Finite Group Databasebeta

← #14313320

Subgroups — #14313320

Order 1920.

468 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5648C211yesmaximal, characteristic
2#11749173C211yesmaximal, characteristic
3#11749126C211yesmaximal, characteristic
4#11746360C211yesmaximal, characteristic, complemented
5C3×#64759C211yesmaximal, characteristic, complemented
6#11746003C211yesmaximal, characteristic, complemented
7#11746002C211yesmaximal, characteristic, complemented
8#10602663—31nomaximal, Hall
9C2×C5×#237C2211yescharacteristic
10C22×C5×Dic6C411yescharacteristic, complemented
11C3×C5×#123C2211yescharacteristic
12C5×#935C2211yescharacteristic
13C5×#929C411yescharacteristic, complemented
14C5×#896—21no—
15C5×#888—21no—
16C5×#886C411yescharacteristic, complemented
17C5×#885—21no—
18C5×#878—21no—
19C5×#877C411yescharacteristic, complemented
20#91529—21no—
21D3×#681—21no—
22#91118C2211yescharacteristic
23#91117C2211yescharacteristic
24C3×#3966C2211yescharacteristic
25C3×#3965C2211yescharacteristic
26#90996—21no—
27#90962—21no—
28#69145—51nomaximal, Hall
29C5×#536—31no—
30#65529—31no—
31#65526—31no—
32#64759—31no—
33#64759—31no—
34#64759—31no—
35#64759D311yescharacteristic, complemented
36C2×C3×C5×D4C2311yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C2×C5×#67C2×C411yescharacteristic
39C2×C5×#67D411yescharacteristic
40C22×C5×Dic3C2×C411yescharacteristic
41C22×C5×Dic3C2×C411yescharacteristic
42C22×C5×Dic3D411yescharacteristic
43C5×#237—41no—
44C5×#237—41no—
45C2×C4×C5×D3D411yescharacteristic
46C2×C5×Dic6—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6—41no—
49C2×C5×Dic6—41no—
50C2×C5×Dic6D411yescharacteristic
51C3×C5×C4⋊C4—21no—
52C3×C5×C22⋊C4—21no—
53C3×C5×C22⋊C4C2×C411yescharacteristic
54#6719—21no—
55#6710—21no—
56C5×#217—21no—
57C5×#217C2×C411yescharacteristic
58C5×(C2×D3)⋊C4—21no—
59C5×(C2×D3)⋊C4—21no—
60C5×C4⋊Dic3—21no—
61C5×Dic3⋊C4—21no—
62C5×Dic3⋊C4—21no—
63C5×Dic3⋊C4—21no—
64C4×C5×Dic3—21no—
65C3×C22⋊Dic5—21no—
66C3×#681—21no—
67Dic3⋊Dic5—41no—
68Dic3×Dic5—41no—
69#6650—41no—
70D3×#168—41no—
71#5648D511yescharacteristic
72#4745—51no—
73#4740—51no—
74C3×#352—51no—
75#4539—51no—
76#4476—51no—
77#4472—51no—
78C2×C5×#41—31no—
79C22×C5×Q8—31no—
80C5×C4⋊Q8—61no—
81C5×#124—61no—
82C5×#123—31no—
83C5×#123—31no—
84C5×#123—31no—
85C5×#123C2×D311yescharacteristic
86C5×C22⋊Q8—61no—
87C5×C22⋊Q8—61no—
88C5×#117—31no—
89#4072—61no—
90C2×#681—61no—
91#3968—61no—
92#3966—31no—
93#3966—61no—
94#3966C2×D311yescharacteristic
95#3965—31no—
96#3965C2×D311yescharacteristic
97#2123—151noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C5×D3C22⋊C411yescharacteristic
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×Dic15—41no—
107C5×#67—41no—
108C5×#67—41no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3C22⋊C411yescharacteristic
117C2×C5×Dic3C22⋊C411yescharacteristic
118C2×C5×Dic3C22⋊C411yescharacteristic
119C4×C5×D3—21no—
120C4×C5×D3—21no—
121C5×Dic6—41no—
122C5×Dic6—42no—
123C5×Dic6—41no—
124C5×Dic6—41no—
125C2×C3×Dic5—41no—
126C3⋊#168—41no—
127C3×#168—41no—
128C2×#237C2×D511yescharacteristic
129C22×Dic6Dic511yescharacteristic, complemented
130C3×#123C2×D511yescharacteristic
131#935C2×D511yescharacteristic
132#929Dic511yescharacteristic, complemented
133D3×M16—101no—
134#896—21no—
135#888—21no—
136#886Dic511yescharacteristic, complemented
137#885—21no—
138#878—21no—
139#877—101no—
140#877Dic511yescharacteristic, complemented
141C3×#100—51no—
142C3×#99—51no—
143#834—51no—
144#833—51no—
145#824—101no—
146#806—101no—
147C5×#41—121no—
148C5×#41—121no—
149C2×C5×Q8—31no—
150C2×C5×Q8—61no—
151C2×C5×Q8—61no—
152C2×C5×Q8—121no—
153C2×C5×Q8—121no—
154C2×C5×D4—31no—
155C2×C5×D4—31no—
156C2×C5×D4C22×D311yescharacteristic
157C22×C4×C5—31no—
158C22×C4×C5—31no—
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C22×C4×C5C4×D311yescharacteristic
162C5×C4⋊C4—21no—
163C5×C4⋊C4—61no—
164C5×C4⋊C4—61no—
165C5×C4⋊C4—61no—
166C5×C4⋊C4—61no—
167C5×C22⋊C4—21no—
168C5×C22⋊C4—31no—
169C5×C22⋊C4—61no—
170C5×C22⋊C4—61no—
171C5×C22⋊C4—61no—
172C5×C22⋊C4C4×D311yescharacteristic
173C42×C5—61no—
174C22⋊Dic5—21no—
175C22⋊Dic5—61no—
176C4⋊Dic5—121no—
177C4×Dic5—121no—
178#681—21no—
179#681—61no—
180#681—121no—
181C2×#168—121no—
182#536—31no—
183#413—151no—
184#410—151no—
185#352—51no—
186#352—151no—
187#352—151no—
188#352—151no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5C2×C22⋊C411yescharacteristic
194C2×C5×D3—21no—
195C2×C5×D3—41no—
196C3×C4×C5—21no—
197C3×C4×C5—41no—
198C3×C4×C5—41no—
199Dic15—81no—
200C3×Dic5—81no—
201C5×Dic3—21no—
202C5×Dic3—21no—
203C5×Dic3—41no—
204C5×Dic3—41no—
205C5×Dic3#9911yescharacteristic
206C5×Dic3#9911yescharacteristic
207C2×C3×D4C22×D511yescharacteristic
208C22×C3×C4C2×Dic511yescharacteristic
209C2×#67C2×Dic511yescharacteristic
210C2×#67C22⋊D511yescharacteristic
211C22×Dic3C2×Dic511yescharacteristic
212C22×Dic3C2×Dic511yescharacteristic
213C22×Dic3C22⋊D511yescharacteristic
214#237—41no—
215#237—41no—
216C2×C4×D3C22⋊D511yescharacteristic
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—41no—
220C2×Dic6—41no—
221C2×Dic6C22⋊D511yescharacteristic
222C3×M16—101no—
223C3×C4⋊C4—21no—
224C3×C22⋊C4—21no—
225C3×C22⋊C4—101no—
226C3×C22⋊C4C2×Dic511yescharacteristic
227#217—21no—
228#217—101no—
229#217C2×Dic511yescharacteristic
230(C2×D3)⋊C4—21no—
231(C2×D3)⋊C4—21no—
232C4⋊Dic3—21no—
233Dic3⋊C4—21no—
234Dic3⋊C4—21no—
235Dic3⋊C4—21no—
236Dic3⋊C4—201no—
237C4×Dic3—21no—
238C4×Dic3—201no—
239#208—101no—
240ΓL(1,𝔽25)—201no—
241D3×C8—201no—
242C23×C5—31no—
243C23×C5C2×C4×D311yescharacteristic
244C23×C5D3×D411yescharacteristic
245C5×Q8—121no—
246C5×Q8—121no—
247C5×Q8—121no—
248C5×Q8—122no—
249C5×D4—41no—
250C5×D4—121no—
251C5×D4—121no—
252C2×C4×C5—21no—
253C2×C4×C5—21no—
254C2×C4×C5—31no—
255C2×C4×C5—31no—
256C2×C4×C5—31no—
257C2×C4×C5—41no—
258C2×C4×C5—61no—
259C2×C4×C5—61no—
260C2×C4×C5—61no—
261C2×C4×C5—61no—
262C2×C4×C5—61no—
263C2×C4×C5—61no—
264C2×C4×C5—61no—
265C2×C4×C5—61no—
266C2×C4×C5—121no—
267C2×C4×C5D3×D411yescharacteristic
268C2×Dic5—41no—
269C2×Dic5—121no—
270#168—41no—
271#168—121no—
272C2×#41—31no—
273C22×Q8—31no—
274C2×M16—301no—
275C4⋊Q8—61no—
276#124—61no—
277#123—31no—
278#123—31no—
279#123—31no—
280#123D3×D511yescharacteristic
281C22⋊Q8—61no—
282C22⋊Q8—61no—
283#117—31no—
284#117—301no—
285#101—301no—
286#100—51no—
287#100—151no—
288#99—51no—
289#99—151no—
290#99—301no—
291C2×C3×C5—21no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5C2×#9911yescharacteristic
295C5×D3—41no—
296C23×C3C22×Dic511yescharacteristic
297C23×C3C2×C22⋊D511yescharacteristic
298C22×D3C22⋊Dic511yescharacteristic
299C3×D4—41no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—41no—
303C2×C3×C4—201no—
304C2×C3×C4C2×C22⋊D511yescharacteristic
305#67—41no—
306#67—41no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—41no—
314C2×Dic3—201no—
315C2×Dic3C22⋊Dic511yescharacteristic
316C2×Dic3C22⋊Dic511yescharacteristic
317C2×Dic3C22⋊Dic511yescharacteristic
318C4×D3—21no—
319C4×D3—21no—
320Dic6—41no—
321Dic6—42no—
322Dic6—41no—
323Dic6—41no—
324C3×C8—201no—
325C3⋊C8—201no—
326C22×C5—21no—
327C22×C5—21no—
328C22×C5—41no—
329C22×C5—41no—
330C22×C5—61no—
331C22×C5—121no—
332C22×C5D3×C22⋊C411yescharacteristic
333C4×C5—21no—
334C4×C5—31no—
335C4×C5—31no—
336C4×C5—41no—
337C4×C5—41no—
338C4×C5—61no—
339C4×C5—61no—
340C4×C5—121no—
341C4×C5—121no—
342Dic5—81no—
343Dic5—241no—
344#41—121no—
345#41—121no—
346C2×Q8—31no—
347C2×Q8—61no—
348C2×Q8—61no—
349C2×Q8—121no—
350C2×Q8—121no—
351C2×D4—31no—
352C2×D4—31no—
353C2×D4C2×D3×D511yescharacteristic
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4D3×Dic511yescharacteristic
359M16—101no—
360M16—301no—
361M16—601no—
362C2×C8—601no—
363C4⋊C4—21no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—601no—
369C22⋊C4—21no—
370C22⋊C4—31no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C22⋊C4—101no—
375C22⋊C4—301no—
376C22⋊C4D3×Dic511yescharacteristic
377C42—61no—
378C42—601no—
379C3×C5#212311yescharacteristic, complemented, Hall
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3C2×C22⋊Dic511yescharacteristic
385C2×D3—21no—
386C2×D3—41no—
387C3×C4—21no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—401no—
391Dic3—21no—
392Dic3—21no—
393Dic3—41no—
394Dic3—41no—
395Dic3—401no—
396Dic3#396611yescharacteristic
397Dic3#396611yescharacteristic
398C2×C5—21no—
399C2×C5—41no—
400C2×C5—41no—
401C2×C5—121no—
402C2×C5D3×#9911yescharacteristic
403C23—31no—
404C23C2×D3×Dic511yescharacteristic
405C23D3×C22⋊D511yescharacteristic
406Q8—121no—
407Q8—121no—
408Q8—121no—
409Q8—122no—
410D4—41no—
411D4—121no—
412D4—121no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—31no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—41no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—121no—
428C2×C4—201no—
429C2×C4—601no—
430C2×C4D3×C22⋊D511yescharacteristic
431C8—201no—
432C8—601no—
433C2×C3—21no—
434C2×C3—41no—
435C2×C3—41no—
436C2×C3C2×#396611yescharacteristic
437D3—41no—
438C5#6914511yescharacteristic, complemented, Sylow
439C22—21no—
440C22—21no—
441C22—41no—
442C22—41no—
443C22—61no—
444C22—121no—
445C22D3×C22⋊Dic511yescharacteristic
446C4—21no—
447C4—31no—
448C4—31no—
449C4—41no—
450C4—41no—
451C4—61no—
452C4—61no—
453C4—121no—
454C4—121no—
455C4—401no—
456C4—1201no—
457C3#1060266311yescharacteristic, complemented, Sylow
458C2—21no—
459C2—41no—
460C2—41no—
461C2—121no—
462C2D3×#396611yescharacteristic
subgroupG/H
centerC2D3×#3966
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#123C22
socleC2×C3×C5C2×#99
prime radicalC2×C5×#237C22
cosocleC2×C3×C5×D4C23
hypercenter#123D3×D5
hypocenterC3×C5#2123
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
4. #11746360C2semidirect
5. C3×#64759C2semidirect
6. #11746003C2semidirect
7. #11746002C2semidirect
10. C22×C5×Dic6C4semidirect
13. C5×#929C4semidirect
16. C5×#886C4semidirect
19. C5×#877C4semidirect
35. #64759D3semidirect
129. C22×Dic6Dic5semidirect
132. #929Dic5semidirect
136. #886Dic5semidirect
140. #877Dic5semidirect
379. C3×C5#2123semidirect
438. C5#69145semidirect
457. C3#10602663semidirect

Maximal subgroups

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

subgroupindex
C5×#56482
#117491732
#117491262
#117463602
C3×#647592
#117460032
#117460022
#106026633
#691455