Finite Group Databasebeta

← C3×#10617506 #14322389

Subgroups — C3×#10617506 #14322389

Order 1920.

2320 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D4×D5C211yesmaximal, characteristic
2C22×C3×C22⋊AGL(1,𝔽5)C212yesmaximal, complemented
3C3×#65800C212yesmaximal, complemented
4C3×#65779C218yesmaximal, complemented
5C3×#65764C212yesmaximal, complemented
6#10617506C311yesmaximal, characteristic, direct product factor, Hall
7C24×C3×D5C2211yescharacteristic
8C24×C3×D5C2211yescharacteristic
9C23×C3×AGL(1,𝔽5)C2214yescomplemented
10C22×C3×C5×D4C411yescharacteristic, complemented
11C22×C3×C22⋊D5C411yescharacteristic, complemented
12C22×C3×C22⋊D5C411yescharacteristic, complemented
13C2×C3×D4×D5—28no—
14C2×C3×D4×D5C414yescomplemented
15C2×C3×D4×D5C2214yes—
16C22×C3×D20C411yescharacteristic, complemented
17C22×C3×C4×D5C2211yescharacteristic
18C2×C3×C22⋊AGL(1,𝔽5)—28no—
19C2×C3×C22⋊AGL(1,𝔽5)C2214yes—
20C2×C3×C22⋊AGL(1,𝔽5)C2214yescomplemented
21C2×C3×C22⋊AGL(1,𝔽5)C2218yescomplemented
22C3×(C2×AGL(1,𝔽5))⋊C4C2218yescomplemented
23C3×#2308—51nomaximal, Hall
24C22×D4×D5C2×C311yescharacteristic
25C22×C22⋊AGL(1,𝔽5)C2×C312yescomplemented
26#65800C2×C312yescomplemented
27#65779C2×C318yescomplemented
28#65764C2×C312yescomplemented
29C24×C3×C5C2×C411yescharacteristic
30C24×C3×C5C2×C411yescharacteristic, complemented
31C23×C3×D5—24no—
32C23×C3×D5—44no—
33C23×C3×D5—44no—
34C23×C3×D5C2×C411yescharacteristic
35C23×C3×D5C2×C412yes—
36C23×C3×D5C2×C411yescharacteristic, complemented
37C23×C3×D5C2×C412yescomplemented
38C23×C3×D5D418yes—
39C23×C3×D5C2312yes—
40C23×C3×D5C2311yescharacteristic
41C23×C3×D5C2312yes—
42C22×C3×AGL(1,𝔽5)—28no—
43C22×C3×AGL(1,𝔽5)—48no—
44C22×C3×AGL(1,𝔽5)C2318yes—
45C2×C3×C5×D4—24no—
46C2×C3×C5×D4C2×C414yescomplemented
47C22×C3×C4×C5C2×C411yescharacteristic, complemented
48C2×C3×C22⋊D5—24no—
49C2×C3×C22⋊D5—24no—
50C2×C3×C22⋊D5C2×C414yescomplemented
51C2×C3×C22⋊D5C2×C414yescomplemented
52C22×C3×Dic5C2×C411yescharacteristic, complemented
53C3×D4×D5—216no—
54C3×D4×D5—28no—
55C3×D4×D5—28no—
56C2×C3×D20—24no—
57C2×C3×D20C2×C414yescomplemented
58C2×C3×C4×D5—24no—
59C2×C3×C4×D5C2×C412yescomplemented
60C2×C3×C4×D5C2312yes—
61C3×C22⋊AGL(1,𝔽5)—28no—
62C3×C22⋊AGL(1,𝔽5)—28no—
63C3×C22⋊AGL(1,𝔽5)—48no—
64C23×C3×D4—51no—
65C22×C3×C22⋊C4—52no—
66C3×#386—58no—
67C3×#381—52no—
68C3×#379—52no—
69C24×D5C22×C311yescharacteristic
70C24×D5C22×C311yescharacteristic
71C23×AGL(1,𝔽5)C22×C314yescomplemented
72C22×C5×D4C3×C411yescharacteristic, complemented
73C22×C22⋊D5C3×C411yescharacteristic, complemented
74C22×C22⋊D5C3×C411yescharacteristic, complemented
75C2×D4×D5—28no—
76C2×D4×D5C3×C414yescomplemented
77C2×D4×D5C22×C314yes—
78C22×D20C3×C411yescharacteristic, complemented
79C22×C4×D5C22×C311yescharacteristic
80C2×C22⋊AGL(1,𝔽5)—28no—
81C2×C22⋊AGL(1,𝔽5)C22×C314yes—
82C2×C22⋊AGL(1,𝔽5)C22×C314yescomplemented
83C2×C22⋊AGL(1,𝔽5)C22×C318yescomplemented
84(C2×AGL(1,𝔽5))⋊C4C22×C318yescomplemented
85#2308—51noSylow
86C23×C3×C5—22no—
87C23×C3×C5—42no—
88C23×C3×C5—42no—
89C23×C3×C5C22⋊C414yescomplemented
90C23×C3×C5C22×C412yes—
91C23×C3×C5C22×C411yescharacteristic
92C23×C3×C5C22×C412yes—
93C22×C3×D5—28no—
94C22×C3×D5—24no—
95C22×C3×D5—22no—
96C22×C3×D5—24no—
97C22×C3×D5—24no—
98C22×C3×D5—28no—
99C22×C3×D5—416no—
100C22×C3×D5—44no—
101C22×C3×D5—42no—
102C22×C3×D5—44no—
103C22×C3×D5—42no—
104C22×C3×D5—416no—
105C22×C3×D5C22⋊C414yescomplemented
106C22×C3×D5C22⋊C418yescomplemented
107C22×C3×D5C22×C412yes—
108C22×C3×D5C22×C411yescharacteristic
109C22×C3×D5C22×C412yes—
110C22×C3×D5C2×D414yes—
111C22×C3×D5C2×D414yes—
112C22×C3×D5C2×D414yes—
113C22×C3×D5C2411yescharacteristic
114C2×C3×AGL(1,𝔽5)—28no—
115C2×C3×AGL(1,𝔽5)—216no—
116C2×C3×AGL(1,𝔽5)—416no—
117C3×C5×D4—28no—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5C22×C412yes—
120C3×C22⋊D5—28no—
121C3×C22⋊D5—28no—
122C2×C3×Dic5—22no—
123C2×C3×Dic5C22×C412yes—
124C3×D20—28no—
125C3×C4×D5—24no—
126C3×C4×D5—24no—
127C25×C3—51no—
128C25×C3—51no—
129C22×C3×D4—51no—
130C22×C3×D4—51no—
131C22×C3×D4—54no—
132C22×C3×D4—54no—
133C22×C3×D4—51no—
134C22×C3×D4—108no—
135C22×C3×D4AGL(1,𝔽5)11yescharacteristic, complemented
136C23×C3×C4—51no—
137C23×C3×C4—54no—
138C2×C3×C22⋊C4—54no—
139C2×C3×C22⋊C4—54no—
140C2×C3×C22⋊C4—58no—
141C2×C3×C22⋊C4—108no—
142C3×#95—58no—
143C24×C5C2×C3×C411yescharacteristic
144C24×C5C2×C3×C411yescharacteristic, complemented
145C23×D5—24no—
146C23×D5—44no—
147C23×D5—44no—
148C23×D5C2×C3×C411yescharacteristic
149C23×D5C2×C3×C412yes—
150C23×D5C2×C3×C411yescharacteristic, complemented
151C23×D5C2×C3×C412yescomplemented
152C23×D5C3×D418yes—
153C23×D5C23×C312yes—
154C23×D5C23×C311yescharacteristic
155C23×D5C23×C312yes—
156C22×AGL(1,𝔽5)—28no—
157C22×AGL(1,𝔽5)—48no—
158C22×AGL(1,𝔽5)C23×C318yes—
159C2×C5×D4—24no—
160C2×C5×D4C2×C3×C414yescomplemented
161C22×C4×C5C2×C3×C411yescharacteristic, complemented
162C2×C22⋊D5—24no—
163C2×C22⋊D5—24no—
164C2×C22⋊D5C2×C3×C414yescomplemented
165C2×C22⋊D5C2×C3×C414yescomplemented
166C22×Dic5C2×C3×C411yescharacteristic, complemented
167D4×D5—216no—
168D4×D5—28no—
169D4×D5—28no—
170C2×D20—24no—
171C2×D20C2×C3×C414yescomplemented
172C2×C4×D5—24no—
173C2×C4×D5C2×C3×C412yescomplemented
174C2×C4×D5C23×C312yes—
175C22⋊AGL(1,𝔽5)—28no—
176C22⋊AGL(1,𝔽5)—28no—
177C22⋊AGL(1,𝔽5)—48no—
178C23×D4—51no—
179C22×C22⋊C4—52no—
180#386—58no—
181#381—52no—
182#379—52no—
183C22×C3×C5—22no—
184C22×C3×C5—24no—
185C22×C3×C5—22no—
186C22×C3×C5—24no—
187C22×C3×C5—44no—
188C22×C3×C5—44no—
189C22×C3×C5C2×C22⋊C412yes—
190C22×C3×C5C2×C22⋊C414yes—
191C22×C3×C5C23×C411yescharacteristic
192C2×C3×D5—22no—
193C2×C3×D5—24no—
194C2×C3×D5—28no—
195C2×C3×D5—28no—
196C2×C3×D5—28no—
197C2×C3×D5—22no—
198C2×C3×D5—24no—
199C2×C3×D5—48no—
200C2×C3×D5—44no—
201C2×C3×D5—48no—
202C2×C3×D5—44no—
203C2×C3×D5—48no—
204C2×C3×D5C2×C22⋊C412yes—
205C2×C3×D5C2×C22⋊C414yes—
206C2×C3×D5C22×D412yes—
207C2×C3×D5H(5,𝔽2)14yes—
208C3×AGL(1,𝔽5)—48no—
209C3×C4×C5—22no—
210C3×Dic5—22no—
211C24×C3—51no—
212C24×C3—52no—
213C24×C3—58no—
214C24×C3—52no—
215C24×C3—51no—
216C24×C3—52no—
217C24×C3—52no—
218C24×C3—51no—
219C24×C3—104no—
220C24×C3—204no—
221C24×C3—204no—
222C24×C3C2×AGL(1,𝔽5)11yescharacteristic
223C24×C3C2×AGL(1,𝔽5)11yescharacteristic, complemented
224C2×C3×D4—24no—
225C2×C3×D4—54no—
226C2×C3×D4—54no—
227C2×C3×D4—54no—
228C2×C3×D4—104no—
229C2×C3×D4—108no—
230C2×C3×D4—108no—
231C2×C3×D4—1016no—
232C2×C3×D4—104no—
233C2×C3×D4—104no—
234C2×C3×D4C2×AGL(1,𝔽5)14yescomplemented
235C22×C3×C4—51no—
236C22×C3×C4—52no—
237C22×C3×C4—52no—
238C22×C3×C4—58no—
239C22×C3×C4—104no—
240C22×C3×C4—108no—
241C22×C3×C4—208no—
242C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
243C3×C22⋊C4—108no—
244C3×C22⋊C4—108no—
245C3×C22⋊C4—208no—
246C23×C5—22no—
247C23×C5—42no—
248C23×C5—42no—
249C23×C5C3×C22⋊C414yescomplemented
250C23×C5C22×C3×C412yes—
251C23×C5C22×C3×C411yescharacteristic
252C23×C5C22×C3×C412yes—
253C22×D5—28no—
254C22×D5—24no—
255C22×D5—22no—
256C22×D5—24no—
257C22×D5—24no—
258C22×D5—28no—
259C22×D5—416no—
260C22×D5—44no—
261C22×D5—42no—
262C22×D5—44no—
263C22×D5—42no—
264C22×D5—416no—
265C22×D5C3×C22⋊C414yescomplemented
266C22×D5C3×C22⋊C418yescomplemented
267C22×D5C22×C3×C412yes—
268C22×D5C22×C3×C411yescharacteristic
269C22×D5C22×C3×C412yes—
270C22×D5C2×C3×D414yes—
271C22×D5C2×C3×D414yes—
272C22×D5C2×C3×D414yes—
273C22×D5C24×C311yescharacteristic
274C2×AGL(1,𝔽5)—28no—
275C2×AGL(1,𝔽5)—216no—
276C2×AGL(1,𝔽5)—416no—
277C5×D4—28no—
278C2×C4×C5—22no—
279C2×C4×C5C22×C3×C412yes—
280C22⋊D5—28no—
281C22⋊D5—28no—
282C2×Dic5—22no—
283C2×Dic5C22×C3×C412yes—
284D20—28no—
285C4×D5—24no—
286C4×D5—24no—
287C25—51no—
288C25—51no—
289C22×D4—51no—
290C22×D4—51no—
291C22×D4—54no—
292C22×D4—54no—
293C22×D4—51no—
294C22×D4—108no—
295C22×D4C3×AGL(1,𝔽5)11yescharacteristic, complemented
296C23×C4—51no—
297C23×C4—54no—
298C2×C22⋊C4—54no—
299C2×C22⋊C4—54no—
300C2×C22⋊C4—58no—
301C2×C22⋊C4—108no—
302#95—58no—
303C2×C3×C5—22no—
304C2×C3×C5—24no—
305C2×C3×C5—42no—
306C2×C3×C5C22×C22⋊C411yescharacteristic
307C2×C3×C5#51812yes—
308C3×D5—22no—
309C3×D5—24no—
310C3×D5—42no—
311C3×D5#53414yes—
312C23×C3—22no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—51no—
316C23×C3—54no—
317C23×C3—54no—
318C23×C3—54no—
319C23×C3—51no—
320C23×C3—52no—
321C23×C3—58no—
322C23×C3—54no—
323C23×C3—52no—
324C23×C3—108no—
325C23×C3—104no—
326C23×C3—108no—
327C23×C3—104no—
328C23×C3—104no—
329C23×C3—102no—
330C23×C3—202no—
331C23×C3—202no—
332C23×C3—204no—
333C23×C3—204no—
334C23×C3—2016no—
335C23×C3—2016no—
336C23×C3C22⋊AGL(1,𝔽5)14yescomplemented
337C23×C3C22×AGL(1,𝔽5)12yes—
338C23×C3C22×AGL(1,𝔽5)11yescharacteristic
339C23×C3C22×AGL(1,𝔽5)12yes—
340C3×D4—28no—
341C3×D4—108no—
342C3×D4—108no—
343C3×D4—108no—
344C2×C3×C4—22no—
345C2×C3×C4—52no—
346C2×C3×C4—104no—
347C2×C3×C4—104no—
348C2×C3×C4—102no—
349C2×C3×C4—108no—
350C2×C3×C4—1016no—
351C2×C3×C4—2016no—
352C2×C3×C4C22×AGL(1,𝔽5)12yes—
353C22×C5—22no—
354C22×C5—24no—
355C22×C5—22no—
356C22×C5—24no—
357C22×C5—44no—
358C22×C5—44no—
359C22×C5C2×C3×C22⋊C412yes—
360C22×C5C2×C3×C22⋊C414yes—
361C22×C5C23×C3×C411yescharacteristic
362C2×D5—22no—
363C2×D5—24no—
364C2×D5—28no—
365C2×D5—28no—
366C2×D5—28no—
367C2×D5—22no—
368C2×D5—24no—
369C2×D5—48no—
370C2×D5—44no—
371C2×D5—48no—
372C2×D5—44no—
373C2×D5—48no—
374C2×D5C2×C3×C22⋊C412yes—
375C2×D5C2×C3×C22⋊C414yes—
376C2×D5C22×C3×D412yes—
377C2×D5C3×H(5,𝔽2)14yes—
378AGL(1,𝔽5)—48no—
379C4×C5—22no—
380Dic5—22no—
381C24—51no—
382C24—52no—
383C24—58no—
384C24—52no—
385C24—51no—
386C24—52no—
387C24—52no—
388C24—51no—
389C24—104no—
390C24—204no—
391C24—204no—
392C24C2×C3×AGL(1,𝔽5)11yescharacteristic
393C24C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
394C2×D4—24no—
395C2×D4—54no—
396C2×D4—54no—
397C2×D4—54no—
398C2×D4—104no—
399C2×D4—108no—
400C2×D4—108no—
401C2×D4—1016no—
402C2×D4—104no—
403C2×D4—104no—
404C2×D4C2×C3×AGL(1,𝔽5)14yescomplemented
405C22×C4—51no—
406C22×C4—52no—
407C22×C4—52no—
408C22×C4—58no—
409C22×C4—104no—
410C22×C4—108no—
411C22×C4—208no—
412C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
413C22⋊C4—108no—
414C22⋊C4—108no—
415C22⋊C4—208no—
416C3×C5#230811yescharacteristic, complemented, Hall
417C22×C3—22no—
418C22×C3—24no—
419C22×C3—24no—
420C22×C3—22no—
421C22×C3—44no—
422C22×C3—44no—
423C22×C3—54no—
424C22×C3—52no—
425C22×C3—52no—
426C22×C3—54no—
427C22×C3—108no—
428C22×C3—108no—
429C22×C3—108no—
430C22×C3—104no—
431C22×C3—102no—
432C22×C3—104no—
433C22×C3—102no—
434C22×C3—204no—
435C22×C3—208no—
436C22×C3—204no—
437C22×C3—208no—
438C22×C3—208no—
439C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
440C22×C3C2×C22⋊AGL(1,𝔽5)14yes—
441C22×C3C23×AGL(1,𝔽5)11yescharacteristic
442C3×C4—22no—
443C3×C4—102no—
444C3×C4—208no—
445C2×C5—22no—
446C2×C5—24no—
447C2×C5—42no—
448C2×C5C22×C3×C22⋊C411yescharacteristic
449C2×C5C3×#51812yes—
450D5—22no—
451D5—24no—
452D5—42no—
453D5C3×#53414yes—
454C23—22no—
455C23—42no—
456C23—42no—
457C23—51no—
458C23—54no—
459C23—54no—
460C23—54no—
461C23—51no—
462C23—52no—
463C23—58no—
464C23—54no—
465C23—52no—
466C23—108no—
467C23—104no—
468C23—108no—
469C23—104no—
470C23—104no—
471C23—102no—
472C23—202no—
473C23—202no—
474C23—204no—
475C23—204no—
476C23—2016no—
477C23—2016no—
478C23C3×C22⋊AGL(1,𝔽5)14yescomplemented
479C23C22×C3×AGL(1,𝔽5)12yes—
480C23C22×C3×AGL(1,𝔽5)11yescharacteristic
481C23C22×C3×AGL(1,𝔽5)12yes—
482D4—28no—
483D4—108no—
484D4—108no—
485D4—108no—
486C2×C4—22no—
487C2×C4—52no—
488C2×C4—104no—
489C2×C4—104no—
490C2×C4—102no—
491C2×C4—108no—
492C2×C4—1016no—
493C2×C4—2016no—
494C2×C4C22×C3×AGL(1,𝔽5)12yes—
495C2×C3—22no—
496C2×C3—24no—
497C2×C3—42no—
498C2×C3—54no—
499C2×C3—102no—
500C2×C3—104no—
501C2×C3—202no—
502C2×C3#6625812yes—
503C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
504C5C3×#230811yescharacteristic, complemented, Sylow
505C22—22no—
506C22—24no—
507C22—24no—
508C22—22no—
509C22—44no—
510C22—44no—
511C22—54no—
512C22—52no—
513C22—52no—
514C22—54no—
515C22—108no—
516C22—108no—
517C22—108no—
518C22—102no—
519C22—104no—
520C22—104no—
521C22—102no—
522C22—204no—
523C22—208no—
524C22—204no—
525C22—208no—
526C22—208no—
527C22C2×C3×C22⋊AGL(1,𝔽5)12yes—
528C22C2×C3×C22⋊AGL(1,𝔽5)14yes—
529C22C23×C3×AGL(1,𝔽5)11yescharacteristic
530C4—22no—
531C4—102no—
532C4—208no—
533C3#1061750611yescharacteristic, direct product factor, Sylow
534C2—22no—
535C2—24no—
536C2—42no—
537C2—54no—
538C2—102no—
539C2—104no—
540C2—202no—
541C2C3×#6625812yes—
542C2C22×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22×C3C23×AGL(1,𝔽5)
commutatorC22×C5C23×C3×C4
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×D4C4
socleC22×C3×C5C23×C4
prime radicalC22×C3×D4×D5C2
cosocleC22×D5C24×C3
hypercenterC22×C3×D4AGL(1,𝔽5)
hypocenterC5C3×#2308
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C22⋊AGL(1,𝔽5)C2semidirect
3. C3×#65800C2semidirect
4. C3×#65779C2semidirect
5. C3×#65764C2semidirect
6. #10617506C3direct (N × H)
9. C23×C3×AGL(1,𝔽5)C22semidirect
10. C22×C3×C5×D4C4semidirect
11. C22×C3×C22⋊D5C4semidirect
12. C22×C3×C22⋊D5C4semidirect
14. C2×C3×D4×D5C4semidirect
16. C22×C3×D20C4semidirect
20. C2×C3×C22⋊AGL(1,𝔽5)C22semidirect
21. C2×C3×C22⋊AGL(1,𝔽5)C22semidirect
22. C3×(C2×AGL(1,𝔽5))⋊C4C22semidirect
25. C22×C22⋊AGL(1,𝔽5)C2×C3semidirect
26. #65800C2×C3semidirect
27. #65779C2×C3semidirect
28. #65764C2×C3semidirect
30. C24×C3×C5C2×C4semidirect
36. C23×C3×D5C2×C4semidirect
37. C23×C3×D5C2×C4semidirect
46. C2×C3×C5×D4C2×C4semidirect
47. C22×C3×C4×C5C2×C4semidirect
50. C2×C3×C22⋊D5C2×C4semidirect
51. C2×C3×C22⋊D5C2×C4semidirect
52. C22×C3×Dic5C2×C4semidirect
57. C2×C3×D20C2×C4semidirect
59. C2×C3×C4×D5C2×C4semidirect
71. C23×AGL(1,𝔽5)C22×C3semidirect
72. C22×C5×D4C3×C4semidirect
73. C22×C22⋊D5C3×C4semidirect
74. C22×C22⋊D5C3×C4semidirect
76. C2×D4×D5C3×C4semidirect
78. C22×D20C3×C4semidirect
82. C2×C22⋊AGL(1,𝔽5)C22×C3semidirect
83. C2×C22⋊AGL(1,𝔽5)C22×C3semidirect
84. (C2×AGL(1,𝔽5))⋊C4C22×C3semidirect
89. C23×C3×C5C22⋊C4semidirect
105. C22×C3×D5C22⋊C4semidirect
106. C22×C3×D5C22⋊C4semidirect
135. C22×C3×D4AGL(1,𝔽5)semidirect
144. C24×C5C2×C3×C4semidirect
150. C23×D5C2×C3×C4semidirect
151. C23×D5C2×C3×C4semidirect
160. C2×C5×D4C2×C3×C4semidirect
161. C22×C4×C5C2×C3×C4semidirect
164. C2×C22⋊D5C2×C3×C4semidirect
165. C2×C22⋊D5C2×C3×C4semidirect
166. C22×Dic5C2×C3×C4semidirect
171. C2×D20C2×C3×C4semidirect
173. C2×C4×D5C2×C3×C4semidirect
223. C24×C3C2×AGL(1,𝔽5)semidirect
234. C2×C3×D4C2×AGL(1,𝔽5)semidirect
242. C22×C3×C4C2×AGL(1,𝔽5)semidirect
249. C23×C5C3×C22⋊C4semidirect
265. C22×D5C3×C22⋊C4semidirect
266. C22×D5C3×C22⋊C4semidirect
295. C22×D4C3×AGL(1,𝔽5)semidirect
336. C23×C3C22⋊AGL(1,𝔽5)semidirect
393. C24C2×C3×AGL(1,𝔽5)semidirect
404. C2×D4C2×C3×AGL(1,𝔽5)semidirect
412. C22×C4C2×C3×AGL(1,𝔽5)semidirect
416. C3×C5#2308semidirect
478. C23C3×C22⋊AGL(1,𝔽5)semidirect
504. C5C3×#2308semidirect
533. C3#10617506direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×D4×D52
C22×C3×C22⋊AGL(1,𝔽5)2
C3×#658002
C3×#657792
C3×#657642
#106175063
C3×#23085