Finite Group Databasebeta

← D5×#4939 #14320786

Subgroups — D5×#4939 #14320786

Order 1920.

2720 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
1C22×D5×D12C211yesmaximal, characteristic
2C2×C3×C42×D5C211yesmaximal, characteristic, complemented
3C2×D5×(C2×D3)⋊C4C214yesmaximal, complemented
4C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#11751040C211yesmaximal, characteristic, complemented
6C5×#4939C211yesmaximal, characteristic, complemented
7#11748908C214yesmaximal, complemented
8#11748768C211yesmaximal, characteristic, complemented
9#11748764C211yesmaximal, characteristic, complemented
10D5×#390—31nomaximal, Hall
11C23×D3×D5C2212yes—
12C22×D60C2211yescharacteristic
13C22×C5×D12C2211yescharacteristic
14C22×C3×C4×D5C2212yes—
15C22×C3×C4×D5C2211yescharacteristic
16C22×#1203C2212yes—
17C22×D5×Dic3C2212yes—
18C2×D5×D12—24no—
19C2×D5×D12—24no—
20C2×D5×D12C418yescomplemented
21C2×C3×C42×C5C2211yescharacteristic, complemented
22C2×#6714C2214yescomplemented
23C2×C4⋊Dic15C2211yescharacteristic, complemented
24C2×C5×(C2×D3)⋊C4C2214yescomplemented
25C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
26C2×C3×C4×Dic5C2212yescomplemented
27C2×C3×C4×Dic5C2211yescharacteristic, complemented
28C3×C42×D5—24no—
29C2×#6668C2212yescomplemented
30C2×#6667C2214yescomplemented
31C2×(C2×D3)⋊Dic5C2214yescomplemented
32D5×(C2×D3)⋊C4—216no—
33D5×C4⋊Dic3—24no—
34C2×#4939—51nomaximal, Hall
35C22×D4×D5—31no—
36C2×D5×C4⋊C4—31no—
37C2×D5×C22⋊C4—34no—
38C2×C42×D5D311yescharacteristic, complemented
39C5×#390—31no—
40#65510—31no—
41#65277—31no—
42#65246—34no—
43#65228—31no—
44C23×D15C2312yes—
45C23×C5×D3C2312yes—
46C23×C3×D5C2311yescharacteristic
47C22×D3×D5—28no—
48C22×D3×D5—24no—
49C22×D3×D5—24no—
50C22×D3×D5—28no—
51C22×D3×D5C2×C418yes—
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2312yes—
55C2×D60—22no—
56C2×D60—22no—
57C2×D60C2×C414yescomplemented
58C22×C5×Dic3C2312yes—
59C2×C5×D12—22no—
60C2×C5×D12—22no—
61C2×C5×D12C2×C414yescomplemented
62C22×C3×Dic5C2312yes—
63C22×C3×Dic5C2311yescharacteristic
64C2×C3×C4×D5—24no—
65C2×C3×C4×D5—24no—
66C2×C3×C4×D5C2×C414yes—
67C2×C3×C4×D5D414yes—
68C2×C3×C4×D5D414yes—
69C2×C3×C4×D5D418yescomplemented
70C2×#1203—24no—
71C2×#1203—24no—
72C2×#1203C2×C418yescomplemented
73C2×D5×Dic3—24no—
74C2×D5×Dic3—28no—
75D5×D12—232no—
76C3×C42×C5—22no—
77#6714—28no—
78C4⋊Dic15—22no—
79C5×(C2×D3)⋊C4—28no—
80C5×C4⋊Dic3—22no—
81C3×C4×Dic5—22no—
82C3×C4×Dic5—24no—
83#6668—24no—
84#6667—28no—
85(C2×D3)⋊Dic5—28no—
86C23×D12—51no—
87C22×C3×C42—51no—
88C22×(C2×D3)⋊C4—54no—
89C22×C4⋊Dic3—51no—
90#4939—51no—
91#4939—51no—
92#4939—54no—
93#4939—51no—
94#4939D511yescharacteristic, direct product factor
95C24×D5—32no—
96C22×C5×D4—31no—
97C22×C22⋊D5—32no—
98C2×D4×D5—38no—
99C2×D4×D5—64no—
100C2×D4×D5—64no—
101C22×D20—31no—
102C22×C4×D5—32no—
103C22×C4×D5C2×D312yes—
104C22×C4×D5C2×D311yescharacteristic
105C2×C5×C4⋊C4—31no—
106C2×C5×C22⋊C4—34no—
107C2×C42×C5C2×D311yescharacteristic, complemented
108C2×C22⋊Dic5—34no—
109C2×#685—34no—
110C2×#685—34no—
111C2×C4⋊Dic5—31no—
112C2×#683—32no—
113C2×C4×Dic5C2×D312yescomplemented
114C2×C4×Dic5C2×D311yescharacteristic, complemented
115D5×C4⋊C4—64no—
116D5×C22⋊C4—616no—
117C42×D5—24no—
118C2×#390—151noSylow
119C23×C3×C5C2411yescharacteristic
120C22×D15—24no—
121C22×D15—22no—
122C22×D15—22no—
123C22×D15—24no—
124C22×D15C22×C414yes—
125C22×C5×D3—24no—
126C22×C5×D3—22no—
127C22×C5×D3—22no—
128C22×C5×D3—24no—
129C22×C5×D3C22×C414yes—
130C22×C3×D5C22×C412yes—
131C22×C3×D5C2×D412yes—
132C22×C3×D5C2×D412yes—
133C22×C3×D5C2×D414yes—
134C22×C3×D5#4114yes—
135C2×D3×D5—216no—
136C2×D3×D5—232no—
137C2×D3×D5—416no—
138C2×D3×D5—48no—
139C2×D3×D5—48no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C22×C412yes—
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2×D414yescomplemented
146C2×Dic15—24no—
147C2×Dic15—22no—
148D60—28no—
149C2×C5×Dic3—24no—
150C2×C5×Dic3—22no—
151C5×D12—28no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C22×C412yes—
155C2×C3×Dic5C2×D412yes—
156C2×C3×Dic5C2×D412yes—
157C2×C3×Dic5C2×D414yescomplemented
158C3×C4×D5—216no—
159C3×C4×D5C22⋊C4116yescomplemented
160#1203—216no—
161D5×Dic3—48no—
162C24×D3—52no—
163C23×C3×C4—51no—
164C23×C3×C4—52no—
165C23×Dic3—52no—
166C22×D12—52no—
167C22×D12—51no—
168C22×D12—58no—
169C22×D12—104no—
170C22×D12—104no—
171C22×D12C2×D511yescharacteristic
172C2×C3×C42—52no—
173C2×C3×C42—51no—
174C2×C3×C42—104no—
175C2×C3×C42C2×D511yescharacteristic, complemented
176C2×(C2×D3)⋊C4—54no—
177C2×(C2×D3)⋊C4—54no—
178C2×(C2×D3)⋊C4—54no—
179C2×(C2×D3)⋊C4—1016no—
180C2×(C2×D3)⋊C4C2×D514yescomplemented
181C2×C4⋊Dic3—51no—
182C2×C4⋊Dic3—52no—
183C2×C4⋊Dic3—104no—
184C2×C4⋊Dic3C2×D511yescharacteristic, complemented
185C24×C5—32no—
186C23×D5—32no—
187C23×D5—38no—
188C23×D5—64no—
189C23×D5—68no—
190C23×D5—68no—
191C23×D5—64no—
192C23×D5C22×D311yescharacteristic
193C2×C5×D4—34no—
194C2×C5×D4—62no—
195C2×C5×D4—62no—
196C22×C4×C5—32no—
197C22×C4×C5C22×D312yes—
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—38no—
200C2×C22⋊D5—64no—
201C2×C22⋊D5—64no—
202C22×Dic5—32no—
203C22×Dic5C22×D312yes—
204C22×Dic5C22×D311yescharacteristic
205D4×D5—632no—
206C2×D20—34no—
207C2×D20—62no—
208C2×D20—62no—
209C2×C4×D5—24no—
210C2×C4×D5—24no—
211C2×C4×D5—68no—
212C2×C4×D5—64no—
213C2×C4×D5C4×D314yes—
214C2×C4×D5D1214yes—
215C2×C4×D5D1218yescomplemented
216C2×C4×D5#6714yes—
217C5×C4⋊C4—62no—
218C5×C22⋊C4—68no—
219C42×C5—22no—
220C22⋊Dic5—68no—
221#685—68no—
222#685—68no—
223C4⋊Dic5—62no—
224#683—64no—
225C4×Dic5—22no—
226C4×Dic5—24no—
227C23×D4—151no—
228C22×C4⋊C4—151no—
229C22×C22⋊C4—154no—
230C22×C42—51no—
231#390—31no—
232#390—154no—
233#390—151no—
234#390—151no—
235#390—151no—
236C22×C3×C5C23×C411yescharacteristic
237C22×C3×C5C22×D411yescharacteristic
238C22×C3×C5C22×D412yes—
239C22×C3×C5C22×D411yescharacteristic
240C22×C3×C5C2×#4112yes—
241C2×D15—24no—
242C2×D15—28no—
243C2×D15—44no—
244C2×D15—42no—
245C2×D15—42no—
246C2×C5×D3—24no—
247C2×C5×D3—28no—
248C2×C5×D3—44no—
249C2×C5×D3—42no—
250C2×C5×D3—42no—
251C2×C3×D5C2×C22⋊C414yes—
252C2×C3×D5C4×D418yes—
253C2×C3×D5#12118yes—
254C2×C3×D5#12414yes—
255C2×C3×D5#12714yes—
256D3×D5—432no—
257C3×C4×C5—24no—
258C3×C4×C5C2×C22⋊C414yescomplemented
259Dic15—42no—
260C3×Dic5—24no—
261C3×Dic5C2×C22⋊C414yescomplemented
262C5×Dic3—42no—
263C24×C3—51no—
264C23×D3—52no—
265C23×D3—58no—
266C23×D3—108no—
267C23×D3—104no—
268C23×D3—104no—
269C23×D3—108no—
270C23×D3C22×D512yes—
271C22×C3×C4—51no—
272C22×C3×C4—54no—
273C22×C3×C4—54no—
274C22×C3×C4—54no—
275C22×C3×C4—52no—
276C22×C3×C4—58no—
277C22×C3×C4—104no—
278C22×C3×C4—104no—
279C22×C3×C4C22×D512yes—
280C22×C3×C4C22×D511yescharacteristic
281C22×Dic3—52no—
282C22×Dic3—104no—
283C22×Dic3—108no—
284C22×Dic3C22×D512yes—
285C2×D12—22no—
286C2×D12—22no—
287C2×D12—58no—
288C2×D12—54no—
289C2×D12—1032no—
290C2×D12—104no—
291C2×D12—104no—
292C2×D12—102no—
293C2×D12—102no—
294C2×D12C4×D514yescomplemented
295C3×C42—22no—
296C3×C42—104no—
297C3×C42—102no—
298(C2×D3)⋊C4—28no—
299(C2×D3)⋊C4—108no—
300(C2×D3)⋊C4—108no—
301(C2×D3)⋊C4—108no—
302C4⋊Dic3—22no—
303C4⋊Dic3—104no—
304C4⋊Dic3—102no—
305C23×C5—34no—
306C23×C5—64no—
307C23×C5—62no—
308C23×C5—64no—
309C23×C5—62no—
310C23×C5C23×D311yescharacteristic
311C22×D5—34no—
312C22×D5—64no—
313C22×D5—62no—
314C22×D5—64no—
315C22×D5—62no—
316C22×D5—632no—
317C22×D5—616no—
318C22×D5—128no—
319C22×D5—128no—
320C22×D5—1216no—
321C22×D5C2×C4×D312yes—
322C22×D5C2×D1214yes—
323C22×D5C2×D1212yes—
324C22×D5#23514yes—
325C22×D5C2×#6712yes—
326C5×D4—68no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—62no—
330C2×C4×C5—64no—
331C2×C4×C5C2×C4×D312yes—
332C2×C4×C5C2×D1212yes—
333C2×C4×C5C2×D1214yescomplemented
334C2×C4×C5C2×#6712yes—
335C22⋊D5—616no—
336C2×Dic5—22no—
337C2×Dic5—22no—
338C2×Dic5—62no—
339C2×Dic5—64no—
340C2×Dic5C2×C4×D312yes—
341C2×Dic5C2×D1212yes—
342C2×Dic5C2×D1214yescomplemented
343C2×Dic5C2×#6712yes—
344D20—68no—
345C4×D5—216no—
346C4×D5—128no—
347C4×D5(C2×D3)⋊C4116yescomplemented
348C25—152no—
349C22×D4—31no—
350C22×D4—158no—
351C22×D4—152no—
352C22×D4—151no—
353C22×D4—304no—
354C22×D4—304no—
355C23×C4—51no—
356C23×C4—52no—
357C23×C4—152no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—152no—
360C2×C4⋊C4—151no—
361C2×C4⋊C4—304no—
362C2×C22⋊C4—34no—
363C2×C22⋊C4—154no—
364C2×C22⋊C4—154no—
365C2×C22⋊C4—154no—
366C2×C22⋊C4—3016no—
367C2×C42—52no—
368C2×C42—51no—
369C2×C42—104no—
370C2×C42D3×D511yescharacteristic, complemented
371C2×C3×C5C22×C22⋊C411yescharacteristic
372C2×C3×C5C2×C4×D412yes—
373C2×C3×C5C2×#12112yes—
374C2×C3×C5C2×#12411yescharacteristic
375C2×C3×C5C2×#12711yescharacteristic
376D15—44no—
377C3×D5#39018yescomplemented
378C5×D3—44no—
379C23×C3—52no—
380C23×C3—52no—
381C23×C3—54no—
382C23×C3—52no—
383C23×C3—54no—
384C23×C3C23×D511yescharacteristic
385C22×D3—24no—
386C22×D3—22no—
387C22×D3—22no—
388C22×D3—24no—
389C22×D3—54no—
390C22×D3—1016no—
391C22×D3—1032no—
392C22×D3—104no—
393C22×D3—102no—
394C22×D3—102no—
395C22×D3—104no—
396C22×D3—208no—
397C22×D3—2016no—
398C22×D3—208no—
399C22×D3C2×C4×D514yes—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—52no—
403C2×C3×C4—52no—
404C2×C3×C4—52no—
405C2×C3×C4—516no—
406C2×C3×C4—54no—
407C2×C3×C4—1016no—
408C2×C3×C4—102no—
409C2×C3×C4—102no—
410C2×C3×C4C2×C4×D512yes—
411C2×C3×C4D4×D512yes—
412C2×C3×C4D4×D512yes—
413C2×C3×C4D4×D514yescomplemented
414C2×Dic3—22no—
415C2×Dic3—24no—
416C2×Dic3—102no—
417C2×Dic3—104no—
418C2×Dic3—208no—
419D12—28no—
420D12—1016no—
421D12—108no—
422C22×C5—68no—
423C22×C5—64no—
424C22×C5—122no—
425C22×C5—122no—
426C22×C5—124no—
427C22×C5C22×C4×D311yescharacteristic
428C22×C5C22×D1212yes—
429C22×C5C22×D1211yescharacteristic
430C22×C5C2×#23512yes—
431C22×C5C22×#6711yescharacteristic
432C2×D5—68no—
433C2×D5—64no—
434C2×D5—122no—
435C2×D5—122no—
436C2×D5—124no—
437C2×D5—1232no—
438C2×D5C4×D1218yes—
439C2×D5#87414yes—
440C2×D5#87514yes—
441C2×D5C2×(C2×D3)⋊C414yes—
442C2×D5#93018yes—
443C4×C5—24no—
444C4×C5—122no—
445C4×C5C2×(C2×D3)⋊C414yescomplemented
446Dic5—24no—
447Dic5—122no—
448Dic5C2×(C2×D3)⋊C414yescomplemented
449C24—32no—
450C24—51no—
451C24—158no—
452C24—152no—
453C24—308no—
454C24—304no—
455C24—304no—
456C24—308no—
457C2×D4—34no—
458C2×D4—62no—
459C2×D4—62no—
460C2×D4—158no—
461C2×D4—154no—
462C2×D4—3032no—
463C2×D4—304no—
464C2×D4—304no—
465C2×D4—302no—
466C2×D4—302no—
467C22×C4—32no—
468C22×C4—51no—
469C22×C4—54no—
470C22×C4—54no—
471C22×C4—54no—
472C22×C4—52no—
473C22×C4—58no—
474C22×C4—104no—
475C22×C4—104no—
476C22×C4—152no—
477C22×C4—308no—
478C22×C4—304no—
479C22×C4C2×D3×D512yes—
480C22×C4C2×D3×D511yescharacteristic
481C4⋊C4—62no—
482C4⋊C4—304no—
483C4⋊C4—302no—
484C22⋊C4—68no—
485C22⋊C4—308no—
486C22⋊C4—308no—
487C22⋊C4—308no—
488C42—22no—
489C42—104no—
490C42—102no—
491C3×C5C2×#39011yescharacteristic, complemented, Hall
492C22×C3—54no—
493C22×C3—54no—
494C22×C3—58no—
495C22×C3—58no—
496C22×C3—54no—
497C22×C3C22×C4×D511yescharacteristic
498C22×C3C2×D4×D511yescharacteristic
499C22×C3C2×D4×D512yes—
500C22×C3C2×D4×D511yescharacteristic
501C22×C3D5×#4112yes—
502C2×D3—24no—
503C2×D3—28no—
504C2×D3—42no—
505C2×D3—44no—
506C2×D3—42no—
507C2×D3—104no—
508C2×D3—108no—
509C2×D3—2032no—
510C2×D3—202no—
511C2×D3—204no—
512C2×D3—202no—
513C3×C4—24no—
514C3×C4—54no—
515C3×C4—104no—
516C3×C4D5×C22⋊C414yescomplemented
517Dic3—42no—
518Dic3—202no—
519C2×C5—124no—
520C2×C5C2×C4×D1212yes—
521C2×C5C2×#87411yescharacteristic
522C2×C5C2×#87511yescharacteristic
523C2×C5C22×(C2×D3)⋊C411yescharacteristic
524C2×C5C2×#93012yes—
525D5—124no—
526D5#493918yesdirect product factor
527C23—34no—
528C23—52no—
529C23—54no—
530C23—52no—
531C23—54no—
532C23—52no—
533C23—64no—
534C23—62no—
535C23—64no—
536C23—62no—
537C23—154no—
538C23—3016no—
539C23—3032no—
540C23—304no—
541C23—302no—
542C23—304no—
543C23—302no—
544C23—608no—
545C23—608no—
546C23—6016no—
547C23C22×D3×D511yescharacteristic
548D4—68no—
549D4—3016no—
550D4—308no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—52no—
554C2×C4—52no—
555C2×C4—52no—
556C2×C4—516no—
557C2×C4—54no—
558C2×C4—64no—
559C2×C4—62no—
560C2×C4—1016no—
561C2×C4—102no—
562C2×C4—102no—
563C2×C4—304no—
564C2×C4—302no—
565C2×C4—608no—
566C2×C4C4×D3×D512yes—
567C2×C4D5×D1212yes—
568C2×C4D5×D1214yescomplemented
569C2×C4D5×#6712yes—
570C2×C3—58no—
571C2×C3C2×D5×C22⋊C411yescharacteristic
572C2×C3C4×D4×D512yes—
573C2×C3D5×#12112yes—
574C2×C3D5×#12411yescharacteristic
575C2×C3D5×#12711yescharacteristic
576D3—44no—
577D3—204no—
578C5C2×#493911yescharacteristic, complemented, Sylow
579C22—58no—
580C22—54no—
581C22—54no—
582C22—54no—
583C22—58no—
584C22—68no—
585C22—64no—
586C22—122no—
587C22—122no—
588C22—124no—
589C22—308no—
590C22—304no—
591C22—6032no—
592C22—602no—
593C22—602no—
594C22—604no—
595C22C2×C4×D3×D511yescharacteristic
596C22C2×D5×D1212yes—
597C22C2×D5×D1211yescharacteristic
598C22D5×#23512yes—
599C22C2×D5×#6711yescharacteristic
600C4—24no—
601C4—54no—
602C4—104no—
603C4—122no—
604C4—602no—
605C4D5×(C2×D3)⋊C414yescomplemented
606C3D5×#39011yescharacteristic, complemented, Sylow
607C2—58no—
608C2—124no—
609C2—604no—
610C2C4×D5×D1212yes—
611C2D5×#87411yescharacteristic
612C2D5×#87511yescharacteristic
613C2C2×D5×(C2×D3)⋊C411yescharacteristic
614C2D5×#93012yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D5×D12C2
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#390
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C42×D5C2semidirect
3. C2×D5×(C2×D3)⋊C4C2semidirect
4. C2×D5×C4⋊Dic3C2semidirect
5. #11751040C2semidirect
6. C5×#4939C2semidirect
7. #11748908C2semidirect
8. #11748768C2semidirect
9. #11748764C2semidirect
20. C2×D5×D12C4semidirect
21. C2×C3×C42×C5C22semidirect
22. C2×#6714C22semidirect
23. C2×C4⋊Dic15C22semidirect
24. C2×C5×(C2×D3)⋊C4C22semidirect
25. C2×C5×C4⋊Dic3C22semidirect
26. C2×C3×C4×Dic5C22semidirect
27. C2×C3×C4×Dic5C22semidirect
29. C2×#6668C22semidirect
30. C2×#6667C22semidirect
31. C2×(C2×D3)⋊Dic5C22semidirect
38. C2×C42×D5D3semidirect
57. C2×D60C2×C4semidirect
61. C2×C5×D12C2×C4semidirect
69. C2×C3×C4×D5D4semidirect
72. C2×#1203C2×C4semidirect
94. #4939D5direct (N × H)
107. C2×C42×C5C2×D3semidirect
113. C2×C4×Dic5C2×D3semidirect
114. C2×C4×Dic5C2×D3semidirect
145. C2×C3×C4×C5C2×D4semidirect
157. C2×C3×Dic5C2×D4semidirect
159. C3×C4×D5C22⋊C4semidirect
175. C2×C3×C42C2×D5semidirect
180. C2×(C2×D3)⋊C4C2×D5semidirect
184. C2×C4⋊Dic3C2×D5semidirect
215. C2×C4×D5D12semidirect
258. C3×C4×C5C2×C22⋊C4semidirect
261. C3×Dic5C2×C22⋊C4semidirect
294. C2×D12C4×D5semidirect
333. C2×C4×C5C2×D12semidirect
342. C2×Dic5C2×D12semidirect
347. C4×D5(C2×D3)⋊C4semidirect
370. C2×C42D3×D5semidirect
377. C3×D5#390semidirect
413. C2×C3×C4D4×D5semidirect
445. C4×C5C2×(C2×D3)⋊C4semidirect
448. Dic5C2×(C2×D3)⋊C4semidirect
491. C3×C5C2×#390semidirect
516. C3×C4D5×C22⋊C4semidirect
526. D5#4939direct (N × H)
568. C2×C4D5×D12semidirect
578. C5C2×#4939semidirect
605. C4D5×(C2×D3)⋊C4semidirect
606. C3D5×#390semidirect

Maximal subgroups

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

subgroupindex
C22×D5×D122
C2×C3×C42×D52
C2×D5×(C2×D3)⋊C42
C2×D5×C4⋊Dic32
#117510402
C5×#49392
#117489082
#117487682
#117487642
D5×#3903
C2×#49395