Finite Group Databasebeta

← #14289426

Subgroups — #14289426

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#550C211yesmaximal, characteristic
2#11751177C211yesmaximal, characteristic, complemented
3#11751122C211yesmaximal, characteristic, complemented
4#11751109C211yesmaximal, characteristic, complemented
5#11746365C211yesmaximal, characteristic, complemented
6#11746356C211yesmaximal, characteristic, complemented
7D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
8#10602712—31nomaximal, Hall
9C2×C3×C5×#41—21no—
10C3×C5×#127—21no—
11C3×C5×#127C2211yescharacteristic
12C3×C5×#121—22no—
13C3×C5×#121—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4C2211yescharacteristic
17C2×#6716—22no—
18#91758C2211yescharacteristic
19#91119—21no—
20#91116—21no—
21#91092—21no—
22#91091—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71919—51nomaximal, Hall
27C5×#550D311yescharacteristic
28#65365—31no—
29#65310—31no—
30#65297—31no—
31#64764—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C3×C5×#41—42no—
35C3×C5×#41—42no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4—22no—
38C2×C3×C5×D4—22no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C2×C3×C5×D4D412yes—
43C22×C3×C4×C5—22no—
44C22×C3×C4×C5—21no—
45C2×Dic30—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—22no—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52C3×C42×C5C2311yescharacteristic
53#6716—44no—
54C4⋊Dic15—21no—
55C4⋊Dic15—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C3×#550D511yescharacteristic
60#5076—51no—
61#5021—51no—
62#5008—51no—
63#4544—51no—
64#4535—51no—
65D4⋊(C3⋊C8)—51no—
66C2×C5×#41—21no—
67C5×#127—21no—
68C5×#127C2×D311yescharacteristic
69C5×#121—22no—
70C5×#121—21no—
71C4×C5×Q8C2×D311yescharacteristic
72C4×C5×D4—21no—
73C4×C5×D4C2×D311yescharacteristic
74C2×#687—62no—
75#4015—31no—
76#3967—61no—
77#3964—61no—
78#3940—61no—
79#3939—61no—
80C4⋊#168—31no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1631—151noSylow
84C23×C3×C5—21no—
85C23×C3×C5—22no—
86C3×C5×Q8—21no—
87C3×C5×Q8SD1612yescomplemented
88C3×C5×D4—21no—
89C3×C5×D4—21no—
90C3×C5×D4—44no—
91C3×C5×D4—42no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C3×C5×D4—82no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—44no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×Dic15—41no—
107Dic30—42no—
108C3⋊#168—22no—
109C3⋊#168—41no—
110C3⋊#168—41no—
111C2×C3×#41—21no—
112C3×#127—21no—
113C3×#127C2×D511yescharacteristic
114C3×#121—22no—
115C3×#121—21no—
116C3×C4×Q8C2×D511yescharacteristic
117C3×C4×D4—21no—
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)—51no—
127C4×C3⋊C8—51no—
128C5×#41—42no—
129C5×#41—42no—
130C2×C5×Q8#6711yescharacteristic
131C2×C5×D4—22no—
132C2×C5×D4—22no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135C2×C5×D4#6711yescharacteristic
136C2×C5×D4#6712yes—
137C22×C4×C5—22no—
138C22×C4×C5—21no—
139C2×Dic10—61no—
140C5×C4⋊C4—21no—
141C5×C4⋊C4#6711yescharacteristic
142C5×C4⋊C4#6711yescharacteristic
143C5×C22⋊C4—22no—
144C5×C22⋊C4—21no—
145C42×C5—21no—
146C42×C5C22×D311yescharacteristic
147#687—124no—
148C4⋊Dic5—61no—
149C4⋊Dic5—61no—
150C2×#168—61no—
151C2×#168—61no—
152C2×#168—61no—
153#550D1511yescharacteristic
154#492—151no—
155#477—151no—
156#476—151no—
157#331—151no—
158Q8⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5—42no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5—42no—
164C22×C3×C5—42no—
165C22×C3×C5—41no—
166C22×C3×C5#12011yescharacteristic
167C3×C4×C5—22no—
168C3×C4×C5—21no—
169C3×C4×C5—41no—
170C3×C4×C5—41no—
171C3×C4×C5C2×SD1611yescharacteristic
172C3×C4×C5#13511yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C3×C4×C5#13711yescharacteristic
175Dic15—81no—
176C3×#41—42no—
177C3×#41—42no—
178C2×C3×Q8C22⋊D511yescharacteristic
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4C22⋊D511yescharacteristic
184C2×C3×D4C22⋊D512yes—
185C22×C3×C4—22no—
186C22×C3×C4—21no—
187C2×Dic6—101no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4C22⋊D511yescharacteristic
190C3×C4⋊C4C22⋊D511yescharacteristic
191C3×C22⋊C4—22no—
192C3×C22⋊C4—21no—
193C3×C42—21no—
194C3×C42C22×D511yescharacteristic
195#214—204no—
196C4⋊Dic3—101no—
197C4⋊Dic3—101no—
198C2×C3⋊C8—101no—
199C2×C3⋊C8—101no—
200C2×C3⋊C8—101no—
201C23×C5—21no—
202C23×C5—22no—
203C5×Q8—21no—
204C5×Q8#21412yescomplemented
205C5×D4—21no—
206C5×D4—21no—
207C5×D4—42no—
208C5×D4—44no—
209C5×D4—41no—
210C5×D4—41no—
211C5×D4—41no—
212C5×D4—41no—
213C5×D4—82no—
214C2×C4×C5—21no—
215C2×C4×C5—21no—
216C2×C4×C5—21no—
217C2×C4×C5—44no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5C2×#6711yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222C2×C4×C5C2×#6711yescharacteristic
223C2×Dic5—121no—
224Dic10—122no—
225#168—62no—
226#168—121no—
227#168—121no—
228C2×#41—21no—
229C2×SD16—302no—
230C4⋊Q8—151no—
231#127—21no—
232#127C2×D1511yescharacteristic
233#121—22no—
234#121—21no—
235C4×Q8C2×D1511yescharacteristic
236C4×D4—21no—
237C4×D4C2×D1511yescharacteristic
238#107—301no—
239#106—301no—
240C4⋊C8—151no—
241C4⋊C8—151no—
242#103—301no—
243#102—301no—
244C4×C8—151no—
245C2×C3×C5—81no—
246C2×C3×C5—82no—
247C2×C3×C5#45011yescharacteristic
248C2×C3×C5#45211yescharacteristic
249C2×C3×C5#45311yescharacteristic
250C23×C3—21no—
251C23×C3—22no—
252C3×Q8—21no—
253C3×Q8#68712yescomplemented
254C3×D4—21no—
255C3×D4—21no—
256C3×D4—42no—
257C3×D4—44no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—82no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—44no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4C2×C22⋊D511yescharacteristic
270C2×C3×C4C2×C22⋊D511yescharacteristic
271C2×C3×C4C2×C22⋊D511yescharacteristic
272C2×Dic3—201no—
273Dic6—202no—
274C3⋊C8—102no—
275C3⋊C8—201no—
276C3⋊C8—201no—
277C22×C5—42no—
278C22×C5—41no—
279C22×C5—41no—
280C22×C5—42no—
281C22×C5—42no—
282C22×C5—41no—
283C22×C5#95311yescharacteristic
284C4×C5—22no—
285C4×C5—21no—
286C4×C5—41no—
287C4×C5—41no—
288C4×C5#93211yescharacteristic
289C4×C5C2×#21411yescharacteristic
290C4×C5#95011yescharacteristic
291C4×C5#95111yescharacteristic
292Dic5—241no—
293#41—42no—
294#41—42no—
295C2×Q8—301no—
296C2×Q8#122011yescharacteristic
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4#122011yescharacteristic
302C2×D4#122012yes—
303C22×C4—22no—
304C22×C4—21no—
305SD16—604no—
306C2×C8—301no—
307C2×C8—301no—
308C2×C8—301no—
309C4⋊C4—21no—
310C4⋊C4—301no—
311C4⋊C4—301no—
312C4⋊C4#122011yescharacteristic
313C4⋊C4#122011yescharacteristic
314C22⋊C4—22no—
315C22⋊C4—21no—
316C42—21no—
317C42C22×D1511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—42no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—42no—
323C22×C3—42no—
324C22×C3—41no—
325C22×C3#409911yescharacteristic
326C3×C4—22no—
327C3×C4—21no—
328C3×C4—41no—
329C3×C4—41no—
330C3×C4#407811yescharacteristic
331C3×C4C2×#68711yescharacteristic
332C3×C4#409611yescharacteristic
333C3×C4#409711yescharacteristic
334Dic3—401no—
335C2×C5—81no—
336C2×C5—82no—
337C2×C5#521811yescharacteristic
338C2×C5#523911yescharacteristic
339C2×C5#524111yescharacteristic
340C23—21no—
341C23—22no—
342Q8—21no—
343Q8—602no—
344Q8#671612yescomplemented
345D4—21no—
346D4—21no—
347D4—42no—
348D4—44no—
349D4—41no—
350D4—41no—
351D4—41no—
352D4—41no—
353D4—82no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—44no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—601no—
361C2×C4C2×#122011yescharacteristic
362C2×C4C2×#122011yescharacteristic
363C2×C4C2×#122011yescharacteristic
364C8—302no—
365C8—601no—
366C8—601no—
367C2×C3—81no—
368C2×C3—82no—
369C2×C3#6550711yescharacteristic
370C2×C3#6552811yescharacteristic
371C2×C3#6553011yescharacteristic
372C5#7191911yescharacteristic, complemented, Sylow
373C22—42no—
374C22—41no—
375C22—41no—
376C22—42no—
377C22—42no—
378C22—41no—
379C22#9184211yescharacteristic
380C4—22no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—1201no—
385C4#9182111yescharacteristic
386C4C2×#671611yescharacteristic
387C4#9183911yescharacteristic
388C4#9184011yescharacteristic
389C3#1060271211yescharacteristic, complemented, Sylow
390C2—81no—
391C2—82no—
392C2#1175131911yescharacteristic
393C2#1175134011yescharacteristic
394C2#1175134211yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
Fitting, prime radicalC3×C5×#550C2
socleC22×C3×C5#120
hypercenter#550D15
hypocenterC3×C5#1631
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
2. #11751177C2semidirect
3. #11751122C2semidirect
4. #11751109C2semidirect
5. #11746365C2semidirect
6. #11746356C2semidirect
7. D4⋊(C3⋊#168)C2semidirect
87. C3×C5×Q8SD16semidirect
204. C5×Q8#214semidirect
253. C3×Q8#687semidirect
318. C3×C5#1631semidirect
344. Q8#6716semidirect
372. C5#71919semidirect
389. C3#10602712semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5502
#117511772
#117511222
#117511092
#117463652
#117463562
D4⋊(C3⋊#168)2
#106027123
#719195