Finite Group Databasebeta

← C3×C5×#3187 #14276221

Subgroups — C3×C5×#3187 #14276221

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×C5×#121C211yesmaximal, characteristic
3C3×C5×#483C212yesmaximal, complemented
4C3×C5×#481C212yesmaximal, complemented
5C3×C5×#465C214yesmaximal, complemented
6C3×C5×#450C212yesmaximal, complemented
7C3×C5×#448C212yesmaximal, complemented
8C2×C3×C5×C22⋊C8C211yesmaximal, characteristic, complemented
9C5×#3187C311yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C5×Q8C2211yescharacteristic, complemented
11C22×C3×C5×D4—21no—
12C22×C3×C5×D4C2211yescharacteristic
13C23×C3×C4×C5C2211yescharacteristic
14C2×C3×C5×SD16C2214yescomplemented
15C22×C3×C5×C8C2212yescomplemented
16C3×C5×C22⋊Q8—21no—
17C3×C5×C22⋊Q8—21no—
18C3×C5×C22⋊Q8C2212yes—
19C3×C5×C22⋊Q8C2212yescomplemented
20C3×C5×#121—21no—
21C3×C5×#121—21no—
22C3×C5×#121C2212yes—
23C3×C5×#121C2212yes—
24C2×C3×C5×C4⋊C4—21no—
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
27C2×C3×C5×C22⋊C4—21no—
28C2×C3×C5×C22⋊C4—21no—
29C3×C5×#106C2214yescomplemented
30C3×C5×#103C2214yescomplemented
31C3×C5×#102C2214yescomplemented
32C3×C5×C22⋊C8C2212yes—
33C3×C5×C22⋊C8C2212yescomplemented
34C3×#3187C511yesmaximal, characteristic, direct product factor, Hall
35C2×C5×C22⋊Q8C2×C311yescharacteristic, complemented
36C2×C5×#121C2×C311yescharacteristic
37C5×#483C2×C312yescomplemented
38C5×#481C2×C312yescomplemented
39C5×#465C2×C314yescomplemented
40C5×#450C2×C312yescomplemented
41C5×#448C2×C312yescomplemented
42C2×C5×C22⋊C8C2×C311yescharacteristic, complemented
43C24×C3×C5—21no—
44C24×C3×C5D411yescharacteristic
45C2×C3×C5×Q8—21no—
46C2×C3×C5×Q8—42no—
47C2×C3×C5×Q8C2312yes—
48C2×C3×C5×D4—22no—
49C2×C3×C5×D4—22no—
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4—42no—
52C2×C3×C5×D4—44no—
53C2×C3×C5×D4C2312yes—
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5—42no—
58C22×C3×C4×C5D411yescharacteristic
59C22×C3×C4×C5D411yescharacteristic
60C22×C3×C4×C5D411yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C3×C5×SD16—44no—
65C2×C3×C5×C8—42no—
66C2×C3×C5×C8C2314yes—
67C3×C5×C4⋊C4—22no—
68C3×C5×C4⋊C4—22no—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72C3×C5×C4⋊C4C2312yes—
73C3×C5×C22⋊C4—22no—
74C3×C5×C22⋊C4—22no—
75C3×C5×C22⋊C4—22no—
76C3×C5×C22⋊C4—22no—
77C2×C3×C22⋊Q8C2×C511yescharacteristic, complemented
78C2×C3×#121C2×C511yescharacteristic
79C3×#483C2×C512yescomplemented
80C3×#481C2×C512yescomplemented
81C3×#465C2×C514yescomplemented
82C3×#450C2×C512yescomplemented
83C3×#448C2×C512yescomplemented
84C2×C3×C22⋊C8C2×C511yescharacteristic, complemented
85C22×C5×Q8C22×C311yescharacteristic, complemented
86C22×C5×D4—21no—
87C22×C5×D4C22×C311yescharacteristic
88C23×C4×C5C22×C311yescharacteristic
89C2×C5×SD16C22×C314yescomplemented
90C22×C5×C8C22×C312yescomplemented
91C5×C22⋊Q8—21no—
92C5×C22⋊Q8—21no—
93C5×C22⋊Q8C22×C312yes—
94C5×C22⋊Q8C22×C312yescomplemented
95C5×#121—21no—
96C5×#121—21no—
97C5×#121C22×C312yes—
98C5×#121C22×C312yes—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4C22×C311yescharacteristic
101C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C5×#106C22×C314yescomplemented
105C5×#103C22×C314yescomplemented
106C5×#102C22×C314yescomplemented
107C5×C22⋊C8C22×C312yes—
108C5×C22⋊C8C22×C312yescomplemented
109#3187C3×C511yescharacteristic, direct product factor, Sylow
110C23×C3×C5—22no—
111C23×C3×C5—41no—
112C23×C3×C5—41no—
113C23×C3×C5—42no—
114C23×C3×C5—42no—
115C23×C3×C5—42no—
116C23×C3×C5SD1614yescomplemented
117C23×C3×C5C2×D411yescharacteristic
118C23×C3×C5C2×D411yescharacteristic
119C23×C3×C5C2×D411yescharacteristic
120C3×C5×Q8—24no—
121C3×C5×Q8—42no—
122C3×C5×D4—24no—
123C3×C5×D4—42no—
124C3×C5×D4—44no—
125C3×C5×D4—44no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5—41no—
134C2×C3×C4×C5—41no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5—42no—
137C2×C3×C4×C5—42no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C3×C5×C8—24no—
143C22×C3×Q8C22×C511yescharacteristic, complemented
144C22×C3×D4—21no—
145C22×C3×D4C22×C511yescharacteristic
146C23×C3×C4C22×C511yescharacteristic
147C2×C3×SD16C22×C514yescomplemented
148C22×C3×C8C22×C512yescomplemented
149C3×C22⋊Q8—21no—
150C3×C22⋊Q8—21no—
151C3×C22⋊Q8C22×C512yes—
152C3×C22⋊Q8C22×C512yescomplemented
153C3×#121—21no—
154C3×#121—21no—
155C3×#121C22×C512yes—
156C3×#121C22×C512yes—
157C2×C3×C4⋊C4—21no—
158C2×C3×C4⋊C4C22×C511yescharacteristic
159C2×C3×C4⋊C4C22×C511yescharacteristic, complemented
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—21no—
162C3×#106C22×C514yescomplemented
163C3×#103C22×C514yescomplemented
164C3×#102C22×C514yescomplemented
165C3×C22⋊C8C22×C512yes—
166C3×C22⋊C8C22×C512yescomplemented
167C24×C5—21no—
168C24×C5C3×D411yescharacteristic
169C2×C5×Q8—21no—
170C2×C5×Q8—42no—
171C2×C5×Q8C23×C312yes—
172C2×C5×D4—22no—
173C2×C5×D4—22no—
174C2×C5×D4—21no—
175C2×C5×D4—42no—
176C2×C5×D4—44no—
177C2×C5×D4C23×C312yes—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—42no—
182C22×C4×C5C3×D411yescharacteristic
183C22×C4×C5C3×D411yescharacteristic
184C22×C4×C5C3×D411yescharacteristic
185C22×C4×C5C23×C311yescharacteristic
186C22×C4×C5C23×C311yescharacteristic
187C22×C4×C5C23×C311yescharacteristic
188C5×SD16—44no—
189C2×C5×C8—42no—
190C2×C5×C8C23×C314yes—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4C23×C312yes—
196C5×C4⋊C4C23×C312yes—
197C5×C22⋊C4—22no—
198C5×C22⋊C4—22no—
199C5×C22⋊C4—22no—
200C5×C22⋊C4—22no—
201C2×C22⋊Q8C2×C3×C511yescharacteristic, complemented
202C2×#121C2×C3×C511yescharacteristic
203#483C2×C3×C512yescomplemented
204#481C2×C3×C512yescomplemented
205#465C2×C3×C514yescomplemented
206#450C2×C3×C512yescomplemented
207#448C2×C3×C512yescomplemented
208C2×C22⋊C8C2×C3×C511yescharacteristic, complemented
209C22×C3×C5—21no—
210C22×C3×C5—21no—
211C22×C3×C5—21no—
212C22×C3×C5—21no—
213C22×C3×C5—21no—
214C22×C3×C5—21no—
215C22×C3×C5—44no—
216C22×C3×C5—42no—
217C22×C3×C5—42no—
218C22×C3×C5—42no—
219C22×C3×C5—84no—
220C22×C3×C5C2×SD1612yes—
221C22×C3×C5C2×SD1612yes—
222C22×C3×C5C2×SD1612yes—
223C22×C3×C5C22×D411yescharacteristic
224C3×C4×C5—21no—
225C3×C4×C5—21no—
226C3×C4×C5—21no—
227C3×C4×C5—42no—
228C3×C4×C5—42no—
229C3×C4×C5—42no—
230C3×C4×C5H(5,𝔽2)12yes—
231C24×C3—21no—
232C24×C3C5×D411yescharacteristic
233C2×C3×Q8—21no—
234C2×C3×Q8—42no—
235C2×C3×Q8C23×C512yes—
236C2×C3×D4—22no—
237C2×C3×D4—22no—
238C2×C3×D4—21no—
239C2×C3×D4—42no—
240C2×C3×D4—44no—
241C2×C3×D4C23×C512yes—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—42no—
246C22×C3×C4C5×D411yescharacteristic
247C22×C3×C4C5×D411yescharacteristic
248C22×C3×C4C5×D411yescharacteristic
249C22×C3×C4C23×C511yescharacteristic
250C22×C3×C4C23×C511yescharacteristic
251C22×C3×C4C23×C511yescharacteristic
252C3×SD16—44no—
253C2×C3×C8—42no—
254C2×C3×C8C23×C514yes—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—22no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4C23×C512yes—
260C3×C4⋊C4C23×C512yes—
261C3×C22⋊C4—22no—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—22no—
264C3×C22⋊C4—22no—
265C23×C5—22no—
266C23×C5—41no—
267C23×C5—41no—
268C23×C5—42no—
269C23×C5—42no—
270C23×C5—42no—
271C23×C5C3×SD1614yescomplemented
272C23×C5C2×C3×D411yescharacteristic
273C23×C5C2×C3×D411yescharacteristic
274C23×C5C2×C3×D411yescharacteristic
275C5×Q8—24no—
276C5×Q8—42no—
277C5×D4—24no—
278C5×D4—42no—
279C5×D4—44no—
280C5×D4—44no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—42no—
291C2×C4×C5—42no—
292C2×C4×C5—42no—
293C2×C4×C5C2×C3×D411yescharacteristic
294C2×C4×C5C2×C3×D411yescharacteristic
295C2×C4×C5C2×C3×D411yescharacteristic
296C2×C4×C5C24×C311yescharacteristic
297C5×C8—24no—
298C22×Q8C22×C3×C511yescharacteristic, complemented
299C22×D4—21no—
300C22×D4C22×C3×C511yescharacteristic
301C23×C4C22×C3×C511yescharacteristic
302C2×SD16C22×C3×C514yescomplemented
303C22×C8C22×C3×C512yescomplemented
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8C22×C3×C512yes—
307C22⋊Q8C22×C3×C512yescomplemented
308#121—21no—
309#121—21no—
310#121C22×C3×C512yes—
311#121C22×C3×C512yes—
312C2×C4⋊C4—21no—
313C2×C4⋊C4C22×C3×C511yescharacteristic
314C2×C4⋊C4C22×C3×C511yescharacteristic, complemented
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317#106C22×C3×C514yescomplemented
318#103C22×C3×C514yescomplemented
319#102C22×C3×C514yescomplemented
320C22⋊C8C22×C3×C512yes—
321C22⋊C8C22×C3×C512yescomplemented
322C2×C3×C5—22no—
323C2×C3×C5—22no—
324C2×C3×C5—22no—
325C2×C3×C5—82no—
326C2×C3×C5#53411yescharacteristic
327C2×C3×C5C22×SD1611yescharacteristic
328C2×C3×C5#57511yescharacteristic
329C23×C3—22no—
330C23×C3—41no—
331C23×C3—41no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3C5×SD1614yescomplemented
336C23×C3C2×C5×D411yescharacteristic
337C23×C3C2×C5×D411yescharacteristic
338C23×C3C2×C5×D411yescharacteristic
339C3×Q8—24no—
340C3×Q8—42no—
341C3×D4—24no—
342C3×D4—42no—
343C3×D4—44no—
344C3×D4—44no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—42no—
357C2×C3×C4C2×C5×D411yescharacteristic
358C2×C3×C4C2×C5×D411yescharacteristic
359C2×C3×C4C2×C5×D411yescharacteristic
360C2×C3×C4C24×C511yescharacteristic
361C3×C8—24no—
362C22×C5—21no—
363C22×C5—21no—
364C22×C5—21no—
365C22×C5—21no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—44no—
369C22×C5—42no—
370C22×C5—42no—
371C22×C5—42no—
372C22×C5—84no—
373C22×C5C2×C3×SD1612yes—
374C22×C5C2×C3×SD1612yes—
375C22×C5C2×C3×SD1612yes—
376C22×C5C22×C3×D411yescharacteristic
377C4×C5—21no—
378C4×C5—21no—
379C4×C5—21no—
380C4×C5—42no—
381C4×C5—42no—
382C4×C5—42no—
383C4×C5C3×H(5,𝔽2)12yes—
384C24—21no—
385C24C3×C5×D411yescharacteristic
386C2×Q8—21no—
387C2×Q8—42no—
388C2×Q8C23×C3×C512yes—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—42no—
393C2×D4—44no—
394C2×D4C23×C3×C512yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—42no—
399C22×C4C3×C5×D411yescharacteristic
400C22×C4C3×C5×D411yescharacteristic
401C22×C4C3×C5×D411yescharacteristic
402C22×C4C23×C3×C511yescharacteristic
403C22×C4C23×C3×C511yescharacteristic
404C22×C4C23×C3×C511yescharacteristic
405SD16—44no—
406C2×C8—42no—
407C2×C8C23×C3×C514yes—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4C23×C3×C512yes—
413C4⋊C4C23×C3×C512yes—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C3×C5#318711yescharacteristic, direct product factor, Hall
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—44no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—84no—
430C22×C3C2×C5×SD1612yes—
431C22×C3C2×C5×SD1612yes—
432C22×C3C2×C5×SD1612yes—
433C22×C3C22×C5×D411yescharacteristic
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—42no—
440C3×C4C5×H(5,𝔽2)12yes—
441C2×C5—22no—
442C2×C5—22no—
443C2×C5—22no—
444C2×C5—82no—
445C2×C5C3×#53411yescharacteristic
446C2×C5C22×C3×SD1611yescharacteristic
447C2×C5C3×#57511yescharacteristic
448C23—22no—
449C23—41no—
450C23—41no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23C3×C5×SD1614yescomplemented
455C23C2×C3×C5×D411yescharacteristic
456C23C2×C3×C5×D411yescharacteristic
457C23C2×C3×C5×D411yescharacteristic
458Q8—24no—
459Q8—42no—
460D4—24no—
461D4—42no—
462D4—44no—
463D4—44no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4C2×C3×C5×D411yescharacteristic
477C2×C4C2×C3×C5×D411yescharacteristic
478C2×C4C2×C3×C5×D411yescharacteristic
479C2×C4C24×C3×C511yescharacteristic
480C8—24no—
481C2×C3—22no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—82no—
485C2×C3C5×#53411yescharacteristic
486C2×C3C22×C5×SD1611yescharacteristic
487C2×C3C5×#57511yescharacteristic
488C5C3×#318711yescharacteristic, direct product factor, Sylow
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—44no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—84no—
500C22C2×C3×C5×SD1612yes—
501C22C2×C3×C5×SD1612yes—
502C22C2×C3×C5×SD1612yes—
503C22C22×C3×C5×D411yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4C3×C5×H(5,𝔽2)12yes—
511C3C5×#318711yescharacteristic, direct product factor, Sylow
512C2—22no—
513C2—22no—
514C2—22no—
515C2—82no—
516C2C3×C5×#53411yescharacteristic
517C2C22×C3×C5×SD1611yescharacteristic
518C2C3×C5×#57511yescharacteristic
subgroupG/H
center, socleC22×C3×C5C22×D4
commutator, Frattini, cosocleC2×C4C24×C3×C5
prime radicalC2×C3×C5×#121C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C23×C3×C4×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×#483C2semidirect
4. C3×C5×#481C2semidirect
5. C3×C5×#465C2semidirect
6. C3×C5×#450C2semidirect
7. C3×C5×#448C2semidirect
8. C2×C3×C5×C22⋊C8C2semidirect
9. C5×#3187C3direct (N × H)
10. C22×C3×C5×Q8C22semidirect
14. C2×C3×C5×SD16C22semidirect
15. C22×C3×C5×C8C22semidirect
19. C3×C5×C22⋊Q8C22semidirect
26. C2×C3×C5×C4⋊C4C22semidirect
29. C3×C5×#106C22semidirect
30. C3×C5×#103C22semidirect
31. C3×C5×#102C22semidirect
33. C3×C5×C22⋊C8C22semidirect
34. C3×#3187C5direct (N × H)
35. C2×C5×C22⋊Q8C2×C3semidirect
37. C5×#483C2×C3semidirect
38. C5×#481C2×C3semidirect
39. C5×#465C2×C3semidirect
40. C5×#450C2×C3semidirect
41. C5×#448C2×C3semidirect
42. C2×C5×C22⋊C8C2×C3semidirect
77. C2×C3×C22⋊Q8C2×C5semidirect
79. C3×#483C2×C5semidirect
80. C3×#481C2×C5semidirect
81. C3×#465C2×C5semidirect
82. C3×#450C2×C5semidirect
83. C3×#448C2×C5semidirect
84. C2×C3×C22⋊C8C2×C5semidirect
85. C22×C5×Q8C22×C3semidirect
89. C2×C5×SD16C22×C3semidirect
90. C22×C5×C8C22×C3semidirect
94. C5×C22⋊Q8C22×C3semidirect
101. C2×C5×C4⋊C4C22×C3semidirect
104. C5×#106C22×C3semidirect
105. C5×#103C22×C3semidirect
106. C5×#102C22×C3semidirect
108. C5×C22⋊C8C22×C3semidirect
109. #3187C3×C5direct (N × H)
116. C23×C3×C5SD16semidirect
143. C22×C3×Q8C22×C5semidirect
147. C2×C3×SD16C22×C5semidirect
148. C22×C3×C8C22×C5semidirect
152. C3×C22⋊Q8C22×C5semidirect
159. C2×C3×C4⋊C4C22×C5semidirect
162. C3×#106C22×C5semidirect
163. C3×#103C22×C5semidirect
164. C3×#102C22×C5semidirect
166. C3×C22⋊C8C22×C5semidirect
201. C2×C22⋊Q8C2×C3×C5semidirect
203. #483C2×C3×C5semidirect
204. #481C2×C3×C5semidirect
205. #465C2×C3×C5semidirect
206. #450C2×C3×C5semidirect
207. #448C2×C3×C5semidirect
208. C2×C22⋊C8C2×C3×C5semidirect
271. C23×C5C3×SD16semidirect
298. C22×Q8C22×C3×C5semidirect
302. C2×SD16C22×C3×C5semidirect
303. C22×C8C22×C3×C5semidirect
307. C22⋊Q8C22×C3×C5semidirect
314. C2×C4⋊C4C22×C3×C5semidirect
317. #106C22×C3×C5semidirect
318. #103C22×C3×C5semidirect
319. #102C22×C3×C5semidirect
321. C22⋊C8C22×C3×C5semidirect
335. C23×C3C5×SD16semidirect
418. C3×C5#3187direct (N × H)
454. C23C3×C5×SD16semidirect
488. C5C3×#3187direct (N × H)
511. C3C5×#3187direct (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×C5×#1212
C3×C5×#4832
C3×C5×#4812
C3×C5×#4652
C3×C5×#4502
C3×C5×#4482
C2×C3×C5×C22⋊C82
C5×#31873
C3×#31875