Finite Group Databasebeta

← C3×#10614131 #14331614

Subgroups — C3×#10614131 #14331614

Order 1920.

1888 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#709C211yesmaximal, characteristic, complemented
2C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
3C2×C3×C4×C22⋊D5C212yesmaximal, complemented
4C3×#65512C212yesmaximal, complemented
5C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
6C3×#65280C211yesmaximal, characteristic, complemented
7C3×#65268C211yesmaximal, characteristic, complemented
8C3×#65249C211yesmaximal, characteristic, complemented
9C3×#65248C212yesmaximal, complemented
10C3×#65236C211yesmaximal, characteristic, complemented
11C3×C4×#685C212yesmaximal, complemented
12#10614131C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C22×C3×C22⋊D5C2212yes—
17C22×C3×C22⋊D5C2212yes—
18C2×C3×#709—24no—
19C2×C3×#709—28no—
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2212yes—
22C22×C3×Dic10C2211yescharacteristic
23C3×C4×C5×D4—24no—
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C42×C5C2211yescharacteristic
28C2×C3×C22⋊Dic5C2212yes—
29C2×C3×C22⋊Dic5C2212yes—
30C3×C4×C22⋊D5—28no—
31C2×C3×#685C2212yes—
32C2×C3×#685C2212yes—
33C2×C3×#685C2212yes—
34C2×C3×#683C2212yes—
35C2×C3×C4×Dic5C2212yes—
36C3×#3963C2211yescharacteristic
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#3963C2211yescharacteristic
40C3×#2388—51nomaximal, Hall
41C22×#709C2×C311yescharacteristic, complemented
42C2×C4×C5×D4C2×C311yescharacteristic, complemented
43C2×C4×C22⋊D5C2×C312yescomplemented
44#65512C2×C312yescomplemented
45C4×C22⋊Dic5C2×C311yescharacteristic, complemented
46#65280C2×C311yescharacteristic, complemented
47#65268C2×C311yescharacteristic, complemented
48#65249C2×C311yescharacteristic, complemented
49#65248C2×C312yescomplemented
50#65236C2×C311yescharacteristic, complemented
51C4×#685C2×C312yescomplemented
52C24×C3×C5C2311yescharacteristic
53C24×C3×C5C2311yescharacteristic
54C23×C3×D5C2312yes—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4—22no—
58C22×C3×C4×C5—24no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—24no—
61C22×C3×C4×C5D414yescomplemented
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C2×C3×C22⋊D5—24no—
68C2×C3×C22⋊D5—24no—
69C2×C3×C22⋊D5—24no—
70C2×C3×C22⋊D5—24no—
71C2×C3×C22⋊D5—24no—
72C2×C3×C22⋊D5—24no—
73C22×C3×Dic5C2312yes—
74C22×C3×Dic5C2312yes—
75C22×C3×Dic5C2312yes—
76C3×#709—232no—
77C2×C3×D20—24no—
78C2×C3×D20—22no—
79C2×C3×C4×D5—24no—
80C2×C3×C4×D5—24no—
81C2×C3×C4×D5D418yescomplemented
82C2×C3×Dic10—22no—
83C2×C3×Dic10—24no—
84C3×C5×C4⋊C4—22no—
85C3×C5×C22⋊C4—22no—
86C3×C5×C22⋊C4—22no—
87C3×C42×C5—22no—
88C3×C22⋊Dic5—24no—
89C3×C22⋊Dic5—24no—
90C3×#685—24no—
91C3×#685—24no—
92C3×#685—24no—
93C3×#683—24no—
94C3×C4×Dic5—24no—
95C22×C3×#41—51no—
96C2×C3×C4×D4—52no—
97C2×C3×C4×D4D511yescharacteristic, complemented
98C3×#395—51no—
99C3×#394—51no—
100C3×#394—52no—
101C3×#393—51no—
102C3×#392—52no—
103C3×#392—51no—
104C3×C4×C22⋊C4—51no—
105C3×C4×C22⋊C4—52no—
106C22×C5×D4C22×C311yescharacteristic
107C23×C4×C5C22×C311yescharacteristic
108C23×C4×C5C22×C311yescharacteristic
109C22×C22⋊D5C22×C312yes—
110C22×C22⋊D5C22×C312yes—
111C2×#709—24no—
112C2×#709—28no—
113C22×D20C22×C311yescharacteristic
114C22×C4×D5C22×C312yes—
115C22×Dic10C22×C311yescharacteristic
116C4×C5×D4—24no—
117C2×C5×C4⋊C4C22×C311yescharacteristic
118C2×C5×C22⋊C4C22×C311yescharacteristic
119C2×C5×C22⋊C4C22×C311yescharacteristic
120C2×C42×C5C22×C311yescharacteristic
121C2×C22⋊Dic5C22×C312yes—
122C2×C22⋊Dic5C22×C312yes—
123C4×C22⋊D5—28no—
124C2×#685C22×C312yes—
125C2×#685C22×C312yes—
126C2×#685C22×C312yes—
127C2×#683C22×C312yes—
128C2×C4×Dic5C22×C312yes—
129#3963C22×C311yescharacteristic
130#3963C22×C312yes—
131#3963C22×C312yes—
132#3963C22×C311yescharacteristic
133#2388—51noSylow
134C23×C3×C5—22no—
135C23×C3×C5—21no—
136C23×C3×C5—22no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—21no—
140C23×C3×C5—21no—
141C23×C3×C5—21no—
142C23×C3×C5C2×D412yes—
143C23×C3×C5#4112yescomplemented
144C23×C3×C5C2411yescharacteristic
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5—22no—
150C22×C3×D5—22no—
151C22×C3×D5C2×D414yes—
152C3×C5×D4—28no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—28no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—21no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—44no—
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2×D414yes—
164C2×C3×C4×C5C2×D412yes—
165C2×C3×C4×C5#4112yescomplemented
166C3×C22⋊D5—216no—
167C3×C22⋊D5—216no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5C2×D414yes—
176C2×C3×Dic5#4114yescomplemented
177C3×D20—28no—
178C3×C4×D5—216no—
179C3×Dic10—28no—
180C2×C3×#41—108no—
181C2×C3×#41—104no—
182C22×C3×Q8—51no—
183C22×C3×D4—52no—
184C22×C3×D4—52no—
185C22×C3×D4—51no—
186C22×C3×D4C2×D511yescharacteristic
187C23×C3×C4—52no—
188C23×C3×C4C2×D511yescharacteristic
189C23×C3×C4C2×D511yescharacteristic
190C3×C4×D4—24no—
191C3×C4×D4—108no—
192C2×C3×C4⋊C4—52no—
193C2×C3×C4⋊C4C2×D511yescharacteristic
194C2×C3×C22⋊C4—52no—
195C2×C3×C22⋊C4—52no—
196C2×C3×C22⋊C4—52no—
197C2×C3×C22⋊C4—52no—
198C2×C3×C22⋊C4—52no—
199C2×C3×C22⋊C4C2×D511yescharacteristic
200C2×C3×C22⋊C4C2×D511yescharacteristic
201C2×C3×C42—52no—
202C2×C3×C42C2×D511yescharacteristic
203C3×#95—51no—
204C3×#95—52no—
205C3×#95—52no—
206C3×#95—51no—
207C24×C5C23×C311yescharacteristic
208C24×C5C23×C311yescharacteristic
209C23×D5C23×C312yes—
210C2×C5×D4—22no—
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C22×C4×C5—24no—
214C22×C4×C5—22no—
215C22×C4×C5—24no—
216C22×C4×C5C3×D414yescomplemented
217C22×C4×C5C23×C311yescharacteristic
218C22×C4×C5C23×C311yescharacteristic
219C22×C4×C5C23×C311yescharacteristic
220C22×C4×C5C23×C311yescharacteristic
221C22×C4×C5C23×C311yescharacteristic
222C2×C22⋊D5—24no—
223C2×C22⋊D5—24no—
224C2×C22⋊D5—24no—
225C2×C22⋊D5—24no—
226C2×C22⋊D5—24no—
227C2×C22⋊D5—24no—
228C22×Dic5C23×C312yes—
229C22×Dic5C23×C312yes—
230C22×Dic5C23×C312yes—
231#709—232no—
232C2×D20—24no—
233C2×D20—22no—
234C2×C4×D5—24no—
235C2×C4×D5—24no—
236C2×C4×D5C3×D418yescomplemented
237C2×Dic10—22no—
238C2×Dic10—24no—
239C5×C4⋊C4—22no—
240C5×C22⋊C4—22no—
241C5×C22⋊C4—22no—
242C42×C5—22no—
243C22⋊Dic5—24no—
244C22⋊Dic5—24no—
245#685—24no—
246#685—24no—
247#685—24no—
248#683—24no—
249C4×Dic5—24no—
250C22×#41—51no—
251C2×C4×D4—52no—
252C2×C4×D4C3×D511yescharacteristic, complemented
253#395—51no—
254#394—51no—
255#394—52no—
256#393—51no—
257#392—52no—
258#392—51no—
259C4×C22⋊C4—51no—
260C4×C22⋊C4—52no—
261C22×C3×C5—22no—
262C22×C3×C5—24no—
263C22×C3×C5—22no—
264C22×C3×C5—22no—
265C22×C3×C5—22no—
266C22×C3×C5—41no—
267C22×C3×C5—42no—
268C22×C3×C5—42no—
269C22×C3×C5—42no—
270C22×C3×C5—41no—
271C22×C3×C5C22×D412yes—
272C22×C3×C5C22×D411yescharacteristic
273C22×C3×C5C2×#4111yescharacteristic
274C22×C3×C5C2×#4111yescharacteristic
275C22×C3×C5C2×#4112yes—
276C2×C3×D5—24no—
277C2×C3×D5—24no—
278C2×C3×D5—24no—
279C2×C3×D5—42no—
280C2×C3×D5—42no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C3×C4×C5—22no—
284C3×C4×C5—22no—
285C3×C4×C5—41no—
286C3×C4×C5—41no—
287C3×C4×C5#12014yes—
288C3×Dic5—24no—
289C3×Dic5—24no—
290C3×Dic5—42no—
291C24×C3—52no—
292C24×C3C22×D511yescharacteristic
293C24×C3C22×D511yescharacteristic
294C3×#41—1032no—
295C2×C3×Q8—104no—
296C2×C3×Q8—102no—
297C2×C3×D4—22no—
298C2×C3×D4—22no—
299C2×C3×D4—22no—
300C2×C3×D4—104no—
301C2×C3×D4—104no—
302C2×C3×D4—104no—
303C2×C3×D4—104no—
304C2×C3×D4—104no—
305C2×C3×D4—104no—
306C2×C3×D4—104no—
307C2×C3×D4—102no—
308C22×C3×C4—24no—
309C22×C3×C4—24no—
310C22×C3×C4—22no—
311C22×C3×C4—52no—
312C22×C3×C4—52no—
313C22×C3×C4—58no—
314C22×C3×C4—52no—
315C22×C3×C4—104no—
316C22×C3×C4—104no—
317C22×C3×C4C22⋊D514yescomplemented
318C22×C3×C4C22×D511yescharacteristic
319C22×C3×C4C22×D511yescharacteristic
320C22×C3×C4C22×D511yescharacteristic
321C22×C3×C4C22×D511yescharacteristic
322C22×C3×C4C22×D511yescharacteristic
323C3×C4⋊C4—22no—
324C3×C4⋊C4—104no—
325C3×C22⋊C4—22no—
326C3×C22⋊C4—22no—
327C3×C22⋊C4—104no—
328C3×C22⋊C4—104no—
329C3×C22⋊C4—104no—
330C3×C22⋊C4—104no—
331C3×C22⋊C4—104no—
332C3×C42—22no—
333C3×C42—104no—
334C23×C5—22no—
335C23×C5—21no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—21no—
340C23×C5—21no—
341C23×C5—21no—
342C23×C5C2×C3×D412yes—
343C23×C5C3×#4112yescomplemented
344C23×C5C24×C311yescharacteristic
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5C2×C3×D414yes—
352C5×D4—28no—
353C2×C4×C5—21no—
354C2×C4×C5—22no—
355C2×C4×C5—21no—
356C2×C4×C5—28no—
357C2×C4×C5—22no—
358C2×C4×C5—21no—
359C2×C4×C5—21no—
360C2×C4×C5—22no—
361C2×C4×C5—44no—
362C2×C4×C5C2×C3×D414yes—
363C2×C4×C5C2×C3×D412yes—
364C2×C4×C5C2×C3×D412yes—
365C2×C4×C5C3×#4112yescomplemented
366C22⋊D5—216no—
367C22⋊D5—216no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5C2×C3×D414yes—
376C2×Dic5C3×#4114yescomplemented
377D20—28no—
378C4×D5—216no—
379Dic10—28no—
380C2×#41—108no—
381C2×#41—104no—
382C22×Q8—51no—
383C22×D4—52no—
384C22×D4—52no—
385C22×D4—51no—
386C22×D4C2×C3×D511yescharacteristic
387C23×C4—52no—
388C23×C4C2×C3×D511yescharacteristic
389C23×C4C2×C3×D511yescharacteristic
390C4×D4—24no—
391C4×D4—108no—
392C2×C4⋊C4—52no—
393C2×C4⋊C4C2×C3×D511yescharacteristic
394C2×C22⋊C4—52no—
395C2×C22⋊C4—52no—
396C2×C22⋊C4—52no—
397C2×C22⋊C4—52no—
398C2×C22⋊C4—52no—
399C2×C22⋊C4C2×C3×D511yescharacteristic
400C2×C22⋊C4C2×C3×D511yescharacteristic
401C2×C42—52no—
402C2×C42C2×C3×D511yescharacteristic
403#95—51no—
404#95—52no—
405#95—52no—
406#95—51no—
407C2×C3×C5—42no—
408C2×C3×C5—42no—
409C2×C3×C5C2×#12011yescharacteristic
410C2×C3×C5#52511yescharacteristic
411C2×C3×C5#52512yes—
412C2×C3×C5#53212yes—
413C2×C3×C5#53211yescharacteristic
414C3×D5—44no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—21no—
423C23×C3—54no—
424C23×C3—102no—
425C23×C3—102no—
426C23×C3—102no—
427C23×C3—102no—
428C23×C3—102no—
429C23×C3—102no—
430C23×C3#70912yescomplemented
431C23×C3C2×C22⋊D512yes—
432C23×C3C23×D511yescharacteristic
433C3×Q8—108no—
434C3×D4—28no—
435C3×D4—108no—
436C3×D4—1016no—
437C3×D4—1016no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—28no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—44no—
447C2×C3×C4—54no—
448C2×C3×C4—54no—
449C2×C3×C4—102no—
450C2×C3×C4—102no—
451C2×C3×C4—102no—
452C2×C3×C4—102no—
453C2×C3×C4—1016no—
454C2×C3×C4—102no—
455C2×C3×C4—102no—
456C2×C3×C4—102no—
457C2×C3×C4#70912yescomplemented
458C2×C3×C4D4×D514yes—
459C2×C3×C4C2×C22⋊D512yes—
460C2×C3×C4C2×C22⋊D512yes—
461C22×C5—22no—
462C22×C5—24no—
463C22×C5—22no—
464C22×C5—22no—
465C22×C5—22no—
466C22×C5—41no—
467C22×C5—42no—
468C22×C5—42no—
469C22×C5—42no—
470C22×C5—41no—
471C22×C5C22×C3×D412yes—
472C22×C5C22×C3×D411yescharacteristic
473C22×C5C2×C3×#4111yescharacteristic
474C22×C5C2×C3×#4111yescharacteristic
475C22×C5C2×C3×#4112yes—
476C2×D5—24no—
477C2×D5—24no—
478C2×D5—24no—
479C2×D5—42no—
480C2×D5—42no—
481C2×D5—42no—
482C2×D5—42no—
483C4×C5—22no—
484C4×C5—22no—
485C4×C5—41no—
486C4×C5—41no—
487C4×C5C3×#12014yes—
488Dic5—24no—
489Dic5—24no—
490Dic5—42no—
491C24—52no—
492C24C22×C3×D511yescharacteristic
493C24C22×C3×D511yescharacteristic
494#41—1032no—
495C2×Q8—104no—
496C2×Q8—102no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—104no—
501C2×D4—104no—
502C2×D4—104no—
503C2×D4—104no—
504C2×D4—104no—
505C2×D4—104no—
506C2×D4—104no—
507C2×D4—102no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—52no—
512C22×C4—52no—
513C22×C4—58no—
514C22×C4—52no—
515C22×C4—104no—
516C22×C4—104no—
517C22×C4C3×C22⋊D514yescomplemented
518C22×C4C22×C3×D511yescharacteristic
519C22×C4C22×C3×D511yescharacteristic
520C22×C4C22×C3×D511yescharacteristic
521C22×C4C22×C3×D511yescharacteristic
522C22×C4C22×C3×D511yescharacteristic
523C4⋊C4—22no—
524C4⋊C4—104no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—104no—
528C22⋊C4—104no—
529C22⋊C4—104no—
530C22⋊C4—104no—
531C22⋊C4—104no—
532C42—22no—
533C42—104no—
534C3×C5#238811yescharacteristic, complemented, Hall
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—24no—
539C22×C3—22no—
540C22×C3—41no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—41no—
545C22×C3—104no—
546C22×C3—104no—
547C22×C3—104no—
548C22×C3—202no—
549C22×C3—202no—
550C22×C3—202no—
551C22×C3—202no—
552C22×C3C2×#70911yescharacteristic
553C22×C3C2×#70911yescharacteristic
554C22×C3C2×D4×D512yes—
555C22×C3D5×#4112yes—
556C22×C3C22×C22⋊D511yescharacteristic
557C3×C4—22no—
558C3×C4—22no—
559C3×C4—41no—
560C3×C4—41no—
561C3×C4—104no—
562C3×C4—104no—
563C3×C4—202no—
564C3×C4#408314yes—
565C2×C5—42no—
566C2×C5—42no—
567C2×C5C2×C3×#12011yescharacteristic
568C2×C5C3×#52511yescharacteristic
569C2×C5C3×#52512yes—
570C2×C5C3×#53212yes—
571C2×C5C3×#53211yescharacteristic
572D5—44no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—21no—
581C23—54no—
582C23—102no—
583C23—102no—
584C23—102no—
585C23—102no—
586C23—102no—
587C23—102no—
588C23C3×#70912yescomplemented
589C23C2×C3×C22⋊D512yes—
590C23C23×C3×D511yescharacteristic
591Q8—108no—
592D4—28no—
593D4—108no—
594D4—1016no—
595D4—1016no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—28no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—44no—
605C2×C4—54no—
606C2×C4—54no—
607C2×C4—102no—
608C2×C4—102no—
609C2×C4—102no—
610C2×C4—102no—
611C2×C4—1016no—
612C2×C4—102no—
613C2×C4—102no—
614C2×C4—102no—
615C2×C4C3×#70912yescomplemented
616C2×C4C3×D4×D514yes—
617C2×C4C2×C3×C22⋊D512yes—
618C2×C4C2×C3×C22⋊D512yes—
619C2×C3—42no—
620C2×C3—42no—
621C2×C3—204no—
622C2×C3#6588112yes—
623C2×C3#6588212yes—
624C2×C3#6612511yescharacteristic
625C2×C3C2×#408311yescharacteristic
626C2×C3#6616611yescharacteristic
627C5C3×#238811yescharacteristic, complemented, Sylow
628C22—22no—
629C22—22no—
630C22—22no—
631C22—24no—
632C22—22no—
633C22—41no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—41no—
638C22—104no—
639C22—104no—
640C22—104no—
641C22—202no—
642C22—202no—
643C22—202no—
644C22—202no—
645C22C2×C3×#70911yescharacteristic
646C22C2×C3×#70911yescharacteristic
647C22C2×C3×D4×D512yes—
648C22C3×D5×#4112yes—
649C22C22×C3×C22⋊D511yescharacteristic
650C4—22no—
651C4—22no—
652C4—41no—
653C4—41no—
654C4—104no—
655C4—104no—
656C4—202no—
657C4C3×#408314yes—
658C3#1061413111yescharacteristic, direct product factor, Sylow
659C2—42no—
660C2—42no—
661C2—204no—
662C2C3×#6588112yes—
663C2C3×#6588212yes—
664C2C3×#6612511yescharacteristic
665C2C2×C3×#408311yescharacteristic
666C2C3×#6616611yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D5
commutator, cosocleC23×C5C24×C3
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#2388
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#709C2semidirect
2. C2×C3×C4×C5×D4C2semidirect
3. C2×C3×C4×C22⋊D5C2semidirect
4. C3×#65512C2semidirect
5. C3×C4×C22⋊Dic5C2semidirect
6. C3×#65280C2semidirect
7. C3×#65268C2semidirect
8. C3×#65249C2semidirect
9. C3×#65248C2semidirect
10. C3×#65236C2semidirect
11. C3×C4×#685C2semidirect
12. #10614131C3direct (N × H)
41. C22×#709C2×C3semidirect
42. C2×C4×C5×D4C2×C3semidirect
43. C2×C4×C22⋊D5C2×C3semidirect
44. #65512C2×C3semidirect
45. C4×C22⋊Dic5C2×C3semidirect
46. #65280C2×C3semidirect
47. #65268C2×C3semidirect
48. #65249C2×C3semidirect
49. #65248C2×C3semidirect
50. #65236C2×C3semidirect
51. C4×#685C2×C3semidirect
61. C22×C3×C4×C5D4semidirect
81. C2×C3×C4×D5D4semidirect
97. C2×C3×C4×D4D5semidirect
143. C23×C3×C5#41semidirect
165. C2×C3×C4×C5#41semidirect
176. C2×C3×Dic5#41semidirect
216. C22×C4×C5C3×D4semidirect
236. C2×C4×D5C3×D4semidirect
252. C2×C4×D4C3×D5semidirect
317. C22×C3×C4C22⋊D5semidirect
343. C23×C5C3×#41semidirect
365. C2×C4×C5C3×#41semidirect
376. C2×Dic5C3×#41semidirect
430. C23×C3#709semidirect
457. C2×C3×C4#709semidirect
517. C22×C4C3×C22⋊D5semidirect
534. C3×C5#2388semidirect
588. C23C3×#709semidirect
615. C2×C4C3×#709semidirect
627. C5C3×#2388semidirect
658. C3#10614131direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C2×C3×C4×C5×D42
C2×C3×C4×C22⋊D52
C3×#655122
C3×C4×C22⋊Dic52
C3×#652802
C3×#652682
C3×#652492
C3×#652482
C3×#652362
C3×C4×#6852
#106141313
C3×#23885