Finite Group Databasebeta

← C5×#24028 #11946748

Subgroups — C5×#24028 #11946748

Order 1280.

1250 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3489C211yesmaximal, characteristic
2C5×#3093C211yesmaximal, characteristic, complemented
3C5×#2896C211yesmaximal, characteristic, complemented
4C5×#2499C211yesmaximal, characteristic, complemented
5C5×#2040C211yesmaximal, characteristic, complemented
6C5×#2039C211yesmaximal, characteristic, complemented
7C5×#2038C211yesmaximal, characteristic, complemented
8C5×#2038C211yesmaximal, characteristic, complemented
9C5×#1901C211yesmaximal, characteristic, complemented
10C5×#1871C211yesmaximal, characteristic, complemented
11C5×#1860C211yesmaximal, characteristic, complemented
12C5×#1859C211yesmaximal, characteristic, complemented
13C5×#1793C211yesmaximal, characteristic, complemented
14C5×#1793C211yesmaximal, characteristic, complemented
15C5×#1789C211yesmaximal, characteristic, complemented
16C2×C5×2−1+4C2211yescharacteristic
17C22×C5×#41C2211yescharacteristic
18C22×C5×M16C2211yescharacteristic
19C5×D4×Q8—21no—
20C5×#548—21no—
21C5×#547—21no—
22C5×#547—22no—
23C5×#546—21no—
24C5×#546—22no—
25C5×#537—21no—
26C5×#537C2211yescharacteristic
27C5×#536—21no—
28C5×#536C2211yescharacteristic
29C5×#525—21no—
30C5×#525C2211yescharacteristic
31C2×C5×C22⋊Q8—21no—
32C2×C5×C22⋊Q8C2211yescharacteristic
33C5×#520C2211yescharacteristic
34C2×C5×#117C2211yescharacteristic
35C5×#485—21no—
36C5×#485—21no—
37C5×#482—21no—
38C5×#482—21no—
39C5×#428C2211yescharacteristic, complemented
40C5×#428C2211yescharacteristic, complemented
41C2×C5×#104C2211yescharacteristic
42C2×C5×#104C2211yescharacteristic
43C2×C5×#104C2211yescharacteristic
44C2×C5×#104C2211yescharacteristic
45C2×C5×#104C2211yescharacteristic, complemented
46C2×C5×#104C2211yescharacteristic, complemented
47C5×#419—21no—
48C5×#418—21no—
49C5×#417C2211yescharacteristic
50C5×#417C2211yescharacteristic
51C5×#417C2211yescharacteristic
52C5×#417C2211yescharacteristic
53C5×#417C2211yescharacteristic, complemented
54C5×#417C2211yescharacteristic, complemented
55C5×#416—21no—
56C5×#416—21no—
57C2×C5×#101C2211yescharacteristic, complemented
58C2×C5×#101C2211yescharacteristic, complemented
59C5×#407C2211yescharacteristic
60C5×#397—22no—
61C5×#391C2211yescharacteristic, complemented
62C5×#391C2211yescharacteristic, complemented
63C5×#387—22no—
64C5×#384C2211yescharacteristic, complemented
65C5×#382C2211yescharacteristic, complemented
66C4×C5×C22⋊C4C2211yescharacteristic
67C5×#343C2211yescharacteristic, complemented
68C5×#343C2211yescharacteristic, complemented
69C5×#339C2211yescharacteristic, complemented
70C5×#339C2211yescharacteristic, complemented
71#24028C511yesmaximal, characteristic, direct product factor, Sylow
72C5×2−1+4—22no—
73C5×2−1+4—22no—
74C5×2−1+4—41no—
75C5×2−1+4—41no—
76C2×C5×#41—21no—
77C2×C5×#41—21no—
78C2×C5×#41—21no—
79C2×C5×#41—22no—
80C2×C5×#41—21no—
81C2×C5×#41—22no—
82C2×C5×#41—22no—
83C2×C5×#41—41no—
84C2×C5×#41—41no—
85C2×C5×#41D411yescharacteristic
86C2×C5×#41D411yescharacteristic
87C2×C5×#41C2311yescharacteristic
88C2×C5×#41C2311yescharacteristic
89C2×C5×#41C2311yescharacteristic
90C22×C5×Q8—21no—
91C22×C5×Q8—21no—
92C22×C5×Q8D411yescharacteristic
93C22×C5×Q8C2311yescharacteristic
94C22×C5×D4—21no—
95C22×C5×D4D411yescharacteristic
96C23×C4×C5—21no—
97C23×C4×C5C2311yescharacteristic
98C2×C5×M16—21no—
99C2×C5×M16—41no—
100C2×C5×M16—41no—
101C2×C5×M16C2311yescharacteristic
102C2×C5×M16C2311yescharacteristic
103C2×C5×M16C2311yescharacteristic
104C2×C5×M16C2311yescharacteristic
105C22×C5×C8—21no—
106C5×C4⋊Q8—22no—
107C5×C4⋊Q8—21no—
108C5×#124—22no—
109C5×#124—21no—
110C5×#123—22no—
111C5×#123—22no—
112C5×#123—22no—
113C5×#123—21no—
114C5×#123—22no—
115C5×C22⋊Q8—22no—
116C5×C22⋊Q8—22no—
117C5×C22⋊Q8—22no—
118C5×C22⋊Q8—21no—
119C5×C22⋊Q8—21no—
120C5×C22⋊Q8—21no—
121C5×C22⋊Q8—21no—
122C5×C22⋊Q8—21no—
123C5×C22⋊Q8—21no—
124C5×C22⋊Q8—21no—
125C5×C22⋊Q8—21no—
126C5×C22⋊Q8D411yescharacteristic
127C5×C22⋊Q8D411yescharacteristic
128C5×#121—22no—
129C5×#121—22no—
130C5×#121—22no—
131C5×#121—21no—
132C5×#121—21no—
133C5×#121—22no—
134C5×#121D411yescharacteristic
135C5×#121D411yescharacteristic
136C5×#120—22no—
137C5×#120—21no—
138C4×C5×Q8—21no—
139C4×C5×D4—22no—
140C4×C5×D4—22no—
141C4×C5×D4—21no—
142C4×C5×D4—22no—
143C4×C5×D4—21no—
144C4×C5×D4—21no—
145C5×#117—21no—
146C5×#117—21no—
147C5×#117—21no—
148C5×#117—21no—
149C5×#117—21no—
150C5×#117C2311yescharacteristic
151C2×C5×C4⋊C4—22no—
152C2×C5×C4⋊C4—21no—
153C2×C5×C4⋊C4—22no—
154C2×C5×C4⋊C4D412yes—
155C2×C5×C4⋊C4C2311yescharacteristic
156C2×C5×C4⋊C4C2311yescharacteristic
157C2×C5×C4⋊C4C2311yescharacteristic
158C2×C5×C22⋊C4—22no—
159C2×C5×C22⋊C4—21no—
160C2×C5×C22⋊C4—21no—
161C2×C5×C22⋊C4D412yes—
162C2×C42×C5—21no—
163C2×C42×C5C2311yescharacteristic
164C2×C42×C5C2311yescharacteristic
165C5×#107—21no—
166C5×#107—21no—
167C5×#106—21no—
168C5×#106—21no—
169C5×#104—22no—
170C5×#104—22no—
171C5×#104—41no—
172C5×#104—41no—
173C5×#104—41no—
174C5×#104—41no—
175C5×#103—21no—
176C5×#103—21no—
177C5×#103—21no—
178C5×#103—21no—
179C5×#103—21no—
180C5×#103—21no—
181C5×#102—21no—
182C5×#102—21no—
183C5×#102—21no—
184C5×#102—21no—
185C5×#102—21no—
186C5×#102—21no—
187C5×#101—41no—
188C5×#101—41no—
189C5×C22⋊C8—21no—
190C5×C22⋊C8—21no—
191C5×#95—21no—
192C5×#95—22no—
193C5×#95—22no—
194C5×#95—22no—
195#3489C2×C511yescharacteristic
196#3093C2×C511yescharacteristic, complemented
197#2896C2×C511yescharacteristic, complemented
198#2499C2×C511yescharacteristic, complemented
199#2040C2×C511yescharacteristic, complemented
200#2039C2×C511yescharacteristic, complemented
201#2038C2×C511yescharacteristic, complemented
202#2038C2×C511yescharacteristic, complemented
203#1901C2×C511yescharacteristic, complemented
204#1871C2×C511yescharacteristic, complemented
205#1860C2×C511yescharacteristic, complemented
206#1859C2×C511yescharacteristic, complemented
207#1793C2×C511yescharacteristic, complemented
208#1793C2×C511yescharacteristic, complemented
209#1789C2×C511yescharacteristic, complemented
210C24×C5—21no—
211C24×C5C2×D411yescharacteristic
212C5×#41—21no—
213C5×#41—21no—
214C5×#41—22no—
215C5×#41—22no—
216C5×#41—21no—
217C5×#41—21no—
218C5×#41—21no—
219C5×#41—21no—
220C5×#41—21no—
221C5×#41—21no—
222C5×#41—21no—
223C5×#41—21no—
224C5×#41—42no—
225C5×#41—42no—
226C5×#41—41no—
227C5×#41—41no—
228C5×#41—42no—
229C5×#41—42no—
230C5×#41—42no—
231C5×#41—42no—
232C5×#41—44no—
233C5×#41—44no—
234C5×#41—42no—
235C5×#41—42no—
236C5×#41#4112yes—
237C5×#41#4112yes—
238C2×C5×Q8—22no—
239C2×C5×Q8—21no—
240C2×C5×Q8—21no—
241C2×C5×Q8—21no—
242C2×C5×Q8—21no—
243C2×C5×Q8—21no—
244C2×C5×Q8—21no—
245C2×C5×Q8—21no—
246C2×C5×Q8—22no—
247C2×C5×Q8—41no—
248C2×C5×Q8—42no—
249C2×C5×Q8—42no—
250C2×C5×Q8—42no—
251C2×C5×Q8—42no—
252C2×C5×Q8C2×D411yescharacteristic
253C2×C5×Q8C2×D411yescharacteristic
254C2×C5×Q8C2×D411yescharacteristic
255C2×C5×D4—21no—
256C2×C5×D4—22no—
257C2×C5×D4—22no—
258C2×C5×D4—21no—
259C2×C5×D4—21no—
260C2×C5×D4—21no—
261C2×C5×D4—21no—
262C2×C5×D4—21no—
263C2×C5×D4—22no—
264C2×C5×D4—21no—
265C2×C5×D4—21no—
266C2×C5×D4—41no—
267C2×C5×D4—42no—
268C2×C5×D4—42no—
269C2×C5×D4C2×D411yescharacteristic
270C2×C5×D4C2×D411yescharacteristic
271C2×C5×D4C2×D411yescharacteristic
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5—22no—
278C22×C4×C5—22no—
279C22×C4×C5—21no—
280C22×C4×C5—21no—
281C22×C4×C5—22no—
282C22×C4×C5—21no—
283C22×C4×C5—21no—
284C22×C4×C5—21no—
285C22×C4×C5—21no—
286C22×C4×C5—21no—
287C22×C4×C5—21no—
288C22×C4×C5—21no—
289C22×C4×C5—42no—
290C22×C4×C5—42no—
291C22×C4×C5C2×D412yes—
292C22×C4×C5C2×D411yescharacteristic
293C22×C4×C5C2×D411yescharacteristic
294C22×C4×C5C2×D411yescharacteristic
295C22×C4×C5C2×D411yescharacteristic
296C22×C4×C5C2×D411yescharacteristic
297C22×C4×C5C2×D412yes—
298C22×C4×C5C2411yescharacteristic
299C5×M16—21no—
300C5×M16—21no—
301C5×M16—21no—
302C5×M16—21no—
303C5×M16—21no—
304C5×M16—21no—
305C5×M16—21no—
306C5×M16—21no—
307C5×M16—42no—
308C2×C5×C8—21no—
309C2×C5×C8—21no—
310C2×C5×C8—21no—
311C2×C5×C8—21no—
312C2×C5×C8—42no—
313C5×C4⋊C4—22no—
314C5×C4⋊C4—22no—
315C5×C4⋊C4—22no—
316C5×C4⋊C4—22no—
317C5×C4⋊C4—21no—
318C5×C4⋊C4—22no—
319C5×C4⋊C4—22no—
320C5×C4⋊C4—21no—
321C5×C4⋊C4—21no—
322C5×C4⋊C4—21no—
323C5×C4⋊C4—21no—
324C5×C4⋊C4—21no—
325C5×C4⋊C4—21no—
326C5×C4⋊C4—21no—
327C5×C4⋊C4—44no—
328C5×C4⋊C4C2×D411yescharacteristic
329C5×C4⋊C4C2×D411yescharacteristic
330C5×C22⋊C4—22no—
331C5×C22⋊C4—22no—
332C5×C22⋊C4—22no—
333C5×C22⋊C4—22no—
334C5×C22⋊C4—22no—
335C5×C22⋊C4—21no—
336C5×C22⋊C4—22no—
337C5×C22⋊C4—22no—
338C5×C22⋊C4—21no—
339C5×C22⋊C4—21no—
340C5×C22⋊C4—21no—
341C5×C22⋊C4—21no—
342C5×C22⋊C4—42no—
343C5×C22⋊C4—41no—
344C5×C22⋊C4—41no—
345C42×C5—22no—
346C42×C5—21no—
347C42×C5—21no—
348C42×C5—21no—
349C42×C5—21no—
350C42×C5—21no—
351C42×C5—41no—
352C42×C5—41no—
353C2×2−1+4C22×C511yescharacteristic
354C22×#41C22×C511yescharacteristic
355C22×M16C22×C511yescharacteristic
356D4×Q8—21no—
357#548—21no—
358#547—21no—
359#547—22no—
360#546—21no—
361#546—22no—
362#537—21no—
363#537C22×C511yescharacteristic
364#536—21no—
365#536C22×C511yescharacteristic
366#525—21no—
367#525C22×C511yescharacteristic
368C2×C22⋊Q8—21no—
369C2×C22⋊Q8C22×C511yescharacteristic
370#520C22×C511yescharacteristic
371C2×#117C22×C511yescharacteristic
372#485—21no—
373#485—21no—
374#482—21no—
375#482—21no—
376#428C22×C511yescharacteristic, complemented
377#428C22×C511yescharacteristic, complemented
378C2×#104C22×C511yescharacteristic
379C2×#104C22×C511yescharacteristic
380C2×#104C22×C511yescharacteristic
381C2×#104C22×C511yescharacteristic
382C2×#104C22×C511yescharacteristic, complemented
383C2×#104C22×C511yescharacteristic, complemented
384#419—21no—
385#418—21no—
386#417C22×C511yescharacteristic
387#417C22×C511yescharacteristic
388#417C22×C511yescharacteristic
389#417C22×C511yescharacteristic
390#417C22×C511yescharacteristic, complemented
391#417C22×C511yescharacteristic, complemented
392#416—21no—
393#416—21no—
394C2×#101C22×C511yescharacteristic, complemented
395C2×#101C22×C511yescharacteristic, complemented
396#407C22×C511yescharacteristic
397#397—22no—
398#391C22×C511yescharacteristic, complemented
399#391C22×C511yescharacteristic, complemented
400#387—22no—
401#384C22×C511yescharacteristic, complemented
402#382C22×C511yescharacteristic, complemented
403C4×C22⋊C4C22×C511yescharacteristic
404#343C22×C511yescharacteristic, complemented
405#343C22×C511yescharacteristic, complemented
406#339C22×C511yescharacteristic, complemented
407#339C22×C511yescharacteristic, complemented
408C23×C5—21no—
409C23×C5—21no—
410C23×C5—21no—
411C23×C5—21no—
412C23×C5—21no—
413C23×C5—41no—
414C23×C5—41no—
415C23×C5—42no—
416C23×C5—42no—
417C23×C5—81no—
418C23×C5#12011yescharacteristic
419C23×C5#12011yescharacteristic
420C23×C5C22×D411yescharacteristic
421C5×Q8—21no—
422C5×Q8—21no—
423C5×Q8—21no—
424C5×Q8—21no—
425C5×Q8—21no—
426C5×Q8—42no—
427C5×Q8—44no—
428C5×Q8—41no—
429C5×Q8—41no—
430C5×Q8—41no—
431C5×Q8—41no—
432C5×Q8#12312yes—
433C5×D4—22no—
434C5×D4—22no—
435C5×D4—21no—
436C5×D4—21no—
437C5×D4—21no—
438C5×D4—21no—
439C5×D4—21no—
440C5×D4—42no—
441C5×D4—42no—
442C5×D4—42no—
443C5×D4—42no—
444C5×D4—44no—
445C5×D4—41no—
446C5×D4—41no—
447C5×D4—41no—
448C5×D4—41no—
449C5×D4—81no—
450C5×D4—82no—
451C5×D4#12312yes—
452C2×C4×C5—21no—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5—21no—
460C2×C4×C5—21no—
461C2×C4×C5—21no—
462C2×C4×C5—21no—
463C2×C4×C5—22no—
464C2×C4×C5—22no—
465C2×C4×C5—22no—
466C2×C4×C5—21no—
467C2×C4×C5—22no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—22no—
471C2×C4×C5—21no—
472C2×C4×C5—22no—
473C2×C4×C5—22no—
474C2×C4×C5—42no—
475C2×C4×C5—42no—
476C2×C4×C5—42no—
477C2×C4×C5—44no—
478C2×C4×C5—41no—
479C2×C4×C5—44no—
480C2×C4×C5—41no—
481C2×C4×C5—41no—
482C2×C4×C5—41no—
483C2×C4×C5—41no—
484C2×C4×C5—41no—
485C2×C4×C5—42no—
486C2×C4×C5—41no—
487C2×C4×C5—42no—
488C2×C4×C5—41no—
489C2×C4×C5—42no—
490C2×C4×C5—41no—
491C2×C4×C5—41no—
492C2×C4×C5—41no—
493C2×C4×C5—82no—
494C2×C4×C5#12011yescharacteristic
495C2×C4×C5#12011yescharacteristic
496C2×C4×C5C22×D411yescharacteristic
497C2×C4×C5C22×D411yescharacteristic
498C2×C4×C5C2×#4111yescharacteristic
499C2×C4×C5C2×#4111yescharacteristic
500C2×C4×C5H(5,𝔽2)11yescharacteristic
501C2×C4×C5H(5,𝔽2)11yescharacteristic
502C5×C8—41no—
503C5×C8—41no—
504C5×C8—41no—
505C5×C8—41no—
5062−1+4—22no—
5072−1+4—22no—
5082−1+4—41no—
5092−1+4—41no—
510C2×#41—21no—
511C2×#41—21no—
512C2×#41—21no—
513C2×#41—22no—
514C2×#41—21no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—41no—
518C2×#41—41no—
519C2×#41C5×D411yescharacteristic
520C2×#41C5×D411yescharacteristic
521C2×#41C23×C511yescharacteristic
522C2×#41C23×C511yescharacteristic
523C2×#41C23×C511yescharacteristic
524C22×Q8—21no—
525C22×Q8—21no—
526C22×Q8C5×D411yescharacteristic
527C22×Q8C23×C511yescharacteristic
528C22×D4—21no—
529C22×D4C5×D411yescharacteristic
530C23×C4—21no—
531C23×C4C23×C511yescharacteristic
532C2×M16—21no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16C23×C511yescharacteristic
536C2×M16C23×C511yescharacteristic
537C2×M16C23×C511yescharacteristic
538C2×M16C23×C511yescharacteristic
539C22×C8—21no—
540C4⋊Q8—22no—
541C4⋊Q8—21no—
542#124—22no—
543#124—21no—
544#123—22no—
545#123—22no—
546#123—22no—
547#123—21no—
548#123—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8C5×D411yescharacteristic
561C22⋊Q8C5×D411yescharacteristic
562#121—22no—
563#121—22no—
564#121—22no—
565#121—21no—
566#121—21no—
567#121—22no—
568#121C5×D411yescharacteristic
569#121C5×D411yescharacteristic
570#120—22no—
571#120—21no—
572C4×Q8—21no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—21no—
576C4×D4—22no—
577C4×D4—21no—
578C4×D4—21no—
579#117—21no—
580#117—21no—
581#117—21no—
582#117—21no—
583#117—21no—
584#117C23×C511yescharacteristic
585C2×C4⋊C4—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4C5×D412yes—
589C2×C4⋊C4C23×C511yescharacteristic
590C2×C4⋊C4C23×C511yescharacteristic
591C2×C4⋊C4C23×C511yescharacteristic
592C2×C22⋊C4—22no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4C5×D412yes—
596C2×C42—21no—
597C2×C42C23×C511yescharacteristic
598C2×C42C23×C511yescharacteristic
599#107—21no—
600#107—21no—
601#106—21no—
602#106—21no—
603#104—22no—
604#104—22no—
605#104—41no—
606#104—41no—
607#104—41no—
608#104—41no—
609#103—21no—
610#103—21no—
611#103—21no—
612#103—21no—
613#103—21no—
614#103—21no—
615#102—21no—
616#102—21no—
617#102—21no—
618#102—21no—
619#102—21no—
620#102—21no—
621#101—41no—
622#101—41no—
623C22⋊C8—21no—
624C22⋊C8—21no—
625#95—21no—
626#95—22no—
627#95—22no—
628#95—22no—
629C22×C5—21no—
630C22×C5—21no—
631C22×C5—21no—
632C22×C5—21no—
633C22×C5—22no—
634C22×C5—21no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5—41no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5—41no—
644C22×C5—41no—
645C22×C5—41no—
646C22×C5—81no—
647C22×C5—81no—
648C22×C5—84no—
649C22×C5C2×#12011yescharacteristic
650C22×C5#54611yescharacteristic
651C22×C5#54611yescharacteristic
652C4×C5—21no—
653C4×C5—21no—
654C4×C5—22no—
655C4×C5—42no—
656C4×C5—42no—
657C4×C5—41no—
658C4×C5—41no—
659C4×C5—42no—
660C4×C5—41no—
661C4×C5—41no—
662C4×C5—81no—
663C4×C5—81no—
664C4×C5—81no—
665C4×C5C2×#12311yescharacteristic
666C4×C5#53411yescharacteristic
667C4×C5#54611yescharacteristic
668C4×C5#54611yescharacteristic
669C24—21no—
670C24C2×C5×D411yescharacteristic
671#41—21no—
672#41—21no—
673#41—22no—
674#41—22no—
675#41—21no—
676#41—21no—
677#41—21no—
678#41—21no—
679#41—21no—
680#41—21no—
681#41—21no—
682#41—21no—
683#41—42no—
684#41—42no—
685#41—41no—
686#41—41no—
687#41—42no—
688#41—42no—
689#41—42no—
690#41—42no—
691#41—44no—
692#41—44no—
693#41—42no—
694#41—42no—
695#41C5×#4112yes—
696#41C5×#4112yes—
697C2×Q8—22no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—22no—
706C2×Q8—41no—
707C2×Q8—42no—
708C2×Q8—42no—
709C2×Q8—42no—
710C2×Q8—42no—
711C2×Q8C2×C5×D411yescharacteristic
712C2×Q8C2×C5×D411yescharacteristic
713C2×Q8C2×C5×D411yescharacteristic
714C2×D4—21no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—41no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4C2×C5×D411yescharacteristic
729C2×D4C2×C5×D411yescharacteristic
730C2×D4C2×C5×D411yescharacteristic
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4C2×C5×D412yes—
751C22×C4C2×C5×D411yescharacteristic
752C22×C4C2×C5×D411yescharacteristic
753C22×C4C2×C5×D411yescharacteristic
754C22×C4C2×C5×D411yescharacteristic
755C22×C4C2×C5×D411yescharacteristic
756C22×C4C2×C5×D412yes—
757C22×C4C24×C511yescharacteristic
758M16—21no—
759M16—21no—
760M16—21no—
761M16—21no—
762M16—21no—
763M16—21no—
764M16—21no—
765M16—21no—
766M16—42no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—42no—
772C4⋊C4—22no—
773C4⋊C4—22no—
774C4⋊C4—22no—
775C4⋊C4—22no—
776C4⋊C4—21no—
777C4⋊C4—22no—
778C4⋊C4—22no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—44no—
787C4⋊C4C2×C5×D411yescharacteristic
788C4⋊C4C2×C5×D411yescharacteristic
789C22⋊C4—22no—
790C22⋊C4—22no—
791C22⋊C4—22no—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—21no—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C42—22no—
805C42—21no—
806C42—21no—
807C42—21no—
808C42—21no—
809C42—21no—
810C42—41no—
811C42—41no—
812C2×C5—21no—
813C2×C5—21no—
814C2×C5—41no—
815C2×C5—41no—
816C2×C5—42no—
817C2×C5—81no—
818C2×C5—81no—
819C2×C5#240511yescharacteristic
820C2×C5#301811yescharacteristic
821C2×C5#302011yescharacteristic
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—41no—
828C23—41no—
829C23—42no—
830C23—42no—
831C23—81no—
832C23C5×#12011yescharacteristic
833C23C5×#12011yescharacteristic
834C23C22×C5×D411yescharacteristic
835Q8—21no—
836Q8—21no—
837Q8—21no—
838Q8—21no—
839Q8—21no—
840Q8—42no—
841Q8—44no—
842Q8—41no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8C5×#12312yes—
847D4—22no—
848D4—22no—
849D4—21no—
850D4—21no—
851D4—21no—
852D4—21no—
853D4—21no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—44no—
858D4—42no—
859D4—41no—
860D4—41no—
861D4—41no—
862D4—41no—
863D4—81no—
864D4—82no—
865D4C5×#12312yes—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—42no—
900C2×C4—41no—
901C2×C4—42no—
902C2×C4—41no—
903C2×C4—42no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—82no—
908C2×C4C5×#12011yescharacteristic
909C2×C4C5×#12011yescharacteristic
910C2×C4C22×C5×D411yescharacteristic
911C2×C4C22×C5×D411yescharacteristic
912C2×C4C2×C5×#4111yescharacteristic
913C2×C4C2×C5×#4111yescharacteristic
914C2×C4C5×H(5,𝔽2)11yescharacteristic
915C2×C4C5×H(5,𝔽2)11yescharacteristic
916C8—41no—
917C8—41no—
918C8—41no—
919C8—41no—
920C5#2402811yescharacteristic, direct product factor, Sylow
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—22no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—81no—
939C22—81no—
940C22—84no—
941C22C2×C5×#12011yescharacteristic
942C22C5×#54611yescharacteristic
943C22C5×#54611yescharacteristic
944C4—21no—
945C4—21no—
946C4—22no—
947C4—42no—
948C4—42no—
949C4—41no—
950C4—41no—
951C4—42no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4C2×C5×#12311yescharacteristic
958C4C5×#53411yescharacteristic
959C4C5×#54611yescharacteristic
960C4C5×#54611yescharacteristic
961C2—21no—
962C2—21no—
963C2—41no—
964C2—41no—
965C2—42no—
966C2—81no—
967C2—81no—
968C2C5×#240511yescharacteristic
969C2C5×#301811yescharacteristic
970C2C5×#302011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3093C2semidirect
3. C5×#2896C2semidirect
4. C5×#2499C2semidirect
5. C5×#2040C2semidirect
6. C5×#2039C2semidirect
7. C5×#2038C2semidirect
8. C5×#2038C2semidirect
9. C5×#1901C2semidirect
10. C5×#1871C2semidirect
11. C5×#1860C2semidirect
12. C5×#1859C2semidirect
13. C5×#1793C2semidirect
14. C5×#1793C2semidirect
15. C5×#1789C2semidirect
39. C5×#428C22semidirect
40. C5×#428C22semidirect
45. C2×C5×#104C22semidirect
46. C2×C5×#104C22semidirect
53. C5×#417C22semidirect
54. C5×#417C22semidirect
57. C2×C5×#101C22semidirect
58. C2×C5×#101C22semidirect
61. C5×#391C22semidirect
62. C5×#391C22semidirect
64. C5×#384C22semidirect
65. C5×#382C22semidirect
67. C5×#343C22semidirect
68. C5×#343C22semidirect
69. C5×#339C22semidirect
70. C5×#339C22semidirect
71. #24028C5direct (N × H)
196. #3093C2×C5semidirect
197. #2896C2×C5semidirect
198. #2499C2×C5semidirect
199. #2040C2×C5semidirect
200. #2039C2×C5semidirect
201. #2038C2×C5semidirect
202. #2038C2×C5semidirect
203. #1901C2×C5semidirect
204. #1871C2×C5semidirect
205. #1860C2×C5semidirect
206. #1859C2×C5semidirect
207. #1793C2×C5semidirect
208. #1793C2×C5semidirect
209. #1789C2×C5semidirect
376. #428C22×C5semidirect
377. #428C22×C5semidirect
382. C2×#104C22×C5semidirect
383. C2×#104C22×C5semidirect
390. #417C22×C5semidirect
391. #417C22×C5semidirect
394. C2×#101C22×C5semidirect
395. C2×#101C22×C5semidirect
398. #391C22×C5semidirect
399. #391C22×C5semidirect
401. #384C22×C5semidirect
402. #382C22×C5semidirect
404. #343C22×C5semidirect
405. #343C22×C5semidirect
406. #339C22×C5semidirect
407. #339C22×C5semidirect
920. C5#24028direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34892
C5×#30932
C5×#28962
C5×#24992
C5×#20402
C5×#20392
C5×#20382
C5×#19012
C5×#18712
C5×#18602
C5×#18592
C5×#17932
C5×#17892
#240285