Finite Group Databasebeta

← #14288841

Subgroups — #14288841

Order 1920.

672 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D12×D20C211yesmaximal, characteristic, complemented
2C3×#65132C211yesmaximal, characteristic, complemented
3#11747035C211yesmaximal, characteristic, complemented
4#11747033C211yesmaximal, characteristic, complemented
5#11746306C211yesmaximal, characteristic, complemented
6C5×#4483C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10598987—31nomaximal, Hall
9C2×D3×D20—21no—
10C2×D5×D12—21no—
11#91763C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C2×C3×D40—21no—
14C3×#4020C2211yescharacteristic, complemented
15C3×C4×D20C2211yescharacteristic
16#91476—22no—
17#91460—21no—
18#91450—21no—
19C2×#6653—22no—
20C2×#6652—21no—
21C3×C5×C4⋊C8C2211yescharacteristic, complemented
22C4⋊(C3⋊#168)C2211yescharacteristic, complemented
23C4×C5×C3⋊C8C2211yescharacteristic, complemented
24C3×#3953—21no—
25#90964—21no—
26#71015—51nomaximal, Hall
27D4×D20—31no—
28#65304—31no—
29#65132D311yescharacteristic, complemented
30#64984—31no—
31C5×D4⋊C8—31no—
32#64705—31no—
33#64679—31no—
34C22×D3×D5—22no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60D412yes—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20D411yescharacteristic
44C2×C3×C4×D5—21no—
45C2×#1203—22no—
46C2×#1202—22no—
47D3×D20—42no—
48D3×D20—42no—
49D5×D12—42no—
50D5×D12—42no—
51C2×C3×C5×C8—21no—
52C3×C42×C5C2311yescharacteristic
53C2×C3⋊#168—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×C4⋊Dic3D411yescharacteristic
56C2×C5×C3⋊C8—21no—
57C3×#685—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C3×D40—42no—
60#6667—22no—
61#6653—44no—
62#6652—42no—
63D4×D12—51no—
64C3×#459—51no—
65#5073—51no—
66#5072—51no—
67D4⋊(C3⋊C8)—51no—
68#4485—51no—
69#4483D511yescharacteristic, complemented
70C2×D4×D5—61no—
71C22×D20—61no—
72C4×C5×D4—31no—
73C2×#686—61no—
74#4076—61no—
75C2×D40—21no—
76C2×D40—62no—
77#4041—61no—
78#4028—62no—
79#4020—31no—
80#4020C2×D311yescharacteristic, complemented
81C4×D20C2×D311yescharacteristic
82C5×C4⋊C8C2×D311yescharacteristic, complemented
83C4×C5×C8—31no—
84#3953—21no—
85#3941—61no—
86C4⋊#168—31no—
87#1619—151noSylow
88C22×D15—22no—
89C22×C5×D3—21no—
90C22×C3×D5—21no—
91C22×C3×D5—41no—
92C2×D3×D5—44no—
93C2×D3×D5—44no—
94C2×D3×D5—82no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98D60—42no—
99D60—41no—
100D60—41no—
101D60—41no—
102D60—41no—
103C2×C5×Dic3—21no—
104C5×D12—21no—
105C5×D12D812yescomplemented
106C4×C5×D3—41no—
107C4×C5×D3—41no—
108C2×C3×Dic5—21no—
109C3×D20—21no—
110C3×D20—42no—
111C3×D20—41no—
112C3×D20—41no—
113C3×D20—41no—
114C3×D20—41no—
115C3×D20D812yescomplemented
116C3×C4×D5—41no—
117C3×C4×D5—41no—
118#1203—44no—
119#1202—44no—
120C3×C5×C8—41no—
121C3⋊#168—41no—
122C5×C3⋊C8—22no—
123C2×D3×D4—101no—
124C22×D12—101no—
125C2×C3×D8—101no—
126C3×#127—51no—
127C3×C4×D4—51no—
128C2×#213—102no—
129C2×#213—101no—
130#930—101no—
131#895—101no—
132#882—102no—
133#874—51no—
134C4×D12C2×D511yescharacteristic
135C3×C4⋊C8C2×D511yescharacteristic, complemented
136C3×#102—101no—
137#832—101no—
138C4⋊(C3⋊C8)—51no—
139C4×C3⋊C8C2×D511yescharacteristic, complemented
140C23×D5—62no—
141C2×C5×D4—31no—
142C22×C4×C5—61no—
143C2×C22⋊D5—62no—
144D4×D5—122no—
145D4×D5—122no—
146C2×D20—21no—
147C2×D20—21no—
148C2×D20—21no—
149C2×D20—32no—
150C2×D20—62no—
151C2×D20—61no—
152C2×D20—61no—
153C2×D20—122no—
154C2×D20—122no—
155C2×D20#6711yescharacteristic
156C2×C4×D5—21no—
157C2×C5×C8—21no—
158C2×C5×C8—61no—
159C5×C4⋊C4—31no—
160C5×C22⋊C4—61no—
161C42×C5C22×D311yescharacteristic
162#686—122no—
163#685—21no—
164#685—62no—
165C4⋊Dic5#6711yescharacteristic
166C2×#168—61no—
167D40—42no—
168D40—124no—
169D42—151no—
170#493—151no—
171#459—51no—
172#459—151no—
173#331—151no—
174D4⋊C8—31no—
175D4⋊C8—151no—
176C22×C3×C5#12011yescharacteristic
177C2×D15—42no—
178C2×D15—42no—
179C2×D15—42no—
180C2×C5×D3—22no—
181C2×C5×D3—41no—
182C2×C5×D3—41no—
183C2×C3×D5—22no—
184C2×C3×D5—41no—
185C2×C3×D5—41no—
186C2×C3×D5—81no—
187C2×C3×D5—81no—
188C2×C3×D5—81no—
189D3×D5—88no—
190C3×C4×C5—21no—
191C3×C4×C5C2×D811yescharacteristic
192C3×C4×C5C2×D811yescharacteristic
193C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
194C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
195C3×Dic5—41no—
196C5×Dic3—41no—
197C23×D3—102no—
198C2×C3×D4—51no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C22×C3×C4—101no—
203C2×#67—102no—
204D3×D4—202no—
205D3×D4—202no—
206C2×D12—52no—
207C2×D12—102no—
208C2×D12—101no—
209C2×D12—101no—
210C2×D12—202no—
211C2×D12—202no—
212C2×D12D2011yescharacteristic
213C2×C4×D3—21no—
214C3×D8—202no—
215C2×C3×C8—21no—
216C3×C4⋊C4—51no—
217C3×C22⋊C4—101no—
218C3×C42C22×D511yescharacteristic
219#213—204no—
220#213—202no—
221(C2×D3)⋊C4—21no—
222(C2×D3)⋊C4—102no—
223C4⋊Dic3D2011yescharacteristic
224C2×C3⋊C8—21no—
225C2×C3⋊C8—101no—
226C23×C5—61no—
227C22×D5—21no—
228C22×D5—41no—
229C22×D5—62no—
230C22×D5—124no—
231C22×D5—124no—
232C22×D5—242no—
233C5×D4—32no—
234C5×D4—61no—
235C2×C4×C5—61no—
236C2×C4×C5—121no—
237C2×C4×C5—121no—
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×C4×C5C2×#6711yescharacteristic
241C22⋊D5—124no—
242C2×Dic5—21no—
243D20—21no—
244D20—42no—
245D20—41no—
246D20—41no—
247D20—41no—
248D20—41no—
249D20—122no—
250D20—124no—
251D20—121no—
252D20—121no—
253D20—121no—
254D20—121no—
255D20#21312yescomplemented
256C4×D5—41no—
257C4×D5—41no—
258C5×C8—41no—
259C5×C8—62no—
260#168—121no—
261C22×D4—301no—
262C22×D4—301no—
263C2×D8—101no—
264C2×D8—302no—
265C2×D8—301no—
266#127—51no—
267#127—151no—
268#121—301no—
269#121—301no—
270#120—302no—
271C4×D4—31no—
272C4×D4—51no—
273C4⋊C8—151no—
274C4⋊C8D3×D511yescharacteristic, complemented
275#102—101no—
276#102—301no—
277C4×C8—31no—
278C2×C3×C5#44711yescharacteristic
279C2×C3×C5#44711yescharacteristic
280C2×C3×C5#45311yescharacteristic
281D15—82no—
282C3×D5—42no—
283C3×D5—161no—
284C5×D3—42no—
285C23×C3—101no—
286C23×C3—201no—
287C22×D3—21no—
288C22×D3—102no—
289C22×D3—204no—
290C22×D3—204no—
291C22×D3—402no—
292C3×D4—52no—
293C3×D4—101no—
294C3×D4—202no—
295C3×D4—201no—
296C3×D4—201no—
297C3×D4—201no—
298C3×D4—201no—
299C2×C3×C4—101no—
300C2×C3×C4—201no—
301C2×C3×C4—201no—
302C2×C3×C4C2×D2011yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4D4×D511yescharacteristic
305#67—204no—
306C2×Dic3—21no—
307D12—21no—
308D12—202no—
309D12—204no—
310D12—201no—
311D12—201no—
312D12—201no—
313D12—201no—
314D12D4012yescomplemented
315C4×D3—41no—
316C4×D3—41no—
317C3×C8—41no—
318C3⋊C8—22no—
319C3⋊C8—201no—
320C22×C5—62no—
321C22×C5—121no—
322C22×C5—121no—
323C22×C5#93711yescharacteristic
324C2×D5—22no—
325C2×D5—41no—
326C2×D5—41no—
327C2×D5—81no—
328C2×D5—81no—
329C2×D5—81no—
330C2×D5—122no—
331C2×D5—122no—
332C2×D5—122no—
333C2×D5—248no—
334C4×C5—21no—
335C4×C5—121no—
336C4×C5D3×D811yescharacteristic
337C4×C5#91111yescharacteristic
338C4×C5C2×#21311yescharacteristic
339C4×C5#94911yescharacteristic
340Dic5—41no—
341C24—302no—
342C2×D4—31no—
343C2×D4—51no—
344C2×D4—101no—
345C2×D4—101no—
346C2×D4—101no—
347C2×D4—152no—
348C2×D4—302no—
349C2×D4—302no—
350C2×D4—301no—
351C2×D4—301no—
352C2×D4—602no—
353C2×D4—602no—
354C2×D4—602no—
355C2×D4—602no—
356C22×C4—61no—
357C22×C4—101no—
358D8—202no—
359D8—604no—
360D8—602no—
361C2×C8—21no—
362C2×C8—61no—
363C2×C8—301no—
364C4⋊C4—31no—
365C4⋊C4—51no—
366C22⋊C4—61no—
367C22⋊C4—101no—
368C22⋊C4—302no—
369C42C2×D3×D511yescharacteristic
370C3×C5#161911yescharacteristic, complemented, Hall
371C22×C3—102no—
372C22×C3—201no—
373C22×C3—201no—
374C22×C3—401no—
375C22×C3—401no—
376C22×C3—401no—
377C22×C3#402811yescharacteristic
378C2×D3—22no—
379C2×D3—41no—
380C2×D3—41no—
381C2×D3—202no—
382C2×D3—202no—
383C2×D3—202no—
384C2×D3—408no—
385C3×C4—21no—
386C3×C4—201no—
387C3×C4C2×D4011yescharacteristic
388C3×C4#405411yescharacteristic
389C3×C4D5×D811yescharacteristic
390C3×C4#406011yescharacteristic
391Dic3—41no—
392C2×C5—122no—
393C2×C5#503611yescharacteristic
394C2×C5#515611yescharacteristic
395C2×C5#519811yescharacteristic
396D5—42no—
397D5—161no—
398D5—242no—
399C23—61no—
400C23—101no—
401C23—201no—
402C23—302no—
403C23—604no—
404C23—604no—
405C23—1202no—
406D4—32no—
407D4—52no—
408D4—61no—
409D4—101no—
410D4—202no—
411D4—201no—
412D4—201no—
413D4—201no—
414D4—201no—
415D4—602no—
416D4—604no—
417D4—604no—
418D4—601no—
419D4—601no—
420D4—601no—
421D4—601no—
422C2×C4—61no—
423C2×C4—101no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4—201no—
427C2×C4—201no—
428C2×C4D3×D2011yescharacteristic
429C2×C4#677711yescharacteristic
430C2×C4D5×#6711yescharacteristic
431C8—41no—
432C8—62no—
433C8—601no—
434C2×C3—202no—
435C2×C3—801no—
436C2×C3#6502111yescharacteristic
437C2×C3#6506211yescharacteristic
438C2×C3#6511111yescharacteristic
439D3—42no—
440D3—402no—
441C5#7101511yescharacteristic, complemented, Sylow
442C22—62no—
443C22—102no—
444C22—121no—
445C22—121no—
446C22—201no—
447C22—201no—
448C22—401no—
449C22—401no—
450C22—401no—
451C22—602no—
452C22—602no—
453C22—602no—
454C22—1208no—
455C22#9147411yescharacteristic
456C4—21no—
457C4—121no—
458C4—201no—
459C4D3×D4011yescharacteristic
460C4#9125411yescharacteristic
461C4D5×#21311yescharacteristic
462C4#9150211yescharacteristic
463C3#1059898711yescharacteristic, complemented, Sylow
464C2—122no—
465C2—202no—
466C2—801no—
467C2—1202no—
468C2#1174748011yescharacteristic
469C2#1174811211yescharacteristic
470C2#1174824211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1619
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. D12×D20C2semidirect
2. C3×#65132C2semidirect
3. #11747035C2semidirect
4. #11747033C2semidirect
5. #11746306C2semidirect
6. C5×#4483C2semidirect
7. #11745835C2semidirect
14. C3×#4020C22semidirect
21. C3×C5×C4⋊C8C22semidirect
22. C4⋊(C3⋊#168)C22semidirect
23. C4×C5×C3⋊C8C22semidirect
29. #65132D3semidirect
69. #4483D5semidirect
80. #4020C2×D3semidirect
82. C5×C4⋊C8C2×D3semidirect
105. C5×D12D8semidirect
115. C3×D20D8semidirect
135. C3×C4⋊C8C2×D5semidirect
139. C4×C3⋊C8C2×D5semidirect
255. D20#213semidirect
274. C4⋊C8D3×D5semidirect
314. D12D40semidirect
370. C3×C5#1619semidirect
441. C5#71015semidirect
463. C3#10598987semidirect

Maximal subgroups

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

subgroupindex
D12×D202
C3×#651322
#117470352
#117470332
#117463062
C5×#44832
#117458352
#105989873
#710155