Finite Group Databasebeta

← #14331631

Subgroups — #14331631

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×Dic5×#67C211yesmaximal, characteristic, complemented
3C2×Dic5×D12C211yesmaximal, characteristic, complemented
4C2×#91405C211yesmaximal, characteristic, complemented
5#11751062C211yesmaximal, characteristic, complemented
6C5×#4960C211yesmaximal, characteristic, complemented
7C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
8#11749523C211yesmaximal, characteristic, complemented
9#11749493C211yesmaximal, characteristic, complemented
10#11748938C211yesmaximal, characteristic, complemented
11#11748929C211yesmaximal, characteristic, complemented
12#11748875C211yesmaximal, characteristic, complemented
13Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14#11748758C211yesmaximal, characteristic, complemented
15#11748757C211yesmaximal, characteristic, complemented
16#10608396—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C2×#6782—24no—
27C2×#6782—24no—
28C2×#6782—24no—
29C22×D3×Dic5C2211yescharacteristic
30C22×D3×Dic5C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×#6719C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×#6714C2211yescharacteristic
35C2×C4⋊Dic15C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C22⋊Dic5C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40C2×C3×C4×Dic5C2211yescharacteristic
41Dic5×#67—24no—
42C2×Dic3⋊Dic5C2211yescharacteristic
43C2×#6668C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×(C2×D3)⋊Dic5C2211yescharacteristic
47C2×(C2×D3)⋊Dic5C2211yescharacteristic
48C2×(C2×D3)⋊Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50Dic5×D12—24no—
51#91405—24no—
52#91115C2211yescharacteristic
53C5×C3⋊#95C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#3963C2211yescharacteristic
56#90994C2211yescharacteristic
57#90994C2211yescharacteristic
58#73580—51nomaximal, Hall
59C22×#711—31no—
60C2×D4×Dic5—31no—
61C2×D4×Dic5—31no—
62C2×#4027—31no—
63C5×#392—31no—
64#65512—31no—
65#65512—31no—
66#65511—31no—
67#65250—31no—
68#65250—31no—
69#65236—31no—
70C22⋊C4×Dic5—31no—
71C22⋊C4×Dic5D311yescharacteristic, complemented
72#64955—31no—
73#64945—31no—
74C24×C3×C5C2311yescharacteristic
75C23×D15C2311yescharacteristic
76C23×C5×D3C2311yescharacteristic
77C23×C5×D3C2311yescharacteristic
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—
89C2×C5×#67—22no—
90C2×C5×#67—22no—
91C2×C5×#67—22no—
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C2×C5×D12—22no—
95C2×C5×D12—22no—
96C2×C5×D12—22no—
97C22×C3×Dic5—22no—
98C22×C3×Dic5—22no—
99C22×C3×Dic5D414yescomplemented
100C22×C3×Dic5C2311yescharacteristic
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×#1203—22no—
111C2×#1203—22no—
112C2×#1203—22no—
113C2×#1200—22no—
114C2×#1200—22no—
115C2×#1200D414yescomplemented
116#6782—232no—
117C2×D3×Dic5—22no—
118C2×D3×Dic5—22no—
119C2×D3×Dic5—22no—
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—
127C4⋊Dic15—22no—
128C5×(C2×D3)⋊C4—22no—
129C5×(C2×D3)⋊C4—22no—
130C3×C22⋊Dic5—22no—
131C3×C4×Dic5—22no—
132C3×C4×Dic5—22no—
133Dic3⋊Dic5—22no—
134#6668—22no—
135#6667—22no—
136(C2×D3)⋊Dic5—22no—
137(C2×D3)⋊Dic5—22no—
138(C2×D3)⋊Dic5—22no—
139(C2×D3)⋊Dic5—22no—
140Dic3×Dic5—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#4960D511yescharacteristic, complemented
150C4×(C2×D3)⋊C4—51no—
151C4×(C2×D3)⋊C4—51no—
152#4673—51no—
153#4672—51no—
154#4671—51no—
155#4656—51no—
156C22×C5×D4—31no—
157C22×C5×D4—31no—
158C22×C5×D4—31no—
159C22×C22⋊D5—31no—
160C22×C22⋊D5—31no—
161C22×C22⋊D5—31no—
162C23×Dic5—31no—
163C23×Dic5—31no—
164C23×Dic5C2×D311yescharacteristic
165C2×#711—64no—
166C2×#711—64no—
167C2×#711—64no—
168C22×C4×D5—31no—
169C22×Dic10—31no—
170C2×C5×C22⋊C4—31no—
171C2×C5×C22⋊C4—31no—
172C2×C5×C22⋊C4C2×D311yescharacteristic
173C2×C22⋊Dic5—31no—
174C2×C22⋊Dic5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5C2×D311yescharacteristic
179D4×Dic5—64no—
180D4×Dic5—64no—
181C2×#685—31no—
182C2×#685—31no—
183C2×#685—31no—
184C2×C4⋊Dic5—31no—
185C2×C4⋊Dic5—31no—
186C2×#683—31no—
187C2×C4×Dic5—31no—
188C2×C4×Dic5C2×D311yescharacteristic
189C2×C4×Dic5C2×D311yescharacteristic
190#4027—64no—
191C5×#95—31no—
192#3963—31no—
193#3963—31no—
194#3963—31no—
195#3963C2×D311yescharacteristic
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—21no—
220C22×C5×D3—21no—
221C22×C5×D3—21no—
222C22×C5×D3—21no—
223C22×C5×D3—21no—
224C22×C5×D3—21no—
225C22×C5×D3C2×D412yes—
226C22×C5×D3#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#4112yescomplemented
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×Dic15—21no—
242C2×Dic15C2×D412yes—
243C5×#67—28no—
244C5×#67—28no—
245C2×C5×Dic3—21no—
246C2×C5×Dic3—21no—
247C2×C5×Dic3—21no—
248C2×C5×Dic3—21no—
249C2×C5×Dic3C2×D412yes—
250C2×C5×Dic3#4112yescomplemented
251C5×D12—28no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5—21no—
256C2×C3×Dic5—28no—
257C2×C3×Dic5—21no—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5C2×D412yes—
261C2×C3×Dic5C2×D412yes—
262C2×C3×Dic5C2×D412yes—
263C2×C3×Dic5C2×D412yes—
264C2×C3×Dic5#4112yescomplemented
265#1204—28no—
266#1203—28no—
267#1203—28no—
268#1200—28no—
269D3×Dic5—28no—
270D3×Dic5—44no—
271C23×C3×C4—51no—
272C22×#67—51no—
273C22×#67C2×D511yescharacteristic
274C22×#67C2×D511yescharacteristic
275C2×#235—104no—
276C2×#235—104no—
277C2×#235—104no—
278C22×D12—51no—
279C22×D12—51no—
280C22×D12C2×D511yescharacteristic
281C22×C4×D3—51no—
282C22×C4×D3—51no—
283C22×C4×D3—51no—
284C22×Dic6—51no—
285C2×C3×C22⋊C4—51no—
286C2×C3×C22⋊C4C2×D511yescharacteristic
287C2×C3×C42—51no—
288C2×C3×C42—51no—
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×Dic3—51no—
304C4×D12—104no—
305C4×D12—104no—
306C3×#95—51no—
307C3×#95—51no—
308C3⋊#95—51no—
309C3⋊#95—51no—
310C3⋊#95—51no—
311C3⋊#95C2×D511yescharacteristic
312C24×C5—31no—
313C24×C5—31no—
314C24×C5C22×D311yescharacteristic
315C23×D5—31no—
316C2×C5×D4—62no—
317C2×C5×D4—62no—
318C2×C5×D4—62no—
319C2×C5×D4—62no—
320C2×C5×D4—62no—
321C2×C5×D4—62no—
322C2×C5×D4—62no—
323C2×C5×D4—62no—
324C2×C5×D4—62no—
325C22×C4×C5—31no—
326C22×C4×C5—31no—
327C22×C4×C5C22×D311yescharacteristic
328C22×C4×C5C22×D311yescharacteristic
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—
336C2×C22⋊D5—62no—
337C2×C22⋊D5—62no—
338C22×Dic5—22no—
339C22×Dic5—22no—
340C22×Dic5—31no—
341C22×Dic5—34no—
342C22×Dic5—31no—
343C22×Dic5—31no—
344C22×Dic5—62no—
345C22×Dic5—62no—
346C22×Dic5—62no—
347C22×Dic5—62no—
348C22×Dic5—62no—
349C22×Dic5D1214yescomplemented
350C22×Dic5C22×D311yescharacteristic
351C22×Dic5C22×D311yescharacteristic
352C22×Dic5C22×D311yescharacteristic
353C22×Dic5C22×D311yescharacteristic
354#711—632no—
355C2×C4×D5—34no—
356C2×C4×D5—62no—
357C2×C4×D5—62no—
358C2×Dic10—62no—
359C2×Dic10—62no—
360C2×Dic10—62no—
361C5×C22⋊C4—22no—
362C5×C22⋊C4—62no—
363C5×C22⋊C4—62no—
364C22⋊Dic5—22no—
365C22⋊Dic5—62no—
366C22⋊Dic5—62no—
367C22⋊Dic5—62no—
368C22⋊Dic5—62no—
369C22⋊Dic5—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373C4⋊Dic5—62no—
374C4⋊Dic5—62no—
375#683—62no—
376C4×Dic5—22no—
377C4×Dic5—22no—
378C4×Dic5—62no—
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—31no—
389#392—151no—
390#392—151no—
391C4×C22⋊C4—51no—
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—22no—
419C2×C5×D3—22no—
420C2×C5×D3—22no—
421C2×C5×D3—41no—
422C2×C5×D3—41no—
423C2×C5×D3—41no—
424C2×C5×D3—41no—
425C2×C5×D3—41no—
426C2×C5×D3—41no—
427C2×C5×D3—41no—
428C2×C5×D3—41no—
429C3×C4×C5—22no—
430C3×C4×C5—41no—
431Dic15—22no—
432Dic15—41no—
433Dic15—41no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—41no—
437C3×Dic5#12014yes—
438C5×Dic3—22no—
439C5×Dic3—22no—
440C24×C3C22×D511yescharacteristic
441C23×D3—51no—
442C23×D3C22×D511yescharacteristic
443C23×D3C22×D511yescharacteristic
444C22×C3×C4—51no—
445C22×C3×C4—54no—
446C22×C3×C4—51no—
447C22×C3×C4—51no—
448C22×C3×C4—51no—
449C22×C3×C4—102no—
450C22×C3×C4—102no—
451C22×C3×C4C22×D511yescharacteristic
452C22×C3×C4C22×D511yescharacteristic
453C2×#67—22no—
454C2×#67—22no—
455C2×#67—22no—
456C2×#67—22no—
457C2×#67—22no—
458C2×#67—22no—
459C2×#67—102no—
460C2×#67—102no—
461C2×#67—102no—
462C22×Dic3—51no—
463C22×Dic3—51no—
464C22×Dic3—51no—
465C22×Dic3C22×D511yescharacteristic
466C22×Dic3C22×D511yescharacteristic
467#235—1032no—
468C2×D12—22no—
469C2×D12—22no—
470C2×D12—22no—
471C2×D12—102no—
472C2×D12—102no—
473C2×D12—102no—
474C2×D12—102no—
475C2×D12—102no—
476C2×D12—102no—
477C2×C4×D3—54no—
478C2×C4×D3—54no—
479C2×C4×D3—102no—
480C2×C4×D3—102no—
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×C22⋊C4—22no—
490C3×C22⋊C4—102no—
491C3×C42—102no—
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—102no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5—21no—
512C23×C5—21no—
513C23×C5—32no—
514C23×C5—32no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5—61no—
520C23×C5—61no—
521C23×C5—61no—
522C23×C5—61no—
523C23×C5—61no—
524C23×C5—61no—
525C23×C5—61no—
526C23×C5—61no—
527C23×C5C2×D1212yes—
528C23×C5C23×D311yescharacteristic
529C22×D5—32no—
530C22×D5—61no—
531C22×D5—61no—
532C22×D5—61no—
533C22×D5—61no—
534C22×D5—61no—
535C22×D5—61no—
536C5×D4—68no—
537C5×D4—68no—
538C5×D4—68no—
539C2×C4×C5—21no—
540C2×C4×C5—21no—
541C2×C4×C5—21no—
542C2×C4×C5—21no—
543C2×C4×C5—21no—
544C2×C4×C5—32no—
545C2×C4×C5—32no—
546C2×C4×C5—61no—
547C2×C4×C5—61no—
548C2×C4×C5—61no—
549C2×C4×C5—61no—
550C2×C4×C5#23512yescomplemented
551C22⋊D5—68no—
552C22⋊D5—68no—
553C22⋊D5—68no—
554C2×Dic5—21no—
555C2×Dic5—21no—
556C2×Dic5—21no—
557C2×Dic5—21no—
558C2×Dic5—28no—
559C2×Dic5—21no—
560C2×Dic5—21no—
561C2×Dic5—21no—
562C2×Dic5—32no—
563C2×Dic5—61no—
564C2×Dic5—61no—
565C2×Dic5—68no—
566C2×Dic5—61no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—61no—
571C2×Dic5—61no—
572C2×Dic5—124no—
573C2×Dic5C2×D1212yes—
574C2×Dic5C2×D1212yes—
575C2×Dic5#23512yescomplemented
576C2×Dic5D3×D412yes—
577C2×Dic5D3×D412yes—
578C4×D5—68no—
579Dic10—68no—
580C2×#41—304no—
581C2×#41—304no—
582C2×#41—304no—
583C22×Q8—151no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—151no—
588C22×D4—151no—
589C22×D4—151no—
590C23×C4—51no—
591C23×C4—151no—
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—151no—
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—51no—
614C2×C42—151no—
615#95—31no—
616#95—51no—
617#95—51no—
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—
630C5×D3—42no—
631C5×D3—42no—
632C23×C3—21no—
633C23×C3—21no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3D4×D512yes—
639C23×C3C23×D511yescharacteristic
640C22×D3—21no—
641C22×D3—21no—
642C22×D3—21no—
643C22×D3—21no—
644C22×D3—21no—
645C22×D3—21no—
646C22×D3—21no—
647C22×D3—21no—
648C22×D3—21no—
649C22×D3—21no—
650C22×D3—21no—
651C22×D3—21no—
652C22×D3—52no—
653C22×D3—101no—
654C22×D3—101no—
655C22×D3—101no—
656C22×D3—101no—
657C22×D3—101no—
658C22×D3—101no—
659C22×D3D4×D512yes—
660C22×D3#71112yescomplemented
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—52no—
669C2×C3×C4—52no—
670C2×C3×C4—52no—
671C2×C3×C4—108no—
672C2×C3×C4—101no—
673C2×C3×C4—101no—
674C2×C3×C4—101no—
675C2×C3×C4—101no—
676C2×C3×C4—101no—
677C2×C3×C4—101no—
678C2×C3×C4—101no—
679C2×C3×C4#71112yescomplemented
680#67—28no—
681#67—28no—
682#67—108no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—52no—
688C2×Dic3—101no—
689C2×Dic3—101no—
690C2×Dic3—101no—
691C2×Dic3—101no—
692C2×Dic3—101no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3D4×D512yes—
697C2×Dic3#71112yescomplemented
698D12—28no—
699D12—108no—
700D12—108no—
701C4×D3—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—62no—
716C22×C5—62no—
717C22×C5—62no—
718C22×C5—121no—
719C22×C5—121no—
720C22×C5—121no—
721C22×C5—121no—
722C22×C5—121no—
723C22×C5—121no—
724C22×C5—121no—
725C22×C5—121no—
726C22×C5C22×D1211yescharacteristic
727C22×C5C2×#23511yescharacteristic
728C22×C5C2×#23511yescharacteristic
729C22×C5C2×D3×D411yescharacteristic
730C22×C5C2×D3×D411yescharacteristic
731C22×C5D3×#4111yescharacteristic
732C22×C5D3×#4111yescharacteristic
733C2×D5—62no—
734C2×D5—62no—
735C2×D5—62no—
736C2×D5—121no—
737C2×D5—121no—
738C2×D5—121no—
739C2×D5—121no—
740C4×C5—22no—
741C4×C5—41no—
742C4×C5—62no—
743C4×C5—62no—
744Dic5—22no—
745Dic5—22no—
746Dic5—41no—
747Dic5—62no—
748Dic5—121no—
749Dic5—121no—
750Dic5#88214yes—
751C24—31no—
752C24—31no—
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—62no—
763C2×D4—62no—
764C2×D4—62no—
765C2×D4—62no—
766C2×D4—62no—
767C2×D4—62no—
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—51no—
780C22×C4—54no—
781C22×C4—51no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—102no—
785C22×C4—102no—
786C22×C4—154no—
787C22×C4—154no—
788C22×C4—151no—
789C22×C4—151no—
790C22×C4—151no—
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—302no—
801C4⋊C4—302no—
802C4⋊C4—302no—
803C22⋊C4—22no—
804C22⋊C4—62no—
805C22⋊C4—62no—
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—102no—
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×C3C2×D4×D511yescharacteristic
827C22×C3C2×D4×D511yescharacteristic
828C22×C3C2×D4×D511yescharacteristic
829C22×C3C2×#71111yescharacteristic
830C22×C3C2×#71111yescharacteristic
831C22×C3C2×#71111yescharacteristic
832C22×C3D5×#4111yescharacteristic
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
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—22no—
855C3×C4—41no—
856C3×C4—54no—
857C3×C4—102no—
858C3×C4—102no—
859C3×C4—201no—
860Dic3—22no—
861Dic3—22no—
862Dic3—102no—
863Dic3—201no—
864Dic3—201no—
865C2×C5—42no—
866C2×C5—122no—
867C2×C5—122no—
868C2×C5#547711yescharacteristic
869C2×C5C2×#88211yescharacteristic
870C2×C5#552411yescharacteristic
871C2×C5#554711yescharacteristic
872C2×C5#554711yescharacteristic
873C2×C5#554811yescharacteristic
874C2×C5#554811yescharacteristic
875D5—122no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—32no—
883C23—32no—
884C23—61no—
885C23—61no—
886C23—61no—
887C23—61no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—152no—
897C23—301no—
898C23—301no—
899C23—301no—
900C23—301no—
901C23—301no—
902C23—301no—
903C23D5×D1212yes—
904C23C22×D3×D511yescharacteristic
905Q8—308no—
906D4—68no—
907D4—68no—
908D4—68no—
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—52no—
922C2×C4—52no—
923C2×C4—52no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—108no—
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—308no—
938C2×C4—308no—
939C2×C4—301no—
940C2×C4—301no—
941C2×C4—301no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—604no—
948C2×C4#678212yescomplemented
949C2×C3—42no—
950C2×C3#6592011yescharacteristic
951C2×C3#6592011yescharacteristic
952C2×C3D5×#12011yescharacteristic
953C2×C3#6593011yescharacteristic
954C2×C3#6593011yescharacteristic
955C2×C3#6594011yescharacteristic
956C2×C3#6605011yescharacteristic
957D3—42no—
958D3—42no—
959D3—202no—
960C5#7358011yescharacteristic, complemented, Sylow
961C22—22no—
962C22—22no—
963C22—22no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—62no—
969C22—62no—
970C22—62no—
971C22—62no—
972C22—62no—
973C22—62no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22—121no—
978C22—121no—
979C22—121no—
980C22—121no—
981C22—121no—
982C22—302no—
983C22—302no—
984C22—302no—
985C22—601no—
986C22—601no—
987C22—601no—
988C22—601no—
989C22C2×D5×D1211yescharacteristic
990C22D5×#23511yescharacteristic
991C22D3×D4×D511yescharacteristic
992C22D3×D4×D511yescharacteristic
993C22D3×#71111yescharacteristic
994C22D3×#71111yescharacteristic
995C22C2×#678211yescharacteristic
996C4—22no—
997C4—41no—
998C4—54no—
999C4—62no—
1000C4—62no—
1001C4—102no—
1002C4—102no—
1003C4—201no—
1004C4—302no—
1005C4—601no—
1006C4—601no—
1007C3#1060839611yescharacteristic, complemented, Sylow
1008C2—42no—
1009C2—122no—
1010C2—122no—
1011C2—602no—
1012C2#1175284311yescharacteristic
1013C2#1175287111yescharacteristic
1014C2D5×#88211yescharacteristic
1015C2#1175324911yescharacteristic
1016C2#1175433011yescharacteristic
1017C2#1175476711yescharacteristic
1018C2#1175477511yescharacteristic
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×Dic5×#67C2semidirect
3. C2×Dic5×D12C2semidirect
4. C2×#91405C2semidirect
5. #11751062C2semidirect
6. C5×#4960C2semidirect
7. C3×C22⋊C4×Dic5C2semidirect
8. #11749523C2semidirect
9. #11749493C2semidirect
10. #11748938C2semidirect
11. #11748929C2semidirect
12. #11748875C2semidirect
13. Dic5×(C2×D3)⋊C4C2semidirect
14. #11748758C2semidirect
15. #11748757C2semidirect
71. C22⋊C4×Dic5D3semidirect
99. C22×C3×Dic5D4semidirect
115. C2×#1200D4semidirect
122. C2×D3×Dic5D4semidirect
149. #4960D5semidirect
226. C22×C5×D3#41semidirect
232. C2×C3×C4×C5#41semidirect
250. C2×C5×Dic3#41semidirect
264. C2×C3×Dic5#41semidirect
349. C22×Dic5D12semidirect
550. C2×C4×C5#235semidirect
575. C2×Dic5#235semidirect
660. C22×D3#711semidirect
679. C2×C3×C4#711semidirect
697. C2×Dic3#711semidirect
818. C3×C5#2388semidirect
948. C2×C4#6782semidirect
960. C5#73580semidirect
1007. C3#10608396semidirect

Maximal subgroups

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

subgroupindex
C22×#67822
C2×Dic5×#672
C2×Dic5×D122
C2×#914052
#117510622
C5×#49602
C3×C22⋊C4×Dic52
#117495232
#117494932
#117489382
#117489292
#117488752
Dic5×(C2×D3)⋊C42
#117487582
#117487572
#106083963
#735805