Finite Group Databasebeta

← #14331633

Subgroups — #14331633

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×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×Dic3×D20C211yesmaximal, characteristic, complemented
4C2×#91395C211yesmaximal, characteristic, complemented
5#11751062C211yesmaximal, characteristic, complemented
6C5×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#65249C211yesmaximal, characteristic, complemented
8#11749522C211yesmaximal, characteristic, complemented
9#11749491C211yesmaximal, characteristic, complemented
10#11748938C211yesmaximal, characteristic, complemented
11#11748923C211yesmaximal, characteristic, complemented
12#11748881C211yesmaximal, characteristic, complemented
13Dic3×#685C211yesmaximal, characteristic, complemented
14#11748755C211yesmaximal, characteristic, complemented
15#11748736C211yesmaximal, characteristic, complemented
16#10605311—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×C5×Dic3C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×D20C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×#1202C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C2×#6779—24no—
27C2×#6779—24no—
28C2×#6779—24no—
29C22×D5×Dic3C2211yescharacteristic
30C22×D5×Dic3C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×C4⋊Dic15C2211yescharacteristic
36C2×C5×#217C2211yescharacteristic
37C2×C4×C5×Dic3C2211yescharacteristic
38C2×C4×C5×Dic3C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41Dic3×C22⋊D5—24no—
42C2×Dic3⋊Dic5C2211yescharacteristic
43C2×#6668C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×#6665C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50Dic3×D20—24no—
51#91395—24no—
52#91115C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C5×C3⋊#95C2211yescharacteristic
55C3×#3963C2211yescharacteristic
56#90994C2211yescharacteristic
57#90994C2211yescharacteristic
58#76665—51nomaximal, Hall
59C22×#709—31no—
60C2×C4×C22⋊D5—31no—
61C2×C4×D20—31no—
62C2×C4×D20—31no—
63C4×C5×C22⋊C4—31no—
64#65250—31no—
65#65250—31no—
66#65249—31no—
67#65249D311yescharacteristic, complemented
68C4×#685—31no—
69C4×#685—31no—
70#64962—31no—
71#64961—31no—
72#64960—31no—
73#64945—31no—
74C24×C3×C5C2311yescharacteristic
75C23×D15C2311yescharacteristic
76C23×C3×D5C2311yescharacteristic
77C23×C3×D5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—22no—
81C2×#1220—22no—
82C2×#1220—22no—
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×C5×Dic3—22no—
87C22×C5×Dic3—22no—
88C22×C5×Dic3D414yescomplemented
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C2×C3×C22⋊D5—22no—
94C2×C3×C22⋊D5—22no—
95C2×C3×C22⋊D5—22no—
96C2×C3×C22⋊D5—22no—
97C2×C3×C22⋊D5—22no—
98C2×C3×C22⋊D5—22no—
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C2×C3×D20—22no—
102C2×C3×D20—22no—
103C2×C3×D20—22no—
104C2×#1204—22no—
105C2×#1204—22no—
106C2×#1204—22no—
107C2×#1202—22no—
108C2×#1202—22no—
109C2×#1202—22no—
110C2×#1202—22no—
111C2×#1202—22no—
112C2×#1202—22no—
113C2×#1200—22no—
114C2×#1200—22no—
115C2×#1200D414yescomplemented
116#6779—232no—
117C2×D5×Dic3—22no—
118C2×D5×Dic3—22no—
119C2×D5×Dic3—22no—
120C2×D5×Dic3—22no—
121C2×D5×Dic3—22no—
122C2×D5×Dic3D414yescomplemented
123C3×C5×C22⋊C4—22no—
124#6719—22no—
125#6714—22no—
126#6714—22no—
127C4⋊Dic15—22no—
128C5×#217—22no—
129C4×C5×Dic3—22no—
130C4×C5×Dic3—22no—
131C3×#685—22no—
132C3×#685—22no—
133Dic3⋊Dic5—22no—
134#6668—22no—
135#6667—22no—
136#6665—22no—
137#6665—22no—
138#6665—22no—
139#6665—22no—
140Dic3×Dic5—22no—
141C22×#237—51no—
142C2×D4×Dic3—51no—
143C2×D4×Dic3—51no—
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⋊C4D511yescharacteristic, complemented
154#4666—51no—
155#4656—51no—
156C23×C4×C5—31no—
157C22×C22⋊D5—31no—
158C22×C22⋊D5C2×D311yescharacteristic
159C22×C22⋊D5C2×D311yescharacteristic
160C2×#709—64no—
161C2×#709—64no—
162C2×#709—64no—
163C22×D20—31no—
164C22×D20—31no—
165C22×D20C2×D311yescharacteristic
166C22×C4×D5—31no—
167C22×C4×D5—31no—
168C22×C4×D5—31no—
169C22×Dic10—31no—
170C2×C5×C22⋊C4—31no—
171C2×C5×C22⋊C4C2×D311yescharacteristic
172C2×C42×C5—31no—
173C2×C42×C5—31no—
174C2×C22⋊Dic5—31no—
175C4×C22⋊D5—64no—
176C2×#685—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#685—31no—
182C2×#685—31no—
183C2×#685C2×D311yescharacteristic
184C2×#685C2×D311yescharacteristic
185C2×C4⋊Dic5—31no—
186C2×C4⋊Dic5—31no—
187C2×#683—31no—
188C2×C4×Dic5—31no—
189C4×D20—64no—
190C4×D20—64no—
191C5×#95—31no—
192C5×#95—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×C5C2×D412yes—
205C23×C3×C5C2411yescharacteristic
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15—21no—
210C22×D15—21no—
211C22×D15—21no—
212C22×D15C2×D412yes—
213C22×C3×D5—21no—
214C22×C3×D5—21no—
215C22×C3×D5—21no—
216C22×C3×D5—21no—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5—21no—
222C22×C3×D5—21no—
223C22×C3×D5—21no—
224C22×C3×D5—21no—
225C22×C3×D5C2×D412yes—
226C22×C3×D5#4112yescomplemented
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5#4112yescomplemented
233#1220—28no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15C2×D412yes—
243C2×C5×Dic3—21no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—28no—
248C2×C5×Dic3—21no—
249C2×C5×Dic3—21no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3C2×D412yes—
252C2×C5×Dic3C2×D412yes—
253C2×C5×Dic3C2×D412yes—
254C2×C5×Dic3C2×D412yes—
255C2×C5×Dic3#4112yescomplemented
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×Dic5C2×D412yes—
263C2×C3×Dic5#4112yescomplemented
264C3×D20—28no—
265#1204—28no—
266#1202—28no—
267#1202—28no—
268#1200—28no—
269D5×Dic3—28no—
270D5×Dic3—44no—
271C22×C3×D4—51no—
272C22×C3×D4—51no—
273C22×C3×D4—51no—
274C22×#67—51no—
275C22×#67—51no—
276C22×#67—51no—
277C23×Dic3—51no—
278C23×Dic3—51no—
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⋊C4C2×D511yescharacteristic
288C2×#217—51no—
289C2×#217—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217C2×D511yescharacteristic
294D4×Dic3—104no—
295D4×Dic3—104no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—51no—
299C2×C4⋊Dic3—51no—
300C2×C4⋊Dic3—51no—
301C2×Dic3⋊C4—51no—
302C2×C4×Dic3—51no—
303C2×C4×Dic3C2×D511yescharacteristic
304C2×C4×Dic3C2×D511yescharacteristic
305#67⋊C4—104no—
306C3×#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95C2×D511yescharacteristic
311C3⋊#95C2×D511yescharacteristic
312C24×C5C22×D311yescharacteristic
313C23×D5—31no—
314C23×D5C22×D311yescharacteristic
315C23×D5C22×D311yescharacteristic
316C22×C4×C5—31no—
317C22×C4×C5—34no—
318C22×C4×C5—31no—
319C22×C4×C5—31no—
320C22×C4×C5—31no—
321C22×C4×C5—62no—
322C22×C4×C5—62no—
323C22×C4×C5C22×D311yescharacteristic
324C22×C4×C5C22×D311yescharacteristic
325C2×C22⋊D5—22no—
326C2×C22⋊D5—22no—
327C2×C22⋊D5—22no—
328C2×C22⋊D5—22no—
329C2×C22⋊D5—22no—
330C2×C22⋊D5—22no—
331C2×C22⋊D5—62no—
332C2×C22⋊D5—62no—
333C2×C22⋊D5—62no—
334C22×Dic5—31no—
335C22×Dic5—31no—
336C22×Dic5—31no—
337C22×Dic5C22×D311yescharacteristic
338C22×Dic5C22×D311yescharacteristic
339#709—632no—
340C2×D20—22no—
341C2×D20—22no—
342C2×D20—22no—
343C2×D20—62no—
344C2×D20—62no—
345C2×D20—62no—
346C2×D20—62no—
347C2×D20—62no—
348C2×D20—62no—
349C2×C4×D5—34no—
350C2×C4×D5—34no—
351C2×C4×D5—62no—
352C2×C4×D5—62no—
353C2×C4×D5—62no—
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×C22⋊C4—22no—
362C5×C22⋊C4—62no—
363C42×C5—62no—
364C42×C5—62no—
365C22⋊Dic5—62no—
366#685—22no—
367#685—22no—
368#685—62no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—62no—
374#685—62no—
375C4⋊Dic5—62no—
376C4⋊Dic5—62no—
377#683—62no—
378C4×Dic5—62no—
379C22×#41—151no—
380C2×C4×D4—151no—
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—31no—
392C4×C22⋊C4—151no—
393C4×C22⋊C4—151no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—41no—
398C22×C3×C5—41no—
399C22×C3×C5—41no—
400C22×C3×C5—41no—
401C22×C3×C5C22×D411yescharacteristic
402C22×C3×C5C22×D411yescharacteristic
403C22×C3×C5C22×D411yescharacteristic
404C22×C3×C5C2×#4111yescharacteristic
405C22×C3×C5C2×#4111yescharacteristic
406C22×C3×C5C2×#4111yescharacteristic
407C22×C3×C5C2×#4111yescharacteristic
408C2×D15—22no—
409C2×D15—22no—
410C2×D15—22no—
411C2×D15—41no—
412C2×D15—41no—
413C2×D15—41no—
414C2×D15—41no—
415C2×C3×D5—22no—
416C2×C3×D5—22no—
417C2×C3×D5—22no—
418C2×C3×D5—22no—
419C2×C3×D5—22no—
420C2×C3×D5—22no—
421C2×C3×D5—41no—
422C2×C3×D5—41no—
423C2×C3×D5—41no—
424C2×C3×D5—41no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428C2×C3×D5—41no—
429C3×C4×C5—22no—
430C3×C4×C5—41no—
431Dic15—22no—
432Dic15—41no—
433Dic15—41no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C5×Dic3—22no—
437C5×Dic3—22no—
438C5×Dic3—41no—
439C5×Dic3#12014yes—
440C24×C3—51no—
441C24×C3—51no—
442C24×C3C22×D511yescharacteristic
443C23×D3—51no—
444C2×C3×D4—102no—
445C2×C3×D4—102no—
446C2×C3×D4—102no—
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×C4C22×D511yescharacteristic
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—51no—
469C22×Dic3—54no—
470C22×Dic3—51no—
471C22×Dic3—51no—
472C22×Dic3—102no—
473C22×Dic3—102no—
474C22×Dic3—102no—
475C22×Dic3—102no—
476C22×Dic3—102no—
477C22×Dic3D2014yescomplemented
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—22no—
490C3×C22⋊C4—102no—
491C3×C22⋊C4—102no—
492#217—22no—
493#217—102no—
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—102no—
502C4⋊Dic3—102no—
503Dic3⋊C4—102no—
504C4×Dic3—22no—
505C4×Dic3—22no—
506C4×Dic3—102no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5—21no—
512C23×C5—21no—
513C23×C5D3×D412yes—
514C23×C5C23×D311yescharacteristic
515C22×D5—21no—
516C22×D5—21no—
517C22×D5—21no—
518C22×D5—21no—
519C22×D5—21no—
520C22×D5—21no—
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—21no—
526C22×D5—21no—
527C22×D5—32no—
528C22×D5—61no—
529C22×D5—61no—
530C22×D5—61no—
531C22×D5—61no—
532C22×D5—61no—
533C22×D5—61no—
534C22×D5D3×D412yes—
535C22×D5#23712yescomplemented
536C2×C4×C5—21no—
537C2×C4×C5—21no—
538C2×C4×C5—21no—
539C2×C4×C5—21no—
540C2×C4×C5—21no—
541C2×C4×C5—32no—
542C2×C4×C5—32no—
543C2×C4×C5—32no—
544C2×C4×C5—32no—
545C2×C4×C5—32no—
546C2×C4×C5—68no—
547C2×C4×C5—61no—
548C2×C4×C5—61no—
549C2×C4×C5—61no—
550C2×C4×C5—61no—
551C2×C4×C5—61no—
552C2×C4×C5—61no—
553C2×C4×C5—61no—
554C2×C4×C5#23712yescomplemented
555C22⋊D5—28no—
556C22⋊D5—28no—
557C22⋊D5—68no—
558C2×Dic5—21no—
559C2×Dic5—21no—
560C2×Dic5—21no—
561C2×Dic5—21no—
562C2×Dic5—32no—
563C2×Dic5—61no—
564C2×Dic5—61no—
565C2×Dic5—61no—
566C2×Dic5—61no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5D3×D412yes—
572C2×Dic5#23712yescomplemented
573D20—28no—
574D20—68no—
575D20—68no—
576C4×D5—68no—
577C4×D5—68no—
578C4×D5—124no—
579Dic10—68no—
580C2×#41—304no—
581C2×#41—304no—
582C2×#41—304no—
583C22×Q8—151no—
584C22×D4—51no—
585C22×D4—51no—
586C22×D4—51no—
587C22×D4—151no—
588C22×D4—151no—
589C22×D4—151no—
590C23×C4—31no—
591C23×C4—151no—
592C23×C4—151no—
593C23×C4—151no—
594C4×D4—304no—
595C4×D4—304no—
596C4×D4—304no—
597C2×C4⋊C4—151no—
598C2×C4⋊C4—151no—
599C2×C4⋊C4—151no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—51no—
602C2×C22⋊C4—51no—
603C2×C22⋊C4—151no—
604C2×C22⋊C4—151no—
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⋊C4D3×D511yescharacteristic
612C2×C42—31no—
613C2×C42—31no—
614C2×C42—151no—
615#95—31no—
616#95—31no—
617#95—51no—
618#95—151no—
619#95—151no—
620#95—151no—
621C2×C3×C5—42no—
622C2×C3×C5C2×#12011yescharacteristic
623C2×C3×C5#52511yescharacteristic
624C2×C3×C5#52511yescharacteristic
625C2×C3×C5#52511yescharacteristic
626C2×C3×C5#53211yescharacteristic
627C2×C3×C5#53211yescharacteristic
628C2×C3×C5#53211yescharacteristic
629D15—42no—
630C3×D5—42no—
631C3×D5—42no—
632C23×C3—21no—
633C23×C3—21no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—52no—
639C23×C3—52no—
640C23×C3—101no—
641C23×C3—101no—
642C23×C3—101no—
643C23×C3—101no—
644C23×C3—101no—
645C23×C3—101no—
646C23×C3—101no—
647C23×C3—101no—
648C23×C3—101no—
649C23×C3—101no—
650C23×C3—101no—
651C23×C3—101no—
652C23×C3C2×D2012yes—
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—108no—
662C3×D4—108no—
663C3×D4—108no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—52no—
670C2×C3×C4—52no—
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—21no—
682C2×Dic3—21no—
683C2×Dic3—28no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—52no—
688C2×Dic3—101no—
689C2×Dic3—101no—
690C2×Dic3—108no—
691C2×Dic3—101no—
692C2×Dic3—101no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3—204no—
698C2×Dic3C2×D2012yes—
699C2×Dic3C2×D2012yes—
700C2×Dic3#70912yescomplemented
701C2×Dic3D4×D512yes—
702C2×Dic3D4×D512yes—
703C4×D3—108no—
704Dic6—108no—
705C22×C5—22no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—41no—
709C22×C5—41no—
710C22×C5—41no—
711C22×C5—41no—
712C22×C5C2×D3×D411yescharacteristic
713C22×C5C2×D3×D411yescharacteristic
714C22×C5C2×D3×D411yescharacteristic
715C22×C5C2×#23711yescharacteristic
716C22×C5C2×#23711yescharacteristic
717C22×C5C2×#23711yescharacteristic
718C22×C5D3×#4111yescharacteristic
719C2×D5—22no—
720C2×D5—22no—
721C2×D5—22no—
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—22no—
725C2×D5—41no—
726C2×D5—41no—
727C2×D5—41no—
728C2×D5—41no—
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—41no—
743C4×C5—62no—
744C4×C5—62no—
745C4×C5—121no—
746Dic5—22no—
747Dic5—22no—
748Dic5—62no—
749Dic5—121no—
750Dic5—121no—
751C24—51no—
752C24—51no—
753C24—151no—
754C24C2×D3×D511yescharacteristic
755#41—3032no—
756C2×Q8—302no—
757C2×Q8—302no—
758C2×Q8—302no—
759C2×D4—102no—
760C2×D4—102no—
761C2×D4—102no—
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—62no—
785C22×C4—62no—
786C22×C4—154no—
787C22×C4—154no—
788C22×C4—151no—
789C22×C4—151no—
790C22×C4—151no—
791C22×C4—302no—
792C22×C4—302no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4C2×D3×D511yescharacteristic
799C22×C4C2×D3×D511yescharacteristic
800C4⋊C4—302no—
801C4⋊C4—302no—
802C4⋊C4—302no—
803C22⋊C4—22no—
804C22⋊C4—62no—
805C22⋊C4—102no—
806C22⋊C4—102no—
807C22⋊C4—302no—
808C22⋊C4—302no—
809C22⋊C4—302no—
810C22⋊C4—302no—
811C22⋊C4—302no—
812C22⋊C4—302no—
813C22⋊C4—302no—
814C22⋊C4—302no—
815C42—62no—
816C42—62no—
817C42—302no—
818C3×C5#238811yescharacteristic, complemented, Hall
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—102no—
827C22×C3—102no—
828C22×C3—102no—
829C22×C3—102no—
830C22×C3—102no—
831C22×C3—102no—
832C22×C3—201no—
833C22×C3—201no—
834C22×C3—201no—
835C22×C3—201no—
836C22×C3—201no—
837C22×C3—201no—
838C22×C3—201no—
839C22×C3—201no—
840C22×C3C22×D2011yescharacteristic
841C22×C3C2×#70911yescharacteristic
842C22×C3C2×#70911yescharacteristic
843C22×C3C2×D4×D511yescharacteristic
844C22×C3C2×D4×D511yescharacteristic
845C22×C3D5×#4111yescharacteristic
846C22×C3D5×#4111yescharacteristic
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—41no—
856C3×C4—102no—
857C3×C4—102no—
858Dic3—22no—
859Dic3—22no—
860Dic3—41no—
861Dic3—102no—
862Dic3—201no—
863Dic3—201no—
864Dic3#402814yes—
865C2×C5—42no—
866C2×C5#558611yescharacteristic
867C2×C5#558611yescharacteristic
868C2×C5D3×#12011yescharacteristic
869C2×C5#559611yescharacteristic
870C2×C5#559611yescharacteristic
871C2×C5#560611yescharacteristic
872C2×C5#571611yescharacteristic
873D5—42no—
874D5—42no—
875D5—122no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—52no—
883C23—52no—
884C23—101no—
885C23—101no—
886C23—101no—
887C23—101no—
888C23—101no—
889C23—101no—
890C23—101no—
891C23—101no—
892C23—101no—
893C23—101no—
894C23—101no—
895C23—101no—
896C23—152no—
897C23—301no—
898C23—301no—
899C23—301no—
900C23—301no—
901C23—301no—
902C23—301no—
903C23D3×D2012yes—
904C23C22×D3×D511yescharacteristic
905Q8—308no—
906D4—108no—
907D4—108no—
908D4—108no—
909D4—308no—
910D4—308no—
911D4—308no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—32no—
918C2×C4—32no—
919C2×C4—32no—
920C2×C4—32no—
921C2×C4—32no—
922C2×C4—52no—
923C2×C4—52no—
924C2×C4—68no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—101no—
933C2×C4—101no—
934C2×C4—101no—
935C2×C4—101no—
936C2×C4—152no—
937C2×C4—308no—
938C2×C4—308no—
939C2×C4—301no—
940C2×C4—301no—
941C2×C4—301no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—604no—
948C2×C4#677912yescomplemented
949C2×C3—42no—
950C2×C3—202no—
951C2×C3—202no—
952C2×C3#6581111yescharacteristic
953C2×C3C2×#402811yescharacteristic
954C2×C3#6585811yescharacteristic
955C2×C3#6588111yescharacteristic
956C2×C3#6588111yescharacteristic
957C2×C3#6588211yescharacteristic
958C2×C3#6588211yescharacteristic
959D3—202no—
960C5#7666511yescharacteristic, complemented, Sylow
961C22—22no—
962C22—22no—
963C22—22no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—102no—
969C22—102no—
970C22—102no—
971C22—102no—
972C22—102no—
973C22—102no—
974C22—201no—
975C22—201no—
976C22—201no—
977C22—201no—
978C22—201no—
979C22—201no—
980C22—201no—
981C22—201no—
982C22—302no—
983C22—302no—
984C22—302no—
985C22—601no—
986C22—601no—
987C22—601no—
988C22—601no—
989C22C2×D3×D2011yescharacteristic
990C22D3×#70911yescharacteristic
991C22D3×D4×D511yescharacteristic
992C22D3×D4×D511yescharacteristic
993C22D5×#23711yescharacteristic
994C22D5×#23711yescharacteristic
995C22C2×#677911yescharacteristic
996C4—22no—
997C4—34no—
998C4—41no—
999C4—62no—
1000C4—62no—
1001C4—102no—
1002C4—102no—
1003C4—121no—
1004C4—302no—
1005C4—601no—
1006C4—601no—
1007C3#1060531111yescharacteristic, complemented, Sylow
1008C2—42no—
1009C2—202no—
1010C2—202no—
1011C2—602no—
1012C2#1175283111yescharacteristic
1013C2#1175287511yescharacteristic
1014C2D3×#402811yescharacteristic
1015C2#1175325011yescharacteristic
1016C2#1175435611yescharacteristic
1017C2#1175475811yescharacteristic
1018C2#1175477711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FittingC2×C3×C5×C22⋊C4C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2388
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6779C2semidirect
2. C2×Dic3×C22⋊D5C2semidirect
3. C2×Dic3×D20C2semidirect
4. C2×#91395C2semidirect
5. #11751062C2semidirect
6. C5×Dic3×C22⋊C4C2semidirect
7. C3×#65249C2semidirect
8. #11749522C2semidirect
9. #11749491C2semidirect
10. #11748938C2semidirect
11. #11748923C2semidirect
12. #11748881C2semidirect
13. Dic3×#685C2semidirect
14. #11748755C2semidirect
15. #11748736C2semidirect
67. #65249D3semidirect
88. C22×C5×Dic3D4semidirect
115. C2×#1200D4semidirect
122. C2×D5×Dic3D4semidirect
153. Dic3×C22⋊C4D5semidirect
226. C22×C3×D5#41semidirect
232. C2×C3×C4×C5#41semidirect
255. C2×C5×Dic3#41semidirect
263. C2×C3×Dic5#41semidirect
477. C22×Dic3D20semidirect
535. C22×D5#237semidirect
554. C2×C4×C5#237semidirect
572. C2×Dic5#237semidirect
675. C2×C3×C4#709semidirect
700. C2×Dic3#709semidirect
818. C3×C5#2388semidirect
948. C2×C4#6779semidirect
960. C5#76665semidirect
1007. C3#10605311semidirect

Maximal subgroups

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

subgroupindex
C22×#67792
C2×Dic3×C22⋊D52
C2×Dic3×D202
C2×#913952
#117510622
C5×Dic3×C22⋊C42
C3×#652492
#117495222
#117494912
#117489382
#117489232
#117488812
Dic3×#6852
#117487552
#117487362
#106053113
#766655