Finite Group Databasebeta

← #14454279

Subgroups — #14454279

Order 1920.

1020 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5553C211yesmaximal, characteristic, complemented
2C3×#65884C211yesmaximal, characteristic, complemented
3C2×#91298C211yesmaximal, characteristic, complemented
4C2×#91297C211yesmaximal, characteristic, complemented
5#11751112C211yesmaximal, characteristic, complemented
6#11748548C211yesmaximal, characteristic, complemented
7#11748538C211yesmaximal, characteristic, complemented
8#11748522C211yesmaximal, characteristic, complemented
9#11748517C211yesmaximal, characteristic, complemented
10#11748511C211yesmaximal, characteristic, complemented
11#11748510C211yesmaximal, characteristic, complemented
12#11747069C211yesmaximal, characteristic, complemented
13#11747048C211yesmaximal, characteristic, complemented
14#11747042C211yesmaximal, characteristic, complemented
15#11747026C211yesmaximal, characteristic, complemented
16#10615308—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic
18C2×C5×#235C2211yescharacteristic, complemented
19C2×C3×#709C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic
22C2×#6710C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic, complemented
24C5×#940—21no—
25C5×#930C2211yescharacteristic
26C5×#930C2211yescharacteristic, complemented
27C5×#893—21no—
28C5×#884—21no—
29C5×#884—21no—
30C5×#874C2211yescharacteristic, complemented
31C4×C5×Dic6C2211yescharacteristic, complemented
32C3×#4083—21no—
33C3×#4076C2211yescharacteristic
34C3×#4070C2211yescharacteristic
35C3×#4040—21no—
36C3×#4030—21no—
37C3×D5×C22⋊C4—21no—
38C3×#4021C2211yescharacteristic
39C3×C4×D20C2211yescharacteristic
40C2×#6661C2211yescharacteristic, complemented
41C2×#6656C2211yescharacteristic, complemented
42C2×#6656C2211yescharacteristic, complemented
43C2×#6655C2211yescharacteristic
44C2×#6655C2211yescharacteristic
45#91298—24no—
46#91297—24no—
47C2×#6652C2211yescharacteristic
48C2×#6652C2211yescharacteristic
49C2×#6652C2211yescharacteristic
50C2×#6652C2211yescharacteristic
51#91114C2211yescharacteristic
52#91114C2211yescharacteristic, complemented
53C4⋊(C3⋊#168)C2211yescharacteristic, complemented
54#91087C2211yescharacteristic, complemented
55#90989C2211yescharacteristic, complemented
56#90972C2211yescharacteristic, complemented
57#90970C2211yescharacteristic, complemented
58#90966C2211yescharacteristic, complemented
59#90966C2211yescharacteristic, complemented
60#90964C2211yescharacteristic
61#90964C2211yescharacteristic
62#83507—51nomaximal, Hall
63C5×#550—31no—
64C2×#4096—31no—
65C2×#4095—31no—
66#65884D311yescharacteristic, complemented
67#65528—31no—
68#65527—31no—
69#65363—31no—
70#65361—31no—
71#65331—31no—
72#65327—31no—
73#65326—31no—
74#65325—31no—
75#65317—31no—
76#65315—31no—
77#65300—31no—
78C23×C3×D5—21no—
79C2×C3×C5×D4D411yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×C5×#67—21no—
83C2×C5×#67—21no—
84C2×C5×#67—21no—
85C2×C5×#67—21no—
86C5×#235—22no—
87C5×#235—22no—
88C5×#235—41no—
89C5×#235—41no—
90C2×C5×D12—21no—
91C2×C5×D12—21no—
92C2×C5×D12C2311yescharacteristic
93C2×C5×D12C2311yescharacteristic
94C2×C4×C5×D3—21no—
95C2×C4×C5×D3—21no—
96C2×C5×Dic6C2311yescharacteristic
97C2×C3×C22⋊D5—21no—
98C2×C3×C22⋊D5—21no—
99C3×#709—22no—
100C3×#709—41no—
101C2×C3×D20—22no—
102C2×C3×D20—21no—
103C2×C3×D20—41no—
104C2×C3×D20C2311yescharacteristic
105C2×C3×D20C2311yescharacteristic
106C2×C3×C4×D5—21no—
107C2×C3×C4×D5—21no—
108C2×C3×Dic10C2311yescharacteristic
109C3×C5×C4⋊C4D411yescharacteristic
110C3×C5×C22⋊C4D411yescharacteristic
111C3×C5×C22⋊C4D411yescharacteristic
112C3×C42×C5C2311yescharacteristic
113#6710—22no—
114C2×C3⋊#168—22no—
115C2×C3⋊#168C2311yescharacteristic
116C2×C3⋊#168C2311yescharacteristic
117C2×C3⋊#168C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119C5×(C2×D3)⋊C4—21no—
120C5×(C2×D3)⋊C4—21no—
121C5×C4⋊Dic3C2311yescharacteristic
122C5×Dic3⋊C4—21no—
123C4×C5×Dic3—21no—
124C3×C22⋊Dic5—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×#685—21no—
129C3×C4⋊Dic5C2311yescharacteristic
130C3×#683—21no—
131#6661—22no—
132#6656—22no—
133#6656—41no—
134#6655—22no—
135#6655D414yescomplemented
136#6652—22no—
137#6652—22no—
138#6652—22no—
139#6652—41no—
140C3×#546—51no—
141C2×#950—51no—
142C2×#932—51no—
143#5553D511yescharacteristic, complemented
144#5238—51no—
145#5217—51no—
146#5058—51no—
147#5054—51no—
148#5049—51no—
149#5047—51no—
150#5038—51no—
151#5037—51no—
152#5018—51no—
153#5015—51no—
154#5011—51no—
155C2×C5×#41—31no—
156C2×C5×#41—31no—
157C2×#709C2×D311yescharacteristic
158C22×D20C2×D311yescharacteristic
159C5×#127—31no—
160C5×#127—61no—
161C5×#121—31no—
162C5×#121—31no—
163C5×#121—61no—
164C5×#121—61no—
165C4×C5×Q8—31no—
166C4×C5×D4—61no—
167C4×C5×D4C2×D311yescharacteristic
168#4096—64no—
169#4095—64no—
170C2×#689—31no—
171C2×#688—31no—
172C2×#688—31no—
173#4083—21no—
174C2×#687—31no—
175C2×#687—31no—
176C2×#686—31no—
177C2×#686—31no—
178C2×#686—31no—
179C2×#686—31no—
180#4076C2×D311yescharacteristic
181#4070C2×D311yescharacteristic
182C2×#681—31no—
183C22×#168—31no—
184#4040—21no—
185#4030—21no—
186D5×C22⋊C4—21no—
187#4021C2×D311yescharacteristic
188C4×D20C2×D311yescharacteristic
189#3967—31no—
190#3964—31no—
191#3964—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3941—31no—
196#3941—31no—
197#3939—31no—
198C4⋊#168—31no—
199#3935—31no—
200#3268—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—42no—
208C22×C3×D5—42no—
209C22×C3×D5—81no—
210C3×C5×D4—41no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2×D411yescharacteristic
218C2×C3×C4×C5C2×D411yescharacteristic
219C2×C3×C4×C5C2411yescharacteristic
220C5×#67—42no—
221C5×#67—42no—
222C5×#67—81no—
223C5×#67—81no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C5×D12—21no—
227C5×D12—21no—
228C5×D12—21no—
229C5×D12—21no—
230C5×D12—42no—
231C5×D12—81no—
232C4×C5×D3—42no—
233C4×C5×D3—42no—
234C5×Dic6—21no—
235C5×Dic6C2×D412yes—
236C3×C22⋊D5—42no—
237C3×C22⋊D5—81no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C3×D20—21no—
241C3×D20—21no—
242C3×D20—21no—
243C3×D20—42no—
244C3×D20C2×D412yes—
245C3×C4×D5—42no—
246C3×C4×D5—81no—
247C3×Dic10—21no—
248C3×Dic10—21no—
249C3⋊#168—21no—
250C3⋊#168—21no—
251C3⋊#168—21no—
252C3⋊#168C2×D412yes—
253C2×C3×#41—51no—
254C22×C3×D4—51no—
255C2×#235C2×D511yescharacteristic
256C2×#235C2×D511yescharacteristic, complemented
257C3×#124—51no—
258C3×#123—101no—
259C3×C22⋊Q8—51no—
260C3×#121—51no—
261C3×#121—101no—
262C3×#120—101no—
263C3×C4×D4—51no—
264C3×C4×D4C2×D511yescharacteristic
265C2×C3×C22⋊C4—101no—
266#950—104no—
267C2×#216—51no—
268C2×#215—51no—
269C2×#215—51no—
270#940—21no—
271C2×#214—51no—
272C2×#214—51no—
273#932—104no—
274C2×#213—51no—
275C2×#213—51no—
276C2×#213—51no—
277C2×#213—51no—
278#930C2×D511yescharacteristic
279#930C2×D511yescharacteristic, complemented
280C2×#208—51no—
281C22×C3⋊C8—51no—
282#893—21no—
283#884—21no—
284#884—21no—
285#874C2×D511yescharacteristic, complemented
286C4×Dic6C2×D511yescharacteristic, complemented
287#835—51no—
288#832—51no—
289#832—51no—
290#830—51no—
291#830—51no—
292#810—51no—
293#809—51no—
294#809—51no—
295#807—51no—
296C4⋊(C3⋊C8)—51no—
297#803—51no—
298C23×D5—21no—
299C5×#41—62no—
300C5×#41—62no—
301C5×#41—121no—
302C5×#41—121no—
303C2×C5×Q8—31no—
304C2×C5×D4—31no—
305C2×C5×D4—31no—
306C2×C5×D4—61no—
307C2×C5×D4—61no—
308C2×C5×D4—61no—
309C2×C5×D4—61no—
310C2×C5×D4—61no—
311C2×C5×D4—61no—
312C2×C5×D4#6711yescharacteristic
313C22×C4×C5—61no—
314C22×C4×C5—61no—
315C22×C4×C5C22×D311yescharacteristic
316C22×C4×C5C22×D311yescharacteristic
317C2×C22⋊D5—21no—
318C2×C22⋊D5—21no—
319#709—22no—
320#709—41no—
321C2×D20—22no—
322C2×D20—21no—
323C2×D20—41no—
324C2×D20C22×D311yescharacteristic
325C2×D20C22×D311yescharacteristic
326C2×C4×D5—21no—
327C2×C4×D5—21no—
328C2×Dic10C22×D311yescharacteristic
329C5×C4⋊C4—31no—
330C5×C4⋊C4—61no—
331C5×C4⋊C4#6711yescharacteristic
332C5×C22⋊C4—61no—
333C5×C22⋊C4—61no—
334C5×C22⋊C4#6711yescharacteristic
335C5×C22⋊C4#6711yescharacteristic
336C42×C5—61no—
337C42×C5C22×D311yescharacteristic
338C22⋊Dic5—21no—
339#689—62no—
340#688—34no—
341#688—62no—
342#687—62no—
343#687—121no—
344#686—62no—
345#686—62no—
346#686—62no—
347#686—121no—
348#685—21no—
349#685—21no—
350#685—21no—
351#685—21no—
352C4⋊Dic5C22×D311yescharacteristic
353#683—21no—
354#681—62no—
355C2×#168—31no—
356C2×#168—31no—
357C2×#168—31no—
358C2×#168—31no—
359C2×#168—62no—
360C2×AGL(1,ℤ/8)—151no—
361C2×#135—151no—
362#550—31no—
363#546—51no—
364#496—151no—
365#468—151no—
366#466—151no—
367#464—151no—
368#459—151no—
369#452—151no—
370#449—151no—
371#449—151no—
372#447—151no—
373#440—151no—
374#435—151no—
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—21no—
378C22×C3×C5—21no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5C22×D411yescharacteristic
382C2×C5×D3—41no—
383C2×C5×D3—41no—
384C2×C5×D3—41no—
385C2×C5×D3—41no—
386C2×C5×D3—41no—
387C2×C5×D3—41no—
388C2×C3×D5—22no—
389C2×C3×D5—41no—
390C2×C3×D5—41no—
391C2×C3×D5—41no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—84no—
395C3×C4×C5—21no—
396C3×C4×C5—21no—
397C3×C4×C5—21no—
398C3×C4×C5—21no—
399C3×C4×C5C22×D411yescharacteristic
400C3×C4×C5H(5,𝔽2)11yescharacteristic
401C3×Dic5—41no—
402C3×Dic5—41no—
403C5×Dic3—22no—
404C5×Dic3—41no—
405C24×C3—101no—
406C3×#41—102no—
407C3×#41—201no—
408C2×C3×Q8—51no—
409C2×C3×D4—51no—
410C2×C3×D4—51no—
411C2×C3×D4—102no—
412C2×C3×D4—101no—
413C2×C3×D4—101no—
414C2×C3×D4—101no—
415C2×C3×D4—201no—
416C2×C3×D4C22⋊D511yescharacteristic
417C22×C3×C4—101no—
418C22×C3×C4—101no—
419C22×C3×C4C22×D511yescharacteristic
420C22×C3×C4C22×D511yescharacteristic
421C2×#67—21no—
422C2×#67—21no—
423C2×#67—21no—
424C2×#67—21no—
425#235—22no—
426#235—22no—
427#235—41no—
428#235—41no—
429C2×D12—21no—
430C2×D12—21no—
431C2×D12C22×D511yescharacteristic
432C2×D12C22×D511yescharacteristic
433C2×C4×D3—21no—
434C2×C4×D3—21no—
435C2×Dic6C22×D511yescharacteristic
436C3×C4⋊C4—51no—
437C3×C4⋊C4—101no—
438C3×C4⋊C4C22⋊D511yescharacteristic
439C3×C22⋊C4—101no—
440C3×C22⋊C4—101no—
441C3×C22⋊C4—101no—
442C3×C22⋊C4—101no—
443C3×C22⋊C4—101no—
444C3×C22⋊C4C22⋊D511yescharacteristic
445C3×C22⋊C4C22⋊D511yescharacteristic
446C3×C42C22×D511yescharacteristic
447#216—102no—
448#215—102no—
449#215—201no—
450#214—54no—
451#214—102no—
452#213—102no—
453#213—102no—
454#213—102no—
455#213—201no—
456(C2×D3)⋊C4—21no—
457(C2×D3)⋊C4—21no—
458C4⋊Dic3C22×D511yescharacteristic
459Dic3⋊C4—21no—
460C4×Dic3—21no—
461#208—102no—
462C2×C3⋊C8—51no—
463C2×C3⋊C8—51no—
464C2×C3⋊C8—51no—
465C2×C3⋊C8—51no—
466C2×C3⋊C8—102no—
467C23×C5—61no—
468C23×C5—61no—
469C23×C5C2×#6711yescharacteristic
470C23×C5C2×#6711yescharacteristic
471C22×D5—21no—
472C22×D5—21no—
473C22×D5—42no—
474C22×D5—42no—
475C22×D5—81no—
476C5×Q8—32no—
477C5×Q8—61no—
478C5×D4—41no—
479C5×D4—61no—
480C5×D4—61no—
481C5×D4—61no—
482C5×D4—61no—
483C5×D4—122no—
484C5×D4—122no—
485C5×D4—122no—
486C5×D4—241no—
487C5×D4—241no—
488C5×D4—241no—
489C2×C4×C5—21no—
490C2×C4×C5—21no—
491C2×C4×C5—21no—
492C2×C4×C5—21no—
493C2×C4×C5—61no—
494C2×C4×C5—61no—
495C2×C4×C5—122no—
496C2×C4×C5—122no—
497C2×C4×C5C2×#6711yescharacteristic
498C2×C4×C5C2×#6711yescharacteristic
499C2×C4×C5C2×#6711yescharacteristic
500C2×C4×C5C2×#6711yescharacteristic
501C2×C4×C5C23×D311yescharacteristic
502C22⋊D5—42no—
503C22⋊D5—81no—
504C2×Dic5—21no—
505C2×Dic5—21no—
506D20—21no—
507D20—21no—
508D20—21no—
509D20—42no—
510D20D3×D412yes—
511C4×D5—42no—
512C4×D5—81no—
513Dic10—21no—
514Dic10—21no—
515#168—32no—
516#168—61no—
517#168—61no—
518#168—61no—
519C2×#41—31no—
520C2×#41—31no—
521C2×#41—51no—
522C22×D4—51no—
523AGL(1,ℤ/8)—304no—
524#135—304no—
525C2×Q16—151no—
526C2×SD16—151no—
527C2×SD16—151no—
528C2×SD16—151no—
529C2×SD16—151no—
530C2×D8—151no—
531C2×D8—151no—
532C2×D8—151no—
533C2×D8—151no—
534C2×M16—151no—
535C22×C8—151no—
536#127—31no—
537#127—61no—
538#124—51no—
539#123—101no—
540C22⋊Q8—51no—
541#121—31no—
542#121—31no—
543#121—51no—
544#121—61no—
545#121—61no—
546#121—101no—
547#120—101no—
548C4×Q8—31no—
549C4×D4—51no—
550C4×D4—61no—
551C4×D4D3×D511yescharacteristic
552C2×C22⋊C4—101no—
553#107—151no—
554C4⋊C8—151no—
555#103—151no—
556#103—151no—
557#102—151no—
558#102—151no—
559#102—151no—
560#102—151no—
561C22⋊C8—151no—
562C22⋊C8—151no—
563#97—151no—
564C2×C3×C5—41no—
565C2×C3×C5—41no—
566C2×C3×C5D4211yescharacteristic
567C2×C3×C5#57511yescharacteristic
568C2×C3×C5#57611yescharacteristic
569C3×D5—42no—
570C3×D5—81no—
571C5×D3—81no—
572C5×D3—81no—
573C23×C3—101no—
574C23×C3—101no—
575C23×C3—202no—
576C23×C3—202no—
577C23×C3—401no—
578C23×C3C2×C22⋊D511yescharacteristic
579C23×C3C2×C22⋊D511yescharacteristic
580C22×D3—21no—
581C22×D3—21no—
582C3×Q8—101no—
583C3×Q8—101no—
584C3×D4—41no—
585C3×D4—52no—
586C3×D4—101no—
587C3×D4—101no—
588C3×D4—101no—
589C3×D4—202no—
590C3×D4—202no—
591C3×D4—401no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—202no—
599C2×C3×C4—401no—
600C2×C3×C4C2×C22⋊D511yescharacteristic
601C2×C3×C4C2×C22⋊D511yescharacteristic
602C2×C3×C4C2×C22⋊D511yescharacteristic
603C2×C3×C4C2×C22⋊D511yescharacteristic
604C2×C3×C4C23×D511yescharacteristic
605#67—42no—
606#67—42no—
607#67—81no—
608#67—81no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611D12—21no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—42no—
616D12—81no—
617C4×D3—42no—
618C4×D3—42no—
619Dic6—21no—
620Dic6D4×D512yes—
621C3⋊C8—52no—
622C3⋊C8—101no—
623C3⋊C8—101no—
624C3⋊C8—101no—
625C22×C5—21no—
626C22×C5—21no—
627C22×C5—21no—
628C22×C5—21no—
629C22×C5—21no—
630C22×C5—21no—
631C22×C5—121no—
632C22×C5—121no—
633C22×C5—121no—
634C22×C5—121no—
635C22×C5—121no—
636C22×C5—121no—
637C22×C5C22×#6711yescharacteristic
638C2×D5—22no—
639C2×D5—41no—
640C2×D5—41no—
641C2×D5—41no—
642C2×D5—41no—
643C2×D5—41no—
644C2×D5—84no—
645C4×C5—21no—
646C4×C5—21no—
647C4×C5—21no—
648C4×C5—21no—
649C4×C5—62no—
650C4×C5—121no—
651C4×C5C2×D3×D411yescharacteristic
652C4×C5#100411yescharacteristic
653Dic5—41no—
654Dic5—41no—
655C24—101no—
656#41—62no—
657#41—62no—
658#41—102no—
659#41—121no—
660#41—121no—
661#41—201no—
662C2×Q8—31no—
663C2×Q8—51no—
664C2×D4—31no—
665C2×D4—31no—
666C2×D4—51no—
667C2×D4—51no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—102no—
675C2×D4—101no—
676C2×D4—101no—
677C2×D4—101no—
678C2×D4—201no—
679C2×D4#120111yescharacteristic
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—101no—
683C22×C4—101no—
684C22×C4C2×D3×D511yescharacteristic
685C22×C4C2×D3×D511yescharacteristic
686Q16—302no—
687SD16—154no—
688SD16—302no—
689SD16—302no—
690SD16—601no—
691D8—302no—
692D8—302no—
693D8—302no—
694D8—601no—
695M16—302no—
696C2×C8—151no—
697C2×C8—151no—
698C2×C8—151no—
699C2×C8—151no—
700C2×C8—302no—
701C4⋊C4—31no—
702C4⋊C4—51no—
703C4⋊C4—61no—
704C4⋊C4—101no—
705C4⋊C4#120111yescharacteristic
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—101no—
709C22⋊C4—101no—
710C22⋊C4—101no—
711C22⋊C4—101no—
712C22⋊C4—101no—
713C22⋊C4#120111yescharacteristic
714C22⋊C4#120111yescharacteristic
715C42—61no—
716C42C2×D3×D511yescharacteristic
717C3×C5#326811yescharacteristic, complemented, Hall
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—102no—
725C22×C3—201no—
726C22×C3—201no—
727C22×C3—201no—
728C22×C3—201no—
729C22×C3—201no—
730C22×C3—404no—
731C22×C3C22×C22⋊D511yescharacteristic
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—201no—
743C3×C4—201no—
744C3×C4C2×D4×D511yescharacteristic
745C3×C4#414411yescharacteristic
746Dic3—22no—
747Dic3—41no—
748C2×C5—41no—
749C2×C5—41no—
750C2×C5—241no—
751C2×C5—241no—
752C2×C5D4×#6711yescharacteristic
753C2×C5#582211yescharacteristic
754C2×C5#583511yescharacteristic
755D5—42no—
756D5—81no—
757C23—61no—
758C23—61no—
759C23—101no—
760C23—101no—
761C23—202no—
762C23—202no—
763C23—401no—
764C23C2×#120111yescharacteristic
765C23C2×#120111yescharacteristic
766Q8—32no—
767Q8—61no—
768Q8—101no—
769Q8—101no—
770D4—41no—
771D4—52no—
772D4—61no—
773D4—61no—
774D4—61no—
775D4—61no—
776D4—101no—
777D4—101no—
778D4—101no—
779D4—122no—
780D4—122no—
781D4—122no—
782D4—202no—
783D4—202no—
784D4—241no—
785D4—241no—
786D4—241no—
787D4—401no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—101no—
795C2×C4—101no—
796C2×C4—122no—
797C2×C4—122no—
798C2×C4—202no—
799C2×C4—401no—
800C2×C4C2×#120111yescharacteristic
801C2×C4C2×#120111yescharacteristic
802C2×C4C2×#120111yescharacteristic
803C2×C4C2×#120111yescharacteristic
804C2×C4C22×D3×D511yescharacteristic
805C8—152no—
806C8—301no—
807C8—301no—
808C8—301no—
809C2×C3—41no—
810C2×C3—41no—
811C2×C3—202no—
812C2×C3—401no—
813C2×C3D4×C22⋊D511yescharacteristic
814C2×C3#6615611yescharacteristic
815C2×C3#6616911yescharacteristic
816D3—81no—
817D3—81no—
818C5#8350711yescharacteristic, complemented, Sylow
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—102no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—201no—
833C22—201no—
834C22—201no—
835C22—201no—
836C22—201no—
837C22—404no—
838C22C22×#120111yescharacteristic
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—62no—
844C4—121no—
845C4—201no—
846C4—201no—
847C4D3×D4×D511yescharacteristic
848C4#9202511yescharacteristic
849C3#1061530811yescharacteristic, complemented, Sylow
850C2—41no—
851C2—41no—
852C2—202no—
853C2—241no—
854C2—241no—
855C2—401no—
856C2#1175413811yescharacteristic
857C2D4×#120111yescharacteristic
858C2#1175530111yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3268
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5553C2semidirect
2. C3×#65884C2semidirect
3. C2×#91298C2semidirect
4. C2×#91297C2semidirect
5. #11751112C2semidirect
6. #11748548C2semidirect
7. #11748538C2semidirect
8. #11748522C2semidirect
9. #11748517C2semidirect
10. #11748511C2semidirect
11. #11748510C2semidirect
12. #11747069C2semidirect
13. #11747048C2semidirect
14. #11747042C2semidirect
15. #11747026C2semidirect
18. C2×C5×#235C22semidirect
23. C22×C3⋊#168C22semidirect
26. C5×#930C22semidirect
30. C5×#874C22semidirect
31. C4×C5×Dic6C22semidirect
40. C2×#6661C22semidirect
41. C2×#6656C22semidirect
42. C2×#6656C22semidirect
52. #91114C22semidirect
53. C4⋊(C3⋊#168)C22semidirect
54. #91087C22semidirect
55. #90989C22semidirect
56. #90972C22semidirect
57. #90970C22semidirect
58. #90966C22semidirect
59. #90966C22semidirect
66. #65884D3semidirect
135. #6655D4semidirect
143. #5553D5semidirect
256. C2×#235C2×D5semidirect
279. #930C2×D5semidirect
285. #874C2×D5semidirect
286. C4×Dic6C2×D5semidirect
717. C3×C5#3268semidirect
818. C5#83507semidirect
849. C3#10615308semidirect

Maximal subgroups

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

subgroupindex
C5×#55532
C3×#658842
C2×#912982
C2×#912972
#117511122
#117485482
#117485382
#117485222
#117485172
#117485112
#117485102
#117470692
#117470482
#117470422
#117470262
#106153083
#835075