Finite Group Databasebeta

← #14326065

Subgroups — #14326065

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×C3×#711C211yesmaximal, characteristic
2C2×#91559C211yesmaximal, characteristic, complemented
3C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
4#11751321C211yesmaximal, characteristic, complemented
5C5×#5220C211yesmaximal, characteristic, complemented
6#11749518C211yesmaximal, characteristic, complemented
7#11749518C211yesmaximal, characteristic, complemented
8#11749506C211yesmaximal, characteristic, complemented
9Dic5×#217C211yesmaximal, characteristic, complemented
10#11749471C211yesmaximal, characteristic, complemented
11C2×#90994C211yesmaximal, characteristic, complemented
12D5×C3⋊#95C211yesmaximal, characteristic, complemented
13#11748737C211yesmaximal, characteristic, complemented
14#11748672C211yesmaximal, characteristic, complemented
15#11748672C211yesmaximal, characteristic, complemented
16#10606403—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C2×C3×#711—24no—
25C2×C3×#711—24no—
26C2×C3×#711C418yescomplemented
27C22×C3×C4×D5C2211yescharacteristic
28C22×C3×Dic10C2211yescharacteristic
29C22×D5×Dic3C2211yescharacteristic
30C22×D5×Dic3C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×#6719C2211yescharacteristic
34C2×C5×#217C2211yescharacteristic
35C2×C5×#217C2211yescharacteristic
36C2×C5×#217C2211yescharacteristic
37#91559—24no—
38Dic3×C22⋊D5—24no—
39C2×#6668C2211yescharacteristic
40C2×#6668C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#84088—51nomaximal, Hall
58C22×#711D311yescharacteristic
59C2×C4×C22⋊D5—31no—
60C2×#4027—31no—
61C5×#386—31no—
62#65509—31no—
63C2×#3963—31no—
64#65245—31no—
65#65245—31no—
66#65232—31no—
67#65231—31no—
68C22⋊C4×Dic5—31no—
69#64953—31no—
70D5×#95—31no—
71#64935—31no—
72#64935—31no—
73C24×C3×C5C2311yescharacteristic
74C24×C3×C5C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C2×C3×C5×D4—22no—
77C2×C3×C5×D4—22no—
78C2×C3×C5×D4C2×C414yescomplemented
79C22×C3×C4×C5C2311yescharacteristic
80C22×Dic15—22no—
81C22×Dic15—22no—
82C22×Dic15—41no—
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C22×C5×Dic3—22no—
88C22×C5×Dic3—22no—
89C22×C5×Dic3—41no—
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C2×C3×C22⋊D5—22no—
95C2×C3×C22⋊D5—22no—
96C2×C3×C22⋊D5C2×C414yes—
97C2×C3×C22⋊D5C2×C414yescomplemented
98C2×C3×C22⋊D5D414yes—
99C2×C3×C22⋊D5D414yes—
100C22×C3×Dic5—22no—
101C22×C3×Dic5—22no—
102C22×C3×Dic5—22no—
103C22×C3×Dic5—22no—
104C22×C3×Dic5C2×C414yescomplemented
105C22×C3×Dic5C2×C414yescomplemented
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C3×#711—232no—
110C2×C3×C4×D5—22no—
111C2×C3×C4×D5—22no—
112C2×C3×C4×D5C2×C414yescomplemented
113C2×C3×Dic10—22no—
114C2×C3×Dic10—22no—
115C2×C3×Dic10C2×C414yescomplemented
116C2×D5×Dic3—22no—
117C2×D5×Dic3—22no—
118C2×D5×Dic3—22no—
119C2×D5×Dic3—22no—
120C2×D5×Dic3—41no—
121C2×D5×Dic3—41no—
122#6719—22no—
123#6719—22no—
124#6719—41no—
125C5×#217—22no—
126C5×#217—22no—
127C5×#217—41no—
128#6668—22no—
129#6668—22no—
130#6665—22no—
131#6665—22no—
132Dic3×Dic5—22no—
133Dic3×Dic5—22no—
134C22×C3×#41—51no—
135C2×D4×Dic3—51no—
136C2×D4×Dic3—51no—
137#5229—51no—
138#5229—51no—
139#5220—51no—
140#5220—51no—
141#5220—51no—
142#5220D511yescharacteristic, complemented
143#5212—51no—
144#5211—51no—
145#5211—51no—
146C4×#217—51no—
147C2×C3⋊#95—51no—
148C2×C3⋊#95—51no—
149C22×C5×D4C2×D311yescharacteristic
150C23×C4×C5—31no—
151C22×C22⋊D5C2×D311yescharacteristic
152C22×C22⋊D5C2×D311yescharacteristic
153C23×Dic5—31no—
154C23×Dic5C2×D311yescharacteristic
155C23×Dic5C2×D311yescharacteristic
156C2×#711—24no—
157C2×#711—24no—
158C2×#711Dic318yescomplemented
159C22×C4×D5—31no—
160C22×C4×D5—31no—
161C22×C4×D5C2×D311yescharacteristic
162C22×Dic10C2×D311yescharacteristic
163C2×C5×C22⋊C4—31no—
164C2×C5×C22⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C22⋊Dic5—31no—
167C2×C22⋊Dic5—31no—
168C2×C22⋊Dic5—31no—
169C4×C22⋊D5—64no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#683—31no—
173C2×#683—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176#4027—64no—
177C5×#95—31no—
178C5×#95—31no—
179#3963—31no—
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963—31no—
187#3963—31no—
188#3963—31no—
189#2339—151noSylow
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×C5—21no—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C22×C412yes—
202C23×C3×C5C2×D412yes—
203C23×C3×C5C2×D412yes—
204C23×C3×C5C2411yescharacteristic
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5C22×C412yes—
210C22×C3×D5C2×D412yes—
211C22×C3×D5C2×D412yes—
212C3×C5×D4—28no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5C22×C412yes—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—44no—
228C2×Dic15#4112yescomplemented
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×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—44no—
241C2×C5×Dic3#4112yescomplemented
242C3×C22⋊D5—28no—
243C3×C22⋊D5C22⋊C4116yescomplemented
244C2×C3×Dic5—28no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—28no—
250C2×C3×Dic5C22×C412yes—
251C2×C3×Dic5C22×C412yes—
252C2×C3×Dic5C22×C412yes—
253C2×C3×Dic5C2×D412yes—
254C2×C3×Dic5C2×D412yes—
255C3×C4×D5—28no—
256C3×Dic10—28no—
257D5×Dic3—44no—
258D5×Dic3—44no—
259C2×C3×#41—58no—
260C2×C3×#41—104no—
261C2×C3×#41—104no—
262C22×C3×Q8—51no—
263C22×C3×D4—51no—
264C22×C3×D4—51no—
265C22×C3×D4C2×D511yescharacteristic
266C23×C3×C4—51no—
267C23×C3×C4—51no—
268C23×C3×C4—51no—
269C23×Dic3—51no—
270C23×Dic3—51no—
271C23×Dic3—51no—
272C23×Dic3C2×D511yescharacteristic
273C2×#217—51no—
274C2×#217—51no—
275C2×#217—51no—
276C2×#217—51no—
277C2×#217—51no—
278C2×#217C2×D511yescharacteristic
279C2×#217C2×D511yescharacteristic
280C2×#217C2×D511yescharacteristic
281D4×Dic3—104no—
282D4×Dic3—104no—
283C2×C4⋊Dic3—51no—
284C2×C4⋊Dic3—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287C3⋊#95—51no—
288C3⋊#95—51no—
289C3⋊#95—51no—
290C3⋊#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C3⋊#95C2×D511yescharacteristic
298C3⋊#95C2×D511yescharacteristic
299C24×C5C22×D311yescharacteristic
300C24×C5C22×D311yescharacteristic
301C23×D5C22×D311yescharacteristic
302C2×C5×D4—22no—
303C2×C5×D4—22no—
304C2×C5×D4C2×Dic314yescomplemented
305C22×C4×C5—31no—
306C22×C4×C5—31no—
307C22×C4×C5—31no—
308C22×C4×C5—31no—
309C22×C4×C5—62no—
310C22×C4×C5—62no—
311C22×C4×C5—121no—
312C22×C4×C5C22×D311yescharacteristic
313C2×C22⋊D5—22no—
314C2×C22⋊D5—22no—
315C2×C22⋊D5C2×Dic314yes—
316C2×C22⋊D5C2×Dic314yescomplemented
317C2×C22⋊D5#6714yes—
318C2×C22⋊D5#6714yes—
319C22×Dic5—22no—
320C22×Dic5—22no—
321C22×Dic5—22no—
322C22×Dic5—22no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—62no—
328C22×Dic5—62no—
329C22×Dic5—121no—
330C22×Dic5C2×Dic314yescomplemented
331C22×Dic5C2×Dic314yescomplemented
332C22×Dic5C22×D311yescharacteristic
333C22×Dic5C22×D311yescharacteristic
334C22×Dic5C22×D311yescharacteristic
335#711—232no—
336C2×C4×D5—22no—
337C2×C4×D5—22no—
338C2×C4×D5—62no—
339C2×C4×D5—62no—
340C2×C4×D5—62no—
341C2×C4×D5—62no—
342C2×C4×D5—121no—
343C2×C4×D5—121no—
344C2×C4×D5C2×Dic314yescomplemented
345C2×Dic10—22no—
346C2×Dic10—22no—
347C2×Dic10C2×Dic314yescomplemented
348C5×C22⋊C4—62no—
349C5×C22⋊C4—62no—
350C5×C22⋊C4—121no—
351C22⋊Dic5—62no—
352C22⋊Dic5—62no—
353C22⋊Dic5—121no—
354#685—62no—
355#685—62no—
356#683—62no—
357#683—62no—
358C4×Dic5—62no—
359C4×Dic5—62no—
360C22×#41—51no—
361C2×C4×D4—151no—
362C2×C4×D4—151no—
363#391—151no—
364#391—151no—
365#386—31no—
366#386—151no—
367#386—151no—
368#386—151no—
369#381—151no—
370#381—151no—
371#380—151no—
372C4×C22⋊C4—151no—
373C2×#95—151no—
374C2×#95—151no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
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—22no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C2×C22⋊C414yes—
389C22×C3×C5C23×C411yescharacteristic
390C22×C3×C5C22×D411yescharacteristic
391C22×C3×C5C22×D411yescharacteristic
392C22×C3×C5C2×#4111yescharacteristic
393C22×C3×C5C2×#4111yescharacteristic
394C22×C3×C5H(5,𝔽2)11yescharacteristic
395C22×C3×C52−1+411yescharacteristic
396C2×C3×D5—22no—
397C2×C3×D5—22no—
398C2×C3×D5—22no—
399C2×C3×D5—22no—
400C2×C3×D5—22no—
401C2×C3×D5—22no—
402C2×C3×D5C2×C22⋊C414yes—
403C3×C4×C5—22no—
404Dic15—22no—
405Dic15—41no—
406Dic15—41no—
407Dic15—41no—
408C3×Dic5—22no—
409C3×Dic5—22no—
410C3×Dic5C2×C22⋊C414yes—
411C5×Dic3—22no—
412C5×Dic3—41no—
413C5×Dic3—41no—
414C5×Dic3—41no—
415C24×C3—51no—
416C24×C3C22×D511yescharacteristic
417C24×C3C22×D511yescharacteristic
418C3×#41—1032no—
419C2×C3×Q8—54no—
420C2×C3×Q8—102no—
421C2×C3×Q8—102no—
422C2×C3×D4—22no—
423C2×C3×D4—22no—
424C2×C3×D4—54no—
425C2×C3×D4—54no—
426C2×C3×D4—54no—
427C2×C3×D4—54no—
428C2×C3×D4—102no—
429C2×C3×D4—102no—
430C2×C3×D4C4×D514yescomplemented
431C22×C3×C4—51no—
432C22×C3×C4—54no—
433C22×C3×C4—54no—
434C22×C3×C4—51no—
435C22×C3×C4—51no—
436C22×C3×C4—54no—
437C22×C3×C4—102no—
438C22×C3×C4—102no—
439C22×C3×C4—102no—
440C22×C3×C4—102no—
441C22×C3×C4—102no—
442C22×C3×C4—102no—
443C22×C3×C4C22×D511yescharacteristic
444C22×Dic3—22no—
445C22×Dic3—22no—
446C22×Dic3—41no—
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—102no—
452C22×Dic3—102no—
453C22×Dic3—102no—
454C22×Dic3—102no—
455C22×Dic3—102no—
456C22×Dic3—102no—
457C22×Dic3—201no—
458C22×Dic3—201no—
459C22×Dic3—201no—
460C22×Dic3C22×D511yescharacteristic
461C22×Dic3C22×D511yescharacteristic
462C22×Dic3C22×D511yescharacteristic
463C22×Dic3C22×D511yescharacteristic
464#217—22no—
465#217—22no—
466#217—41no—
467#217—102no—
468#217—102no—
469#217—102no—
470#217—102no—
471#217—201no—
472C4⋊Dic3—102no—
473C4⋊Dic3—102no—
474C4×Dic3—102no—
475C4×Dic3—102no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—21no—
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—21no—
482C23×C5—21no—
483C23×C5—21no—
484C23×C5—21no—
485C23×C5—21no—
486C23×C5C22×Dic312yes—
487C23×C5C22×Dic312yes—
488C23×C5C2×#6712yes—
489C23×C5C2×#6712yes—
490C23×C5C23×D311yescharacteristic
491C22×D5—21no—
492C22×D5—21no—
493C22×D5—21no—
494C22×D5—21no—
495C22×D5C22×Dic312yes—
496C22×D5C2×#6712yes—
497C22×D5C2×#6712yes—
498C5×D4—28no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—32no—
502C2×C4×C5—61no—
503C2×C4×C5—61no—
504C2×C4×C5—61no—
505C2×C4×C5—61no—
506C2×C4×C5—61no—
507C2×C4×C5—61no—
508C2×C4×C5—61no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—124no—
514C2×C4×C5C22×Dic312yes—
515C22⋊D5—28no—
516C22⋊D5#217116yescomplemented
517C2×Dic5—28no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—28no—
523C2×Dic5—32no—
524C2×Dic5—61no—
525C2×Dic5—61no—
526C2×Dic5—61no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—124no—
536C2×Dic5C22×Dic312yes—
537C2×Dic5C22×Dic312yes—
538C2×Dic5C22×Dic312yes—
539C2×Dic5C2×#6712yes—
540C2×Dic5C2×#6712yes—
541C4×D5—28no—
542C4×D5—124no—
543C4×D5—124no—
544Dic10—28no—
545C2×#41—58no—
546C2×#41—104no—
547C2×#41—104no—
548C22×Q8—51no—
549C22×D4—51no—
550C22×D4—51no—
551C22×D4D3×D511yescharacteristic
552C23×C4—31no—
553C23×C4—51no—
554C23×C4—51no—
555C23×C4—51no—
556C23×C4—151no—
557C23×C4—151no—
558C23×C4—151no—
559C4×D4—304no—
560C4×D4—304no—
561C2×C4⋊C4—151no—
562C2×C4⋊C4—151no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4—151no—
571C2×C42—151no—
572C2×C42—151no—
573#95—31no—
574#95—31no—
575#95—151no—
576#95—151no—
577#95—151no—
578#95—151no—
579#95—151no—
580#95—151no—
581#95—151no—
582#95—151no—
583#95—151no—
584#95—151no—
585C2×C3×C5—24no—
586C2×C3×C5—42no—
587C2×C3×C5C22×C22⋊C411yescharacteristic
588C2×C3×C5C4×#4111yescharacteristic
589C2×C3×C5#52011yescharacteristic
590C2×C3×C5#54611yescharacteristic
591C2×C3×C5#54611yescharacteristic
592C2×C3×C5#54711yescharacteristic
593C2×C3×C5#54711yescharacteristic
594C3×D5—24no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—52no—
606C23×C3—52no—
607C23×C3—52no—
608C23×C3—101no—
609C23×C3—101no—
610C23×C3—101no—
611C23×C3—101no—
612C23×C3C2×C4×D512yes—
613C23×C3C2×C4×D512yes—
614C23×C3D4×D512yes—
615C23×C3D4×D512yes—
616C23×C3C23×D511yescharacteristic
617C3×Q8—108no—
618C3×D4—28no—
619C3×D4—516no—
620C3×D4—108no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—52no—
624C2×C3×C4—52no—
625C2×C3×C4—52no—
626C2×C3×C4—52no—
627C2×C3×C4—52no—
628C2×C3×C4—108no—
629C2×C3×C4—108no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—108no—
635C2×C3×C4C2×C4×D512yes—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
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—44no—
648C2×Dic3—52no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658C2×Dic3—101no—
659C2×Dic3—101no—
660C2×Dic3—204no—
661C2×Dic3—204no—
662C2×Dic3—204no—
663C2×Dic3#71112yescomplemented
664C22×C5—22no—
665C22×C5—22no—
666C22×C5—22no—
667C22×C5—22no—
668C22×C5—22no—
669C22×C5—22no—
670C22×C5—22no—
671C22×C5—22no—
672C22×C5—22no—
673C22×C5—41no—
674C22×C5—41no—
675C22×C5—41no—
676C22×C5—41no—
677C22×C5C2×#21714yes—
678C22×C5D3×#4111yescharacteristic
679C22×C5D3×#4111yescharacteristic
680C22×C5#100911yescharacteristic
681C22×C5#101011yescharacteristic
682C22×C5C23×Dic311yescharacteristic
683C22×C5C22×#6711yescharacteristic
684C22×C5C22×#6711yescharacteristic
685C2×D5—22no—
686C2×D5—22no—
687C2×D5—22no—
688C2×D5—22no—
689C2×D5—22no—
690C2×D5—22no—
691C2×D5C2×#21714yes—
692C4×C5—22no—
693C4×C5—62no—
694C4×C5—121no—
695C4×C5—121no—
696C4×C5—121no—
697Dic5—22no—
698Dic5—22no—
699Dic5—62no—
700Dic5—121no—
701Dic5—121no—
702Dic5—121no—
703Dic5C2×#21714yes—
704C24—51no—
705C24C2×D3×D511yescharacteristic
706C24C2×D3×D511yescharacteristic
707#41—1032no—
708C2×Q8—54no—
709C2×Q8—102no—
710C2×Q8—102no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—54no—
714C2×D4—54no—
715C2×D4—54no—
716C2×D4—54no—
717C2×D4—102no—
718C2×D4—102no—
719C2×D4D5×Dic314yescomplemented
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—51no—
725C22×C4—54no—
726C22×C4—54no—
727C22×C4—51no—
728C22×C4—51no—
729C22×C4—54no—
730C22×C4—62no—
731C22×C4—62no—
732C22×C4—102no—
733C22×C4—102no—
734C22×C4—102no—
735C22×C4—102no—
736C22×C4—102no—
737C22×C4—102no—
738C22×C4—121no—
739C22×C4—151no—
740C22×C4—151no—
741C22×C4—151no—
742C22×C4—151no—
743C22×C4—302no—
744C22×C4—302no—
745C22×C4—302no—
746C22×C4—302no—
747C22×C4—302no—
748C22×C4—302no—
749C22×C4—601no—
750C22×C4—601no—
751C22×C4—601no—
752C22×C4C2×D3×D511yescharacteristic
753C4⋊C4—302no—
754C4⋊C4—302no—
755C22⋊C4—62no—
756C22⋊C4—62no—
757C22⋊C4—121no—
758C22⋊C4—302no—
759C22⋊C4—302no—
760C22⋊C4—302no—
761C22⋊C4—302no—
762C22⋊C4—601no—
763C42—302no—
764C42—302no—
765C3×C5#233911yescharacteristic, complemented, Hall
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—54no—
780C22×C3—102no—
781C22×C3—102no—
782C22×C3—102no—
783C22×C3—102no—
784C22×C3—102no—
785C22×C3—102no—
786C22×C3D5×C22⋊C414yes—
787C22×C3C22×C4×D511yescharacteristic
788C22×C3C2×D4×D511yescharacteristic
789C22×C3C2×D4×D511yescharacteristic
790C22×C3C2×#71111yescharacteristic
791C22×C3#414411yescharacteristic
792C22×C3D5×#4111yescharacteristic
793C22×C3#415011yescharacteristic
794C3×C4—22no—
795C3×C4—54no—
796C3×C4—102no—
797C3×C4—102no—
798Dic3—22no—
799Dic3—41no—
800Dic3—41no—
801Dic3—41no—
802Dic3—102no—
803Dic3—201no—
804Dic3—201no—
805Dic3—201no—
806C2×C5—24no—
807C2×C5—42no—
808C2×C5#582411yescharacteristic
809C2×C5#582411yescharacteristic
810C2×C5Dic3×#4111yescharacteristic
811C2×C5#582711yescharacteristic
812C2×C5#582911yescharacteristic
813C2×C5#582911yescharacteristic
814C2×C5C22×#21711yescharacteristic
815D5—24no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—52no—
827C23—52no—
828C23—52no—
829C23—101no—
830C23—101no—
831C23—101no—
832C23—101no—
833C23C2×D5×Dic312yes—
834C23C2×D5×Dic312yes—
835C23D5×#6712yes—
836C23D5×#6712yes—
837C23C22×D3×D511yescharacteristic
838Q8—108no—
839D4—28no—
840D4—516no—
841D4—108no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—32no—
845C2×C4—52no—
846C2×C4—52no—
847C2×C4—52no—
848C2×C4—52no—
849C2×C4—52no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—108no—
862C2×C4—108no—
863C2×C4—101no—
864C2×C4—101no—
865C2×C4—101no—
866C2×C4—101no—
867C2×C4—108no—
868C2×C4—124no—
869C2×C4—152no—
870C2×C4—301no—
871C2×C4—301no—
872C2×C4—301no—
873C2×C4—301no—
874C2×C4—301no—
875C2×C4—301no—
876C2×C4—301no—
877C2×C4—301no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—301no—
881C2×C4—604no—
882C2×C4—604no—
883C2×C4—604no—
884C2×C4C2×D5×Dic312yes—
885C2×C3—24no—
886C2×C3—42no—
887C2×C3—104no—
888C2×C3C2×D5×C22⋊C411yescharacteristic
889C2×C3C4×#71111yescharacteristic
890C2×C3#6588011yescharacteristic
891C2×C3#6592511yescharacteristic
892C2×C3#6594411yescharacteristic
893C2×C3#6594511yescharacteristic
894C2×C3#6598911yescharacteristic
895C5#8408811yescharacteristic, complemented, Sylow
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—54no—
910C22—102no—
911C22—102no—
912C22—102no—
913C22—102no—
914C22—102no—
915C22—102no—
916C22D5×#21714yes—
917C22#9202011yescharacteristic
918C22D3×#71111yescharacteristic
919C22#9202411yescharacteristic
920C22#9202711yescharacteristic
921C22C22×D5×Dic311yescharacteristic
922C22C2×D5×#6711yescharacteristic
923C22C2×D5×#6711yescharacteristic
924C4—22no—
925C4—54no—
926C4—62no—
927C4—102no—
928C4—102no—
929C4—121no—
930C4—121no—
931C4—121no—
932C4—302no—
933C4—601no—
934C4—601no—
935C4—601no—
936C3#1060640311yescharacteristic, complemented, Sylow
937C2—24no—
938C2—42no—
939C2—104no—
940C2#1175479011yescharacteristic
941C2#1175479211yescharacteristic
942C2Dic3×#71111yescharacteristic
943C2#1175492311yescharacteristic
944C2#1175506311yescharacteristic
945C2#1175506411yescharacteristic
946C2C2×D5×#21711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×#711C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2339
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×#91559C2semidirect
3. C2×Dic3×C22⋊D5C2semidirect
4. #11751321C2semidirect
5. C5×#5220C2semidirect
6. #11749518C2semidirect
7. #11749518C2semidirect
8. #11749506C2semidirect
9. Dic5×#217C2semidirect
10. #11749471C2semidirect
11. C2×#90994C2semidirect
12. D5×C3⋊#95C2semidirect
13. #11748737C2semidirect
14. #11748672C2semidirect
15. #11748672C2semidirect
26. C2×C3×#711C4semidirect
78. C2×C3×C5×D4C2×C4semidirect
97. C2×C3×C22⋊D5C2×C4semidirect
104. C22×C3×Dic5C2×C4semidirect
105. C22×C3×Dic5C2×C4semidirect
112. C2×C3×C4×D5C2×C4semidirect
115. C2×C3×Dic10C2×C4semidirect
142. #5220D5semidirect
158. C2×#711Dic3semidirect
228. C2×Dic15#41semidirect
241. C2×C5×Dic3#41semidirect
243. C3×C22⋊D5C22⋊C4semidirect
304. C2×C5×D4C2×Dic3semidirect
316. C2×C22⋊D5C2×Dic3semidirect
330. C22×Dic5C2×Dic3semidirect
331. C22×Dic5C2×Dic3semidirect
344. C2×C4×D5C2×Dic3semidirect
347. C2×Dic10C2×Dic3semidirect
430. C2×C3×D4C4×D5semidirect
516. C22⋊D5#217semidirect
663. C2×Dic3#711semidirect
719. C2×D4D5×Dic3semidirect
765. C3×C5#2339semidirect
895. C5#84088semidirect
936. C3#10606403semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7112
C2×#915592
C2×Dic3×C22⋊D52
#117513212
C5×#52202
#117495182
#117495062
Dic5×#2172
#117494712
C2×#909942
D5×C3⋊#952
#117487372
#117486722
#106064033
#840885