Finite Group Databasebeta

← C5×#26928 #11949648

Subgroups — C5×#26928 #11949648

Order 1280.

948 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#483C211yesmaximal, characteristic, complemented
2C2×C5×#461C211yesmaximal, characteristic, complemented
3C5×#2429C211yesmaximal, characteristic, complemented
4C5×#2361C211yesmaximal, characteristic
5C5×#2088C211yesmaximal, characteristic, complemented
6C5×#2043C211yesmaximal, characteristic, complemented
7C5×#2000C211yesmaximal, characteristic
8C5×#2000C211yesmaximal, characteristic
9C5×#1968C211yesmaximal, characteristic, complemented
10C5×#1927C211yesmaximal, characteristic, complemented
11C5×#1923C211yesmaximal, characteristic, complemented
12C5×#1880C211yesmaximal, characteristic, complemented
13C5×#1872C211yesmaximal, characteristic, complemented
14C5×#1864C211yesmaximal, characteristic, complemented
15C4×C5×#103C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C22×C5×SD16C2211yescharacteristic
18C2×C5×C4⋊Q8C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×C4×C5×Q8C2211yescharacteristic
23C2×C4×C5×D4—21no—
24C2×C4×C5×D4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C5×#483—24no—
27C5×#461—24no—
28C2×C5×#106C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×C4⋊C8C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#103C2211yescharacteristic
36C2×C5×#103C2211yescharacteristic
37C2×C5×#102C2211yescharacteristic
38C2×C5×#102C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C2×C5×C22⋊C8C2211yescharacteristic
41C2×C4×C5×C8C2211yescharacteristic
42C5×#398—21no—
43C5×#396—21no—
44C5×#391C2211yescharacteristic
45C5×#390C2211yescharacteristic
46C5×#389—21no—
47C5×#389C2211yescharacteristic
48C5×#389C2211yescharacteristic
49C5×#388—21no—
50C5×#388—21no—
51C5×#386—21no—
52C5×#385—21no—
53C4×C5×C4⋊C4C2211yescharacteristic
54C4×C5×C22⋊C4C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26928C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×Q8C2311yescharacteristic
64C22×C5×D4—21no—
65C22×C5×D4C2311yescharacteristic
66C23×C4×C5—21no—
67C23×C4×C5—21no—
68C23×C4×C5C2311yescharacteristic
69C2×C5×SD16—22no—
70C2×C5×SD16—22no—
71C2×C5×SD16—22no—
72C2×C5×SD16—22no—
73C2×C5×SD16—41no—
74C2×C5×SD16—41no—
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C22×C5×C8C2311yescharacteristic
78C22×C5×C8C2311yescharacteristic
79C5×C4⋊Q8—22no—
80C5×C4⋊Q8—41no—
81C5×C22⋊Q8—22no—
82C5×C22⋊Q8—22no—
83C5×C22⋊Q8—41no—
84C5×C22⋊Q8—41no—
85C5×#121—22no—
86C5×#121—22no—
87C4×C5×Q8—22no—
88C4×C5×Q8—41no—
89C4×C5×D4—22no—
90C4×C5×D4—41no—
91C4×C5×D4—44no—
92C2×C5×C4⋊C4—22no—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—21no—
97C2×C5×C4⋊C4—21no—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4—41no—
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
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×C5—21no—
117C2×C42×C5C2311yescharacteristic
118C2×C42×C5C2311yescharacteristic
119C5×#106—22no—
120C5×#106—22no—
121C5×C4⋊C8—22no—
122C5×#103—22no—
123C5×#103—22no—
124C5×#103—22no—
125C5×#103—22no—
126C5×#103—41no—
127C5×#103D414yescomplemented
128C5×#102—22no—
129C5×#102—41no—
130C5×C22⋊C8—22no—
131C5×C22⋊C8—41no—
132C4×C5×C8—41no—
133C5×#95—21no—
134C5×#95—21no—
135C5×#95—21no—
136C5×#95—21no—
137C5×#95—21no—
138C5×#95D411yescharacteristic
139C5×#95D411yescharacteristic
140C2×#483C2×C511yescharacteristic, complemented
141C2×#461C2×C511yescharacteristic, complemented
142#2429C2×C511yescharacteristic, complemented
143#2361C2×C511yescharacteristic
144#2088C2×C511yescharacteristic, complemented
145#2043C2×C511yescharacteristic, complemented
146#2000C2×C511yescharacteristic
147#2000C2×C511yescharacteristic
148#1968C2×C511yescharacteristic, complemented
149#1927C2×C511yescharacteristic, complemented
150#1923C2×C511yescharacteristic, complemented
151#1880C2×C511yescharacteristic, complemented
152#1872C2×C511yescharacteristic, complemented
153#1864C2×C511yescharacteristic, complemented
154C4×#103C2×C511yescharacteristic, complemented
155C24×C5—21no—
156C24×C5C2×D411yescharacteristic
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—21no—
166C2×C5×Q8—21no—
167C2×C5×Q8—21no—
168C2×C5×Q8C2×D412yes—
169C2×C5×D4—24no—
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4—21no—
174C2×C5×D4—21no—
175C2×C5×D4—42no—
176C2×C5×D4—42no—
177C2×C5×D4#4112yes—
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—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—42no—
192C22×C4×C5—42no—
193C22×C4×C5—42no—
194C22×C4×C5—42no—
195C22×C4×C5—81no—
196C22×C4×C5—81no—
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5C2×D411yescharacteristic
201C22×C4×C5C2×D411yescharacteristic
202C22×C4×C5C2411yescharacteristic
203C5×SD16—44no—
204C5×SD16—44no—
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×C8—21no—
213C2×C5×C8—21no—
214C2×C5×C8—21no—
215C2×C5×C8—21no—
216C2×C5×C8C2×D412yes—
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—42no—
225C5×C4⋊C4—42no—
226C5×C4⋊C4—42no—
227C5×C4⋊C4—42no—
228C5×C4⋊C4—42no—
229C5×C4⋊C4—42no—
230C5×C4⋊C4—42no—
231C5×C4⋊C4—42no—
232C5×C4⋊C4C2×D412yes—
233C5×C4⋊C4#4112yes—
234C5×C4⋊C4#4112yes—
235C5×C22⋊C4—24no—
236C5×C22⋊C4—41no—
237C5×C22⋊C4—42no—
238C5×C22⋊C4—42no—
239C5×C22⋊C4—42no—
240C5×C22⋊C4—42no—
241C5×C22⋊C4—81no—
242C5×C22⋊C4SD1614yescomplemented
243C42×C5—21no—
244C42×C5—21no—
245C42×C5—21no—
246C42×C5—21no—
247C42×C5—42no—
248C42×C5—42no—
249C22×SD16C22×C511yescharacteristic
250C22×SD16C22×C511yescharacteristic
251C2×C4⋊Q8C22×C511yescharacteristic
252C2×C22⋊Q8C22×C511yescharacteristic
253C2×C22⋊Q8C22×C511yescharacteristic
254C2×#121C22×C511yescharacteristic
255C2×C4×Q8C22×C511yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4C22×C511yescharacteristic
258C22×C4⋊C4C22×C511yescharacteristic
259#483—24no—
260#461—24no—
261C2×#106C22×C511yescharacteristic
262C2×#106C22×C511yescharacteristic
263C2×C4⋊C8C22×C511yescharacteristic
264C2×#103C22×C511yescharacteristic
265C2×#103C22×C511yescharacteristic
266C2×#103C22×C511yescharacteristic
267C2×#103C22×C511yescharacteristic
268C2×#103C22×C511yescharacteristic
269C2×#103C22×C511yescharacteristic
270C2×#102C22×C511yescharacteristic
271C2×#102C22×C511yescharacteristic
272C2×C22⋊C8C22×C511yescharacteristic
273C2×C22⋊C8C22×C511yescharacteristic
274C2×C4×C8C22×C511yescharacteristic
275#398—21no—
276#396—21no—
277#391C22×C511yescharacteristic
278#390C22×C511yescharacteristic
279#389—21no—
280#389C22×C511yescharacteristic
281#389C22×C511yescharacteristic
282#388—21no—
283#388—21no—
284#386—21no—
285#385—21no—
286C4×C4⋊C4C22×C511yescharacteristic
287C4×C22⋊C4C22×C511yescharacteristic
288#340C22×C511yescharacteristic
289#340C22×C511yescharacteristic
290#340C22×C511yescharacteristic
291#340C22×C511yescharacteristic
292#336C22×C511yescharacteristic
293#336C22×C511yescharacteristic
294C23×C5—21no—
295C23×C5—21no—
296C23×C5—21no—
297C23×C5—21no—
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—22no—
301C23×C5—41no—
302C23×C5—41no—
303C23×C5—41no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5C2×SD1612yes—
308C23×C5C22×D411yescharacteristic
309C5×Q8—22no—
310C5×Q8—22no—
311C5×Q8—41no—
312C5×Q8—41no—
313C5×Q8—41no—
314C5×Q8—41no—
315C5×Q8—41no—
316C5×Q8—41no—
317C5×D4—22no—
318C5×D4—22no—
319C5×D4—48no—
320C5×D4—41no—
321C5×D4—41no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—22no—
328C2×C4×C5—21no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—22no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
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×C5C2×SD1612yes—
363C2×C4×C5C2×SD1612yes—
364C2×C4×C5C22×D411yescharacteristic
365C2×C4×C5C2×#4111yescharacteristic
366C2×C4×C5C2×#4111yescharacteristic
367C2×C4×C5C2×#4111yescharacteristic
368C2×C4×C5H(5,𝔽2)11yescharacteristic
369C2×C4×C5H(5,𝔽2)11yescharacteristic
370C5×C8—22no—
371C5×C8—41no—
372C5×C8—41no—
373C5×C8—41no—
374C22×Q8C23×C511yescharacteristic
375C22×Q8C23×C511yescharacteristic
376C22×D4—21no—
377C22×D4C23×C511yescharacteristic
378C23×C4—21no—
379C23×C4—21no—
380C23×C4C23×C511yescharacteristic
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—41no—
386C2×SD16—41no—
387C22×C8C23×C511yescharacteristic
388C22×C8C23×C511yescharacteristic
389C22×C8C23×C511yescharacteristic
390C22×C8C23×C511yescharacteristic
391C4⋊Q8—22no—
392C4⋊Q8—41no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—41no—
396C22⋊Q8—41no—
397#121—22no—
398#121—22no—
399C4×Q8—22no—
400C4×Q8—41no—
401C4×D4—22no—
402C4×D4—41no—
403C4×D4—44no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—41no—
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⋊C4C5×D411yescharacteristic
426C2×C22⋊C4C5×D411yescharacteristic
427C2×C42—21no—
428C2×C42—21no—
429C2×C42C23×C511yescharacteristic
430C2×C42C23×C511yescharacteristic
431#106—22no—
432#106—22no—
433C4⋊C8—22no—
434#103—22no—
435#103—22no—
436#103—22no—
437#103—22no—
438#103—41no—
439#103C5×D414yescomplemented
440#102—22no—
441#102—41no—
442C22⋊C8—22no—
443C22⋊C8—41no—
444C4×C8—41no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95C5×D411yescharacteristic
451#95C5×D411yescharacteristic
452C22×C5—22no—
453C22×C5—22no—
454C22×C5—22no—
455C22×C5—41no—
456C22×C5—41no—
457C22×C5—41no—
458C22×C5—41no—
459C22×C5—42no—
460C22×C5—42no—
461C22×C5—42no—
462C22×C5—81no—
463C22×C5—81no—
464C22×C5—81no—
465C22×C5—81no—
466C22×C5#52511yescharacteristic
467C22×C5D4211yescharacteristic
468C22×C5#54611yescharacteristic
469C22×C5C22×SD1611yescharacteristic
470C22×C5#57511yescharacteristic
471C22×C5#57711yescharacteristic
472C22×C5#57811yescharacteristic
473C4×C5—22no—
474C4×C5—22no—
475C4×C5—42no—
476C4×C5—41no—
477C4×C5—42no—
478C4×C5—41no—
479C4×C5—42no—
480C4×C5—41no—
481C4×C5—42no—
482C4×C5—81no—
483C4×C5—81no—
484C4×C5—81no—
485C4×C5#53211yescharacteristic
486C4×C5#54011yescharacteristic
487C4×C5#54611yescharacteristic
488C4×C5#55311yescharacteristic
489C24—21no—
490C24C2×C5×D411yescharacteristic
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8C2×C5×D412yes—
503C2×D4—24no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4C5×#4112yes—
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—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4C2×C5×D411yescharacteristic
532C22×C4C2×C5×D411yescharacteristic
533C22×C4C2×C5×D411yescharacteristic
534C22×C4C2×C5×D411yescharacteristic
535C22×C4C2×C5×D411yescharacteristic
536C22×C4C24×C511yescharacteristic
537SD16—44no—
538SD16—44no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8C2×C5×D412yes—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4C2×C5×D412yes—
567C4⋊C4C5×#4112yes—
568C4⋊C4C5×#4112yes—
569C22⋊C4—24no—
570C22⋊C4—41no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—81no—
576C22⋊C4C5×SD1614yescomplemented
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—42no—
582C42—42no—
583C2×C5—42no—
584C2×C5—82no—
585C2×C5#246411yescharacteristic
586C2×C5#310111yescharacteristic
587C2×C5#312011yescharacteristic
588C2×C5#327711yescharacteristic
589C2×C5D4×SD1611yescharacteristic
590C2×C5#329811yescharacteristic
591C2×C5#330711yescharacteristic
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C2×C5×SD1612yes—
606C23C22×C5×D411yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615D4—22no—
616D4—22no—
617D4—48no—
618D4—41no—
619D4—41no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
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—84no—
659C2×C4—84no—
660C2×C4C2×C5×SD1612yes—
661C2×C4C2×C5×SD1612yes—
662C2×C4C22×C5×D411yescharacteristic
663C2×C4C2×C5×#4111yescharacteristic
664C2×C4C2×C5×#4111yescharacteristic
665C2×C4C2×C5×#4111yescharacteristic
666C2×C4C5×H(5,𝔽2)11yescharacteristic
667C2×C4C5×H(5,𝔽2)11yescharacteristic
668C8—22no—
669C8—41no—
670C8—41no—
671C8—41no—
672C5#2692811yescharacteristic, direct product factor, Sylow
673C22—22no—
674C22—22no—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22C5×#52511yescharacteristic
688C22C5×D4211yescharacteristic
689C22C5×#54611yescharacteristic
690C22C22×C5×SD1611yescharacteristic
691C22C5×#57511yescharacteristic
692C22C5×#57711yescharacteristic
693C22C5×#57811yescharacteristic
694C4—22no—
695C4—22no—
696C4—41no—
697C4—42no—
698C4—41no—
699C4—42no—
700C4—42no—
701C4—41no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4C5×#53211yescharacteristic
707C4C5×#54011yescharacteristic
708C4C5×#54611yescharacteristic
709C4C5×#55311yescharacteristic
710C2—42no—
711C2—82no—
712C2C5×#246411yescharacteristic
713C2C5×#310111yescharacteristic
714C2C5×#312011yescharacteristic
715C2C5×#327711yescharacteristic
716C2C5×D4×SD1611yescharacteristic
717C2C5×#329811yescharacteristic
718C2C5×#330711yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C4×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#483C2semidirect
2. C2×C5×#461C2semidirect
3. C5×#2429C2semidirect
5. C5×#2088C2semidirect
6. C5×#2043C2semidirect
9. C5×#1968C2semidirect
10. C5×#1927C2semidirect
11. C5×#1923C2semidirect
12. C5×#1880C2semidirect
13. C5×#1872C2semidirect
14. C5×#1864C2semidirect
15. C4×C5×#103C2semidirect
61. #26928C5direct (N × H)
127. C5×#103D4semidirect
140. C2×#483C2×C5semidirect
141. C2×#461C2×C5semidirect
142. #2429C2×C5semidirect
144. #2088C2×C5semidirect
145. #2043C2×C5semidirect
148. #1968C2×C5semidirect
149. #1927C2×C5semidirect
150. #1923C2×C5semidirect
151. #1880C2×C5semidirect
152. #1872C2×C5semidirect
153. #1864C2×C5semidirect
154. C4×#103C2×C5semidirect
242. C5×C22⋊C4SD16semidirect
439. #103C5×D4semidirect
576. C22⋊C4C5×SD16semidirect
672. C5#26928direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4832
C2×C5×#4612
C5×#24292
C5×#23612
C5×#20882
C5×#20432
C5×#20002
C5×#19682
C5×#19272
C5×#19232
C5×#18802
C5×#18722
C5×#18642
C4×C5×#1032
#269285