Finite Group Databasebeta

← #14289649

Subgroups — #14289649

Order 1920.

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

normal subgroups only

This group has 468 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
1C5×#5726C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic, complemented
3#11746883C211yesmaximal, characteristic, complemented
4#11746883C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745836C211yesmaximal, characteristic, complemented
7#11745836C211yesmaximal, characteristic, complemented
8#10602704—31nomaximal, Hall
9C2×C5×#239—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91758C2211yescharacteristic
12C5×#946—21no—
13C5×#895—21no—
14C5×#894—22no—
15C5×D3×C4⋊C4—21no—
16C4×C5×D12C2211yescharacteristic
17C4×C5×D12C2211yescharacteristic
18#91094—22no—
19C4×C3⋊#168C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90985—21no—
23#90985—21no—
24#90967—21no—
25#90967—21no—
26#68434—51nomaximal, Hall
27C5×#547—31no—
28#65382—31no—
29#65297—31no—
30#65297—31no—
31#64767D311yescharacteristic, complemented
32D4⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C5×#239—42no—
37C5×#239—42no—
38C2×C5×D12—22no—
39C2×C5×D12D411yescharacteristic
40C2×C5×D12D411yescharacteristic
41C2×C4×C5×D3—22no—
42C2×C4×C5×D3—21no—
43C2×C4×C5×D3—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4D412yes—
46C3×C42×C5C2311yescharacteristic
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C2×C3⋊#168—21no—
50C5×(C2×D3)⋊C4—22no—
51C5×(C2×D3)⋊C4—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3D411yescharacteristic
54C5×C4⋊Dic3D411yescharacteristic
55C5×Dic3⋊C4—22no—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58#5726D511yescharacteristic
59#5093—51no—
60#4842—51no—
61#4842—51no—
62C3×#332—51no—
63#4483—51no—
64#4483—51no—
65C2×C5×#41—61no—
66C5×C4⋊Q8C2×D311yescharacteristic
67C5×#123—62no—
68C5×C22⋊Q8—61no—
69C5×#121—61no—
70C4×C5×D4—31no—
71C4×C5×D4—31no—
72C2×C5×C4⋊C4—61no—
73#4015—31no—
74#3964—61no—
75#3964—61no—
76#3942—62no—
77#3940—61no—
78#3940—61no—
79C4⋊#168C2×D311yescharacteristic
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1635—151noSylow
83C22×C5×D3—21no—
84C22×C5×D3—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—41no—
92Dic30—42no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—21no—
95C5×D12—21no—
96C5×D12—21no—
97C5×D12—21no—
98C5×D12—44no—
99C5×D12SD1612yes—
100C4×C5×D3—44no—
101C4×C5×D3—41no—
102C4×C5×D3—41no—
103C4×C5×D3—41no—
104C4×C5×D3—41no—
105C3⋊#168—41no—
106C3×#168—41no—
107C3×#168—41no—
108C2×#239—21no—
109C3×C4⋊Q8C2×D511yescharacteristic
110#946—21no—
111#895—21no—
112#894—22no—
113D3×C4⋊C4—21no—
114C4×D12C2×D511yescharacteristic
115C4×D12C2×D511yescharacteristic
116#869—51no—
117C3×C4⋊C8—51no—
118C3×C4⋊C8—51no—
119#821—101no—
120#821—101no—
121#817—101no—
122#817—101no—
123#810—102no—
124C4×C3⋊C8—51no—
125C5×#41—122no—
126C5×#41—122no—
127C2×C5×Q8—21no—
128C2×C5×D4—31no—
129C2×C5×D4—31no—
130C2×C5×D4—62no—
131C22×C4×C5—62no—
132C22×C4×C5—61no—
133C22×C4×C5—61no—
134C2×Dic10—61no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—31no—
137C5×C4⋊C4—31no—
138C5×C4⋊C4—62no—
139C5×C4⋊C4D1212yes—
140C5×C22⋊C4—62no—
141C5×C22⋊C4—61no—
142C5×C22⋊C4—61no—
143C42×C5C22×D311yescharacteristic
144C4⋊Dic5—61no—
145C4⋊Dic5—61no—
146C2×#168—21no—
147C2×#168—21no—
148C2×#168—61no—
149#547—31no—
150#487—151no—
151#476—151no—
152#476—151no—
153#332—51no—
154D4⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×C5×D3—22no—
158C2×C5×D3—41no—
159C2×C5×D3—41no—
160C2×C5×D3—41no—
161C2×C5×D3—41no—
162C2×C5×D3—41no—
163C3×C4×C5—21no—
164C3×C4×C5—42no—
165C3×C4×C5C2×SD1611yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5#13711yescharacteristic
169Dic15—81no—
170C5×Dic3—41no—
171C5×Dic3—41no—
172C2×C3×Q8—21no—
173#239—42no—
174#239—42no—
175C2×D12—22no—
176C2×D12C22⋊D511yescharacteristic
177C2×D12C22⋊D511yescharacteristic
178C2×C4×D3—22no—
179C2×C4×D3—21no—
180C2×C4×D3—21no—
181C2×Dic6—101no—
182C2×C3×C8—101no—
183C2×C3×C8—101no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4C22⋊D512yes—
186C3×C42C22×D511yescharacteristic
187(C2×D3)⋊C4—22no—
188(C2×D3)⋊C4—21no—
189(C2×D3)⋊C4—21no—
190C4⋊Dic3—101no—
191C4⋊Dic3—101no—
192C4⋊Dic3C22⋊D511yescharacteristic
193C4⋊Dic3C22⋊D511yescharacteristic
194Dic3⋊C4—22no—
195C2×C3⋊C8—101no—
196C23×C5—61no—
197C23×C5—61no—
198C5×Q8—41no—
199C5×Q8—41no—
200C5×D4—32no—
201C5×D4—61no—
202C5×D4—61no—
203C5×D4—61no—
204C5×D4—124no—
205C2×C4×C5—22no—
206C2×C4×C5—61no—
207C2×C4×C5—61no—
208C2×C4×C5—124no—
209C2×C4×C5—121no—
210C2×C4×C5—121no—
211C2×C4×C5—121no—
212C2×C4×C5—121no—
213C2×C4×C5C2×D1211yescharacteristic
214C2×C4×C5D3×D411yescharacteristic
215C2×C4×C5D3×D411yescharacteristic
216C2×Dic5—121no—
217Dic10—122no—
218#168—41no—
219#168—41no—
220#168—121no—
221C2×#41—61no—
222C4⋊Q8—151no—
223C4⋊Q8D3×D511yescharacteristic
224#123—62no—
225C22⋊Q8—61no—
226#121—61no—
227C4×D4—31no—
228C4×D4—31no—
229C2×C4⋊C4—61no—
230#106—301no—
231#106—301no—
232C4⋊C8—51no—
233C4⋊C8—51no—
234#103—302no—
235#102—301no—
236#102—301no—
237C4×C8—151no—
238C2×C3×C5#45011yescharacteristic
239C2×C3×C5#45211yescharacteristic
240C2×C3×C5#45411yescharacteristic
241C5×D3—42no—
242C5×D3—81no—
243C22×D3—21no—
244C22×D3—21no—
245C3×Q8—41no—
246C3×Q8—41no—
247C2×C3×C4—22no—
248C2×C3×C4C2×C22⋊D511yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—201no—
254D12—21no—
255D12—21no—
256D12—21no—
257D12—44no—
258D12#68712yes—
259C4×D3—44no—
260C4×D3—41no—
261C4×D3—41no—
262C4×D3—41no—
263C4×D3—41no—
264Dic6—202no—
265C3×C8—201no—
266C3×C8—201no—
267C3⋊C8—201no—
268C22×C5—62no—
269C22×C5—121no—
270C22×C5—121no—
271C22×C5—121no—
272C22×C5—121no—
273C22×C5—121no—
274C22×C5#88211yescharacteristic
275C4×C5—21no—
276C4×C5—42no—
277C4×C5—121no—
278C4×C5—121no—
279C4×C5#91111yescharacteristic
280C4×C5D3×SD1611yescharacteristic
281C4×C5#91611yescharacteristic
282C4×C5#91811yescharacteristic
283Dic5—241no—
284#41—122no—
285#41—122no—
286C2×Q8—21no—
287C2×Q8—301no—
288C2×D4—31no—
289C2×D4—31no—
290C2×D4—62no—
291C22×C4—62no—
292C22×C4—61no—
293C22×C4—61no—
294C2×C8—101no—
295C2×C8—101no—
296C2×C8—301no—
297C4⋊C4—21no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—62no—
301C4⋊C4—301no—
302C4⋊C4—301no—
303C4⋊C4#120312yes—
304C22⋊C4—62no—
305C22⋊C4—61no—
306C22⋊C4—61no—
307C42C2×D3×D511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3#409911yescharacteristic
310C2×D3—22no—
311C2×D3—41no—
312C2×D3—41no—
313C2×D3—41no—
314C2×D3—41no—
315C2×D3—41no—
316C3×C4—21no—
317C3×C4—42no—
318C3×C4#407811yescharacteristic
319C3×C4C2×#68711yescharacteristic
320C3×C4#409611yescharacteristic
321C3×C4#409711yescharacteristic
322Dic3—41no—
323Dic3—41no—
324Dic3—401no—
325C2×C5—122no—
326C2×C5—241no—
327C2×C5#475311yescharacteristic
328C2×C5#477611yescharacteristic
329C2×C5#480811yescharacteristic
330C23—61no—
331C23—61no—
332Q8—41no—
333Q8—41no—
334Q8—602no—
335D4—32no—
336D4—61no—
337D4—61no—
338D4—61no—
339D4—124no—
340C2×C4—22no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—124no—
344C2×C4—121no—
345C2×C4—121no—
346C2×C4—121no—
347C2×C4—121no—
348C2×C4—601no—
349C2×C4C2×#120311yescharacteristic
350C2×C4D3×C22⋊D511yescharacteristic
351C2×C4D3×C22⋊D511yescharacteristic
352C8—201no—
353C8—201no—
354C8—601no—
355C2×C3#6550711yescharacteristic
356C2×C3#6552811yescharacteristic
357C2×C3#6553411yescharacteristic
358D3—42no—
359D3—81no—
360C5#6843411yescharacteristic, complemented, Sylow
361C22—62no—
362C22—121no—
363C22—121no—
364C22—121no—
365C22—121no—
366C22—121no—
367C22#9157011yescharacteristic
368C4—21no—
369C4—42no—
370C4—121no—
371C4—121no—
372C4—1201no—
373C4D3×#68711yescharacteristic
374C4#9149411yescharacteristic
375C4#9151011yescharacteristic
376C4#9151711yescharacteristic
377C3#1060270411yescharacteristic, complemented, Sylow
378C2—122no—
379C2—241no—
380C2#1174905611yescharacteristic
381C2#1174930011yescharacteristic
382C2#1174938711yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC5×#5726C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1635
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. #11751194C2semidirect
3. #11746883C2semidirect
4. #11746883C2semidirect
5. C3×#64767C2semidirect
6. #11745836C2semidirect
7. #11745836C2semidirect
31. #64767D3semidirect
308. C3×C5#1635semidirect
360. C5#68434semidirect
377. C3#10602704semidirect

Maximal subgroups

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

subgroupindex
C5×#57262
#117511942
#117468832
C3×#647672
#117458362
#106027043
#684345