Finite Group Databasebeta

← #14288985

Subgroups — #14288985

Order 1920.

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

normal subgroups only

This group has 472 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#11752641C211yesmaximal, characteristic, complemented
2C3×#64982C211yesmaximal, characteristic, complemented
3#11747083C211yesmaximal, characteristic, complemented
4#11747033C211yesmaximal, characteristic
5#11746277C211yesmaximal, characteristic, complemented
6C5×#4459C211yesmaximal, characteristic, complemented
7#11745861C211yesmaximal, characteristic, complemented
8#10598991—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C4×C5×D12C2211yescharacteristic
11C2×C3×#677—22no—
12C3×#4020C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91435—21no—
15D3×C4⋊Dic5—21no—
16#91410—22no—
17#91384—21no—
18#91365—21no—
19C2×#6657—21no—
20C2×#6652—21no—
21C3×C4×C5×C8C2211yescharacteristic
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90965—21no—
25#90964—21no—
26#71264—51nomaximal, Hall
27#65877—31no—
28#65304—31no—
29#65137—31no—
30#64982D311yescharacteristic, complemented
31C5×D4⋊C8—31no—
32#64701—31no—
33#64676—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×Dic10D412yes—
41C2×D3×Dic5—22no—
42C2×C3×C5×C8—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15D411yescharacteristic
45#6712—21no—
46C4×Dic15—21no—
47C2×C3⋊#168—21no—
48C5×(C2×D3)⋊C4—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C2×C5×C3⋊C8—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C3×#677—44no—
54Dic3⋊Dic5—22no—
55#6668—22no—
56(C2×D3)⋊Dic5—22no—
57#6657—42no—
58#6652—42no—
59#5730—51no—
60C3×#492—51no—
61#5075—51no—
62#5072—51no—
63#4546—51no—
64#4459D511yescharacteristic, complemented
65#4456—51no—
66C4×C5×D4—31no—
67D4×Dic5—61no—
68C2×#686—61no—
69C2×C4⋊Dic5—61no—
70#4070—61no—
71C2×#677—22no—
72C2×#677—61no—
73#4036—61no—
74#4024—62no—
75#4020C2×D311yescharacteristic
76#4015C2×D311yescharacteristic
77C4×Dic10—31no—
78C5×C4⋊C8—31no—
79C4×C5×C8C2×D311yescharacteristic
80#3953—61no—
81#3941—61no—
82C4⋊#168—31no—
83#1622—151noSylow
84C22×C5×D3—21no—
85C22×C3×D5—41no—
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—
94C5×D12—21no—
95C5×D12SD1612yescomplemented
96C4×C5×D3—41no—
97C4×C5×D3—41no—
98C2×C3×Dic5—22no—
99C3×D20—42no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×Dic10—42no—
105D3×Dic5—82no—
106C3×C5×C8—22no—
107C3⋊#168—41no—
108C5×C3⋊C8—41no—
109C2×C3×SD16—102no—
110C3×C4⋊Q8—51no—
111C3×#127—51no—
112#946—102no—
113C2×#214—101no—
114C2×#213—101no—
115#897—101no—
116#893—101no—
117D3×C4⋊C4—101no—
118#890—101no—
119C4×D12C2×D511yescharacteristic
120C4×Dic6—51no—
121C3×C4×C8C2×D511yescharacteristic
122#832—101no—
123#832—101no—
124C4⋊(C3⋊C8)—51no—
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C2×C5×D4—31no—
127C22×C4×C5—61no—
128C22×Dic5—62no—
129C2×D20—21no—
130C2×D20—21no—
131C2×D20—21no—
132C2×Dic10—31no—
133C2×Dic10#6712yes—
134C2×C5×C8—21no—
135C2×C5×C8—61no—
136C5×C4⋊C4—31no—
137C5×C22⋊C4—61no—
138C42×C5C22×D311yescharacteristic
139C22⋊Dic5—62no—
140#686—122no—
141C4⋊Dic5—21no—
142C4⋊Dic5—21no—
143C4⋊Dic5—31no—
144C4⋊Dic5—62no—
145#683—62no—
146#683—61no—
147C4×Dic5—61no—
148C2×#168—61no—
149#677—44no—
150#677—122no—
151#554—151no—
152#492—51no—
153#460—151no—
154#459—151no—
155#333—151no—
156Q8⋊C8—151no—
157D4⋊C8—31no—
158C22×C3×C5#12011yescharacteristic
159C2×C5×D3—22no—
160C2×C5×D3—41no—
161C2×C5×D3—41no—
162C2×C3×D5—81no—
163C2×C3×D5—81no—
164C2×C3×D5—81no—
165C3×C4×C5—21no—
166C3×C4×C5C2×SD1611yescharacteristic
167C3×C4×C5#13511yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170Dic15—41no—
171Dic15—41no—
172C3×Dic5—42no—
173C5×Dic3—41no—
174C2×C3×Q8—52no—
175C2×C3×D4—101no—
176C2×C3×D4—101no—
177C2×C3×D4—101no—
178C2×D12D2011yescharacteristic
179C2×C4×D3—21no—
180C2×C4×D3—102no—
181C2×Dic6—51no—
182C3×SD16—204no—
183C2×C3×C8—21no—
184C3×C4⋊C4—101no—
185C3×C4⋊C4—101no—
186C3×C42C22×D511yescharacteristic
187#214—202no—
188#213—202no—
189(C2×D3)⋊C4—21no—
190(C2×D3)⋊C4—102no—
191C4⋊Dic3—51no—
192C4⋊Dic3—102no—
193C4⋊Dic3D2011yescharacteristic
194Dic3⋊C4—102no—
195Dic3⋊C4—101no—
196C4×Dic3—101no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—101no—
199C23×C5—61no—
200C22×D5—41no—
201C5×D4—32no—
202C5×D4—61no—
203C2×C4×C5—61no—
204C2×C4×C5—121no—
205C2×C4×C5—121no—
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5C2×#6711yescharacteristic
209C2×Dic5—22no—
210C2×Dic5—61no—
211C2×Dic5—61no—
212C2×Dic5—242no—
213D20—42no—
214D20—41no—
215D20—41no—
216D20—41no—
217D20—41no—
218Dic10—42no—
219Dic10—61no—
220Dic10—61no—
221C5×C8—22no—
222C5×C8—121no—
223#168—121no—
224C2×SD16—102no—
225C2×SD16—301no—
226C2×D8—301no—
227C4⋊Q8—51no—
228#127—51no—
229#125—301no—
230C22⋊Q8—302no—
231C22⋊Q8—301no—
232C4×Q8—151no—
233C4×D4—31no—
234C4×D4—301no—
235C2×C4⋊C4—301no—
236C4⋊C8—31no—
237C4⋊C8—151no—
238#102—301no—
239#102—301no—
240C4×C8D3×D511yescharacteristic
241C2×C3×C5#44811yescharacteristic
242C2×C3×C5#44911yescharacteristic
243C2×C3×C5#45311yescharacteristic
244C3×D5—161no—
245C5×D3—42no—
246C23×C3—201no—
247C22×D3—21no—
248C3×Q8—202no—
249C3×D4—202no—
250C3×D4—201no—
251C3×D4—201no—
252C3×D4—201no—
253C3×D4—201no—
254C2×C3×C4—102no—
255C2×C3×C4C2×D2011yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257C2×C3×C4D4×D511yescharacteristic
258C2×Dic3—21no—
259C2×Dic3—101no—
260C2×Dic3—101no—
261D12—21no—
262D12#67712yescomplemented
263C4×D3—41no—
264C4×D3—41no—
265C4×D3—402no—
266Dic6—101no—
267Dic6—101no—
268C3×C8—22no—
269C3⋊C8—41no—
270C3⋊C8—201no—
271C22×C5—62no—
272C22×C5—121no—
273C22×C5—121no—
274C22×C5#93711yescharacteristic
275C2×D5—81no—
276C2×D5—81no—
277C2×D5—81no—
278C4×C5—21no—
279C4×C5—121no—
280C4×C5D3×SD1611yescharacteristic
281C4×C5#91411yescharacteristic
282C4×C5#91511yescharacteristic
283C4×C5#91611yescharacteristic
284Dic5—42no—
285Dic5—121no—
286Dic5—121no—
287C2×Q8—52no—
288C2×Q8—151no—
289C2×D4—31no—
290C2×D4—101no—
291C2×D4—101no—
292C2×D4—101no—
293C22×C4—61no—
294C22×C4—302no—
295SD16—204no—
296SD16—602no—
297D8—602no—
298C2×C8—21no—
299C2×C8—61no—
300C2×C8—301no—
301C4⋊C4—31no—
302C4⋊C4—101no—
303C4⋊C4—101no—
304C4⋊C4—151no—
305C4⋊C4—302no—
306C4⋊C4—302no—
307C4⋊C4—301no—
308C22⋊C4—61no—
309C22⋊C4—302no—
310C42—301no—
311C42C2×D3×D511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3—401no—
314C22×C3—401no—
315C22×C3—401no—
316C22×C3#402811yescharacteristic
317C2×D3—22no—
318C2×D3—41no—
319C2×D3—41no—
320C3×C4—21no—
321C3×C4—202no—
322C3×C4C2×#67711yescharacteristic
323C3×C4#405511yescharacteristic
324C3×C4#405711yescharacteristic
325C3×C4#406211yescharacteristic
326Dic3—41no—
327Dic3—201no—
328Dic3—201no—
329C2×C5—122no—
330C2×C5#507711yescharacteristic
331C2×C5#517011yescharacteristic
332C2×C5#517211yescharacteristic
333D5—161no—
334C23—61no—
335C23—201no—
336Q8—202no—
337Q8—301no—
338Q8—301no—
339D4—32no—
340D4—61no—
341D4—202no—
342D4—201no—
343D4—201no—
344D4—201no—
345D4—201no—
346C2×C4—61no—
347C2×C4—102no—
348C2×C4—121no—
349C2×C4—121no—
350C2×C4—301no—
351C2×C4—301no—
352C2×C4—1202no—
353C2×C4D3×D2011yescharacteristic
354C2×C4#677711yescharacteristic
355C2×C4D5×#6711yescharacteristic
356C8—22no—
357C8—121no—
358C8—601no—
359C2×C3—801no—
360C2×C3#6502711yescharacteristic
361C2×C3#6507011yescharacteristic
362C2×C3#6511111yescharacteristic
363D3—42no—
364C5#7126411yescharacteristic, complemented, Sylow
365C22—62no—
366C22—121no—
367C22—121no—
368C22—401no—
369C22—401no—
370C22—401no—
371C22#9147411yescharacteristic
372C4—21no—
373C4—121no—
374C4—202no—
375C4—601no—
376C4—601no—
377C4D3×#67711yescharacteristic
378C4#9125711yescharacteristic
379C4#9127411yescharacteristic
380C4#9127611yescharacteristic
381C3#1059899111yescharacteristic, complemented, Sylow
382C2—122no—
383C2—801no—
384C2#1174711411yescharacteristic
385C2#1174788911yescharacteristic
386C2#1174812411yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11747033C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1622
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. #11752641C2semidirect
2. C3×#64982C2semidirect
3. #11747083C2semidirect
5. #11746277C2semidirect
6. C5×#4459C2semidirect
7. #11745861C2semidirect
30. #64982D3semidirect
64. #4459D5semidirect
95. C5×D12SD16semidirect
262. D12#677semidirect
312. C3×C5#1622semidirect
364. C5#71264semidirect
381. C3#10598991semidirect

Maximal subgroups

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

subgroupindex
#117526412
C3×#649822
#117470832
#117470332
#117462772
C5×#44592
#117458612
#105989913
#712645