Finite Group Databasebeta

← #14313555

Subgroups — #14313555

Order 1920.

476 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 72 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#11752544C211yesmaximal, characteristic
2#11751862C212yesmaximal
3#11746725C211yesmaximal, characteristic, complemented
4C3×#64854C211yesmaximal, characteristic, complemented
5#11746557C212yesmaximal, complemented
6#10604355—31nomaximal, Hall
7C2×D3×Dic10C411yescharacteristic, complemented
8C2×#6765C2211yescharacteristic
9#91923—22no—
10#91758C411yescharacteristic, complemented
11C5×#872C411yescharacteristic, complemented
12C3×#4021C2211yescharacteristic
13#91457—22no—
14#91422—22no—
15#91389C411yescharacteristic, complemented
16#91364C2211yescharacteristic
17#91228C2212yes—
18C3×#3999C2212yes—
19#91172—22no—
20#69159—51nomaximal, Hall
21#65860—31no—
22#65745—32no—
23#64854—31no—
24#64854—32no—
25#64854D311yescharacteristic, complemented
26C2×Dic30C2×C411yescharacteristic
27C2×Dic30C2×C411yescharacteristic
28C2×C4×C5×D3C2×C411yescharacteristic
29C2×C3×D20C2311yescharacteristic
30C2×C3×Dic10C2×C411yescharacteristic
31C2×#1204—21no—
32C2×#1201D412yes—
33C2×D3×Dic5—21no—
34C2×D5×Dic3D412yes—
35D3×Dic10—42no—
36#6765—42no—
37#6763—22no—
38C3×C22⋊AGL(1,𝔽5)—22no—
39Dic3⋊AGL(1,𝔽5)—42no—
40Dic3×AGL(1,𝔽5)—42no—
41C3×C42×C5C2×C411yescharacteristic
42C4⋊Dic15—22no—
43C5×(C2×D3)⋊C4—21no—
44C5×Dic3⋊C4—21no—
45C4×C5×Dic3C2×C411yescharacteristic
46C3×#685—22no—
47Dic3⋊Dic5—22no—
48#6665—22no—
49#5675—51no—
50#4740—52no—
51C3×#354—51no—
52#4541—51no—
53#4473—52no—
54C2×#709—31no—
55C22×Dic10—31no—
56#4130—62no—
57C5×#117—31no—
58#4043—62no—
59#4032—62no—
60#4021—31no—
61#4021C2×D311yescharacteristic
62#4015—31no—
63#4015—31no—
64#4011—62no—
65#3999—32no—
66#3999C2×D312yes—
67#2129—151noSylow
68C22×C5×D3C22⋊C411yescharacteristic
69C22×C3×D5C2×D412yes—
70C2×ΓL(1,𝔽16)—42no—
71C2×C3×AGL(1,𝔽5)—42no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×Dic15—21no—
75C2×Dic15C22⋊C412yes—
76Dic30—41no—
77Dic30—41no—
78C2×C5×Dic3—21no—
79C2×C5×Dic3C22⋊C411yescharacteristic
80C4×C5×D3—22no—
81C2×C3×Dic5—21no—
82C3×D20—41no—
83C3×Dic10—41no—
84#1204—42no—
85#1201—42no—
86D3×Dic5—42no—
87D5×Dic3—22no—
88D5×Dic3—22no—
89C2×D3×Q8—51no—
90C2×#237—51no—
91C3×#124—51no—
92#944—51no—
93#936—51no—
94#883—102no—
95#878—102no—
96#877—102no—
97#872AGL(1,𝔽5)11yescharacteristic, complemented
98#869—51no—
99C3×#99—52no—
100#834—52no—
101#806—102no—
102C22×C4×C5—31no—
103C2×C22⋊D5—32no—
104C22×Dic5—61no—
105#709—122no—
106C2×D20C22×D311yescharacteristic
107C2×C4×D5—32no—
108C2×Dic10—31no—
109C2×Dic10—31no—
110C2×Dic10—61no—
111C2×Dic10—122no—
112C2×Dic10C4×D311yescharacteristic
113C22⋊AGL(1,𝔽5)—22no—
114C22⋊AGL(1,𝔽5)—62no—
115C4⋊AGL(1,𝔽5)—122no—
116C4×AGL(1,𝔽5)—122no—
117C5×C4⋊C4—61no—
118C5×C22⋊C4—61no—
119C42×C5—31no—
120C42×C5C4×D311yescharacteristic
121#685—22no—
122#685—62no—
123C4⋊Dic5—62no—
124C4⋊Dic5—62no—
125#536—151no—
126#410—152no—
127#354—51no—
128#354—152no—
129#354—151no—
130C22×C3×C5C2×C22⋊C411yescharacteristic
131C2×C5×D3—21no—
132C2×C5×D3—41no—
133C2×C3×D5—22no—
134C2×C3×D5—42no—
135ΓL(1,𝔽16)—82no—
136C3×AGL(1,𝔽5)—82no—
137C3×C4×C5—21no—
138C3×C4×C5—41no—
139Dic15—22no—
140Dic15—41no—
141C3×Dic5—41no—
142C5×Dic3—41no—
143C5×Dic3#9912yes—
144C2×C3×Q8—51no—
145C2×C3×D4—51no—
146C2×#67—52no—
147C22×Dic3—52no—
148D3×Q8—202no—
149#237—202no—
150C2×C4×D3—101no—
151C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
152C2×Dic6—51no—
153C2×Dic6—51no—
154C2×Dic6—101no—
155C3×C22⋊C4—102no—
156C3×C22⋊C4—102no—
157C3×C42C2×AGL(1,𝔽5)11yescharacteristic
158#217—102no—
159#217—102no—
160(C2×D3)⋊C4—21no—
161C4⋊Dic3—102no—
162Dic3⋊C4—21no—
163Dic3⋊C4—102no—
164Dic3⋊C4—202no—
165C4×Dic3—202no—
166C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
167C23×C5—31no—
168C22×D5D3×D412yes—
169C2×AGL(1,𝔽5)—42no—
170C2×AGL(1,𝔽5)—122no—
171C2×C4×C5—21no—
172C2×C4×C5—31no—
173C2×C4×C5—62no—
174C2×C4×C5—61no—
175C2×C4×C5C2×C4×D311yescharacteristic
176C22⋊D5—122no—
177C2×Dic5—21no—
178C2×Dic5—32no—
179C2×Dic5—61no—
180C2×Dic5—122no—
181D20—41no—
182C4×D5—62no—
183C4×D5—62no—
184Dic10—41no—
185Dic10—122no—
186Dic10—121no—
187Dic10—121no—
188C2×#41—151no—
189C22×Q8—151no—
190C4⋊Q8—151no—
191C4⋊Q8—151no—
192#124—51no—
193#124—151no—
194#123—302no—
195C22⋊Q8—302no—
196#117—31no—
197#117—302no—
198#99—52no—
199#99—152no—
200#99—302no—
201C2×C3×C5—21no—
202C2×C3×C5C2×#9911yescharacteristic
203C3×D5—42no—
204C5×D3—41no—
205C23×C3—52no—
206C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
207C3×Q8—201no—
208C3×D4—201no—
209C2×C3×C4—21no—
210C2×C3×C4—101no—
211C2×C3×C4—202no—
212C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
213#67—202no—
214C2×Dic3—21no—
215C2×Dic3—52no—
216C2×Dic3—102no—
217C2×Dic3—102no—
218C2×Dic3—101no—
219C2×Dic3—202no—
220C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
221C4×D3—22no—
222C4×D3—202no—
223Dic6—201no—
224Dic6—202no—
225Dic6—201no—
226C22×C5—61no—
227C22×C5—121no—
228C22×C5D3×C22⋊C411yescharacteristic
229C2×D5—22no—
230C2×D5—42no—
231AGL(1,𝔽5)—82no—
232AGL(1,𝔽5)—242no—
233C4×C5—21no—
234C4×C5—32no—
235C4×C5—41no—
236C4×C5—121no—
237Dic5—41no—
238Dic5—62no—
239Dic5—121no—
240#41—602no—
241C2×Q8—51no—
242C2×Q8—151no—
243C2×Q8—151no—
244C2×Q8—301no—
245C2×Q8—602no—
246C2×D4—51no—
247C2×D4—152no—
248C22×C4—31no—
249C22×C4—152no—
250C22×C4—301no—
251C4⋊C4—61no—
252C4⋊C4—302no—
253C4⋊C4—302no—
254C4⋊C4—602no—
255C22⋊C4—61no—
256C22⋊C4—102no—
257C22⋊C4—102no—
258C22⋊C4—302no—
259C22⋊C4—302no—
260C42—31no—
261C42—602no—
262C42D3×AGL(1,𝔽5)11yescharacteristic
263C3×C5#212911yescharacteristic, complemented, Hall
264C22×C3—102no—
265C22×C3—202no—
266C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
267C2×D3—21no—
268C2×D3—41no—
269C3×C4—21no—
270C3×C4—41no—
271C3×C4—201no—
272C3×C4—402no—
273Dic3—41no—
274Dic3—102no—
275Dic3—201no—
276Dic3—402no—
277Dic3#399912yes—
278C2×C5—21no—
279C2×C5—121no—
280C2×C5D3×#9911yescharacteristic
281D5—42no—
282C23—31no—
283C23—52no—
284Q8—201no—
285Q8—601no—
286Q8—601no—
287Q8—602no—
288D4—201no—
289D4—602no—
290C2×C4—21no—
291C2×C4—31no—
292C2×C4—62no—
293C2×C4—61no—
294C2×C4—101no—
295C2×C4—152no—
296C2×C4—202no—
297C2×C4—302no—
298C2×C4—302no—
299C2×C4—301no—
300C2×C4—602no—
301C2×C4—602no—
302C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
303C2×C3—21no—
304C2×C3—202no—
305C2×C3C2×#399911yescharacteristic
306D3—41no—
307C5#6915911yescharacteristic, complemented, Sylow
308C22—61no—
309C22—102no—
310C22—121no—
311C22—202no—
312C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
313C4—21no—
314C4—32no—
315C4—41no—
316C4—121no—
317C4—201no—
318C4—302no—
319C4—402no—
320C4—601no—
321C4—1202no—
322C3#1060435511yescharacteristic, complemented, Sylow
323C2—21no—
324C2—121no—
325C2—202no—
326C2D3×#399911yescharacteristic
subgroupG/H
centerC2D3×#3999
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC2×C3×C5C2×#99
prime radicalC2×#6765C22
cosocleC2×C3×D20C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#2129
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #11746725C2semidirect
4. C3×#64854C2semidirect
5. #11746557C2semidirect
7. C2×D3×Dic10C4semidirect
10. #91758C4semidirect
11. C5×#872C4semidirect
15. #91389C4semidirect
25. #64854D3semidirect
97. #872AGL(1,𝔽5)semidirect
263. C3×C5#2129semidirect
307. C5#69159semidirect
322. C3#10604355semidirect

Maximal subgroups

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

subgroupindex
#117525442
#117518622
#117467252
C3×#648542
#117465572
#106043553
#691595