Finite Group Databasebeta

← #14290863

Subgroups — #14290863

Order 1920.

480 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 88 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#11752561C211yesmaximal, characteristic
2C5×#4841C211yesmaximal, characteristic, complemented
3#11746966C211yesmaximal, characteristic, complemented
4#11746947C211yesmaximal, characteristic, complemented
5#11746304C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10601844—31nomaximal, Hall
9C2×#6769—21no—
10C4×D60C2211yescharacteristic
11C2×C5×#204—21no—
12C4×C5×D12C2211yescharacteristic
13C5×#869C2211yescharacteristic
14C3×#4015C2211yescharacteristic
15#91466—21no—
16#91438—22no—
17#91437—21no—
18#91369—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×#816—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90988—21no—
24#90986—22no—
25#90969—21no—
26#68439—51nomaximal, Hall
27#65885—31no—
28C5×#461—31no—
29#65376—31no—
30#65368—31no—
31D4⋊#168—31no—
32#64706D311yescharacteristic, complemented
33#64703—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C5×Dic6—21no—
39C2×C3×Dic10—21no—
40C2×#1203—22no—
41C2×#1200—22no—
42#6769—42no—
43#6769—42no—
44C2×C3×C5×C8—21no—
45C3×C42×C5C2311yescharacteristic
46#6714—21no—
47C4⋊Dic15D411yescharacteristic
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C5×#204—42no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5D412yes—
56C2×C3×#168—21no—
57#6669—22no—
58(C2×D3)⋊Dic5—22no—
59#5726—51no—
60#5080—51no—
61#4846—51no—
62#4841D511yescharacteristic, complemented
63C3×#332—51no—
64#4483—51no—
65#4483—51no—
66C2×#709—61no—
67C2×C5×SD16—61no—
68C5×C4⋊Q8—31no—
69C4×C5×D4—31no—
70#4084—61no—
71#4070—61no—
72D5×C4⋊C4—61no—
73#4029—62no—
74C4×D20—31no—
75#4015C2×D311yescharacteristic
76C5×C4⋊C8C2×D311yescharacteristic
77C5×#103—61no—
78#3941—61no—
79#3940—62no—
80#3939—61no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1654—151noSylow
84C22×D15—21no—
85C22×C5×D3—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90D60—21no—
91D60SD1612yescomplemented
92C4×D15—41no—
93C4×D15—41no—
94C2×C5×Dic3—21no—
95C2×C5×Dic3—41no—
96C5×D12—21no—
97C5×D12—21no—
98C4×C5×D3—41no—
99C4×C5×D3—41no—
100C5×Dic6—41no—
101C5×Dic6—41no—
102C2×C3×Dic5—22no—
103C3×Dic10—41no—
104C3×Dic10—41no—
105#1203—44no—
106#1200—44no—
107C3×C5×C8—41no—
108C3⋊#168—22no—
109C3×#168—41no—
110C2×#239—101no—
111C3×C4⋊Q8—51no—
112#946—101no—
113C2×#204—21no—
114#895—101no—
115#894—102no—
116D3×C4⋊C4—101no—
117C4×D12—51no—
118C4×D12C2×D511yescharacteristic
119#869C2×D511yescharacteristic
120C3×C4⋊C8—51no—
121C3×C4⋊C8C2×D511yescharacteristic
122#821—101no—
123#818—101no—
124#816—21no—
125#808—102no—
126C4×C3⋊C8—51no—
127C2×C5×Q8—61no—
128C2×C5×D4—31no—
129C22×C4×C5—61no—
130C2×C22⋊D5—62no—
131#709—122no—
132#709—122no—
133C2×D20—31no—
134C2×C4×D5—62no—
135C2×C4×D5—61no—
136C2×Dic10—21no—
137C5×SD16—122no—
138C2×C5×C8—21no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C5×C22⋊C4—61no—
143C42×C5C22×D311yescharacteristic
144C22⋊Dic5—62no—
145#685—61no—
146C4⋊Dic5—21no—
147C4⋊Dic5—31no—
148C4⋊Dic5D1212yes—
149#683—62no—
150C2×#168—21no—
151C2×#168—61no—
152#547—151no—
153#498—151no—
154#474—151no—
155#461—31no—
156#332—51no—
157D4⋊C8—151no—
158D4⋊C8—151no—
159C22×C3×C5#12011yescharacteristic
160C2×D15—22no—
161C2×D15—41no—
162C2×D15—41no—
163C2×C5×D3—41no—
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C3×C4×C5—21no—
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171Dic15—41no—
172C3×Dic5—42no—
173C5×Dic3—41no—
174C5×Dic3—81no—
175C2×C3×Q8—101no—
176#239—202no—
177#239—202no—
178C2×D12—51no—
179C2×D12—102no—
180C2×D12C22⋊D511yescharacteristic
181C2×C4×D3—21no—
182C2×C4×D3—102no—
183C2×C4×D3—101no—
184C2×Dic6—21no—
185C2×C3×C8—21no—
186C2×C3×C8—101no—
187C3×C4⋊C4—52no—
188C3×C4⋊C4—101no—
189C3×C42C22×D511yescharacteristic
190(C2×D3)⋊C4—21no—
191(C2×D3)⋊C4—102no—
192(C2×D3)⋊C4—101no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—51no—
196C4⋊Dic3C22⋊D511yescharacteristic
197Dic3⋊C4—102no—
198C2×C3⋊C8—101no—
199#204—42no—
200C23×C5—61no—
201C22×D5—61no—
202C5×Q8—121no—
203C5×Q8—121no—
204C5×D4—61no—
205C5×D4—61no—
206C2×C4×C5—61no—
207C2×C4×C5—121no—
208C2×C4×C5—121no—
209C2×C4×C5—121no—
210C2×C4×C5C2×D1211yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C22⋊D5—124no—
214C2×Dic5—22no—
215C2×Dic5—61no—
216D20—32no—
217D20—61no—
218C4×D5—124no—
219C4×D5—121no—
220C4×D5—121no—
221Dic10—41no—
222Dic10—41no—
223C5×C8—41no—
224#168—41no—
225#168—62no—
226C2×#41—301no—
227C2×SD16—61no—
228C4⋊Q8—31no—
229C4⋊Q8—51no—
230#123—302no—
231C22⋊Q8—301no—
232#121—301no—
233C4×D4—31no—
234C4×D4—151no—
235C2×C4⋊C4—301no—
236#107—301no—
237#106—302no—
238C4⋊C8—51no—
239C4⋊C8D3×D511yescharacteristic
240#103—61no—
241#102—301no—
242C4×C8—151no—
243C2×C3×C5#44911yescharacteristic
244C2×C3×C5#45011yescharacteristic
245C2×C3×C5#45611yescharacteristic
246D15—42no—
247C5×D3—81no—
248C22×D3—21no—
249C22×D3—101no—
250C3×Q8—201no—
251C3×Q8—201no—
252C2×C3×C4—102no—
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4C2×C22⋊D511yescharacteristic
256C2×Dic3—21no—
257C2×Dic3—41no—
258C2×Dic3—101no—
259D12—21no—
260D12—21no—
261D12—52no—
262D12—101no—
263D12—204no—
264C4×D3—41no—
265C4×D3—41no—
266C4×D3—204no—
267C4×D3—201no—
268C4×D3—201no—
269Dic6—41no—
270Dic6—41no—
271C3×C8—41no—
272C3×C8—201no—
273C3⋊C8—102no—
274C22×C5—121no—
275C22×C5—121no—
276C22×C5—121no—
277C22×C5#88211yescharacteristic
278C2×D5—62no—
279C2×D5—121no—
280C2×D5—121no—
281C4×C5—21no—
282C4×C5—121no—
283C4×C5—241no—
284C4×C5#91111yescharacteristic
285C4×C5D3×SD1611yescharacteristic
286C4×C5#91411yescharacteristic
287C4×C5#91911yescharacteristic
288Dic5—42no—
289Dic5—121no—
290#41—602no—
291#41—602no—
292C2×Q8—61no—
293C2×Q8—101no—
294C2×D4—31no—
295C2×D4—151no—
296C2×D4—302no—
297C22×C4—61no—
298C22×C4—302no—
299C22×C4—301no—
300SD16—122no—
301C2×C8—21no—
302C2×C8—101no—
303C2×C8—301no—
304C4⋊C4—31no—
305C4⋊C4—52no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—101no—
309C4⋊C4—151no—
310C4⋊C4—302no—
311C22⋊C4—61no—
312C22⋊C4—302no—
313C22⋊C4—301no—
314C42C2×D3×D511yescharacteristic
315C3×C5#165411yescharacteristic, complemented, Hall
316C22×C3#408311yescharacteristic
317C2×D3—41no—
318C2×D3—41no—
319C2×D3—41no—
320C2×D3—102no—
321C2×D3—201no—
322C2×D3—201no—
323C3×C4—21no—
324C3×C4—202no—
325C3×C4D5×SD1611yescharacteristic
326C3×C4#406011yescharacteristic
327C3×C4#407811yescharacteristic
328C3×C4#409611yescharacteristic
329Dic3—41no—
330Dic3—81no—
331Dic3—201no—
332C2×C5—241no—
333C2×C5#475211yescharacteristic
334C2×C5#477611yescharacteristic
335C2×C5#481011yescharacteristic
336D5—122no—
337C23—61no—
338C23—301no—
339Q8—121no—
340Q8—121no—
341Q8—201no—
342Q8—201no—
343D4—61no—
344D4—61no—
345D4—152no—
346D4—301no—
347D4—604no—
348C2×C4—61no—
349C2×C4—102no—
350C2×C4—121no—
351C2×C4—121no—
352C2×C4—121no—
353C2×C4—301no—
354C2×C4—604no—
355C2×C4—601no—
356C2×C4—601no—
357C2×C4D5×D1211yescharacteristic
358C2×C4#677711yescharacteristic
359C2×C4D3×C22⋊D511yescharacteristic
360C8—41no—
361C8—201no—
362C8—302no—
363C2×C3#6532611yescharacteristic
364C2×C3#6545811yescharacteristic
365C2×C3#6549411yescharacteristic
366D3—81no—
367D3—202no—
368C5#6843911yescharacteristic, complemented, Sylow
369C22—121no—
370C22—121no—
371C22—121no—
372C22—302no—
373C22—601no—
374C22—601no—
375C22#9147511yescharacteristic
376C4—21no—
377C4—121no—
378C4—202no—
379C4—241no—
380C4—601no—
381C4#9125511yescharacteristic
382C4#9125811yescharacteristic
383C4#9149611yescharacteristic
384C4#9151911yescharacteristic
385C3#1060184411yescharacteristic, complemented, Sylow
386C2—241no—
387C2—602no—
388C2#1174751711yescharacteristic
389C2#1174811811yescharacteristic
390C2#1174825811yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752561C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1654
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
2. C5×#4841C2semidirect
3. #11746966C2semidirect
4. #11746947C2semidirect
5. #11746304C2semidirect
6. C3×#64706C2semidirect
7. #11745836C2semidirect
32. #64706D3semidirect
62. #4841D5semidirect
91. D60SD16semidirect
315. C3×C5#1654semidirect
368. C5#68439semidirect
385. C3#10601844semidirect

Maximal subgroups

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

subgroupindex
#117525612
C5×#48412
#117469662
#117469472
#117463042
C3×#647062
#117458362
#106018443
#684395