Finite Group Databasebeta

← #14326765

Subgroups — #14326765

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×C4⋊C4C211yesmaximal, characteristic
2#11751081C211yesmaximal, characteristic, complemented
3C3×#65270C211yesmaximal, characteristic, complemented
4#11748786C211yesmaximal, characteristic
5#11748782C211yesmaximal, characteristic
6#11748782C211yesmaximal, characteristic
7#11748719C211yesmaximal, characteristic
8#11748719C211yesmaximal, characteristic
9C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic
10#11748693C211yesmaximal, characteristic, complemented
11#11748683C211yesmaximal, characteristic, complemented
12#11748682C211yesmaximal, characteristic, complemented
13#11748677C211yesmaximal, characteristic, complemented
14#11748651C211yesmaximal, characteristic, complemented
15Dic5×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#10613891—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C2×C5×Dic3⋊C4C2211yescharacteristic
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C5×D3×C4⋊C4C418yescomplemented
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×Dic3⋊Dic5C2211yescharacteristic
30C2×Dic3⋊Dic5C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×(C2×D3)⋊Dic5C2211yescharacteristic
34C2×(C2×D3)⋊Dic5C2211yescharacteristic
35C2×(C2×D3)⋊Dic5C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38C2×Dic3×Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#74962—51nomaximal, Hall
54C22×C5×C4⋊C4—31no—
55#65501—31no—
56#65501—31no—
57#65501—31no—
58C4×C22⋊Dic5—31no—
59C4×C22⋊Dic5—31no—
60C4×C22⋊Dic5—31no—
61#65274—31no—
62#65274—31no—
63#65270—31no—
64#65270—31no—
65#65270—31no—
66#65270D311yescharacteristic, complemented
67C4⋊C4×Dic5—31no—
68C4⋊C4×Dic5—31no—
69C23×C5×D3C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C2×C4×C5×D3—22no—
81C2×C4×C5×D3—22no—
82C2×C4×C5×D3—41no—
83C2×C4×C5×D3—41no—
84C2×C4×C5×D3—41no—
85C2×C4×C5×D3—41no—
86C2×C4×C5×D3C2×C414yes—
87C2×C4×C5×D3C2×C414yes—
88C2×C4×C5×D3C2×C414yes—
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C3×C5×C4⋊C4C2×C414yes—
94C4⋊Dic15—41no—
95C4×Dic15—41no—
96C5×C4⋊Dic3C2×C414yes—
97C5×Dic3⋊C4C2×C414yes—
98C5×Dic3⋊C4C2×C414yes—
99C3×C4⋊Dic5—41no—
100C3×C4×Dic5—41no—
101Dic3⋊Dic5—22no—
102Dic3⋊Dic5—22no—
103Dic3⋊Dic5—41no—
104Dic3⋊Dic5—41no—
105(C2×D3)⋊Dic5—22no—
106(C2×D3)⋊Dic5—22no—
107(C2×D3)⋊Dic5—22no—
108(C2×D3)⋊Dic5Q814yes—
109Dic3×Dic5—22no—
110Dic3×Dic5—22no—
111Dic3×Dic5—41no—
112Dic3×Dic5—41no—
113C2×D3×C4⋊C4D511yescharacteristic
114C3×#387—51no—
115#4987—51no—
116#4980—51no—
117#4976—51no—
118C4×(C2×D3)⋊C4—51no—
119C4×Dic3⋊C4—51no—
120#4667—51no—
121#4667—51no—
122#4666—51no—
123#4666—51no—
124#4654—51no—
125#4653—51no—
126#4649—51no—
127#4647—51no—
128C23×C4×C5—31no—
129C23×C4×C5—31no—
130C23×C4×C5—31no—
131C2×C5×C4⋊C4—31no—
132C2×C5×C4⋊C4—31no—
133C2×C5×C4⋊C4—31no—
134C2×C5×C4⋊C4—38no—
135C2×C5×C4⋊C4C2×D311yescharacteristic
136C2×C22⋊Dic5—31no—
137C2×C22⋊Dic5—31no—
138C2×C22⋊Dic5—31no—
139C2×C22⋊Dic5—31no—
140C2×C4⋊Dic5—31no—
141C2×C4⋊Dic5—31no—
142C2×C4⋊Dic5—31no—
143C2×C4⋊Dic5—31no—
144C2×C4⋊Dic5—31no—
145C2×C4⋊Dic5C2×D311yescharacteristic
146C2×C4×Dic5—31no—
147C2×C4×Dic5—31no—
148C2×C4×Dic5—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5C2×D311yescharacteristic
152#3963—31no—
153#3963—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#3963C2×D311yescharacteristic
161#3963C2×D311yescharacteristic
162#3963C2×D311yescharacteristic
163#3963C2×D311yescharacteristic
164#2345—151noSylow
165C23×C3×C5C2411yescharacteristic
166C22×C5×D3—21no—
167C22×C5×D3—21no—
168C22×C5×D3—21no—
169C22×C5×D3—21no—
170C22×C5×D3C22×C412yes—
171C22×C5×D3C2×Q812yes—
172C22×C5×D3#4112yes—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5C22×C412yes—
180C2×C3×C4×C5C22×C412yes—
181C2×C3×C4×C5C22×C412yes—
182C2×Dic15—21no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—21no—
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15C2×Q812yes—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3C22×C412yes—
199C2×C5×Dic3C22×C412yes—
200C2×C5×Dic3C22×C412yes—
201C2×C5×Dic3#4112yes—
202C2×C5×Dic3#4112yes—
203C4×C5×D3—28no—
204C4×C5×D3—44no—
205C4×C5×D3—44no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5C2×Q812yes—
218C22×C4×D3C2×D511yescharacteristic
219C22×C4×D3C2×D511yescharacteristic
220C22×C4×D3C2×D511yescharacteristic
221C2×C3×C4⋊C4—51no—
222C2×C3×C4⋊C4C2×D511yescharacteristic
223C2×C3×C42—51no—
224C2×(C2×D3)⋊C4—51no—
225C2×(C2×D3)⋊C4—51no—
226C2×(C2×D3)⋊C4—51no—
227C2×(C2×D3)⋊C4—51no—
228C2×C4⋊Dic3—51no—
229C2×C4⋊Dic3C2×D511yescharacteristic
230C2×Dic3⋊C4—51no—
231C2×Dic3⋊C4—51no—
232C2×Dic3⋊C4—51no—
233C2×Dic3⋊C4—51no—
234C2×Dic3⋊C4C2×D511yescharacteristic
235C2×Dic3⋊C4C2×D511yescharacteristic
236C2×C4×Dic3—51no—
237C2×C4×Dic3—51no—
238C2×C4×Dic3—51no—
239C2×C4×Dic3—51no—
240C2×C4×Dic3—51no—
241D3×C4⋊C4Dic518yescomplemented
242C3×#95—51no—
243C3×#95—51no—
244C3×#95—51no—
245C3×#95—51no—
246C3⋊#95—51no—
247C3⋊#95—51no—
248C3⋊#95—51no—
249C3⋊#95—51no—
250C3⋊#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C24×C5—31no—
255C22×C4×C5—31no—
256C22×C4×C5—31no—
257C22×C4×C5—31no—
258C22×C4×C5—34no—
259C22×C4×C5—34no—
260C22×C4×C5—34no—
261C22×C4×C5—62no—
262C22×C4×C5—62no—
263C22×C4×C5—121no—
264C22×C4×C5—121no—
265C22×C4×C5—121no—
266C22×C4×C5—121no—
267C22×C4×C5C22×D311yescharacteristic
268C22×C4×C5C22×D311yescharacteristic
269C22×C4×C5C22×D311yescharacteristic
270C22×Dic5—31no—
271C22×Dic5—31no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5C22×D311yescharacteristic
275C22×Dic5C22×D311yescharacteristic
276C22×Dic5C22×D311yescharacteristic
277C22×Dic5C22×D311yescharacteristic
278C5×C4⋊C4—34no—
279C5×C4⋊C4—34no—
280C5×C4⋊C4—34no—
281C5×C4⋊C4C4×D314yes—
282C22⋊Dic5—34no—
283C22⋊Dic5—62no—
284C22⋊Dic5—62no—
285C22⋊Dic5—62no—
286C4⋊Dic5—41no—
287C4⋊Dic5—62no—
288C4⋊Dic5—62no—
289C4⋊Dic5—121no—
290C4⋊Dic5—121no—
291C4⋊Dic5—121no—
292C4×Dic5—41no—
293C4×Dic5—62no—
294C4×Dic5—62no—
295C4×Dic5—121no—
296C4×Dic5—121no—
297C4×Dic5—121no—
298C22×C4⋊C4—31no—
299#389—151no—
300#389—151no—
301#387—51no—
302#387—151no—
303#387—151no—
304#387—151no—
305#380—151no—
306#380—151no—
307#380—151no—
308C4×C4⋊C4—151no—
309C4×C4⋊C4—151no—
310C4×C22⋊C4—151no—
311C4×C22⋊C4—151no—
312C4×C22⋊C4—151no—
313C22×C3×C5C23×C411yescharacteristic
314C22×C3×C5C22×Q811yescharacteristic
315C22×C3×C5C2×#4111yescharacteristic
316C22×C3×C5C2×#4111yescharacteristic
317C22×C3×C5C2×#4111yescharacteristic
318C22×C3×C5H(5,𝔽2)11yescharacteristic
319C22×C3×C5H(5,𝔽2)11yescharacteristic
320C2×C5×D3—22no—
321C2×C5×D3—22no—
322C2×C5×D3—22no—
323C2×C5×D3—22no—
324C2×C5×D3—22no—
325C2×C5×D3—22no—
326C2×C5×D3C4×Q814yes—
327C3×C4×C5—22no—
328C3×C4×C5—22no—
329C3×C4×C5—22no—
330Dic15—22no—
331Dic15—41no—
332Dic15—41no—
333Dic15—41no—
334C3×Dic5—22no—
335C3×Dic5—41no—
336C3×Dic5—41no—
337C3×Dic5—41no—
338C5×Dic3—22no—
339C5×Dic3—22no—
340C5×Dic3#11714yes—
341C23×D3C22×D511yescharacteristic
342C22×C3×C4—51no—
343C22×C3×C4—51no—
344C22×C3×C4—51no—
345C22×C3×C4—51no—
346C22×C3×C4C22×D511yescharacteristic
347C22×C3×C4C22×D511yescharacteristic
348C22×C3×C4C22×D511yescharacteristic
349C22×Dic3—51no—
350C22×Dic3—51no—
351C22×Dic3—51no—
352C22×Dic3—51no—
353C22×Dic3C22×D511yescharacteristic
354C22×Dic3C22×D511yescharacteristic
355C22×Dic3C22×D511yescharacteristic
356C2×C4×D3—22no—
357C2×C4×D3—22no—
358C2×C4×D3—41no—
359C2×C4×D3—41no—
360C2×C4×D3—41no—
361C2×C4×D3—41no—
362C2×C4×D3C2×Dic514yes—
363C2×C4×D3C2×Dic514yes—
364C2×C4×D3C2×Dic514yes—
365C3×C4⋊C4—201no—
366C3×C4⋊C4C2×Dic514yes—
367C3×C42—201no—
368(C2×D3)⋊C4—54no—
369(C2×D3)⋊C4—102no—
370(C2×D3)⋊C4—102no—
371(C2×D3)⋊C4—102no—
372C4⋊Dic3—201no—
373C4⋊Dic3C2×Dic514yes—
374Dic3⋊C4—102no—
375Dic3⋊C4—102no—
376Dic3⋊C4—201no—
377Dic3⋊C4—201no—
378Dic3⋊C4C2×Dic514yes—
379Dic3⋊C4C2×Dic514yes—
380C4×Dic3—102no—
381C4×Dic3—102no—
382C4×Dic3—201no—
383C4×Dic3—201no—
384C4×Dic3—201no—
385C23×C5—32no—
386C23×C5—32no—
387C23×C5—32no—
388C23×C5—61no—
389C23×C5—61no—
390C23×C5—61no—
391C23×C5—61no—
392C23×C5C23×D311yescharacteristic
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—32no—
400C2×C4×C5—32no—
401C2×C4×C5—32no—
402C2×C4×C5—32no—
403C2×C4×C5—32no—
404C2×C4×C5—68no—
405C2×C4×C5—61no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—61no—
409C2×C4×C5—124no—
410C2×C4×C5—124no—
411C2×C4×C5C2×C4×D312yes—
412C2×C4×C5C2×C4×D312yes—
413C2×C4×C5C2×C4×D312yes—
414C2×Dic5—21no—
415C2×Dic5—21no—
416C2×Dic5—21no—
417C2×Dic5—21no—
418C2×Dic5—21no—
419C2×Dic5—21no—
420C2×Dic5—21no—
421C2×Dic5—21no—
422C2×Dic5—21no—
423C2×Dic5—21no—
424C2×Dic5—21no—
425C2×Dic5—32no—
426C2×Dic5—61no—
427C2×Dic5—61no—
428C2×Dic5—61no—
429C2×Dic5—61no—
430C2×Dic5—61no—
431C2×Dic5—61no—
432C2×Dic5—61no—
433C2×Dic5—61no—
434C2×Dic5—61no—
435C2×Dic5—61no—
436C2×Dic5—61no—
437C2×Dic5D3×Q812yes—
438C23×C4—31no—
439C23×C4—31no—
440C23×C4—31no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—31no—
443C2×C4⋊C4—31no—
444C2×C4⋊C4—38no—
445C2×C4⋊C4—51no—
446C2×C4⋊C4—151no—
447C2×C4⋊C4—151no—
448C2×C4⋊C4—151no—
449C2×C4⋊C4—151no—
450C2×C4⋊C4—151no—
451C2×C4⋊C4D3×D511yescharacteristic
452C2×C22⋊C4—151no—
453C2×C22⋊C4—151no—
454C2×C22⋊C4—151no—
455C2×C22⋊C4—151no—
456C2×C42—51no—
457C2×C42—151no—
458C2×C42—151no—
459C2×C42—151no—
460C2×C42—151no—
461C2×C42—151no—
462#95—51no—
463#95—51no—
464#95—51no—
465#95—51no—
466#95—151no—
467#95—151no—
468#95—151no—
469#95—151no—
470#95—151no—
471#95—151no—
472#95—151no—
473#95—151no—
474C2×C3×C5C2×#11711yescharacteristic
475C2×C3×C5C2×C4×Q811yescharacteristic
476C2×C3×C5#51811yescharacteristic
477C2×C3×C5#55311yescharacteristic
478C2×C3×C5#55311yescharacteristic
479C2×C3×C5#55411yescharacteristic
480C2×C3×C5#55411yescharacteristic
481C5×D3—24no—
482C23×C3C23×D511yescharacteristic
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3Q8×D512yes—
488C22×D3#71312yes—
489C22×D3C22×Dic512yes—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—52no—
497C2×C3×C4—101no—
498C2×C3×C4—101no—
499C2×C3×C4—101no—
500C2×C3×C4—101no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4—101no—
504C2×C3×C4—101no—
505C2×C3×C4—101no—
506C2×C3×C4—101no—
507C2×C3×C4—101no—
508C2×C3×C4C22×Dic512yes—
509C2×C3×C4C22×Dic512yes—
510C2×C3×C4C22×Dic512yes—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—52no—
516C2×Dic3—101no—
517C2×Dic3—101no—
518C2×Dic3—101no—
519C2×Dic3—101no—
520C2×Dic3—101no—
521C2×Dic3—101no—
522C2×Dic3—101no—
523C2×Dic3—101no—
524C2×Dic3—101no—
525C2×Dic3—101no—
526C2×Dic3—101no—
527C2×Dic3#70912yes—
528C2×Dic3#70912yes—
529C2×Dic3C22×Dic512yes—
530C2×Dic3C22×Dic512yes—
531C2×Dic3C22×Dic512yes—
532C4×D3—28no—
533C4×D3—44no—
534C4×D3—44no—
535C22×C5—34no—
536C22×C5—62no—
537C22×C5—62no—
538C22×C5—62no—
539C22×C5—62no—
540C22×C5—62no—
541C22×C5—62no—
542C22×C5C22×C4×D311yescharacteristic
543C22×C5#100411yescharacteristic
544C22×C5C2×D3×Q811yescharacteristic
545C22×C5D3×#4111yescharacteristic
546C22×C5D3×#4111yescharacteristic
547C22×C5D3×#4111yescharacteristic
548C22×C5#100911yescharacteristic
549C4×C5—22no—
550C4×C5—22no—
551C4×C5—22no—
552C4×C5—34no—
553C4×C5—62no—
554C4×C5—62no—
555Dic5—22no—
556Dic5—41no—
557Dic5—41no—
558Dic5—41no—
559Dic5—62no—
560Dic5—121no—
561Dic5—121no—
562Dic5—121no—
563C24—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—34no—
568C22×C4—34no—
569C22×C4—34no—
570C22×C4—51no—
571C22×C4—51no—
572C22×C4—51no—
573C22×C4—51no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—121no—
577C22×C4—121no—
578C22×C4—121no—
579C22×C4—121no—
580C22×C4—151no—
581C22×C4—151no—
582C22×C4—151no—
583C22×C4—151no—
584C22×C4C2×D3×D511yescharacteristic
585C22×C4C2×D3×D511yescharacteristic
586C22×C4C2×D3×D511yescharacteristic
587C4⋊C4—34no—
588C4⋊C4—34no—
589C4⋊C4—34no—
590C4⋊C4—201no—
591C4⋊C4—302no—
592C4⋊C4—302no—
593C4⋊C4—601no—
594C4⋊C4—601no—
595C4⋊C4—601no—
596C4⋊C4D3×Dic514yes—
597C22⋊C4—154no—
598C22⋊C4—302no—
599C22⋊C4—302no—
600C22⋊C4—302no—
601C42—201no—
602C42—302no—
603C42—302no—
604C42—601no—
605C42—601no—
606C42—601no—
607C3×C5#234511yescharacteristic, complemented, Hall
608C22×C3C2×#70911yescharacteristic
609C22×C3C2×#70911yescharacteristic
610C22×C3#414411yescharacteristic
611C22×C3#414411yescharacteristic
612C22×C3C2×Q8×D511yescharacteristic
613C22×C3C2×#71311yescharacteristic
614C22×C3C23×Dic511yescharacteristic
615C2×D3—22no—
616C2×D3—22no—
617C2×D3—22no—
618C2×D3—22no—
619C2×D3—22no—
620C2×D3—22no—
621C2×D3Q8×Dic514yes—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—22no—
625C3×C4—102no—
626C3×C4—201no—
627C3×C4—201no—
628C3×C4—201no—
629Dic3—22no—
630Dic3—22no—
631Dic3—102no—
632Dic3—201no—
633Dic3—201no—
634Dic3—201no—
635Dic3#407214yes—
636C2×C5—64no—
637C2×C5D3×#11711yescharacteristic
638C2×C5#554511yescharacteristic
639C2×C5C4×D3×Q811yescharacteristic
640C2×C5#563611yescharacteristic
641C2×C5#566111yescharacteristic
642C2×C5#569011yescharacteristic
643C2×C5#570911yescharacteristic
644C23—32no—
645C23—32no—
646C23—32no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23C22×D3×D511yescharacteristic
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—32no—
659C2×C4—32no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—52no—
664C2×C4—68no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—101no—
670C2×C4—101no—
671C2×C4—101no—
672C2×C4—101no—
673C2×C4—101no—
674C2×C4—101no—
675C2×C4—101no—
676C2×C4—101no—
677C2×C4—101no—
678C2×C4—101no—
679C2×C4—101no—
680C2×C4—124no—
681C2×C4—124no—
682C2×C4—152no—
683C2×C4—301no—
684C2×C4—301no—
685C2×C4—301no—
686C2×C4—301no—
687C2×C4—301no—
688C2×C4—301no—
689C2×C4—301no—
690C2×C4—301no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—301no—
694C2×C4C2×D3×Dic512yes—
695C2×C4C2×D3×Dic512yes—
696C2×C4C2×D3×Dic512yes—
697C2×C3#6584511yescharacteristic
698C2×C3#6584511yescharacteristic
699C2×C3#6584811yescharacteristic
700C2×C3#6584811yescharacteristic
701C2×C3C2×#407211yescharacteristic
702C2×C3#6613211yescharacteristic
703C2×C3C2×Q8×Dic511yescharacteristic
704D3—24no—
705C5#7496211yescharacteristic, complemented, Sylow
706C22—34no—
707C22—62no—
708C22—62no—
709C22—62no—
710C22—62no—
711C22—62no—
712C22—62no—
713C22D3×#70911yescharacteristic
714C22D3×#70911yescharacteristic
715C22#9202511yescharacteristic
716C22#9202711yescharacteristic
717C22D3×Q8×D511yescharacteristic
718C22D3×#71311yescharacteristic
719C22C22×D3×Dic511yescharacteristic
720C4—22no—
721C4—22no—
722C4—22no—
723C4—34no—
724C4—62no—
725C4—62no—
726C4—102no—
727C4—201no—
728C4—201no—
729C4—201no—
730C4—302no—
731C4—601no—
732C4—601no—
733C4—601no—
734C3#1061389111yescharacteristic, complemented, Sylow
735C2—64no—
736C2#1175370911yescharacteristic
737C2#1175371811yescharacteristic
738C2#1175374711yescharacteristic
739C2#1175375911yescharacteristic
740C2D3×#407211yescharacteristic
741C2#1175491411yescharacteristic
742C2D3×Q8×Dic511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2345
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11751081C2semidirect
3. C3×#65270C2semidirect
10. #11748693C2semidirect
11. #11748683C2semidirect
12. #11748682C2semidirect
13. #11748677C2semidirect
14. #11748651C2semidirect
15. Dic5×Dic3⋊C4C2semidirect
26. C5×D3×C4⋊C4C4semidirect
66. #65270D3semidirect
241. D3×C4⋊C4Dic5semidirect
607. C3×C5#2345semidirect
705. C5#74962semidirect
734. C3#10613891semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×C4⋊C42
#117510812
C3×#652702
#117487862
#117487822
#117487192
C4×(C2×D3)⋊Dic52
#117486932
#117486832
#117486822
#117486772
#117486512
Dic5×Dic3⋊C42
#106138913
#749625