Finite Group Databasebeta

← #14277608

Subgroups — #14277608

Order 1920.

256 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 59 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#11751227C211yesmaximal, characteristic
2C3×C5×#349C211yesmaximal, characteristic, complemented
3#11746374C211yesmaximal, characteristic, complemented
4#10598021—31nomaximal, Hall
5C22×C4×D15C411yescharacteristic
6C2×C3×C5×M16C2211yescharacteristic
7C2×#6710C411yescharacteristic
8C3×C5×M32—21no—
9#91104—21no—
10#91104—21no—
11#91096—21no—
12#67530—51nomaximal, Hall
13#65415—31no—
14C5×#349D311yescharacteristic, complemented
15#64773—31no—
16C23×D15C811yescharacteristic
17C22×C3×C4×C5C2×C411yescharacteristic
18C22×Dic15C811yescharacteristic
19C2×C4×D15—21no—
20C2×C4×D15—21no—
21C2×C4×D15—41no—
22C2×C4×D15—41no—
23C3×C5×M16—41no—
24C2×C3×C5×C8D411yescharacteristic
25C2×C3×C5×C8D411yescharacteristic
26#6710—41no—
27C2×C3⋊#168—21no—
28C3×C5×C16—41no—
29C3⋊#672—41no—
30#5126—51no—
31C3×#349D511yescharacteristic, complemented
32#4553—51no—
33C22×C4×D5—31no—
34C2×C5×M16C2×D311yescharacteristic
35C2×#681—31no—
36C5×M32—21no—
37#3952—61no—
38#3952—61no—
39#3944—61no—
40#1320—151noSylow
41C23×C3×C5C2×C811yescharacteristic
42C22×D15—21no—
43C22×D15—42no—
44C22×D15—41no—
45C2×C3×C4×C5—21no—
46C2×C3×C4×C5—21no—
47C2×C3×C4×C5C22⋊C411yescharacteristic
48C2×C3×C4×C5M1611yescharacteristic
49C2×Dic15—21no—
50C2×Dic15—41no—
51C4×D15—42no—
52C4×D15—41no—
53C4×D15—41no—
54C3×C5×C8—21no—
55C3×C5×C8—21no—
56C3⋊#168—41no—
57C22×C4×D3—51no—
58C2×C3×M16C2×D511yescharacteristic
59C2×#208—51no—
60C3×M32—21no—
61(C2×D3)⋊C8—101no—
62(C2×D3)⋊C8—101no—
63#812—101no—
64C23×D5—31no—
65C22×C4×C5C4×D311yescharacteristic
66C22×Dic5—31no—
67C2×C4×D5—61no—
68C2×C4×D5—61no—
69C2×C4×D5—121no—
70C2×C4×D5—121no—
71C5×M16—41no—
72C2×C5×C8D1211yescharacteristic
73C2×C5×C8#6711yescharacteristic
74#681—121no—
75C2×#168—61no—
76C5×C16—41no—
77#672—121no—
78#407—151no—
79#349—151no—
80#349D1511yescharacteristic, complemented
81C22×C3×C5—21no—
82C22×C3×C5—41no—
83C22×C3×C5C22⋊C811yescharacteristic
84C2×D15—22no—
85C2×D15—41no—
86C2×D15—42no—
87C2×D15—41no—
88C2×D15—42no—
89C3×C4×C5—21no—
90C3×C4×C5#9911yescharacteristic
91C3×C4×C5#10011yescharacteristic
92Dic15—41no—
93C23×D3—51no—
94C22×C3×C4C4×D511yescharacteristic
95C22×Dic3—51no—
96C2×C4×D3—101no—
97C2×C4×D3—101no—
98C2×C4×D3—201no—
99C2×C4×D3—201no—
100C3×M16—41no—
101C2×C3×C8D2011yescharacteristic
102C2×C3×C8C22⋊D511yescharacteristic
103#208—201no—
104C2×C3⋊C8—101no—
105C3×C16—41no—
106C3⋊C16—201no—
107C23×C5D3×C811yescharacteristic
108C22×D5—61no—
109C22×D5—122no—
110C22×D5—121no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5ΓL(1,𝔽25)11yescharacteristic
114C2×C4×C5(C2×D3)⋊C411yescharacteristic
115C2×Dic5—61no—
116C2×Dic5—121no—
117C4×D5—122no—
118C4×D5—121no—
119C4×D5—121no—
120C5×C8—21no—
121C5×C8—21no—
122#168—121no—
123C23×C4—151no—
124C2×M16—151no—
125C2×M16C2×D1511yescharacteristic
126M32—21no—
127M32—301no—
128C22⋊C8—301no—
129C22⋊C8—301no—
130C2×C3×C5—21no—
131C2×C3×C5—41no—
132C2×C3×C5#32311yescharacteristic
133D15—42no—
134C23×C3C8×D511yescharacteristic
135C22×D3—101no—
136C22×D3—202no—
137C22×D3—201no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4#67611yescharacteristic
141C2×C3×C4#68511yescharacteristic
142C2×Dic3—101no—
143C2×Dic3—201no—
144C4×D3—202no—
145C4×D3—201no—
146C4×D3—201no—
147C3×C8—21no—
148C3×C8—21no—
149C3⋊C8—201no—
150C22×C5—21no—
151C22×C5—41no—
152C22×C5(C2×D3)⋊C811yescharacteristic
153C2×D5—62no—
154C2×D5—121no—
155C2×D5—122no—
156C2×D5—121no—
157C2×D5—122no—
158C4×C5—21no—
159C4×C5#80611yescharacteristic
160C4×C5#82311yescharacteristic
161Dic5—121no—
162C24—151no—
163C22×C4—151no—
164C22×C4—301no—
165C22×C4—301no—
166C22×C4—601no—
167C22×C4—601no—
168C22×C4C4×D1511yescharacteristic
169M16—41no—
170M16—601no—
171C2×C8—301no—
172C2×C8D6011yescharacteristic
173C2×C8#122011yescharacteristic
174C16—41no—
175C16—601no—
176C3×C5#132011yescharacteristic, complemented, Hall
177C22×C3—21no—
178C22×C3—41no—
179C22×C3#395211yescharacteristic
180C2×D3—102no—
181C2×D3—201no—
182C2×D3—202no—
183C2×D3—201no—
184C2×D3—202no—
185C3×C4—21no—
186C3×C4#393811yescharacteristic
187C3×C4#395511yescharacteristic
188Dic3—201no—
189C2×C5—21no—
190C2×C5—41no—
191C2×C5#446811yescharacteristic
192D5—122no—
193C23—301no—
194C23—601no—
195C23—602no—
196C23C8×D1511yescharacteristic
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—301no—
200C2×C4—602no—
201C2×C4—601no—
202C2×C4—601no—
203C2×C4—601no—
204C2×C4#670511yescharacteristic
205C2×C4#671411yescharacteristic
206C8—21no—
207C8—21no—
208C8—601no—
209C2×C3—21no—
210C2×C3—41no—
211C2×C3#6468811yescharacteristic
212D3—202no—
213C5#6753011yescharacteristic, complemented, Sylow
214C22—21no—
215C22—41no—
216C22—302no—
217C22—601no—
218C22—602no—
219C22—602no—
220C22—601no—
221C22#9110411yescharacteristic
222C4—21no—
223C4—601no—
224C4#9109011yescharacteristic
225C4#9110711yescharacteristic
226C3#1059802111yescharacteristic, complemented, Sylow
227C2—21no—
228C2—41no—
229C2—602no—
230C2#1174628911yescharacteristic
subgroupG/H
centerC4#91090
commutatorC23×C3×C5C2×C8
FrattiniC2×M16C2×D15
FittingC3×C5×#349C2
socleC2×C3×C5#323
prime radicalC23×D15C8
cosocleC2×C3×C5×M16C22
hypercenter#349D15
hypocenterC3×C5#1320
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. C3×C5×#349C2semidirect
3. #11746374C2semidirect
14. C5×#349D3semidirect
31. C3×#349D5semidirect
80. #349D15semidirect
176. C3×C5#1320semidirect
213. C5#67530semidirect
226. C3#10598021semidirect

Maximal subgroups

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

subgroupindex
#117512272
C3×C5×#3492
#117463742
#105980213
#675305