Finite Group Databasebeta

← C5×#26146 #11948866

Subgroups — C5×#26146 #11948866

Order 1280.

954 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#481C211yesmaximal, characteristic, complemented
2C2×C5×#428C211yesmaximal, characteristic, complemented
3C5×#2414C211yesmaximal, characteristic
4C5×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C5×#2093C211yesmaximal, characteristic, complemented
6C5×#2084C211yesmaximal, characteristic, complemented
7C5×#2076C211yesmaximal, characteristic, complemented
8C5×#2034C211yesmaximal, characteristic, complemented
9C5×#1925C211yesmaximal, characteristic, complemented
10C5×#1920C211yesmaximal, characteristic, complemented
11C5×#1895C211yesmaximal, characteristic, complemented
12C5×#1874C211yesmaximal, characteristic, complemented
13C5×#1870C211yesmaximal, characteristic, complemented
14C5×#1854C211yesmaximal, characteristic, complemented
15C5×#1852C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C2×C5×#121C2211yescharacteristic
18C2×C5×#121C2211yescharacteristic
19C2×C4×C5×D4—21no—
20C2×C4×C5×D4C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C5×#481—24no—
25C5×#428—24no—
26C2×C5×#107C2211yescharacteristic
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×#106C2211yescharacteristic
31C2×C5×#106C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C2×C5×C22⋊C8C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C5×#394—21no—
40C5×#392—21no—
41C5×#390—21no—
42C5×#390C2211yescharacteristic
43C5×#389—21no—
44C5×#389C2211yescharacteristic
45C5×#388—21no—
46C5×#385—21no—
47C5×#385—21no—
48C5×#384C2211yescharacteristic
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52C4×C5×C4⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26146C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×D4—21no—
63C22×C5×D4—21no—
64C22×C5×D4D411yescharacteristic
65C22×C5×D4C2311yescharacteristic
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C2×C5×M16—22no—
71C2×C5×M16—22no—
72C2×C5×M16—22no—
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C5×#121—22no—
78C5×#121—22no—
79C5×#121—22no—
80C5×#121—41no—
81C4×C5×D4—22no—
82C4×C5×D4—22no—
83C4×C5×D4—44no—
84C5×#117—22no—
85C5×#117—41no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—22no—
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⋊C4D411yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
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×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⋊C4—21no—
111C2×C5×C22⋊C4D411yescharacteristic
112C2×C5×C22⋊C4D411yescharacteristic
113C2×C42×C5—21no—
114C2×C42×C5—21no—
115C2×C42×C5C2311yescharacteristic
116C5×#107—22no—
117C5×#107—22no—
118C5×#107—41no—
119C5×#106—22no—
120C5×#106—22no—
121C5×#106D414yescomplemented
122C5×#102—22no—
123C5×#102—22no—
124C5×#102—22no—
125C5×#102—41no—
126C5×C22⋊C8—22no—
127C5×C22⋊C8—22no—
128C5×C22⋊C8—22no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95—21no—
134C2×#481C2×C511yescharacteristic, complemented
135C2×#428C2×C511yescharacteristic, complemented
136#2414C2×C511yescharacteristic
137D4×C4⋊C4C2×C511yescharacteristic, complemented
138#2093C2×C511yescharacteristic, complemented
139#2084C2×C511yescharacteristic, complemented
140#2076C2×C511yescharacteristic, complemented
141#2034C2×C511yescharacteristic, complemented
142#1925C2×C511yescharacteristic, complemented
143#1920C2×C511yescharacteristic, complemented
144#1895C2×C511yescharacteristic, complemented
145#1874C2×C511yescharacteristic, complemented
146#1870C2×C511yescharacteristic, complemented
147#1854C2×C511yescharacteristic, complemented
148#1852C2×C511yescharacteristic, complemented
149C24×C5—21no—
150C24×C5C2×D411yescharacteristic
151C24×C5C2×D411yescharacteristic
152C2×C5×D4—22no—
153C2×C5×D4—22no—
154C2×C5×D4—22no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—21no—
161C2×C5×D4—42no—
162C2×C5×D4—42no—
163C2×C5×D4—42no—
164C2×C5×D4—81no—
165C2×C5×D4—81no—
166C2×C5×D4—81no—
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—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—42no—
185C22×C4×C5—42no—
186C22×C4×C5—42no—
187C22×C4×C5—42no—
188C22×C4×C5—81no—
189C22×C4×C5—81no—
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5#4112yes—
195C22×C4×C5#4112yes—
196C22×C4×C5C2411yescharacteristic
197C5×M16—28no—
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—21no—
208C2×C5×C8C2×D412yes—
209C2×C5×C8#4112yes—
210C5×C4⋊C4—22no—
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—21no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4—42no—
224C5×C4⋊C4—42no—
225C5×C4⋊C4—42no—
226C5×C4⋊C4—81no—
227C5×C4⋊C4—81no—
228C5×C4⋊C4C2×D412yes—
229C5×C4⋊C4C2×D412yes—
230C5×C22⋊C4—22no—
231C5×C22⋊C4—22no—
232C5×C22⋊C4—42no—
233C5×C22⋊C4—42no—
234C5×C22⋊C4—42no—
235C5×C22⋊C4—42no—
236C5×C22⋊C4—42no—
237C5×C22⋊C4—42no—
238C5×C22⋊C4—81no—
239C5×C22⋊C4—81no—
240C42×C5—21no—
241C42×C5—21no—
242C42×C5—42no—
243C42×C5—42no—
244C22×M16C22×C511yescharacteristic
245C2×#121C22×C511yescharacteristic
246C2×#121C22×C511yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C22×C511yescharacteristic
249C2×#117C22×C511yescharacteristic
250C22×C4⋊C4C22×C511yescharacteristic
251C22×C4⋊C4C22×C511yescharacteristic
252#481—24no—
253#428—24no—
254C2×#107C22×C511yescharacteristic
255C2×#107C22×C511yescharacteristic
256C2×#107C22×C511yescharacteristic
257C2×#106C22×C511yescharacteristic
258C2×#106C22×C511yescharacteristic
259C2×#106C22×C511yescharacteristic
260C2×#102C22×C511yescharacteristic
261C2×#102C22×C511yescharacteristic
262C2×#102C22×C511yescharacteristic
263C2×#102C22×C511yescharacteristic
264C2×C22⋊C8C22×C511yescharacteristic
265C2×C22⋊C8C22×C511yescharacteristic
266C2×C22⋊C8C22×C511yescharacteristic
267#394—21no—
268#392—21no—
269#390—21no—
270#390C22×C511yescharacteristic
271#389—21no—
272#389C22×C511yescharacteristic
273#388—21no—
274#385—21no—
275#385—21no—
276#384C22×C511yescharacteristic
277#380C22×C511yescharacteristic
278#380C22×C511yescharacteristic
279#380C22×C511yescharacteristic
280C4×C4⋊C4C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#340C22×C511yescharacteristic
287#336C22×C511yescharacteristic
288#336C22×C511yescharacteristic
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—21no—
295C23×C5—21no—
296C23×C5—21no—
297C23×C5—21no—
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5#12312yes—
309C23×C5#13712yes—
310C23×C5C22×D411yescharacteristic
311C5×D4—28no—
312C5×D4—41no—
313C5×D4—41no—
314C5×D4—41no—
315C5×D4—41no—
316C5×D4—84no—
317C5×D4—84no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—22no—
329C2×C4×C5—21no—
330C2×C4×C5—22no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
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—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—84no—
358C2×C4×C5—84no—
359C2×C4×C5#12312yes—
360C2×C4×C5AGL(1,ℤ/8)12yes—
361C2×C4×C5C22×D411yescharacteristic
362C2×C4×C5C2×#4111yescharacteristic
363C2×C4×C5C2×#4111yescharacteristic
364C2×C4×C5C2×#4111yescharacteristic
365C2×C4×C5H(5,𝔽2)11yescharacteristic
366C2×C4×C52−1+411yescharacteristic
367C5×C8—22no—
368C5×C8—22no—
369C5×C8—41no—
370C5×C8—41no—
371C22×D4—21no—
372C22×D4—21no—
373C22×D4C5×D411yescharacteristic
374C22×D4C23×C511yescharacteristic
375C23×C4—21no—
376C23×C4—21no—
377C23×C4C23×C511yescharacteristic
378C23×C4C23×C511yescharacteristic
379C2×M16—22no—
380C2×M16—22no—
381C2×M16—22no—
382C22×C8C23×C511yescharacteristic
383C22×C8C23×C511yescharacteristic
384C22×C8C23×C511yescharacteristic
385C22×C8C23×C511yescharacteristic
386#121—22no—
387#121—22no—
388#121—22no—
389#121—41no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—44no—
393#117—22no—
394#117—41no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—41no—
404C2×C4⋊C4C5×D411yescharacteristic
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×C4⋊C4C23×C511yescharacteristic
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⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4C5×D411yescharacteristic
421C2×C22⋊C4C5×D411yescharacteristic
422C2×C42—21no—
423C2×C42—21no—
424C2×C42C23×C511yescharacteristic
425#107—22no—
426#107—22no—
427#107—41no—
428#106—22no—
429#106—22no—
430#106C5×D414yescomplemented
431#102—22no—
432#102—22no—
433#102—22no—
434#102—41no—
435C22⋊C8—22no—
436C22⋊C8—22no—
437C22⋊C8—22no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443C22×C5—22no—
444C22×C5—22no—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—41no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5—41no—
454C22×C5—41no—
455C22×C5—41no—
456C22×C5—41no—
457C22×C5—81no—
458C22×C5—81no—
459C22×C5—81no—
460C22×C5—81no—
461C22×C5—81no—
462C22×C5—81no—
463C22×C5—81no—
464C22×C5C2×#12311yescharacteristic
465C22×C5D4211yescharacteristic
466C22×C5#54711yescharacteristic
467C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
468C22×C5C2×#13711yescharacteristic
469C22×C5#57611yescharacteristic
470C22×C5#57711yescharacteristic
471C4×C5—22no—
472C4×C5—22no—
473C4×C5—41no—
474C4×C5—41no—
475C4×C5—42no—
476C4×C5—42no—
477C4×C5—81no—
478C4×C5—81no—
479C4×C5—81no—
480C4×C5—81no—
481C4×C5—81no—
482C4×C5#52511yescharacteristic
483C4×C5#53911yescharacteristic
484C4×C5#54811yescharacteristic
485C4×C5#55311yescharacteristic
486C24—21no—
487C24C2×C5×D411yescharacteristic
488C24C2×C5×D411yescharacteristic
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—81no—
502C2×D4—81no—
503C2×D4—81no—
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—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4C2×C5×D411yescharacteristic
528C22×C4C2×C5×D411yescharacteristic
529C22×C4C2×C5×D411yescharacteristic
530C22×C4C2×C5×D411yescharacteristic
531C22×C4C5×#4112yes—
532C22×C4C5×#4112yes—
533C22×C4C24×C511yescharacteristic
534M16—28no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8C2×C5×D412yes—
546C2×C8C5×#4112yes—
547C4⋊C4—22no—
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—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—81no—
564C4⋊C4—81no—
565C4⋊C4C2×C5×D412yes—
566C4⋊C4C2×C5×D412yes—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C2×C5—42no—
582C2×C5—42no—
583C2×C5—161no—
584C2×C5#244311yescharacteristic
585C2×C5#309211yescharacteristic
586C2×C5#309611yescharacteristic
587C2×C5#326611yescharacteristic
588C2×C5#327411yescharacteristic
589C2×C5#334611yescharacteristic
590C2×C5#335411yescharacteristic
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C5×#12312yes—
611C23C5×#13712yes—
612C23C22×C5×D411yescharacteristic
613D4—28no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—84no—
619D4—84no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
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—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—84no—
660C2×C4—84no—
661C2×C4C5×#12312yes—
662C2×C4C5×AGL(1,ℤ/8)12yes—
663C2×C4C22×C5×D411yescharacteristic
664C2×C4C2×C5×#4111yescharacteristic
665C2×C4C2×C5×#4111yescharacteristic
666C2×C4C2×C5×#4111yescharacteristic
667C2×C4C5×H(5,𝔽2)11yescharacteristic
668C2×C4C5×2−1+411yescharacteristic
669C8—22no—
670C8—22no—
671C8—41no—
672C8—41no—
673C5#2614611yescharacteristic, direct product factor, Sylow
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22C2×C5×#12311yescharacteristic
696C22C5×D4211yescharacteristic
697C22C5×#54711yescharacteristic
698C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
699C22C2×C5×#13711yescharacteristic
700C22C5×#57611yescharacteristic
701C22C5×#57711yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—41no—
707C4—41no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4—81no—
713C4C5×#52511yescharacteristic
714C4C5×#53911yescharacteristic
715C4C5×#54811yescharacteristic
716C4C5×#55311yescharacteristic
717C2—42no—
718C2—42no—
719C2—161no—
720C2C5×#244311yescharacteristic
721C2C5×#309211yescharacteristic
722C2C5×#309611yescharacteristic
723C2C5×#326611yescharacteristic
724C2C5×#327411yescharacteristic
725C2C5×#334611yescharacteristic
726C2C5×#335411yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#2414C2
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
1. C2×C5×#481C2semidirect
2. C2×C5×#428C2semidirect
4. C5×D4×C4⋊C4C2semidirect
5. C5×#2093C2semidirect
6. C5×#2084C2semidirect
7. C5×#2076C2semidirect
8. C5×#2034C2semidirect
9. C5×#1925C2semidirect
10. C5×#1920C2semidirect
11. C5×#1895C2semidirect
12. C5×#1874C2semidirect
13. C5×#1870C2semidirect
14. C5×#1854C2semidirect
15. C5×#1852C2semidirect
61. #26146C5direct (N × H)
121. C5×#106D4semidirect
134. C2×#481C2×C5semidirect
135. C2×#428C2×C5semidirect
137. D4×C4⋊C4C2×C5semidirect
138. #2093C2×C5semidirect
139. #2084C2×C5semidirect
140. #2076C2×C5semidirect
141. #2034C2×C5semidirect
142. #1925C2×C5semidirect
143. #1920C2×C5semidirect
144. #1895C2×C5semidirect
145. #1874C2×C5semidirect
146. #1870C2×C5semidirect
147. #1854C2×C5semidirect
148. #1852C2×C5semidirect
430. #106C5×D4semidirect
673. C5#26146direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4812
C2×C5×#4282
C5×#24142
C5×D4×C4⋊C42
C5×#20932
C5×#20842
C5×#20762
C5×#20342
C5×#19252
C5×#19202
C5×#18952
C5×#18742
C5×#18702
C5×#18542
C5×#18522
#261465