Finite Group Databasebeta

← #14329007

Subgroups — #14329007

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4024C211yesmaximal, characteristic
2C2×#91528C211yesmaximal, characteristic
3C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
4#11751052C211yesmaximal, characteristic
5C5×#4951C211yesmaximal, characteristic
6#11749486C211yesmaximal, characteristic
7#11749486C211yesmaximal, characteristic
8Dic5×#217C211yesmaximal, characteristic
9#11748699C211yesmaximal, characteristic, complemented
10#11748697C211yesmaximal, characteristic, complemented
11#11748691C211yesmaximal, characteristic, complemented
12#11748681C211yesmaximal, characteristic, complemented
13#11748672C211yesmaximal, characteristic, complemented
14#11748637C211yesmaximal, characteristic, complemented
15Dic3×#683C211yesmaximal, characteristic, complemented
16#10607210—31nomaximal, Hall
17C23×C3×Dic5C2211yescharacteristic
18C22×C3×Dic10C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×#6719C2211yescharacteristic
21C2×#6719C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C5×#217C2211yescharacteristic
25C2×C5×#217C2211yescharacteristic
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C3×#4024C418yescomplemented
33C2×#6668C2211yescharacteristic
34C2×#6668C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×#6668C2211yescharacteristic
37#91528—24no—
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44Dic3×Dic10—24no—
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#82748—51nomaximal, Hall
56C2×#4024D311yescharacteristic
57C2×#4023—31no—
58C2×C4×Dic10—31no—
59C5×#388—31no—
60C4⋊C4×Dic5—31no—
61#65261—31no—
62#65240—31no—
63#65234—31no—
64#65234—31no—
65C22⋊C4×Dic5—31no—
66C4×#683—31no—
67#64944—31no—
68#64942—31no—
69#64938—31no—
70#64935—31no—
71C24×C3×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C3×Dic5—22no—
83C22×C3×Dic5—22no—
84C22×C3×Dic5C2×C414yes—
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×C3×Dic10—22no—
90C2×C3×Dic10—22no—
91C2×C3×Dic10C2×C414yes—
92C3×C5×C22⋊C4C2×C414yes—
93#6719—22no—
94#6719—22no—
95C4⋊Dic15—22no—
96C4×Dic15—22no—
97C5×#217—22no—
98C5×#217—22no—
99C5×C4⋊Dic3—22no—
100C4×C5×Dic3—22no—
101C3×C22⋊Dic5C2×C414yes—
102C3×C4⋊Dic5C2×C414yes—
103C3×#683C2×C414yes—
104C3×#683C2×C414yes—
105#6668—22no—
106#6668—22no—
107#6668—22no—
108#6668D414yes—
109Dic3×Dic5—22no—
110Dic3×Dic5—22no—
111Dic3×Dic5—22no—
112Dic3×Dic5—22no—
113Dic3×Dic5—22no—
114Dic3×Dic5—22no—
115C2×C3×C22⋊Q8—51no—
116C2×Q8×Dic3—51no—
117C2×#926—51no—
118#5229—51no—
119C4×#217—51no—
120#4984—51no—
121#4980—51no—
122#4980—51no—
123Dic3×C4⋊C4—51no—
124Dic3×C4⋊C4—51no—
125Dic3×C4⋊C4—51no—
126#4951—51no—
127#4951—51no—
128#4951—51no—
129#4951D511yescharacteristic
130C23×Dic5C2×D311yescharacteristic
131C22×Dic10C2×D311yescharacteristic
132C2×C5×C4⋊C4—31no—
133C2×C5×C22⋊C4—31no—
134C2×C5×C22⋊C4—31no—
135C2×C5×C22⋊C4C2×D311yescharacteristic
136C2×C42×C5—31no—
137C2×C22⋊Dic5—31no—
138C2×C22⋊Dic5—31no—
139C2×C22⋊Dic5C2×D311yescharacteristic
140C2×C4⋊Dic5—31no—
141C2×C4⋊Dic5C2×D311yescharacteristic
142C2×#683—31no—
143C2×#683—31no—
144C2×#683—31no—
145C2×#683—31no—
146C2×#683C2×D311yescharacteristic
147C2×#683C2×D311yescharacteristic
148C2×C4×Dic5—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—31no—
154C2×C4×Dic5—31no—
155#4024Dic318yescomplemented
156#4023—64no—
157C4×Dic10—64no—
158C5×#95—31no—
159C5×#95—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#2362—151noSylow
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5—21no—
172C23×C3×C5—21no—
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5C22×C412yes—
176C23×C3×C5C2411yescharacteristic
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5C22×C412yes—
182C2×C3×C4×C5C22×C412yes—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15C2×D412yes—
194C2×Dic15#4112yes—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3C2×D412yes—
206C2×C5×Dic3#4112yes—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—28no—
214C2×C3×Dic5C22×C412yes—
215C2×C3×Dic5C22×C412yes—
216C2×C3×Dic5C22×C412yes—
217C2×C3×Dic5C22×C412yes—
218C2×C3×Dic5C2×D412yes—
219C2×C3×Dic5#4112yes—
220C3×Dic10—28no—
221C22×C3×Q8—51no—
222C23×C3×C4—51no—
223C3×C22⋊Q8—58no—
224C2×C3×C4⋊C4—51no—
225C2×C3×C4⋊C4—51no—
226C2×C3×C4⋊C4—51no—
227C2×C3×C22⋊C4—51no—
228C2×C3×C22⋊C4C2×D511yescharacteristic
229C2×#217—51no—
230C2×#217—51no—
231C2×#217C2×D511yescharacteristic
232C2×#217C2×D511yescharacteristic
233Q8×Dic3—104no—
234#926—104no—
235C2×C4⋊Dic3—51no—
236C2×C4⋊Dic3—51no—
237C2×C4⋊Dic3—51no—
238C2×C4⋊Dic3—51no—
239C2×C4⋊Dic3—51no—
240C2×C4⋊Dic3C2×D511yescharacteristic
241C2×C4×Dic3—51no—
242C2×C4×Dic3—51no—
243C2×C4×Dic3—51no—
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3C2×D511yescharacteristic
249C3⋊#95—51no—
250C3⋊#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95C2×D511yescharacteristic
258C3⋊#95C2×D511yescharacteristic
259C24×C5C22×D311yescharacteristic
260C22×C4×C5—31no—
261C22×C4×C5—31no—
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5C22×D311yescharacteristic
265C22×C4×C5C22×D311yescharacteristic
266C22×Dic5—22no—
267C22×Dic5—22no—
268C22×Dic5—31no—
269C22×Dic5—31no—
270C22×Dic5—31no—
271C22×Dic5—31no—
272C22×Dic5C2×Dic314yes—
273C22×Dic5C22×D311yescharacteristic
274C22×Dic5C22×D311yescharacteristic
275C22×Dic5C22×D311yescharacteristic
276C22×Dic5C22×D311yescharacteristic
277C2×Dic10—22no—
278C2×Dic10—22no—
279C2×Dic10C2×Dic314yes—
280C5×C4⋊C4—62no—
281C5×C22⋊C4—62no—
282C5×C22⋊C4—62no—
283C5×C22⋊C4C2×Dic314yes—
284C42×C5—62no—
285C22⋊Dic5—62no—
286C22⋊Dic5—62no—
287C22⋊Dic5C2×Dic314yes—
288C4⋊Dic5—62no—
289C4⋊Dic5C2×Dic314yes—
290#683—34no—
291#683—62no—
292#683—62no—
293#683—62no—
294#683C2×Dic314yes—
295#683C2×Dic314yes—
296C4×Dic5—62no—
297C4×Dic5—62no—
298C4×Dic5—62no—
299C4×Dic5—62no—
300C4×Dic5—62no—
301C4×Dic5—62no—
302C4×Dic5—62no—
303C2×C22⋊Q8—51no—
304C2×C4×Q8—151no—
305C2×#117—151no—
306#391—151no—
307#389—151no—
308#388—31no—
309#388—151no—
310#388—151no—
311#388—151no—
312#387—151no—
313#387—151no—
314C4×C4⋊C4—151no—
315C4×C4⋊C4—151no—
316C4×C4⋊C4—151no—
317C4×C22⋊C4—151no—
318C22×C3×C5—22no—
319C22×C3×C5—22no—
320C22×C3×C5—22no—
321C22×C3×C5—41no—
322C22×C3×C5—41no—
323C22×C3×C5—41no—
324C22×C3×C5—41no—
325C22×C3×C5C23×C411yescharacteristic
326C22×C3×C5C22×D411yescharacteristic
327C22×C3×C5C2×#4111yescharacteristic
328C22×C3×C5C2×#4111yescharacteristic
329C22×C3×C5C2×#4111yescharacteristic
330C22×C3×C52−1+411yescharacteristic
331C22×C3×C52−1+411yescharacteristic
332C3×C4×C5—22no—
333C3×C4×C5—22no—
334Dic15—22no—
335Dic15—22no—
336Dic15—41no—
337Dic15—41no—
338C3×Dic5—22no—
339C3×Dic5—22no—
340C3×Dic5—22no—
341C3×Dic5C4×D414yes—
342C5×Dic3—22no—
343C5×Dic3—22no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C24×C3C22×D511yescharacteristic
347C2×C3×Q8—54no—
348C2×C3×Q8—102no—
349C2×C3×Q8—102no—
350C22×C3×C4—51no—
351C22×C3×C4—54no—
352C22×C3×C4—51no—
353C22×C3×C4—51no—
354C22×C3×C4—51no—
355C22×C3×C4—102no—
356C22×C3×C4—102no—
357C22×C3×C4C22×D511yescharacteristic
358C22×C3×C4C22×D511yescharacteristic
359C22×Dic3—51no—
360C22×Dic3—51no—
361C22×Dic3—51no—
362C22×Dic3—51no—
363C22×Dic3C22×D511yescharacteristic
364C22×Dic3C22×D511yescharacteristic
365C22×Dic3C22×D511yescharacteristic
366C22×Dic3C22×D511yescharacteristic
367C3×C4⋊C4—54no—
368C3×C4⋊C4—54no—
369C3×C4⋊C4—54no—
370C3×C22⋊C4—54no—
371C3×C22⋊C4C4×D514yes—
372#217—22no—
373#217—22no—
374#217—102no—
375#217—102no—
376C4⋊Dic3—22no—
377C4⋊Dic3—54no—
378C4⋊Dic3—102no—
379C4⋊Dic3—102no—
380C4⋊Dic3—102no—
381C4⋊Dic3—102no—
382C4×Dic3—22no—
383C4×Dic3—102no—
384C4×Dic3—102no—
385C4×Dic3—102no—
386C4×Dic3—102no—
387C4×Dic3—102no—
388C4×Dic3—102no—
389C4×Dic3—102no—
390C23×C5—21no—
391C23×C5—21no—
392C23×C5—21no—
393C23×C5—21no—
394C23×C5—21no—
395C23×C5—21no—
396C23×C5C22×Dic312yes—
397C23×C5C23×D311yescharacteristic
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—32no—
403C2×C4×C5—32no—
404C2×C4×C5—61no—
405C2×C4×C5—61no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5—61no—
412C2×C4×C5—61no—
413C2×C4×C5—61no—
414C2×C4×C5C22×Dic312yes—
415C2×C4×C5C22×Dic312yes—
416C2×Dic5—21no—
417C2×Dic5—21no—
418C2×Dic5—21no—
419C2×Dic5—21no—
420C2×Dic5—21no—
421C2×Dic5—21no—
422C2×Dic5—28no—
423C2×Dic5—32no—
424C2×Dic5—32no—
425C2×Dic5—61no—
426C2×Dic5—61no—
427C2×Dic5—61no—
428C2×Dic5—61no—
429C2×Dic5—61no—
430C2×Dic5—61no—
431C2×Dic5—61no—
432C2×Dic5—61no—
433C2×Dic5—61no—
434C2×Dic5—61no—
435C2×Dic5D3×D412yes—
436C2×Dic5#23712yes—
437C2×Dic5C22×Dic312yes—
438C2×Dic5C22×Dic312yes—
439C2×Dic5C22×Dic312yes—
440C2×Dic5C22×Dic312yes—
441Dic10—28no—
442C22×Q8—51no—
443C23×C4—51no—
444C22⋊Q8—58no—
445C4×Q8—304no—
446#117—304no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—51no—
449C2×C4⋊C4—51no—
450C2×C4⋊C4—51no—
451C2×C4⋊C4—151no—
452C2×C4⋊C4—151no—
453C2×C4⋊C4—151no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—151no—
456C2×C22⋊C4—31no—
457C2×C22⋊C4—31no—
458C2×C22⋊C4—51no—
459C2×C22⋊C4—151no—
460C2×C22⋊C4—151no—
461C2×C22⋊C4D3×D511yescharacteristic
462C2×C42—31no—
463C2×C42—151no—
464C2×C42—151no—
465C2×C42—151no—
466C2×C42—151no—
467C2×C42—151no—
468C2×C42—151no—
469C2×C42—151no—
470#95—31no—
471#95—31no—
472#95—151no—
473#95—151no—
474#95—151no—
475#95—151no—
476#95—151no—
477#95—151no—
478#95—151no—
479#95—151no—
480C2×C3×C5—42no—
481C2×C3×C5C2×C4×D411yescharacteristic
482C2×C3×C5C4×#4111yescharacteristic
483C2×C3×C5#51911yescharacteristic
484C2×C3×C5#54711yescharacteristic
485C2×C3×C5#54811yescharacteristic
486C2×C3×C5#55211yescharacteristic
487C2×C3×C5#55611yescharacteristic
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3C2×C4×D512yes—
495C23×C3C23×D511yescharacteristic
496C3×Q8—108no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—52no—
502C2×C3×C4—52no—
503C2×C3×C4—52no—
504C2×C3×C4—52no—
505C2×C3×C4—52no—
506C2×C3×C4—52no—
507C2×C3×C4—108no—
508C2×C3×C4—101no—
509C2×C3×C4—101no—
510C2×C3×C4—101no—
511C2×C3×C4—101no—
512C2×C3×C4—101no—
513C2×C3×C4—101no—
514C2×C3×C4C2×C4×D512yes—
515C2×C3×C4C2×C4×D512yes—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—52no—
527C2×Dic3—52no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3—101no—
531C2×Dic3—101no—
532C2×Dic3—101no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3—101no—
536C2×Dic3—101no—
537C2×Dic3—101no—
538C2×Dic3D4×D512yes—
539C2×Dic3#71112yes—
540C22×C5—22no—
541C22×C5—22no—
542C22×C5—22no—
543C22×C5—41no—
544C22×C5—41no—
545C22×C5—41no—
546C22×C5—41no—
547C22×C5C2×D3×D411yescharacteristic
548C22×C5C2×#23711yescharacteristic
549C22×C5#100711yescharacteristic
550C22×C5#100711yescharacteristic
551C22×C5D3×#4111yescharacteristic
552C22×C5D3×#4111yescharacteristic
553C22×C5C23×Dic311yescharacteristic
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—62no—
557C4×C5—62no—
558C4×C5—121no—
559C4×C5—121no—
560Dic5—22no—
561Dic5—22no—
562Dic5—22no—
563Dic5—62no—
564Dic5—62no—
565Dic5—121no—
566Dic5—121no—
567Dic5D4×Dic314yes—
568C24C2×D3×D511yescharacteristic
569C2×Q8—54no—
570C2×Q8—102no—
571C2×Q8—102no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—51no—
577C22×C4—54no—
578C22×C4—51no—
579C22×C4—51no—
580C22×C4—51no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—151no—
584C22×C4—151no—
585C22×C4—151no—
586C22×C4—151no—
587C22×C4C2×D3×D511yescharacteristic
588C22×C4C2×D3×D511yescharacteristic
589C4⋊C4—54no—
590C4⋊C4—54no—
591C4⋊C4—54no—
592C4⋊C4—62no—
593C4⋊C4—154no—
594C4⋊C4—302no—
595C4⋊C4—302no—
596C4⋊C4—302no—
597C4⋊C4—302no—
598C22⋊C4—54no—
599C22⋊C4—62no—
600C22⋊C4—62no—
601C22⋊C4—302no—
602C22⋊C4—302no—
603C22⋊C4D5×Dic314yes—
604C42—62no—
605C42—302no—
606C42—302no—
607C42—302no—
608C42—302no—
609C42—302no—
610C42—302no—
611C42—302no—
612C3×C5#236211yescharacteristic, complemented, Hall
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3C22×C4×D511yescharacteristic
621C22×C3C2×D4×D511yescharacteristic
622C22×C3C2×#71111yescharacteristic
623C22×C3D5×#4111yescharacteristic
624C22×C3D5×#4111yescharacteristic
625C22×C3#415011yescharacteristic
626C22×C3#415011yescharacteristic
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—54no—
630C3×C4—102no—
631C3×C4—102no—
632C3×C4—102no—
633Dic3—22no—
634Dic3—22no—
635Dic3—41no—
636Dic3—41no—
637Dic3—102no—
638Dic3—102no—
639Dic3—201no—
640Dic3—201no—
641C2×C5—42no—
642C2×C5#563111yescharacteristic
643C2×C5#563311yescharacteristic
644C2×C5#563911yescharacteristic
645C2×C5#564111yescharacteristic
646C2×C5C2×D4×Dic311yescharacteristic
647C2×C5#581211yescharacteristic
648C2×C5Dic3×#4111yescharacteristic
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23C2×D5×Dic312yes—
656C23C22×D3×D511yescharacteristic
657Q8—108no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—52no—
665C2×C4—52no—
666C2×C4—52no—
667C2×C4—52no—
668C2×C4—52no—
669C2×C4—52no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—108no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—152no—
688C2×C4—152no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—301no—
694C2×C4—301no—
695C2×C4—301no—
696C2×C4—301no—
697C2×C4—301no—
698C2×C4—301no—
699C2×C4C2×D5×Dic312yes—
700C2×C4C2×D5×Dic312yes—
701C2×C3—42no—
702C2×C3#6585011yescharacteristic
703C2×C3C4×#71111yescharacteristic
704C2×C3C4×D4×D511yescharacteristic
705C2×C3#6593211yescharacteristic
706C2×C3#6598911yescharacteristic
707C2×C3#6600511yescharacteristic
708C2×C3#6604211yescharacteristic
709C5#8274811yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22#9200411yescharacteristic
718C22#9200411yescharacteristic
719C22D3×D4×D511yescharacteristic
720C22D5×#23711yescharacteristic
721C22D3×#71111yescharacteristic
722C22#9202411yescharacteristic
723C22C22×D5×Dic311yescharacteristic
724C4—22no—
725C4—22no—
726C4—54no—
727C4—62no—
728C4—62no—
729C4—102no—
730C4—102no—
731C4—102no—
732C4—121no—
733C4—121no—
734C4—302no—
735C4—302no—
736C4—601no—
737C4—601no—
738C3#1060721011yescharacteristic, complemented, Sylow
739C2—42no—
740C2#1175277711yescharacteristic
741C2#1175285811yescharacteristic
742C2#1175286411yescharacteristic
743C2#1175294311yescharacteristic
744C2#1175418811yescharacteristic
745C2D4×D5×Dic311yescharacteristic
746C2Dic3×#71111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2362
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×Dic3×Dic10C2semidirect
9. #11748699C2semidirect
10. #11748697C2semidirect
11. #11748691C2semidirect
12. #11748681C2semidirect
13. #11748672C2semidirect
14. #11748637C2semidirect
15. Dic3×#683C2semidirect
32. C3×#4024C4semidirect
155. #4024Dic3semidirect
612. C3×C5#2362semidirect
709. C5#82748semidirect
738. C3#10607210semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40242
C2×#915282
C2×Dic3×Dic102
#117510522
C5×#49512
#117494862
Dic5×#2172
#117486992
#117486972
#117486912
#117486812
#117486722
#117486372
Dic3×#6832
#106072103
#827485