Finite Group Databasebeta

← C5×#82578 #14323369

Subgroups — C5×#82578 #14323369

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#120C211yesmaximal, characteristic
2C22×C5×#217C211yesmaximal, characteristic, complemented
3C2×C5×D4×Dic3C211yesmaximal, characteristic, complemented
4C5×#5247C211yesmaximal, characteristic, complemented
5C5×#5221C212yesmaximal, complemented
6C5×#5220C212yesmaximal, complemented
7C5×#5220C211yesmaximal, characteristic, complemented
8C5×#4951C212yesmaximal, complemented
9C5×#4951C212yesmaximal, complemented
10C5×#4950C211yesmaximal, characteristic, complemented
11C5×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
12C5×#2321—31nomaximal, Hall
13C25×C3×C5C2211yescharacteristic
14C22×C3×C5×D4C2211yescharacteristic
15C22×C3×C5×D4C2212yes—
16C23×C5×Dic3C2211yescharacteristic
17C23×C5×Dic3C2211yescharacteristic
18C23×C5×Dic3C2211yescharacteristic, complemented
19C3×C5×#120C418yescomplemented
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2212yes—
22C2×C5×#217—24no—
23C2×C5×#217C2211yescharacteristic
24C2×C5×#217C2211yescharacteristic
25C2×C5×#217C2212yes—
26C2×C5×#217C2212yes—
27C2×C5×#217C2212yes—
28C2×C5×#217C2212yes—
29C2×C5×#217C2211yescharacteristic, complemented
30C2×C5×#217C2212yescomplemented
31C5×D4×Dic3—24no—
32C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
33C2×C5×C4⋊Dic3C2212yescomplemented
34C2×C4×C5×Dic3C2211yescharacteristic, complemented
35C2×C4×C5×Dic3C2212yescomplemented
36C5×C3⋊#95C2212yescomplemented
37C5×C3⋊#95C2212yescomplemented
38C5×C3⋊#95C2212yescomplemented
39#82578C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#120D311yescharacteristic
41C2×C4×C5×D4—31no—
42C22×C5×C22⋊C4—31no—
43C5×#390—32no—
44C5×#388—32no—
45C5×#388—32no—
46C5×#386—31no—
47C5×#386—32no—
48C5×#385—31no—
49C5×#379—31no—
50C4×C5×C22⋊C4—31no—
51C24×C3×C5—22no—
52C24×C3×C5—22no—
53C24×C3×C5—42no—
54C24×C3×C5—42no—
55C24×C3×C5C2×C414yescomplemented
56C24×C3×C5C2312yes—
57C24×C3×C5C2311yescharacteristic
58C24×C3×C5C2311yescharacteristic
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4—22no—
61C2×C3×C5×D4—42no—
62C2×C3×C5×D4—42no—
63C2×C3×C5×D4C2×C414yes—
64C2×C3×C5×D4C2×C418yescomplemented
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2312yes—
67C22×C5×Dic3—22no—
68C22×C5×Dic3—22no—
69C22×C5×Dic3—42no—
70C22×C5×Dic3—42no—
71C22×C5×Dic3—42no—
72C22×C5×Dic3D414yescomplemented
73C22×C5×Dic3C2311yescharacteristic
74C22×C5×Dic3C2312yes—
75C22×C5×Dic3C2311yescharacteristic
76C22×C5×Dic3C2312yes—
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C3×C5×C22⋊C4C2×C418yescomplemented
80C3×C5×C22⋊C4C2×C414yescomplemented
81C5×#217—22no—
82C5×#217—22no—
83C5×#217—22no—
84C5×#217—24no—
85C5×#217—24no—
86C5×#217—42no—
87C5×#217—42no—
88C5×#217—42no—
89C5×C4⋊Dic3—22no—
90C5×C4⋊Dic3—42no—
91C4×C5×Dic3—22no—
92C4×C5×Dic3—42no—
93C2×C3×#120C2×C511yescharacteristic
94C22×#217C2×C511yescharacteristic, complemented
95C2×D4×Dic3C2×C511yescharacteristic, complemented
96#5247C2×C511yescharacteristic, complemented
97#5221C2×C512yescomplemented
98#5220C2×C512yescomplemented
99#5220C2×C511yescharacteristic, complemented
100#4951C2×C512yescomplemented
101#4951C2×C512yescomplemented
102#4950C2×C511yescharacteristic, complemented
103Dic3×C22⋊C4C2×C511yescharacteristic, complemented
104C25×C5C2×D311yescharacteristic
105C22×C5×D4C2×D311yescharacteristic
106C22×C5×D4C2×D312yes—
107C23×C4×C5—31no—
108C23×C4×C5—31no—
109C23×C4×C5—31no—
110C5×#120Dic318yescomplemented
111C4×C5×D4—64no—
112C2×C5×C4⋊C4—31no—
113C2×C5×C4⋊C4—32no—
114C2×C5×C22⋊C4—31no—
115C2×C5×C22⋊C4—31no—
116C2×C5×C22⋊C4—32no—
117C2×C5×C22⋊C4—32no—
118C2×C5×C22⋊C4—31no—
119C2×C5×C22⋊C4—32no—
120C2×C5×C22⋊C4—32no—
121C2×C5×C22⋊C4—32no—
122C2×C5×C22⋊C4—64no—
123C2×C5×C22⋊C4C2×D311yescharacteristic
124C2×C5×C22⋊C4C2×D312yes—
125C2×C42×C5—31no—
126C2×C42×C5—32no—
127C5×#95—32no—
128C5×#95—32no—
129C5×#95—32no—
130#2321—31noSylow
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5—28no—
134C23×C3×C5—22no—
135C23×C3×C5—21no—
136C23×C3×C5—21no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—22no—
140C23×C3×C5—22no—
141C23×C3×C5—22no—
142C23×C3×C5—22no—
143C23×C3×C5—22no—
144C23×C3×C5—48no—
145C23×C3×C5—44no—
146C23×C3×C5—44no—
147C23×C3×C5—48no—
148C23×C3×C5C22×C414yes—
149C23×C3×C5C22×C412yes—
150C23×C3×C5C22×C412yes—
151C23×C3×C5C2×D412yes—
152C23×C3×C5#4112yes—
153C23×C3×C5C2411yescharacteristic
154C3×C5×D4—28no—
155C3×C5×D4—48no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—21no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5C22×C412yes—
161C2×C3×C4×C5C22×C414yes—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—21no—
165C2×C5×Dic3—21no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3—22no—
173C2×C5×Dic3—22no—
174C2×C5×Dic3—44no—
175C2×C5×Dic3—44no—
176C2×C5×Dic3—44no—
177C2×C5×Dic3C2×D412yes—
178C2×C5×Dic3C2×D412yes—
179C25×C3C22×C511yescharacteristic
180C22×C3×D4C22×C511yescharacteristic
181C22×C3×D4C22×C512yes—
182C23×Dic3C22×C511yescharacteristic
183C23×Dic3C22×C511yescharacteristic
184C23×Dic3C22×C511yescharacteristic, complemented
185C3×#120C4×C518yescomplemented
186C2×C3×C22⋊C4C22×C511yescharacteristic
187C2×C3×C22⋊C4C22×C512yes—
188C2×#217—24no—
189C2×#217C22×C511yescharacteristic
190C2×#217C22×C511yescharacteristic
191C2×#217C22×C512yes—
192C2×#217C22×C512yes—
193C2×#217C22×C512yes—
194C2×#217C22×C512yes—
195C2×#217C22×C511yescharacteristic, complemented
196C2×#217C22×C512yescomplemented
197D4×Dic3—24no—
198C2×C4⋊Dic3C22×C511yescharacteristic, complemented
199C2×C4⋊Dic3C22×C512yescomplemented
200C2×C4×Dic3C22×C511yescharacteristic, complemented
201C2×C4×Dic3C22×C512yescomplemented
202C3⋊#95C22×C512yescomplemented
203C3⋊#95C22×C512yescomplemented
204C3⋊#95C22×C512yescomplemented
205C24×C5—22no—
206C24×C5—22no—
207C24×C5—42no—
208C24×C5—42no—
209C24×C5C2×Dic314yescomplemented
210C24×C5C22×D312yes—
211C24×C5C22×D311yescharacteristic
212C24×C5C22×D311yescharacteristic
213C2×C5×D4—22no—
214C2×C5×D4—22no—
215C2×C5×D4—42no—
216C2×C5×D4—42no—
217C2×C5×D4C2×Dic314yes—
218C2×C5×D4C2×Dic318yescomplemented
219C22×C4×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5—34no—
222C22×C4×C5—31no—
223C22×C4×C5—32no—
224C22×C4×C5—32no—
225C22×C4×C5—31no—
226C22×C4×C5—62no—
227C22×C4×C5—62no—
228C22×C4×C5—122no—
229C22×C4×C5—122no—
230C22×C4×C5—122no—
231C22×C4×C5C22×D311yescharacteristic
232C22×C4×C5C22×D312yes—
233C5×C4⋊C4—62no—
234C5×C4⋊C4—122no—
235C5×C22⋊C4—64no—
236C5×C22⋊C4—64no—
237C5×C22⋊C4—62no—
238C5×C22⋊C4—62no—
239C5×C22⋊C4—62no—
240C5×C22⋊C4—122no—
241C5×C22⋊C4—122no—
242C5×C22⋊C4—122no—
243C5×C22⋊C4C2×Dic318yescomplemented
244C5×C22⋊C4C2×Dic314yescomplemented
245C42×C5—62no—
246C42×C5—122no—
247C2×#120C5×D311yescharacteristic
248C2×C4×D4—31no—
249C22×C22⋊C4—31no—
250#390—32no—
251#388—32no—
252#388—32no—
253#386—32no—
254#386—31no—
255#385—31no—
256#379—31no—
257C4×C22⋊C4—31no—
258C22×C3×C5—24no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—24no—
262C22×C3×C5—22no—
263C22×C3×C5—24no—
264C22×C3×C5—24no—
265C22×C3×C5—24no—
266C22×C3×C5—24no—
267C22×C3×C5—416no—
268C22×C3×C5—41no—
269C22×C3×C5—42no—
270C22×C3×C5—41no—
271C22×C3×C5—42no—
272C22×C3×C5—42no—
273C22×C3×C5—42no—
274C22×C3×C5—42no—
275C22×C3×C5C4×D414yes—
276C22×C3×C5C23×C411yescharacteristic
277C22×C3×C5C22×D411yescharacteristic
278C22×C3×C5C2×#4111yescharacteristic
279C22×C3×C5H(5,𝔽2)12yes—
280C22×C3×C5H(5,𝔽2)12yes—
281C3×C4×C5—22no—
282C3×C4×C5—24no—
283C5×Dic3—22no—
284C5×Dic3—22no—
285C5×Dic3—41no—
286C5×Dic3—41no—
287C5×Dic3—42no—
288C5×Dic3—42no—
289C24×C3—22no—
290C24×C3—22no—
291C24×C3—42no—
292C24×C3—42no—
293C24×C3C2×C4×C514yescomplemented
294C24×C3C23×C512yes—
295C24×C3C23×C511yescharacteristic
296C24×C3C23×C511yescharacteristic
297C2×C3×D4—22no—
298C2×C3×D4—22no—
299C2×C3×D4—42no—
300C2×C3×D4—42no—
301C2×C3×D4C2×C4×C514yes—
302C2×C3×D4C2×C4×C518yescomplemented
303C22×C3×C4C23×C511yescharacteristic
304C22×C3×C4C23×C512yes—
305C22×Dic3—22no—
306C22×Dic3—22no—
307C22×Dic3—42no—
308C22×Dic3—42no—
309C22×Dic3—42no—
310C22×Dic3C5×D414yescomplemented
311C22×Dic3C23×C512yes—
312C22×Dic3C23×C511yescharacteristic
313C22×Dic3C23×C512yes—
314C22×Dic3C23×C511yescharacteristic
315C22×Dic3C23×C511yescharacteristic
316C22×Dic3C23×C511yescharacteristic
317C3×C22⋊C4C2×C4×C518yescomplemented
318C3×C22⋊C4C2×C4×C514yescomplemented
319#217—22no—
320#217—22no—
321#217—22no—
322#217—24no—
323#217—24no—
324#217—42no—
325#217—42no—
326#217—42no—
327C4⋊Dic3—22no—
328C4⋊Dic3—42no—
329C4×Dic3—22no—
330C4×Dic3—42no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—28no—
334C23×C5—22no—
335C23×C5—21no—
336C23×C5—21no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—48no—
345C23×C5—44no—
346C23×C5—44no—
347C23×C5—48no—
348C23×C5D3×D412yes—
349C23×C5#23712yes—
350C23×C5C22×Dic314yes—
351C23×C5C22×Dic312yes—
352C23×C5C22×Dic312yes—
353C23×C5C23×D311yescharacteristic
354C5×D4—28no—
355C5×D4—48no—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—32no—
361C2×C4×C5—32no—
362C2×C4×C5—62no—
363C2×C4×C5—62no—
364C2×C4×C5—61no—
365C2×C4×C5—62no—
366C2×C4×C5—61no—
367C2×C4×C5—62no—
368C2×C4×C5—62no—
369C2×C4×C5—62no—
370C2×C4×C5—62no—
371C2×C4×C5—62no—
372C2×C4×C5—62no—
373C2×C4×C5—62no—
374C2×C4×C5—124no—
375C2×C4×C5—124no—
376C2×C4×C5—124no—
377C2×C4×C5C22×Dic312yes—
378C2×C4×C5C22×Dic314yes—
379C25C2×C5×D311yescharacteristic
380C22×D4C2×C5×D311yescharacteristic
381C22×D4C2×C5×D312yes—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—31no—
385#120C5×Dic318yescomplemented
386C4×D4—64no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—32no—
389C2×C22⋊C4—32no—
390C2×C22⋊C4—32no—
391C2×C22⋊C4—31no—
392C2×C22⋊C4—31no—
393C2×C22⋊C4—31no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—64no—
398C2×C22⋊C4C2×C5×D311yescharacteristic
399C2×C22⋊C4C2×C5×D312yes—
400C2×C42—31no—
401C2×C42—32no—
402#95—32no—
403#95—32no—
404#95—32no—
405C2×C3×C5—24no—
406C2×C3×C5—42no—
407C2×C3×C5—44no—
408C2×C3×C5C2×C4×D411yescharacteristic
409C2×C3×C5#51812yes—
410C2×C3×C5#53411yescharacteristic
411C2×C3×C5#53511yescharacteristic
412C2×C3×C5#53812yes—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—28no—
416C23×C3—22no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—48no—
427C23×C3—44no—
428C23×C3—44no—
429C23×C3—48no—
430C23×C3C22×C4×C514yes—
431C23×C3C22×C4×C512yes—
432C23×C3C22×C4×C512yes—
433C23×C3C2×C5×D412yes—
434C23×C3C5×#4112yes—
435C23×C3C24×C511yescharacteristic
436C3×D4—28no—
437C3×D4—48no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4C22×C4×C512yes—
443C2×C3×C4C22×C4×C514yes—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—44no—
457C2×Dic3—44no—
458C2×Dic3—44no—
459C2×Dic3C2×C5×D412yes—
460C2×Dic3C2×C5×D412yes—
461C22×C5—24no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—24no—
465C22×C5—22no—
466C22×C5—24no—
467C22×C5—24no—
468C22×C5—24no—
469C22×C5—24no—
470C22×C5—416no—
471C22×C5—41no—
472C22×C5—42no—
473C22×C5—41no—
474C22×C5—42no—
475C22×C5—42no—
476C22×C5—42no—
477C22×C5—42no—
478C22×C5D4×Dic314yes—
479C22×C5C2×D3×D411yescharacteristic
480C22×C5C2×#23711yescharacteristic
481C22×C5#100412yes—
482C22×C5#100412yes—
483C22×C5C23×Dic311yescharacteristic
484C4×C5—22no—
485C4×C5—24no—
486C4×C5—62no—
487C4×C5—62no—
488C4×C5—121no—
489C4×C5—121no—
490C4×C5—122no—
491C4×C5—122no—
492C24—22no—
493C24—22no—
494C24—42no—
495C24—42no—
496C24C2×C5×Dic314yescomplemented
497C24C22×C5×D312yes—
498C24C22×C5×D311yescharacteristic
499C24C22×C5×D311yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4C2×C5×Dic314yes—
505C2×D4C2×C5×Dic318yescomplemented
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—34no—
509C22×C4—32no—
510C22×C4—32no—
511C22×C4—31no—
512C22×C4—31no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4—122no—
516C22×C4—122no—
517C22×C4—122no—
518C22×C4C22×C5×D311yescharacteristic
519C22×C4C22×C5×D312yes—
520C4⋊C4—62no—
521C4⋊C4—122no—
522C22⋊C4—64no—
523C22⋊C4—64no—
524C22⋊C4—62no—
525C22⋊C4—62no—
526C22⋊C4—62no—
527C22⋊C4—122no—
528C22⋊C4—122no—
529C22⋊C4—122no—
530C22⋊C4C2×C5×Dic318yescomplemented
531C22⋊C4C2×C5×Dic314yescomplemented
532C42—62no—
533C42—122no—
534C3×C5#232111yescharacteristic, complemented, Hall
535C22×C3—24no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—24no—
539C22×C3—22no—
540C22×C3—24no—
541C22×C3—24no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—416no—
545C22×C3—41no—
546C22×C3—42no—
547C22×C3—41no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3C4×C5×D414yes—
553C22×C3C23×C4×C511yescharacteristic
554C22×C3C22×C5×D411yescharacteristic
555C22×C3C2×C5×#4111yescharacteristic
556C22×C3C5×H(5,𝔽2)12yes—
557C22×C3C5×H(5,𝔽2)12yes—
558C3×C4—22no—
559C3×C4—24no—
560Dic3—22no—
561Dic3—22no—
562Dic3—41no—
563Dic3—41no—
564Dic3—42no—
565Dic3—42no—
566C2×C5—24no—
567C2×C5—44no—
568C2×C5—42no—
569C2×C5#558911yescharacteristic
570C2×C5#559211yescharacteristic
571C2×C5#559312yes—
572C2×C5C2×D4×Dic311yescharacteristic
573C2×C5#579812yes—
574C23—22no—
575C23—22no—
576C23—28no—
577C23—22no—
578C23—21no—
579C23—21no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—48no—
588C23—44no—
589C23—44no—
590C23—48no—
591C23C5×D3×D412yes—
592C23C5×#23712yes—
593C23C22×C5×Dic314yes—
594C23C22×C5×Dic312yes—
595C23C22×C5×Dic312yes—
596C23C23×C5×D311yescharacteristic
597D4—28no—
598D4—48no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—32no—
604C2×C4—32no—
605C2×C4—62no—
606C2×C4—62no—
607C2×C4—61no—
608C2×C4—62no—
609C2×C4—61no—
610C2×C4—62no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—124no—
618C2×C4—124no—
619C2×C4—124no—
620C2×C4C22×C5×Dic312yes—
621C2×C4C22×C5×Dic314yes—
622C2×C3—24no—
623C2×C3—44no—
624C2×C3—42no—
625C2×C3C2×C4×C5×D411yescharacteristic
626C2×C3C5×#51812yes—
627C2×C3C5×#53411yescharacteristic
628C2×C3C5×#53511yescharacteristic
629C2×C3C5×#53812yes—
630C5#8257811yescharacteristic, direct product factor, Sylow
631C22—24no—
632C22—22no—
633C22—22no—
634C22—24no—
635C22—22no—
636C22—24no—
637C22—24no—
638C22—24no—
639C22—24no—
640C22—416no—
641C22—41no—
642C22—42no—
643C22—42no—
644C22—41no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22C5×D4×Dic314yes—
649C22C2×C5×D3×D411yescharacteristic
650C22C2×C5×#23711yescharacteristic
651C22C5×#100412yes—
652C22C5×#100412yes—
653C22C23×C5×Dic311yescharacteristic
654C4—22no—
655C4—24no—
656C4—62no—
657C4—62no—
658C4—121no—
659C4—122no—
660C4—121no—
661C4—122no—
662C3C5×#232111yescharacteristic, complemented, Sylow
663C2—24no—
664C2—44no—
665C2—42no—
666C2C5×#558911yescharacteristic
667C2C5×#559211yescharacteristic
668C2C5×#559312yes—
669C2C2×C5×D4×Dic311yescharacteristic
670C2C5×#579812yes—
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
Fitting, prime radicalC2×C3×C5×#120C2
socleC23×C3×C5C24
cosocleC23×C3C24×C5
hypercenterC2×C5×#120D3
hypocenterC3C5×#2321
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C5×#120

Complements

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

NH ≅ G/Ntype
2. C22×C5×#217C2semidirect
3. C2×C5×D4×Dic3C2semidirect
4. C5×#5247C2semidirect
5. C5×#5221C2semidirect
6. C5×#5220C2semidirect
7. C5×#5220C2semidirect
8. C5×#4951C2semidirect
9. C5×#4951C2semidirect
10. C5×#4950C2semidirect
11. C5×Dic3×C22⋊C4C2semidirect
18. C23×C5×Dic3C22semidirect
19. C3×C5×#120C4semidirect
29. C2×C5×#217C22semidirect
30. C2×C5×#217C22semidirect
32. C2×C5×C4⋊Dic3C22semidirect
33. C2×C5×C4⋊Dic3C22semidirect
34. C2×C4×C5×Dic3C22semidirect
35. C2×C4×C5×Dic3C22semidirect
36. C5×C3⋊#95C22semidirect
37. C5×C3⋊#95C22semidirect
38. C5×C3⋊#95C22semidirect
39. #82578C5direct (N × H)
55. C24×C3×C5C2×C4semidirect
64. C2×C3×C5×D4C2×C4semidirect
72. C22×C5×Dic3D4semidirect
79. C3×C5×C22⋊C4C2×C4semidirect
80. C3×C5×C22⋊C4C2×C4semidirect
94. C22×#217C2×C5semidirect
95. C2×D4×Dic3C2×C5semidirect
96. #5247C2×C5semidirect
97. #5221C2×C5semidirect
98. #5220C2×C5semidirect
99. #5220C2×C5semidirect
100. #4951C2×C5semidirect
101. #4951C2×C5semidirect
102. #4950C2×C5semidirect
103. Dic3×C22⋊C4C2×C5semidirect
110. C5×#120Dic3semidirect
184. C23×Dic3C22×C5semidirect
185. C3×#120C4×C5semidirect
195. C2×#217C22×C5semidirect
196. C2×#217C22×C5semidirect
198. C2×C4⋊Dic3C22×C5semidirect
199. C2×C4⋊Dic3C22×C5semidirect
200. C2×C4×Dic3C22×C5semidirect
201. C2×C4×Dic3C22×C5semidirect
202. C3⋊#95C22×C5semidirect
203. C3⋊#95C22×C5semidirect
204. C3⋊#95C22×C5semidirect
209. C24×C5C2×Dic3semidirect
218. C2×C5×D4C2×Dic3semidirect
243. C5×C22⋊C4C2×Dic3semidirect
244. C5×C22⋊C4C2×Dic3semidirect
293. C24×C3C2×C4×C5semidirect
302. C2×C3×D4C2×C4×C5semidirect
310. C22×Dic3C5×D4semidirect
317. C3×C22⋊C4C2×C4×C5semidirect
318. C3×C22⋊C4C2×C4×C5semidirect
385. #120C5×Dic3semidirect
496. C24C2×C5×Dic3semidirect
505. C2×D4C2×C5×Dic3semidirect
530. C22⋊C4C2×C5×Dic3semidirect
531. C22⋊C4C2×C5×Dic3semidirect
534. C3×C5#2321semidirect
630. C5#82578direct (N × H)
662. C3C5×#2321semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1202
C22×C5×#2172
C2×C5×D4×Dic32
C5×#52472
C5×#52212
C5×#52202
C5×#49512
C5×#49502
C5×Dic3×C22⋊C42
C5×#23213
#825785