Finite Group Databasebeta

← C3×C5×#2496 #14275530

Subgroups — C3×C5×#2496 #14275530

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#126C212yesmaximal
2C3×C5×#400C212yesmaximal, complemented
3C3×C5×#397C212yesmaximal
4C3×C5×#389C211yesmaximal, characteristic, complemented
5C3×C5×#389C211yesmaximal, characteristic, complemented
6C3×C5×#387C212yesmaximal, complemented
7C3×C5×#384C211yesmaximal, characteristic, complemented
8C3×C5×#380C211yesmaximal, characteristic
9C3×C5×#380C211yesmaximal, characteristic
10C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
11C3×C4×C5×C22⋊C4C211yesmaximal, characteristic
12C5×#2496C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C3×C5×#126—28no—
15C2×C3×C5×C4⋊C4C2212yes—
16C2×C3×C5×C4⋊C4C2212yes—
17C2×C3×C5×C4⋊C4C2212yes—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2212yes—
23C2×C3×C5×C22⋊C4C2212yes—
24C2×C3×C5×C22⋊C4C2212yes—
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C42×C5C2212yes—
28C2×C3×C42×C5C2211yescharacteristic
29C2×C3×C42×C5C2211yescharacteristic
30C3×C5×#95C2211yescharacteristic
31C3×C5×#95C2211yescharacteristic
32C3×C5×#95C2212yes—
33C3×C5×#95C2212yes—
34C3×C5×#95C2212yes—
35C3×C5×#95C2212yes—
36C3×C5×#95C2212yes—
37C3×#2496C511yesmaximal, characteristic, direct product factor, Hall
38C2×C5×#126C2×C312yes—
39C5×#400C2×C312yescomplemented
40C5×#397C2×C312yes—
41C5×#389C2×C311yescharacteristic, complemented
42C5×#389C2×C311yescharacteristic, complemented
43C5×#387C2×C312yescomplemented
44C5×#384C2×C311yescharacteristic, complemented
45C5×#380C2×C311yescharacteristic
46C5×#380C2×C311yescharacteristic
47C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
48C4×C5×C22⋊C4C2×C311yescharacteristic
49C24×C3×C5C2311yescharacteristic
50C22×C3×C4×C5—22no—
51C22×C3×C4×C5—22no—
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2312yes—
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2311yescharacteristic
63C3×C5×C4⋊C4—24no—
64C3×C5×C4⋊C4—24no—
65C3×C5×C4⋊C4—24no—
66C3×C5×C4⋊C4—24no—
67C3×C5×C4⋊C4—22no—
68C3×C5×C4⋊C4—22no—
69C3×C5×C4⋊C4—22no—
70C3×C5×C4⋊C4—22no—
71C3×C5×C22⋊C4—24no—
72C3×C5×C22⋊C4—24no—
73C3×C5×C22⋊C4—22no—
74C3×C5×C22⋊C4D414yes—
75C3×C42×C5—24no—
76C3×C42×C5—22no—
77C3×C42×C5—22no—
78C2×C3×#126C2×C512yes—
79C3×#400C2×C512yescomplemented
80C3×#397C2×C512yes—
81C3×#389C2×C511yescharacteristic, complemented
82C3×#389C2×C511yescharacteristic, complemented
83C3×#387C2×C512yescomplemented
84C3×#384C2×C511yescharacteristic, complemented
85C3×#380C2×C511yescharacteristic
86C3×#380C2×C511yescharacteristic
87C3×C4×C4⋊C4C2×C511yescharacteristic, complemented
88C3×C4×C22⋊C4C2×C511yescharacteristic
89C23×C4×C5C22×C311yescharacteristic
90C5×#126—28no—
91C2×C5×C4⋊C4C22×C311yescharacteristic
92C2×C5×C4⋊C4C22×C311yescharacteristic
93C2×C5×C4⋊C4C22×C311yescharacteristic
94C2×C5×C4⋊C4C22×C311yescharacteristic
95C2×C5×C4⋊C4C22×C312yes—
96C2×C5×C4⋊C4C22×C312yes—
97C2×C5×C4⋊C4C22×C312yes—
98C2×C5×C4⋊C4C22×C312yes—
99C2×C5×C22⋊C4C22×C311yescharacteristic
100C2×C5×C22⋊C4C22×C312yes—
101C2×C5×C22⋊C4C22×C312yes—
102C2×C5×C22⋊C4C22×C311yescharacteristic
103C2×C42×C5C22×C311yescharacteristic
104C2×C42×C5C22×C311yescharacteristic
105C2×C42×C5C22×C312yes—
106C5×#95C22×C311yescharacteristic
107C5×#95C22×C311yescharacteristic
108C5×#95C22×C312yes—
109C5×#95C22×C312yes—
110C5×#95C22×C312yes—
111C5×#95C22×C312yes—
112C5×#95C22×C312yes—
113#2496C3×C511yescharacteristic, direct product factor, Sylow
114C23×C3×C5—21no—
115C23×C3×C5—21no—
116C23×C3×C5—21no—
117C23×C3×C5—21no—
118C23×C3×C5—21no—
119C23×C3×C5—21no—
120C23×C3×C5C2×D412yes—
121C23×C3×C5C2411yescharacteristic
122C2×C3×C4×C5—21no—
123C2×C3×C4×C5—21no—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—21no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—44no—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5#4112yes—
150C2×C3×C4×C5#4112yes—
151C2×C3×C4×C5#4112yes—
152C2×C3×C4×C5#4112yes—
153C23×C3×C4C22×C511yescharacteristic
154C3×#126—28no—
155C2×C3×C4⋊C4C22×C511yescharacteristic
156C2×C3×C4⋊C4C22×C511yescharacteristic
157C2×C3×C4⋊C4C22×C511yescharacteristic
158C2×C3×C4⋊C4C22×C511yescharacteristic
159C2×C3×C4⋊C4C22×C512yes—
160C2×C3×C4⋊C4C22×C512yes—
161C2×C3×C4⋊C4C22×C512yes—
162C2×C3×C4⋊C4C22×C512yes—
163C2×C3×C22⋊C4C22×C511yescharacteristic
164C2×C3×C22⋊C4C22×C512yes—
165C2×C3×C22⋊C4C22×C512yes—
166C2×C3×C22⋊C4C22×C511yescharacteristic
167C2×C3×C42C22×C511yescharacteristic
168C2×C3×C42C22×C511yescharacteristic
169C2×C3×C42C22×C512yes—
170C3×#95C22×C511yescharacteristic
171C3×#95C22×C511yescharacteristic
172C3×#95C22×C512yes—
173C3×#95C22×C512yes—
174C3×#95C22×C512yes—
175C3×#95C22×C512yes—
176C3×#95C22×C512yes—
177C24×C5C23×C311yescharacteristic
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5C23×C312yes—
182C22×C4×C5C23×C312yes—
183C22×C4×C5C23×C311yescharacteristic
184C22×C4×C5C23×C312yes—
185C22×C4×C5C23×C312yes—
186C22×C4×C5C23×C311yescharacteristic
187C22×C4×C5C23×C311yescharacteristic
188C22×C4×C5C23×C311yescharacteristic
189C22×C4×C5C23×C311yescharacteristic
190C22×C4×C5C23×C311yescharacteristic
191C5×C4⋊C4—24no—
192C5×C4⋊C4—24no—
193C5×C4⋊C4—24no—
194C5×C4⋊C4—24no—
195C5×C4⋊C4—22no—
196C5×C4⋊C4—22no—
197C5×C4⋊C4—22no—
198C5×C4⋊C4—22no—
199C5×C22⋊C4—24no—
200C5×C22⋊C4—24no—
201C5×C22⋊C4—22no—
202C5×C22⋊C4C3×D414yes—
203C42×C5—24no—
204C42×C5—22no—
205C42×C5—22no—
206C2×#126C2×C3×C512yes—
207#400C2×C3×C512yescomplemented
208#397C2×C3×C512yes—
209#389C2×C3×C511yescharacteristic, complemented
210#389C2×C3×C511yescharacteristic, complemented
211#387C2×C3×C512yescomplemented
212#384C2×C3×C511yescharacteristic, complemented
213#380C2×C3×C511yescharacteristic
214#380C2×C3×C511yescharacteristic
215C4×C4⋊C4C2×C3×C511yescharacteristic, complemented
216C4×C22⋊C4C2×C3×C511yescharacteristic
217C22×C3×C5—22no—
218C22×C3×C5—22no—
219C22×C3×C5—22no—
220C22×C3×C5—41no—
221C22×C3×C5—41no—
222C22×C3×C5—41no—
223C22×C3×C5—41no—
224C22×C3×C5C22×D411yescharacteristic
225C22×C3×C5C2×#4111yescharacteristic
226C22×C3×C5C2×#4111yescharacteristic
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5C2×#4111yescharacteristic
229C22×C3×C52−1+411yescharacteristic
230C22×C3×C52−1+411yescharacteristic
231C3×C4×C5—22no—
232C3×C4×C5—22no—
233C3×C4×C5—22no—
234C3×C4×C5—41no—
235C3×C4×C5—42no—
236C3×C4×C5—42no—
237C3×C4×C5—42no—
238C3×C4×C5—42no—
239C3×C4×C5—41no—
240C3×C4×C5#12614yescomplemented
241C24×C3C23×C511yescharacteristic
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4C23×C511yescharacteristic
246C22×C3×C4C23×C511yescharacteristic
247C22×C3×C4C23×C512yes—
248C22×C3×C4C23×C512yes—
249C22×C3×C4C23×C512yes—
250C22×C3×C4C23×C512yes—
251C22×C3×C4C23×C511yescharacteristic
252C22×C3×C4C23×C511yescharacteristic
253C22×C3×C4C23×C511yescharacteristic
254C22×C3×C4C23×C511yescharacteristic
255C3×C4⋊C4—24no—
256C3×C4⋊C4—24no—
257C3×C4⋊C4—24no—
258C3×C4⋊C4—24no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—22no—
263C3×C22⋊C4—24no—
264C3×C22⋊C4—24no—
265C3×C22⋊C4—22no—
266C3×C22⋊C4C5×D414yes—
267C3×C42—24no—
268C3×C42—22no—
269C3×C42—22no—
270C23×C5—21no—
271C23×C5—21no—
272C23×C5—21no—
273C23×C5—21no—
274C23×C5—21no—
275C23×C5—21no—
276C23×C5C2×C3×D412yes—
277C23×C5C24×C311yescharacteristic
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—22no—
295C2×C4×C5—22no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—21no—
302C2×C4×C5—44no—
303C2×C4×C5C2×C3×D412yes—
304C2×C4×C5C2×C3×D412yes—
305C2×C4×C5C3×#4112yes—
306C2×C4×C5C3×#4112yes—
307C2×C4×C5C3×#4112yes—
308C2×C4×C5C3×#4112yes—
309C23×C4C22×C3×C511yescharacteristic
310#126—28no—
311C2×C4⋊C4C22×C3×C512yes—
312C2×C4⋊C4C22×C3×C512yes—
313C2×C4⋊C4C22×C3×C512yes—
314C2×C4⋊C4C22×C3×C511yescharacteristic
315C2×C4⋊C4C22×C3×C511yescharacteristic
316C2×C4⋊C4C22×C3×C511yescharacteristic
317C2×C4⋊C4C22×C3×C511yescharacteristic
318C2×C4⋊C4C22×C3×C512yes—
319C2×C22⋊C4C22×C3×C512yes—
320C2×C22⋊C4C22×C3×C512yes—
321C2×C22⋊C4C22×C3×C511yescharacteristic
322C2×C22⋊C4C22×C3×C511yescharacteristic
323C2×C42C22×C3×C512yes—
324C2×C42C22×C3×C511yescharacteristic
325C2×C42C22×C3×C511yescharacteristic
326#95C22×C3×C511yescharacteristic
327#95C22×C3×C511yescharacteristic
328#95C22×C3×C512yes—
329#95C22×C3×C512yes—
330#95C22×C3×C512yes—
331#95C22×C3×C512yes—
332#95C22×C3×C512yes—
333C2×C3×C5—42no—
334C2×C3×C5C2×#12611yescharacteristic
335C2×C3×C5#53211yescharacteristic
336C2×C3×C5#54111yescharacteristic
337C2×C3×C5#54711yescharacteristic
338C2×C3×C5#54711yescharacteristic
339C2×C3×C5#55211yescharacteristic
340C2×C3×C5#55611yescharacteristic
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3C2×C5×D412yes—
348C23×C3C24×C511yescharacteristic
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—21no—
373C2×C3×C4—44no—
374C2×C3×C4C2×C5×D412yes—
375C2×C3×C4C2×C5×D412yes—
376C2×C3×C4C5×#4112yes—
377C2×C3×C4C5×#4112yes—
378C2×C3×C4C5×#4112yes—
379C2×C3×C4C5×#4112yes—
380C22×C5—22no—
381C22×C5—22no—
382C22×C5—22no—
383C22×C5—41no—
384C22×C5—41no—
385C22×C5—41no—
386C22×C5—41no—
387C22×C5C22×C3×D411yescharacteristic
388C22×C5C2×C3×#4111yescharacteristic
389C22×C5C2×C3×#4111yescharacteristic
390C22×C5C2×C3×#4111yescharacteristic
391C22×C5C2×C3×#4111yescharacteristic
392C22×C5C3×2−1+411yescharacteristic
393C22×C5C3×2−1+411yescharacteristic
394C4×C5—22no—
395C4×C5—22no—
396C4×C5—22no—
397C4×C5—41no—
398C4×C5—42no—
399C4×C5—42no—
400C4×C5—42no—
401C4×C5—42no—
402C4×C5—41no—
403C4×C5C3×#12614yescomplemented
404C24C23×C3×C511yescharacteristic
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4C23×C3×C511yescharacteristic
409C22×C4C23×C3×C511yescharacteristic
410C22×C4C23×C3×C512yes—
411C22×C4C23×C3×C512yes—
412C22×C4C23×C3×C512yes—
413C22×C4C23×C3×C512yes—
414C22×C4C23×C3×C511yescharacteristic
415C22×C4C23×C3×C511yescharacteristic
416C22×C4C23×C3×C511yescharacteristic
417C22×C4C23×C3×C511yescharacteristic
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—22no—
429C22⋊C4C3×C5×D414yes—
430C42—24no—
431C42—22no—
432C42—22no—
433C3×C5#249611yescharacteristic, direct product factor, Hall
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3C22×C5×D411yescharacteristic
442C22×C3C2×C5×#4111yescharacteristic
443C22×C3C2×C5×#4111yescharacteristic
444C22×C3C2×C5×#4111yescharacteristic
445C22×C3C2×C5×#4111yescharacteristic
446C22×C3C5×2−1+411yescharacteristic
447C22×C3C5×2−1+411yescharacteristic
448C3×C4—22no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—41no—
457C3×C4C5×#12614yescomplemented
458C2×C5—42no—
459C2×C5C2×C3×#12611yescharacteristic
460C2×C5C3×#53211yescharacteristic
461C2×C5C3×#54111yescharacteristic
462C2×C5C3×#54711yescharacteristic
463C2×C5C3×#54711yescharacteristic
464C2×C5C3×#55211yescharacteristic
465C2×C5C3×#55611yescharacteristic
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23C2×C3×C5×D412yes—
473C23C24×C3×C511yescharacteristic
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—44no—
499C2×C4C2×C3×C5×D412yes—
500C2×C4C2×C3×C5×D412yes—
501C2×C4C3×C5×#4112yes—
502C2×C4C3×C5×#4112yes—
503C2×C4C3×C5×#4112yes—
504C2×C4C3×C5×#4112yes—
505C2×C3—42no—
506C2×C3C2×C5×#12611yescharacteristic
507C2×C3C5×#53211yescharacteristic
508C2×C3C5×#54111yescharacteristic
509C2×C3C5×#54711yescharacteristic
510C2×C3C5×#54711yescharacteristic
511C2×C3C5×#55211yescharacteristic
512C2×C3C5×#55611yescharacteristic
513C5C3×#249611yescharacteristic, direct product factor, Sylow
514C22—22no—
515C22—22no—
516C22—22no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22C22×C3×C5×D411yescharacteristic
522C22C2×C3×C5×#4111yescharacteristic
523C22C2×C3×C5×#4111yescharacteristic
524C22C2×C3×C5×#4111yescharacteristic
525C22C2×C3×C5×#4111yescharacteristic
526C22C3×C5×2−1+411yescharacteristic
527C22C3×C5×2−1+411yescharacteristic
528C4—22no—
529C4—22no—
530C4—22no—
531C4—41no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—42no—
536C4—41no—
537C4C3×C5×#12614yescomplemented
538C3C5×#249611yescharacteristic, direct product factor, Sylow
539C2—42no—
540C2C2×C3×C5×#12611yescharacteristic
541C2C3×C5×#53211yescharacteristic
542C2C3×C5×#54111yescharacteristic
543C2C3×C5×#54711yescharacteristic
544C2C3×C5×#54711yescharacteristic
545C2C3×C5×#55211yescharacteristic
546C2C3×C5×#55611yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC24×C3×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C5×#400C2semidirect
4. C3×C5×#389C2semidirect
5. C3×C5×#389C2semidirect
6. C3×C5×#387C2semidirect
7. C3×C5×#384C2semidirect
10. C3×C4×C5×C4⋊C4C2semidirect
12. C5×#2496C3direct (N × H)
37. C3×#2496C5direct (N × H)
39. C5×#400C2×C3semidirect
41. C5×#389C2×C3semidirect
42. C5×#389C2×C3semidirect
43. C5×#387C2×C3semidirect
44. C5×#384C2×C3semidirect
47. C4×C5×C4⋊C4C2×C3semidirect
79. C3×#400C2×C5semidirect
81. C3×#389C2×C5semidirect
82. C3×#389C2×C5semidirect
83. C3×#387C2×C5semidirect
84. C3×#384C2×C5semidirect
87. C3×C4×C4⋊C4C2×C5semidirect
113. #2496C3×C5direct (N × H)
207. #400C2×C3×C5semidirect
209. #389C2×C3×C5semidirect
210. #389C2×C3×C5semidirect
211. #387C2×C3×C5semidirect
212. #384C2×C3×C5semidirect
215. C4×C4⋊C4C2×C3×C5semidirect
240. C3×C4×C5#126semidirect
403. C4×C5C3×#126semidirect
433. C3×C5#2496direct (N × H)
457. C3×C4C5×#126semidirect
513. C5C3×#2496direct (N × H)
537. C4C3×C5×#126semidirect
538. C3C5×#2496direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1262
C3×C5×#4002
C3×C5×#3972
C3×C5×#3892
C3×C5×#3872
C3×C5×#3842
C3×C5×#3802
C3×C4×C5×C4⋊C42
C3×C4×C5×C22⋊C42
C5×#24963
C3×#24965