Finite Group Databasebeta

← #14313491

Subgroups — #14313491

Order 1920.

572 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 70 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#11752752C211yesmaximal, characteristic
2#11751852C212yesmaximal, complemented
3#11746724C211yesmaximal, characteristic, complemented
4C3×#64853C211yesmaximal, characteristic, complemented
5#11746556C212yesmaximal, complemented
6#10604546—31nomaximal, Hall
7C2×#6777C2211yescharacteristic
8C2×#6766C411yescharacteristic, complemented
9D3×C22⋊AGL(1,𝔽5)—22no—
10#91761C411yescharacteristic, complemented
11C5×#875C411yescharacteristic, complemented
12C3×#4020C2211yescharacteristic
13#91474—22no—
14#91463C411yescharacteristic, complemented
15#91408—22no—
16#91368C2211yescharacteristic
17#91228C2212yes—
18C3×#3999C2212yes—
19#91172—22no—
20#69150—51nomaximal, Hall
21#66008—31no—
22D5⋊#99—32no—
23#64928—32no—
24#64853—31no—
25#64853D311yescharacteristic, complemented
26C22×D3×D5D412yes—
27C2×D3×AGL(1,𝔽5)—42no—
28C2×C4×D15C2×C411yescharacteristic
29C2×C5×D12C2×C411yescharacteristic
30C2×C5×Dic6C2×C411yescharacteristic, complemented
31C2×C3×D20—22no—
32C2×C3×D20C2×C411yescharacteristic, complemented
33C2×C3×D20C2311yescharacteristic
34C2×#1202—21no—
35C2×#1201—22no—
36C2×#1201D412yes—
37C2×D5×Dic3—21no—
38#6777—42no—
39#6766—42no—
40#6763—22no—
41C3×C22⋊AGL(1,𝔽5)—22no—
42(C2×D3)⋊AGL(1,𝔽5)—42no—
43C3×C42×C5C2×C411yescharacteristic, complemented
44#6714—21no—
45#6712—21no—
46C4×Dic15C2×C411yescharacteristic, complemented
47C5×(C2×D3)⋊C4—22no—
48#6665—22no—
49#5715—51no—
50D3×#99—52no—
51C3×#353—51no—
52#4545—51no—
53#4473—52no—
54C2×#713—31no—
55C2×D4×D5—31no—
56C2×C22⋊AGL(1,𝔽5)—62no—
57C5×#124—31no—
58#4093—31no—
59#4086—31no—
60#4030—62no—
61#4028—62no—
62#4020C2×D311yescharacteristic
63#4018—31no—
64#4011—62no—
65#3999—32no—
66#3999C2×D312yes—
67#2127—151noSylow
68C22×D15C22⋊C411yescharacteristic
69C22×C5×D3C22⋊C412yes—
70C22×C3×D5—21no—
71C22×C3×D5C2×D412yes—
72C2×D3×D5—22no—
73C2×D3×D5—22no—
74C2×D3×D5—82no—
75C2×ΓL(1,𝔽16)—42no—
76C2×C3×AGL(1,𝔽5)—42no—
77D3×AGL(1,𝔽5)—84no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5C22×C411yescharacteristic
80C2×Dic15—21no—
81C2×Dic15C22⋊C411yescharacteristic
82C4×D15—22no—
83C2×C5×Dic3—21no—
84C5×D12—41no—
85C5×Dic6—41no—
86C3×D20—41no—
87C3×D20—41no—
88C3×D20—82no—
89#1202—42no—
90#1201—42no—
91#1201—82no—
92D5×Dic3—42no—
93C2×#237—51no—
94C2×D3×D4—51no—
95C3×#127—51no—
96#940—51no—
97#939—102no—
98#937—102no—
99#936—51no—
100D3×C22⋊C4—102no—
101#875AGL(1,𝔽5)11yescharacteristic, complemented
102#872—51no—
103C3×#99—52no—
104#834—52no—
105#806—102no—
106C23×D5—32no—
107C22×AGL(1,𝔽5)—122no—
108C2×C5×Q8—31no—
109C2×C5×D4—31no—
110C2×C22⋊D5—32no—
111C2×C22⋊D5—62no—
112#713—122no—
113D4×D5—122no—
114C2×D20—22no—
115C2×D20—61no—
116C2×D20C4×D311yescharacteristic, complemented
117C2×D20C22×D311yescharacteristic
118C2×C4×D5—31no—
119C2×C4×D5—61no—
120C22⋊AGL(1,𝔽5)—22no—
121C22⋊AGL(1,𝔽5)—62no—
122C22⋊AGL(1,𝔽5)—122no—
123C5×C22⋊C4—62no—
124C42×C5C4×D311yescharacteristic, complemented
125#685—61no—
126#685—62no—
127#683—61no—
128C4×Dic5—31no—
129#535—151no—
130C2×#99—152no—
131#354—152no—
132#353—51no—
133#353—151no—
134C22×C3×C5C2×C22⋊C411yescharacteristic
135C2×D15—41no—
136C2×D15#9912yes—
137C2×C5×D3—22no—
138C2×C5×D3—42no—
139C2×C3×D5—22no—
140C2×C3×D5—42no—
141C2×C3×D5—42no—
142C2×C3×D5—41no—
143D3×D5—44no—
144D3×D5—82no—
145ΓL(1,𝔽16)—82no—
146C3×AGL(1,𝔽5)—82no—
147C3×C4×C5—21no—
148C3×C4×C5—41no—
149Dic15—21no—
150Dic15—41no—
151C5×Dic3—41no—
152C23×D3—52no—
153C2×C3×D4—51no—
154C2×C3×D4—51no—
155C2×C3×D4—102no—
156C2×#67—52no—
157C2×#67—101no—
158C2×#67—102no—
159C22×Dic3—101no—
160#237—202no—
161D3×D4—202no—
162C2×D12C2×AGL(1,𝔽5)11yescharacteristic
163C2×C4×D3—51no—
164C2×C4×D3—202no—
165C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
166C3×C22⋊C4—102no—
167C3×C42C2×AGL(1,𝔽5)11yescharacteristic, complemented
168#217—102no—
169#217—102no—
170(C2×D3)⋊C4—22no—
171(C2×D3)⋊C4—101no—
172(C2×D3)⋊C4—202no—
173Dic3⋊C4—101no—
174C4×Dic3—51no—
175C23×C5—32no—
176C22×D5—21no—
177C22×D5—31no—
178C22×D5—62no—
179C22×D5—62no—
180C22×D5—242no—
181C22×D5D3×D412yes—
182C2×AGL(1,𝔽5)—42no—
183C2×AGL(1,𝔽5)—122no—
184C2×AGL(1,𝔽5)—244no—
185C5×Q8—121no—
186C5×D4—121no—
187C2×C4×C5—21no—
188C2×C4×C5—61no—
189C2×C4×C5C2×C4×D311yescharacteristic
190C22⋊D5—122no—
191C22⋊D5—242no—
192C2×Dic5—31no—
193C2×Dic5—61no—
194D20—41no—
195D20—41no—
196D20—82no—
197D20—122no—
198C4×D5—62no—
199C4×D5—122no—
200C2×#41—151no—
201C22×D4—151no—
202#127—51no—
203#127—151no—
204#124—31no—
205#124—151no—
206#121—302no—
207#120—302no—
208#117—151no—
209C2×C22⋊C4—302no—
210#99—52no—
211#99—152no—
212#99—302no—
213C2×C3×C5—21no—
214C2×C3×C5C2×#9911yescharacteristic
215D15—22no—
216C3×D5—42no—
217C3×D5—81no—
218C5×D3—42no—
219C23×C3—52no—
220C23×C3—101no—
221C22×D3—51no—
222C22×D3—102no—
223C22×D3—102no—
224C22×D3—402no—
225C22×D3C22⋊AGL(1,𝔽5)12yes—
226C3×D4—201no—
227C3×D4—201no—
228C3×D4—402no—
229C2×C3×C4—21no—
230C2×C3×C4—202no—
231C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
232#67—202no—
233#67—202no—
234#67—402no—
235C2×Dic3—21no—
236C2×Dic3—51no—
237C2×Dic3—101no—
238C2×Dic3—202no—
239C2×Dic3—202no—
240D12—41no—
241C4×D3—102no—
242C4×D3—404no—
243Dic6—41no—
244C22×C5—62no—
245C22×C5—122no—
246C22×C5D3×C22⋊C411yescharacteristic
247C2×D5—22no—
248C2×D5—32no—
249C2×D5—42no—
250C2×D5—42no—
251C2×D5—41no—
252C2×D5—124no—
253C2×D5—121no—
254C2×D5—242no—
255AGL(1,𝔽5)—82no—
256AGL(1,𝔽5)—242no—
257C4×C5—21no—
258C4×C5—41no—
259C4×C5—121no—
260Dic5—61no—
261Dic5—121no—
262C24—152no—
263#41—602no—
264C2×Q8—31no—
265C2×D4—31no—
266C2×D4—51no—
267C2×D4—51no—
268C2×D4—102no—
269C2×D4—152no—
270C2×D4—301no—
271C2×D4—302no—
272C2×D4—602no—
273C22×C4—151no—
274C22×C4—301no—
275C22×C4—602no—
276C4⋊C4—301no—
277C22⋊C4—62no—
278C22⋊C4—102no—
279C22⋊C4—301no—
280C22⋊C4—302no—
281C22⋊C4—302no—
282C22⋊C4—602no—
283C42—151no—
284C42D3×AGL(1,𝔽5)11yescharacteristic, complemented
285C3×C5#212711yescharacteristic, complemented, Hall
286C22×C3—102no—
287C22×C3—202no—
288C22×C3—202no—
289C22×C3—201no—
290C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
291C2×D3—22no—
292C2×D3—42no—
293C2×D3—52no—
294C2×D3—204no—
295C2×D3—201no—
296C2×D3—402no—
297C3×C4—21no—
298C3×C4—41no—
299C3×C4—402no—
300Dic3—41no—
301Dic3—101no—
302Dic3—201no—
303Dic3—402no—
304C2×C5—21no—
305C2×C5—122no—
306C2×C5D3×#9911yescharacteristic
307D5—42no—
308D5—62no—
309D5—81no—
310C23—32no—
311C23—52no—
312C23—101no—
313C23—151no—
314C23—302no—
315C23—302no—
316C23—1202no—
317Q8—121no—
318D4—121no—
319D4—201no—
320D4—201no—
321D4—402no—
322D4—602no—
323D4—602no—
324D4—1202no—
325C2×C4—21no—
326C2×C4—61no—
327C2×C4—151no—
328C2×C4—202no—
329C2×C4—302no—
330C2×C4—301no—
331C2×C4—602no—
332C2×C4—602no—
333C2×C4—1204no—
334C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
335C2×C3—21no—
336C2×C3—202no—
337C2×C3—401no—
338C2×C3D5⋊#9911yescharacteristic
339D3—42no—
340D3—102no—
341C5#6915011yescharacteristic, complemented, Sylow
342C22—62no—
343C22—102no—
344C22—122no—
345C22—152no—
346C22—202no—
347C22—202no—
348C22—201no—
349C22—601no—
350C22—604no—
351C22—1202no—
352C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
353C4—21no—
354C4—41no—
355C4—121no—
356C4—301no—
357C4—402no—
358C4—601no—
359C4—1202no—
360C3#1060454611yescharacteristic, complemented, Sylow
361C2—21no—
362C2—122no—
363C2—202no—
364C2—302no—
365C2—401no—
366C2#1175185211yescharacteristic
subgroupG/H
centerC2#11751852
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC2×C3×C5C2×#99
prime radical#11752752C2
cosocleC2×C3×D20C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#2127
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
2. #11751852C2semidirect
3. #11746724C2semidirect
4. C3×#64853C2semidirect
5. #11746556C2semidirect
8. C2×#6766C4semidirect
10. #91761C4semidirect
11. C5×#875C4semidirect
14. #91463C4semidirect
25. #64853D3semidirect
30. C2×C5×Dic6C2×C4semidirect
32. C2×C3×D20C2×C4semidirect
43. C3×C42×C5C2×C4semidirect
46. C4×Dic15C2×C4semidirect
101. #875AGL(1,𝔽5)semidirect
116. C2×D20C4×D3semidirect
124. C42×C5C4×D3semidirect
165. C2×Dic6C2×AGL(1,𝔽5)semidirect
167. C3×C42C2×AGL(1,𝔽5)semidirect
284. C42D3×AGL(1,𝔽5)semidirect
285. C3×C5#2127semidirect
341. C5#69150semidirect
360. C3#10604546semidirect

Maximal subgroups

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

subgroupindex
#117527522
#117518522
#117467242
C3×#648532
#117465562
#106045463
#691505