Finite Group Databasebeta

← #14329060

Subgroups — #14329060

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91770C211yesmaximal, characteristic, complemented
2C2×#91558C211yesmaximal, characteristic
3C2×#91398C211yesmaximal, characteristic, complemented
4C5×#4957C211yesmaximal, characteristic, complemented
5C3×#65233C211yesmaximal, characteristic, complemented
6#11749501C211yesmaximal, characteristic, complemented
7#11749487C211yesmaximal, characteristic, complemented
8#11749483C211yesmaximal, characteristic, complemented
9#11748918C211yesmaximal, characteristic, complemented
10#11748909C211yesmaximal, characteristic, complemented
11#11748886C211yesmaximal, characteristic, complemented
12#11748818C211yesmaximal, characteristic, complemented
13C4×#6667C211yesmaximal, characteristic, complemented
14#11748669C211yesmaximal, characteristic, complemented
15#11748645C211yesmaximal, characteristic, complemented
16#10608036—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×#1203C2211yescharacteristic
22C22×D3×Dic5C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6712C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic
27#91770—24no—
28C2×C5×#217C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C4×C5×Dic3C2211yescharacteristic
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic
37#91558C418yescomplemented
38C2×#6669C2211yescharacteristic
39C2×#6669C2211yescharacteristic
40C2×#6667C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×(C2×D3)⋊Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46C2×Dic3×Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48#91398—24no—
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#75480—51nomaximal, Hall
56C2×#4085—31no—
57C2×#4027—31no—
58C2×#4023—31no—
59C5×#390—31no—
60#65509—31no—
61#65279—31no—
62#65261—31no—
63#65246—31no—
64#65246—31no—
65#65245—31no—
66#65233D311yescharacteristic, complemented
67C22⋊C4×Dic5—31no—
68C22⋊C4×Dic5—31no—
69C4×#685—31no—
70C4×#683—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15C2311yescharacteristic
73C23×C5×D3C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C2×#1220—22no—
77C2×#1220—22no—
78C2×#1220C2×C414yes—
79C22×Dic15—22no—
80C22×Dic15—22no—
81C22×Dic15—41no—
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C2×C4×D15—22no—
86C2×C4×D15—22no—
87C2×C4×D15—41no—
88C2×C5×#67—41no—
89C2×C5×#67—41no—
90C2×C5×#67C2×C414yescomplemented
91C22×C5×Dic3C2311yescharacteristic
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C2×#1203—41no—
99C2×#1203—41no—
100C2×#1203C2×C414yescomplemented
101C2×D3×Dic5—22no—
102C2×D3×Dic5—22no—
103C2×D3×Dic5C2×C414yescomplemented
104C3×C5×C22⋊C4—22no—
105#6714—22no—
106#6712D414yescomplemented
107C4×Dic15—22no—
108C5×#217—22no—
109C5×(C2×D3)⋊C4—22no—
110C5×(C2×D3)⋊C4—22no—
111C5×Dic3⋊C4—41no—
112C4×C5×Dic3—41no—
113C3×C22⋊Dic5—41no—
114C3×C22⋊Dic5C2×C414yescomplemented
115C3×#683—41no—
116C3×C4×Dic5—22no—
117#6669—22no—
118#6669C2×C414yescomplemented
119#6667—22no—
120#6667—41no—
121#6667C2×C414yescomplemented
122(C2×D3)⋊Dic5—22no—
123(C2×D3)⋊Dic5—22no—
124Dic3×Dic5—22no—
125Dic3×Dic5—22no—
126Dic3×Dic5—41no—
127C2×#884—51no—
128C2×#67⋊C4—51no—
129C2×#872—51no—
130C3×#388—51no—
131#4988—51no—
132#4976—51no—
133#4958—51no—
134#4957—51no—
135#4957D511yescharacteristic, complemented
136Dic3×C22⋊C4—51no—
137C4×(C2×D3)⋊C4—51no—
138#4669—51no—
139#4666—51no—
140#4665—51no—
141#4649—51no—
142C22×C5×D4—31no—
143C22×C22⋊D5—31no—
144C22×C22⋊D5—31no—
145C23×Dic5—31no—
146C23×Dic5—31no—
147C22×C4×D5—31no—
148C2×C5×C4⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C5×C22⋊C4—31no—
152C2×C5×C22⋊C4C2×D311yescharacteristic
153C2×C42×C5—31no—
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5—31no—
156C2×C22⋊Dic5C2×D311yescharacteristic
157C2×C22⋊Dic5C2×D311yescharacteristic
158#4085—38no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#683—31no—
164C2×#683—31no—
165C2×#683—31no—
166C2×#683C2×D311yescharacteristic
167C2×C4×Dic5—31no—
168C2×C4×Dic5—31no—
169C2×C4×Dic5—31no—
170C2×C4×Dic5—31no—
171C2×C4×Dic5C2×D311yescharacteristic
172#4027—64no—
173#4023—64no—
174#3963—31no—
175#3963—31no—
176#3963—31no—
177#3963—31no—
178#3963C2×D311yescharacteristic
179#3963C2×D311yescharacteristic
180#2363—151noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5C22×C412yes—
188C23×C3×C5C2411yescharacteristic
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—21no—
193C22×D15—21no—
194C22×D15—21no—
195C22×D15C22×C412yes—
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3—21no—
201C22×C5×D3—21no—
202C22×C5×D3C22×C412yes—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5C2×D412yes—
209#1220—28no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—44no—
215C2×Dic15C22×C412yes—
216C2×Dic15C2×D412yes—
217C2×Dic15C2×D412yes—
218C2×Dic15#4112yes—
219C2×Dic15#4112yes—
220C4×D15—44no—
221C5×#67—44no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3C22×C412yes—
230C2×C5×Dic3#4112yes—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5C22×C412yes—
242C2×C3×Dic5C22×C412yes—
243#1203—44no—
244D3×Dic5—28no—
245C22×#67—51no—
246C22×#67C2×D511yescharacteristic
247C23×Dic3—51no—
248C22×D12—51no—
249C22×C4×D3—51no—
250C22×C4×D3—51no—
251C2×C3×C4⋊C4—51no—
252C2×C3×C22⋊C4—51no—
253C2×C3×C22⋊C4—51no—
254C2×C3×C22⋊C4C2×D511yescharacteristic
255C2×C3×C42—51no—
256C2×#217C2×D511yescharacteristic
257C2×(C2×D3)⋊C4—51no—
258C2×(C2×D3)⋊C4—51no—
259C2×(C2×D3)⋊C4—51no—
260C2×(C2×D3)⋊C4—51no—
261C2×(C2×D3)⋊C4—51no—
262C2×(C2×D3)⋊C4—51no—
263C2×(C2×D3)⋊C4C2×D511yescharacteristic
264C2×(C2×D3)⋊C4C2×D511yescharacteristic
265C2×Dic3⋊C4—51no—
266C2×Dic3⋊C4—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4C2×D511yescharacteristic
269C2×C4×Dic3—51no—
270C2×C4×Dic3—51no—
271C2×C4×Dic3—51no—
272C2×C4×Dic3—51no—
273C2×C4×Dic3C2×D511yescharacteristic
274#884—58no—
275#67⋊C4—104no—
276#872—104no—
277C3×#95—51no—
278C3×#95—51no—
279C3⋊#95—51no—
280C3⋊#95—51no—
281C3⋊#95—51no—
282C3⋊#95—51no—
283C24×C5—31no—
284C24×C5C22×D311yescharacteristic
285C23×D5—31no—
286C2×C5×D4—34no—
287C2×C5×D4—121no—
288C2×C5×D4—121no—
289C22×C4×C5—31no—
290C22×C4×C5—31no—
291C22×C4×C5—31no—
292C22×C4×C5C22×D311yescharacteristic
293C22×C4×C5C22×D311yescharacteristic
294C2×C22⋊D5—34no—
295C2×C22⋊D5—34no—
296C2×C22⋊D5—62no—
297C2×C22⋊D5—62no—
298C2×C22⋊D5—121no—
299C2×C22⋊D5—121no—
300C22×Dic5—31no—
301C22×Dic5—31no—
302C22×Dic5—31no—
303C22×Dic5—34no—
304C22×Dic5—62no—
305C22×Dic5—62no—
306C22×Dic5—62no—
307C22×Dic5—62no—
308C22×Dic5—121no—
309C22×Dic5C22×D311yescharacteristic
310C22×Dic5C22×D311yescharacteristic
311C22×Dic5C22×D311yescharacteristic
312C22×Dic5C22×D311yescharacteristic
313C2×C4×D5—62no—
314C2×C4×D5—62no—
315C2×C4×D5—121no—
316C5×C4⋊C4—121no—
317C5×C22⋊C4—22no—
318C5×C22⋊C4—62no—
319C5×C22⋊C4—62no—
320C5×C22⋊C4—62no—
321C42×C5—121no—
322C22⋊Dic5—41no—
323C22⋊Dic5—62no—
324C22⋊Dic5—62no—
325C22⋊Dic5C4×D314yescomplemented
326#685—34no—
327#685—62no—
328#685—62no—
329#685—121no—
330#683—34no—
331#683—34no—
332#683—41no—
333#683—62no—
334C4×Dic5—22no—
335C4×Dic5—62no—
336C4×Dic5—62no—
337C4×Dic5—62no—
338C4×Dic5—121no—
339C2×#121—151no—
340C2×C4×D4—151no—
341C2×#117—151no—
342#390—31no—
343#390—151no—
344#390—151no—
345#389—151no—
346#388—51no—
347#388—151no—
348#386—151no—
349#386—151no—
350C4×C4⋊C4—151no—
351C4×C22⋊C4—151no—
352C4×C22⋊C4—151no—
353C4×C22⋊C4—151no—
354C22×C3×C5—22no—
355C22×C3×C5—22no—
356C22×C3×C5—22no—
357C22×C3×C5—41no—
358C22×C3×C5—41no—
359C22×C3×C5—41no—
360C22×C3×C5—41no—
361C22×C3×C5C23×C411yescharacteristic
362C22×C3×C5C22×D411yescharacteristic
363C22×C3×C5C2×#4111yescharacteristic
364C22×C3×C5C2×#4111yescharacteristic
365C22×C3×C5C2×#4111yescharacteristic
366C22×C3×C5H(5,𝔽2)11yescharacteristic
367C22×C3×C5H(5,𝔽2)11yescharacteristic
368C2×D15—22no—
369C2×D15—22no—
370C2×D15—22no—
371C2×D15—41no—
372C2×D15—41no—
373C2×D15—41no—
374C2×D15—41no—
375C2×C5×D3—22no—
376C2×C5×D3—22no—
377C2×C5×D3—22no—
378C2×C5×D3—41no—
379C2×C5×D3—41no—
380C2×C5×D3—41no—
381C2×C5×D3—41no—
382C3×C4×C5—22no—
383C3×C4×C5—41no—
384Dic15—22no—
385Dic15—22no—
386Dic15C4×D414yes—
387C3×Dic5—22no—
388C3×Dic5—22no—
389C3×Dic5—41no—
390C3×Dic5—41no—
391C5×Dic3—22no—
392C5×Dic3—22no—
393C5×Dic3—41no—
394C24×C3C22×D511yescharacteristic
395C23×D3—51no—
396C23×D3C22×D511yescharacteristic
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4—51no—
400C22×C3×C4—51no—
401C22×C3×C4C22×D511yescharacteristic
402C22×C3×C4C22×D511yescharacteristic
403C2×#67—41no—
404C2×#67—41no—
405C2×#67—54no—
406C2×#67—102no—
407C2×#67—102no—
408C2×#67C4×D514yescomplemented
409C22×Dic3—51no—
410C22×Dic3—51no—
411C22×Dic3—51no—
412C22×Dic3—102no—
413C22×Dic3—102no—
414C22×Dic3—201no—
415C22×Dic3C22×D511yescharacteristic
416C22×Dic3C22×D511yescharacteristic
417C22×Dic3C22×D511yescharacteristic
418C2×D12—54no—
419C2×D12—201no—
420C2×D12—201no—
421C2×C4×D3—54no—
422C2×C4×D3—102no—
423C2×C4×D3—102no—
424C2×C4×D3—102no—
425C2×C4×D3—102no—
426C2×C4×D3—201no—
427C3×C4⋊C4—201no—
428C3×C22⋊C4—22no—
429C3×C22⋊C4—54no—
430C3×C22⋊C4—201no—
431C3×C42—102no—
432#217—22no—
433(C2×D3)⋊C4—22no—
434(C2×D3)⋊C4—22no—
435(C2×D3)⋊C4—54no—
436(C2×D3)⋊C4—102no—
437(C2×D3)⋊C4—102no—
438(C2×D3)⋊C4—102no—
439(C2×D3)⋊C4—102no—
440(C2×D3)⋊C4—201no—
441Dic3⋊C4—41no—
442Dic3⋊C4—54no—
443Dic3⋊C4—54no—
444Dic3⋊C4—102no—
445C4×Dic3—41no—
446C4×Dic3—102no—
447C4×Dic3—102no—
448C4×Dic3—102no—
449C4×Dic3—201no—
450C23×C5—21no—
451C23×C5—21no—
452C23×C5—21no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—32no—
457C23×C5—61no—
458C23×C5—61no—
459C23×C5—61no—
460C23×C5—61no—
461C23×C5—61no—
462C23×C5—61no—
463C23×C5C2×C4×D312yes—
464C23×C5C23×D311yescharacteristic
465C22×D5—32no—
466C22×D5—61no—
467C22×D5—61no—
468C22×D5—61no—
469C22×D5—61no—
470C22×D5—61no—
471C22×D5—61no—
472C5×D4—124no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—32no—
479C2×C4×C5—32no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—61no—
487C2×C4×C5D3×D412yes—
488C22⋊D5—68no—
489C22⋊D5—124no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—21no—
499C2×Dic5—21no—
500C2×Dic5—32no—
501C2×Dic5—32no—
502C2×Dic5—32no—
503C2×Dic5—32no—
504C2×Dic5—32no—
505C2×Dic5—68no—
506C2×Dic5—61no—
507C2×Dic5—61no—
508C2×Dic5—61no—
509C2×Dic5—61no—
510C2×Dic5—124no—
511C2×Dic5C2×C4×D312yes—
512C2×Dic5C2×C4×D312yes—
513C4×D5—124no—
514C22×D4—31no—
515C22×D4—151no—
516C22×D4—151no—
517C23×C4—151no—
518C23×C4—151no—
519C23×C4—151no—
520#121—158no—
521C4×D4—304no—
522#117—304no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—51no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—151no—
527C2×C4⋊C4—151no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—51no—
532C2×C22⋊C4—51no—
533C2×C22⋊C4—151no—
534C2×C22⋊C4—151no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C22⋊C4—151no—
538C2×C22⋊C4—151no—
539C2×C22⋊C4D3×D511yescharacteristic
540C2×C42—31no—
541C2×C42—51no—
542C2×C42—151no—
543C2×C42—151no—
544C2×C42—151no—
545C2×C42—151no—
546#95—51no—
547#95—51no—
548#95—151no—
549#95—151no—
550#95—151no—
551#95—151no—
552C2×C3×C5—42no—
553C2×C3×C5C2×C4×D411yescharacteristic
554C2×C3×C5C4×#4111yescharacteristic
555C2×C3×C5#51811yescharacteristic
556C2×C3×C5#54611yescharacteristic
557C2×C3×C5#55011yescharacteristic
558C2×C3×C5#55311yescharacteristic
559C2×C3×C5#55511yescharacteristic
560D15—42no—
561C5×D3—42no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3C2×C4×D512yes—
569C23×C3C23×D511yescharacteristic
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—52no—
577C22×D3—101no—
578C22×D3—101no—
579C22×D3—101no—
580C22×D3—101no—
581C22×D3—101no—
582C22×D3—101no—
583C22×D3C2×C4×D512yes—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—52no—
590C2×C3×C4—52no—
591C2×C3×C4—101no—
592C2×C3×C4—101no—
593C2×C3×C4—101no—
594C2×C3×C4—101no—
595C2×C3×C4—101no—
596C2×C3×C4—101no—
597C2×C3×C4—101no—
598C2×C3×C4—101no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4D4×D512yes—
602#67—44no—
603#67—108no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—52no—
612C2×Dic3—52no—
613C2×Dic3—52no—
614C2×Dic3—52no—
615C2×Dic3—52no—
616C2×Dic3—101no—
617C2×Dic3—101no—
618C2×Dic3—101no—
619C2×Dic3—101no—
620C2×Dic3—204no—
621C2×Dic3C2×C4×D512yes—
622C2×Dic3#71112yes—
623D12—204no—
624C4×D3—108no—
625C4×D3—204no—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—41no—
630C22×C5—41no—
631C22×C5—41no—
632C22×C5—41no—
633C22×C5—62no—
634C22×C5—62no—
635C22×C5—62no—
636C22×C5—121no—
637C22×C5—121no—
638C22×C5—121no—
639C22×C5—121no—
640C22×C5C22×C4×D311yescharacteristic
641C22×C5C2×D3×D411yescharacteristic
642C22×C5#100411yescharacteristic
643C22×C5D3×#4111yescharacteristic
644C22×C5D3×#4111yescharacteristic
645C22×C5D3×#4111yescharacteristic
646C22×C5#100911yescharacteristic
647C2×D5—62no—
648C2×D5—62no—
649C2×D5—62no—
650C2×D5—121no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C4×C5—22no—
655C4×C5—41no—
656C4×C5—62no—
657C4×C5—62no—
658C4×C5—121no—
659Dic5—22no—
660Dic5—22no—
661Dic5—34no—
662Dic5—41no—
663Dic5—41no—
664Dic5—62no—
665Dic5—62no—
666C24—31no—
667C24—151no—
668C24C2×D3×D511yescharacteristic
669C2×D4—34no—
670C2×D4—121no—
671C2×D4—121no—
672C2×D4—154no—
673C2×D4—154no—
674C2×D4—302no—
675C2×D4—302no—
676C2×D4—601no—
677C2×D4—601no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—51no—
682C22×C4—51no—
683C22×C4—51no—
684C22×C4—51no—
685C22×C4—154no—
686C22×C4—151no—
687C22×C4—151no—
688C22×C4—151no—
689C22×C4—302no—
690C22×C4—302no—
691C22×C4—302no—
692C22×C4—302no—
693C22×C4—302no—
694C22×C4—302no—
695C22×C4—601no—
696C22×C4—601no—
697C22×C4C2×D3×D511yescharacteristic
698C22×C4C2×D3×D511yescharacteristic
699C4⋊C4—121no—
700C4⋊C4—154no—
701C4⋊C4—154no—
702C4⋊C4—201no—
703C4⋊C4—302no—
704C22⋊C4—22no—
705C22⋊C4—54no—
706C22⋊C4—62no—
707C22⋊C4—62no—
708C22⋊C4—62no—
709C22⋊C4—154no—
710C22⋊C4—201no—
711C22⋊C4—302no—
712C22⋊C4—302no—
713C22⋊C4—302no—
714C22⋊C4—302no—
715C22⋊C4—601no—
716C42—102no—
717C42—121no—
718C42—302no—
719C42—302no—
720C42—302no—
721C42—601no—
722C3×C5#236311yescharacteristic, complemented, Hall
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3C22×C4×D511yescharacteristic
731C22×C3C2×D4×D511yescharacteristic
732C22×C3C2×#71111yescharacteristic
733C22×C3#414411yescharacteristic
734C22×C3#414411yescharacteristic
735C22×C3D5×#4111yescharacteristic
736C22×C3D5×#4111yescharacteristic
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—22no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—102no—
745C2×D3—102no—
746C2×D3—102no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—201no—
750C2×D3—201no—
751C3×C4—22no—
752C3×C4—41no—
753C3×C4—102no—
754C3×C4—102no—
755C3×C4—201no—
756C3×C4—201no—
757Dic3—22no—
758Dic3—22no—
759Dic3—41no—
760Dic3—54no—
761Dic3—102no—
762Dic3—102no—
763C2×C5—42no—
764C2×C5—122no—
765C2×C5#552211yescharacteristic
766C2×C5C4×D3×D411yescharacteristic
767C2×C5#554511yescharacteristic
768C2×C5#559911yescharacteristic
769C2×C5#565411yescharacteristic
770C2×C5#567011yescharacteristic
771C2×C5#570911yescharacteristic
772D5—122no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—32no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23—61no—
785C23—61no—
786C23—152no—
787C23—301no—
788C23—301no—
789C23—301no—
790C23—301no—
791C23—301no—
792C23—301no—
793C23C4×D3×D512yes—
794C23C22×D3×D511yescharacteristic
795D4—124no—
796D4—308no—
797D4—604no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—52no—
806C2×C4—52no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—101no—
815C2×C4—101no—
816C2×C4—101no—
817C2×C4—101no—
818C2×C4—101no—
819C2×C4—101no—
820C2×C4—101no—
821C2×C4—101no—
822C2×C4—101no—
823C2×C4—101no—
824C2×C4—152no—
825C2×C4—152no—
826C2×C4—152no—
827C2×C4—152no—
828C2×C4—152no—
829C2×C4—308no—
830C2×C4—301no—
831C2×C4—301no—
832C2×C4—301no—
833C2×C4—301no—
834C2×C4—604no—
835C2×C4—604no—
836C2×C4#679012yes—
837C2×C3—42no—
838C2×C3#6582011yescharacteristic
839C2×C3C4×#71111yescharacteristic
840C2×C3C4×D4×D511yescharacteristic
841C2×C3#6593511yescharacteristic
842C2×C3#6594411yescharacteristic
843C2×C3#6600411yescharacteristic
844C2×C3#6605211yescharacteristic
845D3—42no—
846D3—202no—
847C5#7548011yescharacteristic, complemented, Sylow
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—62no—
856C22—62no—
857C22—62no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—302no—
863C22—302no—
864C22—302no—
865C22—601no—
866C22—601no—
867C22—601no—
868C22—601no—
869C22C2×C4×D3×D511yescharacteristic
870C22#9201611yescharacteristic
871C22D3×#71111yescharacteristic
872C22#9202411yescharacteristic
873C22#9202511yescharacteristic
874C22#9202711yescharacteristic
875C22C2×#679011yescharacteristic
876C4—22no—
877C4—41no—
878C4—62no—
879C4—62no—
880C4—102no—
881C4—102no—
882C4—121no—
883C4—154no—
884C4—201no—
885C4—201no—
886C4—302no—
887C4—302no—
888C3#1060803611yescharacteristic, complemented, Sylow
889C2—42no—
890C2—122no—
891C2—602no—
892C2#1175282311yescharacteristic
893C2#1175300111yescharacteristic
894C2#1175301211yescharacteristic
895C2#1175320211yescharacteristic
896C2C4×#679011yescharacteristic
897C2#1175482611yescharacteristic
898C2#1175495611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91558C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2363
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#91770C2semidirect
3. C2×#91398C2semidirect
4. C5×#4957C2semidirect
5. C3×#65233C2semidirect
6. #11749501C2semidirect
7. #11749487C2semidirect
8. #11749483C2semidirect
9. #11748918C2semidirect
10. #11748909C2semidirect
11. #11748886C2semidirect
12. #11748818C2semidirect
13. C4×#6667C2semidirect
14. #11748669C2semidirect
15. #11748645C2semidirect
37. #91558C4semidirect
66. #65233D3semidirect
90. C2×C5×#67C2×C4semidirect
100. C2×#1203C2×C4semidirect
103. C2×D3×Dic5C2×C4semidirect
106. #6712D4semidirect
114. C3×C22⋊Dic5C2×C4semidirect
118. #6669C2×C4semidirect
121. #6667C2×C4semidirect
135. #4957D5semidirect
325. C22⋊Dic5C4×D3semidirect
408. C2×#67C4×D5semidirect
722. C3×C5#2363semidirect
847. C5#75480semidirect
888. C3#10608036semidirect

Maximal subgroups

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

subgroupindex
C2×#917702
C2×#915582
C2×#913982
C5×#49572
C3×#652332
#117495012
#117494872
#117494832
#117489182
#117489092
#117488862
#117488182
C4×#66672
#117486692
#117486452
#106080363
#754805