Finite Group Databasebeta

← #14419669

Subgroups — #14419669

Order 1920.

744 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#11752693C211yesmaximal, characteristic
2#11750809C211yesmaximal, characteristic, complemented
3C5×D3×#97C211yesmaximal, characteristic, complemented
4C3×#64997C211yesmaximal, characteristic, complemented
5#11747824C211yesmaximal, characteristic, complemented
6#11747819C211yesmaximal, characteristic, complemented
7#11747725C211yesmaximal, characteristic, complemented
8#11747719C211yesmaximal, characteristic, complemented
9#11747711C211yesmaximal, characteristic, complemented
10#11747705C211yesmaximal, characteristic, complemented
11C8×#1203C211yesmaximal, characteristic, complemented
12C8×#1201C211yesmaximal, characteristic, complemented
13#11746938C211yesmaximal, characteristic, complemented
14#11746876C211yesmaximal, characteristic, complemented
15#11746874C211yesmaximal, characteristic, complemented
16#10610212—31nomaximal, Hall
17C2×#6705C2211yescharacteristic
18C2×C8×D15C2211yescharacteristic
19#91761C2211yescharacteristic
20C2×C5×D3×C8C2211yescharacteristic
21C2×C5×D3×C8C2211yescharacteristic
22C42×C5×D3C2211yescharacteristic
23C2×C3×#676C2211yescharacteristic
24C2×C3×C8×D5C2211yescharacteristic
25C3×#4018C2211yescharacteristic
26C4×#1204C2211yescharacteristic
27#91454C411yescharacteristic
28#91452C411yescharacteristic
29C4×#1203C2211yescharacteristic
30C4×#1202C2211yescharacteristic
31C4×#1201C2211yescharacteristic
32#91380C411yescharacteristic
33#91379C411yescharacteristic
34#91363C411yescharacteristic
35#91353C411yescharacteristic
36#91352C411yescharacteristic
37#91351C411yescharacteristic
38C3×C5×#97C2211yescharacteristic
39#91099C2211yescharacteristic
40C8×Dic15C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42C5×#815C2211yescharacteristic
43C5×#815C2211yescharacteristic
44C5×#803C2211yescharacteristic
45C3×#3947C2211yescharacteristic
46C3×C8×Dic5C2211yescharacteristic
47C3×C4×#168C2211yescharacteristic
48Dic3⋊#168C2211yescharacteristic
49Dic3⋊#168C2211yescharacteristic
50#90983C2211yescharacteristic
51#90983C2211yescharacteristic
52#90982C2211yescharacteristic
53#90982C2211yescharacteristic
54#90957C2211yescharacteristic
55#90957C2211yescharacteristic
56(C2×D3)⋊#168C2211yescharacteristic
57(C2×D3)⋊#168C2211yescharacteristic
58#90955C2211yescharacteristic
59#90955C2211yescharacteristic
60#78558—51nomaximal, Hall
61#65813—31no—
62C2×C5×#97—31no—
63#65400—31no—
64#65400—31no—
65C8×C22⋊D5—31no—
66C8×C22⋊D5—31no—
67#65214—31no—
68#64998—31no—
69#64998—31no—
70#64997—31no—
71#64997D311yescharacteristic, complemented
72#64995—31no—
73#64995—31no—
74#64990—31no—
75#64990—31no—
76C2×C4×D15C2311yescharacteristic
77C2×C4×C5×D3C2×C411yescharacteristic
78C2×C4×C5×D3C2×C411yescharacteristic
79C2×C4×C5×D3C2311yescharacteristic
80C2×C3×C4×D5C2311yescharacteristic
81C2×#1204C2×C411yescharacteristic
82C2×#1203C2×C411yescharacteristic
83C2×#1202C2×C411yescharacteristic
84C2×#1201C2×C411yescharacteristic
85C2×C3×C5×C8C2311yescharacteristic
86C2×C3×C5×C8C2311yescharacteristic
87C3×C42×C5C2311yescharacteristic
88#6714C2×C411yescharacteristic
89#6714C2×C411yescharacteristic
90#6712C2×C411yescharacteristic
91#6712C2×C411yescharacteristic
92C4×Dic15C2311yescharacteristic
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95#6705—22no—
96C8×D15—22no—
97C4×C5×Dic3C2×C411yescharacteristic
98C4×C5×Dic3C2×C411yescharacteristic
99C4×C5×Dic3C2311yescharacteristic
100C2×C5×C3⋊C8C2311yescharacteristic
101C2×C5×C3⋊C8C2311yescharacteristic
102C5×D3×C8—22no—
103C5×D3×C8—22no—
104C3×#685C2×C411yescharacteristic
105C3×#685C2×C411yescharacteristic
106C3×#683C2×C411yescharacteristic
107C3×#683C2×C411yescharacteristic
108C3×C4×Dic5C2311yescharacteristic
109C2×C3×#168C2311yescharacteristic
110C2×C3×#168C2311yescharacteristic
111C3×#676—22no—
112C3×C8×D5—22no—
113Dic3⋊Dic5C2×C411yescharacteristic
114Dic3⋊Dic5C2×C411yescharacteristic
115#6669C2×C411yescharacteristic
116#6669C2×C411yescharacteristic
117#6668C2×C411yescharacteristic
118#6668C2×C411yescharacteristic
119#6667C2×C411yescharacteristic
120#6667C2×C411yescharacteristic
121(C2×D3)⋊Dic5C2×C411yescharacteristic
122(C2×D3)⋊Dic5C2×C411yescharacteristic
123#6665C2×C411yescharacteristic
124#6665C2×C411yescharacteristic
125#5528—51no—
126C3×#405—51no—
127#5127—51no—
128#5127—51no—
129#5111—51no—
130C8×#67—51no—
131#5000—51no—
132#4708—51no—
133#4706—51no—
134D3×#97D511yescharacteristic, complemented
135#4701—51no—
136#4690—51no—
137C8×D12—51no—
138#4685—51no—
139#4679—51no—
140C22×C5×C8—31no—
141C22×C5×C8—31no—
142C2×C42×C5—31no—
143#4076—31no—
144#4075—31no—
145#4075—31no—
146C4×C22⋊D5—31no—
147C4×C22⋊D5—31no—
148#4070—31no—
149C2×#676—31no—
150C2×#676C2×D311yescharacteristic
151C2×C8×D5—31no—
152C2×C8×D5C2×D311yescharacteristic
153#4022—31no—
154#4022—31no—
155#4021—31no—
156C4×D20—31no—
157#4018—31no—
158#4018C2×D311yescharacteristic
159#4016—31no—
160C4×Dic10—31no—
161C5×#97—31no—
162C5×#97—31no—
163C5×#97—31no—
164C5×#97C2×D311yescharacteristic
165C22⋊#168—31no—
166C22⋊#168—31no—
167#3952—31no—
168#3952—31no—
169#3952—31no—
170#3952—31no—
171#3947—31no—
172#3947C2×D311yescharacteristic
173#3946—31no—
174#3946—31no—
175#3946—31no—
176#3946—31no—
177C8×Dic5—31no—
178C8×Dic5C2×D311yescharacteristic
179C4⋊#168—31no—
180C4⋊#168—31no—
181C4×#168—31no—
182C4×#168C2×D311yescharacteristic
183#2968—151noSylow
184C22×D15C22×C411yescharacteristic
185C22×C5×D3C22×C411yescharacteristic
186C22×C3×D5C22×C411yescharacteristic
187C2×C3×C4×C5C22×C411yescharacteristic
188C2×C3×C4×C5C22×C411yescharacteristic
189C2×C3×C4×C5C2411yescharacteristic
190C2×Dic15C22×C411yescharacteristic
191C2×Dic15C22×C411yescharacteristic
192C2×Dic15C22×C411yescharacteristic
193C4×D15—21no—
194C4×D15—21no—
195C2×C5×Dic3C22×C411yescharacteristic
196C2×C5×Dic3C22×C411yescharacteristic
197C2×C5×Dic3C22×C411yescharacteristic
198C4×C5×D3—22no—
199C4×C5×D3—21no—
200C4×C5×D3—21no—
201C4×C5×D3—41no—
202C2×C3×Dic5C22×C411yescharacteristic
203C2×C3×Dic5C22×C411yescharacteristic
204C2×C3×Dic5C22×C411yescharacteristic
205C3×C4×D5—21no—
206C3×C4×D5—21no—
207#1204—41no—
208#1203—22no—
209#1202—41no—
210#1201—22no—
211C3×C5×C8#4112yes—
212C3×C5×C8#4112yes—
213C3⋊#168—21no—
214C3⋊#168—21no—
215C3×#168—21no—
216C3×#168—21no—
217C5×C3⋊C8—21no—
218C5×C3⋊C8—21no—
219C2×C3×M16—51no—
220C22×C3×C8—51no—
221C3×#117—51no—
222C4×#67—51no—
223C4×#67—51no—
224C2×ΓL(1,𝔽25)—51no—
225C2×D3×C8—51no—
226C2×D3×C8C2×D511yescharacteristic
227C2×D3×C8C2×D511yescharacteristic
228#898—51no—
229#896—51no—
230#894—51no—
231#889—51no—
232#885—51no—
233#884—51no—
234#883—51no—
235#879—51no—
236C4×D12—51no—
237#872—51no—
238C42×D3C2×D511yescharacteristic
239C4×Dic6—51no—
240C3×#97—51no—
241C3×#97C2×D511yescharacteristic
242C3×C4×C8—51no—
243C3×C4×C8—51no—
244#830—51no—
245#830—51no—
246(C2×D3)⋊C8—51no—
247(C2×D3)⋊C8—51no—
248(C2×D3)⋊C8—51no—
249(C2×D3)⋊C8—51no—
250#815—51no—
251#815C2×D511yescharacteristic
252#815C2×D511yescharacteristic
253Dic3⋊C8—51no—
254Dic3⋊C8—51no—
255Dic3⋊C8—51no—
256Dic3⋊C8—51no—
257C8×Dic3—51no—
258C4⋊(C3⋊C8)—51no—
259C4⋊(C3⋊C8)—51no—
260#803C2×D511yescharacteristic
261C4×C3⋊C8—51no—
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5—31no—
265C2×C22⋊D5—31no—
266C2×C22⋊D5—31no—
267C2×D20—31no—
268C2×C4×D5—31no—
269C2×C4×D5C22×D311yescharacteristic
270C2×Dic10—31no—
271C2×C5×C8—31no—
272C2×C5×C8—31no—
273C2×C5×C8—62no—
274C2×C5×C8—62no—
275C2×C5×C8C22×D311yescharacteristic
276C2×C5×C8C22×D311yescharacteristic
277C42×C5—31no—
278C42×C5—31no—
279C42×C5—31no—
280C42×C5C22×D311yescharacteristic
281C22⋊Dic5—31no—
282C22⋊Dic5—31no—
283#685—31no—
284#685—31no—
285#685—31no—
286#685—31no—
287#685—31no—
288#685—31no—
289#685C4×D311yescharacteristic
290#685C4×D311yescharacteristic
291C4⋊Dic5—31no—
292C4⋊Dic5—31no—
293#683—31no—
294#683—31no—
295#683—31no—
296#683—31no—
297#683—31no—
298#683—31no—
299#683C4×D311yescharacteristic
300#683C4×D311yescharacteristic
301C4×Dic5—31no—
302C4×Dic5C22×D311yescharacteristic
303C2×#168—31no—
304C2×#168—31no—
305C2×#168C22×D311yescharacteristic
306C2×#168C22×D311yescharacteristic
307#676—22no—
308#676—62no—
309C8×D5—22no—
310C8×D5—62no—
311#529—151no—
312#446—151no—
313#446—151no—
314#435—151no—
315#435—151no—
316#435—151no—
317#435—151no—
318C8×D4—151no—
319C8×D4—151no—
320#433—151no—
321#433—151no—
322#431—151no—
323#405—51no—
324#405—151no—
325C2×#97—31no—
326C22×C3×C5C23×C411yescharacteristic
327C2×D15—21no—
328C2×D15—21no—
329C2×D15—21no—
330C2×C5×D3—21no—
331C2×C5×D3—21no—
332C2×C5×D3#13112yes—
333C2×C3×D5—21no—
334C2×C3×D5—21no—
335C2×C3×D5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—21no—
338C3×C4×C5C2×#4111yescharacteristic
339C3×C4×C5C2×#4111yescharacteristic
340Dic15—21no—
341Dic15—21no—
342Dic15—21no—
343C3×Dic5—21no—
344C3×Dic5—21no—
345C3×Dic5—21no—
346C5×Dic3—21no—
347C5×Dic3—21no—
348C5×Dic3—21no—
349C22×C3×C4—51no—
350C2×#67—51no—
351C2×#67—51no—
352C2×D12—51no—
353C2×C4×D3—51no—
354C2×C4×D3C4×D511yescharacteristic
355C2×C4×D3C4×D511yescharacteristic
356C2×C4×D3C22×D511yescharacteristic
357C2×Dic6—51no—
358C3×M16—102no—
359C2×C3×C8—51no—
360C2×C3×C8—51no—
361C2×C3×C8—102no—
362C2×C3×C8C22×D511yescharacteristic
363C2×C3×C8C22×D511yescharacteristic
364C3×C4⋊C4—51no—
365C3×C4⋊C4—51no—
366C3×C22⋊C4—51no—
367C3×C22⋊C4—51no—
368C3×C42—51no—
369C3×C42C22×D511yescharacteristic
370#217—51no—
371#217—51no—
372(C2×D3)⋊C4—51no—
373(C2×D3)⋊C4—51no—
374(C2×D3)⋊C4—51no—
375(C2×D3)⋊C4—51no—
376(C2×D3)⋊C4—51no—
377(C2×D3)⋊C4—51no—
378C4⋊Dic3—51no—
379C4⋊Dic3—51no—
380Dic3⋊C4—51no—
381Dic3⋊C4—51no—
382Dic3⋊C4—51no—
383Dic3⋊C4—51no—
384Dic3⋊C4—51no—
385Dic3⋊C4—51no—
386C4×Dic3—51no—
387C4×Dic3C4×D511yescharacteristic
388C4×Dic3C4×D511yescharacteristic
389C4×Dic3C22×D511yescharacteristic
390C2×C3⋊C8—51no—
391C2×C3⋊C8—51no—
392C2×C3⋊C8C22×D511yescharacteristic
393C2×C3⋊C8C22×D511yescharacteristic
394ΓL(1,𝔽25)—102no—
395D3×C8—22no—
396D3×C8—22no—
397D3×C8—102no—
398C23×C5—31no—
399C22×D5—31no—
400C22×D5C2×C4×D311yescharacteristic
401C2×C4×C5—31no—
402C2×C4×C5—31no—
403C2×C4×C5—31no—
404C2×C4×C5—62no—
405C2×C4×C5—61no—
406C2×C4×C5—61no—
407C2×C4×C5—121no—
408C2×C4×C5C2×C4×D311yescharacteristic
409C2×C4×C5C2×C4×D311yescharacteristic
410C2×C4×C5C23×D311yescharacteristic
411C22⋊D5—62no—
412C22⋊D5—62no—
413C2×Dic5—31no—
414C2×Dic5—31no—
415C2×Dic5—31no—
416C2×Dic5C2×C4×D311yescharacteristic
417C2×Dic5C2×C4×D311yescharacteristic
418C2×Dic5C2×C4×D311yescharacteristic
419D20—121no—
420C4×D5—21no—
421C4×D5—21no—
422C4×D5—61no—
423C4×D5—61no—
424Dic10—121no—
425C5×C8—61no—
426C5×C8—61no—
427C5×C8#23512yes—
428C5×C8#23512yes—
429#168—21no—
430#168—21no—
431#168—61no—
432#168—61no—
433C2×M16—51no—
434C2×M16—151no—
435C22×C8—31no—
436C22×C8—31no—
437C22×C8—51no—
438C22×C8—151no—
439#126—151no—
440#126—151no—
441#125—151no—
442#124—151no—
443#123—151no—
444#123—151no—
445C22⋊Q8—151no—
446#121—151no—
447C4×Q8—151no—
448C4×D4—151no—
449C4×D4—151no—
450C4×D4—151no—
451#117—51no—
452#117—151no—
453C2×C42—31no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456C4⋊C8—151no—
457C4⋊C8—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460C22⋊C8—151no—
461C22⋊C8—151no—
462C22⋊C8—151no—
463C22⋊C8—151no—
464C22⋊C8—151no—
465C22⋊C8—151no—
466#97—31no—
467#97—31no—
468#97—31no—
469#97—51no—
470#97—151no—
471#97D3×D511yescharacteristic
472C4×C8—51no—
473C4×C8—51no—
474C4×C8—151no—
475C4×C8—151no—
476C2×C3×C5C4×#4111yescharacteristic
477C2×C3×C5C2×#13111yescharacteristic
478C2×C3×C5#56811yescharacteristic
479D15—41no—
480C3×D5—41no—
481C5×D3—22no—
482C23×C3—51no—
483C22×D3—51no—
484C22×D3C2×C4×D511yescharacteristic
485C2×C3×C4—51no—
486C2×C3×C4—51no—
487C2×C3×C4—51no—
488C2×C3×C4—101no—
489C2×C3×C4—101no—
490C2×C3×C4C2×C4×D511yescharacteristic
491C2×C3×C4C2×C4×D511yescharacteristic
492C2×C3×C4C23×D511yescharacteristic
493#67—102no—
494#67—201no—
495C2×Dic3—51no—
496C2×Dic3—51no—
497C2×Dic3—51no—
498C2×Dic3C2×C4×D511yescharacteristic
499C2×Dic3C2×C4×D511yescharacteristic
500C2×Dic3C2×C4×D511yescharacteristic
501D12—102no—
502C4×D3—22no—
503C4×D3—21no—
504C4×D3—21no—
505C4×D3—41no—
506C4×D3—101no—
507C4×D3—101no—
508Dic6—201no—
509C3×C8—101no—
510C3×C8—101no—
511C3×C8#70912yes—
512C3×C8#70912yes—
513C3⋊C8—21no—
514C3⋊C8—21no—
515C3⋊C8—101no—
516C3⋊C8—101no—
517C22×C5—32no—
518C22×C5—61no—
519C22×C5—61no—
520C22×C5C22×C4×D311yescharacteristic
521C2×D5—21no—
522C2×D5—21no—
523C2×D5—21no—
524C2×D5—61no—
525C2×D5—61no—
526C2×D5—61no—
527C4×C5—21no—
528C4×C5—21no—
529C4×C5—61no—
530C4×C5—61no—
531C4×C5—61no—
532C4×C5C2×#23511yescharacteristic
533C4×C5C2×#23511yescharacteristic
534Dic5—21no—
535Dic5—21no—
536Dic5—21no—
537Dic5—61no—
538Dic5—61no—
539Dic5—61no—
540C2×Q8—151no—
541C2×D4—151no—
542C2×D4—151no—
543C2×D4—151no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—51no—
548C22×C4—151no—
549M16—102no—
550M16—302no—
551C2×C8—31no—
552C2×C8—31no—
553C2×C8—51no—
554C2×C8—51no—
555C2×C8—62no—
556C2×C8—62no—
557C2×C8—102no—
558C2×C8—151no—
559C2×C8—151no—
560C2×C8—302no—
561C2×C8C2×D3×D511yescharacteristic
562C2×C8C2×D3×D511yescharacteristic
563C4⋊C4—51no—
564C4⋊C4—51no—
565C4⋊C4—151no—
566C4⋊C4—151no—
567C4⋊C4—151no—
568C4⋊C4—151no—
569C4⋊C4—151no—
570C4⋊C4—151no—
571C4⋊C4—151no—
572C4⋊C4—151no—
573C22⋊C4—51no—
574C22⋊C4—51no—
575C22⋊C4—151no—
576C22⋊C4—151no—
577C22⋊C4—151no—
578C22⋊C4—151no—
579C22⋊C4—151no—
580C22⋊C4—151no—
581C22⋊C4—151no—
582C22⋊C4—151no—
583C42—31no—
584C42—31no—
585C42—31no—
586C42—51no—
587C42—151no—
588C42C2×D3×D511yescharacteristic
589C3×C5#296811yescharacteristic, complemented, Hall
590C22×C3—101no—
591C22×C3—101no—
592C22×C3—101no—
593C22×C3C22×C4×D511yescharacteristic
594C2×D3—21no—
595C2×D3—21no—
596C2×D3—101no—
597C2×D3—101no—
598C2×D3—101no—
599C2×D3#405312yes—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—101no—
603C3×C4—101no—
604C3×C4—101no—
605C3×C4C2×#70911yescharacteristic
606C3×C4C2×#70911yescharacteristic
607Dic3—21no—
608Dic3—21no—
609Dic3—21no—
610Dic3—101no—
611Dic3—101no—
612Dic3—101no—
613C2×C5—62no—
614C2×C5C4×#23511yescharacteristic
615C2×C5D3×#13111yescharacteristic
616C2×C5#575011yescharacteristic
617D5—41no—
618D5—121no—
619C23—31no—
620C23—51no—
621C23—151no—
622Q8—601no—
623D4—302no—
624D4—302no—
625D4—601no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—51no—
630C2×C4—51no—
631C2×C4—51no—
632C2×C4—62no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—101no—
636C2×C4—101no—
637C2×C4—121no—
638C2×C4—151no—
639C2×C4—151no—
640C2×C4—151no—
641C2×C4—301no—
642C2×C4—301no—
643C2×C4C4×D3×D511yescharacteristic
644C2×C4C4×D3×D511yescharacteristic
645C2×C4C22×D3×D511yescharacteristic
646C8—61no—
647C8—61no—
648C8—101no—
649C8—101no—
650C8—301no—
651C8—301no—
652C8#677112yes—
653C8#677112yes—
654C2×C3—201no—
655C2×C3C4×#70911yescharacteristic
656C2×C3C2×#405311yescharacteristic
657C2×C3#6607911yescharacteristic
658D3—22no—
659D3—201no—
660C5#7855811yescharacteristic, complemented, Sylow
661C22—32no—
662C22—61no—
663C22—61no—
664C22—101no—
665C22—101no—
666C22—101no—
667C22—301no—
668C22—301no—
669C22—301no—
670C22C2×C4×D3×D511yescharacteristic
671C4—21no—
672C4—21no—
673C4—61no—
674C4—61no—
675C4—61no—
676C4—101no—
677C4—101no—
678C4—101no—
679C4—301no—
680C4—301no—
681C4—301no—
682C4C2×#677111yescharacteristic
683C4C2×#677111yescharacteristic
684C3#1061021211yescharacteristic, complemented, Sylow
685C2—62no—
686C2—201no—
687C2—601no—
688C2C4×#677111yescharacteristic
689C2D3×#405311yescharacteristic
690C2#1175401611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×#97C22
prime radical#91454C4
cosocleC2×C3×C4×C5C24
hypercenter#97D3×D5
hypocenterC3×C5#2968
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ #97

Complements

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

NH ≅ G/Ntype
2. #11750809C2semidirect
3. C5×D3×#97C2semidirect
4. C3×#64997C2semidirect
5. #11747824C2semidirect
6. #11747819C2semidirect
7. #11747725C2semidirect
8. #11747719C2semidirect
9. #11747711C2semidirect
10. #11747705C2semidirect
11. C8×#1203C2semidirect
12. C8×#1201C2semidirect
13. #11746938C2semidirect
14. #11746876C2semidirect
15. #11746874C2semidirect
71. #64997D3semidirect
134. D3×#97D5semidirect
589. C3×C5#2968semidirect
660. C5#78558semidirect
684. C3#10610212semidirect

Maximal subgroups

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

subgroupindex
#117526932
#117508092
C5×D3×#972
C3×#649972
#117478242
#117478192
#117477252
#117477192
#117477112
#117477052
C8×#12032
C8×#12012
#117469382
#117468762
#117468742
#106102123
#785585