Finite Group Databasebeta

← #14416619

Subgroups — #14416619

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11755200C211yesmaximal, characteristic, complemented
2C2×#91523C211yesmaximal, characteristic
3#11753406C211yesmaximal, characteristic, complemented
4#11750905C211yesmaximal, characteristic, complemented
5C5×#4817C211yesmaximal, characteristic, complemented
6C3×#65078C211yesmaximal, characteristic, complemented
7#11749256C211yesmaximal, characteristic, complemented
8#11749223C211yesmaximal, characteristic, complemented
9#11748145C211yesmaximal, characteristic, complemented
10#11747746C211yesmaximal, characteristic, complemented
11#11747743C211yesmaximal, characteristic, complemented
12#11747603C211yesmaximal, characteristic, complemented
13#11747470C211yesmaximal, characteristic, complemented
14#11747440C211yesmaximal, characteristic, complemented
15#11747224C211yesmaximal, characteristic, complemented
16#10611503—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×#6768C2211yescharacteristic
19C2×C8×D15C2211yescharacteristic
20#91781C2211yescharacteristic
21C5×Q8×Dic3C2211yescharacteristic
22C2×C5×#215C2211yescharacteristic
23C5×#893C2211yescharacteristic
24C3×Q8×Dic5C2211yescharacteristic
25C2×C3×#689C2211yescharacteristic
26C3×#4033C2211yescharacteristic
27#91523C418yescomplemented
28#91446—21no—
29#91428—21no—
30#91428C2211yescharacteristic
31#91418—21no—
32#91418C2211yescharacteristic
33Dic5×D12C2211yescharacteristic
34#91405—21no—
35C4×#1200—21no—
36C4×#1200C2211yescharacteristic
37#91400—21no—
38C4×D3×Dic5—21no—
39#91347—21no—
40#91347C2211yescharacteristic
41Dic3×Dic10C2211yescharacteristic
42C2×#6658C2211yescharacteristic
43C2×#6654C2211yescharacteristic
44C2×#6648C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic
46#91119C2211yescharacteristic
47#91105C2211yescharacteristic
48#91093C2211yescharacteristic
49C5×#821C2211yescharacteristic
50C5×#815C2211yescharacteristic
51C5×#807C2211yescharacteristic
52C3×#3948C2211yescharacteristic
53C3×#3947C2211yescharacteristic
54C3×#3940C2211yescharacteristic
55#90990C2211yescharacteristic
56#90985C2211yescharacteristic
57#90970C2211yescharacteristic
58#90966C2211yescharacteristic
59#90953C2211yescharacteristic
60#90952C2211yescharacteristic
61#79828—51nomaximal, Hall
62C2×#4062—31no—
63C4×#713—31no—
64C4×#711—31no—
65C5×#440—31no—
66#65453—31no—
67#65319—31no—
68#65303—31no—
69#65178—31no—
70#65169—31no—
71#65093—31no—
72#65078D311yescharacteristic, complemented
73#65074—31no—
74#65061—31no—
75#64999—31no—
76D5×#97—31no—
77C2×C3×C5×Q8C2311yescharacteristic
78#6821—22no—
79#6821C2×C414yescomplemented
80C2×D60—21no—
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×C4×D15C2311yescharacteristic
84C2×C5×D12C2311yescharacteristic
85C2×C4×C5×D3—21no—
86C2×C3×Dic10C2311yescharacteristic
87C2×#1203—21no—
88C2×#1200—21no—
89C2×#1200—21no—
90C2×#1200D411yescharacteristic
91C2×#1200D411yescharacteristic
92C2×D3×Dic5—21no—
93C2×D3×Dic5—21no—
94#6768—22no—
95#6768C2×C414yescomplemented
96C2×C3×C5×C8C2311yescharacteristic
97C3×C5×C4⋊C4C2311yescharacteristic
98#6714—21no—
99C4⋊Dic15C2311yescharacteristic
100C4×Dic15—21no—
101C2×C3⋊#168C2311yescharacteristic
102C8×D15—22no—
103C5×#215C2×C414yescomplemented
104C5×(C2×D3)⋊C4—21no—
105C5×C4⋊Dic3—21no—
106C5×C4⋊Dic3C2311yescharacteristic
107C4×C5×Dic3—21no—
108C4×C5×Dic3C2311yescharacteristic
109C2×C5×C3⋊C8C2311yescharacteristic
110C3×#689C2×C414yescomplemented
111C3×C4⋊Dic5—21no—
112C3×C4⋊Dic5C2311yescharacteristic
113C3×#683—21no—
114C3×C4×Dic5—21no—
115C3×C4×Dic5—21no—
116C3×C4×Dic5C2311yescharacteristic
117C2×C3×#168C2311yescharacteristic
118#6668—21no—
119#6667—21no—
120#6667—21no—
121#6667—21no—
122(C2×D3)⋊Dic5—21no—
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5D411yescharacteristic
126Dic3×Dic5D411yescharacteristic
127#6658C2×C414yescomplemented
128#6654C2×C414yescomplemented
129#6648C2×C414yescomplemented
130C2×#919—51no—
131C4×#239—51no—
132C4×#239—51no—
133C3×#441—51no—
134#5184—51no—
135#5026—51no—
136#5026—51no—
137#4869—51no—
138#4860—51no—
139#4817—51no—
140#4817D511yescharacteristic, complemented
141#4804—51no—
142#4804—51no—
143#4711—51no—
144D3×#97—51no—
145C2×#713—31no—
146C2×#711—31no—
147C2×C5×SD16—31no—
148C4×C5×Q8—31no—
149C4×C5×D4—31no—
150Q8×Dic5C2×D311yescharacteristic
151C2×#689C2×D311yescharacteristic
152D4×Dic5—31no—
153C2×#686—31no—
154C4×C22⋊D5—61no—
155C2×C4×Dic5—61no—
156#4062—38no—
157C2×#677—31no—
158C2×C8×D5—31no—
159C2×C8×D5—31no—
160#4039—31no—
161#4039—61no—
162#4038—31no—
163#4038—31no—
164#4038—61no—
165#4033C2×D311yescharacteristic
166#4027—61no—
167#4023—61no—
168C4×D20—31no—
169C4×D20—61no—
170C42×D5—31no—
171C42×D5—61no—
172C4×Dic10—31no—
173C5×#107—31no—
174C5×#103C2×D311yescharacteristic
175C5×#102—31no—
176C5×#97—31no—
177#3967—31no—
178#3964—31no—
179#3953—31no—
180#3950—31no—
181#3948C2×D311yescharacteristic
182#3947—31no—
183#3947C2×D311yescharacteristic
184#3942—31no—
185#3941—31no—
186#3940—31no—
187#3940C2×D311yescharacteristic
188#3935—31no—
189#2943—151noSylow
190C22×D15—21no—
191C22×D15C2×D411yescharacteristic
192C22×C5×D3—21no—
193C3×C5×Q8—21no—
194C3×C5×Q8C22×C412yes—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5C2411yescharacteristic
198C2×Dic15—21no—
199C2×Dic15C2×D411yescharacteristic
200D60—24no—
201D60—21no—
202D60C22×C412yes—
203C4×D15—24no—
204C4×D15C22×C412yes—
205C4×D15#4112yes—
206C2×C5×Dic3—21no—
207C2×C5×Dic3C2×D411yescharacteristic
208C2×C5×Dic3C2×D411yescharacteristic
209C5×D12—21no—
210C5×D12C22×C412yes—
211C4×C5×D3—42no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C3×Dic10—21no—
217C3×Dic10C22×C412yes—
218#1203—24no—
219#1200—41no—
220#1200—41no—
221#1200—42no—
222#1200—42no—
223D3×Dic5—24no—
224D3×Dic5—42no—
225C3×C5×C8—21no—
226C3⋊#168—21no—
227C3×#168C22×C412yes—
228C5×C3⋊C8C22×C412yes—
229C2×#239—51no—
230C2×#239—51no—
231C2×C3×Q16—51no—
232C3×C4×Q8—51no—
233C3×C4×Q8—51no—
234Q8×Dic3—51no—
235Q8×Dic3C2×D511yescharacteristic
236C2×#215—51no—
237C2×#215C2×D511yescharacteristic
238#919—58no—
239C2×D24—51no—
240C2×D3×C8—51no—
241C2×D3×C8—51no—
242#893—51no—
243#893—101no—
244#893—101no—
245#893C2×D511yescharacteristic
246#892—51no—
247#892—51no—
248#892—101no—
249#892—101no—
250C4×D12—51no—
251C4×D12—51no—
252C4×D12—101no—
253C4×D12—101no—
254C42×D3—51no—
255C42×D3—101no—
256C42×D3—101no—
257C3×#106—51no—
258C3×#103—51no—
259C3×#103C2×D511yescharacteristic
260C3×#97—51no—
261#835—51no—
262#835—51no—
263#821—51no—
264#821C2×D511yescharacteristic
265#817—51no—
266#815—51no—
267#815C2×D511yescharacteristic
268#809—51no—
269#809—51no—
270#807—51no—
271#807C2×D511yescharacteristic
272#803—51no—
273C2×C5×Q8C22×D311yescharacteristic
274C2×C5×D4—31no—
275C22×C4×C5—61no—
276C2×C22⋊D5—61no—
277C22×Dic5—61no—
278C22×Dic5—61no—
279#713—34no—
280#713—62no—
281#711—34no—
282#711—62no—
283C2×D20—31no—
284C2×D20—61no—
285C2×C4×D5—31no—
286C2×C4×D5—31no—
287C2×C4×D5—31no—
288C2×C4×D5—61no—
289C2×C4×D5—61no—
290C2×C4×D5—61no—
291C2×Dic10C22×D311yescharacteristic
292C5×SD16—34no—
293C2×C5×C8—31no—
294C2×C5×C8C22×D311yescharacteristic
295C5×C4⋊C4—31no—
296C5×C4⋊C4—61no—
297C5×C4⋊C4C22×D311yescharacteristic
298C5×C22⋊C4—61no—
299C42×C5—31no—
300C42×C5—61no—
301C22⋊Dic5—61no—
302#689C4×D314yescomplemented
303#686—34no—
304#685—61no—
305#685—61no—
306#685—61no—
307#685—61no—
308C4⋊Dic5—21no—
309C4⋊Dic5—31no—
310C4⋊Dic5C22×D311yescharacteristic
311#683—21no—
312#683—61no—
313C4×Dic5—21no—
314C4×Dic5—21no—
315C4×Dic5—31no—
316C4×Dic5—31no—
317C4×Dic5—61no—
318C4×Dic5—61no—
319C4×Dic5—61no—
320C4×Dic5C22×D311yescharacteristic
321C2×#168—31no—
322C2×#168C22×D311yescharacteristic
323#677—34no—
324C8×D5—34no—
325C8×D5—62no—
326C2×#135—151no—
327C4×#41—151no—
328C4×#41—151no—
329#442—151no—
330#442—151no—
331#441—51no—
332#441—151no—
333#440—31no—
334#440—151no—
335#440—151no—
336#440—151no—
337#427—151no—
338#416—151no—
339#416—151no—
340C2×#97—151no—
341C22×C3×C5C22×D411yescharacteristic
342C2×D15—21no—
343C2×D15—21no—
344C2×D15—22no—
345C2×D15—41no—
346C2×D15—41no—
347C2×D15C4×D412yes—
348C2×C5×D3—22no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C3×C4×C5—22no—
352C3×C4×C5—41no—
353C3×C4×C5C23×C411yescharacteristic
354C3×C4×C5C2×#4111yescharacteristic
355Dic15—41no—
356Dic15C4×D412yes—
357C3×Dic5—22no—
358C3×Dic5—21no—
359C3×Dic5—21no—
360C3×Dic5—41no—
361C5×Dic3—21no—
362C5×Dic3—21no—
363C5×Dic3—41no—
364C2×C3×Q8—51no—
365C2×C3×Q8C22×D511yescharacteristic
366#239—54no—
367#239—54no—
368#239—102no—
369#239—102no—
370C2×D12—51no—
371C2×D12—101no—
372C2×D12—101no—
373C2×D12C22×D511yescharacteristic
374C2×C4×D3—21no—
375C2×C4×D3—51no—
376C2×C4×D3—51no—
377C2×C4×D3—51no—
378C2×C4×D3—101no—
379C2×C4×D3—101no—
380C2×C4×D3—101no—
381C2×C4×D3—101no—
382C2×C4×D3—101no—
383C3×Q16—54no—
384C2×C3×C8—51no—
385C2×C3×C8C22×D511yescharacteristic
386C3×C4⋊C4—51no—
387C3×C4⋊C4—101no—
388C3×C4⋊C4—101no—
389C3×C4⋊C4C22×D511yescharacteristic
390C3×C42—51no—
391C3×C42—101no—
392C3×C42—101no—
393#215—54no—
394#215C4×D514yescomplemented
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—101no—
397(C2×D3)⋊C4—101no—
398(C2×D3)⋊C4—101no—
399(C2×D3)⋊C4—101no—
400(C2×D3)⋊C4—101no—
401C4⋊Dic3—21no—
402C4⋊Dic3—51no—
403C4⋊Dic3—101no—
404C4⋊Dic3C22×D511yescharacteristic
405C4×Dic3—21no—
406C4×Dic3—51no—
407C4×Dic3—51no—
408C4×Dic3—101no—
409C4×Dic3—101no—
410C4×Dic3—101no—
411C4×Dic3C22×D511yescharacteristic
412C2×C3⋊C8—51no—
413C2×C3⋊C8C22×D511yescharacteristic
414D24—54no—
415D3×C8—54no—
416D3×C8—102no—
417C23×C5—61no—
418C22×D5—31no—
419C22×D5—61no—
420C5×Q8—21no—
421C5×Q8C2×C4×D312yes—
422C5×D4—32no—
423C5×D4—61no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—31no—
427C2×C4×C5—31no—
428C2×C4×C5—61no—
429C2×C4×C5—122no—
430C2×C4×C5C23×D311yescharacteristic
431C22⋊D5—64no—
432C2×Dic5—21no—
433C2×Dic5—21no—
434C2×Dic5—31no—
435C2×Dic5—64no—
436C2×Dic5—61no—
437C2×Dic5—122no—
438C2×Dic5D3×D411yescharacteristic
439C2×Dic5D3×D411yescharacteristic
440D20—32no—
441D20—64no—
442D20—61no—
443C4×D5—32no—
444C4×D5—32no—
445C4×D5—64no—
446C4×D5—121no—
447C4×D5—121no—
448C4×D5—122no—
449C4×D5—122no—
450Dic10—21no—
451Dic10C2×C4×D312yes—
452C5×C8—21no—
453C5×C8—32no—
454#168—61no—
455#168C2×C4×D312yes—
456C2×#41—151no—
457C2×#41—151no—
458#135—158no—
459C2×Q16—51no—
460C2×SD16—31no—
461C2×SD16—151no—
462C2×D8—151no—
463C22×C8—151no—
464C22×C8—151no—
465C4×Q8—31no—
466C4×Q8—51no—
467C4×Q8—51no—
468C4×Q8—151no—
469C4×D4—31no—
470C4×D4—151no—
471C4×D4—151no—
472C4×D4—151no—
473C4×D4—301no—
474C4×D4—301no—
475C4×D4—301no—
476C4×D4—301no—
477#117—151no—
478#117—151no—
479#117—301no—
480#117—301no—
481C2×C42—151no—
482C2×C42—301no—
483C2×C42—301no—
484#107—31no—
485#107—151no—
486#106—51no—
487#106—151no—
488#103—51no—
489#103—151no—
490#103—151no—
491#103D3×D511yescharacteristic
492#102—31no—
493#102—151no—
494#102—151no—
495#102—151no—
496#97—31no—
497#97—51no—
498#97—151no—
499#97—151no—
500C2×C3×C5C2×C4×D411yescharacteristic
501C2×C3×C5#57511yescharacteristic
502C2×C3×C5#57511yescharacteristic
503D15—22no—
504D15—42no—
505C5×D3—42no—
506C22×D3—21no—
507C22×D3—51no—
508C22×D3—101no—
509C3×Q8—21no—
510C3×Q8—52no—
511C3×Q8—101no—
512C3×Q8C2×C4×D512yes—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—51no—
516C2×C3×C4—51no—
517C2×C3×C4—101no—
518C2×C3×C4—101no—
519C2×C3×C4C23×D511yescharacteristic
520C2×Dic3—21no—
521C2×Dic3—51no—
522C2×Dic3—101no—
523C2×Dic3D4×D511yescharacteristic
524C2×Dic3D4×D511yescharacteristic
525D12—21no—
526D12—52no—
527D12—104no—
528D12—104no—
529D12—101no—
530D12C2×C4×D512yes—
531C4×D3—42no—
532C4×D3—52no—
533C4×D3—52no—
534C4×D3—104no—
535C4×D3—104no—
536C4×D3—201no—
537C4×D3—201no—
538C4×D3—202no—
539C4×D3—202no—
540C4×D3—202no—
541C3×C8—21no—
542C3×C8—52no—
543C3⋊C8—101no—
544C3⋊C8C2×C4×D512yes—
545C22×C5—62no—
546C22×C5—121no—
547C22×C5—121no—
548C22×C5C2×D3×D411yescharacteristic
549C2×D5—32no—
550C2×D5—61no—
551C2×D5—61no—
552C2×D5—62no—
553C2×D5—121no—
554C2×D5—121no—
555C4×C5—22no—
556C4×C5—41no—
557C4×C5—61no—
558C4×C5—61no—
559C4×C5—121no—
560C4×C5C22×C4×D311yescharacteristic
561C4×C5D3×#4111yescharacteristic
562Dic5—21no—
563Dic5—21no—
564Dic5—22no—
565Dic5—32no—
566Dic5—41no—
567Dic5—121no—
568#41—154no—
569#41—154no—
570#41—302no—
571#41—302no—
572C2×Q8—51no—
573C2×Q8C2×D3×D511yescharacteristic
574C2×D4—31no—
575C2×D4—151no—
576C2×D4—301no—
577C2×D4—301no—
578C22×C4—61no—
579C22×C4—151no—
580C22×C4—151no—
581C22×C4—151no—
582C22×C4—301no—
583C22×C4—301no—
584C22×C4—301no—
585C22×C4—301no—
586C22×C4—301no—
587Q16—54no—
588SD16—34no—
589SD16—154no—
590D8—154no—
591C2×C8—31no—
592C2×C8—51no—
593C2×C8—154no—
594C2×C8—151no—
595C2×C8—302no—
596C2×C8C2×D3×D511yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—51no—
599C4⋊C4—61no—
600C4⋊C4—101no—
601C4⋊C4—101no—
602C4⋊C4—151no—
603C4⋊C4—301no—
604C4⋊C4C2×D3×D511yescharacteristic
605C22⋊C4—61no—
606C22⋊C4—301no—
607C22⋊C4—301no—
608C22⋊C4—301no—
609C22⋊C4—301no—
610C22⋊C4—301no—
611C42—31no—
612C42—51no—
613C42—61no—
614C42—101no—
615C42—101no—
616C42—151no—
617C42—151no—
618C42—301no—
619C42—301no—
620C42—301no—
621C3×C5#294311yescharacteristic, complemented, Hall
622C22×C3C2×D4×D511yescharacteristic
623C2×D3—22no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—52no—
627C2×D3—101no—
628C2×D3—101no—
629C2×D3—102no—
630C2×D3—201no—
631C2×D3—201no—
632C3×C4—22no—
633C3×C4—41no—
634C3×C4—101no—
635C3×C4—101no—
636C3×C4—102no—
637C3×C4—201no—
638C3×C4C22×C4×D511yescharacteristic
639C3×C4D5×#4111yescharacteristic
640Dic3—21no—
641Dic3—21no—
642Dic3—41no—
643Dic3—52no—
644Dic3—201no—
645C2×C5—122no—
646C2×C5C4×D3×D411yescharacteristic
647C2×C5#577711yescharacteristic
648C2×C5#577711yescharacteristic
649D5—62no—
650D5—122no—
651C23—61no—
652C23—151no—
653C23—301no—
654Q8—21no—
655Q8—52no—
656Q8—101no—
657Q8C4×D3×D512yes—
658D4—32no—
659D4—61no—
660D4—152no—
661D4—304no—
662D4—304no—
663D4—301no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—51no—
669C2×C4—51no—
670C2×C4—61no—
671C2×C4—101no—
672C2×C4—101no—
673C2×C4—122no—
674C2×C4—151no—
675C2×C4—152no—
676C2×C4—152no—
677C2×C4—304no—
678C2×C4—304no—
679C2×C4—301no—
680C2×C4—601no—
681C2×C4—601no—
682C2×C4—602no—
683C2×C4—602no—
684C2×C4—602no—
685C2×C4C22×D3×D511yescharacteristic
686C8—21no—
687C8—32no—
688C8—52no—
689C8—301no—
690C2×C3C4×D4×D511yescharacteristic
691C2×C3#6610711yescharacteristic
692C2×C3#6611111yescharacteristic
693D3—42no—
694D3—102no—
695D3—202no—
696C5#7982811yescharacteristic, complemented, Sylow
697C22—62no—
698C22—121no—
699C22—121no—
700C22—152no—
701C22—301no—
702C22—301no—
703C22—302no—
704C22—601no—
705C22—601no—
706C22D3×D4×D511yescharacteristic
707C4—22no—
708C4—41no—
709C4—61no—
710C4—61no—
711C4—101no—
712C4—101no—
713C4—102no—
714C4—121no—
715C4—152no—
716C4—201no—
717C4—601no—
718C4C2×C4×D3×D511yescharacteristic
719C4#9202411yescharacteristic
720C3#1061150311yescharacteristic, complemented, Sylow
721C2—122no—
722C2—302no—
723C2—602no—
724C2#1175320311yescharacteristic
725C2#1175407411yescharacteristic
726C2#1175410111yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×#91523C2
cosocleC2×C3×C4×C5C24
hypercenter#103D3×D5
hypocenterC3×C5#2943
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #11755200C2semidirect
3. #11753406C2semidirect
4. #11750905C2semidirect
5. C5×#4817C2semidirect
6. C3×#65078C2semidirect
7. #11749256C2semidirect
8. #11749223C2semidirect
9. #11748145C2semidirect
10. #11747746C2semidirect
11. #11747743C2semidirect
12. #11747603C2semidirect
13. #11747470C2semidirect
14. #11747440C2semidirect
15. #11747224C2semidirect
27. #91523C4semidirect
72. #65078D3semidirect
79. #6821C2×C4semidirect
95. #6768C2×C4semidirect
103. C5×#215C2×C4semidirect
110. C3×#689C2×C4semidirect
127. #6658C2×C4semidirect
128. #6654C2×C4semidirect
129. #6648C2×C4semidirect
140. #4817D5semidirect
302. #689C4×D3semidirect
394. #215C4×D5semidirect
621. C3×C5#2943semidirect
696. C5#79828semidirect
720. C3#10611503semidirect

Maximal subgroups

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

subgroupindex
#117552002
C2×#915232
#117534062
#117509052
C5×#48172
C3×#650782
#117492562
#117492232
#117481452
#117477462
#117477432
#117476032
#117474702
#117474402
#117472242
#106115033
#798285