Finite Group Databasebeta

← #14327477

Subgroups — #14327477

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×#91418C211yesmaximal, characteristic
2C2×#91404C211yesmaximal, characteristic, complemented
3C2×#91403C211yesmaximal, characteristic, complemented
4#11750766C211yesmaximal, characteristic
5C5×#4653C211yesmaximal, characteristic, complemented
6C3×#64938C211yesmaximal, characteristic, complemented
7#11748904C211yesmaximal, characteristic
8#11748876C211yesmaximal, characteristic, complemented
9#11748876C211yesmaximal, characteristic, complemented
10#11748875C211yesmaximal, characteristic, complemented
11#11748727C211yesmaximal, characteristic, complemented
12#11748726C211yesmaximal, characteristic, complemented
13C4×#6667C211yesmaximal, characteristic, complemented
14#11748682C211yesmaximal, characteristic, complemented
15#11748580C211yesmaximal, characteristic, complemented
16#10607036—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C22×#1200C2211yescharacteristic
21C22×#1200C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C5×Dic3⋊C4C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×Dic3⋊Dic5C2211yescharacteristic
34C2×#6668C2211yescharacteristic
35C2×#6668C2211yescharacteristic
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42#91418C418yescomplemented
43#91404—24no—
44#91403—24no—
45C3×C5×#95C2211yescharacteristic
46#91115C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#73771—51nomaximal, Hall
56C2×#4039—31no—
57C2×D5×C4⋊C4—31no—
58C2×#4018—31no—
59C5×#387—31no—
60#65279—31no—
61#65270—31no—
62C4×#685—31no—
63#64959—31no—
64#64956—31no—
65#64956—31no—
66#64955—31no—
67#64954—31no—
68#64954—31no—
69#64939—31no—
70#64938D311yescharacteristic, complemented
71C23×D15C2311yescharacteristic
72C23×D15C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C2×D60—22no—
79C2×D60—22no—
80C2×D60C2×C414yes—
81C2×C4×D15—22no—
82C2×C4×D15—22no—
83C2×C4×D15—41no—
84C22×C5×Dic3C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C2×#1200—22no—
93C2×#1200—22no—
94C2×#1200—22no—
95C2×#1200—22no—
96C2×#1200—22no—
97C2×#1200—22no—
98C2×#1200—41no—
99C2×#1200C2×C414yes—
100C2×#1200C2×C414yescomplemented
101#6714—22no—
102#6714—22no—
103#6714—41no—
104C5×C4⋊Dic3C2×C414yescomplemented
105C5×Dic3⋊C4—22no—
106C4×C5×Dic3—22no—
107C3×#683—22no—
108C3×#683D414yescomplemented
109C3×C4×Dic5—41no—
110C3×C4×Dic5—41no—
111C3×C4×Dic5C2×C414yescomplemented
112Dic3⋊Dic5—22no—
113#6668—22no—
114#6668—22no—
115#6667—22no—
116#6667—22no—
117#6667—41no—
118#6667C2×C414yes—
119#6667C2×C414yescomplemented
120Dic3×Dic5—22no—
121C2×#892—51no—
122C2×D3×C4⋊C4—51no—
123C2×C4×D12—51no—
124C3×C4×C4⋊C4—51no—
125#4987—51no—
126#4987—51no—
127#4940—51no—
128#4940—51no—
129C4×(C2×D3)⋊C4—51no—
130C4×(C2×D3)⋊C4—51no—
131#4936—51no—
132#4665—51no—
133#4665—51no—
134#4653—51no—
135#4653D511yescharacteristic, complemented
136C22×D20—31no—
137C22×C4×D5—31no—
138C22×C4×D5—31no—
139C22×C4×D5—31no—
140C22×C4×D5—31no—
141C2×C5×C4⋊C4—31no—
142C2×C5×C4⋊C4—31no—
143C2×C42×C5—31no—
144C2×#685—31no—
145C2×#685—31no—
146C2×#685—31no—
147C2×#685—31no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
151C2×#685—31no—
152C2×C4⋊Dic5—31no—
153C2×#683—31no—
154C2×#683—31no—
155C2×#683C2×D311yescharacteristic
156C2×#683C2×D311yescharacteristic
157C2×C4×Dic5—31no—
158C2×C4×Dic5C2×D311yescharacteristic
159C2×C4×Dic5C2×D311yescharacteristic
160C2×C4×Dic5C2×D311yescharacteristic
161#4039—38no—
162D5×C4⋊C4—64no—
163#4018—64no—
164C5×#95—31no—
165C5×#95—31no—
166C5×#95—31no—
167C5×#95C2×D311yescharacteristic
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#3963—31no—
173#3963C2×D311yescharacteristic
174#2352—151noSylow
175C23×C3×C5C2411yescharacteristic
176C22×D15—21no—
177C22×D15—21no—
178C22×D15—21no—
179C22×D15—21no—
180C22×D15—21no—
181C22×D15—21no—
182C22×D15—21no—
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15C22×C412yes—
187C22×D15C22×C412yes—
188C22×D15#4112yes—
189C22×D15#4112yes—
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×C5—21no—
197C2×C3×C4×C5C22×C412yes—
198C2×C3×C4×C5C2×D412yes—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204C2×Dic15—21no—
205D60—28no—
206C4×D15—44no—
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×Dic3C22×C412yes—
218C2×C5×Dic3C22×C412yes—
219C2×C3×Dic5—21no—
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×Dic5C22×C412yes—
227C2×C3×Dic5C22×C412yes—
228C2×C3×Dic5C2×D412yes—
229C2×C3×Dic5C2×D412yes—
230C2×C3×Dic5#4112yes—
231#1200—28no—
232#1200—28no—
233#1200—44no—
234C22×D12—51no—
235C22×C4×D3—51no—
236C22×C4×D3—51no—
237C22×C4×D3—51no—
238C22×C4×D3—51no—
239C2×C3×C4⋊C4—51no—
240C2×C3×C4⋊C4—51no—
241C2×C3×C42—51no—
242C2×C3×C42—51no—
243C2×C3×C42—51no—
244C2×(C2×D3)⋊C4—51no—
245C2×(C2×D3)⋊C4—51no—
246C2×(C2×D3)⋊C4—51no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4—51no—
249C2×(C2×D3)⋊C4—51no—
250C2×(C2×D3)⋊C4—51no—
251C2×(C2×D3)⋊C4—51no—
252C2×C4⋊Dic3—51no—
253C2×C4⋊Dic3—51no—
254C2×C4⋊Dic3C2×D511yescharacteristic
255C2×Dic3⋊C4—51no—
256C2×Dic3⋊C4C2×D511yescharacteristic
257C2×C4×Dic3—51no—
258C2×C4×Dic3C2×D511yescharacteristic
259#892—104no—
260D3×C4⋊C4—104no—
261C4×D12—58no—
262C3×#95—51no—
263C3×#95C2×D511yescharacteristic
264C3⋊#95—51no—
265C3⋊#95—51no—
266C3⋊#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95C2×D511yescharacteristic
270C3⋊#95C2×D511yescharacteristic
271C3⋊#95C2×D511yescharacteristic
272C23×D5—31no—
273C23×D5—31no—
274C22×C4×C5—31no—
275C22×C4×C5—31no—
276C22×C4×C5—31no—
277C22×C4×C5—31no—
278C22×C4×C5C22×D311yescharacteristic
279C22×C4×C5C22×D311yescharacteristic
280C22×C4×C5C22×D311yescharacteristic
281C22×Dic5—31no—
282C22×Dic5—31no—
283C22×Dic5C22×D311yescharacteristic
284C22×Dic5C22×D311yescharacteristic
285C22×Dic5C22×D311yescharacteristic
286C22×Dic5C22×D311yescharacteristic
287C2×D20—34no—
288C2×D20—62no—
289C2×D20—62no—
290C2×C4×D5—34no—
291C2×C4×D5—34no—
292C2×C4×D5—62no—
293C2×C4×D5—62no—
294C2×C4×D5—62no—
295C2×C4×D5—62no—
296C2×C4×D5—62no—
297C2×C4×D5—62no—
298C2×C4×D5—62no—
299C2×C4×D5—62no—
300C2×C4×D5—121no—
301C2×C4×D5—121no—
302C5×C4⋊C4—34no—
303C5×C4⋊C4—62no—
304C42×C5—62no—
305#685—34no—
306#685—34no—
307#685—62no—
308#685—62no—
309#685—62no—
310#685—62no—
311#685—121no—
312#685—121no—
313C4⋊Dic5—62no—
314#683—22no—
315#683—62no—
316#683—62no—
317#683D1214yescomplemented
318C4×Dic5—41no—
319C4×Dic5—41no—
320C4×Dic5—62no—
321C4×Dic5C4×D314yescomplemented
322C2×C4×D4—151no—
323C2×#117—151no—
324C22×C4⋊C4—151no—
325#388—151no—
326#388—151no—
327#387—31no—
328#387—151no—
329#386—151no—
330#386—151no—
331#382—151no—
332#380—151no—
333#380—151no—
334C4×C4⋊C4—51no—
335C4×C22⋊C4—151no—
336C4×C22⋊C4—151no—
337C22×C3×C5C23×C411yescharacteristic
338C22×C3×C5C22×D411yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C22×C3×C5H(5,𝔽2)11yescharacteristic
343C22×C3×C52−1+411yescharacteristic
344C2×D15—22no—
345C2×D15—22no—
346C2×D15—22no—
347C2×D15—22no—
348C2×D15—22no—
349C2×D15—22no—
350C2×D15—22no—
351C2×D15—22no—
352C2×D15—22no—
353C2×D15—41no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—41no—
357C2×D15#11714yescomplemented
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360C3×C4×C5—41no—
361Dic15—41no—
362Dic15—41no—
363C3×Dic5—22no—
364C3×Dic5—22no—
365C3×Dic5—41no—
366C3×Dic5C4×D414yes—
367C5×Dic3—22no—
368C5×Dic3—22no—
369C5×Dic3—41no—
370C5×Dic3—41no—
371C23×D3—51no—
372C23×D3—51no—
373C22×C3×C4—51no—
374C22×C3×C4—51no—
375C22×C3×C4—51no—
376C22×C3×C4—51no—
377C22×C3×C4C22×D511yescharacteristic
378C22×C3×C4C22×D511yescharacteristic
379C22×C3×C4C22×D511yescharacteristic
380C22×Dic3—51no—
381C22×Dic3—51no—
382C22×Dic3C22×D511yescharacteristic
383C22×Dic3C22×D511yescharacteristic
384C22×Dic3C22×D511yescharacteristic
385C22×Dic3C22×D511yescharacteristic
386C2×D12—54no—
387C2×D12—102no—
388C2×D12—102no—
389C2×C4×D3—54no—
390C2×C4×D3—54no—
391C2×C4×D3—102no—
392C2×C4×D3—102no—
393C2×C4×D3—102no—
394C2×C4×D3—102no—
395C2×C4×D3—102no—
396C2×C4×D3—102no—
397C2×C4×D3—102no—
398C2×C4×D3—102no—
399C2×C4×D3—201no—
400C2×C4×D3—201no—
401C3×C4⋊C4—54no—
402C3×C4⋊C4—102no—
403C3×C42—54no—
404C3×C42—201no—
405C3×C42—201no—
406(C2×D3)⋊C4—54no—
407(C2×D3)⋊C4—54no—
408(C2×D3)⋊C4—102no—
409(C2×D3)⋊C4—102no—
410(C2×D3)⋊C4—102no—
411(C2×D3)⋊C4—102no—
412(C2×D3)⋊C4—201no—
413(C2×D3)⋊C4—201no—
414C4⋊Dic3—102no—
415C4⋊Dic3—102no—
416C4⋊Dic3C4×D514yescomplemented
417Dic3⋊C4—22no—
418Dic3⋊C4—102no—
419C4×Dic3—22no—
420C4×Dic3—102no—
421C23×C5C23×D311yescharacteristic
422C22×D5—32no—
423C22×D5—32no—
424C22×D5—32no—
425C22×D5—32no—
426C22×D5—61no—
427C22×D5—61no—
428C22×D5—61no—
429C22×D5—61no—
430C22×D5—61no—
431C22×D5—61no—
432C22×D5—61no—
433C22×D5—61no—
434C22×D5—61no—
435C22×D5—61no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—32no—
444C2×C4×C5—32no—
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—61no—
452C2×C4×C5—61no—
453C2×C4×C5—61no—
454C2×C4×C5—61no—
455C2×C4×C5C2×C4×D312yes—
456C2×C4×C5C2×D1212yes—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—21no—
463C2×Dic5—21no—
464C2×Dic5—61no—
465C2×Dic5—61no—
466C2×Dic5—61no—
467C2×Dic5—61no—
468C2×Dic5—61no—
469C2×Dic5—61no—
470C2×Dic5C2×C4×D312yes—
471C2×Dic5C2×C4×D312yes—
472C2×Dic5C2×D1212yes—
473C2×Dic5C2×D1212yes—
474C2×Dic5#23512yes—
475D20—68no—
476C4×D5—68no—
477C4×D5—68no—
478C4×D5—124no—
479C4×D5—124no—
480C22×D4—151no—
481C23×C4—151no—
482C23×C4—151no—
483C23×C4—151no—
484C23×C4—151no—
485C4×D4—158no—
486#117—304no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—51no—
491C2×C4⋊C4—151no—
492C2×C4⋊C4—151no—
493C2×C4⋊C4—151no—
494C2×C4⋊C4—304no—
495C2×C22⋊C4—151no—
496C2×C22⋊C4—151no—
497C2×C22⋊C4—151no—
498C2×C22⋊C4—151no—
499C2×C22⋊C4—151no—
500C2×C22⋊C4—151no—
501C2×C22⋊C4—151no—
502C2×C22⋊C4—151no—
503C2×C42—31no—
504C2×C42—51no—
505C2×C42—51no—
506C2×C42—51no—
507C2×C42—151no—
508#95—31no—
509#95—31no—
510#95—31no—
511#95—51no—
512#95—151no—
513#95—151no—
514#95—151no—
515#95—151no—
516#95—151no—
517#95D3×D511yescharacteristic
518C2×C3×C5C2×#11711yescharacteristic
519C2×C3×C5C2×C4×D411yescharacteristic
520C2×C3×C5#52011yescharacteristic
521C2×C3×C5#54611yescharacteristic
522C2×C3×C5#54811yescharacteristic
523C2×C3×C5#55211yescharacteristic
524C2×C3×C5#55311yescharacteristic
525D15—24no—
526D15—42no—
527C23×C3C23×D511yescharacteristic
528C22×D3—52no—
529C22×D3—52no—
530C22×D3—52no—
531C22×D3—52no—
532C22×D3—101no—
533C22×D3—101no—
534C22×D3—101no—
535C22×D3—101no—
536C22×D3—101no—
537C22×D3—101no—
538C22×D3—101no—
539C22×D3—101no—
540C22×D3—101no—
541C22×D3—101no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—52no—
550C2×C3×C4—52no—
551C2×C3×C4—52no—
552C2×C3×C4—52no—
553C2×C3×C4—52no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4—101no—
558C2×C3×C4—101no—
559C2×C3×C4—101no—
560C2×C3×C4—101no—
561C2×C3×C4C2×C4×D512yes—
562C2×C3×C4D4×D512yes—
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—21no—
572C2×Dic3—21no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—101no—
579C2×Dic3C2×C4×D512yes—
580C2×Dic3C2×C4×D512yes—
581D12—108no—
582C4×D3—108no—
583C4×D3—108no—
584C4×D3—204no—
585C4×D3—204no—
586C22×C5C22×C4×D311yescharacteristic
587C22×C5C22×D1211yescharacteristic
588C22×C5C2×#23511yescharacteristic
589C22×C5#100411yescharacteristic
590C22×C5#100711yescharacteristic
591C22×C5D3×#4111yescharacteristic
592C22×C5D3×#4111yescharacteristic
593C2×D5—34no—
594C2×D5—62no—
595C2×D5—62no—
596C2×D5—62no—
597C2×D5—62no—
598C2×D5—62no—
599C2×D5—62no—
600C2×D5—62no—
601C2×D5—62no—
602C2×D5—62no—
603C2×D5—121no—
604C2×D5—121no—
605C2×D5—121no—
606C2×D5—121no—
607C4×C5—22no—
608C4×C5—22no—
609C4×C5—41no—
610C4×C5—62no—
611C4×C5—62no—
612C4×C5—121no—
613C4×C5—121no—
614Dic5—22no—
615Dic5—22no—
616Dic5—41no—
617Dic5—121no—
618Dic5—121no—
619Dic5C4×D1214yes—
620C24—151no—
621C24—151no—
622C2×D4—154no—
623C2×D4—302no—
624C2×D4—302no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—154no—
634C22×C4—154no—
635C22×C4—151no—
636C22×C4—151no—
637C22×C4—302no—
638C22×C4—302no—
639C22×C4—302no—
640C22×C4—302no—
641C22×C4—302no—
642C22×C4—302no—
643C22×C4—302no—
644C22×C4—302no—
645C22×C4—601no—
646C22×C4—601no—
647C22×C4C2×D3×D511yescharacteristic
648C22×C4C2×D3×D511yescharacteristic
649C22×C4C2×D3×D511yescharacteristic
650C4⋊C4—34no—
651C4⋊C4—54no—
652C4⋊C4—62no—
653C4⋊C4—102no—
654C4⋊C4—302no—
655C4⋊C4—302no—
656C4⋊C4—302no—
657C22⋊C4—154no—
658C22⋊C4—154no—
659C22⋊C4—302no—
660C22⋊C4—302no—
661C22⋊C4—302no—
662C22⋊C4—302no—
663C22⋊C4—601no—
664C22⋊C4—601no—
665C42—54no—
666C42—62no—
667C42—201no—
668C42—201no—
669C42—302no—
670C3×C5#235211yescharacteristic, complemented, Hall
671C22×C3C22×C4×D511yescharacteristic
672C22×C3C2×D4×D511yescharacteristic
673C22×C3#414711yescharacteristic
674C22×C3D5×#4111yescharacteristic
675C22×C3D5×#4111yescharacteristic
676C22×C3D5×#4111yescharacteristic
677C22×C3#414911yescharacteristic
678C2×D3—54no—
679C2×D3—102no—
680C2×D3—102no—
681C2×D3—102no—
682C2×D3—102no—
683C2×D3—102no—
684C2×D3—102no—
685C2×D3—102no—
686C2×D3—102no—
687C2×D3—102no—
688C2×D3—201no—
689C2×D3—201no—
690C2×D3—201no—
691C2×D3—201no—
692C3×C4—22no—
693C3×C4—22no—
694C3×C4—41no—
695C3×C4—54no—
696C3×C4—102no—
697C3×C4—102no—
698C3×C4—201no—
699Dic3—22no—
700Dic3—22no—
701Dic3—41no—
702Dic3—41no—
703Dic3—201no—
704Dic3—201no—
705C2×C5C2×C4×D1211yescharacteristic
706C2×C5#550411yescharacteristic
707C2×C5D3×#11711yescharacteristic
708C2×C5#555411yescharacteristic
709C2×C5#555811yescharacteristic
710C2×C5#557611yescharacteristic
711C2×C5#558111yescharacteristic
712D5—64no—
713D5—122no—
714C23—152no—
715C23—152no—
716C23—152no—
717C23—152no—
718C23—301no—
719C23—301no—
720C23—301no—
721C23—301no—
722C23—301no—
723C23—301no—
724C23—301no—
725C23—301no—
726C23—301no—
727C23—301no—
728C23C22×D3×D511yescharacteristic
729D4—308no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—52no—
740C2×C4—52no—
741C2×C4—52no—
742C2×C4—52no—
743C2×C4—52no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—101no—
759C2×C4—101no—
760C2×C4—101no—
761C2×C4—308no—
762C2×C4—308no—
763C2×C4—301no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—301no—
767C2×C4—301no—
768C2×C4—301no—
769C2×C4—604no—
770C2×C4—604no—
771C2×C4C4×D3×D512yes—
772C2×C4D5×D1212yes—
773C2×C3D5×#11711yescharacteristic
774C2×C3C4×D4×D511yescharacteristic
775C2×C3#6590811yescharacteristic
776C2×C3#6596711yescharacteristic
777C2×C3#6598811yescharacteristic
778C2×C3#6602711yescharacteristic
779C2×C3#6604311yescharacteristic
780D3—104no—
781D3—202no—
782C5#7377111yescharacteristic, complemented, Sylow
783C22—154no—
784C22—302no—
785C22—302no—
786C22—302no—
787C22—302no—
788C22—302no—
789C22—302no—
790C22—302no—
791C22—302no—
792C22—302no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—601no—
797C22C2×C4×D3×D511yescharacteristic
798C22C2×D5×D1211yescharacteristic
799C22D5×#23511yescharacteristic
800C22#9202411yescharacteristic
801C22#9202411yescharacteristic
802C22#9202611yescharacteristic
803C22#9202911yescharacteristic
804C4—22no—
805C4—22no—
806C4—41no—
807C4—54no—
808C4—62no—
809C4—62no—
810C4—102no—
811C4—102no—
812C4—121no—
813C4—121no—
814C4—201no—
815C4—601no—
816C4—601no—
817C3#1060703611yescharacteristic, complemented, Sylow
818C2—304no—
819C2—602no—
820C2C4×D5×D1211yescharacteristic
821C2#1175282511yescharacteristic
822C2#1175309411yescharacteristic
823C2#1175326611yescharacteristic
824C2#1175333611yescharacteristic
825C2#1175334111yescharacteristic
826C2#1175338311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D60C22
hypercenter#95D3×D5
hypocenterC3×C5#2352
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#91404C2semidirect
3. C2×#91403C2semidirect
5. C5×#4653C2semidirect
6. C3×#64938C2semidirect
8. #11748876C2semidirect
9. #11748876C2semidirect
10. #11748875C2semidirect
11. #11748727C2semidirect
12. #11748726C2semidirect
13. C4×#6667C2semidirect
14. #11748682C2semidirect
15. #11748580C2semidirect
42. #91418C4semidirect
70. #64938D3semidirect
100. C2×#1200C2×C4semidirect
104. C5×C4⋊Dic3C2×C4semidirect
108. C3×#683D4semidirect
111. C3×C4×Dic5C2×C4semidirect
119. #6667C2×C4semidirect
135. #4653D5semidirect
317. #683D12semidirect
321. C4×Dic5C4×D3semidirect
357. C2×D15#117semidirect
416. C4⋊Dic3C4×D5semidirect
670. C3×C5#2352semidirect
782. C5#73771semidirect
817. C3#10607036semidirect

Maximal subgroups

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

subgroupindex
C2×#914182
C2×#914042
C2×#914032
#117507662
C5×#46532
C3×#649382
#117489042
#117488762
#117488752
#117487272
#117487262
C4×#66672
#117486822
#117485802
#106070363
#737715