Finite Group Databasebeta

← #14423170

Subgroups — #14423170

Order 1920.

692 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
1#11753495C211yesmaximal, characteristic
2#11752366C211yesmaximal, characteristic, complemented
3C3×#65709C211yesmaximal, characteristic, complemented
4#11751928C211yesmaximal, characteristic, complemented
5#11751922C211yesmaximal, characteristic, complemented
6#11751912C211yesmaximal, characteristic, complemented
7#11751894C211yesmaximal, characteristic, complemented
8#11751892C211yesmaximal, characteristic, complemented
9#11751890C211yesmaximal, characteristic, complemented
10#11751889C211yesmaximal, characteristic, complemented
11#11751888C211yesmaximal, characteristic, complemented
12#11751887C211yesmaximal, characteristic, complemented
13#11751828C211yesmaximal, characteristic, complemented
14#11751809C211yesmaximal, characteristic, complemented
15#11751800C211yesmaximal, characteristic, complemented
16#10617356—31nomaximal, Hall
17C2×#6740C2211yescharacteristic
18C2×#6740C2211yescharacteristic
19C2×#6740C2211yescharacteristic
20C2×#6739C2211yescharacteristic
21C2×#6738C2211yescharacteristic
22C2×D3×#170C2211yescharacteristic
23#91783C411yescharacteristic
24C5×#898C411yescharacteristic
25C3×#4033C2211yescharacteristic
26#91420C411yescharacteristic
27#91418C2211yescharacteristic
28#91411C411yescharacteristic
29#91405C2211yescharacteristic
30#91405C2211yescharacteristic
31#91402C2211yescharacteristic
32C4×#1200C2211yescharacteristic
33#91398C2211yescharacteristic
34#91380C411yescharacteristic
35#91355C411yescharacteristic
36#91335C411yescharacteristic
37#91326C411yescharacteristic
38#91233C2211yescharacteristic
39#91233C2211yescharacteristic
40#91231C2211yescharacteristic
41#91231C2211yescharacteristic
42C4⋊(C3⋊#170)C2211yescharacteristic
43C4×C3⋊#170C2211yescharacteristic
44C3×#4002C2211yescharacteristic
45C3×#4002C2211yescharacteristic
46C3×C4⋊#170C2211yescharacteristic
47C3×C4⋊#170C2211yescharacteristic
48C3×C4⋊#170C2211yescharacteristic
49C3×C4×#170C2211yescharacteristic
50#91177C2211yescharacteristic
51#91177C2211yescharacteristic
52Dic3⋊#170C2211yescharacteristic
53Dic3⋊#170C2211yescharacteristic
54#91171C2211yescharacteristic
55#91171C2211yescharacteristic
56#91171C2211yescharacteristic
57#91171C2211yescharacteristic
58(C2×D3)⋊#170C2211yescharacteristic
59(C2×D3)⋊#170C2211yescharacteristic
60#79949—51nomaximal, Hall
61#66040—31no—
62#65709D311yescharacteristic, complemented
63#65708—31no—
64#65707—31no—
65#65706—31no—
66#65705—31no—
67#65704—31no—
68#65697—31no—
69#65696—31no—
70#65695—31no—
71#65694—31no—
72#65693—31no—
73#65693—31no—
74#65684—31no—
75#65681—31no—
76C2×D60C2×C411yescharacteristic
77C2×C4×D15C2×C411yescharacteristic
78C2×C3×Dic10C2×C411yescharacteristic
79C2×#1203C2×C411yescharacteristic
80C2×#1203C2×C411yescharacteristic
81C2×#1200C2×C411yescharacteristic
82C2×#1200C2311yescharacteristic
83C2×#1200C2311yescharacteristic
84C2×D3×Dic5C2311yescharacteristic
85C2×C3⋊#170C2311yescharacteristic
86C2×C3⋊#170C2311yescharacteristic
87C2×C3⋊#170C2311yescharacteristic
88C2×C3⋊#170C2311yescharacteristic
89C2×C3×#170C2311yescharacteristic
90C2×C3×#170C2311yescharacteristic
91C2×C3×#170C2311yescharacteristic
92C2×C3×#170C2311yescharacteristic
93#6740—41no—
94#6740—41no—
95#6740—41no—
96#6739—41no—
97#6738—41no—
98D3×#170—41no—
99C3×C5×C4⋊C4C2×C411yescharacteristic
100#6714C2×C411yescharacteristic
101#6714C2×C411yescharacteristic
102#6714C2×C411yescharacteristic
103#6712C2×C411yescharacteristic
104C5×(C2×D3)⋊C4C2×C411yescharacteristic
105C5×(C2×D3)⋊C4C2×C411yescharacteristic
106C5×(C2×D3)⋊C4C2×C411yescharacteristic
107C5×C4⋊Dic3C2×C411yescharacteristic
108C5×Dic3⋊C4C2×C411yescharacteristic
109C4×C5×Dic3C2×C411yescharacteristic
110C3×#683C2×C411yescharacteristic
111C3×#683C2×C411yescharacteristic
112C3×C4×Dic5C2311yescharacteristic
113C3×C4×Dic5C2311yescharacteristic
114C3×C4×Dic5C2311yescharacteristic
115Dic3⋊Dic5C2×C411yescharacteristic
116#6669C2×C411yescharacteristic
117#6668C2×C411yescharacteristic
118#6668C2×C411yescharacteristic
119#6667C2×C411yescharacteristic
120#6667C2×C411yescharacteristic
121#6667C2×C411yescharacteristic
122(C2×D3)⋊Dic5C2×C411yescharacteristic
123Dic3×Dic5C2×C411yescharacteristic
124Dic3×Dic5C2311yescharacteristic
125#5580—51no—
126C3×#446—51no—
127#5024—51no—
128#4839—51no—
129#4839—51no—
130#4838—51no—
131#4837—51no—
132#4836—51no—
133#4836—51no—
134#4709—51no—
135#4706—51no—
136#4706—51no—
137#4705—51no—
138#4690—51no—
139#4688—51no—
140C2×#704—31no—
141C22×#170—31no—
142C2×#700—31no—
143C2×#700—31no—
144C2×#700—31no—
145C2×D5⋊C8—31no—
146C5×#126—31no—
147#4042—31no—
148#4040—31no—
149#4039—31no—
150#4038—31no—
151#4035—31no—
152#4033C2×D311yescharacteristic
153#4031—31no—
154#4030—31no—
155#4029—31no—
156#4027—31no—
157#4027—31no—
158#4023—31no—
159#4022—31no—
160C42×D5—31no—
161C22⋊#170—31no—
162C22⋊#170—31no—
163#4004—31no—
164#4004—31no—
165#4004—31no—
166#4004—31no—
167#4003—31no—
168#4003—31no—
169#4003—31no—
170#4003—31no—
171#4002—31no—
172#4002—31no—
173#4002C2×D311yescharacteristic
174#4002C2×D311yescharacteristic
175C4⋊#170—31no—
176C4⋊#170—31no—
177C4⋊#170—31no—
178C4⋊#170C2×D311yescharacteristic
179C4⋊#170C2×D311yescharacteristic
180C4⋊#170C2×D311yescharacteristic
181C4×#170—31no—
182C4×#170C2×D311yescharacteristic
183#2995—151noSylow
184C22×D15C22×C411yescharacteristic
185C22×D15C22×C411yescharacteristic
186C22×C5×D3C22×C411yescharacteristic
187C2×C3×C4×C5C22×C411yescharacteristic
188C2×C3×C4×C5C22×C411yescharacteristic
189C2×C3×C4×C5C22×C411yescharacteristic
190C2×Dic15C22×C411yescharacteristic
191C2×Dic15C22×C411yescharacteristic
192D60—41no—
193C4×D15—41no—
194C2×C5×Dic3C22×C411yescharacteristic
195C2×C5×Dic3C22×C411yescharacteristic
196C2×C5×Dic3C22×C411yescharacteristic
197C2×C3×Dic5C22×C411yescharacteristic
198C2×C3×Dic5C22×C411yescharacteristic
199C2×C3×Dic5C22×C411yescharacteristic
200C2×C3×Dic5C2411yescharacteristic
201C3×Dic10—41no—
202#1203—41no—
203#1203—41no—
204#1200—21no—
205#1200—21no—
206#1200—21no—
207#1200—21no—
208#1200—41no—
209D3×Dic5—21no—
210D3×Dic5—21no—
211C3⋊#170—21no—
212C3⋊#170—21no—
213C3⋊#170—21no—
214C3⋊#170—21no—
215C3×#170—21no—
216C3×#170—21no—
217C3×#170—21no—
218C3×#170—21no—
219C3×C4×Q8—51no—
220#947—51no—
221#946—51no—
222C2×ΓL(1,𝔽25)—51no—
223C2×ΓL(1,𝔽25)—51no—
224C2×ΓL(1,𝔽25)—51no—
225C2×ΓL(1,𝔽25)—51no—
226C2×D3×C8—51no—
227C2×D3×C8—51no—
228#898—51no—
229#898AGL(1,𝔽5)11yescharacteristic
230#895—51no—
231#894—51no—
232#894—51no—
233#890—51no—
234C4×D12—51no—
235C4×D12—51no—
236C4×D12—51no—
237#872—51no—
238#872—51no—
239C42×D3—51no—
240C3×C4⋊C8—51no—
241C3×C4⋊C8—51no—
242C3×C4⋊C8—51no—
243C3×#97—51no—
244C3×#97—51no—
245C3×C4×C8—51no—
246(C2×D3)⋊C8—51no—
247(C2×D3)⋊C8—51no—
248(C2×D3)⋊C8—51no—
249(C2×D3)⋊C8—51no—
250(C2×D3)⋊C8—51no—
251(C2×D3)⋊C8—51no—
252Dic3⋊C8—51no—
253Dic3⋊C8—51no—
254Dic3⋊C8—51no—
255Dic3⋊C8—51no—
256C4⋊(C3⋊C8)—51no—
257C4⋊(C3⋊C8)—51no—
258C4⋊(C3⋊C8)—51no—
259#803—51no—
260#803—51no—
261C4×C3⋊C8—51no—
262C2×C22⋊D5—31no—
263C2×C22⋊D5—31no—
264C22×Dic5—31no—
265C2×D20—31no—
266C2×C4×D5—31no—
267C2×C4×D5—31no—
268C2×C4×D5—31no—
269C2×C4×D5—31no—
270C2×Dic10C4×D311yescharacteristic
271#704—121no—
272C2×#170—31no—
273C2×#170—31no—
274C2×#170—31no—
275C2×#170—31no—
276C2×#170—121no—
277C2×#170C22×D311yescharacteristic
278C2×#170C22×D311yescharacteristic
279C2×#170C22×D311yescharacteristic
280C2×#170C22×D311yescharacteristic
281#700—121no—
282#700—121no—
283#700—121no—
284D5⋊C8—121no—
285C5×C4⋊C4—31no—
286C5×C4⋊C4—31no—
287C5×C4⋊C4C4×D311yescharacteristic
288C5×C22⋊C4—31no—
289C5×C22⋊C4—31no—
290C5×C22⋊C4—31no—
291C42×C5—31no—
292C22⋊Dic5—31no—
293#685—31no—
294#685—31no—
295#685—31no—
296#685—31no—
297#685—31no—
298#685—31no—
299C4⋊Dic5—31no—
300#683—31no—
301#683—31no—
302#683—31no—
303#683—31no—
304#683C4×D311yescharacteristic
305#683C4×D311yescharacteristic
306C4×Dic5—31no—
307C4×Dic5—31no—
308C4×Dic5C22×D311yescharacteristic
309C4×Dic5C22×D311yescharacteristic
310C4×Dic5C22×D311yescharacteristic
311#529—151no—
312#446—51no—
313#446—151no—
314#436—151no—
315#436—151no—
316#435—151no—
317#435—151no—
318#435—151no—
319#435—151no—
320#433—151no—
321#433—151no—
322#432—151no—
323#424—151no—
324#424—151no—
325#423—151no—
326C22×C3×C5C23×C411yescharacteristic
327C2×D15—21no—
328C2×D15—21no—
329C2×D15—21no—
330C2×D15—21no—
331C2×D15—21no—
332C2×D15—21no—
333C2×C5×D3—21no—
334C2×C5×D3—21no—
335C2×C5×D3—21no—
336C3×C4×C5—21no—
337C3×C4×C5—21no—
338C3×C4×C5—21no—
339Dic15—21no—
340Dic15—21no—
341C3×Dic5—21no—
342C3×Dic5—21no—
343C3×Dic5—21no—
344C3×Dic5H(5,𝔽2)11yescharacteristic
345C3×Dic52−1+411yescharacteristic
346C5×Dic3—21no—
347C5×Dic3—21no—
348C5×Dic3—21no—
349C2×C3×Q8—51no—
350C2×D12—51no—
351C2×D12—51no—
352C2×D12—51no—
353C2×C4×D3—51no—
354C2×C4×D3—51no—
355C2×C4×D3—51no—
356C2×C4×D3—51no—
357C2×C4×D3—51no—
358C2×C3×C8—51no—
359C2×C3×C8—51no—
360C2×C3×C8—51no—
361C2×C3×C8—51no—
362C3×C4⋊C4—51no—
363C3×C4⋊C4—51no—
364C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
365C3×C42—51no—
366C3×C42—51no—
367C3×C42—51no—
368(C2×D3)⋊C4—51no—
369(C2×D3)⋊C4—51no—
370(C2×D3)⋊C4—51no—
371(C2×D3)⋊C4—51no—
372(C2×D3)⋊C4—51no—
373(C2×D3)⋊C4—51no—
374(C2×D3)⋊C4—51no—
375(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
376(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
377(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
378C4⋊Dic3—51no—
379C4⋊Dic3—51no—
380C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
381Dic3⋊C4—51no—
382Dic3⋊C4—51no—
383Dic3⋊C4—51no—
384Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic
385C4×Dic3—51no—
386C4×Dic3—51no—
387C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
388C2×C3⋊C8—51no—
389C2×C3⋊C8—51no—
390C2×C3⋊C8—51no—
391C2×C3⋊C8—51no—
392ΓL(1,𝔽25)—201no—
393ΓL(1,𝔽25)—201no—
394ΓL(1,𝔽25)—201no—
395ΓL(1,𝔽25)—201no—
396D3×C8—201no—
397D3×C8—201no—
398C23×C5—31no—
399C22×D5—31no—
400C22×D5—31no—
401C2×C4×C5—31no—
402C2×C4×C5—31no—
403C2×C4×C5—31no—
404C2×C4×C5C2×C4×D311yescharacteristic
405C2×C4×C5C2×C4×D311yescharacteristic
406C2×C4×C5C2×C4×D311yescharacteristic
407C22⋊D5—121no—
408C22⋊D5—121no—
409C2×Dic5—31no—
410C2×Dic5—31no—
411C2×Dic5—61no—
412C2×Dic5—61no—
413C2×Dic5C2×C4×D311yescharacteristic
414C2×Dic5C2×C4×D311yescharacteristic
415C2×Dic5C2×C4×D311yescharacteristic
416C2×Dic5C23×D311yescharacteristic
417D20—121no—
418C4×D5—61no—
419C4×D5—61no—
420C4×D5—61no—
421C4×D5—61no—
422C4×D5—121no—
423C4×D5—121no—
424Dic10—41no—
425#170—21no—
426#170—21no—
427#170—21no—
428#170—21no—
429#170—61no—
430#170—61no—
431#170—61no—
432#170—61no—
433C2×M16—151no—
434C2×M16—151no—
435C2×M16—151no—
436C2×M16—151no—
437C22×C8—151no—
438C22×C8—151no—
439#126—31no—
440#126—151no—
441#125—151no—
442#124—151no—
443#123—151no—
444#123—151no—
445C22⋊Q8—151no—
446#121—151no—
447C4×Q8—51no—
448C4×D4—151no—
449C4×D4—151no—
450C4×D4—151no—
451#117—151no—
452#117—151no—
453C2×C42—151no—
454C4⋊C8—51no—
455C4⋊C8—51no—
456C4⋊C8—51no—
457C4⋊C8—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460C4⋊C8—151no—
461C4⋊C8—151no—
462C4⋊C8—151no—
463C4⋊C8—151no—
464C22⋊C8—151no—
465C22⋊C8—151no—
466C22⋊C8—151no—
467C22⋊C8—151no—
468C22⋊C8—151no—
469C22⋊C8—151no—
470#97—51no—
471#97—51no—
472#97—151no—
473#97—151no—
474C4×C8—51no—
475C4×C8—151no—
476C2×C3×C5#52011yescharacteristic
477C2×C3×C5#56811yescharacteristic
478C2×C3×C5#56811yescharacteristic
479D15—41no—
480D15—41no—
481C5×D3—41no—
482C22×D3—51no—
483C22×D3—51no—
484C22×D3C22×AGL(1,𝔽5)11yescharacteristic
485C3×Q8—201no—
486C2×C3×C4—51no—
487C2×C3×C4—51no—
488C2×C3×C4—51no—
489C2×C3×C4—51no—
490C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
491C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
492C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
493C2×Dic3—51no—
494C2×Dic3—51no—
495C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
496C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
497C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
498D12—201no—
499D12—201no—
500D12—201no—
501C4×D3—101no—
502C4×D3—101no—
503C4×D3—101no—
504C4×D3—101no—
505C4×D3—101no—
506C4×D3—101no—
507C4×D3—201no—
508C4×D3—201no—
509C3×C8—101no—
510C3×C8—101no—
511C3×C8—101no—
512C3×C8—101no—
513C3⋊C8—101no—
514C3⋊C8—101no—
515C3⋊C8—101no—
516C3⋊C8—101no—
517C22×C5—61no—
518C22×C5—61no—
519C22×C5—61no—
520C22×C5C22×C4×D311yescharacteristic
521C2×D5—61no—
522C2×D5—61no—
523C2×D5—61no—
524C2×D5—61no—
525C2×D5—61no—
526C2×D5—61no—
527C4×C5—21no—
528C4×C5—21no—
529C4×C5—21no—
530C4×C5—61no—
531C4×C5—61no—
532C4×C5—61no—
533Dic5—21no—
534Dic5—21no—
535Dic5—21no—
536Dic5—61no—
537Dic5—61no—
538Dic5#100711yescharacteristic
539Dic5#100911yescharacteristic
540C2×Q8—51no—
541C2×D4—151no—
542C2×D4—151no—
543C2×D4—151no—
544C22×C4—151no—
545C22×C4—151no—
546C22×C4—151no—
547C22×C4—151no—
548C22×C4—151no—
549M16—601no—
550M16—601no—
551M16—601no—
552M16—601no—
553C2×C8—51no—
554C2×C8—51no—
555C2×C8—51no—
556C2×C8—51no—
557C2×C8—151no—
558C2×C8—151no—
559C2×C8—151no—
560C2×C8—151no—
561C2×C8—601no—
562C2×C8—601no—
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—51no—
566C4⋊C4—51no—
567C4⋊C4—151no—
568C4⋊C4—151no—
569C4⋊C4—151no—
570C4⋊C4—151no—
571C4⋊C4—151no—
572C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4—151no—
577C22⋊C4—151no—
578C22⋊C4—151no—
579C22⋊C4—151no—
580C22⋊C4—151no—
581C22⋊C4—151no—
582C22⋊C4—151no—
583C42—31no—
584C42—51no—
585C42—51no—
586C42—51no—
587C42—151no—
588C42—151no—
589C3×C5#299511yescharacteristic, complemented, Hall
590C22×C3C23×AGL(1,𝔽5)11yescharacteristic
591C2×D3—21no—
592C2×D3—21no—
593C2×D3—21no—
594C2×D3—101no—
595C2×D3—101no—
596C2×D3—101no—
597C2×D3—101no—
598C2×D3—101no—
599C2×D3—101no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—51no—
604C3×C4—51no—
605C3×C4—101no—
606C3×C4—101no—
607C3×C4—101no—
608Dic3—21no—
609Dic3—21no—
610Dic3—21no—
611Dic3—101no—
612Dic3—101no—
613C2×C5—121no—
614C2×C5#557411yescharacteristic
615C2×C5#574511yescharacteristic
616C2×C5#575011yescharacteristic
617D5—121no—
618D5—121no—
619C23—31no—
620C23—151no—
621C23—151no—
622Q8—201no—
623D4—601no—
624D4—601no—
625D4—601no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—51no—
630C2×C4—51no—
631C2×C4—51no—
632C2×C4—51no—
633C2×C4—151no—
634C2×C4—151no—
635C2×C4—301no—
636C2×C4—301no—
637C2×C4—301no—
638C2×C4—301no—
639C2×C4—301no—
640C2×C4—301no—
641C2×C4—601no—
642C2×C4—601no—
643C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
644C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
645C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
646C8—101no—
647C8—101no—
648C8—101no—
649C8—101no—
650C8—301no—
651C8—301no—
652C8—301no—
653C8—301no—
654C2×C3#6626411yescharacteristic
655C2×C3#6626411yescharacteristic
656C2×C3#6626611yescharacteristic
657D3—41no—
658D3—201no—
659D3—201no—
660C5#7994911yescharacteristic, complemented, Sylow
661C22—61no—
662C22—61no—
663C22—61no—
664C22—301no—
665C22—301no—
666C22—301no—
667C22—301no—
668C22—301no—
669C22—301no—
670C22C22×D3×AGL(1,𝔽5)11yescharacteristic
671C4—21no—
672C4—21no—
673C4—21no—
674C4—51no—
675C4—51no—
676C4—61no—
677C4—61no—
678C4—61no—
679C4—101no—
680C4—101no—
681C4—101no—
682C4—301no—
683C4—301no—
684C3#1061735611yescharacteristic, complemented, Sylow
685C2—121no—
686C2—601no—
687C2—601no—
688C2#1175682111yescharacteristic
689C2#1175684211yescharacteristic
690C2#1175685411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radical#91420C4
cosocleC2×C3×Dic5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2995
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11752366C2semidirect
3. C3×#65709C2semidirect
4. #11751928C2semidirect
5. #11751922C2semidirect
6. #11751912C2semidirect
7. #11751894C2semidirect
8. #11751892C2semidirect
9. #11751890C2semidirect
10. #11751889C2semidirect
11. #11751888C2semidirect
12. #11751887C2semidirect
13. #11751828C2semidirect
14. #11751809C2semidirect
15. #11751800C2semidirect
62. #65709D3semidirect
589. C3×C5#2995semidirect
660. C5#79949semidirect
684. C3#10617356semidirect

Maximal subgroups

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

subgroupindex
#117534952
#117523662
C3×#657092
#117519282
#117519222
#117519122
#117518942
#117518922
#117518902
#117518892
#117518882
#117518872
#117518282
#117518092
#117518002
#106173563
#799495