Finite Group Databasebeta

← #14322789

Subgroups — #14322789

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#926C211yesmaximal, characteristic
2#11752424C211yesmaximal, characteristic
3C3×#65765C211yesmaximal, characteristic
4#11752018C212yesmaximal
5#11752017C212yesmaximal
6#11751860C211yesmaximal, characteristic, complemented
7Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
8Dic3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
9#11751840C212yesmaximal, complemented
10#11751839C212yesmaximal, complemented
11#11751751C211yesmaximal, characteristic, complemented
12#10617130—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×#6763C2212yes—
15C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
16C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
17C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
18C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
19C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
20C2×Dic3⋊AGL(1,𝔽5)C2212yes—
21C2×Dic3⋊AGL(1,𝔽5)C2212yes—
22C2×Dic3×AGL(1,𝔽5)C2212yes—
23C2×Dic3×AGL(1,𝔽5)C2212yes—
24#91815C411yescharacteristic, complemented
25C5×#926C411yescharacteristic, complemented
26D5×#217C2211yescharacteristic
27D5×#217C2211yescharacteristic
28#91528C411yescharacteristic, complemented
29#91528C411yescharacteristic, complemented
30D5×C4⋊Dic3C2211yescharacteristic
31D5×C4⋊Dic3C2211yescharacteristic
32C4×D5×Dic3C2211yescharacteristic
33C4×D5×Dic3C2211yescharacteristic
34#91358C411yescharacteristic, complemented
35#91358C411yescharacteristic, complemented
36#91357C411yescharacteristic, complemented
37#91357C411yescharacteristic, complemented
38#91235C2212yes—
39C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
41(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
42(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
43(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
44#73868—51nomaximal, Hall
45D5×#117—31no—
46#65765—31no—
47#65765D311yescharacteristic
48#65711—32no—
49#65711—32no—
50#65700—32no—
51#65700—32no—
52#65689—31no—
53#65688—31no—
54C4×C4⋊AGL(1,𝔽5)—31no—
55C4×C4⋊AGL(1,𝔽5)—31no—
56C23×C3×D5C2311yescharacteristic
57C22×ΓL(1,𝔽16)C2312yes—
58C22×ΓL(1,𝔽16)C2312yes—
59C22×C3×AGL(1,𝔽5)C2312yes—
60C22×C3×AGL(1,𝔽5)C2312yes—
61C22×C3×C4×C5C2×C411yescharacteristic
62C22×C3×Dic5C2×C411yescharacteristic
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5C2×C411yescharacteristic
66C2×C3×C4×D5C2×C411yescharacteristic
67C2×C3×C4×D5C2311yescharacteristic
68C2×C3×C4×D5C2311yescharacteristic
69C2×D5×Dic3C2311yescharacteristic
70C2×D5×Dic3C2311yescharacteristic
71C2×D5×Dic3C2311yescharacteristic
72C2×D5×Dic3C2311yescharacteristic
73#6763—42no—
74C4⋊ΓL(1,𝔽16)—22no—
75C4⋊ΓL(1,𝔽16)—22no—
76C3×C22⋊AGL(1,𝔽5)—42no—
77C3×C4⋊AGL(1,𝔽5)—22no—
78C3×C4⋊AGL(1,𝔽5)—22no—
79Dic3⋊AGL(1,𝔽5)—42no—
80Dic3⋊AGL(1,𝔽5)—42no—
81Dic3×AGL(1,𝔽5)—42no—
82Dic3×AGL(1,𝔽5)—42no—
83#6719C2×C411yescharacteristic
84#6719C2×C411yescharacteristic
85C4⋊Dic15C2×C411yescharacteristic
86C4⋊Dic15C2×C411yescharacteristic
87C4×Dic15C2×C411yescharacteristic
88C4×Dic15C2×C411yescharacteristic
89C5×#217C2×C411yescharacteristic
90C5×#217C2×C411yescharacteristic
91C5×C4⋊Dic3C2×C411yescharacteristic
92C5×C4⋊Dic3C2×C411yescharacteristic
93C4×C5×Dic3C2×C411yescharacteristic
94C4×C5×Dic3C2×C411yescharacteristic
95#6668C2×C411yescharacteristic
96#6668C2×C411yescharacteristic
97#6668C2×C411yescharacteristic
98#6668C2×C411yescharacteristic
99#6665C2×C411yescharacteristic
100#6665C2×C411yescharacteristic
101#6665C2×C411yescharacteristic
102#6665C2×C411yescharacteristic
103Dic3×Dic5C2×C411yescharacteristic
104Dic3×Dic5C2×C411yescharacteristic
105Dic3×Dic5C2×C411yescharacteristic
106Dic3×Dic5C2×C411yescharacteristic
107C2×#926—51no—
108C3×#380—51no—
109#5212—51no—
110#4977—51no—
111#4975—51no—
112Dic3×C4⋊C4—51no—
113Dic3×C4⋊C4—51no—
114#4945—52no—
115#4944—52no—
116#4654—52no—
117#4653—52no—
118C22×C4×D5C2×D311yescharacteristic
119C2×C22⋊AGL(1,𝔽5)—32no—
120C2×C22⋊AGL(1,𝔽5)C2×D312yes—
121C2×C4⋊AGL(1,𝔽5)—31no—
122C2×C4⋊AGL(1,𝔽5)—31no—
123C2×C4⋊AGL(1,𝔽5)—32no—
124C2×C4⋊AGL(1,𝔽5)—32no—
125C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
126C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
127C2×C4×AGL(1,𝔽5)—32no—
128C2×C4×AGL(1,𝔽5)—32no—
129C5×#117—31no—
130#4072—31no—
131#4038—31no—
132#4038—31no—
133D5×C4⋊C4—31no—
134D5×C4⋊C4—31no—
135D5×C22⋊C4—31no—
136D5×C22⋊C4—31no—
137#4023—31no—
138#4023—31no—
139#4018—31no—
140#4018—31no—
141C42×D5—31no—
142C42×D5—31no—
143(C2×AGL(1,𝔽5))⋊C4—32no—
144(C2×AGL(1,𝔽5))⋊C4—32no—
145(C2×AGL(1,𝔽5))⋊C4—32no—
146(C2×AGL(1,𝔽5))⋊C4—32no—
147(C2×AGL(1,𝔽5))⋊C4—32no—
148(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
149#2314—151noSylow
150C23×C3×C5C22×C411yescharacteristic
151C22×C3×D5—21no—
152C22×C3×D5—21no—
153C22×C3×D5—21no—
154C22×C3×D5—21no—
155C22×C3×D5—21no—
156C22×C3×D5—21no—
157C22×C3×D5C22×C411yescharacteristic
158C22×C3×D5C2411yescharacteristic
159C2×ΓL(1,𝔽16)—22no—
160C2×ΓL(1,𝔽16)—22no—
161C2×ΓL(1,𝔽16)—22no—
162C2×ΓL(1,𝔽16)—22no—
163C2×ΓL(1,𝔽16)—22no—
164C2×ΓL(1,𝔽16)—22no—
165C2×C3×AGL(1,𝔽5)—22no—
166C2×C3×AGL(1,𝔽5)—22no—
167C2×C3×AGL(1,𝔽5)—22no—
168C2×C3×AGL(1,𝔽5)—22no—
169C2×C3×AGL(1,𝔽5)—22no—
170C2×C3×AGL(1,𝔽5)—22no—
171C2×C3×C4×C5—22no—
172C2×C3×C4×C5C22×C411yescharacteristic
173C2×C3×C4×C5C22×C411yescharacteristic
174C2×Dic15C22×C411yescharacteristic
175C2×Dic15C22×C411yescharacteristic
176C2×Dic15C22×C411yescharacteristic
177C2×Dic15C22×C411yescharacteristic
178C2×C5×Dic3C22×C411yescharacteristic
179C2×C5×Dic3C22×C411yescharacteristic
180C2×C5×Dic3C22×C411yescharacteristic
181C2×C5×Dic3C22×C411yescharacteristic
182C2×C3×Dic5—22no—
183C2×C3×Dic5C22×C411yescharacteristic
184C2×C3×Dic5C22×C411yescharacteristic
185C3×C4×D5—21no—
186C3×C4×D5—21no—
187C3×C4×D5—22no—
188C3×C4×D5—22no—
189C3×C4×D5#4112yes—
190C3×C4×D5#4112yes—
191D5×Dic3—21no—
192D5×Dic3—21no—
193D5×Dic3—21no—
194D5×Dic3—21no—
195D5×Dic3—21no—
196D5×Dic3—21no—
197D5×Dic3—21no—
198D5×Dic3—21no—
199C23×C3×C4—51no—
200C2×C3×C4⋊C4—51no—
201C2×C3×C4⋊C4—51no—
202C2×C3×C22⋊C4—52no—
203C2×#217—51no—
204C2×#217—51no—
205C2×#217—52no—
206#926—51no—
207#926—51no—
208#926—51no—
209#926—51no—
210#926—51no—
211#926—51no—
212#926—51no—
213#926AGL(1,𝔽5)11yescharacteristic, complemented
214C2×C4⋊Dic3—51no—
215C2×C4⋊Dic3—51no—
216C2×C4⋊Dic3—51no—
217C2×C4⋊Dic3—51no—
218C2×Dic3⋊C4—52no—
219C2×Dic3⋊C4—52no—
220C2×C4×Dic3—51no—
221C2×C4×Dic3—51no—
222C2×C4×Dic3—52no—
223C2×C4×Dic3—52no—
224C3×#95—52no—
225C3⋊#95—52no—
226C3⋊#95—52no—
227C3⋊#95—52no—
228C3⋊#95—52no—
229C3⋊#95—52no—
230C23×D5C22×D311yescharacteristic
231C22×AGL(1,𝔽5)—32no—
232C22×AGL(1,𝔽5)—32no—
233C22×AGL(1,𝔽5)C22×D312yes—
234C22×AGL(1,𝔽5)C22×D312yes—
235C22×C4×C5C4×D311yescharacteristic
236C22×Dic5C4×D311yescharacteristic
237C2×C4×D5—22no—
238C2×C4×D5—22no—
239C2×C4×D5—31no—
240C2×C4×D5—31no—
241C2×C4×D5—31no—
242C2×C4×D5—31no—
243C2×C4×D5C4×D311yescharacteristic
244C2×C4×D5C4×D311yescharacteristic
245C2×C4×D5C22×D311yescharacteristic
246C2×C4×D5C22×D311yescharacteristic
247C22⋊AGL(1,𝔽5)—42no—
248C22⋊AGL(1,𝔽5)—122no—
249C4⋊AGL(1,𝔽5)—22no—
250C4⋊AGL(1,𝔽5)—22no—
251C4⋊AGL(1,𝔽5)—62no—
252C4⋊AGL(1,𝔽5)—62no—
253C4⋊AGL(1,𝔽5)—122no—
254C4⋊AGL(1,𝔽5)—122no—
255C4×AGL(1,𝔽5)—122no—
256C4×AGL(1,𝔽5)—122no—
257C5×C4⋊C4—31no—
258C5×C4⋊C4—31no—
259C5×C22⋊C4—31no—
260C5×C22⋊C4—31no—
261C42×C5—31no—
262C42×C5—31no—
263C22⋊Dic5—31no—
264C22⋊Dic5—31no—
265#685—31no—
266#685—31no—
267#685—31no—
268#685—31no—
269C4⋊Dic5—31no—
270C4⋊Dic5—31no—
271#683—31no—
272#683—31no—
273#683—31no—
274#683—31no—
275C4×Dic5—31no—
276C4×Dic5—31no—
277C4×Dic5—31no—
278C4×Dic5—31no—
279C4×Dic5—31no—
280C4×Dic5—31no—
281C2×#117—151no—
282#388—152no—
283#388—152no—
284#387—152no—
285#387—152no—
286#384—151no—
287#382—151no—
288#380—51no—
289#380—151no—
290C4×C4⋊C4—151no—
291C4×C4⋊C4—151no—
292C22×C3×C5—21no—
293C22×C3×C5—21no—
294C22×C3×C5—21no—
295C22×C3×C5C23×C411yescharacteristic
296C2×C3×D5—21no—
297C2×C3×D5—21no—
298C2×C3×D5—21no—
299C2×C3×D5—41no—
300C2×C3×D5—41no—
301C2×C3×D5—41no—
302C2×C3×D5—41no—
303C2×C3×D5C2×#4111yescharacteristic
304C2×C3×D5C2×#4111yescharacteristic
305C2×C3×D5H(5,𝔽2)11yescharacteristic
306C2×C3×D5H(5,𝔽2)11yescharacteristic
307C2×C3×D52−1+411yescharacteristic
308C2×C3×D52−1+411yescharacteristic
309ΓL(1,𝔽16)—42no—
310ΓL(1,𝔽16)—42no—
311C3×AGL(1,𝔽5)—42no—
312C3×AGL(1,𝔽5)—42no—
313C3×C4×C5—21no—
314C3×C4×C5#11712yes—
315Dic15—21no—
316Dic15—21no—
317Dic15—21no—
318Dic15—21no—
319C3×Dic5—21no—
320C3×Dic5#11712yes—
321C5×Dic3—21no—
322C5×Dic3—21no—
323C5×Dic3—21no—
324C5×Dic3—21no—
325C24×C3—51no—
326C22×C3×C4—51no—
327C22×C3×C4—51no—
328C22×C3×C4—51no—
329C22×C3×C4—51no—
330C22×C3×C4—51no—
331C22×C3×C4—52no—
332C22×C3×C4—52no—
333C22×C3×C4—102no—
334C22×C3×C4—102no—
335C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
336C22×Dic3—51no—
337C22×Dic3—51no—
338C22×Dic3—51no—
339C22×Dic3—51no—
340C22×Dic3—52no—
341C22×Dic3—52no—
342C3×C4⋊C4—102no—
343C3×C4⋊C4—102no—
344C3×C22⋊C4—202no—
345#217—51no—
346#217—51no—
347#217—51no—
348#217—51no—
349#217—51no—
350#217—51no—
351#217—202no—
352#217C2×AGL(1,𝔽5)11yescharacteristic
353#217C2×AGL(1,𝔽5)11yescharacteristic
354C4⋊Dic3—51no—
355C4⋊Dic3—51no—
356C4⋊Dic3—51no—
357C4⋊Dic3—51no—
358C4⋊Dic3—51no—
359C4⋊Dic3—51no—
360C4⋊Dic3—102no—
361C4⋊Dic3—102no—
362C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
363C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
364Dic3⋊C4—202no—
365Dic3⋊C4—202no—
366C4×Dic3—51no—
367C4×Dic3—51no—
368C4×Dic3—51no—
369C4×Dic3—51no—
370C4×Dic3—51no—
371C4×Dic3—51no—
372C4×Dic3—202no—
373C4×Dic3—202no—
374C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
375C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
376C23×C5C2×C4×D311yescharacteristic
377C22×D5—21no—
378C22×D5—21no—
379C22×D5—21no—
380C22×D5—21no—
381C22×D5—21no—
382C22×D5—21no—
383C22×D5C2×C4×D311yescharacteristic
384C22×D5C23×D311yescharacteristic
385C2×AGL(1,𝔽5)—22no—
386C2×AGL(1,𝔽5)—22no—
387C2×AGL(1,𝔽5)—22no—
388C2×AGL(1,𝔽5)—22no—
389C2×AGL(1,𝔽5)—22no—
390C2×AGL(1,𝔽5)—22no—
391C2×AGL(1,𝔽5)—62no—
392C2×AGL(1,𝔽5)—62no—
393C2×AGL(1,𝔽5)—62no—
394C2×AGL(1,𝔽5)—62no—
395C2×AGL(1,𝔽5)—62no—
396C2×AGL(1,𝔽5)—62no—
397C2×C4×C5—22no—
398C2×C4×C5—31no—
399C2×C4×C5—31no—
400C2×C4×C5—31no—
401C2×C4×C5—31no—
402C2×C4×C5C2×C4×D311yescharacteristic
403C2×C4×C5C2×C4×D311yescharacteristic
404C2×Dic5—22no—
405C2×Dic5—31no—
406C2×Dic5—31no—
407C2×Dic5—31no—
408C2×Dic5—31no—
409C2×Dic5C2×C4×D311yescharacteristic
410C2×Dic5C2×C4×D311yescharacteristic
411C4×D5—21no—
412C4×D5—21no—
413C4×D5—22no—
414C4×D5—22no—
415C4×D5—61no—
416C4×D5—61no—
417C4×D5—61no—
418C4×D5—61no—
419C4×D5—61no—
420C4×D5—61no—
421C4×D5—61no—
422C4×D5—61no—
423C4×D5#23712yes—
424C4×D5#23712yes—
425C23×C4—51no—
426#117—31no—
427#117—151no—
428#117—151no—
429#117—151no—
430#117—151no—
431#117—151no—
432#117—151no—
433#117—151no—
434C2×C4⋊C4—51no—
435C2×C4⋊C4—51no—
436C2×C4⋊C4—151no—
437C2×C4⋊C4—151no—
438C2×C4⋊C4—151no—
439C2×C4⋊C4—151no—
440C2×C4⋊C4—152no—
441C2×C4⋊C4—152no—
442C2×C22⋊C4—52no—
443C2×C22⋊C4—151no—
444C2×C22⋊C4—151no—
445C2×C22⋊C4—152no—
446C2×C42—151no—
447C2×C42—151no—
448C2×C42—152no—
449C2×C42—152no—
450#95—52no—
451#95—152no—
452#95—152no—
453#95—152no—
454#95—152no—
455#95—152no—
456C2×C3×C5—41no—
457C2×C3×C5C2×#11711yescharacteristic
458C2×C3×C5#52011yescharacteristic
459C2×C3×C5#52011yescharacteristic
460C3×D5—41no—
461C3×D5#54011yescharacteristic
462C3×D5#54111yescharacteristic
463C3×D5#54211yescharacteristic
464C3×D5#54211yescharacteristic
465C23×C3—51no—
466C23×C3—51no—
467C23×C3—101no—
468C23×C3—101no—
469C23×C3—101no—
470C23×C3—101no—
471C23×C3—101no—
472C23×C3—101no—
473C23×C3C22×AGL(1,𝔽5)11yescharacteristic
474C2×C3×C4—22no—
475C2×C3×C4—51no—
476C2×C3×C4—52no—
477C2×C3×C4—52no—
478C2×C3×C4—51no—
479C2×C3×C4—102no—
480C2×C3×C4—101no—
481C2×C3×C4—101no—
482C2×C3×C4—102no—
483C2×C3×C4—102no—
484C2×C3×C4—102no—
485C2×C3×C4—102no—
486C2×C3×C4—102no—
487C2×C3×C4—102no—
488C2×C3×C4—102no—
489C2×C3×C4—102no—
490C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
491C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
492C2×Dic3—51no—
493C2×Dic3—51no—
494C2×Dic3—51no—
495C2×Dic3—51no—
496C2×Dic3—101no—
497C2×Dic3—101no—
498C2×Dic3—101no—
499C2×Dic3—101no—
500C2×Dic3—101no—
501C2×Dic3—101no—
502C2×Dic3—101no—
503C2×Dic3—101no—
504C2×Dic3—102no—
505C2×Dic3—102no—
506C2×Dic3—102no—
507C2×Dic3—102no—
508C2×Dic3—102no—
509C2×Dic3—102no—
510C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
511C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
512C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
513C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
514C22×C5—21no—
515C22×C5—21no—
516C22×C5—21no—
517C22×C5C22×C4×D311yescharacteristic
518C2×D5—21no—
519C2×D5—21no—
520C2×D5—21no—
521C2×D5—41no—
522C2×D5—41no—
523C2×D5—41no—
524C2×D5—41no—
525C2×D5C2×#23711yescharacteristic
526C2×D5C2×#23711yescharacteristic
527C2×D5#100411yescharacteristic
528C2×D5#100711yescharacteristic
529C2×D5#100911yescharacteristic
530C2×D5#101011yescharacteristic
531AGL(1,𝔽5)—42no—
532AGL(1,𝔽5)—42no—
533AGL(1,𝔽5)—122no—
534AGL(1,𝔽5)—122no—
535C4×C5—21no—
536C4×C5—61no—
537C4×C5—61no—
538C4×C5—61no—
539C4×C5—61no—
540C4×C5#87712yes—
541Dic5—21no—
542Dic5—61no—
543Dic5—61no—
544Dic5—61no—
545Dic5—61no—
546Dic5#87712yes—
547C24—51no—
548C22×C4—51no—
549C22×C4—51no—
550C22×C4—51no—
551C22×C4—51no—
552C22×C4—51no—
553C22×C4—52no—
554C22×C4—52no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—151no—
558C22×C4—151no—
559C22×C4—151no—
560C22×C4—151no—
561C22×C4—152no—
562C22×C4—152no—
563C22×C4D3×AGL(1,𝔽5)11yescharacteristic
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—102no—
567C4⋊C4—102no—
568C4⋊C4—151no—
569C4⋊C4—151no—
570C4⋊C4—151no—
571C4⋊C4—151no—
572C4⋊C4—151no—
573C4⋊C4—151no—
574C4⋊C4—302no—
575C4⋊C4—302no—
576C4⋊C4—602no—
577C4⋊C4—602no—
578C22⋊C4—31no—
579C22⋊C4—31no—
580C22⋊C4—151no—
581C22⋊C4—151no—
582C22⋊C4—151no—
583C22⋊C4—151no—
584C22⋊C4—151no—
585C22⋊C4—151no—
586C22⋊C4—202no—
587C22⋊C4—602no—
588C42—31no—
589C42—31no—
590C42—151no—
591C42—151no—
592C42—151no—
593C42—151no—
594C42—151no—
595C42—151no—
596C42—602no—
597C42—602no—
598C3×C5#231411yescharacteristic, complemented, Hall
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—51no—
603C22×C3—51no—
604C22×C3—51no—
605C22×C3—51no—
606C22×C3—51no—
607C22×C3—51no—
608C22×C3—101no—
609C22×C3—101no—
610C22×C3—101no—
611C22×C3—201no—
612C22×C3—201no—
613C22×C3—201no—
614C22×C3—201no—
615C22×C3C23×AGL(1,𝔽5)11yescharacteristic
616C3×C4—21no—
617C3×C4—52no—
618C3×C4—101no—
619C3×C4—202no—
620C3×C4—202no—
621C3×C4#413012yes—
622Dic3—21no—
623Dic3—21no—
624Dic3—21no—
625Dic3—21no—
626Dic3—101no—
627Dic3—101no—
628Dic3—101no—
629Dic3—101no—
630Dic3—202no—
631Dic3—202no—
632C2×C5—41no—
633C2×C5C2×#87711yescharacteristic
634C2×C5#550411yescharacteristic
635C2×C5#552311yescharacteristic
636D5—41no—
637D5#560311yescharacteristic
638D5#561911yescharacteristic
639D5#562511yescharacteristic
640D5#564311yescharacteristic
641C23—51no—
642C23—51no—
643C23—101no—
644C23—101no—
645C23—101no—
646C23—101no—
647C23—101no—
648C23—101no—
649C23C2×D3×AGL(1,𝔽5)11yescharacteristic
650C2×C4—22no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—51no—
656C2×C4—52no—
657C2×C4—52no—
658C2×C4—51no—
659C2×C4—102no—
660C2×C4—101no—
661C2×C4—101no—
662C2×C4—102no—
663C2×C4—102no—
664C2×C4—102no—
665C2×C4—102no—
666C2×C4—102no—
667C2×C4—102no—
668C2×C4—102no—
669C2×C4—102no—
670C2×C4—151no—
671C2×C4—151no—
672C2×C4—151no—
673C2×C4—151no—
674C2×C4—301no—
675C2×C4—301no—
676C2×C4—301no—
677C2×C4—301no—
678C2×C4—301no—
679C2×C4—301no—
680C2×C4—301no—
681C2×C4—301no—
682C2×C4—302no—
683C2×C4—302no—
684C2×C4—302no—
685C2×C4—302no—
686C2×C4—302no—
687C2×C4—302no—
688C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
689C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
690C2×C3—41no—
691C2×C3—51no—
692C2×C3—51no—
693C2×C3—51no—
694C2×C3—51no—
695C2×C3—201no—
696C2×C3C2×#413011yescharacteristic
697C2×C3#6626611yescharacteristic
698C2×C3#6626611yescharacteristic
699C5#7386811yescharacteristic, complemented, Sylow
700C22—21no—
701C22—21no—
702C22—21no—
703C22—51no—
704C22—51no—
705C22—51no—
706C22—51no—
707C22—51no—
708C22—51no—
709C22—101no—
710C22—101no—
711C22—101no—
712C22—201no—
713C22—201no—
714C22—201no—
715C22—201no—
716C22C22×D3×AGL(1,𝔽5)11yescharacteristic
717C4—21no—
718C4—52no—
719C4—61no—
720C4—61no—
721C4—61no—
722C4—61no—
723C4—101no—
724C4—202no—
725C4—202no—
726C4—301no—
727C4—301no—
728C4—301no—
729C4—301no—
730C4—602no—
731C4—602no—
732C4#9192312yes—
733C3#1061713011yescharacteristic, complemented, Sylow
734C2—41no—
735C2—51no—
736C2—51no—
737C2—51no—
738C2—51no—
739C2—201no—
740C2#1175683611yescharacteristic
741C2#1175683811yescharacteristic
742C2C2×#9192311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2314
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
6. #11751860C2semidirect
7. Dic3×C4⋊AGL(1,𝔽5)C2semidirect
8. Dic3×C4⋊AGL(1,𝔽5)C2semidirect
9. #11751840C2semidirect
10. #11751839C2semidirect
11. #11751751C2semidirect
24. #91815C4semidirect
25. C5×#926C4semidirect
28. #91528C4semidirect
29. #91528C4semidirect
34. #91358C4semidirect
35. #91358C4semidirect
36. #91357C4semidirect
37. #91357C4semidirect
213. #926AGL(1,𝔽5)semidirect
598. C3×C5#2314semidirect
699. C5#73868semidirect
733. C3#10617130semidirect

Maximal subgroups

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

subgroupindex
D5×#9262
#117524242
C3×#657652
#117520182
#117520172
#117518602
Dic3×C4⋊AGL(1,𝔽5)2
#117518402
#117518392
#117517512
#106171303
#738685