Finite Group Databasebeta

← C2×#10614076 #12265524

Subgroups — C2×#10614076 #12265524

Order 1280.

4134 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×D4C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×#4072C211yesmaximal, characteristic, complemented
5C2×#65512C211yesmaximal, characteristic
6C2×#65511C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
8#10614076C2116yesmaximal, direct product factor
9C2×#65283C211yesmaximal, characteristic, complemented
10C2×#65273C211yesmaximal, characteristic, complemented
11C2×#65248C211yesmaximal, characteristic, complemented
12C2×#65241C211yesmaximal, characteristic, complemented
13C2×#65237C211yesmaximal, characteristic, complemented
14C2×#65250C211yesmaximal, characteristic, complemented
15C2×C4×#683C211yesmaximal, characteristic, complemented
16C2×C4×#685C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C22⋊D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C2×C4×C5×D4—28no—
24C2×C4×C5×D4C2218yescomplemented
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C2×C4×C22⋊D5—28no—
36C2×C4×C22⋊D5—28no—
37C2×C4×C22⋊D5C2218yescomplemented
38C2×C4×C22⋊D5C2218yescomplemented
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×#685C2211yescharacteristic
42C22×#685C2211yescharacteristic
43C2×#4072—28no—
44C2×#4072C2218yescomplemented
45C22×C4⋊Dic5C2211yescharacteristic
46C22×C4⋊Dic5C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×#683C2211yescharacteristic
50C22×#683C2211yescharacteristic
51C22×C4×Dic5C2211yescharacteristic
52C22×C4×Dic5C2211yescharacteristic
53C22×C4×Dic5C2211yescharacteristic
54#65512C2218yes—
55#65511C2218yescomplemented
56C4×C22⋊Dic5C2218yescomplemented
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62C2×#3963C2211yescharacteristic
63#65283C2218yescomplemented
64#65273C2218yescomplemented
65#65250C2218yescomplemented
66#65248C2218yescomplemented
67#65241C2218yescomplemented
68#65237C2218yescomplemented
69C4×#685C2218yescomplemented
70C4×#683C2218yescomplemented
71C2×#2392—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—24no—
78C22×C5×D4C2314yes—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—24no—
82C23×C4×C5—24no—
83C23×C4×C5—24no—
84C23×C4×C5D418yescomplemented
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2314yes—
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2314yes—
90C23×C4×C5C2311yescharacteristic
91C23×C4×C5C2311yescharacteristic
92C22×C22⋊D5—24no—
93C22×C22⋊D5—24no—
94C22×C22⋊D5—24no—
95C22×C22⋊D5—24no—
96C22×C22⋊D5—24no—
97C22×C22⋊D5—24no—
98C22×C22⋊D5C2314yes—
99C22×C22⋊D5C2314yes—
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C23×Dic5C2311yescharacteristic
106C23×Dic5C2311yescharacteristic
107C22×C4×D5—24no—
108C22×C4×D5—24no—
109C22×C4×D5—24no—
110C22×C4×D5C2314yes—
111C4×C5×D4—232no—
112C2×C5×C4⋊C4—24no—
113C2×C5×C4⋊C4C2314yes—
114C2×C5×C22⋊C4—24no—
115C2×C5×C22⋊C4—24no—
116C2×C5×C22⋊C4C2314yes—
117C2×C5×C22⋊C4C2314yes—
118C2×C42×C5—24no—
119C2×C42×C5C2314yes—
120C2×C22⋊Dic5—24no—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5—24no—
123C2×C22⋊Dic5—24no—
124C2×C22⋊Dic5—24no—
125C2×C22⋊Dic5—24no—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131C2×C22⋊Dic5C2314yes—
132C4×C22⋊D5—232no—
133C4×C22⋊D5—232no—
134C2×#685—24no—
135C2×#685—24no—
136C2×#685—24no—
137C2×#685—24no—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142#4072—232no—
143C2×C4⋊Dic5—24no—
144C2×C4⋊Dic5—24no—
145C2×C4⋊Dic5C2314yes—
146C2×C4⋊Dic5C2314yes—
147C2×#683—24no—
148C2×#683—24no—
149C2×#683—24no—
150C2×#683—24no—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×C4×Dic5—24no—
156C2×C4×Dic5—24no—
157C2×C4×Dic5D418yescomplemented
158C2×C4×Dic5C2314yes—
159C2×C4×Dic5C2314yes—
160C2×C4×Dic5C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×C4×D4—51no—
168C22×C4×D4—51no—
169C22×C4×D4D511yescharacteristic, complemented
170C22×#117—51no—
171#2392—516no—
172C2×#398—51no—
173C2×#397—51no—
174C2×#396—51no—
175C2×#396—51no—
176C2×#394—51no—
177C2×#394—51no—
178C2×#394—51no—
179C2×#392—51no—
180C2×C4×C4⋊C4—51no—
181C2×C4×C22⋊C4—51no—
182C2×C4×C22⋊C4—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5—22no—
194C24×C5—22no—
195C24×C5C2×D414yes—
196C24×C5#4114yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5—22no—
206C23×D5#4114yes—
207C23×D5C2412yes—
208C2×C5×D4—232no—
209C2×C5×D4—28no—
210C2×C5×D4—28no—
211C2×C5×D4—28no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—232no—
217C22×C4×C5—28no—
218C22×C4×C5—28no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—28no—
226C22×C4×C5—28no—
227C22×C4×C5—28no—
228C22×C4×C5—416no—
229C22×C4×C5C2×D414yes—
230C22×C4×C5C2×D414yes—
231C22×C4×C5C2×D414yes—
232C22×C4×C5C2×D4116yescomplemented
233C22×C4×C5#4114yes—
234C22×C4×C5#4114yes—
235C22×C4×C5C2412yes—
236C22×C4×C5C2412yes—
237C22×C4×C5C2412yes—
238C22×C4×C5C2412yes—
239C22×C4×C5C2412yes—
240C2×C22⋊D5—232no—
241C2×C22⋊D5—232no—
242C2×C22⋊D5—28no—
243C2×C22⋊D5—28no—
244C2×C22⋊D5—28no—
245C2×C22⋊D5—28no—
246C2×C22⋊D5—28no—
247C2×C22⋊D5—28no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—22no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5—22no—
262C22×Dic5—22no—
263C22×Dic5—22no—
264C22×Dic5—22no—
265C22×Dic5—22no—
266C22×Dic5C2×D414yes—
267C22×Dic5C2×D414yes—
268C22×Dic5#4114yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C22×Dic5C2412yes—
273C22×Dic5C2412yes—
274C22×Dic5C2412yes—
275C22×Dic5C2412yes—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—28no—
279C2×C4×D5—416no—
280C5×C4⋊C4—28no—
281C5×C22⋊C4—28no—
282C5×C22⋊C4—28no—
283C42×C5—28no—
284C22⋊Dic5—28no—
285C22⋊Dic5—28no—
286C22⋊Dic5—28no—
287C22⋊Dic5—28no—
288C22⋊Dic5—28no—
289C22⋊Dic5—28no—
290#685—28no—
291#685—28no—
292#685—28no—
293#685—28no—
294C4⋊Dic5—28no—
295C4⋊Dic5—28no—
296#683—28no—
297#683—28no—
298#683—28no—
299#683—28no—
300C4×Dic5—28no—
301C4×Dic5—28no—
302C4×Dic5C2×D4116yescomplemented
303C23×D4—51no—
304C23×D4—51no—
305C23×D4C2×D511yescharacteristic
306C24×C4—51no—
307C24×C4C2×D511yescharacteristic
308C24×C4C2×D511yescharacteristic
309C2×C4×D4—28no—
310C2×C4×D4—58no—
311C2×C4×D4—58no—
312C2×C4×D4—108no—
313C2×C4×D4—108no—
314C2×C4×D4C2×D518yescomplemented
315C2×#117—58no—
316C2×#117—108no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4C2×D511yescharacteristic
324C22×C22⋊C4—51no—
325C22×C22⋊C4—51no—
326C22×C22⋊C4—51no—
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C22⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4—51no—
334C22×C22⋊C4C2×D511yescharacteristic
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C42—51no—
337C22×C42—51no—
338C22×C42—51no—
339C22×C42C2×D511yescharacteristic
340#398—58no—
341#397—58no—
342#396—58no—
343#396—58no—
344#394—58no—
345#394—58no—
346#394—58no—
347#392—58no—
348C4×C4⋊C4—58no—
349C4×C22⋊C4—58no—
350C4×C22⋊C4—58no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95—51no—
356C2×#95—51no—
357C23×C5—28no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—28no—
361C23×C5—28no—
362C23×C5—28no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—44no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5—44no—
383C23×C5C22×D412yes—
384C23×C5C22×D414yes—
385C23×C5C22×D412yes—
386C23×C5C2×#4114yes—
387C23×C5C2×#4112yes—
388C23×C5C2×#4112yes—
389C23×C5C2×#4112yes—
390C23×C5C2×#4112yes—
391C23×C5C2×#4112yes—
392C23×C5C2511yescharacteristic
393C22×D5—28no—
394C22×D5—28no—
395C22×D5—28no—
396C22×D5—22no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5—22no—
400C22×D5—22no—
401C22×D5—22no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5C2×#4114yes—
407C5×D4—232no—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—232no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—44no—
422C2×C4×C5—44no—
423C2×C4×C5—416no—
424C2×C4×C5#121116yes—
425C2×C4×C5C22×D414yes—
426C2×C4×C5C22×D414yes—
427C2×C4×C5C22×D414yes—
428C2×C4×C5C2×#4114yes—
429C2×C4×C5C2×#4114yes—
430C22⋊D5—232no—
431C22⋊D5—232no—
432C2×Dic5—28no—
433C2×Dic5—28no—
434C2×Dic5—28no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452C2×Dic5—22no—
453C2×Dic5—44no—
454C2×Dic5—44no—
455C2×Dic5—44no—
456C2×Dic5—44no—
457C2×Dic5C22×D414yes—
458C2×Dic5C22×D414yes—
459C2×Dic5C2×#4114yes—
460C4×D5—416no—
461C25—51no—
462C25C22×D511yescharacteristic
463C25C22×D511yescharacteristic
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—54no—
468C22×D4—54no—
469C22×D4—104no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4C22×D514yes—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—54no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—104no—
492C23×C4C22⋊D518yescomplemented
493C23×C4C22×D511yescharacteristic
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D514yes—
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D511yescharacteristic
498C23×C4C22×D514yes—
499C23×C4C22×D511yescharacteristic
500C4×D4—232no—
501C4×D4—1032no—
502C4×D4—1032no—
503#117—1032no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—54no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—54no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—104no—
512C2×C4⋊C4—104no—
513C2×C4⋊C4—104no—
514C2×C4⋊C4—104no—
515C2×C4⋊C4—104no—
516C2×C4⋊C4—104no—
517C2×C4⋊C4C22×D514yes—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—54no—
521C2×C22⋊C4—54no—
522C2×C22⋊C4—54no—
523C2×C22⋊C4—54no—
524C2×C22⋊C4—54no—
525C2×C22⋊C4—54no—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—54no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—104no—
531C2×C22⋊C4—104no—
532C2×C22⋊C4—104no—
533C2×C22⋊C4—104no—
534C2×C22⋊C4—104no—
535C2×C22⋊C4—104no—
536C2×C22⋊C4—104no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4C22×D514yes—
541C2×C22⋊C4C22×D514yes—
542C2×C42—24no—
543C2×C42—58no—
544C2×C42—54no—
545C2×C42—54no—
546C2×C42—54no—
547C2×C42—104no—
548C2×C42—104no—
549C2×C42C22×D514yes—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95—54no—
555#95—54no—
556C22×C5—24no—
557C22×C5—24no—
558C22×C5—24no—
559C22×C5—24no—
560C22×C5—24no—
561C22×C5—24no—
562C22×C5—416no—
563C22×C5—416no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5C2×#12114yes—
573C22×C5#52514yes—
574C22×C5#52514yes—
575C22×C5#52514yes—
576C22×C5#52914yes—
577C22×C5#52914yes—
578C22×C5#53214yes—
579C22×C5C23×D411yescharacteristic
580C22×C5C23×D411yescharacteristic
581C22×C5C22×#4111yescharacteristic
582C22×C5C22×#4111yescharacteristic
583C22×C5C22×#4111yescharacteristic
584C22×C5C22×#4111yescharacteristic
585C22×C5C22×#4111yescharacteristic
586C2×D5—24no—
587C2×D5—24no—
588C2×D5—24no—
589C2×D5—416no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C4×C5—24no—
595C4×C5—24no—
596C4×C5—42no—
597C4×C5—42no—
598C4×C5C2×#12118yes—
599Dic5—24no—
600Dic5—24no—
601Dic5—24no—
602Dic5—42no—
603Dic5—42no—
604Dic5—42no—
605Dic5—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—54no—
619C24—52no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24#70914yes—
627C24C2×C22⋊D514yes—
628C24C23×D512yes—
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631C2×D4—232no—
632C2×D4—28no—
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—1032no—
640C2×D4—1032no—
641C2×D4—108no—
642C2×D4—108no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—232no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—28no—
657C22×C4—28no—
658C22×C4—28no—
659C22×C4—416no—
660C22×C4—54no—
661C22×C4—54no—
662C22×C4—54no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—102no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—102no—
674C22×C4—102no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—108no—
689C22×C4—108no—
690C22×C4—108no—
691C22×C4—2016no—
692C22×C4#70914yes—
693C22×C4D4×D514yes—
694C22×C4#71114yes—
695C22×C4C2×C22⋊D514yes—
696C22×C4C2×C22⋊D514yes—
697C22×C4C2×C22⋊D5116yescomplemented
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—28no—
704C4⋊C4—108no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C4⋊C4—108no—
709C4⋊C4—108no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—108no—
713C22⋊C4—108no—
714C22⋊C4—108no—
715C22⋊C4—108no—
716C22⋊C4—108no—
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C42—28no—
723C42—516no—
724C42—108no—
725C42—108no—
726C2×C5—44no—
727C2×C5—44no—
728C2×C5#239218yescomplemented
729C2×C5C22×#12111yescharacteristic
730C2×C5C2×#52511yescharacteristic
731C2×C5C2×#52511yescharacteristic
732C2×C5C2×#52511yescharacteristic
733C2×C5C2×#52911yescharacteristic
734C2×C5C2×#52911yescharacteristic
735C2×C5C2×#53211yescharacteristic
736D5—44no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—54no—
764C23—108no—
765C23—108no—
766C23—108no—
767C23—102no—
768C23—102no—
769C23—102no—
770C23—102no—
771C23—102no—
772C23—102no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23C2×#70914yes—
778C23C2×#70912yes—
779C23C2×#70912yes—
780C23C2×D4×D512yes—
781C23C2×#71112yes—
782C23D5×#4112yes—
783C23D5×#4112yes—
784C23C22×C22⋊D514yes—
785C23C22×C22⋊D512yes—
786C23C24×D511yescharacteristic
787D4—232no—
788D4—1032no—
789D4—1032no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—232no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—416no—
806C2×C4—54no—
807C2×C4—54no—
808C2×C4—54no—
809C2×C4—108no—
810C2×C4—108no—
811C2×C4—108no—
812C2×C4—102no—
813C2×C4—102no—
814C2×C4—102no—
815C2×C4—102no—
816C2×C4—102no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—204no—
831C2×C4—204no—
832C2×C4—204no—
833C2×C4—204no—
834C2×C4—2016no—
835C2×C4#4085116yes—
836C2×C4C2×#70914yes—
837C2×C4C2×D4×D514yes—
838C2×C4C2×#71114yes—
839C2×C4C22×C22⋊D514yes—
840C2×C4C22×C22⋊D514yes—
841C5C2×#239211yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—416no—
851C22—416no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—104no—
859C22—104no—
860C22—104no—
861C22—202no—
862C22—2016no—
863C22—202no—
864C22—202no—
865C22—202no—
866C22#6587214yes—
867C22#6588114yes—
868C22#6588214yes—
869C22#6589114yes—
870C22#6612514yes—
871C22C2×#408514yes—
872C22#6616214yes—
873C22C22×#70911yescharacteristic
874C22C22×#70911yescharacteristic
875C22C22×D4×D511yescharacteristic
876C22C22×#71111yescharacteristic
877C22C2×D5×#4111yescharacteristic
878C22C2×D5×#4111yescharacteristic
879C22C23×C22⋊D511yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—104no—
885C4—104no—
886C4—104no—
887C4—202no—
888C4—202no—
889C4—202no—
890C4—202no—
891C4C2×#408518yes—
892C2—44no—
893C2—44no—
894C2—204no—
895C2#1061407618yesdirect product factor
896C2C2×#6587211yescharacteristic
897C2C2×#6588111yescharacteristic
898C2C2×#6589111yescharacteristic
899C2C2×#6588211yescharacteristic
900C2C2×#6612511yescharacteristic
901C2C22×#408511yescharacteristic
902C2C2×#6616211yescharacteristic
subgroupG/H
centerC23×C4C22×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C4×C5×D4C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC22×C4×D4D5
hypocenterC5C2×#2392
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×D4C2semidirect
2. C22×C4×C22⋊D5C2semidirect
3. C22×C4×C22⋊D5C2semidirect
4. C22×#4072C2semidirect
6. C2×#65511C2semidirect
7. C2×C4×C22⋊Dic5C2semidirect
8. #10614076C2direct (N × H)
9. C2×#65283C2semidirect
10. C2×#65273C2semidirect
11. C2×#65248C2semidirect
12. C2×#65241C2semidirect
13. C2×#65237C2semidirect
14. C2×#65250C2semidirect
15. C2×C4×#683C2semidirect
16. C2×C4×#685C2semidirect
24. C2×C4×C5×D4C22semidirect
37. C2×C4×C22⋊D5C22semidirect
38. C2×C4×C22⋊D5C22semidirect
44. C2×#4072C22semidirect
55. #65511C22semidirect
56. C4×C22⋊Dic5C22semidirect
63. #65283C22semidirect
64. #65273C22semidirect
65. #65250C22semidirect
66. #65248C22semidirect
67. #65241C22semidirect
68. #65237C22semidirect
69. C4×#685C22semidirect
70. C4×#683C22semidirect
84. C23×C4×C5D4semidirect
157. C2×C4×Dic5D4semidirect
169. C22×C4×D4D5semidirect
232. C22×C4×C5C2×D4semidirect
302. C4×Dic5C2×D4semidirect
314. C2×C4×D4C2×D5semidirect
492. C23×C4C22⋊D5semidirect
697. C22×C4C2×C22⋊D5semidirect
728. C2×C5#2392semidirect
841. C5C2×#2392semidirect
895. C2#10614076direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×D42
C22×C4×C22⋊D52
C22×#40722
C2×#655122
C2×#655112
C2×C4×C22⋊Dic52
#106140762
C2×#652832
C2×#652732
C2×#652482
C2×#652412
C2×#652372
C2×#652502
C2×C4×#6832
C2×C4×#6852
C2×#23925