Finite Group Databasebeta

← #14331653

Subgroups — #14331653

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×#6771C211yesmaximal, characteristic, complemented
2C2×C3×C4×D20C211yesmaximal, characteristic, complemented
3C2×C4×#1202C211yesmaximal, characteristic, complemented
4C2×C4×#1201C211yesmaximal, characteristic, complemented
5C4×#6714C211yesmaximal, characteristic, complemented
6C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#11748936C211yesmaximal, characteristic, complemented
8#11748925C211yesmaximal, characteristic, complemented
9#11748924C211yesmaximal, characteristic, complemented
10#11748923C211yesmaximal, characteristic, complemented
11#11748922C211yesmaximal, characteristic, complemented
12#11748921C211yesmaximal, characteristic, complemented
13#11748736C211yesmaximal, characteristic, complemented
14#11748734C211yesmaximal, characteristic, complemented
15C4×#6665C211yesmaximal, characteristic, complemented
16#10605311—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1202C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C22×#1201C2211yescharacteristic
28C2×#6771—24no—
29C2×#6771—24no—
30C2×#6771—24no—
31C2×C3×C42×C5C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×C4×Dic15C2211yescharacteristic
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C4×C5×Dic3C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×C4⋊Dic5C2211yescharacteristic
41C3×C4×D20—24no—
42C2×Dic3⋊Dic5C2211yescharacteristic
43C2×#6669C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×#6665C2211yescharacteristic
49C2×#6665C2211yescharacteristic
50C4×#1202—24no—
51C4×#1201—24no—
52#91115C2211yescharacteristic
53#91115C2211yescharacteristic
54C5×C3⋊#95C2211yescharacteristic
55C5×C3⋊#95C2211yescharacteristic
56#90994C2211yescharacteristic
57#90994C2211yescharacteristic
58#82400—51nomaximal, Hall
59C22×#709—31no—
60C2×C4×C22⋊D5—31no—
61C2×C4×D20—31no—
62C2×C4×D20D311yescharacteristic, complemented
63C4×C5×C22⋊C4—31no—
64#65250—31no—
65#65250—31no—
66#65249—31no—
67#65249—31no—
68C4×#685—31no—
69C4×#685—31no—
70#64962—31no—
71#64961—31no—
72#64960—31no—
73#64945—31no—
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C23×C3×D5C2311yescharacteristic
77C23×C3×D5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C2×C4×D15—22no—
85C2×C4×D15—22no—
86C2×C4×D15D414yescomplemented
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C2×C4×C5×D3—22no—
91C2×C4×C5×D3—22no—
92C2×C4×C5×D3D414yescomplemented
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×C3×D20—22no—
96C2×C3×D20—22no—
97C2×C3×D20—22no—
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5—22no—
102C2×C3×C4×D5—22no—
103C2×C3×C4×D5D414yescomplemented
104C2×#1204—22no—
105C2×#1204—22no—
106C2×#1204—22no—
107C2×#1203—22no—
108C2×#1203—22no—
109C2×#1203—22no—
110C2×#1202—22no—
111C2×#1202—22no—
112C2×#1202—22no—
113C2×#1202—22no—
114C2×#1202—22no—
115C2×#1202—22no—
116C2×#1201—22no—
117C2×#1201—22no—
118C2×#1201—22no—
119C2×#1201—22no—
120C2×#1201—22no—
121C2×#1201—22no—
122#6771—232no—
123C3×C42×C5—22no—
124#6714—22no—
125#6714—22no—
126C4×Dic15—22no—
127C5×(C2×D3)⋊C4—22no—
128C5×(C2×D3)⋊C4—22no—
129C4×C5×Dic3—22no—
130C3×#685—22no—
131C3×#685—22no—
132C3×C4⋊Dic5—22no—
133Dic3⋊Dic5—22no—
134#6669—22no—
135#6667—22no—
136(C2×D3)⋊Dic5—22no—
137#6665—22no—
138#6665—22no—
139#6665—22no—
140#6665—22no—
141C22×#235—51no—
142C2×C3×C4×D4—51no—
143C2×C4×#67—51no—
144C2×C4×#67—51no—
145#5223—51no—
146#5223—51no—
147C4×#217—51no—
148#4991—51no—
149#4979—51no—
150#4960—51no—
151#4959—51no—
152#4959—51no—
153#4947—51no—
154C4×(C2×D3)⋊C4—51no—
155C4×(C2×D3)⋊C4D511yescharacteristic, complemented
156C23×C4×C5—31no—
157C22×C22⋊D5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
160C2×#709—64no—
161C2×#709—64no—
162C2×#709—64no—
163C22×D20—31no—
164C22×D20—31no—
165C22×D20C2×D311yescharacteristic
166C22×C4×D5—31no—
167C22×C4×D5C2×D311yescharacteristic
168C22×C4×D5C2×D311yescharacteristic
169C22×Dic10—31no—
170C2×C5×C22⋊C4—31no—
171C2×C5×C22⋊C4—31no—
172C2×C42×C5—31no—
173C2×C42×C5C2×D311yescharacteristic
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⋊Dic5C2×D311yescharacteristic
187C2×#683—31no—
188C2×C4×Dic5—31no—
189C4×D20—24no—
190C4×D20—64no—
191C5×#95—31no—
192C5×#95—31no—
193#3963—31no—
194#3963—31no—
195#3963—31no—
196#3963—31no—
197#2388—151noSylow
198C23×C3×C5C2411yescharacteristic
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15—21no—
203C22×D15—21no—
204C22×D15—21no—
205C22×D15C2×D412yes—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3—21no—
211C22×C5×D3—21no—
212C22×C5×D3C2×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×C5C2×D412yes—
233C2×C3×C4×C5C2×D412yes—
234C2×C3×C4×C5C2×D412yes—
235C2×C3×C4×C5#4112yescomplemented
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15C2×D412yes—
244C2×Dic15#4112yescomplemented
245C4×D15—28no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—21no—
248C2×C5×Dic3—21no—
249C2×C5×Dic3—21no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3C2×D412yes—
254C2×C5×Dic3#4112yescomplemented
255C4×C5×D3—28no—
256C2×C3×Dic5—21no—
257C2×C3×Dic5—21no—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5C2×D412yes—
262C3×D20—28no—
263C3×C4×D5—28no—
264C3×C4×D5—44no—
265#1204—28no—
266#1203—28no—
267#1202—28no—
268#1202—28no—
269#1201—28no—
270#1201—28no—
271C22×C3×D4—51no—
272C23×C3×C4—51no—
273C23×C3×C4—51no—
274C22×#67—51no—
275C22×#67—51no—
276C22×#67—51no—
277C22×#67—51no—
278C2×#235—104no—
279C2×#235—104no—
280C2×#235—104no—
281C22×D12—51no—
282C22×C4×D3—51no—
283C22×C4×D3C2×D511yescharacteristic
284C22×Dic6—51no—
285C3×C4×D4—104no—
286C2×C3×C4⋊C4—51no—
287C2×C3×C22⋊C4—51no—
288C2×C3×C22⋊C4—51no—
289C2×C3×C42C2×D511yescharacteristic
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217—51no—
294C4×#67—104no—
295C4×#67—104no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—51no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4C2×D511yescharacteristic
301C2×(C2×D3)⋊C4C2×D511yescharacteristic
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×C4×Dic3—51no—
305C2×C4×Dic3C2×D511yescharacteristic
306C3⋊#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95C2×D511yescharacteristic
311C3⋊#95C2×D511yescharacteristic
312C24×C5—31no—
313C23×D5—31no—
314C23×D5C22×D311yescharacteristic
315C23×D5C22×D311yescharacteristic
316C22×C4×C5—31no—
317C22×C4×C5—31no—
318C22×C4×C5—34no—
319C22×C4×C5—31no—
320C22×C4×C5—62no—
321C22×C4×C5—62no—
322C22×C4×C5C22×D311yescharacteristic
323C22×C4×C5C22×D311yescharacteristic
324C22×C4×C5C22×D311yescharacteristic
325C2×C22⋊D5—62no—
326C2×C22⋊D5—62no—
327C2×C22⋊D5—62no—
328C2×C22⋊D5—62no—
329C2×C22⋊D5—62no—
330C2×C22⋊D5—62no—
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—22no—
350C2×C4×D5—22no—
351C2×C4×D5—22no—
352C2×C4×D5—22no—
353C2×C4×D5—22no—
354C2×C4×D5—34no—
355C2×C4×D5—62no—
356C2×C4×D5—62no—
357C2×C4×D5#6714yescomplemented
358C2×Dic10—62no—
359C2×Dic10—62no—
360C2×Dic10—62no—
361C5×C22⋊C4—62no—
362C5×C22⋊C4—62no—
363C42×C5—22no—
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—22no—
376C4⋊Dic5—62no—
377#683—62no—
378C4×Dic5—62no—
379C22×#41—151no—
380C2×C4×D4—51no—
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—151no—
389#392—151no—
390#392—151no—
391C4×C22⋊C4—31no—
392C4×C22⋊C4—151no—
393C4×C22⋊C4—151no—
394C22×C3×C5C22×D411yescharacteristic
395C22×C3×C5C22×D411yescharacteristic
396C22×C3×C5C22×D411yescharacteristic
397C22×C3×C5C2×#4111yescharacteristic
398C22×C3×C5C2×#4111yescharacteristic
399C22×C3×C5C2×#4111yescharacteristic
400C22×C3×C5C2×#4111yescharacteristic
401C2×D15—22no—
402C2×D15—22no—
403C2×D15—22no—
404C2×D15—41no—
405C2×D15—41no—
406C2×D15—41no—
407C2×D15—41no—
408C2×C5×D3—22no—
409C2×C5×D3—22no—
410C2×C5×D3—22no—
411C2×C5×D3—41no—
412C2×C5×D3—41no—
413C2×C5×D3—41no—
414C2×C5×D3—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—
431C3×C4×C5#12014yes—
432Dic15—22no—
433Dic15—22no—
434Dic15—41no—
435C3×Dic5—22no—
436C3×Dic5—41no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3—51no—
441C24×C3—51no—
442C23×D3—51no—
443C23×D3C22×D511yescharacteristic
444C2×C3×D4—102no—
445C2×C3×D4—102no—
446C2×C3×D4—102no—
447C22×C3×C4—51no—
448C22×C3×C4—54no—
449C22×C3×C4—51no—
450C22×C3×C4—102no—
451C22×C3×C4—102no—
452C22×C3×C4—102no—
453C22×C3×C4—102no—
454C22×C3×C4—102no—
455C22×C3×C4C22×D511yescharacteristic
456C22×C3×C4C22×D511yescharacteristic
457C22×C3×C4C22×D511yescharacteristic
458C2×#67—102no—
459C2×#67—102no—
460C2×#67—102no—
461C2×#67—102no—
462C2×#67—102no—
463C2×#67—102no—
464C2×#67—102no—
465C2×#67—102no—
466C2×#67—102no—
467C2×#67—102no—
468C2×#67—102no—
469C2×#67—102no—
470C22×Dic3—51no—
471C22×Dic3—51no—
472C22×Dic3—51no—
473C22×Dic3C22×D511yescharacteristic
474C22×Dic3C22×D511yescharacteristic
475C22×Dic3C22×D511yescharacteristic
476#235—1032no—
477C2×D12—102no—
478C2×D12—102no—
479C2×D12—102no—
480C2×C4×D3—22no—
481C2×C4×D3—22no—
482C2×C4×D3—54no—
483C2×C4×D3—102no—
484C2×C4×D3—102no—
485C2×C4×D3D2014yescomplemented
486C2×Dic6—102no—
487C2×Dic6—102no—
488C2×Dic6—102no—
489C3×C4⋊C4—102no—
490C3×C22⋊C4—102no—
491C3×C22⋊C4—102no—
492C3×C42—22no—
493#217—102no—
494#217—102no—
495#217—102no—
496#217—102no—
497(C2×D3)⋊C4—22no—
498(C2×D3)⋊C4—22no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—102no—
501(C2×D3)⋊C4—102no—
502(C2×D3)⋊C4—102no—
503Dic3⋊C4—102no—
504Dic3⋊C4—102no—
505C4×Dic3—22no—
506C4×Dic3—102no—
507C23×C5—32no—
508C23×C5—61no—
509C23×C5—61no—
510C23×C5—61no—
511C23×C5—61no—
512C23×C5—61no—
513C23×C5—61no—
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×D5#23512yescomplemented
535C22×D5C2×#6712yes—
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—61no—
544C2×C4×C5—61no—
545C2×C4×C5—61no—
546C2×C4×C5—61no—
547C2×C4×C5—68no—
548C2×C4×C5—61no—
549C2×C4×C5—61no—
550C2×C4×C5—61no—
551C2×C4×C5#23512yescomplemented
552C2×C4×C5D3×D412yes—
553C2×C4×C5D3×D412yes—
554C2×C4×C5C2×#6712yes—
555C22⋊D5—68no—
556C22⋊D5—68no—
557C22⋊D5—68no—
558C2×Dic5—21no—
559C2×Dic5—21no—
560C2×Dic5—21no—
561C2×Dic5—21no—
562C2×Dic5—21no—
563C2×Dic5—32no—
564C2×Dic5—32no—
565C2×Dic5—61no—
566C2×Dic5—61no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5C2×#6712yes—
573D20—28no—
574D20—68no—
575D20—68no—
576C4×D5—28no—
577C4×D5—44no—
578C4×D5—68no—
579Dic10—68no—
580C2×#41—304no—
581C2×#41—304no—
582C2×#41—304no—
583C22×Q8—151no—
584C22×D4—51no—
585C22×D4—151no—
586C22×D4—151no—
587C22×D4—151no—
588C22×D4—151no—
589C22×D4—151no—
590C23×C4—31no—
591C23×C4—51no—
592C23×C4—51no—
593C23×C4—151no—
594C4×D4—104no—
595C4×D4—304no—
596C4×D4—304no—
597C2×C4⋊C4—51no—
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—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⋊C4—151no—
612C2×C42—31no—
613C2×C42—151no—
614C2×C42D3×D511yescharacteristic
615#95—31no—
616#95—31no—
617#95—151no—
618#95—151no—
619#95—151no—
620#95—151no—
621C2×C3×C5C2×#12011yescharacteristic
622C2×C3×C5#52511yescharacteristic
623C2×C3×C5#52511yescharacteristic
624C2×C3×C5#52511yescharacteristic
625C2×C3×C5#53211yescharacteristic
626C2×C3×C5#53211yescharacteristic
627C2×C3×C5#53211yescharacteristic
628D15—42no—
629C3×D5—42no—
630C3×D5—42no—
631C5×D3—42no—
632C23×C3—52no—
633C23×C3—52no—
634C23×C3—101no—
635C23×C3—101no—
636C23×C3—101no—
637C23×C3—101no—
638C23×C3—101no—
639C23×C3—101no—
640C23×C3—101no—
641C23×C3—101no—
642C23×C3—101no—
643C23×C3—101no—
644C23×C3—101no—
645C23×C3—101no—
646C23×C3C23×D511yescharacteristic
647C22×D3—21no—
648C22×D3—21no—
649C22×D3—21no—
650C22×D3—21no—
651C22×D3—21no—
652C22×D3—21no—
653C22×D3—52no—
654C22×D3—101no—
655C22×D3—101no—
656C22×D3—101no—
657C22×D3—101no—
658C22×D3—101no—
659C22×D3—101no—
660C22×D3C2×D2012yes—
661C3×D4—108no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—52no—
668C2×C3×C4—101no—
669C2×C3×C4—101no—
670C2×C3×C4—108no—
671C2×C3×C4—101no—
672C2×C3×C4—101no—
673C2×C3×C4—101no—
674C2×C3×C4—204no—
675C2×C3×C4C2×D2012yes—
676C2×C3×C4#70912yescomplemented
677C2×C3×C4D4×D512yes—
678C2×C3×C4D4×D512yes—
679#67—108no—
680#67—108no—
681#67—108no—
682#67—108no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—52no—
691C2×Dic3—52no—
692C2×Dic3—101no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3—101no—
698C2×Dic3—101no—
699C2×Dic3C2×D2012yes—
700C2×Dic3#70912yescomplemented
701D12—108no—
702C4×D3—28no—
703C4×D3—108no—
704Dic6—108no—
705C22×C5—62no—
706C22×C5—62no—
707C22×C5—62no—
708C22×C5—121no—
709C22×C5—121no—
710C22×C5—121no—
711C22×C5—121no—
712C22×C5C2×#23511yescharacteristic
713C22×C5C2×#23511yescharacteristic
714C22×C5C2×D3×D411yescharacteristic
715C22×C5C2×D3×D411yescharacteristic
716C22×C5D3×#4111yescharacteristic
717C22×C5D3×#4111yescharacteristic
718C22×C5C22×#6711yescharacteristic
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—41no—
742C4×C5—62no—
743C4×C5—62no—
744C4×C5—121no—
745C4×C5#93714yes—
746Dic5—22no—
747Dic5—41no—
748Dic5—62no—
749Dic5—62no—
750Dic5—121no—
751C24—31no—
752C24—51no—
753C24—51no—
754C24—151no—
755#41—3032no—
756C2×Q8—302no—
757C2×Q8—302no—
758C2×Q8—302no—
759C2×D4—102no—
760C2×D4—102no—
761C2×D4—102no—
762C2×D4—302no—
763C2×D4—302no—
764C2×D4—302no—
765C2×D4—302no—
766C2×D4—302no—
767C2×D4—302no—
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—31no—
779C22×C4—34no—
780C22×C4—31no—
781C22×C4—51no—
782C22×C4—54no—
783C22×C4—51no—
784C22×C4—62no—
785C22×C4—62no—
786C22×C4—102no—
787C22×C4—102no—
788C22×C4—102no—
789C22×C4—102no—
790C22×C4—102no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—154no—
794C22×C4—151no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4C2×D3×D511yescharacteristic
798C22×C4C2×D3×D511yescharacteristic
799C22×C4C2×D3×D511yescharacteristic
800C4⋊C4—102no—
801C4⋊C4—302no—
802C4⋊C4—302no—
803C22⋊C4—62no—
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—22no—
816C42—62no—
817C42—302no—
818C3×C5#238811yescharacteristic, complemented, Hall
819C22×C3—102no—
820C22×C3—102no—
821C22×C3—102no—
822C22×C3—102no—
823C22×C3—102no—
824C22×C3—102no—
825C22×C3—201no—
826C22×C3—201no—
827C22×C3—201no—
828C22×C3—201no—
829C22×C3—201no—
830C22×C3—201no—
831C22×C3—201no—
832C22×C3—201no—
833C22×C3C22×D2011yescharacteristic
834C22×C3C2×#70911yescharacteristic
835C22×C3C2×#70911yescharacteristic
836C22×C3C2×D4×D511yescharacteristic
837C22×C3C2×D4×D511yescharacteristic
838C22×C3D5×#4111yescharacteristic
839C22×C3D5×#4111yescharacteristic
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—41no—
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—201no—
858C3×C4#402814yes—
859Dic3—22no—
860Dic3—22no—
861Dic3—41no—
862Dic3—102no—
863Dic3—102no—
864Dic3—201no—
865C2×C5—122no—
866C2×C5#554711yescharacteristic
867C2×C5#554711yescharacteristic
868C2×C5#554811yescharacteristic
869C2×C5#554811yescharacteristic
870C2×C5#579111yescharacteristic
871C2×C5C2×#93711yescharacteristic
872C2×C5#583211yescharacteristic
873D5—42no—
874D5—42no—
875D5—122no—
876C23—32no—
877C23—52no—
878C23—52no—
879C23—61no—
880C23—61no—
881C23—61no—
882C23—61no—
883C23—61no—
884C23—61no—
885C23—101no—
886C23—101no—
887C23—101no—
888C23—101no—
889C23—101no—
890C23—101no—
891C23—101no—
892C23—101no—
893C23—101no—
894C23—101no—
895C23—101no—
896C23—101no—
897C23—152no—
898C23—301no—
899C23—301no—
900C23—301no—
901C23—301no—
902C23—301no—
903C23—301no—
904C23C22×D3×D511yescharacteristic
905Q8—308no—
906D4—108no—
907D4—308no—
908D4—308no—
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—52no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—68no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—101no—
929C2×C4—101no—
930C2×C4—108no—
931C2×C4—101no—
932C2×C4—101no—
933C2×C4—101no—
934C2×C4—152no—
935C2×C4—152no—
936C2×C4—204no—
937C2×C4—301no—
938C2×C4—301no—
939C2×C4—301no—
940C2×C4—301no—
941C2×C4—308no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4#677112yescomplemented
946C2×C4D3×D2012yes—
947C2×C4#677712yes—
948C2×C4D5×#6712yes—
949C2×C3—202no—
950C2×C3—202no—
951C2×C3#6581111yescharacteristic
952C2×C3C2×#402811yescharacteristic
953C2×C3#6585811yescharacteristic
954C2×C3#6588111yescharacteristic
955C2×C3#6588111yescharacteristic
956C2×C3#6588211yescharacteristic
957C2×C3#6588211yescharacteristic
958D3—42no—
959D3—202no—
960C5#8240011yescharacteristic, complemented, Sylow
961C22—62no—
962C22—62no—
963C22—62no—
964C22—102no—
965C22—102no—
966C22—102no—
967C22—102no—
968C22—102no—
969C22—102no—
970C22—121no—
971C22—121no—
972C22—121no—
973C22—121no—
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×#677111yescharacteristic
990C22C2×D3×D2011yescharacteristic
991C22C2×#677711yescharacteristic
992C22D5×#23511yescharacteristic
993C22D3×#70911yescharacteristic
994C22#9201611yescharacteristic
995C22C2×D5×#6711yescharacteristic
996C4—22no—
997C4—41no—
998C4—62no—
999C4—62no—
1000C4—102no—
1001C4—121no—
1002C4—201no—
1003C4—302no—
1004C4—302no—
1005C4—601no—
1006C4#9147414yes—
1007C3#1060531111yescharacteristic, complemented, Sylow
1008C2—122no—
1009C2—202no—
1010C2—202no—
1011C2—602no—
1012C2#1175267511yescharacteristic
1013C2#1175267911yescharacteristic
1014C2#1175273911yescharacteristic
1015C2#1175274711yescharacteristic
1016C2#1175431111yescharacteristic
1017C2#1175452511yescharacteristic
1018C2C2×#9147411yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2388
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#6771C2semidirect
2. C2×C3×C4×D20C2semidirect
3. C2×C4×#1202C2semidirect
4. C2×C4×#1201C2semidirect
5. C4×#6714C2semidirect
6. C4×C5×(C2×D3)⋊C4C2semidirect
7. #11748936C2semidirect
8. #11748925C2semidirect
9. #11748924C2semidirect
10. #11748923C2semidirect
11. #11748922C2semidirect
12. #11748921C2semidirect
13. #11748736C2semidirect
14. #11748734C2semidirect
15. C4×#6665C2semidirect
62. C2×C4×D20D3semidirect
86. C2×C4×D15D4semidirect
92. C2×C4×C5×D3D4semidirect
103. C2×C3×C4×D5D4semidirect
155. C4×(C2×D3)⋊C4D5semidirect
226. C22×C3×D5#41semidirect
235. C2×C3×C4×C5#41semidirect
244. C2×Dic15#41semidirect
254. C2×C5×Dic3#41semidirect
357. C2×C4×D5#67semidirect
485. C2×C4×D3D20semidirect
534. C22×D5#235semidirect
551. C2×C4×C5#235semidirect
676. C2×C3×C4#709semidirect
700. C2×Dic3#709semidirect
818. C3×C5#2388semidirect
945. C2×C4#6771semidirect
960. C5#82400semidirect
1007. C3#10605311semidirect

Maximal subgroups

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

subgroupindex
C22×#67712
C2×C3×C4×D202
C2×C4×#12022
C2×C4×#12012
C4×#67142
C4×C5×(C2×D3)⋊C42
#117489362
#117489252
#117489242
#117489232
#117489222
#117489212
#117487362
#117487342
C4×#66652
#106053113
#824005