Finite Group Databasebeta

← C3×C5×#2423 #14275457

Subgroups — C3×C5×#2423 #14275457

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic
2C2×C3×C4×C5×Q8C211yesmaximal, characteristic, complemented
3C3×C5×#399C212yesmaximal
4C3×C5×#398C212yesmaximal, complemented
5C3×C5×#391C211yesmaximal, characteristic, complemented
6C3×C5×#389C211yesmaximal, characteristic, complemented
7C3×C5×#388C212yesmaximal
8C3×C5×#387C212yesmaximal, complemented
9C3×C5×#384C211yesmaximal, characteristic, complemented
10C3×C5×#380C211yesmaximal, characteristic
11C3×C4×C5×C22⋊C4C211yesmaximal, characteristic
12C5×#2423C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C3×C5×C22⋊Q8—24no—
16C3×C4×C5×Q8—24no—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2212yes—
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2212yes—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2212yes—
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C4⋊C4C2212yes—
25C2×C3×C5×C22⋊C4C2212yes—
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2212yes—
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C42×C5C2211yescharacteristic
30C2×C3×C42×C5C2212yes—
31C2×C3×C42×C5C2211yescharacteristic
32C3×C5×#95C2211yescharacteristic
33C3×C5×#95C2211yescharacteristic
34C3×C5×#95C2212yes—
35C3×C5×#95C2212yes—
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×#2423C511yesmaximal, characteristic, direct product factor, Hall
39C2×C5×C22⋊Q8C2×C311yescharacteristic
40C2×C4×C5×Q8C2×C311yescharacteristic, complemented
41C5×#399C2×C312yes—
42C5×#398C2×C312yescomplemented
43C5×#391C2×C311yescharacteristic, complemented
44C5×#389C2×C311yescharacteristic, complemented
45C5×#388C2×C312yes—
46C5×#387C2×C312yescomplemented
47C5×#384C2×C311yescharacteristic, complemented
48C5×#380C2×C311yescharacteristic
49C4×C5×C22⋊C4C2×C311yescharacteristic
50C24×C3×C5C2311yescharacteristic
51C2×C3×C5×Q8—22no—
52C2×C3×C5×Q8—22no—
53C2×C3×C5×Q8D414yes—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2312yes—
59C22×C3×C4×C5C2312yes—
60C22×C3×C4×C5C2312yes—
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C3×C5×C4⋊C4—24no—
68C3×C5×C4⋊C4—22no—
69C3×C5×C4⋊C4—22no—
70C3×C5×C4⋊C4—24no—
71C3×C5×C4⋊C4—24no—
72C3×C5×C4⋊C4—22no—
73C3×C5×C4⋊C4—42no—
74C3×C5×C4⋊C4—42no—
75C3×C5×C22⋊C4—24no—
76C3×C5×C22⋊C4—22no—
77C3×C5×C22⋊C4—42no—
78C3×C5×C22⋊C4Q814yescomplemented
79C3×C42×C5—24no—
80C3×C42×C5—22no—
81C3×C42×C5—22no—
82C2×C3×C22⋊Q8C2×C511yescharacteristic
83C2×C3×C4×Q8C2×C511yescharacteristic, complemented
84C3×#399C2×C512yes—
85C3×#398C2×C512yescomplemented
86C3×#391C2×C511yescharacteristic, complemented
87C3×#389C2×C511yescharacteristic, complemented
88C3×#388C2×C512yes—
89C3×#387C2×C512yescomplemented
90C3×#384C2×C511yescharacteristic, complemented
91C3×#380C2×C511yescharacteristic
92C3×C4×C22⋊C4C2×C511yescharacteristic
93C22×C5×Q8C22×C311yescharacteristic
94C23×C4×C5C22×C311yescharacteristic
95C5×C22⋊Q8—24no—
96C4×C5×Q8—24no—
97C2×C5×C4⋊C4C22×C311yescharacteristic
98C2×C5×C4⋊C4C22×C311yescharacteristic
99C2×C5×C4⋊C4C22×C312yes—
100C2×C5×C4⋊C4C22×C311yescharacteristic
101C2×C5×C4⋊C4C22×C312yes—
102C2×C5×C4⋊C4C22×C312yes—
103C2×C5×C4⋊C4C22×C312yes—
104C2×C5×C4⋊C4C22×C312yes—
105C2×C5×C22⋊C4C22×C311yescharacteristic
106C2×C5×C22⋊C4C22×C312yes—
107C2×C5×C22⋊C4C22×C312yes—
108C2×C5×C22⋊C4C22×C311yescharacteristic
109C2×C42×C5C22×C311yescharacteristic
110C2×C42×C5C22×C311yescharacteristic
111C2×C42×C5C22×C312yes—
112C5×#95C22×C311yescharacteristic
113C5×#95C22×C311yescharacteristic
114C5×#95C22×C312yes—
115C5×#95C22×C312yes—
116C5×#95C22×C312yes—
117C5×#95C22×C312yes—
118#2423C3×C511yescharacteristic, direct product factor, Sylow
119C23×C3×C5—21no—
120C23×C3×C5—21no—
121C23×C3×C5—21no—
122C23×C3×C5—21no—
123C23×C3×C5—21no—
124C23×C3×C5—21no—
125C23×C3×C5C2×Q812yes—
126C23×C3×C5C2411yescharacteristic
127C3×C5×Q8—28no—
128C2×C3×C4×C5—21no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—44no—
152C2×C3×C4×C5C2×D414yes—
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2×Q812yes—
155C2×C3×C4×C5C2×Q812yes—
156C2×C3×C4×C5#4112yes—
157C2×C3×C4×C5#4112yes—
158C2×C3×C4×C5#4112yes—
159C22×C3×Q8C22×C511yescharacteristic
160C23×C3×C4C22×C511yescharacteristic
161C3×C22⋊Q8—24no—
162C3×C4×Q8—24no—
163C2×C3×C4⋊C4C22×C511yescharacteristic
164C2×C3×C4⋊C4C22×C511yescharacteristic
165C2×C3×C4⋊C4C22×C512yes—
166C2×C3×C4⋊C4C22×C511yescharacteristic
167C2×C3×C4⋊C4C22×C512yes—
168C2×C3×C4⋊C4C22×C512yes—
169C2×C3×C4⋊C4C22×C512yes—
170C2×C3×C4⋊C4C22×C512yes—
171C2×C3×C22⋊C4C22×C511yescharacteristic
172C2×C3×C22⋊C4C22×C512yes—
173C2×C3×C22⋊C4C22×C512yes—
174C2×C3×C22⋊C4C22×C511yescharacteristic
175C2×C3×C42C22×C511yescharacteristic
176C2×C3×C42C22×C511yescharacteristic
177C2×C3×C42C22×C512yes—
178C3×#95C22×C511yescharacteristic
179C3×#95C22×C511yescharacteristic
180C3×#95C22×C512yes—
181C3×#95C22×C512yes—
182C3×#95C22×C512yes—
183C3×#95C22×C512yes—
184C24×C5C23×C311yescharacteristic
185C2×C5×Q8—22no—
186C2×C5×Q8—22no—
187C2×C5×Q8C3×D414yes—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5C23×C311yescharacteristic
192C22×C4×C5C23×C312yes—
193C22×C4×C5C23×C312yes—
194C22×C4×C5C23×C312yes—
195C22×C4×C5C23×C311yescharacteristic
196C22×C4×C5C23×C312yes—
197C22×C4×C5C23×C311yescharacteristic
198C22×C4×C5C23×C311yescharacteristic
199C22×C4×C5C23×C311yescharacteristic
200C22×C4×C5C23×C311yescharacteristic
201C5×C4⋊C4—24no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—24no—
205C5×C4⋊C4—24no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—42no—
208C5×C4⋊C4—42no—
209C5×C22⋊C4—24no—
210C5×C22⋊C4—22no—
211C5×C22⋊C4—42no—
212C5×C22⋊C4C3×Q814yescomplemented
213C42×C5—24no—
214C42×C5—22no—
215C42×C5—22no—
216C2×C22⋊Q8C2×C3×C511yescharacteristic
217C2×C4×Q8C2×C3×C511yescharacteristic, complemented
218#399C2×C3×C512yes—
219#398C2×C3×C512yescomplemented
220#391C2×C3×C511yescharacteristic, complemented
221#389C2×C3×C511yescharacteristic, complemented
222#388C2×C3×C512yes—
223#387C2×C3×C512yescomplemented
224#384C2×C3×C511yescharacteristic, complemented
225#380C2×C3×C511yescharacteristic
226C4×C22⋊C4C2×C3×C511yescharacteristic
227C22×C3×C5—22no—
228C22×C3×C5—22no—
229C22×C3×C5—22no—
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5—41no—
233C22×C3×C5—41no—
234C22×C3×C5C22×D411yescharacteristic
235C22×C3×C5C22×Q811yescharacteristic
236C22×C3×C5C2×#4111yescharacteristic
237C22×C3×C5C2×#4111yescharacteristic
238C22×C3×C5C2×#4111yescharacteristic
239C22×C3×C5H(5,𝔽2)11yescharacteristic
240C22×C3×C52−1+411yescharacteristic
241C3×C4×C5—24no—
242C3×C4×C5—22no—
243C3×C4×C5—22no—
244C3×C4×C5—22no—
245C3×C4×C5—41no—
246C3×C4×C5—42no—
247C3×C4×C5—41no—
248C3×C4×C5—42no—
249C3×C4×C5—42no—
250C3×C4×C5#12314yes—
251C24×C3C23×C511yescharacteristic
252C2×C3×Q8—22no—
253C2×C3×Q8—22no—
254C2×C3×Q8C5×D414yes—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4C23×C512yes—
259C22×C3×C4C23×C511yescharacteristic
260C22×C3×C4C23×C511yescharacteristic
261C22×C3×C4C23×C512yes—
262C22×C3×C4C23×C512yes—
263C22×C3×C4C23×C512yes—
264C22×C3×C4C23×C511yescharacteristic
265C22×C3×C4C23×C511yescharacteristic
266C22×C3×C4C23×C511yescharacteristic
267C22×C3×C4C23×C511yescharacteristic
268C3×C4⋊C4—24no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—24no—
273C3×C4⋊C4—22no—
274C3×C4⋊C4—42no—
275C3×C4⋊C4—42no—
276C3×C22⋊C4—24no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4C5×Q814yescomplemented
280C3×C42—24no—
281C3×C42—22no—
282C3×C42—22no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5C2×C3×Q812yes—
290C23×C5C24×C311yescharacteristic
291C5×Q8—28no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—22no—
296C2×C4×C5—22no—
297C2×C4×C5—21no—
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—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—21no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—44no—
316C2×C4×C5C2×C3×D414yes—
317C2×C4×C5C2×C3×D412yes—
318C2×C4×C5C2×C3×Q812yes—
319C2×C4×C5C2×C3×Q812yes—
320C2×C4×C5C3×#4112yes—
321C2×C4×C5C3×#4112yes—
322C2×C4×C5C3×#4112yes—
323C22×Q8C22×C3×C511yescharacteristic
324C23×C4C22×C3×C511yescharacteristic
325C22⋊Q8—24no—
326C4×Q8—24no—
327C2×C4⋊C4C22×C3×C511yescharacteristic
328C2×C4⋊C4C22×C3×C512yes—
329C2×C4⋊C4C22×C3×C511yescharacteristic
330C2×C4⋊C4C22×C3×C512yes—
331C2×C4⋊C4C22×C3×C511yescharacteristic
332C2×C4⋊C4C22×C3×C512yes—
333C2×C4⋊C4C22×C3×C512yes—
334C2×C4⋊C4C22×C3×C512yes—
335C2×C22⋊C4C22×C3×C512yes—
336C2×C22⋊C4C22×C3×C511yescharacteristic
337C2×C22⋊C4C22×C3×C512yes—
338C2×C22⋊C4C22×C3×C511yescharacteristic
339C2×C42C22×C3×C511yescharacteristic
340C2×C42C22×C3×C512yes—
341C2×C42C22×C3×C511yescharacteristic
342#95C22×C3×C511yescharacteristic
343#95C22×C3×C511yescharacteristic
344#95C22×C3×C512yes—
345#95C22×C3×C512yes—
346#95C22×C3×C512yes—
347#95C22×C3×C512yes—
348C2×C3×C5—42no—
349C2×C3×C5C2×#12311yescharacteristic
350C2×C3×C5#53311yescharacteristic
351C2×C3×C5#54211yescharacteristic
352C2×C3×C5D4×Q811yescharacteristic
353C2×C3×C5#55011yescharacteristic
354C2×C3×C5#55211yescharacteristic
355C2×C3×C5#55411yescharacteristic
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3C2×C5×Q812yes—
363C23×C3C24×C511yescharacteristic
364C3×Q8—28no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
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—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
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—44no—
389C2×C3×C4C2×C5×D414yes—
390C2×C3×C4C2×C5×D412yes—
391C2×C3×C4C2×C5×Q812yes—
392C2×C3×C4C2×C5×Q812yes—
393C2×C3×C4C5×#4112yes—
394C2×C3×C4C5×#4112yes—
395C2×C3×C4C5×#4112yes—
396C22×C5—22no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—41no—
402C22×C5—41no—
403C22×C5C22×C3×D411yescharacteristic
404C22×C5C22×C3×Q811yescharacteristic
405C22×C5C2×C3×#4111yescharacteristic
406C22×C5C2×C3×#4111yescharacteristic
407C22×C5C2×C3×#4111yescharacteristic
408C22×C5C3×H(5,𝔽2)11yescharacteristic
409C22×C5C3×2−1+411yescharacteristic
410C4×C5—24no—
411C4×C5—22no—
412C4×C5—22no—
413C4×C5—22no—
414C4×C5—41no—
415C4×C5—42no—
416C4×C5—41no—
417C4×C5—42no—
418C4×C5—42no—
419C4×C5C3×#12314yes—
420C24C23×C3×C511yescharacteristic
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8C3×C5×D414yes—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4C23×C3×C512yes—
428C22×C4C23×C3×C511yescharacteristic
429C22×C4C23×C3×C511yescharacteristic
430C22×C4C23×C3×C512yes—
431C22×C4C23×C3×C512yes—
432C22×C4C23×C3×C512yes—
433C22×C4C23×C3×C511yescharacteristic
434C22×C4C23×C3×C511yescharacteristic
435C22×C4C23×C3×C511yescharacteristic
436C22×C4C23×C3×C511yescharacteristic
437C4⋊C4—24no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C4⋊C4—22no—
443C4⋊C4—42no—
444C4⋊C4—42no—
445C22⋊C4—24no—
446C22⋊C4—22no—
447C22⋊C4—42no—
448C22⋊C4C3×C5×Q814yescomplemented
449C42—24no—
450C42—22no—
451C42—22no—
452C3×C5#242311yescharacteristic, direct product factor, Hall
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3C22×C5×D411yescharacteristic
461C22×C3C22×C5×Q811yescharacteristic
462C22×C3C2×C5×#4111yescharacteristic
463C22×C3C2×C5×#4111yescharacteristic
464C22×C3C2×C5×#4111yescharacteristic
465C22×C3C5×H(5,𝔽2)11yescharacteristic
466C22×C3C5×2−1+411yescharacteristic
467C3×C4—24no—
468C3×C4—22no—
469C3×C4—22no—
470C3×C4—22no—
471C3×C4—41no—
472C3×C4—42no—
473C3×C4—41no—
474C3×C4—42no—
475C3×C4—42no—
476C3×C4C5×#12314yes—
477C2×C5—42no—
478C2×C5C2×C3×#12311yescharacteristic
479C2×C5C3×#53311yescharacteristic
480C2×C5C3×#54211yescharacteristic
481C2×C5C3×D4×Q811yescharacteristic
482C2×C5C3×#55011yescharacteristic
483C2×C5C3×#55211yescharacteristic
484C2×C5C3×#55411yescharacteristic
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23C2×C3×C5×Q812yes—
492C23C24×C3×C511yescharacteristic
493Q8—28no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—44no—
518C2×C4C2×C3×C5×D414yes—
519C2×C4C2×C3×C5×D412yes—
520C2×C4C2×C3×C5×Q812yes—
521C2×C4C2×C3×C5×Q812yes—
522C2×C4C3×C5×#4112yes—
523C2×C4C3×C5×#4112yes—
524C2×C4C3×C5×#4112yes—
525C2×C3—42no—
526C2×C3C2×C5×#12311yescharacteristic
527C2×C3C5×#53311yescharacteristic
528C2×C3C5×#54211yescharacteristic
529C2×C3C5×D4×Q811yescharacteristic
530C2×C3C5×#55011yescharacteristic
531C2×C3C5×#55211yescharacteristic
532C2×C3C5×#55411yescharacteristic
533C5C3×#242311yescharacteristic, direct product factor, Sylow
534C22—22no—
535C22—22no—
536C22—22no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22C22×C3×C5×D411yescharacteristic
542C22C22×C3×C5×Q811yescharacteristic
543C22C2×C3×C5×#4111yescharacteristic
544C22C2×C3×C5×#4111yescharacteristic
545C22C2×C3×C5×#4111yescharacteristic
546C22C3×C5×H(5,𝔽2)11yescharacteristic
547C22C3×C5×2−1+411yescharacteristic
548C4—24no—
549C4—22no—
550C4—22no—
551C4—22no—
552C4—41no—
553C4—42no—
554C4—41no—
555C4—42no—
556C4—42no—
557C4C3×C5×#12314yes—
558C3C5×#242311yescharacteristic, direct product factor, Sylow
559C2—42no—
560C2C2×C3×C5×#12311yescharacteristic
561C2C3×C5×#53311yescharacteristic
562C2C3×C5×#54211yescharacteristic
563C2C3×C5×D4×Q811yescharacteristic
564C2C3×C5×#55011yescharacteristic
565C2C3×C5×#55211yescharacteristic
566C2C3×C5×#55411yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC24×C3×C5C23
LCSG ▷ C23 ▷ 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×Q8C2semidirect
4. C3×C5×#398C2semidirect
5. C3×C5×#391C2semidirect
6. C3×C5×#389C2semidirect
8. C3×C5×#387C2semidirect
9. C3×C5×#384C2semidirect
12. C5×#2423C3direct (N × H)
38. C3×#2423C5direct (N × H)
40. C2×C4×C5×Q8C2×C3semidirect
42. C5×#398C2×C3semidirect
43. C5×#391C2×C3semidirect
44. C5×#389C2×C3semidirect
46. C5×#387C2×C3semidirect
47. C5×#384C2×C3semidirect
78. C3×C5×C22⋊C4Q8semidirect
83. C2×C3×C4×Q8C2×C5semidirect
85. C3×#398C2×C5semidirect
86. C3×#391C2×C5semidirect
87. C3×#389C2×C5semidirect
89. C3×#387C2×C5semidirect
90. C3×#384C2×C5semidirect
118. #2423C3×C5direct (N × H)
212. C5×C22⋊C4C3×Q8semidirect
217. C2×C4×Q8C2×C3×C5semidirect
219. #398C2×C3×C5semidirect
220. #391C2×C3×C5semidirect
221. #389C2×C3×C5semidirect
223. #387C2×C3×C5semidirect
224. #384C2×C3×C5semidirect
279. C3×C22⋊C4C5×Q8semidirect
448. C22⋊C4C3×C5×Q8semidirect
452. C3×C5#2423direct (N × H)
533. C5C3×#2423direct (N × H)
558. C3C5×#2423direct (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×C22⋊Q82
C2×C3×C4×C5×Q82
C3×C5×#3992
C3×C5×#3982
C3×C5×#3912
C3×C5×#3892
C3×C5×#3882
C3×C5×#3872
C3×C5×#3842
C3×C5×#3802
C3×C4×C5×C22⋊C42
C5×#24233
C3×#24235