Finite Group Databasebeta

← C2×#10610890 #12977875

Subgroups — C2×#10610890 #12977875

Order 1280.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65848C211yesmaximal, characteristic
2C2×#65845C211yesmaximal, characteristic, complemented
3C22×C5×#107C211yesmaximal, characteristic, complemented
4C2×#65403C211yesmaximal, characteristic, complemented
5C2×#65400C211yesmaximal, characteristic, complemented
6C2×#65259C211yesmaximal, characteristic, complemented
7C2×#65257C211yesmaximal, characteristic, complemented
8C2×#65166C211yesmaximal, characteristic, complemented
9C2×#65179C211yesmaximal, characteristic, complemented
10#10610890C2116yesmaximal, direct product factor
11C2×#65177C211yesmaximal, characteristic, complemented
12C2×#65171C211yesmaximal, characteristic, complemented
13C2×#65175C211yesmaximal, characteristic, complemented
14C2×#65170C211yesmaximal, characteristic, complemented
15C2×#65165C211yesmaximal, characteristic, complemented
16C2×#65178C211yesmaximal, characteristic, complemented
17C23×C5×C8C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C2×#4076—21no—
21C2×#4076C2211yescharacteristic
22C2×C4×C22⋊D5—21no—
23C2×C4×C22⋊D5—21no—
24C2×C4×C22⋊D5C2211yescharacteristic
25C2×#4070—21no—
26C2×#4070C2211yescharacteristic
27C22×#677C2211yescharacteristic
28C22×#676C2211yescharacteristic
29#65848—24no—
30#65848C2218yes—
31C2×#4044—21no—
32#65845—24no—
33#65845C2218yescomplemented
34C2×#4043C2211yescharacteristic
35C2×#4042—21no—
36C2×#4041C2211yescharacteristic
37C2×#4040—21no—
38C2×#4039C2211yescharacteristic
39C2×#4038C2211yescharacteristic
40C2×D5×C4⋊C4C2211yescharacteristic
41C2×#4036C2211yescharacteristic
42C2×#4035—21no—
43C2×#4034C2211yescharacteristic
44C2×#4033C2211yescharacteristic
45C2×C5×#107C2211yescharacteristic
46C2×C5×#107C2211yescharacteristic
47C2×C5×#107C2211yescharacteristic
48C2×C5×#107C2211yescharacteristic
49C2×C5×#107C2218yescomplemented
50C2×C22⋊#168C2211yescharacteristic
51#65403C2218yescomplemented
52C2×#3953C2211yescharacteristic
53#65400C2218yescomplemented
54C2×#3952C2211yescharacteristic
55C2×#3949C2211yescharacteristic
56C2×#3948C2211yescharacteristic
57C2×#3947C2211yescharacteristic
58C2×#3946C2211yescharacteristic
59#65259C2218yescomplemented
60C2×#3942C2211yescharacteristic
61C2×#3942C2211yescharacteristic
62#65257C2218yescomplemented
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3940C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3939C2211yescharacteristic
68C2×#3939C2211yescharacteristic
69#65179C2218yescomplemented
70#65178C2218yescomplemented
71#65177C2218yescomplemented
72#65175C2218yescomplemented
73#65171C2218yescomplemented
74#65170C2218yescomplemented
75#65166C2218yescomplemented
76#65165C2218yescomplemented
77C2×#3346—51nomaximal, Sylow
78C23×C4×C5—21no—
79C23×C4×C5—21no—
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C22×C22⋊D5D411yescharacteristic
83C22×D20—21no—
84C22×D20C2311yescharacteristic
85C22×C4×D5—21no—
86C22×C4×D5—21no—
87C22×C4×D5C2311yescharacteristic
88C22×Dic10—21no—
89C22×Dic10C2311yescharacteristic
90C22×C5×C8—24no—
91C22×C5×C8C2311yescharacteristic
92C22×C5×C8C2314yes—
93C22×C5×C8C2311yescharacteristic
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—21no—
96C2×C5×C4⋊C4—22no—
97C2×C5×C4⋊C4—22no—
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2314yes—
103C2×C5×C4⋊C4C2314yes—
104C2×C22⋊Dic5—21no—
105C2×C22⋊Dic5D411yescharacteristic
106#4076—22no—
107#4076—28no—
108#4076C2314yes—
109C4×C22⋊D5—28no—
110C4×C22⋊D5—28no—
111C4×C22⋊D5D414yes—
112C4×C22⋊D5C2314yes—
113C2×#685—21no—
114C2×#685—21no—
115C2×#685—21no—
116C2×#685—21no—
117C2×#685—21no—
118C2×#685D411yescharacteristic
119C2×C4⋊Dic5—21no—
120C2×C4⋊Dic5—21no—
121C2×C4⋊Dic5C2311yescharacteristic
122C2×C4⋊Dic5C2311yescharacteristic
123#4070—22no—
124#4070—28no—
125#4070C2314yes—
126C2×#683—21no—
127C2×#683—21no—
128C2×#683—21no—
129C2×#683—21no—
130C2×#683—21no—
131C2×#683D411yescharacteristic
132C2×C4×Dic5—21no—
133C2×C4×Dic5—21no—
134C2×C4×Dic5C2311yescharacteristic
135C22×#168C2311yescharacteristic
136C22×#168C2311yescharacteristic
137C2×#677—24no—
138C2×#677C2314yes—
139C2×#676—24no—
140C2×#676C2314yes—
141#4044—28no—
142#4043—22no—
143#4043C2314yes—
144#4042—28no—
145#4041—22no—
146#4041C2314yes—
147#4040—28no—
148#4039—22no—
149#4039C2314yes—
150#4038—22no—
151#4038C2314yes—
152D5×C4⋊C4—22no—
153D5×C4⋊C4C2314yes—
154#4036—22no—
155#4036C2314yes—
156#4035—28no—
157#4034—22no—
158#4034C2314yes—
159#4033—22no—
160#4033C2314yes—
161C5×#107C2314yes—
162C5×#107C2314yes—
163C5×#107C2314yes—
164C5×#107C2314yes—
165C22⋊#168C2314yes—
166#3953C2314yes—
167#3952C2314yes—
168#3949C2314yes—
169#3948C2314yes—
170#3947C2314yes—
171#3946C2314yes—
172#3942C2314yes—
173#3942C2314yes—
174#3941C2314yes—
175#3941C2314yes—
176#3940C2314yes—
177#3940C2314yes—
178#3939C2314yes—
179#3939C2314yes—
180C2×#554—51no—
181C2×#553—51no—
182#3346—516no—
183C2×#501—51no—
184C2×#484—51no—
185C2×#481—51no—
186C2×#485—51no—
187C2×#480—51no—
188C2×#479—51no—
189C2×#474—51no—
190C2×#468—51no—
191C2×#465—51no—
192C2×#440—51no—
193C2×#435—51no—
194C2×#428—51no—
195C22×#107D511yescharacteristic, complemented
196C24×C5C2×D411yescharacteristic
197C23×D5—21no—
198C23×D5C2×D411yescharacteristic
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—24no—
206C22×C4×C5—24no—
207C22×C4×C5—82no—
208C22×C4×C5—82no—
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D412yes—
211C22×C4×C5C2412yes—
212C22×C4×C5C2411yescharacteristic
213C2×C22⋊D5—24no—
214C2×C22⋊D5—24no—
215C2×C22⋊D5—44no—
216C2×C22⋊D5C2×D414yes—
217C22×Dic5—21no—
218C22×Dic5—21no—
219C22×Dic5—21no—
220C22×Dic5C2×D411yescharacteristic
221C22×Dic5C2×D411yescharacteristic
222C22×Dic5C2×D411yescharacteristic
223C2×D20—22no—
224C2×D20—22no—
225C2×D20—21no—
226C2×D20—24no—
227C2×D20—82no—
228C2×D20C2412yes—
229C2×C4×D5—22no—
230C2×C4×D5—22no—
231C2×C4×D5—24no—
232C2×C4×D5—24no—
233C2×C4×D5—82no—
234C2×C4×D5—82no—
235C2×C4×D5C2×D412yes—
236C2×C4×D5C2412yes—
237C2×Dic10—22no—
238C2×Dic10—22no—
239C2×Dic10—21no—
240C2×Dic10—24no—
241C2×Dic10—82no—
242C2×Dic10C2412yes—
243C2×C5×C8—22no—
244C2×C5×C8—28no—
245C2×C5×C8#4114yes—
246C2×C5×C8C2412yes—
247C2×C5×C8C2412yes—
248C5×C4⋊C4—21no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4—24no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—24no—
254C5×C4⋊C4C2412yes—
255C5×C4⋊C4C2412yes—
256C5×C4⋊C4C2412yes—
257C5×C4⋊C4C2412yes—
258C22⋊Dic5—24no—
259C22⋊Dic5C2×D414yes—
260#685—24no—
261#685—24no—
262#685—24no—
263#685—24no—
264#685—24no—
265#685C2×D414yes—
266C4⋊Dic5—21no—
267C4⋊Dic5—21no—
268C4⋊Dic5—24no—
269C4⋊Dic5—24no—
270C4⋊Dic5C2412yes—
271C4⋊Dic5C2412yes—
272#683—24no—
273#683—24no—
274#683—24no—
275#683—24no—
276#683—24no—
277#683C2×D414yes—
278C4×Dic5—24no—
279C4×Dic5—24no—
280C4×Dic5C2×D412yes—
281C4×Dic5C2412yes—
282C2×#168—22no—
283C2×#168—22no—
284C2×#168C2412yes—
285C2×#168C2412yes—
286#677—28no—
287#676—28no—
288C22×SD16—51no—
289C22×M16—51no—
290C23×C8C2×D511yescharacteristic
291#554—58no—
292#554—104no—
293#553—58no—
294#553—104no—
295C2×C4⋊Q8—51no—
296C2×#126—101no—
297C2×#125—51no—
298C2×#125—101no—
299C2×#123—101no—
300C2×C22⋊Q8—51no—
301C2×C22⋊Q8—51no—
302C2×C22⋊Q8—101no—
303C2×C22⋊Q8—101no—
304C2×#121—51no—
305C2×#121—51no—
306C2×#121—101no—
307C2×C4×Q8—51no—
308C2×C4×D4—51no—
309C2×C4×D4—51no—
310C2×C4×D4—101no—
311C2×C4×D4—101no—
312C2×#117—51no—
313C22×C4⋊C4—51no—
314C22×C4⋊C4C2×D511yescharacteristic
315C22×C4⋊C4C2×D511yescharacteristic
316#501—58no—
317#485—58no—
318#484—58no—
319#481—58no—
320#480—58no—
321#479—58no—
322#474—58no—
323#468—58no—
324#465—58no—
325#440—58no—
326#435—58no—
327#428—58no—
328C2×#107—51no—
329C2×#107—51no—
330C2×#107C2×D511yescharacteristic
331C2×#107C2×D511yescharacteristic
332C2×#107C2×D511yescharacteristic
333C2×#107C2×D511yescharacteristic
334C2×#107C2×D518yescomplemented
335C2×#106—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×C4⋊C8—51no—
339C2×#103—51no—
340C2×#103—51no—
341C2×#103—51no—
342C2×#102—51no—
343C2×#102—51no—
344C2×#102—51no—
345C2×C22⋊C8—51no—
346C2×C22⋊C8—51no—
347C2×#97—51no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5#13714yes—
351C23×C5C22×D412yes—
352C23×C5C22×D411yescharacteristic
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—42no—
358C22×D5—42no—
359C22×D5—42no—
360C22×D5C22×D412yes—
361C2×C4×C5—22no—
362C2×C4×C5—24no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—42no—
370C2×C4×C5—42no—
371C2×C4×C5—42no—
372C2×C4×C5—42no—
373C2×C4×C5—84no—
374C2×C4×C5—84no—
375C2×C4×C5C22×D412yes—
376C2×C4×C5C22×D411yescharacteristic
377C2×C4×C5C2×#4112yes—
378C2×C4×C52−1+412yes—
379C2×C4×C5C2511yescharacteristic
380C22⋊D5—28no—
381C22⋊D5—48no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—42no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391C2×Dic5C22×D412yes—
392C2×Dic5C22×D412yes—
393C2×Dic5C22×D412yes—
394D20—22no—
395D20—22no—
396D20—42no—
397D20—84no—
398C4×D5—24no—
399C4×D5—22no—
400C4×D5—22no—
401C4×D5—84no—
402C4×D5—84no—
403Dic10—22no—
404Dic10—22no—
405Dic10—42no—
406Dic10—84no—
407C5×C8—22no—
408C5×C8C2×#4114yes—
409#168—22no—
410#168—22no—
411C22×Q8—51no—
412C22×Q8—101no—
413C22×D4—51no—
414C22×D4—51no—
415C22×D4—101no—
416C22×D4—101no—
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—51no—
420C23×C4—101no—
421C23×C4—101no—
422C23×C4C22×D511yescharacteristic
423C2×SD16—54no—
424C2×SD16—104no—
425C2×M16—54no—
426C2×M16—104no—
427C22×C8—24no—
428C22×C8—51no—
429C22×C8—51no—
430C22×C8C22×D511yescharacteristic
431C22×C8C22×D514yes—
432C22×C8C22×D511yescharacteristic
433C4⋊Q8—54no—
434C4⋊Q8—102no—
435#126—108no—
436#125—54no—
437#125—102no—
438#125—108no—
439#123—108no—
440C22⋊Q8—54no—
441C22⋊Q8—54no—
442C22⋊Q8—108no—
443C22⋊Q8—108no—
444C22⋊Q8—102no—
445C22⋊Q8—102no—
446#121—54no—
447#121—54no—
448#121—102no—
449#121—108no—
450#121—102no—
451C4×Q8—54no—
452C4×Q8—102no—
453C4×D4—54no—
454C4×D4—54no—
455C4×D4—54no—
456C4×D4—102no—
457C4×D4—108no—
458C4×D4—108no—
459#117—54no—
460#117—102no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—54no—
469C2×C4⋊C4—102no—
470C2×C4⋊C4—101no—
471C2×C4⋊C4—101no—
472C2×C4⋊C4—101no—
473C2×C4⋊C4—101no—
474C2×C4⋊C4—101no—
475C2×C4⋊C4—101no—
476C2×C4⋊C4—101no—
477C2×C4⋊C4C22×D511yescharacteristic
478C2×C4⋊C4C22×D511yescharacteristic
479C2×C4⋊C4C22×D511yescharacteristic
480C2×C4⋊C4C22×D511yescharacteristic
481C2×C4⋊C4C22×D514yes—
482C2×C4⋊C4C22×D514yes—
483C2×C22⋊C4—51no—
484C2×C22⋊C4—51no—
485C2×C22⋊C4—101no—
486C2×C22⋊C4—101no—
487C2×C22⋊C4—101no—
488C2×C22⋊C4—101no—
489C2×C22⋊C4—101no—
490C2×C22⋊C4—101no—
491C2×C42—51no—
492C2×C42—101no—
493C2×C42—101no—
494#107—54no—
495#107—54no—
496#107C22×D514yes—
497#107C22×D514yes—
498#107C22×D514yes—
499#107C22×D514yes—
500#106—54no—
501#106—54no—
502#106—54no—
503C4⋊C8—54no—
504#103—54no—
505#103—54no—
506#103—54no—
507#102—54no—
508#102—54no—
509#102—54no—
510C22⋊C8—54no—
511C22⋊C8—54no—
512#97—54no—
513C22×C5—28no—
514C22×C5—22no—
515C22×C5—22no—
516C22×C5#54712yes—
517C22×C5C2×#13714yes—
518C22×C5C2×#13712yes—
519C22×C5#57612yes—
520C22×C5C23×D411yescharacteristic
521C2×D5—22no—
522C2×D5—22no—
523C2×D5—22no—
524C2×D5—44no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—42no—
528C2×D5—84no—
529C4×C5—22no—
530C4×C5—42no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5#54712yes—
535C4×C5C22×#4111yescharacteristic
536C4×C5C2×2−1+411yescharacteristic
537Dic5—22no—
538Dic5—22no—
539Dic5—22no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543C24—51no—
544C24—101no—
545C24D4×D511yescharacteristic
546C2×Q8—52no—
547C2×Q8—104no—
548C2×Q8—101no—
549C2×Q8—102no—
550C2×Q8—102no—
551C2×Q8—402no—
552C2×D4—54no—
553C2×D4—52no—
554C2×D4—104no—
555C2×D4—104no—
556C2×D4—104no—
557C2×D4—102no—
558C2×D4—101no—
559C2×D4—102no—
560C2×D4—204no—
561C2×D4—402no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—51no—
571C22×C4—51no—
572C22×C4—51no—
573C22×C4—52no—
574C22×C4—52no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4—104no—
578C22×C4—104no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—402no—
585C22×C4—402no—
586C22×C4D4×D512yes—
587C22×C4D4×D511yescharacteristic
588C22×C4C23×D512yes—
589C22×C4C23×D511yescharacteristic
590SD16—108no—
591M16—108no—
592C2×C8—22no—
593C2×C8—28no—
594C2×C8—52no—
595C2×C8—52no—
596C2×C8—102no—
597C2×C8—102no—
598C2×C8#70914yes—
599C2×C8C23×D512yes—
600C2×C8C23×D512yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—24no—
607C4⋊C4—54no—
608C4⋊C4—52no—
609C4⋊C4—52no—
610C4⋊C4—104no—
611C4⋊C4—104no—
612C4⋊C4—104no—
613C4⋊C4—104no—
614C4⋊C4—104no—
615C4⋊C4—104no—
616C4⋊C4—101no—
617C4⋊C4—101no—
618C4⋊C4—104no—
619C4⋊C4C23×D512yes—
620C4⋊C4C23×D512yes—
621C4⋊C4C23×D512yes—
622C4⋊C4C23×D512yes—
623C22⋊C4—54no—
624C22⋊C4—54no—
625C22⋊C4—104no—
626C22⋊C4—104no—
627C22⋊C4—104no—
628C22⋊C4—104no—
629C22⋊C4—104no—
630C22⋊C4—104no—
631C42—52no—
632C42—52no—
633C42—104no—
634C42—104no—
635C2×C5—24no—
636C2×C5#334614yescomplemented
637C2×C5C2×#54711yescharacteristic
638C2×C5C22×#13711yescharacteristic
639C2×C5C2×#57611yescharacteristic
640D5—42no—
641D5—82no—
642C23—22no—
643C23—22no—
644C23—52no—
645C23—102no—
646C23—102no—
647C23—102no—
648C23—102no—
649C23—202no—
650C23—202no—
651C23—202no—
652C23#406414yes—
653C23C2×D4×D512yes—
654C23C2×D4×D511yescharacteristic
655Q8—102no—
656Q8—102no—
657Q8—202no—
658Q8—404no—
659D4—108no—
660D4—102no—
661D4—102no—
662D4—208no—
663D4—202no—
664D4—404no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—52no—
678C2×C4—52no—
679C2×C4—52no—
680C2×C4—84no—
681C2×C4—84no—
682C2×C4—102no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—104no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—202no—
692C2×C4—202no—
693C2×C4—202no—
694C2×C4—404no—
695C2×C4—404no—
696C2×C4C2×#70912yes—
697C2×C4C2×D4×D512yes—
698C2×C4C2×D4×D511yescharacteristic
699C2×C4#414712yes—
700C2×C4C24×D511yescharacteristic
701C8—22no—
702C8—102no—
703C8—102no—
704C8C2×#70914yes—
705C5C2×#334611yescharacteristic, complemented, Sylow
706C22—22no—
707C22—22no—
708C22—28no—
709C22—102no—
710C22—102no—
711C22—102no—
712C22—204no—
713C22—202no—
714C22—202no—
715C22—202no—
716C22—404no—
717C22#6584112yes—
718C22#6609112yes—
719C22C2×#406414yes—
720C22C2×#406412yes—
721C22C22×D4×D511yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—102no—
728C4—102no—
729C4—102no—
730C4—202no—
731C4—202no—
732C4—202no—
733C4#6584112yes—
734C4C22×#70911yescharacteristic
735C4C2×#414711yescharacteristic
736C2—24no—
737C2—202no—
738C2—402no—
739C2#1061089014yesdirect product factor
740C2C2×#6584111yescharacteristic
741C2C2×#6609111yescharacteristic
742C2C22×#406411yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C5×#107C2
socleC23×C5C22×D4
prime radicalC2×#65848C2
hypercenterC22×#107D5
hypocenterC5C2×#3346
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. C2×#65845C2semidirect
3. C22×C5×#107C2semidirect
4. C2×#65403C2semidirect
5. C2×#65400C2semidirect
6. C2×#65259C2semidirect
7. C2×#65257C2semidirect
8. C2×#65166C2semidirect
9. C2×#65179C2semidirect
10. #10610890C2direct (N × H)
11. C2×#65177C2semidirect
12. C2×#65171C2semidirect
13. C2×#65175C2semidirect
14. C2×#65170C2semidirect
15. C2×#65165C2semidirect
16. C2×#65178C2semidirect
33. #65845C22semidirect
49. C2×C5×#107C22semidirect
51. #65403C22semidirect
53. #65400C22semidirect
59. #65259C22semidirect
62. #65257C22semidirect
69. #65179C22semidirect
70. #65178C22semidirect
71. #65177C22semidirect
72. #65175C22semidirect
73. #65171C22semidirect
74. #65170C22semidirect
75. #65166C22semidirect
76. #65165C22semidirect
195. C22×#107D5semidirect
334. C2×#107C2×D5semidirect
636. C2×C5#3346semidirect
705. C5C2×#3346semidirect
739. C2#10610890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658482
C2×#658452
C22×C5×#1072
C2×#654032
C2×#654002
C2×#652592
C2×#652572
C2×#651662
C2×#651792
#106108902
C2×#651772
C2×#651712
C2×#651752
C2×#651702
C2×#651652
C2×#651782
C2×#33465