Finite Group Databasebeta

← C2×C3×C5×#388 #14275323

Subgroups — C2×C3×C5×#388 #14275323

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×C3×C5×C22⋊C4C211yesmaximal, characteristic
3C22×C3×C5×C22⋊C4C211yesmaximal, characteristic
4C22×C3×C5×C22⋊C4C211yesmaximal, characteristic
5C22×C3×C42×C5C211yesmaximal, characteristic, complemented
6C3×C5×#388C218yesmaximal, direct product factor
7C2×C3×C5×#95C211yesmaximal, characteristic, complemented
8C2×C3×C5×#95C211yesmaximal, characteristic, complemented
9C2×C5×#388C311yesmaximal, characteristic, direct product factor, Hall
10C25×C3×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×C4×C5C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2211yescharacteristic
17C2×C3×C5×C4⋊C4—24no—
18C2×C3×C5×C4⋊C4C2214yescomplemented
19C2×C3×C5×C22⋊C4—24no—
20C2×C3×C5×C22⋊C4—24no—
21C2×C3×C5×C22⋊C4C418yescomplemented
22C2×C3×C5×C22⋊C4C2214yes—
23C2×C3×C5×C22⋊C4C2214yes—
24C2×C3×C5×C22⋊C4C2214yes—
25C2×C3×C42×C5—24no—
26C2×C3×C42×C5C2214yescomplemented
27C3×C5×#95C2214yescomplemented
28C3×C5×#95C2214yescomplemented
29C2×C3×#388C511yesmaximal, characteristic, direct product factor, Hall
30C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
31C22×C5×C22⋊C4C2×C311yescharacteristic
32C22×C5×C22⋊C4C2×C311yescharacteristic
33C22×C5×C22⋊C4C2×C311yescharacteristic
34C22×C42×C5C2×C311yescharacteristic, complemented
35C5×#388C2×C318yesdirect product factor
36C2×C5×#95C2×C311yescharacteristic, complemented
37C2×C5×#95C2×C311yescharacteristic, complemented
38C24×C3×C5—22no—
39C24×C3×C5—22no—
40C24×C3×C5—22no—
41C24×C3×C5—22no—
42C24×C3×C5—22no—
43C24×C3×C5—22no—
44C24×C3×C5C2×C414yes—
45C24×C3×C5C2312yes—
46C24×C3×C5C2311yescharacteristic
47C22×C3×C4×C5—22no—
48C22×C3×C4×C5—22no—
49C22×C3×C4×C5—22no—
50C22×C3×C4×C5—22no—
51C22×C3×C4×C5—22no—
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5C2×C414yes—
62C22×C3×C4×C5C2×C414yes—
63C22×C3×C4×C5D414yes—
64C22×C3×C4×C5D414yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2312yes—
69C22×C3×C4×C5C2312yes—
70C22×C3×C4×C5C2312yes—
71C3×C5×C4⋊C4—28no—
72C3×C5×C22⋊C4—28no—
73C3×C5×C22⋊C4—28no—
74C3×C5×C22⋊C4C2×C4116yescomplemented
75C3×C42×C5—28no—
76C22×C3×C4⋊C4C2×C511yescharacteristic, complemented
77C22×C3×C22⋊C4C2×C511yescharacteristic
78C22×C3×C22⋊C4C2×C511yescharacteristic
79C22×C3×C22⋊C4C2×C511yescharacteristic
80C22×C3×C42C2×C511yescharacteristic, complemented
81C3×#388C2×C518yesdirect product factor
82C2×C3×#95C2×C511yescharacteristic, complemented
83C2×C3×#95C2×C511yescharacteristic, complemented
84C25×C5C22×C311yescharacteristic
85C23×C4×C5C22×C311yescharacteristic
86C23×C4×C5C22×C311yescharacteristic
87C23×C4×C5C22×C311yescharacteristic
88C23×C4×C5C22×C311yescharacteristic
89C23×C4×C5C22×C311yescharacteristic
90C23×C4×C5C22×C311yescharacteristic
91C2×C5×C4⋊C4—24no—
92C2×C5×C4⋊C4C22×C314yescomplemented
93C2×C5×C22⋊C4—24no—
94C2×C5×C22⋊C4—24no—
95C2×C5×C22⋊C4C3×C418yescomplemented
96C2×C5×C22⋊C4C22×C314yes—
97C2×C5×C22⋊C4C22×C314yes—
98C2×C5×C22⋊C4C22×C314yes—
99C2×C42×C5—24no—
100C2×C42×C5C22×C314yescomplemented
101C5×#95C22×C314yescomplemented
102C5×#95C22×C314yescomplemented
103C2×#388C3×C511yescharacteristic, direct product factor, Sylow
104C23×C3×C5—28no—
105C23×C3×C5—28no—
106C23×C3×C5—28no—
107C23×C3×C5—22no—
108C23×C3×C5—22no—
109C23×C3×C5—22no—
110C23×C3×C5—22no—
111C23×C3×C5—22no—
112C23×C3×C5—22no—
113C23×C3×C5—44no—
114C23×C3×C5—44no—
115C23×C3×C5—44no—
116C23×C3×C5—44no—
117C23×C3×C5C22×C414yes—
118C23×C3×C5C22×C412yes—
119C23×C3×C5C2×D412yes—
120C23×C3×C5C2×D412yes—
121C23×C3×C5#4112yes—
122C23×C3×C5#4112yes—
123C23×C3×C5#4112yes—
124C23×C3×C5#4112yes—
125C23×C3×C5C2411yescharacteristic
126C2×C3×C4×C5—28no—
127C2×C3×C4×C5—28no—
128C2×C3×C4×C5—28no—
129C2×C3×C4×C5—28no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
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—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—44no—
145C2×C3×C4×C5—44no—
146C2×C3×C4×C5C22×C414yes—
147C2×C3×C4×C5C22×C414yes—
148C2×C3×C4×C5C2×D414yes—
149C2×C3×C4×C5C2×D414yes—
150C25×C3C22×C511yescharacteristic
151C23×C3×C4C22×C511yescharacteristic
152C23×C3×C4C22×C511yescharacteristic
153C23×C3×C4C22×C511yescharacteristic
154C23×C3×C4C22×C511yescharacteristic
155C23×C3×C4C22×C511yescharacteristic
156C23×C3×C4C22×C511yescharacteristic
157C2×C3×C4⋊C4—24no—
158C2×C3×C4⋊C4C22×C514yescomplemented
159C2×C3×C22⋊C4—24no—
160C2×C3×C22⋊C4—24no—
161C2×C3×C22⋊C4C4×C518yescomplemented
162C2×C3×C22⋊C4C22×C514yes—
163C2×C3×C22⋊C4C22×C514yes—
164C2×C3×C22⋊C4C22×C514yes—
165C2×C3×C42—24no—
166C2×C3×C42C22×C514yescomplemented
167C3×#95C22×C514yescomplemented
168C3×#95C22×C514yescomplemented
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5—22no—
174C24×C5—22no—
175C24×C5C2×C3×C414yes—
176C24×C5C23×C312yes—
177C24×C5C23×C311yescharacteristic
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5C2×C3×C414yes—
193C22×C4×C5C2×C3×C414yes—
194C22×C4×C5C3×D414yes—
195C22×C4×C5C3×D414yes—
196C22×C4×C5C23×C312yes—
197C22×C4×C5C23×C312yes—
198C22×C4×C5C23×C312yes—
199C22×C4×C5C23×C312yes—
200C22×C4×C5C23×C312yes—
201C22×C4×C5C23×C312yes—
202C5×C4⋊C4—28no—
203C5×C22⋊C4—28no—
204C5×C22⋊C4—28no—
205C5×C22⋊C4C2×C3×C4116yescomplemented
206C42×C5—28no—
207C22×C4⋊C4C2×C3×C511yescharacteristic, complemented
208C22×C22⋊C4C2×C3×C511yescharacteristic
209C22×C22⋊C4C2×C3×C511yescharacteristic
210C22×C22⋊C4C2×C3×C511yescharacteristic
211C22×C42C2×C3×C511yescharacteristic, complemented
212#388C2×C3×C518yesdirect product factor
213C2×#95C2×C3×C511yescharacteristic, complemented
214C2×#95C2×C3×C511yescharacteristic, complemented
215C22×C3×C5—24no—
216C22×C3×C5—24no—
217C22×C3×C5—24no—
218C22×C3×C5—42no—
219C22×C3×C5—42no—
220C22×C3×C5—42no—
221C22×C3×C5—42no—
222C22×C3×C5—416no—
223C22×C3×C5#11714yes—
224C22×C3×C5C4×D414yes—
225C22×C3×C5C4×D414yes—
226C22×C3×C5#12114yes—
227C22×C3×C5#12314yes—
228C22×C3×C5#12414yes—
229C22×C3×C5#12614yes—
230C22×C3×C5C23×C411yescharacteristic
231C22×C3×C5C22×D411yescharacteristic
232C22×C3×C5C22×D411yescharacteristic
233C22×C3×C5C2×#4111yescharacteristic
234C22×C3×C5C2×#4111yescharacteristic
235C22×C3×C5C2×#4111yescharacteristic
236C22×C3×C5C2×#4111yescharacteristic
237C3×C4×C5—24no—
238C3×C4×C5—24no—
239C3×C4×C5—24no—
240C3×C4×C5—24no—
241C3×C4×C5—42no—
242C3×C4×C5—42no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3C2×C4×C514yes—
250C24×C3C23×C512yes—
251C24×C3C23×C511yescharacteristic
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4C2×C4×C514yes—
267C22×C3×C4C2×C4×C514yes—
268C22×C3×C4C5×D414yes—
269C22×C3×C4C5×D414yes—
270C22×C3×C4C23×C512yes—
271C22×C3×C4C23×C512yes—
272C22×C3×C4C23×C512yes—
273C22×C3×C4C23×C512yes—
274C22×C3×C4C23×C512yes—
275C22×C3×C4C23×C512yes—
276C3×C4⋊C4—28no—
277C3×C22⋊C4—28no—
278C3×C22⋊C4—28no—
279C3×C22⋊C4C2×C4×C5116yescomplemented
280C3×C42—28no—
281C23×C5—28no—
282C23×C5—28no—
283C23×C5—28no—
284C23×C5—22no—
285C23×C5—22no—
286C23×C5—22no—
287C23×C5—22no—
288C23×C5—22no—
289C23×C5—22no—
290C23×C5—44no—
291C23×C5—44no—
292C23×C5—44no—
293C23×C5—44no—
294C23×C5C22×C3×C414yes—
295C23×C5C22×C3×C412yes—
296C23×C5C2×C3×D412yes—
297C23×C5C2×C3×D412yes—
298C23×C5C3×#4112yes—
299C23×C5C3×#4112yes—
300C23×C5C3×#4112yes—
301C23×C5C3×#4112yes—
302C23×C5C24×C311yescharacteristic
303C2×C4×C5—28no—
304C2×C4×C5—28no—
305C2×C4×C5—28no—
306C2×C4×C5—28no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—44no—
322C2×C4×C5—44no—
323C2×C4×C5C22×C3×C414yes—
324C2×C4×C5C22×C3×C414yes—
325C2×C4×C5C2×C3×D414yes—
326C2×C4×C5C2×C3×D414yes—
327C25C22×C3×C511yescharacteristic
328C23×C4C22×C3×C511yescharacteristic
329C23×C4C22×C3×C511yescharacteristic
330C23×C4C22×C3×C511yescharacteristic
331C23×C4C22×C3×C511yescharacteristic
332C23×C4C22×C3×C511yescharacteristic
333C23×C4C22×C3×C511yescharacteristic
334C2×C4⋊C4—24no—
335C2×C4⋊C4C22×C3×C514yescomplemented
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4C3×C4×C518yescomplemented
339C2×C22⋊C4C22×C3×C514yes—
340C2×C22⋊C4C22×C3×C514yes—
341C2×C22⋊C4C22×C3×C514yes—
342C2×C42—24no—
343C2×C42C22×C3×C514yescomplemented
344#95C22×C3×C514yescomplemented
345#95C22×C3×C514yescomplemented
346C2×C3×C5—44no—
347C2×C3×C5#38818yesdirect product factor
348C2×C3×C5C2×#11711yescharacteristic
349C2×C3×C5C2×C4×D411yescharacteristic
350C2×C3×C5C2×C4×D411yescharacteristic
351C2×C3×C5C2×#12111yescharacteristic
352C2×C3×C5C2×#12311yescharacteristic
353C2×C3×C5C2×#12411yescharacteristic
354C2×C3×C5C2×#12611yescharacteristic
355C23×C3—28no—
356C23×C3—28no—
357C23×C3—28no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—44no—
365C23×C3—44no—
366C23×C3—44no—
367C23×C3—44no—
368C23×C3C22×C4×C514yes—
369C23×C3C22×C4×C512yes—
370C23×C3C2×C5×D412yes—
371C23×C3C2×C5×D412yes—
372C23×C3C5×#4112yes—
373C23×C3C5×#4112yes—
374C23×C3C5×#4112yes—
375C23×C3C5×#4112yes—
376C23×C3C24×C511yescharacteristic
377C2×C3×C4—28no—
378C2×C3×C4—28no—
379C2×C3×C4—28no—
380C2×C3×C4—28no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—44no—
396C2×C3×C4—44no—
397C2×C3×C4C22×C4×C514yes—
398C2×C3×C4C22×C4×C514yes—
399C2×C3×C4C2×C5×D414yes—
400C2×C3×C4C2×C5×D414yes—
401C22×C5—24no—
402C22×C5—24no—
403C22×C5—24no—
404C22×C5—416no—
405C22×C5—42no—
406C22×C5—42no—
407C22×C5—42no—
408C22×C5—42no—
409C22×C5C3×#11714yes—
410C22×C5C3×C4×D414yes—
411C22×C5C3×C4×D414yes—
412C22×C5C3×#12114yes—
413C22×C5C3×#12314yes—
414C22×C5C3×#12414yes—
415C22×C5C3×#12614yes—
416C22×C5C23×C3×C411yescharacteristic
417C22×C5C22×C3×D411yescharacteristic
418C22×C5C22×C3×D411yescharacteristic
419C22×C5C2×C3×#4111yescharacteristic
420C22×C5C2×C3×#4111yescharacteristic
421C22×C5C2×C3×#4111yescharacteristic
422C22×C5C2×C3×#4111yescharacteristic
423C4×C5—24no—
424C4×C5—24no—
425C4×C5—24no—
426C4×C5—24no—
427C4×C5—42no—
428C4×C5—42no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24C2×C3×C4×C514yes—
436C24C23×C3×C512yes—
437C24C23×C3×C511yescharacteristic
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4C2×C3×C4×C514yes—
453C22×C4C2×C3×C4×C514yes—
454C22×C4C3×C5×D414yes—
455C22×C4C3×C5×D414yes—
456C22×C4C23×C3×C512yes—
457C22×C4C23×C3×C512yes—
458C22×C4C23×C3×C512yes—
459C22×C4C23×C3×C512yes—
460C22×C4C23×C3×C512yes—
461C22×C4C23×C3×C512yes—
462C4⋊C4—28no—
463C22⋊C4—28no—
464C22⋊C4—28no—
465C22⋊C4C2×C3×C4×C5116yescomplemented
466C42—28no—
467C3×C5C2×#38811yescharacteristic, direct product factor, Hall
468C22×C3—24no—
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—416no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3C5×#11714yes—
477C22×C3C4×C5×D414yes—
478C22×C3C4×C5×D414yes—
479C22×C3C5×#12114yes—
480C22×C3C5×#12314yes—
481C22×C3C5×#12414yes—
482C22×C3C5×#12614yes—
483C22×C3C23×C4×C511yescharacteristic
484C22×C3C22×C5×D411yescharacteristic
485C22×C3C22×C5×D411yescharacteristic
486C22×C3C2×C5×#4111yescharacteristic
487C22×C3C2×C5×#4111yescharacteristic
488C22×C3C2×C5×#4111yescharacteristic
489C22×C3C2×C5×#4111yescharacteristic
490C3×C4—24no—
491C3×C4—24no—
492C3×C4—24no—
493C3×C4—24no—
494C3×C4—42no—
495C3×C4—42no—
496C2×C5—44no—
497C2×C5C3×#38818yesdirect product factor
498C2×C5C2×C3×#11711yescharacteristic
499C2×C5C2×C3×C4×D411yescharacteristic
500C2×C5C2×C3×C4×D411yescharacteristic
501C2×C5C2×C3×#12111yescharacteristic
502C2×C5C2×C3×#12311yescharacteristic
503C2×C5C2×C3×#12411yescharacteristic
504C2×C5C2×C3×#12611yescharacteristic
505C23—28no—
506C23—28no—
507C23—28no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—44no—
515C23—44no—
516C23—44no—
517C23—44no—
518C23C22×C3×C4×C514yes—
519C23C22×C3×C4×C512yes—
520C23C2×C3×C5×D412yes—
521C23C2×C3×C5×D412yes—
522C23C3×C5×#4112yes—
523C23C3×C5×#4112yes—
524C23C3×C5×#4112yes—
525C23C3×C5×#4112yes—
526C23C24×C3×C511yescharacteristic
527C2×C4—28no—
528C2×C4—28no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—28no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—28no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4C22×C3×C4×C514yes—
548C2×C4C22×C3×C4×C514yes—
549C2×C4C2×C3×C5×D414yes—
550C2×C4C2×C3×C5×D414yes—
551C2×C3—44no—
552C2×C3C5×#38818yesdirect product factor
553C2×C3C2×C5×#11711yescharacteristic
554C2×C3C2×C4×C5×D411yescharacteristic
555C2×C3C2×C4×C5×D411yescharacteristic
556C2×C3C2×C5×#12111yescharacteristic
557C2×C3C2×C5×#12311yescharacteristic
558C2×C3C2×C5×#12411yescharacteristic
559C2×C3C2×C5×#12611yescharacteristic
560C5C2×C3×#38811yescharacteristic, direct product factor, Sylow
561C22—24no—
562C22—24no—
563C22—24no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—416no—
569C22C3×C5×#11714yes—
570C22C3×C4×C5×D414yes—
571C22C3×C4×C5×D414yes—
572C22C3×C5×#12114yes—
573C22C3×C5×#12314yes—
574C22C3×C5×#12414yes—
575C22C3×C5×#12614yes—
576C22C23×C3×C4×C511yescharacteristic
577C22C22×C3×C5×D411yescharacteristic
578C22C22×C3×C5×D411yescharacteristic
579C22C2×C3×C5×#4111yescharacteristic
580C22C2×C3×C5×#4111yescharacteristic
581C22C2×C3×C5×#4111yescharacteristic
582C22C2×C3×C5×#4111yescharacteristic
583C4—24no—
584C4—24no—
585C4—24no—
586C4—24no—
587C4—42no—
588C4—42no—
589C3C2×C5×#38811yescharacteristic, direct product factor, Sylow
590C2—44no—
591C2C3×C5×#38818yesdirect product factor
592C2C2×C3×C5×#11711yescharacteristic
593C2C2×C3×C4×C5×D411yescharacteristic
594C2C2×C3×C4×C5×D411yescharacteristic
595C2C2×C3×C5×#12111yescharacteristic
596C2C2×C3×C5×#12311yescharacteristic
597C2C2×C3×C5×#12411yescharacteristic
598C2C2×C3×C5×#12611yescharacteristic
subgroupG/H
center, socleC24×C3×C5C23
commutatorC22C23×C3×C4×C5
Frattini, cosocleC23C24×C3×C5
prime radicalC25×C3×C5C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×C4⋊C4C2semidirect
5. C22×C3×C42×C5C2semidirect
6. C3×C5×#388C2direct (N × H)
7. C2×C3×C5×#95C2semidirect
8. C2×C3×C5×#95C2semidirect
9. C2×C5×#388C3direct (N × H)
18. C2×C3×C5×C4⋊C4C22semidirect
21. C2×C3×C5×C22⋊C4C4semidirect
26. C2×C3×C42×C5C22semidirect
27. C3×C5×#95C22semidirect
28. C3×C5×#95C22semidirect
29. C2×C3×#388C5direct (N × H)
30. C22×C5×C4⋊C4C2×C3semidirect
34. C22×C42×C5C2×C3semidirect
35. C5×#388C2×C3direct (N × H)
36. C2×C5×#95C2×C3semidirect
37. C2×C5×#95C2×C3semidirect
74. C3×C5×C22⋊C4C2×C4semidirect
76. C22×C3×C4⋊C4C2×C5semidirect
80. C22×C3×C42C2×C5semidirect
81. C3×#388C2×C5direct (N × H)
82. C2×C3×#95C2×C5semidirect
83. C2×C3×#95C2×C5semidirect
92. C2×C5×C4⋊C4C22×C3semidirect
95. C2×C5×C22⋊C4C3×C4semidirect
100. C2×C42×C5C22×C3semidirect
101. C5×#95C22×C3semidirect
102. C5×#95C22×C3semidirect
103. C2×#388C3×C5direct (N × H)
158. C2×C3×C4⋊C4C22×C5semidirect
161. C2×C3×C22⋊C4C4×C5semidirect
166. C2×C3×C42C22×C5semidirect
167. C3×#95C22×C5semidirect
168. C3×#95C22×C5semidirect
205. C5×C22⋊C4C2×C3×C4semidirect
207. C22×C4⋊C4C2×C3×C5semidirect
211. C22×C42C2×C3×C5semidirect
212. #388C2×C3×C5direct (N × H)
213. C2×#95C2×C3×C5semidirect
214. C2×#95C2×C3×C5semidirect
279. C3×C22⋊C4C2×C4×C5semidirect
335. C2×C4⋊C4C22×C3×C5semidirect
338. C2×C22⋊C4C3×C4×C5semidirect
343. C2×C42C22×C3×C5semidirect
344. #95C22×C3×C5semidirect
345. #95C22×C3×C5semidirect
347. C2×C3×C5#388direct (N × H)
465. C22⋊C4C2×C3×C4×C5semidirect
467. C3×C5C2×#388direct (N × H)
497. C2×C5C3×#388direct (N × H)
552. C2×C3C5×#388direct (N × H)
560. C5C2×C3×#388direct (N × H)
589. C3C2×C5×#388direct (N × H)
591. C2C3×C5×#388direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×C4⋊C42
C22×C3×C5×C22⋊C42
C22×C3×C42×C52
C3×C5×#3882
C2×C3×C5×#952
C2×C5×#3883
C2×C3×#3885