Finite Group Databasebeta

← C3×C5×#2454 #14275488

Subgroups — C3×C5×#2454 #14275488

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#125C211yesmaximal, characteristic, complemented
2C2×C3×C4×C5×D4C211yesmaximal, characteristic
3C3×C5×#399C212yesmaximal, complemented
4C3×C5×#396C212yesmaximal, complemented
5C3×C5×#390C211yesmaximal, characteristic
6C3×C5×#390C211yesmaximal, characteristic
7C3×C5×#389C211yesmaximal, characteristic, complemented
8C3×C5×#389C211yesmaximal, characteristic, complemented
9C3×C5×#385C212yesmaximal, complemented
10C3×C5×#380C212yesmaximal, complemented
11C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
12C5×#2454C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2212yes—
15C3×C5×#125—24no—
16C3×C4×C5×D4—24no—
17C2×C3×C5×C4⋊C4C2212yes—
18C2×C3×C5×C4⋊C4C2212yes—
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C4⋊C4C2212yes—
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2212yes—
27C2×C3×C5×C22⋊C4C2212yes—
28C2×C3×C5×C22⋊C4C2212yes—
29C2×C3×C5×C22⋊C4C2212yes—
30C2×C3×C5×C22⋊C4C2212yes—
31C2×C3×C42×C5C2211yescharacteristic
32C2×C3×C42×C5C2211yescharacteristic
33C2×C3×C42×C5C2211yescharacteristic
34C3×C5×#95C2211yescharacteristic
35C3×C5×#95C2211yescharacteristic
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×#2454C511yesmaximal, characteristic, direct product factor, Hall
39C2×C5×#125C2×C311yescharacteristic, complemented
40C2×C4×C5×D4C2×C311yescharacteristic
41C5×#399C2×C312yescomplemented
42C5×#396C2×C312yescomplemented
43C5×#390C2×C311yescharacteristic
44C5×#390C2×C311yescharacteristic
45C5×#389C2×C311yescharacteristic, complemented
46C5×#389C2×C311yescharacteristic, complemented
47C5×#385C2×C312yescomplemented
48C5×#380C2×C312yescomplemented
49C4×C5×C4⋊C4C2×C311yescharacteristic, complemented
50C24×C3×C5C2312yes—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4Q814yes—
54C22×C3×C4×C5—24no—
55C22×C3×C4×C5—24no—
56C22×C3×C4×C5—42no—
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2312yes—
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C3×C5×C4⋊C4—24no—
68C3×C5×C4⋊C4—24no—
69C3×C5×C4⋊C4—22no—
70C3×C5×C4⋊C4—22no—
71C3×C5×C4⋊C4—22no—
72C3×C5×C4⋊C4—22no—
73C3×C5×C4⋊C4—42no—
74C3×C5×C4⋊C4—42no—
75C3×C5×C4⋊C4D414yes—
76C3×C5×C22⋊C4—24no—
77C3×C5×C22⋊C4—24no—
78C3×C5×C22⋊C4—42no—
79C3×C5×C22⋊C4—42no—
80C3×C5×C22⋊C4—42no—
81C3×C42×C5—22no—
82C3×C42×C5—22no—
83C3×C42×C5—22no—
84C2×C3×#125C2×C511yescharacteristic, complemented
85C2×C3×C4×D4C2×C511yescharacteristic
86C3×#399C2×C512yescomplemented
87C3×#396C2×C512yescomplemented
88C3×#390C2×C511yescharacteristic
89C3×#390C2×C511yescharacteristic
90C3×#389C2×C511yescharacteristic, complemented
91C3×#389C2×C511yescharacteristic, complemented
92C3×#385C2×C512yescomplemented
93C3×#380C2×C512yescomplemented
94C3×C4×C4⋊C4C2×C511yescharacteristic, complemented
95C22×C5×D4C22×C311yescharacteristic
96C23×C4×C5C22×C312yes—
97C5×#125—24no—
98C4×C5×D4—24no—
99C2×C5×C4⋊C4C22×C311yescharacteristic
100C2×C5×C4⋊C4C22×C311yescharacteristic
101C2×C5×C4⋊C4C22×C312yes—
102C2×C5×C4⋊C4C22×C312yes—
103C2×C5×C4⋊C4C22×C311yescharacteristic
104C2×C5×C4⋊C4C22×C311yescharacteristic
105C2×C5×C4⋊C4C22×C312yes—
106C2×C5×C4⋊C4C22×C312yes—
107C2×C5×C4⋊C4C22×C311yescharacteristic
108C2×C5×C22⋊C4C22×C312yes—
109C2×C5×C22⋊C4C22×C312yes—
110C2×C5×C22⋊C4C22×C312yes—
111C2×C5×C22⋊C4C22×C312yes—
112C2×C5×C22⋊C4C22×C312yes—
113C2×C42×C5C22×C311yescharacteristic
114C2×C42×C5C22×C311yescharacteristic
115C2×C42×C5C22×C311yescharacteristic
116C5×#95C22×C311yescharacteristic
117C5×#95C22×C311yescharacteristic
118C5×#95C22×C312yes—
119C5×#95C22×C312yes—
120#2454C3×C511yescharacteristic, direct product factor, Sylow
121C23×C3×C5—22no—
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5C2×Q814yes—
128C23×C3×C5C2411yescharacteristic
129C3×C5×D4—28no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—21no—
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—22no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—48no—
155C2×C3×C4×C5C2×D414yes—
156C2×C3×C4×C5C2×D412yes—
157C2×C3×C4×C5C2×Q812yes—
158C2×C3×C4×C5#4112yes—
159C2×C3×C4×C5#4112yes—
160C2×C3×C4×C5#4112yes—
161C22×C3×D4C22×C511yescharacteristic
162C23×C3×C4C22×C512yes—
163C3×#125—24no—
164C3×C4×D4—24no—
165C2×C3×C4⋊C4C22×C511yescharacteristic
166C2×C3×C4⋊C4C22×C511yescharacteristic
167C2×C3×C4⋊C4C22×C512yes—
168C2×C3×C4⋊C4C22×C512yes—
169C2×C3×C4⋊C4C22×C511yescharacteristic
170C2×C3×C4⋊C4C22×C511yescharacteristic
171C2×C3×C4⋊C4C22×C512yes—
172C2×C3×C4⋊C4C22×C512yes—
173C2×C3×C4⋊C4C22×C511yescharacteristic
174C2×C3×C22⋊C4C22×C512yes—
175C2×C3×C22⋊C4C22×C512yes—
176C2×C3×C22⋊C4C22×C512yes—
177C2×C3×C22⋊C4C22×C512yes—
178C2×C3×C22⋊C4C22×C512yes—
179C2×C3×C42C22×C511yescharacteristic
180C2×C3×C42C22×C511yescharacteristic
181C2×C3×C42C22×C511yescharacteristic
182C3×#95C22×C511yescharacteristic
183C3×#95C22×C511yescharacteristic
184C3×#95C22×C512yes—
185C3×#95C22×C512yes—
186C24×C5C23×C312yes—
187C2×C5×D4—22no—
188C2×C5×D4—22no—
189C2×C5×D4C3×Q814yes—
190C22×C4×C5—24no—
191C22×C4×C5—24no—
192C22×C4×C5—42no—
193C22×C4×C5C23×C311yescharacteristic
194C22×C4×C5C23×C311yescharacteristic
195C22×C4×C5C23×C311yescharacteristic
196C22×C4×C5C23×C311yescharacteristic
197C22×C4×C5C23×C312yes—
198C22×C4×C5C23×C312yes—
199C22×C4×C5C23×C312yes—
200C22×C4×C5C23×C311yescharacteristic
201C22×C4×C5C23×C311yescharacteristic
202C22×C4×C5C23×C311yescharacteristic
203C5×C4⋊C4—24no—
204C5×C4⋊C4—24no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—22no—
208C5×C4⋊C4—22no—
209C5×C4⋊C4—42no—
210C5×C4⋊C4—42no—
211C5×C4⋊C4C3×D414yes—
212C5×C22⋊C4—24no—
213C5×C22⋊C4—24no—
214C5×C22⋊C4—42no—
215C5×C22⋊C4—42no—
216C5×C22⋊C4—42no—
217C42×C5—22no—
218C42×C5—22no—
219C42×C5—22no—
220C2×#125C2×C3×C511yescharacteristic, complemented
221C2×C4×D4C2×C3×C511yescharacteristic
222#399C2×C3×C512yescomplemented
223#396C2×C3×C512yescomplemented
224#390C2×C3×C511yescharacteristic
225#390C2×C3×C511yescharacteristic
226#389C2×C3×C511yescharacteristic, complemented
227#389C2×C3×C511yescharacteristic, complemented
228#385C2×C3×C512yescomplemented
229#380C2×C3×C512yescomplemented
230C4×C4⋊C4C2×C3×C511yescharacteristic, complemented
231C22×C3×C5—24no—
232C22×C3×C5—24no—
233C22×C3×C5—24no—
234C22×C3×C5—42no—
235C22×C3×C5—42no—
236C22×C3×C5—42no—
237C22×C3×C5—42no—
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C22×Q811yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C22×C3×C5H(5,𝔽2)11yescharacteristic
244C22×C3×C5H(5,𝔽2)11yescharacteristic
245C3×C4×C5—22no—
246C3×C4×C5—22no—
247C3×C4×C5—24no—
248C3×C4×C5—41no—
249C3×C4×C5—42no—
250C3×C4×C5—41no—
251C3×C4×C5—41no—
252C3×C4×C5—41no—
253C3×C4×C5—42no—
254C3×C4×C5C22⋊Q814yes—
255C24×C3C23×C512yes—
256C2×C3×D4—22no—
257C2×C3×D4—22no—
258C2×C3×D4C5×Q814yes—
259C22×C3×C4—24no—
260C22×C3×C4—24no—
261C22×C3×C4—42no—
262C22×C3×C4C23×C511yescharacteristic
263C22×C3×C4C23×C512yes—
264C22×C3×C4C23×C511yescharacteristic
265C22×C3×C4C23×C511yescharacteristic
266C22×C3×C4C23×C511yescharacteristic
267C22×C3×C4C23×C512yes—
268C22×C3×C4C23×C512yes—
269C22×C3×C4C23×C511yescharacteristic
270C22×C3×C4C23×C511yescharacteristic
271C22×C3×C4C23×C511yescharacteristic
272C3×C4⋊C4—24no—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—22no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—42no—
279C3×C4⋊C4—42no—
280C3×C4⋊C4C5×D414yes—
281C3×C22⋊C4—24no—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—42no—
284C3×C22⋊C4—42no—
285C3×C22⋊C4—42no—
286C3×C42—22no—
287C3×C42—22no—
288C3×C42—22no—
289C23×C5—22no—
290C23×C5—22no—
291C23×C5—22no—
292C23×C5—22no—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5C2×C3×Q814yes—
296C23×C5C24×C311yescharacteristic
297C5×D4—28no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—22no—
308C2×C4×C5—21no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—48no—
323C2×C4×C5C2×C3×D414yes—
324C2×C4×C5C2×C3×D412yes—
325C2×C4×C5C2×C3×Q812yes—
326C2×C4×C5C3×#4112yes—
327C2×C4×C5C3×#4112yes—
328C2×C4×C5C3×#4112yes—
329C22×D4C22×C3×C511yescharacteristic
330C23×C4C22×C3×C512yes—
331#125—24no—
332C4×D4—24no—
333C2×C4⋊C4C22×C3×C512yes—
334C2×C4⋊C4C22×C3×C512yes—
335C2×C4⋊C4C22×C3×C511yescharacteristic
336C2×C4⋊C4C22×C3×C511yescharacteristic
337C2×C4⋊C4C22×C3×C511yescharacteristic
338C2×C4⋊C4C22×C3×C511yescharacteristic
339C2×C4⋊C4C22×C3×C512yes—
340C2×C4⋊C4C22×C3×C512yes—
341C2×C4⋊C4C22×C3×C511yescharacteristic
342C2×C22⋊C4C22×C3×C512yes—
343C2×C22⋊C4C22×C3×C512yes—
344C2×C22⋊C4C22×C3×C512yes—
345C2×C22⋊C4C22×C3×C512yes—
346C2×C22⋊C4C22×C3×C512yes—
347C2×C42C22×C3×C511yescharacteristic
348C2×C42C22×C3×C511yescharacteristic
349C2×C42C22×C3×C511yescharacteristic
350#95C22×C3×C511yescharacteristic
351#95C22×C3×C511yescharacteristic
352#95C22×C3×C512yes—
353#95C22×C3×C512yes—
354C2×C3×C5—44no—
355C2×C3×C5C2×C22⋊Q811yescharacteristic
356C2×C3×C5#52911yescharacteristic
357C2×C3×C5#54011yescharacteristic
358C2×C3×C5#54611yescharacteristic
359C2×C3×C5#55011yescharacteristic
360C2×C3×C5#55411yescharacteristic
361C2×C3×C5#55411yescharacteristic
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3C2×C5×Q814yes—
369C23×C3C24×C511yescharacteristic
370C3×D4—28no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—48no—
396C2×C3×C4C2×C5×D414yes—
397C2×C3×C4C2×C5×D412yes—
398C2×C3×C4C2×C5×Q812yes—
399C2×C3×C4C5×#4112yes—
400C2×C3×C4C5×#4112yes—
401C2×C3×C4C5×#4112yes—
402C22×C5—24no—
403C22×C5—24no—
404C22×C5—24no—
405C22×C5—42no—
406C22×C5—42no—
407C22×C5—42no—
408C22×C5—42no—
409C22×C5C22×C3×D411yescharacteristic
410C22×C5C22×C3×Q811yescharacteristic
411C22×C5C2×C3×#4111yescharacteristic
412C22×C5C2×C3×#4111yescharacteristic
413C22×C5C2×C3×#4111yescharacteristic
414C22×C5C3×H(5,𝔽2)11yescharacteristic
415C22×C5C3×H(5,𝔽2)11yescharacteristic
416C4×C5—22no—
417C4×C5—22no—
418C4×C5—24no—
419C4×C5—41no—
420C4×C5—42no—
421C4×C5—41no—
422C4×C5—41no—
423C4×C5—41no—
424C4×C5—42no—
425C4×C5C3×C22⋊Q814yes—
426C24C23×C3×C512yes—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4C3×C5×Q814yes—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—42no—
433C22×C4C23×C3×C511yescharacteristic
434C22×C4C23×C3×C512yes—
435C22×C4C23×C3×C511yescharacteristic
436C22×C4C23×C3×C511yescharacteristic
437C22×C4C23×C3×C511yescharacteristic
438C22×C4C23×C3×C512yes—
439C22×C4C23×C3×C512yes—
440C22×C4C23×C3×C511yescharacteristic
441C22×C4C23×C3×C511yescharacteristic
442C22×C4C23×C3×C511yescharacteristic
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—42no—
450C4⋊C4—42no—
451C4⋊C4C3×C5×D414yes—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C42—22no—
458C42—22no—
459C42—22no—
460C3×C5#245411yescharacteristic, direct product factor, Hall
461C22×C3—24no—
462C22×C3—24no—
463C22×C3—24no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3C22×C5×D411yescharacteristic
469C22×C3C22×C5×Q811yescharacteristic
470C22×C3C2×C5×#4111yescharacteristic
471C22×C3C2×C5×#4111yescharacteristic
472C22×C3C2×C5×#4111yescharacteristic
473C22×C3C5×H(5,𝔽2)11yescharacteristic
474C22×C3C5×H(5,𝔽2)11yescharacteristic
475C3×C4—22no—
476C3×C4—22no—
477C3×C4—24no—
478C3×C4—41no—
479C3×C4—42no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—41no—
483C3×C4—42no—
484C3×C4C5×C22⋊Q814yes—
485C2×C5—44no—
486C2×C5C2×C3×C22⋊Q811yescharacteristic
487C2×C5C3×#52911yescharacteristic
488C2×C5C3×#54011yescharacteristic
489C2×C5C3×#54611yescharacteristic
490C2×C5C3×#55011yescharacteristic
491C2×C5C3×#55411yescharacteristic
492C2×C5C3×#55411yescharacteristic
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23C2×C3×C5×Q814yes—
500C23C24×C3×C511yescharacteristic
501D4—28no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—48no—
527C2×C4C2×C3×C5×D414yes—
528C2×C4C2×C3×C5×D412yes—
529C2×C4C2×C3×C5×Q812yes—
530C2×C4C3×C5×#4112yes—
531C2×C4C3×C5×#4112yes—
532C2×C4C3×C5×#4112yes—
533C2×C3—44no—
534C2×C3C2×C5×C22⋊Q811yescharacteristic
535C2×C3C5×#52911yescharacteristic
536C2×C3C5×#54011yescharacteristic
537C2×C3C5×#54611yescharacteristic
538C2×C3C5×#55011yescharacteristic
539C2×C3C5×#55411yescharacteristic
540C2×C3C5×#55411yescharacteristic
541C5C3×#245411yescharacteristic, direct product factor, Sylow
542C22—24no—
543C22—24no—
544C22—24no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22C22×C3×C5×D411yescharacteristic
550C22C22×C3×C5×Q811yescharacteristic
551C22C2×C3×C5×#4111yescharacteristic
552C22C2×C3×C5×#4111yescharacteristic
553C22C2×C3×C5×#4111yescharacteristic
554C22C3×C5×H(5,𝔽2)11yescharacteristic
555C22C3×C5×H(5,𝔽2)11yescharacteristic
556C4—22no—
557C4—22no—
558C4—24no—
559C4—41no—
560C4—42no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—42no—
565C4C3×C5×C22⋊Q814yes—
566C3C5×#245411yescharacteristic, direct product factor, Sylow
567C2—44no—
568C2C2×C3×C5×C22⋊Q811yescharacteristic
569C2C3×C5×#52911yescharacteristic
570C2C3×C5×#54011yescharacteristic
571C2C3×C5×#54611yescharacteristic
572C2C3×C5×#55011yescharacteristic
573C2C3×C5×#55411yescharacteristic
574C2C3×C5×#55411yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC22×C3×C5×D4C22
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×#125C2semidirect
3. C3×C5×#399C2semidirect
4. C3×C5×#396C2semidirect
7. C3×C5×#389C2semidirect
8. C3×C5×#389C2semidirect
9. C3×C5×#385C2semidirect
10. C3×C5×#380C2semidirect
11. C3×C4×C5×C4⋊C4C2semidirect
12. C5×#2454C3direct (N × H)
38. C3×#2454C5direct (N × H)
39. C2×C5×#125C2×C3semidirect
41. C5×#399C2×C3semidirect
42. C5×#396C2×C3semidirect
45. C5×#389C2×C3semidirect
46. C5×#389C2×C3semidirect
47. C5×#385C2×C3semidirect
48. C5×#380C2×C3semidirect
49. C4×C5×C4⋊C4C2×C3semidirect
84. C2×C3×#125C2×C5semidirect
86. C3×#399C2×C5semidirect
87. C3×#396C2×C5semidirect
90. C3×#389C2×C5semidirect
91. C3×#389C2×C5semidirect
92. C3×#385C2×C5semidirect
93. C3×#380C2×C5semidirect
94. C3×C4×C4⋊C4C2×C5semidirect
120. #2454C3×C5direct (N × H)
220. C2×#125C2×C3×C5semidirect
222. #399C2×C3×C5semidirect
223. #396C2×C3×C5semidirect
226. #389C2×C3×C5semidirect
227. #389C2×C3×C5semidirect
228. #385C2×C3×C5semidirect
229. #380C2×C3×C5semidirect
230. C4×C4⋊C4C2×C3×C5semidirect
460. C3×C5#2454direct (N × H)
541. C5C3×#2454direct (N × H)
566. C3C5×#2454direct (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×#1252
C2×C3×C4×C5×D42
C3×C5×#3992
C3×C5×#3962
C3×C5×#3902
C3×C5×#3892
C3×C5×#3852
C3×C5×#3802
C3×C4×C5×C4⋊C42
C5×#24543
C3×#24545