Finite Group Databasebeta

← C3×C5×#2413 #14275447

Subgroups — C3×C5×#2413 #14275447

Order 1920.

1220 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#123C211yesmaximal, characteristic
2C2×C3×C5×#123C211yesmaximal, characteristic
3C2×C3×C5×#117C211yesmaximal, characteristic, complemented
4C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×C5×#398C212yesmaximal, complemented
6C3×C5×#396C212yesmaximal, complemented
7C3×C5×#389C212yesmaximal, complemented
8C3×C5×#388C212yesmaximal, complemented
9C3×C5×#386C211yesmaximal, characteristic
10C3×C5×#385C211yesmaximal, characteristic, complemented
11C3×C5×#381C211yesmaximal, characteristic, complemented
12C5×#2413C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2211yescharacteristic
17C3×C5×#123—24no—
18C3×C5×#123—24no—
19C3×C5×#117—24no—
20C2×C3×C5×C4⋊C4—24no—
21C2×C3×C5×C4⋊C4C2212yes—
22C2×C3×C5×C4⋊C4C2212yes—
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2212yes—
26C2×C3×C5×C4⋊C4C2211yescharacteristic
27C2×C3×C5×C4⋊C4C2212yes—
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2212yes—
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2212yes—
34C2×C3×C5×C22⋊C4C2211yescharacteristic
35C2×C3×C42×C5C2212yes—
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×C5×#95C2212yes—
39C3×C5×#95C2212yes—
40C3×#2413C511yesmaximal, characteristic, direct product factor, Hall
41C2×C5×#123C2×C311yescharacteristic
42C2×C5×#123C2×C311yescharacteristic
43C2×C5×#117C2×C311yescharacteristic, complemented
44C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
45C5×#398C2×C312yescomplemented
46C5×#396C2×C312yescomplemented
47C5×#389C2×C312yescomplemented
48C5×#388C2×C312yescomplemented
49C5×#386C2×C311yescharacteristic
50C5×#385C2×C311yescharacteristic, complemented
51C5×#381C2×C311yescharacteristic, complemented
52C24×C3×C5C2311yescharacteristic
53C24×C3×C5C2311yescharacteristic
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—24no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—22no—
64C22×C3×C4×C5D414yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2312yes—
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2312yes—
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2312yes—
74C3×C5×C4⋊C4—24no—
75C3×C5×C4⋊C4—24no—
76C3×C5×C4⋊C4—24no—
77C3×C5×C4⋊C4—22no—
78C3×C5×C4⋊C4—22no—
79C3×C5×C4⋊C4—24no—
80C3×C5×C4⋊C4—24no—
81C3×C5×C22⋊C4—22no—
82C3×C5×C22⋊C4—22no—
83C3×C5×C22⋊C4—22no—
84C3×C5×C22⋊C4—22no—
85C3×C5×C22⋊C4—24no—
86C3×C5×C22⋊C4—24no—
87C3×C5×C22⋊C4D414yes—
88C3×C42×C5—24no—
89C2×C3×#123C2×C511yescharacteristic
90C2×C3×#123C2×C511yescharacteristic
91C2×C3×#117C2×C511yescharacteristic, complemented
92C22×C3×C4⋊C4C2×C511yescharacteristic, complemented
93C3×#398C2×C512yescomplemented
94C3×#396C2×C512yescomplemented
95C3×#389C2×C512yescomplemented
96C3×#388C2×C512yescomplemented
97C3×#386C2×C511yescharacteristic
98C3×#385C2×C511yescharacteristic, complemented
99C3×#381C2×C511yescharacteristic, complemented
100C22×C5×D4C22×C311yescharacteristic
101C23×C4×C5C22×C311yescharacteristic
102C23×C4×C5C22×C311yescharacteristic
103C23×C4×C5C22×C311yescharacteristic
104C5×#123—24no—
105C5×#123—24no—
106C5×#117—24no—
107C2×C5×C4⋊C4—24no—
108C2×C5×C4⋊C4C22×C312yes—
109C2×C5×C4⋊C4C22×C312yes—
110C2×C5×C4⋊C4C22×C311yescharacteristic
111C2×C5×C4⋊C4C22×C312yes—
112C2×C5×C4⋊C4C22×C312yes—
113C2×C5×C4⋊C4C22×C312yes—
114C2×C5×C4⋊C4C22×C311yescharacteristic
115C2×C5×C22⋊C4C22×C311yescharacteristic
116C2×C5×C22⋊C4C22×C311yescharacteristic
117C2×C5×C22⋊C4C22×C312yes—
118C2×C5×C22⋊C4C22×C311yescharacteristic
119C2×C5×C22⋊C4C22×C312yes—
120C2×C5×C22⋊C4C22×C311yescharacteristic
121C2×C5×C22⋊C4C22×C311yescharacteristic
122C2×C42×C5C22×C312yes—
123C5×#95C22×C312yes—
124C5×#95C22×C312yes—
125C5×#95C22×C312yes—
126C5×#95C22×C312yes—
127#2413C3×C511yescharacteristic, direct product factor, Sylow
128C23×C3×C5—22no—
129C23×C3×C5—22no—
130C23×C3×C5—21no—
131C23×C3×C5—21no—
132C23×C3×C5—22no—
133C23×C3×C5—21no—
134C23×C3×C5—22no—
135C23×C3×C5C2×D412yes—
136C23×C3×C5C2×D412yes—
137C23×C3×C5#4112yes—
138C23×C3×C5C2411yescharacteristic
139C3×C5×D4—44no—
140C2×C3×C4×C5—28no—
141C2×C3×C4×C5—28no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—44no—
164C2×C3×C4×C5C2×D414yes—
165C2×C3×C4×C5C2×D412yes—
166C2×C3×C4×C5C2×D412yes—
167C2×C3×C4×C5#4114yes—
168C22×C3×D4C22×C511yescharacteristic
169C23×C3×C4C22×C511yescharacteristic
170C23×C3×C4C22×C511yescharacteristic
171C23×C3×C4C22×C511yescharacteristic
172C3×#123—24no—
173C3×#123—24no—
174C3×#117—24no—
175C2×C3×C4⋊C4—24no—
176C2×C3×C4⋊C4C22×C512yes—
177C2×C3×C4⋊C4C22×C512yes—
178C2×C3×C4⋊C4C22×C511yescharacteristic
179C2×C3×C4⋊C4C22×C512yes—
180C2×C3×C4⋊C4C22×C512yes—
181C2×C3×C4⋊C4C22×C512yes—
182C2×C3×C4⋊C4C22×C511yescharacteristic
183C2×C3×C22⋊C4C22×C511yescharacteristic
184C2×C3×C22⋊C4C22×C511yescharacteristic
185C2×C3×C22⋊C4C22×C512yes—
186C2×C3×C22⋊C4C22×C511yescharacteristic
187C2×C3×C22⋊C4C22×C512yes—
188C2×C3×C22⋊C4C22×C511yescharacteristic
189C2×C3×C22⋊C4C22×C511yescharacteristic
190C2×C3×C42C22×C512yes—
191C3×#95C22×C512yes—
192C3×#95C22×C512yes—
193C3×#95C22×C512yes—
194C3×#95C22×C512yes—
195C24×C5C23×C311yescharacteristic
196C24×C5C23×C311yescharacteristic
197C2×C5×D4—22no—
198C2×C5×D4—22no—
199C2×C5×D4—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—24no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5C3×D414yes—
208C22×C4×C5C23×C312yes—
209C22×C4×C5C23×C311yescharacteristic
210C22×C4×C5C23×C311yescharacteristic
211C22×C4×C5C23×C312yes—
212C22×C4×C5C23×C311yescharacteristic
213C22×C4×C5C23×C311yescharacteristic
214C22×C4×C5C23×C312yes—
215C22×C4×C5C23×C311yescharacteristic
216C22×C4×C5C23×C312yes—
217C5×C4⋊C4—24no—
218C5×C4⋊C4—24no—
219C5×C4⋊C4—24no—
220C5×C4⋊C4—22no—
221C5×C4⋊C4—22no—
222C5×C4⋊C4—24no—
223C5×C4⋊C4—24no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—22no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4—24no—
229C5×C22⋊C4—24no—
230C5×C22⋊C4C3×D414yes—
231C42×C5—24no—
232C2×#123C2×C3×C511yescharacteristic
233C2×#123C2×C3×C511yescharacteristic
234C2×#117C2×C3×C511yescharacteristic, complemented
235C22×C4⋊C4C2×C3×C511yescharacteristic, complemented
236#398C2×C3×C512yescomplemented
237#396C2×C3×C512yescomplemented
238#389C2×C3×C512yescomplemented
239#388C2×C3×C512yescomplemented
240#386C2×C3×C511yescharacteristic
241#385C2×C3×C511yescharacteristic, complemented
242#381C2×C3×C511yescharacteristic, complemented
243C22×C3×C5—22no—
244C22×C3×C5—22no—
245C22×C3×C5—24no—
246C22×C3×C5—24no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5—41no—
250C22×C3×C5—42no—
251C22×C3×C5—42no—
252C22×C3×C5#12114yes—
253C22×C3×C5C22×D411yescharacteristic
254C22×C3×C5C22×D411yescharacteristic
255C22×C3×C5C2×#4111yescharacteristic
256C22×C3×C5C2×#4112yes—
257C22×C3×C52−1+412yes—
258C3×C4×C5—22no—
259C3×C4×C5—22no—
260C3×C4×C5—24no—
261C3×C4×C5—24no—
262C3×C4×C5—42no—
263C3×C4×C5—41no—
264C3×C4×C5—41no—
265C3×C4×C5—41no—
266C3×C4×C5—42no—
267C24×C3C23×C511yescharacteristic
268C24×C3C23×C511yescharacteristic
269C2×C3×D4—22no—
270C2×C3×D4—22no—
271C2×C3×D4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—24no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4C5×D414yes—
280C22×C3×C4C23×C511yescharacteristic
281C22×C3×C4C23×C512yes—
282C22×C3×C4C23×C511yescharacteristic
283C22×C3×C4C23×C512yes—
284C22×C3×C4C23×C511yescharacteristic
285C22×C3×C4C23×C512yes—
286C22×C3×C4C23×C511yescharacteristic
287C22×C3×C4C23×C511yescharacteristic
288C22×C3×C4C23×C512yes—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—24no—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—24no—
295C3×C4⋊C4—24no—
296C3×C22⋊C4—22no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—22no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4C5×D414yes—
303C3×C42—24no—
304C23×C5—22no—
305C23×C5—22no—
306C23×C5—21no—
307C23×C5—21no—
308C23×C5—22no—
309C23×C5—21no—
310C23×C5—22no—
311C23×C5C2×C3×D412yes—
312C23×C5C2×C3×D412yes—
313C23×C5C3×#4112yes—
314C23×C5C24×C311yescharacteristic
315C5×D4—44no—
316C2×C4×C5—28no—
317C2×C4×C5—28no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—21no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—44no—
340C2×C4×C5C2×C3×D414yes—
341C2×C4×C5C2×C3×D412yes—
342C2×C4×C5C2×C3×D412yes—
343C2×C4×C5C3×#4114yes—
344C22×D4C22×C3×C511yescharacteristic
345C23×C4C22×C3×C511yescharacteristic
346C23×C4C22×C3×C511yescharacteristic
347C23×C4C22×C3×C511yescharacteristic
348#123—24no—
349#123—24no—
350#117—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4C22×C3×C512yes—
353C2×C4⋊C4C22×C3×C512yes—
354C2×C4⋊C4C22×C3×C512yes—
355C2×C4⋊C4C22×C3×C511yescharacteristic
356C2×C4⋊C4C22×C3×C512yes—
357C2×C4⋊C4C22×C3×C511yescharacteristic
358C2×C4⋊C4C22×C3×C512yes—
359C2×C22⋊C4C22×C3×C511yescharacteristic
360C2×C22⋊C4C22×C3×C511yescharacteristic
361C2×C22⋊C4C22×C3×C511yescharacteristic
362C2×C22⋊C4C22×C3×C512yes—
363C2×C22⋊C4C22×C3×C511yescharacteristic
364C2×C22⋊C4C22×C3×C512yes—
365C2×C22⋊C4C22×C3×C511yescharacteristic
366C2×C42C22×C3×C512yes—
367#95C22×C3×C512yes—
368#95C22×C3×C512yes—
369#95C22×C3×C512yes—
370#95C22×C3×C512yes—
371C2×C3×C5—24no—
372C2×C3×C5—81no—
373C2×C3×C5C2×#12111yescharacteristic
374C2×C3×C5#52511yescharacteristic
375C2×C3×C5#53611yescharacteristic
376C2×C3×C5#54712yes—
377C2×C3×C5#55212yes—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—22no—
383C23×C3—21no—
384C23×C3—22no—
385C23×C3C2×C5×D412yes—
386C23×C3C2×C5×D412yes—
387C23×C3C5×#4112yes—
388C23×C3C24×C511yescharacteristic
389C3×D4—44no—
390C2×C3×C4—28no—
391C2×C3×C4—28no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—44no—
414C2×C3×C4C2×C5×D414yes—
415C2×C3×C4C2×C5×D412yes—
416C2×C3×C4C2×C5×D412yes—
417C2×C3×C4C5×#4114yes—
418C22×C5—22no—
419C22×C5—22no—
420C22×C5—24no—
421C22×C5—24no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5—41no—
425C22×C5—42no—
426C22×C5—42no—
427C22×C5C3×#12114yes—
428C22×C5C22×C3×D411yescharacteristic
429C22×C5C22×C3×D411yescharacteristic
430C22×C5C2×C3×#4111yescharacteristic
431C22×C5C2×C3×#4112yes—
432C22×C5C3×2−1+412yes—
433C4×C5—22no—
434C4×C5—22no—
435C4×C5—24no—
436C4×C5—24no—
437C4×C5—42no—
438C4×C5—41no—
439C4×C5—41no—
440C4×C5—41no—
441C4×C5—42no—
442C24C23×C3×C511yescharacteristic
443C24C23×C3×C511yescharacteristic
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4C3×C5×D414yes—
455C22×C4C23×C3×C511yescharacteristic
456C22×C4C23×C3×C512yes—
457C22×C4C23×C3×C511yescharacteristic
458C22×C4C23×C3×C512yes—
459C22×C4C23×C3×C511yescharacteristic
460C22×C4C23×C3×C512yes—
461C22×C4C23×C3×C511yescharacteristic
462C22×C4C23×C3×C511yescharacteristic
463C22×C4C23×C3×C512yes—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—24no—
470C4⋊C4—24no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4C3×C5×D414yes—
478C42—24no—
479C3×C5#241311yescharacteristic, direct product factor, Hall
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—24no—
483C22×C3—24no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3C5×#12114yes—
490C22×C3C22×C5×D411yescharacteristic
491C22×C3C22×C5×D411yescharacteristic
492C22×C3C2×C5×#4111yescharacteristic
493C22×C3C2×C5×#4112yes—
494C22×C3C5×2−1+412yes—
495C3×C4—22no—
496C3×C4—22no—
497C3×C4—24no—
498C3×C4—24no—
499C3×C4—42no—
500C3×C4—41no—
501C3×C4—41no—
502C3×C4—41no—
503C3×C4—42no—
504C2×C5—24no—
505C2×C5—81no—
506C2×C5C2×C3×#12111yescharacteristic
507C2×C5C3×#52511yescharacteristic
508C2×C5C3×#53611yescharacteristic
509C2×C5C3×#54712yes—
510C2×C5C3×#55212yes—
511C23—22no—
512C23—22no—
513C23—21no—
514C23—21no—
515C23—22no—
516C23—21no—
517C23—22no—
518C23C2×C3×C5×D412yes—
519C23C2×C3×C5×D412yes—
520C23C3×C5×#4112yes—
521C23C24×C3×C511yescharacteristic
522D4—44no—
523C2×C4—28no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—28no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—44no—
547C2×C4C2×C3×C5×D414yes—
548C2×C4C2×C3×C5×D412yes—
549C2×C4C2×C3×C5×D412yes—
550C2×C4C3×C5×#4114yes—
551C2×C3—24no—
552C2×C3—81no—
553C2×C3C2×C5×#12111yescharacteristic
554C2×C3C5×#52511yescharacteristic
555C2×C3C5×#53611yescharacteristic
556C2×C3C5×#54712yes—
557C2×C3C5×#55212yes—
558C5C3×#241311yescharacteristic, direct product factor, Sylow
559C22—22no—
560C22—22no—
561C22—24no—
562C22—24no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—42no—
567C22—42no—
568C22C3×C5×#12114yes—
569C22C22×C3×C5×D411yescharacteristic
570C22C22×C3×C5×D411yescharacteristic
571C22C2×C3×C5×#4111yescharacteristic
572C22C2×C3×C5×#4112yes—
573C22C3×C5×2−1+412yes—
574C4—22no—
575C4—22no—
576C4—24no—
577C4—24no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C3C5×#241311yescharacteristic, direct product factor, Sylow
584C2—24no—
585C2—81no—
586C2C2×C3×C5×#12111yescharacteristic
587C2C3×C5×#52511yescharacteristic
588C2C3×C5×#53611yescharacteristic
589C2C3×C5×#54712yes—
590C2C3×C5×#55212yes—
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC22×C3×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C3×C5×#117C2semidirect
4. C22×C3×C5×C4⋊C4C2semidirect
5. C3×C5×#398C2semidirect
6. C3×C5×#396C2semidirect
7. C3×C5×#389C2semidirect
8. C3×C5×#388C2semidirect
10. C3×C5×#385C2semidirect
11. C3×C5×#381C2semidirect
12. C5×#2413C3direct (N × H)
40. C3×#2413C5direct (N × H)
43. C2×C5×#117C2×C3semidirect
44. C22×C5×C4⋊C4C2×C3semidirect
45. C5×#398C2×C3semidirect
46. C5×#396C2×C3semidirect
47. C5×#389C2×C3semidirect
48. C5×#388C2×C3semidirect
50. C5×#385C2×C3semidirect
51. C5×#381C2×C3semidirect
91. C2×C3×#117C2×C5semidirect
92. C22×C3×C4⋊C4C2×C5semidirect
93. C3×#398C2×C5semidirect
94. C3×#396C2×C5semidirect
95. C3×#389C2×C5semidirect
96. C3×#388C2×C5semidirect
98. C3×#385C2×C5semidirect
99. C3×#381C2×C5semidirect
127. #2413C3×C5direct (N × H)
234. C2×#117C2×C3×C5semidirect
235. C22×C4⋊C4C2×C3×C5semidirect
236. #398C2×C3×C5semidirect
237. #396C2×C3×C5semidirect
238. #389C2×C3×C5semidirect
239. #388C2×C3×C5semidirect
241. #385C2×C3×C5semidirect
242. #381C2×C3×C5semidirect
479. C3×C5#2413direct (N × H)
558. C5C3×#2413direct (N × H)
583. C3C5×#2413direct (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×#1232
C2×C3×C5×#1172
C22×C3×C5×C4⋊C42
C3×C5×#3982
C3×C5×#3962
C3×C5×#3892
C3×C5×#3882
C3×C5×#3862
C3×C5×#3852
C3×C5×#3812
C5×#24133
C3×#24135