Finite Group Databasebeta

← #14460018

Subgroups — #14460018

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5631C211yesmaximal, characteristic
2#11754233C211yesmaximal, characteristic, complemented
3#11751146C211yesmaximal, characteristic, complemented
4C3×#65340C211yesmaximal, characteristic, complemented
5#11749305C211yesmaximal, characteristic, complemented
6#11749251C211yesmaximal, characteristic, complemented
7#11749211C211yesmaximal, characteristic, complemented
8#11749187C211yesmaximal, characteristic, complemented
9#11748538C211yesmaximal, characteristic, complemented
10#67×#168C211yesmaximal, characteristic, complemented
11#11748388C211yesmaximal, characteristic, complemented
12#11747416C211yesmaximal, characteristic, complemented
13#11747353C211yesmaximal, characteristic, complemented
14#11747264C211yesmaximal, characteristic, complemented
15#11747208C211yesmaximal, characteristic, complemented
16#10615241—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18C2×C5×#235C2211yescharacteristic
19C3×C5×C22⋊Q8C2211yescharacteristic
20#91815C2211yescharacteristic
21C5×#944C2211yescharacteristic
22C4×C5×#67C2211yescharacteristic
23C5×#897C2211yescharacteristic
24C5×#894—21no—
25C5×#893C2211yescharacteristic
26C5×D3×C4⋊C4—21no—
27C5×#884—21no—
28C5×#883—21no—
29C2×C3×#689C2211yescharacteristic
30C3×#4070C2211yescharacteristic
31C22×C3×#168C2211yescharacteristic
32#91530—21no—
33#91525—21no—
34#91469C2211yescharacteristic
35#91369C2211yescharacteristic
36#91367—21no—
37#91338C2211yescharacteristic
38Dic3×Dic10C2211yescharacteristic
39#91325—21no—
40C2×#6661C2211yescharacteristic
41C2×#6656C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic
43#91119C2211yescharacteristic
44#91119C2211yescharacteristic
45#91114C2211yescharacteristic
46#91092C2211yescharacteristic
47#91091C2211yescharacteristic
48C3×#3967C2211yescharacteristic
49C3×#3942C2211yescharacteristic
50C3×#3939C2211yescharacteristic
51Dic3⋊#168C2211yescharacteristic
52#90973C2211yescharacteristic
53#90973C2211yescharacteristic
54#90972C2211yescharacteristic
55#90967C2211yescharacteristic
56#90967C2211yescharacteristic
57#90966C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#80776—51nomaximal, Hall
61C5×#547—31no—
62#65876—31no—
63#65528—31no—
64#65528—31no—
65#65522—31no—
66#65522—31no—
67#65379—31no—
68#65370—31no—
69#65340—31no—
70#65340D311yescharacteristic, complemented
71#65334—31no—
72#65334—31no—
73C4×#687—31no—
74D4×#168—31no—
75#65296—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C2×C5×#67—21no—
79C2×C5×#67D411yescharacteristic
80C5×#239—22no—
81C5×#239—41no—
82C5×#235—22no—
83C5×#235—41no—
84C2×C5×D12—21no—
85C2×C5×D12C2311yescharacteristic
86C2×C4×C5×D3—21no—
87C2×C4×C5×D3—21no—
88C2×C4×C5×D3—21no—
89C2×C4×C5×D3C2311yescharacteristic
90C2×C5×Dic6C2311yescharacteristic
91C2×C3×Dic10C2311yescharacteristic
92C2×#1204—21no—
93C3×C5×C4⋊C4—21no—
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C22⋊C4—21no—
96#6719—21no—
97C4⋊Dic15C2311yescharacteristic
98C4⋊Dic15C2311yescharacteristic
99C4×Dic15—21no—
100C2×C3⋊#168C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102C5×#217D411yescharacteristic
103C5×(C2×D3)⋊C4—21no—
104C5×(C2×D3)⋊C4—21no—
105C5×(C2×D3)⋊C4D411yescharacteristic
106C5×C4⋊Dic3—21no—
107C5×Dic3⋊C4—21no—
108C5×Dic3⋊C4—21no—
109C5×Dic3⋊C4D411yescharacteristic
110C4×C5×Dic3C2311yescharacteristic
111C3×C22⋊Dic5—21no—
112C3×#689—41no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×#683—21no—
115C2×C3×#168—41no—
116C2×C3×#168C2311yescharacteristic
117C2×C3×#168C2311yescharacteristic
118Dic3⋊Dic5—21no—
119#6669—21no—
120#6668—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125#6661—41no—
126#6656—22no—
127D3×#168—41no—
128#5641—51no—
129#5631D511yescharacteristic
130C3×#467—51no—
131#5187—51no—
132#5182—51no—
133#5113—51no—
134C8×#67—51no—
135#5047—51no—
136#5045—51no—
137#4890—51no—
138#4888—51no—
139#4813—51no—
140#4804—51no—
141#4792—51no—
142#4788—51no—
143C2×C5×#41—31no—
144C2×C5×#41—31no—
145C5×C4⋊Q8—31no—
146C5×#123—61no—
147C5×#123—61no—
148C5×C22⋊Q8—31no—
149C5×C22⋊Q8C2×D311yescharacteristic
150C5×#121—61no—
151C4×C5×D4—31no—
152C4×C5×D4—31no—
153C2×C5×C4⋊C4—61no—
154C2×#689—31no—
155C2×#689C2×D311yescharacteristic
156#4082—61no—
157C2×#687—31no—
158#4072—31no—
159#4072—31no—
160#4070—31no—
161#4070C2×D311yescharacteristic
162C22×#168—31no—
163C22×#168C2×D311yescharacteristic
164#4033—61no—
165#4025—61no—
166#4025—61no—
167#4015—31no—
168C4×Dic10—31no—
169#3967—31no—
170#3967—31no—
171#3967—31no—
172#3967—31no—
173#3967—31no—
174#3967C2×D311yescharacteristic
175#3964—31no—
176#3964—31no—
177#3964—31no—
178C22⋊#168—31no—
179C22⋊#168—31no—
180#3942C2×D311yescharacteristic
181#3940—31no—
182#3939—31no—
183#3939C2×D311yescharacteristic
184C4⋊#168—31no—
185C4×#168—31no—
186#3302—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×C5×D3—21no—
189C22×C5×D3C2×D411yescharacteristic
190C3×C5×Q8—21no—
191C3×C5×Q8—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2411yescharacteristic
198C2×Dic15—21no—
199C2×Dic15—21no—
200C5×#67—22no—
201C5×#67—42no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3C2×D411yescharacteristic
204C2×C5×Dic3C2×D411yescharacteristic
205C2×C5×Dic3C2×D411yescharacteristic
206C5×D12—21no—
207C5×D12—42no—
208C5×D12#4112yes—
209C4×C5×D3—21no—
210C4×C5×D3—21no—
211C4×C5×D3—42no—
212C4×C5×D3—42no—
213C4×C5×D3—42no—
214C5×Dic6—21no—
215C5×Dic6—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C3×Dic10—21no—
219C3×Dic10—21no—
220#1204—42no—
221C3⋊#168—21no—
222C3⋊#168—21no—
223C3×#168—21no—
224C3×#168—21no—
225C2×#239C2×D511yescharacteristic
226C2×#235C2×D511yescharacteristic
227C2×C3×Q16—51no—
228C22×C3×C8—51no—
229C3×C22⋊Q8—51no—
230C3×C22⋊Q8C2×D511yescharacteristic
231#946—51no—
232Q8×Dic3—51no—
233#944C2×D511yescharacteristic
234C2×#216—51no—
235C2×#215—51no—
236C4×#67C2×D511yescharacteristic
237#926—51no—
238C2×D3×C8—51no—
239#898—101no—
240#897C2×D511yescharacteristic
241#894—21no—
242#893C2×D511yescharacteristic
243#892—51no—
244D3×C4⋊C4—21no—
245#888—51no—
246#887—101no—
247#885—101no—
248#884—21no—
249#883—21no—
250#879—101no—
251C3×#107—51no—
252C3×#103—51no—
253C3×#103—51no—
254#835—51no—
255#835—51no—
256#830—51no—
257#821—51no—
258#821—51no—
259(C2×D3)⋊C8—51no—
260#816—51no—
261#816—51no—
262Dic3⋊C8—51no—
263C8×Dic3—51no—
264#810—51no—
265#809—51no—
266#808—51no—
267#807—51no—
268C5×#41—62no—
269C5×#41—62no—
270C5×#41—121no—
271C5×#41—121no—
272C2×C5×Q8—31no—
273C2×C5×Q8C22×D311yescharacteristic
274C2×C5×D4—31no—
275C2×C5×D4—31no—
276C2×C5×D4—61no—
277C2×C5×D4—61no—
278C22×C4×C5—31no—
279C22×C4×C5—61no—
280C22×C4×C5—61no—
281C22×C4×C5—61no—
282C22×C4×C5C22×D311yescharacteristic
283C2×Dic10—61no—
284C2×Dic10C22×D311yescharacteristic
285C5×C4⋊C4—21no—
286C5×C4⋊C4—31no—
287C5×C4⋊C4—61no—
288C5×C4⋊C4—61no—
289C5×C4⋊C4—61no—
290C5×C4⋊C4C22×D311yescharacteristic
291C5×C22⋊C4—21no—
292C5×C22⋊C4—31no—
293C5×C22⋊C4—31no—
294C5×C22⋊C4—61no—
295C5×C22⋊C4—61no—
296C42×C5—31no—
297C22⋊Dic5—21no—
298C22⋊Dic5—61no—
299C22⋊Dic5—61no—
300C22⋊Dic5—61no—
301#689—41no—
302#689—121no—
303#687—62no—
304C4⋊Dic5—31no—
305C4⋊Dic5—31no—
306C4⋊Dic5—61no—
307C4⋊Dic5C22×D311yescharacteristic
308#683—21no—
309#683—61no—
310#683—61no—
311C4×Dic5—61no—
312C4×Dic5—61no—
313C4×Dic5—61no—
314C2×#168—31no—
315C2×#168—31no—
316C2×#168—41no—
317C2×#168—121no—
318C2×#168C22×D311yescharacteristic
319C2×#168C22×D311yescharacteristic
320#556—151no—
321#547—31no—
322#487—151no—
323#485—151no—
324#485—151no—
325#474—151no—
326#467—51no—
327#467—151no—
328#462—151no—
329#452—151no—
330#452—151no—
331C4×SD16—151no—
332C8×D4—151no—
333#416—151no—
334#416—151no—
335C22×C3×C5—21no—
336C22×C3×C5—21no—
337C22×C3×C5—21no—
338C22×C3×C5C22×D411yescharacteristic
339C2×C5×D3—21no—
340C2×C5×D3—22no—
341C2×C5×D3—21no—
342C2×C5×D3—21no—
343C2×C5×D3—41no—
344C2×C5×D3—41no—
345C3×C4×C5—21no—
346C3×C4×C5—41no—
347C3×C4×C5—41no—
348C3×C4×C5C2×#4111yescharacteristic
349C3×C4×C5H(5,𝔽2)11yescharacteristic
350Dic15—41no—
351Dic15—41no—
352C3×Dic5—41no—
353C3×Dic5—41no—
354C5×Dic3—21no—
355C5×Dic3—21no—
356C5×Dic3—41no—
357C5×Dic3#13512yes—
358C2×C3×Q8—51no—
359C2×C3×Q8C22×D511yescharacteristic
360C22×C3×C4C22×D511yescharacteristic
361C2×#67—21no—
362C2×#67C22⋊D511yescharacteristic
363#239—22no—
364#239—41no—
365#235—22no—
366#235—41no—
367C2×D12—21no—
368C2×D12C22×D511yescharacteristic
369C2×C4×D3—21no—
370C2×C4×D3—21no—
371C2×C4×D3—21no—
372C2×C4×D3C22×D511yescharacteristic
373C2×Dic6—101no—
374C2×Dic6C22×D511yescharacteristic
375C3×Q16—201no—
376C2×C3×C8—51no—
377C2×C3×C8—51no—
378C2×C3×C8—201no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—51no—
381C3×C4⋊C4—101no—
382C3×C4⋊C4C22×D511yescharacteristic
383C3×C22⋊C4—21no—
384C3×C22⋊C4—101no—
385#217—101no—
386#217C22⋊D511yescharacteristic
387#216—201no—
388#215—102no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—101no—
392(C2×D3)⋊C4—101no—
393(C2×D3)⋊C4C22⋊D511yescharacteristic
394C4⋊Dic3—21no—
395C4⋊Dic3—51no—
396C4⋊Dic3—51no—
397C4⋊Dic3—101no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—101no—
401Dic3⋊C4—101no—
402Dic3⋊C4C22⋊D511yescharacteristic
403C4×Dic3—101no—
404C4×Dic3—101no—
405C4×Dic3—101no—
406C4×Dic3C22×D511yescharacteristic
407C2×C3⋊C8—51no—
408C2×C3⋊C8—51no—
409D3×C8—201no—
410C23×C5—31no—
411C23×C5—61no—
412C23×C5D3×D411yescharacteristic
413C5×Q8—21no—
414C5×Q8—21no—
415C5×Q8—61no—
416C5×Q8—61no—
417C5×D4—32no—
418C5×D4—62no—
419C5×D4—61no—
420C5×D4—122no—
421C5×D4—122no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—31no—
427C2×C4×C5—31no—
428C2×C4×C5—31no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—122no—
433C2×C4×C5—122no—
434C2×C4×C5—122no—
435C2×C4×C5D3×D411yescharacteristic
436C2×C4×C5C23×D311yescharacteristic
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—61no—
440C2×Dic5—61no—
441Dic10—21no—
442Dic10—21no—
443Dic10—122no—
444#168—21no—
445#168—21no—
446#168—61no—
447#168—61no—
448C2×#41—31no—
449C2×#41—31no—
450C2×Q16—51no—
451C2×Q16—151no—
452C2×SD16—151no—
453C22×C8—51no—
454C22×C8—151no—
455C4⋊Q8—31no—
456C4⋊Q8—151no—
457#126—301no—
458#126—301no—
459#124—301no—
460#123—61no—
461#123—61no—
462C22⋊Q8—31no—
463C22⋊Q8—51no—
464C22⋊Q8—151no—
465C22⋊Q8D3×D511yescharacteristic
466#121—61no—
467C4×Q8—151no—
468C4×Q8—301no—
469C4×D4—31no—
470C4×D4—31no—
471#117—151no—
472#117—151no—
473C2×C4⋊C4—61no—
474#107—51no—
475#107—151no—
476#106—151no—
477C4⋊C8—151no—
478#103—51no—
479#103—51no—
480#103—151no—
481#103—151no—
482#103—151no—
483#103—151no—
484#103—151no—
485#102—151no—
486#102—151no—
487#102—151no—
488C22⋊C8—151no—
489C22⋊C8—151no—
490C4×C8—151no—
491C2×C3×C5—41no—
492C2×C3×C5#54611yescharacteristic
493C2×C3×C5C2×#13511yescharacteristic
494C2×C3×C5#57811yescharacteristic
495C5×D3—41no—
496C5×D3—42no—
497C23×C3C2×C22⋊D511yescharacteristic
498C22×D3—21no—
499C22×D3C2×C22⋊D511yescharacteristic
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—101no—
503C3×Q8—101no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—101no—
509C2×C3×C4—101no—
510C2×C3×C4C2×C22⋊D511yescharacteristic
511C2×C3×C4C23×D511yescharacteristic
512#67—22no—
513#67—42no—
514C2×Dic3—21no—
515C2×Dic3—101no—
516C2×Dic3—101no—
517C2×Dic3C2×C22⋊D511yescharacteristic
518C2×Dic3C2×C22⋊D511yescharacteristic
519C2×Dic3C2×C22⋊D511yescharacteristic
520D12—21no—
521D12—42no—
522D12#71112yes—
523C4×D3—21no—
524C4×D3—21no—
525C4×D3—42no—
526C4×D3—42no—
527C4×D3—42no—
528Dic6—21no—
529Dic6—21no—
530Dic6—202no—
531C3×C8—101no—
532C3×C8—101no—
533C3⋊C8—101no—
534C3⋊C8—101no—
535C22×C5—21no—
536C22×C5—21no—
537C22×C5—21no—
538C22×C5—61no—
539C22×C5—61no—
540C22×C5—61no—
541C22×C5—62no—
542C22×C5—121no—
543C22×C5—121no—
544C22×C5C2×D3×D411yescharacteristic
545C4×C5—21no—
546C4×C5—32no—
547C4×C5—41no—
548C4×C5—41no—
549C4×C5—61no—
550C4×C5—61no—
551C4×C5—121no—
552C4×C5#100411yescharacteristic
553C4×C5D3×#4111yescharacteristic
554Dic5—41no—
555Dic5—41no—
556Dic5—121no—
557Dic5—121no—
558#41—62no—
559#41—62no—
560#41—121no—
561#41—121no—
562C2×Q8—31no—
563C2×Q8—51no—
564C2×Q8—301no—
565C2×Q8C2×D3×D511yescharacteristic
566C2×D4—31no—
567C2×D4—31no—
568C2×D4—61no—
569C2×D4—61no—
570C22×C4—31no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4C2×D3×D511yescharacteristic
575Q16—201no—
576Q16—601no—
577SD16—302no—
578C2×C8—51no—
579C2×C8—51no—
580C2×C8—151no—
581C2×C8—151no—
582C2×C8—201no—
583C2×C8—601no—
584C4⋊C4—21no—
585C4⋊C4—31no—
586C4⋊C4—51no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—101no—
591C4⋊C4—151no—
592C4⋊C4—151no—
593C4⋊C4—301no—
594C4⋊C4—301no—
595C4⋊C4—301no—
596C4⋊C4C2×D3×D511yescharacteristic
597C22⋊C4—21no—
598C22⋊C4—31no—
599C22⋊C4—31no—
600C22⋊C4—61no—
601C22⋊C4—61no—
602C22⋊C4—101no—
603C22⋊C4—301no—
604C22⋊C4—301no—
605C22⋊C4—301no—
606C42—31no—
607C42—301no—
608C42—301no—
609C42—301no—
610C3×C5#330211yescharacteristic, complemented, Hall
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3C22×C22⋊D511yescharacteristic
615C2×D3—21no—
616C2×D3—22no—
617C2×D3—21no—
618C2×D3—21no—
619C2×D3—41no—
620C2×D3—41no—
621C3×C4—21no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—201no—
625C3×C4—201no—
626C3×C4C2×#71111yescharacteristic
627C3×C4#414411yescharacteristic
628Dic3—21no—
629Dic3—21no—
630Dic3—41no—
631Dic3—201no—
632Dic3—201no—
633Dic3#409612yes—
634C2×C5—41no—
635C2×C5—121no—
636C2×C5—122no—
637C2×C5#561011yescharacteristic
638C2×C5#576611yescharacteristic
639C2×C5D3×#13511yescharacteristic
640C23—31no—
641C23—61no—
642C23D3×C22⋊D511yescharacteristic
643Q8—21no—
644Q8—21no—
645Q8—61no—
646Q8—61no—
647Q8—101no—
648Q8—101no—
649Q8—602no—
650D4—32no—
651D4—62no—
652D4—61no—
653D4—122no—
654D4—122no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—101no—
666C2×C4—101no—
667C2×C4—122no—
668C2×C4—122no—
669C2×C4—122no—
670C2×C4—301no—
671C2×C4—301no—
672C2×C4D3×C22⋊D511yescharacteristic
673C2×C4C22×D3×D511yescharacteristic
674C8—101no—
675C8—101no—
676C8—301no—
677C8—301no—
678C2×C3—41no—
679C2×C3#6614011yescharacteristic
680C2×C3C2×#409611yescharacteristic
681C2×C3#6617211yescharacteristic
682D3—41no—
683D3—42no—
684C5#8077611yescharacteristic, complemented, Sylow
685C22—21no—
686C22—21no—
687C22—21no—
688C22—61no—
689C22—61no—
690C22—61no—
691C22—62no—
692C22—121no—
693C22—121no—
694C22C2×D3×C22⋊D511yescharacteristic
695C4—21no—
696C4—32no—
697C4—41no—
698C4—41no—
699C4—61no—
700C4—61no—
701C4—121no—
702C4—201no—
703C4—201no—
704C4—601no—
705C4—601no—
706C4D3×#71111yescharacteristic
707C4#9202511yescharacteristic
708C3#1061524111yescharacteristic, complemented, Sylow
709C2—41no—
710C2—121no—
711C2—122no—
712C2#1175494211yescharacteristic
713C2#1175510511yescharacteristic
714C2D3×#409611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC5×#5631C2
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11754233C2semidirect
3. #11751146C2semidirect
4. C3×#65340C2semidirect
5. #11749305C2semidirect
6. #11749251C2semidirect
7. #11749211C2semidirect
8. #11749187C2semidirect
9. #11748538C2semidirect
10. #67×#168C2semidirect
11. #11748388C2semidirect
12. #11747416C2semidirect
13. #11747353C2semidirect
14. #11747264C2semidirect
15. #11747208C2semidirect
70. #65340D3semidirect
610. C3×C5#3302semidirect
684. C5#80776semidirect
708. C3#10615241semidirect

Maximal subgroups

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

subgroupindex
C5×#56312
#117542332
#117511462
C3×#653402
#117493052
#117492512
#117492112
#117491872
#117485382
#67×#1682
#117483882
#117474162
#117473532
#117472642
#117472082
#106152413
#807765