Finite Group Databasebeta

← C3×Dic5×#121 #14321435

Subgroups — C3×Dic5×#121 #14321435

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C2×C3×D4×Dic5C212yesmaximal, complemented
3C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
4C22×C3×C4×Dic5C211yesmaximal, characteristic, complemented
5C3×#65510C211yesmaximal, characteristic, complemented
6C3×#65509C212yesmaximal, complemented
7C3×#65501C211yesmaximal, characteristic, complemented
8C3×#65274C211yesmaximal, characteristic, complemented
9C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
10C3×#65240C212yesmaximal, complemented
11C3×C22⋊C4×Dic5C212yesmaximal, complemented
12Dic5×#121C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2212yes—
14C22×C3×C5×D4C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C23×C3×Dic5C2212yes—
18C23×C3×Dic5C2211yescharacteristic
19C3×C5×#121C418yescomplemented
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2212yes—
22C2×C3×C22⋊Dic5C2212yes—
23C2×C3×C22⋊Dic5C2212yes—
24C2×C3×C22⋊Dic5C2212yes—
25C2×C3×C22⋊Dic5C2212yes—
26C3×D4×Dic5—28no—
27C3×D4×Dic5—24no—
28C2×C3×C4⋊Dic5C2212yes—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×C4×Dic5—24no—
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C2×C3×C4×Dic5C2212yes—
36C2×C3×C4×Dic5C2211yescharacteristic
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#3963C2212yes—
40C3×C4×#121—51nomaximal, Hall
41C2×C5×#121C2×C311yescharacteristic
42C2×D4×Dic5C2×C311yescharacteristic, complemented
43C2×D4×Dic5C2×C312yescomplemented
44C22×C4×Dic5C2×C311yescharacteristic, complemented
45#65510C2×C311yescharacteristic, complemented
46#65509C2×C312yescomplemented
47#65501C2×C311yescharacteristic, complemented
48#65274C2×C311yescharacteristic, complemented
49C4⋊C4×Dic5C2×C311yescharacteristic, complemented
50#65240C2×C312yescomplemented
51C22⋊C4×Dic5C2×C312yescomplemented
52C24×C3×C5C2312yes—
53C24×C3×C5C2311yescharacteristic
54C2×C3×C5×D4—24no—
55C2×C3×C5×D4—24no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4C2×C418yescomplemented
59C2×C3×C5×D4C2×C414yescomplemented
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5C2×C414yescomplemented
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×Dic5—22no—
67C22×C3×Dic5—22no—
68C22×C3×Dic5—22no—
69C22×C3×Dic5—22no—
70C22×C3×Dic5—22no—
71C22×C3×Dic5—24no—
72C22×C3×Dic5—24no—
73C22×C3×Dic5—24no—
74C22×C3×Dic5D414yescomplemented
75C22×C3×Dic5C2312yes—
76C22×C3×Dic5C2312yes—
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2311yescharacteristic
80C22×C3×Dic5C2311yescharacteristic
81C3×C5×C4⋊C4C2×C414yescomplemented
82C3×C5×C22⋊C4C2×C418yescomplemented
83C3×C22⋊Dic5—24no—
84C3×C22⋊Dic5—24no—
85C3×C22⋊Dic5—24no—
86C3×C22⋊Dic5—24no—
87C3×C4⋊Dic5—22no—
88C3×C4⋊Dic5—22no—
89C3×C4⋊Dic5—24no—
90C3×C4×Dic5—22no—
91C3×C4×Dic5—24no—
92C3×C4×Dic5—22no—
93C3×C4×Dic5—22no—
94C3×C4×Dic5D414yescomplemented
95C2×C3×#121D511yescharacteristic
96C2×C3×C4×D4—51no—
97C2×C3×C4×D4—52no—
98C22×C3×C42—51no—
99C3×#390—51no—
100C3×#389—51no—
101C3×#388—52no—
102C3×#386—52no—
103C3×#380—51no—
104C3×C4×C4⋊C4—51no—
105C3×C4×C22⋊C4—52no—
106C22×C5×D4C22×C312yes—
107C22×C5×D4C22×C311yescharacteristic
108C23×C4×C5C22×C311yescharacteristic
109C23×Dic5C22×C311yescharacteristic
110C23×Dic5C22×C312yes—
111C23×Dic5C22×C311yescharacteristic
112C5×#121C3×C418yescomplemented
113C2×C5×C4⋊C4C22×C311yescharacteristic
114C2×C5×C22⋊C4C22×C312yes—
115C2×C22⋊Dic5C22×C312yes—
116C2×C22⋊Dic5C22×C312yes—
117C2×C22⋊Dic5C22×C312yes—
118C2×C22⋊Dic5C22×C312yes—
119D4×Dic5—28no—
120D4×Dic5—24no—
121C2×C4⋊Dic5C22×C312yes—
122C2×C4⋊Dic5C22×C311yescharacteristic
123C2×C4⋊Dic5C22×C311yescharacteristic
124C2×C4×Dic5—24no—
125C2×C4×Dic5C22×C311yescharacteristic
126C2×C4×Dic5C22×C311yescharacteristic
127C2×C4×Dic5C22×C311yescharacteristic
128C2×C4×Dic5C22×C312yes—
129C2×C4×Dic5C22×C311yescharacteristic
130#3963C22×C312yes—
131#3963C22×C312yes—
132#3963C22×C312yes—
133C4×#121—51noSylow
134C23×C3×C5—21no—
135C23×C3×C5—21no—
136C23×C3×C5—21no—
137C23×C3×C5—21no—
138C23×C3×C5—22no—
139C23×C3×C5—22no—
140C23×C3×C5—22no—
141C23×C3×C5—22no—
142C23×C3×C5—22no—
143C23×C3×C5—22no—
144C23×C3×C5C22×C414yes—
145C23×C3×C5C22×C412yes—
146C23×C3×C5C2×D412yes—
147C23×C3×C5#4112yes—
148C23×C3×C5C2411yescharacteristic
149C3×C5×D4—216no—
150C3×C5×D4—28no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—28no—
156C2×C3×C4×C5C22×C412yes—
157C2×C3×C4×C5C22×C414yes—
158C2×C3×C4×C5C22×C412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5#4112yes—
161C2×C3×Dic5—28no—
162C2×C3×Dic5—21no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—28no—
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×Dic5—48no—
176C2×C3×Dic5C2×D412yes—
177C2×C3×Dic5C2×D412yes—
178C2×C3×Dic5C2×D412yes—
179C2×C3×Dic5C2×D412yes—
180C2×C3×Dic5#4112yes—
181C2×C3×Dic5#4112yes—
182C22×C3×D4C2×D512yes—
183C22×C3×D4C2×D511yescharacteristic
184C23×C3×C4—51no—
185C23×C3×C4—52no—
186C23×C3×C4—51no—
187C23×C3×C4C2×D511yescharacteristic
188C3×#121Dic518yesdirect product factor
189C3×C4×D4—104no—
190C3×C4×D4—108no—
191C2×C3×C4⋊C4—51no—
192C2×C3×C4⋊C4—51no—
193C2×C3×C4⋊C4—52no—
194C2×C3×C4⋊C4C2×D511yescharacteristic
195C2×C3×C22⋊C4—52no—
196C2×C3×C22⋊C4—52no—
197C2×C3×C22⋊C4—52no—
198C2×C3×C22⋊C4—52no—
199C2×C3×C22⋊C4C2×D512yes—
200C2×C3×C42—51no—
201C2×C3×C42—51no—
202C2×C3×C42—52no—
203C2×C3×C42—51no—
204C2×C3×C42—51no—
205C2×C3×C42—104no—
206C3×#95—52no—
207C3×#95—52no—
208C3×#95—52no—
209C24×C5C23×C312yes—
210C24×C5C23×C311yescharacteristic
211C2×C5×D4—24no—
212C2×C5×D4—24no—
213C2×C5×D4—22no—
214C2×C5×D4—22no—
215C2×C5×D4C2×C3×C418yescomplemented
216C2×C5×D4C2×C3×C414yescomplemented
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5C2×C3×C414yescomplemented
220C22×C4×C5C23×C311yescharacteristic
221C22×C4×C5C23×C312yes—
222C22×C4×C5C23×C311yescharacteristic
223C22×Dic5—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—24no—
229C22×Dic5—24no—
230C22×Dic5—24no—
231C22×Dic5C3×D414yescomplemented
232C22×Dic5C23×C312yes—
233C22×Dic5C23×C312yes—
234C22×Dic5C23×C311yescharacteristic
235C22×Dic5C23×C311yescharacteristic
236C22×Dic5C23×C311yescharacteristic
237C22×Dic5C23×C311yescharacteristic
238C5×C4⋊C4C2×C3×C414yescomplemented
239C5×C22⋊C4C2×C3×C418yescomplemented
240C22⋊Dic5—24no—
241C22⋊Dic5—24no—
242C22⋊Dic5—24no—
243C22⋊Dic5—24no—
244C4⋊Dic5—22no—
245C4⋊Dic5—22no—
246C4⋊Dic5—24no—
247C4×Dic5—22no—
248C4×Dic5—22no—
249C4×Dic5—22no—
250C4×Dic5—24no—
251C4×Dic5C3×D414yescomplemented
252C2×#121C3×D511yescharacteristic
253C2×C4×D4—51no—
254C2×C4×D4—52no—
255C22×C42—51no—
256#390—51no—
257#389—51no—
258#388—52no—
259#386—52no—
260#380—51no—
261C4×C4⋊C4—51no—
262C4×C22⋊C4—52no—
263C22×C3×C5—22no—
264C22×C3×C5—22no—
265C22×C3×C5—22no—
266C22×C3×C5—22no—
267C22×C3×C5—22no—
268C22×C3×C5—22no—
269C22×C3×C5—24no—
270C22×C3×C5—24no—
271C22×C3×C5—24no—
272C22×C3×C5—42no—
273C22×C3×C5—42no—
274C22×C3×C5—42no—
275C22×C3×C5—42no—
276C22×C3×C5C4×D414yescomplemented
277C22×C3×C5C23×C411yescharacteristic
278C22×C3×C5C22×D411yescharacteristic
279C22×C3×C5C22×D411yescharacteristic
280C22×C3×C5C2×#4111yescharacteristic
281C22×C3×C5C2×#4111yescharacteristic
282C22×C3×C5C2×#4111yescharacteristic
283C22×C3×C5C2×#4111yescharacteristic
284C3×C4×C5—22no—
285C3×C4×C5—24no—
286C3×C4×C5C4×D414yescomplemented
287C3×Dic5—22no—
288C3×Dic5—22no—
289C3×Dic5—22no—
290C3×Dic5—42no—
291C3×Dic5—42no—
292C3×Dic5#12114yesdirect product factor
293C24×C3C22×D512yes—
294C24×C3C22×D511yescharacteristic
295C2×C3×D4—24no—
296C2×C3×D4—24no—
297C2×C3×D4—22no—
298C2×C3×D4—22no—
299C2×C3×D4C2×Dic518yescomplemented
300C2×C3×D4C2×Dic514yescomplemented
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—51no—
304C22×C3×C4—54no—
305C22×C3×C4—51no—
306C22×C3×C4—51no—
307C22×C3×C4—51no—
308C22×C3×C4—52no—
309C22×C3×C4—52no—
310C22×C3×C4—102no—
311C22×C3×C4—102no—
312C22×C3×C4—102no—
313C22×C3×C4—102no—
314C22×C3×C4—104no—
315C22×C3×C4—104no—
316C22×C3×C4—104no—
317C22×C3×C4—102no—
318C22×C3×C4C2×Dic514yescomplemented
319C22×C3×C4C22×D511yescharacteristic
320C22×C3×C4C22×D512yes—
321C22×C3×C4C22×D511yescharacteristic
322C3×C4⋊C4—104no—
323C3×C4⋊C4—102no—
324C3×C4⋊C4—102no—
325C3×C4⋊C4C2×Dic514yescomplemented
326C3×C22⋊C4—104no—
327C3×C22⋊C4—104no—
328C3×C22⋊C4—104no—
329C3×C22⋊C4—104no—
330C3×C22⋊C4C2×Dic518yescomplemented
331C3×C42—54no—
332C3×C42—102no—
333C3×C42—102no—
334C3×C42—104no—
335C3×C42—102no—
336C23×C5—21no—
337C23×C5—21no—
338C23×C5—21no—
339C23×C5—21no—
340C23×C5—22no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5C22×C3×C414yes—
347C23×C5C22×C3×C412yes—
348C23×C5C2×C3×D412yes—
349C23×C5C3×#4112yes—
350C23×C5C24×C311yescharacteristic
351C5×D4—216no—
352C5×D4—28no—
353C2×C4×C5—21no—
354C2×C4×C5—22no—
355C2×C4×C5—21no—
356C2×C4×C5—22no—
357C2×C4×C5—28no—
358C2×C4×C5C22×C3×C412yes—
359C2×C4×C5C22×C3×C414yes—
360C2×C4×C5C22×C3×C412yes—
361C2×C4×C5C2×C3×D412yes—
362C2×C4×C5C3×#4112yes—
363C2×Dic5—28no—
364C2×Dic5—21no—
365C2×Dic5—21no—
366C2×Dic5—21no—
367C2×Dic5—21no—
368C2×Dic5—21no—
369C2×Dic5—21no—
370C2×Dic5—28no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—48no—
378C2×Dic5C2×C3×D412yes—
379C2×Dic5C2×C3×D412yes—
380C2×Dic5C2×C3×D412yes—
381C2×Dic5C2×C3×D412yes—
382C2×Dic5C3×#4112yes—
383C2×Dic5C3×#4112yes—
384C22×D4C2×C3×D512yes—
385C22×D4C2×C3×D511yescharacteristic
386C23×C4—51no—
387C23×C4—52no—
388C23×C4—51no—
389C23×C4C2×C3×D511yescharacteristic
390#121C3×Dic518yesdirect product factor
391C4×D4—104no—
392C4×D4—108no—
393C2×C4⋊C4—51no—
394C2×C4⋊C4—52no—
395C2×C4⋊C4—51no—
396C2×C4⋊C4C2×C3×D511yescharacteristic
397C2×C22⋊C4—52no—
398C2×C22⋊C4—52no—
399C2×C22⋊C4—52no—
400C2×C22⋊C4—52no—
401C2×C22⋊C4C2×C3×D512yes—
402C2×C42—51no—
403C2×C42—52no—
404C2×C42—51no—
405C2×C42—51no—
406C2×C42—51no—
407C2×C42—104no—
408#95—52no—
409#95—52no—
410#95—52no—
411C2×C3×C5—24no—
412C2×C3×C5—44no—
413C2×C3×C5C2×C4×D411yescharacteristic
414C2×C3×C5C2×C4×D411yescharacteristic
415C2×C3×C5C4×#4111yescharacteristic
416C2×C3×C5C2×#12111yescharacteristic
417C2×C3×C5#52511yescharacteristic
418C2×C3×C5#52911yescharacteristic
419C2×C3×C5#53211yescharacteristic
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3D4×D512yes—
431C23×C3#71112yes—
432C23×C3C22×Dic514yes—
433C23×C3C22×Dic512yes—
434C23×C3C23×D511yescharacteristic
435C3×D4—216no—
436C3×D4—28no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—28no—
442C2×C3×C4—52no—
443C2×C3×C4—52no—
444C2×C3×C4—52no—
445C2×C3×C4—52no—
446C2×C3×C4—52no—
447C2×C3×C4—52no—
448C2×C3×C4—108no—
449C2×C3×C4—108no—
450C2×C3×C4—101no—
451C2×C3×C4—101no—
452C2×C3×C4—101no—
453C2×C3×C4—101no—
454C2×C3×C4—101no—
455C2×C3×C4—101no—
456C2×C3×C4—102no—
457C2×C3×C4—102no—
458C2×C3×C4—102no—
459C2×C3×C4—102no—
460C2×C3×C4—102no—
461C2×C3×C4—102no—
462C2×C3×C4—208no—
463C2×C3×C4D4×D512yes—
464C2×C3×C4#71112yes—
465C2×C3×C4C22×Dic512yes—
466C2×C3×C4C22×Dic514yes—
467C2×C3×C4C22×Dic512yes—
468C22×C5—22no—
469C22×C5—22no—
470C22×C5—22no—
471C22×C5—22no—
472C22×C5—22no—
473C22×C5—22no—
474C22×C5—24no—
475C22×C5—24no—
476C22×C5—24no—
477C22×C5—42no—
478C22×C5—42no—
479C22×C5—42no—
480C22×C5—42no—
481C22×C5C3×C4×D414yescomplemented
482C22×C5C23×C3×C411yescharacteristic
483C22×C5C22×C3×D411yescharacteristic
484C22×C5C22×C3×D411yescharacteristic
485C22×C5C2×C3×#4111yescharacteristic
486C22×C5C2×C3×#4111yescharacteristic
487C22×C5C2×C3×#4111yescharacteristic
488C22×C5C2×C3×#4111yescharacteristic
489C4×C5—22no—
490C4×C5—24no—
491C4×C5C3×C4×D414yescomplemented
492Dic5—22no—
493Dic5—22no—
494Dic5—22no—
495Dic5—42no—
496Dic5—42no—
497Dic5C3×#12114yesdirect product factor
498C24C22×C3×D512yes—
499C24C22×C3×D511yescharacteristic
500C2×D4—24no—
501C2×D4—24no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4C2×C3×Dic518yescomplemented
505C2×D4C2×C3×Dic514yescomplemented
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—51no—
509C22×C4—54no—
510C22×C4—51no—
511C22×C4—51no—
512C22×C4—51no—
513C22×C4—52no—
514C22×C4—52no—
515C22×C4—102no—
516C22×C4—102no—
517C22×C4—102no—
518C22×C4—102no—
519C22×C4—104no—
520C22×C4—104no—
521C22×C4—104no—
522C22×C4—102no—
523C22×C4C2×C3×Dic514yescomplemented
524C22×C4C22×C3×D511yescharacteristic
525C22×C4C22×C3×D512yes—
526C22×C4C22×C3×D511yescharacteristic
527C4⋊C4—104no—
528C4⋊C4—102no—
529C4⋊C4—102no—
530C4⋊C4C2×C3×Dic514yescomplemented
531C22⋊C4—104no—
532C22⋊C4—104no—
533C22⋊C4—104no—
534C22⋊C4—104no—
535C22⋊C4C2×C3×Dic518yescomplemented
536C42—54no—
537C42—102no—
538C42—102no—
539C42—104no—
540C42—102no—
541C3×C5C4×#12111yescharacteristic, complemented, Hall
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—24no—
549C22×C3—24no—
550C22×C3—24no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3D4×Dic514yescomplemented
556C22×C3C2×D4×D511yescharacteristic
557C22×C3C2×D4×D511yescharacteristic
558C22×C3C2×#71111yescharacteristic
559C22×C3C2×#71111yescharacteristic
560C22×C3D5×#4111yescharacteristic
561C22×C3D5×#4111yescharacteristic
562C22×C3C23×Dic511yescharacteristic
563C3×C4—22no—
564C3×C4—24no—
565C3×C4—54no—
566C3×C4—102no—
567C3×C4—102no—
568C3×C4—102no—
569C3×C4—202no—
570C3×C4—202no—
571C3×C4D4×Dic514yescomplemented
572C2×C5—24no—
573C2×C5—44no—
574C2×C5C2×C3×C4×D411yescharacteristic
575C2×C5C2×C3×C4×D411yescharacteristic
576C2×C5C3×C4×#4111yescharacteristic
577C2×C5C2×C3×#12111yescharacteristic
578C2×C5C3×#52511yescharacteristic
579C2×C5C3×#52911yescharacteristic
580C2×C5C3×#53211yescharacteristic
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23C3×D4×D512yes—
592C23C3×#71112yes—
593C23C22×C3×Dic514yes—
594C23C22×C3×Dic512yes—
595C23C23×C3×D511yescharacteristic
596D4—216no—
597D4—28no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—28no—
603C2×C4—52no—
604C2×C4—52no—
605C2×C4—52no—
606C2×C4—52no—
607C2×C4—52no—
608C2×C4—52no—
609C2×C4—108no—
610C2×C4—108no—
611C2×C4—101no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—102no—
620C2×C4—102no—
621C2×C4—102no—
622C2×C4—102no—
623C2×C4—208no—
624C2×C4C3×D4×D512yes—
625C2×C4C3×#71112yes—
626C2×C4C22×C3×Dic512yes—
627C2×C4C22×C3×Dic514yes—
628C2×C4C22×C3×Dic512yes—
629C2×C3—24no—
630C2×C3—44no—
631C2×C3#6593011yescharacteristic
632C2×C3#6593411yescharacteristic
633C2×C3D5×#12111yescharacteristic
634C2×C3#6594011yescharacteristic
635C2×C3C2×D4×Dic511yescharacteristic
636C2×C3C2×D4×Dic511yescharacteristic
637C2×C3#41×Dic511yescharacteristic
638C5C3×C4×#12111yescharacteristic, complemented, Sylow
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—24no—
646C22—24no—
647C22—24no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22C3×D4×Dic514yescomplemented
653C22C2×C3×D4×D511yescharacteristic
654C22C2×C3×D4×D511yescharacteristic
655C22C2×C3×#71111yescharacteristic
656C22C2×C3×#71111yescharacteristic
657C22C3×D5×#4111yescharacteristic
658C22C3×D5×#4111yescharacteristic
659C22C23×C3×Dic511yescharacteristic
660C4—22no—
661C4—24no—
662C4—54no—
663C4—102no—
664C4—102no—
665C4—102no—
666C4—202no—
667C4—202no—
668C4C3×D4×Dic514yescomplemented
669C3Dic5×#12111yescharacteristic, direct product factor, Sylow
670C2—24no—
671C2—44no—
672C2C3×#6593011yescharacteristic
673C2C3×#6593411yescharacteristic
674C2C3×D5×#12111yescharacteristic
675C2C3×#6594011yescharacteristic
676C2C2×C3×D4×Dic511yescharacteristic
677C2C2×C3×D4×Dic511yescharacteristic
678C2C3×#41×Dic511yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
Fitting, prime radicalC2×C3×C5×#121C2
socleC23×C3×C5C24
cosocleC23×C5C24×C3
hypercenterC2×C3×#121D5
hypocenterC5C3×C4×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic5C2semidirect
3. C2×C3×D4×Dic5C2semidirect
4. C22×C3×C4×Dic5C2semidirect
5. C3×#65510C2semidirect
6. C3×#65509C2semidirect
7. C3×#65501C2semidirect
8. C3×#65274C2semidirect
9. C3×C4⋊C4×Dic5C2semidirect
10. C3×#65240C2semidirect
11. C3×C22⋊C4×Dic5C2semidirect
12. Dic5×#121C3direct (N × H)
19. C3×C5×#121C4semidirect
42. C2×D4×Dic5C2×C3semidirect
43. C2×D4×Dic5C2×C3semidirect
44. C22×C4×Dic5C2×C3semidirect
45. #65510C2×C3semidirect
46. #65509C2×C3semidirect
47. #65501C2×C3semidirect
48. #65274C2×C3semidirect
49. C4⋊C4×Dic5C2×C3semidirect
50. #65240C2×C3semidirect
51. C22⋊C4×Dic5C2×C3semidirect
58. C2×C3×C5×D4C2×C4semidirect
59. C2×C3×C5×D4C2×C4semidirect
62. C22×C3×C4×C5C2×C4semidirect
74. C22×C3×Dic5D4semidirect
81. C3×C5×C4⋊C4C2×C4semidirect
82. C3×C5×C22⋊C4C2×C4semidirect
94. C3×C4×Dic5D4semidirect
112. C5×#121C3×C4semidirect
188. C3×#121Dic5direct (N × H)
215. C2×C5×D4C2×C3×C4semidirect
216. C2×C5×D4C2×C3×C4semidirect
219. C22×C4×C5C2×C3×C4semidirect
231. C22×Dic5C3×D4semidirect
238. C5×C4⋊C4C2×C3×C4semidirect
239. C5×C22⋊C4C2×C3×C4semidirect
251. C4×Dic5C3×D4semidirect
276. C22×C3×C5C4×D4semidirect
286. C3×C4×C5C4×D4semidirect
292. C3×Dic5#121direct (N × H)
299. C2×C3×D4C2×Dic5semidirect
300. C2×C3×D4C2×Dic5semidirect
318. C22×C3×C4C2×Dic5semidirect
325. C3×C4⋊C4C2×Dic5semidirect
330. C3×C22⋊C4C2×Dic5semidirect
390. #121C3×Dic5direct (N × H)
481. C22×C5C3×C4×D4semidirect
491. C4×C5C3×C4×D4semidirect
497. Dic5C3×#121direct (N × H)
504. C2×D4C2×C3×Dic5semidirect
505. C2×D4C2×C3×Dic5semidirect
523. C22×C4C2×C3×Dic5semidirect
530. C4⋊C4C2×C3×Dic5semidirect
535. C22⋊C4C2×C3×Dic5semidirect
541. C3×C5C4×#121semidirect
555. C22×C3D4×Dic5semidirect
571. C3×C4D4×Dic5semidirect
638. C5C3×C4×#121semidirect
652. C22C3×D4×Dic5semidirect
668. C4C3×D4×Dic5semidirect
669. C3Dic5×#121direct (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×#1212
C2×C3×D4×Dic52
C22×C3×C4×Dic52
C3×#655102
C3×#655092
C3×#655012
C3×#652742
C3×C4⋊C4×Dic52
C3×#652402
C3×C22⋊C4×Dic52
Dic5×#1213
C3×C4×#1215