Finite Group Databasebeta

← #14288981

Subgroups — #14288981

Order 1920.

472 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 96 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#11756302C211yesmaximal, characteristic, complemented
2C3×#65304C211yesmaximal, characteristic
3#11747083C211yesmaximal, characteristic, complemented
4#11747071C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745863C211yesmaximal, characteristic, complemented
7#11745844C211yesmaximal, characteristic, complemented
8#10598991—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10D4×Dic15—21no—
11C2×C4⋊Dic15—21no—
12#91813—21no—
13#91779—21no—
14#91767—22no—
15#91758C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C2×C3×#686—21no—
18C3×#4020C2211yescharacteristic
19C2×#6657—21no—
20C2×#6657—22no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×#3941—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90965—21no—
26#71016—51nomaximal, Hall
27#65877—31no—
28#65304D311yescharacteristic
29#65137—31no—
30#64982—31no—
31C5×D4⋊C8—31no—
32#64701—31no—
33#64676—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C22×Dic15—22no—
37C2×Dic30D411yescharacteristic
38C2×Dic30D412yes—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45#6719—22no—
46C4⋊Dic15—22no—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15D411yescharacteristic
50#6712—22no—
51#6712—21no—
52C4×Dic15—21no—
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×#686—42no—
56C2×C3×#168—21no—
57#6657—44no—
58#6657—42no—
59#5543—51no—
60C3×#459—51no—
61#5076—51no—
62#5075—51no—
63D4⋊(C3⋊C8)D511yescharacteristic, complemented
64#4484—51no—
65#4481—51no—
66C4×C5×D4C2×D311yescharacteristic
67D4×Dic5—61no—
68C2×#686—21no—
69C2×C4⋊Dic5—61no—
70#4070—61no—
71C2×#677—61no—
72C2×#677—62no—
73#4036—61no—
74#4024—62no—
75#4020C2×D311yescharacteristic
76#4015—31no—
77C4×Dic10—31no—
78C5×C4⋊C8—31no—
79C4×C5×C8—31no—
80#3953—61no—
81#3941—21no—
82C4⋊#168C2×D311yescharacteristic
83#1622—151noSylow
84C23×C3×C5—21no—
85C22×C3×D5—41no—
86C3×C5×D4—21no—
87C3×C5×D4SD1612yescomplemented
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×Dic15—21no—
95C2×Dic15—21no—
96C2×Dic15—22no—
97C2×Dic15—82no—
98Dic30—21no—
99Dic30—21no—
100Dic30—42no—
101C3×D20—42no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3×D20—41no—
106C3×#168—41no—
107C5×C3⋊C8—22no—
108C5×C3⋊C8—41no—
109C2×C3×D8—101no—
110C3×#127—51no—
111C3×C4×D4C2×D511yescharacteristic
112D4×Dic3—101no—
113C2×#214—101no—
114C2×#214—102no—
115C2×C4⋊Dic3—101no—
116#924—101no—
117#890—101no—
118#878—102no—
119#869—51no—
120C4×Dic6—51no—
121C3×C4⋊C8—51no—
122C3×#102—101no—
123#832—101no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C4×C3⋊C8C2×D511yescharacteristic
126C2×C5×D4#6711yescharacteristic
127C22×C4×C5—21no—
128C22×Dic5—62no—
129C2×D20—21no—
130C2×D20—21no—
131C2×D20—21no—
132C2×Dic10—31no—
133C2×Dic10—32no—
134C2×C5×C8—61no—
135C2×C5×C8—61no—
136C5×C4⋊C4#6711yescharacteristic
137C5×C22⋊C4—21no—
138C42×C5C22×D311yescharacteristic
139C22⋊Dic5—62no—
140#686—42no—
141C4⋊Dic5—31no—
142C4⋊Dic5—62no—
143C4⋊Dic5—61no—
144C4⋊Dic5—61no—
145#683—62no—
146#683—61no—
147C4×Dic5—61no—
148C2×#168—21no—
149#677—124no—
150#677—122no—
151#554—151no—
152#492—151no—
153#460—151no—
154#459—51no—
155#333—151no—
156Q8⋊C8—151no—
157D4⋊C8—31no—
158C22×C3×C5—22no—
159C22×C3×C5—41no—
160C22×C3×C5—41no—
161C22×C3×C5#12011yescharacteristic
162C2×C3×D5—81no—
163C2×C3×D5—81no—
164C2×C3×D5—81no—
165C3×C4×C5—21no—
166C3×C4×C5—41no—
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C3×C4×C5#13711yescharacteristic
171Dic15—41no—
172Dic15—42no—
173Dic15—41no—
174C2×C3×D4—101no—
175C2×C3×D4—101no—
176C2×C3×D4—101no—
177C2×C3×D4D2011yescharacteristic
178C22×C3×C4—21no—
179C22×Dic3—102no—
180C2×Dic6—51no—
181C2×Dic6—52no—
182C3×D8—202no—
183C2×C3×C8—101no—
184C3×C4⋊C4D2011yescharacteristic
185C3×C22⋊C4—21no—
186C3×C42C22×D511yescharacteristic
187#217—102no—
188#214—204no—
189#214—202no—
190C4⋊Dic3—51no—
191C4⋊Dic3—102no—
192C4⋊Dic3—101no—
193C4⋊Dic3—101no—
194Dic3⋊C4—102no—
195Dic3⋊C4—101no—
196C4×Dic3—101no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C23×C5—21no—
200C22×D5—41no—
201C5×D4—21no—
202C5×D4#21412yescomplemented
203C2×C4×C5—21no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5C2×#6711yescharacteristic
209C2×Dic5—61no—
210C2×Dic5—61no—
211C2×Dic5—62no—
212C2×Dic5—242no—
213D20—42no—
214D20—41no—
215D20—41no—
216D20—41no—
217D20—41no—
218Dic10—61no—
219Dic10—61no—
220Dic10—122no—
221C5×C8—62no—
222C5×C8—121no—
223#168—41no—
224C2×SD16—301no—
225C2×SD16—302no—
226C2×D8—101no—
227C4⋊Q8—151no—
228#127—51no—
229#125—301no—
230C22⋊Q8—302no—
231C22⋊Q8—301no—
232C4×Q8—151no—
233C4×D4—301no—
234C4×D4D3×D511yescharacteristic
235C2×C4⋊C4—301no—
236C4⋊C8—31no—
237C4⋊C8—51no—
238#102—101no—
239#102—301no—
240C4×C8—31no—
241C2×C3×C5—42no—
242C2×C3×C5#44811yescharacteristic
243C2×C3×C5#44911yescharacteristic
244C2×C3×C5#45311yescharacteristic
245C3×D5—161no—
246C23×C3—21no—
247C23×C3—201no—
248C3×D4—21no—
249C3×D4—202no—
250C3×D4—201no—
251C3×D4—201no—
252C3×D4—201no—
253C3×D4—201no—
254C3×D4#67712yescomplemented
255C2×C3×C4—21no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4C2×D2011yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×Dic3—101no—
262C2×Dic3—101no—
263C2×Dic3—102no—
264C2×Dic3—402no—
265Dic6—101no—
266Dic6—101no—
267Dic6—202no—
268C3×C8—201no—
269C3⋊C8—22no—
270C3⋊C8—41no—
271C22×C5—22no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5#93711yescharacteristic
275C2×D5—81no—
276C2×D5—81no—
277C2×D5—81no—
278C4×C5—21no—
279C4×C5—41no—
280C4×C5#91111yescharacteristic
281C4×C5#91211yescharacteristic
282C4×C5C2×#21411yescharacteristic
283C4×C5#95111yescharacteristic
284Dic5—121no—
285Dic5—122no—
286Dic5—121no—
287C2×Q8—151no—
288C2×Q8—152no—
289C2×D4—101no—
290C2×D4—101no—
291C2×D4—101no—
292C2×D4#120211yescharacteristic
293C22×C4—21no—
294C22×C4—302no—
295SD16—604no—
296SD16—602no—
297D8—202no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—101no—
301C4⋊C4—151no—
302C4⋊C4—302no—
303C4⋊C4—302no—
304C4⋊C4—301no—
305C4⋊C4—301no—
306C4⋊C4—301no—
307C4⋊C4#120211yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—302no—
310C42—301no—
311C42C2×D3×D511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3—22no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—401no—
317C22×C3—401no—
318C22×C3—401no—
319C22×C3#402811yescharacteristic
320C3×C4—21no—
321C3×C4—41no—
322C3×C4C2×#67711yescharacteristic
323C3×C4#405511yescharacteristic
324C3×C4#405711yescharacteristic
325C3×C4#406211yescharacteristic
326Dic3—201no—
327Dic3—202no—
328Dic3—201no—
329C2×C5—42no—
330C2×C5#504011yescharacteristic
331C2×C5#515811yescharacteristic
332C2×C5#519811yescharacteristic
333D5—161no—
334C23—21no—
335C23—201no—
336Q8—301no—
337Q8—301no—
338Q8—602no—
339D4—21no—
340D4—202no—
341D4—201no—
342D4—201no—
343D4—201no—
344D4—201no—
345D4#665712yescomplemented
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—301no—
350C2×C4—301no—
351C2×C4—302no—
352C2×C4—1202no—
353C2×C4C2×#120211yescharacteristic
354C2×C4#679011yescharacteristic
355C2×C4#679011yescharacteristic
356C8—62no—
357C8—121no—
358C8—201no—
359C2×C3—42no—
360C2×C3—801no—
361C2×C3#6502711yescharacteristic
362C2×C3#6507011yescharacteristic
363C2×C3#6511111yescharacteristic
364C5#7101611yescharacteristic, complemented, Sylow
365C22—22no—
366C22—41no—
367C22—41no—
368C22—401no—
369C22—401no—
370C22—401no—
371C22#9157211yescharacteristic
372C4—21no—
373C4—41no—
374C4—601no—
375C4—602no—
376C4—601no—
377C4C2×#665711yescharacteristic
378C4#9131311yescharacteristic
379C4#9148211yescharacteristic
380C4#9149711yescharacteristic
381C3#1059899111yescharacteristic, complemented, Sylow
382C2—42no—
383C2—801no—
384C2#1174854911yescharacteristic
385C2#1174904211yescharacteristic
386C2#1174942111yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC3×#65304C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1622
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756302C2semidirect
3. #11747083C2semidirect
4. #11747071C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745863C2semidirect
7. #11745844C2semidirect
63. D4⋊(C3⋊C8)D5semidirect
87. C3×C5×D4SD16semidirect
202. C5×D4#214semidirect
254. C3×D4#677semidirect
312. C3×C5#1622semidirect
345. D4#6657semidirect
364. C5#71016semidirect
381. C3#10598991semidirect

Maximal subgroups

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

subgroupindex
#117563022
C3×#653042
#117470832
#117470712
C5×D4⋊(C3⋊C8)2
#117458632
#117458442
#105989913
#710165