Finite Group Databasebeta

← #14331674

Subgroups — #14331674

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×#6782C211yesmaximal, characteristic, complemented
2C2×C3×#4027C211yesmaximal, characteristic, complemented
3C2×#91444C211yesmaximal, characteristic, complemented
4C2×#91440C211yesmaximal, characteristic, complemented
5#11751060C211yesmaximal, characteristic, complemented
6C5×#4959C211yesmaximal, characteristic, complemented
7#11749522C211yesmaximal, characteristic, complemented
8#11749521C211yesmaximal, characteristic, complemented
9Dic5×#217C211yesmaximal, characteristic, complemented
10#11748925C211yesmaximal, characteristic, complemented
11#11748875C211yesmaximal, characteristic, complemented
12Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#11748736C211yesmaximal, characteristic, complemented
14#11748733C211yesmaximal, characteristic, complemented
15#11748567C211yesmaximal, characteristic, complemented
16#10608620—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1202C2211yescharacteristic
25C22×#1201C2211yescharacteristic
26C22×#1200C2211yescharacteristic
27C2×#6782—24no—
28C2×#6782—24no—
29C2×#6782—24no—
30C22×D3×Dic5C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×#6712C2211yescharacteristic
36C2×C5×#217C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C5×(C2×D3)⋊C4C2211yescharacteristic
39C2×C5×Dic3⋊C4C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C3×#4027—24no—
44C2×#6667C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47C2×#6665C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50#91444—24no—
51#91440—24no—
52#91115C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#90994C2211yescharacteristic
58#82400—51nomaximal, Hall
59C22×#711—31no—
60C2×#4039—31no—
61C2×#4027—31no—
62C2×#4027D311yescharacteristic, complemented
63C5×#394—31no—
64#65512—31no—
65#65268—31no—
66#65249—31no—
67#65249—31no—
68#65248—31no—
69#65248—31no—
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×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C2×C5×#67—22no—
87C2×C5×#67—22no—
88C2×C5×#67—22no—
89C22×C5×Dic3C2311yescharacteristic
90C22×C5×Dic3C2311yescharacteristic
91C22×C5×Dic3C2311yescharacteristic
92C2×C3×C22⋊D5—22no—
93C2×C3×C22⋊D5—22no—
94C2×C3×C22⋊D5—22no—
95C22×C3×Dic5—22no—
96C22×C3×Dic5—22no—
97C22×C3×Dic5D414yescomplemented
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C2×C3×C4×D5—22no—
102C2×C3×C4×D5—22no—
103C2×C3×C4×D5—22no—
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#6782—232no—
120C2×D3×Dic5—22no—
121C2×D3×Dic5—22no—
122C2×D3×Dic5D414yescomplemented
123C3×C5×C22⋊C4—22no—
124#6719—22no—
125#6714—22no—
126#6714—22no—
127#6712—22no—
128C5×#217—22no—
129C5×(C2×D3)⋊C4—22no—
130C5×(C2×D3)⋊C4—22no—
131C5×Dic3⋊C4—22no—
132C3×#685—22no—
133C3×#683—22no—
134C3×C4×Dic5—22no—
135#6667—22no—
136(C2×D3)⋊Dic5—22no—
137#6665—22no—
138#6665—22no—
139Dic3×Dic5—22no—
140Dic3×Dic5—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#4959D511yescharacteristic, complemented
153#4947—51no—
154C4×(C2×D3)⋊C4—51no—
155C4×(C2×D3)⋊C4—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×Dic5C2×D311yescharacteristic
163C2×#711—64no—
164C2×#711—64no—
165C2×#711—64no—
166C22×D20—31no—
167C22×C4×D5—31no—
168C22×C4×D5C2×D311yescharacteristic
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⋊Dic5—31no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#685—31no—
182C2×#685C2×D311yescharacteristic
183C2×#683—31no—
184C2×#683C2×D311yescharacteristic
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187C2×C4×Dic5C2×D311yescharacteristic
188#4039—64no—
189#4027—24no—
190#4027—64no—
191C5×#95—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×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×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×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—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—21no—
249C2×C5×Dic3—21no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3C2×D412yes—
252C2×C5×Dic3#4112yescomplemented
253C3×C22⋊D5—28no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5—21no—
256C2×C3×Dic5—21no—
257C2×C3×Dic5—21no—
258C2×C3×Dic5—28no—
259C2×C3×Dic5C2×D412yes—
260C2×C3×Dic5C2×D412yes—
261C2×C3×Dic5C2×D412yes—
262C2×C3×Dic5C2×D412yes—
263C2×C3×Dic5#4112yescomplemented
264C3×C4×D5—44no—
265#1204—28no—
266#1203—28no—
267#1202—28no—
268#1201—28no—
269#1200—28no—
270D3×Dic5—28no—
271C22×C3×D4—51no—
272C23×C3×C4—51no—
273C23×C3×C4—51no—
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×D3—51no—
284C22×Dic6—51no—
285C3×C4×D4—104no—
286C2×C3×C4⋊C4—51no—
287C2×C3×C22⋊C4—51no—
288C2×C3×C22⋊C4C2×D511yescharacteristic
289C2×C3×C42—51no—
290C2×#217—51no—
291C2×#217—51no—
292C2×#217—51no—
293C2×#217C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
304C2×C4×Dic3—51no—
305C2×C4×Dic3—51no—
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—22no—
337C22×Dic5—22no—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—34no—
341C22×Dic5—31no—
342C22×Dic5—62no—
343C22×Dic5—62no—
344C22×Dic5#6714yescomplemented
345C22×Dic5C22×D311yescharacteristic
346C22×Dic5C22×D311yescharacteristic
347C22×Dic5C22×D311yescharacteristic
348#711—632no—
349C2×D20—62no—
350C2×D20—62no—
351C2×D20—62no—
352C2×C4×D5—22no—
353C2×C4×D5—22no—
354C2×C4×D5—22no—
355C2×C4×D5—34no—
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—62no—
367C22⋊Dic5—62no—
368#685—22no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—62no—
374#683—22no—
375#683—62no—
376C4×Dic5—22no—
377C4×Dic5—62no—
378C4×Dic5—62no—
379C22×#41—151no—
380C2×C4×D4—51no—
381C2×C4×D4—151no—
382C2×C4×D4—151no—
383#395—151no—
384#394—31no—
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#12014yes—
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—54no—
449C22×C3×C4—51no—
450C22×C3×C4—51no—
451C22×C3×C4—102no—
452C22×C3×C4—102no—
453C22×C3×C4—102no—
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—54no—
481C2×C4×D3—54no—
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×C42—102no—
493#217—22no—
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—22no—
504Dic3⋊C4—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×C5C2×#6712yes—
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×D5#23512yescomplemented
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—28no—
561C2×Dic5—32no—
562C2×Dic5—32no—
563C2×Dic5—61no—
564C2×Dic5—61no—
565C2×Dic5—61no—
566C2×Dic5—61no—
567C2×Dic5—68no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5#23512yescomplemented
572C2×Dic5D3×D412yes—
573C2×Dic5D3×D412yes—
574C2×Dic5C2×#6712yes—
575C2×Dic5C2×#6712yes—
576D20—68no—
577C4×D5—44no—
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—51no—
591C23×C4—51no—
592C23×C4—151no—
593C23×C4—151no—
594C4×D4—104no—
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—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—51no—
613C2×C42—151no—
614C2×C42—151no—
615#95—31no—
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×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—52no—
671C2×C3×C4—52no—
672C2×C3×C4—52no—
673C2×C3×C4—108no—
674C2×C3×C4—101no—
675C2×C3×C4—101no—
676C2×C3×C4—101no—
677C2×C3×C4—101no—
678C2×C3×C4—204no—
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×Dic3D4×D512yes—
700C2×Dic3#71112yescomplemented
701D12—108no—
702C4×D3—108no—
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—41no—
742C4×C5—62no—
743C4×C5—62no—
744C4×C5—121no—
745Dic5—22no—
746Dic5—22no—
747Dic5—62no—
748Dic5—62no—
749Dic5—121no—
750Dic5#93714yes—
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—54no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—102no—
785C22×C4—102no—
786C22×C4—102no—
787C22×C4—102no—
788C22×C4—102no—
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—62no—
806C22⋊C4—62no—
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—102no—
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—54no—
857C3×C4—102no—
858C3×C4—102no—
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—
903C23D5×#6712yes—
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—52no—
923C2×C4—52no—
924C2×C4—52no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—108no—
933C2×C4—101no—
934C2×C4—101no—
935C2×C4—101no—
936C2×C4—101no—
937C2×C4—152no—
938C2×C4—152no—
939C2×C4—204no—
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×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#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—
989C22D5×#23511yescharacteristic
990C22D5×#23511yescharacteristic
991C22D3×D4×D511yescharacteristic
992C22D3×D4×D511yescharacteristic
993C22D3×#71111yescharacteristic
994C22#9202411yescharacteristic
995C22C2×D5×#6711yescharacteristic
996C4—41no—
997C4—41no—
998C4—54no—
999C4—62no—
1000C4—62no—
1001C4—102no—
1002C4—102no—
1003C4—121no—
1004C4—302no—
1005C4—302no—
1006C4—601no—
1007C3#1060862011yescharacteristic, complemented, Sylow
1008C2—42no—
1009C2—122no—
1010C2—202no—
1011C2—602no—
1012C2#1175284311yescharacteristic
1013C2#1175285111yescharacteristic
1014C2#1175324411yescharacteristic
1015C2#1175324911yescharacteristic
1016C2#1175431611yescharacteristic
1017C2#1175479611yescharacteristic
1018C2D5×#93711yescharacteristic
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×#6782C2semidirect
2. C2×C3×#4027C2semidirect
3. C2×#91444C2semidirect
4. C2×#91440C2semidirect
5. #11751060C2semidirect
6. C5×#4959C2semidirect
7. #11749522C2semidirect
8. #11749521C2semidirect
9. Dic5×#217C2semidirect
10. #11748925C2semidirect
11. #11748875C2semidirect
12. Dic5×(C2×D3)⋊C4C2semidirect
13. #11748736C2semidirect
14. #11748733C2semidirect
15. #11748567C2semidirect
62. C2×#4027D3semidirect
97. C22×C3×Dic5D4semidirect
118. C2×#1200D4semidirect
122. C2×D3×Dic5D4semidirect
152. #4959D5semidirect
226. C22×C3×D5#41semidirect
242. C2×Dic15#41semidirect
252. C2×C5×Dic3#41semidirect
263. C2×C3×Dic5#41semidirect
344. C22×Dic5#67semidirect
535. C22×D5#235semidirect
571. C2×Dic5#235semidirect
700. C2×Dic3#711semidirect
818. C3×C5#2388semidirect
960. C5#82400semidirect
1007. C3#10608620semidirect

Maximal subgroups

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

subgroupindex
C22×#67822
C2×C3×#40272
C2×#914442
C2×#914402
#117510602
C5×#49592
#117495222
#117495212
Dic5×#2172
#117489252
#117488752
Dic5×(C2×D3)⋊C42
#117487362
#117487332
#117485672
#106086203
#824005