Finite Group Databasebeta

← C5×#32713 #11955433

Subgroups — C5×#32713 #11955433

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2616C211yesmaximal, characteristic, complemented
2C5×#2615C211yesmaximal, characteristic
3C5×#2077C211yesmaximal, characteristic, complemented
4C5×#2076C211yesmaximal, characteristic, complemented
5C5×#2075C211yesmaximal, characteristic, complemented
6C5×#2036C211yesmaximal, characteristic, complemented
7C5×#2036C211yesmaximal, characteristic, complemented
8C5×#2035C211yesmaximal, characteristic, complemented
9C5×#2034C211yesmaximal, characteristic, complemented
10C5×#2033C211yesmaximal, characteristic, complemented
11C5×#2033C211yesmaximal, characteristic, complemented
12C5×#2000C211yesmaximal, characteristic, complemented
13C5×#2000C211yesmaximal, characteristic, complemented
14C5×#2000C211yesmaximal, characteristic, complemented
15C5×#1780C211yesmaximal, characteristic, complemented
16C22×C5×#41C2211yescharacteristic
17C22×C5×SD16C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×C5×#121C2211yescharacteristic
23C2×C5×#121C2211yescharacteristic
24C2×C5×#107C2211yescharacteristic
25C2×C5×#107C2211yescharacteristic
26C2×C5×#106C2211yescharacteristic
27C2×C5×#103C2211yescharacteristic
28C2×C5×#103C2211yescharacteristic
29C2×C5×#103C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×C22⋊C8C2211yescharacteristic
34C2×C5×C22⋊C8C2211yescharacteristic
35C2×C5×C22⋊C8C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C2×C5×C22⋊C8C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C5×#395—21no—
40C5×#394—21no—
41C5×#394—21no—
42C5×#394—21no—
43C5×#393—21no—
44C5×#392—21no—
45C5×#392—21no—
46C5×#392—21no—
47C5×#380C2211yescharacteristic
48C5×#380C2211yescharacteristic
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52C5×#380C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59#32713C511yesmaximal, characteristic, direct product factor, Sylow
60C2×C5×#41—41no—
61C2×C5×#41—41no—
62C2×C5×#41—41no—
63C2×C5×#41—41no—
64C2×C5×#41—41no—
65C2×C5×#41—41no—
66C22×C5×Q8D411yescharacteristic
67C22×C5×Q8C2311yescharacteristic
68C22×C5×D4—21no—
69C22×C5×D4—21no—
70C22×C5×D4—21no—
71C22×C5×D4D411yescharacteristic
72C22×C5×D4D411yescharacteristic
73C22×C5×D4D411yescharacteristic
74C22×C5×D4C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C2×C5×SD16—41no—
79C2×C5×SD16—41no—
80C2×C5×SD16—41no—
81C22×C5×C8C2311yescharacteristic
82C22×C5×C8C2311yescharacteristic
83C22×C5×C8C2311yescharacteristic
84C22×C5×C8C2311yescharacteristic
85C5×C22⋊Q8—41no—
86C5×C22⋊Q8—41no—
87C5×C22⋊Q8—41no—
88C5×C22⋊Q8—41no—
89C5×C22⋊Q8—41no—
90C5×C22⋊Q8—41no—
91C5×#121—41no—
92C5×#121—41no—
93C5×#121—41no—
94C5×#121—41no—
95C5×#121—41no—
96C5×#121—41no—
97C2×C5×C4⋊C4—21no—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4—21no—
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C5×#107—41no—
119C5×#107—41no—
120C5×#106—41no—
121C5×#103—41no—
122C5×#103—41no—
123C5×#103—41no—
124C5×#102—41no—
125C5×#102—41no—
126C5×#102—41no—
127C5×C22⋊C8—41no—
128C5×C22⋊C8—41no—
129C5×C22⋊C8—41no—
130C5×C22⋊C8—41no—
131C5×C22⋊C8—41no—
132C5×C22⋊C8—41no—
133C5×#95—21no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95—21no—
137C5×#95—21no—
138C5×#95—21no—
139#2616C2×C511yescharacteristic, complemented
140#2615C2×C511yescharacteristic
141#2077C2×C511yescharacteristic, complemented
142#2076C2×C511yescharacteristic, complemented
143#2075C2×C511yescharacteristic, complemented
144#2036C2×C511yescharacteristic, complemented
145#2036C2×C511yescharacteristic, complemented
146#2035C2×C511yescharacteristic, complemented
147#2034C2×C511yescharacteristic, complemented
148#2033C2×C511yescharacteristic, complemented
149#2033C2×C511yescharacteristic, complemented
150#2000C2×C511yescharacteristic, complemented
151#2000C2×C511yescharacteristic, complemented
152#2000C2×C511yescharacteristic, complemented
153#1780C2×C511yescharacteristic, complemented
154C24×C5—21no—
155C24×C5C2×D411yescharacteristic
156C24×C5C2×D411yescharacteristic
157C24×C5C2×D411yescharacteristic
158C5×#41—44no—
159C5×#41—44no—
160C5×#41—44no—
161C5×#41—44no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8—21no—
168C2×C5×Q8—41no—
169C2×C5×Q8—41no—
170C2×C5×Q8—41no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—21no—
176C2×C5×D4—21no—
177C2×C5×D4—41no—
178C2×C5×D4—41no—
179C2×C5×D4—41no—
180C2×C5×D4—41no—
181C2×C5×D4—41no—
182C2×C5×D4—41no—
183C2×C5×D4—41no—
184C2×C5×D4—41no—
185C2×C5×D4—41no—
186C2×C5×D4—42no—
187C2×C5×D4—42no—
188C2×C5×D4—42no—
189C2×C5×D4—81no—
190C2×C5×D4—81no—
191C2×C5×D4—81no—
192C2×C5×D4—81no—
193C2×C5×D4—81no—
194C2×C5×D4—81no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
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×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2411yescharacteristic
224C5×SD16—44no—
225C2×C5×C8—21no—
226C2×C5×C8—21no—
227C2×C5×C8—21no—
228C2×C5×C8—21no—
229C2×C5×C8—21no—
230C2×C5×C8—21no—
231C2×C5×C8—21no—
232C2×C5×C8—21no—
233C2×C5×C8—21no—
234C2×C5×C8—21no—
235C2×C5×C8—21no—
236C2×C5×C8—21no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4—21no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—21no—
245C5×C4⋊C4—21no—
246C5×C4⋊C4—21no—
247C5×C4⋊C4—21no—
248C5×C4⋊C4—21no—
249C5×C4⋊C4—42no—
250C5×C4⋊C4—42no—
251C5×C4⋊C4—42no—
252C5×C22⋊C4—42no—
253C5×C22⋊C4—42no—
254C5×C22⋊C4—42no—
255C5×C22⋊C4—42no—
256C5×C22⋊C4—42no—
257C5×C22⋊C4—42no—
258C5×C22⋊C4—81no—
259C5×C22⋊C4—81no—
260C5×C22⋊C4—81no—
261C5×C22⋊C4—81no—
262C5×C22⋊C4—81no—
263C5×C22⋊C4—81no—
264C22×#41C22×C511yescharacteristic
265C22×SD16C22×C511yescharacteristic
266C2×C22⋊Q8C22×C511yescharacteristic
267C2×C22⋊Q8C22×C511yescharacteristic
268C2×C22⋊Q8C22×C511yescharacteristic
269C2×#121C22×C511yescharacteristic
270C2×#121C22×C511yescharacteristic
271C2×#121C22×C511yescharacteristic
272C2×#107C22×C511yescharacteristic
273C2×#107C22×C511yescharacteristic
274C2×#106C22×C511yescharacteristic
275C2×#103C22×C511yescharacteristic
276C2×#103C22×C511yescharacteristic
277C2×#103C22×C511yescharacteristic
278C2×#102C22×C511yescharacteristic
279C2×#102C22×C511yescharacteristic
280C2×#102C22×C511yescharacteristic
281C2×C22⋊C8C22×C511yescharacteristic
282C2×C22⋊C8C22×C511yescharacteristic
283C2×C22⋊C8C22×C511yescharacteristic
284C2×C22⋊C8C22×C511yescharacteristic
285C2×C22⋊C8C22×C511yescharacteristic
286C2×C22⋊C8C22×C511yescharacteristic
287#395—21no—
288#394—21no—
289#394—21no—
290#394—21no—
291#393—21no—
292#392—21no—
293#392—21no—
294#392—21no—
295#380C22×C511yescharacteristic
296#380C22×C511yescharacteristic
297#380C22×C511yescharacteristic
298#380C22×C511yescharacteristic
299#380C22×C511yescharacteristic
300#380C22×C511yescharacteristic
301#340C22×C511yescharacteristic
302#340C22×C511yescharacteristic
303#340C22×C511yescharacteristic
304#340C22×C511yescharacteristic
305#340C22×C511yescharacteristic
306#340C22×C511yescharacteristic
307C23×C5—21no—
308C23×C5—21no—
309C23×C5—21no—
310C23×C5—21no—
311C23×C5—21no—
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
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—41no—
329C23×C5—41no—
330C23×C5—41no—
331C23×C5—41no—
332C23×C5—41no—
333C23×C5—41no—
334C23×C5—41no—
335C23×C5C22×D411yescharacteristic
336C5×Q8—44no—
337C5×Q8—41no—
338C5×Q8—41no—
339C5×Q8—41no—
340C5×Q8—41no—
341C5×D4—44no—
342C5×D4—44no—
343C5×D4—44no—
344C5×D4—41no—
345C5×D4—41no—
346C5×D4—41no—
347C5×D4—41no—
348C5×D4—84no—
349C5×D4—84no—
350C5×D4—84no—
351C2×C4×C5—21no—
352C2×C4×C5—21no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—21no—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—21no—
359C2×C4×C5—21no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5—41no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
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×C5H(5,𝔽2)11yescharacteristic
394C2×C4×C5H(5,𝔽2)11yescharacteristic
395C2×C4×C5H(5,𝔽2)11yescharacteristic
396C2×C4×C5H(5,𝔽2)11yescharacteristic
397C2×C4×C5H(5,𝔽2)11yescharacteristic
398C2×C4×C5H(5,𝔽2)11yescharacteristic
399C5×C8—41no—
400C5×C8—41no—
401C5×C8—41no—
402C5×C8—41no—
403C2×#41—41no—
404C2×#41—41no—
405C2×#41—41no—
406C2×#41—41no—
407C2×#41—41no—
408C2×#41—41no—
409C22×Q8C5×D411yescharacteristic
410C22×Q8C23×C511yescharacteristic
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4C5×D411yescharacteristic
415C22×D4C5×D411yescharacteristic
416C22×D4C5×D411yescharacteristic
417C22×D4C23×C511yescharacteristic
418C23×C4C23×C511yescharacteristic
419C23×C4C23×C511yescharacteristic
420C23×C4C23×C511yescharacteristic
421C2×SD16—41no—
422C2×SD16—41no—
423C2×SD16—41no—
424C22×C8C23×C511yescharacteristic
425C22×C8C23×C511yescharacteristic
426C22×C8C23×C511yescharacteristic
427C22×C8C23×C511yescharacteristic
428C22⋊Q8—41no—
429C22⋊Q8—41no—
430C22⋊Q8—41no—
431C22⋊Q8—41no—
432C22⋊Q8—41no—
433C22⋊Q8—41no—
434#121—41no—
435#121—41no—
436#121—41no—
437#121—41no—
438#121—41no—
439#121—41no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4C23×C511yescharacteristic
444C2×C4⋊C4C23×C511yescharacteristic
445C2×C4⋊C4C23×C511yescharacteristic
446C2×C4⋊C4C23×C511yescharacteristic
447C2×C4⋊C4C23×C511yescharacteristic
448C2×C4⋊C4C23×C511yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461#107—41no—
462#107—41no—
463#106—41no—
464#103—41no—
465#103—41no—
466#103—41no—
467#102—41no—
468#102—41no—
469#102—41no—
470C22⋊C8—41no—
471C22⋊C8—41no—
472C22⋊C8—41no—
473C22⋊C8—41no—
474C22⋊C8—41no—
475C22⋊C8—41no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482C22×C5—41no—
483C22×C5—41no—
484C22×C5—41no—
485C22×C5—41no—
486C22×C5—41no—
487C22×C5—41no—
488C22×C5—41no—
489C22×C5—41no—
490C22×C5—41no—
491C22×C5—41no—
492C22×C5—41no—
493C22×C5—41no—
494C22×C5—41no—
495C22×C5—41no—
496C22×C5—41no—
497C22×C5—41no—
498C22×C5—41no—
499C22×C5—41no—
500C22×C5—41no—
501C22×C5—41no—
502C22×C5—41no—
503C22×C5—81no—
504C22×C5—81no—
505C22×C5—81no—
506C22×C5—81no—
507C22×C5—81no—
508C22×C5—81no—
509C22×C5—81no—
510C22×C5#53411yescharacteristic
511C22×C5#53411yescharacteristic
512C22×C5#53411yescharacteristic
513C22×C5#57611yescharacteristic
514C22×C5#57711yescharacteristic
515C22×C5#57711yescharacteristic
516C22×C5#57811yescharacteristic
517C4×C5—41no—
518C4×C5—41no—
519C4×C5—41no—
520C4×C5—81no—
521C4×C5—81no—
522C4×C5—81no—
523C4×C5—81no—
524C4×C5—81no—
525C4×C5—81no—
526C4×C5—81no—
527C4×C5#56011yescharacteristic
528C4×C5#56011yescharacteristic
529C4×C5#56011yescharacteristic
530C4×C5H(3,𝔽4)11yescharacteristic
531C24—21no—
532C24C2×C5×D411yescharacteristic
533C24C2×C5×D411yescharacteristic
534C24C2×C5×D411yescharacteristic
535#41—44no—
536#41—44no—
537#41—44no—
538#41—44no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
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×C4C2×C5×D411yescharacteristic
598C22×C4C2×C5×D411yescharacteristic
599C22×C4C2×C5×D411yescharacteristic
600C22×C4C24×C511yescharacteristic
601SD16—44no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C2×C5—81no—
642C2×C5—81no—
643C2×C5—81no—
644C2×C5—161no—
645C2×C5#281211yescharacteristic
646C2×C5#319811yescharacteristic
647C2×C5#319811yescharacteristic
648C2×C5#320011yescharacteristic
649C2×C5#320111yescharacteristic
650C2×C5#320111yescharacteristic
651C2×C5#320311yescharacteristic
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23C22×C5×D411yescharacteristic
681Q8—44no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686D4—44no—
687D4—44no—
688D4—44no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694D4—84no—
695D4—84no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
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×C4C5×H(5,𝔽2)11yescharacteristic
739C2×C4C5×H(5,𝔽2)11yescharacteristic
740C2×C4C5×H(5,𝔽2)11yescharacteristic
741C2×C4C5×H(5,𝔽2)11yescharacteristic
742C2×C4C5×H(5,𝔽2)11yescharacteristic
743C2×C4C5×H(5,𝔽2)11yescharacteristic
744C8—41no—
745C8—41no—
746C8—41no—
747C8—41no—
748C5#3271311yescharacteristic, direct product factor, Sylow
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C5×#53411yescharacteristic
778C22C5×#53411yescharacteristic
779C22C5×#53411yescharacteristic
780C22C5×#57611yescharacteristic
781C22C5×#57711yescharacteristic
782C22C5×#57711yescharacteristic
783C22C5×#57811yescharacteristic
784C4—41no—
785C4—41no—
786C4—41no—
787C4—81no—
788C4—81no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4C5×#56011yescharacteristic
795C4C5×#56011yescharacteristic
796C4C5×#56011yescharacteristic
797C4C5×H(3,𝔽4)11yescharacteristic
798C2—81no—
799C2—81no—
800C2—81no—
801C2—161no—
802C2C5×#281211yescharacteristic
803C2C5×#319811yescharacteristic
804C2C5×#319811yescharacteristic
805C2C5×#320011yescharacteristic
806C2C5×#320111yescharacteristic
807C2C5×#320111yescharacteristic
808C2C5×#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. C5×#2616C2semidirect
3. C5×#2077C2semidirect
4. C5×#2076C2semidirect
5. C5×#2075C2semidirect
6. C5×#2036C2semidirect
7. C5×#2036C2semidirect
8. C5×#2035C2semidirect
9. C5×#2034C2semidirect
10. C5×#2033C2semidirect
11. C5×#2033C2semidirect
12. C5×#2000C2semidirect
13. C5×#2000C2semidirect
14. C5×#2000C2semidirect
15. C5×#1780C2semidirect
59. #32713C5direct (N × H)
139. #2616C2×C5semidirect
141. #2077C2×C5semidirect
142. #2076C2×C5semidirect
143. #2075C2×C5semidirect
144. #2036C2×C5semidirect
145. #2036C2×C5semidirect
146. #2035C2×C5semidirect
147. #2034C2×C5semidirect
148. #2033C2×C5semidirect
149. #2033C2×C5semidirect
150. #2000C2×C5semidirect
151. #2000C2×C5semidirect
152. #2000C2×C5semidirect
153. #1780C2×C5semidirect
748. C5#32713direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26162
C5×#26152
C5×#20772
C5×#20762
C5×#20752
C5×#20362
C5×#20352
C5×#20342
C5×#20332
C5×#20002
C5×#17802
#327135