Finite Group Databasebeta

← C2×#10609827 #12305530

Subgroups — C2×#10609827 #12305530

Order 1280.

2110 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×#399C211yesmaximal, characteristic, complemented
2C2×#65282C211yesmaximal, characteristic, complemented
3C2×#65283C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65275C211yesmaximal, characteristic, complemented
6C2×#65272C211yesmaximal, characteristic, complemented
7C2×#65274C211yesmaximal, characteristic, complemented
8C2×#65248C211yesmaximal, characteristic
9C2×#65238C211yesmaximal, characteristic, complemented
10C2×#65241C211yesmaximal, characteristic, complemented
11C2×#65250C211yesmaximal, characteristic
12C2×#65250C211yesmaximal, characteristic
13C2×#65240C211yesmaximal, characteristic, complemented
14#10609827C2116yesmaximal, direct product factor
15C2×#64946C211yesmaximal, characteristic, complemented
16C2×#64958C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C5×#399C2218yescomplemented
43C2×C5×#95C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65283C2218yescomplemented
54#65283C2218yescomplemented
55#65282C2218yescomplemented
56#65275C2218yescomplemented
57#65274C2218yescomplemented
58#65272C2218yescomplemented
59#65250C2218yes—
60#65250C2218yes—
61#65248C2218yes—
62#65241C2218yescomplemented
63#65240C2218yescomplemented
64#65238C2218yescomplemented
65#64958C2218yescomplemented
66#64946C2218yescomplemented
67C2×#2837—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—42no—
77C22×C22⋊D5—42no—
78C22×C22⋊D5—42no—
79C22×C22⋊D5C2314yes—
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C2×C5×C4⋊C4—24no—
88C2×C5×C4⋊C4—42no—
89C2×C5×C4⋊C4—42no—
90C2×C5×C4⋊C4C2314yes—
91C2×C5×C4⋊C4C2314yes—
92C2×C5×C4⋊C4C2314yes—
93C2×C5×C22⋊C4—24no—
94C2×C5×C22⋊C4—42no—
95C2×C5×C22⋊C4—42no—
96C2×C5×C22⋊C4C2314yes—
97C2×C5×C22⋊C4C2314yes—
98C2×C5×C22⋊C4C2314yes—
99C2×C22⋊Dic5—42no—
100C2×C22⋊Dic5—42no—
101C2×C22⋊Dic5—42no—
102C2×C22⋊Dic5C2314yes—
103C2×C22⋊Dic5C2314yes—
104C2×C22⋊Dic5C2314yes—
105C2×#685—24no—
106C2×#685—42no—
107C2×#685—42no—
108C2×#685—42no—
109C2×#685—42no—
110C2×#685—42no—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×C4⋊Dic5—42no—
118C2×C4⋊Dic5—42no—
119C2×C4⋊Dic5—42no—
120C2×C4⋊Dic5—42no—
121C2×C4⋊Dic5C2314yes—
122C2×C4⋊Dic5C2314yes—
123C2×C4⋊Dic5C2314yes—
124C2×C4⋊Dic5C2314yes—
125C2×#683—42no—
126C2×#683—42no—
127C2×#683—42no—
128C2×#683—42no—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×C4×Dic5—42no—
134C2×C4×Dic5C2314yes—
135C5×#95C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2837—516no—
146C2×#400—51no—
147C2×#399—51no—
148C2×#399D511yescharacteristic, complemented
149C2×#398—51no—
150C2×#398—51no—
151C2×#397—51no—
152C2×#397—51no—
153C2×#396—51no—
154C2×#396—51no—
155C2×#394—51no—
156C2×#394—51no—
157C2×#394—51no—
158C2×#389—51no—
159C2×#388—51no—
160C2×#388—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#4114yes—
196C22×C4×C5C2412yes—
197C22×C4×C5C2412yes—
198C22×C4×C5C2412yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C2×C22⋊D5—44no—
203C2×C22⋊D5—44no—
204C2×C22⋊D5—44no—
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—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C5×C4⋊C4—28no—
235C5×C4⋊C4—44no—
236C5×C4⋊C4—44no—
237C5×C22⋊C4—28no—
238C5×C22⋊C4—44no—
239C5×C22⋊C4—44no—
240C22⋊Dic5—44no—
241C22⋊Dic5—44no—
242C22⋊Dic5—44no—
243#685—28no—
244#685—44no—
245#685—44no—
246#685—44no—
247#685—44no—
248#685—44no—
249C4⋊Dic5—44no—
250C4⋊Dic5—44no—
251C4⋊Dic5—44no—
252C4⋊Dic5—44no—
253#683—44no—
254#683—44no—
255#683—44no—
256#683—44no—
257C4×Dic5—44no—
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×C4⋊C4C2×D511yescharacteristic
269C22×C4⋊C4C2×D511yescharacteristic
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⋊C4—51no—
278C22×C22⋊C4—51no—
279C22×C22⋊C4C2×D511yescharacteristic
280C22×C22⋊C4C2×D511yescharacteristic
281C22×C22⋊C4C2×D511yescharacteristic
282C22×C42—51no—
283#400—58no—
284#399—58no—
285#399C2×D518yescomplemented
286#398—58no—
287#398—58no—
288#397—58no—
289#397—58no—
290#396—58no—
291#396—58no—
292#394—58no—
293#394—58no—
294#394—58no—
295#389—58no—
296#388—58no—
297#388—58no—
298C2×#95—51no—
299C2×#95—51no—
300C2×#95—51no—
301C2×#95—51no—
302C2×#95—51no—
303C2×#95—51no—
304C2×#95—51no—
305C2×#95—51no—
306C2×#95—51no—
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×C5H(5,𝔽2)12yes—
324C23×C5H(5,𝔽2)12yes—
325C23×C5H(5,𝔽2)12yes—
326C23×C5H(5,𝔽2)12yes—
327C23×C52−1+412yes—
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—28no—
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×C5C2×#4114yes—
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—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—44no—
391C2×Dic5—44no—
392C2×Dic5—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5—44no—
397C25—51no—
398C25C22×D511yescharacteristic
399C22×D4—54no—
400C22×D4—202no—
401C22×D4—202no—
402C22×D4—202no—
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—24no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
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—54no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—202no—
428C2×C4⋊C4—202no—
429C2×C4⋊C4—202no—
430C2×C4⋊C4—202no—
431C2×C4⋊C4—202no—
432C2×C4⋊C4—202no—
433C2×C4⋊C4—202no—
434C2×C4⋊C4—202no—
435C2×C4⋊C4C22×D514yes—
436C2×C4⋊C4C22×D514yes—
437C2×C4⋊C4C22×D514yes—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—54no—
442C2×C22⋊C4—54no—
443C2×C22⋊C4—54no—
444C2×C22⋊C4—54no—
445C2×C22⋊C4—54no—
446C2×C22⋊C4—54no—
447C2×C22⋊C4—54no—
448C2×C22⋊C4—54no—
449C2×C22⋊C4—54no—
450C2×C22⋊C4—104no—
451C2×C22⋊C4—202no—
452C2×C22⋊C4—202no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4—202no—
456C2×C22⋊C4—202no—
457C2×C22⋊C4—202no—
458C2×C22⋊C4—202no—
459C2×C22⋊C4C22×D514yes—
460C2×C22⋊C4C22×D514yes—
461C2×C22⋊C4C22×D514yes—
462C2×C42—54no—
463C2×C42—202no—
464#95—54no—
465#95—54no—
466#95—54no—
467#95—54no—
468#95—54no—
469#95—54no—
470#95—54no—
471#95—54no—
472#95—54no—
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×C5#53914yes—
483C22×C5#54014yes—
484C22×C5#54214yes—
485C22×C5#56014yes—
486C22×C5#56214yes—
487C22×C5#56214yes—
488C22×C5#56314yes—
489C22×C5C22×#4111yescharacteristic
490C22×C5C2×H(5,𝔽2)11yescharacteristic
491C22×C5C2×H(5,𝔽2)11yescharacteristic
492C22×C5C2×H(5,𝔽2)11yescharacteristic
493C22×C5C2×H(5,𝔽2)11yescharacteristic
494C22×C5C2×2−1+411yescharacteristic
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—24no—
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—
516Dic5—42no—
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—204no—
535C2×D4—204no—
536C2×D4—204no—
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—52no—
556C22×C4—52no—
557C22×C4—52no—
558C22×C4—52no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—52no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
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#71114yes—
584C22×C4C23×D512yes—
585C22×C4C23×D512yes—
586C22×C4C23×D512yes—
587C22×C4C23×D512yes—
588C22×C4C23×D512yes—
589C22×C4C23×D512yes—
590C4⋊C4—28no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—204no—
594C4⋊C4—204no—
595C4⋊C4—204no—
596C4⋊C4—204no—
597C4⋊C4—204no—
598C4⋊C4—204no—
599C4⋊C4—204no—
600C4⋊C4—204no—
601C22⋊C4—28no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—108no—
605C22⋊C4—204no—
606C22⋊C4—204no—
607C22⋊C4—204no—
608C22⋊C4—204no—
609C22⋊C4—204no—
610C22⋊C4—204no—
611C22⋊C4—204no—
612C22⋊C4—204no—
613C42—204no—
614C2×C5—82no—
615C2×C5#283718yescomplemented
616C2×C5C2×#53911yescharacteristic
617C2×C5C2×#54011yescharacteristic
618C2×C5C2×#54211yescharacteristic
619C2×C5C2×#56011yescharacteristic
620C2×C5C2×#56211yescharacteristic
621C2×C5C2×#56211yescharacteristic
622C2×C5C2×#56311yescharacteristic
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—
652C23C2×#71112yes—
653C23#414412yes—
654C23#414412yes—
655C23#414712yes—
656C23#414912yes—
657C23#414912yes—
658C23#415012yes—
659C23C24×D511yescharacteristic
660D4—2016no—
661C2×C4—28no—
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—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
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—204no—
706C2×C4—204no—
707C2×C4—204no—
708C2×C4—204no—
709C2×C4—204no—
710C2×C4—204no—
711C2×C4—204no—
712C2×C4C2×#71114yes—
713C5C2×#283711yescharacteristic, 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#6597714yes—
731C22#6598014yes—
732C22#6598114yes—
733C22#6599914yes—
734C22#6600014yes—
735C22#6600114yes—
736C22#6605314yes—
737C22C22×#71111yescharacteristic
738C22C2×#414411yescharacteristic
739C22C2×#414411yescharacteristic
740C22C2×#414711yescharacteristic
741C22C2×#414911yescharacteristic
742C22C2×#414911yescharacteristic
743C22C2×#415011yescharacteristic
744C4—24no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—202no—
751C4—202no—
752C4—202no—
753C4—202no—
754C4—202no—
755C4—202no—
756C4—202no—
757C2—82no—
758C2—402no—
759C2#1060982718yesdirect product factor
760C2C2×#6597711yescharacteristic
761C2C2×#6598011yescharacteristic
762C2C2×#6598111yescharacteristic
763C2C2×#6599911yescharacteristic
764C2C2×#6600011yescharacteristic
765C2C2×#6600111yescharacteristic
766C2C2×#6605311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#399C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#399D5
hypocenterC5C2×#2837
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C2×C5×#399C2semidirect
2. C2×#65282C2semidirect
3. C2×#65283C2semidirect
4. C2×#65283C2semidirect
5. C2×#65275C2semidirect
6. C2×#65272C2semidirect
7. C2×#65274C2semidirect
9. C2×#65238C2semidirect
10. C2×#65241C2semidirect
13. C2×#65240C2semidirect
14. #10609827C2direct (N × H)
15. C2×#64946C2semidirect
16. C2×#64958C2semidirect
42. C5×#399C22semidirect
53. #65283C22semidirect
54. #65283C22semidirect
55. #65282C22semidirect
56. #65275C22semidirect
57. #65274C22semidirect
58. #65272C22semidirect
62. #65241C22semidirect
63. #65240C22semidirect
64. #65238C22semidirect
65. #64958C22semidirect
66. #64946C22semidirect
148. C2×#399D5semidirect
285. #399C2×D5semidirect
615. C2×C5#2837semidirect
713. C5C2×#2837semidirect
759. C2#10609827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3992
C2×#652822
C2×#652832
C2×#652752
C2×#652722
C2×#652742
C2×#652482
C2×#652382
C2×#652412
C2×#652502
C2×#652402
#106098272
C2×#649462
C2×#649582
C2×#28375