Finite Group Databasebeta

← #14281850

Subgroups — #14281850

Order 1920.

432 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 118 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#11752506C211yesmaximal, characteristic
2D5⋊(C4⋊(C3⋊C8))C211yesmaximal, characteristic
3C3×#65680C211yesmaximal, characteristic
4#11746493C214yesmaximal, complemented
5#10604645—31nomaximal, Hall
6C2×D5⋊(C3⋊C8)—21no—
7#91758C411yescharacteristic
8C5×#869C411yescharacteristic
9C3×C42×D5C2211yescharacteristic
10#91388—21no—
11#91360—21no—
12#91359C412yes—
13#91358—21no—
14#91333—21no—
15Dic5×Dic6C2212yes—
16#91233—21no—
17C4⋊(C3⋊#170)C2212yes—
18C3×#4003—21no—
19C3×C4⋊#170—21no—
20C3×C4×#170C2212yes—
21#70768—51nomaximal, Hall
22#66062—31no—
23#65680D311yescharacteristic
24D5⋊(C4⋊C8)—31no—
25Q8⋊#170—34no—
26C2×Dic30—21no—
27C2×C5×Dic6C2×C412yes—
28C2×C3×C4×D5C2×C411yescharacteristic
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C4×D5D411yescharacteristic
31C2×C3⋊#170—22no—
32D5⋊(C3⋊C8)—42no—
33C2×C3×#170—22no—
34C3×C42×C5C2×C411yescharacteristic
35C4⋊Dic15—21no—
36C4⋊Dic15C2×C412yes—
37C5×C4⋊Dic3—21no—
38C5×C4⋊Dic3—21no—
39C3×C4×Dic5D411yescharacteristic
40C3×C4×Dic5D411yescharacteristic
41C3×C4×Dic5C2311yescharacteristic
42Dic3⋊Dic5—22no—
43#6669—22no—
44#6665—22no—
45Dic3×Dic5—22no—
46#5470—51no—
47C3×#431—51no—
48C2×C4⋊(C3⋊C8)—51no—
49#4456—54no—
50C2×D5⋊C8—61no—
51C5×C4⋊Q8—31no—
52#4092—32no—
53Q8×Dic5—32no—
54#4043—61no—
55#4038—61no—
56#4036—61no—
57#4033—61no—
58C42×D5C2×D311yescharacteristic
59#4015—31no—
60#4004—61no—
61#4003—21no—
62C4⋊#170—21no—
63C4⋊#170—32no—
64C4×#170C2×D312yes—
65#1481—151noSylow
66C22×C3×D5C22⋊C411yescharacteristic
67C2×C3×C4×C5C22⋊C411yescharacteristic
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22×C411yescharacteristic
70C2×Dic15—22no—
71Dic30—42no—
72C2×C5×Dic3—22no—
73C5×Dic6—24no—
74C2×C3×Dic5C22⋊C411yescharacteristic
75C2×C3×Dic5C2×D411yescharacteristic
76C2×C3×Dic5C2×D411yescharacteristic
77C3×C4×D5—22no—
78C3×C4×D5—41no—
79C3×C4×D5SD1612yes—
80C3×C4×D5Q1612yes—
81C3⋊#170—42no—
82C3×#170—42no—
83C2×C3×C42—51no—
84#926—101no—
85#924—52no—
86#924—101no—
87C22×C3⋊C8—101no—
88#870—101no—
89#869—51no—
90#869AGL(1,𝔽5)11yescharacteristic
91C4×Dic6—52no—
92C4×Dic6—101no—
93C3×C4⋊C8—101no—
94C3×C22⋊C8—101no—
95C3×C4×C8—52no—
96C4⋊(C3⋊C8)—52no—
97C4⋊(C3⋊C8)—101no—
98C2×C5×Q8—32no—
99C2×C4×D5C4×D311yescharacteristic
100C2×C4×D5D1211yescharacteristic
101C2×C4×D5#6711yescharacteristic
102C2×Dic10—61no—
103C2×#170—22no—
104C2×#170—62no—
105D5⋊C8—122no—
106C5×C4⋊C4—61no—
107C5×C4⋊C4—61no—
108C42×C5C4×D311yescharacteristic
109#685—62no—
110C4⋊Dic5—32no—
111C4⋊Dic5—61no—
112C4⋊Dic5—62no—
113#683—62no—
114C4×Dic5—62no—
115C4×Dic5D1211yescharacteristic
116C4×Dic5#6711yescharacteristic
117C4×Dic5C22×D311yescharacteristic
118#533—151no—
119#431—51no—
120C2×C4⋊C8—151no—
121Q8⋊C8—154no—
122C22×C3×C5C2×C22⋊C411yescharacteristic
123C2×C3×D5—21no—
124C2×C3×D5—21no—
125C2×C3×D5#10312yes—
126C3×C4×C5—21no—
127C3×C4×C5#10312yes—
128C3×C4×C5#13112yes—
129Dic15—42no—
130C3×Dic5—21no—
131C3×Dic5—21no—
132C3×Dic5C2×SD1611yescharacteristic
133C3×Dic5C2×Q1611yescharacteristic
134C5×Dic3—42no—
135C22×C3×C4—51no—
136C22×C3×C4—51no—
137C22×C3×C4—51no—
138C2×Dic6—101no—
139C2×Dic6C2×AGL(1,𝔽5)12yes—
140C2×C3×C8—102no—
141C3×C42—51no—
142C3×C42—51no—
143C3×C42—51no—
144C3×C42C2×AGL(1,𝔽5)11yescharacteristic
145#217—102no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C4⋊Dic3—52no—
149C4⋊Dic3—101no—
150Dic3⋊C4—102no—
151Dic3⋊C4—102no—
152C4×Dic3—102no—
153C2×C3⋊C8—102no—
154C2×C3⋊C8—202no—
155C22×D5(C2×D3)⋊C411yescharacteristic
156C5×Q8—64no—
157C2×C4×C5—62no—
158C2×C4×C5(C2×D3)⋊C411yescharacteristic
159C2×C4×C5(C2×D3)⋊C411yescharacteristic
160C2×C4×C5C2×C4×D311yescharacteristic
161C2×Dic5—62no—
162C2×Dic5(C2×D3)⋊C411yescharacteristic
163C2×Dic5C2×D1211yescharacteristic
164C2×Dic5C2×#6711yescharacteristic
165C4×D5—22no—
166C4×D5—41no—
167C4×D5#20412yes—
168C4×D5Dic1212yes—
169Dic10—122no—
170#170—42no—
171#170—122no—
172C22×C8—301no—
173C4⋊Q8—31no—
174C4⋊Q8—151no—
175#125—301no—
176C22⋊Q8—152no—
177C22⋊Q8—301no—
178C4×Q8—152no—
179C4×Q8—301no—
180#117—301no—
181C2×C42—51no—
182C4⋊C8—101no—
183C4⋊C8—152no—
184C4⋊C8—301no—
185C22⋊C8—101no—
186C4×C8—52no—
187C2×C3×C5#40811yescharacteristic
188C2×C3×C5C2×#10311yescharacteristic
189C2×C3×C5#42111yescharacteristic
190C3×D5—22no—
191C23×C3—51no—
192C2×C3×C4—51no—
193C2×C3×C4—52no—
194C2×C3×C4—52no—
195C2×C3×C4—51no—
196C2×C3×C4—51no—
197C2×C3×C4—102no—
198C2×C3×C4—201no—
199C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
200C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
201C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
202C2×Dic3—22no—
203C2×Dic3—102no—
204Dic6—24no—
205Dic6—202no—
206C3×C8—202no—
207C3⋊C8—202no—
208C22×C5C2×(C2×D3)⋊C411yescharacteristic
209C2×D5—21no—
210C2×D5—21no—
211C2×D5#81612yes—
212C4×C5—21no—
213C4×C5—122no—
214C4×C5#81612yes—
215C4×C5#90712yes—
216Dic5—21no—
217Dic5—21no—
218Dic5—122no—
219Dic5C2×#20411yescharacteristic
220Dic5C2×Dic1211yescharacteristic
221C2×Q8—32no—
222C2×Q8—301no—
223C22×C4—51no—
224C22×C4—51no—
225C22×C4—51no—
226C2×C8—102no—
227C2×C8—302no—
228C2×C8—602no—
229C4⋊C4—61no—
230C4⋊C4—61no—
231C4⋊C4—152no—
232C4⋊C4—302no—
233C4⋊C4—302no—
234C4⋊C4—301no—
235C22⋊C4—302no—
236C42—51no—
237C42—51no—
238C42—51no—
239C42—302no—
240C42D3×AGL(1,𝔽5)11yescharacteristic
241C3×C5#148111yescharacteristic, complemented, Hall
242C22×C3—52no—
243C22×C3—101no—
244C22×C3—101no—
245C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
246C3×C4—21no—
247C3×C4—51no—
248C3×C4—51no—
249C3×C4—101no—
250C3×C4—101no—
251C3×C4#400912yes—
252C3×C4#413112yes—
253Dic3—42no—
254Dic3—202no—
255C2×C5#500511yescharacteristic
256C2×C5C2×#81611yescharacteristic
257C2×C5#512911yescharacteristic
258D5—22no—
259C23—51no—
260Q8—64no—
261Q8—602no—
262C2×C4—51no—
263C2×C4—52no—
264C2×C4—52no—
265C2×C4—51no—
266C2×C4—51no—
267C2×C4—62no—
268C2×C4—102no—
269C2×C4—201no—
270C2×C4—302no—
271C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
272C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
273C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
274C8—202no—
275C8—602no—
276C2×C3—102no—
277C2×C3#6577611yescharacteristic
278C2×C3C2×#400911yescharacteristic
279C2×C3#6578411yescharacteristic
280C5#7076811yescharacteristic, complemented, Sylow
281C22—52no—
282C22—101no—
283C22—101no—
284C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
285C4—21no—
286C4—51no—
287C4—51no—
288C4—101no—
289C4—101no—
290C4—122no—
291C4—602no—
292C4#9115412yes—
293C4#9191312yes—
294C3#1060464511yescharacteristic, complemented, Sylow
295C2—102no—
296C2C2×#9115411yescharacteristic
297C2#1175172411yescharacteristic
298C2#1175181111yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1481
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
4. #11746493C2semidirect
241. C3×C5#1481semidirect
280. C5#70768semidirect
294. C3#10604645semidirect

Maximal subgroups

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

subgroupindex
#117525062
D5⋊(C4⋊(C3⋊C8))2
C3×#656802
#117464932
#106046453
#707685