Finite Group Databasebeta

← #14330972

Subgroups — #14330972

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#930C211yesmaximal, characteristic
2#11752424C211yesmaximal, characteristic, complemented
3C3×#65764C211yesmaximal, characteristic, complemented
4#11752055C212yesmaximal, complemented
5#11752019C212yesmaximal, complemented
6#11751934C212yesmaximal, complemented
7#11751933C212yesmaximal, complemented
8#11751841C212yesmaximal, complemented
9#11751840C212yesmaximal, complemented
10#10617256—31nomaximal, Hall
11C22×D3×AGL(1,𝔽5)C2212yes—
12C22×C3×C4×D5C2211yescharacteristic
13C2×D5×#67C2212yes—
14C2×D5×D12C2211yescharacteristic
15C2×#6763C2211yescharacteristic
16C2×#6763C2211yescharacteristic
17C2×C4⋊ΓL(1,𝔽16)C2212yes—
18C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
19C2×Dic3⋊AGL(1,𝔽5)C2212yes—
20C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
21C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
22C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
23C2×Dic3×AGL(1,𝔽5)C2212yes—
24#91819C411yescharacteristic, complemented
25C5×#930C411yescharacteristic, complemented
26#91566C412yescomplemented
27D5×(C2×D3)⋊C4C2212yes—
28#91450C411yescharacteristic, complemented
29#91449C411yescharacteristic, complemented
30#91448C412yescomplemented
31D5×C4⋊Dic3C2211yescharacteristic
32#91235C2212yes—
33C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
34C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
35C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
36(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
37(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
38#74124—51nomaximal, Hall
39D5×#121—31no—
40#65780—32no—
41#65779—32no—
42#65779—32no—
43#65765—31no—
44#65764D311yescharacteristic, complemented
45#65711—32no—
46#65700—32no—
47#65699—32no—
48C23×C3×D5C2311yescharacteristic
49C22×D3×D5C2312yes—
50C22×ΓL(1,𝔽16)C2312yes—
51C22×ΓL(1,𝔽16)C2312yes—
52C22×C3×AGL(1,𝔽5)C2312yes—
53C22×C3×AGL(1,𝔽5)C2312yes—
54C2×D3×AGL(1,𝔽5)—42no—
55C2×D3×AGL(1,𝔽5)—42no—
56C2×D3×AGL(1,𝔽5)—42no—
57C22×C3×C4×C5C2×C411yescharacteristic, complemented
58C2×#1220C2×C412yescomplemented
59C2×D60C2×C411yescharacteristic
60C2×C5×#67C2×C412yescomplemented
61C2×C5×D12C2×C411yescharacteristic
62C22×C3×Dic5C2×C411yescharacteristic, complemented
63C2×C3×C4×D5—42no—
64C2×C3×C4×D5C2×C411yescharacteristic, complemented
65C2×C3×C4×D5C2×C411yescharacteristic, complemented
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×C4×D5C2311yescharacteristic
68D5×#67—42no—
69D5×#67—42no—
70C2×#1203C2×C412yes—
71C2×#1202C2×C412yescomplemented
72C2×#1201C2×C412yescomplemented
73C2×D5×Dic3C2312yes—
74D5×D12—42no—
75#6763—41no—
76#6763—41no—
77C4⋊ΓL(1,𝔽16)—42no—
78C3×C22⋊AGL(1,𝔽5)—42no—
79Dic3⋊AGL(1,𝔽5)—42no—
80(C2×D3)⋊AGL(1,𝔽5)—42no—
81(C2×D3)⋊AGL(1,𝔽5)—42no—
82(C2×D3)⋊AGL(1,𝔽5)—42no—
83Dic3×AGL(1,𝔽5)—42no—
84#6714C2×C412yescomplemented
85C4⋊Dic15C2×C411yescharacteristic, complemented
86C5×(C2×D3)⋊C4C2×C412yescomplemented
87C5×C4⋊Dic3C2×C411yescharacteristic, complemented
88#6668C2×C412yescomplemented
89#6667C2×C412yescomplemented
90(C2×D3)⋊Dic5C2×C412yescomplemented
91C2×#930—51no—
92C3×#381—51no—
93#5212—51no—
94#4957—52no—
95#4956—52no—
96#4670—52no—
97#4668—52no—
98#4665—52no—
99#4654—52no—
100C23×AGL(1,𝔽5)—32no—
101C2×D4×D5—32no—
102C2×D4×D5—31no—
103C22×C4×D5C2×D311yescharacteristic
104C2×C22⋊AGL(1,𝔽5)—31no—
105C2×C22⋊AGL(1,𝔽5)—31no—
106C2×C22⋊AGL(1,𝔽5)—32no—
107C2×C22⋊AGL(1,𝔽5)—32no—
108C2×C22⋊AGL(1,𝔽5)—32no—
109C2×C22⋊AGL(1,𝔽5)C2×D312yes—
110C2×C4⋊AGL(1,𝔽5)—32no—
111C2×C4⋊AGL(1,𝔽5)—32no—
112C2×C4×AGL(1,𝔽5)—32no—
113C5×#121—31no—
114#4085—32no—
115#4084—31no—
116#4076—31no—
117#4041—31no—
118D5×C4⋊C4—31no—
119#4030—32no—
120D5×C22⋊C4—32no—
121(C2×AGL(1,𝔽5))⋊C4—32no—
122(C2×AGL(1,𝔽5))⋊C4—32no—
123(C2×AGL(1,𝔽5))⋊C4—32no—
124(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
125(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
126(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
127#2377—151noSylow
128C23×C3×C5C22×C411yescharacteristic
129C22×D15C22×C412yes—
130C22×C5×D3C22×C412yes—
131C22×C3×D5—22no—
132C22×C3×D5—21no—
133C22×C3×D5—22no—
134C22×C3×D5—21no—
135C22×C3×D5C22×C411yescharacteristic
136C22×C3×D5C2411yescharacteristic
137C2×D3×D5—22no—
138C2×D3×D5—22no—
139C2×D3×D5—22no—
140C2×D3×D5—22no—
141C2×D3×D5—22no—
142C2×D3×D5—22no—
143C2×ΓL(1,𝔽16)—22no—
144C2×ΓL(1,𝔽16)—22no—
145C2×ΓL(1,𝔽16)—22no—
146C2×ΓL(1,𝔽16)—22no—
147C2×ΓL(1,𝔽16)—22no—
148C2×ΓL(1,𝔽16)—22no—
149C2×C3×AGL(1,𝔽5)—22no—
150C2×C3×AGL(1,𝔽5)—22no—
151C2×C3×AGL(1,𝔽5)—22no—
152C2×C3×AGL(1,𝔽5)—22no—
153C2×C3×AGL(1,𝔽5)—22no—
154C2×C3×AGL(1,𝔽5)—22no—
155D3×AGL(1,𝔽5)—48no—
156C2×C3×C4×C5—41no—
157C2×C3×C4×C5C22×C411yescharacteristic
158C2×C3×C4×C5C22×C411yescharacteristic
159#1220—42no—
160C2×Dic15C22×C412yes—
161D60—41no—
162C5×#67—42no—
163C2×C5×Dic3C22×C412yes—
164C5×D12—41no—
165C2×C3×Dic5—41no—
166C2×C3×Dic5C22×C411yescharacteristic
167C2×C3×Dic5C22×C411yescharacteristic
168C3×C4×D5—22no—
169C3×C4×D5—22no—
170C3×C4×D5—41no—
171C3×C4×D5—41no—
172#1203—42no—
173#1202—42no—
174#1201—42no—
175D5×Dic3—22no—
176D5×Dic3—22no—
177C23×C3×C4—51no—
178C22×#67—52no—
179C22×D12—51no—
180C22×C4×D3—52no—
181C2×C3×C22⋊C4—52no—
182C2×#217—51no—
183C2×#217—51no—
184#930—51no—
185#930—52no—
186#930—51no—
187#930—52no—
188#930—51no—
189#930AGL(1,𝔽5)11yescharacteristic, complemented
190C2×(C2×D3)⋊C4—52no—
191C2×(C2×D3)⋊C4—52no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4—52no—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—52no—
196C2×Dic3⋊C4—52no—
197C2×C4×Dic3—52no—
198C3×#95—52no—
199C3×#95—51no—
200C3×#95—51no—
201C3⋊#95—52no—
202C3⋊#95—52no—
203C3⋊#95—52no—
204C23×D5—32no—
205C23×D5C22×D311yescharacteristic
206C22×AGL(1,𝔽5)—32no—
207C22×AGL(1,𝔽5)—32no—
208C22×AGL(1,𝔽5)—122no—
209C22×AGL(1,𝔽5)—122no—
210C22×AGL(1,𝔽5)—122no—
211C22×AGL(1,𝔽5)C22×D312yes—
212C22×AGL(1,𝔽5)C22×D312yes—
213C2×C5×D4—32no—
214C2×C5×D4—31no—
215C22×C4×C5C4×D311yescharacteristic, complemented
216C2×C22⋊D5—32no—
217C2×C22⋊D5—32no—
218C2×C22⋊D5—32no—
219C22×Dic5C4×D311yescharacteristic, complemented
220D4×D5—122no—
221D4×D5—122no—
222D4×D5—122no—
223C2×D20—32no—
224C2×D20—31no—
225C2×C4×D5—32no—
226C2×C4×D5—42no—
227C2×C4×D5C4×D311yescharacteristic, complemented
228C2×C4×D5C4×D311yescharacteristic, complemented
229C2×C4×D5C22×D311yescharacteristic
230C2×C4×D5C22×D311yescharacteristic
231C22⋊AGL(1,𝔽5)—42no—
232C22⋊AGL(1,𝔽5)—122no—
233C22⋊AGL(1,𝔽5)—122no—
234C22⋊AGL(1,𝔽5)—122no—
235C22⋊AGL(1,𝔽5)—121no—
236C22⋊AGL(1,𝔽5)—121no—
237C4⋊AGL(1,𝔽5)—122no—
238C4⋊AGL(1,𝔽5)—122no—
239C4×AGL(1,𝔽5)—122no—
240C5×C4⋊C4—31no—
241C5×C22⋊C4—32no—
242C22⋊Dic5—32no—
243#685—32no—
244#685—32no—
245C4⋊Dic5—31no—
246#683—32no—
247C2×#121—151no—
248#390—152no—
249#388—152no—
250#387—152no—
251#386—152no—
252#386—152no—
253#385—152no—
254#381—51no—
255#380—151no—
256C22×C3×C5—21no—
257C22×C3×C5—21no—
258C22×C3×C5—21no—
259C22×C3×C5C23×C411yescharacteristic
260C2×D15—22no—
261C2×D15—22no—
262C2×D15—22no—
263C2×C5×D3—22no—
264C2×C5×D3—22no—
265C2×C5×D3—22no—
266C2×C3×D5—21no—
267C2×C3×D5—21no—
268C2×C3×D5—21no—
269C2×C3×D5—42no—
270C2×C3×D5—42no—
271C2×C3×D5H(5,𝔽2)12yes—
272C2×C3×D5H(5,𝔽2)11yescharacteristic
273C2×C3×D5H(5,𝔽2)12yes—
274C2×C3×D52−1+411yescharacteristic
275D3×D5—42no—
276D3×D5—42no—
277D3×D5—42no—
278D3×D5—42no—
279ΓL(1,𝔽16)—42no—
280ΓL(1,𝔽16)—42no—
281C3×AGL(1,𝔽5)—42no—
282C3×AGL(1,𝔽5)—42no—
283C3×C4×C5—21no—
284C3×C4×C5—21no—
285Dic15—22no—
286C3×Dic5—21no—
287C3×Dic5—21no—
288C5×Dic3—22no—
289C24×C3—51no—
290C23×D3—52no—
291C22×C3×C4—51no—
292C22×C3×C4—51no—
293C22×C3×C4—51no—
294C22×C3×C4—51no—
295C22×C3×C4—51no—
296C22×C3×C4—52no—
297C22×C3×C4—52no—
298C22×C3×C4—202no—
299C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
300C2×#67—52no—
301C2×#67—52no—
302C2×#67—52no—
303C2×#67—202no—
304C2×#67—202no—
305C2×#67C2×AGL(1,𝔽5)12yescomplemented
306C22×Dic3—52no—
307C22×Dic3—52no—
308C22×Dic3—52no—
309C2×D12—52no—
310C2×D12—51no—
311C2×D12—202no—
312C2×D12C2×AGL(1,𝔽5)11yescharacteristic
313C2×C4×D3—202no—
314C2×C4×D3—202no—
315C2×C4×D3—202no—
316C3×C22⋊C4—202no—
317#217—201no—
318#217—201no—
319(C2×D3)⋊C4—52no—
320(C2×D3)⋊C4—52no—
321(C2×D3)⋊C4—52no—
322(C2×D3)⋊C4—202no—
323(C2×D3)⋊C4—202no—
324(C2×D3)⋊C4—202no—
325(C2×D3)⋊C4C2×AGL(1,𝔽5)12yescomplemented
326C4⋊Dic3—51no—
327C4⋊Dic3—52no—
328C4⋊Dic3—202no—
329C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
330Dic3⋊C4—202no—
331C4×Dic3—202no—
332C23×C5—32no—
333C23×C5C2×C4×D311yescharacteristic
334C22×D5—22no—
335C22×D5—21no—
336C22×D5—22no—
337C22×D5—21no—
338C22×D5—32no—
339C22×D5—62no—
340C22×D5—62no—
341C22×D5—62no—
342C22×D5—62no—
343C22×D5—62no—
344C22×D5—62no—
345C22×D5C2×C4×D311yescharacteristic
346C22×D5C23×D311yescharacteristic
347C2×AGL(1,𝔽5)—22no—
348C2×AGL(1,𝔽5)—22no—
349C2×AGL(1,𝔽5)—22no—
350C2×AGL(1,𝔽5)—22no—
351C2×AGL(1,𝔽5)—22no—
352C2×AGL(1,𝔽5)—22no—
353C2×AGL(1,𝔽5)—62no—
354C2×AGL(1,𝔽5)—62no—
355C2×AGL(1,𝔽5)—62no—
356C2×AGL(1,𝔽5)—62no—
357C2×AGL(1,𝔽5)—62no—
358C2×AGL(1,𝔽5)—62no—
359C2×AGL(1,𝔽5)—128no—
360C5×D4—121no—
361C5×D4—122no—
362C2×C4×C5—32no—
363C2×C4×C5—41no—
364C2×C4×C5C2×C4×D311yescharacteristic
365C2×C4×C5C2×C4×D311yescharacteristic
366C22⋊D5—122no—
367C22⋊D5—122no—
368C22⋊D5—122no—
369C2×Dic5—32no—
370C2×Dic5—41no—
371C2×Dic5C2×C4×D311yescharacteristic
372C2×Dic5C2×C4×D311yescharacteristic
373D20—121no—
374D20—122no—
375C4×D5—22no—
376C4×D5—22no—
377C4×D5—41no—
378C4×D5—41no—
379C4×D5—62no—
380C4×D5—62no—
381C22×D4—151no—
382C22×D4—152no—
383C23×C4—51no—
384C23×C4—152no—
385#121—31no—
386#121—152no—
387#121—151no—
388#121—151no—
389#121—152no—
390#121—151no—
391C2×C4⋊C4—151no—
392C2×C4⋊C4—152no—
393C2×C4⋊C4—152no—
394C2×C22⋊C4—52no—
395C2×C22⋊C4—152no—
396C2×C22⋊C4—152no—
397C2×C22⋊C4—152no—
398C2×C22⋊C4—152no—
399C2×C22⋊C4—151no—
400C2×C22⋊C4—151no—
401C2×C42—152no—
402#95—51no—
403#95—52no—
404#95—51no—
405#95—152no—
406#95—152no—
407#95—152no—
408C2×C3×C5—41no—
409C2×C3×C5#51811yescharacteristic
410C2×C3×C5#51811yescharacteristic
411C2×C3×C5#52011yescharacteristic
412D15—42no—
413C3×D5—41no—
414C3×D5#56012yes—
415C3×D5#56212yes—
416C5×D3—42no—
417C23×C3—51no—
418C23×C3—51no—
419C23×C3—101no—
420C23×C3—102no—
421C23×C3—102no—
422C23×C3—101no—
423C23×C3C22×AGL(1,𝔽5)11yescharacteristic
424C22×D3—52no—
425C22×D3—102no—
426C22×D3—102no—
427C22×D3—102no—
428C22×D3—102no—
429C22×D3—102no—
430C22×D3—102no—
431C22×D3C22×AGL(1,𝔽5)12yes—
432C2×C3×C4—41no—
433C2×C3×C4—51no—
434C2×C3×C4—51no—
435C2×C3×C4—102no—
436C2×C3×C4—102no—
437C2×C3×C4—102no—
438C2×C3×C4—102no—
439C2×C3×C4—102no—
440C2×C3×C4—102no—
441C2×C3×C4—102no—
442C2×C3×C4—102no—
443C2×C3×C4—201no—
444C2×C3×C4—201no—
445C2×C3×C4—201no—
446C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
447C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
448#67—42no—
449#67—202no—
450#67—202no—
451#67—202no—
452C2×Dic3—52no—
453C2×Dic3—102no—
454C2×Dic3—102no—
455C2×Dic3—102no—
456C2×Dic3—102no—
457C2×Dic3—102no—
458C2×Dic3—102no—
459C2×Dic3—102no—
460C2×Dic3—102no—
461C2×Dic3C22×AGL(1,𝔽5)12yes—
462D12—41no—
463D12—201no—
464D12—202no—
465C4×D3—208no—
466C22×C5—21no—
467C22×C5—21no—
468C22×C5—21no—
469C22×C5—62no—
470C22×C5—62no—
471C22×C5—62no—
472C22×C5C22×C4×D311yescharacteristic
473C2×D5—21no—
474C2×D5—21no—
475C2×D5—21no—
476C2×D5—42no—
477C2×D5—42no—
478C2×D5—62no—
479C2×D5—62no—
480C2×D5—62no—
481C2×D5—122no—
482C2×D5—122no—
483C2×D5—122no—
484C2×D5—122no—
485C2×D5#100412yes—
486C2×D5#100911yescharacteristic
487C2×D5#100912yes—
488C2×D5#101011yescharacteristic
489AGL(1,𝔽5)—42no—
490AGL(1,𝔽5)—42no—
491AGL(1,𝔽5)—122no—
492AGL(1,𝔽5)—122no—
493C4×C5—21no—
494C4×C5—21no—
495C4×C5—62no—
496Dic5—21no—
497Dic5—21no—
498Dic5—62no—
499C24—51no—
500C24—152no—
501C2×D4—32no—
502C2×D4—31no—
503C2×D4—152no—
504C2×D4—152no—
505C2×D4—152no—
506C2×D4—152no—
507C2×D4—151no—
508C2×D4—602no—
509C2×D4—602no—
510C2×D4—602no—
511C22×C4—51no—
512C22×C4—51no—
513C22×C4—51no—
514C22×C4—51no—
515C22×C4—51no—
516C22×C4—52no—
517C22×C4—52no—
518C22×C4—152no—
519C22×C4—152no—
520C22×C4—152no—
521C22×C4—202no—
522C22×C4—602no—
523C22×C4—602no—
524C22×C4—602no—
525C22×C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
526C4⋊C4—31no—
527C4⋊C4—152no—
528C4⋊C4—151no—
529C4⋊C4—602no—
530C4⋊C4—602no—
531C22⋊C4—32no—
532C22⋊C4—152no—
533C22⋊C4—152no—
534C22⋊C4—152no—
535C22⋊C4—202no—
536C22⋊C4—602no—
537C22⋊C4—602no—
538C22⋊C4—602no—
539C22⋊C4—601no—
540C22⋊C4—601no—
541C42—602no—
542C3×C5#237711yescharacteristic, complemented, Hall
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—52no—
547C22×C3—52no—
548C22×C3—51no—
549C22×C3—51no—
550C22×C3—101no—
551C22×C3—101no—
552C22×C3—101no—
553C22×C3—202no—
554C22×C3—202no—
555C22×C3C23×AGL(1,𝔽5)11yescharacteristic
556C2×D3—22no—
557C2×D3—22no—
558C2×D3—22no—
559C2×D3—102no—
560C2×D3—102no—
561C2×D3—102no—
562C2×D3—202no—
563C2×D3—202no—
564C2×D3—202no—
565C2×D3—202no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—101no—
569C3×C4—101no—
570C3×C4—202no—
571C3×C4—202no—
572Dic3—22no—
573Dic3—102no—
574Dic3—202no—
575Dic3—202no—
576C2×C5—41no—
577C2×C5—122no—
578C2×C5#548611yescharacteristic
579C2×C5#552111yescharacteristic
580C2×C5#552311yescharacteristic
581D5—41no—
582D5—122no—
583D5#566612yes—
584D5#566712yes—
585C23—32no—
586C23—51no—
587C23—51no—
588C23—102no—
589C23—101no—
590C23—102no—
591C23—101no—
592C23—152no—
593C23—302no—
594C23—302no—
595C23—302no—
596C23—302no—
597C23—302no—
598C23—302no—
599C23C2×D3×AGL(1,𝔽5)11yescharacteristic
600D4—121no—
601D4—122no—
602D4—601no—
603D4—602no—
604D4—602no—
605D4—602no—
606D4—602no—
607C2×C4—32no—
608C2×C4—41no—
609C2×C4—51no—
610C2×C4—51no—
611C2×C4—102no—
612C2×C4—102no—
613C2×C4—102no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—102no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—152no—
620C2×C4—201no—
621C2×C4—201no—
622C2×C4—201no—
623C2×C4—302no—
624C2×C4—302no—
625C2×C4—302no—
626C2×C4—302no—
627C2×C4—302no—
628C2×C4—302no—
629C2×C4—302no—
630C2×C4—302no—
631C2×C4—608no—
632C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
633C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
634C2×C3—41no—
635C2×C3—52no—
636C2×C3—52no—
637C2×C3—201no—
638C2×C3#6625811yescharacteristic
639C2×C3#6625811yescharacteristic
640C2×C3#6626611yescharacteristic
641D3—42no—
642D3—202no—
643C5#7412411yescharacteristic, complemented, Sylow
644C22—21no—
645C22—21no—
646C22—21no—
647C22—52no—
648C22—51no—
649C22—51no—
650C22—52no—
651C22—62no—
652C22—62no—
653C22—62no—
654C22—101no—
655C22—101no—
656C22—101no—
657C22—202no—
658C22—202no—
659C22—302no—
660C22—302no—
661C22—302no—
662C22—602no—
663C22—602no—
664C22—602no—
665C22—602no—
666C22C22×D3×AGL(1,𝔽5)11yescharacteristic
667C4—21no—
668C4—21no—
669C4—62no—
670C4—101no—
671C4—101no—
672C4—202no—
673C4—202no—
674C4—302no—
675C4—602no—
676C4—602no—
677C3#1061725611yescharacteristic, complemented, Sylow
678C2—41no—
679C2—52no—
680C2—52no—
681C2—122no—
682C2—201no—
683C2—602no—
684C2#1175683711yescharacteristic
685C2#1175683811yescharacteristic
686C2#1175687111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalD5×#930C2
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2377
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752424C2semidirect
3. C3×#65764C2semidirect
4. #11752055C2semidirect
5. #11752019C2semidirect
6. #11751934C2semidirect
7. #11751933C2semidirect
8. #11751841C2semidirect
9. #11751840C2semidirect
24. #91819C4semidirect
25. C5×#930C4semidirect
26. #91566C4semidirect
28. #91450C4semidirect
29. #91449C4semidirect
30. #91448C4semidirect
44. #65764D3semidirect
57. C22×C3×C4×C5C2×C4semidirect
58. C2×#1220C2×C4semidirect
60. C2×C5×#67C2×C4semidirect
62. C22×C3×Dic5C2×C4semidirect
64. C2×C3×C4×D5C2×C4semidirect
65. C2×C3×C4×D5C2×C4semidirect
71. C2×#1202C2×C4semidirect
72. C2×#1201C2×C4semidirect
84. #6714C2×C4semidirect
85. C4⋊Dic15C2×C4semidirect
86. C5×(C2×D3)⋊C4C2×C4semidirect
87. C5×C4⋊Dic3C2×C4semidirect
88. #6668C2×C4semidirect
89. #6667C2×C4semidirect
90. (C2×D3)⋊Dic5C2×C4semidirect
189. #930AGL(1,𝔽5)semidirect
215. C22×C4×C5C4×D3semidirect
219. C22×Dic5C4×D3semidirect
227. C2×C4×D5C4×D3semidirect
228. C2×C4×D5C4×D3semidirect
299. C22×C3×C4C2×AGL(1,𝔽5)semidirect
305. C2×#67C2×AGL(1,𝔽5)semidirect
325. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
329. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
525. C22×C4D3×AGL(1,𝔽5)semidirect
542. C3×C5#2377semidirect
643. C5#74124semidirect
677. C3#10617256semidirect

Maximal subgroups

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

subgroupindex
D5×#9302
#117524242
C3×#657642
#117520552
#117520192
#117519342
#117519332
#117518412
#117518402
#106172563
#741245