Finite Group Databasebeta

← #14316819

Subgroups — #14316819

Order 1920.

520 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 79 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×C5×#560C211yesmaximal, characteristic, complemented
2#11751178C211yesmaximal, characteristic, complemented
3#11751154C211yesmaximal, characteristic, complemented
4#11751133C211yesmaximal, characteristic, complemented
5#11746366C211yesmaximal, characteristic, complemented
6#11746360C211yesmaximal, characteristic, complemented
7#11746357C211yesmaximal, characteristic, complemented
8#10602740—31nomaximal, Hall
9#92095C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C3×C5×#126—21no—
12C3×C5×#123—21no—
13C3×C5×#123C2211yescharacteristic
14C3×C5×#121—21no—
15C3×C5×#121—21no—
16C3×C5×#121—21no—
17C3×C5×#120—21no—
18C3×C5×#120C2211yescharacteristic
19#91842—21no—
20#91821—21no—
21#91818—21no—
22#91118C2211yescharacteristic
23#91118C2211yescharacteristic
24#91117C2211yescharacteristic
25#91090—21no—
26#91090—21no—
27#91089—21no—
28#71947—51nomaximal, Hall
29C5×#560D311yescharacteristic, complemented
30#65366—31no—
31#65342—31no—
32#65321—31no—
33#64765—31no—
34#64759—31no—
35#64756—31no—
36C24×C3×C5D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4D411yescharacteristic, complemented
43C2×C3×C5×D4C2311yescharacteristic
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5D411yescharacteristic, complemented
46C2×#1220—21no—
47C2×#1220—21no—
48C2×#1220—41no—
49#6819—41no—
50D4×D15—41no—
51#6817—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4D411yescharacteristic
61C3×C5×C22⋊C4D411yescharacteristic, complemented
62C3×C42×C5D411yescharacteristic, complemented
63#6719—21no—
64#6719—21no—
65#6719—41no—
66#6716—41no—
67#6715—41no—
68#6714—41no—
69#6712—41no—
70#6710—21no—
71C3×#560D511yescharacteristic, complemented
72#5077—51no—
73#5053—51no—
74#5032—51no—
75#4545—51no—
76#4539—51no—
77#4536—51no—
78#4144—31no—
79C5×#127C2×D311yescharacteristic
80C5×#126—21no—
81C5×#123—21no—
82C5×#123C2×D311yescharacteristic
83C5×#121—21no—
84C5×#121—21no—
85C5×#121—21no—
86C5×#120—21no—
87C5×#120C2×D311yescharacteristic
88#4099—61no—
89#4078—61no—
90#4075—61no—
91#3966—31no—
92#3966—31no—
93#3965—31no—
94#3938—61no—
95#3938—61no—
96#3937—61no—
97#2200—151noSylow
98C23×C3×C5—21no—
99C23×C3×C5—21no—
100C23×C3×C5—41no—
101C23×C3×C5—81no—
102C23×C3×C5C2×D411yescharacteristic
103C23×C3×C5C2×D411yescharacteristic
104C22×D15—21no—
105C22×D15—21no—
106C3×C5×D4—41no—
107C3×C5×D4—41no—
108C3×C5×D4—81no—
109C3×C5×D4—81no—
110C3×C5×D4—81no—
111C3×C5×D4—81no—
112C3×C5×D4—81no—
113C2×C3×C4×C5—21no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—41no—
118C2×C3×C4×C5—81no—
119C2×C3×C4×C5C2×D411yescharacteristic
120#1220—41no—
121#1220—41no—
122#1220—41no—
123#1220—82no—
124C2×Dic15—21no—
125C2×Dic15—21no—
126C2×Dic15—41no—
127C2×Dic15—41no—
128D60—21no—
129C4×D15—41no—
130Dic30—21no—
131C3⋊#168—41no—
132#1004—51no—
133C3×#127C2×D511yescharacteristic
134C3×#126—21no—
135C3×#123—21no—
136C3×#123C2×D511yescharacteristic
137C3×#121—21no—
138C3×#121—21no—
139C3×#121—21no—
140C3×#120—21no—
141C3×#120C2×D511yescharacteristic
142#953—101no—
143#932—101no—
144#929—101no—
145#834—51no—
146#834—51no—
147#833—51no—
148#806—101no—
149#806—101no—
150#805—101no—
151C24×C5#6711yescharacteristic
152C2×C5×D4—21no—
153C2×C5×D4—21no—
154C2×C5×D4—21no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4#6711yescharacteristic, complemented
158C2×C5×D4C22×D311yescharacteristic
159C22×C4×C5—21no—
160C22×C4×C5#6711yescharacteristic, complemented
161C2×C22⋊D5—61no—
162C2×C22⋊D5—61no—
163C2×C22⋊D5—121no—
164#711—121no—
165D4×D5—121no—
166#709—61no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4—21no—
172C5×C22⋊C4—21no—
173C5×C22⋊C4—21no—
174C5×C22⋊C4—21no—
175C5×C22⋊C4#6711yescharacteristic
176C5×C22⋊C4#6711yescharacteristic, complemented
177C42×C5#6711yescharacteristic, complemented
178C22⋊Dic5—61no—
179C22⋊Dic5—61no—
180C22⋊Dic5—121no—
181#687—121no—
182#686—121no—
183#685—121no—
184#683—121no—
185#681—61no—
186#560D1511yescharacteristic, complemented
187#458—151no—
188B(4,𝔽2)—151no—
189#453—151no—
190#353—151no—
191#352—151no—
192AΣL(1,𝔽16)—151no—
193C22×C3×C5—21no—
194C22×C3×C5—21no—
195C22×C3×C5—41no—
196C22×C3×C5—41no—
197C22×C3×C5—41no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5—41no—
201C22×C3×C5—42no—
202C22×C3×C5—41no—
203C22×C3×C5—41no—
204C22×C3×C5—81no—
205C22×C3×C5#12011yescharacteristic
206C2×D15—41no—
207C2×D15—81no—
208C2×D15—81no—
209C3×C4×C5—21no—
210C3×C4×C5—41no—
211C3×C4×C5—41no—
212C3×C4×C5—41no—
213C3×C4×C5—41no—
214Dic15—41no—
215Dic15—81no—
216Dic15—81no—
217C24×C3C22⋊D511yescharacteristic
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4C22⋊D511yescharacteristic, complemented
224C2×C3×D4C22×D511yescharacteristic
225C22×C3×C4—21no—
226C22×C3×C4C22⋊D511yescharacteristic, complemented
227C2×#67—101no—
228C2×#67—101no—
229C2×#67—201no—
230#237—201no—
231D3×D4—201no—
232#235—101no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4C22⋊D511yescharacteristic
242C3×C22⋊C4C22⋊D511yescharacteristic, complemented
243C3×C42C22⋊D511yescharacteristic, complemented
244#217—101no—
245#217—101no—
246#217—201no—
247#214—201no—
248#213—201no—
249(C2×D3)⋊C4—201no—
250Dic3⋊C4—201no—
251#208—101no—
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—41no—
255C23×C5—81no—
256C23×C5C2×#6711yescharacteristic
257C23×C5C2×#6711yescharacteristic
258C22×D5—61no—
259C22×D5—61no—
260C5×D4—41no—
261C5×D4—41no—
262C5×D4—81no—
263C5×D4—81no—
264C5×D4—81no—
265C5×D4—81no—
266C5×D4—81no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—41no—
272C2×C4×C5—81no—
273C2×C4×C5C2×#6711yescharacteristic
274C22⋊D5—121no—
275C22⋊D5—121no—
276C22⋊D5—121no—
277C22⋊D5—242no—
278C2×Dic5—61no—
279C2×Dic5—61no—
280C2×Dic5—121no—
281C2×Dic5—121no—
282D20—61no—
283C4×D5—121no—
284Dic10—61no—
285#168—121no—
286H(5,𝔽2)—151no—
287AGL(1,ℤ/8)—301no—
288#127C2×D1511yescharacteristic
289#126—21no—
290#123—21no—
291#123—301no—
292#123C2×D1511yescharacteristic
293#121—21no—
294#121—21no—
295#121—21no—
296#120—21no—
297#120—301no—
298#120C2×D1511yescharacteristic
299#104—301no—
300#100—151no—
301#99—151no—
302#99—151no—
303#99—301no—
304#99—301no—
305C2×C3×C5—21no—
306C2×C3×C5—41no—
307C2×C3×C5—41no—
308C2×C3×C5—81no—
309C2×C3×C5—81no—
310C2×C3×C5B(4,𝔽2)11yescharacteristic
311D15—81no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—41no—
315C23×C3—81no—
316C23×C3C2×C22⋊D511yescharacteristic
317C23×C3C2×C22⋊D511yescharacteristic
318C22×D3—101no—
319C22×D3—101no—
320C3×D4—41no—
321C3×D4—41no—
322C3×D4—81no—
323C3×D4—81no—
324C3×D4—81no—
325C3×D4—81no—
326C3×D4—81no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—41no—
332C2×C3×C4—81no—
333C2×C3×C4C2×C22⋊D511yescharacteristic
334#67—201no—
335#67—201no—
336#67—201no—
337#67—402no—
338C2×Dic3—101no—
339C2×Dic3—101no—
340C2×Dic3—201no—
341C2×Dic3—201no—
342D12—101no—
343C4×D3—201no—
344Dic6—101no—
345C3⋊C8—201no—
346C22×C5—21no—
347C22×C5—21no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5—41no—
352C22×C5—41no—
353C22×C5—41no—
354C22×C5—42no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—81no—
358C22×C5#95311yescharacteristic
359C2×D5—121no—
360C2×D5—241no—
361C2×D5—241no—
362C4×C5—21no—
363C4×C5—41no—
364C4×C5—41no—
365C4×C5—41no—
366C4×C5—41no—
367Dic5—121no—
368Dic5—241no—
369Dic5—241no—
370C24#122011yescharacteristic
371#41—301no—
372#41—601no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—301no—
379C2×D4—301no—
380C2×D4—601no—
381C2×D4—601no—
382C2×D4#122011yescharacteristic, complemented
383C2×D4C22×D1511yescharacteristic
384C22×C4—21no—
385C22×C4#122011yescharacteristic, complemented
386SD16—601no—
387D8—601no—
388M16—301no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—601no—
393C22⋊C4—21no—
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—301no—
399C22⋊C4—301no—
400C22⋊C4—601no—
401C22⋊C4—601no—
402C22⋊C4#122011yescharacteristic
403C22⋊C4#122011yescharacteristic, complemented
404C42#122011yescharacteristic, complemented
405C3×C5#220011yescharacteristic, complemented, Hall
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—42no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—81no—
418C22×C3#409911yescharacteristic
419C2×D3—201no—
420C2×D3—401no—
421C2×D3—401no—
422C3×C4—21no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—41no—
427Dic3—201no—
428Dic3—401no—
429Dic3—401no—
430C2×C5—21no—
431C2×C5—41no—
432C2×C5—41no—
433C2×C5—81no—
434C2×C5—81no—
435C2×C5#524411yescharacteristic
436D5—241no—
437C23—21no—
438C23—21no—
439C23—41no—
440C23—81no—
441C23—301no—
442C23—301no—
443C23C2×#122011yescharacteristic
444C23C2×#122011yescharacteristic
445Q8—301no—
446D4—41no—
447D4—41no—
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452D4—81no—
453D4—301no—
454D4—601no—
455D4—601no—
456D4—601no—
457D4—1202no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—41no—
463C2×C4—81no—
464C2×C4—301no—
465C2×C4—301no—
466C2×C4—601no—
467C2×C4—601no—
468C2×C4—601no—
469C2×C4C2×#122011yescharacteristic
470C8—601no—
471C2×C3—21no—
472C2×C3—41no—
473C2×C3—41no—
474C2×C3—81no—
475C2×C3—81no—
476C2×C3#6553311yescharacteristic
477D3—401no—
478C5#7194711yescharacteristic, complemented, Sylow
479C22—21no—
480C22—21no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—42no—
488C22—41no—
489C22—41no—
490C22—81no—
491C22—601no—
492C22—1201no—
493C22—1201no—
494C22#9184211yescharacteristic
495C4—21no—
496C4—41no—
497C4—41no—
498C4—41no—
499C4—41no—
500C4—601no—
501C4—1201no—
502C4—1201no—
503C3#1060274011yescharacteristic, complemented, Sylow
504C2—21no—
505C2—41no—
506C2—41no—
507C2—81no—
508C2—81no—
509C2—1201no—
510C2#1175134511yescharacteristic
subgroupG/H
centerC2#11751345
commutator, cosocleC2×C3×C5×D4C23
FrattiniC2×D4C22×D15
FittingC3×C5×#560C2
socleC2×C3×C5B(4,𝔽2)
hypercenter#560D15
hypocenterC3×C5#2200
LCSG ▷ C2×C3×C5×D4 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #560

Complements

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

NH ≅ G/Ntype
1. C3×C5×#560C2semidirect
2. #11751178C2semidirect
3. #11751154C2semidirect
4. #11751133C2semidirect
5. #11746366C2semidirect
6. #11746360C2semidirect
7. #11746357C2semidirect
29. C5×#560D3semidirect
42. C2×C3×C5×D4D4semidirect
45. C22×C3×C4×C5D4semidirect
61. C3×C5×C22⋊C4D4semidirect
62. C3×C42×C5D4semidirect
71. C3×#560D5semidirect
157. C2×C5×D4#67semidirect
160. C22×C4×C5#67semidirect
176. C5×C22⋊C4#67semidirect
177. C42×C5#67semidirect
186. #560D15semidirect
223. C2×C3×D4C22⋊D5semidirect
226. C22×C3×C4C22⋊D5semidirect
242. C3×C22⋊C4C22⋊D5semidirect
243. C3×C42C22⋊D5semidirect
382. C2×D4#1220semidirect
385. C22×C4#1220semidirect
403. C22⋊C4#1220semidirect
404. C42#1220semidirect
405. C3×C5#2200semidirect
478. C5#71947semidirect
503. C3#10602740semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5602
#117511782
#117511542
#117511332
#117463662
#117463602
#117463572
#106027403
#719475