Finite Group Databasebeta

← #14326067

Subgroups — #14326067

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×C5×#237C211yesmaximal, characteristic
2C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
3C2×Dic5×#67C211yesmaximal, characteristic, complemented
4#11751321C211yesmaximal, characteristic, complemented
5C3×#65509C211yesmaximal, characteristic, complemented
6#11749519C211yesmaximal, characteristic, complemented
7#11749519C211yesmaximal, characteristic, complemented
8#11749513C211yesmaximal, characteristic, complemented
9Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
10#11749472C211yesmaximal, characteristic, complemented
11C2×#90994C211yesmaximal, characteristic, complemented
12D3×#3963C211yesmaximal, characteristic, complemented
13#11748777C211yesmaximal, characteristic, complemented
14#11748692C211yesmaximal, characteristic, complemented
15#11748692C211yesmaximal, characteristic, complemented
16#10615819—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic
22C23×C5×Dic3C2211yescharacteristic
23C2×C5×#237—24no—
24C2×C5×#237—24no—
25C2×C5×#237C418yescomplemented
26C22×C4×C5×D3C2211yescharacteristic
27C22×C5×Dic6C2211yescharacteristic
28C23×C3×Dic5C2211yescharacteristic
29C22×D3×Dic5C2211yescharacteristic
30C22×D3×Dic5C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×#6719C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C2×C3×C22⋊Dic5C2211yescharacteristic
37#67⋊Dic5—24no—
38Dic5×#67—24no—
39C2×Dic3⋊Dic5C2211yescharacteristic
40C2×Dic3⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#74672—51nomaximal, Hall
58C22×C5×#41—31no—
59C2×D4×Dic5—31no—
60C2×D4×Dic5—31no—
61#65519—31no—
62#65519—31no—
63#65509—31no—
64#65509—31no—
65#65509—31no—
66#65509D311yescharacteristic, complemented
67#65501—31no—
68#65500—31no—
69#65500—31no—
70C4×C22⋊Dic5—31no—
71C2×#3963—31no—
72C2×#3963—31no—
73C24×C3×C5C2311yescharacteristic
74C24×C3×C5C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
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
87C2×C5×#67—22no—
88C2×C5×#67—22no—
89C2×C5×#67C2×C414yes—
90C2×C5×#67C2×C414yescomplemented
91C2×C5×#67D414yes—
92C2×C5×#67D414yes—
93C22×C5×Dic3—22no—
94C22×C5×Dic3—22no—
95C22×C5×Dic3—22no—
96C22×C5×Dic3—22no—
97C22×C5×Dic3C2×C414yescomplemented
98C22×C5×Dic3C2×C414yescomplemented
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C5×#237—232no—
103C2×C4×C5×D3—22no—
104C2×C4×C5×D3—22no—
105C2×C4×C5×D3C2×C414yescomplemented
106C2×C5×Dic6—22no—
107C2×C5×Dic6—22no—
108C2×C5×Dic6C2×C414yescomplemented
109C22×C3×Dic5—22no—
110C22×C3×Dic5—22no—
111C22×C3×Dic5—41no—
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C2×D3×Dic5—22no—
117C2×D3×Dic5—22no—
118C2×D3×Dic5—22no—
119C2×D3×Dic5—22no—
120C2×D3×Dic5—41no—
121C2×D3×Dic5—41no—
122#6719—22no—
123#6719—22no—
124#6719—41no—
125C3×C22⋊Dic5—22no—
126C3×C22⋊Dic5—22no—
127C3×C22⋊Dic5—41no—
128Dic3⋊Dic5—22no—
129Dic3⋊Dic5—22no—
130(C2×D3)⋊Dic5—22no—
131(C2×D3)⋊Dic5—22no—
132Dic3×Dic5—22no—
133Dic3×Dic5—22no—
134C22×#237D511yescharacteristic
135C2×C4×#67—51no—
136C2×#67⋊C4—51no—
137C3×#386—51no—
138#5220—51no—
139C2×C3⋊#95—51no—
140#4956—51no—
141#4956—51no—
142#4943—51no—
143#4942—51no—
144Dic3×C22⋊C4—51no—
145#4664—51no—
146D3×#95—51no—
147#4646—51no—
148#4646—51no—
149C2×C5×#41—38no—
150C2×C5×#41—64no—
151C2×C5×#41—64no—
152C22×C5×Q8—31no—
153C22×C5×D4—31no—
154C22×C5×D4—31no—
155C22×C5×D4C2×D311yescharacteristic
156C23×C4×C5—31no—
157C23×C4×C5—31no—
158C23×C4×C5—31no—
159C23×Dic5—31no—
160C23×Dic5—31no—
161C23×Dic5—31no—
162C23×Dic5C2×D311yescharacteristic
163C2×C22⋊Dic5—31no—
164C2×C22⋊Dic5—31no—
165C2×C22⋊Dic5—31no—
166C2×C22⋊Dic5—31no—
167C2×C22⋊Dic5—31no—
168C2×C22⋊Dic5C2×D311yescharacteristic
169C2×C22⋊Dic5C2×D311yescharacteristic
170C2×C22⋊Dic5C2×D311yescharacteristic
171D4×Dic5—64no—
172D4×Dic5—64no—
173C2×C4⋊Dic5—31no—
174C2×C4⋊Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177#3963—31no—
178#3963—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#3963C2×D311yescharacteristic
188#3963C2×D311yescharacteristic
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×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—
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
229C5×#67—28no—
230C5×#67C22⋊C4116yescomplemented
231C2×C5×Dic3—28no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—28no—
237C2×C5×Dic3C22×C412yes—
238C2×C5×Dic3C22×C412yes—
239C2×C5×Dic3C22×C412yes—
240C2×C5×Dic3C2×D412yes—
241C2×C5×Dic3C2×D412yes—
242C4×C5×D3—28no—
243C5×Dic6—28no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5—44no—
256C2×C3×Dic5#4112yescomplemented
257D3×Dic5—44no—
258D3×Dic5—44no—
259C22×C3×D4C2×D511yescharacteristic
260C23×C3×C4—51no—
261C22×#67C2×D511yescharacteristic
262C22×#67C2×D511yescharacteristic
263C23×Dic3—51no—
264C23×Dic3C2×D511yescharacteristic
265C23×Dic3C2×D511yescharacteristic
266C2×#237—24no—
267C2×#237—24no—
268C2×#237Dic518yescomplemented
269C22×C4×D3—51no—
270C22×C4×D3—51no—
271C22×C4×D3C2×D511yescharacteristic
272C22×Dic6C2×D511yescharacteristic
273C2×C3×C22⋊C4—51no—
274C2×C3×C22⋊C4—51no—
275C2×C3×C22⋊C4—51no—
276C2×#217—51no—
277C2×#217—51no—
278C2×#217—51no—
279C4×#67—104no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×Dic3⋊C4—51no—
283C2×Dic3⋊C4—51no—
284C2×C4×Dic3—51no—
285C2×C4×Dic3—51no—
286#67⋊C4—104no—
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⋊#95—51no—
298C3⋊#95—51no—
299C24×C5—31no—
300C24×C5C22×D311yescharacteristic
301C24×C5C22×D311yescharacteristic
302C5×#41—632no—
303C2×C5×Q8—34no—
304C2×C5×Q8—62no—
305C2×C5×Q8—62no—
306C2×C5×D4—22no—
307C2×C5×D4—22no—
308C2×C5×D4—34no—
309C2×C5×D4—34no—
310C2×C5×D4—34no—
311C2×C5×D4—34no—
312C2×C5×D4—62no—
313C2×C5×D4—62no—
314C2×C5×D4C4×D314yescomplemented
315C22×C4×C5—31no—
316C22×C4×C5—34no—
317C22×C4×C5—34no—
318C22×C4×C5—31no—
319C22×C4×C5—31no—
320C22×C4×C5—34no—
321C22×C4×C5—62no—
322C22×C4×C5—62no—
323C22×C4×C5—62no—
324C22×C4×C5—62no—
325C22×C4×C5—62no—
326C22×C4×C5—62no—
327C22×C4×C5C22×D311yescharacteristic
328C22×Dic5—22no—
329C22×Dic5—22no—
330C22×Dic5—31no—
331C22×Dic5—31no—
332C22×Dic5—31no—
333C22×Dic5—31no—
334C22×Dic5—41no—
335C22×Dic5—62no—
336C22×Dic5—62no—
337C22×Dic5—62no—
338C22×Dic5—62no—
339C22×Dic5—62no—
340C22×Dic5—62no—
341C22×Dic5—121no—
342C22×Dic5—121no—
343C22×Dic5—121no—
344C22×Dic5C22×D311yescharacteristic
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348C22⋊Dic5—22no—
349C22⋊Dic5—22no—
350C22⋊Dic5—41no—
351C22⋊Dic5—62no—
352C22⋊Dic5—62no—
353C22⋊Dic5—62no—
354C22⋊Dic5—62no—
355C22⋊Dic5—121no—
356C4⋊Dic5—62no—
357C4⋊Dic5—62no—
358C4×Dic5—62no—
359C4×Dic5—62no—
360C22×#41—31no—
361C2×C4×D4—151no—
362C2×C4×D4—151no—
363#391—151no—
364#391—151no—
365#386—51no—
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×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—
404Dic15—22no—
405Dic15—41no—
406Dic15—41no—
407Dic15—41no—
408C3×Dic5—22no—
409C3×Dic5—41no—
410C3×Dic5—41no—
411C3×Dic5—41no—
412C5×Dic3—22no—
413C5×Dic3—22no—
414C5×Dic3C2×C22⋊C414yes—
415C24×C3C22×D511yescharacteristic
416C24×C3C22×D511yescharacteristic
417C23×D3C22×D511yescharacteristic
418C2×C3×D4—22no—
419C2×C3×D4—22no—
420C2×C3×D4C2×Dic514yescomplemented
421C22×C3×C4—51no—
422C22×C3×C4—51no—
423C22×C3×C4—51no—
424C22×C3×C4—51no—
425C22×C3×C4—102no—
426C22×C3×C4—102no—
427C22×C3×C4—201no—
428C22×C3×C4C22×D511yescharacteristic
429C2×#67—22no—
430C2×#67—22no—
431C2×#67C2×Dic514yes—
432C2×#67C2×Dic514yescomplemented
433C2×#67C22⋊D514yes—
434C2×#67C22⋊D514yes—
435C22×Dic3—22no—
436C22×Dic3—22no—
437C22×Dic3—22no—
438C22×Dic3—22no—
439C22×Dic3—51no—
440C22×Dic3—51no—
441C22×Dic3—51no—
442C22×Dic3—51no—
443C22×Dic3—102no—
444C22×Dic3—102no—
445C22×Dic3—201no—
446C22×Dic3C2×Dic514yescomplemented
447C22×Dic3C2×Dic514yescomplemented
448C22×Dic3C22×D511yescharacteristic
449C22×Dic3C22×D511yescharacteristic
450C22×Dic3C22×D511yescharacteristic
451#237—232no—
452C2×C4×D3—22no—
453C2×C4×D3—22no—
454C2×C4×D3—102no—
455C2×C4×D3—102no—
456C2×C4×D3—102no—
457C2×C4×D3—102no—
458C2×C4×D3—201no—
459C2×C4×D3—201no—
460C2×C4×D3C2×Dic514yescomplemented
461C2×Dic6—22no—
462C2×Dic6—22no—
463C2×Dic6C2×Dic514yescomplemented
464C3×C22⋊C4—102no—
465C3×C22⋊C4—102no—
466C3×C22⋊C4—201no—
467#217—102no—
468#217—102no—
469#217—201no—
470(C2×D3)⋊C4—102no—
471(C2×D3)⋊C4—102no—
472Dic3⋊C4—102no—
473Dic3⋊C4—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×C5—32no—
487C23×C5—32no—
488C23×C5—32no—
489C23×C5—61no—
490C23×C5—61no—
491C23×C5—61no—
492C23×C5—61no—
493C23×C5C2×C4×D312yes—
494C23×C5C2×C4×D312yes—
495C23×C5D3×D412yes—
496C23×C5D3×D412yes—
497C23×C5C23×D311yescharacteristic
498C5×Q8—68no—
499C5×D4—28no—
500C5×D4—316no—
501C5×D4—68no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—32no—
505C2×C4×C5—32no—
506C2×C4×C5—32no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—68no—
510C2×C4×C5—68no—
511C2×C4×C5—68no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5C2×C4×D312yes—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—32no—
529C2×Dic5—44no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—61no—
538C2×Dic5—61no—
539C2×Dic5—61no—
540C2×Dic5—61no—
541C2×Dic5—124no—
542C2×Dic5—124no—
543C2×Dic5—124no—
544C2×Dic5#23712yescomplemented
545C2×#41—38no—
546C2×#41—64no—
547C2×#41—64no—
548C22×Q8—31no—
549C22×D4—31no—
550C22×D4—31no—
551C22×D4D3×D511yescharacteristic
552C23×C4—31no—
553C23×C4—31no—
554C23×C4—31no—
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—51no—
564C2×C22⋊C4—51no—
565C2×C22⋊C4—51no—
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—51no—
574#95—51no—
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
594C5×D3—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×C3C22×Dic512yes—
606C23×C3C22×Dic512yes—
607C23×C3C2×C22⋊D512yes—
608C23×C3C2×C22⋊D512yes—
609C23×C3C23×D511yescharacteristic
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3C22×Dic512yes—
615C22×D3C2×C22⋊D512yes—
616C22×D3C2×C22⋊D512yes—
617C3×D4—28no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—52no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—101no—
628C2×C3×C4—101no—
629C2×C3×C4—101no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4—204no—
633C2×C3×C4C22×Dic512yes—
634#67—28no—
635#67C22⋊Dic5116yescomplemented
636C2×Dic3—28no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—28no—
642C2×Dic3—52no—
643C2×Dic3—101no—
644C2×Dic3—101no—
645C2×Dic3—101no—
646C2×Dic3—101no—
647C2×Dic3—101no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—204no—
655C2×Dic3C22×Dic512yes—
656C2×Dic3C22×Dic512yes—
657C2×Dic3C22×Dic512yes—
658C2×Dic3C2×C22⋊D512yes—
659C2×Dic3C2×C22⋊D512yes—
660C4×D3—28no—
661C4×D3—204no—
662C4×D3—204no—
663Dic6—28no—
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—34no—
674C22×C5—41no—
675C22×C5—41no—
676C22×C5—41no—
677C22×C5—41no—
678C22×C5—62no—
679C22×C5—62no—
680C22×C5—62no—
681C22×C5—62no—
682C22×C5—62no—
683C22×C5—62no—
684C22×C5D3×C22⋊C414yes—
685C22×C5C22×C4×D311yescharacteristic
686C22×C5C2×D3×D411yescharacteristic
687C22×C5C2×D3×D411yescharacteristic
688C22×C5C2×#23711yescharacteristic
689C22×C5#100411yescharacteristic
690C22×C5D3×#4111yescharacteristic
691C22×C5#101011yescharacteristic
692C4×C5—22no—
693C4×C5—34no—
694C4×C5—62no—
695C4×C5—62no—
696Dic5—22no—
697Dic5—41no—
698Dic5—41no—
699Dic5—41no—
700Dic5—62no—
701Dic5—121no—
702Dic5—121no—
703Dic5—121no—
704C24—31no—
705C24C2×D3×D511yescharacteristic
706C24C2×D3×D511yescharacteristic
707#41—632no—
708C2×Q8—34no—
709C2×Q8—62no—
710C2×Q8—62no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—34no—
714C2×D4—34no—
715C2×D4—34no—
716C2×D4—34no—
717C2×D4—62no—
718C2×D4—62no—
719C2×D4D3×Dic514yescomplemented
720C22×C4—31no—
721C22×C4—34no—
722C22×C4—34no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—34no—
726C22×C4—51no—
727C22×C4—51no—
728C22×C4—51no—
729C22×C4—51no—
730C22×C4—62no—
731C22×C4—62no—
732C22×C4—62no—
733C22×C4—62no—
734C22×C4—62no—
735C22×C4—62no—
736C22×C4—102no—
737C22×C4—102no—
738C22×C4—151no—
739C22×C4—151no—
740C22×C4—151no—
741C22×C4—151no—
742C22×C4—201no—
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—102no—
756C22⋊C4—102no—
757C22⋊C4—201no—
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×C3C2×C22⋊Dic514yes—
780C22×C3D5×#4111yescharacteristic
781C22×C3D5×#4111yescharacteristic
782C22×C3#414911yescharacteristic
783C22×C3#415011yescharacteristic
784C22×C3C23×Dic511yescharacteristic
785C22×C3C22×C22⋊D511yescharacteristic
786C22×C3C22×C22⋊D511yescharacteristic
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3C2×C22⋊Dic514yes—
794C3×C4—22no—
795C3×C4—102no—
796C3×C4—201no—
797C3×C4—201no—
798C3×C4—201no—
799Dic3—22no—
800Dic3—22no—
801Dic3—102no—
802Dic3—201no—
803Dic3—201no—
804Dic3—201no—
805Dic3C2×C22⋊Dic514yes—
806C2×C5—24no—
807C2×C5—42no—
808C2×C5—64no—
809C2×C5C2×D3×C22⋊C411yescharacteristic
810C2×C5C4×#23711yescharacteristic
811C2×C5#554611yescharacteristic
812C2×C5#559111yescharacteristic
813C2×C5#561011yescharacteristic
814C2×C5#561111yescharacteristic
815C2×C5#565511yescharacteristic
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—32no—
827C23—32no—
828C23—32no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23C2×D3×Dic512yes—
834C23C2×D3×Dic512yes—
835C23D3×C22⋊D512yes—
836C23D3×C22⋊D512yes—
837C23C22×D3×D511yescharacteristic
838Q8—68no—
839D4—28no—
840D4—316no—
841D4—68no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—32no—
845C2×C4—32no—
846C2×C4—32no—
847C2×C4—32no—
848C2×C4—32no—
849C2×C4—52no—
850C2×C4—68no—
851C2×C4—68no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—68no—
857C2×C4—101no—
858C2×C4—101no—
859C2×C4—101no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—101no—
863C2×C4—101no—
864C2×C4—101no—
865C2×C4—101no—
866C2×C4—101no—
867C2×C4—101no—
868C2×C4—152no—
869C2×C4—204no—
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×D3×Dic512yes—
885C2×C3—24no—
886C2×C3—42no—
887C2×C3#6615811yescharacteristic
888C2×C3#6615811yescharacteristic
889C2×C3#41×Dic511yescharacteristic
890C2×C3#6616111yescharacteristic
891C2×C3#6616311yescharacteristic
892C2×C3#6616311yescharacteristic
893C2×C3C22×C22⋊Dic511yescharacteristic
894D3—24no—
895C5#7467211yescharacteristic, complemented, Sylow
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—34no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—62no—
914C22—62no—
915C22—62no—
916C22D3×C22⋊Dic514yes—
917C22#9202011yescharacteristic
918C22D5×#23711yescharacteristic
919C22#9202411yescharacteristic
920C22#9202611yescharacteristic
921C22C22×D3×Dic511yescharacteristic
922C22C2×D3×C22⋊D511yescharacteristic
923C22C2×D3×C22⋊D511yescharacteristic
924C4—22no—
925C4—34no—
926C4—62no—
927C4—62no—
928C4—102no—
929C4—201no—
930C4—201no—
931C4—201no—
932C4—302no—
933C4—601no—
934C4—601no—
935C4—601no—
936C3#1061581911yescharacteristic, complemented, Sylow
937C2—24no—
938C2—42no—
939C2—64no—
940C2#1175480611yescharacteristic
941C2#1175481011yescharacteristic
942C2Dic5×#23711yescharacteristic
943C2#1175492011yescharacteristic
944C2#1175506611yescharacteristic
945C2#1175506911yescharacteristic
946C2C2×D3×C22⋊Dic511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#237C2
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×#67⋊Dic5C2semidirect
3. C2×Dic5×#67C2semidirect
4. #11751321C2semidirect
5. C3×#65509C2semidirect
6. #11749519C2semidirect
7. #11749519C2semidirect
8. #11749513C2semidirect
9. Dic3×C22⋊Dic5C2semidirect
10. #11749472C2semidirect
11. C2×#90994C2semidirect
12. D3×#3963C2semidirect
13. #11748777C2semidirect
14. #11748692C2semidirect
15. #11748692C2semidirect
25. C2×C5×#237C4semidirect
66. #65509D3semidirect
78. C2×C3×C5×D4C2×C4semidirect
90. C2×C5×#67C2×C4semidirect
97. C22×C5×Dic3C2×C4semidirect
98. C22×C5×Dic3C2×C4semidirect
105. C2×C4×C5×D3C2×C4semidirect
108. C2×C5×Dic6C2×C4semidirect
228. C2×Dic15#41semidirect
230. C5×#67C22⋊C4semidirect
256. C2×C3×Dic5#41semidirect
268. C2×#237Dic5semidirect
314. C2×C5×D4C4×D3semidirect
420. C2×C3×D4C2×Dic5semidirect
432. C2×#67C2×Dic5semidirect
446. C22×Dic3C2×Dic5semidirect
447. C22×Dic3C2×Dic5semidirect
460. C2×C4×D3C2×Dic5semidirect
463. C2×Dic6C2×Dic5semidirect
544. C2×Dic5#237semidirect
635. #67C22⋊Dic5semidirect
719. C2×D4D3×Dic5semidirect
765. C3×C5#2339semidirect
895. C5#74672semidirect
936. C3#10615819semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2372
C2×#67⋊Dic52
C2×Dic5×#672
#117513212
C3×#655092
#117495192
#117495132
Dic3×C22⋊Dic52
#117494722
C2×#909942
D3×#39632
#117487772
#117486922
#106158193
#746725