Finite Group Databasebeta

← #14326657

Subgroups — #14326657

Order 1920.

1208 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×C4⋊C4C211yesmaximal, characteristic
2C2×#91371C211yesmaximal, characteristic
3C2×#91338C211yesmaximal, characteristic
4#11751081C211yesmaximal, characteristic, complemented
5C3×#65270C211yesmaximal, characteristic, complemented
6#11748782C211yesmaximal, characteristic
7#11748777C211yesmaximal, characteristic
8#11748777C211yesmaximal, characteristic
9#11748719C211yesmaximal, 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#10613890—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#91371—24no—
42#91338—24no—
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74961—51nomaximal, Hall
56C22×C5×C4⋊C4—31no—
57C2×#4072—31no—
58C2×#4072—31no—
59#65501—31no—
60#65500—31no—
61#65500—31no—
62C4×C22⋊Dic5—31no—
63#65274—31no—
64#65274—31no—
65#65270—31no—
66#65270—31no—
67#65270—31no—
68#65270D311yescharacteristic, complemented
69C4⋊C4×Dic5—31no—
70C4⋊C4×Dic5—31no—
71C23×C5×D3C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×Dic15C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C22×C5×Dic3C2311yescharacteristic
82C2×C4×C5×D3—22no—
83C2×C4×C5×D3—22no—
84C2×C4×C5×D3—22no—
85C2×C4×C5×D3—22no—
86C2×C4×C5×D3—22no—
87C2×C4×C5×D3—22no—
88C2×C4×C5×D3C2×C414yes—
89C2×C4×C5×D3C2×C414yes—
90C2×C4×C5×D3C2×C414yes—
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C3×C5×C4⋊C4C2×C414yes—
96C4⋊Dic15—22no—
97C4×Dic15—22no—
98C5×C4⋊Dic3C2×C414yes—
99C5×Dic3⋊C4C2×C414yes—
100C5×Dic3⋊C4C2×C414yes—
101C3×C4⋊Dic5—22no—
102C3×C4×Dic5—22no—
103Dic3⋊Dic5—22no—
104Dic3⋊Dic5—22no—
105Dic3⋊Dic5—22no—
106Dic3⋊Dic5—22no—
107(C2×D3)⋊Dic5—22no—
108(C2×D3)⋊Dic5—22no—
109(C2×D3)⋊Dic5—22no—
110(C2×D3)⋊Dic5D414yes—
111Dic3×Dic5—22no—
112Dic3×Dic5—22no—
113Dic3×Dic5—22no—
114Dic3×Dic5—22no—
115C2×#892—51no—
116C2×D3×C4⋊C4D511yescharacteristic
117C2×#872—51no—
118C3×#387—51no—
119#4980—51no—
120#4976—51no—
121C4×Dic3⋊C4—51no—
122#4667—51no—
123#4666—51no—
124#4664—51no—
125#4664—51no—
126#4654—51no—
127#4653—51no—
128#4649—51no—
129#4647—51no—
130C23×C4×C5—31no—
131C23×C4×C5—31no—
132C23×C4×C5—31no—
133C2×C5×C4⋊C4—31no—
134C2×C5×C4⋊C4—31no—
135C2×C5×C4⋊C4—31no—
136C2×C5×C4⋊C4—38no—
137C2×C5×C4⋊C4C2×D311yescharacteristic
138C2×C22⋊Dic5—31no—
139C2×C22⋊Dic5—31no—
140C2×C22⋊Dic5—31no—
141C2×C22⋊Dic5—31no—
142#4072—64no—
143#4072—64no—
144C2×C4⋊Dic5—31no—
145C2×C4⋊Dic5—31no—
146C2×C4⋊Dic5—31no—
147C2×C4⋊Dic5—31no—
148C2×C4⋊Dic5—31no—
149C2×C4⋊Dic5C2×D311yescharacteristic
150C2×C4×Dic5—31no—
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—31no—
154C2×C4×Dic5—31no—
155C2×C4×Dic5C2×D311yescharacteristic
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963C2×D311yescharacteristic
165#3963C2×D311yescharacteristic
166#3963C2×D311yescharacteristic
167#3963C2×D311yescharacteristic
168#2344—151noSylow
169C23×C3×C5C2411yescharacteristic
170C22×C5×D3—21no—
171C22×C5×D3—21no—
172C22×C5×D3—21no—
173C22×C5×D3—21no—
174C22×C5×D3C22×C412yes—
175C22×C5×D3C2×D412yes—
176C22×C5×D3#4112yes—
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5C22×C412yes—
184C2×C3×C4×C5C22×C412yes—
185C2×C3×C4×C5C22×C412yes—
186C2×Dic15—21no—
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15C2×D412yes—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3C22×C412yes—
203C2×C5×Dic3C22×C412yes—
204C2×C5×Dic3C22×C412yes—
205C2×C5×Dic3#4112yes—
206C2×C5×Dic3#4112yes—
207C4×C5×D3—28no—
208C4×C5×D3—28no—
209C4×C5×D3—28no—
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×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5C2×D412yes—
222C22×C4×D3C2×D511yescharacteristic
223C22×C4×D3C2×D511yescharacteristic
224C22×C4×D3C2×D511yescharacteristic
225C2×C3×C4⋊C4—51no—
226C2×C3×C4⋊C4C2×D511yescharacteristic
227C2×C3×C42—51no—
228C2×(C2×D3)⋊C4—51no—
229C2×(C2×D3)⋊C4—51no—
230C2×(C2×D3)⋊C4—51no—
231C2×(C2×D3)⋊C4—51no—
232C2×C4⋊Dic3—51no—
233C2×C4⋊Dic3C2×D511yescharacteristic
234C2×Dic3⋊C4—51no—
235C2×Dic3⋊C4—51no—
236C2×Dic3⋊C4—51no—
237C2×Dic3⋊C4—51no—
238C2×Dic3⋊C4C2×D511yescharacteristic
239C2×Dic3⋊C4C2×D511yescharacteristic
240C2×C4×Dic3—51no—
241C2×C4×Dic3—51no—
242C2×C4×Dic3—51no—
243C2×C4×Dic3—51no—
244C2×C4×Dic3—51no—
245#892—104no—
246D3×C4⋊C4Dic518yescomplemented
247#872—104no—
248C3×#95—51no—
249C3×#95—51no—
250C3×#95—51no—
251C3×#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95—51no—
260C24×C5—31no—
261C22×C4×C5—31no—
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5—34no—
265C22×C4×C5—34no—
266C22×C4×C5—34no—
267C22×C4×C5—62no—
268C22×C4×C5—62no—
269C22×C4×C5—62no—
270C22×C4×C5—62no—
271C22×C4×C5—62no—
272C22×C4×C5—62no—
273C22×C4×C5C22×D311yescharacteristic
274C22×C4×C5C22×D311yescharacteristic
275C22×C4×C5C22×D311yescharacteristic
276C22×Dic5—31no—
277C22×Dic5—31no—
278C22×Dic5—31no—
279C22×Dic5—31no—
280C22×Dic5C22×D311yescharacteristic
281C22×Dic5C22×D311yescharacteristic
282C22×Dic5C22×D311yescharacteristic
283C22×Dic5C22×D311yescharacteristic
284C5×C4⋊C4—34no—
285C5×C4⋊C4—34no—
286C5×C4⋊C4—34no—
287C5×C4⋊C4C4×D314yes—
288C22⋊Dic5—34no—
289C22⋊Dic5—62no—
290C22⋊Dic5—62no—
291C22⋊Dic5—62no—
292C4⋊Dic5—22no—
293C4⋊Dic5—62no—
294C4⋊Dic5—62no—
295C4⋊Dic5—62no—
296C4⋊Dic5—62no—
297C4⋊Dic5—62no—
298C4×Dic5—22no—
299C4×Dic5—62no—
300C4×Dic5—62no—
301C4×Dic5—62no—
302C4×Dic5—62no—
303C4×Dic5—62no—
304C2×#117—151no—
305C2×#117—151no—
306C22×C4⋊C4—31no—
307#389—151no—
308#389—151no—
309#387—51no—
310#387—151no—
311#387—151no—
312#387—151no—
313#381—151no—
314#381—151no—
315#380—151no—
316C4×C4⋊C4—151no—
317C4×C4⋊C4—151no—
318C4×C22⋊C4—151no—
319C22×C3×C5C23×C411yescharacteristic
320C22×C3×C5C22×D411yescharacteristic
321C22×C3×C5C2×#4111yescharacteristic
322C22×C3×C5C2×#4111yescharacteristic
323C22×C3×C5C2×#4111yescharacteristic
324C22×C3×C52−1+411yescharacteristic
325C22×C3×C52−1+411yescharacteristic
326C2×C5×D3—22no—
327C2×C5×D3—22no—
328C2×C5×D3—22no—
329C2×C5×D3—22no—
330C2×C5×D3—22no—
331C2×C5×D3—22no—
332C2×C5×D3C4×D414yes—
333C3×C4×C5—22no—
334C3×C4×C5—22no—
335C3×C4×C5—22no—
336Dic15—22no—
337Dic15—41no—
338Dic15—41no—
339Dic15—41no—
340C3×Dic5—22no—
341C3×Dic5—41no—
342C3×Dic5—41no—
343C3×Dic5—41no—
344C5×Dic3—22no—
345C5×Dic3—22no—
346C5×Dic3#11714yescomplemented
347C23×D3C22×D511yescharacteristic
348C22×C3×C4—51no—
349C22×C3×C4—51no—
350C22×C3×C4—51no—
351C22×C3×C4—51no—
352C22×C3×C4C22×D511yescharacteristic
353C22×C3×C4C22×D511yescharacteristic
354C22×C3×C4C22×D511yescharacteristic
355C22×Dic3—51no—
356C22×Dic3—51no—
357C22×Dic3—51no—
358C22×Dic3—51no—
359C22×Dic3C22×D511yescharacteristic
360C22×Dic3C22×D511yescharacteristic
361C22×Dic3C22×D511yescharacteristic
362C2×C4×D3—22no—
363C2×C4×D3—22no—
364C2×C4×D3—22no—
365C2×C4×D3—22no—
366C2×C4×D3—22no—
367C2×C4×D3—22no—
368C2×C4×D3C2×Dic514yes—
369C2×C4×D3C2×Dic514yes—
370C2×C4×D3C2×Dic514yes—
371C3×C4⋊C4—102no—
372C3×C4⋊C4C2×Dic514yes—
373C3×C42—102no—
374(C2×D3)⋊C4—54no—
375(C2×D3)⋊C4—102no—
376(C2×D3)⋊C4—102no—
377(C2×D3)⋊C4—102no—
378C4⋊Dic3—102no—
379C4⋊Dic3C2×Dic514yes—
380Dic3⋊C4—102no—
381Dic3⋊C4—102no—
382Dic3⋊C4—102no—
383Dic3⋊C4—102no—
384Dic3⋊C4C2×Dic514yes—
385Dic3⋊C4C2×Dic514yes—
386C4×Dic3—102no—
387C4×Dic3—102no—
388C4×Dic3—102no—
389C4×Dic3—102no—
390C4×Dic3—102no—
391C23×C5—32no—
392C23×C5—32no—
393C23×C5—32no—
394C23×C5—61no—
395C23×C5—61no—
396C23×C5—61no—
397C23×C5—61no—
398C23×C5C23×D311yescharacteristic
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—32no—
406C2×C4×C5—32no—
407C2×C4×C5—32no—
408C2×C4×C5—32no—
409C2×C4×C5—32no—
410C2×C4×C5—68no—
411C2×C4×C5—68no—
412C2×C4×C5—68no—
413C2×C4×C5—61no—
414C2×C4×C5—61no—
415C2×C4×C5—61no—
416C2×C4×C5—61no—
417C2×C4×C5C2×C4×D312yes—
418C2×C4×C5C2×C4×D312yes—
419C2×C4×C5C2×C4×D312yes—
420C2×Dic5—21no—
421C2×Dic5—21no—
422C2×Dic5—21no—
423C2×Dic5—21no—
424C2×Dic5—21no—
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—21no—
428C2×Dic5—21no—
429C2×Dic5—21no—
430C2×Dic5—21no—
431C2×Dic5—32no—
432C2×Dic5—61no—
433C2×Dic5—61no—
434C2×Dic5—61no—
435C2×Dic5—61no—
436C2×Dic5—61no—
437C2×Dic5—61no—
438C2×Dic5—61no—
439C2×Dic5—61no—
440C2×Dic5—61no—
441C2×Dic5—61no—
442C2×Dic5—61no—
443C2×Dic5D3×D412yes—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—31no—
447#117—304no—
448#117—304no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—31no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—38no—
453C2×C4⋊C4—51no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—151no—
456C2×C4⋊C4—151no—
457C2×C4⋊C4—151no—
458C2×C4⋊C4—151no—
459C2×C4⋊C4D3×D511yescharacteristic
460C2×C22⋊C4—151no—
461C2×C22⋊C4—151no—
462C2×C22⋊C4—151no—
463C2×C22⋊C4—151no—
464C2×C42—51no—
465C2×C42—151no—
466C2×C42—151no—
467C2×C42—151no—
468C2×C42—151no—
469C2×C42—151no—
470#95—51no—
471#95—51no—
472#95—51no—
473#95—51no—
474#95—151no—
475#95—151no—
476#95—151no—
477#95—151no—
478#95—151no—
479#95—151no—
480#95—151no—
481#95—151no—
482C2×C3×C5C2×#11711yescharacteristic
483C2×C3×C5C2×C4×D411yescharacteristic
484C2×C3×C5#51911yescharacteristic
485C2×C3×C5#54711yescharacteristic
486C2×C3×C5#54711yescharacteristic
487C2×C3×C5#55211yescharacteristic
488C2×C3×C5#55211yescharacteristic
489C5×D3—24no—
490C23×C3C23×D511yescharacteristic
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3D4×D512yes—
496C22×D3#71112yes—
497C22×D3C22×Dic512yes—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—52no—
505C2×C3×C4—101no—
506C2×C3×C4—101no—
507C2×C3×C4—101no—
508C2×C3×C4—101no—
509C2×C3×C4—101no—
510C2×C3×C4—101no—
511C2×C3×C4—101no—
512C2×C3×C4—101no—
513C2×C3×C4—101no—
514C2×C3×C4—101no—
515C2×C3×C4—101no—
516C2×C3×C4C22×Dic512yes—
517C2×C3×C4C22×Dic512yes—
518C2×C3×C4C22×Dic512yes—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—52no—
524C2×Dic3—101no—
525C2×Dic3—101no—
526C2×Dic3—101no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3—101no—
531C2×Dic3—101no—
532C2×Dic3—101no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3#70912yes—
536C2×Dic3#70912yes—
537C2×Dic3C22×Dic512yes—
538C2×Dic3C22×Dic512yes—
539C2×Dic3C22×Dic512yes—
540C4×D3—28no—
541C4×D3—28no—
542C4×D3—28no—
543C22×C5—34no—
544C22×C5—62no—
545C22×C5—62no—
546C22×C5—62no—
547C22×C5—62no—
548C22×C5—62no—
549C22×C5—62no—
550C22×C5C22×C4×D311yescharacteristic
551C22×C5C2×D3×D411yescharacteristic
552C22×C5#100711yescharacteristic
553C22×C5D3×#4111yescharacteristic
554C22×C5D3×#4111yescharacteristic
555C22×C5D3×#4111yescharacteristic
556C22×C5#101011yescharacteristic
557C4×C5—22no—
558C4×C5—22no—
559C4×C5—22no—
560C4×C5—34no—
561C4×C5—62no—
562C4×C5—62no—
563Dic5—22no—
564Dic5—41no—
565Dic5—41no—
566Dic5—41no—
567Dic5—62no—
568Dic5—121no—
569Dic5—121no—
570Dic5—121no—
571C24—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—34no—
576C22×C4—34no—
577C22×C4—34no—
578C22×C4—51no—
579C22×C4—51no—
580C22×C4—51no—
581C22×C4—51no—
582C22×C4—62no—
583C22×C4—62no—
584C22×C4—62no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—151no—
589C22×C4—151no—
590C22×C4—151no—
591C22×C4—151no—
592C22×C4C2×D3×D511yescharacteristic
593C22×C4C2×D3×D511yescharacteristic
594C22×C4C2×D3×D511yescharacteristic
595C4⋊C4—34no—
596C4⋊C4—34no—
597C4⋊C4—34no—
598C4⋊C4—102no—
599C4⋊C4—302no—
600C4⋊C4—302no—
601C4⋊C4—302no—
602C4⋊C4—302no—
603C4⋊C4—302no—
604C4⋊C4D3×Dic514yes—
605C22⋊C4—154no—
606C22⋊C4—302no—
607C22⋊C4—302no—
608C22⋊C4—302no—
609C42—102no—
610C42—302no—
611C42—302no—
612C42—302no—
613C42—302no—
614C42—302no—
615C3×C5#234411yescharacteristic, complemented, Hall
616C22×C3C2×#70911yescharacteristic
617C22×C3C2×#70911yescharacteristic
618C22×C3C2×D4×D511yescharacteristic
619C22×C3C2×#71111yescharacteristic
620C22×C3#414711yescharacteristic
621C22×C3#414711yescharacteristic
622C22×C3C23×Dic511yescharacteristic
623C2×D3—22no—
624C2×D3—22no—
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—22no—
629C2×D3D4×Dic514yes—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—22no—
633C3×C4—102no—
634C3×C4—201no—
635C3×C4—201no—
636C3×C4—201no—
637Dic3—22no—
638Dic3—22no—
639Dic3—102no—
640Dic3—201no—
641Dic3—201no—
642Dic3—201no—
643Dic3#407214yescomplemented
644C2×C5—64no—
645C2×C5D3×#11711yescharacteristic
646C2×C5C4×D3×D411yescharacteristic
647C2×C5#557211yescharacteristic
648C2×C5#563111yescharacteristic
649C2×C5#565511yescharacteristic
650C2×C5#569311yescharacteristic
651C2×C5#570811yescharacteristic
652C23—32no—
653C23—32no—
654C23—32no—
655C23—61no—
656C23—61no—
657C23—61no—
658C23—61no—
659C23C22×D3×D511yescharacteristic
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—52no—
672C2×C4—68no—
673C2×C4—68no—
674C2×C4—68no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—101no—
680C2×C4—101no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—152no—
691C2×C4—301no—
692C2×C4—301no—
693C2×C4—301no—
694C2×C4—301no—
695C2×C4—301no—
696C2×C4—301no—
697C2×C4—301no—
698C2×C4—301no—
699C2×C4—301no—
700C2×C4—301no—
701C2×C4—301no—
702C2×C4C2×D3×Dic512yes—
703C2×C4C2×D3×Dic512yes—
704C2×C4C2×D3×Dic512yes—
705C2×C3#6584111yescharacteristic
706C2×C3#6584111yescharacteristic
707C2×C3#6584711yescharacteristic
708C2×C3#6584711yescharacteristic
709C2×C3C2×#407211yescharacteristic
710C2×C3C2×D4×Dic511yescharacteristic
711C2×C3#6614611yescharacteristic
712D3—24no—
713C5#7496111yescharacteristic, complemented, Sylow
714C22—34no—
715C22—62no—
716C22—62no—
717C22—62no—
718C22—62no—
719C22—62no—
720C22—62no—
721C22D3×#70911yescharacteristic
722C22D3×#70911yescharacteristic
723C22D3×D4×D511yescharacteristic
724C22D3×#71111yescharacteristic
725C22#9202811yescharacteristic
726C22#9202911yescharacteristic
727C22C22×D3×Dic511yescharacteristic
728C4—22no—
729C4—22no—
730C4—22no—
731C4—34no—
732C4—62no—
733C4—62no—
734C4—102no—
735C4—201no—
736C4—201no—
737C4—201no—
738C4—302no—
739C4—601no—
740C4—601no—
741C4—601no—
742C3#1061389011yescharacteristic, complemented, Sylow
743C2—64no—
744C2#1175335411yescharacteristic
745C2#1175367411yescharacteristic
746C2#1175368511yescharacteristic
747C2#1175374611yescharacteristic
748C2D3×#407211yescharacteristic
749C2D3×D4×Dic511yescharacteristic
750C2#1175514411yescharacteristic
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#2344
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
4. #11751081C2semidirect
5. C3×#65270C2semidirect
10. #11748693C2semidirect
11. #11748683C2semidirect
12. #11748682C2semidirect
13. #11748677C2semidirect
14. #11748651C2semidirect
15. Dic5×Dic3⋊C4C2semidirect
26. C5×D3×C4⋊C4C4semidirect
68. #65270D3semidirect
246. D3×C4⋊C4Dic5semidirect
346. C5×Dic3#117semidirect
615. C3×C5#2344semidirect
643. Dic3#4072semidirect
713. C5#74961semidirect
742. C3#10613890semidirect

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
C2×#913712
C2×#913382
#117510812
C3×#652702
#117487822
#117487772
#117487192
#117486932
#117486832
#117486822
#117486772
#117486512
Dic5×Dic3⋊C42
#106138903
#749615