Finite Group Databasebeta

← C5×#13992 #11936712

Subgroups — C5×#13992 #11936712

Order 1280.

1918 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#385C211yesmaximal, characteristic
2C2×C5×#381C211yesmaximal, characteristic
3C2×C5×#381C211yesmaximal, characteristic
4C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
5C22×C5×#95C211yesmaximal, characteristic
6C5×#1443C212yesmaximal, complemented
7C5×#1442C212yesmaximal, complemented
8C5×#1436C212yesmaximal, complemented
9C5×#1434C212yesmaximal, complemented
10C5×C22⋊#95C211yesmaximal, characteristic
11C5×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C5C2211yescharacteristic
13C24×C4×C5C2211yescharacteristic
14C24×C4×C5C2211yescharacteristic
15C22×C5×C4⋊C4C2212yes—
16C22×C5×C22⋊C4C2211yescharacteristic
17C22×C5×C22⋊C4C2211yescharacteristic
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C42×C5C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C5×#385—24no—
23C5×#381—24no—
24C5×#381C418yescomplemented
25C4×C5×C22⋊C4—24no—
26C2×C5×#95—24no—
27C2×C5×#95C2212yes—
28C2×C5×#95C2212yes—
29C2×C5×#95C2211yescharacteristic
30C2×C5×#95C2211yescharacteristic
31C2×C5×#95C2212yes—
32C2×C5×#95C2212yes—
33C2×C5×#95C2212yes—
34C2×C5×#95C2212yes—
35C2×C5×#95C2212yes—
36C2×C5×#95C2212yes—
37C2×C5×#95C2212yes—
38C2×C5×#95C2212yes—
39C2×C5×#95C2212yes—
40#13992C511yesmaximal, characteristic, direct product factor, Sylow
41C25×C5C2311yescharacteristic
42C23×C4×C5—22no—
43C23×C4×C5—22no—
44C23×C4×C5—22no—
45C23×C4×C5—22no—
46C23×C4×C5—22no—
47C23×C4×C5—22no—
48C23×C4×C5—22no—
49C23×C4×C5—22no—
50C23×C4×C5—22no—
51C23×C4×C5—24no—
52C23×C4×C5—24no—
53C23×C4×C5—22no—
54C23×C4×C5—22no—
55C23×C4×C5—42no—
56C23×C4×C5—42no—
57C23×C4×C5C2×C414yes—
58C23×C4×C5D414yes—
59C23×C4×C5C2312yes—
60C23×C4×C5C2312yes—
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2312yes—
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2312yes—
68C23×C4×C5C2311yescharacteristic
69C2×C5×C4⋊C4—24no—
70C2×C5×C4⋊C4—24no—
71C2×C5×C4⋊C4—42no—
72C2×C5×C22⋊C4—22no—
73C2×C5×C22⋊C4—22no—
74C2×C5×C22⋊C4—22no—
75C2×C5×C22⋊C4—22no—
76C2×C5×C22⋊C4—22no—
77C2×C5×C22⋊C4—22no—
78C2×C5×C22⋊C4—22no—
79C2×C5×C22⋊C4—22no—
80C2×C5×C22⋊C4—22no—
81C2×C5×C22⋊C4C2×C414yes—
82C2×C5×C22⋊C4C2×C414yes—
83C2×C5×C22⋊C4D414yes—
84C2×C42×C5—22no—
85C2×C42×C5—22no—
86C2×C42×C5—24no—
87C2×C42×C5—42no—
88C5×#95—24no—
89C5×#95—24no—
90C5×#95—22no—
91C5×#95—22no—
92C5×#95—24no—
93C5×#95—24no—
94C5×#95—24no—
95C5×#95—24no—
96C5×#95—24no—
97C5×#95—42no—
98C5×#95—42no—
99C5×#95C2×C418yescomplemented
100C5×#95C2×C418yescomplemented
101C2×#385C2×C511yescharacteristic
102C2×#381C2×C511yescharacteristic
103C2×#381C2×C511yescharacteristic
104C2×C4×C22⋊C4C2×C511yescharacteristic
105C22×#95C2×C511yescharacteristic
106#1443C2×C512yescomplemented
107#1442C2×C512yescomplemented
108#1436C2×C512yescomplemented
109#1434C2×C512yescomplemented
110C22⋊#95C2×C511yescharacteristic
111C22⋊#95C2×C511yescharacteristic
112C24×C5—22no—
113C24×C5—22no—
114C24×C5—22no—
115C24×C5—22no—
116C24×C5C22×C412yes—
117C24×C5C2×D412yes—
118C24×C5C2×D412yes—
119C24×C5#4112yes—
120C24×C5#4112yes—
121C24×C5#4112yes—
122C24×C5#4112yes—
123C24×C5C2411yescharacteristic
124C22×C4×C5—21no—
125C22×C4×C5—21no—
126C22×C4×C5—22no—
127C22×C4×C5—28no—
128C22×C4×C5—28no—
129C22×C4×C5—28no—
130C22×C4×C5—28no—
131C22×C4×C5—28no—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—22no—
169C22×C4×C5—22no—
170C22×C4×C5—28no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—44no—
179C22×C4×C5—48no—
180C22×C4×C5—48no—
181C22×C4×C5—48no—
182C22×C4×C5—48no—
183C22×C4×C5—44no—
184C22×C4×C5—44no—
185C22×C4×C5—44no—
186C22×C4×C5—44no—
187C22×C4×C5—44no—
188C22×C4×C5—44no—
189C22×C4×C5C22×C412yes—
190C22×C4×C5C22×C414yes—
191C22×C4×C5C22×C412yes—
192C22×C4×C5C22×C414yes—
193C22×C4×C5C2×D412yes—
194C22×C4×C5C2×D412yes—
195C22×C4×C5C2×D412yes—
196C22×C4×C5C2×D412yes—
197C22×C4×C5#4114yes—
198C22×C4×C5#4114yes—
199C5×C4⋊C4—48no—
200C5×C22⋊C4—28no—
201C5×C22⋊C4—28no—
202C5×C22⋊C4—28no—
203C5×C22⋊C4—44no—
204C42×C5—44no—
205C42×C5—44no—
206C24×C4C22×C511yescharacteristic
207C24×C4C22×C511yescharacteristic
208C24×C4C22×C511yescharacteristic
209C22×C4⋊C4C22×C512yes—
210C22×C22⋊C4C22×C511yescharacteristic
211C22×C22⋊C4C22×C511yescharacteristic
212C22×C22⋊C4C22×C511yescharacteristic
213C22×C22⋊C4C22×C511yescharacteristic
214C22×C42C22×C511yescharacteristic
215C22×C42C22×C511yescharacteristic
216#385—24no—
217#381—24no—
218#381C4×C518yescomplemented
219C4×C22⋊C4—24no—
220C2×#95—24no—
221C2×#95C22×C512yes—
222C2×#95C22×C512yes—
223C2×#95C22×C512yes—
224C2×#95C22×C512yes—
225C2×#95C22×C512yes—
226C2×#95C22×C512yes—
227C2×#95C22×C511yescharacteristic
228C2×#95C22×C512yes—
229C2×#95C22×C511yescharacteristic
230C2×#95C22×C512yes—
231C2×#95C22×C512yes—
232C2×#95C22×C512yes—
233C2×#95C22×C512yes—
234C23×C5—24no—
235C23×C5—24no—
236C23×C5—22no—
237C23×C5—22no—
238C23×C5—24no—
239C23×C5—22no—
240C23×C5—22no—
241C23×C5—24no—
242C23×C5—24no—
243C23×C5—24no—
244C23×C5—24no—
245C23×C5—24no—
246C23×C5—24no—
247C23×C5—24no—
248C23×C5—24no—
249C23×C5—24no—
250C23×C5#11714yes—
251C23×C5C4×D414yes—
252C23×C5C4×D414yes—
253C23×C5#12114yes—
254C23×C5#12314yes—
255C23×C5#12414yes—
256C23×C5#12614yes—
257C23×C5C23×C411yescharacteristic
258C23×C5C22×D411yescharacteristic
259C23×C5C22×D411yescharacteristic
260C23×C5C2×#4111yescharacteristic
261C23×C5C2×#4111yescharacteristic
262C23×C5C2×#4111yescharacteristic
263C23×C5C2×#4111yescharacteristic
264C23×C5C2×#4112yes—
265C23×C5C2×#4112yes—
266C23×C5H(5,𝔽2)12yes—
267C23×C52−1+412yes—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—24no—
271C2×C4×C5—24no—
272C2×C4×C5—24no—
273C2×C4×C5—22no—
274C2×C4×C5—24no—
275C2×C4×C5—22no—
276C2×C4×C5—24no—
277C2×C4×C5—24no—
278C2×C4×C5—24no—
279C2×C4×C5—24no—
280C2×C4×C5—24no—
281C2×C4×C5—24no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—24no—
287C2×C4×C5—22no—
288C2×C4×C5—24no—
289C2×C4×C5—24no—
290C2×C4×C5—24no—
291C2×C4×C5—24no—
292C2×C4×C5—416no—
293C2×C4×C5—416no—
294C2×C4×C5—42no—
295C2×C4×C5—42no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—42no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—42no—
302C2×C4×C5—42no—
303C2×C4×C5—42no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—42no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—42no—
310C2×C4×C5—42no—
311C2×C4×C5—42no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—42no—
320C2×C4×C5—416no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5#12314yes—
329C25C23×C511yescharacteristic
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—24no—
340C23×C4—24no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—42no—
344C23×C4—42no—
345C23×C4C2×C4×C514yes—
346C23×C4C5×D414yes—
347C23×C4C23×C512yes—
348C23×C4C23×C512yes—
349C23×C4C23×C511yescharacteristic
350C23×C4C23×C511yescharacteristic
351C23×C4C23×C512yes—
352C23×C4C23×C511yescharacteristic
353C23×C4C23×C511yescharacteristic
354C23×C4C23×C511yescharacteristic
355C23×C4C23×C512yes—
356C23×C4C23×C511yescharacteristic
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—42no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4C2×C4×C514yes—
370C2×C22⋊C4C2×C4×C514yes—
371C2×C22⋊C4C5×D414yes—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—24no—
375C2×C42—42no—
376#95—24no—
377#95—24no—
378#95—22no—
379#95—22no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—42no—
386#95—42no—
387#95C2×C4×C518yescomplemented
388#95C2×C4×C518yescomplemented
389C22×C5—24no—
390C22×C5—28no—
391C22×C5—28no—
392C22×C5—24no—
393C22×C5—24no—
394C22×C5—24no—
395C22×C5—28no—
396C22×C5—28no—
397C22×C5—24no—
398C22×C5—24no—
399C22×C5#38818yes—
400C22×C5C2×#11711yescharacteristic
401C22×C5C2×C4×D411yescharacteristic
402C22×C5C2×C4×D411yescharacteristic
403C22×C5C4×#4112yes—
404C22×C5#52012yes—
405C22×C5C2×#12111yescharacteristic
406C22×C5C2×#12311yescharacteristic
407C22×C5C2×#12311yescharacteristic
408C22×C5#52511yescharacteristic
409C22×C5C2×#12411yescharacteristic
410C22×C5C2×#12611yescharacteristic
411C22×C5#52912yes—
412C22×C5#53411yescharacteristic
413C22×C5#53611yescharacteristic
414C22×C5#53912yes—
415C22×C5#54612yes—
416C22×C5#54712yes—
417C22×C5#55112yes—
418C22×C5#55112yes—
419C22×C5#55112yes—
420C22×C5#55212yes—
421C22×C5#55212yes—
422C22×C5#55212yes—
423C4×C5—24no—
424C4×C5—42no—
425C4×C5—44no—
426C4×C5—42no—
427C4×C5—42no—
428C4×C5—42no—
429C4×C5—44no—
430C4×C5—44no—
431C4×C5—42no—
432C4×C5—82no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24C22×C4×C512yes—
438C24C2×C5×D412yes—
439C24C2×C5×D412yes—
440C24C5×#4112yes—
441C24C5×#4112yes—
442C24C5×#4112yes—
443C24C5×#4112yes—
444C24C24×C511yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—28no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—44no—
500C22×C4—48no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4C22×C4×C512yes—
511C22×C4C22×C4×C514yes—
512C22×C4C22×C4×C512yes—
513C22×C4C22×C4×C514yes—
514C22×C4C2×C5×D412yes—
515C22×C4C2×C5×D412yes—
516C22×C4C2×C5×D412yes—
517C22×C4C2×C5×D412yes—
518C22×C4C5×#4114yes—
519C22×C4C5×#4114yes—
520C4⋊C4—48no—
521C22⋊C4—28no—
522C22⋊C4—28no—
523C22⋊C4—28no—
524C22⋊C4—44no—
525C42—44no—
526C42—44no—
527C2×C5—28no—
528C2×C5C2×#38811yescharacteristic
529C2×C5C4×#12311yescharacteristic
530C2×C5#232211yescharacteristic
531C2×C5#234312yes—
532C2×C5#235912yes—
533C2×C5#248311yescharacteristic
534C2×C5#248411yescharacteristic
535C2×C5#248611yescharacteristic
536C2×C5#248812yes—
537C2×C5#249312yes—
538C2×C5#253411yescharacteristic
539C23—24no—
540C23—24no—
541C23—22no—
542C23—22no—
543C23—24no—
544C23—22no—
545C23—22no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23C5×#11714yes—
556C23C4×C5×D414yes—
557C23C4×C5×D414yes—
558C23C5×#12114yes—
559C23C5×#12314yes—
560C23C5×#12414yes—
561C23C5×#12614yes—
562C23C23×C4×C511yescharacteristic
563C23C22×C5×D411yescharacteristic
564C23C22×C5×D411yescharacteristic
565C23C2×C5×#4111yescharacteristic
566C23C2×C5×#4111yescharacteristic
567C23C2×C5×#4111yescharacteristic
568C23C2×C5×#4111yescharacteristic
569C23C2×C5×#4112yes—
570C23C2×C5×#4112yes—
571C23C5×H(5,𝔽2)12yes—
572C23C5×2−1+412yes—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—416no—
598C2×C4—416no—
599C2×C4—416no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4C5×#12314yes—
634C5#1399211yescharacteristic, direct product factor, Sylow
635C22—24no—
636C22—24no—
637C22—24no—
638C22—28no—
639C22—28no—
640C22—24no—
641C22—24no—
642C22—24no—
643C22—28no—
644C22—28no—
645C22C5×#38818yes—
646C22C2×C5×#11711yescharacteristic
647C22C2×C4×C5×D411yescharacteristic
648C22C2×C4×C5×D411yescharacteristic
649C22C4×C5×#4112yes—
650C22C5×#52012yes—
651C22C2×C5×#12111yescharacteristic
652C22C2×C5×#12311yescharacteristic
653C22C2×C5×#12311yescharacteristic
654C22C5×#52511yescharacteristic
655C22C2×C5×#12411yescharacteristic
656C22C2×C5×#12611yescharacteristic
657C22C5×#52912yes—
658C22C5×#53411yescharacteristic
659C22C5×#53611yescharacteristic
660C22C5×#53912yes—
661C22C5×#54612yes—
662C22C5×#54712yes—
663C22C5×#55112yes—
664C22C5×#55112yes—
665C22C5×#55112yes—
666C22C5×#55212yes—
667C22C5×#55212yes—
668C22C5×#55212yes—
669C4—24no—
670C4—42no—
671C4—42no—
672C4—44no—
673C4—42no—
674C4—44no—
675C4—42no—
676C4—42no—
677C4—44no—
678C4—82no—
679C2—28no—
680C2C2×C5×#38811yescharacteristic
681C2C4×C5×#12311yescharacteristic
682C2C5×#232211yescharacteristic
683C2C5×#234312yes—
684C2C5×#235912yes—
685C2C5×#248311yescharacteristic
686C2C5×#248411yescharacteristic
687C2C5×#248611yescharacteristic
688C2C5×#248812yes—
689C2C5×#249312yes—
690C2C5×#253411yescharacteristic
subgroupG/H
center, socleC24×C5C24
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

Complements

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

NH ≅ G/Ntype
6. C5×#1443C2semidirect
7. C5×#1442C2semidirect
8. C5×#1436C2semidirect
9. C5×#1434C2semidirect
24. C5×#381C4semidirect
40. #13992C5direct (N × H)
99. C5×#95C2×C4semidirect
100. C5×#95C2×C4semidirect
106. #1443C2×C5semidirect
107. #1442C2×C5semidirect
108. #1436C2×C5semidirect
109. #1434C2×C5semidirect
218. #381C4×C5semidirect
387. #95C2×C4×C5semidirect
388. #95C2×C4×C5semidirect
634. C5#13992direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3852
C2×C5×#3812
C2×C4×C5×C22⋊C42
C22×C5×#952
C5×#14432
C5×#14422
C5×#14362
C5×#14342
C5×C22⋊#952
#139925