Finite Group Databasebeta

← #12100446

Subgroups — #12100446

Order 1280.

2230 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D5C211yesmaximal, characteristic
2C22×D5×M16C211yesmaximal, characteristic, complemented
3C2×C5×#407C211yesmaximal, characteristic, complemented
4C2×#65496C211yesmaximal, characteristic, complemented
5C2×#65415C211yesmaximal, characteristic, complemented
6#10602772C211yesmaximal, characteristic, complemented
7#10602772C211yesmaximal, characteristic, complemented
8#10600751C214yesmaximal, complemented
9#10600750C214yesmaximal, complemented
10C24×C4×C5C2211yescharacteristic
11C23×C22⋊D5C411yescharacteristic
12C23×C4×D5C2211yescharacteristic
13C22×C5×M16C2211yescharacteristic
14C22×C5×M16C2211yescharacteristic
15C22×C22⋊Dic5C411yescharacteristic
16C2×C4×C22⋊D5—24no—
17C2×C4×C22⋊D5—24no—
18C2×C4×C22⋊D5C412yes—
19C2×C4×C22⋊D5C412yes—
20C2×C4×C22⋊D5C2212yes—
21C2×C4×C22⋊D5C2212yes—
22C22×#685C411yescharacteristic
23C22×#683C411yescharacteristic
24C22×C4×Dic5C2211yescharacteristic
25C22×#681C2211yescharacteristic
26C22×#681C2211yescharacteristic
27C2×D5×M16—24no—
28C2×D5×M16—24no—
29C2×D5×M16—24no—
30C22×#676C2212yescomplemented
31C22×C8×D5C2212yescomplemented
32C5×#407—24no—
33C2×C5×C22⋊C8C2214yescomplemented
34#65496—24no—
35C2×C22⋊#168C2214yescomplemented
36#65415—24no—
37C2×#3952C2212yescomplemented
38C2×#3952C2212yescomplemented
39#64770C2214yescomplemented
40#64770C2214yescomplemented
41#20898—51nomaximal, Sylow
42C25×C5C2×C411yescharacteristic
43C24×D5C2×C411yescharacteristic
44C23×C4×C5—22no—
45C23×C4×C5—22no—
46C23×C4×C5—22no—
47C23×C4×C5—22no—
48C23×C4×C5—22no—
49C23×C4×C5—22no—
50C23×C4×C5C2×C411yescharacteristic
51C23×C4×C5C2×C412yes—
52C23×C4×C5C2312yes—
53C23×C4×C5C2311yescharacteristic
54C22×C22⋊D5—24no—
55C22×C22⋊D5—28no—
56C22×C22⋊D5C2×C412yes—
57C22×C22⋊D5C2×C412yes—
58C23×Dic5C2×C411yescharacteristic
59C23×Dic5C2×C411yescharacteristic
60C23×Dic5C2×C411yescharacteristic
61C22×C4×D5—22no—
62C22×C4×D5—22no—
63C22×C4×D5—22no—
64C22×C4×D5—22no—
65C22×C4×D5C2×C411yescharacteristic
66C22×C4×D5C2×C411yescharacteristic
67C22×C4×D5D414yes—
68C22×C4×D5D414yes—
69C22×C4×D5C2311yescharacteristic
70C22×C4×D5C2311yescharacteristic
71C2×C5×M16—22no—
72C2×C5×M16—22no—
73C2×C5×M16—22no—
74C2×C5×M16—22no—
75C2×C5×M16—22no—
76C2×C5×M16D414yescomplemented
77C22×C5×C8C2312yes—
78C22×C5×C8C2312yes—
79C2×C22⋊Dic5—24no—
80C2×C22⋊Dic5C2×C412yes—
81C2×C22⋊Dic5C2×C412yes—
82C4×C22⋊D5—28no—
83C4×C22⋊D5—28no—
84C4×C22⋊D5—24no—
85C4×C22⋊D5—24no—
86C4×C22⋊D5—24no—
87C4×C22⋊D5—24no—
88C2×#685—24no—
89C2×#685C2×C412yes—
90C2×#685C2×C412yes—
91C2×#683—24no—
92C2×#683C2×C412yes—
93C2×#683C2×C412yes—
94C2×C4×Dic5—22no—
95C2×C4×Dic5—22no—
96C2×C4×Dic5C2×C412yes—
97C2×C4×Dic5C2312yes—
98C2×#681—22no—
99C2×#681—22no—
100C2×#681—22no—
101C2×#681—22no—
102C2×#681—22no—
103C2×#681D414yescomplemented
104C22×#168C2312yes—
105C22×#168C2312yes—
106D5×M16—232no—
107C2×#676—24no—
108C2×#676—24no—
109C2×#676—24no—
110C2×C8×D5—24no—
111C2×C8×D5—24no—
112C2×C8×D5—24no—
113C5×C22⋊C8—28no—
114C22⋊#168—28no—
115#3952—24no—
116#3952—24no—
117C23×M16—51no—
118C22×C4×D4—51no—
119C2×#407—51no—
120C2×#407—51no—
121C2×#407D511yescharacteristic, complemented
122#1870—54no—
123#1869—54no—
124#1728—51no—
125#1728—51no—
126C24×C5—22no—
127C24×C5—24no—
128C24×C5—22no—
129C24×C5—22no—
130C24×C5—42no—
131C24×C5C22×C412yes—
132C24×C5C22×C411yescharacteristic
133C23×D5—22no—
134C23×D5—22no—
135C23×D5—24no—
136C23×D5—42no—
137C23×D5C22⋊C414yes—
138C23×D5C22×C411yescharacteristic
139C23×D5C22×C411yescharacteristic
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—24no—
144C22×C4×C5—24no—
145C22×C4×C5—24no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—44no—
153C22×C4×C5—44no—
154C22×C4×C5—44no—
155C22×C4×C5—44no—
156C22×C4×C5C22×C412yes—
157C22×C4×C5C22×C411yescharacteristic
158C22×C4×C5C2×D412yes—
159C22×C4×C5C2×D412yes—
160C22×C4×C5C2×D412yes—
161C22×C4×C5C2×D412yes—
162C22×C4×C5#4112yes—
163C22×C4×C5#4112yes—
164C22×C4×C5C2411yescharacteristic
165C2×C22⋊D5—232no—
166C2×C22⋊D5—24no—
167C2×C22⋊D5—24no—
168C2×C22⋊D5—24no—
169C2×C22⋊D5—24no—
170C2×C22⋊D5—24no—
171C2×C22⋊D5M1618yescomplemented
172C22×Dic5—22no—
173C22×Dic5—22no—
174C22×Dic5—22no—
175C22×Dic5—24no—
176C22×Dic5—22no—
177C22×Dic5—42no—
178C22×Dic5C22⋊C414yes—
179C22×Dic5C22×C412yes—
180C22×Dic5C22×C411yescharacteristic
181C22×Dic5C22×C411yescharacteristic
182C22×Dic5C22×C412yes—
183C2×C4×D5—22no—
184C2×C4×D5—22no—
185C2×C4×D5—22no—
186C2×C4×D5—22no—
187C2×C4×D5—28no—
188C2×C4×D5—28no—
189C2×C4×D5—28no—
190C2×C4×D5—28no—
191C2×C4×D5—21no—
192C2×C4×D5—21no—
193C2×C4×D5—21no—
194C2×C4×D5—21no—
195C2×C4×D5—21no—
196C2×C4×D5—21no—
197C2×C4×D5—21no—
198C2×C4×D5—21no—
199C2×C4×D5C22⋊C414yes—
200C2×C4×D5C22⋊C414yes—
201C2×C4×D5C2×D412yes—
202C2×C4×D5C2×D412yes—
203C2×C4×D5C2×D412yes—
204C2×C4×D5C2×D412yes—
205C5×M16—28no—
206C5×M16—44no—
207C2×C5×C8—22no—
208C2×C5×C8—22no—
209C2×C5×C8—22no—
210C2×C5×C8—22no—
211C2×C5×C8—22no—
212C2×C5×C8C2×D414yescomplemented
213C22⋊Dic5—24no—
214C22⋊Dic5—24no—
215#685—24no—
216#685—24no—
217#683—24no—
218#683—24no—
219C4×Dic5—24no—
220C4×Dic5—22no—
221C4×Dic5—22no—
222#681—28no—
223#681—44no—
224C2×#168—22no—
225C2×#168—22no—
226C2×#168—22no—
227C2×#168—22no—
228C2×#168—22no—
229C2×#168C2×D414yescomplemented
230#676—216no—
231C8×D5—216no—
232C23×D4—51no—
233C24×C4—51no—
234C24×C4C2×D511yescharacteristic
235C22×M16—51no—
236C22×M16—51no—
237C22×M16—52no—
238C22×M16—104no—
239C22×M16—104no—
240C22×M16—104no—
241C22×M16C2×D511yescharacteristic
242C22×M16C2×D511yescharacteristic
243C23×C8—52no—
244C2×C4×D4—52no—
245C2×C4×D4—52no—
246C2×C4×D4—52no—
247C2×C4×D4—52no—
248C2×C4×D4—104no—
249C2×C4×D4—104no—
250C22×C4⋊C4—51no—
251C22×C22⋊C4—51no—
252C22×C22⋊C4—51no—
253C22×C42—51no—
254#407—24no—
255#407—104no—
256#407—104no—
257C2×C22⋊C8—54no—
258C2×C22⋊C8—52no—
259C2×C22⋊C8—52no—
260C2×C22⋊C8C2×D514yescomplemented
261#336—54no—
262#336—54no—
263C23×C5—22no—
264C23×C5—22no—
265C23×C5—28no—
266C23×C5—22no—
267C23×C5—22no—
268C23×C5—22no—
269C23×C5—22no—
270C23×C5—22no—
271C23×C5—22no—
272C23×C5—48no—
273C23×C5—48no—
274C23×C5—44no—
275C23×C5—44no—
276C23×C5C2×C22⋊C412yes—
277C23×C5C4×D412yes—
278C23×C5C4×D412yes—
279C23×C5C2×M1614yescomplemented
280C23×C5C23×C411yescharacteristic
281C22×D5—21no—
282C22×D5—21no—
283C22×D5—22no—
284C22×D5—21no—
285C22×D5—21no—
286C22×D5—22no—
287C22×D5—22no—
288C22×D5—28no—
289C22×D5—28no—
290C22×D5—44no—
291C22×D5—48no—
292C22×D5—48no—
293C22×D5C2×C22⋊C412yes—
294C22×D5C2×C22⋊C412yes—
295C22×D5C2×M1614yes—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—44no—
300C2×C4×C5—42no—
301C2×C4×C5—42no—
302C2×C4×C5—42no—
303C2×C4×C5—42no—
304C2×C4×C5—48no—
305C2×C4×C5C2×C22⋊C412yes—
306C2×C4×C5C4×D412yes—
307C2×C4×C5C4×D412yes—
308C2×C4×C5#12014yes—
309C2×C4×C5#12114yes—
310C2×C4×C5#12114yes—
311C2×C4×C5#12314yes—
312C2×C4×C5C22×D411yescharacteristic
313C2×C4×C5C22×D411yescharacteristic
314C2×C4×C5C22×D411yescharacteristic
315C2×C4×C5C22×D411yescharacteristic
316C2×C4×C5C2×#4111yescharacteristic
317C2×C4×C5C2×#4111yescharacteristic
318C22⋊D5—216no—
319C22⋊D5—216no—
320C2×Dic5—28no—
321C2×Dic5—22no—
322C2×Dic5—21no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—22no—
327C2×Dic5—28no—
328C2×Dic5—22no—
329C2×Dic5—24no—
330C2×Dic5—44no—
331C2×Dic5C2×C22⋊C412yes—
332C2×Dic5C2×C22⋊C412yes—
333C2×Dic5C2×M1614yescomplemented
334C4×D5—22no—
335C4×D5—22no—
336C4×D5—22no—
337C4×D5—22no—
338C4×D5—22no—
339C4×D5—22no—
340C4×D5—22no—
341C4×D5—22no—
342C4×D5—28no—
343C4×D5—28no—
344C5×C8—24no—
345C5×C8—42no—
346#168—24no—
347#168—42no—
348C25—51no—
349C25C4×D511yescharacteristic
350C22×D4—52no—
351C22×D4—52no—
352C22×D4—108no—
353C22×D4—104no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—51no—
361C23×C4—51no—
362C23×C4—51no—
363C23×C4—54no—
364C23×C4—54no—
365C23×C4—51no—
366C23×C4—51no—
367C23×C4—51no—
368C23×C4—51no—
369C23×C4—102no—
370C23×C4—102no—
371C23×C4—102no—
372C23×C4—102no—
373C23×C4C4×D511yescharacteristic
374C23×C4C4×D512yes—
375C23×C4C22×D512yes—
376C23×C4C22×D511yescharacteristic
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16—54no—
383C2×M16—104no—
384C2×M16—104no—
385C2×M16—1032no—
386C2×M16—102no—
387C2×M16—102no—
388C2×M16—102no—
389C2×M16—102no—
390C2×M16—102no—
391C2×M16—104no—
392C2×M16C22⋊D514yescomplemented
393C22×C8—52no—
394C22×C8—52no—
395C22×C8—104no—
396C22×C8—104no—
397C22×C8—104no—
398C22×C8C22×D512yes—
399C22×C8C22×D512yes—
400C4×D4—104no—
401C4×D4—104no—
402C4×D4—104no—
403C4×D4—104no—
404C4×D4—108no—
405C4×D4—108no—
406C2×C4⋊C4—52no—
407C2×C4⋊C4—52no—
408C2×C4⋊C4—104no—
409C2×C22⋊C4—52no—
410C2×C22⋊C4—52no—
411C2×C22⋊C4—52no—
412C2×C22⋊C4—52no—
413C2×C22⋊C4—104no—
414C2×C22⋊C4—104no—
415C2×C42—52no—
416C2×C42—52no—
417C2×C42—102no—
418C2×C42—102no—
419C22⋊C8—28no—
420C22⋊C8—104no—
421C22⋊C8—104no—
422C22⋊C8—108no—
423C22×C5—22no—
424C22×C5—22no—
425C22×C5—24no—
426C22×C5—24no—
427C22×C5—24no—
428C22×C5—24no—
429C22×C5—24no—
430C22×C5—416no—
431C22×C5—42no—
432C22×C5—42no—
433C22×C5—42no—
434C22×C5—42no—
435C22×C5#38614yes—
436C22×C5C22×C22⋊C411yescharacteristic
437C22×C5C2×C4×D411yescharacteristic
438C22×C5C2×C4×D411yescharacteristic
439C22×C5C22×M1612yes—
440C22×C5#56812yes—
441C2×D5—22no—
442C2×D5—24no—
443C2×D5—24no—
444C2×D5—22no—
445C2×D5—22no—
446C2×D5—22no—
447C2×D5—22no—
448C2×D5—416no—
449C2×D5—42no—
450C2×D5—42no—
451C2×D5#40714yescomplemented
452C4×C5—42no—
453C4×C5#38614yes—
454C4×C5C2×#12011yescharacteristic
455C4×C5C2×#12111yescharacteristic
456C4×C5C2×#12111yescharacteristic
457C4×C5C2×#12311yescharacteristic
458Dic5—24no—
459Dic5—22no—
460Dic5—22no—
461Dic5—42no—
462C24—22no—
463C24—24no—
464C24—22no—
465C24—22no—
466C24—42no—
467C24—51no—
468C24—51no—
469C24—54no—
470C24—104no—
471C24—102no—
472C24—102no—
473C24—202no—
474C24C2×C4×D512yes—
475C24C2×C4×D511yescharacteristic
476C2×D4—58no—
477C2×D4—104no—
478C2×D4—104no—
479C2×D4—104no—
480C2×D4—104no—
481C2×D4—1032no—
482C2×D4—104no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—52no—
500C22×C4—51no—
501C22×C4—51no—
502C22×C4—54no—
503C22×C4—52no—
504C22×C4—52no—
505C22×C4—52no—
506C22×C4—52no—
507C22×C4—54no—
508C22×C4—54no—
509C22×C4—52no—
510C22×C4—104no—
511C22×C4—102no—
512C22×C4—102no—
513C22×C4—102no—
514C22×C4—101no—
515C22×C4—101no—
516C22×C4—101no—
517C22×C4—101no—
518C22×C4—101no—
519C22×C4—101no—
520C22×C4—101no—
521C22×C4—101no—
522C22×C4—102no—
523C22×C4—102no—
524C22×C4—108no—
525C22×C4—108no—
526C22×C4—102no—
527C22×C4—102no—
528C22×C4—108no—
529C22×C4—108no—
530C22×C4—102no—
531C22×C4—202no—
532C22×C4C2×C4×D512yes—
533C22×C4C2×C4×D511yescharacteristic
534C22×C4#70912yes—
535C22×C4D4×D512yes—
536C22×C4D4×D512yes—
537C22×C4D4×D512yes—
538C22×C4#71112yes—
539C22×C4C2×C22⋊D512yes—
540C22×C4C23×D511yescharacteristic
541M16—28no—
542M16—44no—
543M16—1016no—
544M16—108no—
545M16—204no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—54no—
552C2×C8—1016no—
553C2×C8—102no—
554C2×C8—102no—
555C2×C8—102no—
556C2×C8—102no—
557C2×C8—102no—
558C2×C8C2×C22⋊D514yescomplemented
559C4⋊C4—104no—
560C4⋊C4—104no—
561C22⋊C4—104no—
562C22⋊C4—104no—
563C22⋊C4—104no—
564C22⋊C4—104no—
565C42—102no—
566C42—102no—
567C42—104no—
568C2×C5—24no—
569C2×C5—44no—
570C2×C5C2×#38611yescharacteristic
571C2×C5C2×#40711yescharacteristic
572C2×C5#287911yescharacteristic
573C2×C5D4×M1612yes—
574C2×C5D4×M1612yes—
575D5—24no—
576D5—42no—
577C23—22no—
578C23—22no—
579C23—28no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—48no—
587C23—48no—
588C23—44no—
589C23—44no—
590C23—52no—
591C23—54no—
592C23—52no—
593C23—108no—
594C23—101no—
595C23—102no—
596C23—101no—
597C23—101no—
598C23—102no—
599C23—102no—
600C23—101no—
601C23—108no—
602C23—204no—
603C23—208no—
604C23—208no—
605C23D5×C22⋊C412yes—
606C23#402712yes—
607C23D5×M1614yescomplemented
608C23C4×C22⋊D512yes—
609C23C22×C4×D511yescharacteristic
610D4—1016no—
611D4—1016no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—44no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—48no—
621C2×C4—52no—
622C2×C4—52no—
623C2×C4—54no—
624C2×C4—108no—
625C2×C4—102no—
626C2×C4—101no—
627C2×C4—101no—
628C2×C4—102no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—108no—
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—108no—
641C2×C4—108no—
642C2×C4—102no—
643C2×C4—104no—
644C2×C4—204no—
645C2×C4D5×C22⋊C412yes—
646C2×C4#402712yes—
647C2×C4#402914yes—
648C2×C4#403014yes—
649C2×C4C4×C22⋊D512yes—
650C2×C4#408314yes—
651C2×C4#408414yes—
652C2×C4C2×#70911yescharacteristic
653C2×C4C2×D4×D511yescharacteristic
654C2×C4C2×D4×D511yescharacteristic
655C2×C4C2×D4×D511yescharacteristic
656C2×C4C2×#71111yescharacteristic
657C2×C4C22×C22⋊D511yescharacteristic
658C8—24no—
659C8—42no—
660C8—104no—
661C8—202no—
662C5#2089811yescharacteristic, complemented, Sylow
663C22—24no—
664C22—22no—
665C22—22no—
666C22—24no—
667C22—24no—
668C22—24no—
669C22—24no—
670C22—416no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—54no—
676C22—102no—
677C22—104no—
678C22—102no—
679C22—104no—
680C22—102no—
681C22—102no—
682C22—102no—
683C22—2016no—
684C22—202no—
685C22—202no—
686C22#6524514yes—
687C22C2×D5×C22⋊C411yescharacteristic
688C22C2×#402711yescharacteristic
689C22C2×D5×M1612yes—
690C22#6607912yes—
691C22C2×C4×C22⋊D511yescharacteristic
692C4—42no—
693C4—102no—
694C4—102no—
695C4—104no—
696C4—202no—
697C4#6524514yes—
698C4C2×#402911yescharacteristic
699C4C2×#403011yescharacteristic
700C4C2×#408311yescharacteristic
701C4C2×#408411yescharacteristic
702C2—24no—
703C2—44no—
704C2—104no—
705C2—202no—
706C2#1061035912yes—
707C2D5×#40711yescharacteristic
708C2#1061036111yescharacteristic
709C2C2×#6524511yescharacteristic
710C2M16×C22⋊D512yes—
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC2×C5×#407C2
prime radicalC23×C22⋊D5C4
cosocleC22×C4×C5C24
hypercenterC2×#407D5
hypocenterC5#20898
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C22×D5×M16C2semidirect
3. C2×C5×#407C2semidirect
4. C2×#65496C2semidirect
5. C2×#65415C2semidirect
6. #10602772C2semidirect
7. #10602772C2semidirect
8. #10600751C2semidirect
9. #10600750C2semidirect
30. C22×#676C22semidirect
31. C22×C8×D5C22semidirect
33. C2×C5×C22⋊C8C22semidirect
35. C2×C22⋊#168C22semidirect
37. C2×#3952C22semidirect
38. C2×#3952C22semidirect
39. #64770C22semidirect
40. #64770C22semidirect
76. C2×C5×M16D4semidirect
103. C2×#681D4semidirect
121. C2×#407D5semidirect
171. C2×C22⋊D5M16semidirect
212. C2×C5×C8C2×D4semidirect
229. C2×#168C2×D4semidirect
260. C2×C22⋊C8C2×D5semidirect
279. C23×C5C2×M16semidirect
333. C2×Dic5C2×M16semidirect
392. C2×M16C22⋊D5semidirect
451. C2×D5#407semidirect
558. C2×C8C2×C22⋊D5semidirect
607. C23D5×M16semidirect
662. C5#20898semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D52
C22×D5×M162
C2×C5×#4072
C2×#654962
C2×#654152
#106027722
#106007512
#106007502
#208985