Finite Group Databasebeta

← #14323236

Subgroups — #14323236

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#893C211yesmaximal, characteristic
2#11752371C211yesmaximal, characteristic, complemented
3C3×#65712C211yesmaximal, characteristic, complemented
4#11751857C211yesmaximal, characteristic
5#11751855C212yesmaximal, complemented
6#11751853C212yesmaximal, complemented
7#11751850C211yesmaximal, characteristic
8Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
9#11751841C212yesmaximal, complemented
10#11751836C212yesmaximal, complemented
11#11751748C211yesmaximal, characteristic, complemented
12#10617176—31nomaximal, Hall
13C2×D5×D12C2211yescharacteristic
14C2×C4×D3×D5C2212yes—
15C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
16C2×C4⋊ΓL(1,𝔽16)C2212yes—
17C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
18C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
19C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
20C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
21C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
22C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
23C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
24C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
25C2×Dic3×AGL(1,𝔽5)C2212yes—
26#91782C411yescharacteristic, complemented
27C5×#893C411yescharacteristic, complemented
28C3×D5×C4⋊C4C2211yescharacteristic
29D5×(C2×D3)⋊C4C2212yes—
30#91446C412yescomplemented
31#91435C411yescharacteristic, complemented
32#91428C411yescharacteristic, complemented
33#91406C412yescomplemented
34C4×D5×Dic3C2211yescharacteristic
35#91235C2212yes—
36C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
37(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
38(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
39(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
40(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42#75969—51nomaximal, Hall
43C4×D4×D5—31no—
44#65780—31no—
45#65780—31no—
46#65765—32no—
47#65764—32no—
48#65712—31no—
49#65712D311yescharacteristic, complemented
50#65700—32no—
51#65700—32no—
52C4×C4⋊AGL(1,𝔽5)—31no—
53#65686—31no—
54C22×D3×D5C2312yes—
55C22×ΓL(1,𝔽16)C2312yes—
56C22×ΓL(1,𝔽16)C2311yescharacteristic
57C22×ΓL(1,𝔽16)C2311yescharacteristic
58C22×C3×AGL(1,𝔽5)C2312yes—
59C22×C3×AGL(1,𝔽5)C2311yescharacteristic
60C22×C3×AGL(1,𝔽5)C2311yescharacteristic
61C2×D60C2×C411yescharacteristic
62C2×C4×D15C2×C412yes—
63C2×C5×D12C2×C411yescharacteristic
64C2×C4×C5×D3C2×C412yes—
65C2×C3×C4×D5C2312yes—
66C2×C3×C4×D5C2311yescharacteristic
67C2×#1203C2×C412yes—
68C2×#1200C2×C412yes—
69C2×D3×Dic5C2×C412yes—
70C2×D5×Dic3C2311yescharacteristic
71C2×D5×Dic3C2311yescharacteristic
72D5×D12—22no—
73D5×D12—22no—
74C4×D3×D5—42no—
75C4×D3×D5—42no—
76C4⋊ΓL(1,𝔽16)—22no—
77C4⋊ΓL(1,𝔽16)—42no—
78C4×ΓL(1,𝔽16)—22no—
79C3×C4⋊AGL(1,𝔽5)—22no—
80C3×C4⋊AGL(1,𝔽5)—42no—
81C3×C4×AGL(1,𝔽5)—22no—
82(C2×D3)⋊AGL(1,𝔽5)—42no—
83(C2×D3)⋊AGL(1,𝔽5)—42no—
84(C2×D3)⋊AGL(1,𝔽5)—42no—
85(C2×D3)⋊AGL(1,𝔽5)—42no—
86Dic3×AGL(1,𝔽5)—42no—
87C3×C5×C4⋊C4C2×C411yescharacteristic
88#6714C2×C412yes—
89C4×Dic15C2×C411yescharacteristic
90C5×(C2×D3)⋊C4C2×C412yes—
91C4×C5×Dic3C2×C411yescharacteristic
92C3×C4⋊Dic5C2×C411yescharacteristic
93C3×#683C2×C412yes—
94#6667C2×C412yes—
95(C2×D3)⋊Dic5C2×C412yes—
96Dic3×Dic5C2×C411yescharacteristic
97Dic3×Dic5C2×C411yescharacteristic
98C2×#893—51no—
99C3×#389—51no—
100#4990—52no—
101#4988—51no—
102#4987—52no—
103#4984—51no—
104Dic3×C4⋊C4—51no—
105#4939—51no—
106#4932—51no—
107#4670—52no—
108#4664—52no—
109C2×D4×D5—31no—
110C22×C4×D5—32no—
111C2×C22⋊AGL(1,𝔽5)—32no—
112C2×C22⋊AGL(1,𝔽5)—32no—
113C2×C22⋊AGL(1,𝔽5)—32no—
114C2×C22⋊AGL(1,𝔽5)—32no—
115C2×C4⋊AGL(1,𝔽5)—31no—
116C2×C4⋊AGL(1,𝔽5)—32no—
117C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
118C2×C4⋊AGL(1,𝔽5)C2×D312yes—
119C2×C4×AGL(1,𝔽5)—31no—
120C2×C4×AGL(1,𝔽5)—32no—
121C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
122C4×C5×D4—31no—
123D4×Dic5—31no—
124C4×C22⋊D5—32no—
125#4039—31no—
126D5×C4⋊C4C2×D311yescharacteristic
127#4027—32no—
128D5×C22⋊C4—32no—
129C4×D20—31no—
130C42×D5—31no—
131(C2×AGL(1,𝔽5))⋊C4—31no—
132(C2×AGL(1,𝔽5))⋊C4—31no—
133(C2×AGL(1,𝔽5))⋊C4—31no—
134(C2×AGL(1,𝔽5))⋊C4—31no—
135(C2×AGL(1,𝔽5))⋊C4—32no—
136(C2×AGL(1,𝔽5))⋊C4—32no—
137(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
138#2319—151noSylow
139C22×D15C22×C412yes—
140C22×C5×D3C22×C412yes—
141C22×C3×D5C2411yescharacteristic
142C2×D3×D5—22no—
143C2×D3×D5—22no—
144C2×D3×D5—22no—
145C2×D3×D5—22no—
146C2×D3×D5—22no—
147C2×D3×D5—22no—
148C2×ΓL(1,𝔽16)—21no—
149C2×ΓL(1,𝔽16)—21no—
150C2×ΓL(1,𝔽16)—22no—
151C2×ΓL(1,𝔽16)—22no—
152C2×ΓL(1,𝔽16)—21no—
153C2×ΓL(1,𝔽16)—21no—
154C2×ΓL(1,𝔽16)—22no—
155C2×ΓL(1,𝔽16)—21no—
156C2×ΓL(1,𝔽16)—21no—
157C2×C3×AGL(1,𝔽5)—21no—
158C2×C3×AGL(1,𝔽5)—21no—
159C2×C3×AGL(1,𝔽5)—22no—
160C2×C3×AGL(1,𝔽5)—22no—
161C2×C3×AGL(1,𝔽5)—21no—
162C2×C3×AGL(1,𝔽5)—21no—
163C2×C3×AGL(1,𝔽5)—22no—
164C2×C3×AGL(1,𝔽5)—21no—
165C2×C3×AGL(1,𝔽5)—21no—
166C2×C3×C4×C5C22×C412yes—
167C2×C3×C4×C5C22×C411yescharacteristic
168C2×Dic15C22×C411yescharacteristic
169C2×Dic15C22×C411yescharacteristic
170D60—22no—
171C4×D15—42no—
172C2×C5×Dic3C22×C411yescharacteristic
173C2×C5×Dic3C22×C411yescharacteristic
174C5×D12—22no—
175C4×C5×D3—42no—
176C2×C3×Dic5C22×C412yes—
177C2×C3×Dic5C22×C411yescharacteristic
178C3×C4×D5—22no—
179C3×C4×D5—22no—
180C3×C4×D5#4112yes—
181C3×C4×D5#4112yes—
182#1203—24no—
183#1200—42no—
184D3×Dic5—42no—
185D5×Dic3—21no—
186D5×Dic3—21no—
187D5×Dic3—21no—
188D5×Dic3—21no—
189C22×D12—51no—
190C22×C4×D3—52no—
191C2×C3×C4⋊C4—51no—
192C2×C3×C4⋊C4—51no—
193C2×C3×C4⋊C4—52no—
194C2×C3×C42—51no—
195C2×(C2×D3)⋊C4—52no—
196C2×(C2×D3)⋊C4—52no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—52no—
199C2×(C2×D3)⋊C4—52no—
200C2×C4⋊Dic3—51no—
201C2×C4⋊Dic3—52no—
202C2×C4×Dic3—51no—
203C2×C4×Dic3—51no—
204C2×C4×Dic3—52no—
205#893—51no—
206#893—52no—
207#893—51no—
208#893—52no—
209#893—51no—
210#893AGL(1,𝔽5)11yescharacteristic, complemented
211C3×#95—52no—
212C3⋊#95—51no—
213C3⋊#95—52no—
214C3⋊#95—51no—
215C3⋊#95—51no—
216C3⋊#95—51no—
217C3⋊#95—52no—
218C23×D5—32no—
219C22×AGL(1,𝔽5)—31no—
220C22×AGL(1,𝔽5)—32no—
221C22×AGL(1,𝔽5)—31no—
222C22×AGL(1,𝔽5)C22×D312yes—
223C22×AGL(1,𝔽5)C22×D311yescharacteristic
224C22×AGL(1,𝔽5)C22×D311yescharacteristic
225C2×C5×D4—31no—
226C22×C4×C5—32no—
227C2×C22⋊D5—32no—
228C22×Dic5—32no—
229D4×D5—62no—
230D4×D5—62no—
231C2×D20—31no—
232C2×C4×D5—31no—
233C2×C4×D5—31no—
234C2×C4×D5—32no—
235C2×C4×D5—32no—
236C2×C4×D5—122no—
237C2×C4×D5—122no—
238C2×C4×D5C22×D312yes—
239C2×C4×D5C22×D311yescharacteristic
240C22⋊AGL(1,𝔽5)—122no—
241C22⋊AGL(1,𝔽5)—122no—
242C22⋊AGL(1,𝔽5)—122no—
243C22⋊AGL(1,𝔽5)—122no—
244C4⋊AGL(1,𝔽5)—22no—
245C4⋊AGL(1,𝔽5)—42no—
246C4⋊AGL(1,𝔽5)—62no—
247C4⋊AGL(1,𝔽5)—122no—
248C4×AGL(1,𝔽5)—22no—
249C4×AGL(1,𝔽5)—62no—
250C4×AGL(1,𝔽5)—122no—
251C5×C4⋊C4C4×D311yescharacteristic
252C5×C22⋊C4—32no—
253C42×C5—31no—
254C22⋊Dic5—32no—
255#685—32no—
256#685—32no—
257C4⋊Dic5C4×D311yescharacteristic
258#683C4×D312yes—
259C4×Dic5—31no—
260C4×Dic5—31no—
261C4×Dic5—31no—
262C2×C4×D4—151no—
263#390—151no—
264#390—151no—
265#389—51no—
266#389—151no—
267#388—152no—
268#388—152no—
269#381—152no—
270#380—152no—
271C4×C4⋊C4—151no—
272#376—151no—
273C22×C3×C5C23×C411yescharacteristic
274C2×D15—22no—
275C2×D15—22no—
276C2×D15—22no—
277C2×C5×D3—22no—
278C2×C5×D3—22no—
279C2×C5×D3—22no—
280C2×C3×D5C2×#4111yescharacteristic
281C2×C3×D5C2×#4111yescharacteristic
282C2×C3×D5H(5,𝔽2)11yescharacteristic
283C2×C3×D5H(5,𝔽2)11yescharacteristic
284C2×C3×D5H(5,𝔽2)11yescharacteristic
285C2×C3×D52−1+411yescharacteristic
286D3×D5—42no—
287D3×D5—42no—
288D3×D5—42no—
289D3×D5—42no—
290ΓL(1,𝔽16)—41no—
291ΓL(1,𝔽16)—42no—
292ΓL(1,𝔽16)—41no—
293C3×AGL(1,𝔽5)—41no—
294C3×AGL(1,𝔽5)—42no—
295C3×AGL(1,𝔽5)—41no—
296C3×C4×C5—22no—
297C3×C4×C5#11712yes—
298Dic15—21no—
299Dic15—21no—
300C3×Dic5—22no—
301C3×Dic5#11712yes—
302C5×Dic3—21no—
303C5×Dic3—21no—
304C23×D3—52no—
305C22×C3×C4—51no—
306C22×C3×C4—52no—
307C22×C3×C4—51no—
308C22×C3×C4—51no—
309C22×C3×C4—52no—
310C22×Dic3—51no—
311C22×Dic3—51no—
312C22×Dic3—51no—
313C22×Dic3—51no—
314C22×Dic3—52no—
315C2×D12—52no—
316C2×D12—51no—
317C2×D12—102no—
318C2×D12—102no—
319C2×D12C2×AGL(1,𝔽5)11yescharacteristic
320C2×C4×D3—52no—
321C2×C4×D3—52no—
322C2×C4×D3—52no—
323C2×C4×D3—202no—
324C2×C4×D3—202no—
325C2×C4×D3C2×AGL(1,𝔽5)12yes—
326C3×C4⋊C4—52no—
327C3×C4⋊C4—51no—
328C3×C4⋊C4—102no—
329C3×C4⋊C4—202no—
330C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
331C3×C42—102no—
332(C2×D3)⋊C4—52no—
333(C2×D3)⋊C4—52no—
334(C2×D3)⋊C4—52no—
335(C2×D3)⋊C4—202no—
336(C2×D3)⋊C4—202no—
337(C2×D3)⋊C4—202no—
338(C2×D3)⋊C4—202no—
339(C2×D3)⋊C4C2×AGL(1,𝔽5)12yes—
340C4⋊Dic3—102no—
341C4⋊Dic3—202no—
342C4×Dic3—51no—
343C4×Dic3—51no—
344C4×Dic3—51no—
345C4×Dic3—102no—
346C4×Dic3—202no—
347C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
348C23×C5—32no—
349C22×D5—32no—
350C22×D5—62no—
351C22×D5—62no—
352C22×D5—62no—
353C22×D5—62no—
354C22×D5—62no—
355C22×D5—62no—
356C22×D5C23×D311yescharacteristic
357C2×AGL(1,𝔽5)—21no—
358C2×AGL(1,𝔽5)—21no—
359C2×AGL(1,𝔽5)—22no—
360C2×AGL(1,𝔽5)—21no—
361C2×AGL(1,𝔽5)—22no—
362C2×AGL(1,𝔽5)—21no—
363C2×AGL(1,𝔽5)—22no—
364C2×AGL(1,𝔽5)—21no—
365C2×AGL(1,𝔽5)—21no—
366C2×AGL(1,𝔽5)—61no—
367C2×AGL(1,𝔽5)—61no—
368C2×AGL(1,𝔽5)—61no—
369C2×AGL(1,𝔽5)—62no—
370C2×AGL(1,𝔽5)—61no—
371C2×AGL(1,𝔽5)—62no—
372C2×AGL(1,𝔽5)—61no—
373C2×AGL(1,𝔽5)—62no—
374C2×AGL(1,𝔽5)—61no—
375C5×D4—62no—
376C2×C4×C5—31no—
377C2×C4×C5—31no—
378C2×C4×C5—122no—
379C2×C4×C5C2×C4×D312yes—
380C2×C4×C5C2×C4×D311yescharacteristic
381C22⋊D5—64no—
382C2×Dic5—31no—
383C2×Dic5—31no—
384C2×Dic5—122no—
385C2×Dic5C2×C4×D312yes—
386C2×Dic5C2×C4×D311yescharacteristic
387D20—62no—
388C4×D5—22no—
389C4×D5—22no—
390C4×D5—61no—
391C4×D5—61no—
392C4×D5—61no—
393C4×D5—61no—
394C4×D5—122no—
395C4×D5—122no—
396C4×D5#23712yes—
397C4×D5#23912yes—
398C22×D4—151no—
399C23×C4—152no—
400C4×D4—31no—
401C4×D4—151no—
402C4×D4—152no—
403C4×D4—152no—
404C4×D4—151no—
405C4×D4—151no—
406C2×C4⋊C4—51no—
407C2×C4⋊C4—51no—
408C2×C4⋊C4—52no—
409C2×C4⋊C4—151no—
410C2×C4⋊C4—152no—
411C2×C22⋊C4—152no—
412C2×C22⋊C4—152no—
413C2×C22⋊C4—152no—
414C2×C22⋊C4—152no—
415C2×C22⋊C4—152no—
416C2×C42—51no—
417C2×C42—151no—
418C2×C42—151no—
419C2×C42—152no—
420#95—52no—
421#95—151no—
422#95—151no—
423#95—151no—
424#95—151no—
425#95—152no—
426#95—152no—
427C2×C3×C5C2×#11711yescharacteristic
428C2×C3×C5#51811yescharacteristic
429C2×C3×C5#52011yescharacteristic
430D15—42no—
431C3×D5#54011yescharacteristic
432C3×D5#54011yescharacteristic
433C3×D5#54211yescharacteristic
434C3×D5#54211yescharacteristic
435C5×D3—42no—
436C23×C3—51no—
437C22×D3—52no—
438C22×D3—102no—
439C22×D3—102no—
440C22×D3—102no—
441C22×D3—102no—
442C22×D3—102no—
443C22×D3—102no—
444C22×D3C22×AGL(1,𝔽5)12yes—
445C2×C3×C4—51no—
446C2×C3×C4—52no—
447C2×C3×C4—52no—
448C2×C3×C4—52no—
449C2×C3×C4—102no—
450C2×C3×C4—102no—
451C2×C3×C4—102no—
452C2×C3×C4—101no—
453C2×C3×C4—101no—
454C2×C3×C4—102no—
455C2×C3×C4—101no—
456C2×C3×C4—101no—
457C2×C3×C4—102no—
458C2×C3×C4—101no—
459C2×C3×C4—101no—
460C2×C3×C4C22×AGL(1,𝔽5)12yes—
461C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
462C2×Dic3—51no—
463C2×Dic3—51no—
464C2×Dic3—101no—
465C2×Dic3—101no—
466C2×Dic3—101no—
467C2×Dic3—101no—
468C2×Dic3—101no—
469C2×Dic3—101no—
470C2×Dic3—102no—
471C2×Dic3—102no—
472C2×Dic3—101no—
473C2×Dic3—102no—
474C2×Dic3—101no—
475C2×Dic3—101no—
476C2×Dic3—101no—
477C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
478C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
479D12—22no—
480D12—104no—
481D12—102no—
482C4×D3—42no—
483C4×D3—202no—
484C4×D3—202no—
485C4×D3—202no—
486C22×C5—62no—
487C22×C5—62no—
488C22×C5—62no—
489C22×C5C22×C4×D311yescharacteristic
490C2×D5—62no—
491C2×D5—62no—
492C2×D5—62no—
493C2×D5—122no—
494C2×D5—122no—
495C2×D5—122no—
496C2×D5—122no—
497C2×D5C2×#23711yescharacteristic
498C2×D5#100411yescharacteristic
499C2×D5C2×#23911yescharacteristic
500C2×D5#100711yescharacteristic
501C2×D5#100911yescharacteristic
502C2×D5#100911yescharacteristic
503AGL(1,𝔽5)—41no—
504AGL(1,𝔽5)—41no—
505AGL(1,𝔽5)—42no—
506AGL(1,𝔽5)—121no—
507AGL(1,𝔽5)—122no—
508AGL(1,𝔽5)—121no—
509C4×C5—22no—
510C4×C5—61no—
511C4×C5—61no—
512C4×C5#89212yes—
513Dic5—22no—
514Dic5—61no—
515Dic5—61no—
516Dic5#89212yes—
517C24—152no—
518C2×D4—31no—
519C2×D4—152no—
520C2×D4—151no—
521C2×D4—302no—
522C2×D4—302no—
523C22×C4—32no—
524C22×C4—51no—
525C22×C4—52no—
526C22×C4—51no—
527C22×C4—52no—
528C22×C4—51no—
529C22×C4—152no—
530C22×C4—151no—
531C22×C4—151no—
532C22×C4—152no—
533C22×C4—152no—
534C22×C4—151no—
535C22×C4—151no—
536C22×C4—152no—
537C22×C4—602no—
538C22×C4—602no—
539C4⋊C4—52no—
540C4⋊C4—51no—
541C4⋊C4—102no—
542C4⋊C4—202no—
543C4⋊C4—302no—
544C4⋊C4—602no—
545C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
546C22⋊C4—32no—
547C22⋊C4—152no—
548C22⋊C4—152no—
549C22⋊C4—152no—
550C22⋊C4—602no—
551C22⋊C4—602no—
552C22⋊C4—602no—
553C22⋊C4—602no—
554C42—31no—
555C42—102no—
556C42—151no—
557C42—151no—
558C42—151no—
559C42—302no—
560C42—602no—
561C3×C5#231911yescharacteristic, complemented, Hall
562C22×C3—51no—
563C22×C3—51no—
564C22×C3—51no—
565C22×C3—51no—
566C22×C3—51no—
567C22×C3—51no—
568C22×C3C23×AGL(1,𝔽5)11yescharacteristic
569C2×D3—22no—
570C2×D3—22no—
571C2×D3—22no—
572C2×D3—102no—
573C2×D3—102no—
574C2×D3—102no—
575C2×D3—202no—
576C2×D3—202no—
577C2×D3—202no—
578C2×D3—202no—
579C3×C4—22no—
580C3×C4—52no—
581C3×C4—102no—
582C3×C4—202no—
583C3×C4—201no—
584C3×C4—201no—
585C3×C4#413012yes—
586Dic3—21no—
587Dic3—21no—
588Dic3—101no—
589Dic3—101no—
590Dic3—201no—
591Dic3—202no—
592Dic3—201no—
593C2×C5—122no—
594C2×C5C2×#89211yescharacteristic
595C2×C5#554511yescharacteristic
596C2×C5#557411yescharacteristic
597D5—122no—
598D5#561911yescharacteristic
599D5#564311yescharacteristic
600D5#569711yescharacteristic
601D5#573311yescharacteristic
602C23—32no—
603C23—51no—
604C23—152no—
605C23—302no—
606C23—302no—
607C23—302no—
608C23—302no—
609C23—302no—
610C23—302no—
611D4—62no—
612D4—304no—
613D4—302no—
614C2×C4—31no—
615C2×C4—31no—
616C2×C4—51no—
617C2×C4—52no—
618C2×C4—52no—
619C2×C4—52no—
620C2×C4—102no—
621C2×C4—102no—
622C2×C4—101no—
623C2×C4—101no—
624C2×C4—102no—
625C2×C4—101no—
626C2×C4—101no—
627C2×C4—102no—
628C2×C4—102no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—122no—
632C2×C4—151no—
633C2×C4—151no—
634C2×C4—301no—
635C2×C4—301no—
636C2×C4—301no—
637C2×C4—301no—
638C2×C4—301no—
639C2×C4—301no—
640C2×C4—302no—
641C2×C4—301no—
642C2×C4—301no—
643C2×C4—302no—
644C2×C4—302no—
645C2×C4—301no—
646C2×C4—301no—
647C2×C4—602no—
648C2×C4—602no—
649C2×C4—602no—
650C2×C4C2×D3×AGL(1,𝔽5)12yes—
651C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
652C2×C3—51no—
653C2×C3—51no—
654C2×C3—51no—
655C2×C3—51no—
656C2×C3C2×#413011yescharacteristic
657C2×C3#6625811yescharacteristic
658C2×C3#6626611yescharacteristic
659D3—42no—
660D3—202no—
661C5#7596911yescharacteristic, complemented, Sylow
662C22—51no—
663C22—51no—
664C22—51no—
665C22—51no—
666C22—51no—
667C22—51no—
668C22—62no—
669C22—62no—
670C22—62no—
671C22—302no—
672C22—302no—
673C22—302no—
674C22—602no—
675C22—602no—
676C22—602no—
677C22—602no—
678C22C22×D3×AGL(1,𝔽5)11yescharacteristic
679C4—22no—
680C4—52no—
681C4—61no—
682C4—61no—
683C4—102no—
684C4—201no—
685C4—202no—
686C4—201no—
687C4—301no—
688C4—301no—
689C4—601no—
690C4—602no—
691C4—601no—
692C4#9190712yes—
693C3#1061717611yescharacteristic, complemented, Sylow
694C2—51no—
695C2—51no—
696C2—51no—
697C2—51no—
698C2—122no—
699C2—602no—
700C2C2×#9190711yescharacteristic
701C2#1175684511yescharacteristic
702C2#1175685411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalC2×D5×D12C22
cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2319
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11752371C2semidirect
3. C3×#65712C2semidirect
5. #11751855C2semidirect
6. #11751853C2semidirect
8. Dic3×C4⋊AGL(1,𝔽5)C2semidirect
9. #11751841C2semidirect
10. #11751836C2semidirect
11. #11751748C2semidirect
26. #91782C4semidirect
27. C5×#893C4semidirect
30. #91446C4semidirect
31. #91435C4semidirect
32. #91428C4semidirect
33. #91406C4semidirect
49. #65712D3semidirect
210. #893AGL(1,𝔽5)semidirect
561. C3×C5#2319semidirect
661. C5#75969semidirect
693. C3#10617176semidirect

Maximal subgroups

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

subgroupindex
D5×#8932
#117523712
C3×#657122
#117518572
#117518552
#117518532
#117518502
Dic3×C4⋊AGL(1,𝔽5)2
#117518412
#117518362
#117517482
#106171763
#759695