Finite Group Databasebeta

← #14290919

Subgroups — #14290919

Order 1920.

460 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C5×#5684C211yesmaximal, characteristic, complemented
2#11751159C211yesmaximal, characteristic, complemented
3#11747032C211yesmaximal, characteristic, complemented
4#11746915C211yesmaximal, characteristic, complemented
5C3×#64760C211yesmaximal, characteristic, complemented
6#11745850C211yesmaximal, characteristic, complemented
7#11745847C211yesmaximal, characteristic, complemented
8#10602745—31nomaximal, Hall
9C3×C5×#124C2211yescharacteristic
10C2×#6717—21no—
11C2×#6715—21no—
12#91763C2211yescharacteristic
13C5×#946—21no—
14C5×#939—21no—
15C5×#886—21no—
16C5×#884—21no—
17C5×#883—21no—
18C5×#878—21no—
19C5×#875C2211yescharacteristic
20C5×#870C2211yescharacteristic
21C2×#6660—21no—
22C2×#6654—21no—
23#91087C2211yescharacteristic
24C3×#3935C2211yescharacteristic
25C3×#3935C2211yescharacteristic
26#90969—21no—
27#90969—21no—
28#68351—51nomaximal, Hall
29C5×#562—31no—
30#65356—31no—
31#65347—31no—
32#65347—31no—
33#64763—31no—
34#64760—31no—
35#64760D311yescharacteristic, complemented
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4D411yescharacteristic
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×C5×#67—21no—
42C2×C5×#67—21no—
43C22×C5×Dic3—21no—
44C2×C5×D12D411yescharacteristic
45C2×C4×C5×D3—21no—
46C2×C5×Dic6D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C3×C5×C22⋊C4—21no—
49C3×C42×C5C2311yescharacteristic
50#6717—42no—
51#6715—42no—
52C2×C3⋊#168—21no—
53C5×#217—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×(C2×D3)⋊C4—21no—
56C5×(C2×D3)⋊C4—21no—
57C5×C4⋊Dic3—21no—
58C5×C4⋊Dic3D411yescharacteristic
59C5×C4⋊Dic3D411yescharacteristic
60C5×Dic3⋊C4—21no—
61C5×Dic3⋊C4—21no—
62C5×Dic3⋊C4—21no—
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65#6660—42no—
66#6654—42no—
67#5684D511yescharacteristic, complemented
68#5058—51no—
69#4713—51no—
70#4712—51no—
71C3×#329—51no—
72#4465—51no—
73#4464—51no—
74C5×#125—31no—
75C5×#124—31no—
76C5×#124C2×D311yescharacteristic
77C5×#123—61no—
78C5×#123—61no—
79C5×C22⋊Q8—61no—
80C5×C22⋊Q8—61no—
81C5×#121—61no—
82C5×#121—61no—
83C2×#688—61no—
84C2×#688—61no—
85C2×#686—61no—
86C2×#686—61no—
87#4020—31no—
88#3941—61no—
89#3941—61no—
90#3935—31no—
91#3935C2×D311yescharacteristic
92#3935C2×D311yescharacteristic
93#1656—151noSylow
94C23×C3×C5—21no—
95C22×D15—41no—
96C22×C5×D3—21no—
97C3×C5×Q8—41no—
98C3×C5×D4—41no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103D60—41no—
104D60—41no—
105D60—41no—
106D60—42no—
107D60—41no—
108C5×#67—81no—
109C5×#67—81no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—81no—
114C5×D12—41no—
115C4×C5×D3—81no—
116C5×Dic6—41no—
117C3⋊#168—22no—
118C3×#168—22no—
119C3×#168—41no—
120C3×#124C2×D511yescharacteristic
121#946—21no—
122C2×#215—101no—
123#939—21no—
124C2×#213—101no—
125C2×D24—101no—
126C2×#204—101no—
127#886—21no—
128#884—21no—
129#883—21no—
130#878—21no—
131#875C2×D511yescharacteristic
132#874—51no—
133#870C2×D511yescharacteristic
134C3×#97—51no—
135C3×#97—51no—
136#821—101no—
137#821—101no—
138#803—51no—
139C2×C5×Q8—31no—
140C2×C5×Q8D1211yescharacteristic
141C2×C5×D4—31no—
142C2×C5×D4—61no—
143C2×C5×D4—61no—
144C2×C5×D4D1211yescharacteristic
145C22×C4×C5—61no—
146C22×C4×C5—61no—
147C2×D20—61no—
148C2×D20—61no—
149C2×D20—61no—
150C5×C4⋊C4—31no—
151C5×C4⋊C4—31no—
152C5×C4⋊C4—61no—
153C5×C4⋊C4—61no—
154C5×C4⋊C4—61no—
155C5×C4⋊C4—61no—
156C5×C22⋊C4—21no—
157C5×C22⋊C4—21no—
158C5×C22⋊C4—61no—
159C5×C22⋊C4—61no—
160C5×C22⋊C4—61no—
161C5×C22⋊C4—61no—
162C42×C5C22×D311yescharacteristic
163#688—122no—
164#688—122no—
165#686—122no—
166#686—122no—
167C2×#168—21no—
168C2×#168—21no—
169C2×#168—61no—
170#562—31no—
171#496—151no—
172#496—151no—
173#490—151no—
174#330—151no—
175#329—51no—
176#329—151no—
177C22×C3×C5—41no—
178C22×C3×C5—41no—
179C22×C3×C5—41no—
180C22×C3×C5#12011yescharacteristic
181C2×D15—81no—
182C2×D15—81no—
183C2×D15—81no—
184C2×C5×D3—41no—
185C2×C5×D3—41no—
186C2×C5×D3—41no—
187C3×C4×C5—21no—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190C3×C4×C5—41no—
191C5×Dic3—41no—
192C5×Dic3—41no—
193C5×Dic3—41no—
194C2×C3×Q8C22⋊D511yescharacteristic
195C2×C3×D4C22⋊D511yescharacteristic
196C2×#67—21no—
197C2×#67—21no—
198C22×Dic3—21no—
199C2×D12—101no—
200C2×D12—101no—
201C2×D12—101no—
202C2×D12C22⋊D511yescharacteristic
203C2×C4×D3—21no—
204C2×Dic6C22⋊D511yescharacteristic
205C2×C3×C8—101no—
206C2×C3×C8—101no—
207C3×C22⋊C4—21no—
208C3×C22⋊C4—21no—
209C3×C42C22×D511yescharacteristic
210#217—21no—
211#215—202no—
212#213—202no—
213(C2×D3)⋊C4—21no—
214(C2×D3)⋊C4—21no—
215(C2×D3)⋊C4—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3C22⋊D511yescharacteristic
218C4⋊Dic3C22⋊D511yescharacteristic
219Dic3⋊C4—21no—
220Dic3⋊C4—21no—
221Dic3⋊C4—21no—
222C2×C3⋊C8—101no—
223D24—202no—
224#204—202no—
225C23×C5—21no—
226C23×C5—61no—
227C22×D5—121no—
228C5×Q8—41no—
229C5×Q8—121no—
230C5×D4—41no—
231C5×D4—121no—
232C5×D4—241no—
233C5×D4—241no—
234C2×C4×C5—21no—
235C2×C4×C5—61no—
236C2×C4×C5—61no—
237C2×C4×C5—61no—
238C2×C4×C5—241no—
239C2×C4×C5—241no—
240C2×C4×C5C2×D1211yescharacteristic
241C2×C4×C5D3×D411yescharacteristic
242C2×C4×C5D3×D411yescharacteristic
243D20—121no—
244D20—121no—
245D20—121no—
246D20—121no—
247D20—122no—
248#168—22no—
249#168—41no—
250#168—62no—
251C2×SD16—301no—
252C2×SD16—301no—
253C2×D8—301no—
254C2×D8—301no—
255#127—151no—
256#125—31no—
257#124—31no—
258#124D3×D511yescharacteristic
259#123—61no—
260#123—61no—
261C22⋊Q8—61no—
262C22⋊Q8—61no—
263#121—61no—
264#121—61no—
265#102—301no—
266#102—301no—
267#97—51no—
268#97—51no—
269#97—151no—
270C2×C3×C5—81no—
271C2×C3×C5#45311yescharacteristic
272C2×C3×C5#45311yescharacteristic
273C2×C3×C5#45411yescharacteristic
274D15—161no—
275C5×D3—81no—
276C23×C3—21no—
277C22×D3—21no—
278C22×D3—201no—
279C3×Q8—41no—
280C3×D4—41no—
281C2×C3×C4—21no—
282C2×C3×C4C2×C22⋊D511yescharacteristic
283C2×C3×C4C2×C22⋊D511yescharacteristic
284C2×C3×C4C2×C22⋊D511yescharacteristic
285#67—81no—
286#67—81no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—81no—
291D12—41no—
292D12—201no—
293D12—201no—
294D12—201no—
295D12—201no—
296D12—202no—
297C4×D3—81no—
298Dic6—41no—
299C3×C8—102no—
300C3×C8—201no—
301C3⋊C8—102no—
302C22×C5—41no—
303C22×C5—41no—
304C22×C5—41no—
305C22×C5—121no—
306C22×C5—121no—
307C22×C5—121no—
308C22×C5#88211yescharacteristic
309C2×D5—241no—
310C2×D5—241no—
311C2×D5—241no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—21no—
315C4×C5—41no—
316C4×C5—121no—
317C4×C5—121no—
318C4×C5—121no—
319C2×Q8—31no—
320C2×Q8#120311yescharacteristic
321C2×D4—31no—
322C2×D4—61no—
323C2×D4—61no—
324C2×D4—301no—
325C2×D4—301no—
326C2×D4—301no—
327C2×D4#120311yescharacteristic
328C22×C4—61no—
329C22×C4—61no—
330SD16—602no—
331SD16—602no—
332D8—602no—
333D8—602no—
334C2×C8—101no—
335C2×C8—101no—
336C2×C8—301no—
337C4⋊C4—31no—
338C4⋊C4—31no—
339C4⋊C4—61no—
340C4⋊C4—61no—
341C4⋊C4—61no—
342C4⋊C4—61no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C22⋊C4—61no—
349C42C2×D3×D511yescharacteristic
350C3×C5#165611yescharacteristic, complemented, Hall
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3#409911yescharacteristic
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—41no—
358C2×D3—401no—
359C2×D3—401no—
360C2×D3—401no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—41no—
365Dic3—41no—
366Dic3—41no—
367Dic3—41no—
368C2×C5—81no—
369C2×C5—241no—
370C2×C5#474711yescharacteristic
371C2×C5#482211yescharacteristic
372C2×C5#482711yescharacteristic
373D5—481no—
374C23—21no—
375C23—61no—
376C23—601no—
377Q8—41no—
378Q8—121no—
379D4—41no—
380D4—121no—
381D4—241no—
382D4—241no—
383D4—601no—
384D4—601no—
385D4—601no—
386D4—601no—
387D4—602no—
388C2×C4—21no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—241no—
393C2×C4—241no—
394C2×C4C2×#120311yescharacteristic
395C2×C4D3×C22⋊D511yescharacteristic
396C2×C4D3×C22⋊D511yescharacteristic
397C8—102no—
398C8—201no—
399C8—302no—
400C2×C3—81no—
401C2×C3#6553011yescharacteristic
402C2×C3#6553011yescharacteristic
403C2×C3#6553411yescharacteristic
404D3—81no—
405D3—801no—
406C5#6835111yescharacteristic, complemented, Sylow
407C22—41no—
408C22—41no—
409C22—41no—
410C22—121no—
411C22—121no—
412C22—121no—
413C22—1201no—
414C22—1201no—
415C22—1201no—
416C22#9157011yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—41no—
421C4—121no—
422C4—121no—
423C4—121no—
424C3#1060274511yescharacteristic, complemented, Sylow
425C2—81no—
426C2—241no—
427C2—2401no—
428C2#1174914111yescharacteristic
429C2#1174942011yescharacteristic
430C2#1174945911yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5#120
hypercenter#124D3×D5
hypocenterC3×C5#1656
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C5×#5684C2semidirect
2. #11751159C2semidirect
3. #11747032C2semidirect
4. #11746915C2semidirect
5. C3×#64760C2semidirect
6. #11745850C2semidirect
7. #11745847C2semidirect
35. #64760D3semidirect
67. #5684D5semidirect
350. C3×C5#1656semidirect
406. C5#68351semidirect
424. C3#10602745semidirect

Maximal subgroups

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

subgroupindex
C5×#56842
#117511592
#117470322
#117469152
C3×#647602
#117458502
#117458472
#106027453
#683515