Finite Group Databasebeta

← #14289471

Subgroups — #14289471

Order 1920.

512 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#65887C211yesmaximal, characteristic
2#11751109C211yesmaximal, characteristic, complemented
3#11747071C211yesmaximal, characteristic, complemented
4#11746916C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745852C211yesmaximal, characteristic, complemented
7#11745841C211yesmaximal, characteristic, complemented
8#10598981—31nomaximal, Hall
9C2×C3×#709—21no—
10C3×C4×C5×D4C2211yescharacteristic
11#91758C2211yescharacteristic
12C3×#4086—21no—
13C3×#4076—21no—
14C3×#4039—21no—
15C3×#4030—22no—
16C3×#4020C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C2×#6657—22no—
19#91116—21no—
20#91092—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#90990—21no—
25#90971—21no—
26#71919—51nomaximal, Hall
27#65887D311yescharacteristic
28#65297—31no—
29#65139—31no—
30#64982—31no—
31C5×D4⋊C8—31no—
32#64705—31no—
33#64676—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×Dic30—21no—
37C2×C3×C22⋊D5—22no—
38C2×C3×C22⋊D5—22no—
39C3×#709—42no—
40C3×#709—42no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20D412yes—
44C2×C3×C4×D5—22no—
45C2×C3×Dic10D411yescharacteristic
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C3×C42×C5C2311yescharacteristic
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C2×C3⋊#168—21no—
52C2×C5×C3⋊C8—21no—
53C2×C5×C3⋊C8—21no—
54C3×#685—22no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×#683—21no—
57C3×C4×Dic5—21no—
58#6657—44no—
59C3×#550—51no—
60#5076—51no—
61#5021—51no—
62#5008—51no—
63#4544—51no—
64#4535—51no—
65D4⋊(C3⋊C8)D511yescharacteristic, complemented
66C2×#709—21no—
67C4×C5×D4C2×D311yescharacteristic
68#4086—21no—
69#4076—21no—
70C2×#677—62no—
71#4039—21no—
72#4030—22no—
73#4020C2×D311yescharacteristic
74#4015—31no—
75C4×Dic10C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C4×C5×C8—31no—
78#3964—61no—
79#3950—61no—
80#3948—61no—
81#3940—61no—
82C4⋊#168—31no—
83#1631—151noSylow
84C23×C3×C5—21no—
85C22×C3×D5—22no—
86C3×C5×D4—21no—
87C3×C5×D4—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×Dic15—41no—
95Dic30—42no—
96C3×C22⋊D5—44no—
97C3×C22⋊D5—82no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—21no—
100C3×D20—42no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3×C4×D5—44no—
106C3×Dic10—21no—
107C3×Dic10SD1612yescomplemented
108C3⋊#168—41no—
109C5×C3⋊C8—22no—
110C5×C3⋊C8—41no—
111C2×C3×#41—101no—
112C3×#127—51no—
113C3×#127—101no—
114C3×#121—102no—
115C3×#121—101no—
116C3×C4×Q8—51no—
117C3×C4×D4—101no—
118C3×C4×D4C2×D511yescharacteristic
119C2×#214—102no—
120#869—51no—
121#835—101no—
122#832—101no—
123#808—101no—
124#807—101no—
125C4⋊(C3⋊C8)—51no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C4×C3⋊C8C2×D511yescharacteristic
128C2×C5×D4#6711yescharacteristic
129C22×C4×C5—21no—
130C2×C22⋊D5—22no—
131C2×C22⋊D5—22no—
132#709—42no—
133#709—42no—
134C2×D20—21no—
135C2×D20—21no—
136C2×D20#6712yes—
137C2×C4×D5—22no—
138C2×Dic10—61no—
139C2×Dic10#6711yescharacteristic
140C2×C5×C8—61no—
141C2×C5×C8—61no—
142C5×C4⋊C4#6711yescharacteristic
143C5×C22⋊C4—21no—
144C42×C5C22×D311yescharacteristic
145#685—22no—
146C4⋊Dic5—61no—
147C4⋊Dic5—61no—
148C4⋊Dic5#6711yescharacteristic
149#683—21no—
150C4×Dic5—21no—
151C2×#168—61no—
152#677—124no—
153#550—51no—
154#492—151no—
155#477—151no—
156#476—151no—
157#331—151no—
158Q8⋊C8—151no—
159D4⋊C8—31no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5#12011yescharacteristic
164C2×C3×D5—42no—
165C2×C3×D5—42no—
166C2×C3×D5—42no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169C3×C4×C5C2×SD1611yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173Dic15—81no—
174C3×Dic5—22no—
175C3×Dic5—41no—
176C3×#41—202no—
177C3×#41—202no—
178C2×C3×Q8—51no—
179C2×C3×D4—52no—
180C2×C3×D4—102no—
181C2×C3×D4—102no—
182C2×C3×D4—101no—
183C2×C3×D4—101no—
184C2×C3×D4D2011yescharacteristic
185C22×C3×C4—21no—
186C22×C3×C4—102no—
187C2×Dic6—101no—
188C3×C4⋊C4—51no—
189C3×C4⋊C4—101no—
190C3×C4⋊C4D2011yescharacteristic
191C3×C22⋊C4—21no—
192C3×C22⋊C4—102no—
193C3×C42—101no—
194C3×C42C22×D511yescharacteristic
195#214—204no—
196C4⋊Dic3—101no—
197C4⋊Dic3—101no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—101no—
201C23×C5—21no—
202C22×D5—22no—
203C5×D4—21no—
204C5×D4—21no—
205C2×C4×C5—21no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5C2×#6711yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C22⋊D5—44no—
212C22⋊D5—82no—
213C2×Dic5—21no—
214C2×Dic5—21no—
215C2×Dic5—121no—
216D20—42no—
217D20—41no—
218D20—41no—
219D20—41no—
220D20—41no—
221C4×D5—44no—
222Dic10—21no—
223Dic10—122no—
224Dic10#21412yescomplemented
225C5×C8—62no—
226C5×C8—121no—
227#168—121no—
228C2×#41—101no—
229C2×SD16—302no—
230C4⋊Q8—151no—
231#127—51no—
232#127—101no—
233#121—102no—
234#121—101no—
235C4×Q8—51no—
236C4×D4—101no—
237C4×D4D3×D511yescharacteristic
238#107—301no—
239#106—301no—
240C4⋊C8—31no—
241C4⋊C8—151no—
242#103—301no—
243#102—301no—
244C4×C8—31no—
245C2×C3×C5—81no—
246C2×C3×C5#45011yescharacteristic
247C2×C3×C5#45211yescharacteristic
248C2×C3×C5#45311yescharacteristic
249C3×D5—82no—
250C23×C3—21no—
251C23×C3—102no—
252C3×Q8—52no—
253C3×Q8—101no—
254C3×D4—21no—
255C3×D4—21no—
256C3×D4—202no—
257C3×D4—204no—
258C3×D4—201no—
259C3×D4—201no—
260C3×D4—201no—
261C3×D4—201no—
262C3×D4—402no—
263C2×C3×C4—21no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—101no—
267C2×C3×C4—101no—
268C2×C3×C4—204no—
269C2×C3×C4C2×D2011yescharacteristic
270C2×C3×C4D4×D511yescharacteristic
271C2×C3×C4D4×D511yescharacteristic
272C2×Dic3—201no—
273Dic6—202no—
274C3⋊C8—22no—
275C3⋊C8—41no—
276C3⋊C8—201no—
277C22×C5—41no—
278C22×C5—41no—
279C22×C5—41no—
280C22×C5#95311yescharacteristic
281C2×D5—42no—
282C2×D5—42no—
283C2×D5—42no—
284C4×C5—21no—
285C4×C5—41no—
286C4×C5#93211yescharacteristic
287C4×C5C2×#21411yescharacteristic
288C4×C5#95011yescharacteristic
289C4×C5#95111yescharacteristic
290Dic5—22no—
291Dic5—41no—
292Dic5—241no—
293#41—202no—
294#41—202no—
295C2×Q8—51no—
296C2×Q8—301no—
297C2×D4—52no—
298C2×D4—102no—
299C2×D4—102no—
300C2×D4—101no—
301C2×D4—101no—
302C2×D4#120211yescharacteristic
303C22×C4—21no—
304C22×C4—102no—
305SD16—604no—
306C2×C8—61no—
307C2×C8—61no—
308C2×C8—301no—
309C4⋊C4—51no—
310C4⋊C4—101no—
311C4⋊C4—301no—
312C4⋊C4—301no—
313C4⋊C4#120211yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—102no—
316C42—101no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—202no—
323C22×C3—202no—
324C22×C3—202no—
325C22×C3#402811yescharacteristic
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—102no—
329C3×C4—201no—
330C3×C4#405011yescharacteristic
331C3×C4#405511yescharacteristic
332C3×C4#405711yescharacteristic
333C3×C4D5×SD1611yescharacteristic
334Dic3—401no—
335C2×C5—81no—
336C2×C5#521811yescharacteristic
337C2×C5#523911yescharacteristic
338C2×C5#524111yescharacteristic
339D5—82no—
340C23—21no—
341C23—102no—
342Q8—52no—
343Q8—101no—
344Q8—602no—
345D4—21no—
346D4—21no—
347D4—202no—
348D4—204no—
349D4—201no—
350D4—201no—
351D4—201no—
352D4—201no—
353D4—402no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—101no—
358C2×C4—101no—
359C2×C4—204no—
360C2×C4—601no—
361C2×C4C2×#120211yescharacteristic
362C2×C4D5×#6711yescharacteristic
363C2×C4D5×#6711yescharacteristic
364C8—62no—
365C8—121no—
366C8—601no—
367C2×C3—81no—
368C2×C3—402no—
369C2×C3#6502211yescharacteristic
370C2×C3#6506511yescharacteristic
371C2×C3#6511111yescharacteristic
372C5#7191911yescharacteristic, complemented, Sylow
373C22—41no—
374C22—41no—
375C22—41no—
376C22—202no—
377C22—202no—
378C22—202no—
379C22#9156411yescharacteristic
380C4—21no—
381C4—41no—
382C4—102no—
383C4—201no—
384C4—1201no—
385C4#9131111yescharacteristic
386C4#9131311yescharacteristic
387C4D5×#21411yescharacteristic
388C4#9148911yescharacteristic
389C3#1059898111yescharacteristic, complemented, Sylow
390C2—81no—
391C2—402no—
392C2#1174853111yescharacteristic
393C2#1174904511yescharacteristic
394C2#1174941811yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC3×#65887C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1631
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11751109C2semidirect
3. #11747071C2semidirect
4. #11746916C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745852C2semidirect
7. #11745841C2semidirect
65. D4⋊(C3⋊C8)D5semidirect
107. C3×Dic10SD16semidirect
224. Dic10#214semidirect
318. C3×C5#1631semidirect
372. C5#71919semidirect
389. C3#10598981semidirect

Maximal subgroups

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

subgroupindex
C3×#658872
#117511092
#117470712
#117469162
C5×D4⋊(C3⋊C8)2
#117458522
#117458412
#105989813
#719195