Finite Group Databasebeta

← #14280298

Subgroups — #14280298

Order 1920.

1472 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1204C211yesmaximal, characteristic
2C2×#91115C211yesmaximal, characteristic
3C2×C5×C3⋊#95C211yesmaximal, characteristic
4C2×C3×#3963C211yesmaximal, characteristic
5C2×#90994C211yesmaximal, characteristic
6C2×#90994C211yesmaximal, characteristic
7C2×#90994C211yesmaximal, characteristic
8#10600217—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C23×Dic15C2211yescharacteristic
11C23×Dic15C2211yescharacteristic
12C23×C5×Dic3C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C23×C3×Dic5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C22×#1204—22no—
17C22×#1204—22no—
18C22×#1204—22no—
19C22×#1204—22no—
20C22×#1204—22no—
21C22×#1204—22no—
22C22×#1204C414yescomplemented
23#91115—22no—
24C5×C3⋊#95—22no—
25C3×#3963—22no—
26#90994—22no—
27#90994—22no—
28#90994—22no—
29#69424—51nomaximal, Hall
30C23×Dic10—31no—
31C2×C5×#95—31no—
32C2×#3963—31no—
33C2×#3963—31no—
34C2×#3963—31no—
35C2×#3963—31no—
36C2×#3963D311yescharacteristic
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×C5Q812yescomplemented
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×Dic15D412yes—
58C22×Dic15Q812yescomplemented
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×Dic3Q812yescomplemented
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×Dic5Q812yescomplemented
87C2×#1204—28no—
88C2×#1204—28no—
89C2×#1204—28no—
90C2×#1204—28no—
91C2×#1204—28no—
92C2×#1204—28no—
93C2×#1204—28no—
94C23×Dic6—51no—
95C2×C3×#95—51no—
96C2×C3⋊#95—51no—
97C2×C3⋊#95—51no—
98C2×C3⋊#95—51no—
99C2×C3⋊#95—51no—
100C2×C3⋊#95D511yescharacteristic
101C23×C4×C5—31no—
102C23×C4×C5—31no—
103C23×C4×C5C2×D311yescharacteristic
104C23×Dic5—31no—
105C23×Dic5—31no—
106C23×Dic5C2×D311yescharacteristic
107C23×Dic5C2×D311yescharacteristic
108C22×Dic10—34no—
109C22×Dic10—62no—
110C22×Dic10—62no—
111C22×Dic10—62no—
112C22×Dic10—62no—
113C22×Dic10—62no—
114C22×Dic10—62no—
115C5×#95—62no—
116#3963—22no—
117#3963—62no—
118#3963—62no—
119#3963—62no—
120#3963—62no—
121#1446—151noSylow
122C23×C3×C5C22×C411yescharacteristic
123C23×C3×C5C2×D411yescharacteristic
124C23×C3×C5C2×D411yescharacteristic
125C23×C3×C5C2×D411yescharacteristic
126C23×C3×C5C2×D411yescharacteristic
127C23×C3×C5C2×D411yescharacteristic
128C23×C3×C5C2×D411yescharacteristic
129C23×C3×C5C2×Q811yescharacteristic
130C23×C3×C5C2×Q811yescharacteristic
131C23×C3×C5C2×Q811yescharacteristic
132C23×C3×C5C2×Q811yescharacteristic
133C23×C3×C5#4111yescharacteristic
134C23×C3×C5#4111yescharacteristic
135C23×C3×C5#4111yescharacteristic
136C23×C3×C5#4111yescharacteristic
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—41no—
141C2×C3×C4×C5—41no—
142C2×C3×C4×C5—41no—
143C2×C3×C4×C5—41no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—22no—
148C2×Dic15—22no—
149C2×Dic15—22no—
150C2×Dic15—22no—
151C2×Dic15—22no—
152C2×Dic15—22no—
153C2×Dic15—41no—
154C2×Dic15—41no—
155C2×Dic15—41no—
156C2×Dic15—41no—
157C2×Dic15C22⋊C414yes—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—41no—
168C2×C5×Dic3—41no—
169C2×C5×Dic3—41no—
170C2×C5×Dic3—41no—
171C2×C5×Dic3C22⋊C414yes—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5—22no—
178C2×C3×Dic5—22no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5—22no—
181C2×C3×Dic5—41no—
182C2×C3×Dic5—41no—
183C2×C3×Dic5—41no—
184C2×C3×Dic5—41no—
185C2×C3×Dic5C22⋊C414yes—
186#1204—232no—
187C23×C3×C4—51no—
188C23×C3×C4—51no—
189C23×C3×C4C2×D511yescharacteristic
190C23×Dic3—51no—
191C23×Dic3—51no—
192C23×Dic3C2×D511yescharacteristic
193C23×Dic3C2×D511yescharacteristic
194C22×Dic6—54no—
195C22×Dic6—102no—
196C22×Dic6—102no—
197C22×Dic6—102no—
198C22×Dic6—102no—
199C22×Dic6—102no—
200C22×Dic6—102no—
201C3×#95—102no—
202C3⋊#95—22no—
203C3⋊#95—102no—
204C3⋊#95—102no—
205C3⋊#95—102no—
206C3⋊#95—102no—
207C24×C5C22×D311yescharacteristic
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—32no—
215C22×C4×C5—32no—
216C22×C4×C5—32no—
217C22×C4×C5—32no—
218C22×C4×C5—61no—
219C22×C4×C5—61no—
220C22×C4×C5—61no—
221C22×C4×C5—61no—
222C22×C4×C5—61no—
223C22×C4×C5—61no—
224C22×C4×C5—61no—
225C22×C4×C5—61no—
226C22×C4×C5—61no—
227C22×C4×C5—61no—
228C22×C4×C5Dic612yescomplemented
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—32no—
240C22×Dic5—32no—
241C22×Dic5—32no—
242C22×Dic5—32no—
243C22×Dic5—61no—
244C22×Dic5—61no—
245C22×Dic5—61no—
246C22×Dic5—61no—
247C22×Dic5—61no—
248C22×Dic5—61no—
249C22×Dic5—61no—
250C22×Dic5—61no—
251C22×Dic5—61no—
252C22×Dic5—61no—
253C22×Dic5Dic612yescomplemented
254C22×Dic5C4×D312yes—
255C22×Dic5D1212yes—
256C22×Dic5#6712yes—
257C2×Dic10—68no—
258C2×Dic10—68no—
259C2×Dic10—68no—
260C2×Dic10—68no—
261C2×Dic10—68no—
262C2×Dic10—68no—
263C2×Dic10—68no—
264C23×Q8—151no—
265C2×#95—31no—
266C2×#95—51no—
267C2×#95—151no—
268C2×#95—151no—
269C2×#95—151no—
270C2×#95—151no—
271C22×C3×C5C2×C22⋊C411yescharacteristic
272C22×C3×C5C2×C22⋊C411yescharacteristic
273C22×C3×C5C2×C22⋊C411yescharacteristic
274C22×C3×C5C4×Q811yescharacteristic
275C22×C3×C5C4×Q811yescharacteristic
276C22×C3×C5C4×Q811yescharacteristic
277C22×C3×C5C4×Q811yescharacteristic
278C22×C3×C5#12011yescharacteristic
279C22×C3×C5#12011yescharacteristic
280C22×C3×C5#12011yescharacteristic
281C22×C3×C5#12011yescharacteristic
282C22×C3×C5C22⋊Q811yescharacteristic
283C22×C3×C5C22⋊Q811yescharacteristic
284C22×C3×C5C22⋊Q811yescharacteristic
285C22×C3×C5C22⋊Q811yescharacteristic
286C22×C3×C5C22⋊Q811yescharacteristic
287C22×C3×C5C22⋊Q811yescharacteristic
288C22×C3×C5C22⋊Q811yescharacteristic
289C22×C3×C5C22⋊Q811yescharacteristic
290C22×C3×C5C22⋊Q811yescharacteristic
291C22×C3×C5C22⋊Q811yescharacteristic
292C22×C3×C5C22⋊Q811yescharacteristic
293C22×C3×C5C22⋊Q811yescharacteristic
294C22×C3×C5#12411yescharacteristic
295C22×C3×C5#12411yescharacteristic
296C22×C3×C5#12411yescharacteristic
297C22×C3×C5#12411yescharacteristic
298C22×C3×C5#12411yescharacteristic
299C22×C3×C5#12411yescharacteristic
300C22×C3×C5C4⋊Q811yescharacteristic
301C22×C3×C5C4⋊Q811yescharacteristic
302C22×C3×C5C4⋊Q811yescharacteristic
303C22×C3×C5C4⋊Q811yescharacteristic
304C22×C3×C5C4⋊Q811yescharacteristic
305C22×C3×C5C4⋊Q811yescharacteristic
306C3×C4×C5—42no—
307Dic15—24no—
308Dic15—42no—
309C3×Dic5—24no—
310C3×Dic5—42no—
311C5×Dic3—24no—
312C5×Dic3—42no—
313C24×C3C22×D511yescharacteristic
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—52no—
321C22×C3×C4—52no—
322C22×C3×C4—52no—
323C22×C3×C4—52no—
324C22×C3×C4—101no—
325C22×C3×C4—101no—
326C22×C3×C4—101no—
327C22×C3×C4—101no—
328C22×C3×C4—101no—
329C22×C3×C4—101no—
330C22×C3×C4—101no—
331C22×C3×C4—101no—
332C22×C3×C4—101no—
333C22×C3×C4—101no—
334C22×C3×C4Dic1012yescomplemented
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—52no—
346C22×Dic3—52no—
347C22×Dic3—52no—
348C22×Dic3—52no—
349C22×Dic3—101no—
350C22×Dic3—101no—
351C22×Dic3—101no—
352C22×Dic3—101no—
353C22×Dic3—101no—
354C22×Dic3—101no—
355C22×Dic3—101no—
356C22×Dic3—101no—
357C22×Dic3—101no—
358C22×Dic3—101no—
359C22×Dic3Dic1012yescomplemented
360C22×Dic3C4×D512yes—
361C22×Dic3D2012yes—
362C22×Dic3C22⋊D512yes—
363C2×Dic6—108no—
364C2×Dic6—108no—
365C2×Dic6—108no—
366C2×Dic6—108no—
367C2×Dic6—108no—
368C2×Dic6—108no—
369C2×Dic6—108no—
370C23×C5C2×Dic611yescharacteristic
371C23×C5C2×Dic611yescharacteristic
372C23×C5C2×C4×D311yescharacteristic
373C23×C5C2×D1211yescharacteristic
374C23×C5#23511yescharacteristic
375C23×C5#23511yescharacteristic
376C23×C5D3×D411yescharacteristic
377C23×C5D3×D411yescharacteristic
378C23×C5D3×D411yescharacteristic
379C23×C5D3×D411yescharacteristic
380C23×C5#23711yescharacteristic
381C23×C5#23711yescharacteristic
382C23×C5D3×Q811yescharacteristic
383C23×C5D3×Q811yescharacteristic
384C23×C5C2×#6711yescharacteristic
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—34no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—62no—
394C2×C4×C5—62no—
395C2×C4×C5—62no—
396C2×C4×C5—62no—
397C2×C4×C5—62no—
398C2×C4×C5—62no—
399C2×C4×C5—62no—
400C2×C4×C5—62no—
401C2×C4×C5—62no—
402C2×C4×C5—121no—
403C2×C4×C5—121no—
404C2×C4×C5—121no—
405C2×C4×C5—121no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—34no—
416C2×Dic5—41no—
417C2×Dic5—41no—
418C2×Dic5—41no—
419C2×Dic5—41no—
420C2×Dic5—62no—
421C2×Dic5—62no—
422C2×Dic5—62no—
423C2×Dic5—62no—
424C2×Dic5—62no—
425C2×Dic5—62no—
426C2×Dic5—62no—
427C2×Dic5—62no—
428C2×Dic5—62no—
429C2×Dic5—121no—
430C2×Dic5—121no—
431C2×Dic5—121no—
432C2×Dic5—121no—
433C2×Dic5(C2×D3)⋊C414yes—
434Dic10—632no—
435C22×Q8—154no—
436C22×Q8—302no—
437C22×Q8—302no—
438C22×Q8—302no—
439C22×Q8—302no—
440C22×Q8—302no—
441C22×Q8—302no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—51no—
445C23×C4—51no—
446C23×C4—151no—
447C23×C4—151no—
448C23×C4D3×D511yescharacteristic
449#95—62no—
450#95—102no—
451#95—302no—
452#95—302no—
453#95—302no—
454#95—302no—
455C2×C3×C5#37911yescharacteristic
456C2×C3×C5#39111yescharacteristic
457C2×C3×C5#39111yescharacteristic
458C2×C3×C5#39111yescharacteristic
459C2×C3×C5#39111yescharacteristic
460C2×C3×C5#39111yescharacteristic
461C2×C3×C5#39111yescharacteristic
462C2×C3×C5#39311yescharacteristic
463C2×C3×C5#39311yescharacteristic
464C2×C3×C5#39311yescharacteristic
465C2×C3×C5#39311yescharacteristic
466C2×C3×C5#39511yescharacteristic
467C2×C3×C5#39511yescharacteristic
468C2×C3×C5#39511yescharacteristic
469C2×C3×C5#39511yescharacteristic
470C23×C3C2×Dic1011yescharacteristic
471C23×C3C2×Dic1011yescharacteristic
472C23×C3C2×C4×D511yescharacteristic
473C23×C3C2×D2011yescharacteristic
474C23×C3#70911yescharacteristic
475C23×C3#70911yescharacteristic
476C23×C3D4×D511yescharacteristic
477C23×C3D4×D511yescharacteristic
478C23×C3D4×D511yescharacteristic
479C23×C3D4×D511yescharacteristic
480C23×C3#71111yescharacteristic
481C23×C3#71111yescharacteristic
482C23×C3Q8×D511yescharacteristic
483C23×C3Q8×D511yescharacteristic
484C23×C3C2×C22⋊D511yescharacteristic
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—54no—
493C2×C3×C4—102no—
494C2×C3×C4—102no—
495C2×C3×C4—102no—
496C2×C3×C4—102no—
497C2×C3×C4—102no—
498C2×C3×C4—102no—
499C2×C3×C4—102no—
500C2×C3×C4—102no—
501C2×C3×C4—102no—
502C2×C3×C4—201no—
503C2×C3×C4—201no—
504C2×C3×C4—201no—
505C2×C3×C4—201no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3—41no—
519C2×Dic3—54no—
520C2×Dic3—102no—
521C2×Dic3—102no—
522C2×Dic3—102no—
523C2×Dic3—102no—
524C2×Dic3—102no—
525C2×Dic3—102no—
526C2×Dic3—102no—
527C2×Dic3—102no—
528C2×Dic3—102no—
529C2×Dic3—201no—
530C2×Dic3—201no—
531C2×Dic3—201no—
532C2×Dic3—201no—
533C2×Dic3#68514yes—
534Dic6—1032no—
535C22×C5C4×Dic611yescharacteristic
536C22×C5C4×Dic611yescharacteristic
537C22×C5#86911yescharacteristic
538C22×C5#87511yescharacteristic
539C22×C5#87811yescharacteristic
540C22×C5#87811yescharacteristic
541C22×C5#87811yescharacteristic
542C22×C5#87811yescharacteristic
543C22×C5D3×C22⋊C411yescharacteristic
544C22×C5D3×C22⋊C411yescharacteristic
545C22×C5#88211yescharacteristic
546C22×C5#88211yescharacteristic
547C22×C5#88511yescharacteristic
548C22×C5#88511yescharacteristic
549C22×C5#88511yescharacteristic
550C22×C5#88511yescharacteristic
551C22×C5#88711yescharacteristic
552C22×C5#88711yescharacteristic
553C22×C5#88811yescharacteristic
554C22×C5#88811yescharacteristic
555C22×C5#88811yescharacteristic
556C22×C5#88811yescharacteristic
557C22×C5#89611yescharacteristic
558C22×C5#89611yescharacteristic
559C22×C5#89611yescharacteristic
560C22×C5#89611yescharacteristic
561C22×C5#89711yescharacteristic
562C22×C5#89711yescharacteristic
563C22×C5#92411yescharacteristic
564C22×C5#92411yescharacteristic
565C22×C5C2×(C2×D3)⋊C411yescharacteristic
566C22×C5#93611yescharacteristic
567C22×C5#93711yescharacteristic
568C22×C5#93711yescharacteristic
569C22×C5#94411yescharacteristic
570C4×C5—42no—
571C4×C5—64no—
572C4×C5—122no—
573Dic5—24no—
574Dic5—42no—
575Dic5—64no—
576Dic5—122no—
577C24C2×D3×D511yescharacteristic
578C2×Q8—308no—
579C2×Q8—308no—
580C2×Q8—308no—
581C2×Q8—308no—
582C2×Q8—308no—
583C2×Q8—308no—
584C2×Q8—308no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—52no—
596C22×C4—52no—
597C22×C4—52no—
598C22×C4—52no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—101no—
610C22×C4—101no—
611C22×C4—101no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—101no—
615C22×C4—101no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—101no—
619C22×C4—152no—
620C22×C4—152no—
621C22×C4—152no—
622C22×C4—152no—
623C22×C4—301no—
624C22×C4—301no—
625C22×C4—301no—
626C22×C4—301no—
627C22×C4—301no—
628C22×C4—301no—
629C22×C4—301no—
630C22×C4—301no—
631C22×C4—301no—
632C22×C4—301no—
633C22×C4#120412yescomplemented
634C3×C5#144611yescharacteristic, complemented, Hall
635C22×C3C4×Dic1011yescharacteristic
636C22×C3C4×Dic1011yescharacteristic
637C22×C3#401511yescharacteristic
638C22×C3#402111yescharacteristic
639C22×C3#402411yescharacteristic
640C22×C3#402411yescharacteristic
641C22×C3#402411yescharacteristic
642C22×C3#402411yescharacteristic
643C22×C3D5×C22⋊C411yescharacteristic
644C22×C3D5×C22⋊C411yescharacteristic
645C22×C3#402811yescharacteristic
646C22×C3#402811yescharacteristic
647C22×C3#403111yescharacteristic
648C22×C3#403111yescharacteristic
649C22×C3#403111yescharacteristic
650C22×C3#403111yescharacteristic
651C22×C3#403311yescharacteristic
652C22×C3#403311yescharacteristic
653C22×C3#403411yescharacteristic
654C22×C3#403411yescharacteristic
655C22×C3#403411yescharacteristic
656C22×C3#403411yescharacteristic
657C22×C3#404211yescharacteristic
658C22×C3#404211yescharacteristic
659C22×C3#404211yescharacteristic
660C22×C3#404211yescharacteristic
661C22×C3#404311yescharacteristic
662C22×C3#404311yescharacteristic
663C22×C3#407011yescharacteristic
664C22×C3#407011yescharacteristic
665C22×C3C2×#68511yescharacteristic
666C22×C3#408211yescharacteristic
667C22×C3#408311yescharacteristic
668C22×C3#408311yescharacteristic
669C22×C3#409011yescharacteristic
670C3×C4—42no—
671C3×C4—104no—
672C3×C4—202no—
673Dic3—24no—
674Dic3—42no—
675Dic3—104no—
676Dic3—202no—
677C2×C5#464611yescharacteristic
678C2×C5#464611yescharacteristic
679C2×C5#464611yescharacteristic
680C2×C5#464611yescharacteristic
681C2×C5#465611yescharacteristic
682C2×C5#465611yescharacteristic
683C2×C5#467311yescharacteristic
684C2×C5#467311yescharacteristic
685C2×C5#492911yescharacteristic
686C2×C5#494711yescharacteristic
687C2×C5#494711yescharacteristic
688C2×C5#495511yescharacteristic
689C2×C5#497311yescharacteristic
690C2×C5#497911yescharacteristic
691C2×C5#497911yescharacteristic
692C23D5×Dic611yescharacteristic
693C23D3×Dic1011yescharacteristic
694C23D15⋊Q811yescharacteristic
695C23#677111yescharacteristic
696C23C4×D3×D511yescharacteristic
697C23D5×D1211yescharacteristic
698C23D3×D2011yescharacteristic
699C23#677711yescharacteristic
700C23#677911yescharacteristic
701C23#678011yescharacteristic
702C23#678211yescharacteristic
703C23C2×#120411yescharacteristic
704C23D5×#6711yescharacteristic
705C23D3×C22⋊D511yescharacteristic
706C23#679011yescharacteristic
707Q8—3032no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—34no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—54no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—154no—
740C2×C4—201no—
741C2×C4—201no—
742C2×C4—201no—
743C2×C4—201no—
744C2×C4—302no—
745C2×C4—302no—
746C2×C4—302no—
747C2×C4—302no—
748C2×C4—302no—
749C2×C4—302no—
750C2×C4—302no—
751C2×C4—302no—
752C2×C4—302no—
753C2×C4—601no—
754C2×C4—601no—
755C2×C4—601no—
756C2×C4—601no—
757C2×C3#6493511yescharacteristic
758C2×C3#6493511yescharacteristic
759C2×C3#6493511yescharacteristic
760C2×C3#6493511yescharacteristic
761C2×C3#6494511yescharacteristic
762C2×C3#6494511yescharacteristic
763C2×C3#6496211yescharacteristic
764C2×C3#6496211yescharacteristic
765C2×C3#6521811yescharacteristic
766C2×C3#6523611yescharacteristic
767C2×C3#6523611yescharacteristic
768C2×C3#6524411yescharacteristic
769C2×C3#6526311yescharacteristic
770C2×C3#6526811yescharacteristic
771C2×C3#6526811yescharacteristic
772C5#6942411yescharacteristic, complemented, Sylow
773C22#9132311yescharacteristic
774C22#9132411yescharacteristic
775C22#9132511yescharacteristic
776C22#9132711yescharacteristic
777C22#9132811yescharacteristic
778C22#9132911yescharacteristic
779C22#9134911yescharacteristic
780C22#9135011yescharacteristic
781C22#9135211yescharacteristic
782C22#9135311yescharacteristic
783C22#9137711yescharacteristic
784C22#9141711yescharacteristic
785C22#9141911yescharacteristic
786C22#9142211yescharacteristic
787C22#9142911yescharacteristic
788C22#9143011yescharacteristic
789C22#9143611yescharacteristic
790C22#9146411yescharacteristic
791C22C4×#120411yescharacteristic
792C22#9146811yescharacteristic
793C22#9146911yescharacteristic
794C22#9147011yescharacteristic
795C22D5×(C2×D3)⋊C411yescharacteristic
796C22D3×#68511yescharacteristic
797C22#9147311yescharacteristic
798C22#9147411yescharacteristic
799C22#9147511yescharacteristic
800C22#9147611yescharacteristic
801C22#9152511yescharacteristic
802C22#9152611yescharacteristic
803C22#9153411yescharacteristic
804C22#9157411yescharacteristic
805C22#9157511yescharacteristic
806C22#9157611yescharacteristic
807C22#9157711yescharacteristic
808C4—42no—
809C4—64no—
810C4—104no—
811C4—122no—
812C4—202no—
813C4—304no—
814C4—602no—
815C3#1060021711yescharacteristic, complemented, Sylow
816C2#1174856711yescharacteristic
817C2#1174857911yescharacteristic
818C2#1174862811yescharacteristic
819C2#1174863111yescharacteristic
820C2#1174863211yescharacteristic
821C2#1174873611yescharacteristic
822C2#1174875711yescharacteristic
823C2#1174893311yescharacteristic
824C2#1174893411yescharacteristic
825C2#1174893511yescharacteristic
826C2#1174893611yescharacteristic
827C2#1174893711yescharacteristic
828C2#1174893811yescharacteristic
829C2#1174894011yescharacteristic
830C2#1174952411yescharacteristic
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#1446
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
22. C22×#1204C4semidirect
44. C22×C3×C4×C5Q8semidirect
58. C22×Dic15Q8semidirect
72. C22×C5×Dic3Q8semidirect
86. C22×C3×Dic5Q8semidirect
228. C22×C4×C5Dic6semidirect
253. C22×Dic5Dic6semidirect
334. C22×C3×C4Dic10semidirect
359. C22×Dic3Dic10semidirect
633. C22×C4#1204semidirect
634. C3×C5#1446semidirect
772. C5#69424semidirect
815. C3#10600217semidirect

Maximal subgroups

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

subgroupindex
C23×#12042
C2×#911152
C2×C5×C3⋊#952
C2×C3×#39632
C2×#909942
#106002173
#694245