Finite Group Databasebeta

← #14330925

Subgroups — #14330925

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#895C211yesmaximal, characteristic
2#11751081C211yesmaximal, characteristic, complemented
3C3×#65270C211yesmaximal, characteristic, complemented
4#11748903C211yesmaximal, characteristic, complemented
5#11748901C211yesmaximal, characteristic, complemented
6#11748901C211yesmaximal, characteristic, complemented
7#11748901C211yesmaximal, characteristic, complemented
8#11748901C211yesmaximal, characteristic, complemented
9#11748897C211yesmaximal, characteristic, complemented
10#11748797C211yesmaximal, characteristic, complemented
11#11748794C211yesmaximal, characteristic, complemented
12#11748782C211yesmaximal, characteristic, complemented
13#11748777C211yesmaximal, characteristic, complemented
14#11748764C211yesmaximal, characteristic, complemented
15#11748747C211yesmaximal, characteristic, complemented
16#10614370—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic
22C22×D3×Dic5C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic
25C2×C4×Dic15C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C5×#895C418yescomplemented
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×Dic3⋊Dic5C2211yescharacteristic
32C2×Dic3⋊Dic5C2211yescharacteristic
33C2×(C2×D3)⋊Dic5C2211yescharacteristic
34C2×(C2×D3)⋊Dic5C2211yescharacteristic
35C2×(C2×D3)⋊Dic5C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2211yescharacteristic
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×(C2×D3)⋊Dic5C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45#91115C2211yescharacteristic
46#91115C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#75313—51nomaximal, Hall
54C2×C5×#121—31no—
55#65510—31no—
56#65510—31no—
57#65509—31no—
58#65509—31no—
59#65509—31no—
60#65509—31no—
61#65501—31no—
62#65500—31no—
63#65270—31no—
64#65270D311yescharacteristic, complemented
65#65240—31no—
66#65240—31no—
67#65239—31no—
68#65239—31no—
69C23×C5×D3C2311yescharacteristic
70C23×C5×D3C2311yescharacteristic
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
80C2×C5×D12—41no—
81C2×C5×D12—41no—
82C2×C5×D12—41no—
83C2×C5×D12—41no—
84C2×C5×D12—41no—
85C2×C5×D12—41no—
86C2×C5×D12C2×C414yes—
87C2×C5×D12C2×C414yescomplemented
88C2×C5×D12C2×C414yescomplemented
89C2×C4×C5×D3—41no—
90C2×C4×C5×D3—41no—
91C2×C4×C5×D3C2×C414yescomplemented
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C2×D3×Dic5—41no—
97C2×D3×Dic5—41no—
98C2×D3×Dic5—41no—
99C2×D3×Dic5—41no—
100C2×D3×Dic5—41no—
101C2×D3×Dic5—41no—
102C3×C5×C4⋊C4C2×C414yescomplemented
103C4⋊Dic15—41no—
104C4×Dic15—41no—
105C5×(C2×D3)⋊C4C2×C414yescomplemented
106C5×(C2×D3)⋊C4C2×C414yescomplemented
107C3×C4⋊Dic5—41no—
108C3×C4×Dic5—41no—
109Dic3⋊Dic5—41no—
110Dic3⋊Dic5—41no—
111(C2×D3)⋊Dic5—41no—
112(C2×D3)⋊Dic5—41no—
113(C2×D3)⋊Dic5—41no—
114(C2×D3)⋊Dic5—41no—
115(C2×D3)⋊Dic5—41no—
116(C2×D3)⋊Dic5—41no—
117(C2×D3)⋊Dic5—41no—
118(C2×D3)⋊Dic5—41no—
119(C2×D3)⋊Dic5—41no—
120(C2×D3)⋊Dic5—41no—
121C2×#895D511yescharacteristic
122C3×#387—51no—
123#4989—51no—
124#4988—51no—
125#4980—51no—
126#4940—51no—
127#4939—51no—
128#4669—51no—
129#4668—51no—
130#4667—51no—
131#4665—51no—
132#4665—51no—
133#4665—51no—
134#4665—51no—
135#4664—51no—
136C22×C5×D4—31no—
137C22×C5×D4—31no—
138C22×C5×D4—31no—
139C23×C4×C5—31no—
140C23×Dic5—31no—
141C23×Dic5—31no—
142C5×#121—38no—
143C2×C5×C4⋊C4C2×D311yescharacteristic
144C2×C5×C22⋊C4—31no—
145C2×C5×C22⋊C4—31no—
146C2×C22⋊Dic5—31no—
147C2×C22⋊Dic5—31no—
148C2×C22⋊Dic5—31no—
149C2×C22⋊Dic5—31no—
150C2×C22⋊Dic5—31no—
151C2×C22⋊Dic5—31no—
152C2×C22⋊Dic5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5—31no—
156C2×C4⋊Dic5—31no—
157C2×C4⋊Dic5—31no—
158C2×C4⋊Dic5—31no—
159C2×C4⋊Dic5C2×D311yescharacteristic
160C2×C4×Dic5—31no—
161C2×C4×Dic5C2×D311yescharacteristic
162#3963—31no—
163#3963—31no—
164#3963—31no—
165#3963—31no—
166#3963—31no—
167#3963—31no—
168#3963C2×D311yescharacteristic
169#3963C2×D311yescharacteristic
170#3963C2×D311yescharacteristic
171#3963C2×D311yescharacteristic
172#2377—151noSylow
173C23×C3×C5C2411yescharacteristic
174C22×C5×D3—21no—
175C22×C5×D3—21no—
176C22×C5×D3—21no—
177C22×C5×D3—21no—
178C22×C5×D3—21no—
179C22×C5×D3—21no—
180C22×C5×D3—21no—
181C22×C5×D3—21no—
182C22×C5×D3—21no—
183C22×C5×D3—21no—
184C22×C5×D3—21no—
185C22×C5×D3—21no—
186C22×C5×D3—21no—
187C22×C5×D3—21no—
188C22×C5×D3—21no—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3C22×C412yes—
193C22×C5×D3C22×C412yes—
194C22×C5×D3C22×C412yes—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C22×C412yes—
202C2×C3×C4×C5C22×C412yes—
203C2×C3×C4×C5C22×C412yes—
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—21no—
207C2×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C2×C5×Dic3C22×C412yes—
219C5×D12—44no—
220C5×D12—44no—
221C5×D12—44no—
222C4×C5×D3—44no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235D3×Dic5—44no—
236D3×Dic5—44no—
237C22×D12C2×D511yescharacteristic
238C22×D12C2×D511yescharacteristic
239C22×D12C2×D511yescharacteristic
240C22×C4×D3—51no—
241C22×C4×D3—51no—
242C22×C4×D3C2×D511yescharacteristic
243C2×C3×C4⋊C4—51no—
244C2×C3×C4⋊C4C2×D511yescharacteristic
245C2×C3×C42—51no—
246C2×(C2×D3)⋊C4—51no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4—51no—
249C2×(C2×D3)⋊C4—51no—
250C2×(C2×D3)⋊C4—51no—
251C2×(C2×D3)⋊C4—51no—
252C2×(C2×D3)⋊C4—51no—
253C2×(C2×D3)⋊C4—51no—
254C2×(C2×D3)⋊C4—51no—
255C2×(C2×D3)⋊C4—51no—
256C2×(C2×D3)⋊C4C2×D511yescharacteristic
257C2×(C2×D3)⋊C4C2×D511yescharacteristic
258C2×C4⋊Dic3—51no—
259C2×Dic3⋊C4—51no—
260C2×Dic3⋊C4—51no—
261C2×C4×Dic3—51no—
262#895Dic518yescomplemented
263C3×#95—51no—
264C3×#95—51no—
265C3×#95—51no—
266C3×#95—51no—
267C3⋊#95—51no—
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95—51no—
271C3⋊#95—51no—
272C3⋊#95—51no—
273C24×C5—31no—
274C24×C5—31no—
275C24×C5—31no—
276C2×C5×D4—34no—
277C2×C5×D4—34no—
278C2×C5×D4—34no—
279C2×C5×D4—121no—
280C2×C5×D4—121no—
281C2×C5×D4—121no—
282C2×C5×D4—121no—
283C2×C5×D4—121no—
284C2×C5×D4—121no—
285C22×C4×C5—31no—
286C22×C4×C5—34no—
287C22×C4×C5—121no—
288C22×C4×C5—121no—
289C22×C4×C5C22×D311yescharacteristic
290C22×C4×C5C22×D311yescharacteristic
291C22×C4×C5C22×D311yescharacteristic
292C22×Dic5—31no—
293C22×Dic5—31no—
294C22×Dic5—31no—
295C22×Dic5—31no—
296C22×Dic5—121no—
297C22×Dic5—121no—
298C22×Dic5—121no—
299C22×Dic5—121no—
300C22×Dic5—121no—
301C22×Dic5—121no—
302C22×Dic5C22×D311yescharacteristic
303C22×Dic5C22×D311yescharacteristic
304C22×Dic5C22×D311yescharacteristic
305C22×Dic5C22×D311yescharacteristic
306C5×C4⋊C4C4×D314yescomplemented
307C5×C22⋊C4—34no—
308C5×C22⋊C4—34no—
309C22⋊Dic5—121no—
310C22⋊Dic5—121no—
311C22⋊Dic5—121no—
312C22⋊Dic5—121no—
313C22⋊Dic5—121no—
314C22⋊Dic5—121no—
315C22⋊Dic5—121no—
316C22⋊Dic5—121no—
317C22⋊Dic5—121no—
318C22⋊Dic5—121no—
319C4⋊Dic5—41no—
320C4⋊Dic5—121no—
321C4⋊Dic5—121no—
322C4⋊Dic5—121no—
323C4×Dic5—41no—
324C4×Dic5—121no—
325C2×#121—31no—
326#390—151no—
327#390—151no—
328#388—151no—
329#388—151no—
330#387—51no—
331#387—151no—
332#386—151no—
333#386—151no—
334#386—151no—
335#386—151no—
336#385—151no—
337#385—151no—
338#381—151no—
339#380—151no—
340C22×C3×C5C23×C411yescharacteristic
341C22×C3×C5H(5,𝔽2)11yescharacteristic
342C22×C3×C5H(5,𝔽2)11yescharacteristic
343C22×C3×C5H(5,𝔽2)11yescharacteristic
344C22×C3×C5H(5,𝔽2)11yescharacteristic
345C22×C3×C5H(5,𝔽2)11yescharacteristic
346C22×C3×C52−1+411yescharacteristic
347C2×C5×D3—22no—
348C2×C5×D3—22no—
349C2×C5×D3—22no—
350C2×C5×D3—22no—
351C2×C5×D3—22no—
352C2×C5×D3—22no—
353C2×C5×D3—22no—
354C2×C5×D3—22no—
355C2×C5×D3—22no—
356C2×C5×D3—41no—
357C2×C5×D3—41no—
358C2×C5×D3—41no—
359C2×C5×D3—41no—
360C2×C5×D3—41no—
361C2×C5×D3—41no—
362C2×C5×D3—41no—
363C2×C5×D3—41no—
364C2×C5×D3—41no—
365C2×C5×D3—41no—
366C2×C5×D3—41no—
367C2×C5×D3—41no—
368C3×C4×C5—22no—
369C3×C4×C5—22no—
370C3×C4×C5—22no—
371Dic15—41no—
372Dic15—41no—
373Dic15—41no—
374Dic15—41no—
375C3×Dic5—41no—
376C3×Dic5—41no—
377C3×Dic5—41no—
378C3×Dic5—41no—
379C5×Dic3—22no—
380C23×D3C22×D511yescharacteristic
381C23×D3C22×D511yescharacteristic
382C23×D3C22×D511yescharacteristic
383C22×C3×C4—51no—
384C22×C3×C4—51no—
385C22×C3×C4—51no—
386C22×C3×C4—51no—
387C22×C3×C4C22×D511yescharacteristic
388C22×C3×C4C22×D511yescharacteristic
389C22×C3×C4C22×D511yescharacteristic
390C22×Dic3—51no—
391C22×Dic3—51no—
392C22×Dic3—51no—
393C22×Dic3—51no—
394C22×Dic3C22×D511yescharacteristic
395C2×D12—41no—
396C2×D12—41no—
397C2×D12—41no—
398C2×D12—41no—
399C2×D12—41no—
400C2×D12—41no—
401C2×D12C2×Dic514yes—
402C2×D12C2×Dic514yescomplemented
403C2×D12C2×Dic514yescomplemented
404C2×C4×D3—41no—
405C2×C4×D3—41no—
406C2×C4×D3—201no—
407C2×C4×D3—201no—
408C2×C4×D3—201no—
409C2×C4×D3—201no—
410C2×C4×D3—201no—
411C2×C4×D3—201no—
412C2×C4×D3C2×Dic514yescomplemented
413C3×C4⋊C4—201no—
414C3×C4⋊C4C2×Dic514yescomplemented
415C3×C42—201no—
416(C2×D3)⋊C4—201no—
417(C2×D3)⋊C4—201no—
418(C2×D3)⋊C4—201no—
419(C2×D3)⋊C4—201no—
420(C2×D3)⋊C4—201no—
421(C2×D3)⋊C4—201no—
422(C2×D3)⋊C4—201no—
423(C2×D3)⋊C4—201no—
424(C2×D3)⋊C4—201no—
425(C2×D3)⋊C4—201no—
426(C2×D3)⋊C4C2×Dic514yescomplemented
427(C2×D3)⋊C4C2×Dic514yescomplemented
428C4⋊Dic3—201no—
429Dic3⋊C4—201no—
430Dic3⋊C4—201no—
431C4×Dic3—201no—
432C23×C5—32no—
433C23×C5—32no—
434C23×C5—32no—
435C23×C5—61no—
436C23×C5—61no—
437C23×C5—61no—
438C23×C5—61no—
439C23×C5—61no—
440C23×C5—61no—
441C23×C5—61no—
442C23×C5—61no—
443C23×C5—61no—
444C23×C5—61no—
445C23×C5—61no—
446C23×C5—61no—
447C23×C5—61no—
448C23×C5—61no—
449C23×C5—61no—
450C23×C5—61no—
451C23×C5—61no—
452C23×C5—61no—
453C23×C5C23×D311yescharacteristic
454C5×D4—124no—
455C5×D4—124no—
456C5×D4—124no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5—21no—
460C2×C4×C5—21no—
461C2×C4×C5—21no—
462C2×C4×C5—21no—
463C2×C4×C5—32no—
464C2×C4×C5—61no—
465C2×C4×C5—61no—
466C2×C4×C5—124no—
467C2×C4×C5C2×C4×D312yes—
468C2×C4×C5C2×C4×D312yes—
469C2×C4×C5C2×C4×D312yes—
470C2×Dic5—21no—
471C2×Dic5—21no—
472C2×Dic5—21no—
473C2×Dic5—21no—
474C2×Dic5—21no—
475C2×Dic5—21no—
476C2×Dic5—21no—
477C2×Dic5—21no—
478C2×Dic5—21no—
479C2×Dic5—21no—
480C2×Dic5—21no—
481C2×Dic5—21no—
482C2×Dic5—61no—
483C2×Dic5—61no—
484C2×Dic5—61no—
485C2×Dic5—61no—
486C2×Dic5—61no—
487C2×Dic5—61no—
488C2×Dic5—61no—
489C2×Dic5—61no—
490C2×Dic5—61no—
491C2×Dic5—61no—
492C2×Dic5—61no—
493C2×Dic5—61no—
494C2×Dic5—124no—
495C2×Dic5—124no—
496C22×D4—31no—
497C22×D4—31no—
498C22×D4—31no—
499C23×C4—31no—
500C23×C4—151no—
501C23×C4—151no—
502#121—38no—
503C2×C4⋊C4—51no—
504C2×C4⋊C4—151no—
505C2×C4⋊C4—151no—
506C2×C4⋊C4—151no—
507C2×C4⋊C4D3×D511yescharacteristic
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—151no—
511C2×C22⋊C4—151no—
512C2×C22⋊C4—151no—
513C2×C22⋊C4—151no—
514C2×C22⋊C4—151no—
515C2×C22⋊C4—151no—
516C2×C22⋊C4—151no—
517C2×C22⋊C4—151no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—151no—
520C2×C42—51no—
521C2×C42—151no—
522#95—51no—
523#95—51no—
524#95—51no—
525#95—51no—
526#95—151no—
527#95—151no—
528#95—151no—
529#95—151no—
530#95—151no—
531#95—151no—
532C2×C3×C5#51811yescharacteristic
533C2×C3×C5#51811yescharacteristic
534C2×C3×C5#52011yescharacteristic
535C2×C3×C5#56011yescharacteristic
536C2×C3×C5#56011yescharacteristic
537C2×C3×C5#56211yescharacteristic
538C2×C3×C5#56211yescharacteristic
539C5×D3—42no—
540C5×D3—42no—
541C5×D3—42no—
542C23×C3C23×D511yescharacteristic
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3C22×Dic512yes—
562C22×D3C22×Dic512yes—
563C22×D3C22×Dic512yes—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—101no—
571C2×C3×C4—101no—
572C2×C3×C4—101no—
573C2×C3×C4—101no—
574C2×C3×C4—101no—
575C2×C3×C4—101no—
576C2×C3×C4—101no—
577C2×C3×C4—101no—
578C2×C3×C4—101no—
579C2×C3×C4—101no—
580C2×C3×C4—101no—
581C2×C3×C4—101no—
582C2×C3×C4C22×Dic512yes—
583C2×C3×C4C22×Dic512yes—
584C2×C3×C4C22×Dic512yes—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—101no—
588C2×Dic3—101no—
589C2×Dic3—101no—
590C2×Dic3—101no—
591C2×Dic3—101no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594C2×Dic3—101no—
595C2×Dic3—101no—
596C2×Dic3—101no—
597C2×Dic3—101no—
598C2×Dic3—101no—
599C2×Dic3C22×Dic512yes—
600D12—44no—
601D12—44no—
602D12—44no—
603C4×D3—44no—
604C4×D3—204no—
605C4×D3—204no—
606C22×C5—62no—
607C22×C5—62no—
608C22×C5—62no—
609C22×C5—62no—
610C22×C5—62no—
611C22×C5—62no—
612C22×C5—62no—
613C22×C5—62no—
614C22×C5—62no—
615C22×C5—121no—
616C22×C5—121no—
617C22×C5—121no—
618C22×C5—121no—
619C22×C5—121no—
620C22×C5—121no—
621C22×C5—121no—
622C22×C5—121no—
623C22×C5—121no—
624C22×C5—121no—
625C22×C5—121no—
626C22×C5—121no—
627C22×C5C22×C4×D311yescharacteristic
628C22×C5#100411yescharacteristic
629C22×C5#100711yescharacteristic
630C22×C5#100911yescharacteristic
631C22×C5#100911yescharacteristic
632C22×C5#100911yescharacteristic
633C22×C5#100911yescharacteristic
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—22no—
637C4×C5—62no—
638Dic5—41no—
639Dic5—41no—
640Dic5—41no—
641Dic5—41no—
642Dic5—121no—
643Dic5—121no—
644Dic5—121no—
645Dic5—121no—
646C24—31no—
647C24—31no—
648C24—31no—
649C2×D4—34no—
650C2×D4—34no—
651C2×D4—34no—
652C2×D4—121no—
653C2×D4—121no—
654C2×D4—121no—
655C2×D4—121no—
656C2×D4—121no—
657C2×D4—121no—
658C22×C4—31no—
659C22×C4—34no—
660C22×C4—51no—
661C22×C4—51no—
662C22×C4—51no—
663C22×C4—51no—
664C22×C4—121no—
665C22×C4—121no—
666C22×C4—151no—
667C22×C4—151no—
668C22×C4—151no—
669C22×C4—151no—
670C22×C4—601no—
671C22×C4—601no—
672C22×C4—601no—
673C22×C4—601no—
674C22×C4—601no—
675C22×C4—601no—
676C22×C4C2×D3×D511yescharacteristic
677C22×C4C2×D3×D511yescharacteristic
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—201no—
680C4⋊C4—601no—
681C4⋊C4—601no—
682C4⋊C4—601no—
683C4⋊C4D3×Dic514yescomplemented
684C22⋊C4—34no—
685C22⋊C4—34no—
686C22⋊C4—601no—
687C22⋊C4—601no—
688C22⋊C4—601no—
689C22⋊C4—601no—
690C22⋊C4—601no—
691C22⋊C4—601no—
692C22⋊C4—601no—
693C22⋊C4—601no—
694C22⋊C4—601no—
695C22⋊C4—601no—
696C42—201no—
697C42—601no—
698C3×C5#237711yescharacteristic, complemented, Hall
699C22×C3#414411yescharacteristic
700C22×C3#414411yescharacteristic
701C22×C3#414411yescharacteristic
702C22×C3#414411yescharacteristic
703C22×C3#414911yescharacteristic
704C22×C3#415011yescharacteristic
705C22×C3C23×Dic511yescharacteristic
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—41no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—201no—
731C3×C4—201no—
732C3×C4—201no—
733C3×C4—201no—
734Dic3—22no—
735Dic3—201no—
736Dic3—201no—
737Dic3—201no—
738Dic3—201no—
739C2×C5—122no—
740C2×C5—122no—
741C2×C5—122no—
742C2×C5#552111yescharacteristic
743C2×C5#554511yescharacteristic
744C2×C5#557411yescharacteristic
745C2×C5#564711yescharacteristic
746C2×C5#566611yescharacteristic
747C2×C5#570011yescharacteristic
748C2×C5#571111yescharacteristic
749C23—32no—
750C23—32no—
751C23—32no—
752C23—61no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23—61no—
763C23—61no—
764C23—61no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—61no—
770C23C22×D3×D511yescharacteristic
771D4—124no—
772D4—124no—
773D4—124no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—32no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—101no—
784C2×C4—101no—
785C2×C4—101no—
786C2×C4—101no—
787C2×C4—101no—
788C2×C4—101no—
789C2×C4—101no—
790C2×C4—101no—
791C2×C4—101no—
792C2×C4—101no—
793C2×C4—101no—
794C2×C4—101no—
795C2×C4—124no—
796C2×C4—301no—
797C2×C4—301no—
798C2×C4—301no—
799C2×C4—301no—
800C2×C4—301no—
801C2×C4—301no—
802C2×C4—301no—
803C2×C4—301no—
804C2×C4—301no—
805C2×C4—301no—
806C2×C4—301no—
807C2×C4—301no—
808C2×C4—604no—
809C2×C4—604no—
810C2×C4C2×D3×Dic512yes—
811C2×C4C2×D3×Dic512yes—
812C2×C4C2×D3×Dic512yes—
813C2×C3#6595411yescharacteristic
814C2×C3#6595411yescharacteristic
815C2×C3#6595511yescharacteristic
816C2×C3#6595511yescharacteristic
817C2×C3#6613211yescharacteristic
818C2×C3#6613211yescharacteristic
819C2×C3#6616111yescharacteristic
820D3—42no—
821D3—42no—
822D3—42no—
823C5#7531311yescharacteristic, complemented, Sylow
824C22—62no—
825C22—62no—
826C22—62no—
827C22—62no—
828C22—62no—
829C22—62no—
830C22—62no—
831C22—62no—
832C22—62no—
833C22—121no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22#9201811yescharacteristic
846C22#9201811yescharacteristic
847C22#9202511yescharacteristic
848C22#9202711yescharacteristic
849C22#9203011yescharacteristic
850C22#9203511yescharacteristic
851C22C22×D3×Dic511yescharacteristic
852C4—22no—
853C4—22no—
854C4—22no—
855C4—62no—
856C4—201no—
857C4—201no—
858C4—201no—
859C4—201no—
860C4—601no—
861C4—601no—
862C4—601no—
863C4—601no—
864C3#1061437011yescharacteristic, complemented, Sylow
865C2—122no—
866C2—122no—
867C2—122no—
868C2#1175365411yescharacteristic
869C2#1175381411yescharacteristic
870C2#1175394011yescharacteristic
871C2#1175394211yescharacteristic
872C2#1175450311yescharacteristic
873C2#1175491411yescharacteristic
874C2#1175522011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#895C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2377
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
4. #11748903C2semidirect
5. #11748901C2semidirect
6. #11748901C2semidirect
7. #11748901C2semidirect
8. #11748901C2semidirect
9. #11748897C2semidirect
10. #11748797C2semidirect
11. #11748794C2semidirect
12. #11748782C2semidirect
13. #11748777C2semidirect
14. #11748764C2semidirect
15. #11748747C2semidirect
28. C5×#895C4semidirect
64. #65270D3semidirect
87. C2×C5×D12C2×C4semidirect
88. C2×C5×D12C2×C4semidirect
91. C2×C4×C5×D3C2×C4semidirect
102. C3×C5×C4⋊C4C2×C4semidirect
105. C5×(C2×D3)⋊C4C2×C4semidirect
106. C5×(C2×D3)⋊C4C2×C4semidirect
262. #895Dic5semidirect
306. C5×C4⋊C4C4×D3semidirect
402. C2×D12C2×Dic5semidirect
403. C2×D12C2×Dic5semidirect
412. C2×C4×D3C2×Dic5semidirect
414. C3×C4⋊C4C2×Dic5semidirect
426. (C2×D3)⋊C4C2×Dic5semidirect
427. (C2×D3)⋊C4C2×Dic5semidirect
683. C4⋊C4D3×Dic5semidirect
698. C3×C5#2377semidirect
823. C5#75313semidirect
864. C3#10614370semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8952
#117510812
C3×#652702
#117489032
#117489012
#117488972
#117487972
#117487942
#117487822
#117487772
#117487642
#117487472
#106143703
#753135