Finite Group Databasebeta

← #14326069

Subgroups — #14326069

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6769C211yesmaximal, characteristic
2C2×#91406C211yesmaximal, characteristic, complemented
3C2×#91405C211yesmaximal, characteristic, complemented
4#11750766C211yesmaximal, characteristic, complemented
5C5×#4664C211yesmaximal, characteristic, complemented
6C3×#64935C211yesmaximal, characteristic, complemented
7#11748904C211yesmaximal, characteristic, complemented
8#11748889C211yesmaximal, characteristic, complemented
9#11748888C211yesmaximal, characteristic, complemented
10#11748883C211yesmaximal, characteristic, complemented
11#11748883C211yesmaximal, characteristic, complemented
12D3×#3963C211yesmaximal, characteristic, complemented
13#11748876C211yesmaximal, characteristic, complemented
14#11748875C211yesmaximal, characteristic, complemented
15#11748672C211yesmaximal, characteristic, complemented
16#10605852—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic
21C22×#1203C2211yescharacteristic
22C22×#1203C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C22×D3×Dic5C2211yescharacteristic
28C2×#6769—24no—
29C2×#6769—24no—
30C2×#6769C418yescomplemented
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43#91406—24no—
44#91405—24no—
45C3×C5×#95C2211yescharacteristic
46#91115C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#76613—51nomaximal, Hall
58C22×#709—31no—
59C2×#4027—31no—
60C2×#4027—31no—
61C5×#381—31no—
62C2×#3963—31no—
63#65247—31no—
64#65247—31no—
65#64956—31no—
66#64955—31no—
67#64954—31no—
68#64954—31no—
69#64953—31no—
70D5×#95—31no—
71#64935—31no—
72#64935D311yescharacteristic, complemented
73C23×D15C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C2×D60—22no—
82C2×D60—22no—
83C2×D60C2×C414yescomplemented
84C2×C4×D15—22no—
85C2×C4×D15—22no—
86C2×C4×D15—41no—
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C2×C4×C5×D3—22no—
91C2×C4×C5×D3—22no—
92C2×C4×C5×D3C2×C414yescomplemented
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C2×C3×Dic10—22no—
98C2×C3×Dic10—22no—
99C2×C3×Dic10C2×C414yescomplemented
100C2×#1203—22no—
101C2×#1203—22no—
102C2×#1203C2×C414yes—
103C2×#1203C2×C414yescomplemented
104C2×#1203D414yes—
105C2×#1203D414yes—
106C2×#1200—22no—
107C2×#1200—22no—
108C2×#1200—22no—
109C2×#1200—22no—
110C2×#1200—22no—
111C2×#1200—22no—
112C2×#1200—41no—
113C2×#1200C2×C414yescomplemented
114C2×#1200C2×C414yescomplemented
115C2×D3×Dic5—22no—
116C2×D3×Dic5—22no—
117C2×D3×Dic5—22no—
118C2×D3×Dic5—22no—
119C2×D3×Dic5—41no—
120C2×D3×Dic5—41no—
121#6769—232no—
122#6714—22no—
123#6714—22no—
124#6714—41no—
125C5×(C2×D3)⋊C4—22no—
126C5×(C2×D3)⋊C4—22no—
127C3×#683—22no—
128C3×C4×Dic5—22no—
129#6668—22no—
130#6667—22no—
131#6667—22no—
132#6667—41no—
133Dic3×Dic5—22no—
134C22×#239—51no—
135C2×#893—51no—
136C2×C4×D12—51no—
137C3×#391—51no—
138#5229—51no—
139#4987—51no—
140C4×(C2×D3)⋊C4—51no—
141#4665—51no—
142#4665—51no—
143#4665—51no—
144#4665—51no—
145#4664—51no—
146#4664D511yescharacteristic, complemented
147D3×#95—51no—
148D3×#95—51no—
149C23×C4×C5—31no—
150C22×C22⋊D5—31no—
151C22×C22⋊D5—31no—
152C23×Dic5—31no—
153C23×Dic5—31no—
154C2×#709—38no—
155C2×#709—64no—
156C2×#709—64no—
157C22×D20—31no—
158C22×C4×D5—31no—
159C22×C4×D5—31no—
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×Dic10C2×D311yescharacteristic
163C2×C5×C22⋊C4—31no—
164C2×C5×C22⋊C4—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#683—31no—
172C2×#683C2×D311yescharacteristic
173C2×C4×Dic5—31no—
174C2×C4×Dic5C2×D311yescharacteristic
175#4027—64no—
176#4027—64no—
177C5×#95—31no—
178C5×#95—31no—
179C5×#95—31no—
180C5×#95C2×D311yescharacteristic
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963C2×D311yescharacteristic
187#3963C2×D311yescharacteristic
188#3963C2×D311yescharacteristic
189#2339—151noSylow
190C23×C3×C5C2411yescharacteristic
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—21no—
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15C22×C412yes—
202C22×D15C22×C412yes—
203C22×D15C2×D412yes—
204C22×D15C2×D412yes—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—21no—
209C22×C5×D3C22×C412yes—
210C22×C5×D3C2×D412yes—
211C22×C5×D3C2×D412yes—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5C22×C412yes—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15#4112yescomplemented
227D60—28no—
228C4×D15—44no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3C22×C412yes—
238C4×C5×D3—28no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5C22×C412yes—
247C2×C3×Dic5C22×C412yes—
248C2×C3×Dic5C2×D412yes—
249C2×C3×Dic5C2×D412yes—
250C2×C3×Dic5#4112yescomplemented
251C3×Dic10—28no—
252#1203—28no—
253#1203C22⋊C4116yescomplemented
254#1200—28no—
255#1200—28no—
256#1200—44no—
257D3×Dic5—44no—
258D3×Dic5—44no—
259C22×C3×Q8—51no—
260C2×#239—58no—
261C2×#239—104no—
262C2×#239—104no—
263C22×D12—51no—
264C22×D12—51no—
265C22×D12—51no—
266C22×C4×D3—51no—
267C22×C4×D3—51no—
268C22×C4×D3—51no—
269C22×C4×D3—51no—
270C22×C4×D3—51no—
271C22×C4×D3—51no—
272C22×C4×D3C2×D511yescharacteristic
273C2×C3×C4⋊C4—51no—
274C2×C3×C42—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4C2×D511yescharacteristic
282C2×(C2×D3)⋊C4C2×D511yescharacteristic
283C2×C4⋊Dic3—51no—
284C2×C4×Dic3—51no—
285#893—104no—
286C4×D12—104no—
287C3×#95—51no—
288C3×#95—51no—
289C3×#95—51no—
290C3×#95C2×D511yescharacteristic
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95C2×D511yescharacteristic
297C3⋊#95C2×D511yescharacteristic
298C3⋊#95C2×D511yescharacteristic
299C24×C5—31no—
300C23×D5—31no—
301C23×D5—31no—
302C22×C4×C5—31no—
303C22×C4×C5—34no—
304C22×C4×C5—31no—
305C22×C4×C5—31no—
306C22×C4×C5—62no—
307C22×C4×C5—62no—
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×C4×C5C22×D311yescharacteristic
311C2×C22⋊D5—34no—
312C2×C22⋊D5—34no—
313C2×C22⋊D5—34no—
314C2×C22⋊D5—34no—
315C2×C22⋊D5—62no—
316C2×C22⋊D5—62no—
317C22×Dic5—31no—
318C22×Dic5—31no—
319C22×Dic5—62no—
320C22×Dic5—62no—
321C22×Dic5—62no—
322C22×Dic5—62no—
323C22×Dic5—121no—
324C22×Dic5—121no—
325C22×Dic5C22×D311yescharacteristic
326C22×Dic5C22×D311yescharacteristic
327C22×Dic5C22×D311yescharacteristic
328C22×Dic5C22×D311yescharacteristic
329#709—632no—
330C2×D20—34no—
331C2×D20—62no—
332C2×D20—62no—
333C2×C4×D5—34no—
334C2×C4×D5—34no—
335C2×C4×D5—62no—
336C2×C4×D5—62no—
337C2×C4×D5—62no—
338C2×C4×D5—62no—
339C2×C4×D5—62no—
340C2×C4×D5—62no—
341C2×C4×D5—62no—
342C2×C4×D5—62no—
343C2×C4×D5—121no—
344C2×C4×D5—121no—
345C2×Dic10—22no—
346C2×Dic10—22no—
347C2×Dic10C4×D314yescomplemented
348C5×C22⋊C4—62no—
349C5×C22⋊C4—62no—
350#685—62no—
351#685—62no—
352#685—62no—
353#685—62no—
354#685—121no—
355#685—121no—
356#683—22no—
357#683—62no—
358C4×Dic5—22no—
359C4×Dic5—62no—
360C22×#41—151no—
361C2×C4×D4—151no—
362C2×C4×D4—151no—
363#391—51no—
364#391—151no—
365#386—151no—
366#386—151no—
367#386—151no—
368#386—151no—
369#381—31no—
370#381—151no—
371#380—151no—
372C4×C22⋊C4—151no—
373C2×#95—151no—
374C2×#95—151no—
375C22×C3×C5C23×C411yescharacteristic
376C22×C3×C5C22×D411yescharacteristic
377C22×C3×C5C22×D411yescharacteristic
378C22×C3×C5C2×#4111yescharacteristic
379C22×C3×C5C2×#4111yescharacteristic
380C22×C3×C5H(5,𝔽2)11yescharacteristic
381C22×C3×C52−1+411yescharacteristic
382C2×D15—22no—
383C2×D15—22no—
384C2×D15—22no—
385C2×D15—22no—
386C2×D15—22no—
387C2×D15—22no—
388C2×D15—22no—
389C2×D15—22no—
390C2×D15—22no—
391C2×D15—41no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—41no—
395C2×D15C2×C22⋊C414yes—
396C2×C5×D3—22no—
397C2×C5×D3—22no—
398C2×C5×D3—22no—
399C2×C5×D3—22no—
400C2×C5×D3—22no—
401C2×C5×D3—22no—
402C2×C5×D3C2×C22⋊C414yes—
403C3×C4×C5—22no—
404C3×C4×C5—41no—
405C3×C4×C5—41no—
406Dic15—22no—
407Dic15—41no—
408C3×Dic5—22no—
409C3×Dic5—22no—
410C3×Dic5—41no—
411C3×Dic5C2×C22⋊C414yes—
412C5×Dic3—22no—
413C5×Dic3—41no—
414C5×Dic3—41no—
415C23×D3—51no—
416C23×D3—51no—
417C23×D3C22×D511yescharacteristic
418C2×C3×Q8—54no—
419C2×C3×Q8—102no—
420C2×C3×Q8—102no—
421C22×C3×C4—51no—
422C22×C3×C4—51no—
423C22×C3×C4—51no—
424C22×C3×C4—51no—
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C22×C3×C4C22×D511yescharacteristic
428C22×Dic3—51no—
429C22×Dic3—51no—
430C22×Dic3C22×D511yescharacteristic
431C22×Dic3C22×D511yescharacteristic
432C22×Dic3C22×D511yescharacteristic
433#239—1032no—
434C2×D12—54no—
435C2×D12—54no—
436C2×D12—54no—
437C2×D12—54no—
438C2×D12—54no—
439C2×D12—102no—
440C2×D12—102no—
441C2×D12—102no—
442C2×D12—102no—
443C2×C4×D3—22no—
444C2×C4×D3—22no—
445C2×C4×D3—54no—
446C2×C4×D3—54no—
447C2×C4×D3—102no—
448C2×C4×D3—102no—
449C2×C4×D3—102no—
450C2×C4×D3—102no—
451C2×C4×D3—102no—
452C2×C4×D3—102no—
453C2×C4×D3—102no—
454C2×C4×D3—102no—
455C2×C4×D3—102no—
456C2×C4×D3—102no—
457C2×C4×D3—102no—
458C2×C4×D3—102no—
459C2×C4×D3—201no—
460C2×C4×D3—201no—
461C2×C4×D3—201no—
462C2×C4×D3—201no—
463C2×C4×D3C4×D514yescomplemented
464C3×C4⋊C4—102no—
465C3×C42—102no—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—22no—
468(C2×D3)⋊C4—102no—
469(C2×D3)⋊C4—102no—
470(C2×D3)⋊C4—102no—
471(C2×D3)⋊C4—102no—
472(C2×D3)⋊C4—201no—
473(C2×D3)⋊C4—201no—
474C4⋊Dic3—102no—
475C4×Dic3—102no—
476C23×C5—32no—
477C23×C5—32no—
478C23×C5—32no—
479C23×C5—61no—
480C23×C5—61no—
481C23×C5—61no—
482C23×C5—61no—
483C23×C5C23×D311yescharacteristic
484C22×D5—32no—
485C22×D5—32no—
486C22×D5—32no—
487C22×D5—32no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C22×D5—61no—
493C22×D5—61no—
494C22×D5—61no—
495C22×D5—61no—
496C22×D5—61no—
497C22×D5—61no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—32no—
507C2×C4×C5—68no—
508C2×C4×C5—61no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5C2×C4×D312yes—
517C22⋊D5—316no—
518C22⋊D5—68no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—32no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—124no—
533C2×Dic5—124no—
534C2×Dic5C2×C4×D312yes—
535C2×Dic5C2×C4×D312yes—
536C2×Dic5D3×D412yes—
537C2×Dic5D3×D412yes—
538C2×Dic5#23912yescomplemented
539D20—68no—
540C4×D5—68no—
541C4×D5—68no—
542C4×D5—124no—
543C4×D5—124no—
544Dic10—28no—
545C2×#41—158no—
546C2×#41—304no—
547C2×#41—304no—
548C22×Q8—51no—
549C22×D4—151no—
550C22×D4—151no—
551C22×D4—151no—
552C23×C4—31no—
553C23×C4—151no—
554C23×C4—151no—
555C23×C4—151no—
556C23×C4—151no—
557C23×C4—151no—
558C23×C4—151no—
559C4×D4—304no—
560C4×D4—304no—
561C2×C4⋊C4—51no—
562C2×C4⋊C4—151no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—151no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4—151no—
571C2×C42—51no—
572C2×C42—151no—
573#95—31no—
574#95—31no—
575#95—31no—
576#95—51no—
577#95—51no—
578#95—51no—
579#95—151no—
580#95—151no—
581#95—151no—
582#95—151no—
583#95—151no—
584#95D3×D511yescharacteristic
585C2×C3×C5C22×C22⋊C411yescharacteristic
586C2×C3×C5C4×#4111yescharacteristic
587C2×C3×C5#52011yescharacteristic
588C2×C3×C5#54611yescharacteristic
589C2×C3×C5#54611yescharacteristic
590C2×C3×C5#54711yescharacteristic
591C2×C3×C5#54711yescharacteristic
592D15—24no—
593D15—42no—
594C5×D3—24no—
595C23×C3C23×D511yescharacteristic
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—52no—
601C22×D3—52no—
602C22×D3—52no—
603C22×D3—52no—
604C22×D3—101no—
605C22×D3—101no—
606C22×D3—101no—
607C22×D3—101no—
608C22×D3—101no—
609C22×D3—101no—
610C22×D3—101no—
611C22×D3—101no—
612C22×D3—101no—
613C22×D3—101no—
614C22×D3C2×C4×D512yes—
615C22×D3D4×D512yes—
616C22×D3D4×D512yes—
617C3×Q8—108no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—52no—
627C2×C3×C4—52no—
628C2×C3×C4—52no—
629C2×C3×C4—52no—
630C2×C3×C4—52no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4C2×C4×D512yes—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—52no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3C2×C4×D512yes—
654D12—516no—
655D12—108no—
656D12—108no—
657C4×D3—28no—
658C4×D3—108no—
659C4×D3—108no—
660C4×D3—204no—
661C4×D3—204no—
662C4×D3—204no—
663C4×D3—204no—
664C22×C5—34no—
665C22×C5—62no—
666C22×C5—62no—
667C22×C5—62no—
668C22×C5—62no—
669C22×C5—62no—
670C22×C5—62no—
671C22×C5C22×C4×D311yescharacteristic
672C22×C5C2×D3×D411yescharacteristic
673C22×C5C2×D3×D411yescharacteristic
674C22×C5C2×#23911yescharacteristic
675C22×C5#100711yescharacteristic
676C22×C5D3×#4111yescharacteristic
677C22×C5#100911yescharacteristic
678C2×D5—34no—
679C2×D5—62no—
680C2×D5—62no—
681C2×D5—62no—
682C2×D5—62no—
683C2×D5—62no—
684C2×D5—62no—
685C2×D5—62no—
686C2×D5—62no—
687C2×D5—62no—
688C2×D5—121no—
689C2×D5—121no—
690C2×D5—121no—
691C2×D5—121no—
692C4×C5—22no—
693C4×C5—41no—
694C4×C5—41no—
695C4×C5—62no—
696C4×C5—121no—
697C4×C5—121no—
698Dic5—22no—
699Dic5—22no—
700Dic5—41no—
701Dic5—62no—
702Dic5—121no—
703Dic5D3×C22⋊C414yes—
704C24—31no—
705C24—151no—
706C24—151no—
707#41—3032no—
708C2×Q8—54no—
709C2×Q8—102no—
710C2×Q8—102no—
711C2×D4—154no—
712C2×D4—154no—
713C2×D4—154no—
714C2×D4—154no—
715C2×D4—154no—
716C2×D4—302no—
717C2×D4—302no—
718C2×D4—302no—
719C2×D4—302no—
720C22×C4—31no—
721C22×C4—34no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—51no—
725C22×C4—51no—
726C22×C4—51no—
727C22×C4—51no—
728C22×C4—62no—
729C22×C4—62no—
730C22×C4—154no—
731C22×C4—154no—
732C22×C4—151no—
733C22×C4—151no—
734C22×C4—302no—
735C22×C4—302no—
736C22×C4—302no—
737C22×C4—302no—
738C22×C4—302no—
739C22×C4—302no—
740C22×C4—302no—
741C22×C4—302no—
742C22×C4—302no—
743C22×C4—302no—
744C22×C4—302no—
745C22×C4—302no—
746C22×C4—601no—
747C22×C4—601no—
748C22×C4—601no—
749C22×C4—601no—
750C22×C4C2×D3×D511yescharacteristic
751C22×C4C2×D3×D511yescharacteristic
752C22×C4C2×D3×D511yescharacteristic
753C4⋊C4—102no—
754C4⋊C4—302no—
755C22⋊C4—62no—
756C22⋊C4—62no—
757C22⋊C4—302no—
758C22⋊C4—302no—
759C22⋊C4—302no—
760C22⋊C4—302no—
761C22⋊C4—601no—
762C22⋊C4—601no—
763C42—102no—
764C42—302no—
765C3×C5#233911yescharacteristic, complemented, Hall
766C22×C3C22×C4×D511yescharacteristic
767C22×C3C2×D4×D511yescharacteristic
768C22×C3C2×D4×D511yescharacteristic
769C22×C3D5×#4111yescharacteristic
770C22×C3D5×#4111yescharacteristic
771C22×C3#414911yescharacteristic
772C22×C3#415011yescharacteristic
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—54no—
780C2×D3—102no—
781C2×D3—102no—
782C2×D3—102no—
783C2×D3—102no—
784C2×D3—102no—
785C2×D3—102no—
786C2×D3—102no—
787C2×D3—102no—
788C2×D3—102no—
789C2×D3—201no—
790C2×D3—201no—
791C2×D3—201no—
792C2×D3—201no—
793C2×D3D5×C22⋊C414yes—
794C3×C4—22no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—54no—
798C3×C4—102no—
799C3×C4—102no—
800C3×C4—201no—
801Dic3—22no—
802Dic3—41no—
803Dic3—41no—
804Dic3—102no—
805Dic3—201no—
806C2×C5—64no—
807C2×C5C2×D3×C22⋊C411yescharacteristic
808C2×C5C4×#23911yescharacteristic
809C2×C5#557411yescharacteristic
810C2×C5#563011yescharacteristic
811C2×C5#563111yescharacteristic
812C2×C5#567611yescharacteristic
813C2×C5#572611yescharacteristic
814D5—64no—
815D5—122no—
816C23—32no—
817C23—32no—
818C23—32no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—61no—
823C23—152no—
824C23—152no—
825C23—152no—
826C23—152no—
827C23—301no—
828C23—301no—
829C23—301no—
830C23—301no—
831C23—301no—
832C23—301no—
833C23—301no—
834C23—301no—
835C23—301no—
836C23—301no—
837C23C22×D3×D511yescharacteristic
838Q8—108no—
839D4—1516no—
840D4—308no—
841D4—308no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—32no—
851C2×C4—52no—
852C2×C4—52no—
853C2×C4—52no—
854C2×C4—52no—
855C2×C4—52no—
856C2×C4—68no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—101no—
866C2×C4—101no—
867C2×C4—101no—
868C2×C4—101no—
869C2×C4—101no—
870C2×C4—101no—
871C2×C4—101no—
872C2×C4—152no—
873C2×C4—308no—
874C2×C4—308no—
875C2×C4—301no—
876C2×C4—301no—
877C2×C4—301no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—604no—
881C2×C4—604no—
882C2×C4—604no—
883C2×C4—604no—
884C2×C4C4×D3×D512yes—
885C2×C3C2×D5×C22⋊C411yescharacteristic
886C2×C3#6585611yescharacteristic
887C2×C3#6585711yescharacteristic
888C2×C3#6598811yescharacteristic
889C2×C3#6598811yescharacteristic
890C2×C3#6598911yescharacteristic
891C2×C3#6598911yescharacteristic
892D3—24no—
893D3—104no—
894D3—202no—
895C5#7661311yescharacteristic, complemented, Sylow
896C22—34no—
897C22—62no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—154no—
904C22—302no—
905C22—302no—
906C22—302no—
907C22—302no—
908C22—302no—
909C22—302no—
910C22—302no—
911C22—302no—
912C22—302no—
913C22—601no—
914C22—601no—
915C22—601no—
916C22—601no—
917C22#9200411yescharacteristic
918C22C2×C4×D3×D511yescharacteristic
919C22#9201911yescharacteristic
920C22D3×D4×D511yescharacteristic
921C22D3×D4×D511yescharacteristic
922C22#9202411yescharacteristic
923C22D5×#23911yescharacteristic
924C4—22no—
925C4—41no—
926C4—41no—
927C4—54no—
928C4—62no—
929C4—102no—
930C4—102no—
931C4—121no—
932C4—121no—
933C4—201no—
934C4—302no—
935C4—601no—
936C3#1060585211yescharacteristic, complemented, Sylow
937C2—64no—
938C2—304no—
939C2—602no—
940C2#1175252711yescharacteristic
941C2#1175285811yescharacteristic
942C2D3×D5×C22⋊C411yescharacteristic
943C2#1175326011yescharacteristic
944C2#1175340811yescharacteristic
945C2#1175342611yescharacteristic
946C2#1175387011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6769C2
hypercenter#95D3×D5
hypocenterC3×C5#2339
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#91406C2semidirect
3. C2×#91405C2semidirect
4. #11750766C2semidirect
5. C5×#4664C2semidirect
6. C3×#64935C2semidirect
7. #11748904C2semidirect
8. #11748889C2semidirect
9. #11748888C2semidirect
10. #11748883C2semidirect
11. #11748883C2semidirect
12. D3×#3963C2semidirect
13. #11748876C2semidirect
14. #11748875C2semidirect
15. #11748672C2semidirect
30. C2×#6769C4semidirect
72. #64935D3semidirect
83. C2×D60C2×C4semidirect
92. C2×C4×C5×D3C2×C4semidirect
99. C2×C3×Dic10C2×C4semidirect
103. C2×#1203C2×C4semidirect
113. C2×#1200C2×C4semidirect
114. C2×#1200C2×C4semidirect
146. #4664D5semidirect
226. C2×Dic15#41semidirect
250. C2×C3×Dic5#41semidirect
253. #1203C22⋊C4semidirect
347. C2×Dic10C4×D3semidirect
463. C2×C4×D3C4×D5semidirect
538. C2×Dic5#239semidirect
765. C3×C5#2339semidirect
895. C5#76613semidirect
936. C3#10605852semidirect

Maximal subgroups

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

subgroupindex
C22×#67692
C2×#914062
C2×#914052
#117507662
C5×#46642
C3×#649352
#117489042
#117488892
#117488882
#117488832
D3×#39632
#117488762
#117488752
#117486722
#106058523
#766135