Finite Group Databasebeta

← C3×D5×#407 #14411622

Subgroups — C3×D5×#407 #14411622

Order 1920.

2016 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D5C211yesmaximal, characteristic
2C2×C3×D5×M16C212yesmaximal, complemented
3C3×C5×#407C211yesmaximal, characteristic, complemented
4C3×#65496C211yesmaximal, characteristic, complemented
5C3×#65415C212yesmaximal, complemented
6C3×#65015C214yesmaximal, complemented
7C3×D5×C22⋊C8C214yesmaximal, complemented
8D5×#407C311yesmaximal, characteristic, direct product factor, Hall
9C24×C3×D5C411yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×Dic5C411yescharacteristic
12C22×C3×C4×D5—28no—
13C22×C3×C4×D5C411yescharacteristic
14C22×C3×C4×D5C411yescharacteristic
15C22×C3×C4×D5C412yes—
16C22×C3×C4×D5C412yes—
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×C4×D5C2212yes—
19C22×C3×C4×D5C2212yes—
20C22×C3×C4×D5C2211yescharacteristic
21C2×C3×C5×M16C2212yescomplemented
22C2×C3×#681C2212yescomplemented
23C3×D5×M16—28no—
24C2×C3×#676C2214yescomplemented
25C2×C3×C8×D5C2214yescomplemented
26C3×C5×C22⋊C8C2214yescomplemented
27C3×C22⋊#168C2214yescomplemented
28C3×#3952C2218yescomplemented
29C2×C3×#407—51nomaximal, Hall
30C23×C4×D5C2×C311yescharacteristic
31C2×D5×M16C2×C312yescomplemented
32C5×#407C2×C311yescharacteristic, complemented
33#65496C2×C311yescharacteristic, complemented
34#65415C2×C312yescomplemented
35#65015C2×C314yescomplemented
36D5×C22⋊C8C2×C314yescomplemented
37C24×C3×C5C2×C411yescharacteristic
38C23×C3×D5—24no—
39C23×C3×D5—28no—
40C23×C3×D5C2×C411yescharacteristic
41C23×C3×D5C2×C412yes—
42C23×C3×D5C2×C411yescharacteristic
43C23×C3×D5C2×C412yes—
44C22×C3×C4×C5—24no—
45C22×C3×C4×C5C2×C411yescharacteristic
46C22×C3×C4×C5C2×C412yes—
47C22×C3×C4×C5C2312yes—
48C22×C3×C4×C5C2311yescharacteristic
49C22×C3×Dic5—24no—
50C22×C3×Dic5C2×C411yescharacteristic
51C22×C3×Dic5C2×C412yes—
52C22×C3×Dic5C2×C412yes—
53C22×C3×Dic5C2×C411yescharacteristic
54C2×C3×C4×D5—24no—
55C2×C3×C4×D5—24no—
56C2×C3×C4×D5—24no—
57C2×C3×C4×D5—28no—
58C2×C3×C4×D5—28no—
59C2×C3×C4×D5—28no—
60C2×C3×C4×D5—28no—
61C2×C3×C4×D5C2×C412yes—
62C2×C3×C4×D5C2×C412yes—
63C2×C3×C4×D5C2×C412yes—
64C2×C3×C4×D5C2×C412yes—
65C2×C3×C4×D5C2×C412yes—
66C2×C3×C4×D5C2×C411yescharacteristic
67C2×C3×C4×D5C2×C411yescharacteristic
68C2×C3×C4×D5D418yes—
69C2×C3×C4×D5C2312yes—
70C2×C3×C4×D5C2311yescharacteristic
71C2×C3×C4×D5C2311yescharacteristic
72C3×C5×M16—24no—
73C2×C3×C5×C8C2314yescomplemented
74C3×#681—24no—
75C2×C3×#168C2314yescomplemented
76C3×#676—28no—
77C3×C8×D5—28no—
78C24×C3×C4—51no—
79C22×C3×M16—52no—
80C3×#407—51no—
81C3×#407—52no—
82C3×#407—54no—
83C3×#407D511yescharacteristic, direct product factor
84C2×C3×C22⋊C8—54no—
85C24×D5C3×C411yescharacteristic
86C23×C4×C5C22×C311yescharacteristic
87C23×Dic5C3×C411yescharacteristic
88C22×C4×D5—28no—
89C22×C4×D5C3×C411yescharacteristic
90C22×C4×D5C3×C411yescharacteristic
91C22×C4×D5C3×C412yes—
92C22×C4×D5C3×C412yes—
93C22×C4×D5C22×C311yescharacteristic
94C22×C4×D5C22×C312yes—
95C22×C4×D5C22×C312yes—
96C22×C4×D5C22×C311yescharacteristic
97C2×C5×M16C22×C312yescomplemented
98C2×#681C22×C312yescomplemented
99D5×M16—28no—
100C2×#676C22×C314yescomplemented
101C2×C8×D5C22×C314yescomplemented
102C5×C22⋊C8C22×C314yescomplemented
103C22⋊#168C22×C314yescomplemented
104#3952C22×C318yescomplemented
105C2×#407—51noSylow
106C23×C3×C5—22no—
107C23×C3×C5—24no—
108C23×C3×C5C22×C411yescharacteristic
109C23×C3×C5C22×C412yes—
110C22×C3×D5—232no—
111C22×C3×D5—22no—
112C22×C3×D5—24no—
113C22×C3×D5—24no—
114C22×C3×D5—24no—
115C22×C3×D5—24no—
116C22×C3×D5—24no—
117C22×C3×D5—24no—
118C22×C3×D5—24no—
119C22×C3×D5C22⋊C414yes—
120C22×C3×D5M1618yescomplemented
121C22×C3×D5C22×C411yescharacteristic
122C22×C3×D5C22×C412yes—
123C22×C3×D5C22×C411yescharacteristic
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—24no—
126C2×C3×C4×C5—24no—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5C22×C411yescharacteristic
129C2×C3×C4×C5C2×D414yes—
130C2×C3×C4×C5C2411yescharacteristic
131C2×C3×Dic5—22no—
132C2×C3×Dic5—24no—
133C2×C3×Dic5—24no—
134C2×C3×Dic5C22⋊C414yes—
135C2×C3×Dic5C22×C412yes—
136C2×C3×Dic5C22×C411yescharacteristic
137C2×C3×Dic5C22×C411yescharacteristic
138C3×C4×D5—24no—
139C3×C4×D5—24no—
140C3×C4×D5—24no—
141C3×C4×D5—24no—
142C3×C4×D5—24no—
143C3×C4×D5—24no—
144C3×C4×D5C22⋊C414yes—
145C3×C4×D5C22⋊C414yes—
146C3×C4×D5C2×D414yes—
147C3×C4×D5C2×D414yes—
148C3×C5×C8—24no—
149C3×#168—24no—
150C25×C3—51no—
151C23×C3×C4—51no—
152C23×C3×C4—51no—
153C23×C3×C4—51no—
154C23×C3×C4—52no—
155C23×C3×C4—52no—
156C23×C3×C4—51no—
157C23×C3×C4—52no—
158C23×C3×C4—52no—
159C23×C3×C4—51no—
160C23×C3×C4—108no—
161C23×C3×C4C2×D511yescharacteristic
162C2×C3×M16—52no—
163C2×C3×M16—54no—
164C2×C3×M16—108no—
165C2×C3×M16C2×D512yescomplemented
166C22×C3×C8—54no—
167C3×C22⋊C8—54no—
168C3×C22⋊C8—58no—
169C3×C22⋊C8C2×D514yescomplemented
170C24×C5C2×C3×C411yescharacteristic
171C23×D5—24no—
172C23×D5—28no—
173C23×D5C2×C3×C411yescharacteristic
174C23×D5C2×C3×C412yes—
175C23×D5C2×C3×C411yescharacteristic
176C23×D5C2×C3×C412yes—
177C22×C4×C5—24no—
178C22×C4×C5C2×C3×C411yescharacteristic
179C22×C4×C5C2×C3×C412yes—
180C22×C4×C5C23×C312yes—
181C22×C4×C5C23×C311yescharacteristic
182C22×Dic5—24no—
183C22×Dic5C2×C3×C411yescharacteristic
184C22×Dic5C2×C3×C412yes—
185C22×Dic5C2×C3×C412yes—
186C22×Dic5C2×C3×C411yescharacteristic
187C2×C4×D5—24no—
188C2×C4×D5—24no—
189C2×C4×D5—24no—
190C2×C4×D5—28no—
191C2×C4×D5—28no—
192C2×C4×D5—28no—
193C2×C4×D5—28no—
194C2×C4×D5C2×C3×C412yes—
195C2×C4×D5C2×C3×C412yes—
196C2×C4×D5C2×C3×C412yes—
197C2×C4×D5C2×C3×C412yes—
198C2×C4×D5C2×C3×C412yes—
199C2×C4×D5C2×C3×C411yescharacteristic
200C2×C4×D5C2×C3×C411yescharacteristic
201C2×C4×D5C3×D418yes—
202C2×C4×D5C23×C312yes—
203C2×C4×D5C23×C311yescharacteristic
204C2×C4×D5C23×C311yescharacteristic
205C5×M16—24no—
206C2×C5×C8C23×C314yescomplemented
207#681—24no—
208C2×#168C23×C314yescomplemented
209#676—28no—
210C8×D5—28no—
211C24×C4—51no—
212C22×M16—52no—
213#407—51no—
214#407—52no—
215#407—54no—
216#407C3×D511yescharacteristic, direct product factor
217C2×C22⋊C8—54no—
218C22×C3×C5—28no—
219C22×C3×C5—22no—
220C22×C3×C5—22no—
221C22×C3×C5—22no—
222C22×C3×C5C2×C22⋊C412yes—
223C22×C3×C5C2×M1614yescomplemented
224C22×C3×C5C23×C411yescharacteristic
225C2×C3×D5—216no—
226C2×C3×D5—28no—
227C2×C3×D5—22no—
228C2×C3×D5—22no—
229C2×C3×D5—22no—
230C2×C3×D5—28no—
231C2×C3×D5—216no—
232C2×C3×D5C2×C22⋊C412yes—
233C2×C3×D5C2×C22⋊C412yes—
234C2×C3×D5C2×M1614yes—
235C2×C3×D5C2×M1614yescomplemented
236C3×C4×C5—22no—
237C3×C4×C5C2×C22⋊C412yes—
238C3×C4×C5C22×D412yes—
239C3×Dic5—22no—
240C3×Dic5C2×C22⋊C412yes—
241C3×Dic5C2×C22⋊C412yes—
242C24×C3—51no—
243C24×C3—52no—
244C24×C3—52no—
245C24×C3—51no—
246C24×C3—108no—
247C24×C3—104no—
248C24×C3C4×D511yescharacteristic
249C22×C3×C4—24no—
250C22×C3×C4—51no—
251C22×C3×C4—51no—
252C22×C3×C4—51no—
253C22×C3×C4—58no—
254C22×C3×C4—51no—
255C22×C3×C4—51no—
256C22×C3×C4—52no—
257C22×C3×C4—52no—
258C22×C3×C4—51no—
259C22×C3×C4—52no—
260C22×C3×C4—52no—
261C22×C3×C4—52no—
262C22×C3×C4—52no—
263C22×C3×C4—52no—
264C22×C3×C4—52no—
265C22×C3×C4—104no—
266C22×C3×C4—108no—
267C22×C3×C4—108no—
268C22×C3×C4—108no—
269C22×C3×C4—108no—
270C22×C3×C4—104no—
271C22×C3×C4—104no—
272C22×C3×C4—104no—
273C22×C3×C4C4×D511yescharacteristic
274C22×C3×C4C4×D512yes—
275C22×C3×C4C22×D512yes—
276C22×C3×C4C22×D511yescharacteristic
277C3×M16—24no—
278C3×M16—108no—
279C3×M16—104no—
280C2×C3×C8—54no—
281C2×C3×C8—108no—
282C2×C3×C8C22×D514yescomplemented
283C23×C5—22no—
284C23×C5—24no—
285C23×C5C22×C3×C411yescharacteristic
286C23×C5C22×C3×C412yes—
287C22×D5—232no—
288C22×D5—22no—
289C22×D5—24no—
290C22×D5—24no—
291C22×D5—24no—
292C22×D5—24no—
293C22×D5—24no—
294C22×D5—24no—
295C22×D5—24no—
296C22×D5C3×C22⋊C414yes—
297C22×D5C3×M1618yescomplemented
298C22×D5C22×C3×C411yescharacteristic
299C22×D5C22×C3×C412yes—
300C22×D5C22×C3×C411yescharacteristic
301C2×C4×C5—22no—
302C2×C4×C5—24no—
303C2×C4×C5—24no—
304C2×C4×C5C22×C3×C412yes—
305C2×C4×C5C22×C3×C411yescharacteristic
306C2×C4×C5C2×C3×D414yes—
307C2×C4×C5C24×C311yescharacteristic
308C2×Dic5—22no—
309C2×Dic5—24no—
310C2×Dic5—24no—
311C2×Dic5C3×C22⋊C414yes—
312C2×Dic5C22×C3×C412yes—
313C2×Dic5C22×C3×C411yescharacteristic
314C2×Dic5C22×C3×C411yescharacteristic
315C4×D5—24no—
316C4×D5—24no—
317C4×D5—24no—
318C4×D5—24no—
319C4×D5—24no—
320C4×D5—24no—
321C4×D5C3×C22⋊C414yes—
322C4×D5C3×C22⋊C414yes—
323C4×D5C2×C3×D414yes—
324C4×D5C2×C3×D414yes—
325C5×C8—24no—
326#168—24no—
327C25—51no—
328C23×C4—51no—
329C23×C4—51no—
330C23×C4—51no—
331C23×C4—52no—
332C23×C4—52no—
333C23×C4—51no—
334C23×C4—52no—
335C23×C4—52no—
336C23×C4—51no—
337C23×C4—108no—
338C23×C4C2×C3×D511yescharacteristic
339C2×M16—52no—
340C2×M16—54no—
341C2×M16—108no—
342C2×M16C2×C3×D512yescomplemented
343C22×C8—54no—
344C22⋊C8—54no—
345C22⋊C8—58no—
346C22⋊C8C2×C3×D514yescomplemented
347C2×C3×C5—22no—
348C2×C3×C5—24no—
349C2×C3×C5C22×C22⋊C411yescharacteristic
350C2×C3×C5C22×M1612yes—
351C3×D5—22no—
352C3×D5—24no—
353C3×D5#40714yesdirect product factor
354C23×C3—22no—
355C23×C3—24no—
356C23×C3—51no—
357C23×C3—51no—
358C23×C3—52no—
359C23×C3—54no—
360C23×C3—58no—
361C23×C3—104no—
362C23×C3—104no—
363C23×C3—104no—
364C23×C3—104no—
365C23×C3—104no—
366C23×C3—104no—
367C23×C3—1032no—
368C23×C3—102no—
369C23×C3—104no—
370C23×C3C2×C4×D511yescharacteristic
371C23×C3C2×C4×D512yes—
372C2×C3×C4—22no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—51no—
376C2×C3×C4—51no—
377C2×C3×C4—54no—
378C2×C3×C4—54no—
379C2×C3×C4—54no—
380C2×C3×C4—54no—
381C2×C3×C4—54no—
382C2×C3×C4—52no—
383C2×C3×C4—104no—
384C2×C3×C4—104no—
385C2×C3×C4—104no—
386C2×C3×C4—104no—
387C2×C3×C4—104no—
388C2×C3×C4—104no—
389C2×C3×C4—102no—
390C2×C3×C4—104no—
391C2×C3×C4—104no—
392C2×C3×C4C2×C4×D512yes—
393C2×C3×C4C2×C4×D511yescharacteristic
394C2×C3×C4D4×D514yes—
395C2×C3×C4C23×D511yescharacteristic
396C3×C8—24no—
397C3×C8—104no—
398C22×C5—28no—
399C22×C5—22no—
400C22×C5—22no—
401C22×C5—22no—
402C22×C5C2×C3×C22⋊C412yes—
403C22×C5C2×C3×M1614yescomplemented
404C22×C5C23×C3×C411yescharacteristic
405C2×D5—216no—
406C2×D5—28no—
407C2×D5—22no—
408C2×D5—22no—
409C2×D5—22no—
410C2×D5—28no—
411C2×D5—216no—
412C2×D5C2×C3×C22⋊C412yes—
413C2×D5C2×C3×C22⋊C412yes—
414C2×D5C2×C3×M1614yes—
415C2×D5C2×C3×M1614yescomplemented
416C4×C5—22no—
417C4×C5C2×C3×C22⋊C412yes—
418C4×C5C22×C3×D412yes—
419Dic5—22no—
420Dic5C2×C3×C22⋊C412yes—
421Dic5C2×C3×C22⋊C412yes—
422C24—51no—
423C24—52no—
424C24—52no—
425C24—51no—
426C24—104no—
427C24—108no—
428C24C3×C4×D511yescharacteristic
429C22×C4—24no—
430C22×C4—51no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—58no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—52no—
437C22×C4—52no—
438C22×C4—51no—
439C22×C4—52no—
440C22×C4—52no—
441C22×C4—52no—
442C22×C4—52no—
443C22×C4—52no—
444C22×C4—52no—
445C22×C4—104no—
446C22×C4—108no—
447C22×C4—108no—
448C22×C4—108no—
449C22×C4—108no—
450C22×C4—104no—
451C22×C4—104no—
452C22×C4—104no—
453C22×C4C3×C4×D511yescharacteristic
454C22×C4C3×C4×D512yes—
455C22×C4C22×C3×D512yes—
456C22×C4C22×C3×D511yescharacteristic
457M16—24no—
458M16—108no—
459M16—104no—
460C2×C8—54no—
461C2×C8—108no—
462C2×C8C22×C3×D514yescomplemented
463C3×C5C2×#40711yescharacteristic, complemented, Hall
464C22×C3—28no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—52no—
469C22×C3—54no—
470C22×C3—52no—
471C22×C3—54no—
472C22×C3—108no—
473C22×C3—1016no—
474C22×C3—108no—
475C22×C3—1016no—
476C22×C3—102no—
477C22×C3—102no—
478C22×C3—102no—
479C22×C3D5×C22⋊C412yes—
480C22×C3D5×M1614yescomplemented
481C22×C3C22×C4×D511yescharacteristic
482C3×C4—22no—
483C3×C4—52no—
484C3×C4—52no—
485C3×C4—102no—
486C3×C4D5×C22⋊C412yes—
487C3×C4C2×D4×D512yes—
488C2×C5—22no—
489C2×C5—24no—
490C2×C5C22×C3×C22⋊C411yescharacteristic
491C2×C5C22×C3×M1612yes—
492D5—22no—
493D5—24no—
494D5C3×#40714yesdirect product factor
495C23—22no—
496C23—24no—
497C23—51no—
498C23—51no—
499C23—52no—
500C23—54no—
501C23—58no—
502C23—104no—
503C23—104no—
504C23—104no—
505C23—104no—
506C23—104no—
507C23—104no—
508C23—1032no—
509C23—102no—
510C23—104no—
511C23C2×C3×C4×D511yescharacteristic
512C23C2×C3×C4×D512yes—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—51no—
517C2×C4—51no—
518C2×C4—54no—
519C2×C4—54no—
520C2×C4—54no—
521C2×C4—54no—
522C2×C4—54no—
523C2×C4—52no—
524C2×C4—104no—
525C2×C4—104no—
526C2×C4—104no—
527C2×C4—104no—
528C2×C4—104no—
529C2×C4—104no—
530C2×C4—102no—
531C2×C4—104no—
532C2×C4—104no—
533C2×C4C2×C3×C4×D512yes—
534C2×C4C2×C3×C4×D511yescharacteristic
535C2×C4C3×D4×D514yes—
536C2×C4C23×C3×D511yescharacteristic
537C8—24no—
538C8—104no—
539C2×C3—22no—
540C2×C3—24no—
541C2×C3—54no—
542C2×C3—102no—
543C2×C3—104no—
544C2×C3C2×D5×C22⋊C411yescharacteristic
545C2×C3C2×D5×M1612yes—
546C5C2×C3×#40711yescharacteristic, complemented, Sylow
547C22—28no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—52no—
552C22—54no—
553C22—52no—
554C22—54no—
555C22—108no—
556C22—1016no—
557C22—108no—
558C22—1016no—
559C22—102no—
560C22—102no—
561C22—102no—
562C22C3×D5×C22⋊C412yes—
563C22C3×D5×M1614yescomplemented
564C22C22×C3×C4×D511yescharacteristic
565C4—22no—
566C4—52no—
567C4—52no—
568C4—102no—
569C4C3×D5×C22⋊C412yes—
570C4C2×C3×D4×D512yes—
571C3D5×#40711yescharacteristic, direct product factor, Sylow
572C2—22no—
573C2—24no—
574C2—54no—
575C2—102no—
576C2—104no—
577C2C2×C3×D5×C22⋊C411yescharacteristic
578C2C2×C3×D5×M1612yes—
subgroupG/H
centerC2×C3×C4C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#407C2
socleC22×C3×C5C23×C4
prime radicalC24×C3×D5C4
cosocleC2×C4×C5C24×C3
hypercenterC3×#407D5
hypocenterC5C2×C3×#407
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5×M16C2semidirect
3. C3×C5×#407C2semidirect
4. C3×#65496C2semidirect
5. C3×#65415C2semidirect
6. C3×#65015C2semidirect
7. C3×D5×C22⋊C8C2semidirect
8. D5×#407C3direct (N × H)
21. C2×C3×C5×M16C22semidirect
22. C2×C3×#681C22semidirect
24. C2×C3×#676C22semidirect
25. C2×C3×C8×D5C22semidirect
26. C3×C5×C22⋊C8C22semidirect
27. C3×C22⋊#168C22semidirect
28. C3×#3952C22semidirect
31. C2×D5×M16C2×C3semidirect
32. C5×#407C2×C3semidirect
33. #65496C2×C3semidirect
34. #65415C2×C3semidirect
35. #65015C2×C3semidirect
36. D5×C22⋊C8C2×C3semidirect
73. C2×C3×C5×C8C23semidirect
75. C2×C3×#168C23semidirect
83. C3×#407D5direct (N × H)
97. C2×C5×M16C22×C3semidirect
98. C2×#681C22×C3semidirect
100. C2×#676C22×C3semidirect
101. C2×C8×D5C22×C3semidirect
102. C5×C22⋊C8C22×C3semidirect
103. C22⋊#168C22×C3semidirect
104. #3952C22×C3semidirect
120. C22×C3×D5M16semidirect
165. C2×C3×M16C2×D5semidirect
169. C3×C22⋊C8C2×D5semidirect
206. C2×C5×C8C23×C3semidirect
208. C2×#168C23×C3semidirect
216. #407C3×D5direct (N × H)
223. C22×C3×C5C2×M16semidirect
235. C2×C3×D5C2×M16semidirect
282. C2×C3×C8C22×D5semidirect
297. C22×D5C3×M16semidirect
342. C2×M16C2×C3×D5semidirect
346. C22⋊C8C2×C3×D5semidirect
353. C3×D5#407direct (N × H)
403. C22×C5C2×C3×M16semidirect
415. C2×D5C2×C3×M16semidirect
462. C2×C8C22×C3×D5semidirect
463. C3×C5C2×#407semidirect
480. C22×C3D5×M16semidirect
494. D5C3×#407direct (N × H)
546. C5C2×C3×#407semidirect
563. C22C3×D5×M16semidirect
571. C3D5×#407direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D52
C2×C3×D5×M162
C3×C5×#4072
C3×#654962
C3×#654152
C3×#650152
C3×D5×C22⋊C82
D5×#4073
C2×C3×#4075