Finite Group Databasebeta

← C5×#82241 #14327678

Subgroups — C5×#82241 #14327678

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic, complemented
2C2×C4×C5×#67C211yesmaximal, characteristic
3C2×C5×#892C211yesmaximal, characteristic, complemented
4C5×#5212C211yesmaximal, characteristic, complemented
5C5×#4987C211yesmaximal, characteristic, complemented
6C5×#4975C211yesmaximal, characteristic, complemented
7C5×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
8C5×#4957C212yesmaximal
9C5×#4944C212yesmaximal, complemented
10C5×#4940C212yesmaximal, complemented
11C4×C5×Dic3⋊C4C212yesmaximal, complemented
12C5×#2354—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C5×#67C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C3×C5×#117—24no—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2212yes—
20C2×C3×C42×C5C2212yes—
21C2×C5×#217C2212yes—
22C2×C5×#217C2211yescharacteristic
23C4×C5×#67C418yescomplemented
24C2×C5×(C2×D3)⋊C4C2212yes—
25C2×C5×(C2×D3)⋊C4C2212yes—
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C5×C4⋊Dic3C2211yescharacteristic
29C2×C5×Dic3⋊C4C2212yes—
30C2×C5×Dic3⋊C4C2212yes—
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C4×C5×Dic3C2212yes—
33C2×C4×C5×Dic3C2212yes—
34C2×C4×C5×Dic3C2211yescharacteristic
35C5×#892—24no—
36C5×C3⋊#95C2212yes—
37C5×C3⋊#95C2212yes—
38C5×C3⋊#95C2212yes—
39#82241C511yesmaximal, characteristic, direct product factor, Hall
40C2×C4×C5×D4—31no—
41C2×C5×#117—31no—
42C2×C5×#117D311yescharacteristic, complemented
43C5×#390—32no—
44C5×#388—32no—
45C5×#388—32no—
46C5×#384—31no—
47C5×#380—31no—
48C5×#380—31no—
49C4×C5×C4⋊C4—31no—
50C4×C5×C4⋊C4—32no—
51C24×C3×C5C2311yescharacteristic
52C23×C5×D3C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yes—
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2312yes—
59C22×C3×C4×C5C2311yescharacteristic
60C2×C5×#67—22no—
61C2×C5×#67—22no—
62C2×C5×#67C2×C414yes—
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2312yes—
65C22×C5×Dic3C2311yescharacteristic
66C22×C5×Dic3C2311yescharacteristic
67C22×C5×Dic3C2311yescharacteristic
68C2×C4×C5×D3—22no—
69C2×C4×C5×D3—22no—
70C2×C4×C5×D3C2×C414yes—
71C3×C5×C4⋊C4—22no—
72C3×C5×C4⋊C4D414yescomplemented
73C3×C5×C22⋊C4—24no—
74C3×C42×C5—24no—
75C5×#217—42no—
76C5×#217C2×C414yes—
77C5×(C2×D3)⋊C4—24no—
78C5×(C2×D3)⋊C4—42no—
79C5×(C2×D3)⋊C4C2×C414yes—
80C5×C4⋊Dic3—22no—
81C5×C4⋊Dic3—22no—
82C5×Dic3⋊C4—24no—
83C5×Dic3⋊C4—42no—
84C5×Dic3⋊C4C2×C414yes—
85C4×C5×Dic3—24no—
86C4×C5×Dic3—24no—
87C4×C5×Dic3C2×C414yes—
88C2×C3×#117C2×C511yescharacteristic, complemented
89C2×C4×#67C2×C511yescharacteristic
90C2×#892C2×C511yescharacteristic, complemented
91#5212C2×C511yescharacteristic, complemented
92#4987C2×C511yescharacteristic, complemented
93#4975C2×C511yescharacteristic, complemented
94Dic3×C4⋊C4C2×C511yescharacteristic, complemented
95#4957C2×C512yes—
96#4944C2×C512yescomplemented
97#4940C2×C512yescomplemented
98C4×Dic3⋊C4C2×C512yescomplemented
99C22×C5×D4—31no—
100C23×C4×C5—31no—
101C23×C4×C5C2×D311yescharacteristic
102C4×C5×D4—38no—
103C5×#117—24no—
104C5×#117—64no—
105C2×C5×C4⋊C4—31no—
106C2×C5×C4⋊C4—31no—
107C2×C5×C4⋊C4—32no—
108C2×C5×C4⋊C4—31no—
109C2×C5×C4⋊C4—32no—
110C2×C5×C4⋊C4C2×D311yescharacteristic
111C2×C5×C4⋊C4C2×D311yescharacteristic
112C2×C5×C22⋊C4—31no—
113C2×C5×C22⋊C4—31no—
114C2×C5×C22⋊C4—32no—
115C2×C5×C22⋊C4—32no—
116C2×C5×C22⋊C4—32no—
117C2×C5×C22⋊C4C2×D312yes—
118C2×C42×C5—31no—
119C2×C42×C5—32no—
120C2×C42×C5—32no—
121C2×C42×C5C2×D312yes—
122C5×#95—32no—
123C5×#95—32no—
124C5×#95—32no—
125#2354—31noSylow
126C23×C3×C5—21no—
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—21no—
130C23×C3×C5—21no—
131C23×C3×C5—21no—
132C23×C3×C5C22×C412yes—
133C23×C3×C5C2411yescharacteristic
134C22×C5×D3—21no—
135C22×C5×D3—21no—
136C22×C5×D3—21no—
137C22×C5×D3—21no—
138C22×C5×D3—21no—
139C22×C5×D3—21no—
140C22×C5×D3C22×C412yes—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—28no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5C22×C412yes—
150C2×C3×C4×C5C22×C412yes—
151C2×C3×C4×C5C2×D414yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5#4112yes—
154C5×#67—28no—
155C2×C5×Dic3—21no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—21no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3C22×C412yes—
166C2×C5×Dic3C22×C412yes—
167C2×C5×Dic3C22×C412yes—
168C2×C5×Dic3#4112yes—
169C2×C5×Dic3#4112yes—
170C4×C5×D3—28no—
171C23×C3×C4C22×C511yescharacteristic
172C22×#67C22×C511yescharacteristic
173C22×C4×D3C22×C511yescharacteristic
174C3×#117—24no—
175C2×C3×C4⋊C4C22×C511yescharacteristic
176C2×C3×C4⋊C4C22×C511yescharacteristic
177C2×C3×C22⋊C4C22×C512yes—
178C2×C3×C42C22×C512yes—
179C2×#217C22×C512yes—
180C2×#217C22×C511yescharacteristic
181C4×#67C4×C518yescomplemented
182C2×(C2×D3)⋊C4C22×C512yes—
183C2×(C2×D3)⋊C4C22×C512yes—
184C2×(C2×D3)⋊C4C22×C511yescharacteristic
185C2×C4⋊Dic3C22×C511yescharacteristic
186C2×C4⋊Dic3C22×C511yescharacteristic
187C2×Dic3⋊C4C22×C512yes—
188C2×Dic3⋊C4C22×C512yes—
189C2×Dic3⋊C4C22×C511yescharacteristic
190C2×C4×Dic3C22×C512yes—
191C2×C4×Dic3C22×C512yes—
192C2×C4×Dic3C22×C511yescharacteristic
193#892—24no—
194C3⋊#95C22×C512yes—
195C3⋊#95C22×C512yes—
196C3⋊#95C22×C512yes—
197C24×C5—31no—
198C24×C5C22×D311yescharacteristic
199C2×C5×D4—34no—
200C2×C5×D4—62no—
201C2×C5×D4—62no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—31no—
205C22×C4×C5—31no—
206C22×C4×C5—31no—
207C22×C4×C5—34no—
208C22×C4×C5—32no—
209C22×C4×C5—32no—
210C22×C4×C5—62no—
211C22×C4×C5—62no—
212C22×C4×C5C4×D314yes—
213C22×C4×C5C22×D312yes—
214C22×C4×C5C22×D311yescharacteristic
215C22×C4×C5C22×D312yes—
216C22×C4×C5C22×D311yescharacteristic
217C5×C4⋊C4—22no—
218C5×C4⋊C4—34no—
219C5×C4⋊C4—64no—
220C5×C4⋊C4—62no—
221C5×C4⋊C4—62no—
222C5×C4⋊C4—122no—
223C5×C4⋊C4#6714yescomplemented
224C5×C22⋊C4—24no—
225C5×C22⋊C4—34no—
226C5×C22⋊C4—34no—
227C5×C22⋊C4—64no—
228C5×C22⋊C4—122no—
229C5×C22⋊C4—122no—
230C42×C5—24no—
231C42×C5—34no—
232C42×C5—64no—
233C42×C5—64no—
234C2×C4×D4—31no—
235C2×#117—31no—
236C2×#117C5×D311yescharacteristic, complemented
237#390—32no—
238#388—32no—
239#388—32no—
240#384—31no—
241#380—31no—
242#380—31no—
243C4×C4⋊C4—31no—
244C4×C4⋊C4—32no—
245C22×C3×C5—22no—
246C22×C3×C5—22no—
247C22×C3×C5—22no—
248C22×C3×C5—41no—
249C22×C3×C5—41no—
250C22×C3×C5—41no—
251C22×C3×C5—41no—
252C22×C3×C5C23×C411yescharacteristic
253C22×C3×C5C22×D411yescharacteristic
254C22×C3×C5C2×#4111yescharacteristic
255C22×C3×C5C2×#4111yescharacteristic
256C22×C3×C5C2×#4111yescharacteristic
257C22×C3×C5H(5,𝔽2)11yescharacteristic
258C22×C3×C52−1+411yescharacteristic
259C2×C5×D3—22no—
260C2×C5×D3—22no—
261C2×C5×D3—22no—
262C2×C5×D3—41no—
263C2×C5×D3—41no—
264C2×C5×D3—41no—
265C2×C5×D3—41no—
266C3×C4×C5—22no—
267C3×C4×C5—24no—
268C3×C4×C5—42no—
269C3×C4×C5C4×D414yes—
270C5×Dic3—22no—
271C5×Dic3—22no—
272C5×Dic3—42no—
273C5×Dic3—42no—
274C5×Dic3#11714yescomplemented
275C24×C3C23×C511yescharacteristic
276C23×D3C23×C511yescharacteristic
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4C2×C4×C514yes—
280C22×C3×C4C23×C512yes—
281C22×C3×C4C23×C511yescharacteristic
282C22×C3×C4C23×C512yes—
283C22×C3×C4C23×C511yescharacteristic
284C2×#67—22no—
285C2×#67—22no—
286C2×#67C2×C4×C514yes—
287C22×Dic3C23×C512yes—
288C22×Dic3C23×C512yes—
289C22×Dic3C23×C511yescharacteristic
290C22×Dic3C23×C511yescharacteristic
291C22×Dic3C23×C511yescharacteristic
292C2×C4×D3—22no—
293C2×C4×D3—22no—
294C2×C4×D3C2×C4×C514yes—
295C3×C4⋊C4—22no—
296C3×C4⋊C4C5×D414yescomplemented
297C3×C22⋊C4—24no—
298C3×C42—24no—
299#217—42no—
300#217C2×C4×C514yes—
301(C2×D3)⋊C4—24no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4C2×C4×C514yes—
304C4⋊Dic3—22no—
305C4⋊Dic3—22no—
306Dic3⋊C4—24no—
307Dic3⋊C4—42no—
308Dic3⋊C4C2×C4×C514yes—
309C4×Dic3—24no—
310C4×Dic3—24no—
311C4×Dic3C2×C4×C514yes—
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—32no—
319C23×C5—61no—
320C23×C5—61no—
321C23×C5—61no—
322C23×C5—61no—
323C23×C5—61no—
324C23×C5—61no—
325C23×C5C2×C4×D312yes—
326C23×C5C23×D311yescharacteristic
327C5×D4—68no—
328C2×C4×C5—21no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—21no—
332C2×C4×C5—28no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—32no—
337C2×C4×C5—32no—
338C2×C4×C5—32no—
339C2×C4×C5—32no—
340C2×C4×C5—32no—
341C2×C4×C5—61no—
342C2×C4×C5—61no—
343C2×C4×C5—61no—
344C2×C4×C5—61no—
345C2×C4×C5—68no—
346C2×C4×C5—62no—
347C2×C4×C5—62no—
348C2×C4×C5—62no—
349C2×C4×C5—62no—
350C2×C4×C5—62no—
351C2×C4×C5—62no—
352C2×C4×C5C2×C4×D312yes—
353C2×C4×C5C2×C4×D312yes—
354C2×C4×C5#23512yes—
355C2×C4×C5C2×#6714yes—
356C2×C4×C5C2×#6712yes—
357C22×D4—31no—
358C23×C4—31no—
359C23×C4C2×C5×D311yescharacteristic
360C4×D4—38no—
361#117—24no—
362#117—64no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4C2×C5×D311yescharacteristic
369C2×C4⋊C4C2×C5×D311yescharacteristic
370C2×C22⋊C4—31no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4C2×C5×D312yes—
376C2×C42—31no—
377C2×C42—32no—
378C2×C42—32no—
379C2×C42C2×C5×D312yes—
380#95—32no—
381#95—32no—
382#95—32no—
383C2×C3×C5—42no—
384C2×C3×C5C2×#11711yescharacteristic
385C2×C3×C5C2×C4×D411yescharacteristic
386C2×C3×C5#52011yescharacteristic
387C2×C3×C5#54711yescharacteristic
388C2×C3×C5#55011yescharacteristic
389C2×C3×C5#55511yescharacteristic
390C2×C3×C5#55611yescharacteristic
391C5×D3—42no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3C22×C4×C512yes—
399C23×C3C24×C511yescharacteristic
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3C22×C4×C512yes—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—28no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4C22×C4×C512yes—
416C2×C3×C4C22×C4×C512yes—
417C2×C3×C4C2×C5×D414yes—
418C2×C3×C4C2×C5×D412yes—
419C2×C3×C4C5×#4112yes—
420#67—28no—
421C2×Dic3—21no—
422C2×Dic3—21no—
423C2×Dic3—21no—
424C2×Dic3—21no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3C22×C4×C512yes—
432C2×Dic3C22×C4×C512yes—
433C2×Dic3C22×C4×C512yes—
434C2×Dic3C5×#4112yes—
435C2×Dic3C5×#4112yes—
436C4×D3—28no—
437C22×C5—22no—
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5—62no—
445C22×C5—62no—
446C22×C5—62no—
447C22×C5—121no—
448C22×C5—121no—
449C22×C5—121no—
450C22×C5—121no—
451C22×C5C22×C4×D311yescharacteristic
452C22×C5C2×#23511yescharacteristic
453C22×C5D3×#4111yescharacteristic
454C22×C5D3×#4111yescharacteristic
455C22×C5#100911yescharacteristic
456C22×C5#101011yescharacteristic
457C22×C5C22×#6711yescharacteristic
458C4×C5—22no—
459C4×C5—24no—
460C4×C5—34no—
461C4×C5—42no—
462C4×C5—62no—
463C4×C5—62no—
464C4×C5—122no—
465C4×C5—122no—
466C4×C5C4×#6714yes—
467C24—31no—
468C24C22×C5×D311yescharacteristic
469C2×D4—34no—
470C2×D4—62no—
471C2×D4—62no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—34no—
478C22×C4—32no—
479C22×C4—32no—
480C22×C4—62no—
481C22×C4—62no—
482C22×C4C4×C5×D314yes—
483C22×C4C22×C5×D312yes—
484C22×C4C22×C5×D311yescharacteristic
485C22×C4C22×C5×D312yes—
486C22×C4C22×C5×D311yescharacteristic
487C4⋊C4—22no—
488C4⋊C4—34no—
489C4⋊C4—64no—
490C4⋊C4—62no—
491C4⋊C4—62no—
492C4⋊C4—122no—
493C4⋊C4C5×#6714yescomplemented
494C22⋊C4—24no—
495C22⋊C4—34no—
496C22⋊C4—34no—
497C22⋊C4—64no—
498C22⋊C4—122no—
499C22⋊C4—122no—
500C42—24no—
501C42—34no—
502C42—64no—
503C42—64no—
504C3×C5#235411yescharacteristic, complemented, Hall
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3C23×C4×C511yescharacteristic
513C22×C3C22×C5×D411yescharacteristic
514C22×C3C2×C5×#4111yescharacteristic
515C22×C3C2×C5×#4111yescharacteristic
516C22×C3C2×C5×#4111yescharacteristic
517C22×C3C5×H(5,𝔽2)11yescharacteristic
518C22×C3C5×2−1+411yescharacteristic
519C2×D3—22no—
520C2×D3—22no—
521C2×D3—22no—
522C2×D3—41no—
523C2×D3—41no—
524C2×D3—41no—
525C2×D3—41no—
526C3×C4—22no—
527C3×C4—24no—
528C3×C4—42no—
529C3×C4C4×C5×D414yes—
530Dic3—22no—
531Dic3—22no—
532Dic3—42no—
533Dic3—42no—
534Dic3C5×#11714yescomplemented
535C2×C5—42no—
536C2×C5—122no—
537C2×C5D3×#11711yescharacteristic
538C2×C5#552311yescharacteristic
539C2×C5#553211yescharacteristic
540C2×C5#553311yescharacteristic
541C2×C5C2×C4×#6711yescharacteristic
542C2×C5#582411yescharacteristic
543C2×C5#583411yescharacteristic
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—32no—
551C23—61no—
552C23—61no—
553C23—61no—
554C23—61no—
555C23—61no—
556C23—61no—
557C23C2×C4×C5×D312yes—
558C23C23×C5×D311yescharacteristic
559D4—68no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—28no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—32no—
569C2×C4—32no—
570C2×C4—32no—
571C2×C4—32no—
572C2×C4—32no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—61no—
576C2×C4—61no—
577C2×C4—68no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4C2×C4×C5×D312yes—
585C2×C4C2×C4×C5×D312yes—
586C2×C4C5×#23512yes—
587C2×C4C2×C5×#6714yes—
588C2×C4C2×C5×#6712yes—
589C2×C3—42no—
590C2×C3C2×C5×#11711yescharacteristic
591C2×C3C2×C4×C5×D411yescharacteristic
592C2×C3C5×#52011yescharacteristic
593C2×C3C5×#54711yescharacteristic
594C2×C3C5×#55011yescharacteristic
595C2×C3C5×#55511yescharacteristic
596C2×C3C5×#55611yescharacteristic
597D3—42no—
598C5#8224111yescharacteristic, direct product factor, Sylow
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—62no—
607C22—62no—
608C22—62no—
609C22—121no—
610C22—121no—
611C22—121no—
612C22—121no—
613C22C22×C4×C5×D311yescharacteristic
614C22C2×C5×#23511yescharacteristic
615C22C5×D3×#4111yescharacteristic
616C22C5×D3×#4111yescharacteristic
617C22C5×#100911yescharacteristic
618C22C5×#101011yescharacteristic
619C22C22×C5×#6711yescharacteristic
620C4—22no—
621C4—24no—
622C4—34no—
623C4—42no—
624C4—62no—
625C4—62no—
626C4—122no—
627C4—122no—
628C4C4×C5×#6714yes—
629C3C5×#235411yescharacteristic, complemented, Sylow
630C2—42no—
631C2—122no—
632C2C5×D3×#11711yescharacteristic
633C2C5×#552311yescharacteristic
634C2C5×#553211yescharacteristic
635C2C5×#553311yescharacteristic
636C2C2×C4×C5×#6711yescharacteristic
637C2C5×#582411yescharacteristic
638C2C5×#583411yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC22×C5×#67C22
cosocleC23×C3C24×C5
hypercenterC2×C5×#117D3
hypocenterC3C5×#2354
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C5×#117

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#117C2semidirect
3. C2×C5×#892C2semidirect
4. C5×#5212C2semidirect
5. C5×#4987C2semidirect
6. C5×#4975C2semidirect
7. C5×Dic3×C4⋊C4C2semidirect
9. C5×#4944C2semidirect
10. C5×#4940C2semidirect
11. C4×C5×Dic3⋊C4C2semidirect
23. C4×C5×#67C4semidirect
39. #82241C5direct (N × H)
42. C2×C5×#117D3semidirect
72. C3×C5×C4⋊C4D4semidirect
88. C2×C3×#117C2×C5semidirect
90. C2×#892C2×C5semidirect
91. #5212C2×C5semidirect
92. #4987C2×C5semidirect
93. #4975C2×C5semidirect
94. Dic3×C4⋊C4C2×C5semidirect
96. #4944C2×C5semidirect
97. #4940C2×C5semidirect
98. C4×Dic3⋊C4C2×C5semidirect
181. C4×#67C4×C5semidirect
223. C5×C4⋊C4#67semidirect
236. C2×#117C5×D3semidirect
274. C5×Dic3#117semidirect
296. C3×C4⋊C4C5×D4semidirect
493. C4⋊C4C5×#67semidirect
504. C3×C5#2354semidirect
534. Dic3C5×#117semidirect
598. C5#82241direct (N × H)
629. C3C5×#2354semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1172
C2×C4×C5×#672
C2×C5×#8922
C5×#52122
C5×#49872
C5×#49752
C5×Dic3×C4⋊C42
C5×#49572
C5×#49442
C5×#49402
C4×C5×Dic3⋊C42
C5×#23543
#822415