Finite Group Databasebeta

← C2×#10618170 #13007016

Subgroups — C2×#10618170 #13007016

Order 1280.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#533C211yesmaximal, characteristic, complemented
2#10618170C2132yesmaximal, direct product factor
3C2×#66064C211yesmaximal, characteristic, complemented
4C2×#66056C211yesmaximal, characteristic, complemented
5C2×#66055C211yesmaximal, characteristic, complemented
6C2×#66066C211yesmaximal, characteristic, complemented
7C2×#66023C212yesmaximal, complemented
8C2×#66031C212yesmaximal, complemented
9C2×#65980C214yesmaximal, complemented
10C2×#65977C212yesmaximal
11C2×#65959C212yesmaximal, complemented
12C2×#65917C214yesmaximal, complemented
13C2×#65903C212yesmaximal, complemented
14C2×#65902C212yesmaximal, complemented
15C2×#65867C212yesmaximal, complemented
16C2×#65863C212yesmaximal, complemented
17C2×#65813C211yesmaximal, characteristic
18C2×#65804C211yesmaximal, characteristic, complemented
19C5×#533C22116yescomplemented
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×C4⋊Q8C2211yescharacteristic
22C2×C5×#125C2212yes—
23C2×C5×C22⋊Q8C2212yes—
24C2×C5×C22⋊Q8C2212yes—
25C2×C4×C5×Q8C2212yes—
26C2×C4×C5×Q8C2212yes—
27C2×C5×#117C2212yes—
28C22×C42×C5C2211yescharacteristic
29C2×#4093C2212yes—
30C2×#4092C2214yes—
31C2×Q8×Dic5C2212yes—
32C2×Q8×Dic5C2212yes—
33C2×#4090C2212yes—
34C2×#4090C2214yes—
35C2×#4076C2211yescharacteristic
36C2×#4075C2212yes—
37C2×C4×C22⋊D5C2212yes—
38C2×#4072C2212yes—
39C2×#4070C2211yescharacteristic
40C2×#4070C2212yes—
41C2×#4070C2211yescharacteristic
42C2×#4070C2211yescharacteristic
43#66066C22116yescomplemented
44#66064C22116yescomplemented
45#66056C22116yescomplemented
46#66055C22116yescomplemented
47#66031C22132yescomplemented
48#66023C22132yescomplemented
49#65980C22164yescomplemented
50#65977C22132yes—
51#65959C22132yescomplemented
52#65917C22164yescomplemented
53#65903C22132yescomplemented
54#65902C22132yescomplemented
55#65867C22132yescomplemented
56#65863C22132yescomplemented
57C2×#4044C2214yes—
58C2×#4044C2214yes—
59C2×#4044C2214yes—
60C2×#4043C2212yes—
61C2×#4043C2214yes—
62C2×#4043C2212yes—
63C2×#4042C2214yes—
64C2×#4039C2212yes—
65C2×#4038C2212yes—
66C2×D5×C4⋊C4C2212yes—
67C2×#4036C2212yes—
68C2×#4036C2214yes—
69C2×#4036C2214yes—
70C2×#4036C2212yes—
71C2×#4035C2214yes—
72C2×#4035C2214yes—
73C2×#4034C2212yes—
74C2×#4034C2214yes—
75C2×#4034C2212yes—
76C2×#4033C2212yes—
77C2×#4033C2212yes—
78C2×#4033C2212yes—
79C2×#4031C2214yes—
80C2×#4029C2214yes—
81C2×#4025C2214yes—
82C2×#4025C2214yes—
83#65813C22116yes—
84C2×#4022C2214yes—
85C2×#4022C2212yes—
86C2×#4021C2211yescharacteristic
87C2×C4×D20C2211yescharacteristic
88C2×#4018C2214yes—
89C2×#4018C2212yes—
90#65804C22116yescomplemented
91C2×#4016C2214yes—
92C2×#4016C2211yescharacteristic
93C2×#4016C2212yes—
94C2×#4015C2211yescharacteristic
95C2×#4015C2211yescharacteristic
96C2×C4×Dic10C2211yescharacteristic
97C2×C4×Dic10C2214yes—
98C2×C4×Dic10C2212yes—
99C2×C4×Dic10C2211yescharacteristic
100C2×C4×Dic10C2211yescharacteristic
101C2×#3555—51nomaximal, Sylow
102C22×C5×Q8C2312yes—
103C22×C5×Q8C2312yes—
104C23×C4×C5C2311yescharacteristic
105C23×C4×C5C2311yescharacteristic
106C23×C4×C5C2311yescharacteristic
107C22×C22⋊D5C2312yes—
108C22×D20C2311yescharacteristic
109C22×C4×D5C2312yes—
110C22×C4×D5C2314yes—
111C22×Dic10C2311yescharacteristic
112C22×Dic10C2311yescharacteristic
113C22×Dic10C2311yescharacteristic
114C22×Dic10C2312yes—
115C22×Dic10C2314yes—
116C5×C4⋊Q8C2318yes—
117C5×C4⋊Q8C2318yes—
118C5×#125C23116yes—
119C5×C22⋊Q8C23116yes—
120C5×C22⋊Q8C23116yes—
121C4×C5×Q8C23116yes—
122C4×C5×Q8C23116yes—
123C5×#117C23116yes—
124C2×C5×C4⋊C4C2312yes—
125C2×C5×C4⋊C4C2312yes—
126C2×C5×C4⋊C4C2312yes—
127C2×C5×C4⋊C4C2314yes—
128C2×C5×C4⋊C4C2312yes—
129C2×C5×C4⋊C4C2314yes—
130C2×C5×C22⋊C4C2314yes—
131C2×C42×C5C2311yescharacteristic
132C2×C42×C5C2311yescharacteristic
133C2×C42×C5C2314yes—
134C2×C42×C5C2311yescharacteristic
135C2×C42×C5C2311yescharacteristic
136C2×C42×C5C2318yes—
137C2×C22⋊Dic5C2312yes—
138C2×C22⋊Dic5C2312yes—
139C2×C22⋊Dic5C2312yes—
140#4093C23116yes—
141#4092C23132yes—
142Q8×Dic5C23116yes—
143Q8×Dic5C23116yes—
144#4090C23116yes—
145#4090C23132yes—
146#4076C2318yes—
147#4075C23116yes—
148C4×C22⋊D5C23116yes—
149C2×#685C2312yes—
150C2×#685C2312yes—
151C2×#685C2312yes—
152C2×#685C2314yes—
153C2×#685C2312yes—
154C2×#685C2314yes—
155C2×#685C2314yes—
156#4072C23116yes—
157C2×C4⋊Dic5C2311yescharacteristic
158C2×C4⋊Dic5C2311yescharacteristic
159C2×C4⋊Dic5C2312yes—
160C2×C4⋊Dic5C2311yescharacteristic
161C2×C4⋊Dic5C2314yes—
162C2×C4⋊Dic5C2312yes—
163C2×C4⋊Dic5C2312yes—
164C2×C4⋊Dic5C2311yescharacteristic
165C2×C4⋊Dic5C2314yes—
166C2×C4⋊Dic5C2314yes—
167#4070C2318yes—
168#4070C2318yes—
169#4070C23116yes—
170#4070C2318yes—
171C2×#683C2312yes—
172C2×#683C2312yes—
173C2×#683C2312yes—
174C2×#683C2312yes—
175C2×#683C2312yes—
176C2×#683C2312yes—
177C2×#683C2312yes—
178C2×#683C2314yes—
179C2×#683C2314yes—
180C2×#683C2312yes—
181C2×#683C2314yes—
182C2×#683C2314yes—
183C2×#683C2314yes—
184C2×C4×Dic5C2312yes—
185C2×C4×Dic5C2312yes—
186C2×C4×Dic5C2312yes—
187C2×C4×Dic5C2314yes—
188C2×C4×Dic5C2314yes—
189C2×C4×Dic5C2314yes—
190#4044C23132yes—
191#4044C23132yes—
192#4044C23132yes—
193#4043C23116yes—
194#4043C23116yes—
195#4043C23132yes—
196#4042C23132yes—
197#4039C23116yes—
198#4038C23116yes—
199D5×C4⋊C4C23116yes—
200#4036C23116yes—
201#4036C23116yes—
202#4036C23132yes—
203#4036C23132yes—
204#4035C23132yes—
205#4035C23132yes—
206#4034C23116yes—
207#4034C23116yes—
208#4034C23132yes—
209#4033C23116yes—
210#4033C23116yes—
211#4033C23116yes—
212#4031C23132yes—
213#4029C23132yes—
214#4025C23132yes—
215#4025C23132yes—
216#4022C23116yes—
217#4022C23132yes—
218#4021C2318yes—
219C4×D20C2318yes—
220#4018C23116yes—
221#4018C23132yes—
222#4016C23116yes—
223#4016C2318yes—
224#4016C23132yes—
225#4015C2318yes—
226#4015C2318yes—
227C4×Dic10C2318yes—
228C4×Dic10C2318yes—
229C4×Dic10C2318yes—
230C4×Dic10C23116yes—
231C4×Dic10C23132yes—
232#3555—532no—
233C2×#563—54no—
234C2×Q82—51no—
235C2×#557—51no—
236C2×#557—52no—
237C2×#556—51no—
238C2×#556—52no—
239C2×#556—52no—
240C2×#554—51no—
241C2×#552—52no—
242C2×#544—52no—
243C2×#542—52no—
244C2×#541—52no—
245C2×#541—52no—
246C2×#541—54no—
247C2×#533—51no—
248C2×#533D511yescharacteristic, complemented
249C2×#529—51no—
250C24×C5C2411yescharacteristic
251C23×D5C2412yes—
252C2×C5×Q8—28no—
253C2×C5×Q8—44no—
254C2×C5×Q8C2418yes—
255C2×C5×Q8C2418yes—
256C22×C4×C5—24no—
257C22×C4×C5—24no—
258C22×C4×C5—42no—
259C22×C4×C5C2411yescharacteristic
260C22×C4×C5C2411yescharacteristic
261C22×C4×C5C2411yescharacteristic
262C22×C4×C5C2411yescharacteristic
263C22×C4×C5C2414yes—
264C22×C4×C5C2414yes—
265C22×C4×C5C2414yes—
266C22×C4×C5C2414yes—
267C22×C4×C5C2414yes—
268C22×C4×C5C2411yescharacteristic
269C22×C4×C5C2411yescharacteristic
270C2×C22⋊D5—44no—
271C2×C22⋊D5C2418yes—
272C22×Dic5C2412yes—
273C22×Dic5C2412yes—
274C22×Dic5C2412yes—
275C22×Dic5C2412yes—
276C22×Dic5C2412yes—
277C22×Dic5C2412yes—
278C22×Dic5C2412yes—
279C2×D20—24no—
280C2×D20C2414yes—
281C2×C4×D5—28no—
282C2×C4×D5—48no—
283C2×C4×D5C2418yes—
284C2×C4×D5C24116yes—
285C2×Dic10—24no—
286C2×Dic10—24no—
287C2×Dic10—24no—
288C2×Dic10—48no—
289C2×Dic10—44no—
290C2×Dic10C2414yes—
291C2×Dic10C2414yes—
292C2×Dic10C2414yes—
293C2×Dic10C2418yes—
294C2×Dic10C24116yes—
295C5×C4⋊C4C2418yes—
296C5×C4⋊C4C2418yes—
297C5×C4⋊C4C24116yes—
298C5×C4⋊C4C24116yes—
299C5×C4⋊C4C2418yes—
300C5×C4⋊C4C2418yes—
301C5×C22⋊C4C24116yes—
302C42×C5C2414yes—
303C42×C5C2414yes—
304C42×C5C2414yes—
305C42×C5C2414yes—
306C42×C5C24116yes—
307C22⋊Dic5C2418yes—
308C22⋊Dic5C2418yes—
309C22⋊Dic5C2418yes—
310#685C2418yes—
311#685C2418yes—
312#685C2418yes—
313#685C24116yes—
314#685C2418yes—
315#685C24116yes—
316#685C24116yes—
317C4⋊Dic5C2414yes—
318C4⋊Dic5C2414yes—
319C4⋊Dic5C2418yes—
320C4⋊Dic5C2414yes—
321C4⋊Dic5C24116yes—
322C4⋊Dic5C2418yes—
323C4⋊Dic5C2418yes—
324C4⋊Dic5C2414yes—
325C4⋊Dic5C24116yes—
326C4⋊Dic5C24116yes—
327#683C2418yes—
328#683C2418yes—
329#683C2418yes—
330#683C2418yes—
331#683C2418yes—
332#683C2418yes—
333#683C2418yes—
334#683C24116yes—
335#683C24116yes—
336#683C2418yes—
337#683C24116yes—
338#683C24116yes—
339#683C24116yes—
340C4×Dic5C2418yes—
341C4×Dic5C2418yes—
342C4×Dic5C2418yes—
343C4×Dic5C24116yes—
344C4×Dic5C24116yes—
345C4×Dic5C24116yes—
346#563—564no—
347Q82—516no—
348#557—516no—
349#557—532no—
350#556—516no—
351#556—532no—
352#556—532no—
353#554—516no—
354#552—532no—
355#544—532no—
356#542—532no—
357#541—532no—
358#541—532no—
359#541—564no—
360#533—516no—
361#533C2×D5116yescomplemented
362C2×C4⋊Q8—52no—
363C2×C4⋊Q8—54no—
364C2×C4⋊Q8—52no—
365C2×C4⋊Q8—52no—
366C2×C4⋊Q8—54no—
367C2×C4⋊Q8—51no—
368C2×C4⋊Q8—51no—
369C2×C4⋊Q8C2×D511yescharacteristic
370C2×C4⋊Q8C2×D511yescharacteristic
371#529—516no—
372C2×#126—54no—
373C2×#126—54no—
374C2×#126—54no—
375C2×#126—54no—
376C2×#126—54no—
377C2×#126—52no—
378C2×#126—54no—
379C2×#125—54no—
380C2×#125—54no—
381C2×#125—54no—
382C2×#125—52no—
383C2×#125—54no—
384C2×#125—52no—
385C2×#125—51no—
386C2×#125—52no—
387C2×#125—54no—
388C2×#125C2×D512yes—
389C2×#124—52no—
390C2×#124—54no—
391C2×#124—51no—
392C2×#123—52no—
393C2×#123—54no—
394C2×C22⋊Q8—54no—
395C2×C22⋊Q8—51no—
396C2×C22⋊Q8—51no—
397C2×C22⋊Q8—51no—
398C2×C22⋊Q8—52no—
399C2×C22⋊Q8—54no—
400C2×C22⋊Q8—54no—
401C2×C22⋊Q8—52no—
402C2×C22⋊Q8—52no—
403C2×C22⋊Q8C2×D512yes—
404C2×C22⋊Q8C2×D512yes—
405C2×#121—51no—
406C2×C4×Q8—52no—
407C2×C4×Q8—52no—
408C2×C4×Q8—52no—
409C2×C4×Q8—52no—
410C2×C4×Q8—52no—
411C2×C4×Q8—51no—
412C2×C4×Q8—51no—
413C2×C4×Q8—52no—
414C2×C4×Q8—51no—
415C2×C4×Q8—54no—
416C2×C4×Q8C2×D512yes—
417C2×C4×Q8C2×D512yes—
418C2×C4×D4—52no—
419C2×C4×D4—52no—
420C2×C4×D4—51no—
421C2×#117—52no—
422C2×#117—52no—
423C2×#117—52no—
424C2×#117—54no—
425C2×#117C2×D512yes—
426C22×C4⋊C4—52no—
427C22×C42C2×D511yescharacteristic
428C23×C5—22no—
429C23×C5—22no—
430C23×C5—22no—
431C23×C5C2512yes—
432C23×C5C2511yescharacteristic
433C22×D5—24no—
434C22×D5—24no—
435C22×D5—24no—
436C22×D5C2514yes—
437C5×Q8—216no—
438C5×Q8—48no—
439C2×C4×C5—22no—
440C2×C4×C5—22no—
441C2×C4×C5—28no—
442C2×C4×C5—22no—
443C2×C4×C5—28no—
444C2×C4×C5—22no—
445C2×C4×C5—28no—
446C2×C4×C5—28no—
447C2×C4×C5—44no—
448C2×C4×C52−1+414yes—
449C2×C4×C52−1+414yes—
450C2×C4×C5C2518yes—
451C2×C4×C5C2518yes—
452C2×C4×C5C2512yes—
453C2×C4×C5C2512yes—
454C2×C4×C5C2512yes—
455C2×C4×C5C2512yes—
456C2×C4×C5C2512yes—
457C2×C4×C5C2512yes—
458C22⋊D5—48no—
459C2×Dic5—24no—
460C2×Dic5—24no—
461C2×Dic5—24no—
462C2×Dic5—24no—
463C2×Dic5—24no—
464C2×Dic5—24no—
465C2×Dic5—24no—
466C2×Dic5C2514yes—
467C2×Dic5C2514yes—
468C2×Dic5C2514yes—
469C2×Dic5C2514yes—
470C2×Dic5C2514yes—
471C2×Dic5C2514yes—
472C2×Dic5C2514yes—
473D20—28no—
474C4×D5—216no—
475C4×D5—416no—
476Dic10—28no—
477Dic10—28no—
478Dic10—28no—
479Dic10—416no—
480Dic10—48no—
481C22×Q8—51no—
482C22×Q8—51no—
483C22×Q8—51no—
484C22×Q8—52no—
485C22×Q8—54no—
486C22×Q8C22×D512yes—
487C22×Q8C22×D512yes—
488C22×D4—52no—
489C22×D4—51no—
490C23×C4—52no—
491C23×C4—54no—
492C23×C4C22×D511yescharacteristic
493C23×C4C22×D511yescharacteristic
494C23×C4C22×D511yescharacteristic
495C4⋊Q8—516no—
496C4⋊Q8—532no—
497C4⋊Q8—516no—
498C4⋊Q8—516no—
499C4⋊Q8—532no—
500C4⋊Q8—58no—
501C4⋊Q8—58no—
502C4⋊Q8C22×D518yes—
503C4⋊Q8C22×D518yes—
504#126—532no—
505#126—532no—
506#126—532no—
507#126—532no—
508#126—532no—
509#126—516no—
510#126—532no—
511#125—532no—
512#125—532no—
513#125—516no—
514#125—532no—
515#125—532no—
516#125—516no—
517#125—58no—
518#125—516no—
519#125—532no—
520#125C22×D5116yes—
521#124—516no—
522#124—532no—
523#124—58no—
524#123—516no—
525#123—532no—
526C22⋊Q8—532no—
527C22⋊Q8—58no—
528C22⋊Q8—58no—
529C22⋊Q8—58no—
530C22⋊Q8—516no—
531C22⋊Q8—532no—
532C22⋊Q8—516no—
533C22⋊Q8—516no—
534C22⋊Q8—532no—
535C22⋊Q8C22×D5116yes—
536C22⋊Q8C22×D5116yes—
537#121—58no—
538C4×Q8—516no—
539C4×Q8—516no—
540C4×Q8—516no—
541C4×Q8—516no—
542C4×Q8—516no—
543C4×Q8—58no—
544C4×Q8—58no—
545C4×Q8—516no—
546C4×Q8—58no—
547C4×Q8—532no—
548C4×Q8C22×D5116yes—
549C4×Q8C22×D5116yes—
550C4×D4—516no—
551C4×D4—516no—
552C4×D4—58no—
553#117—516no—
554#117—516no—
555#117—516no—
556#117—532no—
557#117C22×D5116yes—
558C2×C4⋊C4—51no—
559C2×C4⋊C4—54no—
560C2×C4⋊C4—52no—
561C2×C4⋊C4—51no—
562C2×C4⋊C4—52no—
563C2×C4⋊C4—52no—
564C2×C4⋊C4—54no—
565C2×C4⋊C4—52no—
566C2×C4⋊C4—52no—
567C2×C4⋊C4—51no—
568C2×C4⋊C4—52no—
569C2×C4⋊C4—51no—
570C2×C4⋊C4—52no—
571C2×C4⋊C4—52no—
572C2×C4⋊C4—54no—
573C2×C4⋊C4—54no—
574C2×C4⋊C4—54no—
575C2×C4⋊C4—52no—
576C2×C4⋊C4—54no—
577C2×C4⋊C4—52no—
578C2×C4⋊C4—54no—
579C2×C4⋊C4—52no—
580C2×C4⋊C4—54no—
581C2×C4⋊C4—516no—
582C2×C4⋊C4C22×D512yes—
583C2×C4⋊C4C22×D512yes—
584C2×C4⋊C4C22×D512yes—
585C2×C4⋊C4C22×D514yes—
586C2×C4⋊C4C22×D514yes—
587C2×C4⋊C4C22×D512yes—
588C2×C22⋊C4—52no—
589C2×C22⋊C4—52no—
590C2×C22⋊C4—52no—
591C2×C22⋊C4—52no—
592C2×C22⋊C4—52no—
593C2×C22⋊C4—52no—
594C2×C22⋊C4—54no—
595C2×C22⋊C4—54no—
596C2×C22⋊C4—52no—
597C2×C22⋊C4—54no—
598C2×C22⋊C4C22×D514yes—
599C2×C42—52no—
600C2×C42—52no—
601C2×C42—52no—
602C2×C42—54no—
603C2×C42—54no—
604C2×C42—54no—
605C2×C42C22×D511yescharacteristic
606C2×C42C22×D514yes—
607C2×C42C22×D511yescharacteristic
608C2×C42C22×D511yescharacteristic
609C2×C42C22×D511yescharacteristic
610C2×C42C22×D518yes—
611C22×C5—22no—
612C22×C5—22no—
613C22×C5—22no—
614C22×C5—44no—
615C22×C5C2×2−1+412yes—
616C22×C5C2×2−1+412yes—
617C22×C5#58512yes—
618C22×C5C2611yescharacteristic
619C2×D5—24no—
620C2×D5—24no—
621C2×D5—24no—
622C2×D5—48no—
623C4×C5—22no—
624C4×C5—22no—
625C4×C5—28no—
626C4×C5—22no—
627C4×C5—28no—
628C4×C5—22no—
629C4×C5C2×2−1+414yes—
630C4×C5C2×2−1+414yes—
631Dic5—24no—
632Dic5—24no—
633Dic5—24no—
634Dic5—24no—
635Dic5—24no—
636Dic5—24no—
637Dic5—24no—
638C24—52no—
639C24C23×D511yescharacteristic
640C2×Q8—28no—
641C2×Q8—44no—
642C2×Q8—54no—
643C2×Q8—54no—
644C2×Q8—54no—
645C2×Q8—58no—
646C2×Q8—516no—
647C2×Q8—104no—
648C2×Q8—104no—
649C2×Q8—104no—
650C2×Q8—204no—
651C2×Q8—208no—
652C2×Q8C23×D518yes—
653C2×Q8C23×D518yes—
654C2×D4—58no—
655C2×D4—54no—
656C2×D4—104no—
657C2×D4—204no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—42no—
661C22×C4—52no—
662C22×C4—52no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—58no—
669C22×C4—516no—
670C22×C4—108no—
671C22×C4—208no—
672C22×C4C23×D514yes—
673C22×C4C23×D514yes—
674C22×C4C23×D514yes—
675C22×C4C23×D514yes—
676C22×C4C23×D511yescharacteristic
677C22×C4C23×D511yescharacteristic
678C22×C4C23×D511yescharacteristic
679C22×C4C23×D511yescharacteristic
680C22×C4C23×D514yes—
681C22×C4C23×D511yescharacteristic
682C22×C4C23×D511yescharacteristic
683C4⋊C4—54no—
684C4⋊C4—516no—
685C4⋊C4—58no—
686C4⋊C4—54no—
687C4⋊C4—58no—
688C4⋊C4—58no—
689C4⋊C4—516no—
690C4⋊C4—58no—
691C4⋊C4—58no—
692C4⋊C4—54no—
693C4⋊C4—58no—
694C4⋊C4—54no—
695C4⋊C4—58no—
696C4⋊C4—58no—
697C4⋊C4—516no—
698C4⋊C4—516no—
699C4⋊C4—516no—
700C4⋊C4—58no—
701C4⋊C4—516no—
702C4⋊C4—58no—
703C4⋊C4—516no—
704C4⋊C4—58no—
705C4⋊C4—516no—
706C4⋊C4C23×D518yes—
707C4⋊C4C23×D518yes—
708C4⋊C4C23×D518yes—
709C4⋊C4C23×D5116yes—
710C4⋊C4C23×D5116yes—
711C4⋊C4C23×D518yes—
712C22⋊C4—58no—
713C22⋊C4—58no—
714C22⋊C4—58no—
715C22⋊C4—58no—
716C22⋊C4—58no—
717C22⋊C4—58no—
718C22⋊C4—516no—
719C22⋊C4—516no—
720C22⋊C4—58no—
721C22⋊C4—516no—
722C22⋊C4C23×D5116yes—
723C42—58no—
724C42—58no—
725C42—58no—
726C42—516no—
727C42—516no—
728C42—516no—
729C42C23×D514yes—
730C42C23×D514yes—
731C42C23×D514yes—
732C42C23×D514yes—
733C42C23×D5116yes—
734C2×C5—42no—
735C2×C5#355514yescomplemented
736C2×C5C22×2−1+411yescharacteristic
737C2×C5C22×2−1+411yescharacteristic
738C2×C5C2×#58511yescharacteristic
739D5—44no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—54no—
744C23—104no—
745C23—104no—
746C23—104no—
747C23C24×D512yes—
748C23C24×D511yescharacteristic
749Q8—216no—
750Q8—48no—
751Q8—108no—
752Q8—108no—
753Q8—108no—
754Q8—208no—
755Q8—2016no—
756D4—108no—
757D4—208no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—28no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—44no—
767C2×C4—54no—
768C2×C4—54no—
769C2×C4—54no—
770C2×C4—54no—
771C2×C4—54no—
772C2×C4—54no—
773C2×C4—54no—
774C2×C4—104no—
775C2×C4—104no—
776C2×C4—104no—
777C2×C4—104no—
778C2×C4—104no—
779C2×C4—104no—
780C2×C4—104no—
781C2×C4—1016no—
782C2×C4—2016no—
783C2×C4#414714yes—
784C2×C4#415014yes—
785C2×C4C24×D518yes—
786C2×C4C24×D518yes—
787C2×C4C24×D512yes—
788C2×C4C24×D512yes—
789C2×C4C24×D512yes—
790C2×C4C24×D512yes—
791C2×C4C24×D512yes—
792C2×C4C24×D512yes—
793C5C2×#355511yescharacteristic, complemented, Sylow
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—104no—
799C22—104no—
800C22—104no—
801C22—208no—
802C22C2×#414712yes—
803C22C2×#415012yes—
804C22#6628312yes—
805C22C25×D511yescharacteristic
806C4—22no—
807C4—22no—
808C4—28no—
809C4—22no—
810C4—22no—
811C4—28no—
812C4—104no—
813C4—104no—
814C4—104no—
815C4—104no—
816C4—104no—
817C4—104no—
818C4—104no—
819C4C2×#414714yes—
820C4C2×#415014yes—
821C2—42no—
822C2—204no—
823C2#1061817014yesdirect product factor
824C2C22×#414711yescharacteristic
825C2C22×#415011yescharacteristic
826C2C2×#6628311yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#533C2
socleC23×C5C25
prime radicalC2×#4076C22
hypercenterC2×#533D5
hypocenterC5C2×#3555
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C5×#533C2semidirect
2. #10618170C2direct (N × H)
3. C2×#66064C2semidirect
4. C2×#66056C2semidirect
5. C2×#66055C2semidirect
6. C2×#66066C2semidirect
7. C2×#66023C2semidirect
8. C2×#66031C2semidirect
9. C2×#65980C2semidirect
11. C2×#65959C2semidirect
12. C2×#65917C2semidirect
13. C2×#65903C2semidirect
14. C2×#65902C2semidirect
15. C2×#65867C2semidirect
16. C2×#65863C2semidirect
18. C2×#65804C2semidirect
19. C5×#533C22semidirect
43. #66066C22semidirect
44. #66064C22semidirect
45. #66056C22semidirect
46. #66055C22semidirect
47. #66031C22semidirect
48. #66023C22semidirect
49. #65980C22semidirect
51. #65959C22semidirect
52. #65917C22semidirect
53. #65903C22semidirect
54. #65902C22semidirect
55. #65867C22semidirect
56. #65863C22semidirect
90. #65804C22semidirect
248. C2×#533D5semidirect
361. #533C2×D5semidirect
735. C2×C5#3555semidirect
793. C5C2×#3555semidirect
823. C2#10618170direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5332
#106181702
C2×#660642
C2×#660562
C2×#660552
C2×#660662
C2×#660232
C2×#660312
C2×#659802
C2×#659772
C2×#659592
C2×#659172
C2×#659032
C2×#659022
C2×#658672
C2×#658632
C2×#658132
C2×#658042
C2×#35555