Finite Group Databasebeta

← #14289656

Subgroups — #14289656

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
1#11756314C211yesmaximal, characteristic
2C3×#65297C211yesmaximal, characteristic, complemented
3#11746942C211yesmaximal, characteristic, complemented
4#11746920C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10598997—31nomaximal, Hall
9C2×#6819—21no—
10C3×C4×C5×D4C2211yescharacteristic
11#91819—21no—
12C2×C4⋊Dic15—21no—
13#91786—21no—
14#91775—22no—
15C4×D60C2211yescharacteristic
16#91758C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C4×C5×C3⋊C8C2211yescharacteristic
20C3×#3964—21no—
21C3×#3940—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90987—21no—
24#90971—22no—
25#90968—21no—
26#71146—51nomaximal, Hall
27#65889—31no—
28#65297D311yescharacteristic, complemented
29#65131—31no—
30#64970—31no—
31C5×D4⋊C8—31no—
32#64706—31no—
33#64679—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×#1220—22no—
37C22×Dic15—22no—
38#6819—42no—
39#6819—42no—
40C2×D60D411yescharacteristic
41C2×C4×D15—21no—
42C2×Dic30—21no—
43C2×C3×Dic10—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C22⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47#6714—22no—
48#6714—21no—
49C4⋊Dic15—22no—
50C4⋊Dic15—21no—
51C4⋊Dic15D412yes—
52C4⋊Dic15D411yescharacteristic
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C2×C3×#168—21no—
58#5555—51no—
59C3×#476—51no—
60#5084—51no—
61#5079—51no—
62D4⋊(C3⋊C8)D511yescharacteristic, complemented
63#4483—51no—
64#4482—51no—
65C2×#711—61no—
66C4×C5×D4C2×D311yescharacteristic
67#4076—61no—
68C2×C4⋊Dic5—61no—
69#4043—61no—
70#4032—62no—
71C4×D20—31no—
72#4015—31no—
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3964—21no—
77#3953—61no—
78#3949—61no—
79#3948—62no—
80#3940—21no—
81C4⋊#168C2×D311yescharacteristic
82#1635—151noSylow
83C23×C3×C5—21no—
84C22×D15—21no—
85C3×C5×D4—21no—
86C3×C5×D4SD1612yes—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93#1220—44no—
94C2×Dic15—22no—
95C2×Dic15—21no—
96C2×Dic15—44no—
97D60—21no—
98D60—21no—
99C4×D15—41no—
100C4×D15—41no—
101Dic30—41no—
102Dic30—41no—
103C2×C3×Dic5—41no—
104C3×Dic10—42no—
105C3×#168—41no—
106C5×C3⋊C8—41no—
107C5×C3⋊C8—41no—
108C2×#237—101no—
109C3×C4⋊Q8—51no—
110C3×C4×D4C2×D511yescharacteristic
111#930—101no—
112C2×C4⋊Dic3—101no—
113#897—101no—
114#886—102no—
115C4×D12—51no—
116#869—51no—
117C3×#106—101no—
118C3×C4⋊C8—51no—
119C3×#102—101no—
120#835—102no—
121#809—101no—
122#808—101no—
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124C4×C3⋊C8C2×D511yescharacteristic
125C2×C5×D4#6711yescharacteristic
126C22×C4×C5—21no—
127C2×C22⋊D5—62no—
128C22×Dic5—62no—
129#711—122no—
130#711—122no—
131C2×D20—31no—
132C2×C4×D5—61no—
133C2×Dic10—21no—
134C2×Dic10—61no—
135C2×C5×C8—61no—
136C2×C5×C8—61no—
137C5×C4⋊C4#6711yescharacteristic
138C5×C22⋊C4—21no—
139C42×C5C22×D311yescharacteristic
140#685—62no—
141#685—61no—
142C4⋊Dic5—21no—
143C4⋊Dic5—21no—
144C4⋊Dic5—32no—
145C4⋊Dic5—31no—
146C4⋊Dic5—62no—
147C4⋊Dic5—61no—
148C2×#168—21no—
149#547—151no—
150#487—151no—
151#476—51no—
152#476—151no—
153#332—151no—
154D4⋊C8—31no—
155D4⋊C8—151no—
156C22×C3×C5—22no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5#12011yescharacteristic
160C2×D15—41no—
161C2×D15—41no—
162C2×D15—41no—
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5C2×SD1611yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5#13711yescharacteristic
169Dic15—42no—
170Dic15—41no—
171C3×Dic5—81no—
172C2×C3×Q8—101no—
173C2×C3×D4D2011yescharacteristic
174C22×C3×C4—21no—
175C2×#67—102no—
176C22×Dic3—102no—
177#237—202no—
178#237—202no—
179C2×D12—51no—
180C2×C4×D3—101no—
181C2×Dic6—101no—
182C2×C3×C8—101no—
183C3×C4⋊C4—101no—
184C3×C4⋊C4—101no—
185C3×C4⋊C4D2011yescharacteristic
186C3×C22⋊C4—21no—
187C3×C42C22×D511yescharacteristic
188(C2×D3)⋊C4—102no—
189(C2×D3)⋊C4—101no—
190C4⋊Dic3—51no—
191C4⋊Dic3—52no—
192C4⋊Dic3—102no—
193C4⋊Dic3—101no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C23×C5—21no—
197C22×D5—61no—
198C5×D4—21no—
199C5×D4#21512yes—
200C2×C4×C5—21no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C22⋊D5—124no—
207C2×Dic5—41no—
208C2×Dic5—62no—
209C2×Dic5—61no—
210C2×Dic5—124no—
211D20—61no—
212D20—61no—
213C4×D5—121no—
214C4×D5—121no—
215Dic10—42no—
216Dic10—121no—
217Dic10—121no—
218C5×C8—121no—
219C5×C8—121no—
220#168—41no—
221C2×#41—301no—
222C4⋊Q8—51no—
223C4⋊Q8—151no—
224#123—302no—
225C22⋊Q8—301no—
226#121—301no—
227C4×D4—151no—
228C4×D4D3×D511yescharacteristic
229C2×C4⋊C4—301no—
230#106—101no—
231#106—301no—
232C4⋊C8—31no—
233C4⋊C8—51no—
234#103—302no—
235#102—101no—
236#102—301no—
237C4×C8—31no—
238C2×C3×C5—42no—
239C2×C3×C5#45011yescharacteristic
240C2×C3×C5#45211yescharacteristic
241C2×C3×C5#45411yescharacteristic
242D15—81no—
243C23×C3—21no—
244C22×D3—101no—
245C3×Q8—202no—
246C3×D4—21no—
247C3×D4#67712yes—
248C2×C3×C4—21no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—201no—
252C2×C3×C4C2×D2011yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255#67—204no—
256C2×Dic3—102no—
257C2×Dic3—101no—
258C2×Dic3—204no—
259D12—101no—
260D12—101no—
261C4×D3—201no—
262C4×D3—201no—
263Dic6—201no—
264Dic6—201no—
265C3×C8—201no—
266C3⋊C8—41no—
267C3⋊C8—41no—
268C22×C5—22no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5#93711yescharacteristic
272C2×D5—121no—
273C2×D5—121no—
274C2×D5—121no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5#91511yescharacteristic
278C4×C5#91611yescharacteristic
279C4×C5C2×#21511yescharacteristic
280C4×C5#94911yescharacteristic
281Dic5—81no—
282Dic5—122no—
283Dic5—121no—
284#41—602no—
285#41—602no—
286C2×Q8—101no—
287C2×Q8—301no—
288C2×D4—151no—
289C2×D4—302no—
290C2×D4#120211yescharacteristic
291C22×C4—21no—
292C22×C4—302no—
293C22×C4—301no—
294C2×C8—61no—
295C2×C8—61no—
296C2×C8—101no—
297C4⋊C4—101no—
298C4⋊C4—101no—
299C4⋊C4—152no—
300C4⋊C4—151no—
301C4⋊C4—302no—
302C4⋊C4—301no—
303C4⋊C4#120211yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—302no—
306C22⋊C4—301no—
307C42C2×D3×D511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3—22no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3#402811yescharacteristic
313C2×D3—201no—
314C2×D3—201no—
315C2×D3—201no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—401no—
319C3×C4C2×#67711yescharacteristic
320C3×C4#405411yescharacteristic
321C3×C4#405811yescharacteristic
322C3×C4#406111yescharacteristic
323Dic3—202no—
324Dic3—201no—
325C2×C5—42no—
326C2×C5#504611yescharacteristic
327C2×C5#517311yescharacteristic
328C2×C5#520111yescharacteristic
329D5—241no—
330C23—21no—
331C23—301no—
332Q8—202no—
333Q8—601no—
334Q8—601no—
335D4—21no—
336D4—301no—
337D4—301no—
338D4—604no—
339D4#665812yes—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—201no—
344C2×C4—301no—
345C2×C4—302no—
346C2×C4—604no—
347C2×C4—601no—
348C2×C4—601no—
349C2×C4C2×#120211yescharacteristic
350C2×C4#679011yescharacteristic
351C2×C4#679011yescharacteristic
352C8—121no—
353C8—121no—
354C8—201no—
355C2×C3—42no—
356C2×C3#6502011yescharacteristic
357C2×C3#6507211yescharacteristic
358C2×C3#6511611yescharacteristic
359D3—401no—
360C5#7114611yescharacteristic, complemented, Sylow
361C22—22no—
362C22—41no—
363C22—41no—
364C22—601no—
365C22—601no—
366C22—601no—
367C22#9157211yescharacteristic
368C4—21no—
369C4—41no—
370C4—401no—
371C4—601no—
372C4—602no—
373C4#9130111yescharacteristic
374C4C2×#665811yescharacteristic
375C4#9148811yescharacteristic
376C4#9149911yescharacteristic
377C3#1059899711yescharacteristic, complemented, Sylow
378C2—42no—
379C2—1201no—
380C2#1174855111yescharacteristic
381C2#1174906311yescharacteristic
382C2#1174946011yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radical#11756314C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1635
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. C3×#65297C2semidirect
3. #11746942C2semidirect
4. #11746920C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. #11745860C2semidirect
7. #11745838C2semidirect
28. #65297D3semidirect
62. D4⋊(C3⋊C8)D5semidirect
308. C3×C5#1635semidirect
360. C5#71146semidirect
377. C3#10598997semidirect

Maximal subgroups

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

subgroupindex
#117563142
C3×#652972
#117469422
#117469202
C5×D4⋊(C3⋊C8)2
#117458602
#117458382
#105989973
#711465