Finite Group Databasebeta

← #14411824

Subgroups — #14411824

Order 1920.

1548 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
1C22×#6771C211yesmaximal, characteristic
2C2×#91267C212yesmaximal, complemented
3#11750827C211yesmaximal, characteristic, complemented
4C5×D3×C22⋊C8C211yesmaximal, characteristic, complemented
5C3×#65015C211yesmaximal, characteristic, complemented
6#11748505C211yesmaximal, characteristic, complemented
7#11748497C211yesmaximal, characteristic, complemented
8D5×#830C211yesmaximal, characteristic, complemented
9#11748144C212yesmaximal, complemented
10#11748139C212yesmaximal, complemented
11#11748136C212yesmaximal, complemented
12#10610331—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×#1204C411yescharacteristic
17C22×#1203C411yescharacteristic
18C22×#1202C411yescharacteristic
19C22×#1201C411yescharacteristic
20C2×#6771—28no—
21C2×#6771C411yescharacteristic
22C2×#6771C411yescharacteristic
23C2×#6771C411yescharacteristic
24C2×#6771C411yescharacteristic
25C2×#6771C2211yescharacteristic
26C2×#6771C2211yescharacteristic
27C2×#6771C2211yescharacteristic
28C2×#6771C2211yescharacteristic
29C2×#6705C2212yescomplemented
30C2×C5×D3×C8C2212yescomplemented
31C2×C3×#676C2212yescomplemented
32C2×#6650C2212yescomplemented
33C2×#6648C2212yescomplemented
34C2×D5×C3⋊C8C2212yescomplemented
35#91267—28no—
36C3×C5×C22⋊C8C2211yescharacteristic
37#91114C2211yescharacteristic
38#91104C2212yescomplemented
39C5×#830C2211yescharacteristic
40C5×(C2×D3)⋊C8C2212yescomplemented
41C3×C22⋊#168C2211yescharacteristic
42C3×#3952C2212yescomplemented
43#90957C2212yescomplemented
44(C2×D3)⋊#168C2212yescomplemented
45#90955C2212yescomplemented
46#78631—51nomaximal, Hall
47C22×#709—31no—
48C2×#4047—32no—
49C2×C5×C22⋊C8—31no—
50#65496—31no—
51#65399—32no—
52#65016—32no—
53#65016—32no—
54#65015—31no—
55#65015D311yescharacteristic, complemented
56D5×C22⋊C8—31no—
57D5×C22⋊C8—31no—
58C23×D15C2×C411yescharacteristic
59C23×C5×D3C2×C411yescharacteristic
60C23×C3×D5C2×C411yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C22×Dic15C2×C411yescharacteristic
63C2×C4×D15—24no—
64C2×C4×D15C2×C411yescharacteristic
65C2×C4×D15C2×C411yescharacteristic
66C2×C4×D15C2311yescharacteristic
67C2×C4×D15C2311yescharacteristic
68C22×C5×Dic3C2×C411yescharacteristic
69C2×C4×C5×D3—24no—
70C2×C4×C5×D3C2×C411yescharacteristic
71C2×C4×C5×D3C2×C411yescharacteristic
72C2×C4×C5×D3C2311yescharacteristic
73C2×C4×C5×D3C2311yescharacteristic
74C22×C3×Dic5C2×C411yescharacteristic
75C2×C3×C4×D5—24no—
76C2×C3×C4×D5C2×C411yescharacteristic
77C2×C3×C4×D5C2×C411yescharacteristic
78C2×C3×C4×D5C2311yescharacteristic
79C2×C3×C4×D5C2311yescharacteristic
80C2×#1204—24no—
81C2×#1204C2×C411yescharacteristic
82C2×#1204C2×C411yescharacteristic
83C2×#1204C2×C411yescharacteristic
84C2×#1204C2×C411yescharacteristic
85C2×#1203—24no—
86C2×#1203C2×C411yescharacteristic
87C2×#1203C2×C411yescharacteristic
88C2×#1203C2×C411yescharacteristic
89C2×#1203C2×C411yescharacteristic
90C2×#1202—24no—
91C2×#1202C2×C411yescharacteristic
92C2×#1202C2×C411yescharacteristic
93C2×#1202C2×C411yescharacteristic
94C2×#1202C2×C411yescharacteristic
95C2×#1201—24no—
96C2×#1201C2×C411yescharacteristic
97C2×#1201C2×C411yescharacteristic
98C2×#1201C2×C411yescharacteristic
99C2×#1201C2×C411yescharacteristic
100#6771—24no—
101#6771—24no—
102#6771—24no—
103#6771—24no—
104#6771—24no—
105#6771—24no—
106#6771—24no—
107#6771D418yes—
108C2×C3×C5×C8C2312yes—
109C2×C3⋊#168C2312yes—
110#6705—24no—
111C2×C5×C3⋊C8C2312yes—
112C5×D3×C8—24no—
113C2×C3×#168C2312yes—
114C3×#676—24no—
115#6650—24no—
116#6648—24no—
117D5×C3⋊C8—24no—
118C22×#235—51no—
119C2×#907—52no—
120C3×#407—51no—
121C2×#830—51no—
122#5129—52no—
123#4727—52no—
124#4727—52no—
125#4726—51no—
126#4726—51no—
127D3×C22⋊C8—51no—
128D3×C22⋊C8D511yescharacteristic, complemented
129C23×C4×C5—31no—
130C22×C22⋊D5—31no—
131C22×C22⋊D5—31no—
132C2×#709—31no—
133C2×#709—31no—
134C2×#709—31no—
135C2×#709—31no—
136C2×#709—31no—
137C2×#709—31no—
138C2×#709—31no—
139C2×#709—31no—
140C2×#709—68no—
141C22×D20—31no—
142C22×C4×D5—31no—
143C22×C4×D5C2×D311yescharacteristic
144C22×Dic10—31no—
145C22×C5×C8—32no—
146C2×#681—32no—
147#4047—68no—
148C2×#676—32no—
149C2×#676C2×D312yescomplemented
150C2×C8×D5—32no—
151C2×C8×D5—32no—
152C5×C22⋊C8—31no—
153C5×C22⋊C8—32no—
154C5×C22⋊C8C2×D311yescharacteristic
155C22⋊#168—31no—
156C22⋊#168—32no—
157C22⋊#168C2×D311yescharacteristic
158#3952—32no—
159#3952—32no—
160#3952—32no—
161#3952C2×D312yescomplemented
162#2880—151noSylow
163C23×C3×C5C22×C411yescharacteristic
164C22×D15—22no—
165C22×D15—22no—
166C22×D15—41no—
167C22×D15C22×C411yescharacteristic
168C22×D15C22×C411yescharacteristic
169C22×C5×D3—22no—
170C22×C5×D3—22no—
171C22×C5×D3—41no—
172C22×C5×D3C22×C411yescharacteristic
173C22×C5×D3C22×C411yescharacteristic
174C22×C3×D5—22no—
175C22×C3×D5—22no—
176C22×C3×D5—41no—
177C22×C3×D5C22×C411yescharacteristic
178C22×C3×D5C22×C411yescharacteristic
179C2×C3×C4×C5—22no—
180C2×C3×C4×C5C22×C411yescharacteristic
181C2×C3×C4×C5C2411yescharacteristic
182C2×Dic15—22no—
183C2×Dic15C22×C411yescharacteristic
184C2×Dic15C22×C411yescharacteristic
185C4×D15—22no—
186C4×D15—22no—
187C4×D15—22no—
188C4×D15C2×D414yes—
189C2×C5×Dic3—22no—
190C2×C5×Dic3C22×C411yescharacteristic
191C2×C5×Dic3C22×C411yescharacteristic
192C4×C5×D3—22no—
193C4×C5×D3—22no—
194C4×C5×D3—22no—
195C4×C5×D3C2×D414yes—
196C2×C3×Dic5—22no—
197C2×C3×Dic5C22×C411yescharacteristic
198C2×C3×Dic5C22×C411yescharacteristic
199C3×C4×D5—22no—
200C3×C4×D5—22no—
201C3×C4×D5—22no—
202C3×C4×D5C2×D414yes—
203#1204—22no—
204#1204—22no—
205#1204—22no—
206#1204C22⋊C414yes—
207#1203—22no—
208#1203—22no—
209#1203—22no—
210#1203C22⋊C414yes—
211#1202—22no—
212#1202—22no—
213#1202—22no—
214#1202C22⋊C414yes—
215#1201—22no—
216#1201—22no—
217#1201—22no—
218#1201C22⋊C414yes—
219C3×C5×C8—22no—
220C3⋊#168—22no—
221C3×#168—22no—
222C5×C3⋊C8—22no—
223C23×C3×C4—51no—
224C22×#67—51no—
225C22×#67—51no—
226C2×#235—51no—
227C2×#235—51no—
228C2×#235—51no—
229C2×#235—51no—
230C2×#235—51no—
231C2×#235—51no—
232C2×#235—51no—
233C2×#235—51no—
234C2×#235—108no—
235C22×D12—51no—
236C22×C4×D3—51no—
237C22×C4×D3C2×D511yescharacteristic
238C22×Dic6—51no—
239C2×C3×M16—52no—
240C22×C3⋊C8—52no—
241#907—108no—
242C2×ΓL(1,𝔽25)—52no—
243C2×ΓL(1,𝔽25)—52no—
244C2×D3×C8—52no—
245C2×D3×C8C2×D512yescomplemented
246C3×C22⋊C8—51no—
247C3×C22⋊C8—52no—
248C3×C22⋊C8C2×D511yescharacteristic
249#830—51no—
250#830—52no—
251#830C2×D511yescharacteristic
252(C2×D3)⋊C8—52no—
253(C2×D3)⋊C8—52no—
254(C2×D3)⋊C8—52no—
255(C2×D3)⋊C8C2×D512yescomplemented
256C24×C5—31no—
257C23×D5—31no—
258C23×D5C4×D311yescharacteristic
259C22×C4×C5—31no—
260C22×C4×C5—31no—
261C22×C4×C5—31no—
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5—64no—
265C22×C4×C5C22×D311yescharacteristic
266C2×C22⋊D5—31no—
267C2×C22⋊D5—31no—
268C2×C22⋊D5—31no—
269C2×C22⋊D5—31no—
270C2×C22⋊D5—31no—
271C2×C22⋊D5—31no—
272C2×C22⋊D5—31no—
273C2×C22⋊D5—31no—
274C2×C22⋊D5—64no—
275C2×C22⋊D5—64no—
276C22×Dic5—31no—
277C22×Dic5C4×D311yescharacteristic
278#709—38no—
279#709—64no—
280#709—64no—
281#709—64no—
282#709—64no—
283#709—64no—
284#709—64no—
285#709—64no—
286C2×D20—31no—
287C2×D20—31no—
288C2×D20—31no—
289C2×D20—31no—
290C2×D20—64no—
291C2×C4×D5—24no—
292C2×C4×D5—31no—
293C2×C4×D5—31no—
294C2×C4×D5—31no—
295C2×C4×D5—31no—
296C2×C4×D5—64no—
297C2×C4×D5C4×D311yescharacteristic
298C2×C4×D5C4×D311yescharacteristic
299C2×C4×D5C22×D311yescharacteristic
300C2×C4×D5C22×D311yescharacteristic
301C2×Dic10—31no—
302C2×Dic10—31no—
303C2×Dic10—31no—
304C2×Dic10—31no—
305C2×Dic10—64no—
306C2×C5×C8—32no—
307C2×C5×C8—64no—
308C2×C5×C8C22×D312yes—
309#681—64no—
310C2×#168—32no—
311C2×#168C22×D312yes—
312#676—24no—
313#676—64no—
314C8×D5—64no—
315C8×D5—64no—
316C22×#41—151no—
317C2×#131—152no—
318#408—152no—
319#408—152no—
320#408—152no—
321#407—51no—
322#407—151no—
323#407—151no—
324C2×C22⋊C8—31no—
325C2×C22⋊C8—151no—
326C2×C22⋊C8—151no—
327C22×C3×C5—21no—
328C22×C3×C5—21no—
329C22×C3×C5#13112yescomplemented
330C22×C3×C5C23×C411yescharacteristic
331C2×D15—21no—
332C2×D15—21no—
333C2×D15—21no—
334C2×D15—21no—
335C2×D15—21no—
336C2×D15—44no—
337C2×D15C2×C22⋊C412yes—
338C2×C5×D3—21no—
339C2×C5×D3—21no—
340C2×C5×D3—21no—
341C2×C5×D3—21no—
342C2×C5×D3—21no—
343C2×C5×D3—44no—
344C2×C5×D3C2×C22⋊C412yes—
345C2×C3×D5—21no—
346C2×C3×D5—21no—
347C2×C3×D5—21no—
348C2×C3×D5—21no—
349C2×C3×D5—21no—
350C2×C3×D5—44no—
351C2×C3×D5C2×C22⋊C412yes—
352C3×C4×C5—21no—
353C3×C4×C5C22×D412yes—
354Dic15—21no—
355Dic15C2×C22⋊C412yes—
356C3×Dic5—21no—
357C3×Dic5C2×C22⋊C412yes—
358C5×Dic3—21no—
359C5×Dic3C2×C22⋊C412yes—
360C24×C3—51no—
361C23×D3—51no—
362C23×D3C4×D511yescharacteristic
363C22×C3×C4—51no—
364C22×C3×C4—51no—
365C22×C3×C4—51no—
366C22×C3×C4—51no—
367C22×C3×C4—51no—
368C22×C3×C4—104no—
369C22×C3×C4C22×D511yescharacteristic
370C2×#67—51no—
371C2×#67—51no—
372C2×#67—51no—
373C2×#67—51no—
374C2×#67—51no—
375C2×#67—51no—
376C2×#67—51no—
377C2×#67—51no—
378C2×#67—104no—
379C2×#67—104no—
380C22×Dic3—51no—
381C22×Dic3C4×D511yescharacteristic
382#235—58no—
383#235—104no—
384#235—104no—
385#235—104no—
386#235—104no—
387#235—104no—
388#235—104no—
389#235—104no—
390C2×D12—51no—
391C2×D12—51no—
392C2×D12—51no—
393C2×D12—51no—
394C2×D12—104no—
395C2×C4×D3—24no—
396C2×C4×D3—51no—
397C2×C4×D3—51no—
398C2×C4×D3—51no—
399C2×C4×D3—51no—
400C2×C4×D3—104no—
401C2×C4×D3C4×D511yescharacteristic
402C2×C4×D3C4×D511yescharacteristic
403C2×C4×D3C22×D511yescharacteristic
404C2×C4×D3C22×D511yescharacteristic
405C2×Dic6—51no—
406C2×Dic6—51no—
407C2×Dic6—51no—
408C2×Dic6—51no—
409C2×Dic6—104no—
410C3×M16—104no—
411C2×C3×C8—52no—
412C2×C3×C8C22×D512yes—
413C2×C3⋊C8—52no—
414C2×C3⋊C8—104no—
415C2×C3⋊C8C22×D512yes—
416ΓL(1,𝔽25)—104no—
417ΓL(1,𝔽25)—104no—
418D3×C8—24no—
419D3×C8—104no—
420C23×C5—31no—
421C23×C5—31no—
422C23×C5—62no—
423C23×C5—62no—
424C23×C5—121no—
425C23×C5C2×C4×D311yescharacteristic
426C22×D5—22no—
427C22×D5—22no—
428C22×D5—31no—
429C22×D5—31no—
430C22×D5—41no—
431C22×D5—62no—
432C22×D5—62no—
433C22×D5—121no—
434C22×D5C2×C4×D311yescharacteristic
435C22×D5C2×C4×D311yescharacteristic
436C2×C4×C5—22no—
437C2×C4×C5—31no—
438C2×C4×C5—34no—
439C2×C4×C5—31no—
440C2×C4×C5—62no—
441C2×C4×C5—62no—
442C2×C4×C5—62no—
443C2×C4×C5—62no—
444C2×C4×C5C2×C4×D311yescharacteristic
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—34no—
447C22⋊D5—34no—
448C22⋊D5—62no—
449C22⋊D5—62no—
450C22⋊D5—62no—
451C22⋊D5—62no—
452C22⋊D5—62no—
453C22⋊D5—62no—
454C2×Dic5—22no—
455C2×Dic5—31no—
456C2×Dic5—31no—
457C2×Dic5—62no—
458C2×Dic5C2×C4×D311yescharacteristic
459C2×Dic5C2×C4×D311yescharacteristic
460D20—34no—
461D20—62no—
462D20—62no—
463D20—62no—
464C4×D5—22no—
465C4×D5—22no—
466C4×D5—22no—
467C4×D5—34no—
468C4×D5—62no—
469C4×D5—62no—
470C4×D5—62no—
471C4×D5D3×D414yes—
472Dic10—34no—
473Dic10—62no—
474Dic10—62no—
475Dic10—62no—
476C5×C8—22no—
477C5×C8—62no—
478#168—22no—
479#168—62no—
480C2×#41—151no—
481C2×#41—151no—
482C2×#41—151no—
483C2×#41—151no—
484C2×#41—151no—
485C2×#41—151no—
486C2×#41—151no—
487C2×#41—151no—
488C2×#41—308no—
489C22×Q8—151no—
490C22×D4—151no—
491C22×D4—151no—
492C22×D4—151no—
493C23×C4—31no—
494C23×C4—51no—
495C23×C4—151no—
496#131—308no—
497C2×M16—52no—
498C2×M16—152no—
499C2×M16—152no—
500C22×C8—32no—
501C22×C8—152no—
502C22×C8—152no—
503C22⋊C8—31no—
504C22⋊C8—32no—
505C22⋊C8—51no—
506C22⋊C8—52no—
507C22⋊C8—152no—
508C22⋊C8—152no—
509C22⋊C8—152no—
510C22⋊C8—151no—
511C22⋊C8—152no—
512C22⋊C8D3×D511yescharacteristic
513C2×C3×C5—22no—
514C2×C3×C5C22×C22⋊C411yescharacteristic
515C2×C3×C5C2×#13111yescharacteristic
516C2×C3×C5#56811yescharacteristic
517D15—22no—
518D15—41no—
519C3×D5—22no—
520C3×D5—41no—
521C5×D3—22no—
522C5×D3—41no—
523C23×C3—51no—
524C23×C3—51no—
525C23×C3—102no—
526C23×C3—102no—
527C23×C3—201no—
528C23×C3C2×C4×D511yescharacteristic
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—41no—
532C22×D3—51no—
533C22×D3—51no—
534C22×D3—102no—
535C22×D3—102no—
536C22×D3—201no—
537C22×D3C2×C4×D511yescharacteristic
538C22×D3C2×C4×D511yescharacteristic
539C2×C3×C4—22no—
540C2×C3×C4—51no—
541C2×C3×C4—54no—
542C2×C3×C4—51no—
543C2×C3×C4—102no—
544C2×C3×C4—102no—
545C2×C3×C4—102no—
546C2×C3×C4—102no—
547C2×C3×C4C2×C4×D511yescharacteristic
548C2×C3×C4C23×D511yescharacteristic
549#67—54no—
550#67—54no—
551#67—102no—
552#67—102no—
553#67—102no—
554#67—102no—
555#67—102no—
556#67—102no—
557C2×Dic3—22no—
558C2×Dic3—51no—
559C2×Dic3—51no—
560C2×Dic3—102no—
561C2×Dic3C2×C4×D511yescharacteristic
562C2×Dic3C2×C4×D511yescharacteristic
563D12—54no—
564D12—102no—
565D12—102no—
566D12—102no—
567C4×D3—22no—
568C4×D3—22no—
569C4×D3—22no—
570C4×D3—54no—
571C4×D3—102no—
572C4×D3—102no—
573C4×D3—102no—
574C4×D3D4×D514yes—
575Dic6—54no—
576Dic6—102no—
577Dic6—102no—
578Dic6—102no—
579C3×C8—22no—
580C3×C8—102no—
581C3⋊C8—22no—
582C3⋊C8—102no—
583C22×C5—21no—
584C22×C5—21no—
585C22×C5—32no—
586C22×C5—61no—
587C22×C5—61no—
588C22×C5—61no—
589C22×C5—61no—
590C22×C5—61no—
591C22×C5—124no—
592C22×C5#90712yescomplemented
593C22×C5C22×C4×D311yescharacteristic
594C2×D5—21no—
595C2×D5—21no—
596C2×D5—21no—
597C2×D5—21no—
598C2×D5—21no—
599C2×D5—32no—
600C2×D5—44no—
601C2×D5—61no—
602C2×D5—61no—
603C2×D5—61no—
604C2×D5—61no—
605C2×D5—61no—
606C2×D5—124no—
607C2×D5D3×C22⋊C412yes—
608C4×C5—21no—
609C4×C5—32no—
610C4×C5—61no—
611C4×C5C2×D3×D412yes—
612Dic5—21no—
613Dic5—32no—
614Dic5—61no—
615Dic5D3×C22⋊C412yes—
616C24—31no—
617C24—51no—
618C24—151no—
619#41—158no—
620#41—304no—
621#41—304no—
622#41—304no—
623#41—304no—
624#41—304no—
625#41—304no—
626#41—304no—
627C2×Q8—151no—
628C2×Q8—151no—
629C2×Q8—151no—
630C2×Q8—151no—
631C2×Q8—304no—
632C2×D4—151no—
633C2×D4—151no—
634C2×D4—151no—
635C2×D4—151no—
636C2×D4—151no—
637C2×D4—151no—
638C2×D4—151no—
639C2×D4—151no—
640C2×D4—151no—
641C2×D4—151no—
642C2×D4—151no—
643C2×D4—151no—
644C2×D4—304no—
645C2×D4—304no—
646C2×D4—304no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—51no—
653C22×C4—51no—
654C22×C4—51no—
655C22×C4—51no—
656C22×C4—51no—
657C22×C4—64no—
658C22×C4—104no—
659C22×C4—151no—
660C22×C4—151no—
661C22×C4—151no—
662C22×C4—151no—
663C22×C4—151no—
664C22×C4—304no—
665C22×C4C2×D3×D511yescharacteristic
666M16—104no—
667M16—304no—
668M16—304no—
669C2×C8—32no—
670C2×C8—52no—
671C2×C8—64no—
672C2×C8—152no—
673C2×C8—304no—
674C2×C8—304no—
675C2×C8C2×D3×D512yes—
676C3×C5#288011yescharacteristic, complemented, Hall
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—52no—
680C22×C3—101no—
681C22×C3—101no—
682C22×C3—101no—
683C22×C3—101no—
684C22×C3—101no—
685C22×C3—204no—
686C22×C3#404712yescomplemented
687C22×C3C22×C4×D511yescharacteristic
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—44no—
694C2×D3—52no—
695C2×D3—101no—
696C2×D3—101no—
697C2×D3—101no—
698C2×D3—101no—
699C2×D3—101no—
700C2×D3—204no—
701C2×D3D5×C22⋊C412yes—
702C3×C4—21no—
703C3×C4—52no—
704C3×C4—101no—
705C3×C4C2×D4×D512yes—
706Dic3—21no—
707Dic3—52no—
708Dic3—101no—
709Dic3D5×C22⋊C412yes—
710C2×C5—22no—
711C2×C5—62no—
712C2×C5—121no—
713C2×C5C2×D3×C22⋊C411yescharacteristic
714C2×C5C2×#90711yescharacteristic
715C2×C5#574511yescharacteristic
716D5—22no—
717D5—41no—
718D5—62no—
719D5—121no—
720C23—31no—
721C23—31no—
722C23—51no—
723C23—51no—
724C23—62no—
725C23—62no—
726C23—102no—
727C23—102no—
728C23—121no—
729C23—151no—
730C23—151no—
731C23—201no—
732C23—302no—
733C23—302no—
734C23—601no—
735C23C4×D3×D511yescharacteristic
736Q8—154no—
737Q8—302no—
738Q8—302no—
739Q8—302no—
740D4—154no—
741D4—154no—
742D4—154no—
743D4—302no—
744D4—302no—
745D4—302no—
746D4—302no—
747D4—302no—
748D4—302no—
749D4—302no—
750D4—302no—
751D4—302no—
752C2×C4—22no—
753C2×C4—31no—
754C2×C4—34no—
755C2×C4—31no—
756C2×C4—51no—
757C2×C4—54no—
758C2×C4—51no—
759C2×C4—62no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—102no—
764C2×C4—102no—
765C2×C4—102no—
766C2×C4—102no—
767C2×C4—151no—
768C2×C4—154no—
769C2×C4—151no—
770C2×C4—302no—
771C2×C4—302no—
772C2×C4—302no—
773C2×C4—302no—
774C2×C4C4×D3×D511yescharacteristic
775C2×C4C22×D3×D511yescharacteristic
776C8—22no—
777C8—62no—
778C8—102no—
779C8—302no—
780C2×C3—22no—
781C2×C3—102no—
782C2×C3—201no—
783C2×C3C2×D5×C22⋊C411yescharacteristic
784C2×C3C2×#404711yescharacteristic
785C2×C3#6607911yescharacteristic
786D3—22no—
787D3—41no—
788D3—102no—
789D3—201no—
790C5#7863111yescharacteristic, complemented, Sylow
791C22—21no—
792C22—21no—
793C22—32no—
794C22—52no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—61no—
800C22—101no—
801C22—101no—
802C22—101no—
803C22—101no—
804C22—101no—
805C22—124no—
806C22—152no—
807C22—204no—
808C22—301no—
809C22—301no—
810C22—301no—
811C22—301no—
812C22—301no—
813C22—604no—
814C22#9126712yescomplemented
815C22C2×C4×D3×D511yescharacteristic
816C4—21no—
817C4—32no—
818C4—52no—
819C4—61no—
820C4—101no—
821C4—152no—
822C4—301no—
823C4D3×D4×D512yes—
824C3#1061033111yescharacteristic, complemented, Sylow
825C2—22no—
826C2—62no—
827C2—102no—
828C2—121no—
829C2—201no—
830C2—302no—
831C2—601no—
832C2D3×D5×C22⋊C411yescharacteristic
833C2C2×#9126711yescharacteristic
834C2#1175404111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C8C22
prime radicalC22×#6771C2
cosocleC2×C3×C4×C5C24
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#2880
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#91267C2semidirect
3. #11750827C2semidirect
4. C5×D3×C22⋊C8C2semidirect
5. C3×#65015C2semidirect
6. #11748505C2semidirect
7. #11748497C2semidirect
8. D5×#830C2semidirect
9. #11748144C2semidirect
10. #11748139C2semidirect
11. #11748136C2semidirect
29. C2×#6705C22semidirect
30. C2×C5×D3×C8C22semidirect
31. C2×C3×#676C22semidirect
32. C2×#6650C22semidirect
33. C2×#6648C22semidirect
34. C2×D5×C3⋊C8C22semidirect
38. #91104C22semidirect
40. C5×(C2×D3)⋊C8C22semidirect
42. C3×#3952C22semidirect
43. #90957C22semidirect
44. (C2×D3)⋊#168C22semidirect
45. #90955C22semidirect
55. #65015D3semidirect
128. D3×C22⋊C8D5semidirect
149. C2×#676C2×D3semidirect
161. #3952C2×D3semidirect
245. C2×D3×C8C2×D5semidirect
255. (C2×D3)⋊C8C2×D5semidirect
329. C22×C3×C5#131semidirect
592. C22×C5#907semidirect
676. C3×C5#2880semidirect
686. C22×C3#4047semidirect
790. C5#78631semidirect
814. C22#91267semidirect
824. C3#10610331semidirect

Maximal subgroups

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

subgroupindex
C22×#67712
C2×#912672
#117508272
C5×D3×C22⋊C82
C3×#650152
#117485052
#117484972
D5×#8302
#117481442
#117481392
#117481362
#106103313
#786315