Finite Group Databasebeta

← #14289455

Subgroups — #14289455

Order 1920.

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

normal subgroups only

This group has 512 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#11752680C211yesmaximal, characteristic
2C5×#4693C211yesmaximal, characteristic, complemented
3#11746963C211yesmaximal, characteristic, complemented
4#11746880C211yesmaximal, characteristic, complemented
5#11746277C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic, complemented
7#11745853C211yesmaximal, characteristic, complemented
8#10602064—31nomaximal, Hall
9C2×#6772—21no—
10C4×Dic30C2211yescharacteristic
11C2×C5×#204—22no—
12C5×#874C2211yescharacteristic
13C5×#869C2211yescharacteristic
14C3×C4×D20C2211yescharacteristic
15#91463—21no—
16#91453—22no—
17#91449—21no—
18#91435—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90988—21no—
23#90986—21no—
24#90975—21no—
25#90964—21no—
26#68188—51nomaximal, Hall
27#66052—31no—
28C5×#492—31no—
29#65380—31no—
30#65373—31no—
31#64764—31no—
32#64679D311yescharacteristic, complemented
33#64676—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12D412yes—
38C2×C5×Dic6—21no—
39C2×C3×D20D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×#1201—22no—
42C2×#1201—22no—
43C2×D3×Dic5—22no—
44#6772—42no—
45#6772—42no—
46C2×C3×C5×C8—21no—
47C3×C42×C5C2311yescharacteristic
48C4⋊Dic15D411yescharacteristic
49#6712—21no—
50C4×Dic15—21no—
51C2×C3⋊#168—21no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3—21no—
54C5×#204—44no—
55C3×#685—21no—
56C3×C4⋊Dic5D411yescharacteristic
57C2×C3×#168—21no—
58(C2×D3)⋊Dic5—22no—
59#5553—51no—
60#5008—51no—
61#4850—51no—
62#4693D511yescharacteristic, complemented
63C3×D4⋊C8—51no—
64#4485—51no—
65#4456—51no—
66C2×#711—61no—
67C2×C5×SD16—62no—
68C5×C4⋊Q8—31no—
69C5×#127—31no—
70#4086—61no—
71#4085—62no—
72#4084—61no—
73D4×Dic5—61no—
74C4×D20C2×D311yescharacteristic
75C4×Dic10—31no—
76C4×C5×C8C2×D311yescharacteristic
77#3942—61no—
78#3941—61no—
79#3940—61no—
80#3939—61no—
81C4⋊#168—31no—
82C4⋊#168C2×D311yescharacteristic
83#1631—151noSylow
84C22×C5×D3—22no—
85C22×C3×D5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91Dic30—21no—
92Dic30SD1612yescomplemented
93C2×C5×Dic3—41no—
94C5×D12—42no—
95C5×D12—41no—
96C5×D12—41no—
97C5×D12—41no—
98C5×D12—41no—
99C5×Dic6—42no—
100C2×C3×Dic5—21no—
101C3×D20—21no—
102C3×D20—21no—
103C3×C4×D5—41no—
104C3×C4×D5—41no—
105#1201—44no—
106#1201—82no—
107D3×Dic5—44no—
108C3×C5×C8—22no—
109C3⋊#168—41no—
110C3×#168—41no—
111C2×#235—101no—
112C3×C4×D4—51no—
113#940—101no—
114#930—101no—
115C2×#204—22no—
116#893—101no—
117#884—102no—
118#874C2×D511yescharacteristic
119#869C2×D511yescharacteristic
120C4×Dic6—51no—
121C3×C4⋊C8—51no—
122C3×C4×C8C2×D511yescharacteristic
123#832—101no—
124#818—101no—
125#816—101no—
126#808—101no—
127C4⋊(C3⋊C8)—51no—
128C2×C5×Q8—61no—
129C2×C5×D4—32no—
130C2×C5×D4—61no—
131C2×C5×D4—61no—
132C2×C22⋊D5—62no—
133C2×C22⋊D5—62no—
134C22×Dic5—62no—
135#711—122no—
136#711—122no—
137C2×D20D1211yescharacteristic
138C2×C4×D5—21no—
139C2×Dic10—31no—
140C5×SD16—124no—
141C2×C5×C8—21no—
142C5×C4⋊C4—61no—
143C5×C4⋊C4—61no—
144C42×C5C22×D311yescharacteristic
145C22⋊Dic5—62no—
146#685—21no—
147C4⋊Dic5—31no—
148C4⋊Dic5D1211yescharacteristic
149#683—61no—
150C4×Dic5—61no—
151C2×#168—21no—
152C2×#168—61no—
153#550—151no—
154#492—31no—
155#477—151no—
156#476—151no—
157#331—151no—
158Q8⋊C8—151no—
159D4⋊C8—51no—
160C22×C3×C5#12011yescharacteristic
161C2×C5×D3—42no—
162C2×C5×D3—42no—
163C2×C5×D3—42no—
164C2×C3×D5—41no—
165C2×C3×D5—41no—
166C2×C3×D5—41no—
167C3×C4×C5—21no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5#13711yescharacteristic
172Dic15—22no—
173Dic15—41no—
174C3×Dic5—41no—
175C5×Dic3—81no—
176C2×C3×D4—51no—
177C22×C3×C4—101no—
178C2×#67—102no—
179C2×#67—102no—
180#235—202no—
181#235—202no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12C22⋊D512yes—
185C2×C4×D3—102no—
186C2×Dic6—21no—
187C2×Dic6—51no—
188C2×C3×C8—21no—
189C2×C3×C8—101no—
190C3×C4⋊C4—51no—
191C3×C22⋊C4—101no—
192C3×C42C22×D511yescharacteristic
193(C2×D3)⋊C4—102no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—51no—
197Dic3⋊C4—101no—
198C4×Dic3—101no—
199C2×C3⋊C8—101no—
200#204—44no—
201C23×C5—62no—
202C22×D5—21no—
203C5×Q8—122no—
204C5×D4—122no—
205C5×D4—121no—
206C5×D4—121no—
207C5×D4—121no—
208C5×D4—121no—
209C2×C4×C5—121no—
210C2×C4×C5C2×D1211yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C22⋊D5—124no—
214C22⋊D5—242no—
215C2×Dic5—21no—
216C2×Dic5—61no—
217C2×Dic5—61no—
218C2×Dic5—124no—
219D20—21no—
220D20—21no—
221C4×D5—41no—
222C4×D5—41no—
223Dic10—32no—
224Dic10—61no—
225C5×C8—22no—
226#168—41no—
227#168—121no—
228C2×#41—301no—
229C2×SD16—62no—
230C4⋊Q8—31no—
231#127—31no—
232#127—301no—
233#121—302no—
234#121—301no—
235C4×Q8—151no—
236C4×D4—51no—
237C4×D4—301no—
238#107—301no—
239#106—301no—
240C4⋊C8—51no—
241C4⋊C8—151no—
242#103—301no—
243#102—301no—
244C4×C8D3×D511yescharacteristic
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45211yescharacteristic
247C2×C3×C5#45311yescharacteristic
248C3×D5—81no—
249C5×D3—82no—
250C23×C3—101no—
251C22×D3—22no—
252C3×D4—101no—
253C3×D4—101no—
254C2×C3×C4—101no—
255C2×C3×C4—201no—
256C2×C3×C4—201no—
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4C2×C22⋊D511yescharacteristic
260#67—204no—
261#67—402no—
262C2×Dic3—41no—
263C2×Dic3—101no—
264C2×Dic3—101no—
265D12—42no—
266D12—41no—
267D12—41no—
268D12—41no—
269D12—41no—
270C4×D3—204no—
271Dic6—42no—
272Dic6—52no—
273Dic6—101no—
274C3×C8—22no—
275C3×C8—201no—
276C3⋊C8—201no—
277C22×C5—122no—
278C22×C5—122no—
279C22×C5—122no—
280C22×C5#88211yescharacteristic
281C2×D5—41no—
282C2×D5—41no—
283C2×D5—41no—
284C4×C5—21no—
285C4×C5—241no—
286C4×C5#90411yescharacteristic
287C4×C5#90911yescharacteristic
288C4×C5#91111yescharacteristic
289C4×C5D3×SD1611yescharacteristic
290Dic5—41no—
291Dic5—62no—
292Dic5—121no—
293#41—602no—
294#41—602no—
295C2×Q8—61no—
296C2×Q8—151no—
297C2×D4—32no—
298C2×D4—51no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4—302no—
302C2×D4—302no—
303C22×C4—101no—
304C22×C4—302no—
305SD16—124no—
306C2×C8—21no—
307C2×C8—101no—
308C2×C8—301no—
309C4⋊C4—51no—
310C4⋊C4—61no—
311C4⋊C4—61no—
312C4⋊C4—151no—
313C4⋊C4—301no—
314C22⋊C4—101no—
315C22⋊C4—302no—
316C42—301no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—201no—
320C22×C3—201no—
321C22×C3—201no—
322C22×C3#408311yescharacteristic
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—42no—
326C3×C4—21no—
327C3×C4—201no—
328C3×C4D5×SD1611yescharacteristic
329C3×C4#406011yescharacteristic
330C3×C4#406111yescharacteristic
331C3×C4#406211yescharacteristic
332Dic3—81no—
333Dic3—102no—
334Dic3—201no—
335C2×C5—242no—
336C2×C5#473311yescharacteristic
337C2×C5#477611yescharacteristic
338C2×C5#482211yescharacteristic
339D5—81no—
340C23—62no—
341C23—101no—
342Q8—122no—
343Q8—152no—
344Q8—301no—
345D4—101no—
346D4—101no—
347D4—122no—
348D4—121no—
349D4—121no—
350D4—121no—
351D4—121no—
352D4—604no—
353D4—1202no—
354C2×C4—101no—
355C2×C4—121no—
356C2×C4—201no—
357C2×C4—201no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—604no—
361C2×C4D5×D1211yescharacteristic
362C2×C4#677711yescharacteristic
363C2×C4D3×C22⋊D511yescharacteristic
364C8—22no—
365C8—201no—
366C8—601no—
367C2×C3—401no—
368C2×C3#6536611yescharacteristic
369C2×C3#6545811yescharacteristic
370C2×C3#6546211yescharacteristic
371D3—82no—
372C5#6818811yescharacteristic, complemented, Sylow
373C22—122no—
374C22—122no—
375C22—122no—
376C22—201no—
377C22—201no—
378C22—201no—
379C22#9147511yescharacteristic
380C4—21no—
381C4—201no—
382C4—241no—
383C4—302no—
384C4—601no—
385C4#9125511yescharacteristic
386C4#9125811yescharacteristic
387C4#9126011yescharacteristic
388C4#9126911yescharacteristic
389C3#1060206411yescharacteristic, complemented, Sylow
390C2—242no—
391C2—401no—
392C2#1174711611yescharacteristic
393C2#1174811811yescharacteristic
394C2#1174815511yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11752680C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1631
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×#4693C2semidirect
3. #11746963C2semidirect
4. #11746880C2semidirect
5. #11746277C2semidirect
6. C3×#64679C2semidirect
7. #11745853C2semidirect
32. #64679D3semidirect
62. #4693D5semidirect
92. Dic30SD16semidirect
318. C3×C5#1631semidirect
372. C5#68188semidirect
389. C3#10602064semidirect

Maximal subgroups

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

subgroupindex
#117526802
C5×#46932
#117469632
#117468802
#117462772
C3×#646792
#117458532
#106020643
#681885