Finite Group Databasebeta

← #14288931

Subgroups — #14288931

Order 1920.

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

normal subgroups only

This group has 556 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#11752538C211yesmaximal, characteristic, complemented
2C3×#65137C211yesmaximal, characteristic, complemented
3#11747035C211yesmaximal, characteristic, complemented
4#11747033C211yesmaximal, characteristic, complemented
5#11746306C211yesmaximal, characteristic, complemented
6C5×#4483C211yesmaximal, characteristic, complemented
7#11745841C211yesmaximal, characteristic, complemented
8#10598979—31nomaximal, Hall
9C2×#6769—21no—
10#91763C2211yescharacteristic
11C4×C5×D12C2211yescharacteristic
12C2×C3×#677—21no—
13C3×#4020C2211yescharacteristic
14C3×C4×Dic10C2211yescharacteristic
15#91460—21no—
16#91451—21no—
17#91420—22no—
18#91418—21no—
19C2×#6653—22no—
20C2×#6652—21no—
21C3×C5×C4⋊C8C2211yescharacteristic
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24C3×#3953—21no—
25#90964—21no—
26#71032—51nomaximal, Hall
27#65887—31no—
28#65304—31no—
29#65137D311yescharacteristic, complemented
30#64984—31no—
31C5×D4⋊C8—31no—
32#64705—31no—
33#64676—31no—
34C2×D60—21no—
35C2×D60—21no—
36C2×D60D412yes—
37C2×C5×D12D411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×Dic10D411yescharacteristic
43C2×#1203—22no—
44C2×#1203—22no—
45C2×#1200—22no—
46#6769—42no—
47#6769—42no—
48C2×C3×C5×C8—21no—
49C3×C42×C5C2311yescharacteristic
50C2×C3⋊#168—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C2×C5×C3⋊C8—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C3×#677—42no—
58#6667—22no—
59#6653—44no—
60#6652—42no—
61#5577—51no—
62C3×#460—51no—
63#5073—51no—
64#5072—51no—
65#4535—51no—
66#4485—51no—
67#4483D511yescharacteristic, complemented
68C2×#709—61no—
69C4×C5×D4—31no—
70#4086—61no—
71C2×#686—61no—
72#4076—61no—
73C2×D40—62no—
74C2×#677—21no—
75#4039—61no—
76#4030—62no—
77#4020—31no—
78#4020C2×D311yescharacteristic
79C4×Dic10C2×D311yescharacteristic
80C5×C4⋊C8C2×D311yescharacteristic
81C4×C5×C8—31no—
82#3953—21no—
83#3941—61no—
84C4⋊#168—31no—
85#1621—151noSylow
86C22×D15—22no—
87C22×C5×D3—21no—
88C22×C3×D5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92D60—42no—
93D60—41no—
94D60—41no—
95D60—41no—
96D60—41no—
97C2×C5×Dic3—21no—
98C5×D12—21no—
99C5×D12—21no—
100C4×C5×D3—41no—
101C4×C5×D3—41no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—21no—
104C3×D20—42no—
105C3×D20—41no—
106C3×D20—41no—
107C3×D20—41no—
108C3×D20—41no—
109C3×Dic10—21no—
110C3×Dic10D812yescomplemented
111#1203—44no—
112#1203—82no—
113#1200—44no—
114C3×C5×C8—41no—
115C3⋊#168—41no—
116C5×C3⋊C8—22no—
117C2×#239—101no—
118C2×C3×SD16—101no—
119C3×#127—51no—
120C3×C4×Q8—51no—
121C2×#213—102no—
122C2×#213—101no—
123#895—102no—
124#895—101no—
125#874—51no—
126#874—101no—
127C4×D12—101no—
128C4×D12C2×D511yescharacteristic
129C3×C4⋊C8C2×D511yescharacteristic
130C3×#102—101no—
131#832—101no—
132C4⋊(C3⋊C8)—51no—
133C4×C3⋊C8C2×D511yescharacteristic
134C2×C5×D4—31no—
135C22×C4×C5—61no—
136C2×C22⋊D5—62no—
137C2×C22⋊D5—62no—
138#709—122no—
139#709—122no—
140C2×D20—21no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20—32no—
144C2×D20—61no—
145C2×D20—61no—
146C2×C4×D5—62no—
147C2×Dic10#6711yescharacteristic
148C2×C5×C8—21no—
149C2×C5×C8—61no—
150C5×C4⋊C4—31no—
151C5×C22⋊C4—61no—
152C42×C5C22×D311yescharacteristic
153#686—122no—
154#685—62no—
155C4⋊Dic5#6711yescharacteristic
156#683—21no—
157C4×Dic5—21no—
158C2×#168—61no—
159D40—124no—
160#677—42no—
161#550—151no—
162#493—151no—
163#460—51no—
164#459—151no—
165#331—151no—
166Q8⋊C8—151no—
167D4⋊C8—31no—
168C22×C3×C5#12011yescharacteristic
169C2×D15—42no—
170C2×D15—42no—
171C2×D15—42no—
172C2×C5×D3—41no—
173C2×C5×D3—41no—
174C2×C5×D3—41no—
175C2×C3×D5—81no—
176C2×C3×D5—81no—
177C2×C3×D5—81no—
178C3×C4×C5—21no—
179C3×C4×C5C2×D811yescharacteristic
180C3×C4×C5#13511yescharacteristic
181C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
182C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
183C3×Dic5—22no—
184C3×Dic5—41no—
185C5×Dic3—41no—
186C2×C3×Q8—51no—
187C2×C3×D4—101no—
188C2×C3×D4—101no—
189C2×C3×D4—101no—
190#239—202no—
191#239—202no—
192C2×D12—52no—
193C2×D12—102no—
194C2×D12—101no—
195C2×D12—101no—
196C2×D12—102no—
197C2×D12D2011yescharacteristic
198C2×C4×D3—21no—
199C2×C4×D3—102no—
200C3×SD16—202no—
201C2×C3×C8—21no—
202C3×C4⋊C4—51no—
203C3×C4⋊C4—101no—
204C3×C42—101no—
205C3×C42C22×D511yescharacteristic
206#213—204no—
207#213—202no—
208(C2×D3)⋊C4—21no—
209(C2×D3)⋊C4—102no—
210C4⋊Dic3D2011yescharacteristic
211C2×C3⋊C8—21no—
212C2×C3⋊C8—101no—
213C23×C5—61no—
214C22×D5—41no—
215C22×D5—62no—
216C5×D4—61no—
217C5×D4—61no—
218C2×C4×C5—61no—
219C2×C4×C5—121no—
220C2×C4×C5—121no—
221C2×C4×C5D3×D411yescharacteristic
222C2×C4×C5D3×D411yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C22⋊D5—124no—
225C22⋊D5—242no—
226C2×Dic5—21no—
227C2×Dic5—21no—
228D20—42no—
229D20—41no—
230D20—41no—
231D20—41no—
232D20—41no—
233D20—122no—
234D20—121no—
235D20—121no—
236D20—121no—
237D20—121no—
238C4×D5—124no—
239Dic10—21no—
240Dic10#21312yescomplemented
241C5×C8—41no—
242C5×C8—62no—
243#168—121no—
244C2×#41—301no—
245C2×SD16—101no—
246C2×D8—302no—
247C2×D8—301no—
248#127—51no—
249#127—151no—
250#127—301no—
251#121—302no—
252#121—301no—
253C4×Q8—51no—
254C4×D4—31no—
255C4×D4—301no—
256C4⋊C8—151no—
257C4⋊C8D3×D511yescharacteristic
258#102—101no—
259#102—301no—
260C4×C8—31no—
261C2×C3×C5#44711yescharacteristic
262C2×C3×C5#44911yescharacteristic
263C2×C3×C5#45311yescharacteristic
264D15—82no—
265C3×D5—161no—
266C5×D3—81no—
267C23×C3—201no—
268C22×D3—21no—
269C22×D3—102no—
270C3×Q8—52no—
271C3×Q8—101no—
272C3×D4—202no—
273C3×D4—201no—
274C3×D4—201no—
275C3×D4—201no—
276C3×D4—201no—
277C2×C3×C4—101no—
278C2×C3×C4—101no—
279C2×C3×C4C2×D2011yescharacteristic
280C2×C3×C4D4×D511yescharacteristic
281C2×C3×C4D4×D511yescharacteristic
282C2×Dic3—21no—
283D12—21no—
284D12—21no—
285D12—202no—
286D12—204no—
287D12—201no—
288D12—201no—
289D12—201no—
290D12—201no—
291D12—402no—
292C4×D3—41no—
293C4×D3—41no—
294C4×D3—204no—
295C3×C8—41no—
296C3⋊C8—22no—
297C3⋊C8—201no—
298C22×C5—121no—
299C22×C5—121no—
300C22×C5—121no—
301C22×C5#93711yescharacteristic
302C2×D5—81no—
303C2×D5—81no—
304C2×D5—81no—
305C2×D5—122no—
306C2×D5—122no—
307C2×D5—122no—
308C4×C5—21no—
309C4×C5—121no—
310C4×C5#91411yescharacteristic
311C4×C5#91611yescharacteristic
312C4×C5C2×#21311yescharacteristic
313C4×C5#94911yescharacteristic
314Dic5—22no—
315Dic5—41no—
316#41—602no—
317#41—602no—
318C2×Q8—51no—
319C2×D4—31no—
320C2×D4—101no—
321C2×D4—101no—
322C2×D4—101no—
323C2×D4—152no—
324C2×D4—302no—
325C2×D4—302no—
326C2×D4—301no—
327C2×D4—301no—
328C22×C4—61no—
329C22×C4—302no—
330SD16—202no—
331D8—604no—
332D8—602no—
333C2×C8—21no—
334C2×C8—61no—
335C2×C8—301no—
336C4⋊C4—31no—
337C4⋊C4—51no—
338C4⋊C4—101no—
339C22⋊C4—61no—
340C22⋊C4—302no—
341C42—101no—
342C42C2×D3×D511yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—401no—
345C22×C3—401no—
346C22×C3—401no—
347C22×C3#402811yescharacteristic
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—41no—
351C2×D3—202no—
352C2×D3—202no—
353C2×D3—202no—
354C3×C4—21no—
355C3×C4—102no—
356C3×C4—201no—
357C3×C4#405011yescharacteristic
358C3×C4#405411yescharacteristic
359C3×C4D5×D811yescharacteristic
360C3×C4#406011yescharacteristic
361Dic3—41no—
362C2×C5—241no—
363C2×C5#503611yescharacteristic
364C2×C5#517211yescharacteristic
365C2×C5#519811yescharacteristic
366D5—161no—
367D5—242no—
368C23—61no—
369C23—201no—
370C23—302no—
371Q8—52no—
372Q8—101no—
373D4—61no—
374D4—61no—
375D4—202no—
376D4—201no—
377D4—201no—
378D4—201no—
379D4—201no—
380D4—602no—
381D4—604no—
382D4—601no—
383D4—601no—
384D4—601no—
385D4—601no—
386D4—1202no—
387C2×C4—61no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4—604no—
393C2×C4D3×D2011yescharacteristic
394C2×C4#677711yescharacteristic
395C2×C4D5×#6711yescharacteristic
396C8—41no—
397C8—62no—
398C8—601no—
399C2×C3—801no—
400C2×C3#6502311yescharacteristic
401C2×C3#6506211yescharacteristic
402C2×C3#6511111yescharacteristic
403D3—81no—
404D3—402no—
405C5#7103211yescharacteristic, complemented, Sylow
406C22—121no—
407C22—121no—
408C22—121no—
409C22—401no—
410C22—401no—
411C22—401no—
412C22—602no—
413C22—602no—
414C22—602no—
415C22#9147411yescharacteristic
416C4—21no—
417C4—102no—
418C4—121no—
419C4—201no—
420C4#9125311yescharacteristic
421C4#9127211yescharacteristic
422C4D5×#21311yescharacteristic
423C4#9150211yescharacteristic
424C3#1059897911yescharacteristic, complemented, Sylow
425C2—241no—
426C2—801no—
427C2—1202no—
428C2#1174748011yescharacteristic
429C2#1174789011yescharacteristic
430C2#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#1621
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. #11752538C2semidirect
2. C3×#65137C2semidirect
3. #11747035C2semidirect
4. #11747033C2semidirect
5. #11746306C2semidirect
6. C5×#4483C2semidirect
7. #11745841C2semidirect
29. #65137D3semidirect
67. #4483D5semidirect
110. C3×Dic10D8semidirect
240. Dic10#213semidirect
343. C3×C5#1621semidirect
405. C5#71032semidirect
424. C3#10598979semidirect

Maximal subgroups

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

subgroupindex
#117525382
C3×#651372
#117470352
#117470332
#117463062
C5×#44832
#117458412
#105989793
#710325