Finite Group Databasebeta

← #14331639

Subgroups — #14331639

Order 1920.

1888 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6779C211yesmaximal, characteristic, complemented
2C2×C5×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×#91556C211yesmaximal, characteristic, complemented
4C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
5#11751324C211yesmaximal, characteristic, complemented
6C3×#65512C211yesmaximal, characteristic, complemented
7#11749524C211yesmaximal, characteristic, complemented
8#11749522C211yesmaximal, characteristic, complemented
9#11749510C211yesmaximal, characteristic, complemented
10#11749490C211yesmaximal, characteristic, complemented
11Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
12#11748937C211yesmaximal, characteristic, complemented
13#11748928C211yesmaximal, characteristic, complemented
14#11748881C211yesmaximal, characteristic, complemented
15Dic3×#685C211yesmaximal, characteristic, complemented
16#10614131—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×#1204C2211yescharacteristic
25C22×#1202C2211yescharacteristic
26C22×#1200C2211yescharacteristic
27C2×#6779—24no—
28C2×#6779—24no—
29C2×#6779—24no—
30C22×D5×Dic3C2211yescharacteristic
31C2×#6719C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×C5×#217C2211yescharacteristic
35C2×C5×#217C2211yescharacteristic
36C5×D4×Dic3—24no—
37C2×C5×C4⋊Dic3C2211yescharacteristic
38C2×C4×C5×Dic3C2211yescharacteristic
39C2×C3×C22⋊Dic5C2211yescharacteristic
40C2×C3×C22⋊Dic5C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42#91556—24no—
43Dic3×C22⋊D5—24no—
44C2×#6669C2211yescharacteristic
45C2×#6668C2211yescharacteristic
46C2×#6667C2211yescharacteristic
47C2×#6667C2211yescharacteristic
48C2×#6665C2211yescharacteristic
49C2×#6665C2211yescharacteristic
50C2×Dic3×Dic5C2211yescharacteristic
51C2×Dic3×Dic5C2211yescharacteristic
52#91115C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#90994C2211yescharacteristic
58#76665—51nomaximal, Hall
59C22×#709—31no—
60C2×C4×C5×D4—31no—
61C2×C4×C22⋊D5—31no—
62C2×C4×C22⋊D5—31no—
63#65512—31no—
64#65512D311yescharacteristic, complemented
65C4×C22⋊Dic5—31no—
66#65280—31no—
67#65268—31no—
68#65249—31no—
69#65248—31no—
70#65248—31no—
71#65236—31no—
72C4×#685—31no—
73C4×#685—31no—
74C24×C3×C5C2311yescharacteristic
75C24×C3×C5C2311yescharacteristic
76C23×D15C2311yescharacteristic
77C23×C3×D5C2311yescharacteristic
78C2×C3×C5×D4—22no—
79C2×C3×C5×D4—22no—
80C2×C3×C5×D4—22no—
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—22no—
83C2×#1220—22no—
84C2×#1220—22no—
85C2×#1220—22no—
86C2×#1220—22no—
87C2×#1220—22no—
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×C5×Dic3—22no—
92C22×C5×Dic3—22no—
93C22×C5×Dic3—22no—
94C22×C5×Dic3—22no—
95C22×C5×Dic3—22no—
96C22×C5×Dic3D414yescomplemented
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C2×C3×C22⋊D5—22no—
102C2×C3×C22⋊D5—22no—
103C2×C3×C22⋊D5—22no—
104C2×C3×C22⋊D5—22no—
105C2×C3×C22⋊D5—22no—
106C2×C3×C22⋊D5—22no—
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C2×#1204—22no—
111C2×#1204—22no—
112C2×#1204—22no—
113C2×#1202—22no—
114C2×#1202—22no—
115C2×#1202—22no—
116C2×#1200—22no—
117C2×#1200—22no—
118C2×#1200D414yescomplemented
119#6779—232no—
120C2×D5×Dic3—22no—
121C2×D5×Dic3—22no—
122C2×D5×Dic3D414yescomplemented
123#6719—22no—
124#6719—22no—
125#6714—22no—
126C5×#217—22no—
127C5×#217—22no—
128C5×C4⋊Dic3—22no—
129C4×C5×Dic3—22no—
130C3×C22⋊Dic5—22no—
131C3×C22⋊Dic5—22no—
132C3×#685—22no—
133#6669—22no—
134#6668—22no—
135#6667—22no—
136#6667—22no—
137#6665—22no—
138#6665—22no—
139Dic3×Dic5—22no—
140Dic3×Dic5—22no—
141C22×#237—51no—
142C2×D4×Dic3—51no—
143C2×D4×Dic3D511yescharacteristic, complemented
144C2×#67⋊C4—51no—
145C3×#392—51no—
146#5223—51no—
147#5223—51no—
148#5222—51no—
149#4961—51no—
150#4961—51no—
151#4947—51no—
152Dic3×C22⋊C4—51no—
153Dic3×C22⋊C4—51no—
154#4666—51no—
155#4656—51no—
156C22×C5×D4C2×D311yescharacteristic
157C23×C4×C5—31no—
158C23×C4×C5—31no—
159C22×C22⋊D5—31no—
160C22×C22⋊D5—31no—
161C22×C22⋊D5C2×D311yescharacteristic
162C22×C22⋊D5C2×D311yescharacteristic
163C2×#709—64no—
164C2×#709—64no—
165C2×#709—64no—
166C22×D20—31no—
167C22×C4×D5—31no—
168C22×C4×D5—31no—
169C22×Dic10—31no—
170C4×C5×D4—64no—
171C2×C5×C4⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C5×C22⋊C4—31no—
174C2×C42×C5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5C2×D311yescharacteristic
178C2×C22⋊Dic5C2×D311yescharacteristic
179C4×C22⋊D5—64no—
180C4×C22⋊D5—64no—
181C2×#685—31no—
182C2×#685—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685C2×D311yescharacteristic
187C2×#683—31no—
188C2×#683—31no—
189C2×C4×Dic5—31no—
190C2×C4×Dic5—31no—
191#3963—31no—
192#3963—31no—
193#3963—31no—
194#3963—31no—
195#3963—31no—
196#3963C2×D311yescharacteristic
197#2388—151noSylow
198C23×C3×C5—21no—
199C23×C3×C5—21no—
200C23×C3×C5—21no—
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5—21no—
206C23×C3×C5—21no—
207C23×C3×C5—21no—
208C23×C3×C5—21no—
209C23×C3×C5—21no—
210C23×C3×C5C2×D412yes—
211C23×C3×C5#4112yescomplemented
212C23×C3×C5C2411yescharacteristic
213C22×D15—21no—
214C22×D15—21no—
215C22×D15—21no—
216C22×D15—21no—
217C22×D15—21no—
218C22×D15—21no—
219C22×D15C2×D412yes—
220C22×C3×D5—21no—
221C22×C3×D5—21no—
222C22×C3×D5—21no—
223C22×C3×D5—21no—
224C22×C3×D5—21no—
225C22×C3×D5—21no—
226C22×C3×D5C2×D412yes—
227C3×C5×D4—28no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5#4112yescomplemented
231#1220—28no—
232#1220—28no—
233C2×Dic15—21no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15C2×D412yes—
241C2×Dic15#4112yescomplemented
242C2×C5×Dic3—21no—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—28no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—21no—
248C2×C5×Dic3—21no—
249C2×C5×Dic3—21no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—44no—
252C2×C5×Dic3C2×D412yes—
253C2×C5×Dic3C2×D412yes—
254C2×C5×Dic3C2×D412yes—
255C2×C5×Dic3C2×D412yes—
256C3×C22⋊D5—28no—
257C3×C22⋊D5—28no—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5C2×D412yes—
266C2×C3×Dic5#4112yescomplemented
267#1204—28no—
268#1202—28no—
269#1200—28no—
270D5×Dic3—28no—
271C22×C3×D4—51no—
272C22×C3×D4—51no—
273C22×C3×D4C2×D511yescharacteristic
274C22×#67—51no—
275C22×#67—51no—
276C22×#67—51no—
277C23×Dic3—51no—
278C23×Dic3C2×D511yescharacteristic
279C23×Dic3C2×D511yescharacteristic
280C2×#237—104no—
281C2×#237—104no—
282C2×#237—104no—
283C22×C4×D3—51no—
284C22×Dic6—51no—
285C2×C3×C22⋊C4—51no—
286C2×C3×C22⋊C4—51no—
287C2×C3×C22⋊C4—51no—
288C2×#217—51no—
289C2×#217—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217C2×D511yescharacteristic
293C2×#217C2×D511yescharacteristic
294D4×Dic3—24no—
295D4×Dic3—104no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—51no—
299C2×C4⋊Dic3—51no—
300C2×C4⋊Dic3C2×D511yescharacteristic
301C2×Dic3⋊C4—51no—
302C2×C4×Dic3—51no—
303C2×C4×Dic3—51no—
304C2×C4×Dic3C2×D511yescharacteristic
305#67⋊C4—104no—
306C3×#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C24×C5C22×D311yescharacteristic
313C24×C5C22×D311yescharacteristic
314C23×D5—31no—
315C23×D5C22×D311yescharacteristic
316C2×C5×D4—22no—
317C2×C5×D4—22no—
318C2×C5×D4—22no—
319C22×C4×C5—31no—
320C22×C4×C5—34no—
321C22×C4×C5—31no—
322C22×C4×C5—31no—
323C22×C4×C5—31no—
324C22×C4×C5—62no—
325C22×C4×C5—62no—
326C22×C4×C5—62no—
327C22×C4×C5—62no—
328C22×C4×C5—62no—
329C22×C4×C5C22×D311yescharacteristic
330C2×C22⋊D5—22no—
331C2×C22⋊D5—22no—
332C2×C22⋊D5—22no—
333C2×C22⋊D5—22no—
334C2×C22⋊D5—22no—
335C2×C22⋊D5—22no—
336C2×C22⋊D5—62no—
337C2×C22⋊D5—62no—
338C2×C22⋊D5—62no—
339C2×C22⋊D5—62no—
340C2×C22⋊D5—62no—
341C2×C22⋊D5—62no—
342C22×Dic5—31no—
343C22×Dic5—31no—
344C22×Dic5—31no—
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348#709—632no—
349C2×D20—62no—
350C2×D20—62no—
351C2×D20—62no—
352C2×C4×D5—34no—
353C2×C4×D5—34no—
354C2×C4×D5—62no—
355C2×C4×D5—62no—
356C2×C4×D5—62no—
357C2×C4×D5—62no—
358C2×Dic10—62no—
359C2×Dic10—62no—
360C2×Dic10—62no—
361C5×C4⋊C4—62no—
362C5×C22⋊C4—62no—
363C5×C22⋊C4—62no—
364C42×C5—62no—
365C22⋊Dic5—22no—
366C22⋊Dic5—22no—
367C22⋊Dic5—62no—
368C22⋊Dic5—62no—
369#685—22no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—62no—
374#685—62no—
375#683—62no—
376#683—62no—
377C4×Dic5—62no—
378C4×Dic5—62no—
379C22×#41—151no—
380C2×C4×D4—31no—
381C2×C4×D4—151no—
382C2×C4×D4—151no—
383#395—151no—
384#394—151no—
385#394—151no—
386#394—151no—
387#393—151no—
388#392—51no—
389#392—151no—
390#392—151no—
391C4×C22⋊C4—151no—
392C4×C22⋊C4—151no—
393C4×C22⋊C4—151no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—41no—
401C22×C3×C5—41no—
402C22×C3×C5—41no—
403C22×C3×C5—41no—
404C22×C3×C5—41no—
405C22×C3×C5—41no—
406C22×C3×C5—41no—
407C22×C3×C5—41no—
408C22×C3×C5C22×D411yescharacteristic
409C22×C3×C5C22×D411yescharacteristic
410C22×C3×C5C22×D411yescharacteristic
411C22×C3×C5C2×#4111yescharacteristic
412C22×C3×C5C2×#4111yescharacteristic
413C22×C3×C5C2×#4111yescharacteristic
414C22×C3×C5C2×#4111yescharacteristic
415C2×D15—22no—
416C2×D15—22no—
417C2×D15—22no—
418C2×D15—41no—
419C2×D15—41no—
420C2×D15—41no—
421C2×D15—41no—
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—22no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428C2×C3×D5—41no—
429C3×C4×C5—22no—
430Dic15—22no—
431Dic15—22no—
432Dic15—41no—
433C3×Dic5—22no—
434C3×Dic5—22no—
435C3×Dic5—41no—
436C5×Dic3—22no—
437C5×Dic3—41no—
438C5×Dic3—41no—
439C5×Dic3#12014yes—
440C24×C3—51no—
441C24×C3C22×D511yescharacteristic
442C24×C3C22×D511yescharacteristic
443C23×D3—51no—
444C2×C3×D4—22no—
445C2×C3×D4—22no—
446C2×C3×D4—22no—
447C2×C3×D4—102no—
448C2×C3×D4—102no—
449C2×C3×D4—102no—
450C2×C3×D4—102no—
451C2×C3×D4—102no—
452C2×C3×D4—102no—
453C22×C3×C4—51no—
454C22×C3×C4—51no—
455C22×C3×C4—51no—
456C22×C3×C4C22×D511yescharacteristic
457C2×#67—102no—
458C2×#67—102no—
459C2×#67—102no—
460C2×#67—102no—
461C2×#67—102no—
462C2×#67—102no—
463C2×#67—102no—
464C2×#67—102no—
465C2×#67—102no—
466C22×Dic3—22no—
467C22×Dic3—22no—
468C22×Dic3—22no—
469C22×Dic3—22no—
470C22×Dic3—22no—
471C22×Dic3—51no—
472C22×Dic3—51no—
473C22×Dic3—54no—
474C22×Dic3—51no—
475C22×Dic3—102no—
476C22×Dic3—102no—
477C22×Dic3C22⋊D514yescomplemented
478C22×Dic3C22×D511yescharacteristic
479C22×Dic3C22×D511yescharacteristic
480C22×Dic3C22×D511yescharacteristic
481C22×Dic3C22×D511yescharacteristic
482#237—1032no—
483C2×C4×D3—54no—
484C2×C4×D3—102no—
485C2×C4×D3—102no—
486C2×Dic6—102no—
487C2×Dic6—102no—
488C2×Dic6—102no—
489C3×C22⋊C4—102no—
490C3×C22⋊C4—102no—
491C3×C22⋊C4—102no—
492#217—22no—
493#217—22no—
494#217—102no—
495#217—102no—
496#217—102no—
497#217—102no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—102no—
501C4⋊Dic3—22no—
502C4⋊Dic3—102no—
503Dic3⋊C4—102no—
504C4×Dic3—22no—
505C4×Dic3—102no—
506C4×Dic3—102no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5—21no—
512C23×C5—21no—
513C23×C5—21no—
514C23×C5—21no—
515C23×C5—21no—
516C23×C5—21no—
517C23×C5—21no—
518C23×C5—21no—
519C23×C5D3×D412yes—
520C23×C5#23712yescomplemented
521C23×C5C23×D311yescharacteristic
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—21no—
526C22×D5—21no—
527C22×D5—21no—
528C22×D5—32no—
529C22×D5—61no—
530C22×D5—61no—
531C22×D5—61no—
532C22×D5—61no—
533C22×D5—61no—
534C22×D5—61no—
535C22×D5D3×D412yes—
536C5×D4—28no—
537C2×C4×C5—21no—
538C2×C4×C5—21no—
539C2×C4×C5—32no—
540C2×C4×C5—32no—
541C2×C4×C5—32no—
542C2×C4×C5—32no—
543C2×C4×C5—68no—
544C2×C4×C5—61no—
545C2×C4×C5—61no—
546C2×C4×C5—61no—
547C2×C4×C5—61no—
548C2×C4×C5—61no—
549C2×C4×C5—61no—
550C2×C4×C5—61no—
551C2×C4×C5—61no—
552C2×C4×C5—124no—
553C2×C4×C5#23712yescomplemented
554C22⋊D5—28no—
555C22⋊D5—28no—
556C22⋊D5—68no—
557C22⋊D5—68no—
558C2×Dic5—21no—
559C2×Dic5—21no—
560C2×Dic5—21no—
561C2×Dic5—21no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—32no—
566C2×Dic5—32no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—61no—
573C2×Dic5—61no—
574C2×Dic5D3×D412yes—
575C2×Dic5#23712yescomplemented
576D20—68no—
577C4×D5—68no—
578C4×D5—68no—
579Dic10—68no—
580C2×#41—304no—
581C2×#41—304no—
582C2×#41—304no—
583C22×Q8—151no—
584C22×D4—51no—
585C22×D4—51no—
586C22×D4—151no—
587C22×D4—151no—
588C22×D4—151no—
589C22×D4D3×D511yescharacteristic
590C23×C4—31no—
591C23×C4—31no—
592C23×C4—151no—
593C23×C4—151no—
594C4×D4—64no—
595C4×D4—304no—
596C4×D4—304no—
597C2×C4⋊C4—31no—
598C2×C4⋊C4—151no—
599C2×C4⋊C4—151no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—31no—
602C2×C22⋊C4—51no—
603C2×C22⋊C4—51no—
604C2×C22⋊C4—51no—
605C2×C22⋊C4—151no—
606C2×C22⋊C4—151no—
607C2×C22⋊C4—151no—
608C2×C22⋊C4—151no—
609C2×C22⋊C4—151no—
610C2×C22⋊C4—151no—
611C2×C22⋊C4—151no—
612C2×C42—31no—
613C2×C42—151no—
614C2×C42—151no—
615#95—51no—
616#95—151no—
617#95—151no—
618#95—151no—
619#95—151no—
620#95—151no—
621C2×C3×C5—42no—
622C2×C3×C5—42no—
623C2×C3×C5C2×#12011yescharacteristic
624C2×C3×C5#52511yescharacteristic
625C2×C3×C5#52511yescharacteristic
626C2×C3×C5#52511yescharacteristic
627C2×C3×C5#53211yescharacteristic
628C2×C3×C5#53211yescharacteristic
629C2×C3×C5#53211yescharacteristic
630D15—42no—
631C3×D5—42no—
632C23×C3—21no—
633C23×C3—21no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—21no—
639C23×C3—21no—
640C23×C3—21no—
641C23×C3—21no—
642C23×C3—21no—
643C23×C3—21no—
644C23×C3—52no—
645C23×C3—101no—
646C23×C3—101no—
647C23×C3—101no—
648C23×C3—101no—
649C23×C3—101no—
650C23×C3—101no—
651C23×C3#70912yescomplemented
652C23×C3C2×C22⋊D512yes—
653C23×C3C23×D511yescharacteristic
654C22×D3—52no—
655C22×D3—101no—
656C22×D3—101no—
657C22×D3—101no—
658C22×D3—101no—
659C22×D3—101no—
660C22×D3—101no—
661C3×D4—28no—
662C3×D4—108no—
663C3×D4—108no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—52no—
667C2×C3×C4—52no—
668C2×C3×C4—101no—
669C2×C3×C4—101no—
670C2×C3×C4—101no—
671C2×C3×C4—101no—
672C2×C3×C4—101no—
673C2×C3×C4—101no—
674C2×C3×C4—101no—
675C2×C3×C4#70912yescomplemented
676#67—108no—
677#67—108no—
678#67—108no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—28no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—44no—
689C2×Dic3—52no—
690C2×Dic3—52no—
691C2×Dic3—101no—
692C2×Dic3—101no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—108no—
696C2×Dic3—101no—
697C2×Dic3—101no—
698C2×Dic3—101no—
699C2×Dic3D4×D512yes—
700C2×Dic3D4×D512yes—
701C2×Dic3C2×C22⋊D512yes—
702C2×Dic3C2×C22⋊D512yes—
703C4×D3—108no—
704Dic6—108no—
705C22×C5—22no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—22no—
710C22×C5—22no—
711C22×C5—41no—
712C22×C5—41no—
713C22×C5—41no—
714C22×C5—41no—
715C22×C5—41no—
716C22×C5—41no—
717C22×C5—41no—
718C22×C5—41no—
719C22×C5C2×D3×D411yescharacteristic
720C22×C5C2×D3×D411yescharacteristic
721C22×C5C2×D3×D411yescharacteristic
722C22×C5C2×#23711yescharacteristic
723C22×C5C2×#23711yescharacteristic
724C22×C5C2×#23711yescharacteristic
725C22×C5D3×#4111yescharacteristic
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—41no—
730C2×D5—41no—
731C2×D5—41no—
732C2×D5—41no—
733C2×D5—62no—
734C2×D5—62no—
735C2×D5—62no—
736C2×D5—121no—
737C2×D5—121no—
738C2×D5—121no—
739C2×D5—121no—
740C4×C5—22no—
741C4×C5—34no—
742C4×C5—62no—
743C4×C5—121no—
744C4×C5—121no—
745Dic5—22no—
746Dic5—22no—
747Dic5—41no—
748Dic5—62no—
749Dic5—62no—
750Dic5—121no—
751C24—51no—
752C24—151no—
753C24C2×D3×D511yescharacteristic
754C24C2×D3×D511yescharacteristic
755#41—3032no—
756C2×Q8—302no—
757C2×Q8—302no—
758C2×Q8—302no—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—102no—
763C2×D4—102no—
764C2×D4—102no—
765C2×D4—102no—
766C2×D4—102no—
767C2×D4—102no—
768C2×D4—302no—
769C2×D4—302no—
770C2×D4—302no—
771C2×D4—302no—
772C2×D4—302no—
773C2×D4—302no—
774C2×D4—302no—
775C2×D4—302no—
776C2×D4—302no—
777C22×C4—31no—
778C22×C4—34no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—62no—
786C22×C4—62no—
787C22×C4—62no—
788C22×C4—62no—
789C22×C4—62no—
790C22×C4—154no—
791C22×C4—154no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—151no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—302no—
799C22×C4C2×D3×D511yescharacteristic
800C4⋊C4—62no—
801C4⋊C4—302no—
802C4⋊C4—302no—
803C22⋊C4—62no—
804C22⋊C4—62no—
805C22⋊C4—102no—
806C22⋊C4—102no—
807C22⋊C4—102no—
808C22⋊C4—302no—
809C22⋊C4—302no—
810C22⋊C4—302no—
811C22⋊C4—302no—
812C22⋊C4—302no—
813C22⋊C4—302no—
814C22⋊C4—302no—
815C42—62no—
816C42—302no—
817C42—302no—
818C3×C5#238811yescharacteristic, complemented, Hall
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—102no—
834C22×C3—102no—
835C22×C3—102no—
836C22×C3—201no—
837C22×C3—201no—
838C22×C3—201no—
839C22×C3—201no—
840C22×C3C2×#70911yescharacteristic
841C22×C3C2×#70911yescharacteristic
842C22×C3C2×D4×D511yescharacteristic
843C22×C3C2×D4×D511yescharacteristic
844C22×C3D5×#4111yescharacteristic
845C22×C3D5×#4111yescharacteristic
846C22×C3C22×C22⋊D511yescharacteristic
847C2×D3—102no—
848C2×D3—102no—
849C2×D3—102no—
850C2×D3—201no—
851C2×D3—201no—
852C2×D3—201no—
853C2×D3—201no—
854C3×C4—22no—
855C3×C4—102no—
856C3×C4—102no—
857C3×C4—201no—
858Dic3—22no—
859Dic3—41no—
860Dic3—41no—
861Dic3—102no—
862Dic3—102no—
863Dic3—201no—
864Dic3#408314yes—
865C2×C5—42no—
866C2×C5—42no—
867C2×C5#558611yescharacteristic
868C2×C5#558611yescharacteristic
869C2×C5D3×#12011yescharacteristic
870C2×C5#559611yescharacteristic
871C2×C5#559611yescharacteristic
872C2×C5#560611yescharacteristic
873C2×C5#571611yescharacteristic
874D5—42no—
875D5—122no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—52no—
889C23—101no—
890C23—101no—
891C23—101no—
892C23—101no—
893C23—101no—
894C23—101no—
895C23—152no—
896C23—301no—
897C23—301no—
898C23—301no—
899C23—301no—
900C23—301no—
901C23—301no—
902C23#677912yescomplemented
903C23D3×C22⋊D512yes—
904C23C22×D3×D511yescharacteristic
905Q8—308no—
906D4—28no—
907D4—108no—
908D4—108no—
909D4—308no—
910D4—308no—
911D4—308no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—52no—
919C2×C4—52no—
920C2×C4—68no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—101no—
930C2×C4—101no—
931C2×C4—101no—
932C2×C4—101no—
933C2×C4—101no—
934C2×C4—101no—
935C2×C4—101no—
936C2×C4—124no—
937C2×C4—152no—
938C2×C4—152no—
939C2×C4—308no—
940C2×C4—308no—
941C2×C4—301no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—301no—
948C2×C4#677912yescomplemented
949C2×C3—42no—
950C2×C3—42no—
951C2×C3—202no—
952C2×C3#6588111yescharacteristic
953C2×C3#6588111yescharacteristic
954C2×C3#6588211yescharacteristic
955C2×C3#6588211yescharacteristic
956C2×C3#6612511yescharacteristic
957C2×C3C2×#408311yescharacteristic
958C2×C3#6616611yescharacteristic
959D3—202no—
960C5#7666511yescharacteristic, complemented, Sylow
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—102no—
976C22—102no—
977C22—102no—
978C22—201no—
979C22—201no—
980C22—201no—
981C22—201no—
982C22—302no—
983C22—302no—
984C22—302no—
985C22—601no—
986C22—601no—
987C22—601no—
988C22—601no—
989C22D3×D4×D511yescharacteristic
990C22D3×D4×D511yescharacteristic
991C22D5×#23711yescharacteristic
992C22#9202411yescharacteristic
993C22C2×#677911yescharacteristic
994C22C2×#677911yescharacteristic
995C22C2×D3×C22⋊D511yescharacteristic
996C4—22no—
997C4—34no—
998C4—62no—
999C4—102no—
1000C4—102no—
1001C4—121no—
1002C4—121no—
1003C4—201no—
1004C4—302no—
1005C4—302no—
1006C4—601no—
1007C3#1061413111yescharacteristic, complemented, Sylow
1008C2—42no—
1009C2—42no—
1010C2—202no—
1011C2—602no—
1012C2#1175475811yescharacteristic
1013C2#1175476011yescharacteristic
1014C2#1175477411yescharacteristic
1015C2#1175477711yescharacteristic
1016C2#1175480311yescharacteristic
1017C2D3×#408311yescharacteristic
1018C2#1175538811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FittingC22×C3×C5×D4C22
hypercenterC22×D4D3×D5
hypocenterC3×C5#2388
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6779C2semidirect
2. C2×C5×D4×Dic3C2semidirect
3. C2×#91556C2semidirect
4. C2×Dic3×C22⋊D5C2semidirect
5. #11751324C2semidirect
6. C3×#65512C2semidirect
7. #11749524C2semidirect
8. #11749522C2semidirect
9. #11749510C2semidirect
10. #11749490C2semidirect
11. Dic3×C22⋊Dic5C2semidirect
12. #11748937C2semidirect
13. #11748928C2semidirect
14. #11748881C2semidirect
15. Dic3×#685C2semidirect
64. #65512D3semidirect
96. C22×C5×Dic3D4semidirect
118. C2×#1200D4semidirect
122. C2×D5×Dic3D4semidirect
143. C2×D4×Dic3D5semidirect
211. C23×C3×C5#41semidirect
230. C2×C3×C4×C5#41semidirect
241. C2×Dic15#41semidirect
266. C2×C3×Dic5#41semidirect
477. C22×Dic3C22⋊D5semidirect
520. C23×C5#237semidirect
553. C2×C4×C5#237semidirect
575. C2×Dic5#237semidirect
651. C23×C3#709semidirect
675. C2×C3×C4#709semidirect
818. C3×C5#2388semidirect
902. C23#6779semidirect
948. C2×C4#6779semidirect
960. C5#76665semidirect
1007. C3#10614131semidirect

Maximal subgroups

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

subgroupindex
C22×#67792
C2×C5×D4×Dic32
C2×#915562
C2×Dic3×C22⋊D52
#117513242
C3×#655122
#117495242
#117495222
#117495102
#117494902
Dic3×C22⋊Dic52
#117489372
#117489282
#117488812
Dic3×#6852
#106141313
#766655