Finite Group Databasebeta

← #14331652

Subgroups — #14331652

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×C4×#1220C211yesmaximal, characteristic, complemented
3C2×C4×C5×#67C211yesmaximal, characteristic, complemented
4C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
5#11749524C211yesmaximal, characteristic, complemented
6#11749523C211yesmaximal, characteristic, complemented
7#11749522C211yesmaximal, characteristic, complemented
8#11749521C211yesmaximal, characteristic, complemented
9#11748920C211yesmaximal, characteristic, complemented
10#11748733C211yesmaximal, characteristic, complemented
11#11748732C211yesmaximal, characteristic, complemented
12C4×#6667C211yesmaximal, characteristic, complemented
13C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
14C4×#6665C211yesmaximal, characteristic, complemented
15#11748567C211yesmaximal, characteristic, complemented
16#10614131—31nomaximal, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×#1204C2211yescharacteristic
25C22×#1203C2211yescharacteristic
26C22×#1202C2211yescharacteristic
27C22×#1201C2211yescharacteristic
28C2×#6771—24no—
29C2×#6771—24no—
30C2×#6771—24no—
31C2×#6719C2211yescharacteristic
32C4×#1220—24no—
33C2×#6714C2211yescharacteristic
34C2×#6712C2211yescharacteristic
35C2×C4×Dic15C2211yescharacteristic
36C2×C5×#217C2211yescharacteristic
37C4×C5×#67—24no—
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×Dic3⋊C4C2211yescharacteristic
40C2×C4×C5×Dic3C2211yescharacteristic
41C2×C3×C22⋊Dic5C2211yescharacteristic
42C3×C4×C22⋊D5—24no—
43C2×C3×#685C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C2×C3×C4×Dic5C2211yescharacteristic
46C2×#6667C2211yescharacteristic
47C2×#6667C2211yescharacteristic
48C2×(C2×D3)⋊Dic5C2211yescharacteristic
49C2×(C2×D3)⋊Dic5C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51C2×#6665C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#90994C2211yescharacteristic
58#82400—51nomaximal, Hall
59C22×#709—31no—
60C2×C4×C5×D4—31no—
61C2×C4×C22⋊D5—31no—
62C2×C4×C22⋊D5D311yescharacteristic, complemented
63#65512—31no—
64#65512—31no—
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
75C23×D15C2311yescharacteristic
76C23×C5×D3C2311yescharacteristic
77C23×C3×D5C2311yescharacteristic
78C22×C3×C4×C5—22no—
79C22×C3×C4×C5—22no—
80C22×C3×C4×C5—22no—
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×#1220—22no—
84C2×#1220—22no—
85C2×#1220—22no—
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C2×C4×D15—22no—
90C2×C4×D15—22no—
91C2×C4×D15D414yescomplemented
92C2×C5×#67—22no—
93C2×C5×#67—22no—
94C2×C5×#67—22no—
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C2×C4×C5×D3—22no—
99C2×C4×C5×D3—22no—
100C2×C4×C5×D3D414yescomplemented
101C2×C3×C22⋊D5—22no—
102C2×C3×C22⋊D5—22no—
103C2×C3×C22⋊D5—22no—
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C2×C3×C4×D5—22no—
108C2×C3×C4×D5—22no—
109C2×C3×C4×D5D414yescomplemented
110C2×#1204—22no—
111C2×#1204—22no—
112C2×#1204—22no—
113C2×#1203—22no—
114C2×#1203—22no—
115C2×#1203—22no—
116C2×#1202—22no—
117C2×#1202—22no—
118C2×#1202—22no—
119C2×#1201—22no—
120C2×#1201—22no—
121C2×#1201—22no—
122#6771—232no—
123#6719—22no—
124#6714—22no—
125#6712—22no—
126C4×Dic15—22no—
127C5×#217—22no—
128C5×(C2×D3)⋊C4—22no—
129C5×Dic3⋊C4—22no—
130C4×C5×Dic3—22no—
131C3×C22⋊Dic5—22no—
132C3×#685—22no—
133C3×#683—22no—
134C3×C4×Dic5—22no—
135#6667—22no—
136#6667—22no—
137(C2×D3)⋊Dic5—22no—
138(C2×D3)⋊Dic5—22no—
139#6665—22no—
140#6665—22no—
141C22×#235—51no—
142C2×C3×C4×D4—51no—
143C2×C4×#67—51no—
144C2×C4×#67D511yescharacteristic, complemented
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)⋊C4—51no—
156C22×C5×D4—31no—
157C23×C4×C5—31no—
158C23×C4×C5C2×D311yescharacteristic
159C22×C22⋊D5—31no—
160C22×C22⋊D5—31no—
161C22×C22⋊D5—31no—
162C22×C22⋊D5C2×D311yescharacteristic
163C2×#709—64no—
164C2×#709—64no—
165C2×#709—64no—
166C22×D20—31no—
167C22×C4×D5—31no—
168C22×C4×D5C2×D311yescharacteristic
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⋊Dic5—31no—
178C2×C22⋊Dic5C2×D311yescharacteristic
179C4×C22⋊D5—24no—
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×#683C2×D311yescharacteristic
189C2×C4×Dic5—31no—
190C2×C4×Dic5C2×D311yescharacteristic
191#3963—31no—
192#3963—31no—
193#3963—31no—
194#3963—31no—
195#3963—31no—
196#3963—31no—
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#4112yescomplemented
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×C5×D3—21no—
214C22×C5×D3—21no—
215C22×C5×D3—21no—
216C22×C5×D3—21no—
217C22×C5×D3—21no—
218C22×C5×D3—21no—
219C22×C5×D3C2×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—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—44no—
231C2×C3×C4×C5C2×D412yes—
232C2×C3×C4×C5C2×D412yes—
233C2×C3×C4×C5C2×D412yes—
234#1220—28no—
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×Dic15#4112yescomplemented
244C4×D15—28no—
245C5×#67—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—
256C3×C22⋊D5—28no—
257C2×C3×Dic5—21no—
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×Dic5C2×D412yes—
265C2×C3×Dic5#4112yescomplemented
266C3×C4×D5—28no—
267#1204—28no—
268#1203—28no—
269#1202—28no—
270#1201—28no—
271C22×C3×D4—51no—
272C23×C3×C4—51no—
273C23×C3×C4C2×D511yescharacteristic
274C22×#67—51no—
275C22×#67—51no—
276C22×#67—51no—
277C22×#67C2×D511yescharacteristic
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×C42—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217C2×D511yescharacteristic
294C4×#67—24no—
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)⋊C4—51no—
301C2×(C2×D3)⋊C4C2×D511yescharacteristic
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4C2×D511yescharacteristic
304C2×C4×Dic3—51no—
305C2×C4×Dic3C2×D511yescharacteristic
306C3⋊#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95—51no—
312C24×C5—31no—
313C24×C5C22×D311yescharacteristic
314C23×D5—31no—
315C23×D5C22×D311yescharacteristic
316C2×C5×D4—62no—
317C2×C5×D4—62no—
318C2×C5×D4—62no—
319C22×C4×C5—22no—
320C22×C4×C5—22no—
321C22×C4×C5—22no—
322C22×C4×C5—31no—
323C22×C4×C5—31no—
324C22×C4×C5—34no—
325C22×C4×C5—31no—
326C22×C4×C5—62no—
327C22×C4×C5—62no—
328C22×C4×C5C22×D311yescharacteristic
329C22×C4×C5C22×D311yescharacteristic
330C2×C22⋊D5—22no—
331C2×C22⋊D5—22no—
332C2×C22⋊D5—22no—
333C2×C22⋊D5—62no—
334C2×C22⋊D5—62no—
335C2×C22⋊D5—62no—
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—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×C4⋊C4—62no—
362C5×C22⋊C4—62no—
363C5×C22⋊C4—62no—
364C42×C5—62no—
365C22⋊Dic5—22no—
366C22⋊Dic5—62no—
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—22no—
376#683—62no—
377C4×Dic5—22no—
378C4×Dic5—62no—
379C22×#41—151no—
380C2×C4×D4—31no—
381C2×C4×D4—51no—
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—151no—
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×C5×D3—22no—
416C2×C5×D3—22no—
417C2×C5×D3—22no—
418C2×C5×D3—41no—
419C2×C5×D3—41no—
420C2×C5×D3—41no—
421C2×C5×D3—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—41no—
430C3×C4×C5#12014yes—
431Dic15—22no—
432Dic15—22no—
433Dic15—41no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—41no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3—41no—
440C24×C3—51no—
441C24×C3C22×D511yescharacteristic
442C23×D3—51no—
443C23×D3C22×D511yescharacteristic
444C2×C3×D4—102no—
445C2×C3×D4—102no—
446C2×C3×D4—102no—
447C22×C3×C4—22no—
448C22×C3×C4—22no—
449C22×C3×C4—22no—
450C22×C3×C4—51no—
451C22×C3×C4—51no—
452C22×C3×C4—54no—
453C22×C3×C4—51no—
454C22×C3×C4—102no—
455C22×C3×C4—102no—
456C22×C3×C4C22×D511yescharacteristic
457C22×C3×C4C22×D511yescharacteristic
458C2×#67—22no—
459C2×#67—22no—
460C2×#67—22no—
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×D3C22⋊D514yescomplemented
486C2×Dic6—102no—
487C2×Dic6—102no—
488C2×Dic6—102no—
489C3×C4⋊C4—102no—
490C3×C22⋊C4—102no—
491C3×C22⋊C4—102no—
492C3×C42—102no—
493#217—22no—
494#217—102no—
495#217—102no—
496#217—102no—
497(C2×D3)⋊C4—22no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—102no—
501(C2×D3)⋊C4—102no—
502(C2×D3)⋊C4—102no—
503Dic3⋊C4—22no—
504Dic3⋊C4—102no—
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×C5—32no—
514C23×C5—61no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5—61no—
520C23×C5#23512yescomplemented
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×D5C2×#6712yes—
536C5×D4—68no—
537C2×C4×C5—21no—
538C2×C4×C5—21no—
539C2×C4×C5—21no—
540C2×C4×C5—32no—
541C2×C4×C5—32no—
542C2×C4×C5—44no—
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×C5D3×D412yes—
552C2×C4×C5D3×D412yes—
553C2×C4×C5C2×#6712yes—
554C22⋊D5—28no—
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—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×Dic5#23512yescomplemented
575C2×Dic5C2×#6712yes—
576D20—68no—
577C4×D5—28no—
578C4×D5—68no—
579Dic10—68no—
580C2×#41—304no—
581C2×#41—304no—
582C2×#41—304no—
583C22×Q8—151no—
584C22×D4—31no—
585C22×D4—51no—
586C22×D4—151no—
587C22×D4—151no—
588C22×D4—151no—
589C22×D4—151no—
590C23×C4—31no—
591C23×C4—51no—
592C23×C4—151no—
593C23×C4D3×D511yescharacteristic
594C4×D4—64no—
595C4×D4—104no—
596C4×D4—304no—
597C2×C4⋊C4—31no—
598C2×C4⋊C4—51no—
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—51no—
614C2×C42—151no—
615#95—151no—
616#95—151no—
617#95—151no—
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—
631C5×D3—42no—
632C23×C3—21no—
633C23×C3—21no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—52no—
639C23×C3—101no—
640C23×C3—101no—
641C23×C3—101no—
642C23×C3—101no—
643C23×C3—101no—
644C23×C3—101no—
645C23×C3#70912yescomplemented
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×C22⋊D512yes—
661C3×D4—108no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—44no—
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—108no—
673C2×C3×C4—101no—
674C2×C3×C4—101no—
675C2×C3×C4—101no—
676C2×C3×C4D4×D512yes—
677C2×C3×C4D4×D512yes—
678C2×C3×C4C2×C22⋊D512yes—
679#67—28no—
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×Dic3#70912yescomplemented
700C2×Dic3C2×C22⋊D512yes—
701D12—108no—
702C4×D3—28no—
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×C5—62no—
713C22×C5—62no—
714C22×C5—62no—
715C22×C5—121no—
716C22×C5—121no—
717C22×C5—121no—
718C22×C5—121no—
719C22×C5C2×#23511yescharacteristic
720C22×C5C2×#23511yescharacteristic
721C22×C5C2×D3×D411yescharacteristic
722C22×C5C2×D3×D411yescharacteristic
723C22×C5D3×#4111yescharacteristic
724C22×C5D3×#4111yescharacteristic
725C22×C5C22×#6711yescharacteristic
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—41no—
741C4×C5—62no—
742C4×C5—62no—
743C4×C5—121no—
744C4×C5#93714yes—
745Dic5—22no—
746Dic5—22no—
747Dic5—41no—
748Dic5—62no—
749Dic5—62no—
750Dic5—121no—
751C24—31no—
752C24—51no—
753C24—151no—
754C24C2×D3×D511yescharacteristic
755#41—3032no—
756C2×Q8—302no—
757C2×Q8—302no—
758C2×Q8—302no—
759C2×D4—62no—
760C2×D4—62no—
761C2×D4—62no—
762C2×D4—102no—
763C2×D4—102no—
764C2×D4—102no—
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—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—34no—
783C22×C4—31no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—54no—
787C22×C4—51no—
788C22×C4—62no—
789C22×C4—62no—
790C22×C4—102no—
791C22×C4—102no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—154no—
795C22×C4—151no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4C2×D3×D511yescharacteristic
799C22×C4C2×D3×D511yescharacteristic
800C4⋊C4—62no—
801C4⋊C4—102no—
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—62no—
816C42—102no—
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—201no—
830C22×C3—201no—
831C22×C3—201no—
832C22×C3—201no—
833C22×C3C2×#70911yescharacteristic
834C22×C3C2×#70911yescharacteristic
835C22×C3C2×D4×D511yescharacteristic
836C22×C3C2×D4×D511yescharacteristic
837C22×C3D5×#4111yescharacteristic
838C22×C3D5×#4111yescharacteristic
839C22×C3C22×C22⋊D511yescharacteristic
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—41no—
855C3×C4—102no—
856C3×C4—102no—
857C3×C4—201no—
858C3×C4#408314yes—
859Dic3—22no—
860Dic3—22no—
861Dic3—41no—
862Dic3—102no—
863Dic3—102no—
864Dic3—201no—
865C2×C5—42no—
866C2×C5—122no—
867C2×C5#554711yescharacteristic
868C2×C5#554711yescharacteristic
869C2×C5#554811yescharacteristic
870C2×C5#554811yescharacteristic
871C2×C5#579111yescharacteristic
872C2×C5C2×#93711yescharacteristic
873C2×C5#583211yescharacteristic
874D5—42no—
875D5—122no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—32no—
883C23—52no—
884C23—61no—
885C23—61no—
886C23—61no—
887C23—61no—
888C23—61no—
889C23—61no—
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—
903C23#677112yescomplemented
904C23C22×D3×D511yescharacteristic
905Q8—308no—
906D4—68no—
907D4—108no—
908D4—308no—
909D4—308no—
910D4—308no—
911D4—308no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—44no—
918C2×C4—52no—
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—101no—
931C2×C4—101no—
932C2×C4—108no—
933C2×C4—101no—
934C2×C4—101no—
935C2×C4—101no—
936C2×C4—152no—
937C2×C4—152no—
938C2×C4—301no—
939C2×C4—301no—
940C2×C4—301no—
941C2×C4—301no—
942C2×C4—308no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4D5×#6712yes—
947C2×C4D3×C22⋊D512yes—
948C2×C4#679012yes—
949C2×C3—42no—
950C2×C3—202no—
951C2×C3#6588111yescharacteristic
952C2×C3#6588111yescharacteristic
953C2×C3#6588211yescharacteristic
954C2×C3#6588211yescharacteristic
955C2×C3#6612511yescharacteristic
956C2×C3C2×#408311yescharacteristic
957C2×C3#6616611yescharacteristic
958D3—42no—
959D3—202no—
960C5#8240011yescharacteristic, complemented, Sylow
961C22—22no—
962C22—22no—
963C22—22no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—62no—
969C22—62no—
970C22—62no—
971C22—102no—
972C22—102no—
973C22—102no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22—121no—
978C22—201no—
979C22—201no—
980C22—201no—
981C22—201no—
982C22—302no—
983C22—302no—
984C22—302no—
985C22—601no—
986C22—601no—
987C22—601no—
988C22—601no—
989C22C2×#677111yescharacteristic
990C22D5×#23511yescharacteristic
991C22D3×#70911yescharacteristic
992C22#9201611yescharacteristic
993C22C2×D5×#6711yescharacteristic
994C22C2×D3×C22⋊D511yescharacteristic
995C22C2×#679011yescharacteristic
996C4—41no—
997C4—62no—
998C4—62no—
999C4—102no—
1000C4—102no—
1001C4—121no—
1002C4—201no—
1003C4—302no—
1004C4—302no—
1005C4—601no—
1006C4#9157714yes—
1007C3#1061413111yescharacteristic, complemented, Sylow
1008C2—42no—
1009C2—122no—
1010C2—202no—
1011C2—602no—
1012C2#1175431111yescharacteristic
1013C2#1175452511yescharacteristic
1014C2#1175453811yescharacteristic
1015C2#1175453911yescharacteristic
1016C2#1175455411yescharacteristic
1017C2#1175455511yescharacteristic
1018C2C2×#9157711yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2388
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#6771C2semidirect
2. C2×C4×#1220C2semidirect
3. C2×C4×C5×#67C2semidirect
4. C2×C3×C4×C22⋊D5C2semidirect
5. #11749524C2semidirect
6. #11749523C2semidirect
7. #11749522C2semidirect
8. #11749521C2semidirect
9. #11748920C2semidirect
10. #11748733C2semidirect
11. #11748732C2semidirect
12. C4×#6667C2semidirect
13. C4×(C2×D3)⋊Dic5C2semidirect
14. C4×#6665C2semidirect
15. #11748567C2semidirect
62. C2×C4×C22⋊D5D3semidirect
91. C2×C4×D15D4semidirect
100. C2×C4×C5×D3D4semidirect
109. C2×C3×C4×D5D4semidirect
144. C2×C4×#67D5semidirect
204. C23×C3×C5#41semidirect
243. C2×Dic15#41semidirect
254. C2×C5×Dic3#41semidirect
265. C2×C3×Dic5#41semidirect
357. C2×C4×D5#67semidirect
485. C2×C4×D3C22⋊D5semidirect
520. C23×C5#235semidirect
574. C2×Dic5#235semidirect
645. C23×C3#709semidirect
699. C2×Dic3#709semidirect
818. C3×C5#2388semidirect
903. C23#6771semidirect
960. C5#82400semidirect
1007. C3#10614131semidirect

Maximal subgroups

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

subgroupindex
C22×#67712
C2×C4×#12202
C2×C4×C5×#672
C2×C3×C4×C22⋊D52
#117495242
#117495232
#117495222
#117495212
#117489202
#117487332
#117487322
C4×#66672
C4×(C2×D3)⋊Dic52
C4×#66652
#117485672
#106141313
#824005