Finite Group Databasebeta

← C2×C3×#64954 #14320282

Subgroups — C2×C3×#64954 #14320282

Order 1920.

3152 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D20C211yesmaximal, characteristic
2C23×C3×C4×D5C211yesmaximal, characteristic, complemented
3C22×C3×#685C211yesmaximal, characteristic, complemented
4C22×C3×#685C211yesmaximal, characteristic, complemented
5C22×C3×#685C211yesmaximal, characteristic, complemented
6C2×C3×C5×#95C211yesmaximal, characteristic, complemented
7C2×C3×#3963C211yesmaximal, characteristic, complemented
8C3×#64954C218yesmaximal, direct product factor
9C2×#64954C311yesmaximal, characteristic, direct product factor, Hall
10C24×C3×D5C2211yescharacteristic
11C24×C3×D5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×C4×C5C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×C3×D20—24no—
18C22×C3×D20—24no—
19C22×C3×D20C418yescomplemented
20C22×C3×D20C2214yes—
21C22×C3×C4×D5—24no—
22C22×C3×C4×D5—24no—
23C22×C3×C4×D5—24no—
24C22×C3×C4×D5C2214yescomplemented
25C2×C3×#685—24no—
26C2×C3×#685—24no—
27C2×C3×#685—24no—
28C2×C3×#685C2214yescomplemented
29C2×C3×#685C2214yescomplemented
30C2×C3×#685C2214yescomplemented
31C3×C5×#95C2214yescomplemented
32C3×#3963C2214yescomplemented
33C2×C3×#386—51nomaximal, Hall
34C23×D20C2×C311yescharacteristic
35C23×C4×D5C2×C311yescharacteristic, complemented
36C22×#685C2×C311yescharacteristic, complemented
37C22×#685C2×C311yescharacteristic, complemented
38C22×#685C2×C311yescharacteristic, complemented
39C2×C5×#95C2×C311yescharacteristic, complemented
40C2×#3963C2×C311yescharacteristic, complemented
41#64954C2×C318yesdirect product factor
42C24×C3×C5C2311yescharacteristic
43C23×C3×D5—22no—
44C23×C3×D5—22no—
45C23×C3×D5—22no—
46C23×C3×D5—22no—
47C23×C3×D5—22no—
48C23×C3×D5—22no—
49C23×C3×D5—22no—
50C23×C3×D5—22no—
51C23×C3×D5—22no—
52C23×C3×D5—22no—
53C23×C3×D5C2×C414yes—
54C23×C3×D5C2×C414yescomplemented
55C23×C3×D5D414yes—
56C23×C3×D5D414yes—
57C23×C3×D5C2312yes—
58C23×C3×D5C2312yes—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—22no—
64C22×C3×C4×C5—22no—
65C22×C3×C4×C5—22no—
66C22×C3×C4×C5C2×C414yescomplemented
67C22×C3×C4×C5D414yescomplemented
68C22×C3×C4×C5C2312yes—
69C22×C3×C4×C5C2312yes—
70C22×C3×C4×C5C2312yes—
71C22×C3×Dic5—22no—
72C22×C3×Dic5—22no—
73C22×C3×Dic5—22no—
74C22×C3×Dic5—22no—
75C22×C3×Dic5—22no—
76C22×C3×Dic5D414yescomplemented
77C22×C3×Dic5C2312yes—
78C22×C3×Dic5C2312yes—
79C2×C3×D20—232no—
80C2×C3×D20—28no—
81C2×C3×D20—28no—
82C2×C3×D20C2×C4116yescomplemented
83C2×C3×C4×D5—232no—
84C2×C3×C4×D5—28no—
85C2×C3×C4×D5—28no—
86C2×C3×C4×D5—28no—
87C3×#685—28no—
88C3×#685—28no—
89C3×#685—28no—
90C23×C3×D4—51no—
91C24×C3×C4—51no—
92C22×C3×C22⋊C4—51no—
93C22×C3×C22⋊C4—51no—
94C22×C3×C22⋊C4—51no—
95C3×#386—58no—
96C2×C3×#95—51no—
97C2×C3×#95D511yescharacteristic, complemented
98C24×D5C22×C311yescharacteristic
99C24×D5C22×C311yescharacteristic
100C23×C4×C5C22×C311yescharacteristic
101C23×C4×C5C22×C311yescharacteristic
102C23×C4×C5C22×C311yescharacteristic
103C23×Dic5C22×C311yescharacteristic
104C23×Dic5C22×C311yescharacteristic
105C22×D20—24no—
106C22×D20—24no—
107C22×D20C3×C418yescomplemented
108C22×D20C22×C314yes—
109C22×C4×D5—24no—
110C22×C4×D5—24no—
111C22×C4×D5—24no—
112C22×C4×D5C22×C314yescomplemented
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—24no—
116C2×#685C22×C314yescomplemented
117C2×#685C22×C314yescomplemented
118C2×#685C22×C314yescomplemented
119C5×#95C22×C314yescomplemented
120#3963C22×C314yescomplemented
121C2×#386—51noSylow
122C23×C3×C5C22×C412yes—
123C23×C3×C5C2×D412yes—
124C23×C3×C5C2×D412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5C2×D412yes—
127C23×C3×C5#4112yes—
128C23×C3×C5#4112yes—
129C23×C3×C5C2411yescharacteristic
130C22×C3×D5—28no—
131C22×C3×D5—28no—
132C22×C3×D5—28no—
133C22×C3×D5—28no—
134C22×C3×D5—28no—
135C22×C3×D5—28no—
136C22×C3×D5—22no—
137C22×C3×D5—22no—
138C22×C3×D5—22no—
139C22×C3×D5—22no—
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×D5C22⋊C4116yescomplemented
154C22×C3×D5C22×C414yes—
155C22×C3×D5C22×C414yescomplemented
156C22×C3×D5C2×D414yes—
157C22×C3×D5C2×D414yes—
158C2×C3×C4×C5—28no—
159C2×C3×C4×C5—28no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5—22no—
167C2×C3×C4×C5—44no—
168C2×C3×C4×C5C22×C414yescomplemented
169C2×C3×C4×C5C2×D414yescomplemented
170C2×C3×Dic5—28no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—44no—
177C2×C3×Dic5C2×D414yescomplemented
178C3×D20—232no—
179C3×C4×D5—232no—
180C25×C3—51no—
181C25×C3—51no—
182C22×C3×D4—58no—
183C22×C3×D4—54no—
184C22×C3×D4—104no—
185C22×C3×D4—104no—
186C23×C3×C4—51no—
187C23×C3×C4—51no—
188C23×C3×C4—54no—
189C23×C3×C4—104no—
190C23×C3×C4—104no—
191C23×C3×C4—104no—
192C23×C3×C4C2×D511yescharacteristic
193C23×C3×C4C2×D511yescharacteristic
194C23×C3×C4C2×D511yescharacteristic
195C2×C3×C22⋊C4—54no—
196C2×C3×C22⋊C4—54no—
197C2×C3×C22⋊C4—54no—
198C2×C3×C22⋊C4—104no—
199C2×C3×C22⋊C4—104no—
200C2×C3×C22⋊C4—104no—
201C3×#95—54no—
202C3×#95C2×D514yescomplemented
203C24×C5C23×C311yescharacteristic
204C23×D5—22no—
205C23×D5—22no—
206C23×D5—22no—
207C23×D5—22no—
208C23×D5—22no—
209C23×D5—22no—
210C23×D5—22no—
211C23×D5—22no—
212C23×D5—22no—
213C23×D5—22no—
214C23×D5C2×C3×C414yes—
215C23×D5C2×C3×C414yescomplemented
216C23×D5C3×D414yes—
217C23×D5C3×D414yes—
218C23×D5C23×C312yes—
219C23×D5C23×C312yes—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—22no—
227C22×C4×C5C2×C3×C414yescomplemented
228C22×C4×C5C3×D414yescomplemented
229C22×C4×C5C23×C312yes—
230C22×C4×C5C23×C312yes—
231C22×C4×C5C23×C312yes—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5C3×D414yescomplemented
238C22×Dic5C23×C312yes—
239C22×Dic5C23×C312yes—
240C2×D20—232no—
241C2×D20—28no—
242C2×D20—28no—
243C2×D20C2×C3×C4116yescomplemented
244C2×C4×D5—232no—
245C2×C4×D5—28no—
246C2×C4×D5—28no—
247C2×C4×D5—28no—
248#685—28no—
249#685—28no—
250#685—28no—
251C23×D4—51no—
252C24×C4—51no—
253C22×C22⋊C4—51no—
254C22×C22⋊C4—51no—
255C22×C22⋊C4—51no—
256#386—58no—
257C2×#95—51no—
258C2×#95C3×D511yescharacteristic, complemented
259C22×C3×C5C2×C22⋊C414yes—
260C22×C3×C5C4×D414yes—
261C22×C3×C5C4×D414yes—
262C22×C3×C5#12014yes—
263C22×C3×C5#12114yes—
264C22×C3×C5#12114yes—
265C22×C3×C5#12314yes—
266C22×C3×C5C23×C411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C22×D411yescharacteristic
269C22×C3×C5C22×D411yescharacteristic
270C22×C3×C5C22×D411yescharacteristic
271C22×C3×C5C2×#4111yescharacteristic
272C22×C3×C5C2×#4111yescharacteristic
273C2×C3×D5—24no—
274C2×C3×D5—24no—
275C2×C3×D5—24no—
276C2×C3×D5—24no—
277C2×C3×D5—24no—
278C2×C3×D5—24no—
279C2×C3×D5—232no—
280C2×C3×D5—24no—
281C2×C3×D5—24no—
282C2×C3×D5—24no—
283C2×C3×D5—42no—
284C2×C3×D5—42no—
285C2×C3×D5—42no—
286C2×C3×D5—42no—
287C2×C3×D5—416no—
288C2×C3×D5C2×C22⋊C418yescomplemented
289C3×C4×C5—24no—
290C3×C4×C5—24no—
291C3×C4×C5—42no—
292C3×Dic5—24no—
293C3×Dic5—42no—
294C24×C3—54no—
295C24×C3—54no—
296C24×C3—54no—
297C24×C3—52no—
298C24×C3—54no—
299C24×C3—52no—
300C24×C3—102no—
301C24×C3—102no—
302C24×C3—102no—
303C24×C3—102no—
304C24×C3—102no—
305C24×C3—102no—
306C24×C3—102no—
307C24×C3—102no—
308C24×C3—102no—
309C24×C3—102no—
310C24×C3C22×D511yescharacteristic
311C2×C3×D4—516no—
312C2×C3×D4—108no—
313C2×C3×D4—108no—
314C2×C3×D4—1032no—
315C22×C3×C4—22no—
316C22×C3×C4—22no—
317C22×C3×C4—22no—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—22no—
322C22×C3×C4—54no—
323C22×C3×C4—52no—
324C22×C3×C4—52no—
325C22×C3×C4—108no—
326C22×C3×C4—108no—
327C22×C3×C4—1032no—
328C22×C3×C4—102no—
329C22×C3×C4—102no—
330C22×C3×C4—108no—
331C22×C3×C4—102no—
332C22×C3×C4—102no—
333C22×C3×C4—102no—
334C22×C3×C4C4×D514yescomplemented
335C22×C3×C4D2014yescomplemented
336C22×C3×C4C22×D512yes—
337C22×C3×C4C22×D512yes—
338C22×C3×C4C22×D512yes—
339C3×C22⋊C4—108no—
340C3×C22⋊C4—108no—
341C3×C22⋊C4—108no—
342C23×C5C22×C3×C412yes—
343C23×C5C2×C3×D412yes—
344C23×C5C2×C3×D412yes—
345C23×C5C2×C3×D412yes—
346C23×C5C2×C3×D412yes—
347C23×C5C3×#4112yes—
348C23×C5C3×#4112yes—
349C23×C5C24×C311yescharacteristic
350C22×D5—28no—
351C22×D5—28no—
352C22×D5—28no—
353C22×D5—28no—
354C22×D5—28no—
355C22×D5—28no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—28no—
361C22×D5—28no—
362C22×D5—28no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—44no—
370C22×D5—44no—
371C22×D5—44no—
372C22×D5—44no—
373C22×D5C3×C22⋊C4116yescomplemented
374C22×D5C22×C3×C414yes—
375C22×D5C22×C3×C414yescomplemented
376C22×D5C2×C3×D414yes—
377C22×D5C2×C3×D414yes—
378C2×C4×C5—28no—
379C2×C4×C5—28no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—44no—
388C2×C4×C5C22×C3×C414yescomplemented
389C2×C4×C5C2×C3×D414yescomplemented
390C2×Dic5—28no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—44no—
397C2×Dic5C2×C3×D414yescomplemented
398D20—232no—
399C4×D5—232no—
400C25—51no—
401C25—51no—
402C22×D4—58no—
403C22×D4—54no—
404C22×D4—104no—
405C22×D4—104no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—54no—
409C23×C4—104no—
410C23×C4—104no—
411C23×C4—104no—
412C23×C4C2×C3×D511yescharacteristic
413C23×C4C2×C3×D511yescharacteristic
414C23×C4C2×C3×D511yescharacteristic
415C2×C22⋊C4—54no—
416C2×C22⋊C4—54no—
417C2×C22⋊C4—54no—
418C2×C22⋊C4—104no—
419C2×C22⋊C4—104no—
420C2×C22⋊C4—104no—
421#95—54no—
422#95C2×C3×D514yescomplemented
423C2×C3×C5#38618yescomplemented
424C2×C3×C5C22×C22⋊C411yescharacteristic
425C2×C3×C5C2×C4×D411yescharacteristic
426C2×C3×C5C2×C4×D411yescharacteristic
427C2×C3×C5C2×#12011yescharacteristic
428C2×C3×C5C2×#12111yescharacteristic
429C2×C3×C5C2×#12111yescharacteristic
430C2×C3×C5C2×#12311yescharacteristic
431C3×D5—28no—
432C3×D5—44no—
433C23×C3—54no—
434C23×C3—54no—
435C23×C3—54no—
436C23×C3—516no—
437C23×C3—54no—
438C23×C3—102no—
439C23×C3—102no—
440C23×C3—102no—
441C23×C3—102no—
442C23×C3—108no—
443C23×C3—108no—
444C23×C3—108no—
445C23×C3—108no—
446C23×C3—108no—
447C23×C3—108no—
448C23×C3—102no—
449C23×C3—102no—
450C23×C3—102no—
451C23×C3—102no—
452C23×C3—102no—
453C23×C3—102no—
454C23×C3—108no—
455C23×C3—108no—
456C23×C3—108no—
457C23×C3—204no—
458C23×C3—204no—
459C23×C3—204no—
460C23×C3—204no—
461C23×C3C2×C4×D512yes—
462C23×C3C2×D2012yes—
463C23×C3#70912yes—
464C23×C3D4×D512yes—
465C23×C3D4×D512yes—
466C23×C3D4×D512yes—
467C23×C3#71312yes—
468C23×C3C23×D511yescharacteristic
469C3×D4—1032no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—28no—
475C2×C3×C4—28no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—44no—
480C2×C3×C4—54no—
481C2×C3×C4—1032no—
482C2×C3×C4—102no—
483C2×C3×C4—102no—
484C2×C3×C4—108no—
485C2×C3×C4—102no—
486C2×C3×C4—102no—
487C2×C3×C4—102no—
488C2×C3×C4—204no—
489C2×C3×C4C2×C4×D514yescomplemented
490C2×C3×C4C2×D2014yescomplemented
491C22×C5C2×C3×C22⋊C414yes—
492C22×C5C3×C4×D414yes—
493C22×C5C3×C4×D414yes—
494C22×C5C3×#12014yes—
495C22×C5C3×#12114yes—
496C22×C5C3×#12114yes—
497C22×C5C3×#12314yes—
498C22×C5C23×C3×C411yescharacteristic
499C22×C5C22×C3×D411yescharacteristic
500C22×C5C22×C3×D411yescharacteristic
501C22×C5C22×C3×D411yescharacteristic
502C22×C5C22×C3×D411yescharacteristic
503C22×C5C2×C3×#4111yescharacteristic
504C22×C5C2×C3×#4111yescharacteristic
505C2×D5—232no—
506C2×D5—24no—
507C2×D5—24no—
508C2×D5—24no—
509C2×D5—24no—
510C2×D5—24no—
511C2×D5—24no—
512C2×D5—24no—
513C2×D5—24no—
514C2×D5—24no—
515C2×D5—416no—
516C2×D5—42no—
517C2×D5—42no—
518C2×D5—42no—
519C2×D5—42no—
520C2×D5C2×C3×C22⋊C418yescomplemented
521C4×C5—24no—
522C4×C5—24no—
523C4×C5—42no—
524Dic5—24no—
525Dic5—42no—
526C24—54no—
527C24—54no—
528C24—54no—
529C24—52no—
530C24—54no—
531C24—52no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24—102no—
536C24—102no—
537C24—102no—
538C24—102no—
539C24—102no—
540C24—102no—
541C24—102no—
542C24C22×C3×D511yescharacteristic
543C2×D4—516no—
544C2×D4—108no—
545C2×D4—108no—
546C2×D4—1032no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—54no—
555C22×C4—52no—
556C22×C4—52no—
557C22×C4—108no—
558C22×C4—108no—
559C22×C4—1032no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—108no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4C3×C4×D514yescomplemented
567C22×C4C3×D2014yescomplemented
568C22×C4C22×C3×D512yes—
569C22×C4C22×C3×D512yes—
570C22×C4C22×C3×D512yes—
571C22⋊C4—108no—
572C22⋊C4—108no—
573C22⋊C4—108no—
574C3×C5C2×#38611yescharacteristic, complemented, Hall
575C22×C3—58no—
576C22×C3—104no—
577C22×C3—104no—
578C22×C3—104no—
579C22×C3—104no—
580C22×C3—104no—
581C22×C3—104no—
582C22×C3—1032no—
583C22×C3—104no—
584C22×C3—104no—
585C22×C3—104no—
586C22×C3—202no—
587C22×C3—202no—
588C22×C3—202no—
589C22×C3—202no—
590C22×C3—2016no—
591C22×C3C4×D2014yes—
592C22×C3D5×C22⋊C414yes—
593C22×C3#402814yes—
594C22×C3#403014yes—
595C22×C3#403914yes—
596C22×C3#404014yes—
597C22×C3#404114yes—
598C22×C3C22×C4×D511yescharacteristic
599C22×C3C22×D2011yescharacteristic
600C22×C3C2×#70911yescharacteristic
601C22×C3C2×D4×D511yescharacteristic
602C22×C3C2×D4×D511yescharacteristic
603C22×C3C2×D4×D511yescharacteristic
604C22×C3C2×#71311yescharacteristic
605C3×C4—24no—
606C3×C4—24no—
607C3×C4—42no—
608C3×C4—104no—
609C3×C4—202no—
610C2×C5C3×#38618yescomplemented
611C2×C5C22×C3×C22⋊C411yescharacteristic
612C2×C5C2×C3×C4×D411yescharacteristic
613C2×C5C2×C3×C4×D411yescharacteristic
614C2×C5C2×C3×#12011yescharacteristic
615C2×C5C2×C3×#12111yescharacteristic
616C2×C5C2×C3×#12111yescharacteristic
617C2×C5C2×C3×#12311yescharacteristic
618D5—28no—
619D5—44no—
620C23—54no—
621C23—54no—
622C23—54no—
623C23—516no—
624C23—54no—
625C23—102no—
626C23—102no—
627C23—102no—
628C23—102no—
629C23—108no—
630C23—108no—
631C23—108no—
632C23—108no—
633C23—108no—
634C23—108no—
635C23—102no—
636C23—102no—
637C23—102no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—108no—
642C23—108no—
643C23—108no—
644C23—204no—
645C23—204no—
646C23—204no—
647C23—204no—
648C23C2×C3×C4×D512yes—
649C23C2×C3×D2012yes—
650C23C3×#70912yes—
651C23C3×D4×D512yes—
652C23C3×D4×D512yes—
653C23C3×D4×D512yes—
654C23C3×#71312yes—
655C23C23×C3×D511yescharacteristic
656D4—1032no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—28no—
662C2×C4—28no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—44no—
667C2×C4—54no—
668C2×C4—1032no—
669C2×C4—102no—
670C2×C4—102no—
671C2×C4—108no—
672C2×C4—102no—
673C2×C4—102no—
674C2×C4—102no—
675C2×C4—204no—
676C2×C4C2×C3×C4×D514yescomplemented
677C2×C4C2×C3×D2014yescomplemented
678C2×C3—108no—
679C2×C3—204no—
680C2×C3#6495418yesdirect product factor
681C2×C3C2×C4×D2011yescharacteristic
682C2×C3C2×D5×C22⋊C411yescharacteristic
683C2×C3C2×#402811yescharacteristic
684C2×C3C2×#403011yescharacteristic
685C2×C3C2×#403911yescharacteristic
686C2×C3C2×#404011yescharacteristic
687C2×C3C2×#404111yescharacteristic
688C5C2×C3×#38611yescharacteristic, complemented, Sylow
689C22—58no—
690C22—1032no—
691C22—104no—
692C22—104no—
693C22—104no—
694C22—104no—
695C22—104no—
696C22—104no—
697C22—104no—
698C22—104no—
699C22—104no—
700C22—2016no—
701C22—202no—
702C22—202no—
703C22—202no—
704C22—202no—
705C22C3×C4×D2014yes—
706C22C3×D5×C22⋊C414yes—
707C22C3×#402814yes—
708C22C3×#403014yes—
709C22C3×#403914yes—
710C22C3×#404014yes—
711C22C3×#404114yes—
712C22C22×C3×C4×D511yescharacteristic
713C22C22×C3×D2011yescharacteristic
714C22C2×C3×#70911yescharacteristic
715C22C2×C3×D4×D511yescharacteristic
716C22C2×C3×D4×D511yescharacteristic
717C22C2×C3×D4×D511yescharacteristic
718C22C2×C3×#71311yescharacteristic
719C4—24no—
720C4—24no—
721C4—42no—
722C4—104no—
723C4—202no—
724C3C2×#6495411yescharacteristic, direct product factor, Sylow
725C2—108no—
726C2—204no—
727C2C3×#6495418yesdirect product factor
728C2C2×C3×C4×D2011yescharacteristic
729C2C2×C3×D5×C22⋊C411yescharacteristic
730C2C2×C3×#402811yescharacteristic
731C2C2×C3×#403011yescharacteristic
732C2C2×C3×#403911yescharacteristic
733C2C2×C3×#404011yescharacteristic
734C2C2×C3×#404111yescharacteristic
subgroupG/H
centerC24×C3C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C5×#95C2
socleC24×C3×C5C23
prime radicalC23×C3×D20C2
cosocleC23×C5C24×C3
hypercenterC2×C3×#95D5
hypocenterC5C2×C3×#386
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
2. C23×C3×C4×D5C2semidirect
3. C22×C3×#685C2semidirect
4. C22×C3×#685C2semidirect
5. C22×C3×#685C2semidirect
6. C2×C3×C5×#95C2semidirect
7. C2×C3×#3963C2semidirect
8. C3×#64954C2direct (N × H)
9. C2×#64954C3direct (N × H)
19. C22×C3×D20C4semidirect
24. C22×C3×C4×D5C22semidirect
28. C2×C3×#685C22semidirect
29. C2×C3×#685C22semidirect
30. C2×C3×#685C22semidirect
31. C3×C5×#95C22semidirect
32. C3×#3963C22semidirect
35. C23×C4×D5C2×C3semidirect
36. C22×#685C2×C3semidirect
37. C22×#685C2×C3semidirect
38. C22×#685C2×C3semidirect
39. C2×C5×#95C2×C3semidirect
40. C2×#3963C2×C3semidirect
41. #64954C2×C3direct (N × H)
54. C23×C3×D5C2×C4semidirect
66. C22×C3×C4×C5C2×C4semidirect
67. C22×C3×C4×C5D4semidirect
76. C22×C3×Dic5D4semidirect
82. C2×C3×D20C2×C4semidirect
97. C2×C3×#95D5semidirect
107. C22×D20C3×C4semidirect
112. C22×C4×D5C22×C3semidirect
116. C2×#685C22×C3semidirect
117. C2×#685C22×C3semidirect
118. C2×#685C22×C3semidirect
119. C5×#95C22×C3semidirect
120. #3963C22×C3semidirect
153. C22×C3×D5C22⋊C4semidirect
155. C22×C3×D5C22×C4semidirect
168. C2×C3×C4×C5C22×C4semidirect
169. C2×C3×C4×C5C2×D4semidirect
177. C2×C3×Dic5C2×D4semidirect
202. C3×#95C2×D5semidirect
215. C23×D5C2×C3×C4semidirect
227. C22×C4×C5C2×C3×C4semidirect
228. C22×C4×C5C3×D4semidirect
237. C22×Dic5C3×D4semidirect
243. C2×D20C2×C3×C4semidirect
258. C2×#95C3×D5semidirect
288. C2×C3×D5C2×C22⋊C4semidirect
334. C22×C3×C4C4×D5semidirect
335. C22×C3×C4D20semidirect
373. C22×D5C3×C22⋊C4semidirect
375. C22×D5C22×C3×C4semidirect
388. C2×C4×C5C22×C3×C4semidirect
389. C2×C4×C5C2×C3×D4semidirect
397. C2×Dic5C2×C3×D4semidirect
422. #95C2×C3×D5semidirect
423. C2×C3×C5#386semidirect
489. C2×C3×C4C2×C4×D5semidirect
490. C2×C3×C4C2×D20semidirect
520. C2×D5C2×C3×C22⋊C4semidirect
566. C22×C4C3×C4×D5semidirect
567. C22×C4C3×D20semidirect
574. C3×C5C2×#386semidirect
610. C2×C5C3×#386semidirect
676. C2×C4C2×C3×C4×D5semidirect
677. C2×C4C2×C3×D20semidirect
680. C2×C3#64954direct (N × H)
688. C5C2×C3×#386semidirect
724. C3C2×#64954direct (N × H)
727. C2C3×#64954direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D202
C23×C3×C4×D52
C22×C3×#6852
C2×C3×C5×#952
C2×C3×#39632
C3×#649542
C2×#649543
C2×C3×#3865