Finite Group Databasebeta

← #14326028

Subgroups — #14326028

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×#6782C211yesmaximal, characteristic
2C2×C5×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×#67⋊Dic5C211yesmaximal, characteristic, complemented
4#11751059C211yesmaximal, characteristic, complemented
5C3×#65232C211yesmaximal, characteristic, complemented
6#11749498C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748934C211yesmaximal, characteristic, complemented
9#11748914C211yesmaximal, characteristic, complemented
10#11748883C211yesmaximal, characteristic, complemented
11#11748882C211yesmaximal, characteristic, complemented
12#11748881C211yesmaximal, characteristic, complemented
13#11748880C211yesmaximal, characteristic, complemented
14D3×#3963C211yesmaximal, characteristic, complemented
15#11748631C211yesmaximal, characteristic, complemented
16#10614061—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C5×#67C2211yescharacteristic
20C23×C5×Dic3C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C22×#1204C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1200C2211yescharacteristic
26C2×#6782—24no—
27C2×#6782—24no—
28C2×#6782C418yescomplemented
29C22×D3×Dic5C2211yescharacteristic
30C22×D3×Dic5C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×#6714C2211yescharacteristic
34C2×C5×(C2×D3)⋊C4C2211yescharacteristic
35C2×C5×Dic3⋊C4C2211yescharacteristic
36C2×C4×C5×Dic3C2211yescharacteristic
37C5×#67⋊C4—24no—
38C2×C3×C22⋊Dic5C2211yescharacteristic
39#67⋊Dic5—24no—
40C2×Dic3⋊Dic5C2211yescharacteristic
41C2×#6667C2211yescharacteristic
42C2×#6667C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#90994C2211yescharacteristic
56#90994C2211yescharacteristic
57#74121—51nomaximal, Hall
58C22×#711—31no—
59C2×C4×C5×D4—31no—
60C2×D4×Dic5—31no—
61#65502—31no—
62#65502—31no—
63C2×#3963—31no—
64C2×#3963—31no—
65#65276—31no—
66#65263—31no—
67#65247—31no—
68#65247—31no—
69#65232—31no—
70#65232D311yescharacteristic, complemented
71C4×#685—31no—
72#65218—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×C414yescomplemented
81C22×Dic15—22no—
82C22×Dic15—22no—
83C22×Dic15—41no—
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×Dic15C2311yescharacteristic
87C2×C5×#67C2×C414yes—
88C2×C5×#67D414yes—
89C2×C5×#67D414yes—
90C22×C5×Dic3—22no—
91C22×C5×Dic3—22no—
92C22×C5×Dic3—41no—
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C2×C4×C5×D3—22no—
97C2×C4×C5×D3—22no—
98C2×C4×C5×D3—41no—
99C22×C3×Dic5—22no—
100C22×C3×Dic5—22no—
101C22×C3×Dic5C2×C414yescomplemented
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C2×#1204—22no—
107C2×#1204—22no—
108C2×#1204C2×C414yescomplemented
109C2×#1203—22no—
110C2×#1203—22no—
111C2×#1203C2×C414yescomplemented
112C2×#1200—22no—
113C2×#1200—22no—
114C2×#1200C2×C414yescomplemented
115#6782—232no—
116C2×D3×Dic5—22no—
117C2×D3×Dic5—22no—
118C2×D3×Dic5—22no—
119C2×D3×Dic5—22no—
120C2×D3×Dic5—41no—
121C2×D3×Dic5C2×C414yescomplemented
122C3×C5×C22⋊C4—22no—
123#6714—22no—
124#6714—41no—
125C5×(C2×D3)⋊C4—22no—
126C5×Dic3⋊C4—22no—
127C4×C5×Dic3—22no—
128C3×C22⋊Dic5—22no—
129Dic3⋊Dic5—22no—
130#6667—22no—
131#6667—41no—
132(C2×D3)⋊Dic5—22no—
133Dic3×Dic5—22no—
134C22×#235—51no—
135C2×#67⋊C4—51no—
136C2×#67⋊C4D511yescharacteristic, complemented
137C3×#381—51no—
138C2×C3⋊#95—51no—
139#4958—51no—
140#4958—51no—
141#4667—51no—
142#4666—51no—
143#4665—51no—
144#4665—51no—
145#4664—51no—
146D3×#95—51no—
147#4646—51no—
148#4646—51no—
149C22×C5×D4—31no—
150C23×C4×C5—31no—
151C23×C4×C5—31no—
152C22×C22⋊D5—31no—
153C22×C22⋊D5—31no—
154C23×Dic5—31no—
155C23×Dic5—31no—
156C23×Dic5—31no—
157C23×Dic5C2×D311yescharacteristic
158C2×#711—38no—
159C2×#711—64no—
160C2×#711—64no—
161C22×C4×D5—31no—
162C22×Dic10—31no—
163C4×C5×D4—64no—
164C2×C5×C4⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4C2×D311yescharacteristic
167C2×C42×C5—31no—
168C2×C22⋊Dic5—31no—
169C2×C22⋊Dic5C2×D311yescharacteristic
170D4×Dic5—64no—
171C2×#685—31no—
172C2×#685—31no—
173C2×#685—31no—
174C2×#685—31no—
175C2×C4⋊Dic5—31no—
176C2×C4×Dic5—31no—
177#3963—31no—
178#3963—31no—
179#3963—31no—
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963—31no—
185#3963C2×D311yescharacteristic
186#3963C2×D311yescharacteristic
187#3963C2×D311yescharacteristic
188#3963C2×D311yescharacteristic
189#2339—151noSylow
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5C22×C412yes—
195C23×C3×C5C2×D412yes—
196C23×C3×C5C2×D412yes—
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×D3C22×C412yes—
210C22×C5×D3C2×D412yes—
211C22×C5×D3C2×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—
218#1220—28no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—44no—
227C2×Dic15C22×C412yes—
228C2×Dic15#4112yescomplemented
229C5×#67C22⋊C4116yescomplemented
230C2×C5×Dic3—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—44no—
236C2×C5×Dic3C22×C412yes—
237C2×C5×Dic3C2×D412yes—
238C2×C5×Dic3C2×D412yes—
239C2×C5×Dic3#4112yescomplemented
240C4×C5×D3—44no—
241C2×C3×Dic5—28no—
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×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5C22×C412yes—
253C2×C3×Dic5C22×C412yes—
254#1204—28no—
255#1203—28no—
256#1200—28no—
257D3×Dic5—28no—
258D3×Dic5—44no—
259C23×C3×C4—51no—
260C22×#67—51no—
261C22×#67C2×D511yescharacteristic
262C23×Dic3—51no—
263C23×Dic3C2×D511yescharacteristic
264C2×#235—58no—
265C2×#235—104no—
266C2×#235—104no—
267C22×D12—51no—
268C22×C4×D3—51no—
269C22×C4×D3—51no—
270C22×C4×D3—51no—
271C22×C4×D3C2×D511yescharacteristic
272C22×Dic6—51no—
273C2×C3×C22⋊C4—51no—
274C2×C3×C22⋊C4C2×D511yescharacteristic
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4C2×D511yescharacteristic
281C2×Dic3⋊C4—51no—
282C2×Dic3⋊C4C2×D511yescharacteristic
283C2×C4×Dic3—51no—
284C2×C4×Dic3C2×D511yescharacteristic
285#67⋊C4—24no—
286#67⋊C4—104no—
287C3×#95—51no—
288C3×#95—51no—
289C3×#95—51no—
290C3×#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95—51no—
296C3⋊#95—51no—
297C3⋊#95—51no—
298C3⋊#95—51no—
299C24×C5—31no—
300C24×C5C22×D311yescharacteristic
301C23×D5—31no—
302C2×C5×D4—34no—
303C2×C5×D4—34no—
304C2×C5×D4—34no—
305C22×C4×C5—31no—
306C22×C4×C5—31no—
307C22×C4×C5—31no—
308C22×C4×C5—62no—
309C22×C4×C5—62no—
310C22×C4×C5—62no—
311C22×C4×C5—62no—
312C22×C4×C5—121no—
313C22×C4×C5—121no—
314C22×C4×C5C22×D311yescharacteristic
315C22×C4×C5C22×D311yescharacteristic
316C2×C22⋊D5—34no—
317C2×C22⋊D5—34no—
318C2×C22⋊D5—62no—
319C2×C22⋊D5—62no—
320C2×C22⋊D5—62no—
321C2×C22⋊D5—62no—
322C22×Dic5—22no—
323C22×Dic5—22no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—34no—
327C22×Dic5—31no—
328C22×Dic5—62no—
329C22×Dic5—62no—
330C22×Dic5—62no—
331C22×Dic5—62no—
332C22×Dic5—62no—
333C22×Dic5—62no—
334C22×Dic5—121no—
335C22×Dic5—121no—
336C22×Dic5C4×D314yescomplemented
337C22×Dic5C22×D311yescharacteristic
338C22×Dic5C22×D311yescharacteristic
339C22×Dic5C22×D311yescharacteristic
340C22×Dic5C22×D311yescharacteristic
341#711—632no—
342C2×C4×D5—34no—
343C2×C4×D5—62no—
344C2×C4×D5—62no—
345C2×Dic10—34no—
346C2×Dic10—62no—
347C2×Dic10—62no—
348C5×C4⋊C4—62no—
349C5×C22⋊C4—22no—
350C5×C22⋊C4—62no—
351C42×C5—62no—
352C22⋊Dic5—22no—
353C22⋊Dic5—62no—
354#685—62no—
355#685—62no—
356#685—121no—
357#685—121no—
358C4⋊Dic5—62no—
359C4×Dic5—62no—
360C22×#41—151no—
361C2×C4×D4—31no—
362C2×C4×D4—151no—
363#391—151no—
364#391—151no—
365#386—151no—
366#386—151no—
367#386—151no—
368#386—151no—
369#381—51no—
370#381—151no—
371#380—151no—
372C4×C22⋊C4—151no—
373C2×#95—151no—
374C2×#95—151no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—22no—
380C22×C3×C5—22no—
381C22×C3×C5C2×C22⋊C414yes—
382C22×C3×C5C23×C411yescharacteristic
383C22×C3×C5C22×D411yescharacteristic
384C22×C3×C5C22×D411yescharacteristic
385C22×C3×C5C2×#4111yescharacteristic
386C22×C3×C5C2×#4111yescharacteristic
387C22×C3×C5H(5,𝔽2)11yescharacteristic
388C22×C3×C52−1+411yescharacteristic
389C2×D15—22no—
390C2×D15—22no—
391C2×D15—22no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—41no—
395C2×D15—41no—
396C2×C5×D3—22no—
397C2×C5×D3—22no—
398C2×C5×D3—22no—
399C2×C5×D3—22no—
400C2×C5×D3—22no—
401C2×C5×D3—22no—
402C2×C5×D3C2×C22⋊C414yes—
403C3×C4×C5—41no—
404C3×C4×C5—41no—
405Dic15—22no—
406Dic15—22no—
407Dic15—41no—
408C3×Dic5—22no—
409C3×Dic5—22no—
410C3×Dic5—41no—
411C3×Dic5—41no—
412C5×Dic3—22no—
413C5×Dic3—41no—
414C5×Dic3C2×C22⋊C414yes—
415C24×C3C22×D511yescharacteristic
416C23×D3—51no—
417C23×D3C22×D511yescharacteristic
418C22×C3×C4—54no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—51no—
422C22×C3×C4—51no—
423C22×C3×C4—102no—
424C22×C3×C4—102no—
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—54no—
428C2×#67—102no—
429C2×#67—102no—
430C2×#67C4×D514yes—
431C2×#67D2014yes—
432C2×#67C22⋊D514yes—
433C22×Dic3—22no—
434C22×Dic3—22no—
435C22×Dic3—41no—
436C22×Dic3—51no—
437C22×Dic3—51no—
438C22×Dic3—51no—
439C22×Dic3—102no—
440C22×Dic3—102no—
441C22×Dic3—201no—
442C22×Dic3C22×D511yescharacteristic
443C22×Dic3C22×D511yescharacteristic
444C22×Dic3C22×D511yescharacteristic
445#235—1032no—
446C2×D12—54no—
447C2×D12—102no—
448C2×D12—102no—
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—
464C3×C22⋊C4—22no—
465C3×C22⋊C4—102no—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—102no—
468(C2×D3)⋊C4—102no—
469(C2×D3)⋊C4—102no—
470(C2×D3)⋊C4—201no—
471(C2×D3)⋊C4—201no—
472Dic3⋊C4—22no—
473Dic3⋊C4—102no—
474C4×Dic3—22no—
475C4×Dic3—102no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—21no—
479C23×C5—21no—
480C23×C5—32no—
481C23×C5—32no—
482C23×C5—32no—
483C23×C5—61no—
484C23×C5—61no—
485C23×C5—61no—
486C23×C5—61no—
487C23×C5C2×C4×D312yes—
488C23×C5D3×D412yes—
489C23×C5D3×D412yes—
490C23×C5C23×D311yescharacteristic
491C22×D5—32no—
492C22×D5—61no—
493C22×D5—61no—
494C22×D5—61no—
495C22×D5—61no—
496C22×D5—61no—
497C22×D5—61no—
498C5×D4—316no—
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—32no—
506C2×C4×C5—32no—
507C2×C4×C5—32no—
508C2×C4×C5—32no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—124no—
515C2×C4×C5—124no—
516C22⋊D5—68no—
517C22⋊D5—68no—
518C2×Dic5—28no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—32no—
530C2×Dic5—32no—
531C2×Dic5—68no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—61no—
538C2×Dic5—61no—
539C2×Dic5—124no—
540C2×Dic5—124no—
541C2×Dic5C2×C4×D312yes—
542C2×Dic5C2×C4×D312yes—
543C4×D5—68no—
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—31no—
554C23×C4—51no—
555C23×C4—151no—
556C23×C4—151no—
557C23×C4—151no—
558C23×C4—151no—
559C4×D4—64no—
560C4×D4—304no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—151no—
563C2×C22⋊C4—31no—
564C2×C22⋊C4—51no—
565C2×C22⋊C4—151no—
566C2×C22⋊C4—151no—
567C2×C22⋊C4—151no—
568C2×C22⋊C4—151no—
569C2×C22⋊C4—151no—
570C2×C22⋊C4D3×D511yescharacteristic
571C2×C42—31no—
572C2×C42—151no—
573#95—51no—
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#95—151no—
585C2×C3×C5—24no—
586C2×C3×C5C22×C22⋊C411yescharacteristic
587C2×C3×C5C4×#4111yescharacteristic
588C2×C3×C5#52011yescharacteristic
589C2×C3×C5#54611yescharacteristic
590C2×C3×C5#54611yescharacteristic
591C2×C3×C5#54711yescharacteristic
592C2×C3×C5#54711yescharacteristic
593D15—42no—
594C5×D3—24no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3C2×C4×D512yes—
600C23×C3C2×D2012yes—
601C23×C3C2×C22⋊D512yes—
602C23×C3C23×D511yescharacteristic
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—52no—
608C22×D3—101no—
609C22×D3—101no—
610C22×D3—101no—
611C22×D3—101no—
612C22×D3—101no—
613C22×D3—101no—
614C22×D3C2×C4×D512yes—
615C22×D3C2×D2012yes—
616C22×D3C2×C22⋊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—52no—
624C2×C3×C4—52no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—101no—
628C2×C3×C4—101no—
629C2×C3×C4—108no—
630C2×C3×C4—101no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636#67—108no—
637#67#685116yescomplemented
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—44no—
644C2×Dic3—52no—
645C2×Dic3—52no—
646C2×Dic3—101no—
647C2×Dic3—101no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—204no—
654C2×Dic3C2×C4×D512yes—
655C2×Dic3C2×D2012yes—
656C2×Dic3#71112yescomplemented
657C2×Dic3C2×C22⋊D512yes—
658D12—108no—
659C4×D3—44no—
660C4×D3—108no—
661C4×D3—108no—
662C4×D3—204no—
663Dic6—108no—
664C22×C5—22no—
665C22×C5—22no—
666C22×C5—22no—
667C22×C5—22no—
668C22×C5—22no—
669C22×C5—22no—
670C22×C5—34no—
671C22×C5—62no—
672C22×C5—62no—
673C22×C5—62no—
674C22×C5—62no—
675C22×C5—62no—
676C22×C5—62no—
677C22×C5D3×C22⋊C414yes—
678C22×C5C22×C4×D311yescharacteristic
679C22×C5C2×D3×D411yescharacteristic
680C22×C5C2×D3×D411yescharacteristic
681C22×C5D3×#4111yescharacteristic
682C22×C5D3×#4111yescharacteristic
683C22×C5#100911yescharacteristic
684C22×C5#101011yescharacteristic
685C2×D5—62no—
686C2×D5—62no—
687C2×D5—62no—
688C2×D5—121no—
689C2×D5—121no—
690C2×D5—121no—
691C2×D5—121no—
692C4×C5—34no—
693C4×C5—41no—
694C4×C5—41no—
695C4×C5—62no—
696C4×C5—121no—
697Dic5—22no—
698Dic5—22no—
699Dic5—41no—
700Dic5—41no—
701Dic5—62no—
702Dic5—62no—
703Dic5—121no—
704C24—31no—
705C24—151no—
706C24C2×D3×D511yescharacteristic
707#41—3032no—
708C2×Q8—154no—
709C2×Q8—302no—
710C2×Q8—302no—
711C2×D4—34no—
712C2×D4—34no—
713C2×D4—34no—
714C2×D4—154no—
715C2×D4—154no—
716C2×D4—302no—
717C2×D4—302no—
718C2×D4—302no—
719C2×D4—302no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—54no—
724C22×C4—51no—
725C22×C4—51no—
726C22×C4—51no—
727C22×C4—51no—
728C22×C4—62no—
729C22×C4—62no—
730C22×C4—62no—
731C22×C4—62no—
732C22×C4—102no—
733C22×C4—102no—
734C22×C4—121no—
735C22×C4—121no—
736C22×C4—154no—
737C22×C4—154no—
738C22×C4—151no—
739C22×C4—151no—
740C22×C4—151no—
741C22×C4—302no—
742C22×C4—302no—
743C22×C4—302no—
744C22×C4—302no—
745C22×C4—302no—
746C22×C4—302no—
747C22×C4—302no—
748C22×C4—302no—
749C22×C4—601no—
750C22×C4—601no—
751C22×C4C2×D3×D511yescharacteristic
752C22×C4C2×D3×D511yescharacteristic
753C4⋊C4—62no—
754C4⋊C4—302no—
755C22⋊C4—22no—
756C22⋊C4—62no—
757C22⋊C4—102no—
758C22⋊C4—302no—
759C22⋊C4—302no—
760C22⋊C4—302no—
761C22⋊C4—601no—
762C22⋊C4—601no—
763C42—62no—
764C42—302no—
765C3×C5#233911yescharacteristic, complemented, Hall
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3C2×#68514yes—
773C22×C3C22×C4×D511yescharacteristic
774C22×C3C22×D2011yescharacteristic
775C22×C3C2×#71111yescharacteristic
776C22×C3#414411yescharacteristic
777C22×C3D5×#4111yescharacteristic
778C22×C3#415011yescharacteristic
779C22×C3C22×C22⋊D511yescharacteristic
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—102no—
787C2×D3—102no—
788C2×D3—102no—
789C2×D3—201no—
790C2×D3—201no—
791C2×D3—201no—
792C2×D3—201no—
793C2×D3C2×#68514yes—
794C3×C4—41no—
795C3×C4—41no—
796C3×C4—102no—
797C3×C4—102no—
798C3×C4—201no—
799C3×C4—201no—
800Dic3—22no—
801Dic3—41no—
802Dic3—102no—
803Dic3—102no—
804Dic3—201no—
805Dic3C2×#68514yes—
806C2×C5—24no—
807C2×C5—64no—
808C2×C5C2×D3×C22⋊C411yescharacteristic
809C2×C5#552211yescharacteristic
810C2×C5#552311yescharacteristic
811C2×C5#565411yescharacteristic
812C2×C5#565411yescharacteristic
813C2×C5#565511yescharacteristic
814C2×C5#565511yescharacteristic
815D5—122no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—32no—
821C23—32no—
822C23—32no—
823C23—61no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—152no—
828C23—301no—
829C23—301no—
830C23—301no—
831C23—301no—
832C23—301no—
833C23—301no—
834C23C4×D3×D512yes—
835C23D3×D2012yes—
836C23D3×C22⋊D512yes—
837C23C22×D3×D511yescharacteristic
838Q8—308no—
839D4—316no—
840D4—308no—
841D4—308no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—32no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—52no—
853C2×C4—52no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—108no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—101no—
863C2×C4—101no—
864C2×C4—101no—
865C2×C4—101no—
866C2×C4—101no—
867C2×C4—101no—
868C2×C4—101no—
869C2×C4—101no—
870C2×C4—124no—
871C2×C4—124no—
872C2×C4—152no—
873C2×C4—152no—
874C2×C4—308no—
875C2×C4—308no—
876C2×C4—301no—
877C2×C4—301no—
878C2×C4—301no—
879C2×C4—301no—
880C2×C4—301no—
881C2×C4—301no—
882C2×C4—301no—
883C2×C4—604no—
884C2×C4—604no—
885C2×C3—24no—
886C2×C3C4×#71111yescharacteristic
887C2×C3#6588011yescharacteristic
888C2×C3#6588811yescharacteristic
889C2×C3#6588911yescharacteristic
890C2×C3C22×#68511yescharacteristic
891C2×C3#6614011yescharacteristic
892C2×C3#6615811yescharacteristic
893D3—24no—
894D3—202no—
895C5#7412111yescharacteristic, complemented, Sylow
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—34no—
903C22—62no—
904C22—62no—
905C22—62no—
906C22—62no—
907C22—62no—
908C22—62no—
909C22—302no—
910C22—302no—
911C22—302no—
912C22—601no—
913C22—601no—
914C22—601no—
915C22—601no—
916C22D3×#68514yes—
917C22C2×C4×D3×D511yescharacteristic
918C22C2×D3×D2011yescharacteristic
919C22#9202011yescharacteristic
920C22D3×#71111yescharacteristic
921C22#9202411yescharacteristic
922C22#9202711yescharacteristic
923C22C2×D3×C22⋊D511yescharacteristic
924C4—34no—
925C4—41no—
926C4—41no—
927C4—62no—
928C4—102no—
929C4—102no—
930C4—121no—
931C4—201no—
932C4—201no—
933C4—302no—
934C4—302no—
935C4—601no—
936C3#1061406111yescharacteristic, complemented, Sylow
937C2—24no—
938C2—64no—
939C2—602no—
940C2#1175282311yescharacteristic
941C2#1175282411yescharacteristic
942C2#1175287911yescharacteristic
943C2#1175327111yescharacteristic
944C2C2×D3×#68511yescharacteristic
945C2#1175480911yescharacteristic
946C2#1175481011yescharacteristic
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#2339
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×C5×#67⋊C4C2semidirect
3. C2×#67⋊Dic5C2semidirect
4. #11751059C2semidirect
5. C3×#65232C2semidirect
6. #11749498C2semidirect
7. C2×#90994C2semidirect
8. #11748934C2semidirect
9. #11748914C2semidirect
10. #11748883C2semidirect
11. #11748882C2semidirect
12. #11748881C2semidirect
13. #11748880C2semidirect
14. D3×#3963C2semidirect
15. #11748631C2semidirect
28. C2×#6782C4semidirect
70. #65232D3semidirect
80. C2×#1220C2×C4semidirect
101. C22×C3×Dic5C2×C4semidirect
108. C2×#1204C2×C4semidirect
111. C2×#1203C2×C4semidirect
114. C2×#1200C2×C4semidirect
121. C2×D3×Dic5C2×C4semidirect
136. C2×#67⋊C4D5semidirect
228. C2×Dic15#41semidirect
229. C5×#67C22⋊C4semidirect
239. C2×C5×Dic3#41semidirect
336. C22×Dic5C4×D3semidirect
637. #67#685semidirect
656. C2×Dic3#711semidirect
765. C3×C5#2339semidirect
895. C5#74121semidirect
936. C3#10614061semidirect

Maximal subgroups

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

subgroupindex
C22×#67822
C2×C5×#67⋊C42
C2×#67⋊Dic52
#117510592
C3×#652322
#117494982
C2×#909942
#117489342
#117489142
#117488832
#117488822
#117488812
#117488802
D3×#39632
#117486312
#106140613
#741215