Finite Group Databasebeta

← C3×C5×#2437 #14275471

Subgroups — C3×C5×#2437 #14275471

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C212yesmaximal, complemented
2C22×C3×C5×C22⋊C4C212yesmaximal
3C3×C5×#399C211yesmaximal, characteristic, complemented
4C3×C5×#396C212yesmaximal, complemented
5C3×C5×#393C211yesmaximal, characteristic, complemented
6C3×C5×#385C212yesmaximal, complemented
7C3×C5×#385C212yesmaximal, complemented
8C3×C5×#380C212yesmaximal, complemented
9C3×C5×#379C211yesmaximal, characteristic
10C5×#2437C311yesmaximal, characteristic, direct product factor, Hall
11C25×C3×C5C2211yescharacteristic
12C22×C3×C5×Q8C2211yescharacteristic, complemented
13C23×C3×C4×C5C2212yes—
14C23×C3×C4×C5C2212yes—
15C3×C5×C22⋊Q8—28no—
16C2×C3×C5×C4⋊C4C2212yescomplemented
17C2×C3×C5×C4⋊C4C2212yescomplemented
18C2×C3×C5×C4⋊C4C2212yescomplemented
19C2×C3×C5×C4⋊C4C2212yescomplemented
20C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
21C2×C3×C5×C22⋊C4—28no—
22C2×C3×C5×C22⋊C4C2212yes—
23C2×C3×C5×C22⋊C4C2212yes—
24C2×C3×C5×C22⋊C4C2212yes—
25C2×C3×C5×C22⋊C4C2212yes—
26C2×C3×C5×C22⋊C4C2212yes—
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2212yes—
30C3×C5×#95C2211yescharacteristic, complemented
31C3×C5×#95C2212yescomplemented
32C3×C5×#95C2212yescomplemented
33C3×C5×#95C2211yescharacteristic, complemented
34C3×#2437C511yesmaximal, characteristic, direct product factor, Hall
35C2×C5×C22⋊Q8C2×C312yescomplemented
36C22×C5×C22⋊C4C2×C312yes—
37C5×#399C2×C311yescharacteristic, complemented
38C5×#396C2×C312yescomplemented
39C5×#393C2×C311yescharacteristic, complemented
40C5×#385C2×C312yescomplemented
41C5×#385C2×C312yescomplemented
42C5×#380C2×C312yescomplemented
43C5×#379C2×C311yescharacteristic
44C24×C3×C5—24no—
45C24×C3×C5—24no—
46C24×C3×C5—41no—
47C24×C3×C5—41no—
48C24×C3×C5Q814yescomplemented
49C24×C3×C5C2311yescharacteristic
50C24×C3×C5C2312yes—
51C2×C3×C5×Q8—24no—
52C2×C3×C5×Q8—41no—
53C22×C3×C4×C5—24no—
54C22×C3×C4×C5—24no—
55C22×C3×C4×C5—24no—
56C22×C3×C4×C5—24no—
57C22×C3×C4×C5—42no—
58C22×C3×C4×C5—42no—
59C22×C3×C4×C5C2312yes—
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2312yes—
66C3×C5×C4⋊C4—24no—
67C3×C5×C4⋊C4—24no—
68C3×C5×C4⋊C4—24no—
69C3×C5×C4⋊C4—42no—
70C3×C5×C4⋊C4—41no—
71C3×C5×C22⋊C4—24no—
72C3×C5×C22⋊C4—24no—
73C3×C5×C22⋊C4—24no—
74C3×C5×C22⋊C4—24no—
75C3×C5×C22⋊C4—24no—
76C3×C5×C22⋊C4—41no—
77C3×C5×C22⋊C4—41no—
78C3×C5×C22⋊C4D418yes—
79C2×C3×C22⋊Q8C2×C512yescomplemented
80C22×C3×C22⋊C4C2×C512yes—
81C3×#399C2×C511yescharacteristic, complemented
82C3×#396C2×C512yescomplemented
83C3×#393C2×C511yescharacteristic, complemented
84C3×#385C2×C512yescomplemented
85C3×#385C2×C512yescomplemented
86C3×#380C2×C512yescomplemented
87C3×#379C2×C511yescharacteristic
88C25×C5C22×C311yescharacteristic
89C22×C5×Q8C22×C311yescharacteristic, complemented
90C23×C4×C5C22×C312yes—
91C23×C4×C5C22×C312yes—
92C5×C22⋊Q8—28no—
93C2×C5×C4⋊C4C22×C312yescomplemented
94C2×C5×C4⋊C4C22×C312yescomplemented
95C2×C5×C4⋊C4C22×C312yescomplemented
96C2×C5×C4⋊C4C22×C312yescomplemented
97C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
98C2×C5×C22⋊C4—28no—
99C2×C5×C22⋊C4C22×C312yes—
100C2×C5×C22⋊C4C22×C312yes—
101C2×C5×C22⋊C4C22×C312yes—
102C2×C5×C22⋊C4C22×C312yes—
103C2×C5×C22⋊C4C22×C312yes—
104C2×C5×C22⋊C4C22×C311yescharacteristic
105C2×C5×C22⋊C4C22×C311yescharacteristic
106C2×C5×C22⋊C4C22×C312yes—
107C5×#95C22×C311yescharacteristic, complemented
108C5×#95C22×C312yescomplemented
109C5×#95C22×C312yescomplemented
110C5×#95C22×C311yescharacteristic, complemented
111#2437C3×C511yescharacteristic, direct product factor, Sylow
112C23×C3×C5—22no—
113C23×C3×C5—22no—
114C23×C3×C5—22no—
115C23×C3×C5—22no—
116C23×C3×C5—216no—
117C23×C3×C5—22no—
118C23×C3×C5—22no—
119C23×C3×C5—21no—
120C23×C3×C5—21no—
121C23×C3×C5—44no—
122C23×C3×C5—44no—
123C23×C3×C5—48no—
124C23×C3×C5—44no—
125C23×C3×C5C2×D414yes—
126C23×C3×C5C2×Q812yes—
127C23×C3×C5C2×Q814yes—
128C23×C3×C5#4114yes—
129C23×C3×C5C2411yescharacteristic
130C3×C5×Q8—44no—
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—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—48no—
149C2×C3×C4×C5—48no—
150C2×C3×C4×C5C2×D414yes—
151C2×C3×C4×C5C2×D414yes—
152C25×C3C22×C511yescharacteristic
153C22×C3×Q8C22×C511yescharacteristic, complemented
154C23×C3×C4C22×C512yes—
155C23×C3×C4C22×C512yes—
156C3×C22⋊Q8—28no—
157C2×C3×C4⋊C4C22×C512yescomplemented
158C2×C3×C4⋊C4C22×C512yescomplemented
159C2×C3×C4⋊C4C22×C512yescomplemented
160C2×C3×C4⋊C4C22×C512yescomplemented
161C2×C3×C4⋊C4C22×C511yescharacteristic, complemented
162C2×C3×C22⋊C4—28no—
163C2×C3×C22⋊C4C22×C512yes—
164C2×C3×C22⋊C4C22×C512yes—
165C2×C3×C22⋊C4C22×C512yes—
166C2×C3×C22⋊C4C22×C512yes—
167C2×C3×C22⋊C4C22×C512yes—
168C2×C3×C22⋊C4C22×C511yescharacteristic
169C2×C3×C22⋊C4C22×C511yescharacteristic
170C2×C3×C22⋊C4C22×C512yes—
171C3×#95C22×C511yescharacteristic, complemented
172C3×#95C22×C512yescomplemented
173C3×#95C22×C512yescomplemented
174C3×#95C22×C511yescharacteristic, complemented
175C24×C5—24no—
176C24×C5—24no—
177C24×C5—41no—
178C24×C5—41no—
179C24×C5C3×Q814yescomplemented
180C24×C5C23×C311yescharacteristic
181C24×C5C23×C312yes—
182C2×C5×Q8—24no—
183C2×C5×Q8—41no—
184C22×C4×C5—24no—
185C22×C4×C5—24no—
186C22×C4×C5—24no—
187C22×C4×C5—24no—
188C22×C4×C5—42no—
189C22×C4×C5—42no—
190C22×C4×C5C23×C312yes—
191C22×C4×C5C23×C311yescharacteristic
192C22×C4×C5C23×C311yescharacteristic
193C22×C4×C5C23×C312yes—
194C22×C4×C5C23×C312yes—
195C22×C4×C5C23×C312yes—
196C22×C4×C5C23×C312yes—
197C5×C4⋊C4—24no—
198C5×C4⋊C4—24no—
199C5×C4⋊C4—24no—
200C5×C4⋊C4—42no—
201C5×C4⋊C4—41no—
202C5×C22⋊C4—24no—
203C5×C22⋊C4—24no—
204C5×C22⋊C4—24no—
205C5×C22⋊C4—24no—
206C5×C22⋊C4—24no—
207C5×C22⋊C4—41no—
208C5×C22⋊C4—41no—
209C5×C22⋊C4C3×D418yes—
210C2×C22⋊Q8C2×C3×C512yescomplemented
211C22×C22⋊C4C2×C3×C512yes—
212#399C2×C3×C511yescharacteristic, complemented
213#396C2×C3×C512yescomplemented
214#393C2×C3×C511yescharacteristic, complemented
215#385C2×C3×C512yescomplemented
216#385C2×C3×C512yescomplemented
217#380C2×C3×C512yescomplemented
218#379C2×C3×C511yescharacteristic
219C22×C3×C5—24no—
220C22×C3×C5—24no—
221C22×C3×C5—24no—
222C22×C3×C5—24no—
223C22×C3×C5—24no—
224C22×C3×C5—24no—
225C22×C3×C5—24no—
226C22×C3×C5—22no—
227C22×C3×C5—416no—
228C22×C3×C5—41no—
229C22×C3×C5—42no—
230C22×C3×C5—41no—
231C22×C3×C5C22⋊Q818yescomplemented
232C22×C3×C5C22×D412yes—
233C22×C3×C5C22×Q811yescharacteristic
234C22×C3×C5C2×#4112yes—
235C22×C3×C5H(5,𝔽2)11yescharacteristic
236C22×C3×C5H(5,𝔽2)11yescharacteristic
237C3×C4×C5—24no—
238C3×C4×C5—24no—
239C3×C4×C5—42no—
240C3×C4×C5—41no—
241C3×C4×C5—42no—
242C3×C4×C5—42no—
243C3×C4×C5—41no—
244C24×C3—24no—
245C24×C3—24no—
246C24×C3—41no—
247C24×C3—41no—
248C24×C3C5×Q814yescomplemented
249C24×C3C23×C511yescharacteristic
250C24×C3C23×C512yes—
251C2×C3×Q8—24no—
252C2×C3×Q8—41no—
253C22×C3×C4—24no—
254C22×C3×C4—24no—
255C22×C3×C4—24no—
256C22×C3×C4—24no—
257C22×C3×C4—42no—
258C22×C3×C4—42no—
259C22×C3×C4C23×C511yescharacteristic
260C22×C3×C4C23×C512yes—
261C22×C3×C4C23×C512yes—
262C22×C3×C4C23×C511yescharacteristic
263C22×C3×C4C23×C512yes—
264C22×C3×C4C23×C512yes—
265C22×C3×C4C23×C512yes—
266C3×C4⋊C4—24no—
267C3×C4⋊C4—24no—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—42no—
270C3×C4⋊C4—41no—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—24no—
273C3×C22⋊C4—24no—
274C3×C22⋊C4—24no—
275C3×C22⋊C4—24no—
276C3×C22⋊C4—41no—
277C3×C22⋊C4—41no—
278C3×C22⋊C4C5×D418yes—
279C23×C5—22no—
280C23×C5—22no—
281C23×C5—22no—
282C23×C5—22no—
283C23×C5—216no—
284C23×C5—22no—
285C23×C5—22no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—44no—
289C23×C5—44no—
290C23×C5—48no—
291C23×C5—44no—
292C23×C5C2×C3×D414yes—
293C23×C5C2×C3×Q812yes—
294C23×C5C2×C3×Q814yes—
295C23×C5C3×#4114yes—
296C23×C5C24×C311yescharacteristic
297C5×Q8—44no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—48no—
316C2×C4×C5—48no—
317C2×C4×C5C2×C3×D414yes—
318C2×C4×C5C2×C3×D414yes—
319C25C22×C3×C511yescharacteristic
320C22×Q8C22×C3×C511yescharacteristic, complemented
321C23×C4C22×C3×C512yes—
322C23×C4C22×C3×C512yes—
323C22⋊Q8—28no—
324C2×C4⋊C4C22×C3×C512yescomplemented
325C2×C4⋊C4C22×C3×C512yescomplemented
326C2×C4⋊C4C22×C3×C512yescomplemented
327C2×C4⋊C4C22×C3×C512yescomplemented
328C2×C4⋊C4C22×C3×C511yescharacteristic, complemented
329C2×C22⋊C4—28no—
330C2×C22⋊C4C22×C3×C512yes—
331C2×C22⋊C4C22×C3×C512yes—
332C2×C22⋊C4C22×C3×C512yes—
333C2×C22⋊C4C22×C3×C512yes—
334C2×C22⋊C4C22×C3×C512yes—
335C2×C22⋊C4C22×C3×C511yescharacteristic
336C2×C22⋊C4C22×C3×C511yescharacteristic
337C2×C22⋊C4C22×C3×C512yes—
338#95C22×C3×C511yescharacteristic, complemented
339#95C22×C3×C512yescomplemented
340#95C22×C3×C512yescomplemented
341#95C22×C3×C511yescharacteristic, complemented
342C2×C3×C5—28no—
343C2×C3×C5—42no—
344C2×C3×C5C2×C22⋊Q812yes—
345C2×C3×C5#54311yescharacteristic
346C2×C3×C5D4211yescharacteristic
347C2×C3×C5#54612yes—
348C2×C3×C5#55111yescharacteristic
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—216no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—44no—
359C23×C3—44no—
360C23×C3—48no—
361C23×C3—44no—
362C23×C3C2×C5×D414yes—
363C23×C3C2×C5×Q812yes—
364C23×C3C2×C5×Q814yes—
365C23×C3C5×#4114yes—
366C23×C3C24×C511yescharacteristic
367C3×Q8—44no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
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—48no—
386C2×C3×C4—48no—
387C2×C3×C4C2×C5×D414yes—
388C2×C3×C4C2×C5×D414yes—
389C22×C5—24no—
390C22×C5—24no—
391C22×C5—24no—
392C22×C5—24no—
393C22×C5—24no—
394C22×C5—24no—
395C22×C5—24no—
396C22×C5—22no—
397C22×C5—416no—
398C22×C5—41no—
399C22×C5—42no—
400C22×C5—41no—
401C22×C5C3×C22⋊Q818yescomplemented
402C22×C5C22×C3×D412yes—
403C22×C5C22×C3×Q811yescharacteristic
404C22×C5C2×C3×#4112yes—
405C22×C5C3×H(5,𝔽2)11yescharacteristic
406C22×C5C3×H(5,𝔽2)11yescharacteristic
407C4×C5—24no—
408C4×C5—24no—
409C4×C5—42no—
410C4×C5—41no—
411C4×C5—42no—
412C4×C5—42no—
413C4×C5—41no—
414C24—24no—
415C24—24no—
416C24—41no—
417C24—41no—
418C24C3×C5×Q814yescomplemented
419C24C23×C3×C511yescharacteristic
420C24C23×C3×C512yes—
421C2×Q8—24no—
422C2×Q8—41no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4C23×C3×C511yescharacteristic
430C22×C4C23×C3×C512yes—
431C22×C4C23×C3×C512yes—
432C22×C4C23×C3×C511yescharacteristic
433C22×C4C23×C3×C512yes—
434C22×C4C23×C3×C512yes—
435C22×C4C23×C3×C512yes—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—24no—
439C4⋊C4—42no—
440C4⋊C4—41no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4C3×C5×D418yes—
449C3×C5#243711yescharacteristic, direct product factor, Hall
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—24no—
453C22×C3—24no—
454C22×C3—24no—
455C22×C3—24no—
456C22×C3—24no—
457C22×C3—22no—
458C22×C3—416no—
459C22×C3—41no—
460C22×C3—42no—
461C22×C3—41no—
462C22×C3C5×C22⋊Q818yescomplemented
463C22×C3C22×C5×D412yes—
464C22×C3C22×C5×Q811yescharacteristic
465C22×C3C2×C5×#4112yes—
466C22×C3C5×H(5,𝔽2)11yescharacteristic
467C22×C3C5×H(5,𝔽2)11yescharacteristic
468C3×C4—24no—
469C3×C4—24no—
470C3×C4—42no—
471C3×C4—41no—
472C3×C4—42no—
473C3×C4—42no—
474C3×C4—41no—
475C2×C5—28no—
476C2×C5—42no—
477C2×C5C2×C3×C22⋊Q812yes—
478C2×C5C3×#54311yescharacteristic
479C2×C5C3×D4211yescharacteristic
480C2×C5C3×#54612yes—
481C2×C5C3×#55111yescharacteristic
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—216no—
488C23—22no—
489C23—21no—
490C23—21no—
491C23—44no—
492C23—44no—
493C23—48no—
494C23—44no—
495C23C2×C3×C5×D414yes—
496C23C2×C3×C5×Q812yes—
497C23C2×C3×C5×Q814yes—
498C23C3×C5×#4114yes—
499C23C24×C3×C511yescharacteristic
500Q8—44no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—48no—
519C2×C4—48no—
520C2×C4C2×C3×C5×D414yes—
521C2×C4C2×C3×C5×D414yes—
522C2×C3—28no—
523C2×C3—42no—
524C2×C3C2×C5×C22⋊Q812yes—
525C2×C3C5×#54311yescharacteristic
526C2×C3C5×D4211yescharacteristic
527C2×C3C5×#54612yes—
528C2×C3C5×#55111yescharacteristic
529C5C3×#243711yescharacteristic, direct product factor, Sylow
530C22—24no—
531C22—24no—
532C22—24no—
533C22—24no—
534C22—24no—
535C22—24no—
536C22—24no—
537C22—22no—
538C22—416no—
539C22—41no—
540C22—42no—
541C22—41no—
542C22C3×C5×C22⋊Q818yescomplemented
543C22C22×C3×C5×D412yes—
544C22C22×C3×C5×Q811yescharacteristic
545C22C2×C3×C5×#4112yes—
546C22C3×C5×H(5,𝔽2)11yescharacteristic
547C22C3×C5×H(5,𝔽2)11yescharacteristic
548C4—24no—
549C4—24no—
550C4—42no—
551C4—41no—
552C4—42no—
553C4—42no—
554C4—41no—
555C3C5×#243711yescharacteristic, direct product factor, Sylow
556C2—28no—
557C2—42no—
558C2C2×C3×C5×C22⋊Q812yes—
559C2C3×C5×#54311yescharacteristic
560C2C3×C5×D4211yescharacteristic
561C2C3×C5×#54612yes—
562C2C3×C5×#55111yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC25×C3×C5C22
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×C22⋊Q8C2semidirect
3. C3×C5×#399C2semidirect
4. C3×C5×#396C2semidirect
5. C3×C5×#393C2semidirect
6. C3×C5×#385C2semidirect
7. C3×C5×#385C2semidirect
8. C3×C5×#380C2semidirect
10. C5×#2437C3direct (N × H)
12. C22×C3×C5×Q8C22semidirect
16. C2×C3×C5×C4⋊C4C22semidirect
17. C2×C3×C5×C4⋊C4C22semidirect
18. C2×C3×C5×C4⋊C4C22semidirect
19. C2×C3×C5×C4⋊C4C22semidirect
20. C2×C3×C5×C4⋊C4C22semidirect
30. C3×C5×#95C22semidirect
31. C3×C5×#95C22semidirect
32. C3×C5×#95C22semidirect
33. C3×C5×#95C22semidirect
34. C3×#2437C5direct (N × H)
35. C2×C5×C22⋊Q8C2×C3semidirect
37. C5×#399C2×C3semidirect
38. C5×#396C2×C3semidirect
39. C5×#393C2×C3semidirect
40. C5×#385C2×C3semidirect
41. C5×#385C2×C3semidirect
42. C5×#380C2×C3semidirect
48. C24×C3×C5Q8semidirect
79. C2×C3×C22⋊Q8C2×C5semidirect
81. C3×#399C2×C5semidirect
82. C3×#396C2×C5semidirect
83. C3×#393C2×C5semidirect
84. C3×#385C2×C5semidirect
85. C3×#385C2×C5semidirect
86. C3×#380C2×C5semidirect
89. C22×C5×Q8C22×C3semidirect
93. C2×C5×C4⋊C4C22×C3semidirect
94. C2×C5×C4⋊C4C22×C3semidirect
95. C2×C5×C4⋊C4C22×C3semidirect
96. C2×C5×C4⋊C4C22×C3semidirect
97. C2×C5×C4⋊C4C22×C3semidirect
107. C5×#95C22×C3semidirect
108. C5×#95C22×C3semidirect
109. C5×#95C22×C3semidirect
110. C5×#95C22×C3semidirect
111. #2437C3×C5direct (N × H)
153. C22×C3×Q8C22×C5semidirect
157. C2×C3×C4⋊C4C22×C5semidirect
158. C2×C3×C4⋊C4C22×C5semidirect
159. C2×C3×C4⋊C4C22×C5semidirect
160. C2×C3×C4⋊C4C22×C5semidirect
161. C2×C3×C4⋊C4C22×C5semidirect
171. C3×#95C22×C5semidirect
172. C3×#95C22×C5semidirect
173. C3×#95C22×C5semidirect
174. C3×#95C22×C5semidirect
179. C24×C5C3×Q8semidirect
210. C2×C22⋊Q8C2×C3×C5semidirect
212. #399C2×C3×C5semidirect
213. #396C2×C3×C5semidirect
214. #393C2×C3×C5semidirect
215. #385C2×C3×C5semidirect
216. #385C2×C3×C5semidirect
217. #380C2×C3×C5semidirect
231. C22×C3×C5C22⋊Q8semidirect
248. C24×C3C5×Q8semidirect
320. C22×Q8C22×C3×C5semidirect
324. C2×C4⋊C4C22×C3×C5semidirect
325. C2×C4⋊C4C22×C3×C5semidirect
326. C2×C4⋊C4C22×C3×C5semidirect
327. C2×C4⋊C4C22×C3×C5semidirect
328. C2×C4⋊C4C22×C3×C5semidirect
338. #95C22×C3×C5semidirect
339. #95C22×C3×C5semidirect
340. #95C22×C3×C5semidirect
341. #95C22×C3×C5semidirect
401. C22×C5C3×C22⋊Q8semidirect
418. C24C3×C5×Q8semidirect
449. C3×C5#2437direct (N × H)
462. C22×C3C5×C22⋊Q8semidirect
529. C5C3×#2437direct (N × H)
542. C22C3×C5×C22⋊Q8semidirect
555. C3C5×#2437direct (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
C22×C3×C5×C22⋊C42
C3×C5×#3992
C3×C5×#3962
C3×C5×#3932
C3×C5×#3852
C3×C5×#3802
C3×C5×#3792
C5×#24373
C3×#24375