Finite Group Databasebeta

← #14326209

Subgroups — #14326209

Order 1920.

1744 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6782C211yesmaximal, characteristic
2C2×#91325C211yesmaximal, characteristic, complemented
3C2×#91324C211yesmaximal, characteristic, complemented
4#11751058C211yesmaximal, characteristic, complemented
5C5×#4957C211yesmaximal, characteristic, complemented
6C3×#65231C211yesmaximal, characteristic, complemented
7#11749483C211yesmaximal, characteristic, complemented
8#11749482C211yesmaximal, characteristic, complemented
9Dic5×#217C211yesmaximal, characteristic, complemented
10#11748909C211yesmaximal, characteristic, complemented
11#11748909C211yesmaximal, characteristic, complemented
12#11748887C211yesmaximal, characteristic, complemented
13#11748886C211yesmaximal, characteristic, complemented
14#11748882C211yesmaximal, characteristic, complemented
15#11748881C211yesmaximal, characteristic, complemented
16#10608032—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C22×C5×#67C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C22×#1203C2211yescharacteristic
22C22×#1200C2211yescharacteristic
23C2×#6782—24no—
24C2×#6782—24no—
25C2×#6782C418yescomplemented
26C22×D3×Dic5C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×C4×Dic15C2211yescharacteristic
33C2×C5×#217C2211yescharacteristic
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×Dic3⋊C4C2211yescharacteristic
37C2×C4×C5×Dic3C2211yescharacteristic
38C2×C3×C22⋊Dic5C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×Dic3⋊Dic5C2211yescharacteristic
42C2×#6669C2211yescharacteristic
43C2×#6667C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×(C2×D3)⋊Dic5C2211yescharacteristic
46C2×(C2×D3)⋊Dic5C2211yescharacteristic
47C2×Dic3×Dic5C2211yescharacteristic
48C2×Dic3×Dic5C2211yescharacteristic
49C2×Dic3×Dic5C2211yescharacteristic
50C2×Dic3×Dic5C2211yescharacteristic
51#91325—24no—
52#91324—24no—
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#73877—51nomaximal, Hall
58C22×#711—31no—
59C2×#4033—31no—
60C2×C4×Dic10—31no—
61C5×#390—31no—
62#65510—31no—
63#65276—31no—
64#65246—31no—
65#65246—31no—
66#65246—31no—
67#65246—31no—
68#65231—31no—
69#65231D311yescharacteristic, complemented
70C22⋊C4×Dic5—31no—
71C22⋊C4×Dic5—31no—
72C4×#685—31no—
73C24×C3×C5C2311yescharacteristic
74C23×D15C2311yescharacteristic
75C23×C5×D3C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C2×#1220—22no—
79C2×#1220—22no—
80C2×#1220C2×C414yes—
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C2×C5×#67—22no—
85C2×C5×#67—22no—
86C2×C5×#67C2×C414yes—
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2311yescharacteristic
90C22×C3×Dic5—22no—
91C22×C3×Dic5—22no—
92C22×C3×Dic5C2×C414yes—
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C2×#1204C2×C414yes—
98C2×#1204D414yes—
99C2×#1204D414yes—
100C2×#1203—22no—
101C2×#1203—22no—
102C2×#1203C2×C414yes—
103C2×#1200—22no—
104C2×#1200—22no—
105C2×#1200C2×C414yes—
106#6782—232no—
107C2×D3×Dic5—22no—
108C2×D3×Dic5—22no—
109C2×D3×Dic5C2×C414yes—
110C3×C5×C22⋊C4—41no—
111#6719—22no—
112#6714—22no—
113#6714—41no—
114#6712—22no—
115C4×Dic15—22no—
116C5×#217—22no—
117C5×(C2×D3)⋊C4—22no—
118C5×(C2×D3)⋊C4—41no—
119C5×Dic3⋊C4—22no—
120C4×C5×Dic3—22no—
121C3×C22⋊Dic5—41no—
122C3×#683—22no—
123C3×#683—22no—
124Dic3⋊Dic5—22no—
125#6669—22no—
126#6667—22no—
127#6667—41no—
128(C2×D3)⋊Dic5—22no—
129(C2×D3)⋊Dic5—41no—
130Dic3×Dic5—22no—
131Dic3×Dic5—22no—
132Dic3×Dic5—22no—
133Dic3×Dic5—22no—
134C22×#235—51no—
135C2×#887—51no—
136C2×#887—51no—
137C3×#380—51no—
138C4×#217—51no—
139#4988—51no—
140#4988—51no—
141#4957—51no—
142#4957—51no—
143#4957—51no—
144#4957D511yescharacteristic, complemented
145#4667—51no—
146#4667—51no—
147#4666—51no—
148#4666—51no—
149C22×C5×D4—31no—
150C22×C22⋊D5—31no—
151C22×C22⋊D5—31no—
152C23×Dic5—31no—
153C23×Dic5C2×D311yescharacteristic
154C2×#711—38no—
155C2×#711—64no—
156C2×#711—64no—
157C22×C4×D5—31no—
158C22×Dic10—31no—
159C2×C5×C4⋊C4—31no—
160C2×C5×C22⋊C4—31no—
161C2×C5×C22⋊C4—31no—
162C2×C5×C22⋊C4—31no—
163C2×C5×C22⋊C4C2×D311yescharacteristic
164C2×C42×C5—31no—
165C2×C22⋊Dic5—31no—
166C2×C22⋊Dic5—31no—
167C2×C22⋊Dic5—31no—
168C2×C22⋊Dic5C2×D311yescharacteristic
169C2×#685—31no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#685—31no—
173C2×C4⋊Dic5—31no—
174C2×#683—31no—
175C2×#683—31no—
176C2×#683C2×D311yescharacteristic
177C2×#683C2×D311yescharacteristic
178C2×C4×Dic5—31no—
179C2×C4×Dic5—31no—
180C2×C4×Dic5—31no—
181C2×C4×Dic5—31no—
182C2×C4×Dic5—31no—
183#4033—64no—
184C4×Dic10—64no—
185#3963—31no—
186#3963—31no—
187#3963C2×D311yescharacteristic
188#3963C2×D311yescharacteristic
189#2341—151noSylow
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5C22×C412yes—
197C23×C3×C5C2411yescharacteristic
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15—21no—
202C22×D15—21no—
203C22×D15—21no—
204C22×D15C22×C412yes—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—21no—
209C22×C5×D3—21no—
210C22×C5×D3—21no—
211C22×C5×D3C22×C412yes—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218#1220—28no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15C22×C412yes—
225C2×Dic15C2×D412yes—
226C2×Dic15C2×D412yes—
227C2×Dic15#4112yescomplemented
228C5×#67—28no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3C22×C412yes—
235C2×C5×Dic3C2×D412yes—
236C2×C5×Dic3C2×D412yes—
237C2×C5×Dic3#4112yescomplemented
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—28no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5C22×C412yes—
248C2×C3×Dic5C22×C412yes—
249C2×C3×Dic5C2×D412yes—
250C2×C3×Dic5C2×D412yes—
251#1204C22⋊C4116yescomplemented
252#1203—28no—
253#1200—28no—
254D3×Dic5—28no—
255C23×C3×C4—51no—
256C22×#67—51no—
257C22×#67C2×D511yescharacteristic
258C2×#235—58no—
259C2×#235—104no—
260C2×#235—104no—
261C22×D12—51no—
262C22×C4×D3—51no—
263C22×C4×D3—51no—
264C22×Dic6—51no—
265C2×C3×C4⋊C4—51no—
266C2×C3×C4⋊C4—51no—
267C2×C3×C22⋊C4—51no—
268C2×C3×C22⋊C4C2×D511yescharacteristic
269C2×#217—51no—
270C2×#217C2×D511yescharacteristic
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4C2×D511yescharacteristic
278C2×(C2×D3)⋊C4C2×D511yescharacteristic
279C2×Dic3⋊C4—51no—
280C2×Dic3⋊C4—51no—
281C2×Dic3⋊C4—51no—
282C2×Dic3⋊C4C2×D511yescharacteristic
283C2×C4×Dic3—51no—
284C2×C4×Dic3—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287C2×C4×Dic3—51no—
288C2×C4×Dic3C2×D511yescharacteristic
289#887—104no—
290#887—104no—
291C3×#95—51no—
292C3×#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C24×C5—31no—
296C24×C5C22×D311yescharacteristic
297C23×D5—31no—
298C2×C5×D4—34no—
299C2×C5×D4—62no—
300C2×C5×D4—62no—
301C22×C4×C5—31no—
302C22×C4×C5—31no—
303C22×C4×C5—31no—
304C22×C4×C5C22×D311yescharacteristic
305C22×C4×C5C22×D311yescharacteristic
306C2×C22⋊D5—34no—
307C2×C22⋊D5—34no—
308C2×C22⋊D5—62no—
309C2×C22⋊D5—62no—
310C2×C22⋊D5—62no—
311C2×C22⋊D5—62no—
312C22×Dic5—22no—
313C22×Dic5—22no—
314C22×Dic5—31no—
315C22×Dic5—31no—
316C22×Dic5—34no—
317C22×Dic5—31no—
318C22×Dic5—62no—
319C22×Dic5—62no—
320C22×Dic5C4×D314yes—
321C22×Dic5C22×D311yescharacteristic
322C22×Dic5C22×D311yescharacteristic
323C22×Dic5C22×D311yescharacteristic
324C22×Dic5C22×D311yescharacteristic
325#711—632no—
326C2×C4×D5—34no—
327C2×C4×D5—62no—
328C2×C4×D5—62no—
329C2×Dic10—34no—
330C2×Dic10—34no—
331C2×Dic10—34no—
332C5×C4⋊C4—62no—
333C5×C22⋊C4—41no—
334C5×C22⋊C4—62no—
335C5×C22⋊C4—62no—
336C5×C22⋊C4—121no—
337C42×C5—62no—
338C22⋊Dic5—41no—
339C22⋊Dic5—62no—
340C22⋊Dic5—62no—
341C22⋊Dic5—121no—
342#685—62no—
343#685—62no—
344#685—121no—
345#685—121no—
346C4⋊Dic5—62no—
347#683—22no—
348#683—22no—
349#683—62no—
350#683—62no—
351C4×Dic5—62no—
352C4×Dic5—62no—
353C4×Dic5—62no—
354C4×Dic5—62no—
355C4×Dic5—62no—
356C22×#41—151no—
357C2×C4×Q8—151no—
358C2×C4×Q8—151no—
359#390—31no—
360#390—151no—
361#390—151no—
362#390—151no—
363#390—151no—
364#390—151no—
365#380—51no—
366#380—151no—
367#380—151no—
368C4×C22⋊C4—151no—
369C4×C22⋊C4—151no—
370C4×C22⋊C4—151no—
371C22×C3×C5—22no—
372C22×C3×C5—22no—
373C22×C3×C5—22no—
374C22×C3×C5—41no—
375C22×C3×C5—41no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5C23×C411yescharacteristic
379C22×C3×C5C22×D411yescharacteristic
380C22×C3×C5C22×D411yescharacteristic
381C22×C3×C5C2×#4111yescharacteristic
382C22×C3×C5C2×#4111yescharacteristic
383C22×C3×C5H(5,𝔽2)11yescharacteristic
384C22×C3×C52−1+411yescharacteristic
385C2×D15—22no—
386C2×D15—22no—
387C2×D15—22no—
388C2×D15—41no—
389C2×D15—41no—
390C2×D15—41no—
391C2×D15—41no—
392C2×C5×D3—22no—
393C2×C5×D3—22no—
394C2×C5×D3—22no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—41no—
398C2×C5×D3—41no—
399C3×C4×C5—41no—
400C3×C4×C5—41no—
401Dic15—22no—
402Dic15—41no—
403Dic15C2×C22⋊C414yes—
404C3×Dic5—22no—
405C3×Dic5—41no—
406C3×Dic5—41no—
407C3×Dic5C2×C22⋊C414yes—
408C5×Dic3—22no—
409C5×Dic3—41no—
410C5×Dic3C2×C22⋊C414yes—
411C24×C3C22×D511yescharacteristic
412C23×D3—51no—
413C23×D3C22×D511yescharacteristic
414C22×C3×C4—51no—
415C22×C3×C4—54no—
416C22×C3×C4—51no—
417C22×C3×C4—51no—
418C22×C3×C4—51no—
419C22×C3×C4—102no—
420C22×C3×C4—102no—
421C22×C3×C4C22×D511yescharacteristic
422C22×C3×C4C22×D511yescharacteristic
423C2×#67—22no—
424C2×#67—22no—
425C2×#67—54no—
426C2×#67—102no—
427C2×#67—102no—
428C2×#67C4×D514yes—
429C22×Dic3—51no—
430C22×Dic3—51no—
431C22×Dic3—51no—
432C22×Dic3C22×D511yescharacteristic
433C22×Dic3C22×D511yescharacteristic
434C22×Dic3C22×D511yescharacteristic
435#235—1032no—
436C2×D12—54no—
437C2×D12—102no—
438C2×D12—102no—
439C2×C4×D3—54no—
440C2×C4×D3—54no—
441C2×C4×D3—102no—
442C2×C4×D3—102no—
443C2×C4×D3—102no—
444C2×C4×D3—102no—
445C2×Dic6—54no—
446C2×Dic6—54no—
447C2×Dic6—54no—
448C3×C4⋊C4—102no—
449C3×C4⋊C4—102no—
450C3×C22⋊C4—41no—
451C3×C22⋊C4—201no—
452#217—22no—
453#217—102no—
454(C2×D3)⋊C4—22no—
455(C2×D3)⋊C4—41no—
456(C2×D3)⋊C4—102no—
457(C2×D3)⋊C4—102no—
458(C2×D3)⋊C4—102no—
459(C2×D3)⋊C4—201no—
460(C2×D3)⋊C4—201no—
461(C2×D3)⋊C4—201no—
462Dic3⋊C4—22no—
463Dic3⋊C4—102no—
464Dic3⋊C4—102no—
465Dic3⋊C4—102no—
466C4×Dic3—22no—
467C4×Dic3—102no—
468C4×Dic3—102no—
469C4×Dic3—102no—
470C4×Dic3—102no—
471C4×Dic3—102no—
472C23×C5—21no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—32no—
479C23×C5—61no—
480C23×C5—61no—
481C23×C5—61no—
482C23×C5—61no—
483C23×C5—61no—
484C23×C5—61no—
485C23×C5C2×C4×D312yes—
486C23×C5C23×D311yescharacteristic
487C22×D5—32no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C22×D5—61no—
493C22×D5—61no—
494C5×D4—68no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—32no—
502C2×C4×C5—32no—
503C2×C4×C5—32no—
504C2×C4×C5—32no—
505C2×C4×C5—61no—
506C2×C4×C5—61no—
507C2×C4×C5—61no—
508C2×C4×C5—61no—
509C2×C4×C5—61no—
510C22⋊D5—68no—
511C22⋊D5—68no—
512C2×Dic5—21no—
513C2×Dic5—21no—
514C2×Dic5—28no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—32no—
522C2×Dic5—32no—
523C2×Dic5—32no—
524C2×Dic5—32no—
525C2×Dic5—68no—
526C2×Dic5—61no—
527C2×Dic5—61no—
528C2×Dic5—61no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5C2×C4×D312yes—
532C2×Dic5C2×C4×D312yes—
533C2×Dic5D3×D412yes—
534C2×Dic5D3×D412yes—
535C4×D5—68no—
536Dic10—316no—
537C2×#41—158no—
538C2×#41—304no—
539C2×#41—304no—
540C22×Q8—151no—
541C22×D4—31no—
542C22×D4—151no—
543C22×D4—151no—
544C23×C4—51no—
545C23×C4—151no—
546C23×C4—151no—
547C4×Q8—304no—
548C4×Q8—304no—
549C2×C4⋊C4—31no—
550C2×C4⋊C4—51no—
551C2×C4⋊C4—51no—
552C2×C4⋊C4—151no—
553C2×C4⋊C4—151no—
554C2×C4⋊C4—151no—
555C2×C22⋊C4—31no—
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—51no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4—151no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C22⋊C4—151no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4—151no—
566C2×C22⋊C4D3×D511yescharacteristic
567C2×C42—31no—
568C2×C42—151no—
569C2×C42—151no—
570C2×C42—151no—
571C2×C42—151no—
572C2×C42—151no—
573#95—51no—
574#95—51no—
575#95—151no—
576#95—151no—
577C2×C3×C5—42no—
578C2×C3×C5C22×C22⋊C411yescharacteristic
579C2×C3×C5C4×#4111yescharacteristic
580C2×C3×C5#52011yescharacteristic
581C2×C3×C5#54811yescharacteristic
582C2×C3×C5#54811yescharacteristic
583C2×C3×C5#55011yescharacteristic
584C2×C3×C5#55011yescharacteristic
585D15—42no—
586C5×D3—42no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3C2×C4×D512yes—
594C23×C3C23×D511yescharacteristic
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—52no—
602C22×D3—101no—
603C22×D3—101no—
604C22×D3—101no—
605C22×D3—101no—
606C22×D3—101no—
607C22×D3—101no—
608C22×D3C2×C4×D512yes—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—52no—
616C2×C3×C4—52no—
617C2×C3×C4—52no—
618C2×C3×C4—52no—
619C2×C3×C4—108no—
620C2×C3×C4—101no—
621C2×C3×C4—101no—
622C2×C3×C4—101no—
623C2×C3×C4—101no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—101no—
628#67—28no—
629#67—108no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—52no—
636C2×Dic3—52no—
637C2×Dic3—52no—
638C2×Dic3—52no—
639C2×Dic3—101no—
640C2×Dic3—101no—
641C2×Dic3—101no—
642C2×Dic3—101no—
643C2×Dic3—101no—
644C2×Dic3C2×C4×D512yes—
645C2×Dic3D4×D512yes—
646C2×Dic3D4×D512yes—
647C2×Dic3#71112yescomplemented
648D12—108no—
649C4×D3—108no—
650C4×D3—108no—
651Dic6—516no—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—41no—
656C22×C5—41no—
657C22×C5—41no—
658C22×C5—41no—
659C22×C5—62no—
660C22×C5—62no—
661C22×C5—62no—
662C22×C5—121no—
663C22×C5—121no—
664C22×C5—121no—
665C22×C5—121no—
666C22×C5C22×C4×D311yescharacteristic
667C22×C5C2×D3×D411yescharacteristic
668C22×C5C2×D3×D411yescharacteristic
669C22×C5#100411yescharacteristic
670C22×C5#100711yescharacteristic
671C22×C5D3×#4111yescharacteristic
672C22×C5D3×#4111yescharacteristic
673C2×D5—62no—
674C2×D5—62no—
675C2×D5—62no—
676C2×D5—121no—
677C2×D5—121no—
678C2×D5—121no—
679C2×D5—121no—
680C4×C5—34no—
681C4×C5—41no—
682C4×C5—41no—
683C4×C5—62no—
684C4×C5—121no—
685Dic5—22no—
686Dic5—34no—
687Dic5—41no—
688Dic5—41no—
689Dic5—62no—
690Dic5—121no—
691Dic5D3×C22⋊C414yes—
692C24—31no—
693C24—151no—
694C24C2×D3×D511yescharacteristic
695#41—3032no—
696C2×Q8—154no—
697C2×Q8—154no—
698C2×Q8—154no—
699C2×D4—34no—
700C2×D4—62no—
701C2×D4—62no—
702C2×D4—154no—
703C2×D4—154no—
704C2×D4—302no—
705C2×D4—302no—
706C2×D4—302no—
707C2×D4—302no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—51no—
712C22×C4—54no—
713C22×C4—51no—
714C22×C4—51no—
715C22×C4—51no—
716C22×C4—102no—
717C22×C4—102no—
718C22×C4—154no—
719C22×C4—154no—
720C22×C4—151no—
721C22×C4—151no—
722C22×C4—151no—
723C22×C4—302no—
724C22×C4—302no—
725C22×C4—302no—
726C22×C4—302no—
727C22×C4C2×D3×D511yescharacteristic
728C22×C4C2×D3×D511yescharacteristic
729C4⋊C4—62no—
730C4⋊C4—102no—
731C4⋊C4—102no—
732C4⋊C4—302no—
733C4⋊C4—302no—
734C4⋊C4—302no—
735C22⋊C4—41no—
736C22⋊C4—62no—
737C22⋊C4—62no—
738C22⋊C4—121no—
739C22⋊C4—201no—
740C22⋊C4—302no—
741C22⋊C4—302no—
742C22⋊C4—302no—
743C22⋊C4—302no—
744C22⋊C4—601no—
745C22⋊C4—601no—
746C22⋊C4—601no—
747C42—62no—
748C42—302no—
749C42—302no—
750C42—302no—
751C42—302no—
752C42—302no—
753C3×C5#234111yescharacteristic, complemented, Hall
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3C22×C4×D511yescharacteristic
762C22×C3C2×D4×D511yescharacteristic
763C22×C3C2×D4×D511yescharacteristic
764C22×C3C2×#71111yescharacteristic
765C22×C3#414411yescharacteristic
766C22×C3D5×#4111yescharacteristic
767C22×C3#415011yescharacteristic
768C2×D3—22no—
769C2×D3—22no—
770C2×D3—22no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—102no—
776C2×D3—102no—
777C2×D3—102no—
778C2×D3—201no—
779C2×D3—201no—
780C2×D3—201no—
781C2×D3—201no—
782C3×C4—41no—
783C3×C4—41no—
784C3×C4—54no—
785C3×C4—102no—
786C3×C4—201no—
787C3×C4—201no—
788Dic3—22no—
789Dic3—41no—
790Dic3—54no—
791Dic3—102no—
792Dic3—201no—
793Dic3D5×C22⋊C414yes—
794C2×C5—42no—
795C2×C5—122no—
796C2×C5C2×D3×C22⋊C411yescharacteristic
797C2×C5#550411yescharacteristic
798C2×C5#552211yescharacteristic
799C2×C5#559911yescharacteristic
800C2×C5#559911yescharacteristic
801C2×C5#563311yescharacteristic
802C2×C5#563311yescharacteristic
803D5—122no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—32no—
811C23—61no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—61no—
816C23—61no—
817C23—152no—
818C23—301no—
819C23—301no—
820C23—301no—
821C23—301no—
822C23—301no—
823C23—301no—
824C23C4×D3×D512yes—
825C23C22×D3×D511yescharacteristic
826Q8—1516no—
827D4—68no—
828D4—308no—
829D4—308no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—32no—
837C2×C4—32no—
838C2×C4—32no—
839C2×C4—32no—
840C2×C4—52no—
841C2×C4—52no—
842C2×C4—52no—
843C2×C4—52no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—108no—
850C2×C4—101no—
851C2×C4—101no—
852C2×C4—101no—
853C2×C4—101no—
854C2×C4—101no—
855C2×C4—101no—
856C2×C4—101no—
857C2×C4—101no—
858C2×C4—152no—
859C2×C4—152no—
860C2×C4—152no—
861C2×C4—152no—
862C2×C4—308no—
863C2×C4—308no—
864C2×C4—301no—
865C2×C4—301no—
866C2×C4—301no—
867C2×C4—301no—
868C2×C4—301no—
869C2×C3—42no—
870C2×C3C2×D5×C22⋊C411yescharacteristic
871C2×C3C4×#71111yescharacteristic
872C2×C3#6588011yescharacteristic
873C2×C3#6593211yescharacteristic
874C2×C3#6593311yescharacteristic
875C2×C3#6601111yescharacteristic
876C2×C3#6605211yescharacteristic
877D3—42no—
878D3—202no—
879C5#7387711yescharacteristic, complemented, Sylow
880C22—22no—
881C22—22no—
882C22—22no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—62no—
888C22—62no—
889C22—62no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—302no—
895C22—302no—
896C22—302no—
897C22—601no—
898C22—601no—
899C22—601no—
900C22—601no—
901C22#9200411yescharacteristic
902C22C2×C4×D3×D511yescharacteristic
903C22D3×D4×D511yescharacteristic
904C22D3×D4×D511yescharacteristic
905C22D3×#71111yescharacteristic
906C22#9202411yescharacteristic
907C22#9204911yescharacteristic
908C4—34no—
909C4—41no—
910C4—41no—
911C4—54no—
912C4—62no—
913C4—102no—
914C4—121no—
915C4—154no—
916C4—201no—
917C4—201no—
918C4—302no—
919C4—601no—
920C3#1060803211yescharacteristic, complemented, Sylow
921C2—42no—
922C2—122no—
923C2—602no—
924C2#1175282311yescharacteristic
925C2#1175286411yescharacteristic
926C2#1175286511yescharacteristic
927C2D3×D5×C22⋊C411yescharacteristic
928C2#1175429411yescharacteristic
929C2#1175492811yescharacteristic
930C2#1175500611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6782C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2341
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
2. C2×#91325C2semidirect
3. C2×#91324C2semidirect
4. #11751058C2semidirect
5. C5×#4957C2semidirect
6. C3×#65231C2semidirect
7. #11749483C2semidirect
8. #11749482C2semidirect
9. Dic5×#217C2semidirect
10. #11748909C2semidirect
11. #11748909C2semidirect
12. #11748887C2semidirect
13. #11748886C2semidirect
14. #11748882C2semidirect
15. #11748881C2semidirect
25. C2×#6782C4semidirect
69. #65231D3semidirect
144. #4957D5semidirect
227. C2×Dic15#41semidirect
237. C2×C5×Dic3#41semidirect
251. #1204C22⋊C4semidirect
647. C2×Dic3#711semidirect
753. C3×C5#2341semidirect
879. C5#73877semidirect
920. C3#10608032semidirect

Maximal subgroups

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

subgroupindex
C22×#67822
C2×#913252
C2×#913242
#117510582
C5×#49572
C3×#652312
#117494832
#117494822
Dic5×#2172
#117489092
#117488872
#117488862
#117488822
#117488812
#106080323
#738775