Finite Group Databasebeta

← C5×#16452 #11939172

Subgroups — C5×#16452 #11939172

Order 1280.

1310 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#393C211yesmaximal, characteristic
2C2×C5×#387C211yesmaximal, characteristic, complemented
3C5×#1446C211yesmaximal, characteristic, complemented
4C5×#1446C211yesmaximal, characteristic, complemented
5C5×#1445C211yesmaximal, characteristic, complemented
6C5×#1443C211yesmaximal, characteristic, complemented
7C5×#1443C211yesmaximal, characteristic, complemented
8C5×#1442C211yesmaximal, characteristic, complemented
9C5×#1440C211yesmaximal, characteristic
10C5×#1440C211yesmaximal, characteristic
11C5×#1440C211yesmaximal, characteristic
12C5×#1439C211yesmaximal, characteristic
13C5×#1439C211yesmaximal, characteristic
14C5×#1437C211yesmaximal, characteristic
15C5×#1434C211yesmaximal, characteristic, complemented
16C23×C5×Q8C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C5×#393—24no—
28C5×#387—24no—
29C2×C5×#95C2211yescharacteristic
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2211yescharacteristic
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53#16452C511yesmaximal, characteristic, direct product factor, Sylow
54C25×C5C2311yescharacteristic
55C22×C5×Q8—22no—
56C22×C5×Q8—22no—
57C22×C5×Q8—22no—
58C22×C5×Q8—41no—
59C22×C5×Q8—41no—
60C22×C5×Q8—41no—
61C22×C5×Q8—41no—
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×C4×C5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—22no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4—41no—
82C2×C5×C22⋊C4—22no—
83C2×C5×C22⋊C4—22no—
84C2×C5×C22⋊C4—22no—
85C2×C5×C22⋊C4—22no—
86C2×C5×C22⋊C4—22no—
87C2×C5×C22⋊C4—22no—
88C2×C5×C22⋊C4—22no—
89C2×C5×C22⋊C4—22no—
90C2×C5×C22⋊C4—22no—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—41no—
94C2×C5×C22⋊C4—41no—
95C2×C5×C22⋊C4—41no—
96C2×C5×C22⋊C4—41no—
97C2×C5×C22⋊C4—41no—
98C2×C5×C22⋊C4—41no—
99C2×C5×C22⋊C4—41no—
100C2×C5×C22⋊C4—41no—
101C2×C5×C22⋊C4—41no—
102C2×C5×C22⋊C4—41no—
103C2×C42×C5—22no—
104C2×C42×C5—22no—
105C2×C42×C5—41no—
106C5×#95—22no—
107C5×#95—22no—
108C5×#95—22no—
109C5×#95—22no—
110C5×#95—22no—
111C5×#95—22no—
112C5×#95—22no—
113C5×#95—22no—
114C5×#95—22no—
115C5×#95—41no—
116C5×#95—41no—
117C5×#95—41no—
118C5×#95—41no—
119C5×#95—41no—
120C5×#95—41no—
121C5×#95—41no—
122C5×#95—41no—
123C5×#95—41no—
124C5×#95—41no—
125C5×#95—41no—
126C5×#95—41no—
127C5×#95—41no—
128C5×#95—41no—
129C5×#95D414yes—
130C2×#393C2×C511yescharacteristic
131C2×#387C2×C511yescharacteristic, complemented
132#1446C2×C511yescharacteristic, complemented
133#1446C2×C511yescharacteristic, complemented
134#1445C2×C511yescharacteristic, complemented
135#1443C2×C511yescharacteristic, complemented
136#1443C2×C511yescharacteristic, complemented
137#1442C2×C511yescharacteristic, complemented
138#1440C2×C511yescharacteristic
139#1440C2×C511yescharacteristic
140#1440C2×C511yescharacteristic
141#1439C2×C511yescharacteristic
142#1439C2×C511yescharacteristic
143#1437C2×C511yescharacteristic
144#1434C2×C511yescharacteristic, complemented
145C24×C5—21no—
146C24×C5—21no—
147C24×C5—21no—
148C24×C5—21no—
149C24×C5—21no—
150C24×C5—21no—
151C24×C5—21no—
152C24×C5—21no—
153C24×C5—21no—
154C24×C5—21no—
155C24×C5—21no—
156C24×C5—21no—
157C24×C5—21no—
158C24×C5—21no—
159C24×C5#4112yes—
160C24×C5C2411yescharacteristic
161C2×C5×Q8—44no—
162C2×C5×Q8—44no—
163C2×C5×Q8—44no—
164C2×C5×Q8—44no—
165C2×C5×Q8—44no—
166C2×C5×Q8—44no—
167C2×C5×Q8—44no—
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—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—21no—
228C22×C4×C5—21no—
229C22×C4×C5—21no—
230C22×C4×C5—21no—
231C22×C4×C5—21no—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—21no—
236C22×C4×C5—21no—
237C22×C4×C5—21no—
238C22×C4×C5—21no—
239C22×C4×C5—21no—
240C22×C4×C5—21no—
241C22×C4×C5—21no—
242C22×C4×C5—21no—
243C22×C4×C5—21no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5—21no—
247C22×C4×C5—21no—
248C22×C4×C5—21no—
249C22×C4×C5—21no—
250C22×C4×C5—21no—
251C22×C4×C5—21no—
252C22×C4×C5—21no—
253C22×C4×C5—21no—
254C22×C4×C5—21no—
255C22×C4×C5—21no—
256C22×C4×C5—21no—
257C22×C4×C5—21no—
258C22×C4×C5C2×D412yes—
259C22×C4×C5C2×D412yes—
260C22×C4×C5C2×D412yes—
261C22×C4×C5#4112yes—
262C22×C4×C5#4112yes—
263C22×C4×C5#4112yes—
264C22×C4×C5#4112yes—
265C22×C4×C5#4112yes—
266C5×C4⋊C4—28no—
267C5×C4⋊C4—44no—
268C5×C22⋊C4—44no—
269C5×C22⋊C4—44no—
270C5×C22⋊C4—44no—
271C5×C22⋊C4—44no—
272C5×C22⋊C4—44no—
273C5×C22⋊C4—44no—
274C5×C22⋊C4—44no—
275C42×C5—44no—
276C23×Q8C22×C511yescharacteristic
277C22×C4⋊C4C22×C511yescharacteristic
278C22×C4⋊C4C22×C511yescharacteristic
279C22×C22⋊C4C22×C511yescharacteristic
280C22×C22⋊C4C22×C511yescharacteristic
281C22×C22⋊C4C22×C511yescharacteristic
282C22×C22⋊C4C22×C511yescharacteristic
283C22×C22⋊C4C22×C511yescharacteristic
284C22×C22⋊C4C22×C511yescharacteristic
285C22×C22⋊C4C22×C511yescharacteristic
286C22×C42C22×C511yescharacteristic
287#393—24no—
288#387—24no—
289C2×#95C22×C511yescharacteristic
290C2×#95C22×C511yescharacteristic
291C2×#95C22×C511yescharacteristic
292C2×#95C22×C511yescharacteristic
293C2×#95C22×C511yescharacteristic
294C2×#95C22×C511yescharacteristic
295C2×#95C22×C511yescharacteristic
296C2×#95C22×C511yescharacteristic
297C2×#95C22×C511yescharacteristic
298C2×#95C22×C511yescharacteristic
299C2×#95C22×C511yescharacteristic
300C2×#95C22×C511yescharacteristic
301C2×#95C22×C511yescharacteristic
302C2×#95C22×C511yescharacteristic
303C2×#95C22×C511yescharacteristic
304C2×#95C22×C511yescharacteristic
305C2×#95C22×C511yescharacteristic
306C2×#95C22×C511yescharacteristic
307C2×#95C22×C511yescharacteristic
308C2×#95C22×C511yescharacteristic
309C2×#95C22×C511yescharacteristic
310C2×#95C22×C511yescharacteristic
311C2×#95C22×C511yescharacteristic
312C2×#95C22×C511yescharacteristic
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—41no—
321C23×C5—41no—
322C23×C5—41no—
323C23×C5—41no—
324C23×C5—41no—
325C23×C5—41no—
326C23×C5—41no—
327C23×C5—41no—
328C23×C5—41no—
329C23×C5—41no—
330C23×C5—41no—
331C23×C5—41no—
332C23×C5—41no—
333C23×C5—41no—
334C23×C5—41no—
335C23×C5—41no—
336C23×C5—41no—
337C23×C5—41no—
338C23×C5—41no—
339C23×C5—41no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5—41no—
343C23×C5—41no—
344C23×C5—41no—
345C23×C5—41no—
346C23×C5—41no—
347C23×C5—41no—
348C23×C5C22×D411yescharacteristic
349C23×C5C2×#4111yescharacteristic
350C23×C5C2×#4111yescharacteristic
351C23×C5C2×#4111yescharacteristic
352C23×C5C2×#4111yescharacteristic
353C23×C5C2×#4111yescharacteristic
354C23×C5C2×#4111yescharacteristic
355C23×C5H(5,𝔽2)11yescharacteristic
356C23×C5H(5,𝔽2)11yescharacteristic
357C23×C5H(5,𝔽2)11yescharacteristic
358C23×C5H(5,𝔽2)11yescharacteristic
359C23×C5H(5,𝔽2)11yescharacteristic
360C23×C52−1+411yescharacteristic
361C23×C52−1+411yescharacteristic
362C23×C52−1+411yescharacteristic
363C5×Q8—416no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—41no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
401C2×C4×C5—41no—
402C2×C4×C5—41no—
403C2×C4×C5—41no—
404C2×C4×C5—41no—
405C2×C4×C5—41no—
406C2×C4×C5—41no—
407C2×C4×C5—41no—
408C2×C4×C5—41no—
409C2×C4×C5—41no—
410C2×C4×C5—41no—
411C2×C4×C5—41no—
412C2×C4×C5—41no—
413C2×C4×C5—41no—
414C2×C4×C5—41no—
415C2×C4×C5—41no—
416C2×C4×C5—41no—
417C2×C4×C5—41no—
418C2×C4×C5—41no—
419C2×C4×C5—41no—
420C2×C4×C5—41no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—41no—
426C2×C4×C5—41no—
427C2×C4×C5—41no—
428C2×C4×C5—41no—
429C2×C4×C5—41no—
430C2×C4×C5—41no—
431C2×C4×C5—41no—
432C2×C4×C5—41no—
433C2×C4×C5—41no—
434C2×C4×C5—41no—
435C2×C4×C5—41no—
436C2×C4×C5—41no—
437C2×C4×C5—41no—
438C2×C4×C5—41no—
439C2×C4×C5—41no—
440C2×C4×C5—41no—
441C2×C4×C5—41no—
442C2×C4×C5—41no—
443C2×C4×C5—41no—
444C2×C4×C5—41no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—41no—
448C2×C4×C5—41no—
449C2×C4×C5—41no—
450C2×C4×C5—41no—
451C2×C4×C5—41no—
452C2×C4×C5—41no—
453C2×C4×C5—41no—
454C2×C4×C5—41no—
455C2×C4×C5—41no—
456C2×C4×C5—41no—
457C2×C4×C5—41no—
458C2×C4×C5—41no—
459C2×C4×C5—41no—
460C2×C4×C5—41no—
461C2×C4×C5—41no—
462C25C23×C511yescharacteristic
463C22×Q8—22no—
464C22×Q8—22no—
465C22×Q8—22no—
466C22×Q8—41no—
467C22×Q8—41no—
468C22×Q8—41no—
469C22×Q8—41no—
470C23×C4C23×C511yescharacteristic
471C23×C4C23×C511yescharacteristic
472C23×C4C23×C511yescharacteristic
473C23×C4C23×C511yescharacteristic
474C23×C4C23×C511yescharacteristic
475C23×C4C23×C511yescharacteristic
476C23×C4C23×C511yescharacteristic
477C23×C4C23×C511yescharacteristic
478C23×C4C23×C511yescharacteristic
479C23×C4C23×C511yescharacteristic
480C23×C4C23×C511yescharacteristic
481C23×C4C23×C511yescharacteristic
482C23×C4C23×C511yescharacteristic
483C23×C4C23×C511yescharacteristic
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—41no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—41no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—41no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—41no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—41no—
524#95—41no—
525#95—41no—
526#95—41no—
527#95—41no—
528#95—41no—
529#95—41no—
530#95—41no—
531#95—41no—
532#95—41no—
533#95—41no—
534#95—41no—
535#95—41no—
536#95—41no—
537#95C5×D414yes—
538C22×C5—42no—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—81no—
546C22×C5—81no—
547C22×C5—81no—
548C22×C5—81no—
549C22×C5—81no—
550C22×C5—81no—
551C22×C5—81no—
552C22×C5—81no—
553C22×C5#52511yescharacteristic
554C22×C5#52911yescharacteristic
555C22×C5#52911yescharacteristic
556C22×C5#53511yescharacteristic
557C22×C5#53611yescharacteristic
558C22×C5#53811yescharacteristic
559C22×C5#53811yescharacteristic
560C22×C5#53811yescharacteristic
561C22×C5#53811yescharacteristic
562C22×C5#53911yescharacteristic
563C22×C5#53911yescharacteristic
564C22×C5#54111yescharacteristic
565C22×C5#54211yescharacteristic
566C22×C5#54211yescharacteristic
567C22×C5#54211yescharacteristic
568C22×C5#54211yescharacteristic
569C22×C5#54211yescharacteristic
570C22×C5#54211yescharacteristic
571C22×C5#54211yescharacteristic
572C22×C5#54611yescharacteristic
573C22×C5#54611yescharacteristic
574C22×C5#54611yescharacteristic
575C22×C5#54811yescharacteristic
576C22×C5#55111yescharacteristic
577C22×C5#55111yescharacteristic
578C22×C5#55111yescharacteristic
579C22×C5#55211yescharacteristic
580C22×C5#55211yescharacteristic
581C22×C5#55511yescharacteristic
582C22×C5#55611yescharacteristic
583C22×C5#55911yescharacteristic
584C22×C5#56011yescharacteristic
585C22×C5#56211yescharacteristic
586C22×C5#56211yescharacteristic
587C22×C5#56311yescharacteristic
588C4×C5—42no—
589C4×C5—42no—
590C4×C5—42no—
591C4×C5—42no—
592C4×C5—42no—
593C4×C5—42no—
594C4×C5—42no—
595C4×C5—42no—
596C4×C5—81no—
597C4×C5—81no—
598C4×C5—81no—
599C4×C5—81no—
600C4×C5—81no—
601C4×C5—81no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24C5×#4112yes—
617C24C24×C511yescharacteristic
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—44no—
623C2×Q8—44no—
624C2×Q8—44no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4C2×C5×D412yes—
716C22×C4C2×C5×D412yes—
717C22×C4C2×C5×D412yes—
718C22×C4C5×#4112yes—
719C22×C4C5×#4112yes—
720C22×C4C5×#4112yes—
721C22×C4C5×#4112yes—
722C22×C4C5×#4112yes—
723C4⋊C4—28no—
724C4⋊C4—44no—
725C22⋊C4—44no—
726C22⋊C4—44no—
727C22⋊C4—44no—
728C22⋊C4—44no—
729C22⋊C4—44no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C42—44no—
733C2×C5—82no—
734C2×C5#245911yescharacteristic
735C2×C5#247711yescharacteristic
736C2×C5#252711yescharacteristic
737C2×C5#263211yescharacteristic
738C2×C5#265011yescharacteristic
739C2×C5#265311yescharacteristic
740C2×C5#268511yescharacteristic
741C2×C5#269011yescharacteristic
742C2×C5#269611yescharacteristic
743C2×C5#270011yescharacteristic
744C2×C5#273711yescharacteristic
745C2×C5#275111yescharacteristic
746C2×C5#275411yescharacteristic
747C2×C5#277511yescharacteristic
748C2×C5#283011yescharacteristic
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23C22×C5×D411yescharacteristic
785C23C2×C5×#4111yescharacteristic
786C23C2×C5×#4111yescharacteristic
787C23C2×C5×#4111yescharacteristic
788C23C2×C5×#4111yescharacteristic
789C23C2×C5×#4111yescharacteristic
790C23C2×C5×#4111yescharacteristic
791C23C5×H(5,𝔽2)11yescharacteristic
792C23C5×H(5,𝔽2)11yescharacteristic
793C23C5×H(5,𝔽2)11yescharacteristic
794C23C5×H(5,𝔽2)11yescharacteristic
795C23C5×H(5,𝔽2)11yescharacteristic
796C23C5×2−1+411yescharacteristic
797C23C5×2−1+411yescharacteristic
798C23C5×2−1+411yescharacteristic
799Q8—416no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C5#1645211yescharacteristic, direct product factor, Sylow
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22C5×#52511yescharacteristic
915C22C5×#52911yescharacteristic
916C22C5×#52911yescharacteristic
917C22C5×#53511yescharacteristic
918C22C5×#53611yescharacteristic
919C22C5×#53811yescharacteristic
920C22C5×#53811yescharacteristic
921C22C5×#53811yescharacteristic
922C22C5×#53811yescharacteristic
923C22C5×#53911yescharacteristic
924C22C5×#53911yescharacteristic
925C22C5×#54111yescharacteristic
926C22C5×#54211yescharacteristic
927C22C5×#54211yescharacteristic
928C22C5×#54211yescharacteristic
929C22C5×#54211yescharacteristic
930C22C5×#54211yescharacteristic
931C22C5×#54211yescharacteristic
932C22C5×#54211yescharacteristic
933C22C5×#54611yescharacteristic
934C22C5×#54611yescharacteristic
935C22C5×#54611yescharacteristic
936C22C5×#54811yescharacteristic
937C22C5×#55111yescharacteristic
938C22C5×#55111yescharacteristic
939C22C5×#55111yescharacteristic
940C22C5×#55211yescharacteristic
941C22C5×#55211yescharacteristic
942C22C5×#55511yescharacteristic
943C22C5×#55611yescharacteristic
944C22C5×#55911yescharacteristic
945C22C5×#56011yescharacteristic
946C22C5×#56211yescharacteristic
947C22C5×#56211yescharacteristic
948C22C5×#56311yescharacteristic
949C4—42no—
950C4—42no—
951C4—42no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—81no—
958C4—81no—
959C4—81no—
960C4—81no—
961C4—81no—
962C4—81no—
963C2—82no—
964C2C5×#245911yescharacteristic
965C2C5×#247711yescharacteristic
966C2C5×#252711yescharacteristic
967C2C5×#263211yescharacteristic
968C2C5×#265011yescharacteristic
969C2C5×#265311yescharacteristic
970C2C5×#268511yescharacteristic
971C2C5×#269011yescharacteristic
972C2C5×#269611yescharacteristic
973C2C5×#270011yescharacteristic
974C2C5×#273711yescharacteristic
975C2C5×#275111yescharacteristic
976C2C5×#275411yescharacteristic
977C2C5×#277511yescharacteristic
978C2C5×#283011yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutator, Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#387C2semidirect
3. C5×#1446C2semidirect
4. C5×#1446C2semidirect
5. C5×#1445C2semidirect
6. C5×#1443C2semidirect
7. C5×#1443C2semidirect
8. C5×#1442C2semidirect
15. C5×#1434C2semidirect
53. #16452C5direct (N × H)
131. C2×#387C2×C5semidirect
132. #1446C2×C5semidirect
133. #1446C2×C5semidirect
134. #1445C2×C5semidirect
135. #1443C2×C5semidirect
136. #1443C2×C5semidirect
137. #1442C2×C5semidirect
144. #1434C2×C5semidirect
898. C5#16452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3932
C2×C5×#3872
C5×#14462
C5×#14452
C5×#14432
C5×#14422
C5×#14402
C5×#14392
C5×#14372
C5×#14342
#164525