Finite Group Databasebeta

← C5×#32735 #11955455

Subgroups — C5×#32735 #11955455

Order 1280.

766 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2624C211yesmaximal, characteristic, complemented
2C5×#2620C211yesmaximal, characteristic, complemented
3C5×#2100C211yesmaximal, characteristic, complemented
4C5×#2093C211yesmaximal, characteristic, complemented
5C5×#2068C211yesmaximal, characteristic, complemented
6C5×#2067C211yesmaximal, characteristic, complemented
7C5×#2055C211yesmaximal, characteristic, complemented
8C5×#2054C211yesmaximal, characteristic, complemented
9C5×#2042C211yesmaximal, characteristic, complemented
10C5×#2036C211yesmaximal, characteristic, complemented
11C5×#2033C211yesmaximal, characteristic, complemented
12C5×#2012C211yesmaximal, characteristic, complemented
13C5×#2000C211yesmaximal, characteristic, complemented
14C5×#1999C211yesmaximal, characteristic
15C5×#1798C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C22×C5×D8C2211yescharacteristic
18C2×C5×#124C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×#121C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C2×C5×#107C2211yescharacteristic
24C2×C5×#107C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C2×C5×C4⋊C8C2211yescharacteristic
27C2×C5×#103C2211yescharacteristic
28C2×C5×#103C2211yescharacteristic
29C2×C5×#103C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×C22⋊C8C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C5×#399—21no—
38C5×#397—21no—
39C5×#396—21no—
40C5×#396—21no—
41C5×#394—21no—
42C5×#394—21no—
43C5×#394—21no—
44C5×#394—21no—
45C5×#391C2211yescharacteristic
46C5×#390C2211yescharacteristic
47C5×#390C2211yescharacteristic
48C5×#390C2211yescharacteristic
49C5×#389C2211yescharacteristic
50C5×#389C2211yescharacteristic
51C5×#384C2211yescharacteristic
52C5×#380C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#32735C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8C2311yescharacteristic
61C22×C5×D4—21no—
62C22×C5×D4—21no—
63C22×C5×D4C2311yescharacteristic
64C22×C5×D4C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C2×C5×SD16—41no—
67C2×C5×SD16—41no—
68C2×C5×SD16—41no—
69C2×C5×D8—41no—
70C2×C5×D8—41no—
71C2×C5×D8—41no—
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C5×#124—41no—
77C5×#124—41no—
78C5×C22⋊Q8—41no—
79C5×C22⋊Q8—41no—
80C5×#121—41no—
81C5×#121—41no—
82C5×#121—41no—
83C5×#121—41no—
84C5×#117—41no—
85C5×#117—41no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4D411yescharacteristic
92C2×C5×C4⋊C4D411yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4—21no—
110C2×C5×C22⋊C4D411yescharacteristic
111C2×C5×C22⋊C4D411yescharacteristic
112C2×C42×C5C2311yescharacteristic
113C2×C42×C5C2311yescharacteristic
114C5×#107—41no—
115C5×#107—41no—
116C5×C4⋊C8—41no—
117C5×C4⋊C8—41no—
118C5×#103—41no—
119C5×#103—41no—
120C5×#103—41no—
121C5×#102—41no—
122C5×#102—41no—
123C5×#102—41no—
124C5×#102—41no—
125C5×#102—41no—
126C5×C22⋊C8—41no—
127C5×C22⋊C8—41no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133#2624C2×C511yescharacteristic, complemented
134#2620C2×C511yescharacteristic, complemented
135#2100C2×C511yescharacteristic, complemented
136#2093C2×C511yescharacteristic, complemented
137#2068C2×C511yescharacteristic, complemented
138#2067C2×C511yescharacteristic, complemented
139#2055C2×C511yescharacteristic, complemented
140#2054C2×C511yescharacteristic, complemented
141#2042C2×C511yescharacteristic, complemented
142#2036C2×C511yescharacteristic, complemented
143#2033C2×C511yescharacteristic, complemented
144#2012C2×C511yescharacteristic, complemented
145#2000C2×C511yescharacteristic, complemented
146#1999C2×C511yescharacteristic
147#1798C2×C511yescharacteristic, complemented
148C24×C5—21no—
149C24×C5—21no—
150C24×C5C2×D411yescharacteristic
151C2×C5×Q8—21no—
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—21no—
161C2×C5×D4—21no—
162C2×C5×D4—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—42no—
170C2×C5×D4—42no—
171C2×C5×D4—81no—
172C2×C5×D4—81no—
173C2×C5×D4—81no—
174C2×C5×D4—81no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2411yescharacteristic
193C5×SD16—44no—
194C5×D8—44no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8—21no—
199C2×C5×C8—21no—
200C2×C5×C8—21no—
201C2×C5×C8—21no—
202C2×C5×C8—21no—
203C2×C5×C8—21no—
204C2×C5×C8—21no—
205C2×C5×C8—21no—
206C2×C5×C8—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—41no—
218C5×C4⋊C4—41no—
219C5×C4⋊C4—42no—
220C5×C4⋊C4—81no—
221C5×C4⋊C4—81no—
222C5×C4⋊C4—81no—
223C5×C4⋊C4—81no—
224C5×C22⋊C4—41no—
225C5×C22⋊C4—41no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—42no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—42no—
231C5×C22⋊C4—81no—
232C5×C22⋊C4—81no—
233C5×C22⋊C4—81no—
234C5×C22⋊C4—81no—
235C5×C22⋊C4—81no—
236C5×C22⋊C4—81no—
237C5×C22⋊C4—81no—
238C42×C5—21no—
239C42×C5—21no—
240C42×C5—21no—
241C42×C5—21no—
242C22×SD16C22×C511yescharacteristic
243C22×D8C22×C511yescharacteristic
244C2×#124C22×C511yescharacteristic
245C2×C22⋊Q8C22×C511yescharacteristic
246C2×#121C22×C511yescharacteristic
247C2×#121C22×C511yescharacteristic
248C2×#117C22×C511yescharacteristic
249C2×#107C22×C511yescharacteristic
250C2×#107C22×C511yescharacteristic
251C2×C4⋊C8C22×C511yescharacteristic
252C2×C4⋊C8C22×C511yescharacteristic
253C2×#103C22×C511yescharacteristic
254C2×#103C22×C511yescharacteristic
255C2×#103C22×C511yescharacteristic
256C2×#102C22×C511yescharacteristic
257C2×#102C22×C511yescharacteristic
258C2×#102C22×C511yescharacteristic
259C2×#102C22×C511yescharacteristic
260C2×#102C22×C511yescharacteristic
261C2×C22⋊C8C22×C511yescharacteristic
262C2×C22⋊C8C22×C511yescharacteristic
263#399—21no—
264#397—21no—
265#396—21no—
266#396—21no—
267#394—21no—
268#394—21no—
269#394—21no—
270#394—21no—
271#391C22×C511yescharacteristic
272#390C22×C511yescharacteristic
273#390C22×C511yescharacteristic
274#390C22×C511yescharacteristic
275#389C22×C511yescharacteristic
276#389C22×C511yescharacteristic
277#384C22×C511yescharacteristic
278#380C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#340C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#336C22×C511yescharacteristic
284#336C22×C511yescharacteristic
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—41no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5C22×D411yescharacteristic
307C5×Q8—41no—
308C5×Q8—41no—
309C5×Q8—41no—
310C5×Q8—41no—
311C5×D4—41no—
312C5×D4—41no—
313C5×D4—41no—
314C5×D4—41no—
315C5×D4—41no—
316C5×D4—41no—
317C5×D4—41no—
318C5×D4—41no—
319C5×D4—84no—
320C5×D4—84no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5H(5,𝔽2)11yescharacteristic
359C2×C4×C5H(5,𝔽2)11yescharacteristic
360C2×C4×C5H(5,𝔽2)11yescharacteristic
361C2×C4×C5H(5,𝔽2)11yescharacteristic
362C2×C4×C5H(5,𝔽2)11yescharacteristic
363C2×C4×C52−1+411yescharacteristic
364C5×C8—41no—
365C5×C8—41no—
366C5×C8—41no—
367C5×C8—41no—
368C22×Q8C23×C511yescharacteristic
369C22×D4—21no—
370C22×D4—21no—
371C22×D4C23×C511yescharacteristic
372C22×D4C23×C511yescharacteristic
373C23×C4C23×C511yescharacteristic
374C2×SD16—41no—
375C2×SD16—41no—
376C2×SD16—41no—
377C2×D8—41no—
378C2×D8—41no—
379C2×D8—41no—
380C22×C8C23×C511yescharacteristic
381C22×C8C23×C511yescharacteristic
382C22×C8C23×C511yescharacteristic
383C22×C8C23×C511yescharacteristic
384#124—41no—
385#124—41no—
386C22⋊Q8—41no—
387C22⋊Q8—41no—
388#121—41no—
389#121—41no—
390#121—41no—
391#121—41no—
392#117—41no—
393#117—41no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4C5×D411yescharacteristic
400C2×C4⋊C4C5×D411yescharacteristic
401C2×C4⋊C4C23×C511yescharacteristic
402C2×C4⋊C4C23×C511yescharacteristic
403C2×C4⋊C4C23×C511yescharacteristic
404C2×C4⋊C4C23×C511yescharacteristic
405C2×C4⋊C4C23×C511yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4C5×D411yescharacteristic
419C2×C22⋊C4C5×D411yescharacteristic
420C2×C42C23×C511yescharacteristic
421C2×C42C23×C511yescharacteristic
422#107—41no—
423#107—41no—
424C4⋊C8—41no—
425C4⋊C8—41no—
426#103—41no—
427#103—41no—
428#103—41no—
429#102—41no—
430#102—41no—
431#102—41no—
432#102—41no—
433#102—41no—
434C22⋊C8—41no—
435C22⋊C8—41no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5—41no—
447C22×C5—41no—
448C22×C5—81no—
449C22×C5—81no—
450C22×C5—81no—
451C22×C5—81no—
452C22×C5—81no—
453C22×C5—81no—
454C22×C5—81no—
455C22×C5—81no—
456C22×C5—81no—
457C22×C5—81no—
458C22×C5—81no—
459C22×C5—81no—
460C22×C5—81no—
461C22×C5—81no—
462C22×C5#53411yescharacteristic
463C22×C5#53511yescharacteristic
464C22×C5#53711yescharacteristic
465C22×C5#57611yescharacteristic
466C22×C5#57611yescharacteristic
467C22×C5#57711yescharacteristic
468C22×C5#57811yescharacteristic
469C4×C5—41no—
470C4×C5—41no—
471C4×C5—41no—
472C4×C5—41no—
473C4×C5—41no—
474C4×C5—81no—
475C4×C5—81no—
476C4×C5—81no—
477C4×C5—81no—
478C4×C5—81no—
479C4×C5—81no—
480C4×C5#56011yescharacteristic
481C4×C5#56011yescharacteristic
482C4×C5#56211yescharacteristic
483C4×C5#56211yescharacteristic
484C24—21no—
485C24—21no—
486C24C2×C5×D411yescharacteristic
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4—81no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C2×C5×D411yescharacteristic
525C22×C4C2×C5×D411yescharacteristic
526C22×C4C2×C5×D411yescharacteristic
527C22×C4C2×C5×D411yescharacteristic
528C22×C4C24×C511yescharacteristic
529SD16—44no—
530D8—44no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—42no—
556C4⋊C4—81no—
557C4⋊C4—81no—
558C4⋊C4—81no—
559C4⋊C4—81no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C2×C5—81no—
579C2×C5—161no—
580C2×C5—161no—
581C2×C5#281311yescharacteristic
582C2×C5#319811yescharacteristic
583C2×C5#320311yescharacteristic
584C2×C5#322011yescharacteristic
585C2×C5#322511yescharacteristic
586C2×C5#325711yescharacteristic
587C2×C5#326211yescharacteristic
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23C22×C5×D411yescharacteristic
610Q8—41no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—84no—
623D4—84no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4C5×H(5,𝔽2)11yescharacteristic
662C2×C4C5×H(5,𝔽2)11yescharacteristic
663C2×C4C5×H(5,𝔽2)11yescharacteristic
664C2×C4C5×H(5,𝔽2)11yescharacteristic
665C2×C4C5×H(5,𝔽2)11yescharacteristic
666C2×C4C5×2−1+411yescharacteristic
667C8—41no—
668C8—41no—
669C8—41no—
670C8—41no—
671C5#3273511yescharacteristic, direct product factor, Sylow
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22C5×#53411yescharacteristic
694C22C5×#53511yescharacteristic
695C22C5×#53711yescharacteristic
696C22C5×#57611yescharacteristic
697C22C5×#57611yescharacteristic
698C22C5×#57711yescharacteristic
699C22C5×#57811yescharacteristic
700C4—41no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4C5×#56011yescharacteristic
712C4C5×#56011yescharacteristic
713C4C5×#56211yescharacteristic
714C4C5×#56211yescharacteristic
715C2—81no—
716C2—161no—
717C2—161no—
718C2C5×#281311yescharacteristic
719C2C5×#319811yescharacteristic
720C2C5×#320311yescharacteristic
721C2C5×#322011yescharacteristic
722C2C5×#322511yescharacteristic
723C2C5×#325711yescharacteristic
724C2C5×#326211yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C5×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2624C2semidirect
2. C5×#2620C2semidirect
3. C5×#2100C2semidirect
4. C5×#2093C2semidirect
5. C5×#2068C2semidirect
6. C5×#2067C2semidirect
7. C5×#2055C2semidirect
8. C5×#2054C2semidirect
9. C5×#2042C2semidirect
10. C5×#2036C2semidirect
11. C5×#2033C2semidirect
12. C5×#2012C2semidirect
13. C5×#2000C2semidirect
15. C5×#1798C2semidirect
59. #32735C5direct (N × H)
133. #2624C2×C5semidirect
134. #2620C2×C5semidirect
135. #2100C2×C5semidirect
136. #2093C2×C5semidirect
137. #2068C2×C5semidirect
138. #2067C2×C5semidirect
139. #2055C2×C5semidirect
140. #2054C2×C5semidirect
141. #2042C2×C5semidirect
142. #2036C2×C5semidirect
143. #2033C2×C5semidirect
144. #2012C2×C5semidirect
145. #2000C2×C5semidirect
147. #1798C2×C5semidirect
671. C5#32735direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#26242
C5×#26202
C5×#21002
C5×#20932
C5×#20682
C5×#20672
C5×#20552
C5×#20542
C5×#20422
C5×#20362
C5×#20332
C5×#20122
C5×#20002
C5×#19992
C5×#17982
#327355