Finite Group Databasebeta

← #12020708

Subgroups — #12020708

Order 1280.

2398 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4023C211yesmaximal, characteristic
2C2×C4×C22⋊Dic5C211yesmaximal, characteristic
3C22×#3963C211yesmaximal, characteristic
4C2×#65232C211yesmaximal, characteristic
5C2×C22⋊C4×Dic5C211yesmaximal, characteristic
6C5×C22⋊#95C211yesmaximal, characteristic
7#10602337C211yesmaximal, characteristic
8#10600199C212yesmaximal, complemented
9#10600199C212yesmaximal, complemented
10#10600196C212yesmaximal, complemented
11Dic5×#95C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C24×Dic5C2211yescharacteristic
14C24×Dic5C2211yescharacteristic
15C22×C5×C22⋊C4C2211yescharacteristic
16C22×C5×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic5C2211yescharacteristic
18C22×C22⋊Dic5C2211yescharacteristic
19C22×#683C2212yes—
20C22×C4×Dic5C2212yes—
21C22×C4×Dic5C2212yes—
22C22×C4×Dic5C2212yes—
23C2×#4023—24no—
24C2×#4023—24no—
25C2×#4023C418yescomplemented
26C2×C5×#95C2212yes—
27C2×C5×#95C2212yes—
28C4×C22⋊Dic5—24no—
29C2×#3963C418yescomplemented
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35C2×#3963C2211yescharacteristic
36C2×#3963C2211yescharacteristic
37C2×#3963C2211yescharacteristic
38C2×#3963C2212yes—
39C2×#3963C2212yes—
40#65232C418yescomplemented
41C22⋊C4×Dic5—24no—
42#13799—51nomaximal, Sylow
43C25×C5C2311yescharacteristic
44C23×C4×C5—22no—
45C23×C4×C5—22no—
46C23×C4×C5—24no—
47C23×C4×C5—42no—
48C23×C4×C5C2×C414yes—
49C23×C4×C5C2312yes—
50C23×C4×C5C2312yes—
51C23×C4×C5C2311yescharacteristic
52C23×C4×C5C2311yescharacteristic
53C23×Dic5—22no—
54C23×Dic5—22no—
55C23×Dic5—22no—
56C23×Dic5—22no—
57C23×Dic5—22no—
58C23×Dic5—22no—
59C23×Dic5—24no—
60C23×Dic5—42no—
61C23×Dic5C2×C414yes—
62C23×Dic5C2×C414yes—
63C23×Dic5C2×C414yes—
64C23×Dic5C2×C414yes—
65C23×Dic5C2312yes—
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C23×Dic5C2312yes—
70C23×Dic5C2311yescharacteristic
71C2×C5×C22⋊C4—22no—
72C2×C5×C22⋊C4—22no—
73C2×C5×C22⋊C4—22no—
74C2×C5×C22⋊C4—22no—
75C2×C5×C22⋊C4C2×C414yes—
76C2×C5×C22⋊C4C2×C414yes—
77C2×C22⋊Dic5—22no—
78C2×C22⋊Dic5—22no—
79C2×C22⋊Dic5C2×C414yes—
80C2×C22⋊Dic5C2×C414yes—
81C2×C22⋊Dic5D414yes—
82C2×C22⋊Dic5D414yes—
83C2×#683—24no—
84C2×#683—24no—
85C2×#683C2×C418yescomplemented
86C2×C4×Dic5—24no—
87C2×C4×Dic5—24no—
88C2×C4×Dic5—24no—
89C2×C4×Dic5—24no—
90C2×C4×Dic5—24no—
91C2×C4×Dic5—24no—
92C2×C4×Dic5—42no—
93C2×C4×Dic5—42no—
94C2×C4×Dic5C2×C418yescomplemented
95#4023—232no—
96C5×#95—24no—
97C5×#95—42no—
98#3963—24no—
99#3963—24no—
100#3963—24no—
101#3963—42no—
102#3963C2×C414yes—
103#3963C2×C414yes—
104#3963C2×C414yes—
105#3963C2×C414yes—
106#3963C2×C418yescomplemented
107#3963C2×C418yescomplemented
108C22×#117—51no—
109C2×#381—51no—
110C2×C4×C22⋊C4—51no—
111C2×C4×C22⋊C4—51no—
112C22×#95—51no—
113#1436—52no—
114#1436—52no—
115#1434—52no—
116C22⋊#95—51no—
117C22⋊#95D511yescharacteristic
118C4×#95—52no—
119C24×C5—22no—
120C24×C5—22no—
121C24×C5—22no—
122C24×C5—22no—
123C24×C5C22×C412yes—
124C24×C5C22×C412yes—
125C24×C5C22×C412yes—
126C24×C5C2×D412yes—
127C24×C5C2×D412yes—
128C24×C5#4112yes—
129C24×C5#4112yes—
130C24×C5C2411yescharacteristic
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—22no—
134C22×C4×C5—28no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—21no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—28no—
152C22×C4×C5—44no—
153C22×C4×C5—48no—
154C22×C4×C5—48no—
155C22×C4×C5C22×C414yes—
156C22×C4×C5C22×C414yes—
157C22×C4×C5C22×C412yes—
158C22×C4×C5C22×C412yes—
159C22×C4×C5#4114yes—
160C22×Dic5—28no—
161C22×Dic5—28no—
162C22×Dic5—28no—
163C22×Dic5—28no—
164C22×Dic5—28no—
165C22×Dic5—28no—
166C22×Dic5—21no—
167C22×Dic5—21no—
168C22×Dic5—21no—
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—21no—
173C22×Dic5—21no—
174C22×Dic5—21no—
175C22×Dic5—21no—
176C22×Dic5—22no—
177C22×Dic5—22no—
178C22×Dic5—22no—
179C22×Dic5—22no—
180C22×Dic5—22no—
181C22×Dic5—28no—
182C22×Dic5—22no—
183C22×Dic5—21no—
184C22×Dic5—22no—
185C22×Dic5—21no—
186C22×Dic5—22no—
187C22×Dic5—22no—
188C22×Dic5—22no—
189C22×Dic5—22no—
190C22×Dic5—22no—
191C22×Dic5—22no—
192C22×Dic5—28no—
193C22×Dic5—44no—
194C22×Dic5—48no—
195C22×Dic5—48no—
196C22×Dic5C42116yescomplemented
197C22×Dic5C22×C414yes—
198C22×Dic5C22×C412yes—
199C22×Dic5C22×C412yes—
200C22×Dic5C22×C412yes—
201C22×Dic5C22×C412yes—
202C22×Dic5C22×C412yes—
203C22×Dic5C22×C412yes—
204C22×Dic5C22×C412yes—
205C22×Dic5C22×C414yes—
206C22×Dic5C22×C412yes—
207C22×Dic5C2×D414yes—
208C22×Dic5C2×D414yes—
209C22×Dic5#4114yes—
210C5×C22⋊C4—28no—
211C5×C22⋊C4—28no—
212C22⋊Dic5—28no—
213C22⋊Dic5C22⋊C4116yes—
214#683—216no—
215C4×Dic5—216no—
216C4×Dic5—48no—
217C4×Dic5—48no—
218C24×C4—51no—
219C24×C4—51no—
220C24×C4C2×D511yescharacteristic
221C2×#117—58no—
222C2×#117—104no—
223C2×#117—104no—
224C22×C4⋊C4—52no—
225C22×C22⋊C4—51no—
226C22×C22⋊C4—51no—
227C22×C22⋊C4C2×D511yescharacteristic
228C22×C22⋊C4C2×D511yescharacteristic
229C22×C42—52no—
230C22×C42—52no—
231C22×C42—52no—
232#381—58no—
233C4×C22⋊C4—104no—
234C4×C22⋊C4—104no—
235C2×#95—58no—
236C2×#95—51no—
237C2×#95—52no—
238C2×#95—51no—
239C2×#95—51no—
240C2×#95—51no—
241C2×#95—52no—
242C2×#95—52no—
243C2×#95—52no—
244C2×#95—52no—
245C2×#95—52no—
246C2×#95C2×D512yes—
247C2×#95C2×D512yes—
248C23×C5—22no—
249C23×C5—22no—
250C23×C5—24no—
251C23×C5—24no—
252C23×C5—22no—
253C23×C5—22no—
254C23×C5—24no—
255C23×C5—24no—
256C23×C5—24no—
257C23×C5—24no—
258C23×C5—24no—
259C23×C5—24no—
260C23×C5—24no—
261C23×C5—24no—
262C23×C5—24no—
263C23×C5—24no—
264C23×C5C2×C4214yes—
265C23×C5C2×C22⋊C414yes—
266C23×C5#11714yes—
267C23×C5C4×D414yes—
268C23×C5C4×D414yes—
269C23×C5C4×D414yes—
270C23×C5C4×D414yes—
271C23×C5C23×C411yescharacteristic
272C23×C5C23×C411yescharacteristic
273C23×C5C23×C411yescharacteristic
274C23×C5C22×D411yescharacteristic
275C23×C5C22×D411yescharacteristic
276C23×C5C2×#4111yescharacteristic
277C23×C5C2×#4112yes—
278C23×C5C2×#4111yescharacteristic
279C23×C5C2×#4112yes—
280C23×C5H(5,𝔽2)12yes—
281C23×C52−1+412yes—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—24no—
285C2×C4×C5—24no—
286C2×C4×C5—24no—
287C2×C4×C5—22no—
288C2×C4×C5—24no—
289C2×C4×C5—22no—
290C2×C4×C5—24no—
291C2×C4×C5—24no—
292C2×C4×C5—22no—
293C2×C4×C5—24no—
294C2×C4×C5—24no—
295C2×C4×C5—416no—
296C2×C4×C5—42no—
297C2×C4×C5—42no—
298C2×C4×C5—42no—
299C2×C4×C5—42no—
300C2×C4×C5—42no—
301C2×C4×C5—42no—
302C2×C4×C5—42no—
303C2×C4×C5—42no—
304C2×C4×C5—42no—
305C2×C4×C5—42no—
306C2×C4×C5#11714yescomplemented
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—22no—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—22no—
316C2×Dic5—22no—
317C2×Dic5—22no—
318C2×Dic5—22no—
319C2×Dic5—22no—
320C2×Dic5—24no—
321C2×Dic5—22no—
322C2×Dic5—24no—
323C2×Dic5—24no—
324C2×Dic5—24no—
325C2×Dic5—24no—
326C2×Dic5—24no—
327C2×Dic5—24no—
328C2×Dic5—24no—
329C2×Dic5—232no—
330C2×Dic5—22no—
331C2×Dic5—24no—
332C2×Dic5—22no—
333C2×Dic5—24no—
334C2×Dic5—22no—
335C2×Dic5—24no—
336C2×Dic5—416no—
337C2×Dic5—42no—
338C2×Dic5—42no—
339C2×Dic5—42no—
340C2×Dic5—42no—
341C2×Dic5—42no—
342C2×Dic5—42no—
343C2×Dic5C2×C4214yes—
344C2×Dic5C2×C4214yes—
345C2×Dic5C2×C22⋊C418yes—
346C2×Dic5#11714yescomplemented
347C25C22×D511yescharacteristic
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—24no—
351C23×C4—42no—
352C23×C4—54no—
353C23×C4—54no—
354C23×C4—54no—
355C23×C4—52no—
356C23×C4—51no—
357C23×C4—51no—
358C23×C4—51no—
359C23×C4—52no—
360C23×C4—51no—
361C23×C4—54no—
362C23×C4—104no—
363C23×C4—102no—
364C23×C4—102no—
365C23×C4—102no—
366C23×C4—102no—
367C23×C4—102no—
368C23×C4—102no—
369C23×C4—202no—
370C23×C4C4×D514yes—
371C23×C4C22×D512yes—
372C23×C4C22×D512yes—
373C23×C4C22×D511yescharacteristic
374C23×C4C22×D511yescharacteristic
375#117—1032no—
376C2×C4⋊C4—58no—
377C2×C4⋊C4—104no—
378C2×C4⋊C4—104no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—54no—
384C2×C22⋊C4—54no—
385C2×C22⋊C4—54no—
386C2×C22⋊C4—54no—
387C2×C22⋊C4—102no—
388C2×C22⋊C4—102no—
389C2×C22⋊C4C4×D514yes—
390C2×C22⋊C4C4×D514yes—
391C2×C42—58no—
392C2×C42—104no—
393C2×C42—104no—
394C2×C42—104no—
395C2×C42—104no—
396C2×C42—104no—
397C2×C42—104no—
398C2×C42—202no—
399C2×C42—202no—
400#95—24no—
401#95—42no—
402#95—54no—
403#95—54no—
404#95—54no—
405#95—54no—
406#95—58no—
407#95—58no—
408#95—104no—
409#95—104no—
410#95—104no—
411#95—202no—
412C22×C5—28no—
413C22×C5—24no—
414C22×C5—24no—
415C22×C5—28no—
416C22×C5—24no—
417C22×C5—24no—
418C22×C5—28no—
419C22×C5—28no—
420C22×C5—24no—
421C22×C5—24no—
422C22×C5C4×C22⋊C418yes—
423C22×C5C22×C4211yescharacteristic
424C22×C5C22×C22⋊C411yescharacteristic
425C22×C5C2×#11711yescharacteristic
426C22×C5C2×#11711yescharacteristic
427C22×C5C2×#11711yescharacteristic
428C22×C5C2×C4×D411yescharacteristic
429C22×C5C2×C4×D411yescharacteristic
430C22×C5C2×C4×D411yescharacteristic
431C22×C5C2×C4×D411yescharacteristic
432C22×C5C4×#4112yes—
433C22×C5C4×#4112yes—
434C22×C5#51811yescharacteristic
435C22×C5#51911yescharacteristic
436C22×C5#52012yes—
437C22×C5#52012yes—
438C22×C5#54612yes—
439C22×C5#54612yes—
440C22×C5#54712yes—
441C22×C5#54712yes—
442C22×C5#55112yes—
443C22×C5#55112yes—
444C22×C5#55212yes—
445C22×C5#55212yes—
446C4×C5—24no—
447C4×C5—44no—
448C4×C5—42no—
449C4×C5—44no—
450Dic5—28no—
451Dic5—24no—
452Dic5—24no—
453Dic5—24no—
454Dic5—42no—
455Dic5—44no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24C2×C4×D512yes—
461C24C2×C4×D512yes—
462C24C2×C4×D512yes—
463C24D4×D512yes—
464C24D4×D512yes—
465C24#71112yes—
466C24#71312yes—
467C24C23×D511yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—44no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—52no—
493C22×C4—52no—
494C22×C4—52no—
495C22×C4—52no—
496C22×C4—52no—
497C22×C4—52no—
498C22×C4—54no—
499C22×C4—52no—
500C22×C4—54no—
501C22×C4—54no—
502C22×C4—54no—
503C22×C4—516no—
504C22×C4—54no—
505C22×C4—52no—
506C22×C4—108no—
507C22×C4—101no—
508C22×C4—101no—
509C22×C4—101no—
510C22×C4—101no—
511C22×C4—101no—
512C22×C4—102no—
513C22×C4—101no—
514C22×C4—101no—
515C22×C4—102no—
516C22×C4—102no—
517C22×C4—101no—
518C22×C4—101no—
519C22×C4—101no—
520C22×C4—102no—
521C22×C4—102no—
522C22×C4—108no—
523C22×C4—108no—
524C22×C4—108no—
525C22×C4—108no—
526C22×C4—108no—
527C22×C4—108no—
528C22×C4—101no—
529C22×C4—102no—
530C22×C4—102no—
531C22×C4—102no—
532C22×C4—102no—
533C22×C4—102no—
534C22×C4—101no—
535C22×C4—102no—
536C22×C4—102no—
537C22×C4—102no—
538C22×C4—108no—
539C22×C4—204no—
540C22×C4—208no—
541C22×C4—208no—
542C22×C4C2×C4×D514yes—
543C22×C4C2×C4×D512yes—
544C22×C4C2×C4×D514yes—
545C22×C4C2×C4×D512yes—
546C22×C4#71114yes—
547C4⋊C4—1016no—
548C22⋊C4—28no—
549C22⋊C4—28no—
550C22⋊C4—516no—
551C22⋊C4—108no—
552C42—1016no—
553C42—208no—
554C42—208no—
555C2×C5—28no—
556C2×C5C2×C4×C22⋊C411yescharacteristic
557C2×C5C4×#11711yescharacteristic
558C2×C5#227411yescharacteristic
559C2×C5#233912yes—
560C2×C5#234211yescharacteristic
561C2×C5#234211yescharacteristic
562C2×C5#234312yes—
563C2×C5#234411yescharacteristic
564C2×C5#234411yescharacteristic
565C2×C5#235912yes—
566C2×C5#235912yes—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23C42×D514yes—
584C23D5×C22⋊C414yes—
585C23#402714yes—
586C23#402714yes—
587C23#403814yes—
588C23#403914yes—
589C23#403914yes—
590C23C22×C4×D511yescharacteristic
591C23C22×C4×D511yescharacteristic
592C23C22×C4×D511yescharacteristic
593C23C2×D4×D511yescharacteristic
594C23C2×D4×D511yescharacteristic
595C23C2×#71112yes—
596C23C2×#71111yescharacteristic
597C23#414412yes—
598C23C2×#71311yescharacteristic
599C23D5×#4112yes—
600C23#415012yes—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—416no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—54no—
626C2×C4—54no—
627C2×C4—58no—
628C2×C4—54no—
629C2×C4—102no—
630C2×C4—102no—
631C2×C4—102no—
632C2×C4—102no—
633C2×C4—102no—
634C2×C4—102no—
635C2×C4—102no—
636C2×C4—102no—
637C2×C4—102no—
638C2×C4—102no—
639C2×C4—102no—
640C2×C4—102no—
641C2×C4—102no—
642C2×C4—102no—
643C2×C4—104no—
644C2×C4—104no—
645C2×C4—104no—
646C2×C4—104no—
647C2×C4—104no—
648C2×C4—104no—
649C2×C4—104no—
650C2×C4—1032no—
651C2×C4—104no—
652C2×C4—102no—
653C2×C4—104no—
654C2×C4—102no—
655C2×C4—102no—
656C2×C4—104no—
657C2×C4—104no—
658C2×C4—2016no—
659C2×C4—202no—
660C2×C4—202no—
661C2×C4—202no—
662C2×C4—202no—
663C2×C4—202no—
664C2×C4—202no—
665C2×C4#402314yescomplemented
666C5#1379911yescharacteristic, complemented, Sylow
667C22—24no—
668C22—28no—
669C22—28no—
670C22—28no—
671C22—28no—
672C22—24no—
673C22—24no—
674C22—24no—
675C22—24no—
676C22—24no—
677C22#6495518yes—
678C22C2×C42×D511yescharacteristic
679C22C2×#402311yescharacteristic
680C22C2×D5×C22⋊C411yescharacteristic
681C22C2×#402711yescharacteristic
682C22C2×#402711yescharacteristic
683C22#6582011yescharacteristic
684C22C2×#403811yescharacteristic
685C22C2×#403911yescharacteristic
686C22C2×#403911yescharacteristic
687C22#6585011yescharacteristic
688C22D5×#11711yescharacteristic
689C22C4×#71112yes—
690C22C4×#71112yes—
691C22#6588012yes—
692C22#6588012yes—
693C22#6592112yes—
694C22#6592512yes—
695C22#6594412yes—
696C22#6594512yes—
697C22#6597112yes—
698C22#6597612yes—
699C22#6598412yes—
700C22#6598912yes—
701C4—24no—
702C4—44no—
703C4—44no—
704C4—42no—
705C4—108no—
706C4—104no—
707C4—104no—
708C4—104no—
709C4—204no—
710C4—202no—
711C2—28no—
712C2C2×#6495511yescharacteristic
713C2C4×#402311yescharacteristic
714C2#1060516611yescharacteristic
715C2#1060555311yescharacteristic
716C2#1060560911yescharacteristic
717C2#1060574011yescharacteristic
718C2#1060579111yescharacteristic
719C2#1060612312yes—
720C2#1060612612yes—
721C2#1060640312yes—
722C2#1060640612yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC22×C5C22×C42
FittingC5×C22⋊#95C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC22⋊#95D5
hypocenterC5#13799
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
8. #10600199C2semidirect
9. #10600199C2semidirect
10. #10600196C2semidirect
11. Dic5×#95C2semidirect
25. C2×#4023C4semidirect
29. C2×#3963C4semidirect
40. #65232C4semidirect
85. C2×#683C2×C4semidirect
94. C2×C4×Dic5C2×C4semidirect
106. #3963C2×C4semidirect
107. #3963C2×C4semidirect
196. C22×Dic5C42semidirect
306. C2×C4×C5#117semidirect
346. C2×Dic5#117semidirect
665. C2×C4#4023semidirect
666. C5#13799semidirect

Maximal subgroups

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

subgroupindex
C22×#40232
C2×C4×C22⋊Dic52
C22×#39632
C2×#652322
C2×C22⋊C4×Dic52
C5×C22⋊#952
#106023372
#106001992
#106001962
Dic5×#952
#137995