Finite Group Databasebeta

← #14289930

Subgroups — #14289930

Order 1920.

616 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 92 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#11752745C211yesmaximal, characteristic
2#11750947C211yesmaximal, characteristic, complemented
3#11747077C211yesmaximal, characteristic, complemented
4#11746890C211yesmaximal, characteristic, complemented
5C5×#4483C211yesmaximal, characteristic, complemented
6C3×#64705C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic, complemented
8#10598989—31nomaximal, Hall
9C2×#6777—21no—
10C2×D3×D20—21no—
11C4×D60C2211yescharacteristic
12#91758C2211yescharacteristic, complemented
13C4×C5×D12C2211yescharacteristic
14C3×#4020C2211yescharacteristic
15#91474—22no—
16#91465—21no—
17#91456—21no—
18C2×#6659—21no—
19C3×C5×C4⋊C8C2211yescharacteristic, complemented
20#91105—21no—
21#91102—21no—
22C4×C5×C3⋊C8C2211yescharacteristic, complemented
23C3×C4⋊#168C2211yescharacteristic, complemented
24#90975—21no—
25#90965—22no—
26#68392—51nomaximal, Hall
27D4×D20—31no—
28#65308—31no—
29#65135—31no—
30#64983—31no—
31C5×D4⋊C8—31no—
32#64705D311yescharacteristic, complemented
33#64679—31no—
34C22×D3×D5—22no—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×Dic30—21no—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20D412yes—
43C2×#1202—22no—
44C2×#1201—22no—
45#6777—42no—
46#6777—42no—
47D3×D20—42no—
48D3×D20—42no—
49C2×C3×C5×C8—21no—
50C3×C42×C5C2311yescharacteristic
51#6714—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15D411yescharacteristic
55C5×(C2×D3)⋊C4—21no—
56C5×C4⋊Dic3D411yescharacteristic
57C2×C5×C3⋊C8—21no—
58C2×C3×#168—21no—
59#6665—22no—
60#6659—42no—
61#5717—51no—
62#5070—51no—
63#4846—51no—
64#4841—51no—
65C3×#331—51no—
66#4483—51no—
67#4483D511yescharacteristic, complemented
68C2×D4×D5—61no—
69C22×D20—61no—
70C4×C5×D4—31no—
71C2×#687—61no—
72#4076—61no—
73#4041—61no—
74#4028—62no—
75#4020C2×D311yescharacteristic
76C4×D20—31no—
77#4015—31no—
78C5×C4⋊C8C2×D311yescharacteristic, complemented
79C4×C5×C8—31no—
80#3953—61no—
81#3953—62no—
82#3950—61no—
83#3942—61no—
84C4⋊#168C2×D311yescharacteristic, complemented
85#1639—151noSylow
86C22×D15—21no—
87C22×C5×D3—21no—
88C22×C3×D5—22no—
89C2×D3×D5—44no—
90C2×D3×D5—44no—
91C2×D3×D5—82no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15—41no—
97D60—21no—
98D60SD1612yescomplemented
99C4×D15—41no—
100C4×D15—41no—
101Dic30—41no—
102Dic30—41no—
103C2×C5×Dic3—21no—
104C5×D12—21no—
105C5×D12D812yes—
106C4×C5×D3—41no—
107C4×C5×D3—41no—
108C3×D20—42no—
109C3×D20—41no—
110C3×D20—41no—
111C3×D20—41no—
112C3×D20—41no—
113#1202—44no—
114#1201—44no—
115C3×C5×C8—41no—
116C3×#168—41no—
117C5×C3⋊C8—41no—
118C2×D3×D4—101no—
119C2×D3×D4—101no—
120C3×#127—51no—
121#938—101no—
122#938—101no—
123#937—102no—
124C2×#204—101no—
125C4×D12—51no—
126C4×D12C2×D511yescharacteristic
127#869—51no—
128C3×C4⋊C8—51no—
129C3×C4⋊C8C2×D511yescharacteristic, complemented
130#832—102no—
131#821—101no—
132#818—101no—
133#816—101no—
134C4×C3⋊C8C2×D511yescharacteristic, complemented
135C23×D5—62no—
136C2×C5×D4—31no—
137C22×C4×C5—61no—
138C2×C22⋊D5—62no—
139D4×D5—122no—
140D4×D5—122no—
141C2×D20—21no—
142C2×D20—21no—
143C2×D20—31no—
144C2×D20—62no—
145C2×D20—122no—
146C2×D20—122no—
147C2×D20D1212yes—
148C2×C4×D5—61no—
149C2×Dic10—61no—
150C2×C5×C8—21no—
151C2×C5×C8—61no—
152C5×C4⋊C4—31no—
153C5×C22⋊C4—61no—
154C42×C5C22×D311yescharacteristic
155#687—122no—
156#685—62no—
157#685—61no—
158C4⋊Dic5—31no—
159C4⋊Dic5—61no—
160C4⋊Dic5—61no—
161C2×#168—21no—
162D42—151no—
163#486—151no—
164#474—151no—
165#461—151no—
166#331—51no—
167D4⋊C8—31no—
168D4⋊C8—151no—
169C22×C3×C5#12011yescharacteristic
170C2×D15—22no—
171C2×D15—41no—
172C2×D15—41no—
173C2×C5×D3—22no—
174C2×C5×D3—41no—
175C2×C5×D3—41no—
176C2×C3×D5—42no—
177C2×C3×D5—42no—
178C2×C3×D5—42no—
179D3×D5—88no—
180C3×C4×C5—21no—
181C3×C4×C5C2×D811yescharacteristic
182C3×C4×C5C2×SD1611yescharacteristic
183C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185Dic15—41no—
186Dic15—81no—
187C5×Dic3—41no—
188C23×D3—102no—
189C2×C3×D4—52no—
190C2×C3×D4—101no—
191C2×C3×D4—101no—
192C2×#67—102no—
193C2×#67—102no—
194D3×D4—202no—
195D3×D4—202no—
196D3×D4—202no—
197D3×D4—202no—
198C2×D12—51no—
199C2×D12D2011yescharacteristic
200C2×C4×D3—21no—
201C2×C4×D3—101no—
202C2×Dic6—101no—
203C2×C3×C8—21no—
204C2×C3×C8—101no—
205C3×C42C22×D511yescharacteristic
206#217—102no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—101no—
209C4⋊Dic3—51no—
210C4⋊Dic3—101no—
211C4⋊Dic3—101no—
212C4⋊Dic3D2011yescharacteristic
213C2×C3⋊C8—21no—
214#204—202no—
215C23×C5—61no—
216C22×D5—22no—
217C22×D5—61no—
218C22×D5—124no—
219C22×D5—124no—
220C22×D5—242no—
221C5×D4—32no—
222C5×D4—61no—
223C2×C4×C5—61no—
224C2×C4×C5—121no—
225C2×C4×C5—121no—
226C2×C4×C5C2×D1211yescharacteristic
227C2×C4×C5D3×D411yescharacteristic
228C2×C4×C5D3×D411yescharacteristic
229C22⋊D5—124no—
230C2×Dic5—61no—
231C2×Dic5—121no—
232D20—32no—
233D20—42no—
234D20—41no—
235D20—41no—
236D20—41no—
237D20—41no—
238D20—61no—
239D20—124no—
240C4×D5—121no—
241C4×D5—121no—
242Dic10—121no—
243Dic10—121no—
244C5×C8—41no—
245C5×C8—121no—
246#168—41no—
247C22×D4—301no—
248C22×D4—301no—
249C2×SD16—301no—
250C4⋊Q8—151no—
251#127—51no—
252#121—301no—
253#121—301no—
254#120—302no—
255C4×D4—31no—
256C4×D4—151no—
257#107—301no—
258C4⋊C8—51no—
259C4⋊C8D3×D511yescharacteristic, complemented
260#103—301no—
261#102—301no—
262#102—302no—
263C4×C8—31no—
264C2×C3×C5#44711yescharacteristic
265C2×C3×C5#45011yescharacteristic
266C2×C3×C5#45511yescharacteristic
267D15—42no—
268C3×D5—82no—
269C5×D3—42no—
270C23×C3—102no—
271C22×D3—21no—
272C22×D3—101no—
273C22×D3—204no—
274C22×D3—204no—
275C22×D3—402no—
276C3×D4—202no—
277C3×D4—201no—
278C3×D4—201no—
279C3×D4—201no—
280C3×D4—201no—
281C2×C3×C4C2×D2011yescharacteristic
282C2×C3×C4D4×D511yescharacteristic
283C2×C3×C4D4×D511yescharacteristic
284#67—204no—
285#67—204no—
286C2×Dic3—21no—
287C2×Dic3—101no—
288C2×Dic3—201no—
289D12—21no—
290D12—52no—
291D12—101no—
292D12D4012yes—
293C4×D3—41no—
294C4×D3—41no—
295C4×D3—201no—
296C4×D3—201no—
297Dic6—201no—
298Dic6—201no—
299C3×C8—41no—
300C3×C8—201no—
301C3⋊C8—41no—
302C22×C5—62no—
303C22×C5—121no—
304C22×C5—121no—
305C22×C5#88211yescharacteristic
306C2×D5—42no—
307C2×D5—42no—
308C2×D5—42no—
309C2×D5—62no—
310C2×D5—121no—
311C2×D5—121no—
312C2×D5—248no—
313C4×C5—21no—
314C4×C5—121no—
315C4×C5D3×D811yescharacteristic
316C4×C5#91111yescharacteristic
317C4×C5D3×SD1611yescharacteristic
318C4×C5#91411yescharacteristic
319Dic5—121no—
320Dic5—241no—
321C24—302no—
322C2×Q8—301no—
323C2×D4—31no—
324C2×D4—52no—
325C2×D4—101no—
326C2×D4—101no—
327C2×D4—151no—
328C2×D4—302no—
329C2×D4—302no—
330C2×D4—602no—
331C2×D4—602no—
332C2×D4—602no—
333C2×D4—602no—
334C22×C4—61no—
335C22×C4—301no—
336SD16—602no—
337C2×C8—21no—
338C2×C8—61no—
339C2×C8—101no—
340C4⋊C4—31no—
341C4⋊C4—151no—
342C4⋊C4—301no—
343C4⋊C4—301no—
344C22⋊C4—61no—
345C22⋊C4—302no—
346C22⋊C4—301no—
347C42C2×D3×D511yescharacteristic
348C3×C5#163911yescharacteristic, complemented, Hall
349C22×C3—202no—
350C22×C3—202no—
351C22×C3—202no—
352C22×C3#402811yescharacteristic
353C2×D3—22no—
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—102no—
357C2×D3—201no—
358C2×D3—201no—
359C2×D3—408no—
360C3×C4—21no—
361C3×C4C2×D4011yescharacteristic
362C3×C4#405411yescharacteristic
363C3×C4#405711yescharacteristic
364C3×C4D5×SD1611yescharacteristic
365Dic3—41no—
366Dic3—201no—
367Dic3—401no—
368C2×C5—122no—
369C2×C5#474611yescharacteristic
370C2×C5#477311yescharacteristic
371C2×C5#477611yescharacteristic
372D5—82no—
373D5—122no—
374C23—61no—
375C23—102no—
376C23—301no—
377C23—604no—
378C23—604no—
379C23—1202no—
380Q8—601no—
381Q8—601no—
382D4—32no—
383D4—61no—
384D4—152no—
385D4—202no—
386D4—201no—
387D4—201no—
388D4—201no—
389D4—201no—
390D4—301no—
391D4—604no—
392D4—604no—
393C2×C4—61no—
394C2×C4—121no—
395C2×C4—121no—
396C2×C4—301no—
397C2×C4—601no—
398C2×C4—601no—
399C2×C4—601no—
400C2×C4D5×D1211yescharacteristic
401C2×C4D3×D2011yescharacteristic
402C2×C4#679011yescharacteristic
403C8—41no—
404C8—121no—
405C8—201no—
406C2×C3—402no—
407C2×C3#6502111yescharacteristic
408C2×C3#6506511yescharacteristic
409C2×C3#6511411yescharacteristic
410D3—42no—
411D3—202no—
412C5#6839211yescharacteristic, complemented, Sylow
413C22—62no—
414C22—121no—
415C22—121no—
416C22—202no—
417C22—202no—
418C22—202no—
419C22—302no—
420C22—601no—
421C22—601no—
422C22—1208no—
423C22#9147611yescharacteristic
424C4—21no—
425C4—121no—
426C4—601no—
427C4—1201no—
428C4D3×D4011yescharacteristic
429C4#9125311yescharacteristic
430C4#9148211yescharacteristic
431C4#9150511yescharacteristic
432C3#1059898911yescharacteristic, complemented, Sylow
433C2—122no—
434C2—402no—
435C2—602no—
436C2#1174748411yescharacteristic
437C2#1174812111yescharacteristic
438C2#1174825011yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752745C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1639
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. #11750947C2semidirect
3. #11747077C2semidirect
4. #11746890C2semidirect
5. C5×#4483C2semidirect
6. C3×#64705C2semidirect
7. #11745838C2semidirect
12. #91758C22semidirect
19. C3×C5×C4⋊C8C22semidirect
22. C4×C5×C3⋊C8C22semidirect
23. C3×C4⋊#168C22semidirect
32. #64705D3semidirect
67. #4483D5semidirect
78. C5×C4⋊C8C2×D3semidirect
84. C4⋊#168C2×D3semidirect
98. D60SD16semidirect
129. C3×C4⋊C8C2×D5semidirect
134. C4×C3⋊C8C2×D5semidirect
259. C4⋊C8D3×D5semidirect
348. C3×C5#1639semidirect
412. C5#68392semidirect
432. C3#10598989semidirect

Maximal subgroups

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

subgroupindex
#117527452
#117509472
#117470772
#117468902
C5×#44832
C3×#647052
#117458382
#105989893
#683925