Finite Group Databasebeta

← C5×#25238 #11947958

Subgroups — C5×#25238 #11947958

Order 1280.

968 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
1C2×C5×#481C211yesmaximal, characteristic, complemented
2C2×C5×C8×D4C211yesmaximal, characteristic, complemented
3C5×#2487C211yesmaximal, characteristic, complemented
4C5×#2416C211yesmaximal, characteristic
5C5×#2088C211yesmaximal, characteristic, complemented
6C5×#2077C211yesmaximal, characteristic, complemented
7C5×#2065C211yesmaximal, characteristic, complemented
8C5×#2034C211yesmaximal, characteristic, complemented
9C5×#1941C211yesmaximal, characteristic, complemented
10C5×#1934C211yesmaximal, characteristic, complemented
11C5×#1893C211yesmaximal, characteristic, complemented
12C5×#1893C211yesmaximal, characteristic, complemented
13C5×#1853C211yesmaximal, characteristic, complemented
14C5×#1807C211yesmaximal, characteristic, complemented
15C2×C5×#340C211yesmaximal, characteristic, complemented
16C23×C5×C8C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C2×C5×#121—21no—
19C2×C5×#121C2211yescharacteristic
20C2×C5×#121C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C5×#481—24no—
25C5×C8×D4—24no—
26C2×C5×#106C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×C4⋊C8C2211yescharacteristic
31C2×C5×#102C2211yescharacteristic
32C2×C5×#102C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×C22⋊C8C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C2×C4×C5×C8C2211yescharacteristic
38C5×#400—21no—
39C5×#399—21no—
40C5×#396—21no—
41C5×#394—21no—
42C5×#390C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#386—21no—
47C5×#386—21no—
48C5×#385—21no—
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52C5×#380C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60C5×#340C2211yescharacteristic
61#25238C511yesmaximal, 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
70C22×C5×C8—22no—
71C22×C5×C8—22no—
72C22×C5×C8—22no—
73C22×C5×C8—22no—
74C22×C5×C8—41no—
75C22×C5×C8—41no—
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C22×C5×C8C2311yescharacteristic
80C5×#121—22no—
81C5×#121—22no—
82C5×#121—22no—
83C5×#121—41no—
84C5×#121—44no—
85C4×C5×D4—22no—
86C4×C5×D4—22no—
87C2×C5×C4⋊C4—22no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—21no—
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4—21no—
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⋊C4—21no—
112C2×C5×C22⋊C4D411yescharacteristic
113C2×C5×C22⋊C4D411yescharacteristic
114C2×C42×C5C2311yescharacteristic
115C5×#106—22no—
116C5×#106—22no—
117C5×#106—22no—
118C5×#106—41no—
119C5×C4⋊C8—22no—
120C5×#102—22no—
121C5×#102—22no—
122C5×#102—22no—
123C5×#102—41no—
124C5×C22⋊C8—22no—
125C5×C22⋊C8D414yescomplemented
126C4×C5×C8—22no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95—21no—
134C2×#481C2×C511yescharacteristic, complemented
135C2×C8×D4C2×C511yescharacteristic, complemented
136#2487C2×C511yescharacteristic, complemented
137#2416C2×C511yescharacteristic
138#2088C2×C511yescharacteristic, complemented
139#2077C2×C511yescharacteristic, complemented
140#2065C2×C511yescharacteristic, complemented
141#2034C2×C511yescharacteristic, complemented
142#1941C2×C511yescharacteristic, complemented
143#1934C2×C511yescharacteristic, complemented
144#1893C2×C511yescharacteristic, complemented
145#1893C2×C511yescharacteristic, complemented
146#1853C2×C511yescharacteristic, complemented
147#1807C2×C511yescharacteristic, complemented
148C2×#340C2×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—42no—
161C2×C5×D4—42no—
162C2×C5×D4—42no—
163C2×C5×D4—42no—
164C2×C5×D4—42no—
165C2×C5×D4—81no—
166C2×C5×D4SD1614yes—
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—81no—
188C22×C4×C5—81no—
189C22×C4×C5—81no—
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D412yes—
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5#4112yes—
196C22×C4×C5C2411yescharacteristic
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—44no—
207C2×C5×C8—44no—
208C2×C5×C8C2×D412yes—
209C2×C5×C8C2×D412yes—
210C2×C5×C8#4112yes—
211C5×C4⋊C4—22no—
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—21no—
224C5×C4⋊C4—21no—
225C5×C4⋊C4—42no—
226C5×C4⋊C4—42no—
227C5×C4⋊C4—42no—
228C5×C4⋊C4—81no—
229C5×C4⋊C4—81no—
230C5×C4⋊C4#4112yes—
231C5×C22⋊C4—22no—
232C5×C22⋊C4—22no—
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—
240C5×C22⋊C4—81no—
241C42×C5—21no—
242C42×C5—21no—
243C23×C8C22×C511yescharacteristic
244C23×C8C22×C511yescharacteristic
245C2×#121—21no—
246C2×#121C22×C511yescharacteristic
247C2×#121C22×C511yescharacteristic
248C2×C4×D4C22×C511yescharacteristic
249C22×C4⋊C4C22×C511yescharacteristic
250C22×C4⋊C4C22×C511yescharacteristic
251#481—24no—
252C8×D4—24no—
253C2×#106C22×C511yescharacteristic
254C2×#106C22×C511yescharacteristic
255C2×#106C22×C511yescharacteristic
256C2×#106C22×C511yescharacteristic
257C2×C4⋊C8C22×C511yescharacteristic
258C2×#102C22×C511yescharacteristic
259C2×#102C22×C511yescharacteristic
260C2×#102C22×C511yescharacteristic
261C2×#102C22×C511yescharacteristic
262C2×C22⋊C8C22×C511yescharacteristic
263C2×C22⋊C8C22×C511yescharacteristic
264C2×C4×C8C22×C511yescharacteristic
265#400—21no—
266#399—21no—
267#396—21no—
268#394—21no—
269#390C22×C511yescharacteristic
270#389C22×C511yescharacteristic
271#389C22×C511yescharacteristic
272#389C22×C511yescharacteristic
273#386—21no—
274#386—21no—
275#385—21no—
276#380C22×C511yescharacteristic
277#380C22×C511yescharacteristic
278#380C22×C511yescharacteristic
279#380C22×C511yescharacteristic
280#340C22×C511yescharacteristic
281#340C22×C511yescharacteristic
282#340C22×C511yescharacteristic
283#340C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#340C22×C511yescharacteristic
287#340C22×C511yescharacteristic
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—41no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5#12112yes—
306C23×C5C2×SD1612yes—
307C23×C5C2×SD1612yes—
308C23×C5#13512yes—
309C23×C5C22×D411yescharacteristic
310C5×D4—28no—
311C5×D4—41no—
312C5×D4—41no—
313C5×D4—41no—
314C5×D4—41no—
315C5×D4—84no—
316C5×D4—84no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
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—41no—
356C2×C4×C5—84no—
357C2×C4×C5—84no—
358C2×C4×C5#12112yes—
359C2×C4×C5C2×SD1612yes—
360C2×C4×C5C22×D411yescharacteristic
361C2×C4×C5C2×#4111yescharacteristic
362C2×C4×C5C2×#4111yescharacteristic
363C2×C4×C5C2×#4111yescharacteristic
364C2×C4×C5H(5,𝔽2)11yescharacteristic
365C2×C4×C52−1+411yescharacteristic
366C5×C8—22no—
367C5×C8—22no—
368C5×C8—22no—
369C5×C8—41no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4C5×D411yescharacteristic
373C22×D4C23×C511yescharacteristic
374C23×C4—21no—
375C23×C4—21no—
376C23×C4C23×C511yescharacteristic
377C23×C4C23×C511yescharacteristic
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—22no—
382C22×C8—41no—
383C22×C8—41no—
384C22×C8C23×C511yescharacteristic
385C22×C8C23×C511yescharacteristic
386C22×C8C23×C511yescharacteristic
387C22×C8C23×C511yescharacteristic
388#121—22no—
389#121—22no—
390#121—22no—
391#121—41no—
392#121—44no—
393C4×D4—22no—
394C4×D4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
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×C42C23×C511yescharacteristic
423#106—22no—
424#106—22no—
425#106—22no—
426#106—41no—
427C4⋊C8—22no—
428#102—22no—
429#102—22no—
430#102—22no—
431#102—41no—
432C22⋊C8—22no—
433C22⋊C8C5×D414yescomplemented
434C4×C8—22no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442C22×C5—22no—
443C22×C5—22no—
444C22×C5—22no—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—22no—
450C22×C5—22no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5—41no—
454C22×C5—41no—
455C22×C5—81no—
456C22×C5—81no—
457C22×C5—81no—
458C22×C5—81no—
459C22×C5—81no—
460C22×C5—81no—
461C22×C5—81no—
462C22×C5#46514yes—
463C22×C5C2×#12111yescharacteristic
464C22×C5#54611yescharacteristic
465C22×C5#54711yescharacteristic
466C22×C5C22×SD1611yescharacteristic
467C22×C5C2×#13511yescharacteristic
468C22×C5#57611yescharacteristic
469C22×C5#57711yescharacteristic
470C4×C5—22no—
471C4×C5—22no—
472C4×C5—41no—
473C4×C5—42no—
474C4×C5—41no—
475C4×C5—81no—
476C4×C5—81no—
477C4×C5—81no—
478C4×C5—81no—
479C4×C5—81no—
480C4×C5—81no—
481C4×C5#52911yescharacteristic
482C4×C5#53911yescharacteristic
483C4×C5#54611yescharacteristic
484C4×C5#54711yescharacteristic
485C24—21no—
486C24C2×C5×D411yescharacteristic
487C24C2×C5×D411yescharacteristic
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—81no—
502C2×D4C5×SD1614yes—
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—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4C2×C5×D411yescharacteristic
527C22×C4C2×C5×D411yescharacteristic
528C22×C4C2×C5×D411yescharacteristic
529C22×C4C2×C5×D412yes—
530C22×C4C2×C5×D411yescharacteristic
531C22×C4C5×#4112yes—
532C22×C4C24×C511yescharacteristic
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—
543C2×C8—44no—
544C2×C8C2×C5×D412yes—
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—21no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—81no—
565C4⋊C4—81no—
566C4⋊C4C5×#4112yes—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C42—21no—
578C42—21no—
579C2×C5—24no—
580C2×C5—42no—
581C2×C5—161no—
582C2×C5#242511yescharacteristic
583C2×C5C2×#46511yescharacteristic
584C2×C5#306211yescharacteristic
585C2×C5#329511yescharacteristic
586C2×C5#330111yescharacteristic
587C2×C5#333511yescharacteristic
588C2×C5#333911yescharacteristic
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×#12112yes—
607C23C2×C5×SD1612yes—
608C23C2×C5×SD1612yes—
609C23C5×#13512yes—
610C23C22×C5×D411yescharacteristic
611D4—28no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—84no—
617D4—84no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
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—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—84no—
658C2×C4—84no—
659C2×C4C5×#12112yes—
660C2×C4C2×C5×SD1612yes—
661C2×C4C22×C5×D411yescharacteristic
662C2×C4C2×C5×#4111yescharacteristic
663C2×C4C2×C5×#4111yescharacteristic
664C2×C4C2×C5×#4111yescharacteristic
665C2×C4C5×H(5,𝔽2)11yescharacteristic
666C2×C4C5×2−1+411yescharacteristic
667C8—22no—
668C8—22no—
669C8—22no—
670C8—41no—
671C5#2523811yescharacteristic, direct product factor, Sylow
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22C5×#46514yes—
693C22C2×C5×#12111yescharacteristic
694C22C5×#54611yescharacteristic
695C22C5×#54711yescharacteristic
696C22C22×C5×SD1611yescharacteristic
697C22C2×C5×#13511yescharacteristic
698C22C5×#57611yescharacteristic
699C22C5×#57711yescharacteristic
700C4—22no—
701C4—22no—
702C4—42no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4C5×#52911yescharacteristic
712C4C5×#53911yescharacteristic
713C4C5×#54611yescharacteristic
714C4C5×#54711yescharacteristic
715C2—24no—
716C2—42no—
717C2—161no—
718C2C5×#242511yescharacteristic
719C2C2×C5×#46511yescharacteristic
720C2C5×#306211yescharacteristic
721C2C5×#329511yescharacteristic
722C2C5×#330111yescharacteristic
723C2C5×#333511yescharacteristic
724C2C5×#333911yescharacteristic
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×#481C2semidirect
2. C2×C5×C8×D4C2semidirect
3. C5×#2487C2semidirect
5. C5×#2088C2semidirect
6. C5×#2077C2semidirect
7. C5×#2065C2semidirect
8. C5×#2034C2semidirect
9. C5×#1941C2semidirect
10. C5×#1934C2semidirect
11. C5×#1893C2semidirect
12. C5×#1893C2semidirect
13. C5×#1853C2semidirect
14. C5×#1807C2semidirect
15. C2×C5×#340C2semidirect
61. #25238C5direct (N × H)
125. C5×C22⋊C8D4semidirect
134. C2×#481C2×C5semidirect
135. C2×C8×D4C2×C5semidirect
136. #2487C2×C5semidirect
138. #2088C2×C5semidirect
139. #2077C2×C5semidirect
140. #2065C2×C5semidirect
141. #2034C2×C5semidirect
142. #1941C2×C5semidirect
143. #1934C2×C5semidirect
144. #1893C2×C5semidirect
145. #1893C2×C5semidirect
146. #1853C2×C5semidirect
147. #1807C2×C5semidirect
148. C2×#340C2×C5semidirect
433. C22⋊C8C5×D4semidirect
671. C5#25238direct (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×C8×D42
C5×#24872
C5×#24162
C5×#20882
C5×#20772
C5×#20652
C5×#20342
C5×#19412
C5×#19342
C5×#18932
C5×#18532
C5×#18072
C2×C5×#3402
#252385