Finite Group Databasebeta

← #14280246

Subgroups — #14280246

Order 1920.

1216 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×Dic3⋊C4C211yesmaximal, characteristic
2C22×C3×#683C211yesmaximal, characteristic
3C22×#6669C211yesmaximal, characteristic
4C2×#91115C211yesmaximal, characteristic
5C2×#90994C211yesmaximal, characteristic
6C2×#90994C211yesmaximal, characteristic
7C2×#90994C211yesmaximal, characteristic
8#10602361—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C23×Dic15C2211yescharacteristic
11C23×Dic15C2211yescharacteristic
12C23×C5×Dic3C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C23×C3×Dic5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C2×C5×Dic3⋊C4—22no—
17C2×C5×Dic3⋊C4—22no—
18C2×C5×Dic3⋊C4—22no—
19C2×C3×#683—22no—
20C2×C3×#683—22no—
21C2×C3×#683—22no—
22C2×#6669—22no—
23C2×#6669—22no—
24C2×#6669—22no—
25#91115—22no—
26#90994—22no—
27#90994—22no—
28#90994C414yescomplemented
29#71568—51nomaximal, Hall
30C22×C5×C4⋊C4—31no—
31C22×#683—31no—
32C22×#683D311yescharacteristic
33C2×#3963—31no—
34C2×#3963—31no—
35C2×#3963—31no—
36C2×#3963—31no—
37C24×C3×C5C2311yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5D412yes—
45C22×Dic15—21no—
46C22×Dic15—21no—
47C22×Dic15—21no—
48C22×Dic15—21no—
49C22×Dic15—21no—
50C22×Dic15—21no—
51C22×Dic15—21no—
52C22×Dic15—21no—
53C22×Dic15—21no—
54C22×Dic15—21no—
55C22×Dic15C2×C412yes—
56C22×Dic15D412yes—
57C22×Dic15Q812yes—
58C22×Dic15Q812yes—
59C22×C5×Dic3—21no—
60C22×C5×Dic3—21no—
61C22×C5×Dic3—21no—
62C22×C5×Dic3—21no—
63C22×C5×Dic3—21no—
64C22×C5×Dic3—21no—
65C22×C5×Dic3—21no—
66C22×C5×Dic3—21no—
67C22×C5×Dic3—21no—
68C22×C5×Dic3—21no—
69C22×C5×Dic3C2×C412yes—
70C22×C5×Dic3D412yes—
71C22×C5×Dic3D412yes—
72C22×C5×Dic3Q812yes—
73C22×C3×Dic5—21no—
74C22×C3×Dic5—21no—
75C22×C3×Dic5—21no—
76C22×C3×Dic5—21no—
77C22×C3×Dic5—21no—
78C22×C3×Dic5—21no—
79C22×C3×Dic5—21no—
80C22×C3×Dic5—21no—
81C22×C3×Dic5—21no—
82C22×C3×Dic5—21no—
83C22×C3×Dic5C2×C412yes—
84C22×C3×Dic5D412yes—
85C22×C3×Dic5D412yes—
86C22×C3×Dic5Q812yes—
87C5×Dic3⋊C4—28no—
88C3×#683—28no—
89#6669—28no—
90C22×C3×C4⋊C4—51no—
91C22×Dic3⋊C4—51no—
92C22×Dic3⋊C4D511yescharacteristic
93C2×C3⋊#95—51no—
94C2×C3⋊#95—51no—
95C2×C3⋊#95—51no—
96C2×C3⋊#95—51no—
97C23×C4×C5—31no—
98C23×C4×C5—31no—
99C23×C4×C5C2×D311yescharacteristic
100C23×Dic5—31no—
101C23×Dic5—31no—
102C23×Dic5C2×D311yescharacteristic
103C23×Dic5C2×D311yescharacteristic
104C2×C5×C4⋊C4—62no—
105C2×C5×C4⋊C4—62no—
106C2×C5×C4⋊C4—62no—
107C2×#683—22no—
108C2×#683—22no—
109C2×#683—22no—
110C2×#683—62no—
111C2×#683—62no—
112C2×#683—62no—
113#3963—34no—
114#3963—62no—
115#3963—62no—
116#3963—62no—
117#1444—151noSylow
118C23×C3×C5C22×C411yescharacteristic
119C23×C3×C5C2×D411yescharacteristic
120C23×C3×C5C2×D411yescharacteristic
121C23×C3×C5C2×D411yescharacteristic
122C23×C3×C5C2×D411yescharacteristic
123C23×C3×C5C2×D411yescharacteristic
124C23×C3×C5C2×D411yescharacteristic
125C23×C3×C5C2×Q811yescharacteristic
126C23×C3×C5C2×Q811yescharacteristic
127C23×C3×C5C2×Q811yescharacteristic
128C23×C3×C5C2×Q811yescharacteristic
129C23×C3×C5#4111yescharacteristic
130C23×C3×C5#4111yescharacteristic
131C23×C3×C5#4111yescharacteristic
132C23×C3×C5#4111yescharacteristic
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—41no—
137C2×C3×C4×C5—41no—
138C2×C3×C4×C5—41no—
139C2×C3×C4×C5—41no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—22no—
148C2×Dic15—22no—
149C2×Dic15—41no—
150C2×Dic15—41no—
151C2×Dic15—41no—
152C2×Dic15—41no—
153C2×Dic15C4⋊C414yescomplemented
154C2×C5×Dic3—22no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—41no—
164C2×C5×Dic3—41no—
165C2×C5×Dic3—41no—
166C2×C5×Dic3—41no—
167C2×C5×Dic3C4⋊C414yescomplemented
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5—41no—
178C2×C3×Dic5—41no—
179C2×C3×Dic5—41no—
180C2×C3×Dic5—41no—
181C2×C3×Dic5C4⋊C414yescomplemented
182C23×C3×C4—51no—
183C23×C3×C4—51no—
184C23×C3×C4C2×D511yescharacteristic
185C23×Dic3—51no—
186C23×Dic3—51no—
187C23×Dic3C2×D511yescharacteristic
188C23×Dic3C2×D511yescharacteristic
189C2×C3×C4⋊C4—102no—
190C2×C3×C4⋊C4—102no—
191C2×C3×C4⋊C4—102no—
192C2×Dic3⋊C4—22no—
193C2×Dic3⋊C4—22no—
194C2×Dic3⋊C4—22no—
195C2×Dic3⋊C4—102no—
196C2×Dic3⋊C4—102no—
197C2×Dic3⋊C4—102no—
198C3⋊#95—54no—
199C3⋊#95—102no—
200C3⋊#95—102no—
201C3⋊#95—102no—
202C24×C5C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—32no—
210C22×C4×C5—32no—
211C22×C4×C5—32no—
212C22×C4×C5—32no—
213C22×C4×C5—61no—
214C22×C4×C5—61no—
215C22×C4×C5—61no—
216C22×C4×C5—61no—
217C22×C4×C5—61no—
218C22×C4×C5—61no—
219C22×C4×C5—61no—
220C22×C4×C5—61no—
221C22×C4×C5—61no—
222C22×C4×C5—61no—
223C22×C4×C5#6712yes—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—32no—
235C22×Dic5—32no—
236C22×Dic5—32no—
237C22×Dic5—32no—
238C22×Dic5—61no—
239C22×Dic5—61no—
240C22×Dic5—61no—
241C22×Dic5—61no—
242C22×Dic5—61no—
243C22×Dic5—61no—
244C22×Dic5—61no—
245C22×Dic5—61no—
246C22×Dic5—61no—
247C22×Dic5—61no—
248C22×Dic5Dic612yes—
249C22×Dic5C4×D312yes—
250C22×Dic5#6712yes—
251C22×Dic5#6712yes—
252C5×C4⋊C4—68no—
253#683—28no—
254#683—68no—
255C22×C4⋊C4—31no—
256C22×C4⋊C4—51no—
257C22×C4⋊C4—151no—
258C2×#95—151no—
259C2×#95—151no—
260C2×#95—151no—
261C2×#95—151no—
262C22×C3×C5C2×C4⋊C411yescharacteristic
263C22×C3×C5C2×C4⋊C411yescharacteristic
264C22×C3×C5C2×C4⋊C411yescharacteristic
265C22×C3×C5C4×D411yescharacteristic
266C22×C3×C5C4×D411yescharacteristic
267C22×C3×C5C4×D411yescharacteristic
268C22×C3×C5C4×Q811yescharacteristic
269C22×C3×C5#12011yescharacteristic
270C22×C3×C5#12011yescharacteristic
271C22×C3×C5#12011yescharacteristic
272C22×C3×C5#12111yescharacteristic
273C22×C3×C5#12111yescharacteristic
274C22×C3×C5#12111yescharacteristic
275C22×C3×C5C22⋊Q811yescharacteristic
276C22×C3×C5C22⋊Q811yescharacteristic
277C22×C3×C5C22⋊Q811yescharacteristic
278C22×C3×C5C22⋊Q811yescharacteristic
279C22×C3×C5C22⋊Q811yescharacteristic
280C22×C3×C5C22⋊Q811yescharacteristic
281C22×C3×C5C22⋊Q811yescharacteristic
282C22×C3×C5C22⋊Q811yescharacteristic
283C22×C3×C5C22⋊Q811yescharacteristic
284C22×C3×C5#12311yescharacteristic
285C22×C3×C5#12311yescharacteristic
286C22×C3×C5#12311yescharacteristic
287C22×C3×C5#12511yescharacteristic
288C22×C3×C5#12511yescharacteristic
289C22×C3×C5#12511yescharacteristic
290C22×C3×C5#12711yescharacteristic
291C22×C3×C5C4⋊Q811yescharacteristic
292C22×C3×C5C4⋊Q811yescharacteristic
293C22×C3×C5C4⋊Q811yescharacteristic
294C22×C3×C5C4⋊Q811yescharacteristic
295C22×C3×C5C4⋊Q811yescharacteristic
296C22×C3×C5C4⋊Q811yescharacteristic
297C3×C4×C5—42no—
298Dic15—24no—
299Dic15—42no—
300C3×Dic5—24no—
301C3×Dic5—42no—
302C5×Dic3—24no—
303C5×Dic3—42no—
304C24×C3C22×D511yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—52no—
312C22×C3×C4—52no—
313C22×C3×C4—52no—
314C22×C3×C4—52no—
315C22×C3×C4—101no—
316C22×C3×C4—101no—
317C22×C3×C4—101no—
318C22×C3×C4—101no—
319C22×C3×C4—101no—
320C22×C3×C4—101no—
321C22×C3×C4—101no—
322C22×C3×C4—101no—
323C22×C3×C4—101no—
324C22×C3×C4—101no—
325C22×C3×C4C22⋊D512yes—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—52no—
337C22×Dic3—52no—
338C22×Dic3—52no—
339C22×Dic3—52no—
340C22×Dic3—101no—
341C22×Dic3—101no—
342C22×Dic3—101no—
343C22×Dic3—101no—
344C22×Dic3—101no—
345C22×Dic3—101no—
346C22×Dic3—101no—
347C22×Dic3—101no—
348C22×Dic3—101no—
349C22×Dic3—101no—
350C22×Dic3Dic1012yes—
351C22×Dic3C4×D512yes—
352C22×Dic3C22⋊D512yes—
353C22×Dic3C22⋊D512yes—
354C3×C4⋊C4—108no—
355Dic3⋊C4—28no—
356Dic3⋊C4—108no—
357C23×C5C2×Dic611yescharacteristic
358C23×C5C2×C4×D311yescharacteristic
359C23×C5#23511yescharacteristic
360C23×C5#23511yescharacteristic
361C23×C5D3×D411yescharacteristic
362C23×C5D3×D411yescharacteristic
363C23×C5D3×D411yescharacteristic
364C23×C5#23711yescharacteristic
365C23×C5D3×Q811yescharacteristic
366C23×C5D3×Q811yescharacteristic
367C23×C5D3×Q811yescharacteristic
368C23×C5#23911yescharacteristic
369C23×C5C2×#6711yescharacteristic
370C23×C5C2×#6711yescharacteristic
371C23×C5C2×#6711yescharacteristic
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—34no—
376C2×C4×C5—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—62no—
381C2×C4×C5—62no—
382C2×C4×C5—62no—
383C2×C4×C5—62no—
384C2×C4×C5—62no—
385C2×C4×C5—62no—
386C2×C4×C5—62no—
387C2×C4×C5—62no—
388C2×C4×C5—62no—
389C2×C4×C5—121no—
390C2×C4×C5—121no—
391C2×C4×C5—121no—
392C2×C4×C5—121no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—34no—
403C2×Dic5—41no—
404C2×Dic5—41no—
405C2×Dic5—41no—
406C2×Dic5—41no—
407C2×Dic5—62no—
408C2×Dic5—62no—
409C2×Dic5—62no—
410C2×Dic5—62no—
411C2×Dic5—62no—
412C2×Dic5—62no—
413C2×Dic5—62no—
414C2×Dic5—62no—
415C2×Dic5—62no—
416C2×Dic5—121no—
417C2×Dic5—121no—
418C2×Dic5—121no—
419C2×Dic5—121no—
420C2×Dic5Dic3⋊C414yescomplemented
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—151no—
426C23×C4—151no—
427C23×C4D3×D511yescharacteristic
428C2×C4⋊C4—62no—
429C2×C4⋊C4—62no—
430C2×C4⋊C4—62no—
431C2×C4⋊C4—102no—
432C2×C4⋊C4—102no—
433C2×C4⋊C4—102no—
434C2×C4⋊C4—302no—
435C2×C4⋊C4—302no—
436C2×C4⋊C4—302no—
437#95—154no—
438#95—302no—
439#95—302no—
440#95—302no—
441C2×C3×C5#38411yescharacteristic
442C2×C3×C5#38511yescharacteristic
443C2×C3×C5#38511yescharacteristic
444C2×C3×C5#38511yescharacteristic
445C2×C3×C5#38911yescharacteristic
446C2×C3×C5#38911yescharacteristic
447C2×C3×C5#38911yescharacteristic
448C2×C3×C5#39211yescharacteristic
449C2×C3×C5#39511yescharacteristic
450C2×C3×C5#39511yescharacteristic
451C2×C3×C5#39511yescharacteristic
452C2×C3×C5#39811yescharacteristic
453C2×C3×C5#39811yescharacteristic
454C2×C3×C5#39811yescharacteristic
455C2×C3×C5#39911yescharacteristic
456C23×C3C2×Dic1011yescharacteristic
457C23×C3C2×C4×D511yescharacteristic
458C23×C3#70911yescharacteristic
459C23×C3#70911yescharacteristic
460C23×C3D4×D511yescharacteristic
461C23×C3D4×D511yescharacteristic
462C23×C3D4×D511yescharacteristic
463C23×C3#71111yescharacteristic
464C23×C3Q8×D511yescharacteristic
465C23×C3Q8×D511yescharacteristic
466C23×C3Q8×D511yescharacteristic
467C23×C3#71311yescharacteristic
468C23×C3C2×C22⋊D511yescharacteristic
469C23×C3C2×C22⋊D511yescharacteristic
470C23×C3C2×C22⋊D511yescharacteristic
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—54no—
479C2×C3×C4—102no—
480C2×C3×C4—102no—
481C2×C3×C4—102no—
482C2×C3×C4—102no—
483C2×C3×C4—102no—
484C2×C3×C4—102no—
485C2×C3×C4—102no—
486C2×C3×C4—102no—
487C2×C3×C4—102no—
488C2×C3×C4—201no—
489C2×C3×C4—201no—
490C2×C3×C4—201no—
491C2×C3×C4—201no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—54no—
506C2×Dic3—102no—
507C2×Dic3—102no—
508C2×Dic3—102no—
509C2×Dic3—102no—
510C2×Dic3—102no—
511C2×Dic3—102no—
512C2×Dic3—102no—
513C2×Dic3—102no—
514C2×Dic3—102no—
515C2×Dic3—201no—
516C2×Dic3—201no—
517C2×Dic3—201no—
518C2×Dic3—201no—
519C2×Dic3#68314yescomplemented
520C22×C5#88711yescharacteristic
521C22×C5#88811yescharacteristic
522C22×C5#88811yescharacteristic
523C22×C5#88811yescharacteristic
524C22×C5#88911yescharacteristic
525C22×C5#88911yescharacteristic
526C22×C5#89011yescharacteristic
527C22×C5D3×C4⋊C411yescharacteristic
528C22×C5D3×C4⋊C411yescharacteristic
529C22×C5#89311yescharacteristic
530C22×C5#89411yescharacteristic
531C22×C5#89411yescharacteristic
532C22×C5#89611yescharacteristic
533C22×C5#89611yescharacteristic
534C22×C5#89611yescharacteristic
535C22×C5#89611yescharacteristic
536C22×C5C2×Dic3⋊C411yescharacteristic
537C22×C5#92411yescharacteristic
538C22×C5#92411yescharacteristic
539C22×C5C4×#6711yescharacteristic
540C22×C5C4×#6711yescharacteristic
541C22×C5#92911yescharacteristic
542C22×C5#93711yescharacteristic
543C22×C5#93711yescharacteristic
544C22×C5#93811yescharacteristic
545C22×C5#93911yescharacteristic
546C22×C5#93911yescharacteristic
547C22×C5#94011yescharacteristic
548C22×C5#94411yescharacteristic
549C22×C5#94411yescharacteristic
550C22×C5#94411yescharacteristic
551C22×C5#94611yescharacteristic
552C22×C5#94611yescharacteristic
553C22×C5#94611yescharacteristic
554C22×C5#95311yescharacteristic
555C4×C5—42no—
556C4×C5—64no—
557C4×C5—122no—
558Dic5—24no—
559Dic5—42no—
560Dic5—64no—
561Dic5—122no—
562C24C2×D3×D511yescharacteristic
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—32no—
572C22×C4—32no—
573C22×C4—52no—
574C22×C4—52no—
575C22×C4—52no—
576C22×C4—52no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—152no—
598C22×C4—152no—
599C22×C4—152no—
600C22×C4—152no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604C22×C4—301no—
605C22×C4—301no—
606C22×C4—301no—
607C22×C4—301no—
608C22×C4—301no—
609C22×C4—301no—
610C22×C4—301no—
611C22×C4#120112yes—
612C4⋊C4—68no—
613C4⋊C4—108no—
614C4⋊C4—308no—
615C3×C5#144411yescharacteristic, complemented, Hall
616C22×C3#403311yescharacteristic
617C22×C3#403411yescharacteristic
618C22×C3#403411yescharacteristic
619C22×C3#403411yescharacteristic
620C22×C3#403511yescharacteristic
621C22×C3#403511yescharacteristic
622C22×C3#403611yescharacteristic
623C22×C3D5×C4⋊C411yescharacteristic
624C22×C3D5×C4⋊C411yescharacteristic
625C22×C3#403911yescharacteristic
626C22×C3#404011yescharacteristic
627C22×C3#404011yescharacteristic
628C22×C3#404211yescharacteristic
629C22×C3#404211yescharacteristic
630C22×C3#404211yescharacteristic
631C22×C3#404211yescharacteristic
632C22×C3C2×#68311yescharacteristic
633C22×C3#407011yescharacteristic
634C22×C3#407011yescharacteristic
635C22×C3C4×C22⋊D511yescharacteristic
636C22×C3C4×C22⋊D511yescharacteristic
637C22×C3#407511yescharacteristic
638C22×C3#408311yescharacteristic
639C22×C3#408311yescharacteristic
640C22×C3#408411yescharacteristic
641C22×C3#408511yescharacteristic
642C22×C3#408511yescharacteristic
643C22×C3#408611yescharacteristic
644C22×C3#409011yescharacteristic
645C22×C3#409011yescharacteristic
646C22×C3#409011yescharacteristic
647C22×C3#409211yescharacteristic
648C22×C3#409211yescharacteristic
649C22×C3#409211yescharacteristic
650C22×C3#409911yescharacteristic
651C3×C4—42no—
652C3×C4—104no—
653C3×C4—202no—
654Dic3—24no—
655Dic3—42no—
656Dic3—104no—
657Dic3—202no—
658C2×C5#497211yescharacteristic
659C2×C5#497511yescharacteristic
660C2×C5#497611yescharacteristic
661C2×C5#497611yescharacteristic
662C2×C5#497911yescharacteristic
663C2×C5#497911yescharacteristic
664C2×C5#498211yescharacteristic
665C2×C5#498211yescharacteristic
666C2×C5#498311yescharacteristic
667C2×C5#498911yescharacteristic
668C2×C5#498911yescharacteristic
669C2×C5#499311yescharacteristic
670C2×C5#521011yescharacteristic
671C2×C5#522311yescharacteristic
672C2×C5#523011yescharacteristic
673C23D5×Dic611yescharacteristic
674C23D3×Dic1011yescharacteristic
675C23#676911yescharacteristic
676C23D15⋊Q811yescharacteristic
677C23D15⋊Q811yescharacteristic
678C23#677111yescharacteristic
679C23#677311yescharacteristic
680C23C4×D3×D511yescharacteristic
681C23#678011yescharacteristic
682C23C2×#120111yescharacteristic
683C23D5×#6711yescharacteristic
684C23D5×#6711yescharacteristic
685C23D3×C22⋊D511yescharacteristic
686C23D3×C22⋊D511yescharacteristic
687C23#679011yescharacteristic
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—34no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—54no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—121no—
719C2×C4—154no—
720C2×C4—201no—
721C2×C4—201no—
722C2×C4—201no—
723C2×C4—201no—
724C2×C4—302no—
725C2×C4—302no—
726C2×C4—302no—
727C2×C4—302no—
728C2×C4—302no—
729C2×C4—302no—
730C2×C4—302no—
731C2×C4—302no—
732C2×C4—302no—
733C2×C4—601no—
734C2×C4—601no—
735C2×C4—601no—
736C2×C4—601no—
737C2×C3#6526111yescharacteristic
738C2×C3#6526111yescharacteristic
739C2×C3#6526211yescharacteristic
740C2×C3#6526511yescharacteristic
741C2×C3#6526811yescharacteristic
742C2×C3#6526811yescharacteristic
743C2×C3#6526911yescharacteristic
744C2×C3#6527311yescharacteristic
745C2×C3#6527311yescharacteristic
746C2×C3#6527811yescharacteristic
747C2×C3#6527811yescharacteristic
748C2×C3#6528111yescharacteristic
749C2×C3#6549911yescharacteristic
750C2×C3#6551211yescharacteristic
751C2×C3#6551811yescharacteristic
752C5#7156811yescharacteristic, complemented, Sylow
753C22#9132511yescharacteristic
754C22#9132711yescharacteristic
755C22#9132711yescharacteristic
756C22#9132811yescharacteristic
757C22#9132911yescharacteristic
758C22#9132911yescharacteristic
759C22#9133411yescharacteristic
760C22#9134311yescharacteristic
761C22#9134811yescharacteristic
762C22#9134911yescharacteristic
763C22#9135111yescharacteristic
764C22#9135211yescharacteristic
765C22#9135911yescharacteristic
766C22#9136911yescharacteristic
767C22#9137711yescharacteristic
768C22#9138211yescharacteristic
769C22#9138511yescharacteristic
770C22D5×Dic3⋊C411yescharacteristic
771C22D3×#68311yescharacteristic
772C22#9140411yescharacteristic
773C22#9141111yescharacteristic
774C22#9141111yescharacteristic
775C22#9142411yescharacteristic
776C22#9142411yescharacteristic
777C22#9143311yescharacteristic
778C22C4×#120111yescharacteristic
779C22#9144411yescharacteristic
780C22#9144611yescharacteristic
781C22#9154911yescharacteristic
782C22#9156311yescharacteristic
783C22#9156511yescharacteristic
784C22#9156711yescharacteristic
785C22#9156811yescharacteristic
786C22#9157111yescharacteristic
787C22#9157711yescharacteristic
788C4—42no—
789C4—64no—
790C4—104no—
791C4—122no—
792C4—202no—
793C4—304no—
794C4—602no—
795C3#1060236111yescharacteristic, complemented, Sylow
796C2#1174856711yescharacteristic
797C2#1174856811yescharacteristic
798C2#1174857211yescharacteristic
799C2#1174857411yescharacteristic
800C2#1174857511yescharacteristic
801C2#1174859411yescharacteristic
802C2#1174862911yescharacteristic
803C2#1174864111yescharacteristic
804C2#1174866411yescharacteristic
805C2#1174870311yescharacteristic
806C2#1174871611yescharacteristic
807C2#1174881811yescharacteristic
808C2#1174884511yescharacteristic
809C2#1174889411yescharacteristic
810C2#1174952111yescharacteristic
subgroupG/H
center, FrattiniC24C2×D3×D5
commutatorC23×C3×C5C22×C4
FittingC23×C3×C4×C5C22
socle, prime radical, cosocleC24×C3×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1444
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
28. #90994C4semidirect
153. C2×Dic15C4⋊C4semidirect
167. C2×C5×Dic3C4⋊C4semidirect
181. C2×C3×Dic5C4⋊C4semidirect
420. C2×Dic5Dic3⋊C4semidirect
519. C2×Dic3#683semidirect
615. C3×C5#1444semidirect
752. C5#71568semidirect
795. C3#10602361semidirect

Maximal subgroups

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

subgroupindex
C22×C5×Dic3⋊C42
C22×C3×#6832
C22×#66692
C2×#911152
C2×#909942
#106023613
#715685