D3×D511yescharacteristic
174C22×C5C2×D3211yescharacteristic
175C2×D5—61no—
176C2×D5—61no—
177C2×D5—61no—
178C4×C5—61no—
179C4×C5—61no—
180C4×C5—181no—
181Dic5—21no—
182Dic5—61no—
183Dic5—181no—
184C2×C32#70911yescharacteristic
185C2×C32#71111yescharacteristic
186C2×C32#71311yescharacteristic
187C3×D3—201no—
188C4⋊C4—91no—
189C4⋊C4—151no—
190C4⋊C4—451no—
191C22⋊C4—151no—
192C22⋊C4—451no—
193C22⋊C4—451no—
194C42—451no—
195C3×C5—21no—
196C3×C5#87911yescharacteristic, complemented
197C3×C5#89811yescharacteristic, complemented
198C22×C3—21no—
199C22×C3—301no—
200C22×C3—301no—
201C22×C3—301no—
202C22×C3C2×D3×D511yescharacteristic
203C22×C3C2×D3×D511yescharacteristic
204C2×D3—101no—
205C2×D3—101no—
206C2×D3—101no—
207C3×C4—61no—
208C3×C4—61no—
209C3×C4—102no—
210C3×C4—101no—
211C3×C4—101no—
212C3×C4—301no—
213Dic3—21no—
214Dic3—21no—
215Dic3—61no—
216Dic3—61no—
217Dic3—101no—
218Dic3—121no—
219Dic3—301no—
220Dic3—301no—
221Dic3—601no—
222C2×C5#379511yescharacteristic
223C2×C5#379911yescharacteristic
224C2×C5#380511yescharacteristic
225D5—121no—
226C32#404411yescharacteristic, complemented, Sylow
227C23—151no—
228C2×C4—31no—
229C2×C4—31no—
230C2×C4—51no—
231C2×C4—91no—
232C2×C4—151no—
233C2×C4—451no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—601no—
238C2×C3#676611yescharacteristic
239C2×C3#676611yescharacteristic
240C2×C3#676911yescharacteristic
241C2×C3#677111yescharacteristic
242C2×C3#678011yescharacteristic
243C2×C3#678211yescharacteristic
244D3—201no—
245C5#6386111yescharacteristic, complemented, Sylow
246C22—301no—
247C22—301no—
248C22—301no—
249C22D32×D511yescharacteristic
250C4—61no—
251C4—61no—
252C4—101no—
253C4—181no—
254C4—301no—
255C4—901no—
256C3—21no—
257C3#9134511yescharacteristic, complemented
258C3#9136611yescharacteristic, complemented
259C2—601no—
260C2#1062404711yescharacteristic
261C2#1062405011yescharacteristic
262C2#1062405411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, cosocleC22×C32×C5C23
prime radicalC22×C3×D15C22
hypocenterC32×C5#126
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
3. Dic3×Dic15C2semidirect
4. C5×#3724C2semidirect
5. #10623773C2semidirect
6. C3×Dic3⋊Dic5C2semidirect
24. Dic3⋊Dic5D3semidirect
47. #3724D5semidirect
127. C32×C5#126semidirect
196. C3×C5#879semidirect
197. C3×C5#898semidirect
226. C32#4044semidirect
245. C5#63861semidirect
257. C3#91345semidirect
258. C3#91366semidirect

Maximal subgroups

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

subgroupindex
#106238292
#106238112
Dic3×Dic152
C5×#37242
#106237732
C3×Dic3⋊Dic52
C3×#66672
#913663
#913453
#638615