Finite Group Databasebeta

← #14289135

Subgroups — #14289135

Order 1920.

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

normal subgroups only

This group has 512 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#11752532C211yesmaximal, characteristic, complemented
2C3×#65132C211yesmaximal, characteristic, complemented
3#11747033C211yesmaximal, characteristic, complemented
4#11746890C211yesmaximal, characteristic, complemented
5#11746303C211yesmaximal, characteristic, complemented
6C5×#4483C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10598973—31nomaximal, Hall
9C2×#6765—21no—
10#91758C2211yescharacteristic
11C4×C5×D12C2211yescharacteristic
12C2×C3×D40—21no—
13C3×#4020C2211yescharacteristic
14C3×C4×D20C2211yescharacteristic
15#91449—21no—
16#91414—22no—
17D5×C4⋊Dic3—21no—
18#91365—21no—
19C2×#6652—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×#3953—21no—
24#90965—22no—
25#90964—21no—
26#71018—51nomaximal, Hall
27#65885—31no—
28#65304—31no—
29#65132D311yescharacteristic, complemented
30#64983—31no—
31C5×D4⋊C8—31no—
32#64702—31no—
33#64679—31no—
34C2×Dic30—21no—
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20D411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×#1201—22no—
43C2×D5×Dic3—22no—
44#6765—42no—
45#6765—42no—
46C2×C3×C5×C8—21no—
47C3×C42×C5C2311yescharacteristic
48C4⋊Dic15—21no—
49C4⋊Dic15D412yes—
50C2×C3⋊#168—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C2×C5×C3⋊C8—21no—
54C3×#685—21no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×D40—42no—
57#6668—22no—
58(C2×D3)⋊Dic5—22no—
59#6652—42no—
60#5555—51no—
61C3×#459—51no—
62#5072—51no—
63#5070—51no—
64D4⋊(C3⋊C8)—51no—
65#4483D511yescharacteristic, complemented
66#4482—51no—
67C2×#709—61no—
68C4×C5×D4—31no—
69#4084—61no—
70C2×#686—61no—
71#4070—61no—
72C2×D40—21no—
73D5×C4⋊C4—61no—
74#4029—62no—
75#4020C2×D311yescharacteristic
76C4×D20C2×D311yescharacteristic
77#4015—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C4×C5×C8—31no—
80#3953—21no—
81#3953—62no—
82#3941—61no—
83C4⋊#168—31no—
84#1625—151noSylow
85C22×C5×D3—21no—
86C22×C3×D5—21no—
87C22×C3×D5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—22no—
92Dic30—41no—
93Dic30—41no—
94C2×C5×Dic3—21no—
95C5×D12—21no—
96C5×D12—21no—
97C4×C5×D3—41no—
98C4×C5×D3—41no—
99C2×C3×Dic5—21no—
100C3×D20—21no—
101C3×D20—42no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3×D20—41no—
106C3×D20D812yescomplemented
107C3×C4×D5—41no—
108C3×C4×D5—41no—
109#1201—44no—
110D5×Dic3—44no—
111C3×C5×C8—41no—
112C3⋊#168—41no—
113C5×C3⋊C8—41no—
114C2×#237—101no—
115C2×C3×D8—101no—
116C3×#127—51no—
117C3×C4×D4—51no—
118C2×#213—101no—
119#930—101no—
120C2×C4⋊Dic3—101no—
121#897—101no—
122#886—102no—
123C4×D12C2×D511yescharacteristic
124#869—51no—
125C3×C4⋊C8C2×D511yescharacteristic
126C3×#102—101no—
127#832—102no—
128#832—101no—
129C4⋊(C3⋊C8)—51no—
130C4×C3⋊C8C2×D511yescharacteristic
131C2×C5×D4—31no—
132C22×C4×C5—61no—
133C2×C22⋊D5—62no—
134#709—122no—
135#709—122no—
136C2×D20—21no—
137C2×D20—21no—
138C2×D20—21no—
139C2×D20#6711yescharacteristic
140C2×C4×D5—21no—
141C2×C4×D5—62no—
142C2×Dic10—61no—
143C2×C5×C8—21no—
144C2×C5×C8—61no—
145C5×C4⋊C4—31no—
146C5×C22⋊C4—61no—
147C42×C5C22×D311yescharacteristic
148C22⋊Dic5—62no—
149#686—122no—
150#685—21no—
151C4⋊Dic5—32no—
152C4⋊Dic5—61no—
153C4⋊Dic5#6711yescharacteristic
154#683—62no—
155C2×#168—61no—
156D40—42no—
157#547—151no—
158#486—151no—
159#459—51no—
160#459—151no—
161#332—151no—
162D4⋊C8—31no—
163D4⋊C8—151no—
164C22×C3×C5#12011yescharacteristic
165C2×C5×D3—41no—
166C2×C5×D3—41no—
167C2×C5×D3—41no—
168C2×C3×D5—22no—
169C2×C3×D5—41no—
170C2×C3×D5—41no—
171C2×C3×D5—81no—
172C2×C3×D5—81no—
173C2×C3×D5—81no—
174C3×C4×C5—21no—
175C3×C4×C5C2×D811yescharacteristic
176C3×C4×C5#13511yescharacteristic
177C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
178C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
179Dic15—42no—
180C3×Dic5—41no—
181C5×Dic3—41no—
182C2×C3×D4—51no—
183C2×C3×D4—101no—
184C2×C3×D4—101no—
185C2×C3×D4—101no—
186C22×C3×C4—101no—
187C2×#67—102no—
188C22×Dic3—102no—
189#237—202no—
190#237—202no—
191C2×D12D2011yescharacteristic
192C2×C4×D3—21no—
193C2×Dic6—101no—
194C3×D8—202no—
195C2×C3×C8—21no—
196C3×C4⋊C4—51no—
197C3×C22⋊C4—101no—
198C3×C42C22×D511yescharacteristic
199#213—202no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—102no—
202C4⋊Dic3—52no—
203C4⋊Dic3—102no—
204C4⋊Dic3—101no—
205C4⋊Dic3D2011yescharacteristic
206C2×C3⋊C8—21no—
207C2×C3⋊C8—101no—
208C23×C5—61no—
209C22×D5—21no—
210C22×D5—41no—
211C5×D4—61no—
212C5×D4—61no—
213C2×C4×C5—61no—
214C2×C4×C5—121no—
215C2×C4×C5—121no—
216C2×C4×C5D3×D411yescharacteristic
217C2×C4×C5D3×D411yescharacteristic
218C2×C4×C5C2×#6711yescharacteristic
219C22⋊D5—124no—
220C2×Dic5—21no—
221C2×Dic5—62no—
222D20—21no—
223D20—42no—
224D20—41no—
225D20—41no—
226D20—41no—
227D20—41no—
228D20#21312yescomplemented
229C4×D5—41no—
230C4×D5—41no—
231C4×D5—124no—
232Dic10—121no—
233Dic10—121no—
234C5×C8—41no—
235C5×C8—121no—
236#168—121no—
237C2×#41—301no—
238C2×D8—101no—
239C2×D8—301no—
240C4⋊Q8—151no—
241#127—51no—
242#123—302no—
243C22⋊Q8—301no—
244#121—301no—
245C4×D4—31no—
246C4×D4—51no—
247C2×C4⋊C4—301no—
248C4⋊C8—151no—
249C4⋊C8D3×D511yescharacteristic
250#102—101no—
251#102—301no—
252#102—302no—
253C4×C8—31no—
254C2×C3×C5#44711yescharacteristic
255C2×C3×C5#44911yescharacteristic
256C2×C3×C5#45411yescharacteristic
257C3×D5—42no—
258C3×D5—161no—
259C5×D3—81no—
260C23×C3—101no—
261C23×C3—201no—
262C22×D3—21no—
263C3×D4—52no—
264C3×D4—101no—
265C3×D4—202no—
266C3×D4—201no—
267C3×D4—201no—
268C3×D4—201no—
269C3×D4—201no—
270C2×C3×C4—101no—
271C2×C3×C4—201no—
272C2×C3×C4—201no—
273C2×C3×C4C2×D2011yescharacteristic
274C2×C3×C4D4×D511yescharacteristic
275C2×C3×C4D4×D511yescharacteristic
276#67—204no—
277C2×Dic3—21no—
278C2×Dic3—102no—
279C2×Dic3—204no—
280D12—21no—
281D12—21no—
282C4×D3—41no—
283C4×D3—41no—
284Dic6—201no—
285Dic6—201no—
286C3×C8—41no—
287C3⋊C8—41no—
288C3⋊C8—201no—
289C22×C5—121no—
290C22×C5—121no—
291C22×C5—121no—
292C22×C5#93711yescharacteristic
293C2×D5—22no—
294C2×D5—41no—
295C2×D5—41no—
296C2×D5—81no—
297C2×D5—81no—
298C2×D5—81no—
299C4×C5—21no—
300C4×C5—121no—
301C4×C5#91111yescharacteristic
302C4×C5#91211yescharacteristic
303C4×C5C2×#21311yescharacteristic
304C4×C5#94911yescharacteristic
305Dic5—41no—
306Dic5—122no—
307#41—602no—
308#41—602no—
309C2×Q8—301no—
310C2×D4—31no—
311C2×D4—51no—
312C2×D4—101no—
313C2×D4—101no—
314C2×D4—101no—
315C2×D4—302no—
316C22×C4—61no—
317C22×C4—101no—
318C22×C4—302no—
319D8—202no—
320D8—602no—
321C2×C8—21no—
322C2×C8—61no—
323C2×C8—301no—
324C4⋊C4—31no—
325C4⋊C4—51no—
326C4⋊C4—152no—
327C4⋊C4—302no—
328C4⋊C4—301no—
329C22⋊C4—61no—
330C22⋊C4—101no—
331C22⋊C4—302no—
332C42C2×D3×D511yescharacteristic
333C3×C5#162511yescharacteristic, complemented, Hall
334C22×C3—102no—
335C22×C3—201no—
336C22×C3—201no—
337C22×C3—401no—
338C22×C3—401no—
339C22×C3—401no—
340C22×C3#402811yescharacteristic
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C3×C4—21no—
345C3×C4—201no—
346C3×C4#405011yescharacteristic
347C3×C4#405411yescharacteristic
348C3×C4D5×D811yescharacteristic
349C3×C4#406011yescharacteristic
350Dic3—41no—
351Dic3—202no—
352C2×C5—241no—
353C2×C5#503611yescharacteristic
354C2×C5#515811yescharacteristic
355C2×C5#520111yescharacteristic
356D5—42no—
357D5—161no—
358C23—61no—
359C23—101no—
360C23—201no—
361Q8—601no—
362Q8—601no—
363D4—52no—
364D4—61no—
365D4—61no—
366D4—101no—
367D4—202no—
368D4—201no—
369D4—201no—
370D4—201no—
371D4—201no—
372D4—604no—
373C2×C4—61no—
374C2×C4—101no—
375C2×C4—121no—
376C2×C4—121no—
377C2×C4—201no—
378C2×C4—201no—
379C2×C4—302no—
380C2×C4—604no—
381C2×C4D3×D2011yescharacteristic
382C2×C4#677711yescharacteristic
383C2×C4D5×#6711yescharacteristic
384C8—41no—
385C8—121no—
386C8—601no—
387C2×C3—202no—
388C2×C3—801no—
389C2×C3#6502311yescharacteristic
390C2×C3#6506211yescharacteristic
391C2×C3#6511611yescharacteristic
392D3—81no—
393C5#7101811yescharacteristic, complemented, Sylow
394C22—102no—
395C22—121no—
396C22—121no—
397C22—121no—
398C22—201no—
399C22—201no—
400C22—401no—
401C22—401no—
402C22—401no—
403C22#9147411yescharacteristic
404C4—21no—
405C4—121no—
406C4—201no—
407C4—602no—
408C4#9125411yescharacteristic
409C4#9127311yescharacteristic
410C4D5×#21311yescharacteristic
411C4#9150211yescharacteristic
412C3#1059897311yescharacteristic, complemented, Sylow
413C2—202no—
414C2—241no—
415C2—801no—
416C2#1174748011yescharacteristic
417C2#1174814911yescharacteristic
418C2#1174825411yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1625
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. #11752532C2semidirect
2. C3×#65132C2semidirect
3. #11747033C2semidirect
4. #11746890C2semidirect
5. #11746303C2semidirect
6. C5×#4483C2semidirect
7. #11745835C2semidirect
29. #65132D3semidirect
65. #4483D5semidirect
106. C3×D20D8semidirect
228. D20#213semidirect
333. C3×C5#1625semidirect
393. C5#71018semidirect
412. C3#10598973semidirect

Maximal subgroups

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

subgroupindex
#117525322
C3×#651322
#117470332
#117468902
#117463032
C5×#44832
#117458352
#105989733
#710185