Finite Group Databasebeta

← C103×#25316 #39930591

Subgroups — C103×#25316 #39930591

Order 26368.

722 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3140C211yesmaximal, characteristic, complemented
2C103×#3077C211yesmaximal, characteristic, complemented
3C2×#463×C103C211yesmaximal, characteristic
4C103×#2962C211yesmaximal, characteristic, complemented
5C103×#2064C211yesmaximal, characteristic, complemented
6C103×#2063C211yesmaximal, characteristic, complemented
7C103×#2046C211yesmaximal, characteristic, complemented
8C103×#2045C211yesmaximal, characteristic
9C103×#1978C211yesmaximal, characteristic
10C103×#1977C211yesmaximal, characteristic, complemented
11C103×#1967C211yesmaximal, characteristic, complemented
12C103×#1950C211yesmaximal, characteristic, complemented
13C103×#1931C211yesmaximal, characteristic, complemented
14C103×#1930C211yesmaximal, characteristic, complemented
15C4×#100×C103C211yesmaximal, characteristic, complemented
16C22×SD16×C103C2211yescharacteristic
17C22×D8×C103C2211yescharacteristic
18#533×C103C2211yescharacteristic
19C2×#124×C103C2211yescharacteristic
20C2×C4×D4×C103C2211yescharacteristic
21#489×C103—21no—
22#489×C103—21no—
23#488×C103—21no—
24#488×C103—21no—
25#478×C103—21no—
26#478×C103—21no—
27#476×C103—21no—
28#474×C103—21no—
29#463×C103—21no—
30#463×C103—21no—
31#463×C103—21no—
32#463×C103—21no—
33#446×C103—21no—
34#446×C103—21no—
35#446×C103—21no—
36C8×Q8×C103—21no—
37C2×#108×C103C2211yescharacteristic
38C2×#108×C103C2211yescharacteristic
39#428×C103C2211yescharacteristic
40#428×C103C2211yescharacteristic
41#424×C103C2211yescharacteristic
42#424×C103C2211yescharacteristic
43#423×C103C2211yescharacteristic
44C2×C4⋊C8×C103C2211yescharacteristic
45#419×C103C2211yescharacteristic
46#419×C103C2211yescharacteristic
47#418×C103C2211yescharacteristic
48#418×C103C2211yescharacteristic
49#418×C103C2211yescharacteristic
50#418×C103C2211yescharacteristic
51C2×#103×C103C2211yescharacteristic
52C2×#102×C103C2211yescharacteristic
53C2×#101×C103C2211yescharacteristic
54C2×#101×C103C2211yescharacteristic
55C2×#100×C103C2211yescharacteristic
56C2×#100×C103C2211yescharacteristic
57C2×#100×C103C2211yescharacteristic
58C2×#100×C103C2211yescharacteristic
59#405×C103C2211yescharacteristic
60#405×C103C2211yescharacteristic
61C4×M16×C103C2211yescharacteristic
62C4×M16×C103C2211yescharacteristic
63#343×C103C2211yescharacteristic
64#343×C103C2211yescharacteristic
65#341×C103C2211yescharacteristic
66#341×C103C2211yescharacteristic
67C22×Q8×C103C2311yescharacteristic
68C22×D4×C103C2311yescharacteristic
69C22×D4×C103C2311yescharacteristic
70C23×C4×C103—21no—
71C2×SD16×C103—22no—
72C2×SD16×C103—21no—
73C2×SD16×C103—21no—
74C2×SD16×C103—41no—
75C2×D8×C103—22no—
76C2×D8×C103—21no—
77C2×D8×C103—21no—
78C2×D8×C103—41no—
79C2×M16×C103C2311yescharacteristic
80C2×M16×C103C2311yescharacteristic
81C2×M16×C103C2311yescharacteristic
82C2×M16×C103C2311yescharacteristic
83C2×M16×C103C2311yescharacteristic
84C2×M16×C103C2311yescharacteristic
85C22×C8×C103C2311yescharacteristic
86C22×C8×C103C2311yescharacteristic
87C4⋊Q8×C103D411yescharacteristic
88C4⋊Q8×C103D411yescharacteristic
89#125×C103D411yescharacteristic
90#125×C103D411yescharacteristic
91#124×C103—21no—
92#124×C103—21no—
93#124×C103—21no—
94#124×C103—21no—
95C22⋊Q8×C103—21no—
96C22⋊Q8×C103—21no—
97C4×Q8×C103—21no—
98C4×Q8×C103—21no—
99C4×D4×C103—21no—
100C4×D4×C103—21no—
101C4×D4×C103—21no—
102C4×D4×C103—21no—
103#117×C103C2311yescharacteristic
104#117×C103C2311yescharacteristic
105C2×C4⋊C4×C103C2311yescharacteristic
106C2×C22⋊C4×C103—21no—
107C2×C22⋊C4×C103—21no—
108C2×C22⋊C4×C103—21no—
109C2×C42×C103C2311yescharacteristic
110#108×C103—41no—
111#108×C103—41no—
112#107×C103—21no—
113#107×C103—21no—
114#106×C103—21no—
115#106×C103—21no—
116C4⋊C8×C103—21no—
117C4⋊C8×C103—21no—
118C4⋊C8×C103—21no—
119C4⋊C8×C103—21no—
120C4⋊C8×C103—21no—
121C4⋊C8×C103—21no—
122C4⋊C8×C103D411yescharacteristic
123C4⋊C8×C103D411yescharacteristic
124C4⋊C8×C103D411yescharacteristic
125C4⋊C8×C103D411yescharacteristic
126#103×C103—21no—
127#103×C103—21no—
128#103×C103—21no—
129#103×C103—21no—
130#103×C103—21no—
131#103×C103—21no—
132#102×C103—21no—
133#102×C103—21no—
134#102×C103—21no—
135#102×C103—21no—
136#102×C103—21no—
137#102×C103—21no—
138#102×C103—21no—
139#102×C103—21no—
140#102×C103—21no—
141#102×C103—21no—
142#101×C103—22no—
143#101×C103—41no—
144#100×C103—22no—
145#100×C103—22no—
146#100×C103—22no—
147#100×C103—41no—
148#97×C103—21no—
149#97×C103—21no—
150#97×C103—21no—
151#97×C103—21no—
152C4×C8×C103—21no—
153C4×C8×C103—21no—
154C4×C8×C103—21no—
155C4×C8×C103—21no—
156C24×C103—21no—
157C24×C103—21no—
158C2×Q8×C103—21no—
159C2×Q8×C103—21no—
160C2×Q8×C103—21no—
161C2×Q8×C103—21no—
162C2×Q8×C103—21no—
163C2×Q8×C103—21no—
164C2×Q8×C103—21no—
165C2×Q8×C103—21no—
166C2×D4×C103—21no—
167C2×D4×C103—21no—
168C2×D4×C103—21no—
169C2×D4×C103—21no—
170C2×D4×C103—21no—
171C2×D4×C103—21no—
172C2×D4×C103—21no—
173C2×D4×C103—21no—
174C2×D4×C103—21no—
175C2×D4×C103—21no—
176C2×D4×C103—21no—
177C2×D4×C103#4112yes—
178C22×C4×C103—21no—
179C22×C4×C103—21no—
180C22×C4×C103—41no—
181C22×C4×C103—41no—
182C22×C4×C103—82no—
183C22×C4×C103#4111yescharacteristic
184C22×C4×C103#4111yescharacteristic
185C22×C4×C103C2411yescharacteristic
186SD16×C103—42no—
187SD16×C103—42no—
188D8×C103—42no—
189D8×C103—42no—
190M16×C103—21no—
191M16×C103—21no—
192M16×C103—21no—
193M16×C103—21no—
194M16×C103—21no—
195M16×C103—21no—
196M16×C103—21no—
197M16×C103—21no—
198M16×C103—21no—
199M16×C103—21no—
200M16×C103—21no—
201M16×C103#4112yes—
202C2×C8×C103—21no—
203C2×C8×C103—21no—
204C2×C8×C103—21no—
205C2×C8×C103—21no—
206C2×C8×C103—21no—
207C2×C8×C103—21no—
208C2×C8×C103—21no—
209C2×C8×C103—21no—
210C2×C8×C103—21no—
211C2×C8×C103—21no—
212C2×C8×C103C2×D411yescharacteristic
213C2×C8×C103C2×D411yescharacteristic
214C2×C8×C103C2×D411yescharacteristic
215C2×C8×C103C2×D411yescharacteristic
216C4⋊C4×C103—21no—
217C4⋊C4×C103—21no—
218C4⋊C4×C103—21no—
219C4⋊C4×C103—21no—
220C4⋊C4×C103—21no—
221C4⋊C4×C103—21no—
222C4⋊C4×C103—21no—
223C4⋊C4×C103—21no—
224C4⋊C4×C103C2×D411yescharacteristic
225C4⋊C4×C103C2×D411yescharacteristic
226C4⋊C4×C103C2×D411yescharacteristic
227C4⋊C4×C103C2×D411yescharacteristic
228C22⋊C4×C103—21no—
229C22⋊C4×C103—21no—
230C22⋊C4×C103—41no—
231C22⋊C4×C103—41no—
232C22⋊C4×C103—41no—
233C22⋊C4×C103—41no—
234C22⋊C4×C103—41no—
235C22⋊C4×C103—41no—
236C42×C103—21no—
237C42×C103—21no—
238C42×C103C2×D411yescharacteristic
239C42×C103C2×D411yescharacteristic
240C42×C103C2×D411yescharacteristic
241C42×C103C2×D411yescharacteristic
242C23×C103—22no—
243C23×C103—41no—
244C23×C103—41no—
245C23×C103—41no—
246C23×C103—41no—
247C23×C103—41no—
248C23×C103—81no—
249C23×C103—81no—
250C23×C103—81no—
251C23×C103—81no—
252C23×C103C2×#4111yescharacteristic
253Q8×C103—42no—
254Q8×C103—41no—
255Q8×C103—41no—
256Q8×C103—41no—
257Q8×C103—41no—
258Q8×C103—81no—
259D4×C103—22no—
260D4×C103—22no—
261D4×C103—41no—
262D4×C103—41no—
263D4×C103—41no—
264D4×C103—41no—
265D4×C103—41no—
266D4×C103—41no—
267C2×C4×C103—21no—
268C2×C4×C103—21no—
269C2×C4×C103—21no—
270C2×C4×C103—21no—
271C2×C4×C103—41no—
272C2×C4×C103—41no—
273C2×C4×C103—41no—
274C2×C4×C103—41no—
275C2×C4×C103—41no—
276C2×C4×C103—41no—
277C2×C4×C103—82no—
278C2×C4×C103—82no—
279C2×C4×C103—81no—
280C2×C4×C103#12111yescharacteristic
281C2×C4×C103#12111yescharacteristic
282C2×C4×C103#12111yescharacteristic
283C2×C4×C103#12111yescharacteristic
284C2×C4×C103C22×D411yescharacteristic
285C2×C4×C103C22×D411yescharacteristic
286C2×C4×C103C2×#4111yescharacteristic
287C2×C4×C103C2×#4111yescharacteristic
288C2×C4×C103H(5,𝔽2)11yescharacteristic
289C2×C4×C1032−1+411yescharacteristic
290C8×C103—21no—
291C8×C103—21no—
292C8×C103—21no—
293C8×C103—21no—
294C8×C103—22no—
295C8×C103—41no—
296C8×C103—41no—
297C8×C103—41no—
298C8×C103—41no—
299C8×C103—41no—
300C22×C103—21no—
301C22×C103—21no—
302C22×C103—42no—
303C22×C103—82no—
304C22×C103—82no—
305C22×C103—81no—
306C22×C103—81no—
307C22×C103—81no—
308C22×C103—81no—
309C22×C103—81no—
310C22×C103—161no—
311C22×C103—161no—
312C22×C103C2×#12111yescharacteristic
313C22×C103#52911yescharacteristic
314C22×C103#54211yescharacteristic
315C4×C103—21no—
316C4×C103—21no—
317C4×C103—21no—
318C4×C103—21no—
319C4×C103—41no—
320C4×C103—41no—
321C4×C103—41no—
322C4×C103—41no—
323C4×C103—81no—
324C4×C103—81no—
325C4×C103#54611yescharacteristic
326C4×C103#54811yescharacteristic
327C4×C103#54811yescharacteristic
328C4×C103#55011yescharacteristic
329#25316C10311yesmaximal, characteristic, direct product factor, Sylow
330C2×C103—21no—
331C2×C103—21no—
332C2×C103—82no—
333C2×C103—161no—
334C2×C103#242611yescharacteristic
335C2×C103#306711yescharacteristic
336C2×C103#306811yescharacteristic
337#3140C2×C10311yescharacteristic, complemented
338#3077C2×C10311yescharacteristic, complemented
339C2×#463C2×C10311yescharacteristic
340#2962C2×C10311yescharacteristic, complemented
341#2064C2×C10311yescharacteristic, complemented
342#2063C2×C10311yescharacteristic, complemented
343#2046C2×C10311yescharacteristic, complemented
344#2045C2×C10311yescharacteristic
345#1978C2×C10311yescharacteristic
346#1977C2×C10311yescharacteristic, complemented
347#1967C2×C10311yescharacteristic, complemented
348#1950C2×C10311yescharacteristic, complemented
349#1931C2×C10311yescharacteristic, complemented
350#1930C2×C10311yescharacteristic, complemented
351C4×#100C2×C10311yescharacteristic, complemented
352C103#2531611yescharacteristic, direct product factor, Sylow
353C22×SD16C22×C10311yescharacteristic
354C22×D8C22×C10311yescharacteristic
355#533C22×C10311yescharacteristic
356C2×#124C22×C10311yescharacteristic
357C2×C4×D4C22×C10311yescharacteristic
358#489—21no—
359#489—21no—
360#488—21no—
361#488—21no—
362#478—21no—
363#478—21no—
364#476—21no—
365#474—21no—
366#463—21no—
367#463—21no—
368#463—21no—
369#463—21no—
370#446—21no—
371#446—21no—
372#446—21no—
373C8×Q8—21no—
374C2×#108C22×C10311yescharacteristic
375C2×#108C22×C10311yescharacteristic
376#428C22×C10311yescharacteristic
377#428C22×C10311yescharacteristic
378#424C22×C10311yescharacteristic
379#424C22×C10311yescharacteristic
380#423C22×C10311yescharacteristic
381C2×C4⋊C8C22×C10311yescharacteristic
382#419C22×C10311yescharacteristic
383#419C22×C10311yescharacteristic
384#418C22×C10311yescharacteristic
385#418C22×C10311yescharacteristic
386#418C22×C10311yescharacteristic
387#418C22×C10311yescharacteristic
388C2×#103C22×C10311yescharacteristic
389C2×#102C22×C10311yescharacteristic
390C2×#101C22×C10311yescharacteristic
391C2×#101C22×C10311yescharacteristic
392C2×#100C22×C10311yescharacteristic
393C2×#100C22×C10311yescharacteristic
394C2×#100C22×C10311yescharacteristic
395C2×#100C22×C10311yescharacteristic
396#405C22×C10311yescharacteristic
397#405C22×C10311yescharacteristic
398C4×M16C22×C10311yescharacteristic
399C4×M16C22×C10311yescharacteristic
400#343C22×C10311yescharacteristic
401#343C22×C10311yescharacteristic
402#341C22×C10311yescharacteristic
403#341C22×C10311yescharacteristic
404C22×Q8C23×C10311yescharacteristic
405C22×D4C23×C10311yescharacteristic
406C22×D4C23×C10311yescharacteristic
407C23×C4—21no—
408C2×SD16—22no—
409C2×SD16—21no—
410C2×SD16—21no—
411C2×SD16—41no—
412C2×D8—22no—
413C2×D8—21no—
414C2×D8—21no—
415C2×D8—41no—
416C2×M16C23×C10311yescharacteristic
417C2×M16C23×C10311yescharacteristic
418C2×M16C23×C10311yescharacteristic
419C2×M16C23×C10311yescharacteristic
420C2×M16C23×C10311yescharacteristic
421C2×M16C23×C10311yescharacteristic
422C22×C8C23×C10311yescharacteristic
423C22×C8C23×C10311yescharacteristic
424C4⋊Q8D4×C10311yescharacteristic
425C4⋊Q8D4×C10311yescharacteristic
426#125D4×C10311yescharacteristic
427#125D4×C10311yescharacteristic
428#124—21no—
429#124—21no—
430#124—21no—
431#124—21no—
432C22⋊Q8—21no—
433C22⋊Q8—21no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440#117C23×C10311yescharacteristic
441#117C23×C10311yescharacteristic
442C2×C4⋊C4C23×C10311yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C42C23×C10311yescharacteristic
447#108—41no—
448#108—41no—
449#107—21no—
450#107—21no—
451#106—21no—
452#106—21no—
453C4⋊C8—21no—
454C4⋊C8—21no—
455C4⋊C8—21no—
456C4⋊C8—21no—
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8D4×C10311yescharacteristic
460C4⋊C8D4×C10311yescharacteristic
461C4⋊C8D4×C10311yescharacteristic
462C4⋊C8D4×C10311yescharacteristic
463#103—21no—
464#103—21no—
465#103—21no—
466#103—21no—
467#103—21no—
468#103—21no—
469#102—21no—
470#102—21no—
471#102—21no—
472#102—21no—
473#102—21no—
474#102—21no—
475#102—21no—
476#102—21no—
477#102—21no—
478#102—21no—
479#101—22no—
480#101—41no—
481#100—22no—
482#100—22no—
483#100—22no—
484#100—41no—
485#97—21no—
486#97—21no—
487#97—21no—
488#97—21no—
489C4×C8—21no—
490C4×C8—21no—
491C4×C8—21no—
492C4×C8—21no—
493C24—21no—
494C24—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4#41×C10312yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—82no—
520C22×C4#41×C10311yescharacteristic
521C22×C4#41×C10311yescharacteristic
522C22×C4C24×C10311yescharacteristic
523SD16—42no—
524SD16—42no—
525D8—42no—
526D8—42no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16#41×C10312yes—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8C2×D4×C10311yescharacteristic
550C2×C8C2×D4×C10311yescharacteristic
551C2×C8C2×D4×C10311yescharacteristic
552C2×C8C2×D4×C10311yescharacteristic
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4C2×D4×C10311yescharacteristic
562C4⋊C4C2×D4×C10311yescharacteristic
563C4⋊C4C2×D4×C10311yescharacteristic
564C4⋊C4C2×D4×C10311yescharacteristic
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C42—21no—
574C42—21no—
575C42C2×D4×C10311yescharacteristic
576C42C2×D4×C10311yescharacteristic
577C42C2×D4×C10311yescharacteristic
578C42C2×D4×C10311yescharacteristic
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—81no—
586C23—81no—
587C23—81no—
588C23—81no—
589C23C2×#41×C10311yescharacteristic
590Q8—42no—
591Q8—41no—
592Q8—41no—
593Q8—41no—
594Q8—41no—
595Q8—81no—
596D4—22no—
597D4—22no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—82no—
615C2×C4—82no—
616C2×C4—81no—
617C2×C4#121×C10311yescharacteristic
618C2×C4#121×C10311yescharacteristic
619C2×C4#121×C10311yescharacteristic
620C2×C4#121×C10311yescharacteristic
621C2×C4C22×D4×C10311yescharacteristic
622C2×C4C22×D4×C10311yescharacteristic
623C2×C4C2×#41×C10311yescharacteristic
624C2×C4C2×#41×C10311yescharacteristic
625C2×C4H(5,𝔽2)×C10311yescharacteristic
626C2×C42−1+4×C10311yescharacteristic
627C8—21no—
628C8—21no—
629C8—21no—
630C8—21no—
631C8—22no—
632C8—41no—
633C8—41no—
634C8—41no—
635C8—41no—
636C8—41no—
637C22—21no—
638C22—21no—
639C22—42no—
640C22—82no—
641C22—82no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—161no—
648C22—161no—
649C22C2×#121×C10311yescharacteristic
650C22#529×C10311yescharacteristic
651C22#542×C10311yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—81no—
661C4—81no—
662C4#546×C10311yescharacteristic
663C4#548×C10311yescharacteristic
664C4#548×C10311yescharacteristic
665C4#550×C10311yescharacteristic
666C2—21no—
667C2—21no—
668C2—82no—
669C2—161no—
670C2C103×#242611yescharacteristic
671C2C103×#306711yescharacteristic
672C2C103×#306811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D8×C103C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3140C2semidirect
2. C103×#3077C2semidirect
4. C103×#2962C2semidirect
5. C103×#2064C2semidirect
6. C103×#2063C2semidirect
7. C103×#2046C2semidirect
10. C103×#1977C2semidirect
11. C103×#1967C2semidirect
12. C103×#1950C2semidirect
13. C103×#1931C2semidirect
14. C103×#1930C2semidirect
15. C4×#100×C103C2semidirect
329. #25316C103direct (N × H)
337. #3140C2×C103semidirect
338. #3077C2×C103semidirect
340. #2962C2×C103semidirect
341. #2064C2×C103semidirect
342. #2063C2×C103semidirect
343. #2046C2×C103semidirect
346. #1977C2×C103semidirect
347. #1967C2×C103semidirect
348. #1950C2×C103semidirect
349. #1931C2×C103semidirect
350. #1930C2×C103semidirect
351. C4×#100C2×C103semidirect
352. C103#25316direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31402
C103×#30772
C2×#463×C1032
C103×#29622
C103×#20642
C103×#20632
C103×#20462
C103×#20452
C103×#19782
C103×#19772
C103×#19672
C103×#19502
C103×#19312
C103×#19302
C4×#100×C1032
#25316103