Finite Group Databasebeta

← C5×#26126 #11948846

Subgroups — C5×#26126 #11948846

Order 1280.

1008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#480C211yesmaximal, characteristic, complemented
2C22×C5×#107C211yesmaximal, characteristic, complemented
3C5×#2416C211yesmaximal, characteristic
4C5×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C5×#2093C211yesmaximal, characteristic, complemented
6C5×#2083C211yesmaximal, characteristic, complemented
7C5×#2075C211yesmaximal, characteristic, complemented
8C5×#2033C211yesmaximal, characteristic, complemented
9C5×#1925C211yesmaximal, characteristic, complemented
10C5×#1918C211yesmaximal, characteristic, complemented
11C5×#1893C211yesmaximal, characteristic, complemented
12C5×#1874C211yesmaximal, characteristic, complemented
13C5×#1869C211yesmaximal, characteristic, complemented
14C5×#1852C211yesmaximal, characteristic, complemented
15C5×#1852C211yesmaximal, 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
25C5×#480—24no—
26C2×C5×#107—24no—
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#107C2211yescharacteristic
30C2×C5×#107C2211yescharacteristic
31C2×C5×#107C2211yescharacteristic
32C2×C5×#107C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#102C2211yescharacteristic
36C2×C5×#102C2211yescharacteristic
37C2×C5×C22⋊C8C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C5×#396—21no—
41C5×#394—21no—
42C5×#390C2211yescharacteristic
43C5×#389—21no—
44C5×#389C2211yescharacteristic
45C5×#386—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#26126C511yesmaximal, 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×C5—21no—
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C22×C5×C8—22no—
72C22×C5×C8—22no—
73C22×C5×C8—22no—
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C5×#121—22no—
79C5×#121—22no—
80C5×#121—22no—
81C5×#121—41no—
82C5×#121—44no—
83C4×C5×D4—22no—
84C4×C5×D4—22no—
85C4×C5×D4—44no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—22no—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—21no—
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⋊C4—41no—
97C2×C5×C4⋊C4—41no—
98C2×C5×C4⋊C4D411yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
113C2×C5×C22⋊C4D411yescharacteristic
114C2×C5×C22⋊C4D411yescharacteristic
115C2×C42×C5—21no—
116C2×C42×C5C2311yescharacteristic
117C5×#107—22no—
118C5×#107—22no—
119C5×#107—22no—
120C5×#107—22no—
121C5×#107—41no—
122C5×#107D414yescomplemented
123C5×#102—22no—
124C5×#102—22no—
125C5×#102—22no—
126C5×#102—41no—
127C5×C22⋊C8—22no—
128C5×C22⋊C8—22no—
129C5×C22⋊C8—22no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95—21no—
134C5×#95—21no—
135C2×#480C2×C511yescharacteristic, complemented
136C22×#107C2×C511yescharacteristic, complemented
137#2416C2×C511yescharacteristic
138D4×C4⋊C4C2×C511yescharacteristic, complemented
139#2093C2×C511yescharacteristic, complemented
140#2083C2×C511yescharacteristic, complemented
141#2075C2×C511yescharacteristic, complemented
142#2033C2×C511yescharacteristic, complemented
143#1925C2×C511yescharacteristic, complemented
144#1918C2×C511yescharacteristic, complemented
145#1893C2×C511yescharacteristic, complemented
146#1874C2×C511yescharacteristic, complemented
147#1869C2×C511yescharacteristic, complemented
148#1852C2×C511yescharacteristic, complemented
149#1852C2×C511yescharacteristic, complemented
150C24×C5—21no—
151C24×C5C2×D411yescharacteristic
152C24×C5C2×D411yescharacteristic
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—42no—
165C2×C5×D4—42no—
166C2×C5×D4—81no—
167C2×C5×D4D814yes—
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—21no—
185C22×C4×C5—42no—
186C22×C4×C5—42no—
187C22×C4×C5—42no—
188C22×C4×C5—42no—
189C22×C4×C5—42no—
190C22×C4×C5—42no—
191C22×C4×C5—81no—
192C22×C4×C5—81no—
193C22×C4×C5—81no—
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5#4112yes—
199C22×C4×C5#4112yes—
200C22×C4×C5C2411yescharacteristic
201C2×C5×C8—28no—
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×C8—21no—
209C2×C5×C8—21no—
210C2×C5×C8—21no—
211C2×C5×C8—21no—
212C2×C5×C8C2×D412yes—
213C2×C5×C8#4112yes—
214C5×C4⋊C4—22no—
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—21no—
226C5×C4⋊C4—21no—
227C5×C4⋊C4—42no—
228C5×C4⋊C4—42no—
229C5×C4⋊C4—42no—
230C5×C4⋊C4—42no—
231C5×C4⋊C4—42no—
232C5×C4⋊C4—81no—
233C5×C4⋊C4C2×D412yes—
234C5×C4⋊C4C2×D412yes—
235C5×C22⋊C4—22no—
236C5×C22⋊C4—22no—
237C5×C22⋊C4—42no—
238C5×C22⋊C4—42no—
239C5×C22⋊C4—42no—
240C5×C22⋊C4—42no—
241C5×C22⋊C4—42no—
242C5×C22⋊C4—42no—
243C5×C22⋊C4—81no—
244C42×C5—21no—
245C42×C5—21no—
246C42×C5—42no—
247C23×C8C22×C511yescharacteristic
248C2×#121—21no—
249C2×#121C22×C511yescharacteristic
250C2×#121C22×C511yescharacteristic
251C2×C4×D4—21no—
252C2×C4×D4C22×C511yescharacteristic
253C22×C4⋊C4C22×C511yescharacteristic
254C22×C4⋊C4C22×C511yescharacteristic
255C22×C4⋊C4C22×C511yescharacteristic
256#480—24no—
257C2×#107—24no—
258C2×#107C22×C511yescharacteristic
259C2×#107C22×C511yescharacteristic
260C2×#107C22×C511yescharacteristic
261C2×#107C22×C511yescharacteristic
262C2×#107C22×C511yescharacteristic
263C2×#107C22×C511yescharacteristic
264C2×#102C22×C511yescharacteristic
265C2×#102C22×C511yescharacteristic
266C2×#102C22×C511yescharacteristic
267C2×#102C22×C511yescharacteristic
268C2×C22⋊C8C22×C511yescharacteristic
269C2×C22⋊C8C22×C511yescharacteristic
270C2×C22⋊C8C22×C511yescharacteristic
271#396—21no—
272#394—21no—
273#390C22×C511yescharacteristic
274#389—21no—
275#389C22×C511yescharacteristic
276#386—21no—
277#385—21no—
278#385—21no—
279#384C22×C511yescharacteristic
280#380C22×C511yescharacteristic
281#380C22×C511yescharacteristic
282#380C22×C511yescharacteristic
283C4×C4⋊C4C22×C511yescharacteristic
284#340C22×C511yescharacteristic
285#340C22×C511yescharacteristic
286#340C22×C511yescharacteristic
287#340C22×C511yescharacteristic
288#340C22×C511yescharacteristic
289#340C22×C511yescharacteristic
290#336C22×C511yescharacteristic
291#336C22×C511yescharacteristic
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—21no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5#12312yes—
310C23×C5C2×D812yes—
311C23×C5C2×D812yes—
312C23×C5#13712yes—
313C23×C5C22×D411yescharacteristic
314C5×D4—28no—
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—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
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×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—84no—
361C2×C4×C5—84no—
362C2×C4×C5—84no—
363C2×C4×C5#12312yes—
364C2×C4×C5C2×D812yes—
365C2×C4×C5C22×D411yescharacteristic
366C2×C4×C5C2×#4111yescharacteristic
367C2×C4×C5C2×#4111yescharacteristic
368C2×C4×C5C2×#4111yescharacteristic
369C2×C4×C5H(5,𝔽2)11yescharacteristic
370C2×C4×C52−1+411yescharacteristic
371C5×C8—22no—
372C5×C8—22no—
373C5×C8—41no—
374C5×C8—41no—
375C22×D4—21no—
376C22×D4—21no—
377C22×D4C5×D411yescharacteristic
378C22×D4C23×C511yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—21no—
382C23×C4C23×C511yescharacteristic
383C23×C4C23×C511yescharacteristic
384C22×C8—22no—
385C22×C8—22no—
386C22×C8—22no—
387C22×C8C23×C511yescharacteristic
388C22×C8C23×C511yescharacteristic
389C22×C8C23×C511yescharacteristic
390C22×C8C23×C511yescharacteristic
391#121—22no—
392#121—22no—
393#121—22no—
394#121—41no—
395#121—44no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—44no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—41no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4C5×D411yescharacteristic
412C2×C4⋊C4C23×C511yescharacteristic
413C2×C4⋊C4C23×C511yescharacteristic
414C2×C4⋊C4C23×C511yescharacteristic
415C2×C4⋊C4C23×C511yescharacteristic
416C2×C4⋊C4C23×C511yescharacteristic
417C2×C4⋊C4C23×C511yescharacteristic
418C2×C4⋊C4C23×C511yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4C5×D411yescharacteristic
427C2×C22⋊C4C5×D411yescharacteristic
428C2×C42—21no—
429C2×C42C23×C511yescharacteristic
430#107—22no—
431#107—22no—
432#107—22no—
433#107—22no—
434#107—41no—
435#107C5×D414yescomplemented
436#102—22no—
437#102—22no—
438#102—22no—
439#102—41no—
440C22⋊C8—22no—
441C22⋊C8—22no—
442C22⋊C8—22no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448C22×C5—22no—
449C22×C5—22no—
450C22×C5—22no—
451C22×C5—22no—
452C22×C5—22no—
453C22×C5—22no—
454C22×C5—22no—
455C22×C5—22no—
456C22×C5—22no—
457C22×C5—41no—
458C22×C5—41no—
459C22×C5—41no—
460C22×C5—41no—
461C22×C5—81no—
462C22×C5—81no—
463C22×C5—81no—
464C22×C5—81no—
465C22×C5—81no—
466C22×C5—81no—
467C22×C5—81no—
468C22×C5#48014yescomplemented
469C22×C5C2×#12311yescharacteristic
470C22×C5D4211yescharacteristic
471C22×C5#54711yescharacteristic
472C22×C5C22×D811yescharacteristic
473C22×C5C2×#13711yescharacteristic
474C22×C5#57611yescharacteristic
475C22×C5#57811yescharacteristic
476C4×C5—22no—
477C4×C5—22no—
478C4×C5—41no—
479C4×C5—41no—
480C4×C5—42no—
481C4×C5—42no—
482C4×C5—81no—
483C4×C5—81no—
484C4×C5—81no—
485C4×C5—81no—
486C4×C5—81no—
487C4×C5#52511yescharacteristic
488C4×C5#53911yescharacteristic
489C4×C5#54811yescharacteristic
490C4×C5#55311yescharacteristic
491C24—21no—
492C24C2×C5×D411yescharacteristic
493C24C2×C5×D411yescharacteristic
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—81no—
508C2×D4C5×D814yes—
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—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4C2×C5×D411yescharacteristic
536C22×C4C2×C5×D411yescharacteristic
537C22×C4C2×C5×D411yescharacteristic
538C22×C4C2×C5×D411yescharacteristic
539C22×C4C5×#4112yes—
540C22×C4C5×#4112yes—
541C22×C4C24×C511yescharacteristic
542C2×C8—28no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8C2×C5×D412yes—
554C2×C8C5×#4112yes—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—81no—
574C4⋊C4C2×C5×D412yes—
575C4⋊C4C2×C5×D412yes—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—81no—
585C42—21no—
586C42—21no—
587C42—42no—
588C2×C5—24no—
589C2×C5—42no—
590C2×C5—161no—
591C2×C5#244311yescharacteristic
592C2×C5C2×#48011yescharacteristic
593C2×C5#309811yescharacteristic
594C2×C5#327011yescharacteristic
595C2×C5D4×D811yescharacteristic
596C2×C5#333411yescharacteristic
597C2×C5#334611yescharacteristic
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23C5×#12312yes—
616C23C2×C5×D812yes—
617C23C2×C5×D812yes—
618C23C5×#13712yes—
619C23C22×C5×D411yescharacteristic
620D4—28no—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—84no—
626D4—84no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
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×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—84no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4C5×#12312yes—
670C2×C4C2×C5×D812yes—
671C2×C4C22×C5×D411yescharacteristic
672C2×C4C2×C5×#4111yescharacteristic
673C2×C4C2×C5×#4111yescharacteristic
674C2×C4C2×C5×#4111yescharacteristic
675C2×C4C5×H(5,𝔽2)11yescharacteristic
676C2×C4C5×2−1+411yescharacteristic
677C8—22no—
678C8—22no—
679C8—41no—
680C8—41no—
681C5#2612611yescharacteristic, direct product factor, Sylow
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22C5×#48014yescomplemented
703C22C2×C5×#12311yescharacteristic
704C22C5×D4211yescharacteristic
705C22C5×#54711yescharacteristic
706C22C22×C5×D811yescharacteristic
707C22C2×C5×#13711yescharacteristic
708C22C5×#57611yescharacteristic
709C22C5×#57811yescharacteristic
710C4—22no—
711C4—22no—
712C4—42no—
713C4—42no—
714C4—41no—
715C4—41no—
716C4—81no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4C5×#52511yescharacteristic
722C4C5×#53911yescharacteristic
723C4C5×#54811yescharacteristic
724C4C5×#55311yescharacteristic
725C2—24no—
726C2—42no—
727C2—161no—
728C2C5×#244311yescharacteristic
729C2C2×C5×#48011yescharacteristic
730C2C5×#309811yescharacteristic
731C2C5×#327011yescharacteristic
732C2C5×D4×D811yescharacteristic
733C2C5×#333411yescharacteristic
734C2C5×#334611yescharacteristic
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×#480C2semidirect
2. C22×C5×#107C2semidirect
4. C5×D4×C4⋊C4C2semidirect
5. C5×#2093C2semidirect
6. C5×#2083C2semidirect
7. C5×#2075C2semidirect
8. C5×#2033C2semidirect
9. C5×#1925C2semidirect
10. C5×#1918C2semidirect
11. C5×#1893C2semidirect
12. C5×#1874C2semidirect
13. C5×#1869C2semidirect
14. C5×#1852C2semidirect
15. C5×#1852C2semidirect
61. #26126C5direct (N × H)
122. C5×#107D4semidirect
135. C2×#480C2×C5semidirect
136. C22×#107C2×C5semidirect
138. D4×C4⋊C4C2×C5semidirect
139. #2093C2×C5semidirect
140. #2083C2×C5semidirect
141. #2075C2×C5semidirect
142. #2033C2×C5semidirect
143. #1925C2×C5semidirect
144. #1918C2×C5semidirect
145. #1893C2×C5semidirect
146. #1874C2×C5semidirect
147. #1869C2×C5semidirect
148. #1852C2×C5semidirect
149. #1852C2×C5semidirect
435. #107C5×D4semidirect
468. C22×C5#480semidirect
681. C5#26126direct (N × H)
702. C22C5×#480semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4802
C22×C5×#1072
C5×#24162
C5×D4×C4⋊C42
C5×#20932
C5×#20832
C5×#20752
C5×#20332
C5×#19252
C5×#19182
C5×#18932
C5×#18742
C5×#18692
C5×#18522
#261265