Finite Group Databasebeta

← #14276977

Subgroups — #14276977

Order 1920.

312 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 96 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#11752341C211yesmaximal, characteristic
2C3×#65689C211yesmaximal, characteristic
3#11746868C211yesmaximal, characteristic
4#10598527—31nomaximal, Hall
5C2×#6758—21no—
6C2×C3×C4⋊AGL(1,𝔽5)—21no—
7C3×C42×D5C2211yescharacteristic
8#91233—21no—
9#91233C412yescomplemented
10C3×(C2×AGL(1,𝔽5))⋊C4—21no—
11C3×(C2×AGL(1,𝔽5))⋊C4C412yes—
12C4×C3⋊#168C411yescharacteristic, complemented
13C4×C5×C3⋊C8C411yescharacteristic, complemented
14#90982—21no—
15#90955—21no—
16#67631—51nomaximal, Hall
17#65689D311yescharacteristic
18#65682—31no—
19#64974—31no—
20C22×C3×AGL(1,𝔽5)—22no—
21C2×C3×C4×D5C2×C411yescharacteristic
22C2×C3×C4×D5D411yescharacteristic
23C2×C3×C4×D5D411yescharacteristic
24C2×C3⋊#170—22no—
25#6758—41no—
26#6758—41no—
27C3×C4⋊AGL(1,𝔽5)—41no—
28C3×C4⋊AGL(1,𝔽5)—41no—
29C3×C42×C5C2×C411yescharacteristic
30C2×C3⋊#168—21no—
31C2×C5×C3⋊C8—21no—
32C3×C4×Dic5C2×C411yescharacteristic
33C3×C4×Dic5D411yescharacteristic
34C3×C4×Dic5Q811yescharacteristic
35C3×#382—51no—
36#4925—51no—
37#4924—51no—
38C2×C4⋊AGL(1,𝔽5)—21no—
39C2×#700—61no—
40C42×D5C2×D311yescharacteristic
41(C2×AGL(1,𝔽5))⋊C4—21no—
42(C2×AGL(1,𝔽5))⋊C4Dic312yes—
43#4004—32no—
44#4004—61no—
45C4×C5×C8—31no—
46#3952—61no—
47#3946—61no—
48C4×#168—31no—
49#1286—151noSylow
50C22×C3×D5C22⋊C411yescharacteristic
51C2×C3×AGL(1,𝔽5)—42no—
52C2×C3×AGL(1,𝔽5)—42no—
53C2×C3×AGL(1,𝔽5)—42no—
54C2×C3×C4×C5C4211yescharacteristic
55C2×C3×C4×C5C22⋊C411yescharacteristic
56C2×C3×C4×C5C4⋊C411yescharacteristic
57C2×C3×Dic5C22⋊C411yescharacteristic
58C2×C3×Dic5C4⋊C411yescharacteristic
59C2×C3×Dic5C4⋊C411yescharacteristic
60C3×C4×D5—41no—
61C3×C4×D5—41no—
62C3×C4×D5D811yescharacteristic
63C3×C4×D5SD1611yescharacteristic
64C3×C4×D5SD1611yescharacteristic
65C3×C4×D5Q1611yescharacteristic
66C3⋊#170—42no—
67C3⋊#168—41no—
68C5×C3⋊C8—41no—
69C2×C3×C4⋊C4—101no—
70C2×C3×C42—51no—
71C2×#208—101no—
72C3×#95—52no—
73C3×#95—101no—
74#830—101no—
75C4⋊(C3⋊C8)—52no—
76C4⋊(C3⋊C8)—101no—
77C4⋊(C3⋊C8)—101no—
78C4×C3⋊C8—51no—
79C4×C3⋊C8AGL(1,𝔽5)11yescharacteristic, complemented
80C22×AGL(1,𝔽5)—22no—
81C2×C4×D5C2×Dic311yescharacteristic
82C2×C4×D5#6711yescharacteristic
83C2×C4×D5#6711yescharacteristic
84C2×#170—62no—
85C4⋊AGL(1,𝔽5)—41no—
86C4⋊AGL(1,𝔽5)—41no—
87#700—121no—
88#700—121no—
89C2×C5×C8—61no—
90C42×C5C4×D311yescharacteristic
91C4×Dic5Dic611yescharacteristic
92C4×Dic5C4×D311yescharacteristic
93C4×Dic5D1211yescharacteristic
94C2×#168—61no—
95#431—151no—
96#423—151no—
97#382—51no—
98C22×C3×C5#9511yescharacteristic
99C2×C3×D5—21no—
100C2×C3×D5—21no—
101C2×C3×D5#10211yescharacteristic
102C2×C3×D5#10311yescharacteristic
103C3×AGL(1,𝔽5)—82no—
104C3×C4×C5—21no—
105C3×C4×C5—21no—
106C3×C4×C5#10611yescharacteristic
107C3×C4×C5#10711yescharacteristic
108C3×Dic5—21no—
109C3×Dic5—21no—
110C3×Dic5#10211yescharacteristic
111C3×Dic5#10311yescharacteristic
112C22×C3×C4—51no—
113C22×C3×C4—51no—
114C22×C3×C4—51no—
115C22×C3×C4—102no—
116C3×C4⋊C4—201no—
117C3×C4⋊C4—201no—
118C3×C42—51no—
119C3×C42—51no—
120C3×C42—51no—
121C3×C42C2×AGL(1,𝔽5)11yescharacteristic
122#208—201no—
123#208—201no—
124C2×C3⋊C8—21no—
125C2×C3⋊C8—102no—
126C2×C3⋊C8—101no—
127C22×D5#21711yescharacteristic
128C2×AGL(1,𝔽5)—42no—
129C2×AGL(1,𝔽5)—42no—
130C2×AGL(1,𝔽5)—42no—
131C2×C4×C5C4×Dic311yescharacteristic
132C2×C4×C5Dic3⋊C411yescharacteristic
133C2×C4×C5(C2×D3)⋊C411yescharacteristic
134C2×Dic5Dic3⋊C411yescharacteristic
135C2×Dic5C4⋊Dic311yescharacteristic
136C2×Dic5(C2×D3)⋊C411yescharacteristic
137C4×D5—41no—
138C4×D5—41no—
139C4×D5#21311yescharacteristic
140C4×D5#21411yescharacteristic
141C4×D5#21511yescharacteristic
142C4×D5#21611yescharacteristic
143#170—122no—
144C5×C8—121no—
145#168—121no—
146C2×M16—301no—
147C2×C4⋊C4—101no—
148C2×C42—51no—
149C4⋊C8—152no—
150C4⋊C8—301no—
151C4⋊C8—301no—
152C22⋊C8—301no—
153C4×C8—31no—
154C4×C8—151no—
155#95—52no—
156#95—101no—
157C2×C3×C5H(3,ℤ/4)11yescharacteristic
158C2×C3×C5#34011yescharacteristic
159C2×C3×C5#34411yescharacteristic
160C3×D5—21no—
161C3×D5—21no—
162C23×C3—51no—
163C2×C3×C4—51no—
164C2×C3×C4—51no—
165C2×C3×C4—51no—
166C2×C3×C4—51no—
167C2×C3×C4—51no—
168C2×C3×C4—51no—
169C2×C3×C4—51no—
170C2×C3×C4—201no—
171C2×C3×C4—201no—
172C2×C3×C4—202no—
173C2×C3×C4—202no—
174C2×C3×C4—202no—
175C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
176C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
177C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
178C3⋊C8—41no—
179C3⋊C8—201no—
180C3⋊C8—202no—
181C22×C5C3⋊#9511yescharacteristic
182C2×D5—21no—
183C2×D5—21no—
184C2×D5#83211yescharacteristic
185C2×D5#83511yescharacteristic
186AGL(1,𝔽5)—82no—
187C4×C5—21no—
188C4×C5—21no—
189C4×C5#80711yescharacteristic
190C4×C5#80811yescharacteristic
191Dic5—21no—
192Dic5—21no—
193Dic5#80911yescharacteristic
194Dic5#81011yescharacteristic
195C22×C4—51no—
196C22×C4—51no—
197C22×C4—51no—
198C22×C4—102no—
199M16—601no—
200M16—601no—
201C2×C8—61no—
202C2×C8—302no—
203C2×C8—301no—
204C4⋊C4—201no—
205C4⋊C4—201no—
206C42—51no—
207C42—51no—
208C42—51no—
209C42D3×AGL(1,𝔽5)11yescharacteristic
210C3×C5#128611yescharacteristic, complemented, Hall
211C22×C3—51no—
212C22×C3—51no—
213C22×C3—101no—
214C22×C3—101no—
215C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—51no—
219C3×C4—51no—
220C3×C4—101no—
221C3×C4—101no—
222C3×C4—402no—
223C3×C4#399311yescharacteristic
224C3×C4#399411yescharacteristic
225C2×C5#452911yescharacteristic
226C2×C5#453111yescharacteristic
227C2×C5#453311yescharacteristic
228D5—21no—
229D5—21no—
230C23—51no—
231C2×C4—51no—
232C2×C4—51no—
233C2×C4—51no—
234C2×C4—51no—
235C2×C4—51no—
236C2×C4—51no—
237C2×C4—51no—
238C2×C4—201no—
239C2×C4—201no—
240C2×C4—202no—
241C2×C4—202no—
242C2×C4—202no—
243C2×C4Dic3×AGL(1,𝔽5)11yescharacteristic
244C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
245C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
246C8—121no—
247C8—601no—
248C8—602no—
249C2×C3—101no—
250C2×C3—101no—
251C2×C3#6486311yescharacteristic
252C2×C3#6489311yescharacteristic
253C2×C3#6489411yescharacteristic
254C5#6763111yescharacteristic, complemented, Sylow
255C22—51no—
256C22—51no—
257C22—101no—
258C22—101no—
259C22(C2×AGL(1,𝔽5))⋊Dic311yescharacteristic
260C4—21no—
261C4—21no—
262C4—51no—
263C4—51no—
264C4—101no—
265C4—101no—
266C4—402no—
267C4#9115911yescharacteristic
268C4#9116011yescharacteristic
269C3#1059852711yescharacteristic, complemented, Sylow
270C2—101no—
271C2—101no—
272C2#1174651811yescharacteristic
273C2#1174652911yescharacteristic
274C2#1174653711yescharacteristic
subgroupG/H
centerC22(C2×AGL(1,𝔽5))⋊Dic3
commutatorC2×C3×C4×C5C42
Frattini, hypercenterC42D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5#95
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×D5C22
hypocenterC3×C5#1286
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
9. #91233C4semidirect
12. C4×C3⋊#168C4semidirect
13. C4×C5×C3⋊C8C4semidirect
79. C4×C3⋊C8AGL(1,𝔽5)semidirect
210. C3×C5#1286semidirect
254. C5#67631semidirect
269. C3#10598527semidirect

Maximal subgroups

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

subgroupindex
#117523412
C3×#656892
#117468682
#105985273
#676315