Finite Group Databasebeta

← C3×C5×#2543 #14275577

Subgroups — C3×C5×#2543 #14275577

Order 1920.

1448 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic, complemented
2C2×C3×C5×#121C212yesmaximal, complemented
3C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
4C3×C5×#398C211yesmaximal, characteristic, complemented
5C3×C5×#397C211yesmaximal, characteristic, complemented
6C3×C5×#394C211yesmaximal, characteristic, complemented
7C3×C5×#392C211yesmaximal, characteristic, complemented
8C3×C5×#388C212yesmaximal, complemented
9C3×C5×#386C212yesmaximal, complemented
10C3×C5×#386C212yesmaximal, complemented
11C2×C3×C5×#95C211yesmaximal, characteristic, complemented
12C5×#2543C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2212yes—
14C22×C3×C5×D4C2212yes—
15C22×C3×C5×D4C2211yescharacteristic
16C22×C3×C5×D4C2211yescharacteristic
17C23×C3×C4×C5C2212yes—
18C23×C3×C4×C5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C3×C5×#121—28no—
21C3×C5×#121—24no—
22C3×C4×C5×D4—24no—
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2212yes—
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2212yes—
29C2×C3×C5×C22⋊C4C2212yes—
30C2×C3×C5×C22⋊C4C2212yes—
31C2×C3×C5×C22⋊C4C2212yes—
32C2×C3×C5×C22⋊C4C2212yes—
33C2×C3×C42×C5C2211yescharacteristic
34C3×C5×#95C2212yes—
35C3×C5×#95C2211yescharacteristic
36C3×C5×#95C2211yescharacteristic
37C3×C5×#95C2212yes—
38C3×C5×#95C2212yes—
39C3×#2543C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#121C2×C311yescharacteristic, complemented
41C2×C5×#121C2×C312yescomplemented
42C2×C4×C5×D4C2×C311yescharacteristic, complemented
43C5×#398C2×C311yescharacteristic, complemented
44C5×#397C2×C311yescharacteristic, complemented
45C5×#394C2×C311yescharacteristic, complemented
46C5×#392C2×C311yescharacteristic, complemented
47C5×#388C2×C312yescomplemented
48C5×#386C2×C312yescomplemented
49C5×#386C2×C312yescomplemented
50C2×C5×#95C2×C311yescharacteristic, complemented
51C24×C3×C5C2312yes—
52C24×C3×C5C2311yescharacteristic
53C24×C3×C5C2311yescharacteristic
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4—24no—
57C2×C3×C5×D4—24no—
58C2×C3×C5×D4—24no—
59C2×C3×C5×D4—24no—
60C2×C3×C5×D4—22no—
61C2×C3×C5×D4—24no—
62C2×C3×C5×D4—42no—
63C2×C3×C5×D4—42no—
64C2×C3×C5×D4D414yescomplemented
65C22×C3×C4×C5—24no—
66C22×C3×C4×C5—22no—
67C22×C3×C4×C5—24no—
68C22×C3×C4×C5—42no—
69C22×C3×C4×C5—42no—
70C22×C3×C4×C5—42no—
71C22×C3×C4×C5D414yescomplemented
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2312yes—
75C22×C3×C4×C5C2312yes—
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2312yes—
80C3×C5×C4⋊C4—22no—
81C3×C5×C4⋊C4—24no—
82C3×C5×C4⋊C4—22no—
83C3×C5×C22⋊C4—22no—
84C3×C5×C22⋊C4—24no—
85C3×C5×C22⋊C4—22no—
86C3×C5×C22⋊C4—24no—
87C3×C5×C22⋊C4—24no—
88C3×C5×C22⋊C4—24no—
89C3×C5×C22⋊C4—42no—
90C3×C42×C5—22no—
91C2×C3×#121C2×C511yescharacteristic, complemented
92C2×C3×#121C2×C512yescomplemented
93C2×C3×C4×D4C2×C511yescharacteristic, complemented
94C3×#398C2×C511yescharacteristic, complemented
95C3×#397C2×C511yescharacteristic, complemented
96C3×#394C2×C511yescharacteristic, complemented
97C3×#392C2×C511yescharacteristic, complemented
98C3×#388C2×C512yescomplemented
99C3×#386C2×C512yescomplemented
100C3×#386C2×C512yescomplemented
101C2×C3×#95C2×C511yescharacteristic, complemented
102C22×C5×D4C22×C312yes—
103C22×C5×D4C22×C312yes—
104C22×C5×D4C22×C311yescharacteristic
105C22×C5×D4C22×C311yescharacteristic
106C23×C4×C5C22×C312yes—
107C23×C4×C5C22×C311yescharacteristic
108C23×C4×C5C22×C311yescharacteristic
109C5×#121—28no—
110C5×#121—24no—
111C4×C5×D4—24no—
112C2×C5×C4⋊C4C22×C312yes—
113C2×C5×C4⋊C4C22×C311yescharacteristic
114C2×C5×C4⋊C4C22×C311yescharacteristic
115C2×C5×C22⋊C4C22×C311yescharacteristic
116C2×C5×C22⋊C4C22×C312yes—
117C2×C5×C22⋊C4C22×C312yes—
118C2×C5×C22⋊C4C22×C312yes—
119C2×C5×C22⋊C4C22×C312yes—
120C2×C5×C22⋊C4C22×C311yescharacteristic
121C2×C5×C22⋊C4C22×C312yes—
122C2×C42×C5C22×C311yescharacteristic
123C5×#95C22×C312yes—
124C5×#95C22×C311yescharacteristic
125C5×#95C22×C311yescharacteristic
126C5×#95C22×C312yes—
127C5×#95C22×C312yes—
128#2543C3×C511yescharacteristic, direct product factor, Sylow
129C23×C3×C5—22no—
130C23×C3×C5—22no—
131C23×C3×C5—21no—
132C23×C3×C5—21no—
133C23×C3×C5—22no—
134C23×C3×C5—22no—
135C23×C3×C5—22no—
136C23×C3×C5—22no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—22no—
140C23×C3×C5—22no—
141C23×C3×C5—22no—
142C23×C3×C5C2×D412yes—
143C23×C3×C5C2×D412yes—
144C23×C3×C5C2×D412yes—
145C23×C3×C5#4112yes—
146C23×C3×C5C2411yescharacteristic
147C3×C5×D4—28no—
148C3×C5×D4—48no—
149C3×C5×D4—44no—
150C3×C5×D4—48no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—21no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5—22no—
167C2×C3×C4×C5—44no—
168C2×C3×C4×C5—48no—
169C2×C3×C4×C5—44no—
170C2×C3×C4×C5C2×D412yes—
171C2×C3×C4×C5C2×D412yes—
172C2×C3×C4×C5C2×D412yes—
173C2×C3×C4×C5#4114yes—
174C22×C3×D4C22×C512yes—
175C22×C3×D4C22×C512yes—
176C22×C3×D4C22×C511yescharacteristic
177C22×C3×D4C22×C511yescharacteristic
178C23×C3×C4C22×C512yes—
179C23×C3×C4C22×C511yescharacteristic
180C23×C3×C4C22×C511yescharacteristic
181C3×#121—28no—
182C3×#121—24no—
183C3×C4×D4—24no—
184C2×C3×C4⋊C4C22×C512yes—
185C2×C3×C4⋊C4C22×C511yescharacteristic
186C2×C3×C4⋊C4C22×C511yescharacteristic
187C2×C3×C22⋊C4C22×C511yescharacteristic
188C2×C3×C22⋊C4C22×C512yes—
189C2×C3×C22⋊C4C22×C512yes—
190C2×C3×C22⋊C4C22×C512yes—
191C2×C3×C22⋊C4C22×C512yes—
192C2×C3×C22⋊C4C22×C511yescharacteristic
193C2×C3×C22⋊C4C22×C512yes—
194C2×C3×C42C22×C511yescharacteristic
195C3×#95C22×C512yes—
196C3×#95C22×C511yescharacteristic
197C3×#95C22×C511yescharacteristic
198C3×#95C22×C512yes—
199C3×#95C22×C512yes—
200C24×C5C23×C312yes—
201C24×C5C23×C311yescharacteristic
202C24×C5C23×C311yescharacteristic
203C2×C5×D4—22no—
204C2×C5×D4—22no—
205C2×C5×D4—24no—
206C2×C5×D4—24no—
207C2×C5×D4—24no—
208C2×C5×D4—24no—
209C2×C5×D4—22no—
210C2×C5×D4—24no—
211C2×C5×D4—42no—
212C2×C5×D4—42no—
213C2×C5×D4C3×D414yescomplemented
214C22×C4×C5—24no—
215C22×C4×C5—22no—
216C22×C4×C5—24no—
217C22×C4×C5—42no—
218C22×C4×C5—42no—
219C22×C4×C5—42no—
220C22×C4×C5C3×D414yescomplemented
221C22×C4×C5C23×C311yescharacteristic
222C22×C4×C5C23×C311yescharacteristic
223C22×C4×C5C23×C312yes—
224C22×C4×C5C23×C312yes—
225C22×C4×C5C23×C311yescharacteristic
226C22×C4×C5C23×C311yescharacteristic
227C22×C4×C5C23×C311yescharacteristic
228C22×C4×C5C23×C312yes—
229C5×C4⋊C4—22no—
230C5×C4⋊C4—24no—
231C5×C4⋊C4—22no—
232C5×C22⋊C4—22no—
233C5×C22⋊C4—24no—
234C5×C22⋊C4—22no—
235C5×C22⋊C4—24no—
236C5×C22⋊C4—24no—
237C5×C22⋊C4—24no—
238C5×C22⋊C4—42no—
239C42×C5—22no—
240C2×#121C2×C3×C511yescharacteristic, complemented
241C2×#121C2×C3×C512yescomplemented
242C2×C4×D4C2×C3×C511yescharacteristic, complemented
243#398C2×C3×C511yescharacteristic, complemented
244#397C2×C3×C511yescharacteristic, complemented
245#394C2×C3×C511yescharacteristic, complemented
246#392C2×C3×C511yescharacteristic, complemented
247#388C2×C3×C512yescomplemented
248#386C2×C3×C512yescomplemented
249#386C2×C3×C512yescomplemented
250C2×#95C2×C3×C511yescharacteristic, complemented
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—24no—
254C22×C3×C5—24no—
255C22×C3×C5—22no—
256C22×C3×C5—24no—
257C22×C3×C5—41no—
258C22×C3×C5—41no—
259C22×C3×C5—42no—
260C22×C3×C5—42no—
261C22×C3×C5—42no—
262C22×C3×C5—42no—
263C22×C3×C5—42no—
264C22×C3×C5—42no—
265C22×C3×C5—42no—
266C22×C3×C5—42no—
267C22×C3×C5#12114yes—
268C22×C3×C5C22×D411yescharacteristic
269C22×C3×C5C22×D411yescharacteristic
270C22×C3×C5C2×#4111yescharacteristic
271C22×C3×C5C2×#4112yes—
272C22×C3×C5H(5,𝔽2)12yes—
273C3×C4×C5—22no—
274C3×C4×C5—22no—
275C3×C4×C5—22no—
276C3×C4×C5—24no—
277C3×C4×C5—42no—
278C3×C4×C5—41no—
279C3×C4×C5—41no—
280C3×C4×C5—42no—
281C24×C3C23×C512yes—
282C24×C3C23×C511yescharacteristic
283C24×C3C23×C511yescharacteristic
284C2×C3×D4—22no—
285C2×C3×D4—22no—
286C2×C3×D4—24no—
287C2×C3×D4—24no—
288C2×C3×D4—24no—
289C2×C3×D4—24no—
290C2×C3×D4—22no—
291C2×C3×D4—24no—
292C2×C3×D4—42no—
293C2×C3×D4—42no—
294C2×C3×D4C5×D414yescomplemented
295C22×C3×C4—24no—
296C22×C3×C4—22no—
297C22×C3×C4—24no—
298C22×C3×C4—42no—
299C22×C3×C4—42no—
300C22×C3×C4—42no—
301C22×C3×C4C5×D414yescomplemented
302C22×C3×C4C23×C512yes—
303C22×C3×C4C23×C511yescharacteristic
304C22×C3×C4C23×C511yescharacteristic
305C22×C3×C4C23×C512yes—
306C22×C3×C4C23×C511yescharacteristic
307C22×C3×C4C23×C511yescharacteristic
308C22×C3×C4C23×C511yescharacteristic
309C22×C3×C4C23×C512yes—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—22no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—24no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—24no—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—24no—
319C3×C22⋊C4—42no—
320C3×C42—22no—
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—21no—
324C23×C5—21no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5C2×C3×D412yes—
335C23×C5C2×C3×D412yes—
336C23×C5C2×C3×D412yes—
337C23×C5C3×#4112yes—
338C23×C5C24×C311yescharacteristic
339C5×D4—28no—
340C5×D4—48no—
341C5×D4—44no—
342C5×D4—48no—
343C2×C4×C5—21no—
344C2×C4×C5—22no—
345C2×C4×C5—21no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—21no—
350C2×C4×C5—22no—
351C2×C4×C5—21no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—44no—
360C2×C4×C5—48no—
361C2×C4×C5—44no—
362C2×C4×C5C2×C3×D412yes—
363C2×C4×C5C2×C3×D412yes—
364C2×C4×C5C2×C3×D412yes—
365C2×C4×C5C3×#4114yes—
366C22×D4C22×C3×C512yes—
367C22×D4C22×C3×C512yes—
368C22×D4C22×C3×C511yescharacteristic
369C22×D4C22×C3×C511yescharacteristic
370C23×C4C22×C3×C512yes—
371C23×C4C22×C3×C511yescharacteristic
372C23×C4C22×C3×C511yescharacteristic
373#121—28no—
374#121—24no—
375C4×D4—24no—
376C2×C4⋊C4C22×C3×C511yescharacteristic
377C2×C4⋊C4C22×C3×C512yes—
378C2×C4⋊C4C22×C3×C511yescharacteristic
379C2×C22⋊C4C22×C3×C511yescharacteristic
380C2×C22⋊C4C22×C3×C511yescharacteristic
381C2×C22⋊C4C22×C3×C512yes—
382C2×C22⋊C4C22×C3×C512yes—
383C2×C22⋊C4C22×C3×C512yes—
384C2×C22⋊C4C22×C3×C512yes—
385C2×C22⋊C4C22×C3×C512yes—
386C2×C42C22×C3×C511yescharacteristic
387#95C22×C3×C512yes—
388#95C22×C3×C511yescharacteristic
389#95C22×C3×C511yescharacteristic
390#95C22×C3×C512yes—
391#95C22×C3×C512yes—
392C2×C3×C5—24no—
393C2×C3×C5—42no—
394C2×C3×C5—82no—
395C2×C3×C5C2×#12111yescharacteristic
396C2×C3×C5#53211yescharacteristic
397C2×C3×C5#53411yescharacteristic
398C2×C3×C5#54612yes—
399C2×C3×C5#55312yes—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3C2×C5×D412yes—
414C23×C3C2×C5×D412yes—
415C23×C3C2×C5×D412yes—
416C23×C3C5×#4112yes—
417C23×C3C24×C511yescharacteristic
418C3×D4—28no—
419C3×D4—48no—
420C3×D4—44no—
421C3×D4—48no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—44no—
439C2×C3×C4—48no—
440C2×C3×C4—44no—
441C2×C3×C4C2×C5×D412yes—
442C2×C3×C4C2×C5×D412yes—
443C2×C3×C4C2×C5×D412yes—
444C2×C3×C4C5×#4114yes—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—24no—
448C22×C5—24no—
449C22×C5—22no—
450C22×C5—24no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5—42no—
454C22×C5—42no—
455C22×C5—42no—
456C22×C5—42no—
457C22×C5—42no—
458C22×C5—42no—
459C22×C5—42no—
460C22×C5—42no—
461C22×C5C3×#12114yes—
462C22×C5C22×C3×D411yescharacteristic
463C22×C5C22×C3×D411yescharacteristic
464C22×C5C2×C3×#4111yescharacteristic
465C22×C5C2×C3×#4112yes—
466C22×C5C3×H(5,𝔽2)12yes—
467C4×C5—22no—
468C4×C5—22no—
469C4×C5—22no—
470C4×C5—24no—
471C4×C5—42no—
472C4×C5—41no—
473C4×C5—41no—
474C4×C5—42no—
475C24C23×C3×C512yes—
476C24C23×C3×C511yescharacteristic
477C24C23×C3×C511yescharacteristic
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—24no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4C3×C5×D414yescomplemented
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4C3×C5×D414yescomplemented
496C22×C4C23×C3×C512yes—
497C22×C4C23×C3×C511yescharacteristic
498C22×C4C23×C3×C511yescharacteristic
499C22×C4C23×C3×C512yes—
500C22×C4C23×C3×C511yescharacteristic
501C22×C4C23×C3×C511yescharacteristic
502C22×C4C23×C3×C511yescharacteristic
503C22×C4C23×C3×C512yes—
504C4⋊C4—22no—
505C4⋊C4—24no—
506C4⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—24no—
509C22⋊C4—22no—
510C22⋊C4—24no—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—42no—
514C42—22no—
515C3×C5#254311yescharacteristic, direct product factor, Hall
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—24no—
519C22×C3—24no—
520C22×C3—22no—
521C22×C3—24no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—42no—
530C22×C3—42no—
531C22×C3—42no—
532C22×C3C5×#12114yes—
533C22×C3C22×C5×D411yescharacteristic
534C22×C3C22×C5×D411yescharacteristic
535C22×C3C2×C5×#4111yescharacteristic
536C22×C3C2×C5×#4112yes—
537C22×C3C5×H(5,𝔽2)12yes—
538C3×C4—22no—
539C3×C4—22no—
540C3×C4—22no—
541C3×C4—24no—
542C3×C4—42no—
543C3×C4—41no—
544C3×C4—41no—
545C3×C4—42no—
546C2×C5—24no—
547C2×C5—42no—
548C2×C5—82no—
549C2×C5C2×C3×#12111yescharacteristic
550C2×C5C3×#53211yescharacteristic
551C2×C5C3×#53411yescharacteristic
552C2×C5C3×#54612yes—
553C2×C5C3×#55312yes—
554C23—22no—
555C23—22no—
556C23—21no—
557C23—21no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23C2×C3×C5×D412yes—
568C23C2×C3×C5×D412yes—
569C23C2×C3×C5×D412yes—
570C23C3×C5×#4112yes—
571C23C24×C3×C511yescharacteristic
572D4—28no—
573D4—48no—
574D4—44no—
575D4—48no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—44no—
593C2×C4—48no—
594C2×C4—44no—
595C2×C4C2×C3×C5×D412yes—
596C2×C4C2×C3×C5×D412yes—
597C2×C4C2×C3×C5×D412yes—
598C2×C4C3×C5×#4114yes—
599C2×C3—24no—
600C2×C3—42no—
601C2×C3—82no—
602C2×C3C2×C5×#12111yescharacteristic
603C2×C3C5×#53211yescharacteristic
604C2×C3C5×#53411yescharacteristic
605C2×C3C5×#54612yes—
606C2×C3C5×#55312yes—
607C5C3×#254311yescharacteristic, direct product factor, Sylow
608C22—22no—
609C22—22no—
610C22—24no—
611C22—24no—
612C22—22no—
613C22—24no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22C3×C5×#12114yes—
625C22C22×C3×C5×D411yescharacteristic
626C22C22×C3×C5×D411yescharacteristic
627C22C2×C3×C5×#4111yescharacteristic
628C22C2×C3×C5×#4112yes—
629C22C3×C5×H(5,𝔽2)12yes—
630C4—22no—
631C4—22no—
632C4—22no—
633C4—24no—
634C4—42no—
635C4—41no—
636C4—41no—
637C4—42no—
638C3C5×#254311yescharacteristic, direct product factor, Sylow
639C2—24no—
640C2—42no—
641C2—82no—
642C2C2×C3×C5×#12111yescharacteristic
643C2C3×C5×#53211yescharacteristic
644C2C3×C5×#53411yescharacteristic
645C2C3×C5×#54612yes—
646C2C3×C5×#55312yes—
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#121C2semidirect
2. C2×C3×C5×#121C2semidirect
3. C2×C3×C4×C5×D4C2semidirect
4. C3×C5×#398C2semidirect
5. C3×C5×#397C2semidirect
6. C3×C5×#394C2semidirect
7. C3×C5×#392C2semidirect
8. C3×C5×#388C2semidirect
9. C3×C5×#386C2semidirect
10. C3×C5×#386C2semidirect
11. C2×C3×C5×#95C2semidirect
12. C5×#2543C3direct (N × H)
39. C3×#2543C5direct (N × H)
40. C2×C5×#121C2×C3semidirect
41. C2×C5×#121C2×C3semidirect
42. C2×C4×C5×D4C2×C3semidirect
43. C5×#398C2×C3semidirect
44. C5×#397C2×C3semidirect
45. C5×#394C2×C3semidirect
46. C5×#392C2×C3semidirect
47. C5×#388C2×C3semidirect
48. C5×#386C2×C3semidirect
49. C5×#386C2×C3semidirect
50. C2×C5×#95C2×C3semidirect
64. C2×C3×C5×D4D4semidirect
71. C22×C3×C4×C5D4semidirect
91. C2×C3×#121C2×C5semidirect
92. C2×C3×#121C2×C5semidirect
93. C2×C3×C4×D4C2×C5semidirect
94. C3×#398C2×C5semidirect
95. C3×#397C2×C5semidirect
96. C3×#394C2×C5semidirect
97. C3×#392C2×C5semidirect
98. C3×#388C2×C5semidirect
99. C3×#386C2×C5semidirect
100. C3×#386C2×C5semidirect
101. C2×C3×#95C2×C5semidirect
128. #2543C3×C5direct (N × H)
213. C2×C5×D4C3×D4semidirect
220. C22×C4×C5C3×D4semidirect
240. C2×#121C2×C3×C5semidirect
241. C2×#121C2×C3×C5semidirect
242. C2×C4×D4C2×C3×C5semidirect
243. #398C2×C3×C5semidirect
244. #397C2×C3×C5semidirect
245. #394C2×C3×C5semidirect
246. #392C2×C3×C5semidirect
247. #388C2×C3×C5semidirect
248. #386C2×C3×C5semidirect
249. #386C2×C3×C5semidirect
250. C2×#95C2×C3×C5semidirect
294. C2×C3×D4C5×D4semidirect
301. C22×C3×C4C5×D4semidirect
488. C2×D4C3×C5×D4semidirect
495. C22×C4C3×C5×D4semidirect
515. C3×C5#2543direct (N × H)
607. C5C3×#2543direct (N × H)
638. C3C5×#2543direct (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×#1212
C2×C3×C4×C5×D42
C3×C5×#3982
C3×C5×#3972
C3×C5×#3942
C3×C5×#3922
C3×C5×#3882
C3×C5×#3862
C2×C3×C5×#952
C5×#25433
C3×#25435