Finite Group Databasebeta

← C5×#19009 #11941729

Subgroups — C5×#19009 #11941729

Order 1280.

832 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3531C211yesmaximal, characteristic
2C5×#3238C211yesmaximal, characteristic, complemented
3C5×#3218C211yesmaximal, characteristic, complemented
4C5×#3165C211yesmaximal, characteristic, complemented
5C5×#1664C212yesmaximal, complemented
6C5×#1663C212yesmaximal, complemented
7C5×#1661C212yesmaximal, complemented
8C5×#1660C212yesmaximal, complemented
9C5×#1537C211yesmaximal, characteristic, complemented
10C5×#1529C211yesmaximal, characteristic, complemented
11C5×#1529C211yesmaximal, characteristic, complemented
12C5×#564C2211yescharacteristic
13C5×#563—21no—
14C5×#563—21no—
15C5×#563—21no—
16C5×#563—21no—
17C5×#563C2211yescharacteristic
18C5×#563C2211yescharacteristic
19C5×#562—21no—
20C5×#562—21no—
21C5×#562C2211yescharacteristic
22C5×#533—21no—
23C5×#533—21no—
24C5×#533C2211yescharacteristic
25C2×C5×C4⋊Q8C2211yescharacteristic
26C5×#529—21no—
27C5×#529—21no—
28C5×#529—21no—
29C5×#529—21no—
30C5×#529C2211yescharacteristic
31C5×#529C2211yescharacteristic
32C5×#501C2212yes—
33C5×#501C2212yes—
34C5×#501C2212yes—
35C5×#500—21no—
36C5×#498—21no—
37C5×#497C2212yes—
38C5×#491C2212yes—
39C5×#489C2212yes—
40C5×#483—21no—
41C5×#480—21no—
42C5×#477—21no—
43C5×#476—21no—
44C5×#462—21no—
45C5×#461—21no—
46C5×#451—21no—
47C5×#448—21no—
48C5×#432C2211yescharacteristic
49C5×#432C2211yescharacteristic
50C5×#428—21no—
51C5×#428—21no—
52C4×C5×M16C2211yescharacteristic
53C5×#330C2212yes—
54C5×#330C2212yes—
55C5×#330C2212yes—
56C5×#330C2212yes—
57C5×#329C2212yes—
58C5×#329C2212yes—
59#19009C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8—21no—
61C2×C5×Q16—22no—
62C2×C5×SD16—22no—
63C2×C5×M16—21no—
64C5×C4⋊Q8—21no—
65C5×C4⋊Q8—21no—
66C5×C4⋊Q8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8—21no—
70C5×C4⋊Q8—21no—
71C5×C4⋊Q8D411yescharacteristic
72C5×C4⋊Q8D411yescharacteristic
73C5×C4⋊Q8C2312yes—
74C5×#126—21no—
75C5×#126—21no—
76C5×#126—21no—
77C5×#126—21no—
78C5×#126—21no—
79C5×#126—21no—
80C5×#126—21no—
81C5×#126—21no—
82C5×#126—21no—
83C5×#126—21no—
84C5×#125—21no—
85C5×#125—21no—
86C5×#125—21no—
87C5×#125—21no—
88C5×#125—21no—
89C5×#125—21no—
90C5×#125—21no—
91C5×#125—21no—
92C5×#125C2311yescharacteristic
93C5×#125C2311yescharacteristic
94C5×#125C2311yescharacteristic
95C5×#125C2311yescharacteristic
96C5×#124—21no—
97C5×#124—21no—
98C5×#124—21no—
99C5×#124—21no—
100C5×#124C2311yescharacteristic
101C5×#124C2311yescharacteristic
102C5×#123—21no—
103C5×#123—21no—
104C5×#123—21no—
105C5×#123—21no—
106C5×#123—21no—
107C5×#123—21no—
108C5×#123—21no—
109C5×#123—21no—
110C5×#123—21no—
111C5×#123—21no—
112C5×C22⋊Q8—21no—
113C5×C22⋊Q8—21no—
114C5×C22⋊Q8—21no—
115C5×C22⋊Q8—21no—
116C5×C22⋊Q8—21no—
117C5×C22⋊Q8—21no—
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—21no—
129C5×#121—21no—
130C5×#121—21no—
131C5×#121—21no—
132C5×#121D411yescharacteristic
133C5×#121D411yescharacteristic
134C4×C5×Q8—21no—
135C4×C5×Q8—21no—
136C4×C5×Q8—21no—
137C4×C5×Q8—21no—
138C4×C5×Q8D411yescharacteristic
139C4×C5×Q8D411yescharacteristic
140C4×C5×D4—21no—
141C4×C5×D4—21no—
142C4×C5×D4—21no—
143C4×C5×D4—21no—
144C4×C5×D4D411yescharacteristic
145C4×C5×D4D411yescharacteristic
146C5×#117—21no—
147C5×#117—21no—
148C5×#117—21no—
149C5×#117—21no—
150C5×#117D411yescharacteristic
151C5×#117D411yescharacteristic
152C2×C5×C4⋊C4—21no—
153C2×C5×C4⋊C4—21no—
154C2×C42×C5—21no—
155C2×C42×C5—21no—
156C2×C42×C5C2311yescharacteristic
157C5×#107—22no—
158C5×#107—22no—
159C5×#107—22no—
160C5×#106—22no—
161C5×#106—22no—
162C5×#106—22no—
163C5×C4⋊C8—21no—
164C5×C4⋊C8—21no—
165C5×#103—22no—
166C5×#103—22no—
167C5×#103—22no—
168C5×#102—22no—
169C5×C22⋊C8—21no—
170C5×C22⋊C8—21no—
171C5×#97C2312yes—
172C5×#97C2312yes—
173C5×#97C2312yes—
174C4×C5×C8—21no—
175#3531C2×C511yescharacteristic
176#3238C2×C511yescharacteristic, complemented
177#3218C2×C511yescharacteristic, complemented
178#3165C2×C511yescharacteristic, complemented
179#1664C2×C512yescomplemented
180#1663C2×C512yescomplemented
181#1661C2×C512yescomplemented
182#1660C2×C512yescomplemented
183#1537C2×C511yescharacteristic, complemented
184#1529C2×C511yescharacteristic, complemented
185#1529C2×C511yescharacteristic, complemented
186C2×C5×Q8—21no—
187C2×C5×Q8—21no—
188C2×C5×Q8—21no—
189C2×C5×Q8—21no—
190C2×C5×Q8—22no—
191C2×C5×Q8—41no—
192C2×C5×Q8—82no—
193C2×C5×Q8C2×D411yescharacteristic
194C2×C5×Q8C2×D411yescharacteristic
195C2×C5×D4—21no—
196C2×C5×D4—21no—
197C2×C5×D4—21no—
198C2×C5×D4—21no—
199C2×C5×D4C2×D411yescharacteristic
200C2×C5×D4C2×D411yescharacteristic
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—41no—
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D411yescharacteristic
211C5×Q16—82no—
212C5×SD16—82no—
213C5×M16—24no—
214C2×C5×C8—22no—
215C2×C5×C8—22no—
216C2×C5×C8—22no—
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—21no—
225C5×C4⋊C4—21no—
226C5×C4⋊C4—21no—
227C5×C4⋊C4—21no—
228C5×C4⋊C4—21no—
229C5×C4⋊C4—21no—
230C5×C4⋊C4—21no—
231C5×C4⋊C4—21no—
232C5×C4⋊C4—21no—
233C5×C4⋊C4—21no—
234C5×C4⋊C4—21no—
235C5×C4⋊C4—21no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4—21no—
243C5×C4⋊C4—22no—
244C5×C4⋊C4—22no—
245C5×C4⋊C4—41no—
246C5×C4⋊C4—41no—
247C5×C4⋊C4C2×D411yescharacteristic
248C5×C4⋊C4C2×D411yescharacteristic
249C5×C4⋊C4C2×D411yescharacteristic
250C5×C4⋊C4C2×D411yescharacteristic
251C5×C4⋊C4C2×D411yescharacteristic
252C5×C4⋊C4C2×D411yescharacteristic
253C5×C4⋊C4C2×D411yescharacteristic
254C5×C4⋊C4C2×D411yescharacteristic
255C5×C22⋊C4—21no—
256C5×C22⋊C4—21no—
257C5×C22⋊C4—21no—
258C5×C22⋊C4—21no—
259C5×C22⋊C4—21no—
260C5×C22⋊C4—21no—
261C5×C22⋊C4—21no—
262C5×C22⋊C4—21no—
263C5×C22⋊C4—21no—
264C5×C22⋊C4—21no—
265C5×C22⋊C4—21no—
266C5×C22⋊C4—21no—
267C5×C22⋊C4—21no—
268C5×C22⋊C4—21no—
269C5×C22⋊C4—21no—
270C5×C22⋊C4—21no—
271C5×C22⋊C4—21no—
272C5×C22⋊C4—21no—
273C5×C22⋊C4—21no—
274C5×C22⋊C4—21no—
275C42×C5—21no—
276C42×C5—21no—
277C42×C5—21no—
278C42×C5—21no—
279C42×C5—21no—
280C42×C5—21no—
281C42×C5—21no—
282C42×C5—21no—
283C42×C5C2×D411yescharacteristic
284C42×C5C2×D411yescharacteristic
285C42×C5C2×D411yescharacteristic
286C42×C5C2411yescharacteristic
287#564C22×C511yescharacteristic
288#563—21no—
289#563—21no—
290#563—21no—
291#563—21no—
292#563C22×C511yescharacteristic
293#563C22×C511yescharacteristic
294#562—21no—
295#562—21no—
296#562C22×C511yescharacteristic
297#533—21no—
298#533—21no—
299#533C22×C511yescharacteristic
300C2×C4⋊Q8C22×C511yescharacteristic
301#529—21no—
302#529—21no—
303#529—21no—
304#529—21no—
305#529C22×C511yescharacteristic
306#529C22×C511yescharacteristic
307#501C22×C512yes—
308#501C22×C512yes—
309#501C22×C512yes—
310#500—21no—
311#498—21no—
312#497C22×C512yes—
313#491C22×C512yes—
314#489C22×C512yes—
315#483—21no—
316#480—21no—
317#477—21no—
318#476—21no—
319#462—21no—
320#461—21no—
321#451—21no—
322#448—21no—
323#432C22×C511yescharacteristic
324#432C22×C511yescharacteristic
325#428—21no—
326#428—21no—
327C4×M16C22×C511yescharacteristic
328#330C22×C512yes—
329#330C22×C512yes—
330#330C22×C512yes—
331#330C22×C512yes—
332#329C22×C512yes—
333#329C22×C512yes—
334C23×C5—21no—
335C23×C5—21no—
336C23×C5#12011yescharacteristic
337C5×Q8—41no—
338C5×Q8—41no—
339C5×Q8—42no—
340C5×Q8—42no—
341C5×Q8—81no—
342C5×Q8—81no—
343C5×Q8—82no—
344C5×Q8—81no—
345C5×Q8—81no—
346C5×D4—41no—
347C5×D4—41no—
348C5×D4—81no—
349C5×D4—81no—
350C5×D4—81no—
351C5×D4—81no—
352C2×C4×C5—22no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—21no—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—21no—
359C2×C4×C5—21no—
360C2×C4×C5—21no—
361C2×C4×C5—21no—
362C2×C4×C5—21no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—42no—
366C2×C4×C5—42no—
367C2×C4×C5—42no—
368C2×C4×C5—81no—
369C2×C4×C5—81no—
370C2×C4×C5—81no—
371C2×C4×C5—81no—
372C2×C4×C5—82no—
373C2×C4×C5#12011yescharacteristic
374C2×C4×C5#12011yescharacteristic
375C2×C4×C5#12011yescharacteristic
376C2×C4×C5C22×D411yescharacteristic
377C2×C4×C5C22×D411yescharacteristic
378C2×C4×C5C22×D411yescharacteristic
379C5×C8—24no—
380C5×C8—42no—
381C5×C8—42no—
382C22×Q8—21no—
383C2×Q16—22no—
384C2×SD16—22no—
385C2×M16—21no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8—21no—
391C4⋊Q8—21no—
392C4⋊Q8—21no—
393C4⋊Q8C5×D411yescharacteristic
394C4⋊Q8C5×D411yescharacteristic
395C4⋊Q8C23×C512yes—
396#126—21no—
397#126—21no—
398#126—21no—
399#126—21no—
400#126—21no—
401#126—21no—
402#126—21no—
403#126—21no—
404#126—21no—
405#126—21no—
406#125—21no—
407#125—21no—
408#125—21no—
409#125—21no—
410#125—21no—
411#125—21no—
412#125—21no—
413#125—21no—
414#125C23×C511yescharacteristic
415#125C23×C511yescharacteristic
416#125C23×C511yescharacteristic
417#125C23×C511yescharacteristic
418#124—21no—
419#124—21no—
420#124—21no—
421#124—21no—
422#124C23×C511yescharacteristic
423#124C23×C511yescharacteristic
424#123—21no—
425#123—21no—
426#123—21no—
427#123—21no—
428#123—21no—
429#123—21no—
430#123—21no—
431#123—21no—
432#123—21no—
433#123—21no—
434C22⋊Q8—21no—
435C22⋊Q8—21no—
436C22⋊Q8—21no—
437C22⋊Q8—21no—
438C22⋊Q8—21no—
439C22⋊Q8—21no—
440C22⋊Q8—21no—
441C22⋊Q8—21no—
442C22⋊Q8—21no—
443C22⋊Q8—21no—
444C22⋊Q8—21no—
445C22⋊Q8—21no—
446C22⋊Q8—21no—
447C22⋊Q8—21no—
448C22⋊Q8C5×D411yescharacteristic
449C22⋊Q8C5×D411yescharacteristic
450#121—21no—
451#121—21no—
452#121—21no—
453#121—21no—
454#121C5×D411yescharacteristic
455#121C5×D411yescharacteristic
456C4×Q8—21no—
457C4×Q8—21no—
458C4×Q8—21no—
459C4×Q8—21no—
460C4×Q8C5×D411yescharacteristic
461C4×Q8C5×D411yescharacteristic
462C4×D4—21no—
463C4×D4—21no—
464C4×D4—21no—
465C4×D4—21no—
466C4×D4C5×D411yescharacteristic
467C4×D4C5×D411yescharacteristic
468#117—21no—
469#117—21no—
470#117—21no—
471#117—21no—
472#117C5×D411yescharacteristic
473#117C5×D411yescharacteristic
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42C23×C511yescharacteristic
479#107—22no—
480#107—22no—
481#107—22no—
482#106—22no—
483#106—22no—
484#106—22no—
485C4⋊C8—21no—
486C4⋊C8—21no—
487#103—22no—
488#103—22no—
489#103—22no—
490#102—22no—
491C22⋊C8—21no—
492C22⋊C8—21no—
493#97C23×C512yes—
494#97C23×C512yes—
495#97C23×C512yes—
496C4×C8—21no—
497C22×C5—21no—
498C22×C5—21no—
499C22×C5—21no—
500C22×C5—41no—
501C22×C5—41no—
502C22×C5—41no—
503C22×C5—41no—
504C22×C5—41no—
505C22×C5—41no—
506C22×C5C2×#12011yescharacteristic
507C4×C5—21no—
508C4×C5—21no—
509C4×C5—21no—
510C4×C5—21no—
511C4×C5—21no—
512C4×C5—41no—
513C4×C5—41no—
514C4×C5—41no—
515C4×C5—41no—
516C4×C5—41no—
517C4×C5—41no—
518C4×C5—41no—
519C4×C5—41no—
520C4×C5—41no—
521C4×C5—41no—
522C4×C5—82no—
523C4×C5#45612yes—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—41no—
530C2×Q8—82no—
531C2×Q8C2×C5×D411yescharacteristic
532C2×Q8C2×C5×D411yescharacteristic
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4C2×C5×D411yescharacteristic
538C2×D4C2×C5×D411yescharacteristic
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—41no—
546C22×C4C2×C5×D411yescharacteristic
547C22×C4C2×C5×D411yescharacteristic
548C22×C4C2×C5×D411yescharacteristic
549Q16—82no—
550SD16—82no—
551M16—24no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4C2×C5×D411yescharacteristic
586C4⋊C4C2×C5×D411yescharacteristic
587C4⋊C4C2×C5×D411yescharacteristic
588C4⋊C4C2×C5×D411yescharacteristic
589C4⋊C4C2×C5×D411yescharacteristic
590C4⋊C4C2×C5×D411yescharacteristic
591C4⋊C4C2×C5×D411yescharacteristic
592C4⋊C4C2×C5×D411yescharacteristic
593C22⋊C4—21no—
594C22⋊C4—21no—
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42C2×C5×D411yescharacteristic
622C42C2×C5×D411yescharacteristic
623C42C2×C5×D411yescharacteristic
624C42C24×C511yescharacteristic
625C2×C5—41no—
626C2×C5—81no—
627C2×C5—81no—
628C2×C5C2×#45611yescharacteristic
629C2×C5#302111yescharacteristic
630C2×C5#302211yescharacteristic
631C23—21no—
632C23—21no—
633C23C5×#12011yescharacteristic
634Q8—41no—
635Q8—41no—
636Q8—42no—
637Q8—42no—
638Q8—81no—
639Q8—81no—
640Q8—82no—
641Q8—81no—
642Q8—81no—
643D4—41no—
644D4—41no—
645D4—81no—
646D4—81no—
647D4—81no—
648D4—81no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—81no—
666C2×C4—81no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—82no—
670C2×C4C5×#12011yescharacteristic
671C2×C4C5×#12011yescharacteristic
672C2×C4C5×#12011yescharacteristic
673C2×C4C22×C5×D411yescharacteristic
674C2×C4C22×C5×D411yescharacteristic
675C2×C4C22×C5×D411yescharacteristic
676C8—24no—
677C8—42no—
678C8—42no—
679C5#1900911yescharacteristic, direct product factor, Sylow
680C22—21no—
681C22—21no—
682C22—21no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22C2×C5×#12011yescharacteristic
690C4—21no—
691C4—21no—
692C4—21no—
693C4—21no—
694C4—21no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—82no—
706C4C5×#45612yes—
707C2—41no—
708C2—81no—
709C2—81no—
710C2C2×C5×#45611yescharacteristic
711C2C5×#302111yescharacteristic
712C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3531C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3238C2semidirect
3. C5×#3218C2semidirect
4. C5×#3165C2semidirect
5. C5×#1664C2semidirect
6. C5×#1663C2semidirect
7. C5×#1661C2semidirect
8. C5×#1660C2semidirect
9. C5×#1537C2semidirect
10. C5×#1529C2semidirect
11. C5×#1529C2semidirect
59. #19009C5direct (N × H)
176. #3238C2×C5semidirect
177. #3218C2×C5semidirect
178. #3165C2×C5semidirect
179. #1664C2×C5semidirect
180. #1663C2×C5semidirect
181. #1661C2×C5semidirect
182. #1660C2×C5semidirect
183. #1537C2×C5semidirect
184. #1529C2×C5semidirect
185. #1529C2×C5semidirect
679. C5#19009direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35312
C5×#32382
C5×#32182
C5×#31652
C5×#16642
C5×#16632
C5×#16612
C5×#16602
C5×#15372
C5×#15292
#190095