Finite Group Databasebeta

← #14411845

Subgroups — #14411845

Order 1920.

1548 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2C2×#91284C211yesmaximal, characteristic, complemented
3C2×#91283C211yesmaximal, characteristic, complemented
4#11751335C211yesmaximal, characteristic, complemented
5C5×#5234C211yesmaximal, characteristic, complemented
6#11748499C212yesmaximal, complemented
7#11748482C212yesmaximal, complemented
8#11748482C212yesmaximal, complemented
9D5×#830C212yesmaximal, complemented
10#11748341C211yesmaximal, characteristic, complemented
11C2×#90955C211yesmaximal, characteristic, complemented
12#10610394—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C3×D5×#41—24no—
15C3×D5×#41—24no—
16C2×C3×#713C411yescharacteristic
17C2×C3×Q8×D5C411yescharacteristic
18C2×C3×#711C412yes—
19C2×C3×#711C411yescharacteristic
20C2×C3×D4×D5C412yes—
21C2×C3×D4×D5C411yescharacteristic
22C2×C3×#709C2212yes—
23C2×C3×#709C2211yescharacteristic
24C22×C3×C4×D5C2212yes—
25C22×C3×C4×D5C2211yescharacteristic
26C2×#6710C2211yescharacteristic, complemented
27C22×C3⋊#168C2211yescharacteristic, complemented
28C2×C5×#208C2211yescharacteristic, complemented
29C22×C5×C3⋊C8C2211yescharacteristic, complemented
30C2×#6649C2212yescomplemented
31C2×#6649C2212yescomplemented
32#91284—24no—
33#91283—24no—
34C2×D5×C3⋊C8C2212yescomplemented
35C2×D5×C3⋊C8C2212yescomplemented
36#91114C2212yescomplemented
37#91114C2212yescomplemented
38C5×#830C2212yescomplemented
39C5×#830C2212yescomplemented
40#90955C2211yescharacteristic
41#90955C2212yes—
42#90955C2211yescharacteristic
43#90955C2211yescharacteristic, complemented
44#90955C2211yescharacteristic, complemented
45#90955C2212yescomplemented
46#84075—51nomaximal, Hall
47C2×D5×#41D311yescharacteristic
48C2×#4053—31no—
49C2×#4047—31no—
50C5×#408—31no—
51#65523—31no—
52#65415—31no—
53C2×#3952—31no—
54#65016—32no—
55#65016—32no—
56#65015—32no—
57D5×C22⋊C8—32no—
58C23×C3×D5C2×C411yescharacteristic
59C23×C3×D5C2×C412yes—
60C3×C5×#41—22no—
61C3×C5×#41—22no—
62C2×C3×C5×Q8C2×C411yescharacteristic
63C2×C3×C5×D4C2×C412yes—
64C2×C3×C5×D4C2×C411yescharacteristic
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C2×C3×C22⋊D5C2×C412yes—
68C2×C3×C22⋊D5C2×C412yes—
69C2×C3×C22⋊D5C2×C412yes—
70C22×C3×Dic5C2×C411yescharacteristic
71C22×C3×Dic5C2×C412yes—
72C3×#713—24no—
73C3×Q8×D5—24no—
74C3×#711—28no—
75C3×#711—24no—
76C3×D4×D5—28no—
77C3×D4×D5—24no—
78C3×#709—24no—
79C3×#709—24no—
80C3×#709D414yes—
81C3×#709D414yes—
82C2×C3×D20C2×C412yes—
83C2×C3×D20C2×C411yescharacteristic
84C2×C3×C4×D5—22no—
85C2×C3×C4×D5—22no—
86C2×C3×C4×D5—24no—
87C2×C3×C4×D5—24no—
88C2×C3×C4×D5C2×C411yescharacteristic
89C2×C3×C4×D5C2×C412yes—
90C2×C3×C4×D5C2×C412yes—
91C2×C3×C4×D5C2×C411yescharacteristic
92C2×C3×C4×D5C2311yescharacteristic
93C2×C3×C4×D5C2311yescharacteristic
94C2×C3×C4×D5C2312yes—
95C2×C3×Dic10C2×C412yes—
96C2×C3×Dic10C2×C411yescharacteristic
97#6710—22no—
98C2×C3⋊#168—22no—
99C2×C3⋊#168C2311yescharacteristic
100C2×C3⋊#168C2312yes—
101C2×C3⋊#168C2311yescharacteristic
102C5×#208—22no—
103C2×C5×C3⋊C8—22no—
104C2×C5×C3⋊C8C2311yescharacteristic
105C2×C5×C3⋊C8C2311yescharacteristic
106C2×C5×C3⋊C8C2312yes—
107#6649—24no—
108#6649—24no—
109D5×C3⋊C8—24no—
110D5×C3⋊C8—24no—
111C22×C3×#41—51no—
112C2×#948—51no—
113C2×#948—51no—
114#5234—51no—
115#5234—52no—
116#5234—52no—
117#5234D511yescharacteristic, complemented
118#5207—51no—
119#5207—52no—
120C2×#830—51no—
121C2×#830—52no—
122C2×C5×#41C2×D311yescharacteristic
123D5×#41—24no—
124D5×#41—24no—
125C2×#713Dic311yescharacteristic
126C2×Q8×D5Dic311yescharacteristic
127C2×#711Dic312yes—
128C2×#711Dic311yescharacteristic
129C2×D4×D5Dic312yes—
130C2×D4×D5Dic311yescharacteristic
131C2×#709C2×D312yes—
132C2×#709C2×D311yescharacteristic
133C22×C4×D5C2×D311yescharacteristic
134C22×C4×D5C2×D312yes—
135C2×C5×M16—31no—
136C22×C5×C8—31no—
137C2×#681—31no—
138C22×#168—31no—
139#4053—64no—
140#4047—64no—
141C2×#676—32no—
142C2×#676—32no—
143C2×C8×D5—32no—
144C2×C8×D5—32no—
145C5×C22⋊C8—32no—
146C5×C22⋊C8—32no—
147C22⋊#168—32no—
148C22⋊#168—32no—
149#3952—31no—
150#3952—31no—
151#3952—32no—
152#3952—31no—
153#3952—31no—
154#3952—32no—
155#2880—151noSylow
156C23×C3×C5C22×C412yes—
157C23×C3×C5C22×C411yescharacteristic
158C22×C3×D5—22no—
159C22×C3×D5—24no—
160C22×C3×D5—24no—
161C22×C3×D5—22no—
162C22×C3×D5—42no—
163C22×C3×D5—41no—
164C22×C3×D5C22×C411yescharacteristic
165C22×C3×D5C22×C412yes—
166C22×C3×D5C22×C411yescharacteristic
167C3×C5×Q8—22no—
168C3×C5×D4—24no—
169C3×C5×D4—22no—
170C2×C3×C4×C5—22no—
171C2×C3×C4×C5—22no—
172C2×C3×C4×C5C22×C412yes—
173C2×C3×C4×C5C22×C411yescharacteristic
174C2×C3×C4×C5C2×D412yes—
175C2×C3×C4×C5C2×D412yes—
176C2×C3×C4×C5C2411yescharacteristic
177C3×C22⋊D5—24no—
178C3×C22⋊D5—24no—
179C3×C22⋊D5C22⋊C418yes—
180C2×C3×Dic5—22no—
181C2×C3×Dic5—24no—
182C2×C3×Dic5C22×C411yescharacteristic
183C2×C3×Dic5C22×C411yescharacteristic
184C2×C3×Dic5C22×C412yes—
185C3×D20—24no—
186C3×D20C22⋊C414yes—
187C3×C4×D5—24no—
188C3×C4×D5—22no—
189C3×C4×D5—22no—
190C3×C4×D5—21no—
191C3×C4×D5—21no—
192C3×C4×D5—21no—
193C3×C4×D5—21no—
194C3×C4×D5—24no—
195C3×C4×D5C2×D414yes—
196C3×C4×D5C2×D414yes—
197C3×Dic10—24no—
198C3×Dic10C22⋊C414yes—
199C3⋊#168—21no—
200C3⋊#168—21no—
201C3⋊#168—22no—
202C5×C3⋊C8—21no—
203C5×C3⋊C8—21no—
204C5×C3⋊C8—22no—
205C2×C3×#41—51no—
206C2×C3×#41—52no—
207C2×C3×#41—51no—
208C2×C3×#41—51no—
209C2×C3×#41—52no—
210C2×C3×#41—104no—
211C2×C3×#41—104no—
212C2×C3×#41C2×D511yescharacteristic
213C22×C3×Q8—51no—
214C22×C3×D4—52no—
215C22×C3×D4—51no—
216C23×C3×C4—52no—
217C23×C3×C4—51no—
218#948—104no—
219#948—104no—
220C2×#208—51no—
221C2×#208—52no—
222C2×#208—52no—
223C2×#208C2×D511yescharacteristic, complemented
224C22×C3⋊C8—51no—
225C22×C3⋊C8—52no—
226C22×C3⋊C8—52no—
227C22×C3⋊C8C2×D511yescharacteristic, complemented
228#830—52no—
229#830—52no—
230#830—51no—
231#830—52no—
232#830—51no—
233#830—51no—
234#830—51no—
235#830—52no—
236#830C2×D512yescomplemented
237#830C2×D512yescomplemented
238C23×D5C2×Dic311yescharacteristic
239C23×D5C2×Dic312yes—
240C5×#41—22no—
241C5×#41—22no—
242C2×C5×Q8C2×Dic311yescharacteristic
243C2×C5×D4C2×Dic312yes—
244C2×C5×D4C2×Dic311yescharacteristic
245C22×C4×C5C22×D312yes—
246C22×C4×C5C22×D311yescharacteristic
247C2×C22⋊D5C2×Dic312yes—
248C2×C22⋊D5C2×Dic312yes—
249C2×C22⋊D5C2×Dic312yes—
250C22×Dic5C2×Dic311yescharacteristic
251C22×Dic5C2×Dic312yes—
252#713—24no—
253Q8×D5—24no—
254#711—28no—
255#711—24no—
256D4×D5—28no—
257D4×D5—24no—
258#709—24no—
259#709—24no—
260#709#6714yes—
261#709#6714yes—
262C2×D20C2×Dic312yes—
263C2×D20C2×Dic311yescharacteristic
264C2×C4×D5—22no—
265C2×C4×D5—22no—
266C2×C4×D5—24no—
267C2×C4×D5—24no—
268C2×C4×D5C2×Dic311yescharacteristic
269C2×C4×D5C2×Dic312yes—
270C2×C4×D5C2×Dic312yes—
271C2×C4×D5C2×Dic311yescharacteristic
272C2×C4×D5C22×D311yescharacteristic
273C2×C4×D5C22×D311yescharacteristic
274C2×C4×D5C22×D312yes—
275C2×Dic10C2×Dic312yes—
276C2×Dic10C2×Dic311yescharacteristic
277C5×M16—62no—
278C2×C5×C8—31no—
279C2×C5×C8—31no—
280C2×C5×C8—32no—
281C2×C5×C8—62no—
282#681—62no—
283C2×#168—31no—
284C2×#168—32no—
285C2×#168—31no—
286C2×#168—62no—
287#676—64no—
288#676—64no—
289C8×D5—64no—
290C8×D5—64no—
291C22×#41—51no—
292C2×#131—151no—
293C2×#131—151no—
294#408—31no—
295#408—152no—
296#408—152no—
297#408—151no—
298#407—152no—
299#407—151no—
300C2×C22⋊C8—152no—
301C2×C22⋊C8—151no—
302C22×C3×C5—21no—
303C22×C3×C5—21no—
304C22×C3×C5—22no—
305C22×C3×C5—22no—
306C22×C3×C5—22no—
307C22×C3×C5C2×C22⋊C412yes—
308C22×C3×C5C23×C411yescharacteristic
309C2×C3×D5—21no—
310C2×C3×D5—22no—
311C2×C3×D5—21no—
312C2×C3×D5—22no—
313C2×C3×D5—21no—
314C2×C3×D5—21no—
315C2×C3×D5—21no—
316C2×C3×D5—48no—
317C2×C3×D5—44no—
318C2×C3×D5C2×C22⋊C414yes—
319C2×C3×D5#13112yescomplemented
320C3×C4×C5—22no—
321C3×C4×C5C2×C22⋊C412yes—
322C3×C4×C5C22×D411yescharacteristic
323C3×C4×C5C22×D411yescharacteristic
324C3×Dic5—21no—
325C3×Dic5—21no—
326C3×Dic5C2×C22⋊C414yes—
327C24×C3—52no—
328C24×C3—51no—
329C3×#41—22no—
330C3×#41—22no—
331C3×#41—54no—
332C3×#41—54no—
333C3×#41—104no—
334C3×#41—104no—
335C3×#41—108no—
336C3×#41—104no—
337C3×#41—104no—
338C2×C3×Q8—51no—
339C2×C3×Q8—52no—
340C2×C3×Q8—104no—
341C2×C3×Q8C4×D511yescharacteristic
342C2×C3×D4—52no—
343C2×C3×D4—52no—
344C2×C3×D4—52no—
345C2×C3×D4—51no—
346C2×C3×D4—52no—
347C2×C3×D4—108no—
348C2×C3×D4—104no—
349C2×C3×D4C4×D512yes—
350C2×C3×D4C4×D511yescharacteristic
351C22×C3×C4—52no—
352C22×C3×C4—52no—
353C22×C3×C4—51no—
354C22×C3×C4—52no—
355C22×C3×C4—51no—
356C22×C3×C4—52no—
357C22×C3×C4—51no—
358C22×C3×C4—51no—
359C22×C3×C4—51no—
360C22×C3×C4—104no—
361C22×C3×C4—104no—
362C22×C3×C4—102no—
363C22×C3×C4—102no—
364C22×C3×C4C22×D512yes—
365C22×C3×C4C22×D511yescharacteristic
366#208—22no—
367#208—104no—
368#208—104no—
369#208—102no—
370C2×C3⋊C8—22no—
371C2×C3⋊C8—51no—
372C2×C3⋊C8—52no—
373C2×C3⋊C8—51no—
374C2×C3⋊C8—104no—
375C2×C3⋊C8—104no—
376C2×C3⋊C8—102no—
377C2×C3⋊C8C22×D511yescharacteristic
378C2×C3⋊C8C22×D512yes—
379C2×C3⋊C8C22×D511yescharacteristic
380C23×C5C22×Dic312yes—
381C23×C5C22×Dic311yescharacteristic
382C22×D5—22no—
383C22×D5—24no—
384C22×D5—22no—
385C22×D5—24no—
386C22×D5—42no—
387C22×D5—41no—
388C22×D5C22×Dic311yescharacteristic
389C22×D5C22×Dic311yescharacteristic
390C22×D5C22×Dic312yes—
391C5×Q8—22no—
392C5×D4—24no—
393C5×D4—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5C22×Dic312yes—
397C2×C4×C5C22×Dic311yescharacteristic
398C2×C4×C5C2×#6712yes—
399C2×C4×C5C2×#6712yes—
400C2×C4×C5C23×D311yescharacteristic
401C22⋊D5—24no—
402C22⋊D5—24no—
403C22⋊D5#21718yes—
404C2×Dic5—22no—
405C2×Dic5—24no—
406C2×Dic5C22×Dic311yescharacteristic
407C2×Dic5C22×Dic311yescharacteristic
408C2×Dic5C22×Dic312yes—
409D20—24no—
410D20#21714yes—
411C4×D5—24no—
412C4×D5—22no—
413C4×D5—22no—
414C4×D5—21no—
415C4×D5—21no—
416C4×D5—21no—
417C4×D5—21no—
418C4×D5—24no—
419C4×D5C2×#6714yes—
420C4×D5C2×#6714yes—
421Dic10—24no—
422Dic10#21714yes—
423C5×C8—61no—
424C5×C8—62no—
425C5×C8—61no—
426#168—61no—
427#168—62no—
428#168—61no—
429C2×#41—51no—
430C2×#41—52no—
431C2×#41—51no—
432C2×#41—51no—
433C2×#41—52no—
434C2×#41—104no—
435C2×#41—104no—
436C2×#41D3×D511yescharacteristic
437C22×Q8—51no—
438C22×D4—52no—
439C22×D4—51no—
440C23×C4—52no—
441C23×C4—51no—
442#131—304no—
443#131—304no—
444C2×M16—31no—
445C2×M16—152no—
446C2×M16—152no—
447C2×M16—151no—
448C22×C8—31no—
449C22×C8—152no—
450C22×C8—152no—
451C22×C8—151no—
452C22⋊C8—32no—
453C22⋊C8—32no—
454C22⋊C8—151no—
455C22⋊C8—151no—
456C22⋊C8—152no—
457C22⋊C8—151no—
458C22⋊C8—151no—
459C22⋊C8—152no—
460C22⋊C8—152no—
461C22⋊C8—152no—
462C2×C3×C5—22no—
463C2×C3×C5—42no—
464C2×C3×C5C22×C22⋊C411yescharacteristic
465C2×C3×C5C2×#13111yescharacteristic
466C2×C3×C5#56811yescharacteristic
467C3×D5—22no—
468C3×D5—24no—
469C3×D5—41no—
470C23×C3—51no—
471C23×C3—52no—
472C23×C3—51no—
473C23×C3—104no—
474C23×C3—102no—
475C23×C3—104no—
476C23×C3—102no—
477C23×C3—201no—
478C23×C3—202no—
479C23×C3C2×C4×D512yes—
480C23×C3C2×C4×D511yescharacteristic
481C3×Q8—22no—
482C3×Q8—54no—
483C3×Q8—104no—
484C3×D4—24no—
485C3×D4—22no—
486C3×D4—58no—
487C3×D4—54no—
488C3×D4—104no—
489C3×D4—104no—
490C3×D4—104no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—52no—
494C2×C3×C4—54no—
495C2×C3×C4—54no—
496C2×C3×C4—51no—
497C2×C3×C4—51no—
498C2×C3×C4—104no—
499C2×C3×C4—104no—
500C2×C3×C4—104no—
501C2×C3×C4—102no—
502C2×C3×C4—101no—
503C2×C3×C4—101no—
504C2×C3×C4—101no—
505C2×C3×C4—101no—
506C2×C3×C4—102no—
507C2×C3×C4—102no—
508C2×C3×C4C2×C4×D512yes—
509C2×C3×C4C2×C4×D511yescharacteristic
510C2×C3×C4D4×D512yes—
511C2×C3×C4D4×D512yes—
512C2×C3×C4C23×D511yescharacteristic
513C3⋊C8—21no—
514C3⋊C8—21no—
515C3⋊C8—22no—
516C3⋊C8—101no—
517C3⋊C8—101no—
518C3⋊C8—102no—
519C22×C5—21no—
520C22×C5—21no—
521C22×C5—22no—
522C22×C5—22no—
523C22×C5—22no—
524C22×C5C2×#21712yes—
525C22×C5C23×Dic311yescharacteristic
526C2×D5—22no—
527C2×D5—21no—
528C2×D5—22no—
529C2×D5—21no—
530C2×D5—21no—
531C2×D5—21no—
532C2×D5—21no—
533C2×D5—48no—
534C2×D5—44no—
535C2×D5#94812yescomplemented
536C2×D5C2×#21714yes—
537C4×C5—22no—
538C4×C5C2×#21712yes—
539C4×C5C22×#6711yescharacteristic
540C4×C5C22×#6711yescharacteristic
541Dic5—21no—
542Dic5—21no—
543Dic5C2×#21714yes—
544C24—52no—
545C24—51no—
546#41—22no—
547#41—22no—
548#41—54no—
549#41—54no—
550#41—104no—
551#41—104no—
552#41—108no—
553#41—104no—
554#41—104no—
555C2×Q8—51no—
556C2×Q8—52no—
557C2×Q8—104no—
558C2×Q8D5×Dic311yescharacteristic
559C2×D4—52no—
560C2×D4—52no—
561C2×D4—52no—
562C2×D4—51no—
563C2×D4—52no—
564C2×D4—108no—
565C2×D4—104no—
566C2×D4D5×Dic312yes—
567C2×D4D5×Dic311yescharacteristic
568C22×C4—52no—
569C22×C4—52no—
570C22×C4—51no—
571C22×C4—52no—
572C22×C4—51no—
573C22×C4—52no—
574C22×C4—51no—
575C22×C4—51no—
576C22×C4—51no—
577C22×C4—104no—
578C22×C4—104no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4C2×D3×D512yes—
582C22×C4C2×D3×D511yescharacteristic
583M16—62no—
584M16—304no—
585M16—304no—
586M16—302no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—32no—
590C2×C8—62no—
591C2×C8—151no—
592C2×C8—151no—
593C2×C8—152no—
594C2×C8—304no—
595C2×C8—304no—
596C2×C8—302no—
597C3×C5#288011yescharacteristic, complemented, Hall
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—54no—
604C22×C3—52no—
605C22×C3—101no—
606C22×C3—102no—
607C22×C3—102no—
608C22×C3—101no—
609C22×C3—101no—
610C22×C3—101no—
611C22×C3—101no—
612C22×C3—204no—
613C22×C3—208no—
614C22×C3D5×C22⋊C412yes—
615C22×C3C22×C4×D511yescharacteristic
616C3×C4—22no—
617C3×C4—54no—
618C3×C4—101no—
619C3×C4—101no—
620C3×C4D5×C22⋊C412yes—
621C3×C4C2×D4×D511yescharacteristic
622C3×C4C2×D4×D511yescharacteristic
623C2×C5—22no—
624C2×C5—42no—
625C2×C5C2×#94811yescharacteristic
626C2×C5#581911yescharacteristic
627C2×C5C22×#21711yescharacteristic
628D5—22no—
629D5—24no—
630D5—41no—
631C23—51no—
632C23—52no—
633C23—51no—
634C23—104no—
635C23—102no—
636C23—104no—
637C23—102no—
638C23—201no—
639C23—202no—
640C23C2×D5×Dic312yes—
641C23C2×D5×Dic311yescharacteristic
642Q8—22no—
643Q8—54no—
644Q8—104no—
645D4—24no—
646D4—22no—
647D4—58no—
648D4—54no—
649D4—104no—
650D4—104no—
651D4—104no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—52no—
655C2×C4—54no—
656C2×C4—54no—
657C2×C4—51no—
658C2×C4—51no—
659C2×C4—104no—
660C2×C4—104no—
661C2×C4—104no—
662C2×C4—102no—
663C2×C4—101no—
664C2×C4—101no—
665C2×C4—101no—
666C2×C4—101no—
667C2×C4—102no—
668C2×C4—102no—
669C2×C4C2×D5×Dic312yes—
670C2×C4C2×D5×Dic311yescharacteristic
671C2×C4D5×#6712yes—
672C2×C4D5×#6712yes—
673C2×C4C22×D3×D511yescharacteristic
674C8—61no—
675C8—61no—
676C8—62no—
677C8—301no—
678C8—302no—
679C8—301no—
680C2×C3—22no—
681C2×C3—42no—
682C2×C3—102no—
683C2×C3—104no—
684C2×C3—201no—
685C2×C3C2×D5×C22⋊C411yescharacteristic
686C2×C3D5×#13111yescharacteristic
687C2×C3#6608411yescharacteristic
688C5#8407511yescharacteristic, complemented, Sylow
689C22—21no—
690C22—21no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—52no—
695C22—54no—
696C22—102no—
697C22—101no—
698C22—102no—
699C22—101no—
700C22—101no—
701C22—101no—
702C22—101no—
703C22—204no—
704C22—208no—
705C22D5×#21712yes—
706C22C22×D5×Dic311yescharacteristic
707C4—22no—
708C4—54no—
709C4—101no—
710C4—101no—
711C4D5×#21712yes—
712C4C2×D5×#6711yescharacteristic
713C4C2×D5×#6711yescharacteristic
714C3#1061039411yescharacteristic, complemented, Sylow
715C2—22no—
716C2—42no—
717C2—102no—
718C2—104no—
719C2—201no—
720C2D5×#94811yescharacteristic
721C2#1175529611yescharacteristic
722C2C2×D5×#21711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×#41C22
prime radicalC2×C3×D5×#41C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2880
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91284C2semidirect
3. C2×#91283C2semidirect
4. #11751335C2semidirect
5. C5×#5234C2semidirect
6. #11748499C2semidirect
7. #11748482C2semidirect
8. #11748482C2semidirect
9. D5×#830C2semidirect
10. #11748341C2semidirect
11. C2×#90955C2semidirect
26. C2×#6710C22semidirect
27. C22×C3⋊#168C22semidirect
28. C2×C5×#208C22semidirect
29. C22×C5×C3⋊C8C22semidirect
30. C2×#6649C22semidirect
31. C2×#6649C22semidirect
34. C2×D5×C3⋊C8C22semidirect
35. C2×D5×C3⋊C8C22semidirect
36. #91114C22semidirect
37. #91114C22semidirect
38. C5×#830C22semidirect
39. C5×#830C22semidirect
43. #90955C22semidirect
44. #90955C22semidirect
45. #90955C22semidirect
117. #5234D5semidirect
223. C2×#208C2×D5semidirect
227. C22×C3⋊C8C2×D5semidirect
236. #830C2×D5semidirect
237. #830C2×D5semidirect
319. C2×C3×D5#131semidirect
535. C2×D5#948semidirect
597. C3×C5#2880semidirect
688. C5#84075semidirect
714. C3#10610394semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
C2×#912842
C2×#912832
#117513352
C5×#52342
#117484992
#117484822
D5×#8302
#117483412
C2×#909552
#106103943
#840755