Finite Group Databasebeta

← C2×C3×#65250 #14331526

Subgroups — C2×C3×#65250 #14331526

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C22⋊D5C211yesmaximal, characteristic
2C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C22×C3×#685C211yesmaximal, characteristic, complemented
5C22×C3×#685C211yesmaximal, characteristic, complemented
6C22×C3×C4⋊Dic5C211yesmaximal, characteristic, complemented
7C2×C3×#3963C211yesmaximal, characteristic, complemented
8C3×#65250C218yesmaximal, direct product factor
9C2×#65250C311yesmaximal, characteristic, direct product factor, Hall
10C25×C3×C5C2211yescharacteristic
11C24×C3×D5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5—24no—
15C22×C3×C22⋊D5—24no—
16C22×C3×C22⋊D5—24no—
17C22×C3×C22⋊D5C2214yes—
18C23×C3×Dic5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C2×C3×C5×C22⋊C4—24no—
22C2×C3×C5×C22⋊C4C2214yescomplemented
23C2×C3×C22⋊Dic5—24no—
24C2×C3×C22⋊Dic5C2214yescomplemented
25C2×C3×#685—24no—
26C2×C3×#685—24no—
27C2×C3×#685C2214yescomplemented
28C2×C3×#685C2214yescomplemented
29C2×C3×C4⋊Dic5—24no—
30C2×C3×C4⋊Dic5C2214yescomplemented
31C3×#3963C2214yescomplemented
32C2×C3×#394—51nomaximal, Hall
33C23×C22⋊D5C2×C311yescharacteristic
34C22×C5×C22⋊C4C2×C311yescharacteristic, complemented
35C22×C22⋊Dic5C2×C311yescharacteristic, complemented
36C22×#685C2×C311yescharacteristic, complemented
37C22×#685C2×C311yescharacteristic, complemented
38C22×C4⋊Dic5C2×C311yescharacteristic, complemented
39C2×#3963C2×C311yescharacteristic, complemented
40#65250C2×C318yesdirect product factor
41C24×C3×C5—22no—
42C24×C3×C5—22no—
43C24×C3×C5—22no—
44C24×C3×C5—22no—
45C24×C3×C5—22no—
46C24×C3×C5—22no—
47C24×C3×C5D414yes—
48C24×C3×C5C2312yes—
49C24×C3×C5C2311yescharacteristic
50C23×C3×D5—22no—
51C23×C3×D5—22no—
52C23×C3×D5—22no—
53C23×C3×D5—22no—
54C23×C3×D5—22no—
55C23×C3×D5—22no—
56C23×C3×D5D414yes—
57C23×C3×D5C2312yes—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5D414yescomplemented
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2312yes—
66C2×C3×C22⋊D5—232no—
67C2×C3×C22⋊D5—28no—
68C2×C3×C22⋊D5—28no—
69C2×C3×C22⋊D5—28no—
70C22×C3×Dic5—22no—
71C22×C3×Dic5—22no—
72C22×C3×Dic5—22no—
73C22×C3×Dic5—22no—
74C22×C3×Dic5—22no—
75C22×C3×Dic5—22no—
76C22×C3×Dic5—22no—
77C22×C3×Dic5—22no—
78C22×C3×Dic5D414yes—
79C22×C3×Dic5C2312yes—
80C22×C3×Dic5C2312yes—
81C22×C3×Dic5C2312yes—
82C3×C5×C22⋊C4—28no—
83C3×C22⋊Dic5—28no—
84C3×#685—28no—
85C3×#685—28no—
86C3×C4⋊Dic5—28no—
87C23×C3×D4—51no—
88C22×C3×C4⋊C4—51no—
89C22×C3×C22⋊C4—51no—
90C22×C3×C22⋊C4—51no—
91C22×C3×C22⋊C4—51no—
92C22×C3×C22⋊C4D511yescharacteristic, complemented
93C3×#394—58no—
94C2×C3×#95—51no—
95C25×C5C22×C311yescharacteristic
96C24×D5C22×C311yescharacteristic
97C23×C4×C5C22×C311yescharacteristic
98C23×C4×C5C22×C311yescharacteristic
99C22×C22⋊D5—24no—
100C22×C22⋊D5—24no—
101C22×C22⋊D5—24no—
102C22×C22⋊D5C22×C314yes—
103C23×Dic5C22×C311yescharacteristic
104C23×Dic5C22×C311yescharacteristic
105C23×Dic5C22×C311yescharacteristic
106C2×C5×C22⋊C4—24no—
107C2×C5×C22⋊C4C22×C314yescomplemented
108C2×C22⋊Dic5—24no—
109C2×C22⋊Dic5C22×C314yescomplemented
110C2×#685—24no—
111C2×#685—24no—
112C2×#685C22×C314yescomplemented
113C2×#685C22×C314yescomplemented
114C2×C4⋊Dic5—24no—
115C2×C4⋊Dic5C22×C314yescomplemented
116#3963C22×C314yescomplemented
117C2×#394—51noSylow
118C23×C3×C5—28no—
119C23×C3×C5—28no—
120C23×C3×C5—28no—
121C23×C3×C5—22no—
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—44no—
128C23×C3×C5—44no—
129C23×C3×C5—44no—
130C23×C3×C5—44no—
131C23×C3×C5C2×D414yes—
132C23×C3×C5C2×D412yes—
133C23×C3×C5C2×D412yes—
134C23×C3×C5C2×D412yes—
135C23×C3×C5C2×D412yes—
136C23×C3×C5#4112yes—
137C23×C3×C5#4112yes—
138C23×C3×C5#4112yes—
139C23×C3×C5C2411yescharacteristic
140C22×C3×D5—28no—
141C22×C3×D5—28no—
142C22×C3×D5—28no—
143C22×C3×D5—22no—
144C22×C3×D5—22no—
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5—44no—
150C22×C3×D5—44no—
151C22×C3×D5—44no—
152C22×C3×D5—44no—
153C22×C3×D5C2×D414yes—
154C2×C3×C4×C5—28no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—44no—
161C2×C3×C4×C5C2×D414yescomplemented
162C3×C22⋊D5—232no—
163C2×C3×Dic5—28no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—44no—
173C2×C3×Dic5—44no—
174C2×C3×Dic5C2×D414yes—
175C25×C3—51no—
176C25×C3C2×D511yescharacteristic
177C22×C3×D4—54no—
178C22×C3×D4—104no—
179C22×C3×D4—104no—
180C22×C3×D4—104no—
181C23×C3×C4—51no—
182C23×C3×C4—51no—
183C23×C3×C4—51no—
184C23×C3×C4C2×D511yescharacteristic
185C23×C3×C4C2×D511yescharacteristic
186C2×C3×C4⋊C4—54no—
187C2×C3×C4⋊C4—104no—
188C2×C3×C22⋊C4—24no—
189C2×C3×C22⋊C4—54no—
190C2×C3×C22⋊C4—54no—
191C2×C3×C22⋊C4—54no—
192C2×C3×C22⋊C4—104no—
193C2×C3×C22⋊C4—104no—
194C2×C3×C22⋊C4—104no—
195C2×C3×C22⋊C4C2×D514yescomplemented
196C3×#95—54no—
197C24×C5—22no—
198C24×C5—22no—
199C24×C5—22no—
200C24×C5—22no—
201C24×C5—22no—
202C24×C5—22no—
203C24×C5C3×D414yes—
204C24×C5C23×C312yes—
205C24×C5C23×C311yescharacteristic
206C23×D5—22no—
207C23×D5—22no—
208C23×D5—22no—
209C23×D5—22no—
210C23×D5—22no—
211C23×D5—22no—
212C23×D5C3×D414yes—
213C23×D5C23×C312yes—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5C3×D414yescomplemented
220C22×C4×C5C23×C312yes—
221C22×C4×C5C23×C312yes—
222C2×C22⋊D5—232no—
223C2×C22⋊D5—28no—
224C2×C22⋊D5—28no—
225C2×C22⋊D5—28no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5C3×D414yes—
235C22×Dic5C23×C312yes—
236C22×Dic5C23×C312yes—
237C22×Dic5C23×C312yes—
238C5×C22⋊C4—28no—
239C22⋊Dic5—28no—
240#685—28no—
241#685—28no—
242C4⋊Dic5—28no—
243C23×D4—51no—
244C22×C4⋊C4—51no—
245C22×C22⋊C4—51no—
246C22×C22⋊C4—51no—
247C22×C22⋊C4—51no—
248C22×C22⋊C4C3×D511yescharacteristic, complemented
249#394—58no—
250C2×#95—51no—
251C22×C3×C5—24no—
252C22×C3×C5—24no—
253C22×C3×C5—24no—
254C22×C3×C5—42no—
255C22×C3×C5—42no—
256C22×C3×C5—42no—
257C22×C3×C5—42no—
258C22×C3×C5—416no—
259C22×C3×C5#12014yes—
260C22×C3×C5#12114yes—
261C22×C3×C5#12114yes—
262C22×C3×C5#12114yes—
263C22×C3×C5#12314yes—
264C22×C3×C5#12314yes—
265C22×C3×C5#12414yes—
266C22×C3×C5C22×D411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C22×D411yescharacteristic
269C22×C3×C5C22×D411yescharacteristic
270C22×C3×C5C2×#4111yescharacteristic
271C22×C3×C5C2×#4111yescharacteristic
272C22×C3×C5C2×#4111yescharacteristic
273C2×C3×D5—24no—
274C2×C3×D5—24no—
275C2×C3×D5—24no—
276C2×C3×D5—42no—
277C2×C3×D5—42no—
278C2×C3×D5—42no—
279C2×C3×D5—42no—
280C2×C3×D5—416no—
281C3×C4×C5—24no—
282C3×C4×C5—42no—
283C3×Dic5—24no—
284C3×Dic5—42no—
285C3×Dic5—42no—
286C24×C3—22no—
287C24×C3—22no—
288C24×C3—22no—
289C24×C3—22no—
290C24×C3—22no—
291C24×C3—22no—
292C24×C3—54no—
293C24×C3—52no—
294C24×C3—102no—
295C24×C3—102no—
296C24×C3—102no—
297C24×C3—102no—
298C24×C3—102no—
299C24×C3—102no—
300C24×C3D2014yes—
301C24×C3C22×D512yes—
302C24×C3C22×D511yescharacteristic
303C2×C3×D4—108no—
304C2×C3×D4—108no—
305C2×C3×D4—1032no—
306C2×C3×D4—108no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—54no—
313C22×C3×C4—52no—
314C22×C3×C4—52no—
315C22×C3×C4—52no—
316C22×C3×C4—102no—
317C22×C3×C4—102no—
318C22×C3×C4—102no—
319C22×C3×C4—102no—
320C22×C3×C4—102no—
321C22×C3×C4—102no—
322C22×C3×C4—102no—
323C22×C3×C4—102no—
324C22×C3×C4C22⋊D514yescomplemented
325C22×C3×C4C22×D512yes—
326C22×C3×C4C22×D512yes—
327C3×C4⋊C4—108no—
328C3×C22⋊C4—28no—
329C3×C22⋊C4—108no—
330C3×C22⋊C4—108no—
331C3×C22⋊C4—108no—
332C23×C5—28no—
333C23×C5—28no—
334C23×C5—28no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—44no—
342C23×C5—44no—
343C23×C5—44no—
344C23×C5—44no—
345C23×C5C2×C3×D414yes—
346C23×C5C2×C3×D412yes—
347C23×C5C2×C3×D412yes—
348C23×C5C2×C3×D412yes—
349C23×C5C2×C3×D412yes—
350C23×C5C3×#4112yes—
351C23×C5C3×#4112yes—
352C23×C5C3×#4112yes—
353C23×C5C24×C311yescharacteristic
354C22×D5—28no—
355C22×D5—28no—
356C22×D5—28no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—22no—
362C22×D5—22no—
363C22×D5—44no—
364C22×D5—44no—
365C22×D5—44no—
366C22×D5—44no—
367C22×D5C2×C3×D414yes—
368C2×C4×C5—28no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—44no—
375C2×C4×C5C2×C3×D414yescomplemented
376C22⋊D5—232no—
377C2×Dic5—28no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—44no—
387C2×Dic5—44no—
388C2×Dic5C2×C3×D414yes—
389C25—51no—
390C25C2×C3×D511yescharacteristic
391C22×D4—54no—
392C22×D4—104no—
393C22×D4—104no—
394C22×D4—104no—
395C23×C4—51no—
396C23×C4—51no—
397C23×C4—51no—
398C23×C4C2×C3×D511yescharacteristic
399C23×C4C2×C3×D511yescharacteristic
400C2×C4⋊C4—54no—
401C2×C4⋊C4—104no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—54no—
404C2×C22⋊C4—54no—
405C2×C22⋊C4—54no—
406C2×C22⋊C4—104no—
407C2×C22⋊C4—104no—
408C2×C22⋊C4—104no—
409C2×C22⋊C4C2×C3×D514yescomplemented
410#95—54no—
411C2×C3×C5—44no—
412C2×C3×C5#39418yescomplemented
413C2×C3×C5C2×#12011yescharacteristic
414C2×C3×C5C2×#12111yescharacteristic
415C2×C3×C5C2×#12111yescharacteristic
416C2×C3×C5C2×#12111yescharacteristic
417C2×C3×C5C2×#12311yescharacteristic
418C2×C3×C5C2×#12311yescharacteristic
419C2×C3×C5C2×#12411yescharacteristic
420C3×D5—44no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—28no—
428C23×C3—28no—
429C23×C3—28no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—44no—
434C23×C3—54no—
435C23×C3—102no—
436C23×C3—102no—
437C23×C3—102no—
438C23×C3—102no—
439C23×C3—102no—
440C23×C3—102no—
441C23×C3—108no—
442C23×C3—108no—
443C23×C3—108no—
444C23×C3—204no—
445C23×C3—204no—
446C23×C3—204no—
447C23×C3—204no—
448C23×C3C2×D2014yes—
449C23×C3C2×D2012yes—
450C23×C3#70912yes—
451C23×C3D4×D512yes—
452C23×C3D4×D512yes—
453C23×C3#71112yes—
454C23×C3#71112yes—
455C23×C3C2×C22⋊D512yes—
456C23×C3C23×D511yescharacteristic
457C3×D4—1032no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—28no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—44no—
465C2×C3×C4—54no—
466C2×C3×C4—102no—
467C2×C3×C4—102no—
468C2×C3×C4—108no—
469C2×C3×C4—102no—
470C2×C3×C4—102no—
471C2×C3×C4—102no—
472C2×C3×C4—102no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—204no—
476C2×C3×C4—204no—
477C2×C3×C4C2×C22⋊D514yescomplemented
478C22×C5—24no—
479C22×C5—24no—
480C22×C5—24no—
481C22×C5—416no—
482C22×C5—42no—
483C22×C5—42no—
484C22×C5—42no—
485C22×C5—42no—
486C22×C5C3×#12014yes—
487C22×C5C3×#12114yes—
488C22×C5C3×#12114yes—
489C22×C5C3×#12114yes—
490C22×C5C3×#12314yes—
491C22×C5C3×#12314yes—
492C22×C5C3×#12414yes—
493C22×C5C22×C3×D411yescharacteristic
494C22×C5C22×C3×D411yescharacteristic
495C22×C5C22×C3×D411yescharacteristic
496C22×C5C22×C3×D411yescharacteristic
497C22×C5C2×C3×#4111yescharacteristic
498C22×C5C2×C3×#4111yescharacteristic
499C22×C5C2×C3×#4111yescharacteristic
500C2×D5—24no—
501C2×D5—24no—
502C2×D5—24no—
503C2×D5—416no—
504C2×D5—42no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—42no—
508C4×C5—24no—
509C4×C5—42no—
510Dic5—24no—
511Dic5—42no—
512Dic5—42no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—54no—
520C24—52no—
521C24—102no—
522C24—102no—
523C24—102no—
524C24—102no—
525C24—102no—
526C24—102no—
527C24C3×D2014yes—
528C24C22×C3×D512yes—
529C24C22×C3×D511yescharacteristic
530C2×D4—108no—
531C2×D4—108no—
532C2×D4—1032no—
533C2×D4—108no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—54no—
540C22×C4—52no—
541C22×C4—52no—
542C22×C4—52no—
543C22×C4—102no—
544C22×C4—102no—
545C22×C4—102no—
546C22×C4—102no—
547C22×C4—102no—
548C22×C4—102no—
549C22×C4—102no—
550C22×C4—102no—
551C22×C4C3×C22⋊D514yescomplemented
552C22×C4C22×C3×D512yes—
553C22×C4C22×C3×D512yes—
554C4⋊C4—108no—
555C22⋊C4—28no—
556C22⋊C4—108no—
557C22⋊C4—108no—
558C22⋊C4—108no—
559C3×C5C2×#39411yescharacteristic, complemented, Hall
560C22×C3—24no—
561C22×C3—24no—
562C22×C3—24no—
563C22×C3—42no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—42no—
567C22×C3—416no—
568C22×C3—104no—
569C22×C3—104no—
570C22×C3—104no—
571C22×C3—202no—
572C22×C3—202no—
573C22×C3—202no—
574C22×C3—202no—
575C22×C3—2016no—
576C22×C3#402814yes—
577C22×C3#402914yes—
578C22×C3#403114yes—
579C22×C3#403214yes—
580C22×C3#407614yes—
581C22×C3#408414yes—
582C22×C3#408514yes—
583C22×C3C22×D2011yescharacteristic
584C22×C3C2×#70911yescharacteristic
585C22×C3C2×D4×D511yescharacteristic
586C22×C3C2×D4×D511yescharacteristic
587C22×C3C2×#71111yescharacteristic
588C22×C3C2×#71111yescharacteristic
589C22×C3C22×C22⋊D511yescharacteristic
590C3×C4—24no—
591C3×C4—42no—
592C3×C4—104no—
593C3×C4—202no—
594C3×C4—202no—
595C2×C5—44no—
596C2×C5C3×#39418yescomplemented
597C2×C5C2×C3×#12011yescharacteristic
598C2×C5C2×C3×#12111yescharacteristic
599C2×C5C2×C3×#12111yescharacteristic
600C2×C5C2×C3×#12111yescharacteristic
601C2×C5C2×C3×#12311yescharacteristic
602C2×C5C2×C3×#12311yescharacteristic
603C2×C5C2×C3×#12411yescharacteristic
604D5—44no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—28no—
612C23—28no—
613C23—28no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23—54no—
619C23—108no—
620C23—102no—
621C23—102no—
622C23—102no—
623C23—102no—
624C23—102no—
625C23—102no—
626C23—108no—
627C23—108no—
628C23—204no—
629C23—204no—
630C23—204no—
631C23—204no—
632C23C2×C3×D2014yes—
633C23C2×C3×D2012yes—
634C23C3×#70912yes—
635C23C3×D4×D512yes—
636C23C3×D4×D512yes—
637C23C3×#71112yes—
638C23C3×#71112yes—
639C23C2×C3×C22⋊D512yes—
640C23C23×C3×D511yescharacteristic
641D4—1032no—
642C2×C4—28no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—44no—
649C2×C4—54no—
650C2×C4—102no—
651C2×C4—102no—
652C2×C4—108no—
653C2×C4—102no—
654C2×C4—102no—
655C2×C4—102no—
656C2×C4—102no—
657C2×C4—102no—
658C2×C4—102no—
659C2×C4—204no—
660C2×C4—204no—
661C2×C4C2×C3×C22⋊D514yescomplemented
662C2×C3—44no—
663C2×C3—204no—
664C2×C3#6525018yesdirect product factor
665C2×C3C2×#402811yescharacteristic
666C2×C3C2×#402911yescharacteristic
667C2×C3C2×#403111yescharacteristic
668C2×C3C2×#403211yescharacteristic
669C2×C3C2×#407611yescharacteristic
670C2×C3C2×#408411yescharacteristic
671C2×C3C2×#408511yescharacteristic
672C5C2×C3×#39411yescharacteristic, complemented, Sylow
673C22—24no—
674C22—24no—
675C22—24no—
676C22—42no—
677C22—42no—
678C22—416no—
679C22—42no—
680C22—42no—
681C22—104no—
682C22—104no—
683C22—104no—
684C22—202no—
685C22—202no—
686C22—2016no—
687C22—202no—
688C22—202no—
689C22C3×#402814yes—
690C22C3×#402914yes—
691C22C3×#403114yes—
692C22C3×#403214yes—
693C22C3×#407614yes—
694C22C3×#408414yes—
695C22C3×#408514yes—
696C22C22×C3×D2011yescharacteristic
697C22C2×C3×#70911yescharacteristic
698C22C2×C3×D4×D511yescharacteristic
699C22C2×C3×D4×D511yescharacteristic
700C22C2×C3×#71111yescharacteristic
701C22C2×C3×#71111yescharacteristic
702C22C22×C3×C22⋊D511yescharacteristic
703C4—24no—
704C4—42no—
705C4—104no—
706C4—202no—
707C4—202no—
708C3C2×#6525011yescharacteristic, direct product factor, Sylow
709C2—44no—
710C2—204no—
711C2C3×#6525018yesdirect product factor
712C2C2×C3×#402811yescharacteristic
713C2C2×C3×#402911yescharacteristic
714C2C2×C3×#403111yescharacteristic
715C2C2×C3×#403211yescharacteristic
716C2C2×C3×#407611yescharacteristic
717C2C2×C3×#408411yescharacteristic
718C2C2×C3×#408511yescharacteristic
subgroupG/H
centerC24×C3C22×D5
commutator, cosocleC23×C5C24×C3
FrattiniC23C23×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC23×C3×C22⋊D5C2
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C2×C3×#394
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×C22⋊C4C2semidirect
3. C22×C3×C22⋊Dic5C2semidirect
4. C22×C3×#685C2semidirect
5. C22×C3×#685C2semidirect
6. C22×C3×C4⋊Dic5C2semidirect
7. C2×C3×#3963C2semidirect
8. C3×#65250C2direct (N × H)
9. C2×#65250C3direct (N × H)
22. C2×C3×C5×C22⋊C4C22semidirect
24. C2×C3×C22⋊Dic5C22semidirect
27. C2×C3×#685C22semidirect
28. C2×C3×#685C22semidirect
30. C2×C3×C4⋊Dic5C22semidirect
31. C3×#3963C22semidirect
34. C22×C5×C22⋊C4C2×C3semidirect
35. C22×C22⋊Dic5C2×C3semidirect
36. C22×#685C2×C3semidirect
37. C22×#685C2×C3semidirect
38. C22×C4⋊Dic5C2×C3semidirect
39. C2×#3963C2×C3semidirect
40. #65250C2×C3direct (N × H)
63. C22×C3×C4×C5D4semidirect
92. C22×C3×C22⋊C4D5semidirect
107. C2×C5×C22⋊C4C22×C3semidirect
109. C2×C22⋊Dic5C22×C3semidirect
112. C2×#685C22×C3semidirect
113. C2×#685C22×C3semidirect
115. C2×C4⋊Dic5C22×C3semidirect
116. #3963C22×C3semidirect
161. C2×C3×C4×C5C2×D4semidirect
195. C2×C3×C22⋊C4C2×D5semidirect
219. C22×C4×C5C3×D4semidirect
248. C22×C22⋊C4C3×D5semidirect
324. C22×C3×C4C22⋊D5semidirect
375. C2×C4×C5C2×C3×D4semidirect
409. C2×C22⋊C4C2×C3×D5semidirect
412. C2×C3×C5#394semidirect
477. C2×C3×C4C2×C22⋊D5semidirect
551. C22×C4C3×C22⋊D5semidirect
559. C3×C5C2×#394semidirect
596. C2×C5C3×#394semidirect
661. C2×C4C2×C3×C22⋊D5semidirect
664. C2×C3#65250direct (N × H)
672. C5C2×C3×#394semidirect
708. C3C2×#65250direct (N × H)
711. C2C3×#65250direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C22⋊D52
C22×C3×C5×C22⋊C42
C22×C3×C22⋊Dic52
C22×C3×#6852
C22×C3×C4⋊Dic52
C2×C3×#39632
C3×#652502
C2×#652503
C2×C3×#3945