Finite Group Databasebeta

← C5×#82272 #14327342

Subgroups — C5×#82272 #14327342

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 644 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×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C5×#5212C211yesmaximal, characteristic, complemented
5C5×#4987C211yesmaximal, characteristic, complemented
6C5×#4977C211yesmaximal, characteristic, complemented
7C5×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
8C5×#4956C212yesmaximal
9C5×#4945C212yesmaximal, complemented
10C4×C5×(C2×D3)⋊C4C212yesmaximal, complemented
11C5×#4933C212yesmaximal, complemented
12C5×#2352—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C5×#67C2211yescharacteristic
15C22×C4×C5×D3C2212yes—
16C22×C4×C5×D3C2211yescharacteristic
17C3×C5×#117—24no—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2212yes—
21C2×C3×C42×C5C2212yes—
22C2×C5×#217C2212yes—
23C2×C5×#217C2211yescharacteristic
24C4×C5×#67C418yescomplemented
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⋊C4C2211yescharacteristic
31C2×C4×C5×Dic3C2212yes—
32C2×C4×C5×Dic3C2211yescharacteristic
33C5×D3×C4⋊C4—24no—
34C5×C3⋊#95C2212yes—
35C5×C3⋊#95C2212yes—
36C5×C3⋊#95C2212yes—
37C5×C3⋊#95C2212yes—
38C5×C3⋊#95C2212yes—
39#82272C511yesmaximal, characteristic, direct product factor, Hall
40C2×C4×C5×D4—31no—
41C2×C5×#117D311yescharacteristic, complemented
42C22×C5×C4⋊C4—31no—
43C5×#388—32no—
44C5×#387—32no—
45C5×#386—32no—
46C5×#382—31no—
47C5×#380—31no—
48C5×#380—31no—
49C4×C5×C4⋊C4—31no—
50C4×C5×C22⋊C4—32no—
51C24×C3×C5C2311yescharacteristic
52C23×C5×D3C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yescomplemented
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×D3—24no—
71C2×C4×C5×D3—24no—
72C2×C4×C5×D3—42no—
73C2×C4×C5×D3C2×C414yes—
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4D414yescomplemented
76C3×C5×C22⋊C4—24no—
77C3×C42×C5—24no—
78C5×#217—42no—
79C5×#217C2×C414yescomplemented
80C5×(C2×D3)⋊C4—24no—
81C5×(C2×D3)⋊C4C2×C414yes—
82C5×C4⋊Dic3—22no—
83C5×C4⋊Dic3—22no—
84C5×Dic3⋊C4—24no—
85C5×Dic3⋊C4C2×C414yescomplemented
86C4×C5×Dic3—42no—
87C4×C5×Dic3C2×C414yescomplemented
88C2×C3×#117C2×C511yescharacteristic, complemented
89C2×C4×#67C2×C511yescharacteristic
90C2×D3×C4⋊C4C2×C511yescharacteristic, complemented
91#5212C2×C511yescharacteristic, complemented
92#4987C2×C511yescharacteristic, complemented
93#4977C2×C511yescharacteristic, complemented
94Dic3×C4⋊C4C2×C511yescharacteristic, complemented
95#4956C2×C512yes—
96#4945C2×C512yescomplemented
97C4×(C2×D3)⋊C4C2×C512yescomplemented
98#4933C2×C512yescomplemented
99C22×C5×D4—31no—
100C23×C4×C5—31no—
101C23×C4×C5—32no—
102C23×C4×C5C2×D311yescharacteristic
103C4×C5×D4—38no—
104C5×#117—24no—
105C2×C5×C4⋊C4—31no—
106C2×C5×C4⋊C4—31no—
107C2×C5×C4⋊C4—31no—
108C2×C5×C4⋊C4—32no—
109C2×C5×C4⋊C4—64no—
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⋊C4C2×D312yes—
117C2×C42×C5—31no—
118C2×C42×C5—32no—
119C2×C42×C5C2×D312yes—
120C5×#95—32no—
121C5×#95—32no—
122C5×#95—32no—
123C5×#95—32no—
124C5×#95—32no—
125#2352—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×D3C22×C412yes—
139C22×C5×D3#4112yes—
140C22×C5×D3#4112yes—
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—21no—
160C2×C5×Dic3—21no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3C22×C412yes—
168C2×C5×Dic3C22×C412yes—
169C2×C5×Dic3C22×C412yes—
170C4×C5×D3—28no—
171C4×C5×D3—48no—
172C23×C3×C4C22×C511yescharacteristic
173C22×#67C22×C511yescharacteristic
174C22×C4×D3C22×C512yes—
175C22×C4×D3C22×C511yescharacteristic
176C3×#117—24no—
177C2×C3×C4⋊C4C22×C511yescharacteristic
178C2×C3×C4⋊C4C22×C511yescharacteristic
179C2×C3×C22⋊C4C22×C512yes—
180C2×C3×C42C22×C512yes—
181C2×#217C22×C512yes—
182C2×#217C22×C511yescharacteristic
183C4×#67C4×C518yescomplemented
184C2×(C2×D3)⋊C4C22×C512yes—
185C2×(C2×D3)⋊C4C22×C511yescharacteristic
186C2×C4⋊Dic3C22×C511yescharacteristic
187C2×C4⋊Dic3C22×C511yescharacteristic
188C2×Dic3⋊C4C22×C512yes—
189C2×Dic3⋊C4C22×C511yescharacteristic
190C2×C4×Dic3C22×C512yes—
191C2×C4×Dic3C22×C511yescharacteristic
192D3×C4⋊C4—24no—
193C3⋊#95C22×C512yes—
194C3⋊#95C22×C512yes—
195C3⋊#95C22×C512yes—
196C3⋊#95C22×C512yes—
197C3⋊#95C22×C512yes—
198C24×C5—31no—
199C24×C5C22×D311yescharacteristic
200C2×C5×D4—34no—
201C2×C5×D4—62no—
202C2×C5×D4—62no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—31no—
206C22×C4×C5—31no—
207C22×C4×C5—31no—
208C22×C4×C5—34no—
209C22×C4×C5—32no—
210C22×C4×C5—32no—
211C22×C4×C5—64no—
212C22×C4×C5—62no—
213C22×C4×C5—62no—
214C22×C4×C5—64no—
215C22×C4×C5—122no—
216C22×C4×C5C4×D314yescomplemented
217C22×C4×C5C22×D312yes—
218C22×C4×C5C22×D311yescharacteristic
219C22×C4×C5C22×D312yes—
220C22×C4×C5C22×D311yescharacteristic
221C5×C4⋊C4—22no—
222C5×C4⋊C4—34no—
223C5×C4⋊C4—62no—
224C5×C4⋊C4—64no—
225C5×C4⋊C4—62no—
226C5×C4⋊C4#6714yescomplemented
227C5×C22⋊C4—24no—
228C5×C22⋊C4—34no—
229C5×C22⋊C4—34no—
230C5×C22⋊C4—64no—
231C5×C22⋊C4—122no—
232C42×C5—24no—
233C42×C5—34no—
234C42×C5—122no—
235C2×C4×D4—31no—
236C2×#117C5×D311yescharacteristic, complemented
237C22×C4⋊C4—31no—
238#388—32no—
239#387—32no—
240#386—32no—
241#382—31no—
242#380—31no—
243#380—31no—
244C4×C4⋊C4—31no—
245C4×C22⋊C4—32no—
246C22×C3×C5—22no—
247C22×C3×C5—22no—
248C22×C3×C5—22no—
249C22×C3×C5—41no—
250C22×C3×C5—41no—
251C22×C3×C5—41no—
252C22×C3×C5—41no—
253C22×C3×C5C23×C411yescharacteristic
254C22×C3×C5C22×D411yescharacteristic
255C22×C3×C5C2×#4111yescharacteristic
256C22×C3×C5C2×#4111yescharacteristic
257C22×C3×C5C2×#4111yescharacteristic
258C22×C3×C5H(5,𝔽2)11yescharacteristic
259C22×C3×C52−1+411yescharacteristic
260C2×C5×D3—22no—
261C2×C5×D3—22no—
262C2×C5×D3—22no—
263C2×C5×D3—22no—
264C2×C5×D3—22no—
265C2×C5×D3—22no—
266C2×C5×D3#11714yescomplemented
267C3×C4×C5—22no—
268C3×C4×C5—24no—
269C3×C4×C5—42no—
270C3×C4×C5C4×D414yes—
271C5×Dic3—22no—
272C5×Dic3—22no—
273C5×Dic3—22no—
274C5×Dic3—42no—
275C5×Dic3—42no—
276C24×C3C23×C511yescharacteristic
277C23×D3C23×C511yescharacteristic
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4C2×C4×C514yescomplemented
281C22×C3×C4C23×C512yes—
282C22×C3×C4C23×C511yescharacteristic
283C22×C3×C4C23×C512yes—
284C22×C3×C4C23×C511yescharacteristic
285C2×#67—22no—
286C2×#67—22no—
287C2×#67C2×C4×C514yes—
288C22×Dic3C23×C512yes—
289C22×Dic3C23×C512yes—
290C22×Dic3C23×C511yescharacteristic
291C22×Dic3C23×C511yescharacteristic
292C22×Dic3C23×C511yescharacteristic
293C2×C4×D3—22no—
294C2×C4×D3—22no—
295C2×C4×D3—24no—
296C2×C4×D3—24no—
297C2×C4×D3—42no—
298C2×C4×D3C2×C4×C514yes—
299C3×C4⋊C4—22no—
300C3×C4⋊C4C5×D414yescomplemented
301C3×C22⋊C4—24no—
302C3×C42—24no—
303#217—42no—
304#217C2×C4×C514yescomplemented
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4C2×C4×C514yes—
307C4⋊Dic3—22no—
308C4⋊Dic3—22no—
309Dic3⋊C4—24no—
310Dic3⋊C4C2×C4×C514yescomplemented
311C4×Dic3—42no—
312C4×Dic3C2×C4×C514yescomplemented
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—32no—
320C23×C5—32no—
321C23×C5—32no—
322C23×C5—61no—
323C23×C5—61no—
324C23×C5—61no—
325C23×C5—61no—
326C23×C5C2×C4×D312yes—
327C23×C5C23×D311yescharacteristic
328C5×D4—68no—
329C2×C4×C5—21no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—21no—
333C2×C4×C5—28no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—32no—
338C2×C4×C5—32no—
339C2×C4×C5—32no—
340C2×C4×C5—61no—
341C2×C4×C5—61no—
342C2×C4×C5—61no—
343C2×C4×C5—61no—
344C2×C4×C5—61no—
345C2×C4×C5—61no—
346C2×C4×C5—68no—
347C2×C4×C5—62no—
348C2×C4×C5—62no—
349C2×C4×C5—62no—
350C2×C4×C5—62no—
351C2×C4×C5—62no—
352C2×C4×C5—62no—
353C2×C4×C5—128no—
354C2×C4×C5C2×C4×D312yes—
355C2×C4×C5C2×C4×D312yes—
356C2×C4×C5#23512yes—
357C2×C4×C5C2×#6714yes—
358C2×C4×C5C2×#6712yes—
359C22×D4—31no—
360C23×C4—31no—
361C23×C4—32no—
362C23×C4C2×C5×D311yescharacteristic
363C4×D4—38no—
364#117—24no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—64no—
370C2×C4⋊C4C2×C5×D311yescharacteristic
371C2×C4⋊C4C2×C5×D311yescharacteristic
372C2×C22⋊C4—31no—
373C2×C22⋊C4—31no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—32no—
376C2×C22⋊C4C2×C5×D312yes—
377C2×C42—31no—
378C2×C42—32no—
379C2×C42C2×C5×D312yes—
380#95—32no—
381#95—32no—
382#95—32no—
383#95—32no—
384#95—32no—
385C2×C3×C5—42no—
386C2×C3×C5C2×#11711yescharacteristic
387C2×C3×C5C2×C4×D411yescharacteristic
388C2×C3×C5#52011yescharacteristic
389C2×C3×C5#54611yescharacteristic
390C2×C3×C5#54811yescharacteristic
391C2×C3×C5#55211yescharacteristic
392C2×C3×C5#55311yescharacteristic
393C5×D3—24no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3C22×C4×C512yes—
401C23×C3C24×C511yescharacteristic
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3C22×C4×C512yes—
407C22×D3C5×#4112yes—
408C22×D3C5×#4112yes—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—28no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4C22×C4×C512yes—
418C2×C3×C4C22×C4×C512yes—
419C2×C3×C4C2×C5×D414yes—
420C2×C3×C4C2×C5×D412yes—
421C2×C3×C4C5×#4112yes—
422#67—28no—
423C2×Dic3—21no—
424C2×Dic3—21no—
425C2×Dic3—21no—
426C2×Dic3—21no—
427C2×Dic3—21no—
428C2×Dic3—21no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3C22×C4×C512yes—
436C2×Dic3C22×C4×C512yes—
437C2×Dic3C22×C4×C512yes—
438C4×D3—28no—
439C4×D3—48no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—22no—
443C22×C5—34no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5—41no—
447C22×C5—41no—
448C22×C5—62no—
449C22×C5—62no—
450C22×C5—62no—
451C22×C5—62no—
452C22×C5—62no—
453C22×C5—62no—
454C22×C5C22×C4×D311yescharacteristic
455C22×C5C2×#23511yescharacteristic
456C22×C5D3×#4111yescharacteristic
457C22×C5D3×#4111yescharacteristic
458C22×C5#100911yescharacteristic
459C22×C5#101011yescharacteristic
460C22×C5C22×#6711yescharacteristic
461C4×C5—22no—
462C4×C5—24no—
463C4×C5—42no—
464C4×C5—62no—
465C4×C5—62no—
466C4×C5—62no—
467C4×C5—122no—
468C4×C5—122no—
469C4×C5C4×#6714yes—
470C24—31no—
471C24C22×C5×D311yescharacteristic
472C2×D4—34no—
473C2×D4—62no—
474C2×D4—62no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—34no—
481C22×C4—32no—
482C22×C4—32no—
483C22×C4—64no—
484C22×C4—62no—
485C22×C4—62no—
486C22×C4—64no—
487C22×C4—122no—
488C22×C4C4×C5×D314yescomplemented
489C22×C4C22×C5×D312yes—
490C22×C4C22×C5×D311yescharacteristic
491C22×C4C22×C5×D312yes—
492C22×C4C22×C5×D311yescharacteristic
493C4⋊C4—22no—
494C4⋊C4—34no—
495C4⋊C4—62no—
496C4⋊C4—64no—
497C4⋊C4—62no—
498C4⋊C4C5×#6714yescomplemented
499C22⋊C4—24no—
500C22⋊C4—34no—
501C22⋊C4—34no—
502C22⋊C4—64no—
503C22⋊C4—122no—
504C42—24no—
505C42—34no—
506C42—122no—
507C3×C5#235211yescharacteristic, complemented, Hall
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3C23×C4×C511yescharacteristic
516C22×C3C22×C5×D411yescharacteristic
517C22×C3C2×C5×#4111yescharacteristic
518C22×C3C2×C5×#4111yescharacteristic
519C22×C3C2×C5×#4111yescharacteristic
520C22×C3C5×H(5,𝔽2)11yescharacteristic
521C22×C3C5×2−1+411yescharacteristic
522C2×D3—22no—
523C2×D3—22no—
524C2×D3—22no—
525C2×D3—22no—
526C2×D3—22no—
527C2×D3—22no—
528C2×D3C5×#11714yescomplemented
529C3×C4—22no—
530C3×C4—24no—
531C3×C4—42no—
532C3×C4C4×C5×D414yes—
533Dic3—22no—
534Dic3—22no—
535Dic3—22no—
536Dic3—42no—
537Dic3—42no—
538C2×C5—42no—
539C2×C5—64no—
540C2×C5D3×#11711yescharacteristic
541C2×C5#552311yescharacteristic
542C2×C5#552911yescharacteristic
543C2×C5#553011yescharacteristic
544C2×C5C2×C4×#6711yescharacteristic
545C2×C5#582911yescharacteristic
546C2×C5#583111yescharacteristic
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—32no—
554C23—32no—
555C23—32no—
556C23—61no—
557C23—61no—
558C23—61no—
559C23—61no—
560C23C2×C4×C5×D312yes—
561C23C23×C5×D311yescharacteristic
562D4—68no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—28no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—32no—
572C2×C4—32no—
573C2×C4—32no—
574C2×C4—61no—
575C2×C4—61no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—61no—
579C2×C4—61no—
580C2×C4—68no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—128no—
588C2×C4C2×C4×C5×D312yes—
589C2×C4C2×C4×C5×D312yes—
590C2×C4C5×#23512yes—
591C2×C4C2×C5×#6714yes—
592C2×C4C2×C5×#6712yes—
593C2×C3—42no—
594C2×C3C2×C5×#11711yescharacteristic
595C2×C3C2×C4×C5×D411yescharacteristic
596C2×C3C5×#52011yescharacteristic
597C2×C3C5×#54611yescharacteristic
598C2×C3C5×#54811yescharacteristic
599C2×C3C5×#55211yescharacteristic
600C2×C3C5×#55311yescharacteristic
601D3—24no—
602C5#8227211yescharacteristic, direct product factor, Sylow
603C22—22no—
604C22—22no—
605C22—22no—
606C22—34no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—62no—
612C22—62no—
613C22—62no—
614C22—62no—
615C22—62no—
616C22—62no—
617C22C22×C4×C5×D311yescharacteristic
618C22C2×C5×#23511yescharacteristic
619C22C5×D3×#4111yescharacteristic
620C22C5×D3×#4111yescharacteristic
621C22C5×#100911yescharacteristic
622C22C5×#101011yescharacteristic
623C22C22×C5×#6711yescharacteristic
624C4—22no—
625C4—24no—
626C4—42no—
627C4—62no—
628C4—62no—
629C4—62no—
630C4—122no—
631C4—122no—
632C4C4×C5×#6714yes—
633C3C5×#235211yescharacteristic, complemented, Sylow
634C2—42no—
635C2—64no—
636C2C5×D3×#11711yescharacteristic
637C2C5×#552311yescharacteristic
638C2C5×#552911yescharacteristic
639C2C5×#553011yescharacteristic
640C2C2×C4×C5×#6711yescharacteristic
641C2C5×#582911yescharacteristic
642C2C5×#583111yescharacteristic
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×#2352
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×D3×C4⋊C4C2semidirect
4. C5×#5212C2semidirect
5. C5×#4987C2semidirect
6. C5×#4977C2semidirect
7. C5×Dic3×C4⋊C4C2semidirect
9. C5×#4945C2semidirect
10. C4×C5×(C2×D3)⋊C4C2semidirect
11. C5×#4933C2semidirect
24. C4×C5×#67C4semidirect
39. #82272C5direct (N × H)
41. C2×C5×#117D3semidirect
55. C22×C3×C4×C5C2×C4semidirect
75. C3×C5×C4⋊C4D4semidirect
79. C5×#217C2×C4semidirect
85. C5×Dic3⋊C4C2×C4semidirect
87. C4×C5×Dic3C2×C4semidirect
88. C2×C3×#117C2×C5semidirect
90. C2×D3×C4⋊C4C2×C5semidirect
91. #5212C2×C5semidirect
92. #4987C2×C5semidirect
93. #4977C2×C5semidirect
94. Dic3×C4⋊C4C2×C5semidirect
96. #4945C2×C5semidirect
97. C4×(C2×D3)⋊C4C2×C5semidirect
98. #4933C2×C5semidirect
183. C4×#67C4×C5semidirect
216. C22×C4×C5C4×D3semidirect
226. C5×C4⋊C4#67semidirect
236. C2×#117C5×D3semidirect
266. C2×C5×D3#117semidirect
280. C22×C3×C4C2×C4×C5semidirect
300. C3×C4⋊C4C5×D4semidirect
304. #217C2×C4×C5semidirect
310. Dic3⋊C4C2×C4×C5semidirect
312. C4×Dic3C2×C4×C5semidirect
488. C22×C4C4×C5×D3semidirect
498. C4⋊C4C5×#67semidirect
507. C3×C5#2352semidirect
528. C2×D3C5×#117semidirect
602. C5#82272direct (N × H)
633. C3C5×#2352semidirect

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×D3×C4⋊C42
C5×#52122
C5×#49872
C5×#49772
C5×Dic3×C4⋊C42
C5×#49562
C5×#49452
C4×C5×(C2×D3)⋊C42
C5×#49332
C5×#23523
#822725