Finite Group Databasebeta

← #14326774

Subgroups — #14326774

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D5×C4⋊C4C211yesmaximal, characteristic
2#11752371C211yesmaximal, characteristic, complemented
3C3×#65712C211yesmaximal, characteristic, complemented
4#11751855C212yesmaximal
5#11751855C211yesmaximal, characteristic
6#11751848C212yesmaximal
7C4×(C2×D3)⋊AGL(1,𝔽5)C211yesmaximal, characteristic
8#11751846C211yesmaximal, characteristic, complemented
9#11751845C212yesmaximal, complemented
10AGL(1,𝔽5)×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#11751835C212yesmaximal, complemented
12#10617104—31nomaximal, Hall
13C2×C4×D3×D5C2211yescharacteristic
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)C2211yescharacteristic
22C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
23C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×Dic3×AGL(1,𝔽5)C2212yes—
25C2×Dic3×AGL(1,𝔽5)C2212yes—
26C4⋊C4×D15C411yescharacteristic, complemented
27C5×D3×C4⋊C4C411yescharacteristic, complemented
28C3×D5×C4⋊C4C2211yescharacteristic
29#91437C411yescharacteristic, complemented
30D3×C4⋊Dic5C411yescharacteristic, complemented
31D5×C4⋊Dic3C2211yescharacteristic
32#91404C412yescomplemented
33D3×#683C412yescomplemented
34D5×Dic3⋊C4C2212yes—
35#91235C2212yes—
36C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
37(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
38(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
39(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42#76201—51nomaximal, Hall
43C2×D5×C4⋊C4—31no—
44#65765—31no—
45#65765—32no—
46C4×C22⋊AGL(1,𝔽5)—32no—
47C4×C22⋊AGL(1,𝔽5)—31no—
48#65712—31no—
49#65712D311yescharacteristic, complemented
50#65711—32no—
51#65711—32no—
52C4⋊C4×AGL(1,𝔽5)—31no—
53C4⋊C4×AGL(1,𝔽5)—31no—
54C22×D3×D5C2311yescharacteristic
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×C4×D15C2×C411yescharacteristic
62C2×C4×D15C2×C412yes—
63C2×C4×C5×D3C2×C411yescharacteristic
64C2×C4×C5×D3C2×C412yes—
65C2×C3×C4×D5C2312yes—
66C2×C3×C4×D5C2311yescharacteristic
67C2×#1200C2×C411yescharacteristic
68C2×#1200C2×C412yes—
69C2×D3×Dic5C2×C411yescharacteristic
70C2×D3×Dic5C2×C412yes—
71C2×D5×Dic3C2311yescharacteristic
72C2×D5×Dic3C2312yes—
73C4×D3×D5—22no—
74C4×D3×D5—22no—
75C4×D3×D5—42no—
76C4×D3×D5—42no—
77C4⋊ΓL(1,𝔽16)—22no—
78C4⋊ΓL(1,𝔽16)—42no—
79C4×ΓL(1,𝔽16)—22no—
80C3×C4⋊AGL(1,𝔽5)—22no—
81C3×C4⋊AGL(1,𝔽5)—42no—
82C3×C4×AGL(1,𝔽5)—22no—
83(C2×D3)⋊AGL(1,𝔽5)—22no—
84(C2×D3)⋊AGL(1,𝔽5)—24no—
85(C2×D3)⋊AGL(1,𝔽5)Q814yes—
86Dic3×AGL(1,𝔽5)—42no—
87Dic3×AGL(1,𝔽5)—42no—
88C3×C5×C4⋊C4C2×C411yescharacteristic
89C4⋊Dic15C2×C411yescharacteristic
90#6712C2×C412yes—
91C5×C4⋊Dic3C2×C411yescharacteristic
92C5×Dic3⋊C4C2×C412yes—
93C3×C4⋊Dic5C2×C411yescharacteristic
94C3×#683C2×C412yes—
95Dic3⋊Dic5C2×C412yes—
96#6669C2×C412yes—
97#6668C2×C412yes—
98C2×D3×C4⋊C4—51no—
99C3×#389—51no—
100#4987—52no—
101#4987—51no—
102#4984—51no—
103#4978—52no—
104Dic3×C4⋊C4—51no—
105C4×(C2×D3)⋊C4—51no—
106C4×C4⋊Dic3—51no—
107#4666—52no—
108#4655—52no—
109C22×C4×D5—31no—
110C22×C4×D5—32no—
111C2×C22⋊AGL(1,𝔽5)—31no—
112C2×C22⋊AGL(1,𝔽5)—32no—
113C2×C22⋊AGL(1,𝔽5)—31no—
114C2×C4⋊AGL(1,𝔽5)—31no—
115C2×C4⋊AGL(1,𝔽5)—32no—
116C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
117C2×C4⋊AGL(1,𝔽5)C2×D312yes—
118C2×C4×AGL(1,𝔽5)—31no—
119C2×C4×AGL(1,𝔽5)—32no—
120C2×C4×AGL(1,𝔽5)—32no—
121C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
122C2×C5×C4⋊C4—31no—
123C2×C4⋊Dic5—31no—
124C2×#683—32no—
125D5×C4⋊C4—32no—
126D5×C4⋊C4—31no—
127D5×C4⋊C4—31no—
128D5×C4⋊C4—31no—
129D5×C4⋊C4—32no—
130D5×C4⋊C4C2×D311yescharacteristic
131(C2×AGL(1,𝔽5))⋊C4—32no—
132(C2×AGL(1,𝔽5))⋊C4—32no—
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#2345—151noSylow
139C22×D15C22×C411yescharacteristic
140C22×C5×D3C22×C411yescharacteristic
141C22×C3×D5C2411yescharacteristic
142C2×D3×D5—21no—
143C2×D3×D5—21no—
144C2×D3×D5—21no—
145C2×D3×D5—21no—
146C2×D3×D5C2×Q812yes—
147C2×D3×D5#4112yes—
148C2×ΓL(1,𝔽16)—21no—
149C2×ΓL(1,𝔽16)—21no—
150C2×ΓL(1,𝔽16)—22no—
151C2×ΓL(1,𝔽16)—21no—
152C2×ΓL(1,𝔽16)—21no—
153C2×ΓL(1,𝔽16)—22no—
154C2×ΓL(1,𝔽16)—22no—
155C2×ΓL(1,𝔽16)—21no—
156C2×ΓL(1,𝔽16)C2×Q812yes—
157C2×C3×AGL(1,𝔽5)—21no—
158C2×C3×AGL(1,𝔽5)—21no—
159C2×C3×AGL(1,𝔽5)—22no—
160C2×C3×AGL(1,𝔽5)—21no—
161C2×C3×AGL(1,𝔽5)—21no—
162C2×C3×AGL(1,𝔽5)—22no—
163C2×C3×AGL(1,𝔽5)—22no—
164C2×C3×AGL(1,𝔽5)—21no—
165C2×C3×AGL(1,𝔽5)C2×Q812yes—
166C2×C3×C4×C5C22×C412yes—
167C2×C3×C4×C5C22×C411yescharacteristic
168C2×Dic15C22×C412yes—
169C2×Dic15C22×C411yescharacteristic
170C4×D15—22no—
171C4×D15—42no—
172C2×C5×Dic3C22×C412yes—
173C2×C5×Dic3C22×C411yescharacteristic
174C4×C5×D3—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#1200—22no—
183#1200—42no—
184D3×Dic5—22no—
185D3×Dic5—42no—
186D5×Dic3—21no—
187D5×Dic3—21no—
188D5×Dic3—22no—
189D5×Dic3—22no—
190C22×C4×D3—51no—
191C22×C4×D3—52no—
192C2×C3×C4⋊C4—51no—
193C2×C3×C4⋊C4—51no—
194C2×C3×C4⋊C4—52no—
195C2×C3×C42—51no—
196C2×(C2×D3)⋊C4—51no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—51no—
199C2×C4⋊Dic3—51no—
200C2×C4⋊Dic3—51no—
201C2×C4⋊Dic3—52no—
202C2×Dic3⋊C4—52no—
203C2×C4×Dic3—51no—
204C2×C4×Dic3—52no—
205C2×C4×Dic3—52no—
206D3×C4⋊C4—52no—
207D3×C4⋊C4—51no—
208D3×C4⋊C4—51no—
209D3×C4⋊C4—51no—
210D3×C4⋊C4—52no—
211D3×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
212C3×#95—52no—
213C3⋊#95—51no—
214C3⋊#95—52no—
215C3⋊#95—52no—
216C3⋊#95—52no—
217C3⋊#95—51no—
218C3⋊#95—52no—
219C23×D5—31no—
220C22×AGL(1,𝔽5)—31no—
221C22×AGL(1,𝔽5)—31no—
222C22×AGL(1,𝔽5)—32no—
223C22×AGL(1,𝔽5)C22×D312yes—
224C22×AGL(1,𝔽5)C22×D311yescharacteristic
225C22×AGL(1,𝔽5)C22×D311yescharacteristic
226C22×C4×C5—31no—
227C22×C4×C5—32no—
228C22×Dic5—31no—
229C22×Dic5—32no—
230C2×C4×D5—32no—
231C2×C4×D5—31no—
232C2×C4×D5—31no—
233C2×C4×D5—31no—
234C2×C4×D5—32no—
235C2×C4×D5—32no—
236C2×C4×D5—62no—
237C2×C4×D5—62no—
238C2×C4×D5—122no—
239C2×C4×D5—122no—
240C2×C4×D5C22×D312yes—
241C2×C4×D5C22×D311yescharacteristic
242C22⋊AGL(1,𝔽5)—34no—
243C22⋊AGL(1,𝔽5)—64no—
244C22⋊AGL(1,𝔽5)—62no—
245C4⋊AGL(1,𝔽5)—22no—
246C4⋊AGL(1,𝔽5)—42no—
247C4⋊AGL(1,𝔽5)—62no—
248C4⋊AGL(1,𝔽5)—122no—
249C4×AGL(1,𝔽5)—22no—
250C4×AGL(1,𝔽5)—62no—
251C4×AGL(1,𝔽5)—122no—
252C4×AGL(1,𝔽5)—122no—
253C5×C4⋊C4—32no—
254C5×C4⋊C4—31no—
255C5×C4⋊C4C4×D311yescharacteristic
256C4⋊Dic5—31no—
257C4⋊Dic5—32no—
258C4⋊Dic5C4×D311yescharacteristic
259#683—32no—
260#683—32no—
261#683—32no—
262#683C4×D312yes—
263C22×C4⋊C4—151no—
264#389—51no—
265#389—151no—
266#387—152no—
267#387—152no—
268#380—152no—
269#380—151no—
270C4×C4⋊C4—151no—
271C4×C4⋊C4—151no—
272C4×C22⋊C4—152no—
273C4×C22⋊C4—151no—
274C22×C3×C5C23×C411yescharacteristic
275C2×D15—21no—
276C2×D15—21no—
277C2×D15C4×Q812yes—
278C2×C5×D3—21no—
279C2×C5×D3—21no—
280C2×C5×D3C4×Q812yes—
281C2×C3×D5C22×Q811yescharacteristic
282C2×C3×D5C2×#4111yescharacteristic
283C2×C3×D5C2×#4111yescharacteristic
284C2×C3×D5C2×#4111yescharacteristic
285C2×C3×D5H(5,𝔽2)11yescharacteristic
286C2×C3×D5H(5,𝔽2)11yescharacteristic
287D3×D5—22no—
288D3×D5—22no—
289D3×D5—22no—
290D3×D5—22no—
291ΓL(1,𝔽16)—22no—
292ΓL(1,𝔽16)—41no—
293ΓL(1,𝔽16)—42no—
294C3×AGL(1,𝔽5)—22no—
295C3×AGL(1,𝔽5)—41no—
296C3×AGL(1,𝔽5)—42no—
297C3×C4×C5—22no—
298C3×C4×C5#11712yes—
299Dic15—21no—
300Dic15—22no—
301C3×Dic5—22no—
302C3×Dic5#11712yes—
303C5×Dic3—21no—
304C5×Dic3—22no—
305C23×D3—51no—
306C22×C3×C4—51no—
307C22×C3×C4—51no—
308C22×C3×C4—52no—
309C22×C3×C4—51no—
310C22×C3×C4—52no—
311C22×Dic3—51no—
312C22×Dic3—51no—
313C22×Dic3—52no—
314C22×Dic3—51no—
315C22×Dic3—52no—
316C2×C4×D3—51no—
317C2×C4×D3—51no—
318C2×C4×D3—51no—
319C2×C4×D3—52no—
320C2×C4×D3—52no—
321C2×C4×D3—52no—
322C2×C4×D3—102no—
323C2×C4×D3—102no—
324C2×C4×D3—202no—
325C2×C4×D3—202no—
326C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
327C2×C4×D3C2×AGL(1,𝔽5)12yes—
328C3×C4⋊C4—52no—
329C3×C4⋊C4—51no—
330C3×C4⋊C4—102no—
331C3×C4⋊C4—202no—
332C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
333C3×C42—102no—
334(C2×D3)⋊C4—54no—
335(C2×D3)⋊C4—104no—
336(C2×D3)⋊C4—102no—
337C4⋊Dic3—51no—
338C4⋊Dic3—52no—
339C4⋊Dic3—102no—
340C4⋊Dic3—202no—
341C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
342Dic3⋊C4—52no—
343Dic3⋊C4—52no—
344Dic3⋊C4—52no—
345Dic3⋊C4C2×AGL(1,𝔽5)12yes—
346C4×Dic3—102no—
347C4×Dic3—202no—
348C4×Dic3—202no—
349C23×C5—31no—
350C22×D5—31no—
351C22×D5—32no—
352C22×D5—32no—
353C22×D5—61no—
354C22×D5—61no—
355C22×D5—61no—
356C22×D5—61no—
357C22×D5C23×D311yescharacteristic
358C2×AGL(1,𝔽5)—21no—
359C2×AGL(1,𝔽5)—21no—
360C2×AGL(1,𝔽5)—21no—
361C2×AGL(1,𝔽5)—22no—
362C2×AGL(1,𝔽5)—22no—
363C2×AGL(1,𝔽5)—21no—
364C2×AGL(1,𝔽5)—22no—
365C2×AGL(1,𝔽5)—21no—
366C2×AGL(1,𝔽5)—32no—
367C2×AGL(1,𝔽5)—61no—
368C2×AGL(1,𝔽5)—61no—
369C2×AGL(1,𝔽5)—61no—
370C2×AGL(1,𝔽5)—62no—
371C2×AGL(1,𝔽5)—61no—
372C2×AGL(1,𝔽5)—62no—
373C2×AGL(1,𝔽5)—62no—
374C2×AGL(1,𝔽5)—61no—
375C2×AGL(1,𝔽5)D3×Q812yes—
376C2×C4×C5—32no—
377C2×C4×C5—31no—
378C2×C4×C5—62no—
379C2×C4×C5—122no—
380C2×C4×C5C2×C4×D312yes—
381C2×C4×C5C2×C4×D311yescharacteristic
382C2×Dic5—31no—
383C2×Dic5—32no—
384C2×Dic5—62no—
385C2×Dic5—122no—
386C2×Dic5C2×C4×D312yes—
387C2×Dic5C2×C4×D311yescharacteristic
388C4×D5—22no—
389C4×D5—22no—
390C4×D5—61no—
391C4×D5—62no—
392C4×D5—61no—
393C4×D5—62no—
394C4×D5—62no—
395C4×D5—62no—
396C4×D5—122no—
397C4×D5—122no—
398C4×D5#23712yes—
399C4×D5#23912yes—
400C23×C4—151no—
401C23×C4—152no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—51no—
404C2×C4⋊C4—51no—
405C2×C4⋊C4—52no—
406C2×C4⋊C4—152no—
407C2×C4⋊C4—151no—
408C2×C4⋊C4—151no—
409C2×C4⋊C4—152no—
410C2×C4⋊C4—152no—
411C2×C4⋊C4—151no—
412C2×C4⋊C4—151no—
413C2×C4⋊C4—151no—
414C2×C4⋊C4—152no—
415C2×C22⋊C4—151no—
416C2×C22⋊C4—152no—
417C2×C22⋊C4—151no—
418C2×C42—51no—
419C2×C42—151no—
420C2×C42—152no—
421C2×C42—152no—
422#95—52no—
423#95—151no—
424#95—151no—
425#95—152no—
426#95—152no—
427#95—152no—
428#95—152no—
429C2×C3×C5C2×#11711yescharacteristic
430C2×C3×C5C2×C4×Q811yescharacteristic
431C2×C3×C5#51811yescharacteristic
432D15—22no—
433C3×D5#55311yescharacteristic
434C3×D5#55311yescharacteristic
435C3×D5#55411yescharacteristic
436C3×D5#55411yescharacteristic
437C5×D3—22no—
438C23×C3—51no—
439C22×D3—51no—
440C22×D3—52no—
441C22×D3—52no—
442C22×D3—101no—
443C22×D3—101no—
444C22×D3—101no—
445C22×D3—101no—
446C22×D3C22×AGL(1,𝔽5)11yescharacteristic
447C2×C3×C4—51no—
448C2×C3×C4—52no—
449C2×C3×C4—52no—
450C2×C3×C4—52no—
451C2×C3×C4—52no—
452C2×C3×C4—102no—
453C2×C3×C4—102no—
454C2×C3×C4—101no—
455C2×C3×C4—101no—
456C2×C3×C4—102no—
457C2×C3×C4—101no—
458C2×C3×C4—102no—
459C2×C3×C4—101no—
460C2×C3×C4—102no—
461C2×C3×C4—101no—
462C2×C3×C4C22×AGL(1,𝔽5)12yes—
463C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
464C2×Dic3—52no—
465C2×Dic3—51no—
466C2×Dic3—52no—
467C2×Dic3—102no—
468C2×Dic3—102no—
469C2×Dic3—101no—
470C2×Dic3—101no—
471C2×Dic3—101no—
472C2×Dic3—101no—
473C2×Dic3—101no—
474C2×Dic3—102no—
475C2×Dic3—102no—
476C2×Dic3—101no—
477C2×Dic3—101no—
478C2×Dic3—102no—
479C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
480C2×Dic3C22×AGL(1,𝔽5)12yes—
481C4×D3—22no—
482C4×D3—42no—
483C4×D3—102no—
484C4×D3—102no—
485C4×D3—102no—
486C4×D3—202no—
487C4×D3—202no—
488C4×D3—202no—
489C22×C5—32no—
490C22×C5—61no—
491C22×C5—61no—
492C22×C5C22×C4×D311yescharacteristic
493C2×D5—32no—
494C2×D5—61no—
495C2×D5—61no—
496C2×D5—62no—
497C2×D5—62no—
498C2×D5—62no—
499C2×D5—62no—
500C2×D5C2×#23711yescharacteristic
501C2×D5#100411yescharacteristic
502C2×D5C2×D3×Q811yescharacteristic
503C2×D5C2×#23911yescharacteristic
504C2×D5D3×#4111yescharacteristic
505C2×D5#100911yescharacteristic
506AGL(1,𝔽5)—22no—
507AGL(1,𝔽5)—41no—
508AGL(1,𝔽5)—42no—
509AGL(1,𝔽5)—62no—
510AGL(1,𝔽5)—121no—
511AGL(1,𝔽5)—122no—
512C4×C5—22no—
513C4×C5—61no—
514C4×C5—62no—
515C4×C5#89212yes—
516Dic5—22no—
517Dic5—61no—
518Dic5—62no—
519Dic5#89212yes—
520C24—151no—
521C22×C4—31no—
522C22×C4—32no—
523C22×C4—51no—
524C22×C4—51no—
525C22×C4—52no—
526C22×C4—52no—
527C22×C4—51no—
528C22×C4—151no—
529C22×C4—152no—
530C22×C4—151no—
531C22×C4—152no—
532C22×C4—151no—
533C22×C4—152no—
534C22×C4—151no—
535C22×C4—151no—
536C22×C4—152no—
537C22×C4—151no—
538C22×C4—152no—
539C22×C4—302no—
540C22×C4—302no—
541C22×C4—602no—
542C22×C4—602no—
543C4⋊C4—32no—
544C4⋊C4—31no—
545C4⋊C4—52no—
546C4⋊C4—51no—
547C4⋊C4—102no—
548C4⋊C4—152no—
549C4⋊C4—152no—
550C4⋊C4—152no—
551C4⋊C4—152no—
552C4⋊C4—151no—
553C4⋊C4—202no—
554C4⋊C4—302no—
555C4⋊C4—602no—
556C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
557C22⋊C4—154no—
558C22⋊C4—304no—
559C22⋊C4—302no—
560C42—102no—
561C42—302no—
562C42—602no—
563C42—602no—
564C3×C5#234511yescharacteristic, complemented, Hall
565C22×C3—51no—
566C22×C3—51no—
567C22×C3—51no—
568C22×C3—51no—
569C22×C3—51no—
570C22×C3—51no—
571C22×C3C23×AGL(1,𝔽5)11yescharacteristic
572C2×D3—21no—
573C2×D3—21no—
574C2×D3—52no—
575C2×D3—102no—
576C2×D3—102no—
577C2×D3—102no—
578C2×D3—102no—
579C2×D3—101no—
580C2×D3—101no—
581C2×D3Q8×AGL(1,𝔽5)12yes—
582C3×C4—22no—
583C3×C4—52no—
584C3×C4—102no—
585C3×C4—102no—
586C3×C4—202no—
587C3×C4—201no—
588C3×C4#413012yes—
589Dic3—21no—
590Dic3—22no—
591Dic3—102no—
592Dic3—101no—
593Dic3—102no—
594Dic3—201no—
595Dic3—202no—
596C2×C5—62no—
597C2×C5C2×#89211yescharacteristic
598C2×C5#554511yescharacteristic
599C2×C5C4×D3×Q811yescharacteristic
600D5—62no—
601D5#561411yescharacteristic
602D5#563511yescharacteristic
603D5#569511yescharacteristic
604D5#573011yescharacteristic
605C23—31no—
606C23—51no—
607C23—152no—
608C23—152no—
609C23—151no—
610C23—301no—
611C23—301no—
612C23—301no—
613C23—301no—
614C2×C4—31no—
615C2×C4—32no—
616C2×C4—51no—
617C2×C4—52no—
618C2×C4—52no—
619C2×C4—52no—
620C2×C4—52no—
621C2×C4—62no—
622C2×C4—102no—
623C2×C4—102no—
624C2×C4—101no—
625C2×C4—101no—
626C2×C4—101no—
627C2×C4—102no—
628C2×C4—102no—
629C2×C4—101no—
630C2×C4—102no—
631C2×C4—101no—
632C2×C4—122no—
633C2×C4—152no—
634C2×C4—151no—
635C2×C4—152no—
636C2×C4—302no—
637C2×C4—302no—
638C2×C4—302no—
639C2×C4—302no—
640C2×C4—301no—
641C2×C4—301no—
642C2×C4—301no—
643C2×C4—301no—
644C2×C4—302no—
645C2×C4—301no—
646C2×C4—302no—
647C2×C4—301no—
648C2×C4—302no—
649C2×C4—302no—
650C2×C4—301no—
651C2×C4—602no—
652C2×C4—602no—
653C2×C4—602no—
654C2×C4C2×D3×AGL(1,𝔽5)12yes—
655C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
656C2×C3—51no—
657C2×C3—51no—
658C2×C3—51no—
659C2×C3—51no—
660C2×C3C2×#413011yescharacteristic
661C2×C3#6625811yescharacteristic
662C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
663D3—22no—
664D3—102no—
665C5#7620111yescharacteristic, complemented, Sylow
666C22—32no—
667C22—51no—
668C22—51no—
669C22—51no—
670C22—51no—
671C22—51no—
672C22—51no—
673C22—61no—
674C22—61no—
675C22—152no—
676C22—302no—
677C22—302no—
678C22—302no—
679C22—302no—
680C22—301no—
681C22—301no—
682C22C22×D3×AGL(1,𝔽5)11yescharacteristic
683C4—22no—
684C4—52no—
685C4—61no—
686C4—62no—
687C4—102no—
688C4—102no—
689C4—201no—
690C4—202no—
691C4—302no—
692C4—301no—
693C4—302no—
694C4—601no—
695C4—602no—
696C4#9190712yes—
697C3#1061710411yescharacteristic, complemented, Sylow
698C2—51no—
699C2—51no—
700C2—51no—
701C2—51no—
702C2—62no—
703C2—302no—
704C2C2×#9190711yescharacteristic
705C2#1175684511yescharacteristic
706C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2345
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
8. #11751846C2semidirect
9. #11751845C2semidirect
10. AGL(1,𝔽5)×C4⋊Dic3C2semidirect
11. #11751835C2semidirect
26. C4⋊C4×D15C4semidirect
27. C5×D3×C4⋊C4C4semidirect
29. #91437C4semidirect
30. D3×C4⋊Dic5C4semidirect
32. #91404C4semidirect
33. D3×#683C4semidirect
49. #65712D3semidirect
211. D3×C4⋊C4AGL(1,𝔽5)semidirect
564. C3×C5#2345semidirect
665. C5#76201semidirect
697. C3#10617104semidirect

Maximal subgroups

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

subgroupindex
D3×D5×C4⋊C42
#117523712
C3×#657122
#117518552
#117518482
C4×(C2×D3)⋊AGL(1,𝔽5)2
#117518462
#117518452
AGL(1,𝔽5)×C4⋊Dic32
#117518352
#106171043
#762015