Finite Group Databasebeta

← #14288919

Subgroups — #14288919

Order 1920.

556 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#65911C211yesmaximal, characteristic, complemented
2#11751128C211yesmaximal, characteristic, complemented
3#11747035C211yesmaximal, characteristic, complemented
4#11747028C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745852C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10599052—31nomaximal, Hall
9C2×C3×#713—21no—
10C3×C4×C5×Q8C2211yescharacteristic
11C2×#6717—21no—
12#91763C2211yescharacteristic
13C3×#4041—22no—
14C3×#4041—21no—
15C3×#4020—21no—
16C3×#4020C2211yescharacteristic
17C3×C4×D20—21no—
18C3×C4×D20C2211yescharacteristic
19C2×#6653—21no—
20C2×#6653—22no—
21#91093—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C4×C5×C3⋊C8C2211yescharacteristic
25#90968—21no—
26#71918—51nomaximal, Hall
27#65911D311yescharacteristic, complemented
28#65316—31no—
29#65132—31no—
30#64984—31no—
31C5×Q8⋊C8—31no—
32#64705—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C3×#713—42no—
39C3×#713—42no—
40C2×C3×D20—22no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C2×C3×D20—22no—
44C2×C3×D20D411yescharacteristic
45C2×C3×D20D412yes—
46C2×C3×C4×D5—22no—
47C2×C3×C4×D5—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C42×C5—21no—
51C3×C42×C5C2311yescharacteristic
52#6717—42no—
53C2×C3⋊#168—21no—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8—21no—
56C3×#685—22no—
57C3×#685—21no—
58C3×C4⋊Dic5D411yescharacteristic
59#6653—44no—
60#6653—42no—
61C3×#550—51no—
62#5073—51no—
63#5027—51no—
64#5015—51no—
65#4544—51no—
66#4535D511yescharacteristic, complemented
67D4⋊(C3⋊C8)—51no—
68C2×#713—21no—
69C4×C5×Q8C2×D311yescharacteristic
70C2×#688—61no—
71C2×D40—61no—
72C2×D40—62no—
73#4041—22no—
74#4041—21no—
75#4020—21no—
76#4020—31no—
77#4020C2×D311yescharacteristic
78C4×D20—21no—
79C4×D20C2×D311yescharacteristic
80C5×C4⋊C8—31no—
81C4×C5×C8—31no—
82#3953—61no—
83#3941—61no—
84C4⋊#168—31no—
85#1621—151noSylow
86C22×D15—41no—
87C22×C3×D5—21no—
88C22×C3×D5—22no—
89C3×C5×Q8—21no—
90C3×C5×Q8D812yescomplemented
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96D60—42no—
97D60—41no—
98D60—41no—
99D60—41no—
100D60—41no—
101C2×C3×Dic5—21no—
102C3×D20—21no—
103C3×D20—21no—
104C3×D20—44no—
105C3×D20—42no—
106C3×D20—41no—
107C3×D20—41no—
108C3×D20—41no—
109C3×D20—41no—
110C3×D20—82no—
111C3×C4×D5—44no—
112C3×C4×D5—41no—
113C3×C4×D5—41no—
114C3⋊#168—41no—
115C5×C3⋊C8—22no—
116C5×C3⋊C8—41no—
117C2×C3×#41—101no—
118C3×#127—51no—
119C3×#127—101no—
120C3×#121—102no—
121C3×#121—101no—
122C3×C4×Q8C2×D511yescharacteristic
123C3×C4×D4—51no—
124C3×C4×D4—101no—
125C2×#215—101no—
126C2×#213—101no—
127C2×#213—102no—
128#874—51no—
129#809—101no—
130#809—101no—
131C4⋊(C3⋊C8)—51no—
132C4⋊(C3⋊C8)C2×D511yescharacteristic
133C4×C3⋊C8C2×D511yescharacteristic
134C2×C5×Q8#6711yescharacteristic
135#713—42no—
136#713—42no—
137C2×D20—22no—
138C2×D20—21no—
139C2×D20—21no—
140C2×D20—22no—
141C2×D20—61no—
142C2×D20—61no—
143C2×D20—61no—
144C2×D20#6711yescharacteristic
145C2×D20#6712yes—
146C2×C4×D5—22no—
147C2×C4×D5—21no—
148C2×C5×C8—61no—
149C2×C5×C8—61no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4#6711yescharacteristic
152C42×C5—21no—
153C42×C5C22×D311yescharacteristic
154#688—122no—
155#685—22no—
156#685—21no—
157C4⋊Dic5#6711yescharacteristic
158C2×#168—61no—
159D40—124no—
160D40—122no—
161#550—51no—
162#493—151no—
163#460—151no—
164#459—151no—
165#331—151no—
166Q8⋊C8—31no—
167D4⋊C8—151no—
168C22×C3×C5#12011yescharacteristic
169C2×D15—81no—
170C2×D15—81no—
171C2×D15—81no—
172C2×C3×D5—42no—
173C2×C3×D5—41no—
174C2×C3×D5—41no—
175C2×C3×D5—42no—
176C2×C3×D5—42no—
177C2×C3×D5—41no—
178C3×C4×C5—22no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5C2×D811yescharacteristic
182C3×C4×C5#13511yescharacteristic
183C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C3×Dic5—41no—
186C3×#41—202no—
187C3×#41—202no—
188C2×C3×Q8D2011yescharacteristic
189C2×C3×D4—51no—
190C2×C3×D4—52no—
191C2×C3×D4—102no—
192C2×C3×D4—102no—
193C2×C3×D4—101no—
194C2×C3×D4—101no—
195C22×C3×C4—102no—
196C22×C3×C4—101no—
197C2×D12—101no—
198C2×D12—101no—
199C2×D12—101no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—51no—
202C3×C4⋊C4D2011yescharacteristic
203C3×C22⋊C4—102no—
204C3×C22⋊C4—101no—
205C3×C42—21no—
206C3×C42C22×D511yescharacteristic
207#215—202no—
208#213—204no—
209#213—202no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—101no—
213C22×D5—21no—
214C22×D5—22no—
215C22×D5—121no—
216C5×Q8—21no—
217C5×Q8#21312yescomplemented
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5C2×#6711yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222C2×C4×C5C2×#6711yescharacteristic
223C2×Dic5—21no—
224D20—21no—
225D20—21no—
226D20—42no—
227D20—44no—
228D20—41no—
229D20—41no—
230D20—41no—
231D20—41no—
232D20—82no—
233D20—122no—
234D20—121no—
235D20—121no—
236D20—121no—
237D20—121no—
238C4×D5—44no—
239C4×D5—41no—
240C4×D5—41no—
241C5×C8—62no—
242C5×C8—121no—
243#168—121no—
244C2×#41—101no—
245C2×SD16—301no—
246C2×D8—301no—
247C2×D8—302no—
248#127—51no—
249#127—101no—
250#127—151no—
251#121—102no—
252#121—101no—
253C4×Q8D3×D511yescharacteristic
254C4×D4—51no—
255C4×D4—101no—
256C4⋊C8—31no—
257C4⋊C8—151no—
258#102—301no—
259#102—301no—
260C4×C8—31no—
261C2×C3×C5#44711yescharacteristic
262C2×C3×C5#44911yescharacteristic
263C2×C3×C5#45311yescharacteristic
264D15—161no—
265C3×D5—81no—
266C3×D5—82no—
267C23×C3—101no—
268C23×C3—102no—
269C22×D3—201no—
270C3×Q8—21no—
271C3×Q8D4012yescomplemented
272C3×D4—101no—
273C3×D4—101no—
274C3×D4—202no—
275C3×D4—204no—
276C3×D4—201no—
277C3×D4—201no—
278C3×D4—201no—
279C3×D4—201no—
280C3×D4—402no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—101no—
284C2×C3×C4—204no—
285C2×C3×C4—201no—
286C2×C3×C4—201no—
287C2×C3×C4C2×D2011yescharacteristic
288C2×C3×C4D4×D511yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290D12—202no—
291D12—201no—
292D12—201no—
293D12—201no—
294D12—201no—
295C3⋊C8—22no—
296C3⋊C8—41no—
297C3⋊C8—201no—
298C22×C5#95311yescharacteristic
299C2×D5—42no—
300C2×D5—41no—
301C2×D5—41no—
302C2×D5—42no—
303C2×D5—42no—
304C2×D5—41no—
305C2×D5—241no—
306C2×D5—241no—
307C2×D5—241no—
308C4×C5—22no—
309C4×C5—21no—
310C4×C5—41no—
311C4×C5C2×#21311yescharacteristic
312C4×C5#93211yescharacteristic
313C4×C5#94911yescharacteristic
314C4×C5#95011yescharacteristic
315Dic5—41no—
316#41—202no—
317#41—202no—
318C2×Q8#120211yescharacteristic
319C2×D4—51no—
320C2×D4—52no—
321C2×D4—102no—
322C2×D4—102no—
323C2×D4—101no—
324C2×D4—101no—
325C2×D4—301no—
326C2×D4—301no—
327C2×D4—301no—
328C22×C4—102no—
329C22×C4—101no—
330SD16—602no—
331D8—604no—
332D8—602no—
333C2×C8—61no—
334C2×C8—61no—
335C2×C8—301no—
336C4⋊C4—21no—
337C4⋊C4—51no—
338C4⋊C4#120211yescharacteristic
339C22⋊C4—102no—
340C22⋊C4—101no—
341C42—21no—
342C42C2×D3×D511yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—201no—
345C22×C3—202no—
346C22×C3—202no—
347C22×C3—201no—
348C22×C3—202no—
349C22×C3—201no—
350C22×C3#402811yescharacteristic
351C2×D3—401no—
352C2×D3—401no—
353C2×D3—401no—
354C3×C4—21no—
355C3×C4—22no—
356C3×C4—41no—
357C3×C4—201no—
358C3×C4C2×D4011yescharacteristic
359C3×C4#405411yescharacteristic
360C3×C4#406011yescharacteristic
361C3×C4#406511yescharacteristic
362C2×C5#521711yescharacteristic
363C2×C5#523811yescharacteristic
364C2×C5#524111yescharacteristic
365D5—81no—
366D5—82no—
367D5—481no—
368C23—102no—
369C23—101no—
370C23—601no—
371Q8—21no—
372Q8#665312yescomplemented
373D4—101no—
374D4—101no—
375D4—202no—
376D4—204no—
377D4—201no—
378D4—201no—
379D4—201no—
380D4—201no—
381D4—402no—
382D4—602no—
383D4—601no—
384D4—601no—
385D4—601no—
386D4—601no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—101no—
390C2×C4—204no—
391C2×C4—201no—
392C2×C4—201no—
393C2×C4C2×#120211yescharacteristic
394C2×C4D5×#6711yescharacteristic
395C2×C4D5×#6711yescharacteristic
396C8—62no—
397C8—121no—
398C8—601no—
399C2×C3—401no—
400C2×C3—402no—
401C2×C3#6502111yescharacteristic
402C2×C3#6510011yescharacteristic
403C2×C3#6511111yescharacteristic
404D3—801no—
405C5#7191811yescharacteristic, complemented, Sylow
406C22—202no—
407C22—201no—
408C22—201no—
409C22—202no—
410C22—202no—
411C22—201no—
412C22—1201no—
413C22—1201no—
414C22—1201no—
415C22#9156411yescharacteristic
416C4—21no—
417C4—22no—
418C4—41no—
419C4—201no—
420C4C2×#665311yescharacteristic
421C4#9131211yescharacteristic
422C4#9150211yescharacteristic
423C4#9151611yescharacteristic
424C3#1059905211yescharacteristic, complemented, Sylow
425C2—402no—
426C2—401no—
427C2—2401no—
428C2#1174851211yescharacteristic
429C2#1174927211yescharacteristic
430C2#1174941811yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1621
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#65911C2semidirect
2. #11751128C2semidirect
3. #11747035C2semidirect
4. #11747028C2semidirect
5. C5×#4535C2semidirect
6. #11745852C2semidirect
7. #11745835C2semidirect
27. #65911D3semidirect
66. #4535D5semidirect
90. C3×C5×Q8D8semidirect
217. C5×Q8#213semidirect
271. C3×Q8D40semidirect
343. C3×C5#1621semidirect
372. Q8#6653semidirect
405. C5#71918semidirect
424. C3#10599052semidirect

Maximal subgroups

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

subgroupindex
C3×#659112
#117511282
#117470352
#117470282
C5×#45352
#117458522
#117458352
#105990523
#719185