Finite Group Databasebeta

← C5×#29747 #11952467

Subgroups — C5×#29747 #11952467

Order 1280.

1024 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#468C211yesmaximal, characteristic, complemented
2C2×C5×#408C211yesmaximal, characteristic, complemented
3C5×#2616C211yesmaximal, characteristic, complemented
4C5×#2615C211yesmaximal, characteristic
5C5×#2076C211yesmaximal, characteristic, complemented
6C5×#2075C211yesmaximal, characteristic, complemented
7C5×#2036C211yesmaximal, characteristic, complemented
8C5×#2035C211yesmaximal, characteristic, complemented
9C5×#2034C211yesmaximal, characteristic, complemented
10C5×#2033C211yesmaximal, characteristic, complemented
11C5×#2000C211yesmaximal, characteristic, complemented
12C5×#2000C211yesmaximal, characteristic, complemented
13C5×#1893C211yesmaximal, characteristic, complemented
14C5×#1892C211yesmaximal, characteristic, complemented
15C5×#1809C211yesmaximal, characteristic, complemented
16C22×C5×#41C2211yescharacteristic
17C22×C5×SD16C2211yescharacteristic
18C22×C5×M16C2211yescharacteristic
19C23×C5×C8C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×C22⋊Q8C2211yescharacteristic
22C2×C5×C22⋊Q8C2211yescharacteristic
23C2×C5×#121C2211yescharacteristic
24C2×C5×#121C2211yescharacteristic
25C2×C5×#121C2211yescharacteristic
26C5×#468—24no—
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×#103C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C5×#408—24no—
37C2×C5×C22⋊C8C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C2×C5×C22⋊C8C2211yescharacteristic
41C5×#395—21no—
42C5×#394—21no—
43C5×#394—21no—
44C5×#394—21no—
45C5×#393—21no—
46C5×#392—21no—
47C5×#392—21no—
48C5×#392—21no—
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52C5×#380C2211yescharacteristic
53C5×#380C2211yescharacteristic
54C5×#380C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61#29747C511yesmaximal, characteristic, direct product factor, Sylow
62C2×C5×#41—22no—
63C2×C5×#41—22no—
64C2×C5×#41—41no—
65C2×C5×#41—41no—
66C2×C5×#41—41no—
67C2×C5×#41—41no—
68C22×C5×Q8D411yescharacteristic
69C22×C5×Q8C2311yescharacteristic
70C22×C5×D4—21no—
71C22×C5×D4—21no—
72C22×C5×D4—21no—
73C22×C5×D4D411yescharacteristic
74C22×C5×D4D411yescharacteristic
75C22×C5×D4D411yescharacteristic
76C22×C5×D4C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C2×C5×SD16—22no—
81C2×C5×SD16—41no—
82C2×C5×SD16—41no—
83C2×C5×M16—41no—
84C2×C5×M16—41no—
85C2×C5×M16D414yescomplemented
86C22×C5×C8—22no—
87C22×C5×C8—41no—
88C22×C5×C8—41no—
89C22×C5×C8C2311yescharacteristic
90C22×C5×C8C2311yescharacteristic
91C22×C5×C8C2311yescharacteristic
92C22×C5×C8C2311yescharacteristic
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—22no—
95C5×C22⋊Q8—41no—
96C5×C22⋊Q8—41no—
97C5×C22⋊Q8—41no—
98C5×C22⋊Q8—41no—
99C5×#121—22no—
100C5×#121—22no—
101C5×#121—41no—
102C5×#121—41no—
103C5×#121—41no—
104C5×#121—41no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4—21no—
125C2×C5×C22⋊C4—21no—
126C5×#107—22no—
127C5×#107—41no—
128C5×#106—41no—
129C5×#103—22no—
130C5×#103—41no—
131C5×#103—41no—
132C5×#102—22no—
133C5×#102—41no—
134C5×#102—41no—
135C5×C22⋊C8—22no—
136C5×C22⋊C8—22no—
137C5×C22⋊C8—22no—
138C5×C22⋊C8—22no—
139C5×#95—21no—
140C5×#95—21no—
141C5×#95—21no—
142C5×#95—21no—
143C5×#95—21no—
144C5×#95—21no—
145C2×#468C2×C511yescharacteristic, complemented
146C2×#408C2×C511yescharacteristic, complemented
147#2616C2×C511yescharacteristic, complemented
148#2615C2×C511yescharacteristic
149#2076C2×C511yescharacteristic, complemented
150#2075C2×C511yescharacteristic, complemented
151#2036C2×C511yescharacteristic, complemented
152#2035C2×C511yescharacteristic, complemented
153#2034C2×C511yescharacteristic, complemented
154#2033C2×C511yescharacteristic, complemented
155#2000C2×C511yescharacteristic, complemented
156#2000C2×C511yescharacteristic, complemented
157#1893C2×C511yescharacteristic, complemented
158#1892C2×C511yescharacteristic, complemented
159#1809C2×C511yescharacteristic, complemented
160C24×C5—21no—
161C24×C5C2×D411yescharacteristic
162C24×C5C2×D411yescharacteristic
163C24×C5C2×D411yescharacteristic
164C5×#41—44no—
165C5×#41—44no—
166C5×#41—44no—
167C5×#41—44no—
168C2×C5×Q8—22no—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
171C2×C5×Q8—21no—
172C2×C5×Q8—21no—
173C2×C5×Q8—21no—
174C2×C5×Q8—21no—
175C2×C5×Q8—41no—
176C2×C5×Q8—41no—
177C2×C5×D4—22no—
178C2×C5×D4—22no—
179C2×C5×D4—22no—
180C2×C5×D4—21no—
181C2×C5×D4—21no—
182C2×C5×D4—21no—
183C2×C5×D4—21no—
184C2×C5×D4—21no—
185C2×C5×D4—21no—
186C2×C5×D4—41no—
187C2×C5×D4—41no—
188C2×C5×D4—41no—
189C2×C5×D4—41no—
190C2×C5×D4—41no—
191C2×C5×D4—41no—
192C2×C5×D4—42no—
193C2×C5×D4—42no—
194C2×C5×D4—42no—
195C2×C5×D4—81no—
196C2×C5×D4—81no—
197C2×C5×D4—81no—
198C2×C5×D4—81no—
199C2×C5×D4—81no—
200C2×C5×D4—81no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D412yes—
228C22×C4×C5#4112yes—
229C22×C4×C5C2411yescharacteristic
230C5×SD16—44no—
231C5×M16—44no—
232C2×C5×C8—21no—
233C2×C5×C8—21no—
234C2×C5×C8—21no—
235C2×C5×C8—21no—
236C2×C5×C8—21no—
237C2×C5×C8—21no—
238C2×C5×C8—21no—
239C2×C5×C8—21no—
240C2×C5×C8—21no—
241C2×C5×C8—21no—
242C2×C5×C8—44no—
243C2×C5×C8C2×D412yes—
244C2×C5×C8C2×D412yes—
245C5×C4⋊C4—21no—
246C5×C4⋊C4—21no—
247C5×C4⋊C4—21no—
248C5×C4⋊C4—21no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—21no—
255C5×C4⋊C4—21no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—42no—
258C5×C4⋊C4—42no—
259C5×C4⋊C4—42no—
260C5×C22⋊C4—42no—
261C5×C22⋊C4—42no—
262C5×C22⋊C4—42no—
263C5×C22⋊C4—42no—
264C5×C22⋊C4—42no—
265C5×C22⋊C4—42no—
266C5×C22⋊C4—81no—
267C5×C22⋊C4—81no—
268C5×C22⋊C4—81no—
269C5×C22⋊C4—81no—
270C5×C22⋊C4—81no—
271C5×C22⋊C4—81no—
272C22×#41C22×C511yescharacteristic
273C22×SD16C22×C511yescharacteristic
274C22×M16C22×C511yescharacteristic
275C23×C8C22×C511yescharacteristic
276C2×C22⋊Q8C22×C511yescharacteristic
277C2×C22⋊Q8C22×C511yescharacteristic
278C2×C22⋊Q8C22×C511yescharacteristic
279C2×#121C22×C511yescharacteristic
280C2×#121C22×C511yescharacteristic
281C2×#121C22×C511yescharacteristic
282#468—24no—
283C2×#107C22×C511yescharacteristic
284C2×#107C22×C511yescharacteristic
285C2×#106C22×C511yescharacteristic
286C2×#103C22×C511yescharacteristic
287C2×#103C22×C511yescharacteristic
288C2×#103C22×C511yescharacteristic
289C2×#102C22×C511yescharacteristic
290C2×#102C22×C511yescharacteristic
291C2×#102C22×C511yescharacteristic
292#408—24no—
293C2×C22⋊C8C22×C511yescharacteristic
294C2×C22⋊C8C22×C511yescharacteristic
295C2×C22⋊C8C22×C511yescharacteristic
296C2×C22⋊C8C22×C511yescharacteristic
297#395—21no—
298#394—21no—
299#394—21no—
300#394—21no—
301#393—21no—
302#392—21no—
303#392—21no—
304#392—21no—
305#380C22×C511yescharacteristic
306#380C22×C511yescharacteristic
307#380C22×C511yescharacteristic
308#380C22×C511yescharacteristic
309#380C22×C511yescharacteristic
310#380C22×C511yescharacteristic
311#340C22×C511yescharacteristic
312#340C22×C511yescharacteristic
313#340C22×C511yescharacteristic
314#340C22×C511yescharacteristic
315#340C22×C511yescharacteristic
316#340C22×C511yescharacteristic
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—21no—
323C23×C5—21no—
324C23×C5—21no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—21no—
330C23×C5—21no—
331C23×C5—21no—
332C23×C5—21no—
333C23×C5—21no—
334C23×C5—21no—
335C23×C5—21no—
336C23×C5—21no—
337C23×C5—41no—
338C23×C5—41no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—41no—
344C23×C5#12112yes—
345C23×C5C22×D411yescharacteristic
346C5×Q8—44no—
347C5×Q8—41no—
348C5×Q8—41no—
349C5×Q8—41no—
350C5×Q8—41no—
351C5×D4—44no—
352C5×D4—44no—
353C5×D4—44no—
354C5×D4—41no—
355C5×D4—41no—
356C5×D4—41no—
357C5×D4—41no—
358C5×D4—84no—
359C5×D4—84no—
360C5×D4—84no—
361C2×C4×C5—21no—
362C2×C4×C5—21no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—21no—
368C2×C4×C5—21no—
369C2×C4×C5—21no—
370C2×C4×C5—21no—
371C2×C4×C5—21no—
372C2×C4×C5—21no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
381C2×C4×C5—41no—
382C2×C4×C5—41no—
383C2×C4×C5—41no—
384C2×C4×C5—41no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—41no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
401C2×C4×C5—41no—
402C2×C4×C5#12112yes—
403C2×C4×C5C22×D411yescharacteristic
404C2×C4×C5C2×#4111yescharacteristic
405C2×C4×C5H(5,𝔽2)11yescharacteristic
406C2×C4×C5H(5,𝔽2)11yescharacteristic
407C2×C4×C5H(5,𝔽2)11yescharacteristic
408C2×C4×C5H(5,𝔽2)11yescharacteristic
409C5×C8—22no—
410C5×C8—22no—
411C5×C8—41no—
412C5×C8—41no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—41no—
416C2×#41—41no—
417C2×#41—41no—
418C2×#41—41no—
419C22×Q8C5×D411yescharacteristic
420C22×Q8C23×C511yescharacteristic
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C5×D411yescharacteristic
425C22×D4C5×D411yescharacteristic
426C22×D4C5×D411yescharacteristic
427C22×D4C23×C511yescharacteristic
428C23×C4C23×C511yescharacteristic
429C23×C4C23×C511yescharacteristic
430C23×C4C23×C511yescharacteristic
431C2×SD16—22no—
432C2×SD16—41no—
433C2×SD16—41no—
434C2×M16—41no—
435C2×M16—41no—
436C2×M16C5×D414yescomplemented
437C22×C8—22no—
438C22×C8—41no—
439C22×C8—41no—
440C22×C8C23×C511yescharacteristic
441C22×C8C23×C511yescharacteristic
442C22×C8C23×C511yescharacteristic
443C22×C8C23×C511yescharacteristic
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—41no—
447C22⋊Q8—41no—
448C22⋊Q8—41no—
449C22⋊Q8—41no—
450#121—22no—
451#121—22no—
452#121—41no—
453#121—41no—
454#121—41no—
455#121—41no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4C23×C511yescharacteristic
460C2×C4⋊C4C23×C511yescharacteristic
461C2×C4⋊C4C23×C511yescharacteristic
462C2×C4⋊C4C23×C511yescharacteristic
463C2×C4⋊C4C23×C511yescharacteristic
464C2×C4⋊C4C23×C511yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477#107—22no—
478#107—41no—
479#106—41no—
480#103—22no—
481#103—41no—
482#103—41no—
483#102—22no—
484#102—41no—
485#102—41no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—22no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496C22×C5—22no—
497C22×C5—22no—
498C22×C5—22no—
499C22×C5—41no—
500C22×C5—41no—
501C22×C5—41no—
502C22×C5—41no—
503C22×C5—41no—
504C22×C5—41no—
505C22×C5—41no—
506C22×C5—41no—
507C22×C5—41no—
508C22×C5—41no—
509C22×C5—41no—
510C22×C5—41no—
511C22×C5—41no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5—41no—
515C22×C5—41no—
516C22×C5—41no—
517C22×C5—81no—
518C22×C5—81no—
519C22×C5—81no—
520C22×C5—81no—
521C22×C5—81no—
522C22×C5—81no—
523C22×C5—81no—
524C22×C5C2×#12111yescharacteristic
525C22×C5#53411yescharacteristic
526C22×C5#53411yescharacteristic
527C22×C5#57611yescharacteristic
528C22×C5#57711yescharacteristic
529C22×C5#57711yescharacteristic
530C22×C5#57811yescharacteristic
531C4×C5—22no—
532C4×C5—41no—
533C4×C5—41no—
534C4×C5—81no—
535C4×C5—81no—
536C4×C5—81no—
537C4×C5—81no—
538C4×C5—81no—
539C4×C5—81no—
540C4×C5—81no—
541C4×C5#53411yescharacteristic
542C4×C5#53511yescharacteristic
543C4×C5#53811yescharacteristic
544C4×C5#53811yescharacteristic
545C24—21no—
546C24C2×C5×D411yescharacteristic
547C24C2×C5×D411yescharacteristic
548C24C2×C5×D411yescharacteristic
549#41—44no—
550#41—44no—
551#41—44no—
552#41—44no—
553C2×Q8—22no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—41no—
561C2×Q8—41no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4C2×C5×D411yescharacteristic
610C22×C4C2×C5×D411yescharacteristic
611C22×C4C2×C5×D411yescharacteristic
612C22×C4C2×C5×D412yes—
613C22×C4C5×#4112yes—
614C22×C4C24×C511yescharacteristic
615SD16—44no—
616M16—44no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—44no—
628C2×C8C2×C5×D412yes—
629C2×C8C2×C5×D412yes—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—81no—
652C22⋊C4—81no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C22⋊C4—81no—
656C22⋊C4—81no—
657C2×C5—42no—
658C2×C5—81no—
659C2×C5—81no—
660C2×C5—161no—
661C2×C5#261711yescharacteristic
662C2×C5#306211yescharacteristic
663C2×C5#306311yescharacteristic
664C2×C5#319811yescharacteristic
665C2×C5#320011yescharacteristic
666C2×C5#320111yescharacteristic
667C2×C5#320311yescharacteristic
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23C5×#12112yes—
696C23C22×C5×D411yescharacteristic
697Q8—44no—
698Q8—41no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702D4—44no—
703D4—44no—
704D4—44no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4C5×#12112yes—
754C2×C4C22×C5×D411yescharacteristic
755C2×C4C2×C5×#4111yescharacteristic
756C2×C4C5×H(5,𝔽2)11yescharacteristic
757C2×C4C5×H(5,𝔽2)11yescharacteristic
758C2×C4C5×H(5,𝔽2)11yescharacteristic
759C2×C4C5×H(5,𝔽2)11yescharacteristic
760C8—22no—
761C8—22no—
762C8—41no—
763C8—41no—
764C5#2974711yescharacteristic, direct product factor, Sylow
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22C2×C5×#12111yescharacteristic
794C22C5×#53411yescharacteristic
795C22C5×#53411yescharacteristic
796C22C5×#57611yescharacteristic
797C22C5×#57711yescharacteristic
798C22C5×#57711yescharacteristic
799C22C5×#57811yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—81no—
810C4C5×#53411yescharacteristic
811C4C5×#53511yescharacteristic
812C4C5×#53811yescharacteristic
813C4C5×#53811yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—161no—
818C2C5×#261711yescharacteristic
819C2C5×#306211yescharacteristic
820C2C5×#306311yescharacteristic
821C2C5×#319811yescharacteristic
822C2C5×#320011yescharacteristic
823C2C5×#320111yescharacteristic
824C2C5×#320311yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C5×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#468C2semidirect
2. C2×C5×#408C2semidirect
3. C5×#2616C2semidirect
5. C5×#2076C2semidirect
6. C5×#2075C2semidirect
7. C5×#2036C2semidirect
8. C5×#2035C2semidirect
9. C5×#2034C2semidirect
10. C5×#2033C2semidirect
11. C5×#2000C2semidirect
12. C5×#2000C2semidirect
13. C5×#1893C2semidirect
14. C5×#1892C2semidirect
15. C5×#1809C2semidirect
61. #29747C5direct (N × H)
85. C2×C5×M16D4semidirect
145. C2×#468C2×C5semidirect
146. C2×#408C2×C5semidirect
147. #2616C2×C5semidirect
149. #2076C2×C5semidirect
150. #2075C2×C5semidirect
151. #2036C2×C5semidirect
152. #2035C2×C5semidirect
153. #2034C2×C5semidirect
154. #2033C2×C5semidirect
155. #2000C2×C5semidirect
156. #2000C2×C5semidirect
157. #1893C2×C5semidirect
158. #1892C2×C5semidirect
159. #1809C2×C5semidirect
436. C2×M16C5×D4semidirect
764. C5#29747direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4682
C2×C5×#4082
C5×#26162
C5×#26152
C5×#20762
C5×#20752
C5×#20362
C5×#20352
C5×#20342
C5×#20332
C5×#20002
C5×#18932
C5×#18922
C5×#18092
#297475