Finite Group Databasebeta

← #14289332

Subgroups — #14289332

Order 1920.

432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752486C211yesmaximal, characteristic, complemented
2C3×#65137C211yesmaximal, characteristic, complemented
3#11747043C211yesmaximal, characteristic
4#11746895C211yesmaximal, characteristic, complemented
5#11746304C211yesmaximal, characteristic, complemented
6C5×#4486C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10599226—31nomaximal, Hall
9C4×D60C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C2×C3×#677—21no—
12C3×#4020C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91390—21no—
15#91375—21no—
16#91347—21no—
17#91337—22no—
18Dic5×Dic6—21no—
19C2×#6653—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3953—21no—
24#90965—21no—
25#90964—22no—
26#71029—51nomaximal, Hall
27#66066—31no—
28#65377—31no—
29#65137D311yescharacteristic, complemented
30#65132—31no—
31C5×#332—31no—
32#64704—31no—
33#64703—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×Dic6—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43#6714—21no—
44C4⋊Dic15D411yescharacteristic
45C2×C3⋊#168—21no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3D412yes—
48C2×C5×C3⋊C8—21no—
49C3×C4⋊Dic5D411yescharacteristic
50C3×#683—21no—
51C3×C4×Dic5—21no—
52C3×#677—42no—
53Dic3⋊Dic5—22no—
54#6667—22no—
55#6667—22no—
56Dic3×Dic5—22no—
57#6653—42no—
58#5584—51no—
59C3×#460—51no—
60#5072—51no—
61#5070—51no—
62#4535—51no—
63#4486D511yescharacteristic, complemented
64#4483—51no—
65C5×C4⋊Q8—31no—
66#4093—61no—
67Q8×Dic5—61no—
68C2×D40—61no—
69C2×#677—21no—
70#4044—62no—
71#4043—61no—
72#4038—61no—
73#4020C2×D311yescharacteristic
74C4×D20—31no—
75C4×Dic10C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C5×C4⋊C8C2×D311yescharacteristic
78#3953—21no—
79#3953—61no—
80#3941—62no—
81C4×#168—31no—
82#1628—151noSylow
83C22×D15—21no—
84C22×C3×D5—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—21no—
89D60—21no—
90D60—21no—
91C4×D15—41no—
92C4×D15—41no—
93C2×C5×Dic3—22no—
94C5×Dic6—41no—
95C5×Dic6—41no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—21no—
98C3×D20—42no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×Dic10—21no—
104C3×Dic10—21no—
105C3×C5×C8—41no—
106C3⋊#168—41no—
107C5×C3⋊C8—41no—
108C2×C3×SD16—101no—
109C3×#127—51no—
110C3×C4×Q8—51no—
111#946—101no—
112C2×#213—101no—
113#898—102no—
114#892—101no—
115#875—101no—
116C4×D12—51no—
117#869C2×D511yescharacteristic
118C4×Dic6—101no—
119C3×C4⋊C8C2×D511yescharacteristic
120C3×#102—101no—
121#832—101no—
122#832—102no—
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124C4×C3⋊C8—51no—
125C2×C5×Q8—61no—
126C2×D20—21no—
127C2×D20—21no—
128C2×D20—21no—
129C2×D20—31no—
130C2×C4×D5—61no—
131C2×Dic10#6711yescharacteristic
132C2×C5×C8—21no—
133C2×C5×C8—61no—
134C5×C4⋊C4—32no—
135C5×C4⋊C4—61no—
136C42×C5C22×D311yescharacteristic
137#685—62no—
138#685—62no—
139#685—61no—
140C4⋊Dic5—31no—
141C4⋊Dic5—62no—
142C4⋊Dic5#6711yescharacteristic
143#683—21no—
144C4×Dic5—21no—
145C4×Dic5—62no—
146C2×#168—61no—
147D40—122no—
148#677—42no—
149#556—151no—
150#486—151no—
151#460—51no—
152#459—151no—
153#332—31no—
154Q8⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×D15—41no—
158C2×D15—41no—
159C2×D15—41no—
160C2×C3×D5—81no—
161C2×C3×D5—81no—
162C2×C3×D5—81no—
163C3×C4×C5—21no—
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168Dic15—41no—
169C3×Dic5—41no—
170C3×Dic5—41no—
171C5×Dic3—42no—
172C2×C3×Q8—51no—
173C2×C3×D4—101no—
174C2×C3×D4—101no—
175C2×C3×D4—101no—
176C2×D12—51no—
177C2×C4×D3—101no—
178C2×Dic6—21no—
179C3×SD16—202no—
180C2×C3×C8—21no—
181C3×C4⋊C4—51no—
182C3×C4⋊C4—101no—
183C3×C42—101no—
184C3×C42C22×D511yescharacteristic
185#213—202no—
186(C2×D3)⋊C4—102no—
187(C2×D3)⋊C4—102no—
188(C2×D3)⋊C4—101no—
189C4⋊Dic3—21no—
190C4⋊Dic3—51no—
191C4⋊Dic3D2012yes—
192Dic3⋊C4—102no—
193C4×Dic3—102no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—101no—
196C22×D5—41no—
197C22×D5—61no—
198C5×Q8—121no—
199C5×Q8—121no—
200C2×C4×C5—62no—
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C2×Dic5—21no—
205C2×Dic5—21no—
206C2×Dic5—61no—
207D20—42no—
208D20—41no—
209D20—41no—
210D20—41no—
211D20—41no—
212D20—61no—
213D20—61no—
214C4×D5—121no—
215C4×D5—121no—
216Dic10—21no—
217Dic10—21no—
218C5×C8—41no—
219C5×C8—121no—
220#168—121no—
221C2×SD16—101no—
222C2×D8—301no—
223C4⋊Q8—31no—
224#127—51no—
225#126—302no—
226#124—301no—
227C22⋊Q8—301no—
228C4×Q8—51no—
229C4×Q8—301no—
230C4×D4—151no—
231#117—301no—
232C4⋊C8—31no—
233C4⋊C8D3×D511yescharacteristic
234#102—101no—
235#102—302no—
236#102—301no—
237C4×C8—151no—
238C2×C3×C5#44911yescharacteristic
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#45411yescharacteristic
241D15—81no—
242C3×D5—161no—
243C23×C3—201no—
244C22×D3—101no—
245C3×Q8—101no—
246C3×Q8—101no—
247C3×D4—202no—
248C3×D4—201no—
249C3×D4—201no—
250C3×D4—201no—
251C3×D4—201no—
252C2×C3×C4—101no—
253C2×C3×C4—101no—
254C2×C3×C4C2×D2011yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257C2×Dic3—22no—
258C2×Dic3—101no—
259D12—101no—
260D12—101no—
261C4×D3—201no—
262C4×D3—201no—
263Dic6—41no—
264Dic6—41no—
265C3×C8—41no—
266C3⋊C8—41no—
267C3⋊C8—201no—
268C22×C5#93711yescharacteristic
269C2×D5—81no—
270C2×D5—81no—
271C2×D5—81no—
272C2×D5—121no—
273C2×D5—121no—
274C2×D5—121no—
275C4×C5—21no—
276C4×C5—122no—
277C4×C5#91411yescharacteristic
278C4×C5#91611yescharacteristic
279C4×C5#93211yescharacteristic
280C4×C5#95011yescharacteristic
281Dic5—41no—
282Dic5—41no—
283Dic5—121no—
284C2×Q8—51no—
285C2×Q8—61no—
286C2×D4—101no—
287C2×D4—101no—
288C2×D4—101no—
289C2×D4—151no—
290C22×C4—301no—
291SD16—202no—
292D8—602no—
293C2×C8—21no—
294C2×C8—61no—
295C2×C8—301no—
296C4⋊C4—32no—
297C4⋊C4—51no—
298C4⋊C4—61no—
299C4⋊C4—101no—
300C4⋊C4—151no—
301C4⋊C4—302no—
302C22⋊C4—302no—
303C22⋊C4—302no—
304C22⋊C4—301no—
305C42—101no—
306C42—302no—
307C42C2×D3×D511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—401no—
310C22×C3—401no—
311C22×C3—401no—
312C22×C3#402811yescharacteristic
313C2×D3—201no—
314C2×D3—201no—
315C2×D3—201no—
316C3×C4—21no—
317C3×C4—201no—
318C3×C4—201no—
319C3×C4#405711yescharacteristic
320C3×C4#406011yescharacteristic
321C3×C4#406211yescharacteristic
322C3×C4#406511yescharacteristic
323Dic3—42no—
324Dic3—201no—
325C2×C5#503711yescharacteristic
326C2×C5#517211yescharacteristic
327C2×C5#520111yescharacteristic
328D5—161no—
329D5—241no—
330C23—201no—
331C23—301no—
332Q8—101no—
333Q8—101no—
334Q8—121no—
335Q8—121no—
336D4—202no—
337D4—201no—
338D4—201no—
339D4—201no—
340D4—201no—
341D4—301no—
342D4—301no—
343C2×C4—62no—
344C2×C4—101no—
345C2×C4—101no—
346C2×C4—301no—
347C2×C4—601no—
348C2×C4—601no—
349C2×C4D3×D2011yescharacteristic
350C2×C4#677711yescharacteristic
351C2×C4D5×#6711yescharacteristic
352C8—41no—
353C8—121no—
354C8—601no—
355C2×C3—801no—
356C2×C3#6504211yescharacteristic
357C2×C3#6507011yescharacteristic
358C2×C3#6510011yescharacteristic
359D3—401no—
360C5#7102911yescharacteristic, complemented, Sylow
361C22—401no—
362C22—401no—
363C22—401no—
364C22—601no—
365C22—601no—
366C22—601no—
367C22#9147411yescharacteristic
368C4—21no—
369C4—122no—
370C4—201no—
371C4—201no—
372C4—601no—
373C4#9125711yescharacteristic
374C4#9127611yescharacteristic
375C4#9149111yescharacteristic
376C4#9151611yescharacteristic
377C3#1059922611yescharacteristic, complemented, Sylow
378C2—801no—
379C2—1201no—
380C2#1174751211yescharacteristic
381C2#1174788911yescharacteristic
382C2#1174825511yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11747043C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1628
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11752486C2semidirect
2. C3×#65137C2semidirect
4. #11746895C2semidirect
5. #11746304C2semidirect
6. C5×#4486C2semidirect
7. #11745840C2semidirect
29. #65137D3semidirect
63. #4486D5semidirect
308. C3×C5#1628semidirect
360. C5#71029semidirect
377. C3#10599226semidirect

Maximal subgroups

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

subgroupindex
#117524862
C3×#651372
#117470432
#117468952
#117463042
C5×#44862
#117458402
#105992263
#710295