Finite Group Databasebeta

← C2×#10615326 #12977927

Subgroups — C2×#10615326 #12977927

Order 1280.

1834 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
1C2×C5×#552C211yesmaximal, characteristic
2C2×#65876C211yesmaximal, characteristic
3#10615326C2116yesmaximal, direct product factor
4C2×#65352C211yesmaximal, characteristic, complemented
5C2×#65354C211yesmaximal, characteristic, complemented
6C2×#65341C211yesmaximal, characteristic, complemented
7C2×#65340C211yesmaximal, characteristic, complemented
8C2×#65334C211yesmaximal, characteristic, complemented
9C2×#65334C211yesmaximal, characteristic, complemented
10C2×#65310C211yesmaximal, characteristic, complemented
11C2×#65319C211yesmaximal, characteristic, complemented
12C2×#65300C211yesmaximal, characteristic
13C2×#65285C211yesmaximal, characteristic, complemented
14C2×#65287C211yesmaximal, characteristic, complemented
15C2×#65259C211yesmaximal, characteristic, complemented
16C2×#65253C211yesmaximal, characteristic, complemented
17C5×#552—24no—
18C5×#552C2218yes—
19C2×C5×#126—21no—
20C2×C5×#125—21no—
21C2×C5×#125C2211yescharacteristic
22C2×C5×#123—21no—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×D4C2211yescharacteristic
27C2×C5×#117—21no—
28C2×C5×#117C2211yescharacteristic
29C22×C5×C4⋊C4C2211yescharacteristic
30C22×#689C2211yescharacteristic
31C2×#4082—21no—
32C2×#4072C2211yescharacteristic
33C2×#4072C2211yescharacteristic
34C2×#4070C2211yescharacteristic
35C2×#4070C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65876—24no—
39#65876C2218yes—
40C2×#4033—21no—
41C2×#4025—21no—
42C2×#4025—21no—
43C2×#4015C2211yescharacteristic
44C2×C4×Dic10C2211yescharacteristic
45C2×#3967C2211yescharacteristic
46C2×#3967C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65354C2218yescomplemented
51#65352C2218yescomplemented
52#65341C2218yescomplemented
53#65340C2218yescomplemented
54#65334C2218yescomplemented
55#65334C2218yescomplemented
56#65319C2218yescomplemented
57#65310C2218yescomplemented
58#65300C2218yes—
59#65287C2218yescomplemented
60#65285C2218yescomplemented
61#65259C2218yescomplemented
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64C2×#3942C2211yescharacteristic
65#65253C2218yescomplemented
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×#3939C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×#3935C2211yescharacteristic
77C2×#3349—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4D411yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C22×Dic10—21no—
84C22×Dic10C2311yescharacteristic
85C5×#126—28no—
86C5×#125—28no—
87C5×#125—22no—
88C5×#125C2314yes—
89C5×#123—28no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8C2314yes—
93C5×C22⋊Q8C2314yes—
94C4×C5×Q8—22no—
95C4×C5×Q8C2314yes—
96C4×C5×D4D414yes—
97C4×C5×D4C2314yes—
98C5×#117—22no—
99C5×#117—28no—
100C5×#117C2314yes—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—22no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4D411yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2314yes—
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4D411yescharacteristic
117C2×C5×C22⋊C4D411yescharacteristic
118C2×C42×C5—21no—
119C2×C42×C5—21no—
120C2×C42×C5C2311yescharacteristic
121C2×C22⋊Dic5—21no—
122C2×C22⋊Dic5—21no—
123C2×C22⋊Dic5—21no—
124C2×C22⋊Dic5—21no—
125C2×#689—24no—
126C2×#689C2314yes—
127#4082—28no—
128#4072—22no—
129#4072—22no—
130#4072C2314yes—
131#4072C2314yes—
132C2×C4⋊Dic5—21no—
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2311yescharacteristic
135C2×C4⋊Dic5C2311yescharacteristic
136#4070—22no—
137#4070—22no—
138#4070C2314yes—
139#4070C2314yes—
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C2×C4×Dic5—21no—
144C2×C4×Dic5—21no—
145C2×C4×Dic5—21no—
146C2×#681—24no—
147C2×#681C2314yes—
148C22×#168—24no—
149C22×#168C2314yes—
150C22×#168C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154#4033—28no—
155#4025—28no—
156#4025—28no—
157#4015—22no—
158#4015C2314yes—
159C4×Dic10—22no—
160C4×Dic10C2314yes—
161#3967C2314yes—
162#3967C2314yes—
163#3967C2314yes—
164C22⋊#168C2314yes—
165C22⋊#168C2314yes—
166#3942C2314yes—
167#3942C2314yes—
168#3942C2314yes—
169#3940C2314yes—
170#3940C2314yes—
171#3940C2314yes—
172#3940C2314yes—
173#3939C2314yes—
174#3939C2314yes—
175#3939C2314yes—
176#3939C2314yes—
177#3939C2314yes—
178C4⋊#168C2314yes—
179#3935C2314yes—
180C2×#556—51no—
181C2×#552D511yescharacteristic
182#3349—516no—
183C2×#501—51no—
184C2×#484—51no—
185C2×#485—51no—
186C2×#485—51no—
187C2×#485—51no—
188C2×#479—51no—
189C2×#477—51no—
190C2×#470—51no—
191C2×#467—51no—
192C2×#441—51no—
193C2×#435—51no—
194C2×#428—51no—
195C2×#427—51no—
196C24×C5C2×D411yescharacteristic
197C24×C5C2×D411yescharacteristic
198C2×C5×Q8—21no—
199C2×C5×Q8—22no—
200C2×C5×Q8—22no—
201C2×C5×Q8C2412yes—
202C2×C5×D4—42no—
203C2×C5×D4C2×D414yes—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—24no—
213C22×C4×C5—44no—
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D412yes—
219C22×C4×C5C2×D412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2411yescharacteristic
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C2×Dic10—22no—
228C2×Dic10—22no—
229C2×Dic10—24no—
230C2×Dic10—21no—
231C2×Dic10—44no—
232C2×Dic10C2412yes—
233C5×C4⋊C4—21no—
234C5×C4⋊C4—21no—
235C5×C4⋊C4—24no—
236C5×C4⋊C4—24no—
237C5×C4⋊C4—24no—
238C5×C4⋊C4—24no—
239C5×C4⋊C4—24no—
240C5×C4⋊C4—24no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4C2×D414yes—
243C5×C4⋊C4C2412yes—
244C5×C4⋊C4C2412yes—
245C5×C4⋊C4C2412yes—
246C5×C22⋊C4—24no—
247C5×C22⋊C4—24no—
248C5×C22⋊C4—24no—
249C5×C22⋊C4C2×D414yes—
250C5×C22⋊C4C2×D414yes—
251C42×C5—24no—
252C42×C5—24no—
253C42×C5C2×D412yes—
254C42×C5C2412yes—
255C22⋊Dic5—24no—
256C22⋊Dic5—24no—
257C22⋊Dic5—24no—
258C22⋊Dic5—24no—
259#689—28no—
260C4⋊Dic5—21no—
261C4⋊Dic5—21no—
262C4⋊Dic5—21no—
263C4⋊Dic5—24no—
264C4⋊Dic5C2412yes—
265C4⋊Dic5C2412yes—
266C4⋊Dic5C2412yes—
267#683—24no—
268#683—24no—
269#683—24no—
270C4×Dic5—24no—
271C4×Dic5—24no—
272C4×Dic5—24no—
273#681—28no—
274C2×#168—22no—
275C2×#168—22no—
276C2×#168—22no—
277C2×#168—28no—
278C2×#168#4114yes—
279C2×#168C2412yes—
280C2×#168C2412yes—
281C2×#168C2412yes—
282C2×#168C2412yes—
283C22×Q16—51no—
284C22×M16—51no—
285C23×C8—51no—
286#556—58no—
287#556—104no—
288#552—24no—
289#552C2×D518yes—
290C2×C4⋊Q8—51no—
291C2×#126—21no—
292C2×#126—101no—
293C2×#126—101no—
294C2×#125—21no—
295C2×#125C2×D511yescharacteristic
296C2×#124—101no—
297C2×#123—21no—
298C2×C22⋊Q8—51no—
299C2×C22⋊Q8—51no—
300C2×C22⋊Q8C2×D511yescharacteristic
301C2×C22⋊Q8C2×D511yescharacteristic
302C2×C4×Q8—51no—
303C2×C4×Q8—101no—
304C2×C4×Q8C2×D511yescharacteristic
305C2×C4×D4C2×D511yescharacteristic
306C2×#117—21no—
307C2×#117—51no—
308C2×#117—51no—
309C2×#117C2×D511yescharacteristic
310C22×C4⋊C4C2×D511yescharacteristic
311#501—58no—
312#485—58no—
313#485—58no—
314#485—58no—
315#484—58no—
316#479—58no—
317#477—58no—
318#470—58no—
319#467—58no—
320#441—58no—
321#435—58no—
322#428—58no—
323#427—58no—
324C2×#107—51no—
325C2×#107—51no—
326C2×#107—51no—
327C2×#107—51no—
328C2×#107—51no—
329C2×#106—51no—
330C2×#106—51no—
331C2×#106—51no—
332C2×#106—51no—
333C2×C4⋊C8—51no—
334C2×#103—51no—
335C2×#103—51no—
336C2×#103—51no—
337C2×#103—51no—
338C2×#103—51no—
339C2×#103—51no—
340C2×C22⋊C8—51no—
341C2×C22⋊C8—51no—
342C2×#97—51no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5C22×D412yes—
350C23×C5C22×D412yes—
351C23×C5C22×D411yescharacteristic
352C5×Q8—22no—
353C5×Q8—22no—
354C5×Q8—42no—
355C5×D4—44no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—24no—
361C2×C4×C5—24no—
362C2×C4×C5—22no—
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—22no—
370C2×C4×C5—48no—
371C2×C4×C5—42no—
372C2×C4×C5—42no—
373C2×C4×C5—42no—
374C2×C4×C5—42no—
375C2×C4×C5C22×D412yes—
376C2×C4×C5C22×D412yes—
377C2×C4×C5C22×D412yes—
378C2×C4×C5C22×D412yes—
379C2×C4×C5C22×D411yescharacteristic
380C2×C4×C5C2×#4112yes—
381C2×C4×C52−1+412yes—
382C2×C4×C5C2511yescharacteristic
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—42no—
388C2×Dic5—42no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391Dic10—22no—
392Dic10—22no—
393Dic10—48no—
394Dic10—42no—
395#168—22no—
396#168—22no—
397#168—22no—
398#168C2×#4114yes—
399C22×Q8—51no—
400C22×Q8—101no—
401C22×Q8C22×D511yescharacteristic
402C22×D4C22⋊D511yescharacteristic
403C23×C4—21no—
404C23×C4C22×D511yescharacteristic
405C23×C4C22×D511yescharacteristic
406C2×Q16—54no—
407C2×Q16—104no—
408C2×M16—54no—
409C2×M16—104no—
410C22×C8—51no—
411C22×C8—51no—
412C22×C8—54no—
413C22×C8—51no—
414C22×C8—51no—
415C22×C8—104no—
416C4⋊Q8—54no—
417C4⋊Q8—102no—
418#126—28no—
419#126—108no—
420#126—108no—
421#125—28no—
422#125—22no—
423#125C22×D514yes—
424#124—108no—
425#123—28no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—54no—
429C22⋊Q8—54no—
430C22⋊Q8—102no—
431C22⋊Q8—102no—
432C22⋊Q8C22×D514yes—
433C22⋊Q8C22×D514yes—
434C4×Q8—22no—
435C4×Q8—54no—
436C4×Q8—108no—
437C4×Q8—102no—
438C4×Q8C22×D514yes—
439C4×D4C22⋊D514yes—
440C4×D4C22×D514yes—
441#117—22no—
442#117—28no—
443#117—54no—
444#117—54no—
445#117—102no—
446#117—102no—
447#117C22×D514yes—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—51no—
456C2×C4⋊C4—51no—
457C2×C4⋊C4—51no—
458C2×C4⋊C4—101no—
459C2×C4⋊C4—101no—
460C2×C4⋊C4—101no—
461C2×C4⋊C4—101no—
462C2×C4⋊C4C22⋊D511yescharacteristic
463C2×C4⋊C4C22×D511yescharacteristic
464C2×C4⋊C4C22×D511yescharacteristic
465C2×C4⋊C4C22×D514yes—
466C2×C4⋊C4C22×D511yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—101no—
471C2×C22⋊C4—101no—
472C2×C22⋊C4—101no—
473C2×C22⋊C4—101no—
474C2×C22⋊C4C22⋊D511yescharacteristic
475C2×C22⋊C4C22⋊D511yescharacteristic
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—101no—
479C2×C42—101no—
480C2×C42—101no—
481C2×C42C22×D511yescharacteristic
482#107—54no—
483#107—54no—
484#107—54no—
485#107—54no—
486#107—54no—
487#106—54no—
488#106—54no—
489#106—54no—
490#106—54no—
491C4⋊C8—54no—
492#103—54no—
493#103—54no—
494#103—54no—
495#103—54no—
496#103—54no—
497#103—54no—
498C22⋊C8—54no—
499C22⋊C8—54no—
500#97—54no—
501C22×C5—22no—
502C22×C5—22no—
503C22×C5—22no—
504C22×C5—22no—
505C22×C5—22no—
506C22×C5—22no—
507C22×C5—44no—
508C22×C5—44no—
509C22×C5#54712yes—
510C22×C5#57512yes—
511C22×C5#57812yes—
512C22×C5C23×D411yescharacteristic
513C4×C5—22no—
514C4×C5—22no—
515C4×C5—22no—
516C4×C5—22no—
517C4×C5—42no—
518C4×C5—42no—
519C4×C5—42no—
520C4×C5—42no—
521C4×C5#54712yes—
522C4×C5C22×#4111yescharacteristic
523C4×C5C2×2−1+411yescharacteristic
524Dic5—42no—
525Dic5—42no—
526Dic5—42no—
527Dic5—42no—
528C24C2×C22⋊D511yescharacteristic
529C24C2×C22⋊D511yescharacteristic
530C2×Q8—21no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—52no—
534C2×Q8—101no—
535C2×Q8—104no—
536C2×Q8—102no—
537C2×Q8—102no—
538C2×Q8—204no—
539C2×Q8C23×D512yes—
540C2×D4—42no—
541C2×D4C2×C22⋊D514yes—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—44no—
552C22×C4—101no—
553C22×C4—101no—
554C22×C4—101no—
555C22×C4—101no—
556C22×C4C2×C22⋊D512yes—
557C22×C4C2×C22⋊D512yes—
558C22×C4C2×C22⋊D511yescharacteristic
559C22×C4C2×C22⋊D511yescharacteristic
560C22×C4C2×C22⋊D511yescharacteristic
561C22×C4C2×C22⋊D511yescharacteristic
562C22×C4C23×D512yes—
563C22×C4C23×D512yes—
564C22×C4C23×D511yescharacteristic
565Q16—108no—
566M16—108no—
567C2×C8—54no—
568C2×C8—52no—
569C2×C8—52no—
570C2×C8—52no—
571C2×C8—52no—
572C2×C8—108no—
573C2×C8—102no—
574C2×C8—102no—
575C2×C8—102no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—52no—
586C4⋊C4—52no—
587C4⋊C4—52no—
588C4⋊C4—101no—
589C4⋊C4—101no—
590C4⋊C4—101no—
591C4⋊C4—104no—
592C4⋊C4—104no—
593C4⋊C4—104no—
594C4⋊C4—104no—
595C4⋊C4C2×C22⋊D514yes—
596C4⋊C4C23×D512yes—
597C4⋊C4C23×D512yes—
598C4⋊C4C23×D512yes—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—104no—
603C22⋊C4—104no—
604C22⋊C4—104no—
605C22⋊C4—104no—
606C22⋊C4C2×C22⋊D514yes—
607C22⋊C4C2×C22⋊D514yes—
608C42—24no—
609C42—24no—
610C42—104no—
611C42—104no—
612C42—104no—
613C42C2×C22⋊D512yes—
614C42C23×D512yes—
615C2×C5—42no—
616C2×C5—42no—
617C2×C5#334914yescomplemented
618C2×C5C2×#54711yescharacteristic
619C2×C5C2×#57511yescharacteristic
620C2×C5C2×#57811yescharacteristic
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23C22×C22⋊D512yes—
628C23C22×C22⋊D512yes—
629C23C22×C22⋊D511yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—42no—
633Q8—102no—
634Q8—102no—
635Q8—208no—
636Q8—202no—
637D4—44no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—102no—
658C2×C4—102no—
659C2×C4—102no—
660C2×C4—102no—
661C2×C4—202no—
662C2×C4—202no—
663C2×C4—202no—
664C2×C4—202no—
665C2×C4D5×#4112yes—
666C2×C4#415012yes—
667C2×C4C22×C22⋊D512yes—
668C2×C4C22×C22⋊D512yes—
669C2×C4C22×C22⋊D512yes—
670C2×C4C22×C22⋊D512yes—
671C2×C4C22×C22⋊D511yescharacteristic
672C2×C4C24×D511yescharacteristic
673C8—54no—
674C8—102no—
675C8—102no—
676C8—102no—
677C5C2×#334911yescharacteristic, complemented, Sylow
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22#6615612yes—
687C22#6615812yes—
688C22#6617212yes—
689C22C23×C22⋊D511yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—202no—
699C4—202no—
700C4—202no—
701C4—202no—
702C4#6615812yes—
703C4C2×D5×#4111yescharacteristic
704C4C2×#415011yescharacteristic
705C2—42no—
706C2—42no—
707C2#1061532614yesdirect product factor
708C2C2×#6615611yescharacteristic
709C2C2×#6615811yescharacteristic
710C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#552C2
socleC23×C5C22×D4
prime radicalC22×C5×D4D4
hypercenterC2×#552D5
hypocenterC5C2×#3349
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
3. #10615326C2direct (N × H)
4. C2×#65352C2semidirect
5. C2×#65354C2semidirect
6. C2×#65341C2semidirect
7. C2×#65340C2semidirect
8. C2×#65334C2semidirect
9. C2×#65334C2semidirect
10. C2×#65310C2semidirect
11. C2×#65319C2semidirect
13. C2×#65285C2semidirect
14. C2×#65287C2semidirect
15. C2×#65259C2semidirect
16. C2×#65253C2semidirect
50. #65354C22semidirect
51. #65352C22semidirect
52. #65341C22semidirect
53. #65340C22semidirect
54. #65334C22semidirect
55. #65334C22semidirect
56. #65319C22semidirect
57. #65310C22semidirect
59. #65287C22semidirect
60. #65285C22semidirect
61. #65259C22semidirect
65. #65253C22semidirect
617. C2×C5#3349semidirect
677. C5C2×#3349semidirect
707. C2#10615326direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5522
C2×#658762
#106153262
C2×#653522
C2×#653542
C2×#653412
C2×#653402
C2×#653342
C2×#653102
C2×#653192
C2×#653002
C2×#652852
C2×#652872
C2×#652592
C2×#652532
C2×#33495