Finite Group Databasebeta

← #14424132

Subgroups — #14424132

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6769C211yesmaximal, characteristic
2C5×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×#91520C212yesmaximal, complemented
4#11751147C211yesmaximal, characteristic, complemented
5C3×#65339C211yesmaximal, characteristic, complemented
6#11749408C212yesmaximal, complemented
7#11748555C211yesmaximal, characteristic, complemented
8#11748554C211yesmaximal, characteristic, complemented
9#11748505C211yesmaximal, characteristic, complemented
10#11747516C212yesmaximal, complemented
11#11747505C212yesmaximal, complemented
12#10614466—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C2×C5×D3×Q8C2211yescharacteristic, complemented
15C22×C4×C5×D3C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C22×#1203—21no—
18C22×#1200—21no—
19C2×#6769—21no—
20C2×#6769—21no—
21C2×#6769—28no—
22C2×#6769C2212yes—
23C2×#6769C2212yes—
24C3×C5×C22⋊Q8C2211yescharacteristic
25C2×#6717C2212yescomplemented
26C5×#946C2211yescharacteristic, complemented
27C5×#924C2211yescharacteristic
28C5×#897C2211yescharacteristic, complemented
29C5×#896—21no—
30C5×D3×C4⋊C4—21no—
31C5×D3×C4⋊C4C2211yescharacteristic, complemented
32C5×D3×C22⋊C4—21no—
33C5×#878—21no—
34C2×C3×#689C2212yescomplemented
35#91520—28no—
36C2×#6661C2212yescomplemented
37C2×#6660C2212yescomplemented
38C2×#6650C2212yescomplemented
39#91114C2211yescharacteristic
40#91093C2212yescomplemented
41C3×C22⋊#168C2211yescharacteristic
42C3×#3942C2212yescomplemented
43#90970C2212yescomplemented
44#90969C2212yescomplemented
45(C2×D3)⋊#168C2212yescomplemented
46#80184—51nomaximal, Hall
47C22×#709—31no—
48C2×C5×C22⋊Q8—31no—
49C2×#4088—32no—
50#65496—31no—
51#65339—31no—
52#65339D311yescharacteristic, complemented
53#65336—32no—
54#65336—32no—
55#65335—31no—
56#65335—31no—
57#65255—32no—
58C23×D15—21no—
59C23×C5×D3D411yescharacteristic
60C2×C3×C5×Q8C2311yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C2×D60—21no—
63C2×D60—24no—
64C2×D60C2312yes—
65C22×C5×Dic3D411yescharacteristic
66C5×D3×Q8—24no—
67C2×C4×C5×D3—24no—
68C2×C4×C5×D3—21no—
69C2×C4×C5×D3—21no—
70C2×C4×C5×D3D411yescharacteristic
71C2×C4×C5×D3D411yescharacteristic
72C2×C4×C5×D3C2311yescharacteristic
73C2×C4×C5×D3C2311yescharacteristic
74C2×C5×Dic6—21no—
75C2×C5×Dic6C2311yescharacteristic
76C22×C3×Dic5—21no—
77C2×C3×Dic10—21no—
78C2×C3×Dic10—24no—
79C2×C3×Dic10C2312yes—
80C2×#1203—28no—
81C2×#1203—22no—
82C2×#1203—22no—
83C2×#1200—28no—
84C2×#1200—22no—
85C2×#1200—22no—
86#6769—28no—
87#6769—28no—
88#6769—24no—
89#6769—24no—
90#6769—24no—
91#6769D418yes—
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4C2311yescharacteristic
94C3×C5×C22⋊C4—21no—
95#6717—24no—
96C2×C3⋊#168C2312yes—
97C5×#217—21no—
98C5×(C2×D3)⋊C4—21no—
99C5×(C2×D3)⋊C4—21no—
100C5×C4⋊Dic3—21no—
101C5×C4⋊Dic3C2311yescharacteristic
102C5×Dic3⋊C4—21no—
103C5×Dic3⋊C4—21no—
104C5×Dic3⋊C4—21no—
105C3×#689—24no—
106C2×C3×#168C2312yes—
107#6661—24no—
108#6660—24no—
109#6650—24no—
110C22×#239—51no—
111C2×#918—52no—
112D3×C22⋊Q8D511yescharacteristic, complemented
113C3×#451—51no—
114#5228—51no—
115#5187—52no—
116#5046—51no—
117#4808—52no—
118#4803—52no—
119#4731—51no—
120#4726—51no—
121C22×C5×Q8—31no—
122C23×C4×C5—31no—
123C22×C22⋊D5—61no—
124C2×#709—32no—
125C2×#709—32no—
126C2×#709—68no—
127C2×#709—61no—
128C2×#709—61no—
129C22×D20—31no—
130C22×C4×D5—61no—
131C22×Dic10C2×D311yescharacteristic
132C5×C22⋊Q8—31no—
133C5×C22⋊Q8—31no—
134C5×C22⋊Q8—31no—
135C5×C22⋊Q8—61no—
136C5×C22⋊Q8—61no—
137C5×C22⋊Q8C2×D311yescharacteristic
138C2×C5×C4⋊C4—31no—
139C2×C5×C4⋊C4—61no—
140C2×C5×C22⋊C4—61no—
141C2×#689—32no—
142C2×#689C2×D312yescomplemented
143#4088—68no—
144C2×#688—32no—
145C2×#688—32no—
146C2×#681—32no—
147C22⋊#168—31no—
148C22⋊#168—32no—
149C22⋊#168C2×D311yescharacteristic
150#3942—32no—
151#3942C2×D312yescomplemented
152#3941—32no—
153#3941—32no—
154#3007—151noSylow
155C23×C3×C5C2×D411yescharacteristic
156C22×D15—24no—
157C22×D15—22no—
158C22×D15—42no—
159C22×D15—42no—
160C22×C5×D3—22no—
161C22×C5×D3—22no—
162C22×C5×D3—41no—
163C22×C5×D3C2×D411yescharacteristic
164C22×C5×D3C2×D411yescharacteristic
165C3×C5×Q8—22no—
166C2×C3×C4×C5—22no—
167C2×C3×C4×C5—21no—
168C2×C3×C4×C5—21no—
169C2×C3×C4×C5C2×D411yescharacteristic
170C2×C3×C4×C5C2411yescharacteristic
171D60—24no—
172D60—22no—
173D60C2×D414yes—
174C2×C5×Dic3—22no—
175C2×C5×Dic3—21no—
176C2×C5×Dic3—21no—
177C2×C5×Dic3C2×D411yescharacteristic
178C2×C5×Dic3C2×D411yescharacteristic
179C4×C5×D3—22no—
180C4×C5×D3—22no—
181C4×C5×D3—22no—
182C4×C5×D3—42no—
183C4×C5×D3—42no—
184C4×C5×D3C2×D414yes—
185C5×Dic6—22no—
186C5×Dic6—42no—
187C2×C3×Dic5—24no—
188C2×C3×Dic5—22no—
189C3×Dic10—24no—
190C3×Dic10—22no—
191C3×Dic10C2×D414yes—
192#1203—28no—
193#1203—28no—
194#1200—28no—
195#1200—28no—
196C3⋊#168—22no—
197C3×#168—22no—
198C22×C3×Q8—51no—
199C2×#239—52no—
200C2×#239—52no—
201C2×#239—108no—
202C2×#239—101no—
203C2×#239—101no—
204C2×D3×Q8C2×D511yescharacteristic, complemented
205C22×D12—51no—
206C22×D12—101no—
207C22×C4×D3—101no—
208C22×C4×D3C2×D511yescharacteristic
209C2×C3×Q16—52no—
210C3×C22⋊Q8C2×D511yescharacteristic
211#946C2×D511yescharacteristic, complemented
212C2×#216—52no—
213C2×#215—52no—
214#924C2×D511yescharacteristic
215#918—108no—
216C2×#204—52no—
217C2×ΓL(1,𝔽25)—52no—
218#897C2×D511yescharacteristic, complemented
219#896—21no—
220D3×C4⋊C4—21no—
221D3×C4⋊C4C2×D511yescharacteristic, complemented
222D3×C22⋊C4—21no—
223#878—21no—
224C3×#103—52no—
225C3×C22⋊C8—51no—
226#835—52no—
227#830—51no—
228#821—52no—
229(C2×D3)⋊C8—52no—
230#809—52no—
231C24×C5—31no—
232C23×D5—61no—
233C2×C5×Q8—31no—
234C2×C5×Q8—61no—
235C2×C5×Q8—64no—
236C2×C5×Q8C22×D311yescharacteristic
237C22×C4×C5—31no—
238C22×C4×C5—31no—
239C22×C4×C5—31no—
240C22×C4×C5—31no—
241C22×C4×C5—31no—
242C22×C4×C5—64no—
243C22×C4×C5—61no—
244C22×C4×C5—61no—
245C22×C4×C5C22×D311yescharacteristic
246C2×C22⋊D5—62no—
247C2×C22⋊D5—62no—
248C2×C22⋊D5—68no—
249C22×Dic5—21no—
250#709—38no—
251#709—64no—
252#709—64no—
253#709—68no—
254#709—68no—
255#709—64no—
256C2×D20—32no—
257C2×D20—64no—
258C2×D20—61no—
259C2×C4×D5—62no—
260C2×C4×D5—62no—
261C2×C4×D5—68no—
262C2×Dic10—21no—
263C2×Dic10—24no—
264C2×Dic10C22×D312yes—
265C5×C4⋊C4—21no—
266C5×C4⋊C4—31no—
267C5×C4⋊C4—61no—
268C5×C4⋊C4—61no—
269C5×C4⋊C4—61no—
270C5×C4⋊C4—61no—
271C5×C4⋊C4C22×D311yescharacteristic
272C5×C22⋊C4—21no—
273C5×C22⋊C4—61no—
274C5×C22⋊C4—61no—
275C5×C22⋊C4—61no—
276#689—24no—
277#689—64no—
278#688—64no—
279#688—64no—
280#681—64no—
281C2×#168—32no—
282C2×#168C22×D312yes—
283C22×#41—151no—
284C2×#137—152no—
285C2×C22⋊Q8—31no—
286#452—152no—
287#452—152no—
288#451—51no—
289#451—151no—
290#450—151no—
291#450—151no—
292#417—152no—
293#407—151no—
294C22×C3×C5—21no—
295C22×C3×C5—21no—
296C22×C3×C5#13712yescomplemented
297C22×C3×C5C22×D411yescharacteristic
298C2×D15—24no—
299C2×D15—48no—
300C2×D15—42no—
301C2×D15—42no—
302C2×C5×D3—21no—
303C2×C5×D3—21no—
304C2×C5×D3—21no—
305C2×C5×D3—21no—
306C2×C5×D3—21no—
307C2×C5×D3—44no—
308C2×C5×D3#12012yes—
309C3×C4×C5—21no—
310C3×C4×C5—41no—
311C3×C4×C5—41no—
312C3×C4×C5C22×D412yes—
313C3×Dic5—24no—
314C5×Dic3—21no—
315C5×Dic3—41no—
316C5×Dic3—41no—
317C5×Dic3#12012yes—
318C23×D3—101no—
319C23×D3C22⋊D511yescharacteristic
320C2×C3×Q8—52no—
321C2×C3×Q8—104no—
322C2×C3×Q8—101no—
323C2×C3×Q8C22×D511yescharacteristic
324C22×C3×C4—101no—
325C22×C3×C4C22×D511yescharacteristic
326C22×Dic3C22⋊D511yescharacteristic
327#239—58no—
328#239—104no—
329#239—104no—
330#239—108no—
331#239—108no—
332#239—104no—
333D3×Q8—24no—
334C2×D12—52no—
335C2×D12—104no—
336C2×D12—108no—
337C2×D12—102no—
338C2×D12—102no—
339C2×D12—101no—
340C2×C4×D3—24no—
341C2×C4×D3—21no—
342C2×C4×D3—21no—
343C2×C4×D3—108no—
344C2×C4×D3—102no—
345C2×C4×D3—102no—
346C2×C4×D3C22⋊D511yescharacteristic
347C2×C4×D3C22⋊D511yescharacteristic
348C2×C4×D3C22×D511yescharacteristic
349C2×C4×D3C22×D511yescharacteristic
350C2×Dic6—21no—
351C2×Dic6C22×D511yescharacteristic
352C3×Q16—104no—
353C2×C3×C8—52no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4C22×D511yescharacteristic
356C3×C22⋊C4—21no—
357#217—21no—
358#216—104no—
359#215—104no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362C4⋊Dic3—21no—
363C4⋊Dic3C22×D511yescharacteristic
364Dic3⋊C4—21no—
365Dic3⋊C4—21no—
366Dic3⋊C4—21no—
367C2×C3⋊C8—52no—
368#204—104no—
369ΓL(1,𝔽25)—104no—
370C23×C5—31no—
371C23×C5—31no—
372C23×C5—62no—
373C23×C5—62no—
374C23×C5—121no—
375C23×C5D3×D411yescharacteristic
376C22×D5—64no—
377C22×D5—62no—
378C22×D5—122no—
379C22×D5—122no—
380C5×Q8—22no—
381C5×Q8—62no—
382C5×Q8—122no—
383C2×C4×C5—22no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—31no—
387C2×C4×C5—34no—
388C2×C4×C5—31no—
389C2×C4×C5—62no—
390C2×C4×C5—62no—
391C2×C4×C5—62no—
392C2×C4×C5—62no—
393C2×C4×C5—61no—
394C2×C4×C5—61no—
395C2×C4×C5—122no—
396C2×C4×C5—122no—
397C2×C4×C5D3×D411yescharacteristic
398C2×C4×C5C23×D311yescharacteristic
399C22⋊D5—68no—
400C22⋊D5—68no—
401C2×Dic5—24no—
402C2×Dic5—22no—
403D20—34no—
404D20—64no—
405D20—62no—
406C4×D5—68no—
407C4×D5—68no—
408Dic10—24no—
409Dic10—22no—
410Dic10D3×D414yes—
411#168—22no—
412#168—62no—
413C2×#41—152no—
414C2×#41—152no—
415C2×#41—301no—
416C2×#41—301no—
417C2×#41—308no—
418C22×Q8—31no—
419C22×Q8—51no—
420C22×D4—151no—
421C22×D4—301no—
422C23×C4—31no—
423C23×C4—301no—
424#137—308no—
425C2×Q16—52no—
426C2×Q16—152no—
427C2×SD16—152no—
428C2×SD16—152no—
429C2×M16—152no—
430C22⋊Q8—31no—
431C22⋊Q8—31no—
432C22⋊Q8—31no—
433C22⋊Q8—61no—
434C22⋊Q8—61no—
435C22⋊Q8D3×D511yescharacteristic
436C2×C4⋊C4—31no—
437C2×C4⋊C4—61no—
438C2×C22⋊C4—61no—
439#103—52no—
440#103—152no—
441#102—152no—
442#102—152no—
443C22⋊C8—51no—
444C22⋊C8—152no—
445C22⋊C8—151no—
446C2×C3×C5—22no—
447C2×C3×C5C2×#12011yescharacteristic
448C2×C3×C5C2×#13711yescharacteristic
449C2×C3×C5#57511yescharacteristic
450D15—44no—
451C5×D3—22no—
452C5×D3—41no—
453C23×C3C2×C22⋊D511yescharacteristic
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—41no—
457C22×D3—104no—
458C22×D3—102no—
459C22×D3—202no—
460C22×D3—202no—
461C22×D3C2×C22⋊D511yescharacteristic
462C22×D3C2×C22⋊D511yescharacteristic
463C3×Q8—22no—
464C3×Q8—54no—
465C3×Q8—104no—
466C3×Q8—102no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—104no—
471C2×C3×C4—102no—
472C2×C3×C4C2×C22⋊D511yescharacteristic
473C2×C3×C4C23×D511yescharacteristic
474C2×Dic3—22no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3C2×C22⋊D511yescharacteristic
478C2×Dic3C2×C22⋊D511yescharacteristic
479D12—54no—
480D12—104no—
481D12—108no—
482D12—108no—
483D12—102no—
484C4×D3—22no—
485C4×D3—22no—
486C4×D3—22no—
487C4×D3—42no—
488C4×D3—42no—
489C4×D3—108no—
490C4×D3—108no—
491C4×D3D4×D514yes—
492Dic6—22no—
493Dic6—42no—
494C3×C8—102no—
495C3⋊C8—102no—
496C22×C5—21no—
497C22×C5—21no—
498C22×C5—32no—
499C22×C5—61no—
500C22×C5—61no—
501C22×C5—61no—
502C22×C5—61no—
503C22×C5—61no—
504C22×C5—124no—
505C22×C5#91812yescomplemented
506C22×C5C2×D3×D411yescharacteristic
507C2×D5—64no—
508C2×D5—128no—
509C2×D5—122no—
510C2×D5—122no—
511C4×C5—21no—
512C4×C5—32no—
513C4×C5—41no—
514C4×C5—41no—
515C4×C5—61no—
516C4×C5—121no—
517C4×C5—121no—
518C4×C5C2×D3×D412yes—
519Dic5—24no—
520C24—31no—
521C24—301no—
522#41—158no—
523#41—304no—
524#41—304no—
525#41—304no—
526#41—308no—
527#41—308no—
528C2×Q8—31no—
529C2×Q8—52no—
530C2×Q8—61no—
531C2×Q8—64no—
532C2×Q8—104no—
533C2×Q8—101no—
534C2×Q8C2×D3×D511yescharacteristic
535C2×D4—152no—
536C2×D4—304no—
537C2×D4—302no—
538C2×D4—302no—
539C2×D4—308no—
540C2×D4—301no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—64no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—101no—
550C22×C4—302no—
551C22×C4—302no—
552C22×C4—308no—
553C22×C4C2×D3×D511yescharacteristic
554Q16—104no—
555Q16—304no—
556SD16—304no—
557SD16—304no—
558M16—304no—
559C2×C8—52no—
560C2×C8—152no—
561C4⋊C4—21no—
562C4⋊C4—31no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4C2×D3×D511yescharacteristic
568C22⋊C4—21no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C3×C5#300711yescharacteristic, complemented, Hall
573C22×C3—21no—
574C22×C3—21no—
575C22×C3#408812yescomplemented
576C22×C3C22×C22⋊D511yescharacteristic
577C2×D3—21no—
578C2×D3—21no—
579C2×D3—21no—
580C2×D3—21no—
581C2×D3—21no—
582C2×D3—44no—
583C2×D3—104no—
584C2×D3—208no—
585C2×D3—202no—
586C2×D3—202no—
587C2×D3#408312yes—
588C3×C4—21no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—104no—
592C3×C4C2×D4×D512yes—
593Dic3—21no—
594Dic3—41no—
595Dic3—41no—
596Dic3#408312yes—
597C2×C5—22no—
598C2×C5—62no—
599C2×C5—121no—
600C2×C5D3×#12011yescharacteristic
601C2×C5C2×#91811yescharacteristic
602C2×C5#577711yescharacteristic
603D5—124no—
604C23—31no—
605C23—31no—
606C23—62no—
607C23—62no—
608C23—121no—
609C23—304no—
610C23—302no—
611C23—602no—
612C23—602no—
613C23D3×C22⋊D511yescharacteristic
614Q8—22no—
615Q8—54no—
616Q8—62no—
617Q8—104no—
618Q8—102no—
619Q8—122no—
620D4—154no—
621D4—304no—
622D4—308no—
623D4—308no—
624D4—302no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—31no—
629C2×C4—34no—
630C2×C4—31no—
631C2×C4—62no—
632C2×C4—62no—
633C2×C4—62no—
634C2×C4—62no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—104no—
638C2×C4—102no—
639C2×C4—122no—
640C2×C4—122no—
641C2×C4—308no—
642C2×C4—308no—
643C2×C4D3×C22⋊D511yescharacteristic
644C2×C4C22×D3×D511yescharacteristic
645C8—102no—
646C8—302no—
647C2×C3—22no—
648C2×C3C2×#408311yescharacteristic
649C2×C3C2×#408811yescharacteristic
650C2×C3#6615611yescharacteristic
651D3—22no—
652D3—41no—
653D3—204no—
654C5#8018411yescharacteristic, complemented, Sylow
655C22—21no—
656C22—21no—
657C22—32no—
658C22—61no—
659C22—61no—
660C22—61no—
661C22—61no—
662C22—61no—
663C22—124no—
664C22—304no—
665C22—608no—
666C22—602no—
667C22—602no—
668C22#9152012yescomplemented
669C22C2×D3×C22⋊D511yescharacteristic
670C4—21no—
671C4—32no—
672C4—41no—
673C4—41no—
674C4—61no—
675C4—104no—
676C4—121no—
677C4—121no—
678C4D3×D4×D512yes—
679C3#1061446611yescharacteristic, complemented, Sylow
680C2—22no—
681C2—62no—
682C2—121no—
683C2—604no—
684C2D3×#408311yescharacteristic
685C2C2×#9152011yescharacteristic
686C2#1175534811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×#6769C2
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C5×D3×C22⋊Q8C2semidirect
3. C2×#91520C2semidirect
4. #11751147C2semidirect
5. C3×#65339C2semidirect
6. #11749408C2semidirect
7. #11748555C2semidirect
8. #11748554C2semidirect
9. #11748505C2semidirect
10. #11747516C2semidirect
11. #11747505C2semidirect
14. C2×C5×D3×Q8C22semidirect
25. C2×#6717C22semidirect
26. C5×#946C22semidirect
28. C5×#897C22semidirect
31. C5×D3×C4⋊C4C22semidirect
34. C2×C3×#689C22semidirect
36. C2×#6661C22semidirect
37. C2×#6660C22semidirect
38. C2×#6650C22semidirect
40. #91093C22semidirect
42. C3×#3942C22semidirect
43. #90970C22semidirect
44. #90969C22semidirect
45. (C2×D3)⋊#168C22semidirect
52. #65339D3semidirect
112. D3×C22⋊Q8D5semidirect
142. C2×#689C2×D3semidirect
151. #3942C2×D3semidirect
204. C2×D3×Q8C2×D5semidirect
211. #946C2×D5semidirect
218. #897C2×D5semidirect
221. D3×C4⋊C4C2×D5semidirect
296. C22×C3×C5#137semidirect
505. C22×C5#918semidirect
572. C3×C5#3007semidirect
575. C22×C3#4088semidirect
654. C5#80184semidirect
668. C22#91520semidirect
679. C3#10614466semidirect

Maximal subgroups

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

subgroupindex
C22×#67692
C5×D3×C22⋊Q82
C2×#915202
#117511472
C3×#653392
#117494082
#117485552
#117485542
#117485052
#117475162
#117475052
#106144663
#801845