Finite Group Databasebeta

← #14331636

Subgroups — #14331636

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×#91552C211yesmaximal, characteristic, complemented
3C2×#91418C211yesmaximal, characteristic, complemented
4C2×#91405C211yesmaximal, characteristic, complemented
5#11751061C211yesmaximal, characteristic, complemented
6C5×#4961C211yesmaximal, characteristic, complemented
7C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
8#11749523C211yesmaximal, characteristic, complemented
9#11749510C211yesmaximal, characteristic, complemented
10#11748937C211yesmaximal, characteristic, complemented
11#11748932C211yesmaximal, characteristic, complemented
12#11748875C211yesmaximal, characteristic, complemented
13Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14#11748756C211yesmaximal, characteristic, complemented
15#11748579C211yesmaximal, characteristic, complemented
16#10608620—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×#1220C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×#1203C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C22×#1200C2211yescharacteristic
27C2×#6782—24no—
28C2×#6782—24no—
29C2×#6782—24no—
30C22×D3×Dic5C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×C5×#217C2211yescharacteristic
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×C4⋊Dic3C2211yescharacteristic
38C2×C3×C22⋊Dic5C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40C2×C3×C4×Dic5C2211yescharacteristic
41#91552—24no—
42C2×#6669C2211yescharacteristic
43C2×#6668C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×#6667C2211yescharacteristic
46C2×#6667C2211yescharacteristic
47C2×#6667C2211yescharacteristic
48C2×(C2×D3)⋊Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50#91418—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×#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#65248—31no—
70C22⋊C4×Dic5—31no—
71C22⋊C4×Dic5D311yescharacteristic, complemented
72#64962—31no—
73#64955—31no—
74C24×C3×C5C2311yescharacteristic
75C23×D15C2311yescharacteristic
76C23×D15C2311yescharacteristic
77C23×C5×D3C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—22no—
81C2×#1220—22no—
82C2×#1220—22no—
83C2×#1220—22no—
84C2×#1220—22no—
85C2×#1220—22no—
86C22×Dic15C2311yescharacteristic
87C22×Dic15C2311yescharacteristic
88C2×D60—22no—
89C2×D60—22no—
90C2×D60—22no—
91C2×C5×#67—22no—
92C2×C5×#67—22no—
93C2×C5×#67—22no—
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
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×#1200—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#6714—22no—
125#6714—22no—
126C5×#217—22no—
127C5×(C2×D3)⋊C4—22no—
128C5×(C2×D3)⋊C4—22no—
129C5×C4⋊Dic3—22no—
130C3×C22⋊Dic5—22no—
131C3×C4×Dic5—22no—
132C3×C4×Dic5—22no—
133#6669—22no—
134#6668—22no—
135#6667—22no—
136#6667—22no—
137#6667—22no—
138#6667—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#4961D511yescharacteristic, complemented
148#4960—51no—
149#4960—51no—
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×C22⋊D5—31no—
158C22×C22⋊D5—31no—
159C22×C22⋊D5—31no—
160C22×C22⋊D5—31no—
161C23×Dic5—31no—
162C23×Dic5C2×D311yescharacteristic
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×#685—31no—
182C2×#685—31no—
183C2×#683—31no—
184C2×#683—31no—
185C2×C4×Dic5—31no—
186C2×C4×Dic5C2×D311yescharacteristic
187C2×C4×Dic5C2×D311yescharacteristic
188#4039—64no—
189#4027—64no—
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×D15—21no—
213C22×D15—21no—
214C22×D15—21no—
215C22×D15—21no—
216C22×D15—21no—
217C22×D15—21no—
218C22×D15C2×D412yes—
219C22×D15#4112yescomplemented
220C22×C5×D3—21no—
221C22×C5×D3—21no—
222C22×C5×D3—21no—
223C22×C5×D3—21no—
224C22×C5×D3—21no—
225C22×C5×D3—21no—
226C22×C5×D3C2×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#4112yescomplemented
233#1220—28no—
234#1220—28no—
235C2×Dic15—21no—
236C2×Dic15—21no—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15C2×D412yes—
240C2×Dic15#4112yescomplemented
241D60—28no—
242C5×#67—28no—
243C2×C5×Dic3—21no—
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×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—
269#1200—44no—
270D3×Dic5—28no—
271C23×C3×C4—51no—
272C22×#67—51no—
273C22×#67—51no—
274C22×#67C2×D511yescharacteristic
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×D3—51no—
284C22×Dic6—51no—
285C2×C3×C22⋊C4—51no—
286C2×C3×C22⋊C4C2×D511yescharacteristic
287C2×C3×C42—51no—
288C2×C3×C42—51no—
289C2×#217C2×D511yescharacteristic
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⋊Dic3C2×D511yescharacteristic
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×C5C22×D311yescharacteristic
314C23×D5—31no—
315C23×D5—31no—
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—62no—
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—
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—62no—
342C22×Dic5—62no—
343C22×Dic5D1214yescomplemented
344C22×Dic5C22×D311yescharacteristic
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—62no—
369#685—62no—
370#685—62no—
371#685—62no—
372#685—62no—
373#685—62no—
374#683—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—31no—
385#394—151no—
386#394—151no—
387#393—151no—
388#392—151no—
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—22no—
412C2×D15—22no—
413C2×D15—22no—
414C2×D15—41no—
415C2×D15—41no—
416C2×D15—41no—
417C2×D15—41no—
418C2×D15—41no—
419C2×D15—41no—
420C2×D15—41no—
421C2×D15—41no—
422C2×C5×D3—22no—
423C2×C5×D3—22no—
424C2×C5×D3—22no—
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—22no—
433C3×Dic5—22no—
434C3×Dic5—22no—
435C3×Dic5—41no—
436C3×Dic5#12014yes—
437C5×Dic3—22no—
438C5×Dic3—41no—
439C5×Dic3—41no—
440C24×C3C22×D511yescharacteristic
441C23×D3—51no—
442C23×D3—51no—
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—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—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—22no—
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—22no—
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—61no—
515C23×C5—61no—
516C23×C5—61no—
517C23×C5—61no—
518C23×C5—61no—
519C23×C5—61no—
520C23×C5C2×D1212yes—
521C23×C5C23×D311yescharacteristic
522C22×D5—32no—
523C22×D5—32no—
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×D5—61no—
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—32no—
543C2×C4×C5—61no—
544C2×C4×C5—61no—
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#23512yescomplemented
552C22⋊D5—68no—
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—21no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—32no—
565C2×Dic5—32no—
566C2×Dic5—61no—
567C2×Dic5—61no—
568C2×Dic5—61no—
569C2×Dic5—61no—
570C2×Dic5—68no—
571C2×Dic5C2×D1212yes—
572C2×Dic5C2×D1212yes—
573C2×Dic5#23512yescomplemented
574C2×Dic5D3×D412yes—
575C2×Dic5D3×D412yes—
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—151no—
586C22×D4—151no—
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—31no—
598C2×C4⋊C4—151no—
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—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—
630D15—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—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×D3D4×D512yes—
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—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—21no—
691C2×Dic3—52no—
692C2×Dic3—52no—
693C2×Dic3—101no—
694C2×Dic3—101no—
695C2×Dic3—101no—
696C2×Dic3—101no—
697C2×Dic3D4×D512yes—
698D12—108no—
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—121no—
716C22×C5—121no—
717C22×C5—121no—
718C22×C5—121no—
719C22×C5C22×D1211yescharacteristic
720C22×C5C2×#23511yescharacteristic
721C22×C5C2×#23511yescharacteristic
722C22×C5C2×D3×D411yescharacteristic
723C22×C5C2×D3×D411yescharacteristic
724C22×C5D3×#4111yescharacteristic
725C22×C5D3×#4111yescharacteristic
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—121no—
744C4×C5—121no—
745Dic5—22no—
746Dic5—22no—
747Dic5—41no—
748Dic5—62no—
749Dic5—62no—
750Dic5#88214yes—
751C24—31no—
752C24—151no—
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—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—31no—
780C22×C4—51no—
781C22×C4—54no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—102no—
786C22×C4—102no—
787C22×C4—154no—
788C22×C4—154no—
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—62no—
801C4⋊C4—302no—
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—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×C3D5×#4111yescharacteristic
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—54no—
857C3×C4—102no—
858C3×C4—102no—
859C3×C4—201no—
860Dic3—22no—
861Dic3—41no—
862Dic3—41no—
863Dic3—102no—
864Dic3—102no—
865C2×C5—42no—
866C2×C5—122no—
867C2×C5#547711yescharacteristic
868C2×C5C2×#88211yescharacteristic
869C2×C5#552411yescharacteristic
870C2×C5#554711yescharacteristic
871C2×C5#554711yescharacteristic
872C2×C5#554811yescharacteristic
873C2×C5#554811yescharacteristic
874D5—122no—
875D5—122no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—32no—
883C23—61no—
884C23—61no—
885C23—61no—
886C23—61no—
887C23—61no—
888C23—61no—
889C23—152no—
890C23—152no—
891C23—301no—
892C23—301no—
893C23—301no—
894C23—301no—
895C23—301no—
896C23—301no—
897C23—301no—
898C23—301no—
899C23—301no—
900C23—301no—
901C23—301no—
902C23—301no—
903C23D5×D1212yes—
904C23C22×D3×D511yescharacteristic
905Q8—308no—
906D4—68no—
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—52no—
919C2×C4—52no—
920C2×C4—52no—
921C2×C4—52no—
922C2×C4—52no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—108no—
932C2×C4—101no—
933C2×C4—101no—
934C2×C4—101no—
935C2×C4—101no—
936C2×C4—101no—
937C2×C4—101no—
938C2×C4—101no—
939C2×C4—152no—
940C2×C4—152no—
941C2×C4—308no—
942C2×C4—308no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—604no—
948C2×C4#678212yescomplemented
949C2×C3—42no—
950C2×C3D5×#12011yescharacteristic
951C2×C3#6593011yescharacteristic
952C2×C3#6593011yescharacteristic
953C2×C3#6594011yescharacteristic
954C2×C3#6599011yescharacteristic
955C2×C3#6599011yescharacteristic
956C2×C3#6600211yescharacteristic
957D3—42no—
958D3—202no—
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—121no—
972C22—121no—
973C22—121no—
974C22—121no—
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×D5×D1211yescharacteristic
990C22D5×#23511yescharacteristic
991C22D3×D4×D511yescharacteristic
992C22D3×D4×D511yescharacteristic
993C22#9202411yescharacteristic
994C22#9202411yescharacteristic
995C22C2×#678211yescharacteristic
996C4—22no—
997C4—41no—
998C4—54no—
999C4—62no—
1000C4—102no—
1001C4—102no—
1002C4—121no—
1003C4—121no—
1004C4—201no—
1005C4—302no—
1006C4—302no—
1007C3#1060862011yescharacteristic, complemented, Sylow
1008C2—42no—
1009C2—122no—
1010C2—602no—
1011C2—602no—
1012C2#1175285111yescharacteristic
1013C2#1175287211yescharacteristic
1014C2D5×#88211yescharacteristic
1015C2#1175324411yescharacteristic
1016C2#1175433011yescharacteristic
1017C2#1175476911yescharacteristic
1018C2#1175477311yescharacteristic
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×#91552C2semidirect
3. C2×#91418C2semidirect
4. C2×#91405C2semidirect
5. #11751061C2semidirect
6. C5×#4961C2semidirect
7. C3×C22⋊C4×Dic5C2semidirect
8. #11749523C2semidirect
9. #11749510C2semidirect
10. #11748937C2semidirect
11. #11748932C2semidirect
12. #11748875C2semidirect
13. Dic5×(C2×D3)⋊C4C2semidirect
14. #11748756C2semidirect
15. #11748579C2semidirect
71. C22⋊C4×Dic5D3semidirect
99. C22×C3×Dic5D4semidirect
118. C2×#1200D4semidirect
122. C2×D3×Dic5D4semidirect
147. #4961D5semidirect
219. C22×D15#41semidirect
232. C2×C3×C4×C5#41semidirect
240. C2×Dic15#41semidirect
264. C2×C3×Dic5#41semidirect
343. C22×Dic5D12semidirect
551. C2×C4×C5#235semidirect
573. C2×Dic5#235semidirect
679. C2×C3×C4#711semidirect
818. C3×C5#2388semidirect
948. C2×C4#6782semidirect
960. C5#73580semidirect
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×#915522
C2×#914182
C2×#914052
#117510612
C5×#49612
C3×C22⋊C4×Dic52
#117495232
#117495102
#117489372
#117489322
#117488752
Dic5×(C2×D3)⋊C42
#117487562
#117485792
#106086203
#735805