Finite Group Databasebeta

← #13086186

Subgroups — #13086186

Order 1440.

462 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 84 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×#67157C211yesmaximal, characteristic, complemented
2C2×#67150C212yesmaximal, complemented
3C2×C5×#625C211yesmaximal, characteristic, complemented
4C2×C3×#1203C212yesmaximal, complemented
5Dic5×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#91567—32nomaximal
7C22×C3×D15C2212yes—
8C22×C3×C5×D3C2212yes—
9C2×C3⋊Dic15C2211yescharacteristic
10C2×C5×C3⋊Dic3C2211yescharacteristic
11C2×C32×Dic5C2211yescharacteristic
12#67157—22no—
13#67150—24no—
14C5×#625—22no—
15C3×#1203—24no—
16#63914—51nomaximal, Hall
17C2×#1220—32no—
18C2×C5×#67—32no—
19C2×C3×C22⋊D5—32no—
20C2×#1203D312yescomplemented
21C2×#1202—32no—
22C2×#1201—32no—
23Dic3×Dic5—32no—
24Dic3×Dic5—61no—
25C22×C32×C5C2311yescharacteristic
26C2×C3×D15—22no—
27C2×C3×D15—22no—
28C2×C3×D15—22no—
29C2×C3×C5×D3—22no—
30C2×C3×C5×D3—22no—
31C2×C3×C5×D3—22no—
32C3⋊Dic15D412yescomplemented
33C5×C3⋊Dic3D412yescomplemented
34C32×Dic5D412yescomplemented
35#4086—91noHall
36C2×C3×D12—52no—
37C2×#625—52no—
38C2×#625—51no—
39C2×#625D511yescharacteristic, complemented
40C4×C3⋊Dic3—51no—
41C23×C3×C5—32no—
42C22×D15C2×D312yes—
43C22×C5×D3C2×D312yes—
44C22×C3×D5—32no—
45#1220—64no—
46C2×Dic15—32no—
47C2×Dic15—61no—
48C5×#67—64no—
49C2×C5×Dic3—32no—
50C2×C5×Dic3—61no—
51C3×C22⋊D5—64no—
52C2×C3×Dic5—21no—
53C2×C3×Dic5C2×D312yes—
54#1203—24no—
55#1202—64no—
56#1201—64no—
57#940—152no—
58C2×C32×C5C2×D411yescharacteristic
59C2×C32×C5C2×D411yescharacteristic
60C2×C32×C5C2×D411yescharacteristic
61C3×D15—42no—
62C3×C5×D3—42no—
63C2×C5×D4—91no—
64C2×C22⋊D5—32no—
65C2×C22⋊D5—92no—
66C2×D20—91no—
67C4×Dic5—91no—
68C22×C3×D3—52no—
69C22×C3×D3C2×D512yes—
70C2×C32×C4—51no—
71C2×C3⋊Dic3—51no—
72C2×C3⋊Dic3C2×D511yescharacteristic
73C3×D12—104no—
74#625—22no—
75#625—104no—
76#625—102no—
77C22×C3×C5—21no—
78C22×C3×C5—62no—
79C22×C3×C5—62no—
80C22×C3×C5—62no—
81C22×C3×C5C22×D312yes—
82C2×D15—22no—
83C2×D15—22no—
84C2×D15—22no—
85C2×C5×D3—22no—
86C2×C5×D3—22no—
87C2×C5×D3—22no—
88C2×C3×D5—62no—
89C2×C3×D5—62no—
90C2×C3×D5—62no—
91Dic15—34no—
92Dic15—62no—
93C3×Dic5—22no—
94C3×Dic5#6714yescomplemented
95C5×Dic3—34no—
96C5×Dic3—62no—
97C2×C3×D4—152no—
98C2×#67—32no—
99C2×#67—152no—
100C2×#67—152no—
101C2×#67—152no—
102C2×D12—52no—
103C4×Dic3—152no—
104C4×Dic3—301no—
105C32×C5#12711yescharacteristic, complemented, Hall
106C23×C5—32no—
107C22×D5—32no—
108C5×D4—182no—
109C2×C4×C5—91no—
110C22⋊D5—64no—
111C22⋊D5—184no—
112C2×Dic5—91no—
113C2×Dic5D3211yescharacteristic
114D20—182no—
115C22×C32C22×D511yescharacteristic
116C2×C3×D3—22no—
117C2×C3×D3—22no—
118C2×C3×D3—22no—
119C2×C3×D3—102no—
120C2×C3×D3—102no—
121C2×C3×D3—102no—
122C32×C4—52no—
123C3⋊Dic3—52no—
124C3⋊Dic3C22⋊D512yescomplemented
125#127—451noSylow
126C2×C3×C5—21no—
127C2×C3×C5—21no—
128C2×C3×C5—21no—
129C2×C3×C5—122no—
130C2×C3×C5D3×D412yes—
131C2×C3×C5D3×D412yes—
132C2×C3×C5C2×#6712yes—
133D15—42no—
134C3×D5—122no—
135C5×D3—42no—
136C23×C3—32no—
137C23×C3—152no—
138C22×D3—52no—
139C22×D3D3×D512yes—
140C3×D4—304no—
141C2×C3×C4—52no—
142C2×C3×C4—101no—
143#67—64no—
144#67—304no—
145#67—304no—
146#67—304no—
147C2×Dic3—32no—
148C2×Dic3—61no—
149C2×Dic3—152no—
150C2×Dic3—301no—
151D12—104no—
152C22×C5—62no—
153C22×C5—62no—
154C22×C5—62no—
155C22×C5C2×D3211yescharacteristic
156C2×D5—62no—
157C2×D5—62no—
158C2×D5—62no—
159C4×C5—92no—
160Dic5—92no—
161Dic5#62512yescomplemented
162C2×C32D4×D511yescharacteristic
163C2×C32D4×D511yescharacteristic
164C2×C32C2×C22⋊D511yescharacteristic
165C3×D3—42no—
166C3×D3—202no—
167C2×D4—91no—
168C2×D4—152no—
169C2×D4—451no—
170C2×D4—452no—
171C42—451no—
172C3×C5—21no—
173C3×C5#94012yescomplemented
174C22×C3—21no—
175C22×C3—62no—
176C22×C3—62no—
177C22×C3—62no—
178C22×C3—302no—
179C22×C3—302no—
180C22×C3—302no—
181C22×C3C2×D3×D512yes—
182C2×D3—22no—
183C2×D3—22no—
184C2×D3—22no—
185C2×D3—102no—
186C2×D3—102no—
187C2×D3—102no—
188C3×C4—54no—
189C3×C4—102no—
190Dic3—34no—
191Dic3—62no—
192Dic3—154no—
193Dic3—302no—
194C2×C5—122no—
195C2×C5#380211yescharacteristic
196C2×C5#380211yescharacteristic
197C2×C5C2×#62511yescharacteristic
198D5—122no—
199C32#408611yescharacteristic, complemented, Sylow
200C23—32no—
201C23—152no—
202D4—182no—
203D4—304no—
204D4—902no—
205D4—904no—
206C2×C4—51no—
207C2×C4—91no—
208C2×C4—451no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—122no—
213C2×C3—602no—
214C2×C3D5×#6712yes—
215C2×C3D3×C22⋊D512yes—
216C2×C3#679012yes—
217D3—42no—
218D3—202no—
219C5#6391411yescharacteristic, complemented, Sylow
220C22—62no—
221C22—62no—
222C22—62no—
223C22—302no—
224C22—302no—
225C22—302no—
226C22D32×D511yescharacteristic
227C4—52no—
228C4—92no—
229C4—452no—
230C3—21no—
231C3#9156712yescomplemented
232C2—122no—
233C2—602no—
234C2D5×#62511yescharacteristic
235C2#1062403411yescharacteristic
236C2#1062403511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, cosocleC22×C32×C5C23
hypocenterC32×C5#127
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#67157C2semidirect
2. C2×#67150C2semidirect
3. C2×C5×#625C2semidirect
4. C2×C3×#1203C2semidirect
5. Dic5×C3⋊Dic3C2semidirect
20. C2×#1203D3semidirect
32. C3⋊Dic15D4semidirect
33. C5×C3⋊Dic3D4semidirect
34. C32×Dic5D4semidirect
39. C2×#625D5semidirect
94. C3×Dic5#67semidirect
105. C32×C5#127semidirect
124. C3⋊Dic3C22⋊D5semidirect
161. Dic5#625semidirect
173. C3×C5#940semidirect
199. C32#4086semidirect
219. C5#63914semidirect
231. C3#91567semidirect

Maximal subgroups

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

subgroupindex
C2×#671572
C2×#671502
C2×C5×#6252
C2×C3×#12032
Dic5×C3⋊Dic32
#915673
#639145