Finite Group Databasebeta

← #14331676

Subgroups — #14331676

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×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×#91446C211yesmaximal, characteristic, complemented
4C2×#91441C211yesmaximal, characteristic, complemented
5#11751060C211yesmaximal, characteristic, complemented
6C3×#65248C211yesmaximal, characteristic, complemented
7#11749523C211yesmaximal, characteristic, complemented
8#11749521C211yesmaximal, characteristic, complemented
9Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
10#11748925C211yesmaximal, characteristic, complemented
11#11748881C211yesmaximal, characteristic, complemented
12Dic3×#685C211yesmaximal, characteristic, complemented
13#11748757C211yesmaximal, characteristic, complemented
14#11748732C211yesmaximal, characteristic, complemented
15#11748567C211yesmaximal, characteristic, complemented
16#10614131—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C23×C5×Dic3C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×#1200C2211yescharacteristic
27C2×#6779—24no—
28C2×#6779—24no—
29C2×#6779—24no—
30C22×D5×Dic3C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×Dic3⋊C4C2211yescharacteristic
38C2×C4×C5×Dic3C2211yescharacteristic
39C5×#67⋊C4—24no—
40C2×C3×C22⋊Dic5C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×(C2×D3)⋊Dic5C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50#91446—24no—
51#91441—24no—
52#91115C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#90994C2211yescharacteristic
58#76889—51nomaximal, Hall
59C22×#709—31no—
60C2×C4×C5×D4—31no—
61C2×C4×C22⋊D5—31no—
62C2×C4×C22⋊D5—31no—
63#65512—31no—
64#65512—31no—
65C4×C22⋊Dic5—31no—
66#65280—31no—
67#65268—31no—
68#65249—31no—
69#65248—31no—
70#65248D311yescharacteristic, complemented
71#65236—31no—
72C4×#685—31no—
73C4×#685—31no—
74C24×C3×C5C2311yescharacteristic
75C23×D15C2311yescharacteristic
76C23×C5×D3C2311yescharacteristic
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
86C2×C5×#67—22no—
87C2×C5×#67—22no—
88C2×C5×#67—22no—
89C22×C5×Dic3—22no—
90C22×C5×Dic3—22no—
91C22×C5×Dic3D414yescomplemented
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C2×C4×C5×D3—22no—
96C2×C4×C5×D3—22no—
97C2×C4×C5×D3—22no—
98C2×C3×C22⋊D5—22no—
99C2×C3×C22⋊D5—22no—
100C2×C3×C22⋊D5—22no—
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
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×#1201—22no—
114C2×#1201—22no—
115C2×#1201—22no—
116C2×#1200—22no—
117C2×#1200—22no—
118C2×#1200D414yescomplemented
119#6779—232no—
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—
127#6712—22no—
128C5×(C2×D3)⋊C4—22no—
129C5×Dic3⋊C4—22no—
130C4×C5×Dic3—22no—
131C3×C22⋊Dic5—22no—
132C3×#685—22no—
133C3×#685—22no—
134C3×#683—22no—
135#6667—22no—
136(C2×D3)⋊Dic5—22no—
137(C2×D3)⋊Dic5—22no—
138#6665—22no—
139Dic3×Dic5—22no—
140Dic3×Dic5—22no—
141C22×#237—51no—
142C2×#893—51no—
143C2×#67⋊C4—51no—
144C2×#67⋊C4D511yescharacteristic, complemented
145C3×#394—51no—
146#5223—51no—
147#4979—51no—
148#4960—51no—
149#4960—51no—
150#4959—51no—
151#4959—51no—
152Dic3×C22⋊C4—51no—
153Dic3×C22⋊C4—51no—
154#4673—51no—
155#4666—51no—
156C22×C5×D4—31no—
157C23×C4×C5—31no—
158C23×C4×C5—31no—
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×D5—31no—
169C22×Dic10—31no—
170C4×C5×D4—64no—
171C2×C5×C4⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C5×C22⋊C4C2×D311yescharacteristic
174C2×C42×C5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
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×#685C2×D311yescharacteristic
186C2×#685C2×D311yescharacteristic
187C2×#683—31no—
188C2×#683C2×D311yescharacteristic
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×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×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×D3#4112yescomplemented
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—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
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×Dic15C2×D412yes—
242C2×Dic15#4112yescomplemented
243C5×#67—28no—
244C2×C5×Dic3—21no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—21no—
248C2×C5×Dic3—28no—
249C2×C5×Dic3C2×D412yes—
250C2×C5×Dic3C2×D412yes—
251C2×C5×Dic3C2×D412yes—
252C2×C5×Dic3C2×D412yes—
253C2×C5×Dic3#4112yescomplemented
254C4×C5×D3—44no—
255C3×C22⋊D5—28no—
256C2×C3×Dic5—21no—
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×Dic5C2×D412yes—
264C2×C3×Dic5#4112yescomplemented
265#1204—28no—
266#1203—28no—
267#1202—28no—
268#1201—28no—
269#1200—28no—
270D5×Dic3—28no—
271C22×C3×D4—51no—
272C22×#67—51no—
273C22×#67—51no—
274C22×#67—51no—
275C22×#67C2×D511yescharacteristic
276C23×Dic3—51no—
277C23×Dic3C2×D511yescharacteristic
278C2×#237—104no—
279C2×#237—104no—
280C2×#237—104no—
281C22×D12—51no—
282C22×C4×D3—51no—
283C22×C4×D3C2×D511yescharacteristic
284C22×Dic6—51no—
285C2×C3×C4⋊C4—51no—
286C2×C3×C22⋊C4—51no—
287C2×C3×C22⋊C4—51no—
288C2×C3×C22⋊C4—51no—
289C2×C3×C22⋊C4C2×D511yescharacteristic
290C2×#217—51no—
291C2×#217—51no—
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—51no—
296C2×(C2×D3)⋊C4—51no—
297C2×(C2×D3)⋊C4C2×D511yescharacteristic
298C2×Dic3⋊C4—51no—
299C2×Dic3⋊C4C2×D511yescharacteristic
300C2×C4×Dic3—51no—
301C2×C4×Dic3—51no—
302C2×C4×Dic3C2×D511yescharacteristic
303#893—104no—
304#67⋊C4—24no—
305#67⋊C4—104no—
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—31no—
320C22×C4×C5—34no—
321C22×C4×C5—31no—
322C22×C4×C5—31no—
323C22×C4×C5—62no—
324C22×C4×C5—62no—
325C22×C4×C5—62no—
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—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—22no—
363C5×C22⋊C4—62no—
364C42×C5—62no—
365C22⋊Dic5—22no—
366C22⋊Dic5—62no—
367C22⋊Dic5—62no—
368C22⋊Dic5—62no—
369#685—22no—
370#685—22no—
371#685—62no—
372#685—62no—
373#685—62no—
374#685—62no—
375#683—22no—
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—51no—
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—41no—
431Dic15—22no—
432Dic15—22no—
433Dic15—41no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—41no—
437C5×Dic3—22no—
438C5×Dic3—22no—
439C5×Dic3#12014yes—
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—51no—
448C22×C3×C4—51no—
449C22×C3×C4—51no—
450C22×C3×C4C22×D511yescharacteristic
451C22×C3×C4C22×D511yescharacteristic
452C2×#67—22no—
453C2×#67—22no—
454C2×#67—22no—
455C2×#67—102no—
456C2×#67—102no—
457C2×#67—102no—
458C2×#67—102no—
459C2×#67—102no—
460C2×#67—102no—
461C2×#67—102no—
462C2×#67—102no—
463C2×#67—102no—
464C22×Dic3—22no—
465C22×Dic3—22no—
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3—54no—
469C22×Dic3—51no—
470C22×Dic3—102no—
471C22×Dic3—102no—
472C22×Dic3C22⋊D514yescomplemented
473C22×Dic3C22×D511yescharacteristic
474C22×Dic3C22×D511yescharacteristic
475C22×Dic3C22×D511yescharacteristic
476#237—1032no—
477C2×D12—102no—
478C2×D12—102no—
479C2×D12—102no—
480C2×C4×D3—22no—
481C2×C4×D3—22no—
482C2×C4×D3—22no—
483C2×C4×D3—54no—
484C2×C4×D3—102no—
485C2×C4×D3—102no—
486C2×Dic6—102no—
487C2×Dic6—102no—
488C2×Dic6—102no—
489C3×C4⋊C4—102no—
490C3×C22⋊C4—22no—
491C3×C22⋊C4—102no—
492C3×C22⋊C4—102no—
493C3×C22⋊C4—102no—
494#217—102no—
495#217—102no—
496(C2×D3)⋊C4—22no—
497(C2×D3)⋊C4—102no—
498(C2×D3)⋊C4—102no—
499(C2×D3)⋊C4—102no—
500(C2×D3)⋊C4—102no—
501(C2×D3)⋊C4—102no—
502Dic3⋊C4—22no—
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—32no—
514C23×C5—61no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5—61no—
520C23×C5D3×D412yes—
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—68no—
537C2×C4×C5—21no—
538C2×C4×C5—21no—
539C2×C4×C5—21no—
540C2×C4×C5—21no—
541C2×C4×C5—21no—
542C2×C4×C5—21no—
543C2×C4×C5—32no—
544C2×C4×C5—32no—
545C2×C4×C5—32no—
546C2×C4×C5—32no—
547C2×C4×C5—32no—
548C2×C4×C5—68no—
549C2×C4×C5—61no—
550C2×C4×C5—61no—
551C2×C4×C5—61no—
552C2×C4×C5—61no—
553C2×C4×C5—124no—
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×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—31no—
585C22×D4—51no—
586C22×D4—151no—
587C22×D4—151no—
588C22×D4—151no—
589C22×D4—151no—
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—51no—
599C2×C4⋊C4—151no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—51no—
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⋊C4D3×D511yescharacteristic
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×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×C3C2×C22⋊D512yes—
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×D3#70912yescomplemented
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—21no—
668C2×C3×C4—52no—
669C2×C3×C4—52no—
670C2×C3×C4—101no—
671C2×C3×C4—101no—
672C2×C3×C4—101no—
673C2×C3×C4—101no—
674C2×C3×C4—101no—
675C2×C3×C4—101no—
676C2×C3×C4—101no—
677#67—28no—
678#67—108no—
679#67—108no—
680#67—108no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—28no—
686C2×Dic3—52no—
687C2×Dic3—52no—
688C2×Dic3—101no—
689C2×Dic3—101no—
690C2×Dic3—101no—
691C2×Dic3—101no—
692C2×Dic3—108no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3#70912yescomplemented
697C2×Dic3D4×D512yes—
698C2×Dic3D4×D512yes—
699C2×Dic3C2×C22⋊D512yes—
700C2×Dic3C2×C22⋊D512yes—
701D12—108no—
702C4×D3—44no—
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×D3×D411yescharacteristic
720C22×C5C2×D3×D411yescharacteristic
721C22×C5C2×D3×D411yescharacteristic
722C22×C5C2×#23711yescharacteristic
723C22×C5D3×#4111yescharacteristic
724C22×C5D3×#4111yescharacteristic
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—34no—
741C4×C5—41no—
742C4×C5—41no—
743C4×C5—62no—
744C4×C5—62no—
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—31no—
778C22×C4—34no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—62no—
785C22×C4—62no—
786C22×C4—62no—
787C22×C4—62no—
788C22×C4—62no—
789C22×C4—154no—
790C22×C4—154no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—302no—
795C22×C4—302no—
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—22no—
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—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—41no—
856C3×C4—102no—
857C3×C4—102no—
858C3×C4—201no—
859Dic3—22no—
860Dic3—22no—
861Dic3—102no—
862Dic3—102no—
863Dic3—201no—
864Dic3#408314yes—
865C2×C5—42no—
866C2×C5—122no—
867C2×C5D3×#12011yescharacteristic
868C2×C5#559611yescharacteristic
869C2×C5#559611yescharacteristic
870C2×C5#560611yescharacteristic
871C2×C5#565611yescharacteristic
872C2×C5#565611yescharacteristic
873C2×C5#566811yescharacteristic
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—
903C23D3×C22⋊D512yes—
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—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—32no—
919C2×C4—32no—
920C2×C4—32no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—52no—
924C2×C4—52no—
925C2×C4—68no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—101no—
931C2×C4—101no—
932C2×C4—101no—
933C2×C4—101no—
934C2×C4—101no—
935C2×C4—101no—
936C2×C4—101no—
937C2×C4—124no—
938C2×C4—152no—
939C2×C4—152no—
940C2×C4—308no—
941C2×C4—308no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—301no—
948C2×C4—301no—
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#7688911yescharacteristic, 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—
989C22D3×#70911yescharacteristic
990C22D3×#70911yescharacteristic
991C22D3×D4×D511yescharacteristic
992C22D3×D4×D511yescharacteristic
993C22D5×#23711yescharacteristic
994C22#9202411yescharacteristic
995C22C2×D3×C22⋊D511yescharacteristic
996C4—34no—
997C4—41no—
998C4—41no—
999C4—62no—
1000C4—62no—
1001C4—102no—
1002C4—102no—
1003C4—201no—
1004C4—302no—
1005C4—302no—
1006C4—601no—
1007C3#1061413111yescharacteristic, complemented, Sylow
1008C2—42no—
1009C2—122no—
1010C2—202no—
1011C2—602no—
1012C2#1175283111yescharacteristic
1013C2#1175285511yescharacteristic
1014C2#1175322011yescharacteristic
1015C2#1175325011yescharacteristic
1016C2#1175433911yescharacteristic
1017C2#1175480311yescharacteristic
1018C2D3×#408311yescharacteristic
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×C5×#67⋊C4C2semidirect
3. C2×#91446C2semidirect
4. C2×#91441C2semidirect
5. #11751060C2semidirect
6. C3×#65248C2semidirect
7. #11749523C2semidirect
8. #11749521C2semidirect
9. Dic3×C22⋊Dic5C2semidirect
10. #11748925C2semidirect
11. #11748881C2semidirect
12. Dic3×#685C2semidirect
13. #11748757C2semidirect
14. #11748732C2semidirect
15. #11748567C2semidirect
70. #65248D3semidirect
91. C22×C5×Dic3D4semidirect
118. C2×#1200D4semidirect
122. C2×D5×Dic3D4semidirect
144. C2×#67⋊C4D5semidirect
219. C22×C5×D3#41semidirect
242. C2×Dic15#41semidirect
253. C2×C5×Dic3#41semidirect
264. C2×C3×Dic5#41semidirect
472. C22×Dic3C22⋊D5semidirect
575. C2×Dic5#237semidirect
660. C22×D3#709semidirect
696. C2×Dic3#709semidirect
818. C3×C5#2388semidirect
960. C5#76889semidirect
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×#67⋊C42
C2×#914462
C2×#914412
#117510602
C3×#652482
#117495232
#117495212
Dic3×C22⋊Dic52
#117489252
#117488812
Dic3×#6852
#117487572
#117487322
#117485672
#106141313
#768895