Finite Group Databasebeta

← #14289636

Subgroups — #14289636

Order 1920.

468 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 99 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
2#11751109C211yesmaximal, characteristic, complemented
3#11750943C211yesmaximal, characteristic, complemented
4#11750782C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
6#11746307C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, 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
17#91758C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C4×C5×C8C2211yescharacteristic
20#91116—21no—
21#91105—21no—
22#91101—21no—
23#91100—22no—
24#91092—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68204—51nomaximal, Hall
27#65889—31no—
28#65297—31no—
29#65131—31no—
30#64970—31no—
31C5×D4⋊C8D311yescharacteristic, complemented
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×Dic30—21no—
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C3×C42×C5C2311yescharacteristic
49#6714—22no—
50#6714—21no—
51C4⋊Dic15—22no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15D412yes—
56C4⋊Dic15D411yescharacteristic
57C2×C3⋊#168—21no—
58#5555—51no—
59#5008—51no—
60#4842—51no—
61#4681—51no—
62C3×D4⋊C8D511yescharacteristic, complemented
63#4486—51no—
64#4459—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#4015—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8C2×D311yescharacteristic
76#3964—61no—
77#3953—61no—
78#3949—61no—
79#3948—62no—
80#3940—61no—
81C4⋊#168—31no—
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—
97C2×Dic15—41no—
98D60—21no—
99D60—21no—
100C4×D15—41no—
101C4×D15—41no—
102Dic30—41no—
103Dic30—41no—
104Dic30—42no—
105C3×C5×C8—41no—
106C3×C5×C8—41no—
107C3⋊#168—41no—
108C2×#237—101no—
109C3×C4×D4C2×D511yescharacteristic
110#930—101no—
111C2×C4⋊Dic3—101no—
112#897—101no—
113#886—102no—
114C4×D12—51no—
115#869—51no—
116#869—51no—
117C3×C4⋊C8C2×D511yescharacteristic
118C3×C4×C8C2×D511yescharacteristic
119#832—101no—
120#821—101no—
121#817—101no—
122#816—102no—
123#808—101no—
124C4⋊(C3⋊C8)—51no—
125C2×C5×D4D1211yescharacteristic
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—61no—
134C2×Dic10—61no—
135C2×C5×C8—21no—
136C2×C5×C8—21no—
137C5×C4⋊C4D1211yescharacteristic
138C5×C22⋊C4—21no—
139C42×C5C22×D311yescharacteristic
140#685—62no—
141#685—61no—
142C4⋊Dic5—32no—
143C4⋊Dic5—31no—
144C4⋊Dic5—62no—
145C4⋊Dic5—61no—
146C4⋊Dic5—61no—
147C4⋊Dic5—61no—
148C2×#168—61no—
149#547—151no—
150#487—151no—
151#476—151no—
152#476—151no—
153#332—151no—
154D4⋊C8—151no—
155D4⋊C8D1511yescharacteristic, complemented
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—
171Dic15—81no—
172C2×C3×D4D2011yescharacteristic
173C22×C3×C4—21no—
174C2×#67—102no—
175C22×Dic3—102no—
176#237—202no—
177#237—202no—
178C2×D12—51no—
179C2×C4×D3—101no—
180C2×Dic6—101no—
181C2×Dic6—101no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C3×C4⋊C4D2011yescharacteristic
185C3×C22⋊C4—21no—
186C3×C42C22×D511yescharacteristic
187(C2×D3)⋊C4—102no—
188(C2×D3)⋊C4—101no—
189C4⋊Dic3—52no—
190C4⋊Dic3—51no—
191C4⋊Dic3—102no—
192C4⋊Dic3—101no—
193C4⋊Dic3—101no—
194C4⋊Dic3—101no—
195C2×C3⋊C8—101no—
196C23×C5—21no—
197C22×D5—61no—
198C5×D4—21no—
199C5×D4#20412yes—
200C2×C4×C5—21no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5C2×D1211yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C22⋊D5—124no—
207C2×Dic5—62no—
208C2×Dic5—61no—
209C2×Dic5—124no—
210C2×Dic5—121no—
211D20—61no—
212D20—61no—
213C4×D5—121no—
214C4×D5—121no—
215Dic10—121no—
216Dic10—121no—
217Dic10—122no—
218C5×C8—41no—
219C5×C8—41no—
220#168—121no—
221C2×#41—301no—
222C4⋊Q8—151no—
223C4⋊Q8—151no—
224#123—302no—
225C22⋊Q8—301no—
226#121—301no—
227C4×D4—151no—
228C4×D4C2×D1511yescharacteristic
229C2×C4⋊C4—301no—
230#106—301no—
231#106—301no—
232C4⋊C8—151no—
233C4⋊C8C2×D1511yescharacteristic
234#103—302no—
235#102—301no—
236#102—301no—
237C4×C8C2×D1511yescharacteristic
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×D4—21no—
246C3×D4#67712yes—
247C2×C3×C4—21no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4C2×D2011yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252C2×C3×C4D4×D511yescharacteristic
253#67—204no—
254C2×Dic3—102no—
255C2×Dic3—101no—
256C2×Dic3—204no—
257C2×Dic3—201no—
258D12—101no—
259D12—101no—
260C4×D3—201no—
261C4×D3—201no—
262Dic6—201no—
263Dic6—201no—
264Dic6—202no—
265C3×C8—41no—
266C3×C8—41no—
267C3⋊C8—201no—
268C22×C5—22no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5#88211yescharacteristic
272C2×D5—121no—
273C2×D5—121no—
274C2×D5—121no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5C2×#20411yescharacteristic
278C4×C5#90811yescharacteristic
279C4×C5#91211yescharacteristic
280C4×C5#91511yescharacteristic
281Dic5—122no—
282Dic5—121no—
283Dic5—241no—
284#41—602no—
285#41—602no—
286C2×Q8—301no—
287C2×Q8—301no—
288C2×D4—151no—
289C2×D4—302no—
290C2×D4D6011yescharacteristic
291C22×C4—21no—
292C22×C4—302no—
293C22×C4—301no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—301no—
297C4⋊C4—152no—
298C4⋊C4—151no—
299C4⋊C4—302no—
300C4⋊C4—301no—
301C4⋊C4—301no—
302C4⋊C4—301no—
303C4⋊C4D6011yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—302no—
306C22⋊C4—301no—
307C42C22×D1511yescharacteristic
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×C4C2×#67711yescharacteristic
319C3×C4#405411yescharacteristic
320C3×C4#405811yescharacteristic
321C3×C4#406111yescharacteristic
322Dic3—202no—
323Dic3—201no—
324Dic3—401no—
325C2×C5—42no—
326C2×C5#473111yescharacteristic
327C2×C5#478311yescharacteristic
328C2×C5#482711yescharacteristic
329D5—241no—
330C23—21no—
331C23—301no—
332Q8—602no—
333Q8—601no—
334Q8—601no—
335D4—21no—
336D4—301no—
337D4—301no—
338D4—604no—
339D4#670612yes—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—301no—
344C2×C4—302no—
345C2×C4—604no—
346C2×C4—601no—
347C2×C4—601no—
348C2×C4—601no—
349C2×C4C2×D6011yescharacteristic
350C2×C4D4×D1511yescharacteristic
351C2×C4D4×D1511yescharacteristic
352C8—41no—
353C8—41no—
354C8—601no—
355C2×C3—42no—
356C2×C3#6502011yescharacteristic
357C2×C3#6507211yescharacteristic
358C2×C3#6511611yescharacteristic
359D3—401no—
360C5#6820411yescharacteristic, complemented, Sylow
361C22—22no—
362C22—41no—
363C22—41no—
364C22—601no—
365C22—601no—
366C22—601no—
367C22#9177111yescharacteristic
368C4—21no—
369C4—41no—
370C4—601no—
371C4—602no—
372C4—1201no—
373C4C2×#670611yescharacteristic
374C4#9179711yescharacteristic
375C4#9180111yescharacteristic
376C4#9180411yescharacteristic
377C3#1059899711yescharacteristic, complemented, Sylow
378C2—42no—
379C2—1201no—
380C2#1175083211yescharacteristic
381C2#1175088411yescharacteristic
382C2#1175092811yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radical#11756314C2
hypercenterD4⋊C8D15
hypocenterC3×C5#1635
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11751109C2semidirect
3. #11750943C2semidirect
4. #11750782C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. #11746307C2semidirect
7. #11746280C2semidirect
31. C5×D4⋊C8D3semidirect
62. C3×D4⋊C8D5semidirect
155. D4⋊C8D15semidirect
308. C3×C5#1635semidirect
360. C5#68204semidirect
377. C3#10598997semidirect

Maximal subgroups

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

subgroupindex
#117563142
#117511092
#117509432
#117507822
C3×C5×D4⋊C82
#117463072
#117462802
#105989973
#682045