Finite Group Databasebeta

← C2×#10615173 #12971499

Subgroups — C2×#10615173 #12971499

Order 1280.

1678 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#541C211yesmaximal, characteristic
2C2×#65853C211yesmaximal, characteristic
3#10615173C2116yesmaximal, direct product factor
4C2×#65371C211yesmaximal, characteristic, complemented
5C2×#65370C211yesmaximal, characteristic, complemented
6C2×#65354C211yesmaximal, characteristic, complemented
7C2×#65353C211yesmaximal, characteristic, complemented
8C2×#65333C211yesmaximal, characteristic
9C2×#65334C211yesmaximal, characteristic
10C2×#65334C211yesmaximal, characteristic
11C2×#65332C211yesmaximal, characteristic
12C2×#65311C211yesmaximal, characteristic, complemented
13C2×#65311C211yesmaximal, characteristic, complemented
14C2×#65310C211yesmaximal, characteristic, complemented
15C2×#65309C211yesmaximal, characteristic, complemented
16C2×#65289C211yesmaximal, characteristic
17C5×#541—24no—
18C5×#541C2218yes—
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#126—21no—
21C2×C5×#126—21no—
22C2×C5×#125—21no—
23C2×C5×#125—21no—
24C2×C5×#125C2211yescharacteristic
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×Q8C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C2×#4072C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32#65853—24no—
33#65853C2218yes—
34C2×#4036—21no—
35C2×#4034—21no—
36C2×#4024—21no—
37C2×#4024—21no—
38C2×#4016C2211yescharacteristic
39C2×#4016C2211yescharacteristic
40C2×#4015C2211yescharacteristic
41C2×#4015C2211yescharacteristic
42C2×#3967C2211yescharacteristic
43C2×#3967C2211yescharacteristic
44C2×#3967C2211yescharacteristic
45C2×#3967C2211yescharacteristic
46C2×#3967C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×#3967C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×C22⋊#168C2211yescharacteristic
51C2×C22⋊#168C2211yescharacteristic
52#65371C2218yescomplemented
53#65370C2218yescomplemented
54#65354C2218yescomplemented
55#65353C2218yescomplemented
56#65334C2218yes—
57#65334C2218yes—
58#65333C2218yes—
59#65332C2218yes—
60#65311C2218yescomplemented
61#65311C2218yescomplemented
62#65310C2218yescomplemented
63#65309C2218yescomplemented
64#65289C2218yes—
65C2×#3940C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×C4⋊#168C2211yescharacteristic
74C2×C4⋊#168C2211yescharacteristic
75C2×#3935C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3242—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×Q8C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×Dic5—21no—
82C22×Dic10—21no—
83C22×Dic10—21no—
84C5×C4⋊Q8—22no—
85C5×C4⋊Q8C2314yes—
86C5×#126—28no—
87C5×#126—28no—
88C5×#125—28no—
89C5×#125—28no—
90C5×#125—22no—
91C5×#125C2314yes—
92C5×C22⋊Q8—22no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8C2314yes—
95C5×C22⋊Q8C2314yes—
96C4×C5×Q8—22no—
97C4×C5×Q8—22no—
98C4×C5×Q8C2314yes—
99C4×C5×Q8C2314yes—
100C5×#117D414yes—
101C5×#117C2314yes—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4D411yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4D411yescharacteristic
117C2×C5×C22⋊C4D411yescharacteristic
118C2×C42×C5—21no—
119C2×C42×C5—21no—
120C2×C42×C5C2311yescharacteristic
121C2×C42×C5C2311yescharacteristic
122C2×C22⋊Dic5—21no—
123#4072—22no—
124#4072C2314yes—
125C2×C4⋊Dic5—21no—
126C2×C4⋊Dic5—21no—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—22no—
129C2×C4⋊Dic5C2311yescharacteristic
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2314yes—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683—21no—
137C2×#683—21no—
138C2×C4×Dic5—21no—
139C22×#168C2311yescharacteristic
140C22×#168C2311yescharacteristic
141C22×#168C2311yescharacteristic
142C22×#168C2311yescharacteristic
143#4036—28no—
144#4034—28no—
145#4024—28no—
146#4024—28no—
147#4016—22no—
148#4016—22no—
149#4016C2314yes—
150#4016C2314yes—
151#4015—22no—
152#4015—22no—
153#4015C2314yes—
154#4015C2314yes—
155#3967C2314yes—
156#3967C2314yes—
157#3967C2314yes—
158#3967C2314yes—
159#3967C2314yes—
160#3967C2314yes—
161#3967C2314yes—
162#3967C2314yes—
163C22⋊#168C2314yes—
164C22⋊#168C2314yes—
165#3940C2314yes—
166#3940C2314yes—
167#3940C2314yes—
168#3940C2314yes—
169#3939C2314yes—
170#3939C2314yes—
171#3939C2314yes—
172#3939C2314yes—
173C4⋊#168C2314yes—
174C4⋊#168C2314yes—
175#3935C2314yes—
176C4×#168C2314yes—
177C2×#544—51no—
178C2×#541D511yescharacteristic
179#3242—516no—
180C2×#501—51no—
181C2×#499—51no—
182C2×#491—51no—
183C2×#487—51no—
184C2×#484—51no—
185C2×#485—51no—
186C2×#485—51no—
187C2×#483—51no—
188C2×#479—51no—
189C2×#479—51no—
190C2×#477—51no—
191C2×#475—51no—
192C2×#433—51no—
193C24×C5C2×D411yescharacteristic
194C2×C5×Q8—21no—
195C2×C5×Q8—21no—
196C2×C5×Q8—22no—
197C2×C5×Q8—22no—
198C2×C5×Q8—22no—
199C2×C5×Q8—22no—
200C2×C5×Q8C2412yes—
201C2×C5×Q8C2412yes—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D411yescharacteristic
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D412yes—
214C22×C4×C5C2412yes—
215C22×C4×C5C2411yescharacteristic
216C22×Dic5—21no—
217C22×Dic5—21no—
218C22×Dic5—21no—
219C22×Dic5—21no—
220C22×Dic5—24no—
221C22×Dic5—82no—
222C2×Dic10—24no—
223C2×Dic10—24no—
224C2×Dic10—82no—
225C2×Dic10—82no—
226C5×C4⋊C4—24no—
227C5×C4⋊C4—24no—
228C5×C4⋊C4—24no—
229C5×C4⋊C4—24no—
230C5×C4⋊C4—24no—
231C5×C4⋊C4—24no—
232C5×C4⋊C4—24no—
233C5×C4⋊C4—24no—
234C5×C4⋊C4—21no—
235C5×C4⋊C4—21no—
236C5×C4⋊C4C2×D414yes—
237C5×C4⋊C4C2×D414yes—
238C5×C4⋊C4C2412yes—
239C5×C4⋊C4C2412yes—
240C5×C22⋊C4—24no—
241C5×C22⋊C4—24no—
242C5×C22⋊C4C2×D414yes—
243C5×C22⋊C4C2×D414yes—
244C42×C5—24no—
245C42×C5—24no—
246C42×C5C2×D412yes—
247C42×C5C2×D412yes—
248C42×C5C2412yes—
249C42×C5C2412yes—
250C22⋊Dic5—24no—
251C4⋊Dic5—21no—
252C4⋊Dic5—21no—
253C4⋊Dic5—21no—
254C4⋊Dic5—24no—
255C4⋊Dic5—24no—
256C4⋊Dic5—21no—
257C4⋊Dic5—24no—
258C4⋊Dic5C2412yes—
259C4⋊Dic5C2412yes—
260C4⋊Dic5C2412yes—
261C4⋊Dic5C2412yes—
262#683—24no—
263#683—24no—
264#683—24no—
265#683—24no—
266C4×Dic5—24no—
267C2×#168—22no—
268C2×#168—22no—
269C2×#168—22no—
270C2×#168—22no—
271C2×#168C2412yes—
272C2×#168C2412yes—
273C2×#168C2412yes—
274C2×#168C2412yes—
275#544—58no—
276#544—104no—
277#541—24no—
278#541C2×D518yes—
279C2×C4⋊Q8—51no—
280C2×C4⋊Q8—51no—
281C2×C4⋊Q8—101no—
282C2×C4⋊Q8C2×D511yescharacteristic
283C2×#126—21no—
284C2×#126—21no—
285C2×#125—21no—
286C2×#125—21no—
287C2×#125—51no—
288C2×#125—51no—
289C2×#125—101no—
290C2×#125C2×D511yescharacteristic
291C2×C22⋊Q8—101no—
292C2×C22⋊Q8—101no—
293C2×C22⋊Q8C2×D511yescharacteristic
294C2×C22⋊Q8C2×D511yescharacteristic
295C2×C4×Q8C2×D511yescharacteristic
296C2×C4×Q8C2×D511yescharacteristic
297C2×#117—51no—
298C2×#117C2×D511yescharacteristic
299C22×C4⋊C4—51no—
300#501—58no—
301#499—58no—
302#491—58no—
303#487—58no—
304#485—58no—
305#485—58no—
306#484—58no—
307#483—58no—
308#479—58no—
309#479—58no—
310#477—58no—
311#475—58no—
312#433—58no—
313C2×#107—51no—
314C2×#107—51no—
315C2×#107—51no—
316C2×#107—51no—
317C2×#106—51no—
318C2×#106—51no—
319C2×#106—51no—
320C2×#106—51no—
321C2×C4⋊C8—51no—
322C2×C4⋊C8—51no—
323C2×#103—51no—
324C2×#103—51no—
325C2×#103—51no—
326C2×#103—51no—
327C2×#103—51no—
328C2×#103—51no—
329C2×#103—51no—
330C2×#103—51no—
331C2×C22⋊C8—51no—
332C2×C22⋊C8—51no—
333C2×#97—51no—
334C2×C4×C8—51no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5C22×D412yes—
339C23×C5C22×D411yescharacteristic
340C5×Q8—22no—
341C5×Q8—22no—
342C5×Q8—22no—
343C5×Q8—22no—
344C5×Q8—42no—
345C5×Q8—42no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—24no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—42no—
359C2×C4×C5—42no—
360C2×C4×C5—42no—
361C2×C4×C5—42no—
362C2×C4×C5C22×D412yes—
363C2×C4×C5C22×D412yes—
364C2×C4×C5C22×D412yes—
365C2×C4×C5C22×D412yes—
366C2×C4×C5C22×D412yes—
367C2×C4×C5C22×D411yescharacteristic
368C2×C4×C52−1+412yes—
369C2×C4×C52−1+412yes—
370C2×C4×C5C2511yescharacteristic
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—42no—
376C2×Dic5—42no—
377C2×Dic5—42no—
378C2×Dic5—42no—
379C2×Dic5—84no—
380Dic10—84no—
381Dic10—84no—
382#168—22no—
383#168—22no—
384#168—22no—
385#168—22no—
386C22×Q8—101no—
387C22×Q8—101no—
388C22×Q8C22×D511yescharacteristic
389C22×Q8C22×D511yescharacteristic
390C23×C4—101no—
391C23×C4C22×D511yescharacteristic
392C22×C8—51no—
393C22×C8—51no—
394C22×C8—51no—
395C22×C8—51no—
396C4⋊Q8—22no—
397C4⋊Q8—54no—
398C4⋊Q8—54no—
399C4⋊Q8—108no—
400C4⋊Q8—102no—
401C4⋊Q8—102no—
402C4⋊Q8C22×D514yes—
403#126—28no—
404#126—28no—
405#125—28no—
406#125—28no—
407#125—22no—
408#125—54no—
409#125—54no—
410#125—108no—
411#125—102no—
412#125—102no—
413#125C22×D514yes—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—108no—
417C22⋊Q8—108no—
418C22⋊Q8C22×D514yes—
419C22⋊Q8C22×D514yes—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8C22×D514yes—
423C4×Q8C22×D514yes—
424#117—54no—
425#117—102no—
426#117C22⋊D514yes—
427#117C22×D514yes—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—51no—
437C2×C4⋊C4—51no—
438C2×C4⋊C4—54no—
439C2×C4⋊C4—51no—
440C2×C4⋊C4—51no—
441C2×C4⋊C4—101no—
442C2×C4⋊C4—102no—
443C2×C4⋊C4—101no—
444C2×C4⋊C4—101no—
445C2×C4⋊C4—101no—
446C2×C4⋊C4—101no—
447C2×C4⋊C4—101no—
448C2×C4⋊C4—101no—
449C2×C4⋊C4C22⋊D511yescharacteristic
450C2×C4⋊C4C22⋊D511yescharacteristic
451C2×C4⋊C4C22×D511yescharacteristic
452C2×C4⋊C4C22×D511yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—101no—
456C2×C22⋊C4C22⋊D511yescharacteristic
457C2×C22⋊C4C22⋊D511yescharacteristic
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—101no—
461C2×C42C22×D511yescharacteristic
462C2×C42C22×D511yescharacteristic
463#107—54no—
464#107—54no—
465#107—54no—
466#107—54no—
467#106—54no—
468#106—54no—
469#106—54no—
470#106—54no—
471C4⋊C8—54no—
472C4⋊C8—54no—
473#103—54no—
474#103—54no—
475#103—54no—
476#103—54no—
477#103—54no—
478#103—54no—
479#103—54no—
480#103—54no—
481C22⋊C8—54no—
482C22⋊C8—54no—
483#97—54no—
484C4×C8—54no—
485C22×C5—22no—
486C22×C5—22no—
487C22×C5—22no—
488C22×C5—44no—
489C22×C5#53612yes—
490C22×C5#57712yes—
491C22×C5#57812yes—
492C22×C5C23×D411yescharacteristic
493C4×C5—22no—
494C4×C5—22no—
495C4×C5—22no—
496C4×C5—22no—
497C4×C5—22no—
498C4×C5—42no—
499C4×C5—42no—
500C4×C5—42no—
501C4×C5—42no—
502C4×C5#53612yes—
503C4×C5C2×2−1+411yescharacteristic
504C4×C5C2×2−1+411yescharacteristic
505Dic5—42no—
506Dic5—42no—
507Dic5—42no—
508Dic5—42no—
509C24C2×C22⋊D511yescharacteristic
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—104no—
517C2×Q8—104no—
518C2×Q8—402no—
519C2×Q8—402no—
520C2×Q8C23×D512yes—
521C2×Q8C23×D512yes—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—101no—
529C22×C4—101no—
530C22×C4—101no—
531C22×C4—101no—
532C22×C4—104no—
533C22×C4—402no—
534C22×C4C2×C22⋊D512yes—
535C22×C4C2×C22⋊D511yescharacteristic
536C22×C4C2×C22⋊D511yescharacteristic
537C22×C4C2×C22⋊D511yescharacteristic
538C22×C4C2×C22⋊D511yescharacteristic
539C22×C4C2×C22⋊D511yescharacteristic
540C22×C4C23×D512yes—
541C22×C4C23×D511yescharacteristic
542C2×C8—52no—
543C2×C8—52no—
544C2×C8—52no—
545C2×C8—52no—
546C2×C8—102no—
547C2×C8—102no—
548C2×C8—102no—
549C2×C8—102no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—52no—
561C4⋊C4—52no—
562C4⋊C4—52no—
563C4⋊C4—52no—
564C4⋊C4—104no—
565C4⋊C4—101no—
566C4⋊C4—101no—
567C4⋊C4—101no—
568C4⋊C4—101no—
569C4⋊C4—104no—
570C4⋊C4—104no—
571C4⋊C4—104no—
572C4⋊C4—104no—
573C4⋊C4—104no—
574C4⋊C4—104no—
575C4⋊C4C2×C22⋊D514yes—
576C4⋊C4C2×C22⋊D514yes—
577C4⋊C4C23×D512yes—
578C4⋊C4C23×D512yes—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—104no—
582C22⋊C4C2×C22⋊D514yes—
583C22⋊C4C2×C22⋊D514yes—
584C42—24no—
585C42—24no—
586C42—104no—
587C42C2×C22⋊D512yes—
588C42C2×C22⋊D512yes—
589C42C23×D512yes—
590C42C23×D512yes—
591C2×C5—42no—
592C2×C5#324214yescomplemented
593C2×C5C2×#53611yescharacteristic
594C2×C5C2×#57711yescharacteristic
595C2×C5C2×#57811yescharacteristic
596C23—22no—
597C23—22no—
598C23—22no—
599C23C22×C22⋊D512yes—
600C23C22×C22⋊D511yescharacteristic
601Q8—22no—
602Q8—22no—
603Q8—22no—
604Q8—22no—
605Q8—42no—
606Q8—42no—
607Q8—404no—
608Q8—404no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—102no—
626C2×C4—102no—
627C2×C4—102no—
628C2×C4—102no—
629C2×C4—202no—
630C2×C4—202no—
631C2×C4—202no—
632C2×C4—202no—
633C2×C4—404no—
634C2×C4#415012yes—
635C2×C4#415012yes—
636C2×C4C22×C22⋊D512yes—
637C2×C4C22×C22⋊D512yes—
638C2×C4C22×C22⋊D512yes—
639C2×C4C22×C22⋊D512yes—
640C2×C4C22×C22⋊D512yes—
641C2×C4C22×C22⋊D511yescharacteristic
642C2×C4C24×D511yescharacteristic
643C8—102no—
644C8—102no—
645C8—102no—
646C8—102no—
647C5C2×#324211yescharacteristic, complemented, Sylow
648C22—22no—
649C22—22no—
650C22—22no—
651C22—44no—
652C22#6615912yes—
653C22#6617112yes—
654C22#6617212yes—
655C22C23×C22⋊D511yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—22no—
660C4—22no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—42no—
665C4—202no—
666C4—202no—
667C4—202no—
668C4—202no—
669C4#6615912yes—
670C4C2×#415011yescharacteristic
671C4C2×#415011yescharacteristic
672C2—42no—
673C2#1061517314yesdirect product factor
674C2C2×#6615911yescharacteristic
675C2C2×#6617111yescharacteristic
676C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#541C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
hypercenterC2×#541D5
hypocenterC5C2×#3242
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
3. #10615173C2direct (N × H)
4. C2×#65371C2semidirect
5. C2×#65370C2semidirect
6. C2×#65354C2semidirect
7. C2×#65353C2semidirect
12. C2×#65311C2semidirect
13. C2×#65311C2semidirect
14. C2×#65310C2semidirect
15. C2×#65309C2semidirect
52. #65371C22semidirect
53. #65370C22semidirect
54. #65354C22semidirect
55. #65353C22semidirect
60. #65311C22semidirect
61. #65311C22semidirect
62. #65310C22semidirect
63. #65309C22semidirect
592. C2×C5#3242semidirect
647. C5C2×#3242semidirect
673. C2#10615173direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5412
C2×#658532
#106151732
C2×#653712
C2×#653702
C2×#653542
C2×#653532
C2×#653332
C2×#653342
C2×#653322
C2×#653112
C2×#653102
C2×#653092
C2×#652892
C2×#32425