Finite Group Databasebeta

← C13×#19807 #15706146

Subgroups — C13×#19807 #15706146

Order 3328.

684 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3392C211yesmaximal, characteristic, complemented
2C13×#3381C211yesmaximal, characteristic, complemented
3C13×#3295C211yesmaximal, characteristic, complemented
4C13×#3274C211yesmaximal, characteristic
5C13×#1715C211yesmaximal, characteristic, complemented
6C13×#1691C211yesmaximal, characteristic, complemented
7C13×#1678C211yesmaximal, characteristic, complemented
8C13×#1668C211yesmaximal, characteristic, complemented
9C13×#1665C211yesmaximal, characteristic, complemented
10C13×#1639C211yesmaximal, characteristic, complemented
11C13×#1631C211yesmaximal, characteristic, complemented
12C13×#1626C211yesmaximal, characteristic, complemented
13C13×#1622C211yesmaximal, characteristic, complemented
14C13×#1583C211yesmaximal, characteristic, complemented
15C13×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×C13×AGL(1,ℤ/8)—21no—
17C13×#557C2211yescharacteristic, complemented
18C13×#554C2211yescharacteristic
19C13×#550C2211yescharacteristic
20D42×C13C2211yescharacteristic
21C13×#499—21no—
22C13×#498C2211yescharacteristic, complemented
23C13×#493C2211yescharacteristic
24C13×#492—21no—
25C13×#492C2211yescharacteristic, complemented
26C13×#492C2211yescharacteristic, complemented
27C13×#486C2211yescharacteristic
28C13×#486C2211yescharacteristic
29C13×#481—21no—
30C13×#479—21no—
31C13×#478—21no—
32C13×#477C2211yescharacteristic, complemented
33C13×#476C2211yescharacteristic
34C13×#474C2211yescharacteristic
35C13×#469—21no—
36C13×#465—21no—
37C13×#461—21no—
38C13×#461C2211yescharacteristic
39C13×#460—21no—
40C13×#460C2211yescharacteristic
41C13×#460C2211yescharacteristic
42C13×#460C2211yescharacteristic, complemented
43C13×#459C2211yescharacteristic
44C13×#450—21no—
45C13×#449—21no—
46C13×#447—21no—
47C8×Q8×C13C2211yescharacteristic, complemented
48C8×Q8×C13C2211yescharacteristic, complemented
49C4×C13×SD16—21no—
50C4×C13×SD16—21no—
51C4×C13×SD16C2211yescharacteristic
52C4×C13×SD16C2211yescharacteristic
53C13×#436C2211yescharacteristic
54C8×D4×C13C2211yescharacteristic
55C2×C13×#102—21no—
56C13×#335C2211yescharacteristic, complemented
57C13×#334C2211yescharacteristic, complemented
58C13×#333C2211yescharacteristic, complemented
59C13×#332C2211yescharacteristic, complemented
60C13×#331C2211yescharacteristic
61C13×#331C2211yescharacteristic, complemented
62C13×Q8⋊C8C2211yescharacteristic, complemented
63C13×Q8⋊C8C2211yescharacteristic, complemented
64C13×D4⋊C8C2211yescharacteristic
65C13×D4⋊C8C2211yescharacteristic
66C13×#322C2211yescharacteristic, complemented
67C2×C13×#41—21no—
68C22×D4×C13—21no—
69C22×D4×C13—21no—
70C13×AGL(1,ℤ/8)—44no—
71C2×C13×SD16—21no—
72C2×C13×SD16—21no—
73C2×C13×SD16—21no—
74C2×C13×SD16—21no—
75C2×C13×SD16—21no—
76C2×C13×SD16—21no—
77C2×C13×SD16—41no—
78C2×C13×SD16D411yescharacteristic
79C2×C13×SD16D411yescharacteristic
80C2×C13×D8—21no—
81C2×C13×D8—21no—
82C2×C13×D8—21no—
83C2×C13×M16—21no—
84C22×C8×C13—21no—
85C13×C4⋊Q8—21no—
86C13×C4⋊Q8C2311yescharacteristic
87C13×C4⋊Q8C2311yescharacteristic
88C13×#127—21no—
89C13×#127C2311yescharacteristic
90C13×#127C2311yescharacteristic
91C13×#125—21no—
92C13×#125—21no—
93C13×#125—41no—
94C13×C22⋊Q8—21no—
95C13×C22⋊Q8—41no—
96C13×#121—21no—
97C13×#121—21no—
98C13×#121—21no—
99C13×#121—41no—
100C13×#120—41no—
101C4×Q8×C13—21no—
102C4×Q8×C13—21no—
103C4×Q8×C13C2311yescharacteristic
104C4×Q8×C13C2311yescharacteristic
105C4×D4×C13—21no—
106C4×D4×C13—21no—
107C4×D4×C13C2311yescharacteristic
108C4×D4×C13C2311yescharacteristic
109C2×C13×C4⋊C4—21no—
110C13×#107—21no—
111C13×#107—21no—
112C13×#106—21no—
113C13×#106—21no—
114C13×#106—21no—
115C13×#106D411yescharacteristic
116C13×#106D411yescharacteristic
117C13×C4⋊C8—21no—
118C13×C4⋊C8—21no—
119C13×C4⋊C8C2311yescharacteristic
120C13×C4⋊C8C2311yescharacteristic
121C13×C4⋊C8C2311yescharacteristic
122C13×C4⋊C8C2311yescharacteristic
123C13×#103—21no—
124C13×#103—21no—
125C13×#103D411yescharacteristic
126C13×#103D411yescharacteristic
127C13×#102—21no—
128C13×#102—21no—
129C13×#102—21no—
130C13×#102—21no—
131C13×#102—21no—
132C13×#102—21no—
133C13×#102—21no—
134C13×#102—21no—
135C13×#102—41no—
136C13×#102D411yescharacteristic
137C13×#102D411yescharacteristic
138C13×C22⋊C8—21no—
139C13×C22⋊C8—21no—
140C4×C8×C13—21no—
141C4×C8×C13—21no—
142C4×C8×C13C2311yescharacteristic
143C4×C8×C13C2311yescharacteristic
144C4×C8×C13C2311yescharacteristic
145#19807C1311yesmaximal, characteristic, direct product factor, Sylow
146C24×C13—41no—
147C13×#41—42no—
148C13×#41—81no—
149C2×Q8×C13—21no—
150C2×Q8×C13—21no—
151C2×Q8×C13C2×D411yescharacteristic
152C2×Q8×C13C2×D411yescharacteristic
153C2×D4×C13—21no—
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—41no—
160C2×D4×C13—41no—
161C2×D4×C13—41no—
162C2×D4×C13—41no—
163C2×D4×C13—42no—
164C2×D4×C13—42no—
165C2×D4×C13—81no—
166C2×D4×C13—81no—
167C2×D4×C13C2×D411yescharacteristic
168C2×D4×C13C2×D411yescharacteristic
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—41no—
172C22×C4×C13—41no—
173C13×SD16—41no—
174C13×SD16—42no—
175C13×SD16—42no—
176C13×SD16—81no—
177C13×SD16—81no—
178C13×SD16—81no—
179C13×SD16—81no—
180C13×SD16—82no—
181C13×SD16SD1614yescomplemented
182C13×D8—42no—
183C13×D8—42no—
184C13×D8—81no—
185C13×M16—42no—
186C2×C8×C13—21no—
187C2×C8×C13—21no—
188C2×C8×C13—21no—
189C2×C8×C13—21no—
190C2×C8×C13—21no—
191C2×C8×C13—81no—
192C2×C8×C13C2×D411yescharacteristic
193C2×C8×C13C2×D411yescharacteristic
194C2×C8×C13C2×D411yescharacteristic
195C2×C8×C13C2×D411yescharacteristic
196C13×C4⋊C4—21no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—41no—
203C13×C4⋊C4—41no—
204C13×C4⋊C4—41no—
205C13×C4⋊C4—41no—
206C13×C4⋊C4—41no—
207C13×C4⋊C4C2×D411yescharacteristic
208C13×C4⋊C4C2×D411yescharacteristic
209C13×C4⋊C4C2×D411yescharacteristic
210C13×C4⋊C4C2×D411yescharacteristic
211C13×C22⋊C4—21no—
212C13×C22⋊C4—21no—
213C13×C22⋊C4—41no—
214C13×C22⋊C4—41no—
215C13×C22⋊C4—41no—
216C42×C13—21no—
217C42×C13—21no—
218C42×C13—41no—
219C42×C13C2411yescharacteristic
220#3392C2×C1311yescharacteristic, complemented
221#3381C2×C1311yescharacteristic, complemented
222#3295C2×C1311yescharacteristic, complemented
223#3274C2×C1311yescharacteristic
224#1715C2×C1311yescharacteristic, complemented
225#1691C2×C1311yescharacteristic, complemented
226#1678C2×C1311yescharacteristic, complemented
227#1668C2×C1311yescharacteristic, complemented
228#1665C2×C1311yescharacteristic, complemented
229#1639C2×C1311yescharacteristic, complemented
230#1631C2×C1311yescharacteristic, complemented
231#1626C2×C1311yescharacteristic, complemented
232#1622C2×C1311yescharacteristic, complemented
233#1583C2×C1311yescharacteristic, complemented
234SD16⋊C8C2×C1311yescharacteristic, complemented
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—82no—
240C23×C13—82no—
241C23×C13—161no—
242Q8×C13—21no—
243Q8×C13—21no—
244Q8×C13—21no—
245Q8×C13—41no—
246Q8×C13—41no—
247Q8×C13—81no—
248Q8×C13C2×SD1612yes—
249D4×C13—21no—
250D4×C13—21no—
251D4×C13—21no—
252D4×C13—41no—
253D4×C13—41no—
254D4×C13—41no—
255D4×C13—41no—
256D4×C13—41no—
257D4×C13—41no—
258D4×C13—41no—
259D4×C13—41no—
260D4×C13—82no—
261D4×C13—81no—
262D4×C13—81no—
263D4×C13—82no—
264D4×C13—82no—
265D4×C13—161no—
266D4×C13C2×SD1612yes—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—82no—
280C2×C4×C13—161no—
281C2×C4×C13C22×D411yescharacteristic
282C2×C4×C13C22×D411yescharacteristic
283C2×C4×C13H(5,𝔽2)11yescharacteristic
284C8×C13—21no—
285C8×C13—21no—
286C8×C13—21no—
287C8×C13—41no—
288C8×C13—41no—
289C8×C13—41no—
290C8×C13—41no—
291C8×C13—41no—
292C8×C13C2×SD1612yes—
293C2×AGL(1,ℤ/8)—21no—
294#557C22×C1311yescharacteristic, complemented
295#554C22×C1311yescharacteristic
296#550C22×C1311yescharacteristic
297D42C22×C1311yescharacteristic
298#499—21no—
299#498C22×C1311yescharacteristic, complemented
300#493C22×C1311yescharacteristic
301#492—21no—
302#492C22×C1311yescharacteristic, complemented
303#492C22×C1311yescharacteristic, complemented
304#486C22×C1311yescharacteristic
305#486C22×C1311yescharacteristic
306#481—21no—
307#479—21no—
308#478—21no—
309#477C22×C1311yescharacteristic, complemented
310#476C22×C1311yescharacteristic
311#474C22×C1311yescharacteristic
312#469—21no—
313#465—21no—
314#461—21no—
315#461C22×C1311yescharacteristic
316#460—21no—
317#460C22×C1311yescharacteristic
318#460C22×C1311yescharacteristic
319#460C22×C1311yescharacteristic, complemented
320#459C22×C1311yescharacteristic
321#450—21no—
322#449—21no—
323#447—21no—
324C8×Q8C22×C1311yescharacteristic, complemented
325C8×Q8C22×C1311yescharacteristic, complemented
326C4×SD16—21no—
327C4×SD16—21no—
328C4×SD16C22×C1311yescharacteristic
329C4×SD16C22×C1311yescharacteristic
330#436C22×C1311yescharacteristic
331C8×D4C22×C1311yescharacteristic
332C2×#102—21no—
333#335C22×C1311yescharacteristic, complemented
334#334C22×C1311yescharacteristic, complemented
335#333C22×C1311yescharacteristic, complemented
336#332C22×C1311yescharacteristic, complemented
337#331C22×C1311yescharacteristic
338#331C22×C1311yescharacteristic, complemented
339Q8⋊C8C22×C1311yescharacteristic, complemented
340Q8⋊C8C22×C1311yescharacteristic, complemented
341D4⋊C8C22×C1311yescharacteristic
342D4⋊C8C22×C1311yescharacteristic
343#322C22×C1311yescharacteristic, complemented
344C22×C13—22no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—81no—
351C22×C13—81no—
352C22×C13—81no—
353C22×C13—81no—
354C22×C13—81no—
355C22×C13—81no—
356C22×C13—164no—
357C22×C13D4211yescharacteristic
358C4×C13—22no—
359C4×C13—21no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13—41no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—81no—
366C4×C13—81no—
367C4×C13C22×SD1611yescharacteristic
368C4×C13#57511yescharacteristic
369C4×C13#57611yescharacteristic
370C4×C13#57711yescharacteristic
371C2×#41—21no—
372C22×D4—21no—
373C22×D4—21no—
374AGL(1,ℤ/8)—44no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—41no—
382C2×SD16D4×C1311yescharacteristic
383C2×SD16D4×C1311yescharacteristic
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×M16—21no—
388C22×C8—21no—
389C4⋊Q8—21no—
390C4⋊Q8C23×C1311yescharacteristic
391C4⋊Q8C23×C1311yescharacteristic
392#127—21no—
393#127C23×C1311yescharacteristic
394#127C23×C1311yescharacteristic
395#125—21no—
396#125—21no—
397#125—41no—
398C22⋊Q8—21no—
399C22⋊Q8—41no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—41no—
404#120—41no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8C23×C1311yescharacteristic
408C4×Q8C23×C1311yescharacteristic
409C4×D4—21no—
410C4×D4—21no—
411C4×D4C23×C1311yescharacteristic
412C4×D4C23×C1311yescharacteristic
413C2×C4⋊C4—21no—
414#107—21no—
415#107—21no—
416#106—21no—
417#106—21no—
418#106—21no—
419#106D4×C1311yescharacteristic
420#106D4×C1311yescharacteristic
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8C23×C1311yescharacteristic
424C4⋊C8C23×C1311yescharacteristic
425C4⋊C8C23×C1311yescharacteristic
426C4⋊C8C23×C1311yescharacteristic
427#103—21no—
428#103—21no—
429#103D4×C1311yescharacteristic
430#103D4×C1311yescharacteristic
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—41no—
440#102D4×C1311yescharacteristic
441#102D4×C1311yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C1311yescharacteristic
447C4×C8C23×C1311yescharacteristic
448C4×C8C23×C1311yescharacteristic
449C2×C13—42no—
450C2×C13—81no—
451C2×C13—161no—
452C2×C13—161no—
453C2×C13#326811yescharacteristic
454C2×C13D4×SD1611yescharacteristic
455C2×C13#328811yescharacteristic
456C24—41no—
457#41—42no—
458#41—81no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8C2×D4×C1311yescharacteristic
462C2×Q8C2×D4×C1311yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—81no—
476C2×D4—81no—
477C2×D4C2×D4×C1311yescharacteristic
478C2×D4C2×D4×C1311yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—41no—
483SD16—41no—
484SD16—42no—
485SD16—42no—
486SD16—81no—
487SD16—81no—
488SD16—81no—
489SD16—81no—
490SD16—82no—
491SD16C13×SD1614yescomplemented
492D8—42no—
493D8—42no—
494D8—81no—
495M16—42no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—81no—
502C2×C8C2×D4×C1311yescharacteristic
503C2×C8C2×D4×C1311yescharacteristic
504C2×C8C2×D4×C1311yescharacteristic
505C2×C8C2×D4×C1311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4C2×D4×C1311yescharacteristic
518C4⋊C4C2×D4×C1311yescharacteristic
519C4⋊C4C2×D4×C1311yescharacteristic
520C4⋊C4C2×D4×C1311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C42—21no—
527C42—21no—
528C42—41no—
529C42C24×C1311yescharacteristic
530C13#1980711yescharacteristic, direct product factor, Sylow
531C23—21no—
532C23—21no—
533C23—41no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—21no—
539Q8—21no—
540Q8—21no—
541Q8—41no—
542Q8—41no—
543Q8—81no—
544Q8C2×C13×SD1612yes—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—82no—
557D4—81no—
558D4—81no—
559D4—82no—
560D4—82no—
561D4—161no—
562D4C2×C13×SD1612yes—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—82no—
576C2×C4—161no—
577C2×C4C22×D4×C1311yescharacteristic
578C2×C4C22×D4×C1311yescharacteristic
579C2×C4C13×H(5,𝔽2)11yescharacteristic
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8C2×C13×SD1612yes—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—164no—
602C22D42×C1311yescharacteristic
603C4—22no—
604C4—21no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4C22×C13×SD1611yescharacteristic
613C4C13×#57511yescharacteristic
614C4C13×#57611yescharacteristic
615C4C13×#57711yescharacteristic
616C2—42no—
617C2—81no—
618C2—161no—
619C2—161no—
620C2C13×#326811yescharacteristic
621C2D4×C13×SD1611yescharacteristic
622C2C13×#328811yescharacteristic
subgroupG/H
center, socleC22×C13D42
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3274C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3392C2semidirect
2. C13×#3381C2semidirect
3. C13×#3295C2semidirect
5. C13×#1715C2semidirect
6. C13×#1691C2semidirect
7. C13×#1678C2semidirect
8. C13×#1668C2semidirect
9. C13×#1665C2semidirect
10. C13×#1639C2semidirect
11. C13×#1631C2semidirect
12. C13×#1626C2semidirect
13. C13×#1622C2semidirect
14. C13×#1583C2semidirect
15. C13×SD16⋊C8C2semidirect
17. C13×#557C22semidirect
22. C13×#498C22semidirect
25. C13×#492C22semidirect
26. C13×#492C22semidirect
32. C13×#477C22semidirect
42. C13×#460C22semidirect
47. C8×Q8×C13C22semidirect
48. C8×Q8×C13C22semidirect
56. C13×#335C22semidirect
57. C13×#334C22semidirect
58. C13×#333C22semidirect
59. C13×#332C22semidirect
61. C13×#331C22semidirect
62. C13×Q8⋊C8C22semidirect
63. C13×Q8⋊C8C22semidirect
66. C13×#322C22semidirect
145. #19807C13direct (N × H)
181. C13×SD16SD16semidirect
220. #3392C2×C13semidirect
221. #3381C2×C13semidirect
222. #3295C2×C13semidirect
224. #1715C2×C13semidirect
225. #1691C2×C13semidirect
226. #1678C2×C13semidirect
227. #1668C2×C13semidirect
228. #1665C2×C13semidirect
229. #1639C2×C13semidirect
230. #1631C2×C13semidirect
231. #1626C2×C13semidirect
232. #1622C2×C13semidirect
233. #1583C2×C13semidirect
234. SD16⋊C8C2×C13semidirect
294. #557C22×C13semidirect
299. #498C22×C13semidirect
302. #492C22×C13semidirect
303. #492C22×C13semidirect
309. #477C22×C13semidirect
319. #460C22×C13semidirect
324. C8×Q8C22×C13semidirect
325. C8×Q8C22×C13semidirect
333. #335C22×C13semidirect
334. #334C22×C13semidirect
335. #333C22×C13semidirect
336. #332C22×C13semidirect
338. #331C22×C13semidirect
339. Q8⋊C8C22×C13semidirect
340. Q8⋊C8C22×C13semidirect
343. #322C22×C13semidirect
491. SD16C13×SD16semidirect
530. C13#19807direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33922
C13×#33812
C13×#32952
C13×#32742
C13×#17152
C13×#16912
C13×#16782
C13×#16682
C13×#16652
C13×#16392
C13×#16312
C13×#16262
C13×#16222
C13×#15832
C13×SD16⋊C82
#1980713