Finite Group Databasebeta

← C2×#10609279 #12266412

Subgroups — C2×#10609279 #12266412

Order 1280.

2222 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#397C211yesmaximal, characteristic, complemented
2C2×#65283C211yesmaximal, characteristic, complemented
3C2×#65261C211yesmaximal, characteristic, complemented
4C2×#65242C211yesmaximal, characteristic, complemented
5C2×#65241C211yesmaximal, characteristic, complemented
6C2×#65237C211yesmaximal, characteristic, complemented
7C2×#65246C211yesmaximal, characteristic
8C2×#65246C211yesmaximal, characteristic
9C2×#65246C211yesmaximal, characteristic
10#10609279C2116yesmaximal, direct product factor
11C2×#64964C211yesmaximal, characteristic, complemented
12C2×#64964C211yesmaximal, characteristic, complemented
13C2×#64963C211yesmaximal, characteristic, complemented
14C2×#64936C211yesmaximal, characteristic, complemented
15C2×#64936C211yesmaximal, characteristic, complemented
16C2×#64937C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic5C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C5×#397C2218yescomplemented
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65283C2218yescomplemented
54#65261C2218yescomplemented
55#65246C2218yes—
56#65246C2218yes—
57#65246C2218yes—
58#65242C2218yescomplemented
59#65241C2218yescomplemented
60#65237C2218yescomplemented
61#64964C2218yescomplemented
62#64964C2218yescomplemented
63#64963C2218yescomplemented
64#64937C2218yescomplemented
65#64936C2218yescomplemented
66#64936C2218yescomplemented
67C2×#2644—51nomaximal, Sylow
68C25×C5C2311yescharacteristic
69C24×D5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C22×C22⋊D5—24no—
77C22×C22⋊D5—24no—
78C22×C22⋊D5—24no—
79C22×C22⋊D5C2314yes—
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C2×C5×C4⋊C4—42no—
88C2×C5×C4⋊C4C2314yes—
89C2×C5×C22⋊C4—42no—
90C2×C5×C22⋊C4—42no—
91C2×C5×C22⋊C4—42no—
92C2×C5×C22⋊C4C2314yes—
93C2×C5×C22⋊C4C2314yes—
94C2×C5×C22⋊C4C2314yes—
95C2×C22⋊Dic5—42no—
96C2×C22⋊Dic5—42no—
97C2×C22⋊Dic5—42no—
98C2×C22⋊Dic5C2314yes—
99C2×C22⋊Dic5C2314yes—
100C2×C22⋊Dic5C2314yes—
101C2×#685—42no—
102C2×#685—42no—
103C2×#685—42no—
104C2×#685—42no—
105C2×#685—42no—
106C2×#685—42no—
107C2×#685C2314yes—
108C2×#685C2314yes—
109C2×#685C2314yes—
110C2×#685C2314yes—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×C4⋊Dic5—42no—
114C2×C4⋊Dic5—42no—
115C2×C4⋊Dic5C2314yes—
116C2×C4⋊Dic5C2314yes—
117C2×#683—24no—
118C2×#683—24no—
119C2×#683—24no—
120C2×#683—42no—
121C2×#683—42no—
122C2×#683—42no—
123C2×#683C2314yes—
124C2×#683C2314yes—
125C2×#683C2314yes—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×C4×Dic5—24no—
130C2×C4×Dic5—24no—
131C2×C4×Dic5—24no—
132C2×C4×Dic5C2314yes—
133C2×C4×Dic5C2314yes—
134C2×C4×Dic5C2314yes—
135C5×#95C2314yes—
136C5×#95C2314yes—
137C5×#95C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2644—516no—
146C2×#397—51no—
147C2×#397—51no—
148C2×#397—51no—
149C2×#397—51no—
150C2×#397—51no—
151C2×#397D511yescharacteristic, complemented
152C2×#396—51no—
153C2×#396—51no—
154C2×#390—51no—
155C2×#390—51no—
156C2×#390—51no—
157C2×#389—51no—
158C2×#389—51no—
159C2×#389—51no—
160C2×#376—51no—
161C24×C5—22no—
162C24×C5—22no—
163C24×C5—22no—
164C24×C5—22no—
165C24×C5—22no—
166C24×C5—22no—
167C24×C5—22no—
168C24×C5C2412yes—
169C24×C5C2411yescharacteristic
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5—22no—
177C23×D5C2412yes—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5C2412yes—
197C22×C4×C5C2412yes—
198C22×C4×C5C2412yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C2×C22⋊D5—28no—
203C2×C22⋊D5—28no—
204C2×C22⋊D5—28no—
205C2×C22⋊D5—416no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—22no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5—22no—
224C22×Dic5#4114yes—
225C22×Dic5#4114yes—
226C22×Dic5#4114yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C5×C4⋊C4—44no—
235C5×C22⋊C4—44no—
236C5×C22⋊C4—44no—
237C5×C22⋊C4—44no—
238C22⋊Dic5—44no—
239C22⋊Dic5—44no—
240C22⋊Dic5—44no—
241#685—44no—
242#685—44no—
243#685—44no—
244#685—44no—
245#685—44no—
246#685—44no—
247C4⋊Dic5—44no—
248C4⋊Dic5—44no—
249#683—28no—
250#683—28no—
251#683—28no—
252#683—44no—
253#683—44no—
254#683—44no—
255C4×Dic5—28no—
256C4×Dic5—28no—
257C4×Dic5—28no—
258C23×D4—51no—
259C22×C4⋊C4—51no—
260C22×C4⋊C4—51no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4—51no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4—51no—
267C22×C4⋊C4C2×D511yescharacteristic
268C22×C22⋊C4—51no—
269C22×C22⋊C4—51no—
270C22×C22⋊C4—51no—
271C22×C22⋊C4—51no—
272C22×C22⋊C4—51no—
273C22×C22⋊C4—51no—
274C22×C22⋊C4—51no—
275C22×C22⋊C4—51no—
276C22×C22⋊C4—51no—
277C22×C22⋊C4C2×D511yescharacteristic
278C22×C22⋊C4C2×D511yescharacteristic
279C22×C22⋊C4C2×D511yescharacteristic
280C22×C42—51no—
281C22×C42—51no—
282C22×C42—51no—
283#397—58no—
284#397—58no—
285#397—58no—
286#397—58no—
287#397—58no—
288#397C2×D518yescomplemented
289#396—58no—
290#396—58no—
291#390—58no—
292#390—58no—
293#390—58no—
294#389—58no—
295#389—58no—
296#389—58no—
297#376—58no—
298C2×#95—51no—
299C2×#95—51no—
300C2×#95—51no—
301C2×#95—51no—
302C2×#95—51no—
303C2×#95—51no—
304C2×#95—51no—
305C2×#95C2×D511yescharacteristic
306C2×#95C2×D511yescharacteristic
307C2×#95C2×D511yescharacteristic
308C23×C5—22no—
309C23×C5—22no—
310C23×C5—22no—
311C23×C5—22no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—44no—
316C23×C5—44no—
317C23×C5—44no—
318C23×C5—44no—
319C23×C5—44no—
320C23×C5—44no—
321C23×C5—44no—
322C23×C5C2×#4112yes—
323C23×C5C2×#4112yes—
324C23×C5C2×#4112yes—
325C23×C5H(5,𝔽2)12yes—
326C23×C5H(5,𝔽2)12yes—
327C23×C5H(5,𝔽2)12yes—
328C23×C52−1+412yes—
329C23×C5C2511yescharacteristic
330C22×D5—22no—
331C22×D5—22no—
332C22×D5—22no—
333C22×D5—22no—
334C22×D5—22no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—44no—
338C22×D5—44no—
339C22×D5—44no—
340C22×D5—44no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—44no—
363C2×C4×C5—44no—
364C2×C4×C5—44no—
365C2×C4×C5—44no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C22⋊D5—416no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
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—22no—
387C2×Dic5—44no—
388C2×Dic5—44no—
389C2×Dic5—44no—
390C2×Dic5—44no—
391C2×Dic5—44no—
392C2×Dic5—44no—
393C2×Dic5#126116yes—
394C2×Dic5C2×#4114yes—
395C2×Dic5C2×#4114yes—
396C2×Dic5C2×#4114yes—
397C25—51no—
398C25C22×D511yescharacteristic
399C22×D4—54no—
400C22×D4—104no—
401C22×D4—104no—
402C22×D4—104no—
403C23×C4—51no—
404C23×C4—51no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4C22×D511yescharacteristic
411C23×C4C22×D511yescharacteristic
412C23×C4C22×D511yescharacteristic
413C23×C4C22×D511yescharacteristic
414C23×C4C22×D511yescharacteristic
415C23×C4C22×D511yescharacteristic
416C2×C4⋊C4—42no—
417C2×C4⋊C4—54no—
418C2×C4⋊C4—54no—
419C2×C4⋊C4—54no—
420C2×C4⋊C4—54no—
421C2×C4⋊C4—54no—
422C2×C4⋊C4—54no—
423C2×C4⋊C4—54no—
424C2×C4⋊C4—54no—
425C2×C4⋊C4—104no—
426C2×C4⋊C4—104no—
427C2×C4⋊C4—104no—
428C2×C4⋊C4—202no—
429C2×C4⋊C4—202no—
430C2×C4⋊C4—202no—
431C2×C4⋊C4—202no—
432C2×C4⋊C4—202no—
433C2×C4⋊C4C22×D514yes—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—54no—
438C2×C22⋊C4—54no—
439C2×C22⋊C4—54no—
440C2×C22⋊C4—54no—
441C2×C22⋊C4—54no—
442C2×C22⋊C4—54no—
443C2×C22⋊C4—54no—
444C2×C22⋊C4—54no—
445C2×C22⋊C4—54no—
446C2×C22⋊C4—202no—
447C2×C22⋊C4—202no—
448C2×C22⋊C4—202no—
449C2×C22⋊C4—202no—
450C2×C22⋊C4—202no—
451C2×C22⋊C4—202no—
452C2×C22⋊C4—202no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4C22×D514yes—
456C2×C22⋊C4C22×D514yes—
457C2×C22⋊C4C22×D514yes—
458C2×C42—54no—
459C2×C42—54no—
460C2×C42—54no—
461C2×C42—104no—
462C2×C42—104no—
463C2×C42—104no—
464#95—54no—
465#95—54no—
466#95—54no—
467#95—54no—
468#95—54no—
469#95—54no—
470#95—54no—
471#95C22×D514yes—
472#95C22×D514yes—
473#95C22×D514yes—
474C22×C5—42no—
475C22×C5—42no—
476C22×C5—42no—
477C22×C5—42no—
478C22×C5—42no—
479C22×C5—42no—
480C22×C5—42no—
481C22×C5—88no—
482C22×C5C2×#12614yes—
483C22×C5#54014yes—
484C22×C5#54014yes—
485C22×C5#54014yes—
486C22×C5#54214yes—
487C22×C5#54214yes—
488C22×C5#54214yes—
489C22×C5C22×#4111yescharacteristic
490C22×C5C22×#4111yescharacteristic
491C22×C5C22×#4111yescharacteristic
492C22×C5C2×H(5,𝔽2)11yescharacteristic
493C22×C5C2×H(5,𝔽2)11yescharacteristic
494C22×C5C2×H(5,𝔽2)11yescharacteristic
495C22×C5C2×2−1+411yescharacteristic
496C2×D5—42no—
497C2×D5—42no—
498C2×D5—42no—
499C2×D5—42no—
500C2×D5—42no—
501C2×D5—42no—
502C2×D5—42no—
503C2×D5—88no—
504C4×C5—42no—
505C4×C5—42no—
506C4×C5—42no—
507C4×C5—42no—
508C4×C5—42no—
509C4×C5—42no—
510Dic5—42no—
511Dic5—42no—
512Dic5—42no—
513Dic5—42no—
514Dic5—42no—
515Dic5—42no—
516Dic5C2×#12618yes—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—52no—
525C24—102no—
526C24—102no—
527C24—102no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24C23×D512yes—
533C24C23×D511yescharacteristic
534C2×D4—108no—
535C2×D4—108no—
536C2×D4—108no—
537C2×D4—2016no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—54no—
557C22×C4—54no—
558C22×C4—54no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4C23×D512yes—
585C22×C4C23×D512yes—
586C22×C4C23×D512yes—
587C22×C4C23×D512yes—
588C22×C4C23×D512yes—
589C22×C4C23×D512yes—
590C4⋊C4—44no—
591C4⋊C4—108no—
592C4⋊C4—108no—
593C4⋊C4—108no—
594C4⋊C4—204no—
595C4⋊C4—204no—
596C4⋊C4—204no—
597C4⋊C4—204no—
598C4⋊C4—204no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—204no—
603C22⋊C4—204no—
604C22⋊C4—204no—
605C22⋊C4—204no—
606C22⋊C4—204no—
607C22⋊C4—204no—
608C22⋊C4—204no—
609C22⋊C4—204no—
610C22⋊C4—204no—
611C42—108no—
612C42—108no—
613C42—108no—
614C2×C5—82no—
615C2×C5#264418yescomplemented
616C2×C5C22×#12611yescharacteristic
617C2×C5C2×#54011yescharacteristic
618C2×C5C2×#54011yescharacteristic
619C2×C5C2×#54011yescharacteristic
620C2×C5C2×#54211yescharacteristic
621C2×C5C2×#54211yescharacteristic
622C2×C5C2×#54211yescharacteristic
623D5—82no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23—102no—
643C23—102no—
644C23—102no—
645C23—204no—
646C23—204no—
647C23—204no—
648C23—204no—
649C23—204no—
650C23—204no—
651C23—204no—
652C23#414412yes—
653C23#414412yes—
654C23D5×#4112yes—
655C23D5×#4112yes—
656C23D5×#4112yes—
657C23#414912yes—
658C23#415012yes—
659C23C24×D511yescharacteristic
660D4—2016no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—54no—
686C2×C4—54no—
687C2×C4—54no—
688C2×C4—516no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—204no—
708C2×C4—204no—
709C2×C4—204no—
710C2×C4—204no—
711C2×C4—204no—
712C2×C4—204no—
713C5C2×#264411yescharacteristic, complemented, Sylow
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—88no—
722C22—202no—
723C22—202no—
724C22—202no—
725C22—202no—
726C22—202no—
727C22—202no—
728C22—202no—
729C22—408no—
730C22#6594914yes—
731C22#6599614yes—
732C22#6599714yes—
733C22#6599714yes—
734C22#6600314yes—
735C22D5×#12614yes—
736C22#6604414yes—
737C22C2×#414411yescharacteristic
738C22C2×#414411yescharacteristic
739C22C2×D5×#4111yescharacteristic
740C22C2×D5×#4111yescharacteristic
741C22C2×D5×#4111yescharacteristic
742C22C2×#414911yescharacteristic
743C22C2×#415011yescharacteristic
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—58no—
751C4—202no—
752C4—202no—
753C4—202no—
754C4—202no—
755C4—202no—
756C4—202no—
757C2—82no—
758C2—402no—
759C2#1060927918yesdirect product factor
760C2C2×#6594911yescharacteristic
761C2C2×#6599711yescharacteristic
762C2C2×#6599711yescharacteristic
763C2C2×#6599611yescharacteristic
764C2C2×#6600311yescharacteristic
765C2C2×#6604411yescharacteristic
766C2C2×D5×#12611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#397C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#397D5
hypocenterC5C2×#2644
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C2×C5×#397C2semidirect
2. C2×#65283C2semidirect
3. C2×#65261C2semidirect
4. C2×#65242C2semidirect
5. C2×#65241C2semidirect
6. C2×#65237C2semidirect
10. #10609279C2direct (N × H)
11. C2×#64964C2semidirect
12. C2×#64964C2semidirect
13. C2×#64963C2semidirect
14. C2×#64936C2semidirect
15. C2×#64936C2semidirect
16. C2×#64937C2semidirect
42. C5×#397C22semidirect
53. #65283C22semidirect
54. #65261C22semidirect
58. #65242C22semidirect
59. #65241C22semidirect
60. #65237C22semidirect
61. #64964C22semidirect
62. #64964C22semidirect
63. #64963C22semidirect
64. #64937C22semidirect
65. #64936C22semidirect
66. #64936C22semidirect
151. C2×#397D5semidirect
288. #397C2×D5semidirect
615. C2×C5#2644semidirect
713. C5C2×#2644semidirect
759. C2#10609279direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3972
C2×#652832
C2×#652612
C2×#652422
C2×#652412
C2×#652372
C2×#652462
#106092792
C2×#649642
C2×#649632
C2×#649362
C2×#649372
C2×#26445