Finite Group Databasebeta

← #14326076

Subgroups — #14326076

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6772C211yesmaximal, characteristic
2C2×#91440C211yesmaximal, characteristic, complemented
3C2×C4×#1201C211yesmaximal, characteristic, complemented
4#11750747C211yesmaximal, characteristic, complemented
5C5×#4665C211yesmaximal, characteristic, complemented
6C3×D5×#95C211yesmaximal, characteristic, complemented
7#11748905C211yesmaximal, characteristic, complemented
8#11748905C211yesmaximal, characteristic, complemented
9#11748901C211yesmaximal, characteristic, complemented
10#11748887C211yesmaximal, characteristic, complemented
11#11748886C211yesmaximal, characteristic, complemented
12#11748880C211yesmaximal, characteristic, complemented
13D3×#3963C211yesmaximal, characteristic, complemented
14#11748737C211yesmaximal, characteristic, complemented
15#11748694C211yesmaximal, characteristic, complemented
16#10606403—31nomaximal, Hall
17C22×Dic30C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×#1201C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C22×D3×Dic5C2211yescharacteristic
28C2×#6772—24no—
29C2×#6772—24no—
30C2×#6772C418yescomplemented
31C2×#6712C2211yescharacteristic
32C2×C4×Dic15C2211yescharacteristic
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×#6669C2211yescharacteristic
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×Dic3×Dic5C2211yescharacteristic
43#91440—24no—
44C4×#1201—24no—
45C3×C5×#95C2211yescharacteristic
46#91115C2211yescharacteristic
47#91115C2211yescharacteristic
48#91115C2211yescharacteristic
49C5×C3⋊#95C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#73368—51nomaximal, Hall
58C22×#711—31no—
59C2×C4×C22⋊D5—31no—
60C2×#4027—31no—
61C5×#386—31no—
62#65509—31no—
63C2×#3963—31no—
64#65245—31no—
65#65245—31no—
66#65232—31no—
67#65231—31no—
68C22⋊C4×Dic5—31no—
69#64953—31no—
70D5×#95D311yescharacteristic, complemented
71#64935—31no—
72#64935—31no—
73C23×C5×D3C2311yescharacteristic
74C23×C5×D3C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15C2311yescharacteristic
80C22×Dic15C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C2×Dic30—22no—
84C2×Dic30—22no—
85C2×Dic30C2×C414yescomplemented
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C2×C5×D12—22no—
89C2×C5×D12—22no—
90C2×C5×D12C2×C414yescomplemented
91C2×C4×C5×D3—22no—
92C2×C4×C5×D3—22no—
93C2×C4×C5×D3—41no—
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5—22no—
102C2×C3×C4×D5—22no—
103C2×C3×C4×D5—41no—
104C2×C3×C4×D5—41no—
105C2×C3×C4×D5C2×C414yescomplemented
106C2×#1201—22no—
107C2×#1201—22no—
108C2×#1201C2×C414yes—
109C2×#1201C2×C414yescomplemented
110C2×#1201D414yes—
111C2×#1201D414yes—
112C2×D3×Dic5—22no—
113C2×D3×Dic5—22no—
114C2×D3×Dic5—22no—
115C2×D3×Dic5—22no—
116C2×D3×Dic5—22no—
117C2×D3×Dic5—22no—
118C2×D3×Dic5—41no—
119C2×D3×Dic5C2×C414yescomplemented
120C2×D3×Dic5C2×C414yescomplemented
121#6772—232no—
122#6712—22no—
123C4×Dic15—22no—
124C5×(C2×D3)⋊C4—22no—
125C5×(C2×D3)⋊C4—22no—
126C5×(C2×D3)⋊C4—41no—
127#6669—22no—
128(C2×D3)⋊Dic5—22no—
129(C2×D3)⋊Dic5—22no—
130(C2×D3)⋊Dic5—41no—
131#6665—22no—
132#6665—22no—
133Dic3×Dic5—22no—
134C22×#235—51no—
135C2×C4×#67—51no—
136C2×C4×#67—51no—
137C2×C3×#95—51no—
138#5213—51no—
139#5213—51no—
140#5211—51no—
141#4667—51no—
142#4666—51no—
143#4665—51no—
144#4665D511yescharacteristic, complemented
145#4664—51no—
146D3×#95—51no—
147#4646—51no—
148#4646—51no—
149C22×C5×D4—31no—
150C23×C4×C5—31no—
151C22×C22⋊D5—31no—
152C22×C22⋊D5—31no—
153C23×Dic5—31no—
154C23×Dic5—31no—
155C23×Dic5—31no—
156C2×#711—38no—
157C2×#711—64no—
158C2×#711—64no—
159C22×C4×D5C2×D311yescharacteristic
160C22×C4×D5C2×D311yescharacteristic
161C22×C4×D5C2×D311yescharacteristic
162C22×Dic10—31no—
163C2×C5×C22⋊C4—31no—
164C2×C5×C22⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C22⋊Dic5—31no—
167C2×C22⋊Dic5—31no—
168C2×C22⋊Dic5—31no—
169C4×C22⋊D5—64no—
170C2×#685—31no—
171C2×#685—31no—
172C2×#683—31no—
173C2×#683—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176#4027—64no—
177C5×#95—31no—
178C5×#95C2×D311yescharacteristic
179#3963—31no—
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963—31no—
186#3963C2×D311yescharacteristic
187#3963C2×D311yescharacteristic
188#3963C2×D311yescharacteristic
189#2339—151noSylow
190C23×C3×C5C2411yescharacteristic
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3—21no—
194C22×C5×D3—21no—
195C22×C5×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3—21no—
200C22×C5×D3—21no—
201C22×C5×D3C22×C412yes—
202C22×C5×D3C22×C412yes—
203C22×C5×D3C2×D412yes—
204C22×C5×D3C2×D412yes—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5C22×C412yes—
210C22×C3×D5C2×D412yes—
211C22×C3×D5C2×D412yes—
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—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5C22×C412yes—
220C2×C3×C4×C5#4112yescomplemented
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15C22×C412yes—
230C2×Dic15C22×C412yes—
231C2×Dic15C2×D412yes—
232C2×Dic15C2×D412yes—
233Dic30—28no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C5×D12—28no—
241C4×C5×D3—44no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5C22×C412yes—
250C2×C3×Dic5#4112yescomplemented
251C3×C4×D5—28no—
252C3×C4×D5—44no—
253C3×C4×D5—44no—
254#1201—28no—
255#1201C22⋊C4116yescomplemented
256D3×Dic5—28no—
257D3×Dic5—28no—
258D3×Dic5—44no—
259C23×C3×C4—51no—
260C23×C3×C4—51no—
261C23×C3×C4—51no—
262C22×#67—51no—
263C22×#67—51no—
264C2×#235—58no—
265C2×#235—104no—
266C2×#235—104no—
267C22×D12C2×D511yescharacteristic
268C22×C4×D3—51no—
269C22×C4×D3—51no—
270C22×C4×D3—51no—
271C22×C4×D3C2×D511yescharacteristic
272C22×Dic6—51no—
273C2×#217—51no—
274C2×#217—51no—
275C4×#67—104no—
276C4×#67—104no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4C2×D511yescharacteristic
281C2×(C2×D3)⋊C4C2×D511yescharacteristic
282C2×(C2×D3)⋊C4C2×D511yescharacteristic
283C2×Dic3⋊C4—51no—
284C2×Dic3⋊C4—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287C3×#95—51no—
288C3×#95—51no—
289C3×#95—51no—
290C3×#95C2×D511yescharacteristic
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95C2×D511yescharacteristic
299C24×C5—31no—
300C24×C5—31no—
301C23×D5C22×D311yescharacteristic
302C2×C5×D4—34no—
303C2×C5×D4—62no—
304C2×C5×D4—62no—
305C22×C4×C5—31no—
306C22×C4×C5—31no—
307C22×C4×C5—62no—
308C22×C4×C5—62no—
309C22×C4×C5—121no—
310C22×C4×C5C22×D311yescharacteristic
311C22×C4×C5C22×D311yescharacteristic
312C22×C4×C5C22×D311yescharacteristic
313C2×C22⋊D5—34no—
314C2×C22⋊D5—34no—
315C2×C22⋊D5—34no—
316C2×C22⋊D5—34no—
317C2×C22⋊D5—62no—
318C2×C22⋊D5—62no—
319C22×Dic5—31no—
320C22×Dic5—31no—
321C22×Dic5—34no—
322C22×Dic5—34no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—62no—
326C22×Dic5—62no—
327C22×Dic5—62no—
328C22×Dic5—62no—
329C22×Dic5—62no—
330C22×Dic5—62no—
331C22×Dic5—121no—
332C22×Dic5C22×D311yescharacteristic
333C22×Dic5C22×D311yescharacteristic
334C22×Dic5C22×D311yescharacteristic
335#711—632no—
336C2×C4×D5—22no—
337C2×C4×D5—22no—
338C2×C4×D5—22no—
339C2×C4×D5—22no—
340C2×C4×D5—22no—
341C2×C4×D5—22no—
342C2×C4×D5—41no—
343C2×C4×D5—41no—
344C2×C4×D5C4×D314yescomplemented
345C2×Dic10—34no—
346C2×Dic10—62no—
347C2×Dic10—62no—
348C5×C22⋊C4—62no—
349C5×C22⋊C4—62no—
350C5×C22⋊C4—121no—
351C22⋊Dic5—62no—
352C22⋊Dic5—62no—
353C22⋊Dic5—121no—
354#685—62no—
355#685—62no—
356#683—62no—
357#683—62no—
358C4×Dic5—62no—
359C4×Dic5—62no—
360C22×#41—151no—
361C2×C4×D4—151no—
362C2×C4×D4—151no—
363#391—151no—
364#391—151no—
365#386—31no—
366#386—151no—
367#386—151no—
368#386—151no—
369#381—151no—
370#381—151no—
371#380—151no—
372C4×C22⋊C4—151no—
373C2×#95—51no—
374C2×#95—151no—
375C22×C3×C5C23×C411yescharacteristic
376C22×C3×C5C22×D411yescharacteristic
377C22×C3×C5C22×D411yescharacteristic
378C22×C3×C5C2×#4111yescharacteristic
379C22×C3×C5C2×#4111yescharacteristic
380C22×C3×C5H(5,𝔽2)11yescharacteristic
381C22×C3×C52−1+411yescharacteristic
382C2×C5×D3—22no—
383C2×C5×D3—22no—
384C2×C5×D3—22no—
385C2×C5×D3—22no—
386C2×C5×D3—22no—
387C2×C5×D3—22no—
388C2×C5×D3—22no—
389C2×C5×D3—22no—
390C2×C5×D3—22no—
391C2×C5×D3—41no—
392C2×C5×D3—41no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3C2×C22⋊C414yes—
396C2×C3×D5—22no—
397C2×C3×D5—22no—
398C2×C3×D5—22no—
399C2×C3×D5—22no—
400C2×C3×D5—22no—
401C2×C3×D5—22no—
402C2×C3×D5C2×C22⋊C414yes—
403C3×C4×C5—22no—
404C3×C4×C5—22no—
405C3×C4×C5—41no—
406Dic15—22no—
407Dic15—41no—
408Dic15—41no—
409Dic15C2×C22⋊C414yes—
410C3×Dic5—22no—
411C3×Dic5—22no—
412C3×Dic5—41no—
413C5×Dic3—41no—
414C5×Dic3—41no—
415C24×C3—51no—
416C23×D3C22×D511yescharacteristic
417C23×D3C22×D511yescharacteristic
418C22×C3×C4—51no—
419C22×C3×C4—51no—
420C22×C3×C4—54no—
421C22×C3×C4—51no—
422C22×C3×C4—102no—
423C22×C3×C4—102no—
424C22×C3×C4—102no—
425C22×C3×C4—102no—
426C22×C3×C4—102no—
427C22×C3×C4—102no—
428C22×C3×C4—201no—
429C22×C3×C4—201no—
430C22×C3×C4C22×D511yescharacteristic
431C22×C3×C4C22×D511yescharacteristic
432C22×C3×C4C22×D511yescharacteristic
433C2×#67—54no—
434C2×#67—54no—
435C2×#67—54no—
436C2×#67—54no—
437C2×#67—102no—
438C2×#67—102no—
439C22×Dic3—51no—
440C22×Dic3—51no—
441C22×Dic3—51no—
442C22×Dic3—51no—
443C22×Dic3C22×D511yescharacteristic
444C22×Dic3C22×D511yescharacteristic
445#235—1032no—
446C2×D12—22no—
447C2×D12—22no—
448C2×D12C4×D514yescomplemented
449C2×C4×D3—22no—
450C2×C4×D3—22no—
451C2×C4×D3—41no—
452C2×C4×D3—54no—
453C2×C4×D3—54no—
454C2×C4×D3—102no—
455C2×C4×D3—102no—
456C2×C4×D3—102no—
457C2×C4×D3—102no—
458C2×C4×D3—102no—
459C2×C4×D3—102no—
460C2×C4×D3—201no—
461C2×Dic6—54no—
462C2×Dic6—102no—
463C2×Dic6—102no—
464#217—102no—
465#217—102no—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—22no—
468(C2×D3)⋊C4—41no—
469(C2×D3)⋊C4—102no—
470(C2×D3)⋊C4—102no—
471(C2×D3)⋊C4—201no—
472Dic3⋊C4—102no—
473Dic3⋊C4—102no—
474C4×Dic3—102no—
475C4×Dic3—102no—
476C23×C5—32no—
477C23×C5—32no—
478C23×C5—32no—
479C23×C5—32no—
480C23×C5—61no—
481C23×C5—61no—
482C23×C5—61no—
483C23×C5—61no—
484C23×C5—61no—
485C23×C5—61no—
486C23×C5—61no—
487C23×C5—61no—
488C23×C5—61no—
489C23×C5—61no—
490C23×C5C23×D311yescharacteristic
491C22×D5—21no—
492C22×D5—21no—
493C22×D5—21no—
494C22×D5—21no—
495C22×D5C2×C4×D312yes—
496C22×D5D3×D412yes—
497C22×D5D3×D412yes—
498C5×D4—68no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—61no—
507C2×C4×C5—61no—
508C2×C4×C5—61no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5—61no—
512C2×C4×C5—124no—
513C2×C4×C5C2×C4×D312yes—
514C2×C4×C5#23512yescomplemented
515C22⋊D5—316no—
516C22⋊D5—68no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—32no—
525C2×Dic5—32no—
526C2×Dic5—32no—
527C2×Dic5—32no—
528C2×Dic5—68no—
529C2×Dic5—68no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—61no—
538C2×Dic5—124no—
539C2×Dic5C2×C4×D312yes—
540C2×Dic5#23512yescomplemented
541C4×D5—28no—
542C4×D5—44no—
543C4×D5—44no—
544Dic10—68no—
545C2×#41—158no—
546C2×#41—304no—
547C2×#41—304no—
548C22×Q8—151no—
549C22×D4—31no—
550C22×D4—151no—
551C22×D4—151no—
552C23×C4—31no—
553C23×C4—51no—
554C23×C4—51no—
555C23×C4—51no—
556C23×C4—151no—
557C23×C4—151no—
558C23×C4—151no—
559C4×D4—304no—
560C4×D4—304no—
561C2×C4⋊C4—151no—
562C2×C4⋊C4—151no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4—151no—
571C2×C42—151no—
572C2×C42—151no—
573#95—31no—
574#95—51no—
575#95—51no—
576#95—51no—
577#95—151no—
578#95—151no—
579#95—151no—
580#95—151no—
581#95—151no—
582#95—151no—
583#95—151no—
584#95D3×D511yescharacteristic
585C2×C3×C5C22×C22⋊C411yescharacteristic
586C2×C3×C5C4×#4111yescharacteristic
587C2×C3×C5#52011yescharacteristic
588C2×C3×C5#54611yescharacteristic
589C2×C3×C5#54611yescharacteristic
590C2×C3×C5#54711yescharacteristic
591C2×C3×C5#54711yescharacteristic
592C3×D5—24no—
593C5×D3—24no—
594C5×D3—42no—
595C23×C3—52no—
596C23×C3—52no—
597C23×C3—52no—
598C23×C3—101no—
599C23×C3—101no—
600C23×C3—101no—
601C23×C3—101no—
602C23×C3C23×D511yescharacteristic
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3C2×C4×D512yes—
614C22×D3C2×C4×D512yes—
615C22×D3D4×D512yes—
616C22×D3D4×D512yes—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—52no—
625C2×C3×C4—52no—
626C2×C3×C4—108no—
627C2×C3×C4—101no—
628C2×C3×C4—101no—
629C2×C3×C4—101no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—204no—
635C2×C3×C4—204no—
636C2×C3×C4C2×C4×D512yes—
637C2×C3×C4#71112yescomplemented
638#67—516no—
639#67—108no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—52no—
647C2×Dic3—52no—
648C2×Dic3—52no—
649C2×Dic3—52no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658D12—28no—
659C4×D3—44no—
660C4×D3—108no—
661C4×D3—108no—
662C4×D3—204no—
663Dic6—108no—
664C22×C5—34no—
665C22×C5—62no—
666C22×C5—62no—
667C22×C5—62no—
668C22×C5—62no—
669C22×C5—62no—
670C22×C5—62no—
671C22×C5—62no—
672C22×C5—62no—
673C22×C5—62no—
674C22×C5—121no—
675C22×C5—121no—
676C22×C5—121no—
677C22×C5—121no—
678C22×C5C22×C4×D311yescharacteristic
679C22×C5C2×#23511yescharacteristic
680C22×C5C2×#23511yescharacteristic
681C22×C5C2×D3×D411yescharacteristic
682C22×C5C2×D3×D411yescharacteristic
683C22×C5#100411yescharacteristic
684C22×C5#100711yescharacteristic
685C2×D5—22no—
686C2×D5—22no—
687C2×D5—22no—
688C2×D5—22no—
689C2×D5—22no—
690C2×D5—22no—
691C2×D5D3×C22⋊C414yes—
692C4×C5—22no—
693C4×C5—22no—
694C4×C5—41no—
695C4×C5—121no—
696C4×C5—121no—
697Dic5—22no—
698Dic5—22no—
699Dic5—34no—
700Dic5—41no—
701Dic5—62no—
702Dic5—121no—
703Dic5—121no—
704C24—31no—
705C24—31no—
706C24—51no—
707#41—3032no—
708C2×Q8—154no—
709C2×Q8—302no—
710C2×Q8—302no—
711C2×D4—34no—
712C2×D4—62no—
713C2×D4—62no—
714C2×D4—154no—
715C2×D4—154no—
716C2×D4—154no—
717C2×D4—154no—
718C2×D4—302no—
719C2×D4—302no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—51no—
723C22×C4—51no—
724C22×C4—54no—
725C22×C4—51no—
726C22×C4—62no—
727C22×C4—62no—
728C22×C4—102no—
729C22×C4—102no—
730C22×C4—102no—
731C22×C4—102no—
732C22×C4—102no—
733C22×C4—102no—
734C22×C4—121no—
735C22×C4—154no—
736C22×C4—154no—
737C22×C4—151no—
738C22×C4—151no—
739C22×C4—151no—
740C22×C4—151no—
741C22×C4—201no—
742C22×C4—201no—
743C22×C4—302no—
744C22×C4—302no—
745C22×C4—302no—
746C22×C4—302no—
747C22×C4—302no—
748C22×C4—302no—
749C22×C4—601no—
750C22×C4C2×D3×D511yescharacteristic
751C22×C4C2×D3×D511yescharacteristic
752C22×C4C2×D3×D511yescharacteristic
753C4⋊C4—302no—
754C4⋊C4—302no—
755C22⋊C4—62no—
756C22⋊C4—62no—
757C22⋊C4—121no—
758C22⋊C4—302no—
759C22⋊C4—302no—
760C22⋊C4—302no—
761C22⋊C4—302no—
762C22⋊C4—601no—
763C42—302no—
764C42—302no—
765C3×C5#233911yescharacteristic, complemented, Hall
766C22×C3—54no—
767C22×C3—102no—
768C22×C3—102no—
769C22×C3—102no—
770C22×C3—102no—
771C22×C3—102no—
772C22×C3—102no—
773C22×C3C22×C4×D511yescharacteristic
774C22×C3C2×D4×D511yescharacteristic
775C22×C3C2×D4×D511yescharacteristic
776C22×C3C2×#71111yescharacteristic
777C22×C3#414411yescharacteristic
778C22×C3D5×#4111yescharacteristic
779C22×C3#415011yescharacteristic
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3D5×C22⋊C414yes—
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—41no—
797C3×C4—102no—
798C3×C4—102no—
799C3×C4—201no—
800Dic3—41no—
801Dic3—41no—
802Dic3—54no—
803Dic3—102no—
804Dic3—201no—
805Dic3—201no—
806C2×C5—64no—
807C2×C5—122no—
808C2×C5C4×#23511yescharacteristic
809C2×C5C2×D3×C22⋊C411yescharacteristic
810C2×C5#549011yescharacteristic
811C2×C5#549011yescharacteristic
812C2×C5#550411yescharacteristic
813C2×C5#550711yescharacteristic
814C2×C5#550711yescharacteristic
815D5—24no—
816C23—32no—
817C23—32no—
818C23—32no—
819C23—32no—
820C23—52no—
821C23—52no—
822C23—52no—
823C23—61no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—101no—
834C23—101no—
835C23—101no—
836C23—101no—
837C23C22×D3×D511yescharacteristic
838Q8—308no—
839D4—68no—
840D4—1516no—
841D4—308no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—52no—
850C2×C4—52no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—108no—
858C2×C4—101no—
859C2×C4—101no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—101no—
863C2×C4—101no—
864C2×C4—101no—
865C2×C4—124no—
866C2×C4—152no—
867C2×C4—152no—
868C2×C4—152no—
869C2×C4—152no—
870C2×C4—204no—
871C2×C4—204no—
872C2×C4—308no—
873C2×C4—308no—
874C2×C4—301no—
875C2×C4—301no—
876C2×C4—301no—
877C2×C4—301no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—301no—
881C2×C4—301no—
882C2×C4—604no—
883C2×C4#677212yescomplemented
884C2×C4C4×D3×D512yes—
885C2×C3—104no—
886C2×C3C2×D5×C22⋊C411yescharacteristic
887C2×C3C4×#71111yescharacteristic
888C2×C3#6588011yescharacteristic
889C2×C3#6592511yescharacteristic
890C2×C3#6594411yescharacteristic
891C2×C3#6594511yescharacteristic
892C2×C3#6598911yescharacteristic
893D3—24no—
894D3—42no—
895C5#7336811yescharacteristic, complemented, Sylow
896C22—34no—
897C22—54no—
898C22—62no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—62no—
904C22—62no—
905C22—62no—
906C22—62no—
907C22—102no—
908C22—102no—
909C22—102no—
910C22—102no—
911C22—102no—
912C22—102no—
913C22—121no—
914C22—121no—
915C22—121no—
916C22—121no—
917C22C2×#677211yescharacteristic
918C22C2×C4×D3×D511yescharacteristic
919C22D5×#23511yescharacteristic
920C22D3×D4×D511yescharacteristic
921C22D3×D4×D511yescharacteristic
922C22#9202511yescharacteristic
923C22#9203011yescharacteristic
924C4—22no—
925C4—22no—
926C4—41no—
927C4—102no—
928C4—102no—
929C4—121no—
930C4—121no—
931C4—154no—
932C4—201no—
933C4—302no—
934C4—601no—
935C4—601no—
936C3#1060640311yescharacteristic, complemented, Sylow
937C2—64no—
938C2—104no—
939C2—122no—
940C2C4×#677211yescharacteristic
941C2#1175306911yescharacteristic
942C2D3×D5×C22⋊C411yescharacteristic
943C2#1175322811yescharacteristic
944C2#1175367111yescharacteristic
945C2#1175367311yescharacteristic
946C2#1175367511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6772C2
hypercenter#95D3×D5
hypocenterC3×C5#2339
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#91440C2semidirect
3. C2×C4×#1201C2semidirect
4. #11750747C2semidirect
5. C5×#4665C2semidirect
6. C3×D5×#95C2semidirect
7. #11748905C2semidirect
8. #11748905C2semidirect
9. #11748901C2semidirect
10. #11748887C2semidirect
11. #11748886C2semidirect
12. #11748880C2semidirect
13. D3×#3963C2semidirect
14. #11748737C2semidirect
15. #11748694C2semidirect
30. C2×#6772C4semidirect
70. D5×#95D3semidirect
85. C2×Dic30C2×C4semidirect
90. C2×C5×D12C2×C4semidirect
105. C2×C3×C4×D5C2×C4semidirect
109. C2×#1201C2×C4semidirect
119. C2×D3×Dic5C2×C4semidirect
120. C2×D3×Dic5C2×C4semidirect
144. #4665D5semidirect
220. C2×C3×C4×C5#41semidirect
250. C2×C3×Dic5#41semidirect
255. #1201C22⋊C4semidirect
344. C2×C4×D5C4×D3semidirect
448. C2×D12C4×D5semidirect
514. C2×C4×C5#235semidirect
540. C2×Dic5#235semidirect
637. C2×C3×C4#711semidirect
765. C3×C5#2339semidirect
883. C2×C4#6772semidirect
895. C5#73368semidirect
936. C3#10606403semidirect

Maximal subgroups

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

subgroupindex
C22×#67722
C2×#914402
C2×C4×#12012
#117507472
C5×#46652
C3×D5×#952
#117489052
#117489012
#117488872
#117488862
#117488802
D3×#39632
#117487372
#117486942
#106064033
#733685