Finite Group Databasebeta

← #14331675

Subgroups — #14331675

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×#6780C211yesmaximal, characteristic, complemented
2C2×#91770C211yesmaximal, characteristic, complemented
3C2×#91406C211yesmaximal, characteristic, complemented
4C2×#91396C211yesmaximal, characteristic, complemented
5C5×#4959C211yesmaximal, characteristic, complemented
6C3×#65248C211yesmaximal, characteristic, complemented
7#11749523C211yesmaximal, characteristic, complemented
8#11749522C211yesmaximal, characteristic, complemented
9#11749487C211yesmaximal, characteristic, complemented
10#11748925C211yesmaximal, characteristic, complemented
11#11748920C211yesmaximal, characteristic, complemented
12#11748886C211yesmaximal, characteristic, complemented
13#11748884C211yesmaximal, characteristic, complemented
14#11748579C211yesmaximal, characteristic, complemented
15#11748567C211yesmaximal, characteristic, complemented
16#10608620—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C2×#6780—24no—
28C2×#6780—24no—
29C2×#6780—24no—
30C22×D5×Dic3C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34C2×C4×Dic15C2211yescharacteristic
35#91770—24no—
36C2×C5×#217C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×Dic3⋊C4C2211yescharacteristic
40C2×C3×C22⋊Dic5C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×#6667C2211yescharacteristic
46C2×(C2×D3)⋊Dic5C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50#91406—24no—
51#91396—24no—
52C5×C3⋊#95C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#90994C2211yescharacteristic
58#76889—51nomaximal, Hall
59C22×#711—31no—
60C2×#4039—31no—
61C2×#4027—31no—
62C2×#4027—31no—
63C5×#394—31no—
64#65512—31no—
65#65268—31no—
66#65249—31no—
67#65249—31no—
68#65248—31no—
69#65248D311yescharacteristic, complemented
70C22⋊C4×Dic5—31no—
71C22⋊C4×Dic5—31no—
72#64962—31no—
73#64955—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×Dic15—22no—
84C22×Dic15—22no—
85C22×Dic15D414yescomplemented
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C2×C4×D15—22no—
90C2×C4×D15—22no—
91C2×C4×D15—22no—
92C2×C5×#67—22no—
93C2×C5×#67—22no—
94C2×C5×#67—22no—
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
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×D3×Dic5—22no—
117C2×D3×Dic5—22no—
118C2×D3×Dic5D414yescomplemented
119#6780—232no—
120C2×D5×Dic3—22no—
121C2×D5×Dic3—22no—
122C2×D5×Dic3D414yescomplemented
123C3×C5×C22⋊C4—22no—
124#6714—22no—
125#6712—22no—
126C4×Dic15—22no—
127C5×#217—22no—
128C5×(C2×D3)⋊C4—22no—
129C5×(C2×D3)⋊C4—22no—
130C5×Dic3⋊C4—22no—
131C3×C22⋊Dic5—22no—
132C3×#685—22no—
133C3×#685—22no—
134C3×#683—22no—
135#6667—22no—
136#6667—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⋊C4—51no—
145C3×#394—51no—
146#5223—51no—
147#4979—51no—
148#4960—51no—
149#4960—51no—
150#4959—51no—
151#4959D511yescharacteristic, complemented
152Dic3×C22⋊C4—51no—
153Dic3×C22⋊C4—51no—
154#4673—51no—
155#4666—51no—
156C22×C5×D4—31no—
157C22×C22⋊D5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
160C22×C22⋊D5C2×D311yescharacteristic
161C23×Dic5—31no—
162C23×Dic5—31no—
163C2×#711—64no—
164C2×#711—64no—
165C2×#711—64no—
166C22×D20—31no—
167C22×C4×D5—31no—
168C22×C4×D5—31no—
169C22×Dic10—31no—
170C2×C5×C4⋊C4—31no—
171C2×C5×C22⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C5×C22⋊C4—31no—
174C2×C5×C22⋊C4C2×D311yescharacteristic
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5C2×D311yescharacteristic
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#685C2×D311yescharacteristic
182C2×#685C2×D311yescharacteristic
183C2×#683—31no—
184C2×#683C2×D311yescharacteristic
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187C2×C4×Dic5—31no—
188#4039—64no—
189#4027—64no—
190#4027—64no—
191C5×#95—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×D15#4112yescomplemented
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—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—28no—
239C2×Dic15C2×D412yes—
240C2×Dic15C2×D412yes—
241C2×Dic15C2×D412yes—
242C2×Dic15C2×D412yes—
243C2×Dic15#4112yescomplemented
244C4×D15—44no—
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
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—
269D3×Dic5—28no—
270D5×Dic3—28no—
271C22×C3×D4—51no—
272C22×#67—51no—
273C22×#67—51no—
274C22×#67—51no—
275C22×#67C2×D511yescharacteristic
276C23×Dic3—51no—
277C23×Dic3—51no—
278C2×#237—104no—
279C2×#237—104no—
280C2×#237—104no—
281C22×D12—51no—
282C22×C4×D3—51no—
283C22×C4×D3—51no—
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×#217C2×D511yescharacteristic
292C2×(C2×D3)⋊C4—51no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—51no—
296C2×(C2×D3)⋊C4C2×D511yescharacteristic
297C2×(C2×D3)⋊C4C2×D511yescharacteristic
298C2×Dic3⋊C4—51no—
299C2×Dic3⋊C4C2×D511yescharacteristic
300C2×C4×Dic3—51no—
301C2×C4×Dic3—51no—
302C2×C4×Dic3—51no—
303#893—104no—
304#67⋊C4—104no—
305#67⋊C4—104no—
306C3×#95—51no—
307C3⋊#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95C2×D511yescharacteristic
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—31no—
321C22×C4×C5—31no—
322C22×C4×C5C22×D311yescharacteristic
323C22×C4×C5C22×D311yescharacteristic
324C2×C22⋊D5—22no—
325C2×C22⋊D5—22no—
326C2×C22⋊D5—22no—
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—
334C2×C22⋊D5—62no—
335C2×C22⋊D5—62no—
336C22×Dic5—31no—
337C22×Dic5—34no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—34no—
341C22×Dic5—62no—
342C22×Dic5—62no—
343C22×Dic5—62no—
344C22×Dic5—62no—
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348#711—632no—
349C2×D20—62no—
350C2×D20—62no—
351C2×D20—62no—
352C2×C4×D5—34no—
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×C4⋊C4—62no—
362C5×C22⋊C4—22no—
363C5×C22⋊C4—62no—
364C5×C22⋊C4—62no—
365C5×C22⋊C4—62no—
366C22⋊Dic5—22no—
367C22⋊Dic5—62no—
368#685—22no—
369#685—22no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—62no—
374#683—22no—
375#683—62no—
376C4×Dic5—62no—
377C4×Dic5—62no—
378C4×Dic5—62no—
379C22×#41—151no—
380C2×C4×D4—151no—
381C2×C4×D4—151no—
382C2×C4×D4—151no—
383#395—151no—
384#394—31no—
385#394—51no—
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#12014yes—
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—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—51no—
465C22×Dic3—54no—
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3—54no—
469C22×Dic3—102no—
470C22×Dic3—102no—
471C22×Dic3—102no—
472C22×Dic3—102no—
473C22×Dic3C22×D511yescharacteristic
474C22×Dic3C22×D511yescharacteristic
475C22×Dic3C22×D511yescharacteristic
476#237—1032no—
477C2×D12—102no—
478C2×D12—102no—
479C2×D12—102no—
480C2×C4×D3—54no—
481C2×C4×D3—102no—
482C2×C4×D3—102no—
483C2×C4×D3—102no—
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—22no—
495#217—102no—
496(C2×D3)⋊C4—22no—
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—
502Dic3⋊C4—22no—
503Dic3⋊C4—102no—
504C4×Dic3—102no—
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—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—
552C22⋊D5—28no—
553C22⋊D5—68no—
554C22⋊D5—68no—
555C22⋊D5—68no—
556C2×Dic5—21no—
557C2×Dic5—21no—
558C2×Dic5—21no—
559C2×Dic5—21no—
560C2×Dic5—21no—
561C2×Dic5—21no—
562C2×Dic5—21no—
563C2×Dic5—32no—
564C2×Dic5—32no—
565C2×Dic5—32no—
566C2×Dic5—32no—
567C2×Dic5—32no—
568C2×Dic5—68no—
569C2×Dic5—68no—
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—124no—
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—151no—
591C23×C4—151no—
592C23×C4—151no—
593C23×C4—151no—
594C4×D4—304no—
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—31no—
602C2×C22⋊C4—31no—
603C2×C22⋊C4—51no—
604C2×C22⋊C4—51no—
605C2×C22⋊C4—51no—
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—151no—
613C2×C42—151no—
614C2×C42—151no—
615#95—31no—
616#95—51no—
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×C3D4×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×D3D4×D512yes—
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—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—52no—
689C2×Dic3—52no—
690C2×Dic3—52no—
691C2×Dic3—52no—
692C2×Dic3—52no—
693C2×Dic3—108no—
694C2×Dic3—108no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3—101no—
698C2×Dic3—101no—
699C2×Dic3D4×D512yes—
700C2×Dic3#71112yescomplemented
701D12—108no—
702C4×D3—108no—
703C4×D3—204no—
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—41no—
741C4×C5—41no—
742C4×C5—62no—
743C4×C5—62no—
744C4×C5—121no—
745Dic5—22no—
746Dic5—22no—
747Dic5—34no—
748Dic5—41no—
749Dic5—62no—
750Dic5—62no—
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—31no—
779C22×C4—31no—
780C22×C4—51no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—154no—
784C22×C4—154no—
785C22×C4—151no—
786C22×C4—154no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—302no—
790C22×C4—302no—
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—62no—
801C4⋊C4—102no—
802C4⋊C4—302no—
803C22⋊C4—22no—
804C22⋊C4—62no—
805C22⋊C4—62no—
806C22⋊C4—62no—
807C22⋊C4—102no—
808C22⋊C4—102no—
809C22⋊C4—102no—
810C22⋊C4—302no—
811C22⋊C4—302no—
812C22⋊C4—302no—
813C22⋊C4—302no—
814C22⋊C4—302no—
815C42—302no—
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×D4×D511yescharacteristic
834C22×C3C2×D4×D511yescharacteristic
835C22×C3C2×D4×D511yescharacteristic
836C22×C3C2×#71111yescharacteristic
837C22×C3D5×#4111yescharacteristic
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—41no—
855C3×C4—41no—
856C3×C4—102no—
857C3×C4—102no—
858C3×C4—201no—
859Dic3—22no—
860Dic3—22no—
861Dic3—41no—
862Dic3—54no—
863Dic3—102no—
864Dic3—102no—
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—
903C23#679012yes—
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—52no—
921C2×C4—52no—
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—152no—
937C2×C4—152no—
938C2×C4—152no—
939C2×C4—152no—
940C2×C4—152no—
941C2×C4—308no—
942C2×C4—308no—
943C2×C4—308no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—301no—
948C2×C4—604no—
949C2×C3—42no—
950C2×C3—202no—
951C2×C3D5×#12011yescharacteristic
952C2×C3#6593011yescharacteristic
953C2×C3#6593011yescharacteristic
954C2×C3#6594011yescharacteristic
955C2×C3#6599011yescharacteristic
956C2×C3#6599011yescharacteristic
957C2×C3#6600211yescharacteristic
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—
989C22#9201611yescharacteristic
990C22#9201611yescharacteristic
991C22D3×D4×D511yescharacteristic
992C22D3×D4×D511yescharacteristic
993C22D5×#23711yescharacteristic
994C22D3×#71111yescharacteristic
995C22C2×#679011yescharacteristic
996C4—41no—
997C4—41no—
998C4—62no—
999C4—62no—
1000C4—102no—
1001C4—102no—
1002C4—121no—
1003C4—154no—
1004C4—201no—
1005C4—302no—
1006C4—302no—
1007C3#1060862011yescharacteristic, complemented, Sylow
1008C2—42no—
1009C2—122no—
1010C2—202no—
1011C2—602no—
1012C2#1175283411yescharacteristic
1013C2#1175307511yescharacteristic
1014C2#1175322111yescharacteristic
1015C2#1175324511yescharacteristic
1016C2#1175437111yescharacteristic
1017C2#1175482011yescharacteristic
1018C2#1175502011yescharacteristic
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×#6780C2semidirect
2. C2×#91770C2semidirect
3. C2×#91406C2semidirect
4. C2×#91396C2semidirect
5. C5×#4959C2semidirect
6. C3×#65248C2semidirect
7. #11749523C2semidirect
8. #11749522C2semidirect
9. #11749487C2semidirect
10. #11748925C2semidirect
11. #11748920C2semidirect
12. #11748886C2semidirect
13. #11748884C2semidirect
14. #11748579C2semidirect
15. #11748567C2semidirect
69. #65248D3semidirect
85. C22×Dic15D4semidirect
118. C2×D3×Dic5D4semidirect
122. C2×D5×Dic3D4semidirect
151. #4959D5semidirect
212. C22×D15#41semidirect
243. C2×Dic15#41semidirect
254. C2×C5×Dic3#41semidirect
264. C2×C3×Dic5#41semidirect
575. C2×Dic5#237semidirect
700. C2×Dic3#711semidirect
818. C3×C5#2388semidirect
960. C5#76889semidirect
1007. C3#10608620semidirect

Maximal subgroups

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

subgroupindex
C22×#67802
C2×#917702
C2×#914062
C2×#913962
C5×#49592
C3×#652482
#117495232
#117495222
#117494872
#117489252
#117489202
#117488862
#117488842
#117485792
#117485672
#106086203
#768895