Finite Group Databasebeta

← #14283243

Subgroups — #14283243

Order 1920.

484 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 94 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#11752685C211yesmaximal, characteristic
2#11752343C211yesmaximal, characteristic, complemented
3C3×C4×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4#11746503C212yesmaximal, complemented
5#11746497C212yesmaximal
6#10604574—31nomaximal, Hall
7C2×C3×C4⋊AGL(1,𝔽5)—21no—
8C2×C3×C4×AGL(1,𝔽5)—21no—
9#91764C411yescharacteristic, complemented
10C5×#870C411yescharacteristic, complemented
11C3×C42×D5C2211yescharacteristic
12#91450C2211yescharacteristic
13#91444—21no—
14#91418C411yescharacteristic, complemented
15#91402—21no—
16#91387—21no—
17#91360C2211yescharacteristic
18#91348—21no—
19#91333C411yescharacteristic, complemented
20#91233—21no—
21#91232C2212yes—
22#91231—21no—
23C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
24#69470—51nomaximal, Hall
25#66025—31no—
26C4×C4⋊AGL(1,𝔽5)D311yescharacteristic, complemented
27#65684—31no—
28#64869—32no—
29#64868—32no—
30C22×C3×AGL(1,𝔽5)—22no—
31C2×D60C2×C411yescharacteristic
32C2×Dic30C2×C411yescharacteristic
33C2×C3×C4×D5D411yescharacteristic
34C2×C3×C4×D5D411yescharacteristic
35C2×C3×C4×D5C2311yescharacteristic
36C2×#1202—21no—
37C2×#1200—21no—
38C2×C3⋊#170—22no—
39C3×C4⋊AGL(1,𝔽5)—24no—
40C3×C4×AGL(1,𝔽5)—42no—
41C3×C42×C5C2×C411yescharacteristic
42#6714—21no—
43#6714—21no—
44C5×C4⋊Dic3C2×C411yescharacteristic
45C5×C4⋊Dic3C2×C411yescharacteristic
46C5×Dic3⋊C4—21no—
47C5×Dic3⋊C4—21no—
48C3×C4×Dic5C2×C411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50C3×C4×Dic5D411yescharacteristic
51Dic3⋊Dic5—21no—
52#6669—21no—
53#6667—21no—
54#6667—21no—
55#6665—21no—
56Dic3×Dic5—21no—
57#5479—51no—
58C3×C4×C4⋊C4—51no—
59#4926—51no—
60#4452—52no—
61#4451—52no—
62C2×C4⋊AGL(1,𝔽5)—21no—
63C2×C4×AGL(1,𝔽5)—21no—
64C5×#125—31no—
65#4044—61no—
66#4043—31no—
67#4041—31no—
68#4040—61no—
69#4039—31no—
70#4039—61no—
71#4038—61no—
72#4033—31no—
73#4021—31no—
74C42×D5C2×D311yescharacteristic
75(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
76#4004—61no—
77#4003—32no—
78#4002—61no—
79#1509—151noSylow
80C22×D15—21no—
81C22×C3×D5C2×D411yescharacteristic
82C2×C3×AGL(1,𝔽5)—24no—
83C2×C3×AGL(1,𝔽5)—42no—
84C2×C3×AGL(1,𝔽5)—42no—
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×Dic15—21no—
89D60—41no—
90Dic30—41no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C22⋊C411yescharacteristic
95C2×C3×Dic5C2×D411yescharacteristic
96C3×C4×D5—21no—
97C3×C4×D5—21no—
98C3×C4×D5—22no—
99C3×C4×D5—41no—
100#1202—41no—
101#1202—41no—
102#1200—42no—
103C3⋊#170—42no—
104C2×C3×C4⋊C4—101no—
105C2×C3×C42—51no—
106C2×C3×C42—101no—
107#930—51no—
108#929—101no—
109C4×#67—101no—
110#924—51no—
111#876—101no—
112#875—51no—
113C4×D12—51no—
114#872—101no—
115#870AGL(1,𝔽5)11yescharacteristic, complemented
116C4×Dic6—51no—
117C3×#95—52no—
118#830—52no—
119C4⋊(C3⋊C8)—101no—
120#803—101no—
121C22×AGL(1,𝔽5)—22no—
122C2×D20—31no—
123C2×D20—61no—
124C2×C4×D5—61no—
125C2×C4×D5#6711yescharacteristic
126C2×C4×D5#6711yescharacteristic
127C2×C4×D5C22×D311yescharacteristic
128C2×Dic10—31no—
129C2×#170—62no—
130C4⋊AGL(1,𝔽5)—24no—
131C4×AGL(1,𝔽5)—42no—
132C5×C4⋊C4—31no—
133C5×C4⋊C4—31no—
134C5×C4⋊C4—61no—
135C5×C4⋊C4—61no—
136C42×C5C4×D311yescharacteristic
137#685—61no—
138#685—61no—
139#685—61no—
140#685—61no—
141#685—61no—
142C4⋊Dic5—61no—
143#683—61no—
144C4×Dic5—61no—
145C4×Dic5C4×D311yescharacteristic
146C4×Dic5D1211yescharacteristic
147C4×Dic5D1211yescharacteristic
148#529—151no—
149#432—151no—
150C4×C4⋊C4—51no—
151#328—152no—
152#327—152no—
153C22×C3×C5C2×C22⋊C411yescharacteristic
154C2×D15—41no—
155C2×D15—41no—
156C2×D15—41no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
160C2×C3×D5#13711yescharacteristic
161C3×AGL(1,𝔽5)—44no—
162C3×C4×C5—21no—
163C3×C4×C5—21no—
164C3×C4×C5—21no—
165Dic15—41no—
166C3×Dic5—21no—
167C3×Dic5—21no—
168C3×Dic5#10412yes—
169C5×Dic3—41no—
170C5×Dic3—41no—
171C22×C3×C4—51no—
172C22×C3×C4—51no—
173C22×C3×C4—51no—
174C22×C3×C4—102no—
175C2×#67—101no—
176C2×D12—51no—
177C2×C4×D3—101no—
178C2×Dic6—51no—
179C3×C4⋊C4—104no—
180C3×C42—51no—
181C3×C42—51no—
182C3×C42—51no—
183C3×C42—202no—
184C3×C42C2×AGL(1,𝔽5)11yescharacteristic
185#217—101no—
186(C2×D3)⋊C4—101no—
187(C2×D3)⋊C4—101no—
188(C2×D3)⋊C4—101no—
189(C2×D3)⋊C4—101no—
190C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
191C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
192Dic3⋊C4—21no—
193Dic3⋊C4—21no—
194Dic3⋊C4—101no—
195Dic3⋊C4—101no—
196C4×Dic3—101no—
197C2×C3⋊C8—102no—
198C22×D5—61no—
199C22×D5C2×#6711yescharacteristic
200C2×AGL(1,𝔽5)—24no—
201C2×AGL(1,𝔽5)—42no—
202C2×AGL(1,𝔽5)—42no—
203C2×C4×C5—61no—
204C2×C4×C5—61no—
205C2×C4×C5(C2×D3)⋊C411yescharacteristic
206C2×C4×C5(C2×D3)⋊C411yescharacteristic
207C2×C4×C5C2×C4×D311yescharacteristic
208C2×Dic5—61no—
209C2×Dic5(C2×D3)⋊C411yescharacteristic
210C2×Dic5(C2×D3)⋊C411yescharacteristic
211C2×Dic5C2×D1211yescharacteristic
212D20—121no—
213D20—121no—
214D20—121no—
215C4×D5—21no—
216C4×D5—21no—
217C4×D5—22no—
218C4×D5—41no—
219C4×D5—122no—
220Dic10—121no—
221#170—122no—
222#126—301no—
223#125—31no—
224#124—151no—
225#123—301no—
226C22⋊Q8—151no—
227#121—151no—
228C4×Q8—151no—
229C4×D4—151no—
230C4×D4—301no—
231#117—301no—
232C2×C4⋊C4—101no—
233C2×C42—51no—
234C2×C42—101no—
235C4⋊C8—301no—
236C22⋊C8—152no—
237#97—301no—
238#95—52no—
239C2×C3×C5#41011yescharacteristic
240C2×C3×C5#41711yescharacteristic
241C2×C3×C5C2×#10411yescharacteristic
242D15—81no—
243C3×D5—21no—
244C3×D5—21no—
245C23×C3—51no—
246C22×D3—101no—
247C2×C3×C4—51no—
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4—102no—
251C2×C3×C4—101no—
252C2×C3×C4—101no—
253C2×C3×C4—104no—
254C2×C3×C4—201no—
255C2×C3×C4—202no—
256C2×C3×C4—202no—
257C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
258C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
259C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
260#67—201no—
261#67—201no—
262C2×Dic3—21no—
263C2×Dic3—21no—
264C2×Dic3—101no—
265D12—201no—
266C4×D3—202no—
267Dic6—201no—
268C3⋊C8—202no—
269C22×C5C2×(C2×D3)⋊C411yescharacteristic
270C2×D5—21no—
271C2×D5—21no—
272C2×D5—121no—
273C2×D5—121no—
274C2×D5—121no—
275C2×D5#93211yescharacteristic
276C2×D5#94211yescharacteristic
277AGL(1,𝔽5)—44no—
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—121no—
282C4×C5—121no—
283Dic5—21no—
284Dic5—21no—
285Dic5—121no—
286Dic5#80512yes—
287C2×Q8—151no—
288C2×D4—151no—
289C2×D4—301no—
290C22×C4—51no—
291C22×C4—51no—
292C22×C4—51no—
293C22×C4—102no—
294C22×C4—301no—
295C2×C8—302no—
296C4⋊C4—31no—
297C4⋊C4—31no—
298C4⋊C4—61no—
299C4⋊C4—61no—
300C4⋊C4—104no—
301C4⋊C4—301no—
302C4⋊C4—301no—
303C22⋊C4—301no—
304C22⋊C4—301no—
305C22⋊C4—301no—
306C22⋊C4—301no—
307C22⋊C4—301no—
308C42—51no—
309C42—51no—
310C42—51no—
311C42—202no—
312C42—301no—
313C42D3×AGL(1,𝔽5)11yescharacteristic
314C3×C5#150911yescharacteristic, complemented, Hall
315C22×C3—51no—
316C22×C3—51no—
317C22×C3—101no—
318C22×C3—101no—
319C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
320C2×D3—201no—
321C2×D3—201no—
322C2×D3—201no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—52no—
327C3×C4—101no—
328C3×C4—101no—
329C3×C4—204no—
330Dic3—41no—
331Dic3—41no—
332Dic3—201no—
333C2×C5C2×#80511yescharacteristic
334C2×C5#496611yescharacteristic
335C2×C5#500611yescharacteristic
336D5—21no—
337D5—21no—
338D5—241no—
339C23—51no—
340C23—301no—
341Q8—601no—
342D4—601no—
343D4—601no—
344D4—601no—
345C2×C4—51no—
346C2×C4—51no—
347C2×C4—51no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—102no—
351C2×C4—101no—
352C2×C4—101no—
353C2×C4—104no—
354C2×C4—201no—
355C2×C4—202no—
356C2×C4—202no—
357C2×C4—301no—
358C2×C4—602no—
359C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
360C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
361C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
362C8—602no—
363C2×C3—101no—
364C2×C3—101no—
365C2×C3#6578511yescharacteristic
366C2×C3D5⋊#10411yescharacteristic
367C2×C3#6579311yescharacteristic
368D3—401no—
369C5#6947011yescharacteristic, complemented, Sylow
370C22—51no—
371C22—51no—
372C22—101no—
373C22—101no—
374C22—601no—
375C22—601no—
376C22—601no—
377C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—52no—
382C4—101no—
383C4—101no—
384C4—121no—
385C4—121no—
386C4—204no—
387C4—601no—
388C3#1060457411yescharacteristic, complemented, Sylow
389C2—101no—
390C2—101no—
391C2—1201no—
392C2#1175170511yescharacteristic
393C2D5⋊#80511yescharacteristic
394C2#1175181711yescharacteristic
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 radical#91450C22
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1509
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11752343C2semidirect
3. C3×C4×C4⋊AGL(1,𝔽5)C2semidirect
4. #11746503C2semidirect
9. #91764C4semidirect
10. C5×#870C4semidirect
14. #91418C4semidirect
19. #91333C4semidirect
26. C4×C4⋊AGL(1,𝔽5)D3semidirect
115. #870AGL(1,𝔽5)semidirect
314. C3×C5#1509semidirect
369. C5#69470semidirect
388. C3#10604574semidirect

Maximal subgroups

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

subgroupindex
#117526852
#117523432
C3×C4×C4⋊AGL(1,𝔽5)2
#117465032
#117464972
#106045743
#694705