Finite Group Databasebeta

← #14290018

Subgroups — #14290018

Order 1920.

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

normal subgroups only

This group has 500 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#11752536C211yesmaximal, characteristic
2#11751188C211yesmaximal, characteristic, complemented
3C5×#5088C211yesmaximal, characteristic, complemented
4C3×#65379C211yesmaximal, characteristic, complemented
5#11745853C211yesmaximal, characteristic, complemented
6#11745841C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10602000—31nomaximal, Hall
9C2×#6768—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C4×D60C2211yescharacteristic
12C5×#874C2211yescharacteristic
13C2×C3×#689—21no—
14C3×C4×Dic10C2211yescharacteristic
15#91466—21no—
16#91451—21no—
17#91416—22no—
18Dic5×D12—21no—
19#91093—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×#809—22no—
23C4×C5×C3⋊C8C2211yescharacteristic
24C3×#3967—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71061—51nomaximal, Hall
27#66052—31no—
28C5×#486—31no—
29#65379D311yescharacteristic, complemented
30#65376—31no—
31#64764—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12D412yes—
40C2×C3×Dic10D411yescharacteristic
41C2×#1203—22no—
42C2×#1203—22no—
43C2×D3×Dic5—22no—
44#6768—42no—
45#6768—42no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C42×C5C2311yescharacteristic
49#6714—21no—
50C4⋊Dic15D411yescharacteristic
51C2×C3⋊#168—21no—
52C2×C5×C3⋊C8—21no—
53C3×#689—42no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C2×C3×#168—21no—
58(C2×D3)⋊Dic5—22no—
59#5577—51no—
60C3×#462—51no—
61#5088D511yescharacteristic, complemented
62#5087—51no—
63#4535—51no—
64#4485—51no—
65#4483—51no—
66C2×#711—61no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C5×#127—31no—
69C2×#689—21no—
70#4086—61no—
71#4085—62no—
72#4084—61no—
73D4×Dic5—61no—
74C4×D20—31no—
75C4×Dic10C2×D311yescharacteristic
76C5×#102—62no—
77C4×C5×C8—31no—
78#3967—21no—
79#3941—61no—
80#3939—61no—
81C4⋊#168—31no—
82C4⋊#168C2×D311yescharacteristic
83#1641—151noSylow
84C22×D15—21no—
85C22×C5×D3—22no—
86C3×C5×Q8—41no—
87C3×C5×Q8—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×Dic15—21no—
93D60—21no—
94D60—21no—
95C4×D15—41no—
96C4×D15—41no—
97C5×D12—42no—
98C5×D12—41no—
99C5×D12—41no—
100C5×D12—41no—
101C5×D12—41no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—21no—
104C3×Dic10—21no—
105C3×Dic10D812yes—
106#1203—44no—
107#1203—82no—
108D3×Dic5—44no—
109C3⋊#168—41no—
110C3×#168—41no—
111C5×C3⋊C8—41no—
112C2×#239—101no—
113C2×C3×Q16—101no—
114C3×C4⋊Q8C2×D511yescharacteristic
115C3×C4×Q8—51no—
116#895—101no—
117#895—102no—
118#874—101no—
119#874C2×D511yescharacteristic
120C4×D12—51no—
121C4×D12—101no—
122C3×C4⋊C8—51no—
123C3×#103—101no—
124#809—22no—
125#809—101no—
126#807—101no—
127C4⋊(C3⋊C8)—51no—
128C4×C3⋊C8C2×D511yescharacteristic
129C2×C5×Q8—21no—
130C2×C5×D4—32no—
131C2×C5×D4—61no—
132C2×C5×D4—61no—
133C2×C22⋊D5—62no—
134C2×C22⋊D5—62no—
135C22×Dic5—62no—
136#711—122no—
137#711—122no—
138C2×D20—31no—
139C2×C4×D5—61no—
140C2×Dic10#6711yescharacteristic
141C2×C5×C8—61no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—21no—
144C42×C5C22×D311yescharacteristic
145C22⋊Dic5—62no—
146#689—42no—
147#685—61no—
148C4⋊Dic5—31no—
149C4⋊Dic5#6711yescharacteristic
150#683—21no—
151C4×Dic5—21no—
152C2×#168—21no—
153C2×#168—61no—
154#550—151no—
155#486—31no—
156#474—151no—
157#462—51no—
158#331—151no—
159Q8⋊C8—151no—
160D4⋊C8—151no—
161C22×C3×C5#12011yescharacteristic
162C2×D15—41no—
163C2×D15—41no—
164C2×D15—41no—
165C2×C5×D3—42no—
166C2×C5×D3—42no—
167C2×C5×D3—42no—
168C3×C4×C5—21no—
169C3×C4×C5—81no—
170C3×C4×C5C2×D811yescharacteristic
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174Dic15—41no—
175C3×Dic5—22no—
176C3×Dic5—41no—
177C2×C3×Q8—21no—
178C2×C3×Q8—51no—
179#239—202no—
180#239—202no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—51no—
184C2×D12—102no—
185C2×D12—102no—
186C2×D12C22⋊D512yes—
187C2×C4×D3—102no—
188C2×C4×D3—101no—
189C3×Q16—202no—
190C2×C3×C8—101no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—51no—
194C3×C4⋊C4—101no—
195C3×C42—101no—
196C3×C42C22×D511yescharacteristic
197(C2×D3)⋊C4—102no—
198(C2×D3)⋊C4—101no—
199C4⋊Dic3—51no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—101no—
202C23×C5—62no—
203C22×D5—61no—
204C5×Q8—41no—
205C5×Q8—41no—
206C5×D4—122no—
207C5×D4—121no—
208C5×D4—121no—
209C5×D4—121no—
210C5×D4—121no—
211C2×C4×C5—41no—
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5D3×D411yescharacteristic
214C2×C4×C5C2×#6711yescharacteristic
215C22⋊D5—124no—
216C22⋊D5—242no—
217C2×Dic5—21no—
218C2×Dic5—21no—
219C2×Dic5—61no—
220C2×Dic5—124no—
221D20—61no—
222D20—61no—
223C4×D5—121no—
224C4×D5—121no—
225Dic10—21no—
226Dic10#21312yes—
227C5×C8—121no—
228#168—41no—
229#168—121no—
230C2×#41—301no—
231C2×Q16—101no—
232C4⋊Q8D3×D511yescharacteristic
233#127—31no—
234#127—301no—
235#121—301no—
236#121—302no—
237C4×Q8—51no—
238C4×D4—151no—
239C4×D4—301no—
240#107—301no—
241C4⋊C8—51no—
242C4⋊C8—151no—
243#103—101no—
244#102—62no—
245#102—301no—
246C4×C8—31no—
247C2×C3×C5#44711yescharacteristic
248C2×C3×C5#45211yescharacteristic
249C2×C3×C5#45511yescharacteristic
250D15—81no—
251C5×D3—82no—
252C22×D3—22no—
253C22×D3—101no—
254C3×Q8—41no—
255C3×Q8—41no—
256C3×Q8—52no—
257C3×Q8—101no—
258C2×C3×C4—41no—
259C2×C3×C4—101no—
260C2×C3×C4—101no—
261C2×C3×C4D4×D511yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4C2×C22⋊D511yescharacteristic
264C2×Dic3—101no—
265D12—42no—
266D12—41no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12—101no—
271D12—101no—
272D12—204no—
273D12—402no—
274C4×D3—204no—
275C4×D3—201no—
276C4×D3—201no—
277C3×C8—201no—
278C3⋊C8—41no—
279C3⋊C8—201no—
280C22×C5—122no—
281C22×C5—122no—
282C22×C5—122no—
283C22×C5#93711yescharacteristic
284C2×D5—121no—
285C2×D5—121no—
286C2×D5—121no—
287C4×C5—21no—
288C4×C5—81no—
289C4×C5#91811yescharacteristic
290C4×C5#91911yescharacteristic
291C4×C5C2×#21311yescharacteristic
292C4×C5#94911yescharacteristic
293Dic5—22no—
294Dic5—41no—
295Dic5—121no—
296#41—602no—
297#41—602no—
298C2×Q8—21no—
299C2×Q8—51no—
300C2×D4—32no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—151no—
304C2×D4—302no—
305C2×D4—302no—
306C22×C4—302no—
307C22×C4—301no—
308Q16—202no—
309C2×C8—61no—
310C2×C8—101no—
311C2×C8—301no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—51no—
315C4⋊C4—101no—
316C4⋊C4—151no—
317C22⋊C4—302no—
318C22⋊C4—301no—
319C42—101no—
320C42C2×D3×D511yescharacteristic
321C3×C5#164111yescharacteristic, complemented, Hall
322C22×C3#408311yescharacteristic
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—42no—
326C2×D3—201no—
327C2×D3—201no—
328C2×D3—201no—
329C3×C4—21no—
330C3×C4—81no—
331C3×C4—102no—
332C3×C4—201no—
333C3×C4D5×D811yescharacteristic
334C3×C4#405711yescharacteristic
335C3×C4#406111yescharacteristic
336C3×C4#406211yescharacteristic
337Dic3—201no—
338C2×C5—242no—
339C2×C5#503611yescharacteristic
340C2×C5#518711yescharacteristic
341C2×C5#520211yescharacteristic
342D5—241no—
343C23—62no—
344C23—301no—
345Q8—41no—
346Q8—41no—
347Q8—52no—
348Q8—101no—
349D4—122no—
350D4—121no—
351D4—121no—
352D4—121no—
353D4—121no—
354D4—301no—
355D4—301no—
356D4—604no—
357D4—1202no—
358C2×C4—41no—
359C2×C4—101no—
360C2×C4—101no—
361C2×C4—301no—
362C2×C4—604no—
363C2×C4—601no—
364C2×C4—601no—
365C2×C4D5×#6711yescharacteristic
366C2×C4D3×C22⋊D511yescharacteristic
367C2×C4#679011yescharacteristic
368C8—121no—
369C8—201no—
370C8—601no—
371C2×C3#6535011yescharacteristic
372C2×C3#6544511yescharacteristic
373C2×C3#6546211yescharacteristic
374D3—82no—
375D3—401no—
376C5#7106111yescharacteristic, complemented, Sylow
377C22—122no—
378C22—122no—
379C22—122no—
380C22—601no—
381C22—601no—
382C22—601no—
383C22#9157711yescharacteristic
384C4—21no—
385C4—81no—
386C4—102no—
387C4—201no—
388C4—601no—
389C4D5×#21311yescharacteristic
390C4#9147811yescharacteristic
391C4#9152311yescharacteristic
392C4#9152411yescharacteristic
393C3#1060200011yescharacteristic, complemented, Sylow
394C2—242no—
395C2—1201no—
396C2#1174915111yescharacteristic
397C2#1174940711yescharacteristic
398C2#1174941111yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11752536C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1641
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11751188C2semidirect
3. C5×#5088C2semidirect
4. C3×#65379C2semidirect
5. #11745853C2semidirect
6. #11745841C2semidirect
7. #11745838C2semidirect
29. #65379D3semidirect
61. #5088D5semidirect
321. C3×C5#1641semidirect
376. C5#71061semidirect
393. C3#10602000semidirect

Maximal subgroups

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

subgroupindex
#117525362
#117511882
C5×#50882
C3×#653792
#117458532
#117458412
#117458382
#106020003
#710615