Finite Group Databasebeta

← C3×C5×#2324 #14275358

Subgroups — C3×C5×#2324 #14275358

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
3C2×C3×C5×#117C211yesmaximal, characteristic, complemented
4C3×C5×#390C211yesmaximal, characteristic, complemented
5C3×C5×#390C212yesmaximal, complemented
6C3×C5×#389C211yesmaximal, characteristic, complemented
7C3×C5×#388C212yesmaximal, complemented
8C3×C5×#386C212yesmaximal, complemented
9C3×C5×#385C212yesmaximal, complemented
10C3×C5×#380C211yesmaximal, characteristic, complemented
11C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
12C5×#2324C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C22×C3×C5×D4C2212yes—
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2212yes—
17C3×C5×#121C418yescomplemented
18C3×C4×C5×D4—24no—
19C3×C5×#117—24no—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
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
34C2×C3×C42×C5C2212yes—
35C2×C3×C42×C5C2211yescharacteristic
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×C5×#95C2212yes—
39C3×#2324C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#121C2×C311yescharacteristic
41C2×C4×C5×D4C2×C311yescharacteristic, complemented
42C2×C5×#117C2×C311yescharacteristic, complemented
43C5×#390C2×C311yescharacteristic, complemented
44C5×#390C2×C312yescomplemented
45C5×#389C2×C311yescharacteristic, complemented
46C5×#388C2×C312yescomplemented
47C5×#386C2×C312yescomplemented
48C5×#385C2×C312yescomplemented
49C5×#380C2×C311yescharacteristic, complemented
50C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2312yes—
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4—42no—
56C2×C3×C5×D4—42no—
57C2×C3×C5×D4C2×C414yes—
58C2×C3×C5×D4C2×C418yescomplemented
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—24no—
62C22×C3×C4×C5—42no—
63C22×C3×C4×C5—42no—
64C22×C3×C4×C5C2×C414yescomplemented
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2312yes—
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—22no—
77C3×C5×C4⋊C4—22no—
78C3×C5×C4⋊C4—42no—
79C3×C5×C4⋊C4C2×C414yescomplemented
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4—22no—
82C3×C5×C22⋊C4—24no—
83C3×C5×C22⋊C4—42no—
84C3×C5×C22⋊C4—42no—
85C3×C5×C22⋊C4—42no—
86C3×C5×C22⋊C4C2×C418yescomplemented
87C3×C42×C5—22no—
88C3×C42×C5—42no—
89C3×C42×C5D414yescomplemented
90C2×C3×#121C2×C511yescharacteristic
91C2×C3×C4×D4C2×C511yescharacteristic, complemented
92C2×C3×#117C2×C511yescharacteristic, complemented
93C3×#390C2×C511yescharacteristic, complemented
94C3×#390C2×C512yescomplemented
95C3×#389C2×C511yescharacteristic, complemented
96C3×#388C2×C512yescomplemented
97C3×#386C2×C512yescomplemented
98C3×#385C2×C512yescomplemented
99C3×#380C2×C511yescharacteristic, complemented
100C3×C4×C4⋊C4C2×C511yescharacteristic, complemented
101C22×C5×D4C22×C311yescharacteristic
102C22×C5×D4C22×C312yes—
103C23×C4×C5C22×C311yescharacteristic
104C23×C4×C5C22×C312yes—
105C5×#121C3×C418yescomplemented
106C4×C5×D4—24no—
107C5×#117—24no—
108C2×C5×C4⋊C4C22×C311yescharacteristic
109C2×C5×C4⋊C4C22×C311yescharacteristic
110C2×C5×C4⋊C4C22×C311yescharacteristic
111C2×C5×C4⋊C4C22×C311yescharacteristic
112C2×C5×C4⋊C4C22×C312yes—
113C2×C5×C4⋊C4C22×C311yescharacteristic
114C2×C5×C22⋊C4C22×C311yescharacteristic
115C2×C5×C22⋊C4C22×C312yes—
116C2×C5×C22⋊C4C22×C311yescharacteristic
117C2×C5×C22⋊C4C22×C312yes—
118C2×C5×C22⋊C4C22×C312yes—
119C2×C5×C22⋊C4C22×C312yes—
120C2×C5×C22⋊C4C22×C312yes—
121C2×C42×C5C22×C311yescharacteristic
122C2×C42×C5C22×C312yes—
123C2×C42×C5C22×C311yescharacteristic
124C5×#95C22×C312yes—
125C5×#95C22×C312yes—
126C5×#95C22×C312yes—
127#2324C3×C511yescharacteristic, direct product factor, Sylow
128C23×C3×C5—21no—
129C23×C3×C5—22no—
130C23×C3×C5—21no—
131C23×C3×C5—22no—
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—21no—
139C23×C3×C5—22no—
140C23×C3×C5C22×C414yes—
141C23×C3×C5C22×C412yes—
142C23×C3×C5C2411yescharacteristic
143C3×C5×D4—28no—
144C3×C5×D4—48no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—28no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—21no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5—21no—
166C2×C3×C4×C5—48no—
167C2×C3×C4×C5C22×C412yes—
168C2×C3×C4×C5C22×C414yes—
169C2×C3×C4×C5C22×C412yes—
170C2×C3×C4×C5C2×D412yes—
171C2×C3×C4×C5C2×D412yes—
172C2×C3×C4×C5C2×D412yes—
173C2×C3×C4×C5#4112yes—
174C22×C3×D4C22×C511yescharacteristic
175C22×C3×D4C22×C512yes—
176C23×C3×C4C22×C511yescharacteristic
177C23×C3×C4C22×C512yes—
178C3×#121C4×C518yescomplemented
179C3×C4×D4—24no—
180C3×#117—24no—
181C2×C3×C4⋊C4C22×C511yescharacteristic
182C2×C3×C4⋊C4C22×C511yescharacteristic
183C2×C3×C4⋊C4C22×C511yescharacteristic
184C2×C3×C4⋊C4C22×C511yescharacteristic
185C2×C3×C4⋊C4C22×C512yes—
186C2×C3×C4⋊C4C22×C511yescharacteristic
187C2×C3×C22⋊C4C22×C511yescharacteristic
188C2×C3×C22⋊C4C22×C512yes—
189C2×C3×C22⋊C4C22×C511yescharacteristic
190C2×C3×C22⋊C4C22×C512yes—
191C2×C3×C22⋊C4C22×C512yes—
192C2×C3×C22⋊C4C22×C512yes—
193C2×C3×C22⋊C4C22×C512yes—
194C2×C3×C42C22×C511yescharacteristic
195C2×C3×C42C22×C512yes—
196C2×C3×C42C22×C511yescharacteristic
197C3×#95C22×C512yes—
198C3×#95C22×C512yes—
199C3×#95C22×C512yes—
200C24×C5C23×C311yescharacteristic
201C24×C5C23×C312yes—
202C2×C5×D4—22no—
203C2×C5×D4—22no—
204C2×C5×D4—42no—
205C2×C5×D4—42no—
206C2×C5×D4C2×C3×C414yes—
207C2×C5×D4C2×C3×C418yescomplemented
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—24no—
211C22×C4×C5—42no—
212C22×C4×C5—42no—
213C22×C4×C5C2×C3×C414yescomplemented
214C22×C4×C5C23×C311yescharacteristic
215C22×C4×C5C23×C311yescharacteristic
216C22×C4×C5C23×C312yes—
217C22×C4×C5C23×C312yes—
218C22×C4×C5C23×C312yes—
219C22×C4×C5C23×C311yescharacteristic
220C22×C4×C5C23×C311yescharacteristic
221C22×C4×C5C23×C311yescharacteristic
222C22×C4×C5C23×C311yescharacteristic
223C5×C4⋊C4—22no—
224C5×C4⋊C4—22no—
225C5×C4⋊C4—22no—
226C5×C4⋊C4—22no—
227C5×C4⋊C4—42no—
228C5×C4⋊C4C2×C3×C414yescomplemented
229C5×C22⋊C4—22no—
230C5×C22⋊C4—22no—
231C5×C22⋊C4—24no—
232C5×C22⋊C4—42no—
233C5×C22⋊C4—42no—
234C5×C22⋊C4—42no—
235C5×C22⋊C4C2×C3×C418yescomplemented
236C42×C5—22no—
237C42×C5—42no—
238C42×C5C3×D414yescomplemented
239C2×#121C2×C3×C511yescharacteristic
240C2×C4×D4C2×C3×C511yescharacteristic, complemented
241C2×#117C2×C3×C511yescharacteristic, complemented
242#390C2×C3×C511yescharacteristic, complemented
243#390C2×C3×C512yescomplemented
244#389C2×C3×C511yescharacteristic, complemented
245#388C2×C3×C512yescomplemented
246#386C2×C3×C512yescomplemented
247#385C2×C3×C512yescomplemented
248#380C2×C3×C511yescharacteristic, complemented
249C4×C4⋊C4C2×C3×C511yescharacteristic, complemented
250C22×C3×C5—22no—
251C22×C3×C5—24no—
252C22×C3×C5—22no—
253C22×C3×C5—24no—
254C22×C3×C5—22no—
255C22×C3×C5—24no—
256C22×C3×C5—42no—
257C22×C3×C5—41no—
258C22×C3×C5—41no—
259C22×C3×C5—42no—
260C22×C3×C5—41no—
261C22×C3×C5—42no—
262C22×C3×C5—41no—
263C22×C3×C5—42no—
264C22×C3×C5C23×C411yescharacteristic
265C22×C3×C5C22×D411yescharacteristic
266C22×C3×C5C2×#4111yescharacteristic
267C22×C3×C5H(5,𝔽2)11yescharacteristic
268C22×C3×C5H(5,𝔽2)11yescharacteristic
269C22×C3×C5H(5,𝔽2)11yescharacteristic
270C22×C3×C52−1+411yescharacteristic
271C3×C4×C5—22no—
272C3×C4×C5—24no—
273C3×C4×C5—22no—
274C3×C4×C5—22no—
275C3×C4×C5—41no—
276C3×C4×C5—42no—
277C3×C4×C5—41no—
278C3×C4×C5—42no—
279C3×C4×C5C4×D414yes—
280C24×C3C23×C511yescharacteristic
281C24×C3C23×C512yes—
282C2×C3×D4—22no—
283C2×C3×D4—22no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4C2×C4×C514yes—
287C2×C3×D4C2×C4×C518yescomplemented
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—24no—
291C22×C3×C4—42no—
292C22×C3×C4—42no—
293C22×C3×C4C2×C4×C514yescomplemented
294C22×C3×C4C23×C511yescharacteristic
295C22×C3×C4C23×C512yes—
296C22×C3×C4C23×C512yes—
297C22×C3×C4C23×C511yescharacteristic
298C22×C3×C4C23×C512yes—
299C22×C3×C4C23×C511yescharacteristic
300C22×C3×C4C23×C511yescharacteristic
301C22×C3×C4C23×C511yescharacteristic
302C22×C3×C4C23×C511yescharacteristic
303C3×C4⋊C4—22no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—22no—
306C3×C4⋊C4—22no—
307C3×C4⋊C4—42no—
308C3×C4⋊C4C2×C4×C514yescomplemented
309C3×C22⋊C4—22no—
310C3×C22⋊C4—22no—
311C3×C22⋊C4—24no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4C2×C4×C518yescomplemented
316C3×C42—22no—
317C3×C42—42no—
318C3×C42C5×D414yescomplemented
319C23×C5—21no—
320C23×C5—22no—
321C23×C5—21no—
322C23×C5—22no—
323C23×C5—21no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—21no—
330C23×C5—22no—
331C23×C5C22×C3×C414yes—
332C23×C5C22×C3×C412yes—
333C23×C5C24×C311yescharacteristic
334C5×D4—28no—
335C5×D4—48no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5—28no—
345C2×C4×C5—21no—
346C2×C4×C5—21no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—21no—
351C2×C4×C5—21no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—21no—
355C2×C4×C5—22no—
356C2×C4×C5—21no—
357C2×C4×C5—48no—
358C2×C4×C5C22×C3×C412yes—
359C2×C4×C5C22×C3×C414yes—
360C2×C4×C5C22×C3×C412yes—
361C2×C4×C5C2×C3×D412yes—
362C2×C4×C5C2×C3×D412yes—
363C2×C4×C5C2×C3×D412yes—
364C2×C4×C5C3×#4112yes—
365C22×D4C22×C3×C511yescharacteristic
366C22×D4C22×C3×C512yes—
367C23×C4C22×C3×C511yescharacteristic
368C23×C4C22×C3×C512yes—
369#121C3×C4×C518yescomplemented
370C4×D4—24no—
371#117—24no—
372C2×C4⋊C4C22×C3×C511yescharacteristic
373C2×C4⋊C4C22×C3×C511yescharacteristic
374C2×C4⋊C4C22×C3×C511yescharacteristic
375C2×C4⋊C4C22×C3×C511yescharacteristic
376C2×C4⋊C4C22×C3×C512yes—
377C2×C4⋊C4C22×C3×C511yescharacteristic
378C2×C22⋊C4C22×C3×C511yescharacteristic
379C2×C22⋊C4C22×C3×C511yescharacteristic
380C2×C22⋊C4C22×C3×C512yes—
381C2×C22⋊C4C22×C3×C512yes—
382C2×C22⋊C4C22×C3×C512yes—
383C2×C22⋊C4C22×C3×C512yes—
384C2×C22⋊C4C22×C3×C512yes—
385C2×C42C22×C3×C511yescharacteristic
386C2×C42C22×C3×C512yes—
387C2×C42C22×C3×C511yescharacteristic
388#95C22×C3×C512yes—
389#95C22×C3×C512yes—
390#95C22×C3×C512yes—
391C2×C3×C5—42no—
392C2×C3×C5—44no—
393C2×C3×C5C2×C4×D411yescharacteristic
394C2×C3×C5#51811yescharacteristic
395C2×C3×C5#52011yescharacteristic
396C2×C3×C5#53511yescharacteristic
397C2×C3×C5#53711yescharacteristic
398C2×C3×C5#54011yescharacteristic
399C2×C3×C5#54211yescharacteristic
400C23×C3—21no—
401C23×C3—22no—
402C23×C3—21no—
403C23×C3—22no—
404C23×C3—21no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—22no—
412C23×C3C22×C4×C514yes—
413C23×C3C22×C4×C512yes—
414C23×C3C24×C511yescharacteristic
415C3×D4—28no—
416C3×D4—48no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—28no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—48no—
439C2×C3×C4C22×C4×C512yes—
440C2×C3×C4C22×C4×C514yes—
441C2×C3×C4C22×C4×C512yes—
442C2×C3×C4C2×C5×D412yes—
443C2×C3×C4C2×C5×D412yes—
444C2×C3×C4C2×C5×D412yes—
445C2×C3×C4C5×#4112yes—
446C22×C5—22no—
447C22×C5—24no—
448C22×C5—22no—
449C22×C5—24no—
450C22×C5—22no—
451C22×C5—24no—
452C22×C5—42no—
453C22×C5—41no—
454C22×C5—41no—
455C22×C5—42no—
456C22×C5—41no—
457C22×C5—42no—
458C22×C5—41no—
459C22×C5—42no—
460C22×C5C23×C3×C411yescharacteristic
461C22×C5C22×C3×D411yescharacteristic
462C22×C5C2×C3×#4111yescharacteristic
463C22×C5C3×H(5,𝔽2)11yescharacteristic
464C22×C5C3×H(5,𝔽2)11yescharacteristic
465C22×C5C3×H(5,𝔽2)11yescharacteristic
466C22×C5C3×2−1+411yescharacteristic
467C4×C5—22no—
468C4×C5—24no—
469C4×C5—22no—
470C4×C5—22no—
471C4×C5—41no—
472C4×C5—42no—
473C4×C5—41no—
474C4×C5—42no—
475C4×C5C3×C4×D414yes—
476C24C23×C3×C511yescharacteristic
477C24C23×C3×C512yes—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4C2×C3×C4×C514yes—
483C2×D4C2×C3×C4×C518yescomplemented
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4C2×C3×C4×C514yescomplemented
490C22×C4C23×C3×C511yescharacteristic
491C22×C4C23×C3×C512yes—
492C22×C4C23×C3×C512yes—
493C22×C4C23×C3×C511yescharacteristic
494C22×C4C23×C3×C512yes—
495C22×C4C23×C3×C511yescharacteristic
496C22×C4C23×C3×C511yescharacteristic
497C22×C4C23×C3×C511yescharacteristic
498C22×C4C23×C3×C511yescharacteristic
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—42no—
504C4⋊C4C2×C3×C4×C514yescomplemented
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—24no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4C2×C3×C4×C518yescomplemented
512C42—22no—
513C42—42no—
514C42C3×C5×D414yescomplemented
515C3×C5#232411yescharacteristic, direct product factor, Hall
516C22×C3—22no—
517C22×C3—24no—
518C22×C3—22no—
519C22×C3—24no—
520C22×C3—22no—
521C22×C3—24no—
522C22×C3—42no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—42no—
526C22×C3—41no—
527C22×C3—42no—
528C22×C3—41no—
529C22×C3—42no—
530C22×C3C23×C4×C511yescharacteristic
531C22×C3C22×C5×D411yescharacteristic
532C22×C3C2×C5×#4111yescharacteristic
533C22×C3C5×H(5,𝔽2)11yescharacteristic
534C22×C3C5×H(5,𝔽2)11yescharacteristic
535C22×C3C5×H(5,𝔽2)11yescharacteristic
536C22×C3C5×2−1+411yescharacteristic
537C3×C4—22no—
538C3×C4—24no—
539C3×C4—22no—
540C3×C4—22no—
541C3×C4—41no—
542C3×C4—42no—
543C3×C4—41no—
544C3×C4—42no—
545C3×C4C4×C5×D414yes—
546C2×C5—42no—
547C2×C5—44no—
548C2×C5C2×C3×C4×D411yescharacteristic
549C2×C5C3×#51811yescharacteristic
550C2×C5C3×#52011yescharacteristic
551C2×C5C3×#53511yescharacteristic
552C2×C5C3×#53711yescharacteristic
553C2×C5C3×#54011yescharacteristic
554C2×C5C3×#54211yescharacteristic
555C23—21no—
556C23—22no—
557C23—21no—
558C23—22no—
559C23—21no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—22no—
567C23C22×C3×C4×C514yes—
568C23C22×C3×C4×C512yes—
569C23C24×C3×C511yescharacteristic
570D4—28no—
571D4—48no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—28no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—48no—
594C2×C4C22×C3×C4×C512yes—
595C2×C4C22×C3×C4×C514yes—
596C2×C4C22×C3×C4×C512yes—
597C2×C4C2×C3×C5×D412yes—
598C2×C4C2×C3×C5×D412yes—
599C2×C4C2×C3×C5×D412yes—
600C2×C4C3×C5×#4112yes—
601C2×C3—42no—
602C2×C3—44no—
603C2×C3C2×C4×C5×D411yescharacteristic
604C2×C3C5×#51811yescharacteristic
605C2×C3C5×#52011yescharacteristic
606C2×C3C5×#53511yescharacteristic
607C2×C3C5×#53711yescharacteristic
608C2×C3C5×#54011yescharacteristic
609C2×C3C5×#54211yescharacteristic
610C5C3×#232411yescharacteristic, direct product factor, Sylow
611C22—22no—
612C22—24no—
613C22—22no—
614C22—24no—
615C22—22no—
616C22—24no—
617C22—42no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—41no—
622C22—42no—
623C22—41no—
624C22—42no—
625C22C23×C3×C4×C511yescharacteristic
626C22C22×C3×C5×D411yescharacteristic
627C22C2×C3×C5×#4111yescharacteristic
628C22C3×C5×H(5,𝔽2)11yescharacteristic
629C22C3×C5×H(5,𝔽2)11yescharacteristic
630C22C3×C5×H(5,𝔽2)11yescharacteristic
631C22C3×C5×2−1+411yescharacteristic
632C4—22no—
633C4—24no—
634C4—22no—
635C4—22no—
636C4—42no—
637C4—41no—
638C4—41no—
639C4—42no—
640C4C3×C4×C5×D414yes—
641C3C5×#232411yescharacteristic, direct product factor, Sylow
642C2—42no—
643C2—44no—
644C2C2×C3×C4×C5×D411yescharacteristic
645C2C3×C5×#51811yescharacteristic
646C2C3×C5×#52011yescharacteristic
647C2C3×C5×#53511yescharacteristic
648C2C3×C5×#53711yescharacteristic
649C2C3×C5×#54011yescharacteristic
650C2C3×C5×#54211yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutatorC22C23×C3×C4×C5
Frattini, cosocleC23C24×C3×C5
prime radicalC2×C3×C5×#121C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C5×D4C2semidirect
3. C2×C3×C5×#117C2semidirect
4. C3×C5×#390C2semidirect
5. C3×C5×#390C2semidirect
6. C3×C5×#389C2semidirect
7. C3×C5×#388C2semidirect
8. C3×C5×#386C2semidirect
9. C3×C5×#385C2semidirect
10. C3×C5×#380C2semidirect
11. C3×C4×C5×C4⋊C4C2semidirect
12. C5×#2324C3direct (N × H)
17. C3×C5×#121C4semidirect
39. C3×#2324C5direct (N × H)
41. C2×C4×C5×D4C2×C3semidirect
42. C2×C5×#117C2×C3semidirect
43. C5×#390C2×C3semidirect
44. C5×#390C2×C3semidirect
45. C5×#389C2×C3semidirect
46. C5×#388C2×C3semidirect
47. C5×#386C2×C3semidirect
48. C5×#385C2×C3semidirect
49. C5×#380C2×C3semidirect
50. C4×C5×C4⋊C4C2×C3semidirect
58. C2×C3×C5×D4C2×C4semidirect
64. C22×C3×C4×C5C2×C4semidirect
79. C3×C5×C4⋊C4C2×C4semidirect
86. C3×C5×C22⋊C4C2×C4semidirect
89. C3×C42×C5D4semidirect
91. C2×C3×C4×D4C2×C5semidirect
92. C2×C3×#117C2×C5semidirect
93. C3×#390C2×C5semidirect
94. C3×#390C2×C5semidirect
95. C3×#389C2×C5semidirect
96. C3×#388C2×C5semidirect
97. C3×#386C2×C5semidirect
98. C3×#385C2×C5semidirect
99. C3×#380C2×C5semidirect
100. C3×C4×C4⋊C4C2×C5semidirect
105. C5×#121C3×C4semidirect
127. #2324C3×C5direct (N × H)
178. C3×#121C4×C5semidirect
207. C2×C5×D4C2×C3×C4semidirect
213. C22×C4×C5C2×C3×C4semidirect
228. C5×C4⋊C4C2×C3×C4semidirect
235. C5×C22⋊C4C2×C3×C4semidirect
238. C42×C5C3×D4semidirect
240. C2×C4×D4C2×C3×C5semidirect
241. C2×#117C2×C3×C5semidirect
242. #390C2×C3×C5semidirect
243. #390C2×C3×C5semidirect
244. #389C2×C3×C5semidirect
245. #388C2×C3×C5semidirect
246. #386C2×C3×C5semidirect
247. #385C2×C3×C5semidirect
248. #380C2×C3×C5semidirect
249. C4×C4⋊C4C2×C3×C5semidirect
287. C2×C3×D4C2×C4×C5semidirect
293. C22×C3×C4C2×C4×C5semidirect
308. C3×C4⋊C4C2×C4×C5semidirect
315. C3×C22⋊C4C2×C4×C5semidirect
318. C3×C42C5×D4semidirect
369. #121C3×C4×C5semidirect
483. C2×D4C2×C3×C4×C5semidirect
489. C22×C4C2×C3×C4×C5semidirect
504. C4⋊C4C2×C3×C4×C5semidirect
511. C22⋊C4C2×C3×C4×C5semidirect
514. C42C3×C5×D4semidirect
515. C3×C5#2324direct (N × H)
610. C5C3×#2324direct (N × H)
641. C3C5×#2324direct (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
C2×C3×C5×#1172
C3×C5×#3902
C3×C5×#3892
C3×C5×#3882
C3×C5×#3862
C3×C5×#3852
C3×C5×#3802
C3×C4×C5×C4⋊C42
C5×#23243
C3×#23245