Finite Group Databasebeta

← C2×#10609667 #12305535

Subgroups — C2×#10609667 #12305535

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×#398C211yesmaximal, characteristic, complemented
2C2×#65281C211yesmaximal, characteristic, complemented
3C2×#65281C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65280C211yesmaximal, characteristic
6C2×#65280C211yesmaximal, characteristic
7C2×#65269C211yesmaximal, characteristic, complemented
8C2×#65261C211yesmaximal, characteristic, complemented
9C2×#65279C211yesmaximal, characteristic, complemented
10#10609667C2116yesmaximal, direct product factor
11C2×#64964C211yesmaximal, characteristic, complemented
12C2×#64964C211yesmaximal, characteristic, complemented
13C2×#64965C211yesmaximal, characteristic, complemented
14C2×#64948C211yesmaximal, characteristic, complemented
15C2×#64961C211yesmaximal, characteristic
16C2×#64959C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×#685C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C5×#398C2218yescomplemented
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#65281C2218yescomplemented
55#65281C2218yescomplemented
56#65280C2218yes—
57#65280C2218yes—
58#65279C2218yescomplemented
59#65269C2218yescomplemented
60#65261C2218yescomplemented
61#64965C2218yescomplemented
62#64964C2218yescomplemented
63#64964C2218yescomplemented
64#64961C2218yes—
65#64959C2218yescomplemented
66#64948C2218yescomplemented
67C2×#2837—51nomaximal, Sylow
68C24×D5C2311yescharacteristic
69C24×D5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×Dic5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C22×D20—42no—
84C22×D20—42no—
85C22×D20—42no—
86C22×D20C2314yes—
87C2×C5×C4⋊C4—42no—
88C2×C5×C4⋊C4—42no—
89C2×C5×C4⋊C4—42no—
90C2×C5×C4⋊C4—42no—
91C2×C5×C4⋊C4C2314yes—
92C2×C5×C4⋊C4C2314yes—
93C2×C5×C4⋊C4C2314yes—
94C2×C5×C4⋊C4C2314yes—
95C2×#685—24no—
96C2×#685—24no—
97C2×#685—42no—
98C2×#685—42no—
99C2×#685—42no—
100C2×#685—42no—
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×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×C4⋊Dic5—42no—
120C2×C4⋊Dic5C2314yes—
121C2×#683—24no—
122C2×#683—42no—
123C2×#683—42no—
124C2×#683—42no—
125C2×#683—42no—
126C2×#683—42no—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×C4×Dic5—42no—
134C2×C4×Dic5C2314yes—
135C5×#95C2314yes—
136C5×#95C2314yes—
137C5×#95C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2837—516no—
146C2×#400—51no—
147C2×#399—51no—
148C2×#399—51no—
149C2×#398—51no—
150C2×#398D511yescharacteristic, complemented
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×C5C2411yescharacteristic
162C23×D5—22no—
163C23×D5—22no—
164C23×D5—22no—
165C23×D5—22no—
166C23×D5—22no—
167C23×D5—22no—
168C23×D5—22no—
169C23×D5—22no—
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5C2412yes—
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×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
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#4114yes—
224C22×Dic5C2412yes—
225C22×Dic5C2412yes—
226C22×Dic5C2412yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C2×D20—44no—
231C2×D20—44no—
232C2×D20—44no—
233C2×D20—416no—
234C5×C4⋊C4—44no—
235C5×C4⋊C4—44no—
236C5×C4⋊C4—44no—
237C5×C4⋊C4—44no—
238#685—28no—
239#685—28no—
240#685—44no—
241#685—44no—
242#685—44no—
243#685—44no—
244#685—44no—
245#685—44no—
246#685—44no—
247#685—44no—
248#685—44no—
249#685—44no—
250C4⋊Dic5—44no—
251#683—28no—
252#683—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⋊C4C2×D511yescharacteristic
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⋊C4—51no—
280C22×C22⋊C4—51no—
281C22×C22⋊C4—51no—
282C22×C42—51no—
283#400—58no—
284#399—58no—
285#399—58no—
286#398—58no—
287#398C2×D518yescomplemented
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×#95C2×D511yescharacteristic
306C2×#95C2×D511yescharacteristic
307C2×#95C2×D511yescharacteristic
308C23×C5C2×#4112yes—
309C23×C5H(5,𝔽2)12yes—
310C23×C5H(5,𝔽2)12yes—
311C23×C5H(5,𝔽2)12yes—
312C23×C5H(5,𝔽2)12yes—
313C23×C52−1+412yes—
314C23×C52−1+412yes—
315C23×C5C2511yescharacteristic
316C22×D5—22no—
317C22×D5—22no—
318C22×D5—22no—
319C22×D5—22no—
320C22×D5—22no—
321C22×D5—22no—
322C22×D5—22no—
323C22×D5—22no—
324C22×D5—22no—
325C22×D5—22no—
326C22×D5—22no—
327C22×D5—22no—
328C22×D5—22no—
329C22×D5—22no—
330C22×D5—44no—
331C22×D5—44no—
332C22×D5—44no—
333C22×D5—44no—
334C22×D5—44no—
335C22×D5—44no—
336C22×D5—44no—
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—22no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—44no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5—44no—
371C2×C4×C5—44no—
372C2×Dic5—28no—
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×Dic5C2×#4114yes—
396D20—416no—
397C25—51no—
398C25—51no—
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×C4C22×D511yescharacteristic
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—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—42no—
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—104no—
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⋊C4C22×D514yes—
435C2×C4⋊C4C22×D514yes—
436C2×C4⋊C4C22×D514yes—
437C2×C4⋊C4C22×D514yes—
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—54no—
447C2×C22⋊C4—54no—
448C2×C22⋊C4—54no—
449C2×C22⋊C4—54no—
450C2×C22⋊C4—104no—
451C2×C22⋊C4—104no—
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⋊C4—202no—
460C2×C22⋊C4—202no—
461C2×C22⋊C4—202no—
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#95C22×D514yes—
472#95C22×D514yes—
473#95C22×D514yes—
474C22×C5#53914yes—
475C22×C5#54014yes—
476C22×C5#54214yes—
477C22×C5#56014yes—
478C22×C5#56214yes—
479C22×C5#56214yes—
480C22×C5#56314yes—
481C22×C5C22×#4111yescharacteristic
482C22×C5C2×H(5,𝔽2)11yescharacteristic
483C22×C5C2×H(5,𝔽2)11yescharacteristic
484C22×C5C2×H(5,𝔽2)11yescharacteristic
485C22×C5C2×H(5,𝔽2)11yescharacteristic
486C22×C5C2×2−1+411yescharacteristic
487C22×C5C2×2−1+411yescharacteristic
488C2×D5—42no—
489C2×D5—42no—
490C2×D5—42no—
491C2×D5—42no—
492C2×D5—42no—
493C2×D5—42no—
494C2×D5—42no—
495C2×D5—42no—
496C2×D5—42no—
497C2×D5—42no—
498C2×D5—42no—
499C2×D5—42no—
500C2×D5—42no—
501C2×D5—42no—
502C2×D5—88no—
503C2×D5—88no—
504C4×C5—42no—
505C4×C5—42no—
506C4×C5—42no—
507C4×C5—42no—
508C4×C5—42no—
509C4×C5—42no—
510C4×C5—42no—
511Dic5—24no—
512Dic5—42no—
513Dic5—42no—
514Dic5—42no—
515Dic5—42no—
516Dic5—42no—
517C24—52no—
518C24—52no—
519C24—102no—
520C24—102no—
521C24—102no—
522C24—102no—
523C24—102no—
524C24—102no—
525C24—102no—
526C24—102no—
527C24—102no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
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—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—54no—
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×C4C23×D512yes—
584C22×C4C23×D512yes—
585C22×C4C23×D512yes—
586C22×C4C23×D512yes—
587C22×C4C23×D512yes—
588C22×C4C23×D512yes—
589C22×C4C23×D512yes—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—108no—
595C4⋊C4—204no—
596C4⋊C4—204no—
597C4⋊C4—204no—
598C4⋊C4—204no—
599C4⋊C4—204no—
600C4⋊C4—204no—
601C22⋊C4—108no—
602C22⋊C4—108no—
603C22⋊C4—204no—
604C22⋊C4—204no—
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#283718yescomplemented
615C2×C5C2×#53911yescharacteristic
616C2×C5C2×#54011yescharacteristic
617C2×C5C2×#54211yescharacteristic
618C2×C5C2×#56011yescharacteristic
619C2×C5C2×#56211yescharacteristic
620C2×C5C2×#56211yescharacteristic
621C2×C5C2×#56311yescharacteristic
622D5—82no—
623D5—82no—
624C23—102no—
625C23—102no—
626C23—102no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23—102no—
634C23—102no—
635C23—102no—
636C23—102no—
637C23—102no—
638C23—204no—
639C23—204no—
640C23—204no—
641C23—204no—
642C23—204no—
643C23—204no—
644C23—204no—
645C23—204no—
646C23—204no—
647C23—204no—
648C23—204no—
649C23—204no—
650C23—204no—
651C23—204no—
652C23#414412yes—
653C23#414412yes—
654C23#414712yes—
655C23#414712yes—
656C23D5×#4112yes—
657C23#414912yes—
658C23#414912yes—
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—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—54no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—108no—
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—102no—
708C2×C4—204no—
709C2×C4—204no—
710C2×C4—204no—
711C2×C4—204no—
712C2×C4—204no—
713C5C2×#283711yescharacteristic, complemented, Sylow
714C22—202no—
715C22—202no—
716C22—202no—
717C22—202no—
718C22—202no—
719C22—202no—
720C22—202no—
721C22—202no—
722C22—202no—
723C22—202no—
724C22—202no—
725C22—202no—
726C22—202no—
727C22—202no—
728C22—408no—
729C22—408no—
730C22#6595414yes—
731C22#6597414yes—
732C22#6598114yes—
733C22#6599714yes—
734C22#6602614yes—
735C22#6603414yes—
736C22#6606914yes—
737C22C2×#414411yescharacteristic
738C22C2×#414411yescharacteristic
739C22C2×#414711yescharacteristic
740C22C2×#414711yescharacteristic
741C22C2×D5×#4111yescharacteristic
742C22C2×#414911yescharacteristic
743C22C2×#414911yescharacteristic
744C4—42no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—104no—
752C4—202no—
753C4—202no—
754C4—202no—
755C4—202no—
756C4—202no—
757C2—402no—
758C2—402no—
759C2#1060966718yesdirect product factor
760C2C2×#6595411yescharacteristic
761C2C2×#6597411yescharacteristic
762C2C2×#6598111yescharacteristic
763C2C2×#6599711yescharacteristic
764C2C2×#6602611yescharacteristic
765C2C2×#6603411yescharacteristic
766C2C2×#6606911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#398C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#398D5
hypocenterC5C2×#2837
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C2×C5×#398C2semidirect
2. C2×#65281C2semidirect
3. C2×#65281C2semidirect
4. C2×#65283C2semidirect
7. C2×#65269C2semidirect
8. C2×#65261C2semidirect
9. C2×#65279C2semidirect
10. #10609667C2direct (N × H)
11. C2×#64964C2semidirect
12. C2×#64964C2semidirect
13. C2×#64965C2semidirect
14. C2×#64948C2semidirect
16. C2×#64959C2semidirect
42. C5×#398C22semidirect
53. #65283C22semidirect
54. #65281C22semidirect
55. #65281C22semidirect
58. #65279C22semidirect
59. #65269C22semidirect
60. #65261C22semidirect
61. #64965C22semidirect
62. #64964C22semidirect
63. #64964C22semidirect
65. #64959C22semidirect
66. #64948C22semidirect
150. C2×#398D5semidirect
287. #398C2×D5semidirect
614. C2×C5#2837semidirect
713. C5C2×#2837semidirect
759. C2#10609667direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3982
C2×#652812
C2×#652832
C2×#652802
C2×#652692
C2×#652612
C2×#652792
#106096672
C2×#649642
C2×#649652
C2×#649482
C2×#649612
C2×#649592
C2×#28375