Finite Group Databasebeta

← D3×#65238 #14332008

Subgroups — D3×#65238 #14332008

Order 1920.

1816 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×C22⋊C4C211yesmaximal, characteristic
2C2×D3×C22⋊Dic5C212yesmaximal
3C2×D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
4C2×D3×#683C212yesmaximal, complemented
5#11751050C211yesmaximal, characteristic, complemented
6C3×#65238C211yesmaximal, characteristic, complemented
7#11749505C212yesmaximal, complemented
8D3×#3963C211yesmaximal, characteristic, complemented
9#11748798C211yesmaximal, characteristic, complemented
10#11748762C211yesmaximal, characteristic, complemented
11#11748749C212yesmaximal, complemented
12C2×#65238—31nomaximal, Hall
13C24×C5×D3C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C22×D3×Dic5C2212yes—
17C22×D3×Dic5C2212yes—
18C2×C3×C5×C22⋊C4C2211yescharacteristic
19C2×#6719C2212yes—
20C2×C4⋊Dic15C2211yescharacteristic, complemented
21C2×#6712C2212yescomplemented
22C2×C5×#217C2211yescharacteristic
23C2×C5×(C2×D3)⋊C4C2211yescharacteristic
24C2×C5×(C2×D3)⋊C4C2211yescharacteristic
25C5×D3×C22⋊C4—24no—
26C2×C3×C22⋊Dic5C2212yes—
27C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
28C2×C3×#683C2212yescomplemented
29D3×C22⋊Dic5—28no—
30C2×Dic3⋊Dic5C2212yescomplemented
31C2×#6669C2212yescomplemented
32C2×#6668C2212yescomplemented
33C2×(C2×D3)⋊Dic5C2212yes—
34C2×(C2×D3)⋊Dic5C2212yes—
35D3×C4⋊Dic5—24no—
36D3×#683—28no—
37#91115C2211yescharacteristic, complemented
38C3×#3963C2211yescharacteristic, complemented
39#90994C2212yescomplemented
40D3×#399—51nomaximal, Hall
41C22×C5×C22⋊C4—31no—
42C22×C22⋊Dic5—32no—
43C22×C4⋊Dic5—31no—
44C22×#683—32no—
45C2×#3963—31no—
46#65238—31no—
47#65238—32no—
48#65238—31no—
49#65238—31no—
50#65238—32no—
51#65238D311yescharacteristic, direct product factor
52C24×C3×C5C2311yescharacteristic
53C23×C5×D3—22no—
54C23×C5×D3—24no—
55C23×C5×D3—22no—
56C23×C5×D3—24no—
57C23×C5×D3Q814yes—
58C23×C5×D3C2311yescharacteristic
59C23×C5×D3C2311yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C22×Dic15C2312yes—
63C22×Dic15C2312yes—
64C22×C5×Dic3C2311yescharacteristic
65C22×C5×Dic3C2311yescharacteristic
66C2×C4×C5×D3—24no—
67C2×C4×C5×D3—24no—
68C2×C4×C5×D3—22no—
69C2×C4×C5×D3D414yes—
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2312yes—
72C2×D3×Dic5—24no—
73C2×D3×Dic5—24no—
74C2×D3×Dic5—24no—
75C2×D3×Dic5—24no—
76C2×D3×Dic5—24no—
77C2×D3×Dic5D418yes—
78C3×C5×C22⋊C4—22no—
79#6719—24no—
80C4⋊Dic15—22no—
81#6712—24no—
82C5×#217—22no—
83C5×(C2×D3)⋊C4—22no—
84C5×(C2×D3)⋊C4—22no—
85C3×C22⋊Dic5—24no—
86C3×C4⋊Dic5—22no—
87C3×#683—24no—
88Dic3⋊Dic5—24no—
89#6669—24no—
90#6668—24no—
91(C2×D3)⋊Dic5—24no—
92(C2×D3)⋊Dic5—24no—
93C2×D3×C4⋊C4—52no—
94C2×D3×C4⋊C4—51no—
95C2×D3×C22⋊C4—52no—
96C2×D3×C22⋊C4D511yescharacteristic
97C3×#399—51no—
98#4993—52no—
99#4993—51no—
100#4949—51no—
101#4949—52no—
102#4677—51no—
103D3×#95—51no—
104C25×C5—31no—
105C23×C4×C5—31no—
106C23×C4×C5—31no—
107C23×Dic5—32no—
108C23×Dic5—32no—
109C2×C5×C22⋊C4—31no—
110C2×C5×C22⋊C4—31no—
111C2×C5×C22⋊C4—31no—
112C2×C5×C22⋊C4—64no—
113C2×C5×C22⋊C4C2×D311yescharacteristic
114C2×C22⋊Dic5—32no—
115C2×C22⋊Dic5—32no—
116C2×C22⋊Dic5—32no—
117C2×C22⋊Dic5—68no—
118C2×C22⋊Dic5C2×D312yes—
119C2×C4⋊Dic5—31no—
120C2×C4⋊Dic5—32no—
121C2×C4⋊Dic5—64no—
122C2×C4⋊Dic5C2×D311yescharacteristic, complemented
123C2×#683—32no—
124C2×#683—32no—
125C2×#683—32no—
126C2×#683—68no—
127C2×#683C2×D312yescomplemented
128#3963—31no—
129#3963—32no—
130#3963C2×D311yescharacteristic, complemented
131C2×#399—151noSylow
132C23×C3×C5—22no—
133C23×C3×C5—21no—
134C23×C3×C5—21no—
135C23×C3×C5—22no—
136C23×C3×C5C2×Q812yes—
137C23×C3×C5C2411yescharacteristic
138C22×C5×D3—22no—
139C22×C5×D3—21no—
140C22×C5×D3—21no—
141C22×C5×D3—22no—
142C22×C5×D3—216no—
143C22×C5×D3—28no—
144C22×C5×D3—48no—
145C22×C5×D3—44no—
146C22×C5×D3—44no—
147C22×C5×D3C2×D414yes—
148C22×C5×D3C2×D412yes—
149C22×C5×D3C2×Q812yes—
150C22×C5×D3C2×Q812yes—
151C22×C5×D3#4112yes—
152C22×C5×D3#4114yes—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5C2×D412yes—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15—22no—
161C2×Dic15—22no—
162C2×Dic15C2×D414yes—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—21no—
166C2×C5×Dic3C2×D412yes—
167C4×C5×D3—28no—
168C4×C5×D3—44no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5C2×D414yes—
175D3×Dic5—216no—
176D3×Dic5—48no—
177C24×D3C2×D511yescharacteristic
178C22×C4×D3—52no—
179C22×C4×D3—52no—
180C22×C4×D3C2×D511yescharacteristic
181C22×C4×D3C2×D511yescharacteristic
182C2×C3×C4⋊C4—52no—
183C2×C3×C4⋊C4—51no—
184C2×C3×C22⋊C4—52no—
185C2×C3×C22⋊C4C2×D511yescharacteristic
186C2×#217—52no—
187C2×#217C2×D511yescharacteristic
188C2×(C2×D3)⋊C4—52no—
189C2×(C2×D3)⋊C4—52no—
190C2×(C2×D3)⋊C4C2×D511yescharacteristic
191C2×(C2×D3)⋊C4C2×D511yescharacteristic
192C2×C4⋊Dic3—51no—
193C2×C4⋊Dic3—52no—
194C2×Dic3⋊C4—52no—
195C2×Dic3⋊C4—52no—
196C2×Dic3⋊C4—52no—
197D3×C4⋊C4—108no—
198D3×C4⋊C4—104no—
199D3×C22⋊C4—24no—
200D3×C22⋊C4—108no—
201C3×#95—51no—
202C3⋊#95—51no—
203C3⋊#95—52no—
204C24×C5—31no—
205C24×C5—34no—
206C24×C5—31no—
207C24×C5—64no—
208C24×C5—62no—
209C24×C5—62no—
210C24×C5—64no—
211C24×C5C22×D311yescharacteristic
212C22×C4×C5—31no—
213C22×C4×C5—34no—
214C22×C4×C5—31no—
215C22×C4×C5—64no—
216C22×C4×C5—62no—
217C22×C4×C5—64no—
218C22×C4×C5C22×D311yescharacteristic
219C22×C4×C5C22×D311yescharacteristic
220C22×Dic5—32no—
221C22×Dic5—38no—
222C22×Dic5—32no—
223C22×Dic5—64no—
224C22×Dic5—64no—
225C22×Dic5—64no—
226C22×Dic5—64no—
227C22×Dic5—64no—
228C22×Dic5C22×D312yes—
229C22×Dic5C22×D312yes—
230C5×C22⋊C4—22no—
231C5×C22⋊C4—62no—
232C5×C22⋊C4—62no—
233C5×C22⋊C4—62no—
234C22⋊Dic5—24no—
235C22⋊Dic5—64no—
236C22⋊Dic5—64no—
237C22⋊Dic5—64no—
238C4⋊Dic5—22no—
239C4⋊Dic5—64no—
240C4⋊Dic5—62no—
241#683—24no—
242#683—64no—
243#683—64no—
244#683—64no—
245C22×C4⋊C4—152no—
246C22×C4⋊C4—151no—
247C22×C22⋊C4—31no—
248C22×C22⋊C4—152no—
249#399—51no—
250#399—151no—
251#399—152no—
252#399—152no—
253#399—151no—
254#399—151no—
255C2×#95—151no—
256C22×C3×C5—24no—
257C22×C3×C5—22no—
258C22×C3×C5—42no—
259C22×C3×C5—41no—
260C22×C3×C5—41no—
261C22×C3×C5C22×D412yes—
262C22×C3×C5C22×D411yescharacteristic
263C22×C3×C5C22×Q811yescharacteristic
264C22×C3×C5C2×#4111yescharacteristic
265C22×C3×C5C2×#4112yes—
266C2×C5×D3—24no—
267C2×C5×D3—22no—
268C2×C5×D3—42no—
269C2×C5×D3—41no—
270C2×C5×D3—41no—
271C2×C5×D3—416no—
272C2×C5×D3C22⋊Q818yes—
273C2×C5×D3C22⋊Q814yes—
274C2×C5×D3#12318yes—
275C2×C5×D3#12314yes—
276C2×C5×D3#12714yes—
277C3×C4×C5—22no—
278C3×C4×C5—41no—
279Dic15—24no—
280Dic15—42no—
281C3×Dic5—24no—
282C3×Dic5—42no—
283C5×Dic3—22no—
284C5×Dic3—41no—
285C24×C3C22×D511yescharacteristic
286C23×D3—22no—
287C23×D3—24no—
288C23×D3—24no—
289C23×D3—22no—
290C23×D3Dic1014yes—
291C23×D3C22×D511yescharacteristic
292C23×D3C22×D511yescharacteristic
293C22×C3×C4—52no—
294C22×C3×C4—52no—
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D511yescharacteristic
297C22×Dic3—52no—
298C22×Dic3—52no—
299C22×Dic3C22×D511yescharacteristic
300C22×Dic3C22×D511yescharacteristic
301C2×C4×D3—24no—
302C2×C4×D3—24no—
303C2×C4×D3—22no—
304C2×C4×D3—58no—
305C2×C4×D3—104no—
306C2×C4×D3—104no—
307C2×C4×D3—104no—
308C2×C4×D3—104no—
309C2×C4×D3—104no—
310C2×C4×D3C22⋊D514yes—
311C3×C4⋊C4—104no—
312C3×C4⋊C4—102no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—104no—
315#217—22no—
316#217—104no—
317(C2×D3)⋊C4—22no—
318(C2×D3)⋊C4—22no—
319(C2×D3)⋊C4—104no—
320(C2×D3)⋊C4—104no—
321C4⋊Dic3—104no—
322C4⋊Dic3—102no—
323Dic3⋊C4—104no—
324Dic3⋊C4—104no—
325Dic3⋊C4—104no—
326C23×C5—22no—
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—22no—
330C23×C5—34no—
331C23×C5—32no—
332C23×C5—32no—
333C23×C5—32no—
334C23×C5—34no—
335C23×C5—32no—
336C23×C5—616no—
337C23×C5—68no—
338C23×C5—62no—
339C23×C5—61no—
340C23×C5—61no—
341C23×C5—62no—
342C23×C5—128no—
343C23×C5—124no—
344C23×C5—124no—
345C23×C5D3×Q812yes—
346C23×C5C23×D311yescharacteristic
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—21no—
350C2×C4×C5—32no—
351C2×C4×C5—68no—
352C2×C4×C5—62no—
353C2×C4×C5—62no—
354C2×C4×C5—61no—
355C2×C4×C5—124no—
356C2×C4×C5D3×D412yes—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—34no—
363C2×Dic5—616no—
364C2×Dic5—62no—
365C2×Dic5—62no—
366C2×Dic5—62no—
367C2×Dic5—62no—
368C2×Dic5—62no—
369C2×Dic5—128no—
370C2×Dic5D3×D414yes—
371C25—31no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—152no—
375C23×C4—152no—
376C2×C4⋊C4—52no—
377C2×C4⋊C4—51no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—152no—
380C2×C4⋊C4—152no—
381C2×C4⋊C4—152no—
382C2×C4⋊C4—151no—
383C2×C4⋊C4—304no—
384C2×C4⋊C4—308no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—31no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—52no—
389C2×C22⋊C4—64no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C22⋊C4—152no—
393C2×C22⋊C4—308no—
394C2×C22⋊C4D3×D511yescharacteristic
395#95—51no—
396#95—152no—
397#95—151no—
398C2×C3×C5—42no—
399C2×C3×C5C2×C22⋊Q812yes—
400C2×C3×C5C2×C22⋊Q811yescharacteristic
401C2×C3×C5C2×#12312yes—
402C2×C3×C5C2×#12311yescharacteristic
403C2×C3×C5C2×#12711yescharacteristic
404C5×D3—42no—
405C5×D3#39918yescomplemented
406C23×C3—21no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—21no—
410C23×C3C2×Dic1012yes—
411C23×C3C23×D511yescharacteristic
412C22×D3—21no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—21no—
416C22×D3—216no—
417C22×D3—28no—
418C22×D3—48no—
419C22×D3—44no—
420C22×D3—44no—
421C22×D3C2×Dic1012yes—
422C22×D3C2×Dic1012yes—
423C22×D3#70912yes—
424C22×D3D4×D514yes—
425C22×D3#71114yes—
426C22×D3C2×C22⋊D512yes—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—54no—
431C2×C3×C4—102no—
432C2×C3×C4—102no—
433C2×C3×C4—102no—
434C2×C3×C4—102no—
435C2×C3×C4—102no—
436C2×C3×C4C2×C22⋊D512yes—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—21no—
440C2×Dic3—54no—
441C2×Dic3—102no—
442C2×Dic3—102no—
443C2×Dic3—102no—
444C2×Dic3—102no—
445C2×Dic3—102no—
446C2×Dic3C2×C22⋊D512yes—
447C4×D3—28no—
448C4×D3—44no—
449C4×D3—1016no—
450C4×D3—208no—
451C22×C5—22no—
452C22×C5—24no—
453C22×C5—38no—
454C22×C5—34no—
455C22×C5—34no—
456C22×C5—34no—
457C22×C5—38no—
458C22×C5—41no—
459C22×C5—42no—
460C22×C5—41no—
461C22×C5—62no—
462C22×C5—64no—
463C22×C5—1216no—
464C22×C5—121no—
465C22×C5—122no—
466C22×C5—121no—
467C22×C5C2×D3×D412yes—
468C22×C5C2×D3×D411yescharacteristic
469C22×C5C2×D3×Q811yescharacteristic
470C22×C5D3×#4111yescharacteristic
471C22×C5D3×#4112yes—
472C4×C5—22no—
473C4×C5—41no—
474C4×C5—62no—
475C4×C5—121no—
476Dic5—24no—
477Dic5—42no—
478Dic5—64no—
479Dic5—122no—
480C24—31no—
481C24—34no—
482C24—31no—
483C24—62no—
484C24—64no—
485C24—62no—
486C24—64no—
487C24C2×D3×D511yescharacteristic
488C22×C4—31no—
489C22×C4—34no—
490C22×C4—31no—
491C22×C4—52no—
492C22×C4—52no—
493C22×C4—64no—
494C22×C4—62no—
495C22×C4—64no—
496C22×C4—158no—
497C22×C4—152no—
498C22×C4—152no—
499C22×C4—304no—
500C22×C4—304no—
501C22×C4—304no—
502C22×C4—304no—
503C22×C4—304no—
504C22×C4C2×D3×D511yescharacteristic
505C22×C4C2×D3×D511yescharacteristic
506C4⋊C4—104no—
507C4⋊C4—102no—
508C4⋊C4—304no—
509C4⋊C4—304no—
510C4⋊C4—304no—
511C4⋊C4—304no—
512C4⋊C4—302no—
513C22⋊C4—22no—
514C22⋊C4—62no—
515C22⋊C4—62no—
516C22⋊C4—62no—
517C22⋊C4—104no—
518C22⋊C4—304no—
519C22⋊C4—304no—
520C22⋊C4—304no—
521C3×C5C2×#39911yescharacteristic, complemented, Hall
522C22×C3—24no—
523C22×C3—22no—
524C22×C3—42no—
525C22×C3—41no—
526C22×C3—41no—
527C22×C3C22×Dic1011yescharacteristic
528C22×C3C2×#70911yescharacteristic
529C22×C3C2×D4×D512yes—
530C22×C3C2×#71112yes—
531C22×C3C22×C22⋊D511yescharacteristic
532C2×D3—24no—
533C2×D3—22no—
534C2×D3—42no—
535C2×D3—41no—
536C2×D3—41no—
537C2×D3—416no—
538C2×D3#402418yes—
539C2×D3#402918yes—
540C2×D3#407014yes—
541C2×D3#408114yes—
542C2×D3#408614yes—
543C3×C4—22no—
544C3×C4—41no—
545C3×C4—104no—
546C3×C4—202no—
547Dic3—22no—
548Dic3—41no—
549Dic3—104no—
550Dic3—202no—
551C2×C5—38no—
552C2×C5—42no—
553C2×C5—122no—
554C2×C5D3×C22⋊Q811yescharacteristic
555C2×C5D3×C22⋊Q812yes—
556C2×C5D3×#12311yescharacteristic
557C2×C5D3×#12312yes—
558C2×C5D3×#12711yescharacteristic
559C23—21no—
560C23—22no—
561C23—22no—
562C23—21no—
563C23—32no—
564C23—32no—
565C23—34no—
566C23—34no—
567C23—32no—
568C23—32no—
569C23—68no—
570C23—616no—
571C23—61no—
572C23—62no—
573C23—62no—
574C23—61no—
575C23—124no—
576C23—124no—
577C23—128no—
578C23D3×Dic1012yes—
579C23C22×D3×D511yescharacteristic
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—32no—
584C2×C4—54no—
585C2×C4—68no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—61no—
589C2×C4—102no—
590C2×C4—102no—
591C2×C4—102no—
592C2×C4—102no—
593C2×C4—102no—
594C2×C4—124no—
595C2×C4—154no—
596C2×C4—3016no—
597C2×C4—302no—
598C2×C4—302no—
599C2×C4—302no—
600C2×C4—302no—
601C2×C4—302no—
602C2×C4—608no—
603C2×C4D3×C22⋊D512yes—
604C2×C3—42no—
605C2×C3C2×#402412yes—
606C2×C3C2×#402912yes—
607C2×C3C2×#407011yescharacteristic
608C2×C3C2×#408111yescharacteristic
609C2×C3C2×#408611yescharacteristic
610D3—42no—
611D3#6523818yesdirect product factor
612C5D3×#39911yescharacteristic, complemented, Sylow
613C22—22no—
614C22—24no—
615C22—34no—
616C22—34no—
617C22—34no—
618C22—38no—
619C22—38no—
620C22—41no—
621C22—41no—
622C22—42no—
623C22—62no—
624C22—64no—
625C22—1216no—
626C22—121no—
627C22—121no—
628C22—122no—
629C22C2×D3×Dic1011yescharacteristic
630C22D3×#70911yescharacteristic
631C22D3×D4×D512yes—
632C22D3×#71112yes—
633C22C2×D3×C22⋊D511yescharacteristic
634C4—22no—
635C4—41no—
636C4—62no—
637C4—104no—
638C4—121no—
639C4—202no—
640C4—304no—
641C4—602no—
642C3C2×#6523811yescharacteristic, complemented, Sylow
643C2—38no—
644C2—42no—
645C2—122no—
646C2D3×#402412yes—
647C2D3×#402912yes—
648C2D3×#407011yescharacteristic
649C2D3×#408111yescharacteristic
650C2D3×#408611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FittingC2×C3×C5×C22⋊C4C22
prime radicalC24×C5×D3C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#399
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×D3×C4⋊Dic5C2semidirect
4. C2×D3×#683C2semidirect
5. #11751050C2semidirect
6. C3×#65238C2semidirect
7. #11749505C2semidirect
8. D3×#3963C2semidirect
9. #11748798C2semidirect
10. #11748762C2semidirect
11. #11748749C2semidirect
20. C2×C4⋊Dic15C22semidirect
21. C2×#6712C22semidirect
27. C2×C3×C4⋊Dic5C22semidirect
28. C2×C3×#683C22semidirect
30. C2×Dic3⋊Dic5C22semidirect
31. C2×#6669C22semidirect
32. C2×#6668C22semidirect
37. #91115C22semidirect
38. C3×#3963C22semidirect
39. #90994C22semidirect
51. #65238D3direct (N × H)
122. C2×C4⋊Dic5C2×D3semidirect
127. C2×#683C2×D3semidirect
130. #3963C2×D3semidirect
405. C5×D3#399semidirect
521. C3×C5C2×#399semidirect
611. D3#65238direct (N × H)
612. C5D3×#399semidirect
642. C3C2×#65238semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×C22⋊C42
C2×D3×C22⋊Dic52
C2×D3×C4⋊Dic52
C2×D3×#6832
#117510502
C3×#652382
#117495052
D3×#39632
#117487982
#117487622
#117487492
C2×#652383
D3×#3995