Finite Group Databasebeta

← #14326072

Subgroups — #14326072

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6773C211yesmaximal, characteristic
2C2×#91396C211yesmaximal, characteristic, complemented
3C2×#91395C211yesmaximal, characteristic, complemented
4#11750766C211yesmaximal, characteristic, complemented
5C5×#4646C211yesmaximal, characteristic, complemented
6C3×#64953C211yesmaximal, characteristic, complemented
7#11748904C211yesmaximal, characteristic, complemented
8#11748889C211yesmaximal, characteristic, complemented
9#11748888C211yesmaximal, characteristic, complemented
10#11748882C211yesmaximal, characteristic, complemented
11#11748881C211yesmaximal, characteristic, complemented
12#11748872C211yesmaximal, characteristic, complemented
13#11748872C211yesmaximal, characteristic, complemented
14D5×C3⋊#95C211yesmaximal, characteristic, complemented
15#11748692C211yesmaximal, characteristic, complemented
16#10608344—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C5×Dic6C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×#1202C2211yescharacteristic
22C22×#1202C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C22×D5×Dic3C2211yescharacteristic
28C2×#6773—24no—
29C2×#6773—24no—
30C2×#6773C418yescomplemented
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C4×C5×Dic3C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×Dic3⋊Dic5C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43#91396—24no—
44#91395—24no—
45C3×C5×#95C2211yescharacteristic
46#91115C2211yescharacteristic
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#74121—51nomaximal, Hall
58C22×#713—31no—
59C2×#4039—31no—
60C2×C4×D20—31no—
61C5×#391—31no—
62#65519—31no—
63#65276—31no—
64C4×#685—31no—
65#64954—31no—
66#64954—31no—
67#64954—31no—
68#64954—31no—
69#64953—31no—
70#64953D311yescharacteristic, complemented
71D5×#95—31no—
72D5×#95—31no—
73C23×D15C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C2×D60—22no—
82C2×D60—22no—
83C2×D60C2×C414yescomplemented
84C2×C4×D15—22no—
85C2×C4×D15—22no—
86C2×C4×D15—41no—
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C2×C5×Dic6—22no—
92C2×C5×Dic6—22no—
93C2×C5×Dic6C2×C414yescomplemented
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5C2×C414yescomplemented
100C2×#1202—22no—
101C2×#1202—22no—
102C2×#1202C2×C414yes—
103C2×#1202C2×C414yescomplemented
104C2×#1202D414yes—
105C2×#1202D414yes—
106C2×#1200—22no—
107C2×#1200—22no—
108C2×#1200—22no—
109C2×#1200—22no—
110C2×#1200—22no—
111C2×#1200—22no—
112C2×#1200—41no—
113C2×#1200C2×C414yescomplemented
114C2×#1200C2×C414yescomplemented
115C2×D5×Dic3—22no—
116C2×D5×Dic3—22no—
117C2×D5×Dic3—22no—
118C2×D5×Dic3—22no—
119C2×D5×Dic3—41no—
120C2×D5×Dic3—41no—
121#6773—232no—
122#6714—22no—
123#6714—22no—
124#6714—41no—
125C5×Dic3⋊C4—22no—
126C4×C5×Dic3—22no—
127C3×#685—22no—
128C3×#685—22no—
129Dic3⋊Dic5—22no—
130#6667—22no—
131#6667—22no—
132#6667—41no—
133Dic3×Dic5—22no—
134C22×#235—51no—
135C2×#67⋊C4—51no—
136C2×#67⋊C4—51no—
137C3×#381—51no—
138C2×C3⋊#95—51no—
139#4958—51no—
140#4958—51no—
141#4667—51no—
142#4666—51no—
143#4665—51no—
144#4665—51no—
145#4664—51no—
146D3×#95—51no—
147#4646—51no—
148#4646D511yescharacteristic, complemented
149C22×C5×Q8—31no—
150C2×#713—38no—
151C2×#713—64no—
152C2×#713—64no—
153C22×D20—31no—
154C22×D20—31no—
155C22×D20—31no—
156C22×C4×D5—31no—
157C22×C4×D5—31no—
158C22×C4×D5—31no—
159C22×C4×D5—31no—
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×C4×D5C2×D311yescharacteristic
163C2×C5×C4⋊C4—31no—
164C2×C42×C5—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685C2×D311yescharacteristic
172C2×#685C2×D311yescharacteristic
173C2×C4⋊Dic5—31no—
174C2×C4×Dic5—31no—
175#4039—64no—
176C4×D20—64no—
177C5×#95—31no—
178C5×#95—31no—
179C5×#95—31no—
180C5×#95C2×D311yescharacteristic
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963C2×D311yescharacteristic
187#3963C2×D311yescharacteristic
188#3963C2×D311yescharacteristic
189#2339—151noSylow
190C23×C3×C5C2411yescharacteristic
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—21no—
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15C22×C412yes—
202C22×D15C22×C412yes—
203C22×D15C2×D412yes—
204C22×D15C2×D412yes—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5C22×C412yes—
210C22×C3×D5C2×D412yes—
211C22×C3×D5C2×D412yes—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5C22×C412yes—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15#4112yescomplemented
227D60—28no—
228C4×D15—44no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3C22×C412yes—
237C2×C5×Dic3C22×C412yes—
238C2×C5×Dic3C2×D412yes—
239C2×C5×Dic3C2×D412yes—
240C2×C5×Dic3#4112yescomplemented
241C5×Dic6—28no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5C22×C412yes—
251C3×C4×D5—28no—
252#1202—28no—
253#1202C22⋊C4116yescomplemented
254#1200—28no—
255#1200—28no—
256#1200—44no—
257D5×Dic3—44no—
258D5×Dic3—44no—
259C23×C3×C4—51no—
260C22×#67—51no—
261C22×#67—51no—
262C23×Dic3—51no—
263C23×Dic3—51no—
264C2×#235—58no—
265C2×#235—104no—
266C2×#235—104no—
267C22×D12—51no—
268C22×C4×D3—51no—
269C22×C4×D3—51no—
270C22×C4×D3—51no—
271C22×C4×D3—51no—
272C22×Dic6C2×D511yescharacteristic
273C2×C3×C22⋊C4—51no—
274C2×C3×C22⋊C4—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×Dic3⋊C4—51no—
282C2×Dic3⋊C4C2×D511yescharacteristic
283C2×C4×Dic3—51no—
284C2×C4×Dic3C2×D511yescharacteristic
285#67⋊C4—104no—
286#67⋊C4—104no—
287C3×#95—51no—
288C3×#95—51no—
289C3×#95—51no—
290C3×#95C2×D511yescharacteristic
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95C2×D511yescharacteristic
297C3⋊#95C2×D511yescharacteristic
298C3⋊#95C2×D511yescharacteristic
299C23×D5—31no—
300C23×D5—31no—
301C23×D5C22×D311yescharacteristic
302C2×C5×Q8—34no—
303C2×C5×Q8—62no—
304C2×C5×Q8—62no—
305C22×C4×C5—31no—
306C22×C4×C5—31no—
307C22×C4×C5—31no—
308C22×C4×C5—31no—
309C22×C4×C5C22×D311yescharacteristic
310C22×C4×C5C22×D311yescharacteristic
311C22×C4×C5C22×D311yescharacteristic
312C22×Dic5—31no—
313C22×Dic5—31no—
314C22×Dic5C22×D311yescharacteristic
315C22×Dic5C22×D311yescharacteristic
316C22×Dic5C22×D311yescharacteristic
317#713—632no—
318C2×D20—34no—
319C2×D20—34no—
320C2×D20—34no—
321C2×D20—34no—
322C2×D20—34no—
323C2×D20—62no—
324C2×D20—62no—
325C2×D20—62no—
326C2×D20—62no—
327C2×C4×D5—22no—
328C2×C4×D5—22no—
329C2×C4×D5—34no—
330C2×C4×D5—34no—
331C2×C4×D5—62no—
332C2×C4×D5—62no—
333C2×C4×D5—62no—
334C2×C4×D5—62no—
335C2×C4×D5—62no—
336C2×C4×D5—62no—
337C2×C4×D5—62no—
338C2×C4×D5—62no—
339C2×C4×D5—62no—
340C2×C4×D5—62no—
341C2×C4×D5—62no—
342C2×C4×D5—62no—
343C2×C4×D5—121no—
344C2×C4×D5—121no—
345C2×C4×D5—121no—
346C2×C4×D5—121no—
347C2×C4×D5C4×D314yescomplemented
348C5×C4⋊C4—62no—
349C42×C5—62no—
350#685—22no—
351#685—22no—
352#685—62no—
353#685—62no—
354#685—62no—
355#685—62no—
356#685—121no—
357#685—121no—
358C4⋊Dic5—62no—
359C4×Dic5—62no—
360C22×#41—151no—
361C2×C4×D4—151no—
362C2×C4×D4—151no—
363#391—31no—
364#391—151no—
365#386—151no—
366#386—151no—
367#386—151no—
368#386—151no—
369#381—51no—
370#381—151no—
371#380—151no—
372C4×C22⋊C4—151no—
373C2×#95—151no—
374C2×#95—151no—
375C22×C3×C5C23×C411yescharacteristic
376C22×C3×C5C22×D411yescharacteristic
377C22×C3×C5C22×D411yescharacteristic
378C22×C3×C5C2×#4111yescharacteristic
379C22×C3×C5C2×#4111yescharacteristic
380C22×C3×C5H(5,𝔽2)11yescharacteristic
381C22×C3×C52−1+411yescharacteristic
382C2×D15—22no—
383C2×D15—22no—
384C2×D15—22no—
385C2×D15—22no—
386C2×D15—22no—
387C2×D15—22no—
388C2×D15—22no—
389C2×D15—22no—
390C2×D15—22no—
391C2×D15—41no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—41no—
395C2×D15C2×C22⋊C414yes—
396C2×C3×D5—22no—
397C2×C3×D5—22no—
398C2×C3×D5—22no—
399C2×C3×D5—22no—
400C2×C3×D5—22no—
401C2×C3×D5—22no—
402C2×C3×D5C2×C22⋊C414yes—
403C3×C4×C5—22no—
404C3×C4×C5—41no—
405C3×C4×C5—41no—
406Dic15—22no—
407Dic15—41no—
408C3×Dic5—22no—
409C3×Dic5—41no—
410C3×Dic5—41no—
411C5×Dic3—22no—
412C5×Dic3—22no—
413C5×Dic3—41no—
414C5×Dic3C2×C22⋊C414yes—
415C24×C3—51no—
416C23×D3—51no—
417C23×D3—51no—
418C22×C3×C4—51no—
419C22×C3×C4—54no—
420C22×C3×C4—51no—
421C22×C3×C4—51no—
422C22×C3×C4—102no—
423C22×C3×C4—102no—
424C22×C3×C4C22×D511yescharacteristic
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—54no—
428C2×#67—54no—
429C2×#67—54no—
430C2×#67—54no—
431C2×#67—102no—
432C2×#67—102no—
433C22×Dic3—51no—
434C22×Dic3—51no—
435C22×Dic3—102no—
436C22×Dic3—102no—
437C22×Dic3—102no—
438C22×Dic3—102no—
439C22×Dic3—201no—
440C22×Dic3—201no—
441C22×Dic3C22×D511yescharacteristic
442C22×Dic3C22×D511yescharacteristic
443C22×Dic3C22×D511yescharacteristic
444C22×Dic3C22×D511yescharacteristic
445#235—1032no—
446C2×D12—54no—
447C2×D12—102no—
448C2×D12—102no—
449C2×C4×D3—54no—
450C2×C4×D3—54no—
451C2×C4×D3—102no—
452C2×C4×D3—102no—
453C2×C4×D3—102no—
454C2×C4×D3—102no—
455C2×C4×D3—102no—
456C2×C4×D3—102no—
457C2×C4×D3—102no—
458C2×C4×D3—102no—
459C2×C4×D3—201no—
460C2×C4×D3—201no—
461C2×Dic6—22no—
462C2×Dic6—22no—
463C2×Dic6C4×D514yescomplemented
464C3×C22⋊C4—102no—
465C3×C22⋊C4—102no—
466(C2×D3)⋊C4—102no—
467(C2×D3)⋊C4—102no—
468(C2×D3)⋊C4—102no—
469(C2×D3)⋊C4—102no—
470(C2×D3)⋊C4—201no—
471(C2×D3)⋊C4—201no—
472Dic3⋊C4—22no—
473Dic3⋊C4—102no—
474C4×Dic3—22no—
475C4×Dic3—102no—
476C23×C5C23×D311yescharacteristic
477C22×D5—21no—
478C22×D5—21no—
479C22×D5—21no—
480C22×D5—21no—
481C22×D5—32no—
482C22×D5—32no—
483C22×D5—32no—
484C22×D5—32no—
485C22×D5—61no—
486C22×D5—61no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C22×D5—61no—
493C22×D5—61no—
494C22×D5—61no—
495C22×D5C2×C4×D312yes—
496C22×D5D3×D412yes—
497C22×D5D3×D412yes—
498C5×Q8—68no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—32no—
510C2×C4×C5—32no—
511C2×C4×C5—32no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5—61no—
518C2×C4×C5—61no—
519C2×C4×C5C2×C4×D312yes—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—32no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5C2×C4×D312yes—
535D20—316no—
536D20—68no—
537D20—68no—
538C4×D5—28no—
539C4×D5—68no—
540C4×D5—68no—
541C4×D5—124no—
542C4×D5—124no—
543C4×D5—124no—
544C4×D5—124no—
545C2×#41—158no—
546C2×#41—304no—
547C2×#41—304no—
548C22×Q8—31no—
549C22×D4—151no—
550C22×D4—151no—
551C22×D4—151no—
552C23×C4—51no—
553C23×C4—151no—
554C23×C4—151no—
555C23×C4—151no—
556C23×C4—151no—
557C23×C4—151no—
558C23×C4—151no—
559C4×D4—304no—
560C4×D4—304no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—151no—
563C2×C22⋊C4—51no—
564C2×C22⋊C4—51no—
565C2×C22⋊C4—151no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4—151no—
571C2×C42—31no—
572C2×C42—151no—
573#95—31no—
574#95—31no—
575#95—31no—
576#95—51no—
577#95—51no—
578#95—51no—
579#95—151no—
580#95—151no—
581#95—151no—
582#95—151no—
583#95—151no—
584#95D3×D511yescharacteristic
585C2×C3×C5C22×C22⋊C411yescharacteristic
586C2×C3×C5C4×#4111yescharacteristic
587C2×C3×C5#52011yescharacteristic
588C2×C3×C5#54611yescharacteristic
589C2×C3×C5#54611yescharacteristic
590C2×C3×C5#54711yescharacteristic
591C2×C3×C5#54711yescharacteristic
592D15—24no—
593D15—42no—
594C3×D5—24no—
595C23×C3—52no—
596C23×C3—52no—
597C23×C3—52no—
598C23×C3—101no—
599C23×C3—101no—
600C23×C3—101no—
601C23×C3—101no—
602C23×C3C23×D511yescharacteristic
603C22×D3—52no—
604C22×D3—52no—
605C22×D3—52no—
606C22×D3—52no—
607C22×D3—101no—
608C22×D3—101no—
609C22×D3—101no—
610C22×D3—101no—
611C22×D3—101no—
612C22×D3—101no—
613C22×D3—101no—
614C22×D3—101no—
615C22×D3—101no—
616C22×D3—101no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—52no—
626C2×C3×C4—108no—
627C2×C3×C4—101no—
628C2×C3×C4—101no—
629C2×C3×C4—101no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4C2×C4×D512yes—
636#67—516no—
637#67—108no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—52no—
646C2×Dic3—101no—
647C2×Dic3—101no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—204no—
652C2×Dic3—204no—
653C2×Dic3C2×C4×D512yes—
654C2×Dic3C2×C4×D512yes—
655C2×Dic3D4×D512yes—
656C2×Dic3D4×D512yes—
657C2×Dic3#71312yescomplemented
658D12—108no—
659C4×D3—108no—
660C4×D3—108no—
661C4×D3—204no—
662C4×D3—204no—
663Dic6—28no—
664C22×C5C22×C4×D311yescharacteristic
665C22×C5C2×D3×D411yescharacteristic
666C22×C5C2×D3×D411yescharacteristic
667C22×C5D3×#4111yescharacteristic
668C22×C5D3×#4111yescharacteristic
669C22×C5#100911yescharacteristic
670C22×C5#101011yescharacteristic
671C2×D5—22no—
672C2×D5—22no—
673C2×D5—22no—
674C2×D5—22no—
675C2×D5—22no—
676C2×D5—22no—
677C2×D5—34no—
678C2×D5—62no—
679C2×D5—62no—
680C2×D5—62no—
681C2×D5—62no—
682C2×D5—62no—
683C2×D5—62no—
684C2×D5—62no—
685C2×D5—62no—
686C2×D5—62no—
687C2×D5—121no—
688C2×D5—121no—
689C2×D5—121no—
690C2×D5—121no—
691C2×D5D3×C22⋊C414yes—
692C4×C5—22no—
693C4×C5—34no—
694C4×C5—41no—
695C4×C5—41no—
696C4×C5—62no—
697C4×C5—62no—
698C4×C5—121no—
699Dic5—22no—
700Dic5—41no—
701Dic5—41no—
702Dic5—62no—
703Dic5—121no—
704C24—51no—
705C24—151no—
706C24—151no—
707#41—3032no—
708C2×Q8—34no—
709C2×Q8—62no—
710C2×Q8—62no—
711C2×D4—154no—
712C2×D4—154no—
713C2×D4—154no—
714C2×D4—154no—
715C2×D4—154no—
716C2×D4—302no—
717C2×D4—302no—
718C2×D4—302no—
719C2×D4—302no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—51no—
725C22×C4—54no—
726C22×C4—51no—
727C22×C4—51no—
728C22×C4—102no—
729C22×C4—102no—
730C22×C4—154no—
731C22×C4—154no—
732C22×C4—151no—
733C22×C4—151no—
734C22×C4—302no—
735C22×C4—302no—
736C22×C4—302no—
737C22×C4—302no—
738C22×C4—302no—
739C22×C4—302no—
740C22×C4—302no—
741C22×C4—302no—
742C22×C4—302no—
743C22×C4—302no—
744C22×C4—302no—
745C22×C4—302no—
746C22×C4—601no—
747C22×C4—601no—
748C22×C4—601no—
749C22×C4—601no—
750C22×C4C2×D3×D511yescharacteristic
751C22×C4C2×D3×D511yescharacteristic
752C22×C4C2×D3×D511yescharacteristic
753C4⋊C4—62no—
754C4⋊C4—302no—
755C22⋊C4—102no—
756C22⋊C4—102no—
757C22⋊C4—302no—
758C22⋊C4—302no—
759C22⋊C4—302no—
760C22⋊C4—302no—
761C22⋊C4—601no—
762C22⋊C4—601no—
763C42—62no—
764C42—302no—
765C3×C5#233911yescharacteristic, complemented, Hall
766C22×C3—54no—
767C22×C3—102no—
768C22×C3—102no—
769C22×C3—102no—
770C22×C3—102no—
771C22×C3—102no—
772C22×C3—102no—
773C22×C3C22×C4×D511yescharacteristic
774C22×C3C2×D4×D511yescharacteristic
775C22×C3C2×D4×D511yescharacteristic
776C22×C3C2×#71311yescharacteristic
777C22×C3#414711yescharacteristic
778C22×C3D5×#4111yescharacteristic
779C22×C3#414911yescharacteristic
780C2×D3—54no—
781C2×D3—102no—
782C2×D3—102no—
783C2×D3—102no—
784C2×D3—102no—
785C2×D3—102no—
786C2×D3—102no—
787C2×D3—102no—
788C2×D3—102no—
789C2×D3—102no—
790C2×D3—201no—
791C2×D3—201no—
792C2×D3—201no—
793C2×D3—201no—
794C3×C4—22no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—102no—
798C3×C4—201no—
799C3×C4—201no—
800Dic3—22no—
801Dic3—22no—
802Dic3—41no—
803Dic3—102no—
804Dic3—201no—
805Dic3D5×C22⋊C414yes—
806C2×C5C2×D3×C22⋊C411yescharacteristic
807C2×C5#552211yescharacteristic
808C2×C5#552311yescharacteristic
809C2×C5#565411yescharacteristic
810C2×C5#565411yescharacteristic
811C2×C5#565511yescharacteristic
812C2×C5#565511yescharacteristic
813D5—24no—
814D5—64no—
815D5—122no—
816C23—52no—
817C23—52no—
818C23—52no—
819C23—101no—
820C23—101no—
821C23—101no—
822C23—101no—
823C23—152no—
824C23—152no—
825C23—152no—
826C23—152no—
827C23—301no—
828C23—301no—
829C23—301no—
830C23—301no—
831C23—301no—
832C23—301no—
833C23—301no—
834C23—301no—
835C23—301no—
836C23—301no—
837C23C22×D3×D511yescharacteristic
838Q8—68no—
839D4—1516no—
840D4—308no—
841D4—308no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—52no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—108no—
864C2×C4—101no—
865C2×C4—101no—
866C2×C4—101no—
867C2×C4—101no—
868C2×C4—101no—
869C2×C4—101no—
870C2×C4—101no—
871C2×C4—101no—
872C2×C4—152no—
873C2×C4—308no—
874C2×C4—308no—
875C2×C4—301no—
876C2×C4—301no—
877C2×C4—301no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—604no—
881C2×C4—604no—
882C2×C4—604no—
883C2×C4—604no—
884C2×C4C4×D3×D512yes—
885C2×C3—104no—
886C2×C3C2×D5×C22⋊C411yescharacteristic
887C2×C3C4×#71311yescharacteristic
888C2×C3#6590811yescharacteristic
889C2×C3#6596411yescharacteristic
890C2×C3#6596511yescharacteristic
891C2×C3#6601011yescharacteristic
892C2×C3#6606011yescharacteristic
893D3—104no—
894D3—202no—
895C5#7412111yescharacteristic, complemented, Sylow
896C22—54no—
897C22—102no—
898C22—102no—
899C22—102no—
900C22—102no—
901C22—102no—
902C22—102no—
903C22—154no—
904C22—302no—
905C22—302no—
906C22—302no—
907C22—302no—
908C22—302no—
909C22—302no—
910C22—302no—
911C22—302no—
912C22—302no—
913C22—601no—
914C22—601no—
915C22—601no—
916C22—601no—
917C22#9200011yescharacteristic
918C22C2×C4×D3×D511yescharacteristic
919C22#9201911yescharacteristic
920C22D3×D4×D511yescharacteristic
921C22D3×D4×D511yescharacteristic
922C22#9202411yescharacteristic
923C22D3×#71311yescharacteristic
924C4—22no—
925C4—34no—
926C4—41no—
927C4—41no—
928C4—62no—
929C4—62no—
930C4—102no—
931C4—121no—
932C4—201no—
933C4—201no—
934C4—302no—
935C4—601no—
936C3#1060834411yescharacteristic, complemented, Sylow
937C2—104no—
938C2—304no—
939C2—602no—
940C2#1175252111yescharacteristic
941C2#1175283811yescharacteristic
942C2D3×D5×C22⋊C411yescharacteristic
943C2#1175324011yescharacteristic
944C2#1175340311yescharacteristic
945C2#1175341811yescharacteristic
946C2#1175385911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6773C2
hypercenter#95D3×D5
hypocenterC3×C5#2339
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×#91396C2semidirect
3. C2×#91395C2semidirect
4. #11750766C2semidirect
5. C5×#4646C2semidirect
6. C3×#64953C2semidirect
7. #11748904C2semidirect
8. #11748889C2semidirect
9. #11748888C2semidirect
10. #11748882C2semidirect
11. #11748881C2semidirect
12. #11748872C2semidirect
13. #11748872C2semidirect
14. D5×C3⋊#95C2semidirect
15. #11748692C2semidirect
30. C2×#6773C4semidirect
70. #64953D3semidirect
83. C2×D60C2×C4semidirect
93. C2×C5×Dic6C2×C4semidirect
99. C2×C3×C4×D5C2×C4semidirect
103. C2×#1202C2×C4semidirect
113. C2×#1200C2×C4semidirect
114. C2×#1200C2×C4semidirect
148. #4646D5semidirect
226. C2×Dic15#41semidirect
240. C2×C5×Dic3#41semidirect
253. #1202C22⋊C4semidirect
347. C2×C4×D5C4×D3semidirect
463. C2×Dic6C4×D5semidirect
657. C2×Dic3#713semidirect
765. C3×C5#2339semidirect
895. C5#74121semidirect
936. C3#10608344semidirect

Maximal subgroups

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

subgroupindex
C22×#67732
C2×#913962
C2×#913952
#117507662
C5×#46462
C3×#649532
#117489042
#117488892
#117488882
#117488822
#117488812
#117488722
D5×C3⋊#952
#117486922
#106083443
#741215