Finite Group Databasebeta

← C3×C5×#2322 #14275356

Subgroups — C3×C5×#2322 #14275356

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#123C211yesmaximal, characteristic
2C2×C3×C4×C5×D4C211yesmaximal, characteristic
3C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×C5×#389C212yesmaximal, complemented
5C3×C5×#388C212yesmaximal, complemented
6C3×C5×#387C212yesmaximal, complemented
7C3×C5×#386C211yesmaximal, characteristic
8C3×C5×#385C211yesmaximal, characteristic, complemented
9C3×C5×#385C212yesmaximal, complemented
10C3×C5×#381C211yesmaximal, characteristic, complemented
11C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
12C5×#2322C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2211yescharacteristic
17C23×C3×C4×C5C2211yescharacteristic
18C3×C5×#123C418yescomplemented
19C3×C4×C5×D4—24no—
20C2×C3×C5×C4⋊C4—24no—
21C2×C3×C5×C4⋊C4C2212yes—
22C2×C3×C5×C4⋊C4C2212yes—
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2212yes—
25C2×C3×C5×C4⋊C4C2212yes—
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2212yes—
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2212yes—
32C2×C3×C42×C5C2211yescharacteristic
33C2×C3×C42×C5C2212yes—
34C3×C5×#95C2212yes—
35C3×C5×#95C2212yes—
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×C5×#95C2212yes—
39C3×#2322C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#123C2×C311yescharacteristic
41C2×C4×C5×D4C2×C311yescharacteristic
42C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
43C5×#389C2×C312yescomplemented
44C5×#388C2×C312yescomplemented
45C5×#387C2×C312yescomplemented
46C5×#386C2×C311yescharacteristic
47C5×#385C2×C311yescharacteristic, complemented
48C5×#385C2×C312yescomplemented
49C5×#381C2×C311yescharacteristic, complemented
50C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2311yescharacteristic
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4C2×C414yes—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—42no—
61C22×C3×C4×C5—42no—
62C22×C3×C4×C5—42no—
63C22×C3×C4×C5C2×C414yescomplemented
64C22×C3×C4×C5D414yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2312yes—
69C22×C3×C4×C5C2312yes—
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2312yes—
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C3×C5×C4⋊C4—24no—
75C3×C5×C4⋊C4—24no—
76C3×C5×C4⋊C4—22no—
77C3×C5×C4⋊C4—42no—
78C3×C5×C4⋊C4C2×C418yescomplemented
79C3×C5×C22⋊C4—22no—
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4—22no—
82C3×C5×C22⋊C4—42no—
83C3×C5×C22⋊C4C2×C414yescomplemented
84C3×C5×C22⋊C4C2×C418yescomplemented
85C3×C42×C5—22no—
86C3×C42×C5—42no—
87C2×C3×#123C2×C511yescharacteristic
88C2×C3×C4×D4C2×C511yescharacteristic
89C22×C3×C4⋊C4C2×C511yescharacteristic, complemented
90C3×#389C2×C512yescomplemented
91C3×#388C2×C512yescomplemented
92C3×#387C2×C512yescomplemented
93C3×#386C2×C511yescharacteristic
94C3×#385C2×C512yescomplemented
95C3×#385C2×C511yescharacteristic, complemented
96C3×#381C2×C511yescharacteristic, complemented
97C3×C4×C22⋊C4C2×C511yescharacteristic, complemented
98C22×C5×D4C22×C311yescharacteristic
99C23×C4×C5C22×C311yescharacteristic
100C23×C4×C5C22×C311yescharacteristic
101C23×C4×C5C22×C311yescharacteristic
102C23×C4×C5C22×C311yescharacteristic
103C5×#123C3×C418yescomplemented
104C4×C5×D4—24no—
105C2×C5×C4⋊C4—24no—
106C2×C5×C4⋊C4C22×C312yes—
107C2×C5×C4⋊C4C22×C312yes—
108C2×C5×C4⋊C4C22×C311yescharacteristic
109C2×C5×C4⋊C4C22×C312yes—
110C2×C5×C4⋊C4C22×C312yes—
111C2×C5×C22⋊C4C22×C311yescharacteristic
112C2×C5×C22⋊C4C22×C311yescharacteristic
113C2×C5×C22⋊C4C22×C311yescharacteristic
114C2×C5×C22⋊C4C22×C312yes—
115C2×C5×C22⋊C4C22×C311yescharacteristic
116C2×C5×C22⋊C4C22×C312yes—
117C2×C42×C5C22×C311yescharacteristic
118C2×C42×C5C22×C312yes—
119C5×#95C22×C312yes—
120C5×#95C22×C312yes—
121C5×#95C22×C312yes—
122C5×#95C22×C312yes—
123C5×#95C22×C312yes—
124#2322C3×C511yescharacteristic, direct product factor, Sylow
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—22no—
130C23×C3×C5—22no—
131C23×C3×C5C22×C412yes—
132C23×C3×C5C22×C412yes—
133C23×C3×C5C2×D412yes—
134C23×C3×C5#4112yes—
135C23×C3×C5C2411yescharacteristic
136C3×C5×D4—28no—
137C2×C3×C4×C5—28no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
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—22no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—44no—
157C2×C3×C4×C5—44no—
158C2×C3×C4×C5—44no—
159C2×C3×C4×C5C22×C414yes—
160C2×C3×C4×C5C22×C414yes—
161C2×C3×C4×C5C22×C412yes—
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2×D412yes—
164C22×C3×D4C22×C511yescharacteristic
165C23×C3×C4C22×C511yescharacteristic
166C23×C3×C4C22×C511yescharacteristic
167C23×C3×C4C22×C511yescharacteristic
168C23×C3×C4C22×C511yescharacteristic
169C3×#123C4×C518yescomplemented
170C3×C4×D4—24no—
171C2×C3×C4⋊C4—24no—
172C2×C3×C4⋊C4C22×C512yes—
173C2×C3×C4⋊C4C22×C512yes—
174C2×C3×C4⋊C4C22×C511yescharacteristic
175C2×C3×C4⋊C4C22×C512yes—
176C2×C3×C4⋊C4C22×C512yes—
177C2×C3×C22⋊C4C22×C511yescharacteristic
178C2×C3×C22⋊C4C22×C511yescharacteristic
179C2×C3×C22⋊C4C22×C511yescharacteristic
180C2×C3×C22⋊C4C22×C512yes—
181C2×C3×C22⋊C4C22×C511yescharacteristic
182C2×C3×C22⋊C4C22×C512yes—
183C2×C3×C42C22×C511yescharacteristic
184C2×C3×C42C22×C512yes—
185C3×#95C22×C512yes—
186C3×#95C22×C512yes—
187C3×#95C22×C512yes—
188C3×#95C22×C512yes—
189C3×#95C22×C512yes—
190C24×C5C23×C311yescharacteristic
191C24×C5C23×C311yescharacteristic
192C2×C5×D4—22no—
193C2×C5×D4—22no—
194C2×C5×D4C2×C3×C414yes—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—42no—
200C22×C4×C5—42no—
201C22×C4×C5—42no—
202C22×C4×C5C2×C3×C414yescomplemented
203C22×C4×C5C3×D414yes—
204C22×C4×C5C23×C311yescharacteristic
205C22×C4×C5C23×C312yes—
206C22×C4×C5C23×C311yescharacteristic
207C22×C4×C5C23×C312yes—
208C22×C4×C5C23×C312yes—
209C22×C4×C5C23×C311yescharacteristic
210C22×C4×C5C23×C312yes—
211C22×C4×C5C23×C311yescharacteristic
212C22×C4×C5C23×C311yescharacteristic
213C5×C4⋊C4—24no—
214C5×C4⋊C4—24no—
215C5×C4⋊C4—22no—
216C5×C4⋊C4—42no—
217C5×C4⋊C4C2×C3×C418yescomplemented
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—42no—
222C5×C22⋊C4C2×C3×C414yescomplemented
223C5×C22⋊C4C2×C3×C418yescomplemented
224C42×C5—22no—
225C42×C5—42no—
226C2×#123C2×C3×C511yescharacteristic
227C2×C4×D4C2×C3×C511yescharacteristic
228C22×C4⋊C4C2×C3×C511yescharacteristic, complemented
229#389C2×C3×C512yescomplemented
230#388C2×C3×C512yescomplemented
231#387C2×C3×C512yescomplemented
232#386C2×C3×C511yescharacteristic
233#385C2×C3×C512yescomplemented
234#385C2×C3×C511yescharacteristic, complemented
235#381C2×C3×C511yescharacteristic, complemented
236C4×C22⋊C4C2×C3×C511yescharacteristic, complemented
237C22×C3×C5—24no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
241C22×C3×C5—22no—
242C22×C3×C5—24no—
243C22×C3×C5—41no—
244C22×C3×C5—41no—
245C22×C3×C5—42no—
246C22×C3×C5C4×D414yes—
247C22×C3×C5C23×C411yescharacteristic
248C22×C3×C5C22×D411yescharacteristic
249C22×C3×C5C2×#4111yescharacteristic
250C22×C3×C5H(5,𝔽2)12yes—
251C22×C3×C52−1+412yes—
252C3×C4×C5—24no—
253C3×C4×C5—22no—
254C3×C4×C5—24no—
255C3×C4×C5—22no—
256C3×C4×C5—22no—
257C3×C4×C5—41no—
258C3×C4×C5—42no—
259C3×C4×C5—41no—
260C3×C4×C5—42no—
261C24×C3C23×C511yescharacteristic
262C24×C3C23×C511yescharacteristic
263C2×C3×D4—22no—
264C2×C3×D4—22no—
265C2×C3×D4C2×C4×C514yes—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—42no—
271C22×C3×C4—42no—
272C22×C3×C4—42no—
273C22×C3×C4C2×C4×C514yescomplemented
274C22×C3×C4C5×D414yes—
275C22×C3×C4C23×C511yescharacteristic
276C22×C3×C4C23×C512yes—
277C22×C3×C4C23×C511yescharacteristic
278C22×C3×C4C23×C512yes—
279C22×C3×C4C23×C512yes—
280C22×C3×C4C23×C511yescharacteristic
281C22×C3×C4C23×C512yes—
282C22×C3×C4C23×C511yescharacteristic
283C22×C3×C4C23×C511yescharacteristic
284C3×C4⋊C4—24no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—22no—
287C3×C4⋊C4—42no—
288C3×C4⋊C4C2×C4×C518yescomplemented
289C3×C22⋊C4—22no—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—42no—
293C3×C22⋊C4C2×C4×C514yescomplemented
294C3×C22⋊C4C2×C4×C518yescomplemented
295C3×C42—22no—
296C3×C42—42no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—22no—
302C23×C5—22no—
303C23×C5C22×C3×C412yes—
304C23×C5C22×C3×C412yes—
305C23×C5C2×C3×D412yes—
306C23×C5C3×#4112yes—
307C23×C5C24×C311yescharacteristic
308C5×D4—28no—
309C2×C4×C5—28no—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—44no—
329C2×C4×C5—44no—
330C2×C4×C5—44no—
331C2×C4×C5C22×C3×C414yes—
332C2×C4×C5C22×C3×C414yes—
333C2×C4×C5C22×C3×C412yes—
334C2×C4×C5C2×C3×D412yes—
335C2×C4×C5C2×C3×D412yes—
336C22×D4C22×C3×C511yescharacteristic
337C23×C4C22×C3×C511yescharacteristic
338C23×C4C22×C3×C511yescharacteristic
339C23×C4C22×C3×C511yescharacteristic
340C23×C4C22×C3×C511yescharacteristic
341#123C3×C4×C518yescomplemented
342C4×D4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4C22×C3×C512yes—
345C2×C4⋊C4C22×C3×C512yes—
346C2×C4⋊C4C22×C3×C511yescharacteristic
347C2×C4⋊C4C22×C3×C512yes—
348C2×C4⋊C4C22×C3×C512yes—
349C2×C22⋊C4C22×C3×C511yescharacteristic
350C2×C22⋊C4C22×C3×C511yescharacteristic
351C2×C22⋊C4C22×C3×C511yescharacteristic
352C2×C22⋊C4C22×C3×C512yes—
353C2×C22⋊C4C22×C3×C511yescharacteristic
354C2×C22⋊C4C22×C3×C512yes—
355C2×C42C22×C3×C511yescharacteristic
356C2×C42C22×C3×C512yes—
357#95C22×C3×C512yes—
358#95C22×C3×C512yes—
359#95C22×C3×C512yes—
360#95C22×C3×C512yes—
361#95C22×C3×C512yes—
362C2×C3×C5—24no—
363C2×C3×C5—42no—
364C2×C3×C5C2×C4×D411yescharacteristic
365C2×C3×C5#52012yes—
366C2×C3×C5#53411yescharacteristic
367C2×C3×C5#53611yescharacteristic
368C2×C3×C5#53912yes—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3C22×C4×C512yes—
376C23×C3C22×C4×C512yes—
377C23×C3C2×C5×D412yes—
378C23×C3C5×#4112yes—
379C23×C3C24×C511yescharacteristic
380C3×D4—28no—
381C2×C3×C4—28no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—44no—
401C2×C3×C4—44no—
402C2×C3×C4—44no—
403C2×C3×C4C22×C4×C514yes—
404C2×C3×C4C22×C4×C514yes—
405C2×C3×C4C22×C4×C512yes—
406C2×C3×C4C2×C5×D412yes—
407C2×C3×C4C2×C5×D412yes—
408C22×C5—24no—
409C22×C5—22no—
410C22×C5—22no—
411C22×C5—24no—
412C22×C5—22no—
413C22×C5—24no—
414C22×C5—41no—
415C22×C5—41no—
416C22×C5—42no—
417C22×C5C3×C4×D414yes—
418C22×C5C23×C3×C411yescharacteristic
419C22×C5C22×C3×D411yescharacteristic
420C22×C5C2×C3×#4111yescharacteristic
421C22×C5C3×H(5,𝔽2)12yes—
422C22×C5C3×2−1+412yes—
423C4×C5—24no—
424C4×C5—22no—
425C4×C5—24no—
426C4×C5—22no—
427C4×C5—22no—
428C4×C5—41no—
429C4×C5—42no—
430C4×C5—41no—
431C4×C5—42no—
432C24C23×C3×C511yescharacteristic
433C24C23×C3×C511yescharacteristic
434C2×D4—22no—
435C2×D4—22no—
436C2×D4C2×C3×C4×C514yes—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4C2×C3×C4×C514yescomplemented
445C22×C4C3×C5×D414yes—
446C22×C4C23×C3×C511yescharacteristic
447C22×C4C23×C3×C512yes—
448C22×C4C23×C3×C511yescharacteristic
449C22×C4C23×C3×C512yes—
450C22×C4C23×C3×C512yes—
451C22×C4C23×C3×C511yescharacteristic
452C22×C4C23×C3×C512yes—
453C22×C4C23×C3×C511yescharacteristic
454C22×C4C23×C3×C511yescharacteristic
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—42no—
459C4⋊C4C2×C3×C4×C518yescomplemented
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—42no—
464C22⋊C4C2×C3×C4×C514yescomplemented
465C22⋊C4C2×C3×C4×C518yescomplemented
466C42—22no—
467C42—42no—
468C3×C5#232211yescharacteristic, direct product factor, Hall
469C22×C3—24no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—24no—
473C22×C3—22no—
474C22×C3—24no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—42no—
478C22×C3C4×C5×D414yes—
479C22×C3C23×C4×C511yescharacteristic
480C22×C3C22×C5×D411yescharacteristic
481C22×C3C2×C5×#4111yescharacteristic
482C22×C3C5×H(5,𝔽2)12yes—
483C22×C3C5×2−1+412yes—
484C3×C4—24no—
485C3×C4—22no—
486C3×C4—24no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—41no—
490C3×C4—42no—
491C3×C4—41no—
492C3×C4—42no—
493C2×C5—24no—
494C2×C5—42no—
495C2×C5C2×C3×C4×D411yescharacteristic
496C2×C5C3×#52012yes—
497C2×C5C3×#53411yescharacteristic
498C2×C5C3×#53611yescharacteristic
499C2×C5C3×#53912yes—
500C23—22no—
501C23—22no—
502C23—21no—
503C23—21no—
504C23—22no—
505C23—22no—
506C23C22×C3×C4×C512yes—
507C23C22×C3×C4×C512yes—
508C23C2×C3×C5×D412yes—
509C23C3×C5×#4112yes—
510C23C24×C3×C511yescharacteristic
511D4—28no—
512C2×C4—28no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—44no—
532C2×C4—44no—
533C2×C4—44no—
534C2×C4C22×C3×C4×C514yes—
535C2×C4C22×C3×C4×C514yes—
536C2×C4C22×C3×C4×C512yes—
537C2×C4C2×C3×C5×D412yes—
538C2×C4C2×C3×C5×D412yes—
539C2×C3—24no—
540C2×C3—42no—
541C2×C3C2×C4×C5×D411yescharacteristic
542C2×C3C5×#52012yes—
543C2×C3C5×#53411yescharacteristic
544C2×C3C5×#53611yescharacteristic
545C2×C3C5×#53912yes—
546C5C3×#232211yescharacteristic, direct product factor, Sylow
547C22—24no—
548C22—22no—
549C22—22no—
550C22—24no—
551C22—22no—
552C22—24no—
553C22—41no—
554C22—41no—
555C22—42no—
556C22C3×C4×C5×D414yes—
557C22C23×C3×C4×C511yescharacteristic
558C22C22×C3×C5×D411yescharacteristic
559C22C2×C3×C5×#4111yescharacteristic
560C22C3×C5×H(5,𝔽2)12yes—
561C22C3×C5×2−1+412yes—
562C4—24no—
563C4—22no—
564C4—24no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—42no—
571C3C5×#232211yescharacteristic, direct product factor, Sylow
572C2—24no—
573C2—42no—
574C2C2×C3×C4×C5×D411yescharacteristic
575C2C3×C5×#52012yes—
576C2C3×C5×#53411yescharacteristic
577C2C3×C5×#53611yescharacteristic
578C2C3×C5×#53912yes—
subgroupG/H
center, socleC23×C3×C5C24
commutatorC22C23×C3×C4×C5
Frattini, cosocleC23C24×C3×C5
prime radicalC22×C3×C5×D4C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×C3×C5×C4⋊C4C2semidirect
4. C3×C5×#389C2semidirect
5. C3×C5×#388C2semidirect
6. C3×C5×#387C2semidirect
8. C3×C5×#385C2semidirect
9. C3×C5×#385C2semidirect
10. C3×C5×#381C2semidirect
11. C3×C4×C5×C22⋊C4C2semidirect
12. C5×#2322C3direct (N × H)
18. C3×C5×#123C4semidirect
39. C3×#2322C5direct (N × H)
42. C22×C5×C4⋊C4C2×C3semidirect
43. C5×#389C2×C3semidirect
44. C5×#388C2×C3semidirect
45. C5×#387C2×C3semidirect
47. C5×#385C2×C3semidirect
48. C5×#385C2×C3semidirect
49. C5×#381C2×C3semidirect
50. C4×C5×C22⋊C4C2×C3semidirect
63. C22×C3×C4×C5C2×C4semidirect
78. C3×C5×C4⋊C4C2×C4semidirect
83. C3×C5×C22⋊C4C2×C4semidirect
84. C3×C5×C22⋊C4C2×C4semidirect
89. C22×C3×C4⋊C4C2×C5semidirect
90. C3×#389C2×C5semidirect
91. C3×#388C2×C5semidirect
92. C3×#387C2×C5semidirect
94. C3×#385C2×C5semidirect
95. C3×#385C2×C5semidirect
96. C3×#381C2×C5semidirect
97. C3×C4×C22⋊C4C2×C5semidirect
103. C5×#123C3×C4semidirect
124. #2322C3×C5direct (N × H)
169. C3×#123C4×C5semidirect
202. C22×C4×C5C2×C3×C4semidirect
217. C5×C4⋊C4C2×C3×C4semidirect
222. C5×C22⋊C4C2×C3×C4semidirect
223. C5×C22⋊C4C2×C3×C4semidirect
228. C22×C4⋊C4C2×C3×C5semidirect
229. #389C2×C3×C5semidirect
230. #388C2×C3×C5semidirect
231. #387C2×C3×C5semidirect
233. #385C2×C3×C5semidirect
234. #385C2×C3×C5semidirect
235. #381C2×C3×C5semidirect
236. C4×C22⋊C4C2×C3×C5semidirect
273. C22×C3×C4C2×C4×C5semidirect
288. C3×C4⋊C4C2×C4×C5semidirect
293. C3×C22⋊C4C2×C4×C5semidirect
294. C3×C22⋊C4C2×C4×C5semidirect
341. #123C3×C4×C5semidirect
444. C22×C4C2×C3×C4×C5semidirect
459. C4⋊C4C2×C3×C4×C5semidirect
464. C22⋊C4C2×C3×C4×C5semidirect
465. C22⋊C4C2×C3×C4×C5semidirect
468. C3×C5#2322direct (N × H)
546. C5C3×#2322direct (N × H)
571. C3C5×#2322direct (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×C4×C5×D42
C22×C3×C5×C4⋊C42
C3×C5×#3892
C3×C5×#3882
C3×C5×#3872
C3×C5×#3862
C3×C5×#3852
C3×C5×#3812
C3×C4×C5×C22⋊C42
C5×#23223
C3×#23225