Finite Group Databasebeta

← #14289441

Subgroups — #14289441

Order 1920.

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

normal subgroups only

This group has 512 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#11752538C211yesmaximal, characteristic
2#11751186C211yesmaximal, characteristic, complemented
3C5×#5084C211yesmaximal, characteristic, complemented
4C3×#65380C211yesmaximal, characteristic, complemented
5#11745854C211yesmaximal, characteristic, complemented
6#11745840C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10601934—31nomaximal, Hall
9C2×#6769—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C2×#6717—22no—
12#91763C2211yescharacteristic
13C4×C5×D12C2211yescharacteristic
14C3×C4×Dic10C2211yescharacteristic
15#91460—21no—
16#91451—21no—
17#91420—22no—
18#91418—21no—
19C4×C3⋊#168C2211yescharacteristic
20C5×#809—21no—
21C5×#808—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3942—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71160—51nomaximal, Hall
27#65887—31no—
28C5×#476—31no—
29#65380D311yescharacteristic, complemented
30#65374—31no—
31D4⋊#168—31no—
32#64705—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60D412yes—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×#1203—22no—
42C2×#1203—22no—
43C2×#1200—22no—
44#6769—42no—
45#6769—42no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C42×C5C2311yescharacteristic
49#6717—44no—
50C2×C3⋊#168—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C2×C5×C3⋊C8—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C2×C3×#168—21no—
58#6667—22no—
59#5577—51no—
60C3×#477—51no—
61#5085—51no—
62#5084D511yescharacteristic, complemented
63#4535—51no—
64#4485—51no—
65#4483—51no—
66C2×#709—61no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C4×C5×D4—31no—
69C2×#688—62no—
70#4086—61no—
71#4076—61no—
72#4039—61no—
73#4030—62no—
74#4020—31no—
75C4×Dic10C2×D311yescharacteristic
76C5×#106—61no—
77C5×C4⋊C8—31no—
78C5×#102—61no—
79#3942—21no—
80#3939—21no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1631—151noSylow
84C22×D15—22no—
85C22×C5×D3—21no—
86C3×C5×Q8—42no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91D60—42no—
92D60—41no—
93D60—41no—
94D60—41no—
95D60—41no—
96C2×C5×Dic3—21no—
97C5×D12—21no—
98C5×D12—21no—
99C4×C5×D3—41no—
100C4×C5×D3—41no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103C3×Dic10—21no—
104C3×Dic10SD1612yescomplemented
105#1203—44no—
106#1203—82no—
107#1200—44no—
108C3⋊#168—22no—
109C3×#168—41no—
110C5×C3⋊C8—41no—
111C2×#239—101no—
112C3×C4⋊Q8C2×D511yescharacteristic
113C3×C4×Q8—51no—
114C2×#215—102no—
115#895—102no—
116#895—101no—
117#874—51no—
118#874—101no—
119C4×D12—101no—
120C4×D12C2×D511yescharacteristic
121C3×#107—101no—
122C3×C4⋊C8—51no—
123C3×#103—101no—
124#809—21no—
125#808—21no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C4×C3⋊C8—51no—
128C2×C5×Q8—21no—
129C2×C5×D4—31no—
130C22×C4×C5—61no—
131C2×C22⋊D5—62no—
132C2×C22⋊D5—62no—
133#709—122no—
134#709—122no—
135C2×D20—32no—
136C2×D20—61no—
137C2×D20—61no—
138C2×C4×D5—62no—
139C2×Dic10#6711yescharacteristic
140C2×C5×C8—61no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—31no—
144C5×C22⋊C4—61no—
145C42×C5C22×D311yescharacteristic
146#688—124no—
147#685—62no—
148C4⋊Dic5#6711yescharacteristic
149#683—21no—
150C4×Dic5—21no—
151C2×#168—21no—
152C2×#168—61no—
153#550—151no—
154#492—151no—
155#477—51no—
156#476—31no—
157#331—151no—
158Q8⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×D15—42no—
162C2×D15—42no—
163C2×D15—42no—
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C2×C5×D3—41no—
167C3×C4×C5—21no—
168C3×C4×C5—81no—
169C3×C4×C5C2×SD1611yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173C3×Dic5—22no—
174C3×Dic5—41no—
175C5×Dic3—41no—
176C2×C3×Q8—21no—
177C2×C3×Q8—51no—
178#239—202no—
179#239—202no—
180C2×D12—52no—
181C2×D12—102no—
182C2×D12—101no—
183C2×D12—101no—
184C2×D12—102no—
185C2×D12C22⋊D511yescharacteristic
186C2×C4×D3—21no—
187C2×C4×D3—102no—
188C2×C3×C8—101no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—51no—
192C3×C4⋊C4—101no—
193C3×C42—101no—
194C3×C42C22×D511yescharacteristic
195#215—204no—
196(C2×D3)⋊C4—21no—
197(C2×D3)⋊C4—102no—
198C4⋊Dic3C22⋊D511yescharacteristic
199C2×C3⋊C8—21no—
200C2×C3⋊C8—101no—
201C23×C5—61no—
202C22×D5—62no—
203C5×Q8—42no—
204C5×D4—61no—
205C5×D4—61no—
206C2×C4×C5—41no—
207C2×C4×C5—61no—
208C2×C4×C5—121no—
209C2×C4×C5—121no—
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C22⋊D5—124no—
214C22⋊D5—242no—
215C2×Dic5—21no—
216C2×Dic5—21no—
217D20—122no—
218D20—121no—
219D20—121no—
220D20—121no—
221D20—121no—
222C4×D5—124no—
223Dic10—21no—
224Dic10#21512yescomplemented
225C5×C8—121no—
226#168—41no—
227#168—62no—
228C2×#41—301no—
229C2×SD16—302no—
230C4⋊Q8D3×D511yescharacteristic
231#127—151no—
232#127—301no—
233#121—302no—
234#121—301no—
235C4×Q8—51no—
236C4×D4—31no—
237C4×D4—301no—
238#107—101no—
239#106—61no—
240C4⋊C8—31no—
241C4⋊C8—51no—
242#103—101no—
243#102—61no—
244C4×C8—151no—
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45211yescharacteristic
247C2×C3×C5#45311yescharacteristic
248D15—82no—
249C5×D3—81no—
250C22×D3—21no—
251C22×D3—102no—
252C3×Q8—42no—
253C3×Q8—52no—
254C3×Q8—101no—
255C2×C3×C4—41no—
256C2×C3×C4—101no—
257C2×C3×C4—101no—
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4C2×C22⋊D511yescharacteristic
261C2×Dic3—21no—
262D12—21no—
263D12—21no—
264D12—202no—
265D12—204no—
266D12—201no—
267D12—201no—
268D12—201no—
269D12—201no—
270D12—402no—
271C4×D3—41no—
272C4×D3—41no—
273C4×D3—204no—
274C3×C8—201no—
275C3⋊C8—41no—
276C3⋊C8—102no—
277C22×C5—121no—
278C22×C5—121no—
279C22×C5—121no—
280C22×C5#93711yescharacteristic
281C2×D5—122no—
282C2×D5—122no—
283C2×D5—122no—
284C4×C5—21no—
285C4×C5—81no—
286C4×C5—121no—
287C4×C5#91811yescharacteristic
288C4×C5#91911yescharacteristic
289C4×C5C2×#21511yescharacteristic
290C4×C5#94911yescharacteristic
291Dic5—22no—
292Dic5—41no—
293#41—602no—
294#41—602no—
295C2×Q8—21no—
296C2×Q8—51no—
297C2×D4—31no—
298C2×D4—152no—
299C2×D4—302no—
300C2×D4—302no—
301C2×D4—301no—
302C2×D4—301no—
303C22×C4—61no—
304C22×C4—302no—
305SD16—604no—
306C2×C8—61no—
307C2×C8—101no—
308C2×C8—301no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—31no—
312C4⋊C4—51no—
313C4⋊C4—101no—
314C22⋊C4—61no—
315C22⋊C4—302no—
316C42—101no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3#408311yescharacteristic
320C2×D3—41no—
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—202no—
324C2×D3—202no—
325C2×D3—202no—
326C3×C4—21no—
327C3×C4—81no—
328C3×C4—102no—
329C3×C4—201no—
330C3×C4D5×SD1611yescharacteristic
331C3×C4#406011yescharacteristic
332C3×C4#408811yescharacteristic
333C3×C4#409611yescharacteristic
334Dic3—41no—
335C2×C5—241no—
336C2×C5#504611yescharacteristic
337C2×C5#518711yescharacteristic
338C2×C5#519811yescharacteristic
339D5—242no—
340C23—61no—
341C23—302no—
342Q8—42no—
343Q8—52no—
344Q8—101no—
345D4—61no—
346D4—61no—
347D4—602no—
348D4—604no—
349D4—601no—
350D4—601no—
351D4—601no—
352D4—601no—
353D4—1202no—
354C2×C4—41no—
355C2×C4—61no—
356C2×C4—101no—
357C2×C4—101no—
358C2×C4—121no—
359C2×C4—121no—
360C2×C4—604no—
361C2×C4D5×#6711yescharacteristic
362C2×C4D3×C22⋊D511yescharacteristic
363C2×C4#679011yescharacteristic
364C8—121no—
365C8—201no—
366C8—302no—
367C2×C3#6533611yescharacteristic
368C2×C3#6545811yescharacteristic
369C2×C3#6548711yescharacteristic
370D3—81no—
371D3—402no—
372C5#7116011yescharacteristic, complemented, Sylow
373C22—121no—
374C22—121no—
375C22—121no—
376C22—602no—
377C22—602no—
378C22—602no—
379C22#9157711yescharacteristic
380C4—21no—
381C4—81no—
382C4—102no—
383C4—121no—
384C4—201no—
385C4D5×#21511yescharacteristic
386C4#9150211yescharacteristic
387C4#9151911yescharacteristic
388C4#9152011yescharacteristic
389C3#1060193411yescharacteristic, complemented, Sylow
390C2—241no—
391C2—1202no—
392C2#1174916411yescharacteristic
393C2#1174939711yescharacteristic
394C2#1174940811yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11752538C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1631
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11751186C2semidirect
3. C5×#5084C2semidirect
4. C3×#65380C2semidirect
5. #11745854C2semidirect
6. #11745840C2semidirect
7. #11745836C2semidirect
29. #65380D3semidirect
62. #5084D5semidirect
104. C3×Dic10SD16semidirect
224. Dic10#215semidirect
318. C3×C5#1631semidirect
372. C5#71160semidirect
389. C3#10601934semidirect

Maximal subgroups

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

subgroupindex
#117525382
#117511862
C5×#50842
C3×#653802
#117458542
#117458402
#117458362
#106019343
#711605