Finite Group Databasebeta

← #14283400

Subgroups — #14283400

Order 1920.

444 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752342C211yesmaximal, characteristic, complemented
3C3×#65689C211yesmaximal, characteristic, complemented
4#11746503C212yesmaximal, complemented
5#11746497C212yesmaximal
6#10604575—31nomaximal, Hall
7C2×C3×C4⋊AGL(1,𝔽5)—21no—
8#91764C411yescharacteristic, complemented
9C5×#870C411yescharacteristic, complemented
10C3×C42×D5C2211yescharacteristic
11#91450C2211yescharacteristic
12#91444—21no—
13#91418C411yescharacteristic, complemented
14#91402—21no—
15#91387—21no—
16#91360C2211yescharacteristic
17#91348—21no—
18#91333C411yescharacteristic, complemented
19#91232C2212yes—
20#91231—21no—
21C4⋊(C3⋊#170)—21no—
22C3×(C2×AGL(1,𝔽5))⋊C4—21no—
23C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
24#69544—51nomaximal, Hall
25#66025—31no—
26#65689D311yescharacteristic, complemented
27#65683—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)—42no—
40C3×C42×C5C2×C411yescharacteristic
41#6714—21no—
42#6714—21no—
43C5×C4⋊Dic3C2×C411yescharacteristic
44C5×C4⋊Dic3C2×C411yescharacteristic
45C5×Dic3⋊C4—21no—
46C5×Dic3⋊C4—21no—
47C3×C4×Dic5C2×C411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50Dic3⋊Dic5—21no—
51#6669—21no—
52#6667—21no—
53#6667—21no—
54#6665—21no—
55Dic3×Dic5—21no—
56#5479—51no—
57C3×#382—51no—
58#4926—51no—
59#4452—52no—
60#4451—52no—
61C2×C4⋊AGL(1,𝔽5)—21no—
62C5×#125—31no—
63#4044—61no—
64#4043—31no—
65#4041—31no—
66#4040—61no—
67#4039—31no—
68#4039—61no—
69#4038—61no—
70#4033—31no—
71#4021—31no—
72C42×D5C2×D311yescharacteristic
73(C2×AGL(1,𝔽5))⋊C4—21no—
74(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
75#4003—32no—
76#4002—61no—
77C4⋊#170—61no—
78#1512—151noSylow
79C22×D15—21no—
80C22×C3×D5C2×D411yescharacteristic
81C2×C3×AGL(1,𝔽5)—42no—
82C2×C3×AGL(1,𝔽5)—42no—
83C2×C3×AGL(1,𝔽5)—42no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×Dic15—21no—
88D60—41no—
89Dic30—41no—
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C2×C3×Dic5C22⋊C411yescharacteristic
93C2×C3×Dic5C22⋊C411yescharacteristic
94C2×C3×Dic5C2×D411yescharacteristic
95C3×C4×D5—21no—
96C3×C4×D5—21no—
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99#1202—41no—
100#1202—41no—
101#1200—42no—
102C3⋊#170—42no—
103C2×C3×C4⋊C4—101no—
104C2×C3×C42—51no—
105#930—51no—
106#929—101no—
107C4×#67—101no—
108#924—51no—
109#876—101no—
110#875—51no—
111C4×D12—51no—
112#872—101no—
113#870AGL(1,𝔽5)11yescharacteristic, complemented
114C4×Dic6—51no—
115C3×#95—52no—
116C3×#95—101no—
117#830—52no—
118C4⋊(C3⋊C8)—101no—
119#803—101no—
120C22×AGL(1,𝔽5)—22no—
121C2×D20—31no—
122C2×D20—61no—
123C2×C4×D5—61no—
124C2×C4×D5#6711yescharacteristic
125C2×C4×D5#6711yescharacteristic
126C2×C4×D5C22×D311yescharacteristic
127C2×Dic10—31no—
128C2×#170—62no—
129C4⋊AGL(1,𝔽5)—42no—
130C5×C4⋊C4—31no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4—61no—
134C42×C5C4×D311yescharacteristic
135#685—61no—
136#685—61no—
137#685—61no—
138#685—61no—
139#685—61no—
140C4⋊Dic5—61no—
141#683—61no—
142C4×Dic5—61no—
143C4×Dic5C4×D311yescharacteristic
144C4×Dic5D1211yescharacteristic
145C4×Dic5D1211yescharacteristic
146#529—151no—
147#432—151no—
148#382—51no—
149#328—152no—
150#327—152no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C2×D15—41no—
153C2×D15—41no—
154C2×D15—41no—
155C2×C3×D5—21no—
156C2×C3×D5—21no—
157C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
158C2×C3×D5#13711yescharacteristic
159C3×AGL(1,𝔽5)—82no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163Dic15—41no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C3×Dic5—21no—
167C5×Dic3—41no—
168C5×Dic3—41no—
169C22×C3×C4—51no—
170C22×C3×C4—51no—
171C22×C3×C4—51no—
172C22×C3×C4—102no—
173C2×#67—101no—
174C2×D12—51no—
175C2×C4×D3—101no—
176C2×Dic6—51no—
177C3×C4⋊C4—202no—
178C3×C42—51no—
179C3×C42—51no—
180C3×C42—51no—
181C3×C42C2×AGL(1,𝔽5)11yescharacteristic
182#217—101no—
183(C2×D3)⋊C4—101no—
184(C2×D3)⋊C4—101no—
185(C2×D3)⋊C4—101no—
186(C2×D3)⋊C4—101no—
187C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
188C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
189Dic3⋊C4—21no—
190Dic3⋊C4—21no—
191Dic3⋊C4—101no—
192Dic3⋊C4—101no—
193C4×Dic3—101no—
194C2×C3⋊C8—102no—
195C22×D5—61no—
196C22×D5C2×#6711yescharacteristic
197C2×AGL(1,𝔽5)—42no—
198C2×AGL(1,𝔽5)—42no—
199C2×AGL(1,𝔽5)—42no—
200C2×C4×C5—61no—
201C2×C4×C5—61no—
202C2×C4×C5(C2×D3)⋊C411yescharacteristic
203C2×C4×C5(C2×D3)⋊C411yescharacteristic
204C2×C4×C5C2×C4×D311yescharacteristic
205C2×Dic5—61no—
206C2×Dic5(C2×D3)⋊C411yescharacteristic
207C2×Dic5(C2×D3)⋊C411yescharacteristic
208C2×Dic5C2×D1211yescharacteristic
209D20—121no—
210D20—121no—
211D20—121no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—41no—
215C4×D5—41no—
216C4×D5—122no—
217Dic10—121no—
218#170—122no—
219#126—301no—
220#125—31no—
221#124—151no—
222#123—301no—
223C22⋊Q8—151no—
224#121—151no—
225C4×Q8—151no—
226C4×D4—151no—
227C4×D4—301no—
228#117—301no—
229C2×C4⋊C4—101no—
230C2×C42—51no—
231C4⋊C8—301no—
232C22⋊C8—152no—
233#97—301no—
234#95—52no—
235#95—101no—
236C2×C3×C5#41011yescharacteristic
237C2×C3×C5#41711yescharacteristic
238C2×C3×C5#42111yescharacteristic
239D15—81no—
240C3×D5—21no—
241C3×D5—21no—
242C23×C3—51no—
243C22×D3—101no—
244C2×C3×C4—51no—
245C2×C3×C4—51no—
246C2×C3×C4—51no—
247C2×C3×C4—101no—
248C2×C3×C4—101no—
249C2×C3×C4—201no—
250C2×C3×C4—201no—
251C2×C3×C4—202no—
252C2×C3×C4—202no—
253C2×C3×C4—202no—
254C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
255C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
256C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
257#67—201no—
258#67—201no—
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3—101no—
262D12—201no—
263C4×D3—202no—
264Dic6—201no—
265C3⋊C8—202no—
266C22×C5C2×(C2×D3)⋊C411yescharacteristic
267C2×D5—21no—
268C2×D5—21no—
269C2×D5—121no—
270C2×D5—121no—
271C2×D5—121no—
272C2×D5#93211yescharacteristic
273C2×D5#94211yescharacteristic
274AGL(1,𝔽5)—82no—
275C4×C5—21no—
276C4×C5—21no—
277C4×C5—21no—
278C4×C5—121no—
279C4×C5—121no—
280Dic5—21no—
281Dic5—21no—
282Dic5—21no—
283Dic5—121no—
284C2×Q8—151no—
285C2×D4—151no—
286C2×D4—301no—
287C22×C4—51no—
288C22×C4—51no—
289C22×C4—51no—
290C22×C4—102no—
291C22×C4—301no—
292C2×C8—302no—
293C4⋊C4—31no—
294C4⋊C4—31no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C4⋊C4—202no—
298C4⋊C4—301no—
299C4⋊C4—301no—
300C22⋊C4—301no—
301C22⋊C4—301no—
302C22⋊C4—301no—
303C22⋊C4—301no—
304C22⋊C4—301no—
305C42—51no—
306C42—51no—
307C42—51no—
308C42—301no—
309C42D3×AGL(1,𝔽5)11yescharacteristic
310C3×C5#151211yescharacteristic, complemented, Hall
311C22×C3—51no—
312C22×C3—51no—
313C22×C3—101no—
314C22×C3—101no—
315C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
316C2×D3—201no—
317C2×D3—201no—
318C2×D3—201no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—101no—
323C3×C4—101no—
324C3×C4—101no—
325C3×C4—402no—
326Dic3—41no—
327Dic3—41no—
328Dic3—201no—
329C2×C5#496611yescharacteristic
330C2×C5#500511yescharacteristic
331C2×C5#500611yescharacteristic
332D5—21no—
333D5—21no—
334D5—241no—
335C23—51no—
336C23—301no—
337Q8—601no—
338D4—601no—
339D4—601no—
340D4—601no—
341C2×C4—51no—
342C2×C4—51no—
343C2×C4—51no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—101no—
347C2×C4—101no—
348C2×C4—201no—
349C2×C4—201no—
350C2×C4—202no—
351C2×C4—202no—
352C2×C4—202no—
353C2×C4—301no—
354C2×C4—602no—
355C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
356C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
357C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
358C8—602no—
359C2×C3—101no—
360C2×C3—101no—
361C2×C3#6578511yescharacteristic
362C2×C3#6579311yescharacteristic
363C2×C3#6579511yescharacteristic
364D3—401no—
365C5#6954411yescharacteristic, complemented, Sylow
366C22—51no—
367C22—51no—
368C22—101no—
369C22—101no—
370C22—601no—
371C22—601no—
372C22—601no—
373C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—101no—
378C4—101no—
379C4—101no—
380C4—121no—
381C4—121no—
382C4—402no—
383C4—601no—
384C3#1060457511yescharacteristic, complemented, Sylow
385C2—101no—
386C2—101no—
387C2—1201no—
388C2#1175170511yescharacteristic
389C2#1175172011yescharacteristic
390C2#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#1512
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. #11752342C2semidirect
3. C3×#65689C2semidirect
4. #11746503C2semidirect
8. #91764C4semidirect
9. C5×#870C4semidirect
13. #91418C4semidirect
18. #91333C4semidirect
26. #65689D3semidirect
113. #870AGL(1,𝔽5)semidirect
310. C3×C5#1512semidirect
365. C5#69544semidirect
384. C3#10604575semidirect

Maximal subgroups

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

subgroupindex
#117526852
#117523422
C3×#656892
#117465032
#117464972
#106045753
#695445