Finite Group Databasebeta

← C2×#10611223 #12964079

Subgroups — C2×#10611223 #12964079

Order 1280.

2230 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65882C211yesmaximal, characteristic
2C2×C5×#435C211yesmaximal, characteristic, complemented
3C2×#65418C211yesmaximal, characteristic, complemented
4C2×#65417C211yesmaximal, characteristic, complemented
5C2×#65399C211yesmaximal, characteristic, complemented
6C2×C8×C22⋊D5C211yesmaximal, characteristic, complemented
7C2×#65300C211yesmaximal, characteristic, complemented
8#10611223C2116yesmaximal, direct product factor
9C2×#65125C211yesmaximal, characteristic, complemented
10C2×#65122C211yesmaximal, characteristic, complemented
11C2×#65016C211yesmaximal, characteristic, complemented
12C2×#65016C211yesmaximal, characteristic, complemented
13C2×#65018C211yesmaximal, characteristic, complemented
14C2×#65014C211yesmaximal, characteristic, complemented
15C2×#64995C211yesmaximal, characteristic, complemented
16C2×#64994C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C22×#709C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic
20C23×C5×C8C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×#4086C411yescharacteristic
23C2×#4084C411yescharacteristic
24C2×C4×C22⋊D5C2211yescharacteristic
25C2×C4×C22⋊D5C2211yescharacteristic
26C22×#681C2211yescharacteristic
27C23×#168C2211yescharacteristic
28C22×#676C2211yescharacteristic
29C22×#676C2211yescharacteristic
30C22×C8×D5C2211yescharacteristic
31C22×C8×D5C2211yescharacteristic
32#65882C418yes—
33#65882C2218yes—
34C2×#4041C411yescharacteristic
35C2×#4034C411yescharacteristic
36C2×#4031C411yescharacteristic
37C2×#4031C411yescharacteristic
38C2×#4030C411yescharacteristic
39C2×#4030C411yescharacteristic
40C2×C4×D20C2211yescharacteristic
41C2×C42×D5C2211yescharacteristic
42C5×#435C2218yescomplemented
43C2×C5×C4⋊C8C2211yescharacteristic
44C2×C5×C22⋊C8C2211yescharacteristic
45C2×C5×C22⋊C8C2211yescharacteristic
46C2×C5×#97C2211yescharacteristic
47C2×C22⋊#168C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49#65418C2218yescomplemented
50#65417C2218yescomplemented
51#65399C2218yescomplemented
52C8×C22⋊D5C2218yescomplemented
53C2×#3952C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3952C2211yescharacteristic
56C2×#3952C2211yescharacteristic
57C2×#3952C2211yescharacteristic
58C2×#3952C2211yescharacteristic
59C2×#3952C2211yescharacteristic
60C2×#3952C2211yescharacteristic
61C2×#3946C2211yescharacteristic
62C2×#3946C2211yescharacteristic
63C2×C8×Dic5C2211yescharacteristic
64C2×C8×Dic5C2211yescharacteristic
65#65300C2218yescomplemented
66C2×C4⋊#168C2211yescharacteristic
67C2×#3935C2211yescharacteristic
68#65125C2218yescomplemented
69#65122C2218yescomplemented
70#65018C2218yescomplemented
71#65016C2218yescomplemented
72#65016C2218yescomplemented
73#65014C2218yescomplemented
74#64995C2218yescomplemented
75#64994C2218yescomplemented
76C2×#2981—51nomaximal, Sylow
77C22×C5×D4C2×C411yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C22×C22⋊D5C2×C411yescharacteristic
81C22×C22⋊D5C2×C411yescharacteristic
82C22×C22⋊D5C2×C411yescharacteristic
83C22×C22⋊D5C2×C411yescharacteristic
84C22×C22⋊D5C2×C411yescharacteristic
85C22×C22⋊D5C2×C411yescharacteristic
86C2×#709—42no—
87C2×#709—42no—
88C2×#709—42no—
89C2×#709—42no—
90C2×#709C2×C414yes—
91C2×#709C2×C414yes—
92C2×#709C2314yes—
93C2×#709C2314yes—
94C22×D20C2×C411yescharacteristic
95C22×D20C2×C411yescharacteristic
96C22×D20C2×C411yescharacteristic
97C22×C4×D5C2×C411yescharacteristic
98C22×C4×D5C2×C411yescharacteristic
99C22×C4×D5C2311yescharacteristic
100C22×C4×D5C2311yescharacteristic
101C22×C4×D5C2311yescharacteristic
102C22×Dic10C2×C411yescharacteristic
103C22×Dic10C2×C411yescharacteristic
104C2×C5×M16—42no—
105C2×C5×M16C2314yes—
106C22×C5×C8—42no—
107C22×C5×C8C2311yescharacteristic
108C22×C5×C8C2311yescharacteristic
109C22×C5×C8C2311yescharacteristic
110C22×C5×C8C2311yescharacteristic
111C22×C5×C8C2314yes—
112C4×C5×D4C2×C414yes—
113C4×C5×D4C2314yes—
114C2×C5×C4⋊C4C2×C411yescharacteristic
115C2×C5×C22⋊C4C2×C411yescharacteristic
116C2×C5×C22⋊C4C2×C411yescharacteristic
117C2×C42×C5C2311yescharacteristic
118C2×C22⋊Dic5C2×C411yescharacteristic
119C2×C22⋊Dic5C2×C411yescharacteristic
120#4086C2×C418yes—
121#4084C2×C418yes—
122C4×C22⋊D5C2×C414yes—
123C4×C22⋊D5C2×C414yes—
124C4×C22⋊D5C2314yes—
125C4×C22⋊D5C2314yes—
126C2×#685C2×C411yescharacteristic
127C2×#685C2×C411yescharacteristic
128C2×#685C2×C411yescharacteristic
129C2×#685C2×C411yescharacteristic
130C2×C4⋊Dic5C2×C411yescharacteristic
131C2×#683C2×C411yescharacteristic
132C2×#683C2×C411yescharacteristic
133C2×C4×Dic5C2×C411yescharacteristic
134C2×C4×Dic5C2×C411yescharacteristic
135C2×C4×Dic5C2311yescharacteristic
136C2×#681—42no—
137C2×#681C2314yes—
138C22×#168—42no—
139C22×#168C2311yescharacteristic
140C22×#168C2311yescharacteristic
141C22×#168C2311yescharacteristic
142C22×#168C2311yescharacteristic
143C22×#168C2314yes—
144C2×#676—42no—
145C2×#676—42no—
146C2×#676C2314yes—
147C2×#676C2314yes—
148C2×C8×D5—42no—
149C2×C8×D5—42no—
150C2×C8×D5C2314yes—
151C2×C8×D5C2314yes—
152#4041C2×C418yes—
153#4034C2×C418yes—
154#4031C2×C418yes—
155#4031C2×C418yes—
156#4030C2×C418yes—
157#4030C2×C418yes—
158C4×D20C2×C414yes—
159C4×D20C2314yes—
160C42×D5C2×C414yes—
161C42×D5C2314yes—
162C5×C4⋊C8C2314yes—
163C5×C22⋊C8C2314yes—
164C5×C22⋊C8C2314yes—
165C5×#97C2314yes—
166C22⋊#168C2314yes—
167C22⋊#168C2314yes—
168#3952C2314yes—
169#3952C2314yes—
170#3952C2314yes—
171#3952C2314yes—
172#3952C2314yes—
173#3952C2314yes—
174#3952C2314yes—
175#3952C2314yes—
176#3946C2314yes—
177#3946C2314yes—
178C8×Dic5C2314yes—
179C8×Dic5C2314yes—
180C4⋊#168C2314yes—
181#3935C2314yes—
182C2×#532—51no—
183#2981—516no—
184C2×#436—51no—
185C2×#436—51no—
186C2×#435—51no—
187C2×#435—51no—
188C2×#435—51no—
189C2×#435D511yescharacteristic, complemented
190C2×C8×D4—51no—
191C2×C8×D4—51no—
192C2×#432—51no—
193C2×#431—51no—
194C2×#408—51no—
195C2×#408—51no—
196C2×#408—51no—
197C2×#408—51no—
198C24×C5C22×C411yescharacteristic
199C24×C5C22×C411yescharacteristic
200C23×D5C22×C411yescharacteristic
201C23×D5C22×C411yescharacteristic
202C23×D5C22×C411yescharacteristic
203C2×C5×D4—42no—
204C2×C5×D4C22×C414yes—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5C22×C411yescharacteristic
210C22×C4×C5C22×C411yescharacteristic
211C22×C4×C5C22×C411yescharacteristic
212C22×C4×C5C22×C411yescharacteristic
213C22×C4×C5C22×C412yes—
214C22×C4×C5C22×C412yes—
215C22×C4×C5C2412yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2411yescharacteristic
218C2×C22⋊D5—24no—
219C2×C22⋊D5—24no—
220C2×C22⋊D5—42no—
221C2×C22⋊D5—42no—
222C2×C22⋊D5—42no—
223C2×C22⋊D5—42no—
224C2×C22⋊D5C22×C414yes—
225C2×C22⋊D5C22×C414yes—
226C2×C22⋊D5C22×C414yes—
227C2×C22⋊D5C22×C414yes—
228C2×C22⋊D5C22×C414yes—
229C2×C22⋊D5C22×C414yes—
230C22×Dic5C22×C411yescharacteristic
231C22×Dic5C22×C411yescharacteristic
232C22×Dic5C22×C411yescharacteristic
233C22×Dic5C22×C411yescharacteristic
234C22×Dic5C22×C411yescharacteristic
235#709—48no—
236#709—48no—
237#709—44no—
238#709—44no—
239#709—44no—
240#709—44no—
241C2×D20—42no—
242C2×D20—42no—
243C2×D20—42no—
244C2×D20C22×C414yes—
245C2×D20C22×C414yes—
246C2×D20C22×C414yes—
247C2×C4×D5—22no—
248C2×C4×D5—22no—
249C2×C4×D5—22no—
250C2×C4×D5—22no—
251C2×C4×D5—22no—
252C2×C4×D5—22no—
253C2×C4×D5—24no—
254C2×C4×D5—42no—
255C2×C4×D5C22×C414yes—
256C2×C4×D5C22×C412yes—
257C2×C4×D5C22×C412yes—
258C2×C4×D5C22×C412yes—
259C2×C4×D5C22×C414yes—
260C2×C4×D5C2412yes—
261C2×C4×D5C2412yes—
262C2×C4×D5C2412yes—
263C2×Dic10—42no—
264C2×Dic10—42no—
265C2×Dic10C22×C414yes—
266C2×Dic10C22×C414yes—
267C5×M16—44no—
268C2×C5×C8—22no—
269C2×C5×C8—22no—
270C2×C5×C8—22no—
271C2×C5×C8—22no—
272C2×C5×C8—44no—
273C2×C5×C8C2412yes—
274C2×C5×C8C2412yes—
275C2×C5×C8C2412yes—
276C2×C5×C8C2412yes—
277C5×C4⋊C4C22×C414yes—
278C5×C22⋊C4C22×C414yes—
279C5×C22⋊C4C22×C414yes—
280C42×C5C22×C412yes—
281C42×C5C2412yes—
282C22⋊Dic5C22×C414yes—
283C22⋊Dic5C22×C414yes—
284#685C22×C414yes—
285#685C22×C414yes—
286#685C22×C414yes—
287#685C22×C414yes—
288C4⋊Dic5C22×C414yes—
289#683C22×C414yes—
290#683C22×C414yes—
291C4×Dic5C22×C412yes—
292C4×Dic5C22×C414yes—
293C4×Dic5C22×C414yes—
294C4×Dic5C2412yes—
295#681—44no—
296C2×#168—22no—
297C2×#168—22no—
298C2×#168—22no—
299C2×#168—22no—
300C2×#168—44no—
301C2×#168C2412yes—
302C2×#168C2412yes—
303C2×#168C2412yes—
304C2×#168C2412yes—
305#676—44no—
306#676—44no—
307C8×D5—44no—
308C8×D5—44no—
309C22×#41—51no—
310C22×#41—51no—
311C22×M16—51no—
312C22×M16—51no—
313C22×M16—51no—
314C22×M16C2×D511yescharacteristic
315C23×C8—51no—
316C23×C8—51no—
317C23×C8—51no—
318C23×C8C2×D511yescharacteristic
319#532—58no—
320#532—58no—
321C2×C4⋊Q8—51no—
322C2×#127—51no—
323C2×#124—51no—
324C2×#124—51no—
325C2×#121—51no—
326C2×#121—51no—
327C2×#121—51no—
328C2×#121—51no—
329C2×C4×D4—51no—
330C2×C4×D4—51no—
331C2×C4×D4—51no—
332C2×C4×D4C2×D511yescharacteristic
333C22×C42—51no—
334#436—58no—
335#436—58no—
336#435—58no—
337#435—58no—
338#435—58no—
339#435C2×D518yescomplemented
340C8×D4—58no—
341C8×D4—58no—
342#432—58no—
343#431—58no—
344C2×C4⋊C8—51no—
345C2×C4⋊C8—51no—
346C2×C4⋊C8—51no—
347C2×C4⋊C8C2×D511yescharacteristic
348#408—58no—
349#408—58no—
350#408—58no—
351#408—58no—
352C2×C22⋊C8—51no—
353C2×C22⋊C8—51no—
354C2×C22⋊C8—51no—
355C2×C22⋊C8—51no—
356C2×C22⋊C8—51no—
357C2×C22⋊C8—51no—
358C2×C22⋊C8—51no—
359C2×C22⋊C8—51no—
360C2×C22⋊C8—51no—
361C2×C22⋊C8—51no—
362C2×C22⋊C8C2×D511yescharacteristic
363C2×C22⋊C8C2×D511yescharacteristic
364C2×#97—51no—
365C2×#97C2×D511yescharacteristic
366C2×C4×C8—51no—
367C2×C4×C8—51no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5C23×C412yes—
375C23×C5C23×C412yes—
376C23×C5C23×C411yescharacteristic
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5C23×C412yes—
387C22×D5C23×C412yes—
388C22×D5C23×C412yes—
389C5×D4—44no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—24no—
395C2×C4×C5—24no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5C23×C412yes—
401C2×C4×C5C23×C412yes—
402C2×C4×C5C23×C412yes—
403C2×C4×C5C23×C412yes—
404C2×C4×C5C23×C411yescharacteristic
405C2×C4×C5H(5,𝔽2)12yes—
406C2×C4×C5H(5,𝔽2)12yes—
407C2×C4×C5C2511yescharacteristic
408C22⋊D5—28no—
409C22⋊D5—28no—
410C22⋊D5—44no—
411C22⋊D5—44no—
412C22⋊D5—44no—
413C22⋊D5—44no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5#13114yes—
419C2×Dic5C23×C412yes—
420C2×Dic5C23×C412yes—
421C2×Dic5C23×C412yes—
422C2×Dic5C23×C412yes—
423C2×Dic5C23×C412yes—
424D20—44no—
425D20—44no—
426D20—44no—
427C4×D5—24no—
428C4×D5—24no—
429C4×D5—24no—
430C4×D5—22no—
431C4×D5—22no—
432C4×D5—22no—
433C4×D5—22no—
434C4×D5—22no—
435C4×D5—22no—
436C4×D5—28no—
437C4×D5—44no—
438Dic10—44no—
439Dic10—44no—
440C5×C8—22no—
441C5×C8—22no—
442C5×C8—22no—
443C5×C8—22no—
444#168—22no—
445#168—22no—
446#168—22no—
447#168—22no—
448C2×#41—54no—
449C2×#41—54no—
450C2×#41—54no—
451C2×#41—54no—
452C2×#41—202no—
453C2×#41—202no—
454C2×#41—202no—
455C2×#41—202no—
456C22×Q8—51no—
457C22×Q8—51no—
458C22×D4—51no—
459C22×D4—51no—
460C22×D4—51no—
461C22×D4—51no—
462C22×D4—51no—
463C22×D4—51no—
464C22×D4—51no—
465C22×D4—51no—
466C22×D4—51no—
467C22×D4C4×D511yescharacteristic
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4C22×D511yescharacteristic
474C23×C4C22×D511yescharacteristic
475C2×M16—42no—
476C2×M16—54no—
477C2×M16—54no—
478C2×M16—54no—
479C2×M16—202no—
480C2×M16—202no—
481C2×M16—202no—
482C2×M16C22×D514yes—
483C22×C8—42no—
484C22×C8—51no—
485C22×C8—51no—
486C22×C8—51no—
487C22×C8—51no—
488C22×C8—54no—
489C22×C8—54no—
490C22×C8—54no—
491C22×C8—202no—
492C22×C8—202no—
493C22×C8—202no—
494C22×C8C22×D511yescharacteristic
495C22×C8C22×D511yescharacteristic
496C22×C8C22×D511yescharacteristic
497C22×C8C22×D511yescharacteristic
498C22×C8C22×D514yes—
499C4⋊Q8—58no—
500#127—58no—
501#124—58no—
502#124—58no—
503#121—58no—
504#121—58no—
505#121—58no—
506#121—58no—
507C4×D4—54no—
508C4×D4—54no—
509C4×D4—54no—
510C4×D4—54no—
511C4×D4—54no—
512C4×D4—54no—
513C4×D4C4×D514yes—
514C4×D4C22×D514yes—
515C2×C4⋊C4—51no—
516C2×C4⋊C4—51no—
517C2×C4⋊C4—51no—
518C2×C4⋊C4C4×D511yescharacteristic
519C2×C22⋊C4—51no—
520C2×C22⋊C4—51no—
521C2×C22⋊C4—51no—
522C2×C22⋊C4—51no—
523C2×C22⋊C4—51no—
524C2×C22⋊C4—51no—
525C2×C22⋊C4C4×D511yescharacteristic
526C2×C22⋊C4C4×D511yescharacteristic
527C2×C42—51no—
528C2×C42—51no—
529C2×C42—51no—
530C2×C42—54no—
531C2×C42—54no—
532C2×C42C22×D511yescharacteristic
533C4⋊C8—54no—
534C4⋊C8—54no—
535C4⋊C8—54no—
536C4⋊C8C22×D514yes—
537C22⋊C8—54no—
538C22⋊C8—54no—
539C22⋊C8—54no—
540C22⋊C8—54no—
541C22⋊C8—54no—
542C22⋊C8—54no—
543C22⋊C8—54no—
544C22⋊C8—54no—
545C22⋊C8—54no—
546C22⋊C8—54no—
547C22⋊C8C22×D514yes—
548C22⋊C8C22×D514yes—
549#97—54no—
550#97C22×D514yes—
551C4×C8—54no—
552C4×C8—54no—
553C22×C5—22no—
554C22×C5—22no—
555C22×C5—22no—
556C22×C5—22no—
557C22×C5—22no—
558C22×C5—22no—
559C22×C5—44no—
560C22×C5—44no—
561C22×C5#51812yes—
562C22×C5C2×#13112yes—
563C22×C5#56812yes—
564C22×C5C24×C411yescharacteristic
565C2×D5—22no—
566C2×D5—22no—
567C2×D5—22no—
568C2×D5—22no—
569C2×D5—22no—
570C2×D5—22no—
571C2×D5—22no—
572C2×D5—22no—
573C2×D5—22no—
574C2×D5—44no—
575C2×D5—44no—
576C2×D5—44no—
577C4×C5—22no—
578C4×C5—22no—
579C4×C5—22no—
580C4×C5—22no—
581C4×C5#51812yes—
582C4×C5C2×H(5,𝔽2)11yescharacteristic
583C4×C5C2×H(5,𝔽2)11yescharacteristic
584Dic5—22no—
585Dic5—22no—
586Dic5—22no—
587Dic5—22no—
588Dic5C2×#13114yes—
589C24—51no—
590C24—51no—
591C24—51no—
592C24C2×C4×D511yescharacteristic
593C24C2×C4×D511yescharacteristic
594#41—208no—
595#41—208no—
596#41—204no—
597#41—204no—
598#41—204no—
599#41—204no—
600C2×Q8—54no—
601C2×Q8—54no—
602C2×Q8—202no—
603C2×Q8—202no—
604C2×D4—42no—
605C2×D4—54no—
606C2×D4—54no—
607C2×D4—54no—
608C2×D4—54no—
609C2×D4—54no—
610C2×D4—54no—
611C2×D4—54no—
612C2×D4—54no—
613C2×D4—54no—
614C2×D4—104no—
615C2×D4—104no—
616C2×D4—202no—
617C2×D4—202no—
618C2×D4—202no—
619C2×D4—202no—
620C2×D4—202no—
621C2×D4—202no—
622C2×D4—202no—
623C2×D4C2×C4×D514yes—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—54no—
634C22×C4—52no—
635C22×C4—52no—
636C22×C4—52no—
637C22×C4—52no—
638C22×C4—52no—
639C22×C4—52no—
640C22×C4—54no—
641C22×C4—104no—
642C22×C4—102no—
643C22×C4—102no—
644C22×C4—102no—
645C22×C4—102no—
646C22×C4—102no—
647C22×C4—102no—
648C22×C4—202no—
649C22×C4C2×C4×D511yescharacteristic
650C22×C4C2×C4×D511yescharacteristic
651C22×C4C2×C4×D511yescharacteristic
652C22×C4C2×C4×D511yescharacteristic
653C22×C4C2×C4×D512yes—
654C22×C4C2×C4×D512yes—
655C22×C4C23×D512yes—
656C22×C4C23×D512yes—
657C22×C4C23×D511yescharacteristic
658M16—44no—
659M16—204no—
660M16—204no—
661M16—204no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—44no—
667C2×C8—52no—
668C2×C8—52no—
669C2×C8—52no—
670C2×C8—52no—
671C2×C8—102no—
672C2×C8—102no—
673C2×C8—102no—
674C2×C8—102no—
675C2×C8—204no—
676C2×C8—204no—
677C2×C8—204no—
678C2×C8C23×D512yes—
679C2×C8C23×D512yes—
680C2×C8C23×D512yes—
681C2×C8C23×D512yes—
682C4⋊C4—54no—
683C4⋊C4—54no—
684C4⋊C4—54no—
685C4⋊C4C2×C4×D514yes—
686C22⋊C4—54no—
687C22⋊C4—54no—
688C22⋊C4—54no—
689C22⋊C4—54no—
690C22⋊C4—54no—
691C22⋊C4—54no—
692C22⋊C4C2×C4×D514yes—
693C22⋊C4C2×C4×D514yes—
694C42—52no—
695C42—54no—
696C42—54no—
697C42—52no—
698C42C2×C4×D512yes—
699C42C23×D512yes—
700C2×C5—42no—
701C2×C5—42no—
702C2×C5#298114yescomplemented
703C2×C5C2×#51811yescharacteristic
704C2×C5C22×#13111yescharacteristic
705C2×C5C2×#56811yescharacteristic
706D5—42no—
707D5—42no—
708D5—42no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—52no—
716C23—52no—
717C23—52no—
718C23—102no—
719C23—102no—
720C23—102no—
721C23—102no—
722C23—102no—
723C23—102no—
724C23—102no—
725C23—102no—
726C23—102no—
727C23C22×C4×D512yes—
728C23C22×C4×D512yes—
729C23C22×C4×D511yescharacteristic
730Q8—204no—
731Q8—204no—
732D4—44no—
733D4—108no—
734D4—108no—
735D4—204no—
736D4—204no—
737D4—204no—
738D4—204no—
739D4—204no—
740D4—204no—
741D4—204no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—54no—
753C2×C4—52no—
754C2×C4—52no—
755C2×C4—52no—
756C2×C4—52no—
757C2×C4—52no—
758C2×C4—108no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—102no—
763C2×C4—104no—
764C2×C4—104no—
765C2×C4—104no—
766C2×C4—102no—
767C2×C4—102no—
768C2×C4—102no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—102no—
772C2×C4—204no—
773C2×C4C22×C4×D512yes—
774C2×C4C22×C4×D512yes—
775C2×C4C22×C4×D512yes—
776C2×C4C22×C4×D512yes—
777C2×C4C22×C4×D511yescharacteristic
778C2×C4#414412yes—
779C2×C4#414912yes—
780C2×C4C24×D511yescharacteristic
781C8—22no—
782C8—22no—
783C8—22no—
784C8—22no—
785C8—102no—
786C8—102no—
787C8—102no—
788C8—102no—
789C5C2×#298111yescharacteristic, complemented, Sylow
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—102no—
799C22—102no—
800C22—102no—
801C22—102no—
802C22—102no—
803C22—102no—
804C22—102no—
805C22—102no—
806C22—102no—
807C22—204no—
808C22—204no—
809C22—204no—
810C22#6587912yes—
811C22#6607912yes—
812C22D5×#13112yes—
813C22C23×C4×D511yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—54no—
819C4—102no—
820C4—102no—
821C4—102no—
822C4—102no—
823C4#6587912yes—
824C4C2×#414411yescharacteristic
825C4C2×#414911yescharacteristic
826C2—42no—
827C2—42no—
828C2—202no—
829C2—202no—
830C2—202no—
831C2#1061122314yesdirect product factor
832C2C2×#6587911yescharacteristic
833C2C2×#6607911yescharacteristic
834C2C2×D5×#13111yescharacteristic
subgroupG/H
centerC22×C4C23×D5
commutatorC22×C5C24×C4
FrattiniC2×C4C24×D5
FittingC2×C5×#435C2
socleC23×C5C23×C4
prime radicalC2×#65882C2
cosocleC2×C4×C5C25
hypercenterC2×#435D5
hypocenterC5C2×#2981
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×C5×#435C2semidirect
3. C2×#65418C2semidirect
4. C2×#65417C2semidirect
5. C2×#65399C2semidirect
6. C2×C8×C22⋊D5C2semidirect
7. C2×#65300C2semidirect
8. #10611223C2direct (N × H)
9. C2×#65125C2semidirect
10. C2×#65122C2semidirect
11. C2×#65016C2semidirect
12. C2×#65016C2semidirect
13. C2×#65018C2semidirect
14. C2×#65014C2semidirect
15. C2×#64995C2semidirect
16. C2×#64994C2semidirect
42. C5×#435C22semidirect
49. #65418C22semidirect
50. #65417C22semidirect
51. #65399C22semidirect
52. C8×C22⋊D5C22semidirect
65. #65300C22semidirect
68. #65125C22semidirect
69. #65122C22semidirect
70. #65018C22semidirect
71. #65016C22semidirect
72. #65016C22semidirect
73. #65014C22semidirect
74. #64995C22semidirect
75. #64994C22semidirect
189. C2×#435D5semidirect
339. #435C2×D5semidirect
702. C2×C5#2981semidirect
789. C5C2×#2981semidirect
831. C2#10611223direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658822
C2×C5×#4352
C2×#654182
C2×#654172
C2×#653992
C2×C8×C22⋊D52
C2×#653002
#106112232
C2×#651252
C2×#651222
C2×#650162
C2×#650182
C2×#650142
C2×#649952
C2×#649942
C2×#29815