Finite Group Databasebeta

← #14290859

Subgroups — #14290859

Order 1920.

480 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752549C211yesmaximal, characteristic
2C3×#64969C211yesmaximal, characteristic, complemented
3#11747085C211yesmaximal, characteristic, complemented
4#11746900C211yesmaximal, characteristic, complemented
5#11746280C211yesmaximal, characteristic, complemented
6C5×#4459C211yesmaximal, characteristic, complemented
7#11745855C211yesmaximal, characteristic, complemented
8#10598978—31nomaximal, Hall
9C2×#6768—21no—
10C4×D60C2211yescharacteristic
11C4×C5×D12C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91460—21no—
15#91427—22no—
16D3×C4⋊Dic5—21no—
17#91390—21no—
18C2×#6658—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3949—22no—
23#90989—21no—
24#90971—21no—
25#90966—21no—
26#71343—51nomaximal, Hall
27#65889—31no—
28#65296—31no—
29#65130—31no—
30#64969D311yescharacteristic, complemented
31C5×D4⋊C8—31no—
32#64706—31no—
33#64679—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×Dic10—21no—
39C2×C3×Dic10—21no—
40C2×#1203—22no—
41C2×D3×Dic5—22no—
42#6768—42no—
43#6768—42no—
44C2×C3×C5×C8—21no—
45C3×C42×C5C2311yescharacteristic
46#6714—21no—
47C4⋊Dic15D411yescharacteristic
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3D411yescharacteristic
51C2×C5×C3⋊C8—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5D412yes—
56Dic3⋊Dic5—22no—
57#6667—22no—
58#6658—42no—
59#5726—51no—
60C3×#498—51no—
61#5087—51no—
62#5083—51no—
63#4547—51no—
64#4459—51no—
65#4459D511yescharacteristic, complemented
66C2×#711—61no—
67C4×C5×D4—31no—
68#4076—61no—
69C2×C4⋊Dic5—61no—
70C2×#677—61no—
71#4043—61no—
72#4032—62no—
73C4×D20—31no—
74#4015C2×D311yescharacteristic
75#4015C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C4×C5×C8C2×D311yescharacteristic
78#3964—61no—
79#3949—22no—
80#3948—61no—
81#3939—61no—
82C4⋊#168—31no—
83#1654—151noSylow
84C22×D15—21no—
85C22×C5×D3—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90D60—21no—
91D60—21no—
92C4×D15—41no—
93C4×D15—41no—
94C2×C5×Dic3—21no—
95C5×D12—21no—
96C5×D12SD1612yescomplemented
97C4×C5×D3—41no—
98C4×C5×D3—41no—
99C2×C3×Dic5—22no—
100C2×C3×Dic5—41no—
101C3×Dic10—41no—
102C3×Dic10—41no—
103C3×Dic10—41no—
104C3×Dic10—41no—
105#1203—44no—
106D3×Dic5—44no—
107C3×C5×C8—22no—
108C3⋊#168—41no—
109C5×C3⋊C8—41no—
110C2×#239—101no—
111C3×C4⋊Q8—51no—
112C3×C4⋊Q8—51no—
113#946—101no—
114C2×#215—101no—
115#895—101no—
116#894—102no—
117D3×C4⋊C4—101no—
118C4×D12—51no—
119C4×D12C2×D511yescharacteristic
120C3×#106—102no—
121C3×C4×C8C2×D511yescharacteristic
122#835—101no—
123#809—101no—
124#807—101no—
125C4⋊(C3⋊C8)—51no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C2×C5×D4—31no—
128C22×C4×C5—61no—
129C2×C22⋊D5—62no—
130C22×Dic5—62no—
131#711—122no—
132#711—122no—
133C2×D20—31no—
134C2×C4×D5—61no—
135C2×Dic10—21no—
136C2×Dic10—21no—
137C2×C5×C8—21no—
138C2×C5×C8—61no—
139C5×C4⋊C4—31no—
140C5×C22⋊C4—61no—
141C42×C5C22×D311yescharacteristic
142#685—62no—
143#685—61no—
144C4⋊Dic5—21no—
145C4⋊Dic5—21no—
146C4⋊Dic5—21no—
147C4⋊Dic5—31no—
148C4⋊Dic5—62no—
149C4⋊Dic5#6712yes—
150C2×#168—61no—
151#677—122no—
152#547—151no—
153#498—51no—
154#474—151no—
155#461—151no—
156#332—151no—
157D4⋊C8—31no—
158D4⋊C8—151no—
159C22×C3×C5#12011yescharacteristic
160C2×D15—41no—
161C2×D15—41no—
162C2×D15—41no—
163C2×C5×D3—22no—
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C3×C4×C5—21no—
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171Dic15—41no—
172C3×Dic5—42no—
173C3×Dic5—81no—
174C5×Dic3—41no—
175C2×C3×Q8—101no—
176C2×C3×Q8—101no—
177#239—202no—
178#239—202no—
179C2×D12—51no—
180C2×D12—102no—
181C2×D12D2011yescharacteristic
182C2×C4×D3—21no—
183C2×C4×D3—102no—
184C2×C4×D3—101no—
185C2×C3×C8—21no—
186C3×C4⋊C4—52no—
187C3×C4⋊C4—101no—
188C3×C4⋊C4—101no—
189C3×C4⋊C4—101no—
190C3×C42C22×D511yescharacteristic
191#215—202no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—102no—
194(C2×D3)⋊C4—101no—
195C4⋊Dic3—51no—
196C4⋊Dic3D2011yescharacteristic
197Dic3⋊C4—102no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—101no—
200C23×C5—61no—
201C22×D5—61no—
202C5×D4—32no—
203C5×D4—61no—
204C2×C4×C5—61no—
205C2×C4×C5—121no—
206C2×C4×C5—121no—
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C22⋊D5—124no—
211C2×Dic5—22no—
212C2×Dic5—41no—
213C2×Dic5—61no—
214C2×Dic5—124no—
215D20—61no—
216D20—61no—
217C4×D5—121no—
218C4×D5—121no—
219Dic10—41no—
220Dic10—41no—
221Dic10—41no—
222Dic10—41no—
223C5×C8—22no—
224C5×C8—121no—
225#168—121no—
226C2×#41—301no—
227C2×SD16—301no—
228C4⋊Q8—51no—
229C4⋊Q8—51no—
230#123—302no—
231C22⋊Q8—301no—
232#121—301no—
233C4×D4—31no—
234C4×D4—151no—
235C2×C4⋊C4—301no—
236#107—301no—
237#106—102no—
238C4⋊C8—31no—
239C4⋊C8—151no—
240#103—301no—
241#102—301no—
242C4×C8D3×D511yescharacteristic
243C2×C3×C5#44911yescharacteristic
244C2×C3×C5#45011yescharacteristic
245C2×C3×C5#45611yescharacteristic
246D15—81no—
247C5×D3—42no—
248C22×D3—21no—
249C22×D3—101no—
250C3×Q8—201no—
251C3×Q8—201no—
252C3×Q8—201no—
253C3×Q8—201no—
254C2×C3×C4—102no—
255C2×C3×C4—201no—
256C2×C3×C4C2×D2011yescharacteristic
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×Dic3—21no—
260C2×Dic3—101no—
261D12—21no—
262D12—101no—
263D12—101no—
264D12—204no—
265D12#67712yescomplemented
266C4×D3—41no—
267C4×D3—41no—
268C4×D3—204no—
269C4×D3—201no—
270C4×D3—201no—
271C3×C8—22no—
272C3⋊C8—41no—
273C3⋊C8—201no—
274C22×C5—62no—
275C22×C5—121no—
276C22×C5—121no—
277C22×C5#93711yescharacteristic
278C2×D5—121no—
279C2×D5—121no—
280C2×D5—121no—
281C4×C5—21no—
282C4×C5—121no—
283C4×C5D3×SD1611yescharacteristic
284C4×C5#91411yescharacteristic
285C4×C5#91411yescharacteristic
286C4×C5#91611yescharacteristic
287Dic5—42no—
288Dic5—81no—
289Dic5—121no—
290#41—602no—
291#41—602no—
292C2×Q8—101no—
293C2×Q8—101no—
294C2×D4—31no—
295C2×D4—151no—
296C2×D4—302no—
297C22×C4—61no—
298C22×C4—302no—
299C22×C4—301no—
300SD16—602no—
301C2×C8—21no—
302C2×C8—61no—
303C2×C8—301no—
304C4⋊C4—31no—
305C4⋊C4—52no—
306C4⋊C4—101no—
307C4⋊C4—101no—
308C4⋊C4—101no—
309C4⋊C4—151no—
310C4⋊C4—302no—
311C22⋊C4—61no—
312C22⋊C4—302no—
313C22⋊C4—301no—
314C42C2×D3×D511yescharacteristic
315C3×C5#165411yescharacteristic, complemented, Hall
316C22×C3#402811yescharacteristic
317C2×D3—22no—
318C2×D3—41no—
319C2×D3—41no—
320C2×D3—201no—
321C2×D3—201no—
322C2×D3—201no—
323C3×C4—21no—
324C3×C4—202no—
325C3×C4—401no—
326C3×C4C2×#67711yescharacteristic
327C3×C4#405411yescharacteristic
328C3×C4#405711yescharacteristic
329C3×C4#406211yescharacteristic
330Dic3—41no—
331Dic3—201no—
332C2×C5—122no—
333C2×C5#509511yescharacteristic
334C2×C5#516911yescharacteristic
335C2×C5#517211yescharacteristic
336D5—241no—
337C23—61no—
338C23—301no—
339Q8—201no—
340Q8—201no—
341Q8—201no—
342Q8—201no—
343D4—32no—
344D4—61no—
345D4—301no—
346D4—301no—
347D4—604no—
348C2×C4—61no—
349C2×C4—102no—
350C2×C4—121no—
351C2×C4—121no—
352C2×C4—201no—
353C2×C4—301no—
354C2×C4—604no—
355C2×C4—601no—
356C2×C4—601no—
357C2×C4D3×D2011yescharacteristic
358C2×C4#677711yescharacteristic
359C2×C4D5×#6711yescharacteristic
360C8—22no—
361C8—121no—
362C8—601no—
363C2×C3#6502011yescharacteristic
364C2×C3#6507011yescharacteristic
365C2×C3#6511511yescharacteristic
366D3—42no—
367D3—401no—
368C5#7134311yescharacteristic, complemented, Sylow
369C22—62no—
370C22—121no—
371C22—121no—
372C22—601no—
373C22—601no—
374C22—601no—
375C22#9147411yescharacteristic
376C4—21no—
377C4—121no—
378C4—202no—
379C4—401no—
380C4—601no—
381C4D3×#67711yescharacteristic
382C4#9125311yescharacteristic
383C4#9125711yescharacteristic
384C4#9127611yescharacteristic
385C3#1059897811yescharacteristic, complemented, Sylow
386C2—122no—
387C2—1201no—
388C2#1174712011yescharacteristic
389C2#1174788911yescharacteristic
390C2#1174811011yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11752549C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#1654
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
2. C3×#64969C2semidirect
3. #11747085C2semidirect
4. #11746900C2semidirect
5. #11746280C2semidirect
6. C5×#4459C2semidirect
7. #11745855C2semidirect
30. #64969D3semidirect
65. #4459D5semidirect
96. C5×D12SD16semidirect
265. D12#677semidirect
315. C3×C5#1654semidirect
368. C5#71343semidirect
385. C3#10598978semidirect

Maximal subgroups

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

subgroupindex
#117525492
C3×#649692
#117470852
#117469002
#117462802
C5×#44592
#117458552
#105989783
#713435