Finite Group Databasebeta

← #14284087

Subgroups — #14284087

Order 1920.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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×C3×#4036C211yesmaximal, characteristic
2#11752418C211yesmaximal, characteristic
3C4×#6762C211yesmaximal, characteristic
4#11746741C214yesmaximal, complemented
5#10604265—31nomaximal, Hall
6C2×#6762—21no—
7C2×C3×C5×C4⋊C4C411yescharacteristic
8C2×C3×C4⋊Dic5—21no—
9C2×C3×C4⋊Dic5C411yescharacteristic
10C2×C3×#683—21no—
11C2×C3×C4×Dic5C2211yescharacteristic
12C3×#4036—21no—
13C3×#4036—21no—
14C3×#4036C412yes—
15C3×#4036C2212yes—
16#91241—21no—
17#91231C2212yes—
18#91231C2212yes—
19C4⋊(C3⋊#170)—21no—
20C4×C3⋊#170—21no—
21#71735—51nomaximal, Hall
22C2×#4036D311yescharacteristic
23#65759—31no—
24C4×#704—31no—
25#64870—34no—
26C22×C3×C4×C5—21no—
27C22×C3×C4×C5C2×C411yescharacteristic
28C22×C3×Dic5—21no—
29C22×C3×Dic5D411yescharacteristic
30C22×C3×Dic5D411yescharacteristic
31#6762—24no—
32C2×C3⋊#170—22no—
33C2×C3⋊#170—22no—
34C3×C5×C4⋊C4—21no—
35C3×C5×C4⋊C4C2×C412yes—
36C3×C4⋊Dic5—21no—
37C3×C4⋊Dic5—22no—
38C3×C4⋊Dic5—22no—
39C3×C4⋊Dic5C2×C412yes—
40C3×#683—22no—
41C3×#683—22no—
42C3×C4×Dic5C2×C411yescharacteristic
43C3×C4×Dic5D411yescharacteristic
44C3×C4×Dic5D411yescharacteristic
45C3×C4×Dic5C2311yescharacteristic
46C2×C3×#125—51no—
47#4926—51no—
48C4×#208—51no—
49#4543—54no—
50C2×#704—61no—
51C2×C5×C4⋊C4Dic311yescharacteristic
52C2×C4⋊Dic5—21no—
53C2×C4⋊Dic5Dic311yescharacteristic
54C2×#683—21no—
55C2×C4×Dic5C2×D311yescharacteristic
56#4036—21no—
57#4036—21no—
58#4036Dic312yes—
59#4036C2×D312yes—
60C22⋊#170—61no—
61#4002—32no—
62#4002—32no—
63C4⋊#170—61no—
64C4×#170—61no—
65#1528—151noSylow
66C23×C3×C5C22⋊C411yescharacteristic
67C2×C3×C4×C5—22no—
68C2×C3×C4×C5—22no—
69C2×C3×C4×C5—42no—
70C2×C3×C4×C5C22⋊C411yescharacteristic
71C2×C3×C4×C5C22×C411yescharacteristic
72C2×C3×Dic5—22no—
73C2×C3×Dic5—22no—
74C2×C3×Dic5—41no—
75C2×C3×Dic5—42no—
76C2×C3×Dic5C22⋊C411yescharacteristic
77C2×C3×Dic5C22⋊C411yescharacteristic
78C2×C3×Dic5C2×D411yescharacteristic
79C2×C3×Dic5C2×D411yescharacteristic
80C3⋊#170—24no—
81C3⋊#170—42no—
82C3×#125—52no—
83C3×#125—52no—
84C3×#125—101no—
85C3×#125—101no—
86C2×C3×C4⋊C4—51no—
87C2×C3×C4⋊C4—101no—
88C2×C3×C4⋊C4—101no—
89C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
90C2×C3×C42—51no—
91C2×#208—101no—
92#830—101no—
93C4⋊(C3⋊C8)—101no—
94#803—52no—
95#803—52no—
96C4×C3⋊C8—101no—
97C22×C4×C5—21no—
98C22×C4×C5C2×Dic311yescharacteristic
99C22×Dic5—21no—
100C22×Dic5#6711yescharacteristic
101C22×Dic5#6711yescharacteristic
102#704—64no—
103C2×#170—62no—
104C2×#170—62no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4C2×Dic312yes—
107C4⋊Dic5—21no—
108C4⋊Dic5—22no—
109C4⋊Dic5—22no—
110C4⋊Dic5C2×Dic312yes—
111#683—22no—
112#683—22no—
113C4×Dic5C2×Dic311yescharacteristic
114C4×Dic5#6711yescharacteristic
115C4×Dic5#6711yescharacteristic
116C4×Dic5C22×D311yescharacteristic
117C2×#125—51no—
118#432—151no—
119C4×M16—151no—
120#330—154no—
121C22×C3×C5—21no—
122C22×C3×C5—21no—
123C22×C3×C5#10412yes—
124C22×C3×C5C2×C22⋊C411yescharacteristic
125C3×C4×C5—21no—
126C3×C4×C5—42no—
127C3×C4×C5#10112yes—
128C3×Dic5—21no—
129C3×Dic5—21no—
130C3×Dic5—21no—
131C3×Dic5—21no—
132C3×Dic5—42no—
133C22×C3×C4—21no—
134C22×C3×C4—51no—
135C22×C3×C4—51no—
136C22×C3×C4—101no—
137C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
138C3×C4⋊C4—21no—
139C3×C4⋊C4—52no—
140C3×C4⋊C4—102no—
141C3×C4⋊C4—102no—
142C3×C4⋊C4—102no—
143C3×C4⋊C4—102no—
144C3×C4⋊C4—101no—
145C3×C4⋊C4C2×AGL(1,𝔽5)12yes—
146C3×C42—51no—
147C3×C42—51no—
148C3×C42—51no—
149C3×C42—51no—
150#208—104no—
151C2×C3⋊C8—102no—
152C2×C3⋊C8—102no—
153C23×C5#21711yescharacteristic
154C2×C4×C5—22no—
155C2×C4×C5—22no—
156C2×C4×C5—42no—
157C2×C4×C5#21711yescharacteristic
158C2×C4×C5C22×Dic311yescharacteristic
159C2×Dic5—22no—
160C2×Dic5—22no—
161C2×Dic5—41no—
162C2×Dic5—42no—
163C2×Dic5#21711yescharacteristic
164C2×Dic5#21711yescharacteristic
165C2×Dic5C2×#6711yescharacteristic
166C2×Dic5C2×#6711yescharacteristic
167#170—64no—
168#170—122no—
169C2×M16—301no—
170#125—52no—
171#125—52no—
172#125—101no—
173#125—101no—
174C2×C4⋊C4—51no—
175C2×C4⋊C4—101no—
176C2×C4⋊C4—101no—
177C2×C4⋊C4ΓL(1,𝔽16)11yescharacteristic
178C2×C42—51no—
179C4⋊C8—301no—
180C22⋊C8—301no—
181#97—152no—
182#97—152no—
183C4×C8—301no—
184C2×C3×C5—22no—
185C2×C3×C5C2×#10111yescharacteristic
186C2×C3×C5C2×#10411yescharacteristic
187C2×C3×C5#42111yescharacteristic
188C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—42no—
192C2×C3×C4—51no—
193C2×C3×C4—51no—
194C2×C3×C4—51no—
195C2×C3×C4—51no—
196C2×C3×C4—102no—
197C2×C3×C4—102no—
198C2×C3×C4—201no—
199C2×C3×C4—202no—
200C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
201C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
202C3⋊C8—104no—
203C3⋊C8—202no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5#83712yes—
207C22×C5C2×#21711yescharacteristic
208C4×C5—21no—
209C4×C5—42no—
210C4×C5#83612yes—
211Dic5—21no—
212Dic5—21no—
213Dic5—21no—
214Dic5—21no—
215Dic5—42no—
216C22×C4—21no—
217C22×C4—51no—
218C22×C4—51no—
219C22×C4—101no—
220C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
221M16—304no—
222C2×C8—302no—
223C2×C8—302no—
224C4⋊C4—21no—
225C4⋊C4—52no—
226C4⋊C4—102no—
227C4⋊C4—102no—
228C4⋊C4—102no—
229C4⋊C4—102no—
230C4⋊C4—101no—
231C4⋊C4C2×ΓL(1,𝔽16)12yes—
232C42—51no—
233C42—51no—
234C42—51no—
235C42—51no—
236C3×C5#152811yescharacteristic, complemented, Hall
237C22×C3—21no—
238C22×C3—21no—
239C22×C3#400812yes—
240C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
241C3×C4—21no—
242C3×C4—42no—
243C3×C4—101no—
244C3×C4—101no—
245C3×C4—101no—
246C3×C4—101no—
247C3×C4—202no—
248C3×C4#400512yes—
249C2×C5—22no—
250C2×C5C2×#83611yescharacteristic
251C2×C5C2×#83711yescharacteristic
252C2×C5#523611yescharacteristic
253C23#676311yescharacteristic
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—42no—
257C2×C4—51no—
258C2×C4—51no—
259C2×C4—51no—
260C2×C4—51no—
261C2×C4—102no—
262C2×C4—102no—
263C2×C4—201no—
264C2×C4—202no—
265C2×C4#676311yescharacteristic
266C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
267C8—304no—
268C8—602no—
269C2×C3—22no—
270C2×C3C2×#400511yescharacteristic
271C2×C3C2×#400811yescharacteristic
272C2×C3#6578411yescharacteristic
273C5#7173511yescharacteristic, complemented, Sylow
274C22—21no—
275C22—21no—
276C22#9123712yes—
277C22C2×#676311yescharacteristic
278C4—21no—
279C4—42no—
280C4—101no—
281C4—101no—
282C4—101no—
283C4—101no—
284C4—202no—
285C4#9123412yes—
286C3#1060426511yescharacteristic, complemented, Sylow
287C2—22no—
288C2C2×#9123411yescharacteristic
289C2C2×#9123711yescharacteristic
290C2#1175244311yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1528
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11746741C2semidirect
236. C3×C5#1528semidirect
273. C5#71735semidirect
286. C3#10604265semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40362
#117524182
C4×#67622
#117467412
#106042653
#717355