Finite Group Databasebeta

← #14288877

Subgroups — #14288877

Order 1920.

480 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752636C211yesmaximal, characteristic, complemented
2C5×#4848C211yesmaximal, characteristic, complemented
3#11747086C211yesmaximal, characteristic, complemented
4#11747039C211yesmaximal, characteristic
5#11746305C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10601824—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C2×C5×#204—21no—
11C5×#874C2211yescharacteristic
12C4×C5×Dic6C2211yescharacteristic
13C3×#4020C2211yescharacteristic
14#91434—21no—
15Dic3×D20—21no—
16#91407—22no—
17#91368—21no—
18#91364—21no—
19C2×#6659—21no—
20C2×#6652—22no—
21C3×C5×C4⋊C8C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C5×#821—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90967—21no—
26#68402—51nomaximal, Hall
27#65919—31no—
28C5×#460—31no—
29#65364—31no—
30#65362—31no—
31Q8⋊#168—31no—
32#64705D311yescharacteristic, complemented
33#64704—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20D412yes—
42C2×D5×Dic3—22no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15D411yescharacteristic
46#6712—21no—
47C4×Dic15—21no—
48C2×C3⋊#168—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×Dic3⋊C4—21no—
51C4×C5×Dic3—21no—
52C5×#204—42no—
53C2×C3×#168—21no—
54#6665—22no—
55#6665—22no—
56#6665—22no—
57#6659—42no—
58#6652—44no—
59#5713—51no—
60#5073—51no—
61#4848—51no—
62#4848D511yescharacteristic, complemented
63C3×#331—51no—
64#4484—51no—
65#4484—51no—
66C2×C5×SD16—61no—
67C5×#127—31no—
68C4×C5×Q8—31no—
69#4093—61no—
70C2×#687—61no—
71C2×#686—62no—
72#4040—62no—
73#4039—61no—
74#4021—61no—
75#4020C2×D311yescharacteristic
76C4×D20—61no—
77C4×Dic10—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C5×#102—61no—
80#3964—61no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1620—151noSylow
84C22×C5×D3—41no—
85C22×C3×D5—22no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91Dic30—21no—
92Dic30—21no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—21no—
95C5×D12—42no—
96C5×D12—41no—
97C5×D12—41no—
98C5×D12—41no—
99C5×D12—41no—
100C5×Dic6—21no—
101C5×Dic6—21no—
102C3×D20—42no—
103C3×D20—41no—
104C3×D20—41no—
105C3×D20—41no—
106C3×D20—41no—
107D5×Dic3—82no—
108C3×C5×C8—41no—
109C3⋊#168—22no—
110C3×#168—41no—
111C3×#127—51no—
112#936—101no—
113#936—101no—
114#935—102no—
115D4×Dic3—101no—
116D4×Dic3—101no—
117C2×#213—102no—
118C2×#204—21no—
119C2×#204—101no—
120#874C2×D511yescharacteristic
121C4×Dic6—51no—
122C4×Dic6C2×D511yescharacteristic
123C3×C4⋊C8—51no—
124C3×C4⋊C8C2×D511yescharacteristic
125#821—21no—
126#821—101no—
127C4×C3⋊C8—51no—
128C2×C5×Q8—31no—
129C2×C5×D4—61no—
130C2×C5×D4—61no—
131C2×C5×D4—61no—
132C2×D20—21no—
133C2×D20—21no—
134C2×D20D1212yes—
135C2×C4×D5—62no—
136C2×Dic10—31no—
137C5×SD16—122no—
138C2×C5×C8—21no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4—61no—
141C42×C5—61no—
142C42×C5C22×D311yescharacteristic
143#687—122no—
144#686—124no—
145#685—62no—
146#685—62no—
147#685—62no—
148C4⋊Dic5—31no—
149#683—61no—
150C4×Dic5—61no—
151C2×#168—21no—
152C2×#168—61no—
153#559—151no—
154#493—151no—
155#460—31no—
156#460—151no—
157#331—51no—
158Q8⋊C8—151no—
159Q8⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×C5×D3—81no—
162C2×C5×D3—81no—
163C2×C5×D3—81no—
164C2×C3×D5—42no—
165C2×C3×D5—42no—
166C2×C3×D5—42no—
167C3×C4×C5—21no—
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172Dic15—41no—
173Dic15—41no—
174C5×Dic3—41no—
175C5×Dic3—41no—
176C2×C3×D4—52no—
177C2×C3×D4—101no—
178C2×C3×D4—101no—
179C22×Dic3—102no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—21no—
183C2×Dic6—51no—
184C2×Dic6C22⋊D511yescharacteristic
185C2×C3×C8—21no—
186C2×C3×C8—101no—
187C3×C42C22×D511yescharacteristic
188#217—102no—
189#217—102no—
190#217—102no—
191#213—204no—
192C4⋊Dic3—51no—
193C4⋊Dic3C22⋊D511yescharacteristic
194Dic3⋊C4—21no—
195Dic3⋊C4—101no—
196C4×Dic3—21no—
197C4×Dic3—101no—
198C2×C3⋊C8—101no—
199#204—42no—
200#204—202no—
201C23×C5—121no—
202C22×D5—22no—
203C5×Q8—61no—
204C5×Q8—61no—
205C5×D4—122no—
206C5×D4—121no—
207C5×D4—121no—
208C5×D4—121no—
209C5×D4—121no—
210C2×C4×C5—61no—
211C2×C4×C5—61no—
212C2×C4×C5C2×D1211yescharacteristic
213C2×C4×C5D3×D411yescharacteristic
214C2×C4×C5D3×D411yescharacteristic
215C2×Dic5—61no—
216C2×Dic5—61no—
217D20—42no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20—41no—
222C4×D5—242no—
223Dic10—61no—
224Dic10—61no—
225C5×C8—41no—
226#168—41no—
227#168—62no—
228C2×SD16—61no—
229C2×SD16—301no—
230C2×D8—302no—
231#127—31no—
232#127—51no—
233#124—301no—
234#124—301no—
235#123—302no—
236C4×Q8—31no—
237C4×Q8—151no—
238C4×D4—301no—
239C4×D4—301no—
240C4⋊C8—51no—
241C4⋊C8D3×D511yescharacteristic
242#102—61no—
243#102—301no—
244C4×C8—151no—
245C2×C3×C5#44911yescharacteristic
246C2×C3×C5#44911yescharacteristic
247C2×C3×C5#45311yescharacteristic
248C3×D5—82no—
249C5×D3—161no—
250C23×C3—102no—
251C22×D3—41no—
252C3×D4—202no—
253C3×D4—201no—
254C3×D4—201no—
255C3×D4—201no—
256C3×D4—201no—
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4C2×C22⋊D511yescharacteristic
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3—101no—
263C2×Dic3—101no—
264C2×Dic3—402no—
265D12—42no—
266D12—41no—
267D12—41no—
268D12—41no—
269D12—41no—
270Dic6—21no—
271Dic6—21no—
272Dic6—101no—
273Dic6—101no—
274C3×C8—41no—
275C3×C8—201no—
276C3⋊C8—102no—
277C22×C5—241no—
278C22×C5—241no—
279C22×C5—241no—
280C22×C5#88211yescharacteristic
281C2×D5—42no—
282C2×D5—42no—
283C2×D5—42no—
284C4×C5—21no—
285C4×C5—121no—
286C4×C5—121no—
287C4×C5#91111yescharacteristic
288C4×C5#91111yescharacteristic
289C4×C5#91611yescharacteristic
290C4×C5#91611yescharacteristic
291Dic5—121no—
292Dic5—121no—
293C2×Q8—31no—
294C2×Q8—151no—
295C2×D4—52no—
296C2×D4—61no—
297C2×D4—61no—
298C2×D4—61no—
299C2×D4—101no—
300C2×D4—101no—
301C22×C4—302no—
302SD16—122no—
303SD16—602no—
304D8—604no—
305C2×C8—21no—
306C2×C8—101no—
307C2×C8—301no—
308C4⋊C4—31no—
309C4⋊C4—61no—
310C4⋊C4—151no—
311C4⋊C4—301no—
312C22⋊C4—302no—
313C22⋊C4—302no—
314C22⋊C4—302no—
315C42—61no—
316C42—301no—
317C42C2×D3×D511yescharacteristic
318C3×C5#162011yescharacteristic, complemented, Hall
319C22×C3—202no—
320C22×C3—202no—
321C22×C3—202no—
322C22×C3#408311yescharacteristic
323C2×D3—81no—
324C2×D3—81no—
325C2×D3—81no—
326C3×C4—21no—
327C3×C4#406011yescharacteristic
328C3×C4#406211yescharacteristic
329C3×C4#407811yescharacteristic
330C3×C4#409611yescharacteristic
331Dic3—41no—
332Dic3—41no—
333Dic3—201no—
334Dic3—201no—
335C2×C5—481no—
336C2×C5#474711yescharacteristic
337C2×C5#478111yescharacteristic
338C2×C5#478111yescharacteristic
339D5—82no—
340C23—102no—
341C23—121no—
342Q8—61no—
343Q8—61no—
344Q8—301no—
345Q8—301no—
346D4—122no—
347D4—121no—
348D4—121no—
349D4—121no—
350D4—121no—
351D4—202no—
352D4—201no—
353D4—201no—
354D4—201no—
355D4—201no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—1202no—
361C2×C4D5×D1211yescharacteristic
362C2×C4#677711yescharacteristic
363C2×C4D3×C22⋊D511yescharacteristic
364C8—41no—
365C8—201no—
366C8—302no—
367C2×C3—402no—
368C2×C3#6532611yescharacteristic
369C2×C3#6546111yescharacteristic
370C2×C3#6548711yescharacteristic
371D3—161no—
372C5#6840211yescharacteristic, complemented, Sylow
373C22—202no—
374C22—202no—
375C22—202no—
376C22—241no—
377C22—241no—
378C22—241no—
379C22#9147511yescharacteristic
380C4—21no—
381C4—121no—
382C4—121no—
383C4—601no—
384C4—601no—
385C4#9125811yescharacteristic
386C4#9127611yescharacteristic
387C4#9149411yescharacteristic
388C4#9151711yescharacteristic
389C3#1060182411yescharacteristic, complemented, Sylow
390C2—402no—
391C2—481no—
392C2#1174751511yescharacteristic
393C2#1174815311yescharacteristic
394C2#1174824611yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11747039C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1620
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11752636C2semidirect
2. C5×#4848C2semidirect
3. #11747086C2semidirect
5. #11746305C2semidirect
6. C3×#64705C2semidirect
7. #11745842C2semidirect
32. #64705D3semidirect
62. #4848D5semidirect
318. C3×C5#1620semidirect
372. C5#68402semidirect
389. C3#10601824semidirect

Maximal subgroups

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

subgroupindex
#117526362
C5×#48482
#117470862
#117470392
#117463052
C3×#647052
#117458422
#106018243
#684025