Finite Group Databasebeta

← C5×#25219 #11947939

Subgroups — C5×#25219 #11947939

Order 1280.

824 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#483C211yesmaximal, characteristic
2C2×C5×#470C211yesmaximal, characteristic
3C5×#2502C211yesmaximal, characteristic
4C5×#2362C211yesmaximal, characteristic
5C5×#2084C211yesmaximal, characteristic, complemented
6C5×#2072C211yesmaximal, characteristic, complemented
7C5×#2066C211yesmaximal, characteristic, complemented
8C5×#2056C211yesmaximal, characteristic, complemented
9C5×#1948C211yesmaximal, characteristic, complemented
10C5×#1927C211yesmaximal, characteristic, complemented
11C5×#1878C211yesmaximal, characteristic, complemented
12C5×#1873C211yesmaximal, characteristic
13C5×#1851C211yesmaximal, characteristic
14C5×#1803C211yesmaximal, characteristic, complemented
15C5×#1736C211yesmaximal, characteristic
16C22×C5×Q16C2211yescharacteristic
17C22×C5×M16C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C5×#483—24no—
24C5×#470—24no—
25C2×C5×#106C2211yescharacteristic
26C2×C5×#106C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C2×C5×C4⋊C8C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic
30C2×C5×#103C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×#103C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C5×#398—21no—
38C5×#398—21no—
39C5×#391C2211yescharacteristic
40C5×#391C2211yescharacteristic
41C5×#391C2211yescharacteristic
42C5×#389C2211yescharacteristic
43C5×#388—21no—
44C5×#388—21no—
45C5×#387—21no—
46C5×#385—21no—
47C5×#385—21no—
48C5×#384C2211yescharacteristic
49C5×#384C2211yescharacteristic
50C4×C5×C4⋊C4—21no—
51C4×C5×C4⋊C4C2211yescharacteristic
52C4×C5×C22⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#25219C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×Q8C2311yescharacteristic
64C23×C4×C5—21no—
65C23×C4×C5C2311yescharacteristic
66C2×C5×Q16—22no—
67C2×C5×Q16—22no—
68C2×C5×Q16—41no—
69C2×C5×M16—22no—
70C2×C5×M16—22no—
71C2×C5×M16—41no—
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C5×C22⋊Q8—22no—
77C5×C22⋊Q8—22no—
78C5×C22⋊Q8—22no—
79C5×C22⋊Q8D414yes—
80C4×C5×Q8—22no—
81C4×C5×Q8—41no—
82C5×#117—22no—
83C5×#117—41no—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4—22no—
86C2×C5×C4⋊C4—22no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4D411yescharacteristic
105C2×C5×C22⋊C4D411yescharacteristic
106C2×C42×C5—21no—
107C2×C42×C5—21no—
108C2×C42×C5—21no—
109C2×C42×C5C2311yescharacteristic
110C2×C42×C5C2311yescharacteristic
111C5×#106—22no—
112C5×#106—22no—
113C5×#106—22no—
114C5×C4⋊C8—22no—
115C5×C4⋊C8—41no—
116C5×#103—22no—
117C5×#103—22no—
118C5×#103—22no—
119C5×#103—22no—
120C5×#103—22no—
121C5×#103—41no—
122C5×C22⋊C8—22no—
123C5×#95—21no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95D411yescharacteristic
132C5×#95D411yescharacteristic
133C2×#483C2×C511yescharacteristic
134C2×#470C2×C511yescharacteristic
135#2502C2×C511yescharacteristic
136#2362C2×C511yescharacteristic
137#2084C2×C511yescharacteristic, complemented
138#2072C2×C511yescharacteristic, complemented
139#2066C2×C511yescharacteristic, complemented
140#2056C2×C511yescharacteristic, complemented
141#1948C2×C511yescharacteristic, complemented
142#1927C2×C511yescharacteristic, complemented
143#1878C2×C511yescharacteristic, complemented
144#1873C2×C511yescharacteristic
145#1851C2×C511yescharacteristic
146#1803C2×C511yescharacteristic, complemented
147#1736C2×C511yescharacteristic
148C24×C5C2×D411yescharacteristic
149C2×C5×Q8—21no—
150C2×C5×Q8—21no—
151C2×C5×Q8—21no—
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×Q8—21no—
157C2×C5×Q8—21no—
158C2×C5×Q8—21no—
159C2×C5×Q8—21no—
160C2×C5×Q8C2×D412yes—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
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—42no—
174C22×C4×C5—81no—
175C22×C4×C5—81no—
176C22×C4×C5C2×D411yescharacteristic
177C22×C4×C5C2×D411yescharacteristic
178C22×C4×C5C2×D411yescharacteristic
179C22×C4×C5C2×D412yes—
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5#4112yes—
183C22×C4×C5C2411yescharacteristic
184C5×Q16—44no—
185C5×M16—44no—
186C2×C5×C8—21no—
187C2×C5×C8—21no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8#4112yes—
198C5×C4⋊C4—24no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—42no—
210C5×C4⋊C4—42no—
211C5×C4⋊C4—42no—
212C5×C4⋊C4—42no—
213C5×C4⋊C4—81no—
214C5×C4⋊C4—81no—
215C5×C4⋊C4—81no—
216C5×C4⋊C4—81no—
217C5×C4⋊C4C2×D412yes—
218C5×C4⋊C4#4112yes—
219C5×C22⋊C4—24no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—22no—
222C5×C22⋊C4—42no—
223C5×C22⋊C4—42no—
224C42×C5—21no—
225C42×C5—21no—
226C42×C5—21no—
227C42×C5—21no—
228C42×C5—42no—
229C42×C5—42no—
230C42×C5—42no—
231C22×Q16C22×C511yescharacteristic
232C22×M16C22×C511yescharacteristic
233C2×C22⋊Q8C22×C511yescharacteristic
234C2×C22⋊Q8C22×C511yescharacteristic
235C2×C4×Q8C22×C511yescharacteristic
236C2×#117C22×C511yescharacteristic
237C22×C4⋊C4C22×C511yescharacteristic
238#483—24no—
239#470—24no—
240C2×#106C22×C511yescharacteristic
241C2×#106C22×C511yescharacteristic
242C2×#106C22×C511yescharacteristic
243C2×C4⋊C8C22×C511yescharacteristic
244C2×C4⋊C8C22×C511yescharacteristic
245C2×#103C22×C511yescharacteristic
246C2×#103C22×C511yescharacteristic
247C2×#103C22×C511yescharacteristic
248C2×#103C22×C511yescharacteristic
249C2×#103C22×C511yescharacteristic
250C2×#103C22×C511yescharacteristic
251C2×C22⋊C8C22×C511yescharacteristic
252#398—21no—
253#398—21no—
254#391C22×C511yescharacteristic
255#391C22×C511yescharacteristic
256#391C22×C511yescharacteristic
257#389C22×C511yescharacteristic
258#388—21no—
259#388—21no—
260#387—21no—
261#385—21no—
262#385—21no—
263#384C22×C511yescharacteristic
264#384C22×C511yescharacteristic
265C4×C4⋊C4—21no—
266C4×C4⋊C4C22×C511yescharacteristic
267C4×C22⋊C4C22×C511yescharacteristic
268#340C22×C511yescharacteristic
269#340C22×C511yescharacteristic
270#340C22×C511yescharacteristic
271#340C22×C511yescharacteristic
272#340C22×C511yescharacteristic
273#340C22×C511yescharacteristic
274#336C22×C511yescharacteristic
275#336C22×C511yescharacteristic
276C23×C5—21no—
277C23×C5—21no—
278C23×C5—21no—
279C23×C5—21no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5#12112yes—
283C23×C5C22×D411yescharacteristic
284C5×Q8—22no—
285C5×Q8—22no—
286C5×Q8—41no—
287C5×Q8—41no—
288C5×Q8—41no—
289C5×Q8—41no—
290C5×Q8—41no—
291C5×Q8—41no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—21no—
305C2×C4×C5—22no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—84no—
333C2×C4×C5#12112yes—
334C2×C4×C5#13712yes—
335C2×C4×C5#13712yes—
336C2×C4×C5C22×D411yescharacteristic
337C2×C4×C5C2×#4111yescharacteristic
338C2×C4×C5C2×#4111yescharacteristic
339C2×C4×C5C2×#4111yescharacteristic
340C2×C4×C5H(5,𝔽2)11yescharacteristic
341C2×C4×C52−1+411yescharacteristic
342C5×C8—22no—
343C5×C8—41no—
344C5×C8—41no—
345C5×C8—41no—
346C22×Q8C23×C511yescharacteristic
347C22×Q8C23×C511yescharacteristic
348C23×C4—21no—
349C23×C4C23×C511yescharacteristic
350C2×Q16—22no—
351C2×Q16—22no—
352C2×Q16—41no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—41no—
356C22×C8C23×C511yescharacteristic
357C22×C8C23×C511yescharacteristic
358C22×C8C23×C511yescharacteristic
359C22×C8C23×C511yescharacteristic
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8C5×D414yes—
364C4×Q8—22no—
365C4×Q8—41no—
366#117—22no—
367#117—41no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4C23×C511yescharacteristic
380C2×C4⋊C4C23×C511yescharacteristic
381C2×C4⋊C4C23×C511yescharacteristic
382C2×C4⋊C4C23×C511yescharacteristic
383C2×C4⋊C4C23×C511yescharacteristic
384C2×C4⋊C4C23×C511yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4C5×D411yescharacteristic
389C2×C22⋊C4C5×D411yescharacteristic
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C511yescharacteristic
394C2×C42C23×C511yescharacteristic
395#106—22no—
396#106—22no—
397#106—22no—
398C4⋊C8—22no—
399C4⋊C8—41no—
400#103—22no—
401#103—22no—
402#103—22no—
403#103—22no—
404#103—22no—
405#103—41no—
406C22⋊C8—22no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95C5×D411yescharacteristic
416#95C5×D411yescharacteristic
417C22×C5—22no—
418C22×C5—22no—
419C22×C5—22no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5C2×#12111yescharacteristic
425C22×C5#54611yescharacteristic
426C22×C5#54711yescharacteristic
427C22×C5C2×#13711yescharacteristic
428C22×C5C2×#13711yescharacteristic
429C22×C5#57711yescharacteristic
430C22×C5#57711yescharacteristic
431C4×C5—22no—
432C4×C5—22no—
433C4×C5—22no—
434C4×C5—41no—
435C4×C5—42no—
436C4×C5—41no—
437C4×C5—42no—
438C4×C5—42no—
439C4×C5—81no—
440C4×C5—81no—
441C4×C5—81no—
442C4×C5—81no—
443C4×C5—81no—
444C4×C5#52911yescharacteristic
445C4×C5#53911yescharacteristic
446C4×C5#54611yescharacteristic
447C4×C5#54711yescharacteristic
448C24C2×C5×D411yescharacteristic
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×C5×D412yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—42no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4C2×C5×D411yescharacteristic
477C22×C4C2×C5×D411yescharacteristic
478C22×C4C2×C5×D411yescharacteristic
479C22×C4C2×C5×D412yes—
480C22×C4C2×C5×D411yescharacteristic
481C22×C4C2×C5×D411yescharacteristic
482C22×C4C5×#4112yes—
483C22×C4C24×C511yescharacteristic
484Q16—44no—
485M16—44no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8C5×#4112yes—
498C4⋊C4—24no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—81no—
514C4⋊C4—81no—
515C4⋊C4—81no—
516C4⋊C4—81no—
517C4⋊C4C2×C5×D412yes—
518C4⋊C4C5×#4112yes—
519C22⋊C4—24no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—42no—
529C42—42no—
530C42—42no—
531C2×C5—42no—
532C2×C5#242511yescharacteristic
533C2×C5#303911yescharacteristic
534C2×C5#304311yescharacteristic
535C2×C5#331611yescharacteristic
536C2×C5#333111yescharacteristic
537C2×C5#334411yescharacteristic
538C2×C5#335611yescharacteristic
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23C5×#12112yes—
546C23C22×C5×D411yescharacteristic
547Q8—22no—
548Q8—22no—
549Q8—41no—
550Q8—41no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554Q8—41no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4C5×#12112yes—
597C2×C4C5×#13712yes—
598C2×C4C5×#13712yes—
599C2×C4C22×C5×D411yescharacteristic
600C2×C4C2×C5×#4111yescharacteristic
601C2×C4C2×C5×#4111yescharacteristic
602C2×C4C2×C5×#4111yescharacteristic
603C2×C4C5×H(5,𝔽2)11yescharacteristic
604C2×C4C5×2−1+411yescharacteristic
605C8—22no—
606C8—41no—
607C8—41no—
608C8—41no—
609C5#2521911yescharacteristic, direct product factor, Sylow
610C22—22no—
611C22—22no—
612C22—22no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22C2×C5×#12111yescharacteristic
618C22C5×#54611yescharacteristic
619C22C5×#54711yescharacteristic
620C22C2×C5×#13711yescharacteristic
621C22C2×C5×#13711yescharacteristic
622C22C5×#57711yescharacteristic
623C22C5×#57711yescharacteristic
624C4—22no—
625C4—22no—
626C4—22no—
627C4—42no—
628C4—41no—
629C4—42no—
630C4—41no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—81no—
636C4—81no—
637C4C5×#52911yescharacteristic
638C4C5×#53911yescharacteristic
639C4C5×#54611yescharacteristic
640C4C5×#54711yescharacteristic
641C2—42no—
642C2C5×#242511yescharacteristic
643C2C5×#303911yescharacteristic
644C2C5×#304311yescharacteristic
645C2C5×#331611yescharacteristic
646C2C5×#333111yescharacteristic
647C2C5×#334411yescharacteristic
648C2C5×#335611yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC24×C5C2×D4
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
5. C5×#2084C2semidirect
6. C5×#2072C2semidirect
7. C5×#2066C2semidirect
8. C5×#2056C2semidirect
9. C5×#1948C2semidirect
10. C5×#1927C2semidirect
11. C5×#1878C2semidirect
14. C5×#1803C2semidirect
61. #25219C5direct (N × H)
137. #2084C2×C5semidirect
138. #2072C2×C5semidirect
139. #2066C2×C5semidirect
140. #2056C2×C5semidirect
141. #1948C2×C5semidirect
142. #1927C2×C5semidirect
143. #1878C2×C5semidirect
146. #1803C2×C5semidirect
609. C5#25219direct (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×#4702
C5×#25022
C5×#23622
C5×#20842
C5×#20722
C5×#20662
C5×#20562
C5×#19482
C5×#19272
C5×#18782
C5×#18732
C5×#18512
C5×#18032
C5×#17362
#252195