Finite Group Databasebeta

← C5×#26202 #11948922

Subgroups — C5×#26202 #11948922

Order 1280.

944 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2416C211yesmaximal, characteristic
2C5×D4×C4⋊C4C211yesmaximal, characteristic, complemented
3C5×#2100C211yesmaximal, characteristic, complemented
4C5×#2077C211yesmaximal, characteristic, complemented
5C5×#2071C211yesmaximal, characteristic, complemented
6C5×#2034C211yesmaximal, characteristic, complemented
7C5×#1926C211yesmaximal, characteristic, complemented
8C5×#1919C211yesmaximal, characteristic, complemented
9C5×#1893C211yesmaximal, characteristic, complemented
10C5×#1874C211yesmaximal, characteristic, complemented
11C5×#1874C211yesmaximal, characteristic, complemented
12C5×#1869C211yesmaximal, characteristic, complemented
13C5×#1853C211yesmaximal, characteristic, complemented
14C5×#1824C211yesmaximal, characteristic, complemented
15C2×C5×#340C211yesmaximal, characteristic, complemented
16C23×C5×C8C2211yescharacteristic
17C2×C5×#121—21no—
18C2×C5×#121C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C4×C5×D4—21no—
21C2×C4×C5×D4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C2×C5×#106C2211yescharacteristic
26C2×C5×#106C2211yescharacteristic
27C2×C5×#102C2211yescharacteristic
28C2×C5×#102C2211yescharacteristic
29C2×C5×#102C2211yescharacteristic
30C2×C5×#102C2211yescharacteristic
31C2×C5×C22⋊C8C2211yescharacteristic
32C2×C5×C22⋊C8C2211yescharacteristic
33C2×C5×C22⋊C8C2211yescharacteristic
34C5×#396—21no—
35C5×#394—21no—
36C5×#390C2211yescharacteristic
37C5×#389—21no—
38C5×#389C2211yescharacteristic
39C5×#386—21no—
40C5×#385—21no—
41C5×#385—21no—
42C5×#384C2211yescharacteristic
43C5×#380C2211yescharacteristic
44C5×#380C2211yescharacteristic
45C5×#380C2211yescharacteristic
46C4×C5×C4⋊C4C2211yescharacteristic
47C5×#340C2211yescharacteristic
48C5×#340C2211yescharacteristic
49C5×#340C2211yescharacteristic
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#336C2211yescharacteristic
58C5×#336C2211yescharacteristic
59#26202C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×D4—21no—
61C22×C5×D4—21no—
62C22×C5×D4D411yescharacteristic
63C22×C5×D4C2311yescharacteristic
64C23×C4×C5—21no—
65C23×C4×C5—21no—
66C23×C4×C5—21no—
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C22×C5×C8—22no—
70C22×C5×C8—41no—
71C22×C5×C8—41no—
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C5×#121—22no—
77C5×#121—22no—
78C5×#121—22no—
79C5×#121—41no—
80C5×#121—44no—
81C4×C5×D4—22no—
82C4×C5×D4—22no—
83C4×C5×D4—44no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4—41no—
94C2×C5×C4⋊C4—41no—
95C2×C5×C4⋊C4—41no—
96C2×C5×C4⋊C4D411yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
111C2×C5×C22⋊C4D411yescharacteristic
112C2×C5×C22⋊C4D411yescharacteristic
113C2×C42×C5—21no—
114C2×C42×C5C2311yescharacteristic
115C5×#106—22no—
116C5×#106—41no—
117C5×#102—22no—
118C5×#102—41no—
119C5×#102—41no—
120C5×#102—41no—
121C5×C22⋊C8—22no—
122C5×C22⋊C8—41no—
123C5×C22⋊C8—41no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129#2416C2×C511yescharacteristic
130D4×C4⋊C4C2×C511yescharacteristic, complemented
131#2100C2×C511yescharacteristic, complemented
132#2077C2×C511yescharacteristic, complemented
133#2071C2×C511yescharacteristic, complemented
134#2034C2×C511yescharacteristic, complemented
135#1926C2×C511yescharacteristic, complemented
136#1919C2×C511yescharacteristic, complemented
137#1893C2×C511yescharacteristic, complemented
138#1874C2×C511yescharacteristic, complemented
139#1874C2×C511yescharacteristic, complemented
140#1869C2×C511yescharacteristic, complemented
141#1853C2×C511yescharacteristic, complemented
142#1824C2×C511yescharacteristic, complemented
143C2×#340C2×C511yescharacteristic, complemented
144C24×C5—21no—
145C24×C5C2×D411yescharacteristic
146C24×C5C2×D411yescharacteristic
147C2×C5×D4—22no—
148C2×C5×D4—22no—
149C2×C5×D4—21no—
150C2×C5×D4—21no—
151C2×C5×D4—21no—
152C2×C5×D4—21no—
153C2×C5×D4—21no—
154C2×C5×D4—21no—
155C2×C5×D4—42no—
156C2×C5×D4—42no—
157C2×C5×D4—42no—
158C2×C5×D4—42no—
159C2×C5×D4—42no—
160C2×C5×D4—81no—
161C2×C5×D4SD1614yes—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—42no—
180C22×C4×C5—42no—
181C22×C4×C5—42no—
182C22×C4×C5—42no—
183C22×C4×C5—42no—
184C22×C4×C5—42no—
185C22×C4×C5—81no—
186C22×C4×C5—81no—
187C22×C4×C5—81no—
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5#4112yes—
193C22×C4×C5#4112yes—
194C22×C4×C5C2411yescharacteristic
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—
207C2×C5×C8—44no—
208C5×C4⋊C4—22no—
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—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—42no—
222C5×C4⋊C4—42no—
223C5×C4⋊C4—42no—
224C5×C4⋊C4—42no—
225C5×C4⋊C4—42no—
226C5×C4⋊C4—81no—
227C5×C4⋊C4#4112yes—
228C5×C4⋊C4#4112yes—
229C5×C22⋊C4—22no—
230C5×C22⋊C4—22no—
231C5×C22⋊C4—42no—
232C5×C22⋊C4—42no—
233C5×C22⋊C4—42no—
234C5×C22⋊C4—42no—
235C5×C22⋊C4—42no—
236C5×C22⋊C4—42no—
237C5×C22⋊C4—81no—
238C42×C5—21no—
239C42×C5—21no—
240C42×C5—42no—
241C23×C8C22×C511yescharacteristic
242C2×#121—21no—
243C2×#121C22×C511yescharacteristic
244C2×#121C22×C511yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4C22×C511yescharacteristic
247C22×C4⋊C4C22×C511yescharacteristic
248C22×C4⋊C4C22×C511yescharacteristic
249C22×C4⋊C4C22×C511yescharacteristic
250C2×#106C22×C511yescharacteristic
251C2×#106C22×C511yescharacteristic
252C2×#102C22×C511yescharacteristic
253C2×#102C22×C511yescharacteristic
254C2×#102C22×C511yescharacteristic
255C2×#102C22×C511yescharacteristic
256C2×C22⋊C8C22×C511yescharacteristic
257C2×C22⋊C8C22×C511yescharacteristic
258C2×C22⋊C8C22×C511yescharacteristic
259#396—21no—
260#394—21no—
261#390C22×C511yescharacteristic
262#389—21no—
263#389C22×C511yescharacteristic
264#386—21no—
265#385—21no—
266#385—21no—
267#384C22×C511yescharacteristic
268#380C22×C511yescharacteristic
269#380C22×C511yescharacteristic
270#380C22×C511yescharacteristic
271C4×C4⋊C4C22×C511yescharacteristic
272#340C22×C511yescharacteristic
273#340C22×C511yescharacteristic
274#340C22×C511yescharacteristic
275#340C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#340C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#340C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#336C22×C511yescharacteristic
283#336C22×C511yescharacteristic
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—41no—
295C23×C5—41no—
296C23×C5—41no—
297C23×C5—41no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5#12312yes—
302C23×C5C2×SD1612yes—
303C23×C5C2×SD1612yes—
304C23×C5AGL(1,ℤ/8)12yes—
305C23×C5C22×D411yescharacteristic
306C5×D4—28no—
307C5×D4—41no—
308C5×D4—41no—
309C5×D4—41no—
310C5×D4—41no—
311C5×D4—84no—
312C5×D4—84no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
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—84no—
353C2×C4×C5—84no—
354C2×C4×C5—84no—
355C2×C4×C5#12312yes—
356C2×C4×C5C2×SD1612yes—
357C2×C4×C5C2×#4111yescharacteristic
358C2×C4×C5C2×#4111yescharacteristic
359C2×C4×C5C2×#4111yescharacteristic
360C2×C4×C5C2×#4111yescharacteristic
361C2×C4×C5H(5,𝔽2)11yescharacteristic
362C2×C4×C5H(5,𝔽2)11yescharacteristic
363C5×C8—41no—
364C5×C8—41no—
365C5×C8—41no—
366C5×C8—41no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4C5×D411yescharacteristic
370C22×D4C23×C511yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4C23×C511yescharacteristic
375C23×C4C23×C511yescharacteristic
376C22×C8—22no—
377C22×C8—41no—
378C22×C8—41no—
379C22×C8C23×C511yescharacteristic
380C22×C8C23×C511yescharacteristic
381C22×C8C23×C511yescharacteristic
382C22×C8C23×C511yescharacteristic
383#121—22no—
384#121—22no—
385#121—22no—
386#121—41no—
387#121—44no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—44no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—41no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4C5×D411yescharacteristic
404C2×C4⋊C4C23×C511yescharacteristic
405C2×C4⋊C4C23×C511yescharacteristic
406C2×C4⋊C4C23×C511yescharacteristic
407C2×C4⋊C4C23×C511yescharacteristic
408C2×C4⋊C4C23×C511yescharacteristic
409C2×C4⋊C4C23×C511yescharacteristic
410C2×C4⋊C4C23×C511yescharacteristic
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×C42—21no—
421C2×C42C23×C511yescharacteristic
422#106—22no—
423#106—41no—
424#102—22no—
425#102—41no—
426#102—41no—
427#102—41no—
428C22⋊C8—22no—
429C22⋊C8—41no—
430C22⋊C8—41no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436C22×C5—22no—
437C22×C5—22no—
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—22no—
443C22×C5—22no—
444C22×C5—22no—
445C22×C5—41no—
446C22×C5—41no—
447C22×C5—41no—
448C22×C5—41no—
449C22×C5—81no—
450C22×C5—81no—
451C22×C5—81no—
452C22×C5—81no—
453C22×C5—81no—
454C22×C5—81no—
455C22×C5—81no—
456C22×C5#48114yes—
457C22×C5C2×#12311yescharacteristic
458C22×C5#54611yescharacteristic
459C22×C5#54611yescharacteristic
460C22×C5C22×SD1611yescharacteristic
461C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
462C22×C5#57611yescharacteristic
463C22×C5#57811yescharacteristic
464C4×C5—22no—
465C4×C5—22no—
466C4×C5—41no—
467C4×C5—41no—
468C4×C5—42no—
469C4×C5—42no—
470C4×C5—81no—
471C4×C5—81no—
472C4×C5—81no—
473C4×C5—81no—
474C4×C5—81no—
475C4×C5#52911yescharacteristic
476C4×C5#53811yescharacteristic
477C4×C5#55311yescharacteristic
478C4×C5#55311yescharacteristic
479C24—21no—
480C24C2×C5×D411yescharacteristic
481C24C2×C5×D411yescharacteristic
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—81no—
496C2×D4C5×SD1614yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C2×C5×D411yescharacteristic
525C22×C4C2×C5×D411yescharacteristic
526C22×C4C2×C5×D411yescharacteristic
527C22×C4C5×#4112yes—
528C22×C4C5×#4112yes—
529C22×C4C24×C511yescharacteristic
530C2×C8—21no—
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—44no—
543C4⋊C4—22no—
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—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—81no—
562C4⋊C4C5×#4112yes—
563C4⋊C4C5×#4112yes—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C42—21no—
574C42—21no—
575C42—42no—
576C2×C5—24no—
577C2×C5—42no—
578C2×C5—161no—
579C2×C5#244411yescharacteristic
580C2×C5C2×#48111yescharacteristic
581C2×C5#309811yescharacteristic
582C2×C5#329511yescharacteristic
583C2×C5#329811yescharacteristic
584C2×C5#330811yescharacteristic
585C2×C5#331811yescharacteristic
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23C5×#12312yes—
604C23C2×C5×SD1612yes—
605C23C2×C5×SD1612yes—
606C23C5×AGL(1,ℤ/8)12yes—
607C23C22×C5×D411yescharacteristic
608D4—28no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—84no—
614D4—84no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
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—84no—
655C2×C4—84no—
656C2×C4—84no—
657C2×C4C5×#12312yes—
658C2×C4C2×C5×SD1612yes—
659C2×C4C2×C5×#4111yescharacteristic
660C2×C4C2×C5×#4111yescharacteristic
661C2×C4C2×C5×#4111yescharacteristic
662C2×C4C2×C5×#4111yescharacteristic
663C2×C4C5×H(5,𝔽2)11yescharacteristic
664C2×C4C5×H(5,𝔽2)11yescharacteristic
665C8—41no—
666C8—41no—
667C8—41no—
668C8—41no—
669C5#2620211yescharacteristic, direct product factor, Sylow
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22C5×#48114yes—
691C22C2×C5×#12311yescharacteristic
692C22C5×#54611yescharacteristic
693C22C5×#54611yescharacteristic
694C22C22×C5×SD1611yescharacteristic
695C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
696C22C5×#57611yescharacteristic
697C22C5×#57811yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—41no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4C5×#52911yescharacteristic
710C4C5×#53811yescharacteristic
711C4C5×#55311yescharacteristic
712C4C5×#55311yescharacteristic
713C2—24no—
714C2—42no—
715C2—161no—
716C2C5×#244411yescharacteristic
717C2C2×C5×#48111yescharacteristic
718C2C5×#309811yescharacteristic
719C2C5×#329511yescharacteristic
720C2C5×#329811yescharacteristic
721C2C5×#330811yescharacteristic
722C2C5×#331811yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×D4×C4⋊C4C2semidirect
3. C5×#2100C2semidirect
4. C5×#2077C2semidirect
5. C5×#2071C2semidirect
6. C5×#2034C2semidirect
7. C5×#1926C2semidirect
8. C5×#1919C2semidirect
9. C5×#1893C2semidirect
10. C5×#1874C2semidirect
11. C5×#1874C2semidirect
12. C5×#1869C2semidirect
13. C5×#1853C2semidirect
14. C5×#1824C2semidirect
15. C2×C5×#340C2semidirect
59. #26202C5direct (N × H)
130. D4×C4⋊C4C2×C5semidirect
131. #2100C2×C5semidirect
132. #2077C2×C5semidirect
133. #2071C2×C5semidirect
134. #2034C2×C5semidirect
135. #1926C2×C5semidirect
136. #1919C2×C5semidirect
137. #1893C2×C5semidirect
138. #1874C2×C5semidirect
139. #1874C2×C5semidirect
140. #1869C2×C5semidirect
141. #1853C2×C5semidirect
142. #1824C2×C5semidirect
143. C2×#340C2×C5semidirect
669. C5#26202direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#24162
C5×D4×C4⋊C42
C5×#21002
C5×#20772
C5×#20712
C5×#20342
C5×#19262
C5×#19192
C5×#18932
C5×#18742
C5×#18692
C5×#18532
C5×#18242
C2×C5×#3402
#262025