Finite Group Databasebeta

← #14331654

Subgroups — #14331654

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×D60C211yesmaximal, characteristic, complemented
3C2×C4×#1203C211yesmaximal, characteristic, complemented
4C2×C4×#1202C211yesmaximal, characteristic, complemented
5C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×C4×#685C211yesmaximal, characteristic, complemented
7#11748938C211yesmaximal, characteristic, complemented
8#11748932C211yesmaximal, characteristic, complemented
9#11748931C211yesmaximal, characteristic, complemented
10#11748930C211yesmaximal, characteristic, complemented
11#11748925C211yesmaximal, characteristic, complemented
12#11748758C211yesmaximal, characteristic, complemented
13#11748755C211yesmaximal, characteristic, complemented
14C4×#6667C211yesmaximal, characteristic, complemented
15#11748579C211yesmaximal, characteristic, complemented
16#10605311—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1202C2211yescharacteristic
26C22×#1202C2211yescharacteristic
27C22×#1201C2211yescharacteristic
28C2×#6771—24no—
29C2×#6771—24no—
30C2×#6771—24no—
31C2×C3×C42×C5C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×C4⋊Dic15C2211yescharacteristic
35C4×D60—24no—
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C4×C5×Dic3C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C2×Dic3⋊Dic5C2211yescharacteristic
43C2×#6668C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×#6667C2211yescharacteristic
46C2×#6667C2211yescharacteristic
47C2×#6667C2211yescharacteristic
48C2×(C2×D3)⋊Dic5C2211yescharacteristic
49C2×#6665C2211yescharacteristic
50C4×#1203—24no—
51C4×#1202—24no—
52C5×C3⋊#95C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#3963C2211yescharacteristic
56#90994C2211yescharacteristic
57#90994C2211yescharacteristic
58#73580—51nomaximal, Hall
59C22×#709—31no—
60C2×C4×C22⋊D5—31no—
61C2×C4×D20—31no—
62C2×C4×D20—31no—
63C4×C5×C22⋊C4—31no—
64#65250—31no—
65#65250—31no—
66#65249—31no—
67#65249—31no—
68C4×#685—31no—
69C4×#685D311yescharacteristic, complemented
70#64962—31no—
71#64961—31no—
72#64960—31no—
73#64945—31no—
74C23×D15C2311yescharacteristic
75C23×D15C2311yescharacteristic
76C23×C5×D3C2311yescharacteristic
77C23×C3×D5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C2×D60—22no—
84C2×D60—22no—
85C2×D60—22no—
86C2×C4×D15—22no—
87C2×C4×D15—22no—
88C2×C4×D15—22no—
89C2×C4×D15—22no—
90C2×C4×D15—22no—
91C2×C4×D15D414yescomplemented
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C2×C4×C5×D3—22no—
96C2×C4×C5×D3—22no—
97C2×C4×C5×D3D414yescomplemented
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
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×#1203—22no—
111C2×#1203—22no—
112C2×#1203—22no—
113C2×#1202—22no—
114C2×#1202—22no—
115C2×#1202—22no—
116C2×#1202—22no—
117C2×#1202—22no—
118C2×#1202—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#6668—22no—
135#6667—22no—
136#6667—22no—
137#6667—22no—
138#6667—22no—
139(C2×D3)⋊Dic5—22no—
140#6665—22no—
141C22×#235—51no—
142C2×C4×#67—51no—
143C2×C4×D12—51no—
144C2×C4×D12—51no—
145C3×C4×C22⋊C4—51no—
146#4961—51no—
147#4961—51no—
148#4960—51no—
149#4960—51no—
150C4×(C2×D3)⋊C4—51no—
151C4×(C2×D3)⋊C4D511yescharacteristic, complemented
152#4673—51no—
153#4672—51no—
154#4671—51no—
155#4656—51no—
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×D20—31no—
166C22×C4×D5—31no—
167C22×C4×D5—31no—
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⋊Dic5—31no—
187C2×#683—31no—
188C2×C4×Dic5C2×D311yescharacteristic
189C4×D20—64no—
190C4×D20—64no—
191C5×#95—31no—
192C5×#95—31no—
193#3963—31no—
194#3963—31no—
195#3963C2×D311yescharacteristic
196#3963C2×D311yescharacteristic
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×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—21no—
209C22×D15—21no—
210C22×D15—21no—
211C22×D15C2×D412yes—
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×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×Dic15C2×D412yes—
242D60—28no—
243C4×D15—28no—
244C4×D15—44no—
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×Dic3—21no—
252C2×C5×Dic3C2×D412yes—
253C2×C5×Dic3#4112yescomplemented
254C4×C5×D3—28no—
255C2×C3×Dic5—21no—
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×Dic5C2×D412yes—
263C2×C3×Dic5#4112yescomplemented
264C3×C4×D5—28no—
265#1204—28no—
266#1203—28no—
267#1203—28no—
268#1202—28no—
269#1202—28no—
270#1201—28no—
271C23×C3×C4—51no—
272C22×#67—51no—
273C22×#67—51no—
274C22×#67—51no—
275C2×#235—104no—
276C2×#235—104no—
277C2×#235—104no—
278C22×D12—51no—
279C22×D12—51no—
280C22×D12—51no—
281C22×C4×D3—51no—
282C22×C4×D3—51no—
283C22×C4×D3C2×D511yescharacteristic
284C22×Dic6—51no—
285C2×C3×C22⋊C4—51no—
286C2×C3×C22⋊C4—51no—
287C2×C3×C42—51no—
288C2×C3×C42C2×D511yescharacteristic
289C2×#217—51no—
290C4×#67—104no—
291C2×(C2×D3)⋊C4—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)⋊C4—51no—
298C2×(C2×D3)⋊C4C2×D511yescharacteristic
299C2×(C2×D3)⋊C4C2×D511yescharacteristic
300C2×C4⋊Dic3—51no—
301C2×C4⋊Dic3—51no—
302C2×Dic3⋊C4—51no—
303C2×C4×Dic3C2×D511yescharacteristic
304C4×D12—104no—
305C4×D12—104no—
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×D5—31no—
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×Dic5C22×D311yescharacteristic
337C22×Dic5C22×D311yescharacteristic
338C22×Dic5C22×D311yescharacteristic
339#709—632no—
340C2×D20—62no—
341C2×D20—62no—
342C2×D20—62no—
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—34no—
352C2×C4×D5—62no—
353C2×C4×D5—62no—
354C2×C4×D5—62no—
355C2×C4×D5—62no—
356C2×C4×D5—62no—
357C2×C4×D5D1214yescomplemented
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—62no—
376C4⋊Dic5—62no—
377#683—62no—
378C4×Dic5—22no—
379C22×#41—151no—
380C2×C4×D4—151no—
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—51no—
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—22no—
405C2×D15—22no—
406C2×D15—22no—
407C2×D15—41no—
408C2×D15—41no—
409C2×D15—41no—
410C2×D15—41no—
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—22no—
430C3×C4×C5—41no—
431C3×C4×C5#12014yes—
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—
441C23×D3—51no—
442C23×D3—51no—
443C23×D3C22×D511yescharacteristic
444C22×C3×C4—51no—
445C22×C3×C4—51no—
446C22×C3×C4—54no—
447C22×C3×C4—51no—
448C22×C3×C4—102no—
449C22×C3×C4—102no—
450C22×C3×C4C22×D511yescharacteristic
451C22×C3×C4C22×D511yescharacteristic
452C22×C3×C4C22×D511yescharacteristic
453C2×#67—102no—
454C2×#67—102no—
455C2×#67—102no—
456C2×#67—102no—
457C2×#67—102no—
458C2×#67—102no—
459C2×#67—102no—
460C2×#67—102no—
461C2×#67—102no—
462C22×Dic3—51no—
463C22×Dic3—51no—
464C22×Dic3C22×D511yescharacteristic
465C22×Dic3C22×D511yescharacteristic
466C22×Dic3C22×D511yescharacteristic
467#235—1032no—
468C2×D12—102no—
469C2×D12—102no—
470C2×D12—102no—
471C2×D12—102no—
472C2×D12—102no—
473C2×D12—102no—
474C2×D12—102no—
475C2×D12—102no—
476C2×D12—102no—
477C2×C4×D3—22no—
478C2×C4×D3—22no—
479C2×C4×D3—54no—
480C2×C4×D3—102no—
481C2×C4×D3—102no—
482C2×C4×D3—102no—
483C2×C4×D3—102no—
484C2×C4×D3—102no—
485C2×C4×D3D2014yescomplemented
486C2×Dic6—102no—
487C2×Dic6—102no—
488C2×Dic6—102no—
489C3×C22⋊C4—102no—
490C3×C22⋊C4—102no—
491C3×C42—22no—
492C3×C42—102no—
493#217—102no—
494(C2×D3)⋊C4—22no—
495(C2×D3)⋊C4—22no—
496(C2×D3)⋊C4—102no—
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—
502(C2×D3)⋊C4—102no—
503C4⋊Dic3—102no—
504C4⋊Dic3—102no—
505Dic3⋊C4—102no—
506C4×Dic3—22no—
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—32no—
522C22×D5—32no—
523C22×D5—61no—
524C22×D5—61no—
525C22×D5—61no—
526C22×D5—61no—
527C22×D5—61no—
528C22×D5—61no—
529C22×D5—61no—
530C22×D5—61no—
531C22×D5—61no—
532C22×D5—61no—
533C22×D5—61no—
534C22×D5—61no—
535C22×D5C2×D1212yes—
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×C5C2×D1212yes—
552C2×C4×C5#23512yescomplemented
553C2×C4×C5D3×D412yes—
554C2×C4×C5D3×D412yes—
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—61no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5C2×D1212yes—
572C2×Dic5#23512yescomplemented
573D20—68no—
574D20—68no—
575D20—68no—
576C4×D5—28no—
577C4×D5—68no—
578C4×D5—124no—
579Dic10—68no—
580C2×#41—304no—
581C2×#41—304no—
582C2×#41—304no—
583C22×Q8—151no—
584C22×D4—151no—
585C22×D4—151no—
586C22×D4—151no—
587C22×D4—151no—
588C22×D4—151no—
589C22×D4—151no—
590C23×C4—31no—
591C23×C4—51no—
592C23×C4—151no—
593C23×C4—151no—
594C4×D4—304no—
595C4×D4—304no—
596C4×D4—304no—
597C2×C4⋊C4—151no—
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—51no—
614C2×C42D3×D511yescharacteristic
615#95—31no—
616#95—31no—
617#95—51no—
618#95—51no—
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—
629D15—42no—
630C3×D5—42no—
631C5×D3—42no—
632C23×C3—52no—
633C23×C3—101no—
634C23×C3—101no—
635C23×C3—101no—
636C23×C3—101no—
637C23×C3—101no—
638C23×C3—101no—
639C23×C3C23×D511yescharacteristic
640C22×D3—21no—
641C22×D3—21no—
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—21no—
645C22×D3—21no—
646C22×D3—52no—
647C22×D3—52no—
648C22×D3—101no—
649C22×D3—101no—
650C22×D3—101no—
651C22×D3—101no—
652C22×D3—101no—
653C22×D3—101no—
654C22×D3—101no—
655C22×D3—101no—
656C22×D3—101no—
657C22×D3—101no—
658C22×D3—101no—
659C22×D3—101no—
660C22×D3C2×D2012yes—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
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×C4C2×D2012yes—
677C2×C3×C4#70912yescomplemented
678C2×C3×C4D4×D512yes—
679C2×C3×C4D4×D512yes—
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—101no—
692C2×Dic3—101no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3C2×D2012yes—
697C2×Dic3#70912yescomplemented
698D12—108no—
699D12—108no—
700D12—108no—
701C4×D3—28no—
702C4×D3—108no—
703C4×D3—204no—
704Dic6—108no—
705C22×C5—62no—
706C22×C5—62no—
707C22×C5—62no—
708C22×C5—121no—
709C22×C5—121no—
710C22×C5—121no—
711C22×C5—121no—
712C22×C5C22×D1211yescharacteristic
713C22×C5C2×#23511yescharacteristic
714C22×C5C2×#23511yescharacteristic
715C22×C5C2×D3×D411yescharacteristic
716C22×C5C2×D3×D411yescharacteristic
717C22×C5D3×#4111yescharacteristic
718C22×C5D3×#4111yescharacteristic
719C2×D5—22no—
720C2×D5—22no—
721C2×D5—22no—
722C2×D5—41no—
723C2×D5—41no—
724C2×D5—41no—
725C2×D5—41no—
726C2×D5—62no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—121no—
733C2×D5—121no—
734C2×D5—121no—
735C2×D5—121no—
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#88214yes—
746Dic5—22no—
747Dic5—22no—
748Dic5—41no—
749Dic5—62no—
750Dic5—121no—
751C24—31no—
752C24—51no—
753C24—151no—
754C24—151no—
755#41—3032no—
756C2×Q8—302no—
757C2×Q8—302no—
758C2×Q8—302no—
759C2×D4—302no—
760C2×D4—302no—
761C2×D4—302no—
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—51no—
783C22×C4—54no—
784C22×C4—51no—
785C22×C4—62no—
786C22×C4—62no—
787C22×C4—102no—
788C22×C4—102no—
789C22×C4—151no—
790C22×C4—154no—
791C22×C4—151no—
792C22×C4—302no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—302no—
796C22×C4—302no—
797C22×C4C2×D3×D511yescharacteristic
798C22×C4C2×D3×D511yescharacteristic
799C22×C4C2×D3×D511yescharacteristic
800C4⋊C4—302no—
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—102no—
818C3×C5#238811yescharacteristic, complemented, Hall
819C22×C3—102no—
820C22×C3—102no—
821C22×C3—102no—
822C22×C3—201no—
823C22×C3—201no—
824C22×C3—201no—
825C22×C3—201no—
826C22×C3C22×D2011yescharacteristic
827C22×C3C2×#70911yescharacteristic
828C22×C3C2×#70911yescharacteristic
829C22×C3C2×D4×D511yescharacteristic
830C22×C3C2×D4×D511yescharacteristic
831C22×C3D5×#4111yescharacteristic
832C22×C3D5×#4111yescharacteristic
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—102no—
841C2×D3—102no—
842C2×D3—102no—
843C2×D3—102no—
844C2×D3—102no—
845C2×D3—102no—
846C2×D3—201no—
847C2×D3—201no—
848C2×D3—201no—
849C2×D3—201no—
850C2×D3—201no—
851C2×D3—201no—
852C2×D3—201no—
853C2×D3—201no—
854C3×C4—22no—
855C3×C4—41no—
856C3×C4—102no—
857C3×C4—102no—
858C3×C4—201no—
859C3×C4#402814yes—
860Dic3—22no—
861Dic3—22no—
862Dic3—41no—
863Dic3—102no—
864Dic3—201no—
865C2×C5—122no—
866C2×C5#547711yescharacteristic
867C2×C5C2×#88211yescharacteristic
868C2×C5#552411yescharacteristic
869C2×C5#554711yescharacteristic
870C2×C5#554711yescharacteristic
871C2×C5#554811yescharacteristic
872C2×C5#554811yescharacteristic
873D5—42no—
874D5—122no—
875D5—122no—
876C23—32no—
877C23—52no—
878C23—61no—
879C23—61no—
880C23—61no—
881C23—61no—
882C23—61no—
883C23—61no—
884C23—101no—
885C23—101no—
886C23—101no—
887C23—101no—
888C23—101no—
889C23—101no—
890C23—152no—
891C23—152no—
892C23—301no—
893C23—301no—
894C23—301no—
895C23—301no—
896C23—301no—
897C23—301no—
898C23—301no—
899C23—301no—
900C23—301no—
901C23—301no—
902C23—301no—
903C23—301no—
904C23C22×D3×D511yescharacteristic
905Q8—308no—
906D4—308no—
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—52no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—68no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—101no—
930C2×C4—101no—
931C2×C4—101no—
932C2×C4—101no—
933C2×C4—108no—
934C2×C4—101no—
935C2×C4—101no—
936C2×C4—101no—
937C2×C4—152no—
938C2×C4—301no—
939C2×C4—301no—
940C2×C4—308no—
941C2×C4—301no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—604no—
945C2×C4#677112yescomplemented
946C2×C4D5×D1212yes—
947C2×C4D3×D2012yes—
948C2×C4#679012yes—
949C2×C3—202no—
950C2×C3#6581111yescharacteristic
951C2×C3C2×#402811yescharacteristic
952C2×C3#6585811yescharacteristic
953C2×C3#6588111yescharacteristic
954C2×C3#6588111yescharacteristic
955C2×C3#6588211yescharacteristic
956C2×C3#6588211yescharacteristic
957D3—42no—
958D3—202no—
959D3—202no—
960C5#7358011yescharacteristic, complemented, Sylow
961C22—62no—
962C22—62no—
963C22—62no—
964C22—102no—
965C22—102no—
966C22—102no—
967C22—121no—
968C22—121no—
969C22—121no—
970C22—121no—
971C22—201no—
972C22—201no—
973C22—201no—
974C22—201no—
975C22—302no—
976C22—302no—
977C22—302no—
978C22—302no—
979C22—302no—
980C22—302no—
981C22—601no—
982C22—601no—
983C22—601no—
984C22—601no—
985C22—601no—
986C22—601no—
987C22—601no—
988C22—601no—
989C22C2×#677111yescharacteristic
990C22C2×D5×D1211yescharacteristic
991C22C2×D3×D2011yescharacteristic
992C22D5×#23511yescharacteristic
993C22D3×#70911yescharacteristic
994C22#9201611yescharacteristic
995C22C2×#679011yescharacteristic
996C4—22no—
997C4—41no—
998C4—62no—
999C4—62no—
1000C4—102no—
1001C4—102no—
1002C4—121no—
1003C4—201no—
1004C4—302no—
1005C4—601no—
1006C4#9147614yes—
1007C3#1060531111yescharacteristic, complemented, Sylow
1008C2—122no—
1009C2—202no—
1010C2—602no—
1011C2—602no—
1012C2#1175267111yescharacteristic
1013C2#1175267511yescharacteristic
1014C2#1175273011yescharacteristic
1015C2#1175273911yescharacteristic
1016C2#1175455411yescharacteristic
1017C2#1175455511yescharacteristic
1018C2C2×#9147611yescharacteristic
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×C4×D60C2semidirect
3. C2×C4×#1203C2semidirect
4. C2×C4×#1202C2semidirect
5. C4×C5×(C2×D3)⋊C4C2semidirect
6. C3×C4×#685C2semidirect
7. #11748938C2semidirect
8. #11748932C2semidirect
9. #11748931C2semidirect
10. #11748930C2semidirect
11. #11748925C2semidirect
12. #11748758C2semidirect
13. #11748755C2semidirect
14. C4×#6667C2semidirect
15. #11748579C2semidirect
69. C4×#685D3semidirect
91. C2×C4×D15D4semidirect
97. C2×C4×C5×D3D4semidirect
103. C2×C3×C4×D5D4semidirect
151. C4×(C2×D3)⋊C4D5semidirect
212. C22×D15#41semidirect
235. C2×C3×C4×C5#41semidirect
253. C2×C5×Dic3#41semidirect
263. C2×C3×Dic5#41semidirect
357. C2×C4×D5D12semidirect
485. C2×C4×D3D20semidirect
552. C2×C4×C5#235semidirect
572. C2×Dic5#235semidirect
677. C2×C3×C4#709semidirect
697. C2×Dic3#709semidirect
818. C3×C5#2388semidirect
945. C2×C4#6771semidirect
960. C5#73580semidirect
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×C4×D602
C2×C4×#12032
C2×C4×#12022
C4×C5×(C2×D3)⋊C42
C3×C4×#6852
#117489382
#117489322
#117489312
#117489302
#117489252
#117487582
#117487552
C4×#66672
#117485792
#106053113
#735805