Finite Group Databasebeta

← #13041403

Subgroups — #13041403

Order 1280.

1168 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#170C211yesmaximal, characteristic, complemented
2C22×#4004C211yesmaximal, characteristic, complemented
3C2×#65692C211yesmaximal, characteristic, complemented
4C2×#65692C211yesmaximal, characteristic, complemented
5#10606391C211yesmaximal, characteristic
6#10604946C211yesmaximal, characteristic, complemented
7C4×C22⋊#170C211yesmaximal, characteristic, complemented
8#10604241C211yesmaximal, characteristic, complemented
9#10604238C211yesmaximal, characteristic, complemented
10#10604233C211yesmaximal, characteristic, complemented
11#10604230C211yesmaximal, characteristic, complemented
12#10603796C211yesmaximal, characteristic, complemented
13#10603792C211yesmaximal, characteristic, complemented
14#10603785C211yesmaximal, characteristic, complemented
15#10603779C211yesmaximal, characteristic, complemented
16C23×#170C2211yescharacteristic
17C23×#170C2211yescharacteristic
18C23×#170C2211yescharacteristic
19C22×D5⋊C8C2211yescharacteristic
20C2×#4085C411yescharacteristic
21C2×D4×Dic5C2211yescharacteristic
22C22×C4×Dic5C2211yescharacteristic
23C2×#4027C2211yescharacteristic
24C2×#4027C2211yescharacteristic
25C2×C22⋊#170C2211yescharacteristic
26C2×C22⋊#170C2211yescharacteristic
27C2×C22⋊#170C2211yescharacteristic
28C2×C22⋊#170C2211yescharacteristic
29C2×C22⋊#170C2211yescharacteristic
30D4×#170—24no—
31C2×#4004—24no—
32C2×#4004C2211yescharacteristic
33C2×#4004C2211yescharacteristic
34C2×#4004C2211yescharacteristic
35C2×#4004C2211yescharacteristic
36C2×#4004C2211yescharacteristic
37C2×#4003C2211yescharacteristic
38C2×#4003C2211yescharacteristic
39C2×#4003C2211yescharacteristic
40C2×C4⋊#170C2211yescharacteristic
41C2×C4×#170C2211yescharacteristic
42C2×C4×#170C2211yescharacteristic
43C2×C4×#170C2211yescharacteristic
44C2×C4×#170C2211yescharacteristic
45#65692—24no—
46#65692—24no—
47C5×#386C411yescharacteristic
48#65502C411yescharacteristic
49#65246C411yescharacteristic
50#65233C411yescharacteristic
51#65231C411yescharacteristic
52C22⋊C4×Dic5C2211yescharacteristic
53#64959C411yescharacteristic
54#64955C2211yescharacteristic
55#64938C2211yescharacteristic
56#64936C411yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#64918C2211yescharacteristic
60#64918C2211yescharacteristic
61#64918C2211yescharacteristic
62#64918C2211yescharacteristic
63#22985—51nomaximal, Sylow
64C22×C5×D4C2×C411yescharacteristic
65C23×C4×C5C2×C411yescharacteristic
66C22×C22⋊D5C2×C411yescharacteristic
67C22×C22⋊D5C2×C411yescharacteristic
68C23×Dic5C2×C411yescharacteristic
69C23×Dic5C2311yescharacteristic
70C23×Dic5C2311yescharacteristic
71C22×C4×D5C2311yescharacteristic
72C22×#170—22no—
73C22×#170—22no—
74C22×#170—22no—
75C22×#170—22no—
76C22×#170—22no—
77C22×#170—22no—
78C22×#170—41no—
79C22×#170—41no—
80C22×#170—41no—
81C22×#170C2311yescharacteristic
82C22×#170C2311yescharacteristic
83C22×#170C2311yescharacteristic
84C22×#170C2311yescharacteristic
85C22×#170C2311yescharacteristic
86C22×#170C2311yescharacteristic
87C22×#170C2311yescharacteristic
88C22×#170C2311yescharacteristic
89C2×D5⋊C8—22no—
90C2×D5⋊C8—22no—
91C2×D5⋊C8—41no—
92C2×C5×C22⋊C4C2×C411yescharacteristic
93C2×C5×C22⋊C4C2×C411yescharacteristic
94C2×C5×C22⋊C4C2×C411yescharacteristic
95C2×C22⋊Dic5C2×C411yescharacteristic
96C2×C22⋊Dic5C2×C411yescharacteristic
97C2×C22⋊Dic5C2×C411yescharacteristic
98#4085C818yescomplemented
99D4×Dic5—22no—
100D4×Dic5—22no—
101C2×#685C2×C411yescharacteristic
102C2×#685C2×C411yescharacteristic
103C2×#685C2×C411yescharacteristic
104C2×#685C2×C411yescharacteristic
105C2×C4⋊Dic5C2×C411yescharacteristic
106C2×#683C2×C411yescharacteristic
107C2×#683C2×C411yescharacteristic
108C2×#683C2×C411yescharacteristic
109C2×#683C2×C411yescharacteristic
110C2×C4×Dic5—22no—
111C2×C4×Dic5—22no—
112C2×C4×Dic5C2×C411yescharacteristic
113C2×C4×Dic5C2×C411yescharacteristic
114C2×C4×Dic5C2311yescharacteristic
115C2×C4×Dic5C2311yescharacteristic
116C2×C4×Dic5C2311yescharacteristic
117C2×C4×Dic5C2311yescharacteristic
118#4027—22no—
119#4027—22no—
120#4027—22no—
121#4027—22no—
122C22⋊#170—22no—
123C22⋊#170—22no—
124C22⋊#170—22no—
125C22⋊#170—41no—
126C22⋊#170D414yescomplemented
127#4004—22no—
128#4004—22no—
129#4004—22no—
130#4004—22no—
131#4004D414yescomplemented
132#4003—22no—
133#4003—22no—
134#4003—41no—
135C4⋊#170—22no—
136C4×#170—22no—
137C4×#170—22no—
138C4×#170—22no—
139C4×#170—22no—
140C5×#95C2×C411yescharacteristic
141C5×#95C2×C411yescharacteristic
142#3963C2×C411yescharacteristic
143#3963C2×C411yescharacteristic
144#3963C2×C411yescharacteristic
145#3963C2×C411yescharacteristic
146C2×C8×D4—51no—
147C2×C8×D4—51no—
148C2×C8×D4—51no—
149C22×C4⋊C8—51no—
150C4×#121—51no—
151#1954—51no—
152#1939—51no—
153#1923—51no—
154#1923—51no—
155#1869—51no—
156#1869—51no—
157#1850—51no—
158#1850—51no—
159C8×C4⋊C4—51no—
160C4×C22⋊C8—51no—
161C24×C5C22×C411yescharacteristic
162C24×C5C22×C411yescharacteristic
163C23×D5C22×C411yescharacteristic
164C2×C5×D4—22no—
165C2×C5×D4—22no—
166C2×C5×D4C2×C814yescomplemented
167C22×C4×C5—22no—
168C22×C4×C5—22no—
169C22×C4×C5—41no—
170C22×C4×C5C22×C411yescharacteristic
171C22×C4×C5C22×C411yescharacteristic
172C22×C4×C5C22×C411yescharacteristic
173C22×C4×C5C22×C411yescharacteristic
174C22×C4×C5C22×C411yescharacteristic
175C2×C22⋊D5—22no—
176C2×C22⋊D5—22no—
177C2×C22⋊D5—22no—
178C2×C22⋊D5—22no—
179C2×C22⋊D5C2×C814yescomplemented
180C2×C22⋊D5C2×C814yescomplemented
181C22×Dic5—22no—
182C22×Dic5—22no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—21no—
186C22×Dic5—21no—
187C22×Dic5—21no—
188C22×Dic5—21no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—21no—
193C22×Dic5C2×C814yescomplemented
194C22×Dic5C22×C411yescharacteristic
195C22×Dic5C22×C411yescharacteristic
196C22×Dic5C22×C411yescharacteristic
197C22×Dic5C22×C411yescharacteristic
198C22×Dic5C22×C411yescharacteristic
199C22×Dic5C22×C411yescharacteristic
200C22×Dic5C2×D412yes—
201C22×Dic5#4112yes—
202C22×Dic5C2411yescharacteristic
203C2×C4×D5—21no—
204C2×C4×D5—21no—
205C2×C4×D5—21no—
206C2×C4×D5—21no—
207C2×C4×D5—21no—
208C2×C4×D5—21no—
209C2×#170—21no—
210C2×#170—21no—
211C2×#170—21no—
212C2×#170—21no—
213C2×#170—21no—
214C2×#170—21no—
215C2×#170—21no—
216C2×#170—21no—
217C2×#170—21no—
218C2×#170—21no—
219C2×#170—21no—
220C2×#170—21no—
221C2×#170—21no—
222C2×#170—21no—
223C2×#170—21no—
224C2×#170—21no—
225C2×#170—21no—
226C2×#170—21no—
227C2×#170—21no—
228C2×#170—21no—
229C2×#170—44no—
230C2×#170—44no—
231C2×#170—44no—
232C2×#170C2×D412yes—
233C2×#170C2×D412yes—
234C2×#170C2×D412yes—
235C2×#170C2×D412yes—
236D5⋊C8—44no—
237C5×C22⋊C4—22no—
238C5×C22⋊C4—22no—
239C5×C22⋊C4—41no—
240C22⋊Dic5—22no—
241C22⋊Dic5—22no—
242C22⋊Dic5C2×C814yescomplemented
243#685—22no—
244#685—22no—
245#685—41no—
246#685C2×C814yescomplemented
247C4⋊Dic5—22no—
248#683—22no—
249#683—22no—
250#683—22no—
251#683C2×C814yescomplemented
252C4×Dic5—22no—
253C4×Dic5—22no—
254C4×Dic5—21no—
255C4×Dic5—21no—
256C4×Dic5—21no—
257C4×Dic5—21no—
258C4×Dic5—21no—
259C4×Dic5—21no—
260C4×Dic5C2×D412yes—
261C4×Dic5#4112yes—
262C23×C8—51no—
263C23×C8—51no—
264C23×C8—51no—
265C23×C8—51no—
266C2×#121—51no—
267C2×C4×D4—51no—
268C2×C4×D4—51no—
269C2×C4×D4—51no—
270C22×C42—51no—
271C8×D4—104no—
272C8×D4—104no—
273C8×D4—104no—
274C2×C4⋊C8—51no—
275C2×C4⋊C8—51no—
276C2×C4⋊C8—51no—
277C2×C4⋊C8—51no—
278C2×C4⋊C8—51no—
279C2×C4⋊C8—51no—
280C2×C4⋊C8—104no—
281C2×C22⋊C8—51no—
282C2×C22⋊C8—51no—
283C2×C22⋊C8—51no—
284C2×C22⋊C8—51no—
285C2×C22⋊C8—51no—
286C2×C22⋊C8—51no—
287C2×C22⋊C8—51no—
288C2×C22⋊C8—51no—
289C2×C4×C8—51no—
290C2×C4×C8—51no—
291C2×C4×C8—51no—
292C2×C4×C8—51no—
293#390—51no—
294#389—51no—
295#388—51no—
296#388—51no—
297#386—51no—
298#386AGL(1,𝔽5)11yescharacteristic
299#380—51no—
300C4×C4⋊C4—51no—
301C4×C22⋊C4—51no—
302C4×C22⋊C4—51no—
303#336—51no—
304#336—51no—
305#336—51no—
306#336—51no—
307#336—51no—
308#336—51no—
309C23×C5—21no—
310C23×C5—21no—
311C23×C5—21no—
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5C4×D412yes—
320C23×C5C22×C812yes—
321C23×C5C22×C812yes—
322C23×C5#13112yes—
323C23×C5C23×C411yescharacteristic
324C22×D5—21no—
325C22×D5—21no—
326C22×D5—21no—
327C22×D5—21no—
328C22×D5—21no—
329C22×D5—21no—
330C22×D5C22×C812yes—
331C5×D4—28no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—21no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5—21no—
345C2×C4×C5—44no—
346C2×C4×C5C4×D412yes—
347C2×C4×C5C22×C812yes—
348C22⋊D5—28no—
349C22⋊D5—28no—
350C2×Dic5—21no—
351C2×Dic5—21no—
352C2×Dic5—21no—
353C2×Dic5—21no—
354C2×Dic5—21no—
355C2×Dic5—21no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—28no—
361C2×Dic5—21no—
362C2×Dic5—21no—
363C2×Dic5—21no—
364C2×Dic5—21no—
365C2×Dic5—21no—
366C2×Dic5—21no—
367C2×Dic5—41no—
368C2×Dic5—41no—
369C2×Dic5—41no—
370C2×Dic5—41no—
371C2×Dic5C4×D412yes—
372C2×Dic5C4×D412yes—
373C2×Dic5C22×C812yes—
374C2×Dic5C22×C812yes—
375C2×Dic5C22×C812yes—
376C2×Dic5#13112yes—
377C2×Dic5C22×D411yescharacteristic
378C2×Dic5C22×D411yescharacteristic
379C2×Dic5C2×#4111yescharacteristic
380C2×Dic5C2×#4111yescharacteristic
381C2×Dic5H(5,𝔽2)11yescharacteristic
382C2×Dic52−1+411yescharacteristic
383C4×D5—41no—
384C4×D5—41no—
385C4×D5—41no—
386C4×D5—41no—
387#170—22no—
388#170—22no—
389#170—22no—
390#170—22no—
391#170—41no—
392#170—41no—
393#170—41no—
394#170—41no—
395C22×D4—51no—
396C22×D4—51no—
397C22×D4C2×AGL(1,𝔽5)11yescharacteristic
398C23×C4—51no—
399C23×C4—51no—
400C23×C4—51no—
401C23×C4—51no—
402C23×C4C2×AGL(1,𝔽5)11yescharacteristic
403C22×C8—51no—
404C22×C8—51no—
405C22×C8—51no—
406C22×C8—51no—
407C22×C8—51no—
408C22×C8—51no—
409C22×C8—51no—
410C22×C8—51no—
411C22×C8—102no—
412C22×C8—102no—
413C22×C8—102no—
414C22×C8—102no—
415C22×C8—102no—
416C22×C8—102no—
417C22×C8—102no—
418C22×C8—102no—
419C22×C8—201no—
420C22×C8—201no—
421C22×C8—201no—
422C22×C8—201no—
423#121—58no—
424C4×D4—102no—
425C4×D4—102no—
426C4×D4—102no—
427C4×D4—102no—
428C4×D4—102no—
429C4×D4—102no—
430C2×C4⋊C4—51no—
431C2×C4⋊C4—51no—
432C2×C4⋊C4—51no—
433C2×C4⋊C4—51no—
434C2×C4⋊C4—51no—
435C2×C22⋊C4—51no—
436C2×C22⋊C4—51no—
437C2×C22⋊C4—51no—
438C2×C22⋊C4—51no—
439C2×C22⋊C4—51no—
440C2×C22⋊C4—51no—
441C2×C22⋊C4—51no—
442C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
443C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
444C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
445C2×C42—51no—
446C2×C42—51no—
447C2×C42—51no—
448C2×C42—51no—
449C2×C42—51no—
450C2×C42—51no—
451C2×C42—102no—
452C2×C42—102no—
453C4⋊C8—54no—
454C4⋊C8—102no—
455C4⋊C8—102no—
456C4⋊C8—102no—
457C4⋊C8—102no—
458C4⋊C8—102no—
459C22⋊C8—54no—
460C22⋊C8—102no—
461C22⋊C8—102no—
462C22⋊C8—102no—
463C22⋊C8—102no—
464C22⋊C8—102no—
465C22⋊C8—201no—
466C22⋊C8—201no—
467C4×C8—102no—
468C4×C8—102no—
469C4×C8—102no—
470C4×C8—102no—
471#95—51no—
472#95—51no—
473#95—51no—
474#95—51no—
475#95C2×AGL(1,𝔽5)11yescharacteristic
476#95C2×AGL(1,𝔽5)11yescharacteristic
477C22×C5—22no—
478C22×C5—22no—
479C22×C5—22no—
480C22×C5—22no—
481C22×C5—22no—
482C22×C5—22no—
483C22×C5—22no—
484C22×C5—22no—
485C22×C5—22no—
486C22×C5—41no—
487C22×C5—41no—
488C22×C5—41no—
489C22×C5—41no—
490C22×C5C8×D414yescomplemented
491C22×C5C2×C4×D411yescharacteristic
492C22×C5C2×C4×D411yescharacteristic
493C22×C5#52011yescharacteristic
494C22×C5C23×C811yescharacteristic
495C22×C5C2×#13111yescharacteristic
496C22×C5C2×#13111yescharacteristic
497C22×C5#56811yescharacteristic
498C2×D5—22no—
499C2×D5—22no—
500C2×D5—22no—
501C2×D5—41no—
502C2×D5—41no—
503C2×D5—41no—
504C2×D5—41no—
505C4×C5—22no—
506C4×C5—22no—
507C4×C5—41no—
508C4×C5—41no—
509C4×C5—41no—
510Dic5—22no—
511Dic5—22no—
512Dic5—22no—
513Dic5—41no—
514Dic5—41no—
515Dic5C8×D414yescomplemented
516Dic5D4211yescharacteristic
517Dic5#54711yescharacteristic
518Dic5#54811yescharacteristic
519Dic5#55311yescharacteristic
520C24—51no—
521C24C22×AGL(1,𝔽5)11yescharacteristic
522C24C22×AGL(1,𝔽5)11yescharacteristic
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—54no—
526C2×D4—54no—
527C2×D4—102no—
528C2×D4—102no—
529C2×D4—102no—
530C2×D4—102no—
531C2×D4D5⋊C814yescomplemented
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—41no—
535C22×C4—51no—
536C22×C4—51no—
537C22×C4—54no—
538C22×C4—52no—
539C22×C4—52no—
540C22×C4—51no—
541C22×C4—51no—
542C22×C4—51no—
543C22×C4—51no—
544C22×C4—51no—
545C22×C4—101no—
546C22×C4—101no—
547C22×C4—101no—
548C22×C4—101no—
549C22×C4—101no—
550C22×C4—101no—
551C22×C4—101no—
552C22×C4—102no—
553C22×C4—101no—
554C22×C4—101no—
555C22×C4—102no—
556C22×C4—101no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—101no—
560C22×C4—101no—
561C22×C4—101no—
562C22×C4—101no—
563C22×C4C22×AGL(1,𝔽5)11yescharacteristic
564C22×C4C22×AGL(1,𝔽5)11yescharacteristic
565C22×C4C22×AGL(1,𝔽5)11yescharacteristic
566C22×C4C22×AGL(1,𝔽5)11yescharacteristic
567C22×C4C22×AGL(1,𝔽5)11yescharacteristic
568C2×C8—52no—
569C2×C8—52no—
570C2×C8—52no—
571C2×C8—52no—
572C2×C8—101no—
573C2×C8—101no—
574C2×C8—101no—
575C2×C8—101no—
576C2×C8—101no—
577C2×C8—101no—
578C2×C8—101no—
579C2×C8—101no—
580C2×C8—101no—
581C2×C8—101no—
582C2×C8—101no—
583C2×C8—101no—
584C2×C8—101no—
585C2×C8—101no—
586C2×C8—101no—
587C2×C8—101no—
588C2×C8—101no—
589C2×C8—101no—
590C2×C8—101no—
591C2×C8—101no—
592C2×C8—204no—
593C2×C8—204no—
594C2×C8—204no—
595C2×C8—204no—
596C4⋊C4—54no—
597C4⋊C4—102no—
598C4⋊C4—102no—
599C4⋊C4—102no—
600C4⋊C4—102no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—41no—
604C22⋊C4—54no—
605C22⋊C4—54no—
606C22⋊C4—102no—
607C22⋊C4—102no—
608C22⋊C4—102no—
609C22⋊C4—102no—
610C22⋊C4—201no—
611C42—52no—
612C42—52no—
613C42—101no—
614C42—101no—
615C42—101no—
616C42—102no—
617C42—101no—
618C42—101no—
619C42—101no—
620C42—102no—
621C2×C5—24no—
622C2×C5—42no—
623C2×C5#236111yescharacteristic
624C2×C5C2×C8×D411yescharacteristic
625C2×C5C2×C8×D411yescharacteristic
626C2×C5#293311yescharacteristic
627C2×C5#293511yescharacteristic
628C2×C5#298811yescharacteristic
629C2×C5#299411yescharacteristic
630D5—42no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—52no—
642C23—101no—
643C23—101no—
644C23—101no—
645C23—101no—
646C23—101no—
647C23—101no—
648C23C2×D5⋊C812yes—
649C23C2×D5⋊C812yes—
650C23#413112yes—
651C23D4×AGL(1,𝔽5)12yes—
652C23C23×AGL(1,𝔽5)11yescharacteristic
653D4—28no—
654D4—108no—
655D4—108no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—44no—
670C2×C4—52no—
671C2×C4—52no—
672C2×C4—51no—
673C2×C4—51no—
674C2×C4—51no—
675C2×C4—51no—
676C2×C4—52no—
677C2×C4—51no—
678C2×C4—51no—
679C2×C4—52no—
680C2×C4—52no—
681C2×C4—52no—
682C2×C4—102no—
683C2×C4—108no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—101no—
691C2×C4—101no—
692C2×C4—101no—
693C2×C4—101no—
694C2×C4—101no—
695C2×C4—101no—
696C2×C4—101no—
697C2×C4—101no—
698C2×C4—101no—
699C2×C4—201no—
700C2×C4—201no—
701C2×C4—201no—
702C2×C4—201no—
703C2×C4—201no—
704C2×C4—201no—
705C2×C4—201no—
706C2×C4—201no—
707C2×C4C2×D5⋊C812yes—
708C2×C4D4×AGL(1,𝔽5)12yes—
709C8—102no—
710C8—102no—
711C8—102no—
712C8—102no—
713C8—201no—
714C8—201no—
715C8—201no—
716C8—201no—
717C5#2298511yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—102no—
732C22—102no—
733C22—102no—
734C22—201no—
735C22—201no—
736C22—201no—
737C22—201no—
738C22#6569214yescomplemented
739C22C22×D5⋊C811yescharacteristic
740C22C2×#413111yescharacteristic
741C22#6625611yescharacteristic
742C22C2×D4×AGL(1,𝔽5)11yescharacteristic
743C22C2×D4×AGL(1,𝔽5)11yescharacteristic
744C22D5⋊#13111yescharacteristic
745C22#6626611yescharacteristic
746C4—22no—
747C4—22no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—54no—
752C4—51no—
753C4—51no—
754C4—51no—
755C4—51no—
756C4—102no—
757C4—102no—
758C4—102no—
759C4—201no—
760C4—201no—
761C2—24no—
762C2—42no—
763C2—202no—
764C2C2×#6569211yescharacteristic
765C2D4×D5⋊C811yescharacteristic
766C2#1061716511yescharacteristic
767C2#1061721711yescharacteristic
768C2#1061723111yescharacteristic
769C2#1061725311yescharacteristic
770C2#1061730111yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C23×C8
FittingC5×#386C4
socleC23×C5C23×C4
prime radicalC2×#4085C4
cosocleC22×Dic5C24
hypercenter#386AGL(1,𝔽5)
hypocenterC5#22985
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×D4×#170C2semidirect
2. C22×#4004C2semidirect
3. C2×#65692C2semidirect
4. C2×#65692C2semidirect
6. #10604946C2semidirect
7. C4×C22⋊#170C2semidirect
8. #10604241C2semidirect
9. #10604238C2semidirect
10. #10604233C2semidirect
11. #10604230C2semidirect
12. #10603796C2semidirect
13. #10603792C2semidirect
14. #10603785C2semidirect
15. #10603779C2semidirect
98. #4085C8semidirect
126. C22⋊#170D4semidirect
131. #4004D4semidirect
166. C2×C5×D4C2×C8semidirect
179. C2×C22⋊D5C2×C8semidirect
180. C2×C22⋊D5C2×C8semidirect
193. C22×Dic5C2×C8semidirect
242. C22⋊Dic5C2×C8semidirect
246. #685C2×C8semidirect
251. #683C2×C8semidirect
490. C22×C5C8×D4semidirect
515. Dic5C8×D4semidirect
531. C2×D4D5⋊C8semidirect
717. C5#22985semidirect
738. C22#65692semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#1702
C22×#40042
C2×#656922
#106063912
#106049462
C4×C22⋊#1702
#106042412
#106042382
#106042332
#106042302
#106037962
#106037922
#106037852
#106037792
#229855