Finite Group Databasebeta

← #14290635

Subgroups — #14290635

Order 1920.

468 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 101 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
1Q8×D60C211yesmaximal, characteristic
2C3×C5×#475C211yesmaximal, characteristic, complemented
3#11751184C211yesmaximal, characteristic
4#11751181C211yesmaximal, characteristic, complemented
5#11746356C211yesmaximal, characteristic, complemented
6#11746304C211yesmaximal, characteristic
7#11746303C211yesmaximal, characteristic, complemented
8#10601920—31nomaximal, Hall
9C2×Q8×D15—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C4×C5×Q8C2211yescharacteristic
12C2×#6717—21no—
13#91786—21no—
14#91786—22no—
15C4×D60—21no—
16C4×D60C2211yescharacteristic
17#91758—21no—
18#91758C2211yescharacteristic
19C3×C5×#106—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#103—21no—
22#91119—21no—
23#91092—22no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71127—51nomaximal, Hall
27Q8×D20—31no—
28C5×#475D311yescharacteristic, complemented
29#65372—31no—
30#65368—31no—
31Q8⋊#168—31no—
32#64703—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36Q8×D15—42no—
37Q8×D15—42no—
38C2×D60D411yescharacteristic
39C2×C4×D15—22no—
40C2×C4×D15—21no—
41C2×Dic30—22no—
42C2×Dic30—21no—
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C42×C5—21no—
49C3×C42×C5C2311yescharacteristic
50#6717—42no—
51#6714—22no—
52#6714—21no—
53C4⋊Dic15—22no—
54C4⋊Dic15—21no—
55C4⋊Dic15D411yescharacteristic
56C4⋊Dic15D412yes—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59Q8×D12—51no—
60C3×#475D511yescharacteristic, complemented
61#5083—51no—
62#5080—51no—
63#4535—51no—
64#4483—51no—
65#4482—51no—
66C2×Q8×D5—61no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C4×C5×Q8C2×D311yescharacteristic
69C2×#688—61no—
70#4043—62no—
71#4043—61no—
72C4×D20—31no—
73C4×D20—61no—
74#4015—31no—
75#4015—61no—
76C5×#106—21no—
77C5×C4⋊C8C2×D311yescharacteristic
78C5×#103—21no—
79#3967—61no—
80#3940—62no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1651—151noSylow
84C22×D15—21no—
85C3×C5×Q8—21no—
86C3×C5×Q8—41no—
87C3×C5×Q8—41no—
88C3×C5×Q8SD1612yescomplemented
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—21no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15—22no—
97D60—21no—
98D60SD1612yes—
99C4×D15—44no—
100C4×D15—41no—
101C4×D15—41no—
102Dic30—44no—
103Dic30—41no—
104Dic30—41no—
105C3×C5×C8—41no—
106C3⋊#168—22no—
107C3⋊#168—41no—
108C2×D3×Q8—101no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×C4×Q8C2×D511yescharacteristic
111C2×#215—101no—
112#897—102no—
113#897—101no—
114C4×D12—51no—
115C4×D12—101no—
116#869—51no—
117#869—101no—
118C3×#106—21no—
119C3×C4⋊C8C2×D511yescharacteristic
120C3×#103—21no—
121#835—101no—
122#808—102no—
123C4⋊(C3⋊C8)—51no—
124C4×C3⋊C8—51no—
125C2×C5×Q8—21no—
126C2×C5×Q8#6711yescharacteristic
127Q8×D5—122no—
128Q8×D5—122no—
129C2×D20—31no—
130C2×C4×D5—62no—
131C2×C4×D5—61no—
132C2×Dic10—62no—
133C2×Dic10—61no—
134C2×C5×C8—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4#6711yescharacteristic
139C42×C5—21no—
140C42×C5C22×D311yescharacteristic
141#688—122no—
142#685—62no—
143#685—61no—
144C4⋊Dic5—32no—
145C4⋊Dic5—31no—
146C4⋊Dic5—62no—
147C4⋊Dic5—61no—
148C2×#168—61no—
149C2×#168—61no—
150D4×Q8—151no—
151#498—151no—
152#475D1511yescharacteristic, complemented
153#461—151no—
154#332—151no—
155Q8⋊C8—151no—
156D4⋊C8—151no—
157C22×C3×C5#12011yescharacteristic
158C2×D15—22no—
159C2×D15—41no—
160C2×D15—41no—
161C3×C4×C5—22no—
162C3×C4×C5—21no—
163C3×C4×C5—41no—
164C3×C4×C5—81no—
165C3×C4×C5C2×SD1611yescharacteristic
166C3×C4×C5C2×SD1611yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5#13711yescharacteristic
169Dic15—41no—
170Dic15—42no—
171C2×C3×Q8—21no—
172C2×C3×Q8C22⋊D511yescharacteristic
173D3×Q8—202no—
174D3×Q8—202no—
175C2×D12—51no—
176C2×C4×D3—102no—
177C2×C4×D3—101no—
178C2×Dic6—102no—
179C2×Dic6—101no—
180C2×C3×C8—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4C22⋊D511yescharacteristic
185C3×C42—21no—
186C3×C42C22×D511yescharacteristic
187#215—202no—
188(C2×D3)⋊C4—102no—
189(C2×D3)⋊C4—101no—
190C4⋊Dic3—52no—
191C4⋊Dic3—51no—
192C4⋊Dic3—102no—
193C4⋊Dic3—101no—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196C22×D5—61no—
197C5×Q8—21no—
198C5×Q8—41no—
199C5×Q8—41no—
200C5×Q8#21512yescomplemented
201C2×C4×C5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—41no—
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5C2×#6711yescharacteristic
207C2×Dic5—62no—
208C2×Dic5—61no—
209D20—32no—
210D20—61no—
211C4×D5—124no—
212C4×D5—121no—
213C4×D5—121no—
214Dic10—124no—
215Dic10—121no—
216Dic10—121no—
217C5×C8—41no—
218#168—62no—
219#168—121no—
220C22×Q8—301no—
221C2×SD16—301no—
222C4⋊Q8—151no—
223C4⋊Q8—301no—
224C4⋊Q8C2×D1511yescharacteristic
225C22⋊Q8—302no—
226C22⋊Q8—301no—
227C4×Q8C2×D1511yescharacteristic
228C4×D4—151no—
229C4×D4—301no—
230#106—21no—
231#106—302no—
232C4⋊C8—151no—
233C4⋊C8C2×D1511yescharacteristic
234#103—21no—
235#103—301no—
236C4×C8—151no—
237C2×C3×C5#44811yescharacteristic
238C2×C3×C5#45011yescharacteristic
239C2×C3×C5#45611yescharacteristic
240D15—42no—
241C22×D3—101no—
242C3×Q8—21no—
243C3×Q8—41no—
244C3×Q8—41no—
245C3×Q8#68812yescomplemented
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—41no—
249C2×C3×C4D4×D511yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251C2×C3×C4C2×C22⋊D511yescharacteristic
252C2×Dic3—102no—
253C2×Dic3—101no—
254D12—52no—
255D12—101no—
256C4×D3—204no—
257C4×D3—201no—
258C4×D3—201no—
259Dic6—204no—
260Dic6—201no—
261Dic6—201no—
262C3×C8—41no—
263C3⋊C8—102no—
264C3⋊C8—201no—
265C22×C5#93711yescharacteristic
266C2×D5—62no—
267C2×D5—121no—
268C2×D5—121no—
269C4×C5—21no—
270C4×C5—22no—
271C4×C5—41no—
272C4×C5—81no—
273C4×C5D3×SD1611yescharacteristic
274C4×C5#91511yescharacteristic
275C4×C5C2×#21511yescharacteristic
276C4×C5#94911yescharacteristic
277Dic5—121no—
278Dic5—122no—
279C2×Q8—21no—
280C2×Q8—302no—
281C2×Q8—301no—
282C2×Q8—602no—
283C2×Q8—602no—
284C2×Q8#122011yescharacteristic
285C2×D4—151no—
286C22×C4—302no—
287C22×C4—301no—
288SD16—602no—
289C2×C8—21no—
290C2×C8—301no—
291C2×C8—301no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—151no—
296C4⋊C4—152no—
297C4⋊C4—302no—
298C4⋊C4—301no—
299C4⋊C4#122011yescharacteristic
300C22⋊C4—302no—
301C22⋊C4—301no—
302C42—21no—
303C42C22×D1511yescharacteristic
304C3×C5#165111yescharacteristic, complemented, Hall
305C22×C3#408311yescharacteristic
306C2×D3—102no—
307C2×D3—201no—
308C2×D3—201no—
309C3×C4—22no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—81no—
313C3×C4D5×SD1611yescharacteristic
314C3×C4#406111yescharacteristic
315C3×C4C2×#68811yescharacteristic
316C3×C4#409511yescharacteristic
317Dic3—201no—
318Dic3—202no—
319C2×C5#504611yescharacteristic
320C2×C5#517011yescharacteristic
321C2×C5#520511yescharacteristic
322D5—122no—
323C23—301no—
324Q8—21no—
325Q8—41no—
326Q8—41no—
327Q8—604no—
328Q8—601no—
329Q8—601no—
330Q8#671712yescomplemented
331D4—152no—
332D4—301no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—302no—
337C2×C4—301no—
338C2×C4—604no—
339C2×C4—601no—
340C2×C4—601no—
341C2×C4D4×D1511yescharacteristic
342C2×C4D4×D1511yescharacteristic
343C2×C4C2×#122011yescharacteristic
344C8—41no—
345C8—302no—
346C8—601no—
347C2×C3#6533511yescharacteristic
348C2×C3#6545911yescharacteristic
349C2×C3#6549411yescharacteristic
350D3—202no—
351C5#7112711yescharacteristic, complemented, Sylow
352C22—302no—
353C22—601no—
354C22—601no—
355C22#9182611yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—81no—
360C4—602no—
361C4—601no—
362C4SD16×D1511yescharacteristic
363C4#9180411yescharacteristic
364C4C2×#671711yescharacteristic
365C4#9183811yescharacteristic
366C3#1060192011yescharacteristic, complemented, Sylow
367C2—602no—
368C2#1175114711yescharacteristic
369C2#1175127111yescharacteristic
370C2#1175130611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#475C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenter#475D15
hypocenterC3×C5#1651
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. C3×C5×#475C2semidirect
4. #11751181C2semidirect
5. #11746356C2semidirect
7. #11746303C2semidirect
28. C5×#475D3semidirect
60. C3×#475D5semidirect
88. C3×C5×Q8SD16semidirect
152. #475D15semidirect
200. C5×Q8#215semidirect
245. C3×Q8#688semidirect
304. C3×C5#1651semidirect
330. Q8#6717semidirect
351. C5#71127semidirect
366. C3#10601920semidirect

Maximal subgroups

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

subgroupindex
Q8×D602
C3×C5×#4752
#117511842
#117511812
#117463562
#117463042
#117463032
#106019203
#711275