Finite Group Databasebeta

← #14313494

Subgroups — #14313494

Order 1920.

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

normal subgroups only

This group has 572 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#11752744C211yesmaximal, characteristic
2D3×#3999C212yesmaximal, complemented
3#11746725C211yesmaximal, characteristic, complemented
4C3×#64854C211yesmaximal, characteristic, complemented
5#11746555C212yesmaximal, complemented
6#10604353—31nomaximal, Hall
7C2×D3×D20C2211yescharacteristic
8C2×#6769C411yescharacteristic, complemented
9D3×C22⋊AGL(1,𝔽5)—22no—
10#91763C411yescharacteristic, complemented
11C5×#872C411yescharacteristic, complemented
12C3×#4021C2211yescharacteristic
13#91476—22no—
14#91459—22no—
15#91458C2211yescharacteristic
16#91374C411yescharacteristic, complemented
17#91228C2212yes—
18C3×#3999C2212yes—
19#91173—22no—
20#69157—51nomaximal, Hall
21#65859—31no—
22C2×#3999—32no—
23#64854—31no—
24#64854D311yescharacteristic, complemented
25#64853—32no—
26C22×D3×D5D412yes—
27C2×D3×AGL(1,𝔽5)—42no—
28C2×D60—22no—
29C2×D60C2×C411yescharacteristic
30C2×D60C2×C411yescharacteristic, complemented
31C2×C4×C5×D3C2×C411yescharacteristic
32C2×C3×D20C2311yescharacteristic
33C2×C3×Dic10C2×C411yescharacteristic, complemented
34C2×#1203—21no—
35C2×#1202—22no—
36C2×#1202D412yes—
37C2×#1200—21no—
38D3×D20—42no—
39#6769—42no—
40#6763—22no—
41C3×C22⋊AGL(1,𝔽5)—22no—
42(C2×D3)⋊AGL(1,𝔽5)—42no—
43C3×C42×C5C2×C411yescharacteristic, complemented
44C5×(C2×D3)⋊C4—21no—
45C5×Dic3⋊C4—21no—
46C4×C5×Dic3C2×C411yescharacteristic, complemented
47C3×#685—22no—
48#6667—22no—
49#5674—51no—
50D3×#99—52no—
51C3×#354—51no—
52#4541—51no—
53#4474—52no—
54C2×#709—31no—
55C22×D20—31no—
56C2×C22⋊AGL(1,𝔽5)—62no—
57C5×#117—31no—
58#4041—62no—
59#4028—62no—
60#4021—31no—
61#4021C2×D311yescharacteristic
62#4020—31no—
63#4020—31no—
64#3999—32no—
65#3999—62no—
66#3999C2×D312yes—
67#2127—151noSylow
68C22×D15—21no—
69C22×D15C22⋊C412yes—
70C22×C5×D3C22⋊C411yescharacteristic
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
80D60—41no—
81D60—41no—
82D60—82no—
83C2×C5×Dic3—21no—
84C2×C5×Dic3C22⋊C411yescharacteristic
85C4×C5×D3—22no—
86C2×C3×Dic5—21no—
87C3×D20—41no—
88C3×Dic10—41no—
89#1203—42no—
90#1202—42no—
91#1202—82no—
92#1200—42no—
93C2×#239—51no—
94C2×D3×D4—51no—
95C3×#124—51no—
96#947—51no—
97#940—51no—
98#884—102no—
99#882—102no—
100D3×C22⋊C4—102no—
101#874—51no—
102#872AGL(1,𝔽5)11yescharacteristic, complemented
103C3×#99—52no—
104#834—52no—
105#806—102no—
106C23×D5—32no—
107C22×AGL(1,𝔽5)—122no—
108C22×C4×C5—31no—
109C2×C22⋊D5—61no—
110#709—122no—
111C2×D20—32no—
112C2×D20—31no—
113C2×D20—31no—
114C2×D20—62no—
115C2×D20—62no—
116C2×D20—122no—
117C2×D20C22×D311yescharacteristic
118C2×C4×D5—61no—
119C2×Dic10C4×D311yescharacteristic, complemented
120C22⋊AGL(1,𝔽5)—22no—
121C22⋊AGL(1,𝔽5)—62no—
122C22⋊AGL(1,𝔽5)—122no—
123C5×C4⋊C4—61no—
124C5×C22⋊C4—61no—
125C42×C5—31no—
126C42×C5C4×D311yescharacteristic, complemented
127#685—22no—
128#685—62no—
129#535—151no—
130C2×#99—152no—
131#354—51no—
132#354—151no—
133#353—152no—
134C22×C3×C5C2×C22⋊C411yescharacteristic
135C2×D15—22no—
136C2×D15—42no—
137C2×D15—42no—
138C2×D15—41no—
139C2×C5×D3—41no—
140C2×C5×D3#9912yes—
141C2×C3×D5—22no—
142C2×C3×D5—42no—
143D3×D5—44no—
144D3×D5—82no—
145ΓL(1,𝔽16)—82no—
146C3×AGL(1,𝔽5)—82no—
147C3×C4×C5—21no—
148C3×C4×C5—41no—
149C3×Dic5—41no—
150C5×Dic3—21no—
151C5×Dic3—41no—
152C23×D3—52no—
153C2×C3×Q8—51no—
154C2×C3×D4—51no—
155C2×#67—52no—
156C2×#67—102no—
157#239—202no—
158D3×D4—202no—
159C2×D12—51no—
160C2×D12—51no—
161C2×D12—101no—
162C2×D12—102no—
163C2×C4×D3—101no—
164C2×C4×D3—202no—
165C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
166C3×C22⋊C4—102no—
167C3×C22⋊C4—102no—
168C3×C42C2×AGL(1,𝔽5)11yescharacteristic, complemented
169#217—102no—
170(C2×D3)⋊C4—21no—
171(C2×D3)⋊C4—102no—
172(C2×D3)⋊C4—202no—
173Dic3⋊C4—21no—
174C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
175C23×C5—31no—
176C22×D5—32no—
177C22×D5—62no—
178C22×D5—62no—
179C22×D5—61no—
180C22×D5—242no—
181C22×D5D3×D412yes—
182C2×AGL(1,𝔽5)—42no—
183C2×AGL(1,𝔽5)—122no—
184C2×AGL(1,𝔽5)—244no—
185C2×C4×C5—21no—
186C2×C4×C5—31no—
187C2×C4×C5—62no—
188C2×C4×C5—61no—
189C2×C4×C5C2×C4×D311yescharacteristic
190C22⋊D5—122no—
191C2×Dic5—21no—
192D20—41no—
193D20—121no—
194D20—121no—
195D20—122no—
196D20—242no—
197D20—242no—
198C4×D5—122no—
199Dic10—41no—
200C2×#41—151no—
201C22×D4—151no—
202#127—151no—
203#127—151no—
204#124—51no—
205#124—151no—
206#121—302no—
207#120—302no—
208#117—31no—
209C2×C22⋊C4—302no—
210#99—52no—
211#99—152no—
212#99—302no—
213C2×C3×C5—21no—
214C2×C3×C5C2×#9911yescharacteristic
215D15—42no—
216D15—81no—
217C3×D5—42no—
218C5×D3—22no—
219C23×C3—52no—
220C22×D3—52no—
221C22×D3—102no—
222C22×D3—102no—
223C22×D3—101no—
224C22×D3—402no—
225C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
226C3×Q8—201no—
227C3×D4—201no—
228C2×C3×C4—21no—
229C2×C3×C4—101no—
230C2×C3×C4—202no—
231C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
232#67—202no—
233#67—402no—
234C2×Dic3—21no—
235C2×Dic3—202no—
236C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
237D12—201no—
238D12—201no—
239D12—202no—
240D12—402no—
241C4×D3—22no—
242C4×D3—202no—
243C4×D3—404no—
244C22×C5—32no—
245C22×C5—121no—
246C22×C5D3×C22⋊C411yescharacteristic
247C2×D5—22no—
248C2×D5—42no—
249C2×D5—62no—
250C2×D5—124no—
251C2×D5—122no—
252C2×D5—122no—
253C2×D5—121no—
254C2×D5—242no—
255AGL(1,𝔽5)—82no—
256AGL(1,𝔽5)—242no—
257C4×C5—21no—
258C4×C5—41no—
259C4×C5—61no—
260C4×C5—121no—
261Dic5—41no—
262C24—152no—
263#41—602no—
264C2×Q8—51no—
265C2×D4—51no—
266C2×D4—152no—
267C2×D4—151no—
268C2×D4—151no—
269C2×D4—302no—
270C2×D4—302no—
271C2×D4—301no—
272C2×D4—602no—
273C22×C4—31no—
274C22×C4—301no—
275C22×C4—602no—
276C4⋊C4—61no—
277C22⋊C4—61no—
278C22⋊C4—102no—
279C22⋊C4—102no—
280C22⋊C4—302no—
281C22⋊C4—302no—
282C22⋊C4—602no—
283C42—31no—
284C42D3×AGL(1,𝔽5)11yescharacteristic, complemented
285C3×C5#212711yescharacteristic, complemented, Hall
286C22×C3—102no—
287C22×C3—202no—
288C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
289C2×D3—41no—
290C2×D3—102no—
291C2×D3—204no—
292C2×D3—202no—
293C2×D3—202no—
294C2×D3—201no—
295C2×D3—402no—
296C2×D3#399912yes—
297C3×C4—21no—
298C3×C4—41no—
299C3×C4—201no—
300C3×C4—402no—
301Dic3—21no—
302Dic3—41no—
303Dic3—402no—
304C2×C5—21no—
305C2×C5—62no—
306C2×C5D3×#9911yescharacteristic
307D5—42no—
308D5—122no—
309D5—241no—
310C23—31no—
311C23—52no—
312C23—152no—
313C23—302no—
314C23—302no—
315C23—301no—
316C23—1202no—
317Q8—201no—
318D4—201no—
319D4—601no—
320D4—601no—
321D4—602no—
322D4—602no—
323D4—1202no—
324D4—1202no—
325C2×C4—21no—
326C2×C4—31no—
327C2×C4—62no—
328C2×C4—61no—
329C2×C4—101no—
330C2×C4—202no—
331C2×C4—602no—
332C2×C4—602no—
333C2×C4—1204no—
334C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
335C2×C3—21no—
336C2×C3—202no—
337C2×C3C2×#399911yescharacteristic
338D3—22no—
339D3—202no—
340D3—401no—
341C5#6915711yescharacteristic, complemented, Sylow
342C22—32no—
343C22—102no—
344C22—121no—
345C22—202no—
346C22—302no—
347C22—602no—
348C22—602no—
349C22—604no—
350C22—601no—
351C22—1202no—
352C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
353C4—21no—
354C4—41no—
355C4—61no—
356C4—121no—
357C4—201no—
358C4—402no—
359C4—1202no—
360C3#1060435311yescharacteristic, complemented, Sylow
361C2—21no—
362C2—62no—
363C2—202no—
364C2—602no—
365C2—1201no—
366C2D3×#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 radical#11752744C2
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. D3×#3999C2semidirect
3. #11746725C2semidirect
4. C3×#64854C2semidirect
5. #11746555C2semidirect
8. C2×#6769C4semidirect
10. #91763C4semidirect
11. C5×#872C4semidirect
16. #91374C4semidirect
24. #64854D3semidirect
30. C2×D60C2×C4semidirect
33. C2×C3×Dic10C2×C4semidirect
43. C3×C42×C5C2×C4semidirect
46. C4×C5×Dic3C2×C4semidirect
102. #872AGL(1,𝔽5)semidirect
119. C2×Dic10C4×D3semidirect
126. C42×C5C4×D3semidirect
168. C3×C42C2×AGL(1,𝔽5)semidirect
174. C4×Dic3C2×AGL(1,𝔽5)semidirect
284. C42D3×AGL(1,𝔽5)semidirect
285. C3×C5#2127semidirect
341. C5#69157semidirect
360. C3#10604353semidirect

Maximal subgroups

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

subgroupindex
#117527442
D3×#39992
#117467252
C3×#648542
#117465552
#106043533
#691575