Finite Group Databasebeta

← #14301096

Subgroups — #14301096

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
2C2×C3×D5×SD16C211yesmaximal, characteristic
3C2×#91238C211yesmaximal, characteristic, complemented
4#11752439C211yesmaximal, characteristic
5C2×#91236C211yesmaximal, characteristic
6#11746764C211yesmaximal, characteristic, complemented
7#11746763C211yesmaximal, characteristic, complemented
8#10604818—31nomaximal, Hall
9C2×C3×Q8×D5C2211yescharacteristic
10C2×C3×D4×D5C2211yescharacteristic
11C2×#6763—21no—
12C2×#6763—21no—
13Q8×ΓL(1,𝔽16)—22no—
14Q8×ΓL(1,𝔽16)—22no—
15C2×C4⋊ΓL(1,𝔽16)—21no—
16C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
17C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
18C2×C4×ΓL(1,𝔽16)—21no—
19C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
20C2×D5⋊(C3⋊C8)C2211yescharacteristic
21C2×C3×C5×SD16C411yescharacteristic, complemented
22C2×C3×#688C411yescharacteristic, complemented
23C2×C3×#687C411yescharacteristic, complemented
24C3×D5×SD16—22no—
25C3×D5×SD16—22no—
26C2×C3×#677C411yescharacteristic, complemented
27C2×C3×C8×D5C2211yescharacteristic
28#91238—22no—
29#91236—22no—
30#72048—51nomaximal, Hall
31C2×Q8×AGL(1,𝔽5)—31no—
32C2×D5×SD16D311yescharacteristic
33C2×#4009—31no—
34#65780—31no—
35C2×#4007—31no—
36#64893—31no—
37(C2×AGL(1,𝔽5))⋊C8—31no—
38C23×C3×D5—21no—
39C22×ΓL(1,𝔽16)—21no—
40C22×ΓL(1,𝔽16)—21no—
41C22×ΓL(1,𝔽16)D411yescharacteristic
42C22×ΓL(1,𝔽16)D411yescharacteristic
43C2×C3×C5×Q8C2×C411yescharacteristic
44C2×C3×C5×D4C2×C411yescharacteristic
45C2×C3×C22⋊D5—21no—
46C3×Q8×D5—21no—
47C3×Q8×D5—21no—
48C3×Q8×D5D412yes—
49C3×Q8×D5D412yes—
50C3×D4×D5—21no—
51C3×D4×D5—21no—
52C3×D4×D5—21no—
53C3×D4×D5—21no—
54C2×C3×D20C2×C411yescharacteristic
55C2×C3×C4×D5—21no—
56C2×C3×C4×D5C2311yescharacteristic
57C2×C3×Dic10—21no—
58C2×C3×Dic10C2×C411yescharacteristic
59#6763—42no—
60#6763—42no—
61C2×C3⋊#170—21no—
62C4⋊ΓL(1,𝔽16)—24no—
63C4⋊ΓL(1,𝔽16)—21no—
64C4⋊ΓL(1,𝔽16)—21no—
65C4⋊ΓL(1,𝔽16)—21no—
66C4⋊ΓL(1,𝔽16)D412yes—
67C4×ΓL(1,𝔽16)—24no—
68C4×ΓL(1,𝔽16)—21no—
69C4×ΓL(1,𝔽16)—21no—
70D5⋊(C3⋊C8)—21no—
71D5⋊(C3⋊C8)—21no—
72C3×C5×SD16—22no—
73C2×C3×C5×C8C2×C411yescharacteristic
74C3×#688—22no—
75C3×#687—22no—
76C2×C3×#168C2×C411yescharacteristic
77C3×#677—22no—
78C3×C8×D5—21no—
79C3×C8×D5—21no—
80C22×C3×SD16—51no—
81C2×Q8×Dic3—51no—
82C2×#835—51no—
83#5221—51no—
84C2×#832—51no—
85#4551—51no—
86#4550—51no—
87C2×Q8×D5C2×D311yescharacteristic
88C2×D4×D5C2×D311yescharacteristic
89C2×C22⋊AGL(1,𝔽5)—61no—
90C2×C22⋊AGL(1,𝔽5)—61no—
91Q8×AGL(1,𝔽5)—62no—
92Q8×AGL(1,𝔽5)—62no—
93C2×C4⋊AGL(1,𝔽5)—31no—
94C2×C4⋊AGL(1,𝔽5)—31no—
95C2×C4⋊AGL(1,𝔽5)—61no—
96C2×C4×AGL(1,𝔽5)—31no—
97C2×C4×AGL(1,𝔽5)—61no—
98C2×D5⋊C8—31no—
99C2×C5×SD16Dic311yescharacteristic, complemented
100C2×#688Dic311yescharacteristic, complemented
101C2×#687Dic311yescharacteristic, complemented
102D5×SD16—22no—
103D5×SD16—22no—
104C2×#677Dic311yescharacteristic, complemented
105C2×C8×D5C2×D311yescharacteristic
106#4009—62no—
107#4007—62no—
108#1880—151noSylow
109C23×C3×C5—21no—
110C22×C3×D5—21no—
111C22×C3×D5—41no—
112C22×C3×D5—41no—
113C22×C3×D5—41no—
114C22×C3×D5—41no—
115C22×C3×D5—41no—
116C22×C3×D5—41no—
117C22×C3×D5C2×D411yescharacteristic
118C2×ΓL(1,𝔽16)—21no—
119C2×ΓL(1,𝔽16)—21no—
120C2×ΓL(1,𝔽16)—21no—
121C2×ΓL(1,𝔽16)—22no—
122C2×ΓL(1,𝔽16)—21no—
123C2×ΓL(1,𝔽16)—21no—
124C2×ΓL(1,𝔽16)—41no—
125C2×ΓL(1,𝔽16)—41no—
126C2×ΓL(1,𝔽16)—41no—
127C2×ΓL(1,𝔽16)—41no—
128C2×ΓL(1,𝔽16)—41no—
129C2×ΓL(1,𝔽16)SD1612yescomplemented
130C3×C5×Q8—21no—
131C3×C5×Q8C22⋊C412yescomplemented
132C3×C5×D4—21no—
133C3×C5×D4—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5C22×C411yescharacteristic
136C3×C22⋊D5—41no—
137C3×C22⋊D5—41no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5#4111yescharacteristic
140C3×D20—21no—
141C3×D20—21no—
142C3×C4×D5—22no—
143C3×C4×D5—22no—
144C3×C4×D5C2×D411yescharacteristic
145C3×C4×D5C2×D411yescharacteristic
146C3×C4×D5C2×D411yescharacteristic
147C3×C4×D5#4111yescharacteristic
148C3×Dic10—21no—
149C3×Dic10—22no—
150C3×Dic10—22no—
151C3×Dic10C22⋊C412yescomplemented
152C3⋊#170—41no—
153C3×C5×C8—21no—
154C3×#168—21no—
155C22×C3×Q8—51no—
156C22×C3×D4—51no—
157C2×C3×SD16—51no—
158C2×C3×SD16—51no—
159C2×C3×SD16—51no—
160C2×C3×SD16—102no—
161C2×C3×SD16—102no—
162C2×C3×SD16AGL(1,𝔽5)11yescharacteristic, complemented
163C22×C3×C8—51no—
164C2×#217—101no—
165C2×#217—101no—
166Q8×Dic3—102no—
167Q8×Dic3—102no—
168C2×C4⋊Dic3—51no—
169C2×C4⋊Dic3—51no—
170C2×C4⋊Dic3—101no—
171C2×C4×Dic3—51no—
172C2×C4×Dic3—101no—
173C22×C3⋊C8—51no—
174#835—102no—
175#832—102no—
176C23×D5—21no—
177C22×AGL(1,𝔽5)—31no—
178C22×AGL(1,𝔽5)—31no—
179C22×AGL(1,𝔽5)—61no—
180C22×AGL(1,𝔽5)—61no—
181C2×C5×Q8C2×Dic311yescharacteristic
182C2×C5×D4C2×Dic311yescharacteristic
183C2×C22⋊D5—21no—
184Q8×D5—21no—
185Q8×D5—21no—
186Q8×D5#6712yes—
187Q8×D5#6712yes—
188D4×D5—21no—
189D4×D5—21no—
190D4×D5—21no—
191D4×D5—21no—
192C2×D20C2×Dic311yescharacteristic
193C2×C4×D5—21no—
194C2×C4×D5C22×D311yescharacteristic
195C2×Dic10—21no—
196C2×Dic10C2×Dic311yescharacteristic
197C22⋊AGL(1,𝔽5)—122no—
198C22⋊AGL(1,𝔽5)—122no—
199C2×#170—61no—
200C4⋊AGL(1,𝔽5)—32no—
201C4⋊AGL(1,𝔽5)—64no—
202C4⋊AGL(1,𝔽5)—61no—
203C4⋊AGL(1,𝔽5)—61no—
204C4⋊AGL(1,𝔽5)—61no—
205C4×AGL(1,𝔽5)—64no—
206C4×AGL(1,𝔽5)—61no—
207C4×AGL(1,𝔽5)—61no—
208D5⋊C8—61no—
209D5⋊C8—61no—
210C5×SD16—22no—
211C2×C5×C8C2×Dic311yescharacteristic
212#688—22no—
213#687—22no—
214C2×#168C2×Dic311yescharacteristic
215#677—22no—
216C8×D5—21no—
217C8×D5—21no—
218C22×SD16—51no—
219C2×C4×Q8—151no—
220C2×#103—151no—
221C2×#102—151no—
222#390—151no—
223#340—151no—
224#336—151no—
225C22×C3×C5—41no—
226C22×C3×C5—41no—
227C22×C3×C5—41no—
228C22×C3×C5C4×D411yescharacteristic
229C2×C3×D5—41no—
230C2×C3×D5—41no—
231C2×C3×D5—41no—
232C2×C3×D5—81no—
233C2×C3×D5—81no—
234C2×C3×D5—81no—
235C2×C3×D5—81no—
236C2×C3×D5#12011yescharacteristic
237C2×C3×D5#12111yescharacteristic
238C2×C3×D5C2×SD1611yescharacteristic
239C2×C3×D5#13511yescharacteristic
240C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
241C2×C3×D5#13711yescharacteristic
242ΓL(1,𝔽16)—22no—
243ΓL(1,𝔽16)—41no—
244ΓL(1,𝔽16)—42no—
245ΓL(1,𝔽16)—81no—
246C3×C4×C5—22no—
247C3×C4×C5C2×C22⋊C411yescharacteristic
248C3×C4×C5C4×D411yescharacteristic
249C3×Dic5—22no—
250C3×Dic5#12111yescharacteristic
251C3×Dic5#12311yescharacteristic
252C24×C3—101no—
253C2×C3×Q8—52no—
254C2×C3×Q8—52no—
255C2×C3×Q8—51no—
256C2×C3×Q8—101no—
257C2×C3×Q8—101no—
258C2×C3×Q8—101no—
259C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
260C2×C3×D4—51no—
261C2×C3×D4—101no—
262C2×C3×D4—101no—
263C2×C3×D4—101no—
264C2×C3×D4—101no—
265C2×C3×D4—101no—
266C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
267C22×C3×C4—51no—
268C22×C3×C4—101no—
269C22×Dic3—51no—
270C22×Dic3—51no—
271C22×Dic3—101no—
272C22×Dic3—101no—
273C3×SD16—22no—
274C3×SD16—102no—
275C3×SD16—102no—
276C3×SD16—102no—
277C2×C3×C8—51no—
278C2×C3×C8—101no—
279C2×C3×C8—101no—
280C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
281#217—202no—
282#217—202no—
283C4⋊Dic3—52no—
284C4⋊Dic3—101no—
285C4⋊Dic3—104no—
286C4⋊Dic3—101no—
287C4⋊Dic3—101no—
288C4×Dic3—101no—
289C4×Dic3—101no—
290C4×Dic3—104no—
291C2×C3⋊C8—101no—
292C2×C3⋊C8—101no—
293C2×C3⋊C8—101no—
294C23×C5—21no—
295C22×D5—21no—
296C22×D5—41no—
297C22×D5—41no—
298C22×D5—41no—
299C22×D5—41no—
300C22×D5—41no—
301C22×D5—41no—
302C22×D5D3×D411yescharacteristic
303C2×AGL(1,𝔽5)—32no—
304C2×AGL(1,𝔽5)—61no—
305C2×AGL(1,𝔽5)—61no—
306C2×AGL(1,𝔽5)—61no—
307C2×AGL(1,𝔽5)—61no—
308C2×AGL(1,𝔽5)—62no—
309C2×AGL(1,𝔽5)—61no—
310C2×AGL(1,𝔽5)—121no—
311C2×AGL(1,𝔽5)—121no—
312C2×AGL(1,𝔽5)—121no—
313C2×AGL(1,𝔽5)—121no—
314C2×AGL(1,𝔽5)—121no—
315C5×Q8—21no—
316C5×Q8#21712yescomplemented
317C5×D4—21no—
318C5×D4—21no—
319C2×C4×C5—21no—
320C2×C4×C5C22×Dic311yescharacteristic
321C22⋊D5—41no—
322C22⋊D5—41no—
323C2×Dic5—21no—
324C2×Dic5#23711yescharacteristic
325D20—21no—
326D20—21no—
327C4×D5—22no—
328C4×D5—22no—
329C4×D5D3×D411yescharacteristic
330C4×D5#23711yescharacteristic
331C4×D5C2×#6711yescharacteristic
332C4×D5C2×#6711yescharacteristic
333Dic10—21no—
334Dic10—22no—
335Dic10—22no—
336Dic10#21712yescomplemented
337#170—121no—
338C5×C8—21no—
339#168—21no—
340C22×Q8—51no—
341C22×D4—51no—
342C2×SD16—51no—
343C2×SD16—51no—
344C2×SD16—51no—
345C2×SD16—102no—
346C2×SD16—102no—
347C2×SD16ΓL(1,𝔽16)11yescharacteristic, complemented
348C22×C8—51no—
349C22×C8—151no—
350C4×Q8—302no—
351C4×Q8—302no—
352C2×C4⋊C4—151no—
353C2×C4⋊C4—151no—
354C2×C4⋊C4—301no—
355C2×C22⋊C4—301no—
356C2×C22⋊C4—301no—
357C2×C42—151no—
358C2×C42—301no—
359#103—302no—
360#102—302no—
361C2×C3×C5—81no—
362C2×C3×C5#38611yescharacteristic
363C2×C3×C5C4×SD1611yescharacteristic
364C2×C3×C5#44011yescharacteristic
365C3×D5—81no—
366C3×D5#44811yescharacteristic
367C3×D5#44911yescharacteristic
368C3×D5#46011yescharacteristic
369C3×D5#46411yescharacteristic
370C23×C3—21no—
371C23×C3—51no—
372C23×C3—101no—
373C23×C3—201no—
374C23×C3—201no—
375C23×C3—201no—
376C23×C3—201no—
377C23×C3—201no—
378C23×C3—201no—
379C3×Q8—21no—
380C3×Q8—52no—
381C3×Q8—102no—
382C3×Q8—102no—
383C3×Q8—101no—
384C3×Q8C22⋊AGL(1,𝔽5)12yescomplemented
385C3×D4—21no—
386C3×D4—21no—
387C3×D4—101no—
388C3×D4—101no—
389C3×D4—201no—
390C3×D4—201no—
391C2×C3×C4—21no—
392C2×C3×C4—51no—
393C2×C3×C4—51no—
394C2×C3×C4—51no—
395C2×C3×C4—51no—
396C2×C3×C4—51no—
397C2×C3×C4—102no—
398C2×C3×C4—102no—
399C2×C3×C4—101no—
400C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
401C2×Dic3—52no—
402C2×Dic3—101no—
403C2×Dic3—101no—
404C2×Dic3—102no—
405C2×Dic3—101no—
406C2×Dic3—101no—
407C2×Dic3—101no—
408C2×Dic3—201no—
409C2×Dic3—201no—
410C2×Dic3—201no—
411C2×Dic3—201no—
412C2×Dic3—201no—
413C3×C8—21no—
414C3×C8—101no—
415C3⋊C8—201no—
416C22×C5—41no—
417C22×C5—41no—
418C22×C5—41no—
419C22×C5D4×Dic311yescharacteristic
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—41no—
423C2×D5—81no—
424C2×D5—81no—
425C2×D5—81no—
426C2×D5—81no—
427C2×D5D3×SD1611yescharacteristic
428C2×D5#91411yescharacteristic
429C2×D5#91511yescharacteristic
430C2×D5#91611yescharacteristic
431C2×D5#93711yescharacteristic
432C2×D5#93911yescharacteristic
433AGL(1,𝔽5)—62no—
434AGL(1,𝔽5)—121no—
435AGL(1,𝔽5)—122no—
436AGL(1,𝔽5)—241no—
437C4×C5—22no—
438C4×C5D4×Dic311yescharacteristic
439C4×C5C2×#21711yescharacteristic
440Dic5—22no—
441Dic5#93511yescharacteristic
442Dic5#93911yescharacteristic
443C24—101no—
444C2×Q8—52no—
445C2×Q8—52no—
446C2×Q8—51no—
447C2×Q8—101no—
448C2×Q8—101no—
449C2×Q8—101no—
450C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
451C2×D4—51no—
452C2×D4—101no—
453C2×D4—101no—
454C2×D4—101no—
455C2×D4—101no—
456C2×D4—101no—
457C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
458C22×C4—51no—
459C22×C4—101no—
460C22×C4—151no—
461C22×C4—151no—
462C22×C4—301no—
463C22×C4—301no—
464SD16—22no—
465SD16—102no—
466SD16—102no—
467SD16—102no—
468C2×C8—51no—
469C2×C8—101no—
470C2×C8—101no—
471C2×C8—301no—
472C2×C8—301no—
473C2×C8—301no—
474C2×C8C2×ΓL(1,𝔽16)11yescharacteristic
475C4⋊C4—152no—
476C4⋊C4—301no—
477C4⋊C4—301no—
478C4⋊C4—301no—
479C4⋊C4—304no—
480C22⋊C4—602no—
481C22⋊C4—602no—
482C42—301no—
483C42—301no—
484C42—304no—
485C3×C5#188011yescharacteristic, complemented, Hall
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—51no—
490C22×C3—51no—
491C22×C3—51no—
492C22×C3—51no—
493C22×C3—51no—
494C22×C3—51no—
495C22×C3—201no—
496C22×C3—201no—
497C22×C3—201no—
498C22×C3—401no—
499C22×C3—401no—
500C22×C3—401no—
501C22×C3—401no—
502C22×C3D4×AGL(1,𝔽5)11yescharacteristic
503C3×C4—22no—
504C3×C4—51no—
505C3×C4—51no—
506C3×C4—102no—
507C3×C4D4×AGL(1,𝔽5)11yescharacteristic
508C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
509Dic3—102no—
510Dic3—201no—
511Dic3—202no—
512Dic3—401no—
513C2×C5—81no—
514C2×C5Dic3×SD1611yescharacteristic
515C2×C5#516411yescharacteristic
516C2×C5#522011yescharacteristic
517D5—81no—
518D5#516311yescharacteristic
519D5#516611yescharacteristic
520D5#517011yescharacteristic
521D5#517211yescharacteristic
522C23—21no—
523C23—51no—
524C23—101no—
525C23—201no—
526C23—201no—
527C23—201no—
528C23—201no—
529C23—201no—
530C23—201no—
531Q8—21no—
532Q8—52no—
533Q8—102no—
534Q8—102no—
535Q8—101no—
536Q8#676312yescomplemented
537D4—21no—
538D4—21no—
539D4—101no—
540D4—101no—
541D4—201no—
542D4—201no—
543C2×C4—21no—
544C2×C4—51no—
545C2×C4—51no—
546C2×C4—51no—
547C2×C4—51no—
548C2×C4—51no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—101no—
552C2×C4—152no—
553C2×C4—301no—
554C2×C4—301no—
555C2×C4—302no—
556C2×C4—301no—
557C2×C4—301no—
558C2×C4—301no—
559C2×C4—601no—
560C2×C4—601no—
561C2×C4—601no—
562C2×C4—601no—
563C2×C4—601no—
564C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
565C8—21no—
566C8—101no—
567C8—601no—
568C2×C3—51no—
569C2×C3—51no—
570C2×C3—51no—
571C2×C3—51no—
572C2×C3—81no—
573C2×C3—401no—
574C2×C3SD16×AGL(1,𝔽5)11yescharacteristic
575C2×C3#6573511yescharacteristic
576C2×C3#6577911yescharacteristic
577C5#7204811yescharacteristic, complemented, Sylow
578C22—41no—
579C22—41no—
580C22—41no—
581C22—51no—
582C22—51no—
583C22—51no—
584C22—51no—
585C22—51no—
586C22—51no—
587C22—201no—
588C22—201no—
589C22—201no—
590C22—401no—
591C22—401no—
592C22—401no—
593C22—401no—
594C22D4×ΓL(1,𝔽16)11yescharacteristic
595C4—22no—
596C4—51no—
597C4—51no—
598C4—102no—
599C4—302no—
600C4—601no—
601C4—602no—
602C4—1201no—
603C4D4×ΓL(1,𝔽16)11yescharacteristic
604C4C2×#676311yescharacteristic
605C3#1060481811yescharacteristic, complemented, Sylow
606C2—51no—
607C2—51no—
608C2—51no—
609C2—51no—
610C2—81no—
611C2—401no—
612C2SD16×ΓL(1,𝔽16)11yescharacteristic
613C2#1175239411yescharacteristic
614C2#1175243811yescharacteristic
subgroupG/H
centerC22D4×ΓL(1,𝔽16)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC2×C3×C5×SD16C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×D4×D5C22
cosocleC2×C3×C4×D5C23
hypercenterC2×SD16ΓL(1,𝔽16)
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×ΓL(1,𝔽16)C2semidirect
3. C2×#91238C2semidirect
6. #11746764C2semidirect
7. #11746763C2semidirect
21. C2×C3×C5×SD16C4semidirect
22. C2×C3×#688C4semidirect
23. C2×C3×#687C4semidirect
26. C2×C3×#677C4semidirect
99. C2×C5×SD16Dic3semidirect
100. C2×#688Dic3semidirect
101. C2×#687Dic3semidirect
104. C2×#677Dic3semidirect
129. C2×ΓL(1,𝔽16)SD16semidirect
131. C3×C5×Q8C22⋊C4semidirect
151. C3×Dic10C22⋊C4semidirect
162. C2×C3×SD16AGL(1,𝔽5)semidirect
316. C5×Q8#217semidirect
336. Dic10#217semidirect
347. C2×SD16ΓL(1,𝔽16)semidirect
384. C3×Q8C22⋊AGL(1,𝔽5)semidirect
485. C3×C5#1880semidirect
536. Q8#6763semidirect
577. C5#72048semidirect
605. C3#10604818semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×ΓL(1,𝔽16)2
C2×C3×D5×SD162
C2×#912382
#117524392
C2×#912362
#117467642
#117467632
#106048183
#720485