Finite Group Databasebeta

← #14289321

Subgroups — #14289321

Order 1920.

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

normal subgroups only

This group has 432 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#11752480C211yesmaximal, characteristic, complemented
2C5×#4843C211yesmaximal, characteristic
3#11747086C211yesmaximal, characteristic, complemented
4#11746901C211yesmaximal, characteristic, complemented
5#11746305C211yesmaximal, characteristic, complemented
6C3×#64702C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10601812—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C2×C5×D24—21no—
11C5×#874C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91370—21no—
15#91365—21no—
16#91341—22no—
17#91338—21no—
18#91331—21no—
19C2×#6659—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C5×#821—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90967—21no—
25#90966—22no—
26#68433—51nomaximal, Hall
27#65876—31no—
28C5×#459—31no—
29#65364—31no—
30#65359—31no—
31D4⋊#168—31no—
32#64704—31no—
33#64702D311yescharacteristic, complemented
34C2×Dic30D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C3×Dic10—21no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3D411yescharacteristic
49C5×D24—42no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5D412yes—
52C2×C3×#168—21no—
53#6668—22no—
54(C2×D3)⋊Dic5—22no—
55(C2×D3)⋊Dic5—22no—
56Dic3×Dic5—22no—
57#6659—42no—
58#5732—51no—
59#5088—51no—
60#4848—51no—
61#4843D511yescharacteristic
62C3×#332—51no—
63#4484—51no—
64#4483—51no—
65C2×C5×D8—61no—
66C5×#127—31no—
67C4×C5×D4—31no—
68#4082—61no—
69C2×#687—61no—
70#4072—61no—
71#4070—61no—
72#4033—61no—
73#4025—62no—
74#4015C2×D311yescharacteristic
75C4×Dic10—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77C5×#102—61no—
78#3964—61no—
79#3964—62no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1628—151noSylow
83C22×C5×D3—21no—
84C22×C5×D3—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—21no—
89C2×Dic15—21no—
90Dic30—21no—
91Dic30—21no—
92C2×C5×Dic3—21no—
93C5×D12—21no—
94C5×D12—21no—
95C5×D12—42no—
96C5×D12—41no—
97C5×D12—41no—
98C5×D12—41no—
99C5×D12—41no—
100C4×C5×D3—41no—
101C4×C5×D3—41no—
102C2×C3×Dic5—22no—
103C3×Dic10—41no—
104C3×Dic10—41no—
105C3×C5×C8—41no—
106C3⋊#168—41no—
107C3×#168—41no—
108C3×C4⋊Q8—51no—
109#947—101no—
110Q8×Dic3—101no—
111C2×D24—21no—
112C2×#204—101no—
113#898—102no—
114#897—101no—
115#892—101no—
116#874C2×D511yescharacteristic
117C4×D12C2×D511yescharacteristic
118C4×Dic6—51no—
119C3×C4⋊C8—51no—
120C3×C4⋊C8C2×D511yescharacteristic
121#821—21no—
122#821—101no—
123#809—102no—
124C4×C3⋊C8—51no—
125C2×C5×D4—31no—
126C2×C5×D4—61no—
127C2×C5×D4—61no—
128C2×C5×D4—61no—
129C22×C4×C5—61no—
130C2×Dic10—21no—
131C2×Dic10—31no—
132C5×D8—122no—
133C2×C5×C8—21no—
134C5×C4⋊C4—31no—
135C5×C22⋊C4—61no—
136C42×C5C22×D311yescharacteristic
137C22⋊Dic5—62no—
138C22⋊Dic5—62no—
139#687—122no—
140C4⋊Dic5—21no—
141C4⋊Dic5—31no—
142C4⋊Dic5D1212yes—
143#683—62no—
144#683—61no—
145C4×Dic5—62no—
146C4×Dic5—61no—
147C2×#168—21no—
148C2×#168—61no—
149#556—151no—
150#486—151no—
151#460—151no—
152#459—31no—
153#332—51no—
154Q8⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C2×C5×D3—41no—
160C2×C5×D3—81no—
161C2×C5×D3—81no—
162C2×C5×D3—81no—
163C3×C4×C5—21no—
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168Dic15—41no—
169Dic15—41no—
170C3×Dic5—42no—
171C5×Dic3—41no—
172C2×C3×Q8—101no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12—21no—
176C2×D12C22⋊D511yescharacteristic
177C2×C4×D3—21no—
178C2×Dic6—51no—
179C2×C3×C8—21no—
180C2×C3×C8—101no—
181C3×C4⋊C4—52no—
182C3×C4⋊C4—101no—
183C3×C42C22×D511yescharacteristic
184(C2×D3)⋊C4—21no—
185(C2×D3)⋊C4—102no—
186(C2×D3)⋊C4—102no—
187C4⋊Dic3—51no—
188C4⋊Dic3—102no—
189C4⋊Dic3C22⋊D511yescharacteristic
190Dic3⋊C4—101no—
191C4×Dic3—102no—
192C4×Dic3—101no—
193C2×C3⋊C8—101no—
194D24—42no—
195#204—202no—
196C23×C5—61no—
197C23×C5—121no—
198C5×D4—61no—
199C5×D4—61no—
200C5×D4—122no—
201C5×D4—121no—
202C5×D4—121no—
203C5×D4—121no—
204C5×D4—121no—
205C2×C4×C5—61no—
206C2×C4×C5—121no—
207C2×C4×C5—121no—
208C2×C4×C5C2×D1211yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5D3×D411yescharacteristic
211C2×Dic5—22no—
212C2×Dic5—61no—
213C2×Dic5—61no—
214Dic10—41no—
215Dic10—41no—
216Dic10—61no—
217Dic10—61no—
218C5×C8—41no—
219#168—41no—
220#168—121no—
221C2×SD16—301no—
222C2×D8—61no—
223C4⋊Q8—51no—
224#127—31no—
225#126—302no—
226#124—301no—
227C22⋊Q8—301no—
228C4×Q8—151no—
229C4×Q8—301no—
230C4×D4—31no—
231#117—301no—
232C4⋊C8—51no—
233C4⋊C8D3×D511yescharacteristic
234#102—61no—
235#102—302no—
236#102—301no—
237C4×C8—151no—
238C2×C3×C5#44911yescharacteristic
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#45411yescharacteristic
241C5×D3—81no—
242C5×D3—161no—
243C22×D3—21no—
244C22×D3—41no—
245C3×Q8—201no—
246C3×Q8—201no—
247C2×C3×C4—102no—
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251C2×Dic3—21no—
252C2×Dic3—101no—
253C2×Dic3—101no—
254D12—21no—
255D12—21no—
256D12—42no—
257D12—41no—
258D12—41no—
259D12—41no—
260D12—41no—
261C4×D3—41no—
262C4×D3—41no—
263Dic6—101no—
264Dic6—101no—
265C3×C8—41no—
266C3×C8—201no—
267C3⋊C8—201no—
268C22×C5—121no—
269C22×C5—121no—
270C22×C5—121no—
271C22×C5—241no—
272C22×C5—241no—
273C22×C5—241no—
274C22×C5#88211yescharacteristic
275C4×C5—21no—
276C4×C5—121no—
277C4×C5#91111yescharacteristic
278C4×C5#91411yescharacteristic
279C4×C5#91611yescharacteristic
280C4×C5#91911yescharacteristic
281Dic5—42no—
282Dic5—121no—
283Dic5—121no—
284C2×Q8—101no—
285C2×Q8—151no—
286C2×D4—31no—
287C2×D4—61no—
288C2×D4—61no—
289C2×D4—61no—
290C22×C4—61no—
291SD16—602no—
292D8—122no—
293C2×C8—21no—
294C2×C8—101no—
295C2×C8—301no—
296C4⋊C4—31no—
297C4⋊C4—52no—
298C4⋊C4—101no—
299C4⋊C4—151no—
300C4⋊C4—302no—
301C4⋊C4—301no—
302C22⋊C4—61no—
303C22⋊C4—302no—
304C22⋊C4—302no—
305C42—302no—
306C42—301no—
307C42C2×D3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3#408311yescharacteristic
310C2×D3—41no—
311C2×D3—41no—
312C2×D3—41no—
313C2×D3—81no—
314C2×D3—81no—
315C2×D3—81no—
316C3×C4—21no—
317C3×C4—202no—
318C3×C4#405711yescharacteristic
319C3×C4#405811yescharacteristic
320C3×C4#407811yescharacteristic
321C3×C4#409611yescharacteristic
322Dic3—41no—
323Dic3—201no—
324Dic3—201no—
325C2×C5—241no—
326C2×C5—481no—
327C2×C5#475311yescharacteristic
328C2×C5#478111yescharacteristic
329C2×C5#481011yescharacteristic
330C23—61no—
331C23—121no—
332Q8—201no—
333Q8—201no—
334Q8—301no—
335Q8—301no—
336D4—61no—
337D4—61no—
338D4—122no—
339D4—121no—
340D4—121no—
341D4—121no—
342D4—121no—
343C2×C4—61no—
344C2×C4—102no—
345C2×C4—121no—
346C2×C4—121no—
347C2×C4—301no—
348C2×C4—301no—
349C2×C4D5×D1211yescharacteristic
350C2×C4#677711yescharacteristic
351C2×C4D3×C22⋊D511yescharacteristic
352C8—41no—
353C8—201no—
354C8—601no—
355C2×C3#6532611yescharacteristic
356C2×C3#6544711yescharacteristic
357C2×C3#6549011yescharacteristic
358D3—81no—
359D3—161no—
360C5#6843311yescharacteristic, complemented, Sylow
361C22—121no—
362C22—121no—
363C22—121no—
364C22—241no—
365C22—241no—
366C22—241no—
367C22#9147511yescharacteristic
368C4—21no—
369C4—121no—
370C4—202no—
371C4—601no—
372C4—601no—
373C4#9125711yescharacteristic
374C4#9127911yescharacteristic
375C4#9149411yescharacteristic
376C4#9151711yescharacteristic
377C3#1060181211yescharacteristic, complemented, Sylow
378C2—241no—
379C2—481no—
380C2#1174751511yescharacteristic
381C2#1174815911yescharacteristic
382C2#1174825911yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC5×#4843C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1628
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. #11752480C2semidirect
3. #11747086C2semidirect
4. #11746901C2semidirect
5. #11746305C2semidirect
6. C3×#64702C2semidirect
7. #11745836C2semidirect
33. #64702D3semidirect
308. C3×C5#1628semidirect
360. C5#68433semidirect
377. C3#10601812semidirect

Maximal subgroups

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

subgroupindex
#117524802
C5×#48432
#117470862
#117469012
#117463052
C3×#647022
#117458362
#106018123
#684335