Finite Group Databasebeta

← #14327422

Subgroups — #14327422

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic5C211yesmaximal, characteristic
2C22×#6668C211yesmaximal, characteristic, complemented
3C2×#91528C211yesmaximal, characteristic, complemented
4#11751321C211yesmaximal, characteristic
5C5×#5220C211yesmaximal, characteristic
6#11749506C211yesmaximal, characteristic, complemented
7#11749506C211yesmaximal, characteristic, complemented
8#11749487C211yesmaximal, characteristic, complemented
9#11749486C211yesmaximal, characteristic, complemented
10#11749485C211yesmaximal, characteristic, complemented
11Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
12#11748698C211yesmaximal, characteristic, complemented
13#11748697C211yesmaximal, characteristic, complemented
14#11748638C211yesmaximal, characteristic, complemented
15#11748580C211yesmaximal, characteristic, complemented
16#10606404—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6719C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C5×#217C2211yescharacteristic
27C2×C5×#217C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C3×D4×Dic5C418yescomplemented
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×#6668—24no—
34C2×#6668C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×#6668C2211yescharacteristic
37C2×#6668C2211yescharacteristic
38C2×#6668C2211yescharacteristic
39C2×#6668C2211yescharacteristic
40#91528—24no—
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
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#82335—51nomaximal, Hall
56C2×D4×Dic5D311yescharacteristic
57C22×#683—31no—
58C2×#4023—31no—
59C5×#386—31no—
60#65509—31no—
61C4×C22⋊Dic5—31no—
62#65234—31no—
63#65233—31no—
64#65231—31no—
65#65231—31no—
66C22⋊C4×Dic5—31no—
67#64943—31no—
68#64942—31no—
69#64939—31no—
70#64938—31no—
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C2×C3×C5×D4—22no—
74C2×C3×C5×D4—22no—
75C2×C3×C5×D4C2×C414yes—
76C22×C3×C4×C5C2311yescharacteristic
77C22×Dic15—22no—
78C22×Dic15—22no—
79C22×Dic15—41no—
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×C5×Dic3—22no—
85C22×C5×Dic3—22no—
86C22×C5×Dic3—41no—
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C3×Dic5—22no—
92C22×C3×Dic5—22no—
93C22×C3×Dic5—22no—
94C22×C3×Dic5—22no—
95C22×C3×Dic5C2×C414yes—
96C22×C3×Dic5C2×C414yescomplemented
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101#6719—22no—
102#6719—22no—
103#6719—41no—
104C5×#217—22no—
105C5×#217—22no—
106C5×#217—41no—
107C3×C22⋊Dic5C2×C414yes—
108C3×C22⋊Dic5C2×C414yescomplemented
109C3×C4⋊Dic5C2×C414yescomplemented
110C3×C4×Dic5C2×C414yescomplemented
111#6668—22no—
112#6668—22no—
113#6668—22no—
114#6668—22no—
115#6668—22no—
116#6668D414yescomplemented
117Dic3×Dic5—22no—
118Dic3×Dic5—22no—
119Dic3×Dic5—41no—
120Dic3×Dic5—41no—
121C2×C3×C4×D4—51no—
122C2×#926—51no—
123C22×C4⋊Dic3—51no—
124#5220—51no—
125#5220D511yescharacteristic
126#5212—51no—
127#5212—51no—
128#4980—51no—
129#4980—51no—
130#4951—51no—
131#4951—51no—
132Dic3×C22⋊C4—51no—
133Dic3×C22⋊C4—51no—
134#4936—51no—
135C4×C4⋊Dic3—51no—
136C22×C5×D4C2×D311yescharacteristic
137C23×C4×C5—31no—
138C23×Dic5—31no—
139C23×Dic5C2×D311yescharacteristic
140C23×Dic5C2×D311yescharacteristic
141C2×C5×C22⋊C4—31no—
142C2×C5×C22⋊C4—31no—
143C2×C5×C22⋊C4—31no—
144C2×C22⋊Dic5—31no—
145C2×C22⋊Dic5—31no—
146C2×C22⋊Dic5—31no—
147C2×C22⋊Dic5C2×D311yescharacteristic
148C2×C22⋊Dic5C2×D311yescharacteristic
149D4×Dic5Dic318yescomplemented
150C2×C4⋊Dic5C2×D311yescharacteristic
151C2×#683—31no—
152C2×#683—31no—
153C2×#683—31no—
154C2×#683—31no—
155C2×#683—31no—
156C2×#683—31no—
157C2×#683—64no—
158C2×C4×Dic5—31no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5C2×D311yescharacteristic
163#4023—64no—
164C5×#95—31no—
165C5×#95—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963—31no—
174#2352—151noSylow
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5C22×C412yes—
186C23×C3×C5C22×C412yes—
187C23×C3×C5#4112yes—
188C23×C3×C5#4112yes—
189C23×C3×C5C2411yescharacteristic
190C3×C5×D4—28no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5C22×C412yes—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—44no—
206C2×Dic15C2×D412yes—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3—21no—
213C2×C5×Dic3—21no—
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3—44no—
219C2×C5×Dic3C2×D412yes—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—28no—
227C2×C3×Dic5—28no—
228C2×C3×Dic5C22×C412yes—
229C2×C3×Dic5C22×C412yes—
230C2×C3×Dic5C22×C412yes—
231C2×C3×Dic5C22×C412yes—
232C2×C3×Dic5C2×D412yes—
233C2×C3×Dic5#4112yes—
234C22×C3×D4C2×D511yescharacteristic
235C23×C3×C4—51no—
236C23×C3×C4—51no—
237C23×Dic3—51no—
238C23×Dic3C2×D511yescharacteristic
239C3×C4×D4—58no—
240C2×C3×C4⋊C4—51no—
241C2×C3×C22⋊C4—51no—
242C2×C3×C22⋊C4—51no—
243C2×C3×C42—51no—
244C2×#217—51no—
245C2×#217—51no—
246C2×#217—51no—
247C2×#217C2×D511yescharacteristic
248C2×#217C2×D511yescharacteristic
249C2×#217C2×D511yescharacteristic
250#926—104no—
251C2×C4⋊Dic3—51no—
252C2×C4⋊Dic3—51no—
253C2×C4⋊Dic3—51no—
254C2×C4⋊Dic3—51no—
255C2×C4⋊Dic3—51no—
256C2×C4⋊Dic3—51no—
257C2×C4⋊Dic3—104no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3—51no—
260C2×C4×Dic3—51no—
261C2×C4×Dic3—51no—
262C3⋊#95—51no—
263C3⋊#95—51no—
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95C2×D511yescharacteristic
271C3⋊#95C2×D511yescharacteristic
272C24×C5C22×D311yescharacteristic
273C24×C5C22×D311yescharacteristic
274C2×C5×D4—22no—
275C2×C5×D4—22no—
276C2×C5×D4C2×Dic314yes—
277C22×C4×C5—31no—
278C22×C4×C5—31no—
279C22×C4×C5—31no—
280C22×C4×C5—31no—
281C22×C4×C5—62no—
282C22×C4×C5—62no—
283C22×C4×C5—121no—
284C22×C4×C5C22×D311yescharacteristic
285C22×Dic5—22no—
286C22×Dic5—22no—
287C22×Dic5—22no—
288C22×Dic5—22no—
289C22×Dic5—31no—
290C22×Dic5—31no—
291C22×Dic5—31no—
292C22×Dic5—31no—
293C22×Dic5—62no—
294C22×Dic5—62no—
295C22×Dic5—121no—
296C22×Dic5C2×Dic314yes—
297C22×Dic5C2×Dic314yescomplemented
298C22×Dic5C22×D311yescharacteristic
299C22×Dic5C22×D311yescharacteristic
300C22×Dic5C22×D311yescharacteristic
301C22×Dic5C22×D311yescharacteristic
302C5×C22⋊C4—62no—
303C5×C22⋊C4—62no—
304C5×C22⋊C4—121no—
305C22⋊Dic5—62no—
306C22⋊Dic5—62no—
307C22⋊Dic5—121no—
308C22⋊Dic5C2×Dic314yes—
309C22⋊Dic5C2×Dic314yescomplemented
310C4⋊Dic5C2×Dic314yescomplemented
311#683—34no—
312#683—62no—
313#683—62no—
314#683—62no—
315#683—62no—
316#683—62no—
317C4×Dic5—62no—
318C4×Dic5—62no—
319C4×Dic5—121no—
320C4×Dic5—121no—
321C4×Dic5C2×Dic314yescomplemented
322C2×C4×D4—51no—
323C2×#117—151no—
324C22×C4⋊C4—151no—
325#388—151no—
326#388—151no—
327#387—151no—
328#387—151no—
329#386—31no—
330#386—151no—
331#382—151no—
332#380—151no—
333#380—151no—
334C4×C4⋊C4—151no—
335C4×C22⋊C4—151no—
336C4×C22⋊C4—151no—
337C22×C3×C5—22no—
338C22×C3×C5—22no—
339C22×C3×C5—22no—
340C22×C3×C5—22no—
341C22×C3×C5—22no—
342C22×C3×C5—22no—
343C22×C3×C5—22no—
344C22×C3×C5—22no—
345C22×C3×C5—22no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5#11714yescomplemented
351C22×C3×C5C23×C411yescharacteristic
352C22×C3×C5C22×D411yescharacteristic
353C22×C3×C5C2×#4111yescharacteristic
354C22×C3×C5C2×#4111yescharacteristic
355C22×C3×C5C2×#4111yescharacteristic
356C22×C3×C5H(5,𝔽2)11yescharacteristic
357C22×C3×C52−1+411yescharacteristic
358C3×C4×C5—22no—
359Dic15—22no—
360Dic15—41no—
361Dic15—41no—
362Dic15—41no—
363C3×Dic5—22no—
364C3×Dic5—22no—
365C3×Dic5—22no—
366C3×Dic5C4×D414yes—
367C5×Dic3—22no—
368C5×Dic3—41no—
369C5×Dic3—41no—
370C5×Dic3—41no—
371C24×C3C22×D511yescharacteristic
372C24×C3C22×D511yescharacteristic
373C2×C3×D4—22no—
374C2×C3×D4—22no—
375C2×C3×D4C4×D514yes—
376C22×C3×C4—51no—
377C22×C3×C4—54no—
378C22×C3×C4—54no—
379C22×C3×C4—51no—
380C22×C3×C4—51no—
381C22×C3×C4—51no—
382C22×C3×C4—102no—
383C22×C3×C4—102no—
384C22×C3×C4—102no—
385C22×C3×C4—102no—
386C22×C3×C4C22×D511yescharacteristic
387C22×Dic3—22no—
388C22×Dic3—22no—
389C22×Dic3—41no—
390C22×Dic3—51no—
391C22×Dic3—51no—
392C22×Dic3—51no—
393C22×Dic3—51no—
394C22×Dic3—102no—
395C22×Dic3—102no—
396C22×Dic3—201no—
397C22×Dic3C22×D511yescharacteristic
398C22×Dic3C22×D511yescharacteristic
399C22×Dic3C22×D511yescharacteristic
400C22×Dic3C22×D511yescharacteristic
401C3×C4⋊C4—54no—
402C3×C22⋊C4—54no—
403C3×C22⋊C4—54no—
404C3×C42—54no—
405#217—22no—
406#217—22no—
407#217—41no—
408#217—102no—
409#217—102no—
410#217—201no—
411C4⋊Dic3—54no—
412C4⋊Dic3—102no—
413C4⋊Dic3—102no—
414C4⋊Dic3—102no—
415C4⋊Dic3—102no—
416C4⋊Dic3—102no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C4×Dic3—201no—
420C4×Dic3—201no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—21no—
424C23×C5—21no—
425C23×C5—21no—
426C23×C5—21no—
427C23×C5—21no—
428C23×C5—21no—
429C23×C5—21no—
430C23×C5—21no—
431C23×C5#23512yes—
432C23×C5#23512yes—
433C23×C5C22×Dic312yes—
434C23×C5C22×Dic312yes—
435C23×C5C23×D311yescharacteristic
436C5×D4—28no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—32no—
440C2×C4×C5—61no—
441C2×C4×C5—61no—
442C2×C4×C5—61no—
443C2×C4×C5—61no—
444C2×C4×C5—61no—
445C2×C4×C5—61no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5—61no—
449C2×C4×C5—61no—
450C2×C4×C5—61no—
451C2×C4×C5—124no—
452C2×C4×C5C22×Dic312yes—
453C2×Dic5—21no—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—28no—
460C2×Dic5—28no—
461C2×Dic5—32no—
462C2×Dic5—61no—
463C2×Dic5—61no—
464C2×Dic5—61no—
465C2×Dic5—61no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5—61no—
471C2×Dic5—61no—
472C2×Dic5—61no—
473C2×Dic5—124no—
474C2×Dic5D3×D412yes—
475C2×Dic5#23712yes—
476C2×Dic5C22×Dic312yes—
477C2×Dic5C22×Dic312yes—
478C2×Dic5C22×Dic312yes—
479C2×Dic5C22×Dic312yes—
480C22×D4D3×D511yescharacteristic
481C23×C4—31no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—151no—
485C4×D4—58no—
486#117—304no—
487C2×C4⋊C4—51no—
488C2×C4⋊C4—151no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—151no—
491C2×C4⋊C4—151no—
492C2×C4⋊C4—151no—
493C2×C4⋊C4—151no—
494C2×C4⋊C4—304no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—51no—
499C2×C22⋊C4—51no—
500C2×C22⋊C4—151no—
501C2×C22⋊C4—151no—
502C2×C22⋊C4—151no—
503C2×C42—51no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42—151no—
508#95—31no—
509#95—31no—
510#95—151no—
511#95—151no—
512#95—151no—
513#95—151no—
514#95—151no—
515#95—151no—
516#95—151no—
517#95—151no—
518C2×C3×C5—24no—
519C2×C3×C5—42no—
520C2×C3×C5C2×#11711yescharacteristic
521C2×C3×C5C2×C4×D411yescharacteristic
522C2×C3×C5#52011yescharacteristic
523C2×C3×C5#54611yescharacteristic
524C2×C3×C5#54811yescharacteristic
525C2×C3×C5#55211yescharacteristic
526C2×C3×C5#55311yescharacteristic
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3C2×C4×D512yes—
538C23×C3C2×C4×D512yes—
539C23×C3#71112yes—
540C23×C3#71112yes—
541C23×C3C23×D511yescharacteristic
542C3×D4—28no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—52no—
546C2×C3×C4—52no—
547C2×C3×C4—52no—
548C2×C3×C4—52no—
549C2×C3×C4—52no—
550C2×C3×C4—52no—
551C2×C3×C4—108no—
552C2×C3×C4—108no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4—101no—
558C2×C3×C4—101no—
559C2×C3×C4C2×C4×D512yes—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—44no—
572C2×Dic3—52no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—101no—
580C2×Dic3—101no—
581C2×Dic3—101no—
582C2×Dic3—101no—
583C2×Dic3—101no—
584C2×Dic3—204no—
585C2×Dic3D4×D512yes—
586C22×C5—22no—
587C22×C5—22no—
588C22×C5—22no—
589C22×C5—22no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5—22no—
593C22×C5—22no—
594C22×C5—22no—
595C22×C5—41no—
596C22×C5—41no—
597C22×C5—41no—
598C22×C5—41no—
599C22×C5#92614yescomplemented
600C22×C5C2×#23511yescharacteristic
601C22×C5C2×#23511yescharacteristic
602C22×C5C2×D3×D411yescharacteristic
603C22×C5C2×#23711yescharacteristic
604C22×C5#100911yescharacteristic
605C22×C5#101011yescharacteristic
606C22×C5C23×Dic311yescharacteristic
607C4×C5—22no—
608C4×C5—62no—
609C4×C5—121no—
610C4×C5—121no—
611C4×C5—121no—
612Dic5—22no—
613Dic5—22no—
614Dic5—22no—
615Dic5—62no—
616Dic5—121no—
617Dic5—121no—
618Dic5—121no—
619Dic5D4×Dic314yes—
620C24C2×D3×D511yescharacteristic
621C24C2×D3×D511yescharacteristic
622C2×D4—22no—
623C2×D4—22no—
624C2×D4D5×Dic314yes—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—51no—
630C22×C4—54no—
631C22×C4—54no—
632C22×C4—51no—
633C22×C4—51no—
634C22×C4—51no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—102no—
638C22×C4—102no—
639C22×C4—102no—
640C22×C4—102no—
641C22×C4—121no—
642C22×C4—151no—
643C22×C4—151no—
644C22×C4—151no—
645C22×C4—151no—
646C22×C4—302no—
647C22×C4—302no—
648C22×C4—601no—
649C22×C4C2×D3×D511yescharacteristic
650C4⋊C4—54no—
651C4⋊C4—154no—
652C4⋊C4—302no—
653C4⋊C4—302no—
654C4⋊C4—302no—
655C4⋊C4—302no—
656C4⋊C4—302no—
657C22⋊C4—54no—
658C22⋊C4—54no—
659C22⋊C4—62no—
660C22⋊C4—62no—
661C22⋊C4—121no—
662C22⋊C4—302no—
663C22⋊C4—302no—
664C22⋊C4—601no—
665C42—54no—
666C42—302no—
667C42—302no—
668C42—601no—
669C42—601no—
670C3×C5#235211yescharacteristic, complemented, Hall
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3#402314yescomplemented
685C22×C3C22×C4×D511yescharacteristic
686C22×C3C2×D4×D511yescharacteristic
687C22×C3C2×#71111yescharacteristic
688C22×C3C2×#71111yescharacteristic
689C22×C3#414411yescharacteristic
690C22×C3D5×#4111yescharacteristic
691C22×C3#415011yescharacteristic
692C3×C4—22no—
693C3×C4—54no—
694C3×C4—102no—
695C3×C4—102no—
696C3×C4—102no—
697Dic3—22no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—102no—
702Dic3—201no—
703Dic3—201no—
704Dic3—201no—
705C2×C5—24no—
706C2×C5—42no—
707C2×C5#554111yescharacteristic
708C2×C5#555011yescharacteristic
709C2×C5#555211yescharacteristic
710C2×C5#556511yescharacteristic
711C2×C5C2×#92611yescharacteristic
712C2×C5C2×D4×Dic311yescharacteristic
713C2×C5#582711yescharacteristic
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23C2×D5×Dic312yes—
725C23C2×D5×Dic312yes—
726C23#678212yes—
727C23#678212yes—
728C23C22×D3×D511yescharacteristic
729D4—28no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—32no—
733C2×C4—52no—
734C2×C4—52no—
735C2×C4—52no—
736C2×C4—52no—
737C2×C4—52no—
738C2×C4—52no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—108no—
751C2×C4—108no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—124no—
759C2×C4—152no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—301no—
767C2×C4—301no—
768C2×C4—301no—
769C2×C4—301no—
770C2×C4—301no—
771C2×C4—604no—
772C2×C4C2×D5×Dic312yes—
773C2×C3—24no—
774C2×C3—42no—
775C2×C3C2×#402311yescharacteristic
776C2×C3C4×D4×D511yescharacteristic
777C2×C3#6588011yescharacteristic
778C2×C3#6592511yescharacteristic
779C2×C3#6593211yescharacteristic
780C2×C3#6593511yescharacteristic
781C2×C3#6598411yescharacteristic
782C5#8233511yescharacteristic, complemented, Sylow
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22#9152814yescomplemented
797C22#9202011yescharacteristic
798C22D3×D4×D511yescharacteristic
799C22D5×#23711yescharacteristic
800C22#9202711yescharacteristic
801C22C22×D5×Dic311yescharacteristic
802C22C2×#678211yescharacteristic
803C22C2×#678211yescharacteristic
804C4—22no—
805C4—54no—
806C4—62no—
807C4—102no—
808C4—102no—
809C4—102no—
810C4—121no—
811C4—121no—
812C4—121no—
813C4—302no—
814C4—601no—
815C4—601no—
816C4—601no—
817C3#1060640411yescharacteristic, complemented, Sylow
818C2—24no—
819C2—42no—
820C2#1175473011yescharacteristic
821C2D4×D5×Dic311yescharacteristic
822C2#1175477811yescharacteristic
823C2#1175478011yescharacteristic
824C2#1175485911yescharacteristic
825C2#1175492311yescharacteristic
826C2C2×#9152811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
Fitting, prime radicalC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5#2352
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. C22×#6668C2semidirect
3. C2×#91528C2semidirect
6. #11749506C2semidirect
7. #11749506C2semidirect
8. #11749487C2semidirect
9. #11749486C2semidirect
10. #11749485C2semidirect
11. Dic3×C22⋊Dic5C2semidirect
12. #11748698C2semidirect
13. #11748697C2semidirect
14. #11748638C2semidirect
15. #11748580C2semidirect
30. C3×D4×Dic5C4semidirect
96. C22×C3×Dic5C2×C4semidirect
108. C3×C22⋊Dic5C2×C4semidirect
109. C3×C4⋊Dic5C2×C4semidirect
110. C3×C4×Dic5C2×C4semidirect
116. #6668D4semidirect
149. D4×Dic5Dic3semidirect
297. C22×Dic5C2×Dic3semidirect
309. C22⋊Dic5C2×Dic3semidirect
310. C4⋊Dic5C2×Dic3semidirect
321. C4×Dic5C2×Dic3semidirect
350. C22×C3×C5#117semidirect
599. C22×C5#926semidirect
670. C3×C5#2352semidirect
684. C22×C3#4023semidirect
782. C5#82335semidirect
796. C22#91528semidirect
817. C3#10606404semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic52
C22×#66682
C2×#915282
#117513212
C5×#52202
#117495062
#117494872
#117494862
#117494852
Dic3×C22⋊Dic52
#117486982
#117486972
#117486382
#117485802
#106064043
#823355