Finite Group Databasebeta

← #14289272

Subgroups — #14289272

Order 1920.

500 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 92 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#11752558C211yesmaximal, characteristic, complemented
2C5×#4843C211yesmaximal, characteristic
3#11747086C211yesmaximal, characteristic, complemented
4#11746901C211yesmaximal, characteristic, complemented
5#11746305C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10601807—31nomaximal, Hall
9C2×D3×Dic10—21no—
10C4×Dic30C2211yescharacteristic
11C2×C5×D24—21no—
12C5×#874C2211yescharacteristic
13C4×C5×D12C2211yescharacteristic
14C3×#4015C2211yescharacteristic
15#91470—21no—
16#91436—22no—
17#91435—21no—
18#91369—21no—
19C2×#6659—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C5×#821—21no—
23C3×C4⋊#168C2211yescharacteristic
24#90967—21no—
25#90966—22no—
26#68457—51nomaximal, Hall
27D4×Dic10—31no—
28C5×#459—31no—
29#65364—31no—
30#65359—31no—
31D4⋊#168—31no—
32#64706D311yescharacteristic, complemented
33#64704—31no—
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×#1204—22no—
42C2×D3×Dic5—22no—
43D3×Dic10—42no—
44D3×Dic10—42no—
45C2×C3×C5×C8—21no—
46C3×C42×C5C2311yescharacteristic
47C4⋊Dic15D411yescharacteristic
48#6712—21no—
49C4×Dic15—21no—
50C2×C3⋊#168—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C5×D24—42no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5D412yes—
56C2×C3×#168—21no—
57#6669—22no—
58(C2×D3)⋊Dic5—22no—
59#6659—42no—
60#5727—51no—
61#5088—51no—
62#4848—51no—
63#4843D511yescharacteristic
64C3×#332—51no—
65#4484—51no—
66#4483—51no—
67C22×Dic10—61no—
68C2×C5×D8—61no—
69C5×#127—31no—
70C4×C5×D4—31no—
71D4×Dic5—61no—
72C2×#687—61no—
73#4070—61no—
74#4034—61no—
75#4024—62no—
76#4015C2×D311yescharacteristic
77C4×Dic10—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C5×#102—61no—
80#3964—61no—
81#3964—62no—
82C4⋊#168C2×D311yescharacteristic
83C4×#168—31no—
84#1627—151noSylow
85C22×C5×D3—21no—
86C22×C5×D3—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91C2×Dic15—21no—
92Dic30—21no—
93Dic30D812yescomplemented
94C2×C5×Dic3—21no—
95C5×D12—21no—
96C5×D12—42no—
97C5×D12—41no—
98C5×D12—41no—
99C5×D12—41no—
100C5×D12—41no—
101C5×D12SD1612yescomplemented
102C4×C5×D3—41no—
103C4×C5×D3—41no—
104C2×C3×Dic5—22no—
105C3×Dic10—41no—
106C3×Dic10—41no—
107#1204—44no—
108D3×Dic5—44no—
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C3×#168—41no—
112C2×D3×Q8—101no—
113C3×C4⋊Q8—51no—
114#946—101no—
115C2×D24—21no—
116C2×#204—101no—
117#896—102no—
118#893—101no—
119#888—101no—
120#874C2×D511yescharacteristic
121C4×D12C2×D511yescharacteristic
122C4×Dic6—51no—
123C3×C4⋊C8—51no—
124C3×C4⋊C8C2×D511yescharacteristic
125#821—21no—
126#821—101no—
127#809—102no—
128C4×C3⋊C8—51no—
129C2×C5×D4—31no—
130C2×C5×D4—61no—
131C2×C5×D4—61no—
132C2×C5×D4—61no—
133C22×C4×C5—61no—
134C22×Dic5—62no—
135C2×Dic10—21no—
136C2×Dic10—31no—
137C2×Dic10—62no—
138C2×Dic10—122no—
139C2×Dic10—122no—
140C5×D8—122no—
141C2×C5×C8—21no—
142C5×C4⋊C4—31no—
143C5×C22⋊C4—61no—
144C42×C5C22×D311yescharacteristic
145C22⋊Dic5—62no—
146#687—122no—
147C4⋊Dic5—21no—
148C4⋊Dic5—31no—
149C4⋊Dic5D1212yes—
150#683—62no—
151#683—61no—
152C4×Dic5—61no—
153C2×#168—21no—
154C2×#168—61no—
155D4×Q8—151no—
156#486—151no—
157#460—151no—
158#459—31no—
159#332—51no—
160Q8⋊C8—151no—
161D4⋊C8—151no—
162C22×C3×C5#12011yescharacteristic
163C2×C5×D3—22no—
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C2×C5×D3—81no—
167C2×C5×D3—81no—
168C2×C5×D3—81no—
169C3×C4×C5—21no—
170C3×C4×C5C2×D811yescharacteristic
171C3×C4×C5C2×SD1611yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174Dic15—22no—
175Dic15—41no—
176C3×Dic5—42no—
177C5×Dic3—41no—
178C2×C3×Q8—101no—
179D3×Q8—202no—
180D3×Q8—202no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12C22⋊D511yescharacteristic
185C2×C4×D3—21no—
186C2×C4×D3—102no—
187C2×Dic6—51no—
188C2×Dic6—102no—
189C2×C3×C8—21no—
190C2×C3×C8—101no—
191C3×C4⋊C4—52no—
192C3×C4⋊C4—101no—
193C3×C42C22×D511yescharacteristic
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—102no—
196C4⋊Dic3—51no—
197C4⋊Dic3C22⋊D511yescharacteristic
198Dic3⋊C4—102no—
199Dic3⋊C4—101no—
200C4×Dic3—101no—
201C2×C3⋊C8—101no—
202D24—42no—
203#204—202no—
204C23×C5—61no—
205C23×C5—121no—
206C5×D4—32no—
207C5×D4—61no—
208C5×D4—122no—
209C5×D4—121no—
210C5×D4—121no—
211C5×D4—121no—
212C5×D4—121no—
213C2×C4×C5—61no—
214C2×C4×C5—121no—
215C2×C4×C5—121no—
216C2×C4×C5C2×D1211yescharacteristic
217C2×C4×C5D3×D411yescharacteristic
218C2×C4×C5D3×D411yescharacteristic
219C2×Dic5—22no—
220C2×Dic5—61no—
221C2×Dic5—61no—
222C2×Dic5—124no—
223Dic10—32no—
224Dic10—41no—
225Dic10—41no—
226Dic10—61no—
227Dic10—124no—
228C5×C8—41no—
229#168—41no—
230#168—121no—
231C22×Q8—301no—
232C2×SD16—301no—
233C2×D8—61no—
234C4⋊Q8—51no—
235C4⋊Q8—301no—
236#127—31no—
237C22⋊Q8—302no—
238C22⋊Q8—301no—
239C4×Q8—151no—
240C4×D4—31no—
241C4×D4—301no—
242C4⋊C8—51no—
243C4⋊C8D3×D511yescharacteristic
244#102—61no—
245#102—302no—
246#102—301no—
247C4×C8—151no—
248C2×C3×C5#44711yescharacteristic
249C2×C3×C5#44811yescharacteristic
250C2×C3×C5#45411yescharacteristic
251C5×D3—42no—
252C5×D3—161no—
253C22×D3—21no—
254C22×D3—41no—
255C3×Q8—201no—
256C3×Q8—201no—
257C2×C3×C4—102no—
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4C2×C22⋊D511yescharacteristic
261C2×Dic3—21no—
262C2×Dic3—101no—
263C2×Dic3—101no—
264D12—21no—
265D12—42no—
266D12—41no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12#68712yescomplemented
271C4×D3—41no—
272C4×D3—41no—
273C4×D3—204no—
274Dic6—52no—
275Dic6—101no—
276Dic6—204no—
277C3×C8—41no—
278C3×C8—201no—
279C3⋊C8—201no—
280C22×C5—62no—
281C22×C5—121no—
282C22×C5—121no—
283C22×C5—241no—
284C22×C5—241no—
285C22×C5—241no—
286C22×C5#88211yescharacteristic
287C4×C5—21no—
288C4×C5—121no—
289C4×C5D3×D811yescharacteristic
290C4×C5D3×SD1611yescharacteristic
291C4×C5#91411yescharacteristic
292C4×C5#91811yescharacteristic
293Dic5—42no—
294Dic5—62no—
295Dic5—121no—
296C2×Q8—101no—
297C2×Q8—151no—
298C2×Q8—302no—
299C2×Q8—602no—
300C2×Q8—602no—
301C2×D4—31no—
302C2×D4—61no—
303C2×D4—61no—
304C2×D4—61no—
305C22×C4—61no—
306C22×C4—302no—
307SD16—602no—
308D8—122no—
309C2×C8—21no—
310C2×C8—101no—
311C2×C8—301no—
312C4⋊C4—31no—
313C4⋊C4—52no—
314C4⋊C4—101no—
315C4⋊C4—151no—
316C4⋊C4—302no—
317C4⋊C4—301no—
318C22⋊C4—61no—
319C22⋊C4—302no—
320C42—301no—
321C42C2×D3×D511yescharacteristic
322C3×C5#162711yescharacteristic, complemented, Hall
323C22×C3#408311yescharacteristic
324C2×D3—22no—
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—81no—
328C2×D3—81no—
329C2×D3—81no—
330C3×C4—21no—
331C3×C4—202no—
332C3×C4D5×D811yescharacteristic
333C3×C4#405711yescharacteristic
334C3×C4C2×#68711yescharacteristic
335C3×C4#409711yescharacteristic
336Dic3—41no—
337Dic3—102no—
338Dic3—201no—
339C2×C5—122no—
340C2×C5—481no—
341C2×C5#475311yescharacteristic
342C2×C5#477311yescharacteristic
343C2×C5#480611yescharacteristic
344C23—61no—
345C23—121no—
346Q8—152no—
347Q8—201no—
348Q8—201no—
349Q8—301no—
350Q8—604no—
351D4—32no—
352D4—61no—
353D4—122no—
354D4—121no—
355D4—121no—
356D4—121no—
357D4—121no—
358C2×C4—61no—
359C2×C4—102no—
360C2×C4—121no—
361C2×C4—121no—
362C2×C4—301no—
363C2×C4—301no—
364C2×C4—604no—
365C2×C4D5×D1211yescharacteristic
366C2×C4#677711yescharacteristic
367C2×C4D3×C22⋊D511yescharacteristic
368C8—41no—
369C8—201no—
370C8—601no—
371C2×C3#6532911yescharacteristic
372C2×C3#6544511yescharacteristic
373C2×C3#6549011yescharacteristic
374D3—42no—
375D3—161no—
376C5#6845711yescharacteristic, complemented, Sylow
377C22—62no—
378C22—121no—
379C22—121no—
380C22—241no—
381C22—241no—
382C22—241no—
383C22#9147511yescharacteristic
384C4—21no—
385C4—121no—
386C4—202no—
387C4—302no—
388C4—601no—
389C4#9125611yescharacteristic
390C4#9125711yescharacteristic
391C4D3×#68711yescharacteristic
392C4#9151011yescharacteristic
393C3#1060180711yescharacteristic, complemented, Sylow
394C2—122no—
395C2—481no—
396C2#1174749411yescharacteristic
397C2#1174811911yescharacteristic
398C2#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#1627
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. #11752558C2semidirect
3. #11747086C2semidirect
4. #11746901C2semidirect
5. #11746305C2semidirect
6. C3×#64706C2semidirect
7. #11745836C2semidirect
32. #64706D3semidirect
93. Dic30D8semidirect
101. C5×D12SD16semidirect
270. D12#687semidirect
322. C3×C5#1627semidirect
376. C5#68457semidirect
393. C3#10601807semidirect

Maximal subgroups

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

subgroupindex
#117525582
C5×#48432
#117470862
#117469012
#117463052
C3×#647062
#117458362
#106018073
#684575