Finite Group Databasebeta

← C5×#26157 #11948877

Subgroups — C5×#26157 #11948877

Order 1280.

924 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#482C211yesmaximal, characteristic, complemented
2C2×C5×#428C211yesmaximal, characteristic, complemented
3C5×#2416C211yesmaximal, characteristic
4C5×#2354C211yesmaximal, characteristic, complemented
5C5×#2093C211yesmaximal, characteristic, complemented
6C5×#2083C211yesmaximal, characteristic, complemented
7C5×#2076C211yesmaximal, characteristic, complemented
8C5×#2033C211yesmaximal, characteristic, complemented
9C5×#1926C211yesmaximal, characteristic, complemented
10C5×#1919C211yesmaximal, characteristic, complemented
11C5×#1895C211yesmaximal, characteristic, complemented
12C5×#1875C211yesmaximal, characteristic, complemented
13C5×#1870C211yesmaximal, characteristic, complemented
14C5×#1854C211yesmaximal, characteristic, complemented
15C5×#1852C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C2×C5×#121—21no—
18C2×C5×#121C2211yescharacteristic
19C2×C5×#121C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C5×#482—24no—
25C5×#428—24no—
26C2×C5×#107C2211yescharacteristic
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#107C2211yescharacteristic
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×#396—21no—
40C5×#394—21no—
41C5×#390—21no—
42C5×#390C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#388—21no—
45C5×#388—21no—
46C5×#386—21no—
47C5×#384C2211yescharacteristic
48C5×#380C2211yescharacteristic
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C4×C5×C4⋊C4—21no—
52C4×C5×C4⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26157C511yesmaximal, 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×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C2×C5×M16—22no—
70C2×C5×M16—22no—
71C2×C5×M16—22no—
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—
83C5×#117—22no—
84C5×#117—22no—
85C5×#117—41no—
86C5×#117—41no—
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—41no—
93C2×C5×C4⋊C4D411yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
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×C5—21no—
113C2×C42×C5—21no—
114C2×C42×C5—21no—
115C2×C42×C5C2311yescharacteristic
116C5×#107—22no—
117C5×#107—22no—
118C5×#107—22no—
119C5×#107—41no—
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×#482C2×C511yescharacteristic, complemented
135C2×#428C2×C511yescharacteristic, complemented
136#2416C2×C511yescharacteristic
137#2354C2×C511yescharacteristic, complemented
138#2093C2×C511yescharacteristic, complemented
139#2083C2×C511yescharacteristic, complemented
140#2076C2×C511yescharacteristic, complemented
141#2033C2×C511yescharacteristic, complemented
142#1926C2×C511yescharacteristic, complemented
143#1919C2×C511yescharacteristic, complemented
144#1895C2×C511yescharacteristic, complemented
145#1875C2×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—21no—
155C2×C5×D4—21no—
156C2×C5×D4—21no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—41no—
161C2×C5×D4—42no—
162C2×C5×D4—42no—
163C2×C5×D4—42no—
164C2×C5×D4—42no—
165C2×C5×D4—42no—
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—81no—
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5#4112yes—
192C22×C4×C5#4112yes—
193C22×C4×C5C2411yescharacteristic
194C5×M16—28no—
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×C8C2×D412yes—
206C2×C5×C8#4112yes—
207C5×C4⋊C4—22no—
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—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—42no—
221C5×C4⋊C4—42no—
222C5×C4⋊C4—42no—
223C5×C4⋊C4—81no—
224C5×C4⋊C4C2×D412yes—
225C5×C4⋊C4C2×D412yes—
226C5×C22⋊C4—22no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4—42no—
229C5×C22⋊C4—42no—
230C5×C22⋊C4—42no—
231C5×C22⋊C4—42no—
232C5×C22⋊C4—42no—
233C5×C22⋊C4—42no—
234C5×C22⋊C4—81no—
235C5×C22⋊C4—81no—
236C5×C22⋊C4—81no—
237C42×C5—21no—
238C42×C5—21no—
239C42×C5—42no—
240C42×C5—42no—
241C42×C5—42no—
242C22×M16C22×C511yescharacteristic
243C2×#121—21no—
244C2×#121C22×C511yescharacteristic
245C2×#121C22×C511yescharacteristic
246C2×C4×D4C22×C511yescharacteristic
247C2×#117C22×C511yescharacteristic
248C2×#117C22×C511yescharacteristic
249C22×C4⋊C4C22×C511yescharacteristic
250#482—24no—
251#428—24no—
252C2×#107C22×C511yescharacteristic
253C2×#107C22×C511yescharacteristic
254C2×#107C22×C511yescharacteristic
255C2×#107C22×C511yescharacteristic
256C2×#106C22×C511yescharacteristic
257C2×#106C22×C511yescharacteristic
258C2×#102C22×C511yescharacteristic
259C2×#102C22×C511yescharacteristic
260C2×#102C22×C511yescharacteristic
261C2×#102C22×C511yescharacteristic
262C2×C22⋊C8C22×C511yescharacteristic
263C2×C22⋊C8C22×C511yescharacteristic
264C2×C22⋊C8C22×C511yescharacteristic
265#396—21no—
266#394—21no—
267#390—21no—
268#390C22×C511yescharacteristic
269#389C22×C511yescharacteristic
270#388—21no—
271#388—21no—
272#386—21no—
273#384C22×C511yescharacteristic
274#380C22×C511yescharacteristic
275#380C22×C511yescharacteristic
276#380C22×C511yescharacteristic
277C4×C4⋊C4—21no—
278C4×C4⋊C4C22×C511yescharacteristic
279#340C22×C511yescharacteristic
280#340C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285#336C22×C511yescharacteristic
286#336C22×C511yescharacteristic
287C23×C5—21no—
288C23×C5—21no—
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—41no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5#12312yes—
308C23×C5C22×D411yescharacteristic
309C5×D4—44no—
310C5×D4—41no—
311C5×D4—41no—
312C5×D4—41no—
313C5×D4—41no—
314C5×D4—84no—
315C5×D4—84no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—22no—
327C2×C4×C5—21no—
328C2×C4×C5—22no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
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—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—84no—
356C2×C4×C5#12312yes—
357C2×C4×C5AGL(1,ℤ/8)12yes—
358C2×C4×C5C22×D411yescharacteristic
359C2×C4×C5C2×#4111yescharacteristic
360C2×C4×C5C2×#4111yescharacteristic
361C2×C4×C5C2×#4111yescharacteristic
362C2×C4×C5H(5,𝔽2)11yescharacteristic
363C2×C4×C52−1+411yescharacteristic
364C5×C8—22no—
365C5×C8—22no—
366C5×C8—41no—
367C5×C8—41no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4C5×D411yescharacteristic
371C22×D4C23×C511yescharacteristic
372C23×C4—21no—
373C23×C4C23×C511yescharacteristic
374C23×C4C23×C511yescharacteristic
375C2×M16—22no—
376C2×M16—22no—
377C2×M16—22no—
378C22×C8C23×C511yescharacteristic
379C22×C8C23×C511yescharacteristic
380C22×C8C23×C511yescharacteristic
381C22×C8C23×C511yescharacteristic
382#121—22no—
383#121—22no—
384#121—22no—
385#121—41no—
386#121—44no—
387C4×D4—22no—
388C4×D4—22no—
389#117—22no—
390#117—22no—
391#117—41no—
392#117—41no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4C5×D411yescharacteristic
400C2×C4⋊C4C23×C511yescharacteristic
401C2×C4⋊C4C23×C511yescharacteristic
402C2×C4⋊C4C23×C511yescharacteristic
403C2×C4⋊C4C23×C511yescharacteristic
404C2×C4⋊C4C23×C511yescharacteristic
405C2×C4⋊C4C23×C511yescharacteristic
406C2×C4⋊C4C23×C511yescharacteristic
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⋊C4C5×D411yescharacteristic
417C2×C22⋊C4C5×D411yescharacteristic
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42C23×C511yescharacteristic
422#107—22no—
423#107—22no—
424#107—22no—
425#107—41no—
426#106—22no—
427#106C5×D414yescomplemented
428#102—22no—
429#102—22no—
430#102—22no—
431#102—41no—
432C22⋊C8—22no—
433C22⋊C8—22no—
434C22⋊C8—22no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—22no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5—41no—
447C22×C5—41no—
448C22×C5—41no—
449C22×C5—41no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5—41no—
454C22×C5—81no—
455C22×C5—81no—
456C22×C5—81no—
457C22×C5—81no—
458C22×C5—81no—
459C22×C5—81no—
460C22×C5—81no—
461C22×C5C2×#12311yescharacteristic
462C22×C5D4211yescharacteristic
463C22×C5#54711yescharacteristic
464C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
465C22×C5#57511yescharacteristic
466C22×C5#57611yescharacteristic
467C22×C5#57811yescharacteristic
468C4×C5—22no—
469C4×C5—22no—
470C4×C5—41no—
471C4×C5—41no—
472C4×C5—42no—
473C4×C5—42no—
474C4×C5—81no—
475C4×C5—81no—
476C4×C5—81no—
477C4×C5—81no—
478C4×C5—81no—
479C4×C5#52511yescharacteristic
480C4×C5#53911yescharacteristic
481C4×C5#54811yescharacteristic
482C4×C5#55311yescharacteristic
483C24—21no—
484C24C2×C5×D411yescharacteristic
485C24C2×C5×D411yescharacteristic
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—41no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—81no—
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—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—81no—
521C22×C4C2×C5×D411yescharacteristic
522C22×C4C2×C5×D411yescharacteristic
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C2×C5×D411yescharacteristic
525C22×C4C5×#4112yes—
526C22×C4C5×#4112yes—
527C22×C4C24×C511yescharacteristic
528M16—28no—
529C2×C8—21no—
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×C8C2×C5×D412yes—
540C2×C8C5×#4112yes—
541C4⋊C4—22no—
542C4⋊C4—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—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—81no—
558C4⋊C4C2×C5×D412yes—
559C4⋊C4C2×C5×D412yes—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C42—21no—
572C42—21no—
573C42—42no—
574C42—42no—
575C42—42no—
576C2×C5—42no—
577C2×C5—81no—
578C2×C5—161no—
579C2×C5#244311yescharacteristic
580C2×C5#309411yescharacteristic
581C2×C5#309811yescharacteristic
582C2×C5#326911yescharacteristic
583C2×C5#327411yescharacteristic
584C2×C5#334711yescharacteristic
585C2×C5#335311yescharacteristic
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23C5×#12312yes—
607C23C22×C5×D411yescharacteristic
608D4—44no—
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—22no—
626C2×C4—21no—
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×C4C5×#12312yes—
656C2×C4C5×AGL(1,ℤ/8)12yes—
657C2×C4C22×C5×D411yescharacteristic
658C2×C4C2×C5×#4111yescharacteristic
659C2×C4C2×C5×#4111yescharacteristic
660C2×C4C2×C5×#4111yescharacteristic
661C2×C4C5×H(5,𝔽2)11yescharacteristic
662C2×C4C5×2−1+411yescharacteristic
663C8—22no—
664C8—22no—
665C8—41no—
666C8—41no—
667C5#2615711yescharacteristic, direct product factor, Sylow
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×C5×#12311yescharacteristic
690C22C5×D4211yescharacteristic
691C22C5×#54711yescharacteristic
692C22C2×C5×AGL(1,ℤ/8)11yescharacteristic
693C22C5×#57511yescharacteristic
694C22C5×#57611yescharacteristic
695C22C5×#57811yescharacteristic
696C4—22no—
697C4—22no—
698C4—42no—
699C4—42no—
700C4—41no—
701C4—41no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4C5×#52511yescharacteristic
708C4C5×#53911yescharacteristic
709C4C5×#54811yescharacteristic
710C4C5×#55311yescharacteristic
711C2—42no—
712C2—81no—
713C2—161no—
714C2C5×#244311yescharacteristic
715C2C5×#309411yescharacteristic
716C2C5×#309811yescharacteristic
717C2C5×#326911yescharacteristic
718C2C5×#327411yescharacteristic
719C2C5×#334711yescharacteristic
720C2C5×#335311yescharacteristic
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
1. C2×C5×#482C2semidirect
2. C2×C5×#428C2semidirect
4. C5×#2354C2semidirect
5. C5×#2093C2semidirect
6. C5×#2083C2semidirect
7. C5×#2076C2semidirect
8. C5×#2033C2semidirect
9. C5×#1926C2semidirect
10. C5×#1919C2semidirect
11. C5×#1895C2semidirect
12. C5×#1875C2semidirect
13. C5×#1870C2semidirect
14. C5×#1854C2semidirect
15. C5×#1852C2semidirect
61. #26157C5direct (N × H)
121. C5×#106D4semidirect
134. C2×#482C2×C5semidirect
135. C2×#428C2×C5semidirect
137. #2354C2×C5semidirect
138. #2093C2×C5semidirect
139. #2083C2×C5semidirect
140. #2076C2×C5semidirect
141. #2033C2×C5semidirect
142. #1926C2×C5semidirect
143. #1919C2×C5semidirect
144. #1895C2×C5semidirect
145. #1875C2×C5semidirect
146. #1870C2×C5semidirect
147. #1854C2×C5semidirect
148. #1852C2×C5semidirect
427. #106C5×D4semidirect
667. C5#26157direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4822
C2×C5×#4282
C5×#24162
C5×#23542
C5×#20932
C5×#20832
C5×#20762
C5×#20332
C5×#19262
C5×#19192
C5×#18952
C5×#18752
C5×#18702
C5×#18542
C5×#18522
#261575