Finite Group Databasebeta

← C3×C5×#2422 #14275456

Subgroups — C3×C5×#2422 #14275456

Order 1920.

1304 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×#123C212yesmaximal, complemented
2C2×C3×C5×#121C211yesmaximal, characteristic
3C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
4C3×C5×#397C212yesmaximal, complemented
5C3×C5×#394C212yesmaximal, complemented
6C3×C5×#390C211yesmaximal, characteristic, complemented
7C3×C5×#389C211yesmaximal, characteristic, complemented
8C3×C5×#385C212yesmaximal, complemented
9C3×C5×#384C211yesmaximal, characteristic, complemented
10C3×C5×#380C211yesmaximal, characteristic, complemented
11C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
12C5×#2422C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2212yes—
14C22×C3×C5×D4C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2212yes—
17C3×C5×#123—28no—
18C3×C5×#121—24no—
19C3×C4×C5×D4—24no—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2212yes—
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2212yes—
26C2×C3×C5×C22⋊C4C2212yes—
27C2×C3×C5×C22⋊C4C2212yes—
28C2×C3×C5×C22⋊C4C2212yes—
29C2×C3×C5×C22⋊C4C2212yes—
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2212yes—
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C42×C5C2211yescharacteristic
34C2×C3×C42×C5C2211yescharacteristic
35C3×C5×#95C2211yescharacteristic
36C3×C5×#95C2211yescharacteristic
37C3×C5×#95C2212yes—
38C3×C5×#95C2212yes—
39C3×#2422C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#123C2×C312yescomplemented
41C2×C5×#121C2×C311yescharacteristic
42C2×C4×C5×D4C2×C311yescharacteristic, complemented
43C5×#397C2×C312yescomplemented
44C5×#394C2×C312yescomplemented
45C5×#390C2×C311yescharacteristic, complemented
46C5×#389C2×C311yescharacteristic, complemented
47C5×#385C2×C312yescomplemented
48C5×#384C2×C311yescharacteristic, complemented
49C5×#380C2×C311yescharacteristic, complemented
50C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
51C24×C3×C5C2312yes—
52C24×C3×C5C2311yescharacteristic
53C2×C3×C5×D4—24no—
54C2×C3×C5×D4—24no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4—42no—
58C2×C3×C5×D4D414yes—
59C22×C3×C4×C5—24no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—24no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—22no—
64C22×C3×C4×C5—42no—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2312yes—
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4—22no—
76C3×C5×C4⋊C4—24no—
77C3×C5×C4⋊C4—24no—
78C3×C5×C4⋊C4—22no—
79C3×C5×C4⋊C4—42no—
80C3×C5×C22⋊C4—24no—
81C3×C5×C22⋊C4—24no—
82C3×C5×C22⋊C4—24no—
83C3×C5×C22⋊C4—24no—
84C3×C5×C22⋊C4—22no—
85C3×C5×C22⋊C4—24no—
86C3×C5×C22⋊C4D414yescomplemented
87C3×C42×C5—22no—
88C3×C42×C5—22no—
89C2×C3×#123C2×C512yescomplemented
90C2×C3×#121C2×C511yescharacteristic
91C2×C3×C4×D4C2×C511yescharacteristic, complemented
92C3×#397C2×C512yescomplemented
93C3×#394C2×C512yescomplemented
94C3×#390C2×C511yescharacteristic, complemented
95C3×#389C2×C511yescharacteristic, complemented
96C3×#385C2×C512yescomplemented
97C3×#384C2×C511yescharacteristic, complemented
98C3×#380C2×C511yescharacteristic, complemented
99C3×C4×C22⋊C4C2×C511yescharacteristic, complemented
100C22×C5×D4C22×C312yes—
101C22×C5×D4C22×C311yescharacteristic
102C23×C4×C5C22×C311yescharacteristic
103C23×C4×C5C22×C312yes—
104C5×#123—28no—
105C5×#121—24no—
106C4×C5×D4—24no—
107C2×C5×C4⋊C4C22×C311yescharacteristic
108C2×C5×C4⋊C4C22×C311yescharacteristic
109C2×C5×C4⋊C4C22×C311yescharacteristic
110C2×C5×C4⋊C4C22×C312yes—
111C2×C5×C4⋊C4C22×C312yes—
112C2×C5×C4⋊C4C22×C312yes—
113C2×C5×C22⋊C4C22×C311yescharacteristic
114C2×C5×C22⋊C4C22×C312yes—
115C2×C5×C22⋊C4C22×C312yes—
116C2×C5×C22⋊C4C22×C312yes—
117C2×C5×C22⋊C4C22×C312yes—
118C2×C5×C22⋊C4C22×C312yes—
119C2×C5×C22⋊C4C22×C311yescharacteristic
120C2×C42×C5C22×C311yescharacteristic
121C2×C42×C5C22×C311yescharacteristic
122C5×#95C22×C311yescharacteristic
123C5×#95C22×C311yescharacteristic
124C5×#95C22×C312yes—
125C5×#95C22×C312yes—
126#2422C3×C511yescharacteristic, direct product factor, Sylow
127C23×C3×C5—22no—
128C23×C3×C5—21no—
129C23×C3×C5—21no—
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—21no—
137C23×C3×C5—21no—
138C23×C3×C5—22no—
139C23×C3×C5C2×D412yes—
140C23×C3×C5C2×D414yes—
141C23×C3×C5C2411yescharacteristic
142C3×C5×D4—28no—
143C3×C5×D4—48no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—21no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—21no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—21no—
165C2×C3×C4×C5—48no—
166C2×C3×C4×C5—44no—
167C2×C3×C4×C5C2×D412yes—
168C2×C3×C4×C5C2×D412yes—
169C2×C3×C4×C5C2×D412yes—
170C2×C3×C4×C5#4112yes—
171C2×C3×C4×C5#4112yes—
172C2×C3×C4×C5#4112yes—
173C22×C3×D4C22×C512yes—
174C22×C3×D4C22×C511yescharacteristic
175C23×C3×C4C22×C511yescharacteristic
176C23×C3×C4C22×C512yes—
177C3×#123—28no—
178C3×#121—24no—
179C3×C4×D4—24no—
180C2×C3×C4⋊C4C22×C511yescharacteristic
181C2×C3×C4⋊C4C22×C511yescharacteristic
182C2×C3×C4⋊C4C22×C511yescharacteristic
183C2×C3×C4⋊C4C22×C512yes—
184C2×C3×C4⋊C4C22×C512yes—
185C2×C3×C4⋊C4C22×C512yes—
186C2×C3×C22⋊C4C22×C511yescharacteristic
187C2×C3×C22⋊C4C22×C512yes—
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×C42C22×C511yescharacteristic
194C2×C3×C42C22×C511yescharacteristic
195C3×#95C22×C511yescharacteristic
196C3×#95C22×C511yescharacteristic
197C3×#95C22×C512yes—
198C3×#95C22×C512yes—
199C24×C5C23×C312yes—
200C24×C5C23×C311yescharacteristic
201C2×C5×D4—24no—
202C2×C5×D4—24no—
203C2×C5×D4—22no—
204C2×C5×D4—22no—
205C2×C5×D4—42no—
206C2×C5×D4C3×D414yes—
207C22×C4×C5—24no—
208C22×C4×C5—22no—
209C22×C4×C5—24no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—42no—
213C22×C4×C5C23×C311yescharacteristic
214C22×C4×C5C23×C312yes—
215C22×C4×C5C23×C312yes—
216C22×C4×C5C23×C311yescharacteristic
217C22×C4×C5C23×C312yes—
218C22×C4×C5C23×C311yescharacteristic
219C22×C4×C5C23×C311yescharacteristic
220C22×C4×C5C23×C311yescharacteristic
221C22×C4×C5C23×C311yescharacteristic
222C5×C4⋊C4—22no—
223C5×C4⋊C4—22no—
224C5×C4⋊C4—24no—
225C5×C4⋊C4—24no—
226C5×C4⋊C4—22no—
227C5×C4⋊C4—42no—
228C5×C22⋊C4—24no—
229C5×C22⋊C4—24no—
230C5×C22⋊C4—24no—
231C5×C22⋊C4—24no—
232C5×C22⋊C4—22no—
233C5×C22⋊C4—24no—
234C5×C22⋊C4C3×D414yescomplemented
235C42×C5—22no—
236C42×C5—22no—
237C2×#123C2×C3×C512yescomplemented
238C2×#121C2×C3×C511yescharacteristic
239C2×C4×D4C2×C3×C511yescharacteristic, complemented
240#397C2×C3×C512yescomplemented
241#394C2×C3×C512yescomplemented
242#390C2×C3×C511yescharacteristic, complemented
243#389C2×C3×C511yescharacteristic, complemented
244#385C2×C3×C512yescomplemented
245#384C2×C3×C511yescharacteristic, complemented
246#380C2×C3×C511yescharacteristic, complemented
247C4×C22⋊C4C2×C3×C511yescharacteristic, complemented
248C22×C3×C5—24no—
249C22×C3×C5—22no—
250C22×C3×C5—24no—
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—24no—
254C22×C3×C5—41no—
255C22×C3×C5—42no—
256C22×C3×C5—41no—
257C22×C3×C5—42no—
258C22×C3×C5—42no—
259C22×C3×C5—41no—
260C22×C3×C5—41no—
261C22×C3×C5—42no—
262C22×C3×C5C22×D411yescharacteristic
263C22×C3×C5C22×D411yescharacteristic
264C22×C3×C5C2×#4111yescharacteristic
265C22×C3×C5C2×#4111yescharacteristic
266C22×C3×C5C2×#4111yescharacteristic
267C22×C3×C5H(5,𝔽2)11yescharacteristic
268C22×C3×C52−1+411yescharacteristic
269C3×C4×C5—22no—
270C3×C4×C5—22no—
271C3×C4×C5—22no—
272C3×C4×C5—41no—
273C3×C4×C5—42no—
274C3×C4×C5—42no—
275C3×C4×C5—42no—
276C3×C4×C5—41no—
277C3×C4×C5#12314yescomplemented
278C24×C3C23×C512yes—
279C24×C3C23×C511yescharacteristic
280C2×C3×D4—24no—
281C2×C3×D4—24no—
282C2×C3×D4—22no—
283C2×C3×D4—22no—
284C2×C3×D4—42no—
285C2×C3×D4C5×D414yes—
286C22×C3×C4—24no—
287C22×C3×C4—22no—
288C22×C3×C4—24no—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—42no—
292C22×C3×C4C23×C511yescharacteristic
293C22×C3×C4C23×C511yescharacteristic
294C22×C3×C4C23×C512yes—
295C22×C3×C4C23×C512yes—
296C22×C3×C4C23×C512yes—
297C22×C3×C4C23×C511yescharacteristic
298C22×C3×C4C23×C511yescharacteristic
299C22×C3×C4C23×C511yescharacteristic
300C22×C3×C4C23×C511yescharacteristic
301C3×C4⋊C4—22no—
302C3×C4⋊C4—22no—
303C3×C4⋊C4—24no—
304C3×C4⋊C4—24no—
305C3×C4⋊C4—22no—
306C3×C4⋊C4—42no—
307C3×C22⋊C4—24no—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—24no—
310C3×C22⋊C4—24no—
311C3×C22⋊C4—22no—
312C3×C22⋊C4—24no—
313C3×C22⋊C4C5×D414yescomplemented
314C3×C42—22no—
315C3×C42—22no—
316C23×C5—22no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—22no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—22no—
328C23×C5C2×C3×D412yes—
329C23×C5C2×C3×D414yes—
330C23×C5C24×C311yescharacteristic
331C5×D4—28no—
332C5×D4—48no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—22no—
341C2×C4×C5—21no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—21no—
348C2×C4×C5—22no—
349C2×C4×C5—21no—
350C2×C4×C5—21no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—21no—
354C2×C4×C5—48no—
355C2×C4×C5—44no—
356C2×C4×C5C2×C3×D412yes—
357C2×C4×C5C2×C3×D412yes—
358C2×C4×C5C2×C3×D412yes—
359C2×C4×C5C3×#4112yes—
360C2×C4×C5C3×#4112yes—
361C2×C4×C5C3×#4112yes—
362C22×D4C22×C3×C512yes—
363C22×D4C22×C3×C511yescharacteristic
364C23×C4C22×C3×C511yescharacteristic
365C23×C4C22×C3×C512yes—
366#123—28no—
367#121—24no—
368C4×D4—24no—
369C2×C4⋊C4C22×C3×C511yescharacteristic
370C2×C4⋊C4C22×C3×C511yescharacteristic
371C2×C4⋊C4C22×C3×C512yes—
372C2×C4⋊C4C22×C3×C512yes—
373C2×C4⋊C4C22×C3×C511yescharacteristic
374C2×C4⋊C4C22×C3×C512yes—
375C2×C22⋊C4C22×C3×C512yes—
376C2×C22⋊C4C22×C3×C512yes—
377C2×C22⋊C4C22×C3×C512yes—
378C2×C22⋊C4C22×C3×C512yes—
379C2×C22⋊C4C22×C3×C511yescharacteristic
380C2×C22⋊C4C22×C3×C512yes—
381C2×C22⋊C4C22×C3×C511yescharacteristic
382C2×C42C22×C3×C511yescharacteristic
383C2×C42C22×C3×C511yescharacteristic
384#95C22×C3×C511yescharacteristic
385#95C22×C3×C511yescharacteristic
386#95C22×C3×C512yes—
387#95C22×C3×C512yes—
388C2×C3×C5—44no—
389C2×C3×C5—42no—
390C2×C3×C5C2×#12311yescharacteristic
391C2×C3×C5#53211yescharacteristic
392C2×C3×C5#54211yescharacteristic
393C2×C3×C5D4211yescharacteristic
394C2×C3×C5#54711yescharacteristic
395C2×C3×C5#54711yescharacteristic
396C2×C3×C5#55311yescharacteristic
397C23×C3—22no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—22no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—22no—
409C23×C3C2×C5×D412yes—
410C23×C3C2×C5×D414yes—
411C23×C3C24×C511yescharacteristic
412C3×D4—28no—
413C3×D4—48no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
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—21no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—48no—
436C2×C3×C4—44no—
437C2×C3×C4C2×C5×D412yes—
438C2×C3×C4C2×C5×D412yes—
439C2×C3×C4C2×C5×D412yes—
440C2×C3×C4C5×#4112yes—
441C2×C3×C4C5×#4112yes—
442C2×C3×C4C5×#4112yes—
443C22×C5—24no—
444C22×C5—22no—
445C22×C5—24no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—24no—
449C22×C5—41no—
450C22×C5—42no—
451C22×C5—41no—
452C22×C5—42no—
453C22×C5—42no—
454C22×C5—41no—
455C22×C5—41no—
456C22×C5—42no—
457C22×C5C22×C3×D411yescharacteristic
458C22×C5C22×C3×D411yescharacteristic
459C22×C5C2×C3×#4111yescharacteristic
460C22×C5C2×C3×#4111yescharacteristic
461C22×C5C2×C3×#4111yescharacteristic
462C22×C5C3×H(5,𝔽2)11yescharacteristic
463C22×C5C3×2−1+411yescharacteristic
464C4×C5—22no—
465C4×C5—22no—
466C4×C5—22no—
467C4×C5—41no—
468C4×C5—42no—
469C4×C5—42no—
470C4×C5—42no—
471C4×C5—41no—
472C4×C5C3×#12314yescomplemented
473C24C23×C3×C512yes—
474C24C23×C3×C511yescharacteristic
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—42no—
480C2×D4C3×C5×D414yes—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—42no—
487C22×C4C23×C3×C511yescharacteristic
488C22×C4C23×C3×C511yescharacteristic
489C22×C4C23×C3×C512yes—
490C22×C4C23×C3×C512yes—
491C22×C4C23×C3×C512yes—
492C22×C4C23×C3×C511yescharacteristic
493C22×C4C23×C3×C511yescharacteristic
494C22×C4C23×C3×C511yescharacteristic
495C22×C4C23×C3×C511yescharacteristic
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—24no—
499C4⋊C4—24no—
500C4⋊C4—22no—
501C4⋊C4—42no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—24no—
505C22⋊C4—24no—
506C22⋊C4—22no—
507C22⋊C4—24no—
508C22⋊C4C3×C5×D414yescomplemented
509C42—22no—
510C42—22no—
511C3×C5#242211yescharacteristic, direct product factor, Hall
512C22×C3—24no—
513C22×C3—22no—
514C22×C3—24no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—24no—
518C22×C3—41no—
519C22×C3—42no—
520C22×C3—41no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—42no—
526C22×C3C22×C5×D411yescharacteristic
527C22×C3C22×C5×D411yescharacteristic
528C22×C3C2×C5×#4111yescharacteristic
529C22×C3C2×C5×#4111yescharacteristic
530C22×C3C2×C5×#4111yescharacteristic
531C22×C3C5×H(5,𝔽2)11yescharacteristic
532C22×C3C5×2−1+411yescharacteristic
533C3×C4—22no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—41no—
537C3×C4—42no—
538C3×C4—42no—
539C3×C4—42no—
540C3×C4—41no—
541C3×C4C5×#12314yescomplemented
542C2×C5—44no—
543C2×C5—42no—
544C2×C5C2×C3×#12311yescharacteristic
545C2×C5C3×#53211yescharacteristic
546C2×C5C3×#54211yescharacteristic
547C2×C5C3×D4211yescharacteristic
548C2×C5C3×#54711yescharacteristic
549C2×C5C3×#54711yescharacteristic
550C2×C5C3×#55311yescharacteristic
551C23—22no—
552C23—21no—
553C23—21no—
554C23—22no—
555C23—21no—
556C23—21no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—21no—
561C23—21no—
562C23—22no—
563C23C2×C3×C5×D412yes—
564C23C2×C3×C5×D414yes—
565C23C24×C3×C511yescharacteristic
566D4—28no—
567D4—48no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—48no—
590C2×C4—44no—
591C2×C4C2×C3×C5×D412yes—
592C2×C4C2×C3×C5×D412yes—
593C2×C4C2×C3×C5×D412yes—
594C2×C4C3×C5×#4112yes—
595C2×C4C3×C5×#4112yes—
596C2×C4C3×C5×#4112yes—
597C2×C3—44no—
598C2×C3—42no—
599C2×C3C2×C5×#12311yescharacteristic
600C2×C3C5×#53211yescharacteristic
601C2×C3C5×#54211yescharacteristic
602C2×C3C5×D4211yescharacteristic
603C2×C3C5×#54711yescharacteristic
604C2×C3C5×#54711yescharacteristic
605C2×C3C5×#55311yescharacteristic
606C5C3×#242211yescharacteristic, direct product factor, Sylow
607C22—24no—
608C22—22no—
609C22—24no—
610C22—22no—
611C22—22no—
612C22—24no—
613C22—41no—
614C22—42no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22C22×C3×C5×D411yescharacteristic
622C22C22×C3×C5×D411yescharacteristic
623C22C2×C3×C5×#4111yescharacteristic
624C22C2×C3×C5×#4111yescharacteristic
625C22C2×C3×C5×#4111yescharacteristic
626C22C3×C5×H(5,𝔽2)11yescharacteristic
627C22C3×C5×2−1+411yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—41no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4—41no—
636C4C3×C5×#12314yescomplemented
637C3C5×#242211yescharacteristic, direct product factor, Sylow
638C2—44no—
639C2—42no—
640C2C2×C3×C5×#12311yescharacteristic
641C2C3×C5×#53211yescharacteristic
642C2C3×C5×#54211yescharacteristic
643C2C3×C5×D4211yescharacteristic
644C2C3×C5×#54711yescharacteristic
645C2C3×C5×#54711yescharacteristic
646C2C3×C5×#55311yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC2×C3×C5×#121C2
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×#123C2semidirect
3. C2×C3×C4×C5×D4C2semidirect
4. C3×C5×#397C2semidirect
5. C3×C5×#394C2semidirect
6. C3×C5×#390C2semidirect
7. C3×C5×#389C2semidirect
8. C3×C5×#385C2semidirect
9. C3×C5×#384C2semidirect
10. C3×C5×#380C2semidirect
11. C3×C4×C5×C22⋊C4C2semidirect
12. C5×#2422C3direct (N × H)
39. C3×#2422C5direct (N × H)
40. C2×C5×#123C2×C3semidirect
42. C2×C4×C5×D4C2×C3semidirect
43. C5×#397C2×C3semidirect
44. C5×#394C2×C3semidirect
45. C5×#390C2×C3semidirect
46. C5×#389C2×C3semidirect
47. C5×#385C2×C3semidirect
48. C5×#384C2×C3semidirect
49. C5×#380C2×C3semidirect
50. C4×C5×C22⋊C4C2×C3semidirect
86. C3×C5×C22⋊C4D4semidirect
89. C2×C3×#123C2×C5semidirect
91. C2×C3×C4×D4C2×C5semidirect
92. C3×#397C2×C5semidirect
93. C3×#394C2×C5semidirect
94. C3×#390C2×C5semidirect
95. C3×#389C2×C5semidirect
96. C3×#385C2×C5semidirect
97. C3×#384C2×C5semidirect
98. C3×#380C2×C5semidirect
99. C3×C4×C22⋊C4C2×C5semidirect
126. #2422C3×C5direct (N × H)
234. C5×C22⋊C4C3×D4semidirect
237. C2×#123C2×C3×C5semidirect
239. C2×C4×D4C2×C3×C5semidirect
240. #397C2×C3×C5semidirect
241. #394C2×C3×C5semidirect
242. #390C2×C3×C5semidirect
243. #389C2×C3×C5semidirect
244. #385C2×C3×C5semidirect
245. #384C2×C3×C5semidirect
246. #380C2×C3×C5semidirect
247. C4×C22⋊C4C2×C3×C5semidirect
277. C3×C4×C5#123semidirect
313. C3×C22⋊C4C5×D4semidirect
472. C4×C5C3×#123semidirect
508. C22⋊C4C3×C5×D4semidirect
511. C3×C5#2422direct (N × H)
541. C3×C4C5×#123semidirect
606. C5C3×#2422direct (N × H)
636. C4C3×C5×#123semidirect
637. C3C5×#2422direct (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×#1212
C2×C3×C4×C5×D42
C3×C5×#3972
C3×C5×#3942
C3×C5×#3902
C3×C5×#3892
C3×C5×#3852
C3×C5×#3842
C3×C5×#3802
C3×C4×C5×C22⋊C42
C5×#24223
C3×#24225