Finite Group Databasebeta

← #14321971

Subgroups — #14321971

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91464C211yesmaximal, characteristic
2C2×#91442C211yesmaximal, characteristic
3C2×#91325C211yesmaximal, characteristic, complemented
4C42×Dic15C211yesmaximal, characteristic, complemented
5C5×#4940C211yesmaximal, characteristic, complemented
6C3×#65229C211yesmaximal, characteristic, complemented
7#11748935C211yesmaximal, characteristic, complemented
8#11748915C211yesmaximal, characteristic
9#11748886C211yesmaximal, characteristic, complemented
10#11748886C211yesmaximal, characteristic, complemented
11#11748884C211yesmaximal, characteristic, complemented
12#11748884C211yesmaximal, characteristic, complemented
13#11748867C211yesmaximal, characteristic, complemented
14#11748717C211yesmaximal, characteristic, complemented
15#11748709C211yesmaximal, characteristic, complemented
16#10607185—31nomaximal, Hall
17C22×#1204C2211yescharacteristic
18C22×#1201C2211yescharacteristic
19C22×D3×Dic5C2211yescharacteristic
20C22×D5×Dic3C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic
27C2×C4×Dic15C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36C2×#6669C2211yescharacteristic
37C2×#6669C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic
44#91464C418yescomplemented
45#91442—24no—
46#91325—24no—
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#75454—51nomaximal, Hall
56C2×#4033—31no—
57C2×#4031—31no—
58C2×#4027—31no—
59C5×#388—31no—
60#65279—31no—
61#65246—31no—
62#65234—31no—
63C22⋊C4×Dic5—31no—
64C22⋊C4×Dic5—31no—
65#65229D311yescharacteristic, complemented
66C42×Dic5—31no—
67#64955—31no—
68#64955—31no—
69#64939—31no—
70#64935—31no—
71C23×C5×D3C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C22×C5×Dic3C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C2×#1204—22no—
87C2×#1204—22no—
88C2×#1204C2×C414yescomplemented
89C2×#1201—22no—
90C2×#1201—22no—
91C2×#1201C2×C414yes—
92C2×D3×Dic5—22no—
93C2×D3×Dic5—22no—
94C2×D3×Dic5—22no—
95C2×D5×Dic3—22no—
96C2×D5×Dic3—22no—
97C2×D5×Dic3—22no—
98C3×C42×C5—22no—
99C4×Dic15—22no—
100C4×Dic15—22no—
101C4×Dic15—22no—
102C4×Dic15—22no—
103C4×Dic15C2×C414yescomplemented
104C4×Dic15D414yes—
105C5×(C2×D3)⋊C4—22no—
106C5×(C2×D3)⋊C4—22no—
107C5×(C2×D3)⋊C4C2×C414yescomplemented
108C5×Dic3⋊C4—22no—
109C3×#685—22no—
110C3×#685—22no—
111C3×#685C2×C414yescomplemented
112C3×#683—22no—
113#6669—22no—
114#6669—22no—
115(C2×D3)⋊Dic5—22no—
116(C2×D3)⋊Dic5C2×C414yescomplemented
117#6665—22no—
118#6665C2×C414yescomplemented
119Dic3×Dic5—22no—
120Dic3×Dic5—22no—
121C2×#887—51no—
122C2×#885—51no—
123C2×#67⋊C4—51no—
124C3×#388—51no—
125#4990—51no—
126#4957—51no—
127#4945—51no—
128Dic3×C22⋊C4—51no—
129Dic3×C22⋊C4—51no—
130#4940D511yescharacteristic, complemented
131C42×Dic3—51no—
132#4666—51no—
133#4666—51no—
134#4650—51no—
135#4646—51no—
136C22×C22⋊D5—31no—
137C23×Dic5—31no—
138C22×C4×D5—31no—
139C22×Dic10—31no—
140C2×C5×C4⋊C4—31no—
141C2×C5×C22⋊C4—31no—
142C2×C5×C22⋊C4—31no—
143C2×C5×C22⋊C4—31no—
144C2×C42×C5C2×D311yescharacteristic
145C2×C22⋊Dic5—31no—
146C2×C22⋊Dic5—31no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685C2×D311yescharacteristic
150C2×#685C2×D311yescharacteristic
151C2×#685C2×D311yescharacteristic
152C2×#683—31no—
153C2×#683—31no—
154C2×#683C2×D311yescharacteristic
155C2×C4×Dic5—31no—
156C2×C4×Dic5—31no—
157C2×C4×Dic5—31no—
158C2×C4×Dic5—31no—
159C2×C4×Dic5—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5—31no—
163#4033—64no—
164#4031—38no—
165#4027—64no—
166C5×#95—31no—
167C5×#95—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963C2×D311yescharacteristic
173#3963C2×D311yescharacteristic
174C4×#124—151noSylow
175C23×C3×C5C2411yescharacteristic
176C22×C5×D3—21no—
177C22×C5×D3—21no—
178C22×C5×D3—21no—
179C22×C5×D3—21no—
180C22×C5×D3—21no—
181C22×C5×D3—21no—
182C22×C5×D3C22×C412yes—
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5C22×C412yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5C22×C412yes—
197C2×C3×C4×C5C2×D412yes—
198C2×C3×C4×C5#4112yes—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15C22×C412yes—
204C2×Dic15C22×C412yes—
205C2×Dic15C2×D412yes—
206C2×Dic15C2×D412yes—
207C2×Dic15#4112yes—
208C2×Dic15#4112yes—
209C2×Dic15#4112yes—
210C2×Dic15#4112yes—
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—21no—
219C2×C5×Dic3C22×C412yes—
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—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5C22×C412yes—
229#1204—28no—
230#1201—28no—
231D3×Dic5—44no—
232D5×Dic3—44no—
233C22×#67—51no—
234C23×Dic3—51no—
235C22×C4×D3—51no—
236C22×Dic6—51no—
237C2×C3×C4⋊C4—51no—
238C2×C3×C22⋊C4—51no—
239C2×C3×C22⋊C4—51no—
240C2×C3×C22⋊C4—51no—
241C2×C3×C42C2×D511yescharacteristic
242C2×#217—51no—
243C2×#217—51no—
244C2×(C2×D3)⋊C4—51no—
245C2×(C2×D3)⋊C4—51no—
246C2×(C2×D3)⋊C4C2×D511yescharacteristic
247C2×(C2×D3)⋊C4C2×D511yescharacteristic
248C2×(C2×D3)⋊C4C2×D511yescharacteristic
249C2×Dic3⋊C4—51no—
250C2×Dic3⋊C4—51no—
251C2×Dic3⋊C4C2×D511yescharacteristic
252C2×C4×Dic3—51no—
253C2×C4×Dic3—51no—
254C2×C4×Dic3—51no—
255C2×C4×Dic3—51no—
256C2×C4×Dic3—51no—
257C2×C4×Dic3—51no—
258C2×C4×Dic3—51no—
259C2×C4×Dic3—51no—
260#887—104no—
261#885—58no—
262#67⋊C4—104no—
263C3×#95—51no—
264C3×#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95C2×D511yescharacteristic
270C3⋊#95C2×D511yescharacteristic
271C24×C5—31no—
272C23×D5C22×D311yescharacteristic
273C22×C4×C5—31no—
274C22×C4×C5—31no—
275C22×C4×C5—31no—
276C22×C4×C5C22×D311yescharacteristic
277C22×C4×C5C22×D311yescharacteristic
278C22×C4×C5C22×D311yescharacteristic
279C2×C22⋊D5—34no—
280C2×C22⋊D5—62no—
281C2×C22⋊D5—62no—
282C22×Dic5—31no—
283C22×Dic5—31no—
284C22×Dic5—31no—
285C22×Dic5—31no—
286C22×Dic5—62no—
287C22×Dic5—62no—
288C22×Dic5—62no—
289C22×Dic5C22×D311yescharacteristic
290C22×Dic5C22×D311yescharacteristic
291C22×Dic5C22×D311yescharacteristic
292C2×C4×D5—62no—
293C2×C4×D5—62no—
294C2×C4×D5—62no—
295C2×Dic10—34no—
296C2×Dic10—62no—
297C2×Dic10—62no—
298C5×C4⋊C4—62no—
299C5×C22⋊C4—34no—
300C5×C22⋊C4—62no—
301C5×C22⋊C4—62no—
302C42×C5—22no—
303C22⋊Dic5—34no—
304C22⋊Dic5—62no—
305#685—22no—
306#685—22no—
307#685—34no—
308#685—62no—
309#685C4×D314yescomplemented
310#683—22no—
311#683—62no—
312#683—62no—
313C4×Dic5—34no—
314C4×Dic5—34no—
315C4×Dic5—62no—
316C4×Dic5—62no—
317C4×Dic5—62no—
318C4×Dic5—62no—
319C4×Dic5—62no—
320C4×Dic5—62no—
321C2×#124—151no—
322C2×C4×Q8—151no—
323C2×C4×D4—151no—
324#391—151no—
325#390—151no—
326#388—31no—
327#388—51no—
328#388—151no—
329#388—151no—
330#382—151no—
331C4×C22⋊C4—151no—
332C4×C22⋊C4—151no—
333C4×C22⋊C4—151no—
334C4×C22⋊C4—151no—
335C43—151no—
336C22×C3×C5C23×C411yescharacteristic
337C22×C3×C5C22×D411yescharacteristic
338C22×C3×C5C2×#4111yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C22×C3×C5C2×#4111yescharacteristic
343C2×C5×D3—22no—
344C2×C5×D3—22no—
345C2×C5×D3—22no—
346C2×C5×D3—41no—
347C2×C5×D3—41no—
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C3×D5—22no—
351C2×C3×D5—22no—
352C2×C3×D5—22no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C3×C4×C5—22no—
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360Dic15—22no—
361Dic15—22no—
362Dic15C4×D414yes—
363Dic15#12414yescomplemented
364C3×Dic5—22no—
365C3×Dic5—41no—
366C3×Dic5—41no—
367C5×Dic3—22no—
368C5×Dic3—41no—
369C5×Dic3—41no—
370C24×C3—51no—
371C23×D3C22×D511yescharacteristic
372C22×C3×C4—51no—
373C22×C3×C4—51no—
374C22×C3×C4—51no—
375C22×C3×C4C22×D511yescharacteristic
376C22×C3×C4C22×D511yescharacteristic
377C22×C3×C4C22×D511yescharacteristic
378C2×#67—54no—
379C2×#67—102no—
380C2×#67—102no—
381C22×Dic3—51no—
382C22×Dic3—51no—
383C22×Dic3—51no—
384C22×Dic3—51no—
385C22×Dic3—102no—
386C22×Dic3—102no—
387C22×Dic3—102no—
388C22×Dic3C22×D511yescharacteristic
389C22×Dic3C22×D511yescharacteristic
390C22×Dic3C22×D511yescharacteristic
391C2×C4×D3—102no—
392C2×C4×D3—102no—
393C2×C4×D3—102no—
394C2×Dic6—54no—
395C2×Dic6—102no—
396C2×Dic6—102no—
397C3×C4⋊C4—102no—
398C3×C22⋊C4—54no—
399C3×C22⋊C4—102no—
400C3×C22⋊C4—102no—
401C3×C42—22no—
402#217—54no—
403#217—102no—
404(C2×D3)⋊C4—22no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—54no—
407(C2×D3)⋊C4—102no—
408(C2×D3)⋊C4C4×D514yescomplemented
409Dic3⋊C4—22no—
410Dic3⋊C4—102no—
411Dic3⋊C4—102no—
412C4×Dic3—54no—
413C4×Dic3—54no—
414C4×Dic3—102no—
415C4×Dic3—102no—
416C4×Dic3—102no—
417C4×Dic3—102no—
418C4×Dic3—102no—
419C4×Dic3—102no—
420C23×C5—32no—
421C23×C5—61no—
422C23×C5—61no—
423C23×C5—61no—
424C23×C5—61no—
425C23×C5—61no—
426C23×C5—61no—
427C23×C5C23×D311yescharacteristic
428C22×D5—21no—
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—21no—
432C22×D5—21no—
433C22×D5—21no—
434C22×D5C2×C4×D312yes—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—32no—
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×C5C2×C4×D312yes—
451C2×C4×C5D3×D412yes—
452C2×C4×C5#23712yes—
453C22⋊D5—68no—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—32no—
463C2×Dic5—32no—
464C2×Dic5—32no—
465C2×Dic5—32no—
466C2×Dic5—32no—
467C2×Dic5—32no—
468C2×Dic5—32no—
469C2×Dic5—32no—
470C2×Dic5—61no—
471C2×Dic5—61no—
472C2×Dic5—61no—
473C2×Dic5—61no—
474C2×Dic5—124no—
475C2×Dic5C2×C4×D312yes—
476C4×D5—124no—
477Dic10—68no—
478C22×Q8—151no—
479C22×D4—151no—
480C23×C4—151no—
481C23×C4—151no—
482#124—158no—
483C4×Q8—304no—
484C4×D4—304no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—51no—
487C2×C4⋊C4—151no—
488C2×C4⋊C4—151no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—51no—
493C2×C22⋊C4—51no—
494C2×C22⋊C4—51no—
495C2×C22⋊C4—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4—151no—
499C2×C42—151no—
500C2×C42—151no—
501C2×C42—151no—
502C2×C42—151no—
503C2×C42—151no—
504C2×C42—151no—
505C2×C42—151no—
506C2×C42—151no—
507C2×C42D3×D511yescharacteristic
508#95—31no—
509#95—31no—
510#95—51no—
511#95—51no—
512#95—151no—
513#95—151no—
514#95—151no—
515#95—151no—
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C4×#4111yescharacteristic
518C2×C3×C5C4×#4111yescharacteristic
519C2×C3×C5C2×#12411yescharacteristic
520C2×C3×C5#52911yescharacteristic
521C2×C3×C5#52911yescharacteristic
522C2×C3×C5#53211yescharacteristic
523C3×D5—42no—
524C5×D3—42no—
525C23×C3—52no—
526C23×C3—101no—
527C23×C3—101no—
528C23×C3—101no—
529C23×C3—101no—
530C23×C3—101no—
531C23×C3—101no—
532C23×C3C23×D511yescharacteristic
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3C2×C4×D512yes—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—52no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4C2×C4×D512yes—
556C2×C3×C4D4×D512yes—
557C2×C3×C4#71112yes—
558#67—108no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—52no—
568C2×Dic3—52no—
569C2×Dic3—52no—
570C2×Dic3—52no—
571C2×Dic3—52no—
572C2×Dic3—52no—
573C2×Dic3—52no—
574C2×Dic3—52no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3—204no—
580C2×Dic3C2×C4×D512yes—
581C4×D3—204no—
582Dic6—108no—
583C22×C5—62no—
584C22×C5—62no—
585C22×C5—62no—
586C22×C5—121no—
587C22×C5—121no—
588C22×C5—121no—
589C22×C5—121no—
590C22×C5C22×C4×D311yescharacteristic
591C22×C5C2×D3×D411yescharacteristic
592C22×C5C2×#23711yescharacteristic
593C22×C5D3×#4111yescharacteristic
594C22×C5D3×#4111yescharacteristic
595C22×C5D3×#4111yescharacteristic
596C22×C5D3×#4111yescharacteristic
597C2×D5—22no—
598C2×D5—22no—
599C2×D5—22no—
600C2×D5—41no—
601C2×D5—41no—
602C2×D5—41no—
603C2×D5—41no—
604C4×C5—22no—
605C4×C5—22no—
606C4×C5—22no—
607C4×C5—62no—
608C4×C5—121no—
609C4×C5—121no—
610Dic5—22no—
611Dic5—34no—
612Dic5—34no—
613Dic5—41no—
614Dic5—41no—
615Dic5—62no—
616Dic5—62no—
617C24—31no—
618C24—51no—
619C2×Q8—154no—
620C2×Q8—302no—
621C2×Q8—302no—
622C2×D4—154no—
623C2×D4—302no—
624C2×D4—302no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—151no—
632C22×C4—151no—
633C22×C4—151no—
634C22×C4—151no—
635C22×C4—302no—
636C22×C4—302no—
637C22×C4—302no—
638C22×C4—302no—
639C22×C4—302no—
640C22×C4—302no—
641C22×C4C2×D3×D511yescharacteristic
642C22×C4C2×D3×D511yescharacteristic
643C22×C4C2×D3×D511yescharacteristic
644C4⋊C4—62no—
645C4⋊C4—102no—
646C4⋊C4—302no—
647C4⋊C4—302no—
648C22⋊C4—34no—
649C22⋊C4—54no—
650C22⋊C4—62no—
651C22⋊C4—62no—
652C22⋊C4—102no—
653C22⋊C4—102no—
654C22⋊C4—154no—
655C22⋊C4—154no—
656C22⋊C4—302no—
657C22⋊C4—302no—
658C42—22no—
659C42—154no—
660C42—154no—
661C42—302no—
662C42—302no—
663C42—302no—
664C42—302no—
665C42—302no—
666C42—302no—
667C3×C5C4×#12411yescharacteristic, complemented, Hall
668C22×C3—102no—
669C22×C3—102no—
670C22×C3—102no—
671C22×C3—201no—
672C22×C3—201no—
673C22×C3—201no—
674C22×C3—201no—
675C22×C3C22×C4×D511yescharacteristic
676C22×C3C2×D4×D511yescharacteristic
677C22×C3C2×#71111yescharacteristic
678C22×C3D5×#4111yescharacteristic
679C22×C3D5×#4111yescharacteristic
680C22×C3D5×#4111yescharacteristic
681C22×C3D5×#4111yescharacteristic
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C3×C4—22no—
690C3×C4—22no—
691C3×C4—22no—
692C3×C4—102no—
693C3×C4—201no—
694C3×C4—201no—
695Dic3—22no—
696Dic3—41no—
697Dic3—41no—
698Dic3—54no—
699Dic3—54no—
700Dic3—102no—
701Dic3—102no—
702C2×C5—122no—
703C2×C5#552211yescharacteristic
704C2×C5C4×#23711yescharacteristic
705C2×C5C4×D3×D411yescharacteristic
706C2×C5#559611yescharacteristic
707C2×C5#564911yescharacteristic
708C2×C5D3×#12411yescharacteristic
709C2×C5#570611yescharacteristic
710D5—42no—
711C23—32no—
712C23—52no—
713C23—61no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—61no—
718C23—61no—
719C23—101no—
720C23—101no—
721C23—101no—
722C23—101no—
723C23—101no—
724C23—101no—
725C23C22×D3×D511yescharacteristic
726Q8—308no—
727D4—308no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—32no—
735C2×C4—52no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—101no—
745C2×C4—101no—
746C2×C4—101no—
747C2×C4—101no—
748C2×C4—101no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—101no—
752C2×C4—152no—
753C2×C4—152no—
754C2×C4—152no—
755C2×C4—152no—
756C2×C4—152no—
757C2×C4—152no—
758C2×C4—152no—
759C2×C4—152no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—604no—
765C2×C4—604no—
766C2×C4C4×D3×D512yes—
767C2×C4#677712yes—
768C2×C4#678012yes—
769C2×C3—202no—
770C2×C3#6585611yescharacteristic
771C2×C3C4×#71111yescharacteristic
772C2×C3C4×D4×D511yescharacteristic
773C2×C3#6593011yescharacteristic
774C2×C3#6598311yescharacteristic
775C2×C3D5×#12411yescharacteristic
776C2×C3#6604011yescharacteristic
777D3—42no—
778C5#7545411yescharacteristic, complemented, Sylow
779C22—62no—
780C22—62no—
781C22—62no—
782C22—102no—
783C22—102no—
784C22—102no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—201no—
790C22—201no—
791C22—201no—
792C22—201no—
793C22C2×C4×D3×D511yescharacteristic
794C22C2×#677711yescharacteristic
795C22#9201611yescharacteristic
796C22#9201611yescharacteristic
797C22#9201611yescharacteristic
798C22#9201611yescharacteristic
799C22C2×#678011yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—62no—
804C4—102no—
805C4—121no—
806C4—121no—
807C4—154no—
808C4—154no—
809C4—201no—
810C4—201no—
811C4—302no—
812C4—302no—
813C3#1060718511yescharacteristic, complemented, Sylow
814C2—122no—
815C2—202no—
816C2#1175266711yescharacteristic
817C2#1175270211yescharacteristic
818C2C4×#677711yescharacteristic
819C2#1175275111yescharacteristic
820C2C4×#678011yescharacteristic
821C2#1175438611yescharacteristic
822C2#1175444911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1201C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C4×#124
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×#91325C2semidirect
4. C42×Dic15C2semidirect
5. C5×#4940C2semidirect
6. C3×#65229C2semidirect
7. #11748935C2semidirect
9. #11748886C2semidirect
10. #11748886C2semidirect
11. #11748884C2semidirect
12. #11748884C2semidirect
13. #11748867C2semidirect
14. #11748717C2semidirect
15. #11748709C2semidirect
44. #91464C4semidirect
65. #65229D3semidirect
88. C2×#1204C2×C4semidirect
103. C4×Dic15C2×C4semidirect
107. C5×(C2×D3)⋊C4C2×C4semidirect
111. C3×#685C2×C4semidirect
116. (C2×D3)⋊Dic5C2×C4semidirect
118. #6665C2×C4semidirect
130. #4940D5semidirect
309. #685C4×D3semidirect
363. Dic15#124semidirect
408. (C2×D3)⋊C4C4×D5semidirect
667. C3×C5C4×#124semidirect
778. C5#75454semidirect
813. C3#10607185semidirect

Maximal subgroups

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

subgroupindex
C2×#914642
C2×#914422
C2×#913252
C42×Dic152
C5×#49402
C3×#652292
#117489352
#117489152
#117488862
#117488842
#117488672
#117487172
#117487092
#106071853
#754545