Finite Group Databasebeta

← #14323427

Subgroups — #14323427

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4083C211yesmaximal, characteristic
2C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×D5×#217C211yesmaximal, characteristic, complemented
4#11751322C211yesmaximal, characteristic, complemented
5C5×#5220C211yesmaximal, characteristic, complemented
6#11749518C211yesmaximal, characteristic, complemented
7#11749495C211yesmaximal, characteristic, complemented
8#11749489C211yesmaximal, characteristic, complemented
9#11749488C211yesmaximal, characteristic, complemented
10#11749485C211yesmaximal, characteristic, complemented
11#11749485C211yesmaximal, characteristic, complemented
12#11748900C211yesmaximal, characteristic, complemented
13#11748884C211yesmaximal, characteristic, complemented
14#11748791C211yesmaximal, characteristic, complemented
15#11748772C211yesmaximal, characteristic, complemented
16#10606607—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic, complemented
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic, complemented
27C2×#6719C2211yescharacteristic, complemented
28C2×C4⋊Dic15C2211yescharacteristic, complemented
29C2×C4×Dic15C2211yescharacteristic, complemented
30C2×C5×#217C2211yescharacteristic
31C2×C5×#217C2211yescharacteristic
32C2×C5×#217C2211yescharacteristic, complemented
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C3×#4083C418yescomplemented
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37Dic3×C22⋊D5—24no—
38D5×#217—24no—
39C2×#6668C2211yescharacteristic, complemented
40C2×#6668C2211yescharacteristic, complemented
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic, complemented
48C2×Dic3×Dic5C2211yescharacteristic, complemented
49C5×C3⋊#95C2211yescharacteristic, complemented
50C5×C3⋊#95C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#90994C2211yescharacteristic, complemented
54#90994C2211yescharacteristic, complemented
55#82578—51nomaximal, Hall
56C2×#4083D311yescharacteristic
57C2×C4×C22⋊D5—31no—
58C2×D5×C22⋊C4—31no—
59C5×#386—31no—
60#65510—31no—
61#65502—31no—
62#65246—31no—
63#65245—31no—
64#65244—31no—
65#65233—31no—
66#65233—31no—
67#64959—31no—
68#64958—31no—
69#64957—31no—
70#64955—31no—
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×C3×D5—22no—
74C23×C3×D5—22no—
75C23×C3×D5—41no—
76C23×C3×D5—41no—
77C23×C3×D5—41no—
78C23×C3×D5—41no—
79C23×C3×D5C2×C414yescomplemented
80C23×C3×D5C2311yescharacteristic
81C23×C3×D5C2311yescharacteristic
82C2×C3×C5×D4—41no—
83C2×C3×C5×D4—41no—
84C2×C3×C5×D4C2×C414yescomplemented
85C22×C3×C4×C5C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×C5×Dic3—22no—
91C22×C5×Dic3—41no—
92C22×C5×Dic3—41no—
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C2×C3×C22⋊D5—22no—
98C2×C3×C22⋊D5—22no—
99C2×C3×C22⋊D5—41no—
100C2×C3×C22⋊D5—41no—
101C2×C3×C22⋊D5C2×C414yes—
102C2×C3×C22⋊D5C2×C414yescomplemented
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C2×D5×Dic3—22no—
106C2×D5×Dic3—41no—
107C2×D5×Dic3—41no—
108C2×D5×Dic3—41no—
109C2×D5×Dic3—41no—
110C2×D5×Dic3D414yescomplemented
111#6719—22no—
112#6719—22no—
113#6719—41no—
114#6719—41no—
115C4⋊Dic15—41no—
116C4×Dic15—41no—
117C5×#217—22no—
118C5×#217—41no—
119C5×#217—41no—
120C3×C22⋊Dic5C2×C414yescomplemented
121C3×#685C2×C414yescomplemented
122C3×#685C2×C414yescomplemented
123#6668—22no—
124#6668—41no—
125#6665—22no—
126#6665—22no—
127#6665—22no—
128#6665—22no—
129#6665—41no—
130#6665—41no—
131Dic3×Dic5—22no—
132Dic3×Dic5—41no—
133C2×C3×#120—51no—
134C22×#217—51no—
135C2×D4×Dic3—51no—
136#5247—51no—
137#5221—51no—
138#5221—51no—
139#5220—51no—
140#5220—51no—
141#5220D511yescharacteristic, complemented
142#4951—51no—
143#4951—51no—
144#4951—51no—
145#4951—51no—
146#4950—51no—
147Dic3×C22⋊C4—51no—
148C24×D5C2×D311yescharacteristic
149C22×C5×D4C2×D311yescharacteristic
150C23×C4×C5—31no—
151C22×C22⋊D5C2×D311yescharacteristic
152C22×C22⋊D5C2×D311yescharacteristic
153C22×C4×D5—31no—
154C22×C4×D5—31no—
155C2×C5×C22⋊C4—31no—
156C2×C5×C22⋊C4—31no—
157C2×C5×C22⋊C4—31no—
158C2×C22⋊Dic5—31no—
159C2×C22⋊Dic5—31no—
160C2×C22⋊Dic5—31no—
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5C2×D311yescharacteristic
163#4083Dic318yescomplemented
164C4×C22⋊D5—64no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685C2×D311yescharacteristic
172C2×#685C2×D311yescharacteristic
173C2×C4⋊Dic5—31no—
174C2×#683—31no—
175C2×#683—31no—
176C2×C4×Dic5—31no—
177C2×C4×Dic5—31no—
178C2×C4×Dic5—31no—
179D5×C22⋊C4—64no—
180C5×#95—31no—
181C5×#95—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#2321—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5C22×C412yes—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C2411yescharacteristic
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—28no—
213C22×C3×D5—44no—
214C22×C3×D5—44no—
215C22×C3×D5—44no—
216C22×C3×D5—44no—
217C22×C3×D5—44no—
218C22×C3×D5—44no—
219C22×C3×D5C22×C412yes—
220C22×C3×D5C22×C412yes—
221C22×C3×D5C2×D412yes—
222C22×C3×D5#4112yes—
223C3×C5×D4—44no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5C22×C412yes—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15C2×D412yes—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—21no—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—21no—
248C2×C5×Dic3—21no—
249C2×C5×Dic3—21no—
250C2×C5×Dic3—44no—
251C2×C5×Dic3C2×D412yes—
252C3×C22⋊D5—28no—
253C3×C22⋊D5—44no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5—21no—
256C2×C3×Dic5—21no—
257C2×C3×Dic5—21no—
258C2×C3×Dic5C22×C412yes—
259C2×C3×Dic5C22×C412yes—
260D5×Dic3—44no—
261D5×Dic3—44no—
262C25×C3—51no—
263C22×C3×D4—51no—
264C22×C3×D4—51no—
265C22×C3×D4C2×D511yescharacteristic
266C23×Dic3—51no—
267C23×Dic3—51no—
268C23×Dic3C2×D511yescharacteristic, complemented
269C3×#120—58no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×C3×C22⋊C4—51no—
273C2×#217—51no—
274C2×#217—51no—
275C2×#217—51no—
276C2×#217—51no—
277C2×#217—51no—
278C2×#217—51no—
279C2×#217—51no—
280C2×#217—51no—
281C2×#217—51no—
282C2×#217—51no—
283C2×#217—104no—
284C2×#217C2×D511yescharacteristic
285C2×#217C2×D511yescharacteristic
286C2×#217C2×D511yescharacteristic, complemented
287D4×Dic3—104no—
288C2×C4⋊Dic3—51no—
289C2×C4⋊Dic3—51no—
290C2×C4⋊Dic3—51no—
291C2×C4×Dic3—51no—
292C2×C4×Dic3—51no—
293C2×C4×Dic3—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95C2×D511yescharacteristic, complemented
299C3⋊#95C2×D511yescharacteristic, complemented
300C24×C5C22×D311yescharacteristic
301C24×C5C22×D311yescharacteristic
302C23×D5—22no—
303C23×D5—22no—
304C23×D5—41no—
305C23×D5—41no—
306C23×D5—41no—
307C23×D5—41no—
308C23×D5C2×Dic314yescomplemented
309C23×D5C22×D311yescharacteristic
310C23×D5C22×D311yescharacteristic
311C2×C5×D4—41no—
312C2×C5×D4—41no—
313C2×C5×D4C2×Dic314yescomplemented
314C22×C4×C5—31no—
315C22×C4×C5—31no—
316C22×C4×C5—31no—
317C22×C4×C5—31no—
318C22×C4×C5—62no—
319C22×C4×C5—121no—
320C22×C4×C5—121no—
321C22×C4×C5C22×D311yescharacteristic
322C2×C22⋊D5—22no—
323C2×C22⋊D5—22no—
324C2×C22⋊D5—41no—
325C2×C22⋊D5—41no—
326C2×C22⋊D5C2×Dic314yes—
327C2×C22⋊D5C2×Dic314yescomplemented
328C22×Dic5—31no—
329C22×Dic5—31no—
330C22×Dic5—31no—
331C22×Dic5—31no—
332C22×Dic5C22×D311yescharacteristic
333C22×Dic5C22×D311yescharacteristic
334C2×C4×D5—34no—
335C2×C4×D5—62no—
336C2×C4×D5—121no—
337C2×C4×D5—121no—
338C2×C4×D5—121no—
339C2×C4×D5—121no—
340C5×C22⋊C4—62no—
341C5×C22⋊C4—121no—
342C5×C22⋊C4—121no—
343C22⋊Dic5—62no—
344C22⋊Dic5—62no—
345C22⋊Dic5—121no—
346C22⋊Dic5—121no—
347C22⋊Dic5C2×Dic314yescomplemented
348#685—62no—
349#685—62no—
350#685—62no—
351#685—62no—
352#685—121no—
353#685—121no—
354#685C2×Dic314yescomplemented
355#685C2×Dic314yescomplemented
356C4⋊Dic5—121no—
357#683—62no—
358#683—121no—
359C4×Dic5—62no—
360C4×Dic5—121no—
361C4×Dic5—121no—
362C2×#120—51no—
363C2×C4×D4—151no—
364C22×C22⋊C4—151no—
365#390—151no—
366#390—151no—
367#388—151no—
368#388—151no—
369#388—151no—
370#388—151no—
371#386—31no—
372#386—151no—
373#386—151no—
374#385—151no—
375#379—151no—
376C4×C22⋊C4—151no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—22no—
380C22×C3×C5—22no—
381C22×C3×C5—22no—
382C22×C3×C5—22no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5C23×C411yescharacteristic
392C22×C3×C5C22×D411yescharacteristic
393C22×C3×C5C2×#4111yescharacteristic
394C22×C3×C5H(5,𝔽2)11yescharacteristic
395C22×C3×C5H(5,𝔽2)11yescharacteristic
396C22×C3×C5H(5,𝔽2)11yescharacteristic
397C22×C3×C5H(5,𝔽2)11yescharacteristic
398C2×C3×D5—22no—
399C2×C3×D5—22no—
400C2×C3×D5—22no—
401C2×C3×D5—22no—
402C2×C3×D5—22no—
403C2×C3×D5—22no—
404C2×C3×D5—22no—
405C2×C3×D5—22no—
406C2×C3×D5—22no—
407C2×C3×D5—416no—
408C2×C3×D5—41no—
409C2×C3×D5—41no—
410C2×C3×D5—41no—
411C2×C3×D5—41no—
412C2×C3×D5C4×D414yes—
413C3×C4×C5—22no—
414Dic15—22no—
415Dic15—41no—
416Dic15—41no—
417Dic15—41no—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C5×Dic3—22no—
421C5×Dic3—41no—
422C5×Dic3—41no—
423C5×Dic3—41no—
424C24×C3—51no—
425C24×C3—51no—
426C24×C3—54no—
427C24×C3—102no—
428C24×C3—102no—
429C24×C3—201no—
430C24×C3—201no—
431C24×C3—201no—
432C24×C3—201no—
433C24×C3C22×D511yescharacteristic
434C24×C3C22×D511yescharacteristic
435C2×C3×D4—41no—
436C2×C3×D4—41no—
437C2×C3×D4—54no—
438C2×C3×D4—54no—
439C2×C3×D4—102no—
440C2×C3×D4—102no—
441C2×C3×D4—201no—
442C2×C3×D4—201no—
443C2×C3×D4C4×D514yescomplemented
444C22×C3×C4—51no—
445C22×C3×C4—51no—
446C22×C3×C4C22×D511yescharacteristic
447C22×Dic3—22no—
448C22×Dic3—41no—
449C22×Dic3—41no—
450C22×Dic3—51no—
451C22×Dic3—54no—
452C22×Dic3—51no—
453C22×Dic3—51no—
454C22×Dic3—51no—
455C22×Dic3—102no—
456C22×Dic3—201no—
457C22×Dic3—201no—
458C22×Dic3—201no—
459C22×Dic3—201no—
460C22×Dic3C22×D511yescharacteristic
461C22×Dic3C22×D511yescharacteristic
462C22×Dic3C22×D511yescharacteristic
463C22×Dic3C22×D511yescharacteristic
464C3×C22⋊C4—54no—
465C3×C22⋊C4—54no—
466C3×C22⋊C4—54no—
467#217—22no—
468#217—41no—
469#217—41no—
470#217—102no—
471#217—102no—
472#217—102no—
473#217—102no—
474#217—102no—
475#217—102no—
476#217—201no—
477#217—201no—
478#217—201no—
479#217—201no—
480C4⋊Dic3—102no—
481C4⋊Dic3—201no—
482C4⋊Dic3—201no—
483C4×Dic3—102no—
484C4×Dic3—201no—
485C4×Dic3—201no—
486C23×C5—21no—
487C23×C5—21no—
488C23×C5—21no—
489C23×C5—21no—
490C23×C5—21no—
491C23×C5—21no—
492C23×C5—21no—
493C23×C5—21no—
494C23×C5—21no—
495C23×C5—21no—
496C23×C5—21no—
497C23×C5—21no—
498C23×C5C22×Dic312yes—
499C23×C5C22×Dic312yes—
500C23×C5C23×D311yescharacteristic
501C22×D5—21no—
502C22×D5—21no—
503C22×D5—21no—
504C22×D5—21no—
505C22×D5—21no—
506C22×D5—21no—
507C22×D5—21no—
508C22×D5—21no—
509C22×D5—21no—
510C22×D5—21no—
511C22×D5—28no—
512C22×D5—44no—
513C22×D5—44no—
514C22×D5—44no—
515C22×D5—44no—
516C22×D5—44no—
517C22×D5—44no—
518C22×D5D3×D412yes—
519C22×D5#23712yes—
520C22×D5C22×Dic312yes—
521C22×D5C22×Dic312yes—
522C5×D4—44no—
523C2×C4×C5—21no—
524C2×C4×C5—21no—
525C2×C4×C5—32no—
526C2×C4×C5—61no—
527C2×C4×C5—61no—
528C2×C4×C5—61no—
529C2×C4×C5—61no—
530C2×C4×C5—61no—
531C2×C4×C5—61no—
532C2×C4×C5—61no—
533C2×C4×C5—61no—
534C2×C4×C5—61no—
535C2×C4×C5—61no—
536C2×C4×C5—61no—
537C2×C4×C5—124no—
538C2×C4×C5C22×Dic312yes—
539C22⋊D5—28no—
540C22⋊D5—44no—
541C2×Dic5—21no—
542C2×Dic5—21no—
543C2×Dic5—21no—
544C2×Dic5—21no—
545C2×Dic5—32no—
546C2×Dic5—61no—
547C2×Dic5—61no—
548C2×Dic5—61no—
549C2×Dic5—61no—
550C2×Dic5—61no—
551C2×Dic5—61no—
552C2×Dic5—61no—
553C2×Dic5—61no—
554C2×Dic5—61no—
555C2×Dic5—61no—
556C2×Dic5—61no—
557C2×Dic5C22×Dic312yes—
558C2×Dic5C22×Dic312yes—
559C4×D5—124no—
560C4×D5—124no—
561C25—51no—
562C22×D4—51no—
563C22×D4—51no—
564C22×D4D3×D511yescharacteristic
565C23×C4—31no—
566C23×C4—151no—
567C23×C4—151no—
568#120—58no—
569C4×D4—304no—
570C2×C4⋊C4—151no—
571C2×C4⋊C4—151no—
572C2×C4⋊C4—151no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—31no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—51no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—151no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C22⋊C4—151no—
587C2×C22⋊C4—151no—
588C2×C22⋊C4—151no—
589C2×C22⋊C4—304no—
590C2×C42—151no—
591C2×C42—151no—
592C2×C42—151no—
593#95—31no—
594#95—31no—
595#95—151no—
596#95—151no—
597#95—151no—
598#95—151no—
599C2×C3×C5—42no—
600C2×C3×C5—42no—
601C2×C3×C5C2×C4×D411yescharacteristic
602C2×C3×C5#51811yescharacteristic
603C2×C3×C5#51811yescharacteristic
604C2×C3×C5#53411yescharacteristic
605C2×C3×C5#53511yescharacteristic
606C2×C3×C5#53811yescharacteristic
607C2×C3×C5#53811yescharacteristic
608C3×D5—24no—
609C3×D5—42no—
610C23×C3—21no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
615C23×C3—21no—
616C23×C3—21no—
617C23×C3—21no—
618C23×C3—21no—
619C23×C3—21no—
620C23×C3—21no—
621C23×C3—21no—
622C23×C3—52no—
623C23×C3—52no—
624C23×C3—52no—
625C23×C3—52no—
626C23×C3—108no—
627C23×C3—101no—
628C23×C3—101no—
629C23×C3—101no—
630C23×C3—101no—
631C23×C3—101no—
632C23×C3—101no—
633C23×C3—101no—
634C23×C3—101no—
635C23×C3—101no—
636C23×C3—101no—
637C23×C3—204no—
638C23×C3—204no—
639C23×C3—204no—
640C23×C3—204no—
641C23×C3—204no—
642C23×C3—204no—
643C23×C3C2×C4×D512yes—
644C23×C3C2×C4×D512yes—
645C23×C3C23×D511yescharacteristic
646C3×D4—44no—
647C3×D4—108no—
648C3×D4—204no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—52no—
652C2×C3×C4—52no—
653C2×C3×C4—101no—
654C2×C3×C4—101no—
655C2×C3×C4—101no—
656C2×C3×C4—101no—
657C2×C3×C4C2×C4×D512yes—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—44no—
670C2×Dic3—52no—
671C2×Dic3—101no—
672C2×Dic3—101no—
673C2×Dic3—101no—
674C2×Dic3—101no—
675C2×Dic3—101no—
676C2×Dic3—101no—
677C2×Dic3—101no—
678C2×Dic3—101no—
679C2×Dic3—101no—
680C2×Dic3—101no—
681C2×Dic3—101no—
682C2×Dic3—204no—
683C2×Dic3—204no—
684C2×Dic3D4×D512yes—
685C22×C5—22no—
686C22×C5—22no—
687C22×C5—22no—
688C22×C5—22no—
689C22×C5—22no—
690C22×C5—22no—
691C22×C5—41no—
692C22×C5—41no—
693C22×C5—41no—
694C22×C5—41no—
695C22×C5—41no—
696C22×C5—41no—
697C22×C5—41no—
698C22×C5—41no—
699C22×C5C2×D3×D411yescharacteristic
700C22×C5C2×#23711yescharacteristic
701C22×C5#100411yescharacteristic
702C22×C5#100411yescharacteristic
703C22×C5#100411yescharacteristic
704C22×C5#100411yescharacteristic
705C22×C5C23×Dic311yescharacteristic
706C2×D5—22no—
707C2×D5—22no—
708C2×D5—22no—
709C2×D5—22no—
710C2×D5—22no—
711C2×D5—22no—
712C2×D5—22no—
713C2×D5—22no—
714C2×D5—22no—
715C2×D5—416no—
716C2×D5—41no—
717C2×D5—41no—
718C2×D5—41no—
719C2×D5—41no—
720C2×D5D4×Dic314yes—
721C4×C5—22no—
722C4×C5—62no—
723C4×C5—121no—
724C4×C5—121no—
725C4×C5—121no—
726Dic5—22no—
727Dic5—22no—
728Dic5—62no—
729Dic5—121no—
730Dic5—121no—
731Dic5—121no—
732C24—51no—
733C24—51no—
734C24—54no—
735C24—102no—
736C24—102no—
737C24—201no—
738C24—201no—
739C24—201no—
740C24—201no—
741C24C2×D3×D511yescharacteristic
742C24C2×D3×D511yescharacteristic
743C2×D4—41no—
744C2×D4—41no—
745C2×D4—54no—
746C2×D4—54no—
747C2×D4—102no—
748C2×D4—102no—
749C2×D4—201no—
750C2×D4—201no—
751C2×D4D5×Dic314yescomplemented
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—51no—
757C22×C4—51no—
758C22×C4—62no—
759C22×C4—121no—
760C22×C4—121no—
761C22×C4—154no—
762C22×C4—151no—
763C22×C4—151no—
764C22×C4—151no—
765C22×C4—151no—
766C22×C4—302no—
767C22×C4—601no—
768C22×C4—601no—
769C22×C4—601no—
770C22×C4—601no—
771C22×C4C2×D3×D511yescharacteristic
772C4⋊C4—302no—
773C4⋊C4—601no—
774C4⋊C4—601no—
775C22⋊C4—54no—
776C22⋊C4—54no—
777C22⋊C4—54no—
778C22⋊C4—62no—
779C22⋊C4—121no—
780C22⋊C4—121no—
781C22⋊C4—302no—
782C22⋊C4—302no—
783C22⋊C4—302no—
784C22⋊C4—302no—
785C22⋊C4—302no—
786C22⋊C4—302no—
787C22⋊C4—601no—
788C22⋊C4—601no—
789C22⋊C4—601no—
790C22⋊C4—601no—
791C42—302no—
792C42—601no—
793C42—601no—
794C3×C5#232111yescharacteristic, complemented, Hall
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—41no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—54no—
810C22×C3—102no—
811C22×C3—102no—
812C22×C3—102no—
813C22×C3—102no—
814C22×C3—102no—
815C22×C3—102no—
816C22×C3—102no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—2016no—
820C22×C3—201no—
821C22×C3—201no—
822C22×C3—201no—
823C22×C3—201no—
824C22×C3C22×C4×D511yescharacteristic
825C22×C3C2×D4×D511yescharacteristic
826C22×C3#414411yescharacteristic
827C22×C3#414411yescharacteristic
828C22×C3#414411yescharacteristic
829C22×C3D5×#4111yescharacteristic
830C22×C3#414911yescharacteristic
831C3×C4—22no—
832C3×C4—102no—
833C3×C4—102no—
834Dic3—22no—
835Dic3—41no—
836Dic3—41no—
837Dic3—41no—
838Dic3—102no—
839Dic3—201no—
840Dic3—201no—
841Dic3—201no—
842C2×C5—42no—
843C2×C5—42no—
844C2×C5#558911yescharacteristic
845C2×C5#559211yescharacteristic
846C2×C5#559311yescharacteristic
847C2×C5#559311yescharacteristic
848C2×C5C2×D4×Dic311yescharacteristic
849C2×C5#579811yescharacteristic
850C2×C5#579811yescharacteristic
851D5—24no—
852D5—42no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—52no—
866C23—52no—
867C23—52no—
868C23—52no—
869C23—108no—
870C23—101no—
871C23—101no—
872C23—101no—
873C23—101no—
874C23—101no—
875C23—101no—
876C23—101no—
877C23—101no—
878C23—101no—
879C23—101no—
880C23—204no—
881C23—204no—
882C23—204no—
883C23—204no—
884C23—204no—
885C23—204no—
886C23C2×D5×Dic312yes—
887C23C2×D5×Dic312yes—
888C23C22×D3×D511yescharacteristic
889D4—44no—
890D4—108no—
891D4—204no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—32no—
895C2×C4—52no—
896C2×C4—52no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—101no—
909C2×C4—101no—
910C2×C4—101no—
911C2×C4—101no—
912C2×C4—124no—
913C2×C4—152no—
914C2×C4—301no—
915C2×C4—301no—
916C2×C4—301no—
917C2×C4—301no—
918C2×C4—301no—
919C2×C4—301no—
920C2×C4—301no—
921C2×C4—301no—
922C2×C4—301no—
923C2×C4—301no—
924C2×C4—301no—
925C2×C4—604no—
926C2×C4—604no—
927C2×C4C2×D5×Dic312yes—
928C2×C3—42no—
929C2×C3—42no—
930C2×C3—104no—
931C2×C3—202no—
932C2×C3#6582011yescharacteristic
933C2×C3C4×D4×D511yescharacteristic
934C2×C3#6587911yescharacteristic
935C2×C3#6592311yescharacteristic
936C2×C3#6594111yescharacteristic
937C2×C3#6594711yescharacteristic
938C2×C3#6599111yescharacteristic
939C5#8257811yescharacteristic, complemented, Sylow
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—54no—
955C22—102no—
956C22—102no—
957C22—102no—
958C22—102no—
959C22—102no—
960C22—102no—
961C22—102no—
962C22—102no—
963C22—102no—
964C22—2016no—
965C22—201no—
966C22—201no—
967C22—201no—
968C22—201no—
969C22D3×D4×D511yescharacteristic
970C22D5×#23711yescharacteristic
971C22#9202511yescharacteristic
972C22#9202611yescharacteristic
973C22C22×D5×Dic311yescharacteristic
974C22#9204911yescharacteristic
975C22#9204911yescharacteristic
976C4—22no—
977C4—62no—
978C4—102no—
979C4—102no—
980C4—121no—
981C4—121no—
982C4—121no—
983C4—302no—
984C4—601no—
985C4—601no—
986C4—601no—
987C3#1060660711yescharacteristic, complemented, Sylow
988C2—42no—
989C2—42no—
990C2—104no—
991C2—202no—
992C2D4×D5×Dic311yescharacteristic
993C2#1175484211yescharacteristic
994C2#1175484611yescharacteristic
995C2#1175491011yescharacteristic
996C2#1175502211yescharacteristic
997C2#1175502911yescharacteristic
998C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C3×#4083C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2321
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×C22⋊D5C2semidirect
3. C2×D5×#217C2semidirect
4. #11751322C2semidirect
5. C5×#5220C2semidirect
6. #11749518C2semidirect
7. #11749495C2semidirect
8. #11749489C2semidirect
9. #11749488C2semidirect
10. #11749485C2semidirect
11. #11749485C2semidirect
12. #11748900C2semidirect
13. #11748884C2semidirect
14. #11748791C2semidirect
15. #11748772C2semidirect
19. C23×C5×Dic3C22semidirect
26. C2×#6719C22semidirect
27. C2×#6719C22semidirect
28. C2×C4⋊Dic15C22semidirect
29. C2×C4×Dic15C22semidirect
32. C2×C5×#217C22semidirect
34. C3×#4083C4semidirect
39. C2×#6668C22semidirect
40. C2×#6668C22semidirect
47. C2×Dic3×Dic5C22semidirect
48. C2×Dic3×Dic5C22semidirect
49. C5×C3⋊#95C22semidirect
50. C5×C3⋊#95C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
53. #90994C22semidirect
54. #90994C22semidirect
79. C23×C3×D5C2×C4semidirect
84. C2×C3×C5×D4C2×C4semidirect
102. C2×C3×C22⋊D5C2×C4semidirect
110. C2×D5×Dic3D4semidirect
120. C3×C22⋊Dic5C2×C4semidirect
121. C3×#685C2×C4semidirect
122. C3×#685C2×C4semidirect
141. #5220D5semidirect
163. #4083Dic3semidirect
268. C23×Dic3C2×D5semidirect
286. C2×#217C2×D5semidirect
298. C3⋊#95C2×D5semidirect
299. C3⋊#95C2×D5semidirect
308. C23×D5C2×Dic3semidirect
313. C2×C5×D4C2×Dic3semidirect
327. C2×C22⋊D5C2×Dic3semidirect
347. C22⋊Dic5C2×Dic3semidirect
354. #685C2×Dic3semidirect
355. #685C2×Dic3semidirect
443. C2×C3×D4C4×D5semidirect
751. C2×D4D5×Dic3semidirect
794. C3×C5#2321semidirect
939. C5#82578semidirect
987. C3#10606607semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40832
C2×Dic3×C22⋊D52
C2×D5×#2172
#117513222
C5×#52202
#117495182
#117494952
#117494892
#117494882
#117494852
#117489002
#117488842
#117487912
#117487722
#106066073
#825785