Finite Group Databasebeta

← #14289439

Subgroups — #14289439

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#11752677C211yesmaximal, characteristic
2#11751186C211yesmaximal, characteristic, complemented
3C5×#5091C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic, complemented
5#11745854C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601953—31nomaximal, Hall
9C2×#6773—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C2×#6717—22no—
12#91763C2211yescharacteristic
13C4×C5×Dic6C2211yescharacteristic
14C3×C4×D20C2211yescharacteristic
15#91459—22no—
16#91458—21no—
17#91450—21no—
18#91428—21no—
19C4×C3⋊#168C2211yescharacteristic
20C5×#810—21no—
21C5×#807—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3941—21no—
24C3×#3940—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71141—51nomaximal, Hall
27#65911—31no—
28C5×#477—31no—
29#65374—31no—
30#65373D311yescharacteristic, complemented
31Q8⋊#168—31no—
32#64705—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60D412yes—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×D20D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×#1202—22no—
42C2×#1202—22no—
43C2×#1200—22no—
44#6773—42no—
45#6773—42no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C42×C5C2311yescharacteristic
49#6717—44no—
50C2×C3⋊#168—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C5×Dic3⋊C4—21no—
53C4×C5×Dic3—21no—
54C2×C5×C3⋊C8—21no—
55C3×#685—21no—
56C3×C4⋊Dic5D411yescharacteristic
57C2×C3×#168—21no—
58#6667—22no—
59#5553—51no—
60C3×#476—51no—
61#5091D511yescharacteristic, complemented
62#5085—51no—
63D4⋊(C3⋊C8)—51no—
64#4485—51no—
65#4484—51no—
66C2×#713—61no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C4×C5×Q8—31no—
69C2×#688—62no—
70#4041—62no—
71#4041—61no—
72#4020—31no—
73#4020—61no—
74C4×D20—61no—
75C4×D20C2×D311yescharacteristic
76C5×#107—61no—
77C5×C4⋊C8—31no—
78C5×#103—61no—
79#3941—21no—
80#3940—21no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1631—151noSylow
84C22×D15—22no—
85C22×C3×D5—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—
97C2×C5×Dic3—21no—
98C5×Dic6—21no—
99C5×Dic6SD1612yescomplemented
100C2×C3×Dic5—21no—
101C3×D20—21no—
102C3×D20—21no—
103C3×C4×D5—41no—
104C3×C4×D5—41no—
105#1202—44no—
106#1202—82no—
107#1200—44no—
108C3⋊#168—22no—
109C3×#168—41no—
110C5×C3⋊C8—41no—
111C2×#235—101no—
112C3×C4⋊Q8C2×D511yescharacteristic
113C3×C4×D4—51no—
114C2×#215—102no—
115#940—101no—
116#930—101no—
117#893—101no—
118#884—102no—
119#874—51no—
120C4×Dic6C2×D511yescharacteristic
121C3×#106—101no—
122C3×C4⋊C8—51no—
123C3×#102—101no—
124#810—21no—
125#807—21no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C4×C3⋊C8—51no—
128C2×C5×Q8—21no—
129C2×C5×Q8—31no—
130#713—122no—
131#713—122no—
132C2×D20—32no—
133C2×D20—62no—
134C2×D20—61no—
135C2×D20—61no—
136C2×D20—62no—
137C2×D20#6711yescharacteristic
138C2×C4×D5—21no—
139C2×C4×D5—62no—
140C2×C5×C8—61no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—31no—
144C5×C4⋊C4—61no—
145C42×C5—61no—
146C42×C5C22×D311yescharacteristic
147#688—124no—
148#685—21no—
149#685—62no—
150C4⋊Dic5#6711yescharacteristic
151C2×#168—21no—
152C2×#168—61no—
153#550—151no—
154#492—151no—
155#477—31no—
156#476—51no—
157#331—151no—
158Q8⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×D15—42no—
162C2×D15—42no—
163C2×D15—42no—
164C2×C3×D5—41no—
165C2×C3×D5—41no—
166C2×C3×D5—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—41no—
174C5×Dic3—22no—
175C5×Dic3—41no—
176C2×C3×Q8—21no—
177C2×C3×D4—51no—
178C22×C3×C4—101no—
179C2×#67—102no—
180C2×#67—102no—
181#235—202no—
182#235—202no—
183C2×D12—52no—
184C2×D12—101no—
185C2×D12—101no—
186C2×C4×D3—102no—
187C2×Dic6C22⋊D511yescharacteristic
188C2×C3×C8—101no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—51no—
192C3×C22⋊C4—101no—
193C3×C42C22×D511yescharacteristic
194#215—204no—
195(C2×D3)⋊C4—102no—
196C4⋊Dic3C22⋊D511yescharacteristic
197Dic3⋊C4—21no—
198C4×Dic3—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—101no—
201C22×D5—21no—
202C22×D5—62no—
203C5×Q8—32no—
204C5×Q8—42no—
205C5×Q8—61no—
206C2×C4×C5—41no—
207C2×C4×C5—61no—
208C2×C4×C5—61no—
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5C2×#6711yescharacteristic
212C2×Dic5—21no—
213D20—21no—
214D20—21no—
215D20—122no—
216D20—124no—
217D20—121no—
218D20—121no—
219D20—121no—
220D20—121no—
221D20—242no—
222C4×D5—41no—
223C4×D5—41no—
224C4×D5—124no—
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—31no—
236C4×D4—51no—
237C4×D4—301no—
238#107—61no—
239#106—101no—
240C4⋊C8—31no—
241C4⋊C8—51no—
242#103—61no—
243#102—101no—
244C4×C8—151no—
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45211yescharacteristic
247C2×C3×C5#45311yescharacteristic
248D15—82no—
249C3×D5—81no—
250C23×C3—101no—
251C22×D3—102no—
252C3×Q8—42no—
253C3×D4—101no—
254C3×D4—101no—
255C2×C3×C4—41no—
256C2×C3×C4—101no—
257C2×C3×C4—201no—
258C2×C3×C4—201no—
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262#67—204no—
263#67—402no—
264C2×Dic3—21no—
265C2×Dic3—21no—
266D12—202no—
267D12—201no—
268D12—201no—
269D12—201no—
270D12—201no—
271C4×D3—204no—
272Dic6—21no—
273Dic6#68812yescomplemented
274C3×C8—201no—
275C3⋊C8—41no—
276C3⋊C8—102no—
277C22×C5#93711yescharacteristic
278C2×D5—41no—
279C2×D5—41no—
280C2×D5—41no—
281C2×D5—122no—
282C2×D5—122no—
283C2×D5—122no—
284C4×C5—21no—
285C4×C5—62no—
286C4×C5—81no—
287C4×C5—121no—
288C4×C5D3×SD1611yescharacteristic
289C4×C5#91411yescharacteristic
290C4×C5#94211yescharacteristic
291C4×C5#95011yescharacteristic
292Dic5—41no—
293#41—602no—
294#41—602no—
295C2×Q8—21no—
296C2×Q8—31no—
297C2×D4—51no—
298C2×D4—152no—
299C2×D4—302no—
300C2×D4—302no—
301C2×D4—301no—
302C2×D4—301no—
303C22×C4—101no—
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—61no—
314C22⋊C4—101no—
315C22⋊C4—302no—
316C42—61no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—201no—
320C22×C3—201no—
321C22×C3—201no—
322C22×C3#408311yescharacteristic
323C2×D3—202no—
324C2×D3—202no—
325C2×D3—202no—
326C3×C4—21no—
327C3×C4—81no—
328C3×C4—201no—
329C3×C4#406411yescharacteristic
330C3×C4#406511yescharacteristic
331C3×C4C2×#68811yescharacteristic
332C3×C4#409511yescharacteristic
333Dic3—22no—
334Dic3—41no—
335C2×C5#504711yescharacteristic
336C2×C5#516911yescharacteristic
337C2×C5#519811yescharacteristic
338D5—81no—
339D5—242no—
340C23—101no—
341C23—302no—
342Q8—32no—
343Q8—42no—
344Q8—61no—
345D4—101no—
346D4—101no—
347D4—602no—
348D4—604no—
349D4—601no—
350D4—601no—
351D4—601no—
352D4—601no—
353D4—1202no—
354C2×C4—41no—
355C2×C4—61no—
356C2×C4—61no—
357C2×C4—101no—
358C2×C4—201no—
359C2×C4—201no—
360C2×C4—604no—
361C2×C4D5×#6711yescharacteristic
362C2×C4D3×C22⋊D511yescharacteristic
363C2×C4#679011yescharacteristic
364C8—121no—
365C8—201no—
366C8—302no—
367C2×C3—401no—
368C2×C3#6533511yescharacteristic
369C2×C3#6547611yescharacteristic
370C2×C3#6548711yescharacteristic
371D3—402no—
372C5#7114111yescharacteristic, complemented, Sylow
373C22—201no—
374C22—201no—
375C22—201no—
376C22—602no—
377C22—602no—
378C22—602no—
379C22#9157711yescharacteristic
380C4—21no—
381C4—62no—
382C4—81no—
383C4—121no—
384C4—201no—
385C4D3×#68811yescharacteristic
386C4#9150411yescharacteristic
387C4#9151511yescharacteristic
388C4#9151611yescharacteristic
389C3#1060195311yescharacteristic, complemented, Sylow
390C2—401no—
391C2—1202no—
392C2#1174916411yescharacteristic
393C2#1174939811yescharacteristic
394C2#1174940611yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11752677C2
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×#5091C2semidirect
4. C3×#65373C2semidirect
5. #11745854C2semidirect
6. #11745842C2semidirect
7. #11745834C2semidirect
30. #65373D3semidirect
61. #5091D5semidirect
99. C5×Dic6SD16semidirect
273. Dic6#688semidirect
318. C3×C5#1631semidirect
372. C5#71141semidirect
389. C3#10601953semidirect

Maximal subgroups

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

subgroupindex
#117526772
#117511862
C5×#50912
C3×#653732
#117458542
#117458422
#117458342
#106019533
#711415