Finite Group Databasebeta

← C3×#10610597 #14416671

Subgroups — C3×#10610597 #14416671

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#41×Dic5C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic
3C2×C3×#4039C211yesmaximal, characteristic, complemented
4C3×C5×#417C211yesmaximal, characteristic, complemented
5C3×#65420C211yesmaximal, characteristic, complemented
6C3×M16×Dic5C211yesmaximal, characteristic, complemented
7C3×#65253C211yesmaximal, characteristic, complemented
8C3×#65106C212yesmaximal, complemented
9C3×#65077C212yesmaximal, complemented
10C3×#65074C212yesmaximal, complemented
11C3×#65045C212yesmaximal, complemented
12#10610597C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×C3×C4×D5—21no—
16C2×C3×C5×M16C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C3×#4095C418yescomplemented
19C3×Q8×Dic5C2211yescharacteristic, complemented
20C3×Q8×Dic5C2211yescharacteristic, complemented
21C2×C3×#688C2212yes—
22C3×D4×Dic5—21no—
23C3×D4×Dic5—21no—
24C3×D4×Dic5C2211yescharacteristic, complemented
25C3×D4×Dic5C2211yescharacteristic, complemented
26C2×C3×#686C2212yes—
27C2×C3×#685—21no—
28C3×#4072—21no—
29C3×#4072C2211yescharacteristic
30C2×C3×C4×Dic5—21no—
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×C3×#681C2211yescharacteristic
33C3×#4039—21no—
34C3×#4039—21no—
35C3×#4039C2212yes—
36C3×#4039C2212yes—
37C3×C5×#103C2212yescomplemented
38C3×C5×#102C2212yescomplemented
39C3×#3953C2212yes—
40C3×#3953C2212yes—
41C3×#3947C2212yescomplemented
42C3×C8×Dic5C2212yescomplemented
43C3×#3940C2212yescomplemented
44C3×#3939C2212yescomplemented
45C3×C4×AGL(1,ℤ/8)—51nomaximal, Hall
46#41×Dic5C2×C311yescharacteristic, complemented
47C2×#4095C2×C311yescharacteristic
48C2×#4039C2×C311yescharacteristic, complemented
49C5×#417C2×C311yescharacteristic, complemented
50#65420C2×C311yescharacteristic, complemented
51M16×Dic5C2×C311yescharacteristic, complemented
52#65253C2×C311yescharacteristic, complemented
53#65106C2×C312yescomplemented
54#65077C2×C312yescomplemented
55#65074C2×C312yescomplemented
56#65045C2×C312yescomplemented
57C23×C3×D5—21no—
58C3×C5×#41—22no—
59C3×C5×#41C2×C414yescomplemented
60C2×C3×C5×Q8C2311yescharacteristic
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4C2311yescharacteristic
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5—21no—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×Dic5—21no—
67C22×C3×Dic5—21no—
68C22×C3×Dic5D411yescharacteristic
69C22×C3×Dic5D411yescharacteristic
70C2×C3×D20—21no—
71C2×C3×D20—22no—
72C2×C3×D20C2×C414yescomplemented
73C2×C3×D20C2312yes—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5—22no—
76C2×C3×C4×D5—44no—
77C3×C5×M16—22no—
78C2×C3×C5×C8C2312yes—
79C3×C5×C4⋊C4—21no—
80C3×C5×C4⋊C4C2312yes—
81C3×C22⋊Dic5—21no—
82C3×C22⋊Dic5—21no—
83C3×C22⋊Dic5—21no—
84C3×#688C2×C418yescomplemented
85C3×#686C2×C418yescomplemented
86C3×#685—22no—
87C3×#685—22no—
88C3×C4⋊Dic5—21no—
89C3×C4⋊Dic5—21no—
90C3×C4⋊Dic5C2311yescharacteristic
91C3×C4⋊Dic5C2311yescharacteristic
92C3×C4×Dic5—21no—
93C3×C4×Dic5—21no—
94C3×C4×Dic5—21no—
95C3×C4×Dic5D411yescharacteristic
96C3×C4×Dic5D411yescharacteristic
97C3×C4×Dic5C2311yescharacteristic
98C3×C4×Dic5C2311yescharacteristic
99C3×#681C2×C414yescomplemented
100C2×C3×#168C2312yes—
101C2×C3×AGL(1,ℤ/8)—51no—
102C3×C4×#41—51no—
103C2×C3×C4×D4—51no—
104C3×#442—52no—
105C3×#440—52no—
106C3×C4×SD16—52no—
107C3×C4×D8—52no—
108C3×#428—51no—
109C3×#418—51no—
110C3×#417D511yescharacteristic, complemented
111C3×C4×M16—51no—
112C2×C5×#41C22×C311yescharacteristic
113C22×D20C22×C311yescharacteristic
114C22×C4×D5—21no—
115C2×C5×M16C22×C311yescharacteristic
116C2×C5×C4⋊C4C22×C311yescharacteristic
117#4095C3×C418yescomplemented
118Q8×Dic5C22×C311yescharacteristic, complemented
119Q8×Dic5C22×C311yescharacteristic, complemented
120C2×#688C22×C312yes—
121D4×Dic5—21no—
122D4×Dic5—21no—
123D4×Dic5C22×C311yescharacteristic, complemented
124D4×Dic5C22×C311yescharacteristic, complemented
125C2×#686C22×C312yes—
126C2×#685—21no—
127#4072—21no—
128#4072C22×C311yescharacteristic
129C2×C4×Dic5—21no—
130C2×C4×Dic5C22×C311yescharacteristic
131C2×#681C22×C311yescharacteristic
132#4039—21no—
133#4039—21no—
134#4039C22×C312yes—
135#4039C22×C312yes—
136C5×#103C22×C312yescomplemented
137C5×#102C22×C312yescomplemented
138#3953C22×C312yes—
139#3953C22×C312yes—
140#3947C22×C312yescomplemented
141C8×Dic5C22×C312yescomplemented
142#3940C22×C312yescomplemented
143#3939C22×C312yescomplemented
144C4×AGL(1,ℤ/8)—51noSylow
145C23×C3×C5—21no—
146C23×C3×C5C2×D411yescharacteristic
147C22×C3×D5—24no—
148C22×C3×D5—22no—
149C22×C3×D5—42no—
150C22×C3×D5—42no—
151C3×C5×Q8—21no—
152C3×C5×Q8C22×C412yescomplemented
153C3×C5×D4—24no—
154C3×C5×D4—21no—
155C3×C5×D4C22×C412yescomplemented
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—24no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—42no—
160C2×C3×C4×C5C22×C412yes—
161C2×C3×C4×C5C2×D411yescharacteristic
162C2×C3×C4×C5#4112yes—
163C2×C3×C4×C5C2411yescharacteristic
164C2×C3×Dic5—22no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—41no—
168C2×C3×Dic5—42no—
169C2×C3×Dic5—42no—
170C2×C3×Dic5C2×D411yescharacteristic
171C2×C3×Dic5C2×D411yescharacteristic
172C2×C3×Dic5C2×D411yescharacteristic
173C2×C3×Dic5C2×D411yescharacteristic
174C3×D20—24no—
175C3×D20—22no—
176C3×D20C22×C414yes—
177C3×C4×D5—44no—
178C3×C4×D5—44no—
179C3×C5×C8—22no—
180C3×#168C22×C414yescomplemented
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×D4—51no—
183C23×C3×C4—101no—
184C3×AGL(1,ℤ/8)—58no—
185C2×C3×SD16—52no—
186C2×C3×D8—52no—
187C2×C3×M16—51no—
188C2×C3×M16C2×D511yescharacteristic
189C3×C4×Q8—51no—
190C3×C4×Q8—51no—
191C3×C4×D4—51no—
192C3×C4×D4—51no—
193C3×C4×D4—52no—
194C3×C4×D4—52no—
195C3×C4×D4—101no—
196C3×C4×D4—101no—
197C3×C4×D4—101no—
198C3×C4×D4—101no—
199C3×#117—51no—
200C3×#117—101no—
201C2×C3×C4⋊C4C2×D511yescharacteristic
202C2×C3×C22⋊C4—101no—
203C2×C3×C42—51no—
204C2×C3×C42—101no—
205C3×#107—52no—
206C3×#106—52no—
207C3×#103C2×D512yescomplemented
208C3×#102—52no—
209C3×#102—52no—
210C3×#102C2×D512yescomplemented
211C3×#97—52no—
212C3×C4×C8—52no—
213C23×D5—21no—
214C5×#41—22no—
215C5×#41C2×C3×C414yescomplemented
216C2×C5×Q8C23×C311yescharacteristic
217C2×C5×D4—21no—
218C2×C5×D4C23×C311yescharacteristic
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5C23×C311yescharacteristic
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5C3×D411yescharacteristic
225C22×Dic5C3×D411yescharacteristic
226C2×D20—21no—
227C2×D20—22no—
228C2×D20C2×C3×C414yescomplemented
229C2×D20C23×C312yes—
230C2×C4×D5—22no—
231C2×C4×D5—22no—
232C2×C4×D5—44no—
233C5×M16—22no—
234C2×C5×C8C23×C312yes—
235C5×C4⋊C4—21no—
236C5×C4⋊C4C23×C312yes—
237C22⋊Dic5—21no—
238C22⋊Dic5—21no—
239C22⋊Dic5—21no—
240#688C2×C3×C418yescomplemented
241#686C2×C3×C418yescomplemented
242#685—22no—
243#685—22no—
244C4⋊Dic5—21no—
245C4⋊Dic5—21no—
246C4⋊Dic5C23×C311yescharacteristic
247C4⋊Dic5C23×C311yescharacteristic
248C4×Dic5—21no—
249C4×Dic5—21no—
250C4×Dic5—21no—
251C4×Dic5C3×D411yescharacteristic
252C4×Dic5C3×D411yescharacteristic
253C4×Dic5C23×C311yescharacteristic
254C4×Dic5C23×C311yescharacteristic
255#681C2×C3×C414yescomplemented
256C2×#168C23×C312yes—
257C2×AGL(1,ℤ/8)—51no—
258C4×#41—51no—
259C2×C4×D4—51no—
260#442—52no—
261#440—52no—
262C4×SD16—52no—
263C4×D8—52no—
264#428—51no—
265#418—51no—
266#417C3×D511yescharacteristic, complemented
267C4×M16—51no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5—22no—
271C22×C3×C5—41no—
272C22×C3×C5—41no—
273C22×C3×C5C4×D412yes—
274C22×C3×C5C22×D411yescharacteristic
275C2×C3×D5—24no—
276C2×C3×D5—48no—
277C2×C3×D5—42no—
278C2×C3×D5—42no—
279C3×C4×C5—22no—
280C3×C4×C5—42no—
281C3×C4×C5C4×D412yes—
282C3×C4×C5C23×C411yescharacteristic
283C3×C4×C5C2×#4111yescharacteristic
284C3×Dic5—21no—
285C3×Dic5—21no—
286C3×Dic5—21no—
287C3×Dic5—41no—
288C3×Dic5—41no—
289C3×Dic5AGL(1,ℤ/8)12yescomplemented
290C24×C3—101no—
291C3×#41—22no—
292C3×#41C4×D514yescomplemented
293C2×C3×Q8C22×D511yescharacteristic
294C2×C3×D4—21no—
295C2×C3×D4—54no—
296C2×C3×D4—52no—
297C2×C3×D4—101no—
298C2×C3×D4—102no—
299C2×C3×D4C22×D511yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—51no—
303C22×C3×C4—51no—
304C22×C3×C4—102no—
305C22×C3×C4—102no—
306C22×C3×C4—101no—
307C22×C3×C4—101no—
308C22×C3×C4—204no—
309C22×C3×C4C22×D511yescharacteristic
310C3×SD16—58no—
311C3×D8—58no—
312C3×M16—22no—
313C3×M16—54no—
314C2×C3×C8—52no—
315C2×C3×C8C22×D512yes—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—51no—
318C3×C4⋊C4—51no—
319C3×C4⋊C4—101no—
320C3×C4⋊C4—101no—
321C3×C4⋊C4C22×D512yes—
322C3×C22⋊C4—102no—
323C3×C22⋊C4—102no—
324C3×C22⋊C4—101no—
325C3×C22⋊C4—101no—
326C3×C22⋊C4—101no—
327C3×C42—51no—
328C3×C42—51no—
329C3×C42—51no—
330C3×C42—51no—
331C3×C42—101no—
332C3×C42—101no—
333C3×C42—101no—
334C23×C5—21no—
335C23×C5C2×C3×D411yescharacteristic
336C22×D5—24no—
337C22×D5—22no—
338C22×D5—42no—
339C22×D5—42no—
340C5×Q8—21no—
341C5×Q8C22×C3×C412yescomplemented
342C5×D4—24no—
343C5×D4—21no—
344C5×D4C22×C3×C412yescomplemented
345C2×C4×C5—21no—
346C2×C4×C5—24no—
347C2×C4×C5—22no—
348C2×C4×C5—42no—
349C2×C4×C5C22×C3×C412yes—
350C2×C4×C5C2×C3×D411yescharacteristic
351C2×C4×C5C3×#4112yes—
352C2×C4×C5C24×C311yescharacteristic
353C2×Dic5—22no—
354C2×Dic5—21no—
355C2×Dic5—21no—
356C2×Dic5—41no—
357C2×Dic5—42no—
358C2×Dic5—42no—
359C2×Dic5C2×C3×D411yescharacteristic
360C2×Dic5C2×C3×D411yescharacteristic
361C2×Dic5C2×C3×D411yescharacteristic
362C2×Dic5C2×C3×D411yescharacteristic
363D20—24no—
364D20—22no—
365D20C22×C3×C414yes—
366C4×D5—44no—
367C4×D5—44no—
368C5×C8—22no—
369#168C22×C3×C414yescomplemented
370C2×#41C2×C3×D511yescharacteristic
371C22×D4—51no—
372C23×C4—101no—
373AGL(1,ℤ/8)—58no—
374C2×SD16—52no—
375C2×D8—52no—
376C2×M16—51no—
377C2×M16C2×C3×D511yescharacteristic
378C4×Q8—51no—
379C4×Q8—51no—
380C4×D4—51no—
381C4×D4—51no—
382C4×D4—52no—
383C4×D4—52no—
384C4×D4—101no—
385C4×D4—101no—
386C4×D4—101no—
387C4×D4—101no—
388#117—51no—
389#117—101no—
390C2×C4⋊C4C2×C3×D511yescharacteristic
391C2×C22⋊C4—101no—
392C2×C42—51no—
393C2×C42—101no—
394#107—52no—
395#106—52no—
396#103C2×C3×D512yescomplemented
397#102—52no—
398#102—52no—
399#102C2×C3×D512yescomplemented
400#97—52no—
401C4×C8—52no—
402C2×C3×C5—22no—
403C2×C3×C5—42no—
404C2×C3×C5C2×C4×D411yescharacteristic
405C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
406C2×C3×C5#57511yescharacteristic
407C3×D5—44no—
408C23×C3—21no—
409C23×C3—102no—
410C23×C3—104no—
411C23×C3—202no—
412C23×C3—202no—
413C23×C3D4×D511yescharacteristic
414C3×Q8—21no—
415C3×Q8C2×C4×D512yescomplemented
416C3×D4—24no—
417C3×D4—21no—
418C3×D4—54no—
419C3×D4—102no—
420C3×D4—104no—
421C3×D4C2×C4×D512yescomplemented
422C2×C3×C4—21no—
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—42no—
426C2×C3×C4—51no—
427C2×C3×C4—51no—
428C2×C3×C4—51no—
429C2×C3×C4—51no—
430C2×C3×C4—102no—
431C2×C3×C4—101no—
432C2×C3×C4—101no—
433C2×C3×C4—204no—
434C2×C3×C4—204no—
435C2×C3×C4—202no—
436C2×C3×C4—201no—
437C2×C3×C4—202no—
438C2×C3×C4C2×C4×D512yes—
439C2×C3×C4D4×D511yescharacteristic
440C2×C3×C4#71112yes—
441C2×C3×C4C23×D511yescharacteristic
442C3×C8—22no—
443C3×C8—54no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—22no—
447C22×C5—41no—
448C22×C5—41no—
449C22×C5C3×C4×D412yes—
450C22×C5C22×C3×D411yescharacteristic
451C2×D5—24no—
452C2×D5—48no—
453C2×D5—42no—
454C2×D5—42no—
455C4×C5—22no—
456C4×C5—42no—
457C4×C5C3×C4×D412yes—
458C4×C5C23×C3×C411yescharacteristic
459C4×C5C2×C3×#4111yescharacteristic
460Dic5—21no—
461Dic5—21no—
462Dic5—21no—
463Dic5—41no—
464Dic5—41no—
465Dic5C3×AGL(1,ℤ/8)12yescomplemented
466C24—101no—
467#41—22no—
468#41C3×C4×D514yescomplemented
469C2×Q8C22×C3×D511yescharacteristic
470C2×D4—21no—
471C2×D4—54no—
472C2×D4—52no—
473C2×D4—101no—
474C2×D4—102no—
475C2×D4C22×C3×D511yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—51no—
479C22×C4—51no—
480C22×C4—102no—
481C22×C4—102no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—204no—
485C22×C4C22×C3×D511yescharacteristic
486SD16—58no—
487D8—58no—
488M16—22no—
489M16—54no—
490C2×C8—52no—
491C2×C8C22×C3×D512yes—
492C4⋊C4—21no—
493C4⋊C4—51no—
494C4⋊C4—51no—
495C4⋊C4—101no—
496C4⋊C4—101no—
497C4⋊C4C22×C3×D512yes—
498C22⋊C4—102no—
499C22⋊C4—102no—
500C22⋊C4—101no—
501C22⋊C4—101no—
502C22⋊C4—101no—
503C42—51no—
504C42—51no—
505C42—51no—
506C42—51no—
507C42—101no—
508C42—101no—
509C42—101no—
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—104no—
517C22×C3—208no—
518C22×C3—202no—
519C22×C3—202no—
520C22×C3#402712yes—
521C22×C3C2×D4×D511yescharacteristic
522C3×C4—22no—
523C3×C4—42no—
524C3×C4—52no—
525C3×C4—101no—
526C3×C4—101no—
527C3×C4—101no—
528C3×C4—201no—
529C3×C4—201no—
530C3×C4#402712yes—
531C3×C4C22×C4×D511yescharacteristic
532C3×C4C2×#71111yescharacteristic
533C2×C5—22no—
534C2×C5—42no—
535C2×C5C2×C3×C4×D411yescharacteristic
536C2×C5C2×C3×AGL(1,ℤ/8)11yescharacteristic
537C2×C5C3×#57511yescharacteristic
538D5—44no—
539C23—21no—
540C23—102no—
541C23—104no—
542C23—202no—
543C23—202no—
544C23C3×D4×D511yescharacteristic
545Q8—21no—
546Q8C2×C3×C4×D512yescomplemented
547D4—24no—
548D4—21no—
549D4—54no—
550D4—102no—
551D4—104no—
552D4C2×C3×C4×D512yescomplemented
553C2×C4—21no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—42no—
557C2×C4—51no—
558C2×C4—51no—
559C2×C4—51no—
560C2×C4—51no—
561C2×C4—102no—
562C2×C4—101no—
563C2×C4—101no—
564C2×C4—204no—
565C2×C4—204no—
566C2×C4—202no—
567C2×C4—201no—
568C2×C4—202no—
569C2×C4C2×C3×C4×D512yes—
570C2×C4C3×D4×D511yescharacteristic
571C2×C4C3×#71112yes—
572C2×C4C23×C3×D511yescharacteristic
573C8—22no—
574C8—54no—
575C2×C3—22no—
576C2×C3—42no—
577C2×C3—204no—
578C2×C3C2×#402711yescharacteristic
579C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
580C2×C3#6611111yescharacteristic
581C5C3×C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—104no—
588C22—208no—
589C22—202no—
590C22—202no—
591C22C3×#402712yes—
592C22C2×C3×D4×D511yescharacteristic
593C4—22no—
594C4—42no—
595C4—52no—
596C4—101no—
597C4—101no—
598C4—101no—
599C4—201no—
600C4—201no—
601C4C3×#402712yes—
602C4C22×C3×C4×D511yescharacteristic
603C4C2×C3×#71111yescharacteristic
604C3#1061059711yescharacteristic, direct product factor, Sylow
605C2—22no—
606C2—42no—
607C2—204no—
608C2C2×C3×#402711yescharacteristic
609C2C3×D5×AGL(1,ℤ/8)11yescharacteristic
610C2C3×#6611111yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#417C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4095C2
cosocleC2×C4×C5C24×C3
hypercenterC3×#417D5
hypocenterC5C3×C4×AGL(1,ℤ/8)
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#417

Complements

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

NH ≅ G/Ntype
1. C3×#41×Dic5C2semidirect
3. C2×C3×#4039C2semidirect
4. C3×C5×#417C2semidirect
5. C3×#65420C2semidirect
6. C3×M16×Dic5C2semidirect
7. C3×#65253C2semidirect
8. C3×#65106C2semidirect
9. C3×#65077C2semidirect
10. C3×#65074C2semidirect
11. C3×#65045C2semidirect
12. #10610597C3direct (N × H)
18. C3×#4095C4semidirect
19. C3×Q8×Dic5C22semidirect
20. C3×Q8×Dic5C22semidirect
24. C3×D4×Dic5C22semidirect
25. C3×D4×Dic5C22semidirect
37. C3×C5×#103C22semidirect
38. C3×C5×#102C22semidirect
41. C3×#3947C22semidirect
42. C3×C8×Dic5C22semidirect
43. C3×#3940C22semidirect
44. C3×#3939C22semidirect
46. #41×Dic5C2×C3semidirect
48. C2×#4039C2×C3semidirect
49. C5×#417C2×C3semidirect
50. #65420C2×C3semidirect
51. M16×Dic5C2×C3semidirect
52. #65253C2×C3semidirect
53. #65106C2×C3semidirect
54. #65077C2×C3semidirect
55. #65074C2×C3semidirect
56. #65045C2×C3semidirect
59. C3×C5×#41C2×C4semidirect
72. C2×C3×D20C2×C4semidirect
84. C3×#688C2×C4semidirect
85. C3×#686C2×C4semidirect
99. C3×#681C2×C4semidirect
110. C3×#417D5semidirect
117. #4095C3×C4semidirect
118. Q8×Dic5C22×C3semidirect
119. Q8×Dic5C22×C3semidirect
123. D4×Dic5C22×C3semidirect
124. D4×Dic5C22×C3semidirect
136. C5×#103C22×C3semidirect
137. C5×#102C22×C3semidirect
140. #3947C22×C3semidirect
141. C8×Dic5C22×C3semidirect
142. #3940C22×C3semidirect
143. #3939C22×C3semidirect
152. C3×C5×Q8C22×C4semidirect
155. C3×C5×D4C22×C4semidirect
180. C3×#168C22×C4semidirect
207. C3×#103C2×D5semidirect
210. C3×#102C2×D5semidirect
215. C5×#41C2×C3×C4semidirect
228. C2×D20C2×C3×C4semidirect
240. #688C2×C3×C4semidirect
241. #686C2×C3×C4semidirect
255. #681C2×C3×C4semidirect
266. #417C3×D5semidirect
289. C3×Dic5AGL(1,ℤ/8)semidirect
292. C3×#41C4×D5semidirect
341. C5×Q8C22×C3×C4semidirect
344. C5×D4C22×C3×C4semidirect
369. #168C22×C3×C4semidirect
396. #103C2×C3×D5semidirect
399. #102C2×C3×D5semidirect
415. C3×Q8C2×C4×D5semidirect
421. C3×D4C2×C4×D5semidirect
465. Dic5C3×AGL(1,ℤ/8)semidirect
468. #41C3×C4×D5semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
546. Q8C2×C3×C4×D5semidirect
552. D4C2×C3×C4×D5semidirect
581. C5C3×C4×AGL(1,ℤ/8)semidirect
604. C3#10610597direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#41×Dic52
C2×C3×#40952
C2×C3×#40392
C3×C5×#4172
C3×#654202
C3×M16×Dic52
C3×#652532
C3×#651062
C3×#650772
C3×#650742
C3×#650452
#106105973
C3×C4×AGL(1,ℤ/8)5