Finite Group Databasebeta

← C3×#10603801 #14279965

Subgroups — C3×#10603801 #14279965

Order 1920.

1224 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C22×C3×C4×AGL(1,𝔽5)C211yesmaximal, characteristic
3C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
4C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
5C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
6C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
7C3×D5×#95C211yesmaximal, characteristic
8#10603801C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×AGL(1,𝔽5)C2211yescharacteristic
10C23×C3×AGL(1,𝔽5)C2211yescharacteristic
11C23×C3×AGL(1,𝔽5)C2211yescharacteristic
12C23×C3×AGL(1,𝔽5)C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C2×C3×C4⋊AGL(1,𝔽5)—22no—
17C2×C3×C4⋊AGL(1,𝔽5)—22no—
18C2×C3×C4⋊AGL(1,𝔽5)C414yescomplemented
19C2×C3×C4×AGL(1,𝔽5)—22no—
20C2×C3×C4×AGL(1,𝔽5)—22no—
21C2×C3×C4×AGL(1,𝔽5)—22no—
22C3×(C2×AGL(1,𝔽5))⋊C4—22no—
23C3×(C2×AGL(1,𝔽5))⋊C4—22no—
24C3×(C2×AGL(1,𝔽5))⋊C4—22no—
25C3×(C2×AGL(1,𝔽5))⋊C4C414yescomplemented
26C3×C5×#95C411yescharacteristic, complemented
27C3×#3963C411yescharacteristic, complemented
28C3×#3963C411yescharacteristic, complemented
29C3×#3963C411yescharacteristic, complemented
30C3×#1436—51nomaximal, Hall
31C22×C4⋊AGL(1,𝔽5)C2×C311yescharacteristic
32C22×C4×AGL(1,𝔽5)C2×C311yescharacteristic
33C2×(C2×AGL(1,𝔽5))⋊C4C2×C311yescharacteristic
34C2×(C2×AGL(1,𝔽5))⋊C4C2×C311yescharacteristic
35C2×(C2×AGL(1,𝔽5))⋊C4C2×C311yescharacteristic
36C2×(C2×AGL(1,𝔽5))⋊C4C2×C311yescharacteristic
37D5×#95C2×C311yescharacteristic
38C23×C3×D5C2311yescharacteristic
39C22×C3×AGL(1,𝔽5)—21no—
40C22×C3×AGL(1,𝔽5)—21no—
41C22×C3×AGL(1,𝔽5)—21no—
42C22×C3×AGL(1,𝔽5)—21no—
43C22×C3×AGL(1,𝔽5)—21no—
44C22×C3×AGL(1,𝔽5)—21no—
45C22×C3×AGL(1,𝔽5)—21no—
46C22×C3×AGL(1,𝔽5)—21no—
47C22×C3×AGL(1,𝔽5)—21no—
48C22×C3×AGL(1,𝔽5)—21no—
49C22×C3×AGL(1,𝔽5)—21no—
50C22×C3×AGL(1,𝔽5)—21no—
51C22×C3×AGL(1,𝔽5)—21no—
52C22×C3×AGL(1,𝔽5)—21no—
53C22×C3×AGL(1,𝔽5)—21no—
54C22×C3×AGL(1,𝔽5)—21no—
55C22×C3×AGL(1,𝔽5)—21no—
56C22×C3×AGL(1,𝔽5)—21no—
57C22×C3×AGL(1,𝔽5)—21no—
58C22×C3×AGL(1,𝔽5)—21no—
59C22×C3×AGL(1,𝔽5)C2×C412yes—
60C22×C3×AGL(1,𝔽5)C2×C412yes—
61C22×C3×AGL(1,𝔽5)C2×C412yes—
62C22×C3×AGL(1,𝔽5)C2×C412yes—
63C22×C3×AGL(1,𝔽5)D412yes—
64C22×C3×AGL(1,𝔽5)D412yes—
65C22×C3×AGL(1,𝔽5)D412yes—
66C22×C3×AGL(1,𝔽5)Q812yes—
67C22×C3×C4×C5C2×C411yescharacteristic
68C22×C3×C4×C5C2×C411yescharacteristic
69C22×C3×C4×C5C2×C411yescharacteristic
70C22×C3×Dic5C2×C411yescharacteristic
71C22×C3×Dic5C2×C411yescharacteristic
72C22×C3×Dic5C2×C411yescharacteristic
73C2×C3×C4×D5—21no—
74C2×C3×C4×D5—21no—
75C2×C3×C4×D5—21no—
76C2×C3×C4×D5—21no—
77C2×C3×C4×D5—21no—
78C2×C3×C4×D5—21no—
79C2×C3×C4×D5—21no—
80C2×C3×C4×D5—21no—
81C2×C3×C4×D5—21no—
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5—21no—
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5C2×C412yes—
88C2×C3×C4×D5C2×C412yes—
89C2×C3×C4×D5D412yes—
90C2×C3×C4×D5Q812yes—
91C3×C4⋊AGL(1,𝔽5)—28no—
92C3×C4×AGL(1,𝔽5)—28no—
93C22×C3×C4⋊C4—51no—
94C22×C3×C42—51no—
95C2×C3×#95—51no—
96C2×C3×#95—51no—
97C2×C3×#95—51no—
98C2×C3×#95—51no—
99C2×C3×#95—51no—
100C23×AGL(1,𝔽5)C22×C311yescharacteristic
101C23×AGL(1,𝔽5)C22×C311yescharacteristic
102C23×AGL(1,𝔽5)C22×C311yescharacteristic
103C23×AGL(1,𝔽5)C22×C311yescharacteristic
104C22×C4×D5C22×C311yescharacteristic
105C22×C4×D5C22×C311yescharacteristic
106C22×C4×D5C22×C311yescharacteristic
107C2×C4⋊AGL(1,𝔽5)—22no—
108C2×C4⋊AGL(1,𝔽5)—22no—
109C2×C4⋊AGL(1,𝔽5)C3×C414yescomplemented
110C2×C4×AGL(1,𝔽5)—22no—
111C2×C4×AGL(1,𝔽5)—22no—
112C2×C4×AGL(1,𝔽5)—22no—
113(C2×AGL(1,𝔽5))⋊C4—22no—
114(C2×AGL(1,𝔽5))⋊C4—22no—
115(C2×AGL(1,𝔽5))⋊C4—22no—
116(C2×AGL(1,𝔽5))⋊C4C3×C414yescomplemented
117C5×#95C3×C411yescharacteristic, complemented
118#3963C3×C411yescharacteristic, complemented
119#3963C3×C411yescharacteristic, complemented
120#3963C3×C411yescharacteristic, complemented
121#1436—51noSylow
122C23×C3×C5C22×C411yescharacteristic
123C22×C3×D5C22×C411yescharacteristic
124C22×C3×D5C22×C411yescharacteristic
125C22×C3×D5C2×D411yescharacteristic
126C22×C3×D5C2×D411yescharacteristic
127C22×C3×D5C2×D411yescharacteristic
128C22×C3×D5C2×D411yescharacteristic
129C22×C3×D5C2×Q811yescharacteristic
130C22×C3×D5C2×Q811yescharacteristic
131C22×C3×D5#4111yescharacteristic
132C22×C3×D5#4111yescharacteristic
133C22×C3×D5#4111yescharacteristic
134C22×C3×D5#4111yescharacteristic
135C22×C3×D5#4111yescharacteristic
136C22×C3×D5#4111yescharacteristic
137C2×C3×AGL(1,𝔽5)—22no—
138C2×C3×AGL(1,𝔽5)—22no—
139C2×C3×AGL(1,𝔽5)—22no—
140C2×C3×AGL(1,𝔽5)—22no—
141C2×C3×AGL(1,𝔽5)—22no—
142C2×C3×AGL(1,𝔽5)—22no—
143C2×C3×AGL(1,𝔽5)—22no—
144C2×C3×AGL(1,𝔽5)—22no—
145C2×C3×AGL(1,𝔽5)—22no—
146C2×C3×AGL(1,𝔽5)—22no—
147C2×C3×AGL(1,𝔽5)—22no—
148C2×C3×AGL(1,𝔽5)—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—
155C2×C3×AGL(1,𝔽5)—41no—
156C2×C3×AGL(1,𝔽5)—41no—
157C2×C3×AGL(1,𝔽5)—41no—
158C2×C3×AGL(1,𝔽5)—41no—
159C2×C3×AGL(1,𝔽5)—41no—
160C2×C3×AGL(1,𝔽5)—41no—
161C2×C3×AGL(1,𝔽5)—41no—
162C2×C3×AGL(1,𝔽5)—41no—
163C2×C3×AGL(1,𝔽5)C22⋊C414yes—
164C2×C3×AGL(1,𝔽5)C4⋊C414yescomplemented
165C2×C3×C4×C5—21no—
166C2×C3×C4×C5—21no—
167C2×C3×C4×C5—21no—
168C2×C3×C4×C5—21no—
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—21no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5C4212yescomplemented
173C2×C3×C4×C5C4⋊C412yescomplemented
174C2×C3×Dic5—21no—
175C2×C3×Dic5—21no—
176C2×C3×Dic5—21no—
177C2×C3×Dic5—21no—
178C2×C3×Dic5—21no—
179C2×C3×Dic5—21no—
180C2×C3×Dic5—21no—
181C2×C3×Dic5C4212yescomplemented
182C2×C3×Dic5C4⋊C412yescomplemented
183C3×C4×D5—22no—
184C3×C4×D5—22no—
185C3×C4×D5—22no—
186C3×C4×D5—22no—
187C3×C4×D5—22no—
188C3×C4×D5—22no—
189C3×C4×D5—22no—
190C3×C4×D5—22no—
191C3×C4×D5—41no—
192C3×C4×D5—41no—
193C3×C4×D5—41no—
194C3×C4×D5—41no—
195C23×C3×C4—51no—
196C23×C3×C4—51no—
197C23×C3×C4—51no—
198C23×C3×C4—51no—
199C23×C3×C4—51no—
200C23×C3×C4—51no—
201C23×C3×C4—51no—
202C2×C3×C4⋊C4—54no—
203C2×C3×C4⋊C4—102no—
204C2×C3×C4⋊C4—102no—
205C2×C3×C42—102no—
206C2×C3×C42—102no—
207C2×C3×C42—102no—
208C3×#95—54no—
209C3×#95—51no—
210C3×#95—51no—
211C3×#95—51no—
212C3×#95—102no—
213C3×#95—102no—
214C3×#95—102no—
215C3×#95AGL(1,𝔽5)11yescharacteristic, complemented
216C23×D5C23×C311yescharacteristic
217C22×AGL(1,𝔽5)—21no—
218C22×AGL(1,𝔽5)—21no—
219C22×AGL(1,𝔽5)—21no—
220C22×AGL(1,𝔽5)—21no—
221C22×AGL(1,𝔽5)—21no—
222C22×AGL(1,𝔽5)—21no—
223C22×AGL(1,𝔽5)—21no—
224C22×AGL(1,𝔽5)—21no—
225C22×AGL(1,𝔽5)—21no—
226C22×AGL(1,𝔽5)—21no—
227C22×AGL(1,𝔽5)—21no—
228C22×AGL(1,𝔽5)—21no—
229C22×AGL(1,𝔽5)—21no—
230C22×AGL(1,𝔽5)—21no—
231C22×AGL(1,𝔽5)—21no—
232C22×AGL(1,𝔽5)—21no—
233C22×AGL(1,𝔽5)—21no—
234C22×AGL(1,𝔽5)—21no—
235C22×AGL(1,𝔽5)—21no—
236C22×AGL(1,𝔽5)—21no—
237C22×AGL(1,𝔽5)C2×C3×C412yes—
238C22×AGL(1,𝔽5)C2×C3×C412yes—
239C22×AGL(1,𝔽5)C2×C3×C412yes—
240C22×AGL(1,𝔽5)C2×C3×C412yes—
241C22×AGL(1,𝔽5)C3×D412yes—
242C22×AGL(1,𝔽5)C3×D412yes—
243C22×AGL(1,𝔽5)C3×D412yes—
244C22×AGL(1,𝔽5)C3×Q812yes—
245C22×C4×C5C2×C3×C411yescharacteristic
246C22×C4×C5C2×C3×C411yescharacteristic
247C22×C4×C5C2×C3×C411yescharacteristic
248C22×Dic5C2×C3×C411yescharacteristic
249C22×Dic5C2×C3×C411yescharacteristic
250C22×Dic5C2×C3×C411yescharacteristic
251C2×C4×D5—21no—
252C2×C4×D5—21no—
253C2×C4×D5—21no—
254C2×C4×D5—21no—
255C2×C4×D5—21no—
256C2×C4×D5—21no—
257C2×C4×D5—21no—
258C2×C4×D5—21no—
259C2×C4×D5—21no—
260C2×C4×D5—21no—
261C2×C4×D5—21no—
262C2×C4×D5—21no—
263C2×C4×D5—21no—
264C2×C4×D5—21no—
265C2×C4×D5C2×C3×C412yes—
266C2×C4×D5C2×C3×C412yes—
267C2×C4×D5C3×D412yes—
268C2×C4×D5C3×Q812yes—
269C4⋊AGL(1,𝔽5)—28no—
270C4×AGL(1,𝔽5)—28no—
271C22×C4⋊C4—51no—
272C22×C42—51no—
273C2×#95—51no—
274C2×#95—51no—
275C2×#95—51no—
276C2×#95—51no—
277C2×#95—51no—
278C22×C3×C5C2×C4211yescharacteristic
279C22×C3×C5C2×C4⋊C411yescharacteristic
280C22×C3×C5#11711yescharacteristic
281C22×C3×C5C4×D411yescharacteristic
282C22×C3×C5C4×D411yescharacteristic
283C22×C3×C5C4×D411yescharacteristic
284C22×C3×C5C4×Q811yescharacteristic
285C2×C3×D5C2×C22⋊C411yescharacteristic
286C2×C3×D5C2×C4⋊C411yescharacteristic
287C2×C3×D5#11711yescharacteristic
288C2×C3×D5#11711yescharacteristic
289C2×C3×D5C4×D411yescharacteristic
290C2×C3×D5C4×D411yescharacteristic
291C2×C3×D5C4×D411yescharacteristic
292C2×C3×D5C4×D411yescharacteristic
293C2×C3×D5C4×D411yescharacteristic
294C2×C3×D5C4×Q811yescharacteristic
295C2×C3×D5C4×Q811yescharacteristic
296C2×C3×D5C4×Q811yescharacteristic
297C2×C3×D5#12011yescharacteristic
298C2×C3×D5#12111yescharacteristic
299C2×C3×D5#12111yescharacteristic
300C2×C3×D5C22⋊Q811yescharacteristic
301C2×C3×D5C22⋊Q811yescharacteristic
302C2×C3×D5C22⋊Q811yescharacteristic
303C2×C3×D5C22⋊Q811yescharacteristic
304C2×C3×D5#12311yescharacteristic
305C2×C3×D5#12311yescharacteristic
306C2×C3×D5#12311yescharacteristic
307C2×C3×D5#12411yescharacteristic
308C2×C3×D5#12511yescharacteristic
309C2×C3×D5#12511yescharacteristic
310C2×C3×D5#12611yescharacteristic
311C2×C3×D5#12611yescharacteristic
312C2×C3×D5C4⋊Q811yescharacteristic
313C3×AGL(1,𝔽5)—24no—
314C3×AGL(1,𝔽5)—24no—
315C3×AGL(1,𝔽5)—42no—
316C3×AGL(1,𝔽5)—42no—
317C3×C4×C5—22no—
318C3×C4×C5—22no—
319C3×C4×C5—41no—
320C3×Dic5—22no—
321C3×Dic5—22no—
322C3×Dic5—41no—
323C24×C3—51no—
324C22×C3×C4—52no—
325C22×C3×C4—52no—
326C22×C3×C4—52no—
327C22×C3×C4—52no—
328C22×C3×C4—52no—
329C22×C3×C4—52no—
330C22×C3×C4—51no—
331C22×C3×C4—51no—
332C22×C3×C4—52no—
333C22×C3×C4—52no—
334C22×C3×C4—52no—
335C22×C3×C4—52no—
336C22×C3×C4—52no—
337C22×C3×C4—52no—
338C22×C3×C4—51no—
339C22×C3×C4—101no—
340C22×C3×C4—101no—
341C22×C3×C4—101no—
342C22×C3×C4—101no—
343C22×C3×C4—101no—
344C22×C3×C4—101no—
345C22×C3×C4—101no—
346C22×C3×C4—101no—
347C22×C3×C4—101no—
348C22×C3×C4—101no—
349C22×C3×C4—101no—
350C22×C3×C4—101no—
351C22×C3×C4—101no—
352C22×C3×C4—101no—
353C22×C3×C4—101no—
354C22×C3×C4—101no—
355C22×C3×C4—101no—
356C22×C3×C4—101no—
357C22×C3×C4—101no—
358C22×C3×C4—101no—
359C22×C3×C4—101no—
360C22×C3×C4—101no—
361C22×C3×C4—101no—
362C22×C3×C4—101no—
363C22×C3×C4—101no—
364C22×C3×C4—101no—
365C22×C3×C4—101no—
366C22×C3×C4—101no—
367C22×C3×C4—101no—
368C22×C3×C4—101no—
369C22×C3×C4—101no—
370C22×C3×C4—101no—
371C22×C3×C4—101no—
372C22×C3×C4—101no—
373C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
374C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
375C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
376C3×C4⋊C4—108no—
377C3×C42—108no—
378C23×C5C22×C3×C411yescharacteristic
379C22×D5C22×C3×C411yescharacteristic
380C22×D5C22×C3×C411yescharacteristic
381C22×D5C2×C3×D411yescharacteristic
382C22×D5C2×C3×D411yescharacteristic
383C22×D5C2×C3×D411yescharacteristic
384C22×D5C2×C3×D411yescharacteristic
385C22×D5C2×C3×Q811yescharacteristic
386C22×D5C2×C3×Q811yescharacteristic
387C22×D5C3×#4111yescharacteristic
388C22×D5C3×#4111yescharacteristic
389C22×D5C3×#4111yescharacteristic
390C22×D5C3×#4111yescharacteristic
391C22×D5C3×#4111yescharacteristic
392C22×D5C3×#4111yescharacteristic
393C2×AGL(1,𝔽5)—22no—
394C2×AGL(1,𝔽5)—22no—
395C2×AGL(1,𝔽5)—22no—
396C2×AGL(1,𝔽5)—22no—
397C2×AGL(1,𝔽5)—22no—
398C2×AGL(1,𝔽5)—22no—
399C2×AGL(1,𝔽5)—22no—
400C2×AGL(1,𝔽5)—22no—
401C2×AGL(1,𝔽5)—22no—
402C2×AGL(1,𝔽5)—22no—
403C2×AGL(1,𝔽5)—22no—
404C2×AGL(1,𝔽5)—22no—
405C2×AGL(1,𝔽5)—22no—
406C2×AGL(1,𝔽5)—22no—
407C2×AGL(1,𝔽5)—22no—
408C2×AGL(1,𝔽5)—22no—
409C2×AGL(1,𝔽5)—22no—
410C2×AGL(1,𝔽5)—22no—
411C2×AGL(1,𝔽5)—41no—
412C2×AGL(1,𝔽5)—41no—
413C2×AGL(1,𝔽5)—41no—
414C2×AGL(1,𝔽5)—41no—
415C2×AGL(1,𝔽5)—41no—
416C2×AGL(1,𝔽5)—41no—
417C2×AGL(1,𝔽5)—41no—
418C2×AGL(1,𝔽5)—41no—
419C2×AGL(1,𝔽5)C3×C22⋊C414yes—
420C2×AGL(1,𝔽5)C3×C4⋊C414yescomplemented
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5C3×C4212yescomplemented
429C2×C4×C5C3×C4⋊C412yescomplemented
430C2×Dic5—21no—
431C2×Dic5—21no—
432C2×Dic5—21no—
433C2×Dic5—21no—
434C2×Dic5—21no—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5C3×C4212yescomplemented
438C2×Dic5C3×C4⋊C412yescomplemented
439C4×D5—22no—
440C4×D5—22no—
441C4×D5—22no—
442C4×D5—22no—
443C4×D5—22no—
444C4×D5—22no—
445C4×D5—22no—
446C4×D5—22no—
447C4×D5—41no—
448C4×D5—41no—
449C4×D5—41no—
450C4×D5—41no—
451C23×C4—51no—
452C23×C4—51no—
453C23×C4—51no—
454C23×C4—51no—
455C23×C4—51no—
456C23×C4—51no—
457C23×C4—51no—
458C2×C4⋊C4—54no—
459C2×C4⋊C4—102no—
460C2×C4⋊C4—102no—
461C2×C42—102no—
462C2×C42—102no—
463C2×C42—102no—
464#95—54no—
465#95—51no—
466#95—51no—
467#95—51no—
468#95—102no—
469#95—102no—
470#95—102no—
471#95C3×AGL(1,𝔽5)11yescharacteristic, complemented
472C2×C3×C5C4×C22⋊C411yescharacteristic
473C2×C3×C5C4×C4⋊C411yescharacteristic
474C2×C3×C5C4×C4⋊C411yescharacteristic
475C2×C3×C5#38511yescharacteristic
476C2×C3×C5#38711yescharacteristic
477C2×C3×C5#38811yescharacteristic
478C2×C3×C5#38911yescharacteristic
479C3×D5#38511yescharacteristic
480C3×D5#38611yescharacteristic
481C3×D5#38711yescharacteristic
482C3×D5#38711yescharacteristic
483C3×D5#38711yescharacteristic
484C3×D5#38811yescharacteristic
485C3×D5#38911yescharacteristic
486C3×D5#39111yescharacteristic
487C23×C3—51no—
488C23×C3—51no—
489C23×C3—51no—
490C23×C3—51no—
491C23×C3—51no—
492C23×C3—51no—
493C23×C3—51no—
494C23×C3—51no—
495C23×C3—51no—
496C23×C3—51no—
497C23×C3—51no—
498C23×C3—51no—
499C23×C3—51no—
500C23×C3—51no—
501C23×C3C22×AGL(1,𝔽5)11yescharacteristic
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—54no—
510C2×C3×C4—54no—
511C2×C3×C4—52no—
512C2×C3×C4—52no—
513C2×C3×C4—102no—
514C2×C3×C4—102no—
515C2×C3×C4—102no—
516C2×C3×C4—102no—
517C2×C3×C4—102no—
518C2×C3×C4—102no—
519C2×C3×C4—102no—
520C2×C3×C4—102no—
521C2×C3×C4—102no—
522C2×C3×C4—102no—
523C2×C3×C4—102no—
524C2×C3×C4—102no—
525C2×C3×C4—102no—
526C2×C3×C4—102no—
527C2×C3×C4—102no—
528C2×C3×C4—102no—
529C2×C3×C4—102no—
530C2×C3×C4—102no—
531C2×C3×C4—102no—
532C2×C3×C4—102no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—102no—
538C2×C3×C4—102no—
539C2×C3×C4—102no—
540C2×C3×C4—102no—
541C2×C3×C4—102no—
542C2×C3×C4—102no—
543C2×C3×C4—101no—
544C2×C3×C4—101no—
545C2×C3×C4—101no—
546C2×C3×C4—201no—
547C2×C3×C4—201no—
548C2×C3×C4—201no—
549C2×C3×C4—201no—
550C2×C3×C4—201no—
551C2×C3×C4—201no—
552C2×C3×C4—201no—
553C2×C3×C4—201no—
554C2×C3×C4—201no—
555C2×C3×C4—201no—
556C2×C3×C4—201no—
557C2×C3×C4—201no—
558C2×C3×C4C4×AGL(1,𝔽5)12yescomplemented
559C2×C3×C4C4⋊AGL(1,𝔽5)12yescomplemented
560C22×C5C2×C3×C4211yescharacteristic
561C22×C5C2×C3×C4⋊C411yescharacteristic
562C22×C5C3×#11711yescharacteristic
563C22×C5C3×C4×D411yescharacteristic
564C22×C5C3×C4×D411yescharacteristic
565C22×C5C3×C4×D411yescharacteristic
566C22×C5C3×C4×Q811yescharacteristic
567C2×D5C2×C3×C22⋊C411yescharacteristic
568C2×D5C2×C3×C4⋊C411yescharacteristic
569C2×D5C3×#11711yescharacteristic
570C2×D5C3×#11711yescharacteristic
571C2×D5C3×C4×D411yescharacteristic
572C2×D5C3×C4×D411yescharacteristic
573C2×D5C3×C4×D411yescharacteristic
574C2×D5C3×C4×D411yescharacteristic
575C2×D5C3×C4×D411yescharacteristic
576C2×D5C3×C4×Q811yescharacteristic
577C2×D5C3×C4×Q811yescharacteristic
578C2×D5C3×C4×Q811yescharacteristic
579C2×D5C3×#12011yescharacteristic
580C2×D5C3×#12111yescharacteristic
581C2×D5C3×#12111yescharacteristic
582C2×D5C3×C22⋊Q811yescharacteristic
583C2×D5C3×C22⋊Q811yescharacteristic
584C2×D5C3×C22⋊Q811yescharacteristic
585C2×D5C3×C22⋊Q811yescharacteristic
586C2×D5C3×#12311yescharacteristic
587C2×D5C3×#12311yescharacteristic
588C2×D5C3×#12311yescharacteristic
589C2×D5C3×#12411yescharacteristic
590C2×D5C3×#12511yescharacteristic
591C2×D5C3×#12511yescharacteristic
592C2×D5C3×#12611yescharacteristic
593C2×D5C3×#12611yescharacteristic
594C2×D5C3×C4⋊Q811yescharacteristic
595AGL(1,𝔽5)—24no—
596AGL(1,𝔽5)—24no—
597AGL(1,𝔽5)—42no—
598AGL(1,𝔽5)—42no—
599C4×C5—22no—
600C4×C5—22no—
601C4×C5—41no—
602Dic5—22no—
603Dic5—22no—
604Dic5—41no—
605C24—51no—
606C22×C4—52no—
607C22×C4—52no—
608C22×C4—52no—
609C22×C4—52no—
610C22×C4—52no—
611C22×C4—52no—
612C22×C4—51no—
613C22×C4—51no—
614C22×C4—52no—
615C22×C4—52no—
616C22×C4—52no—
617C22×C4—52no—
618C22×C4—52no—
619C22×C4—52no—
620C22×C4—51no—
621C22×C4—101no—
622C22×C4—101no—
623C22×C4—101no—
624C22×C4—101no—
625C22×C4—101no—
626C22×C4—101no—
627C22×C4—101no—
628C22×C4—101no—
629C22×C4—101no—
630C22×C4—101no—
631C22×C4—101no—
632C22×C4—101no—
633C22×C4—101no—
634C22×C4—101no—
635C22×C4—101no—
636C22×C4—101no—
637C22×C4—101no—
638C22×C4—101no—
639C22×C4—101no—
640C22×C4—101no—
641C22×C4—101no—
642C22×C4—101no—
643C22×C4—101no—
644C22×C4—101no—
645C22×C4—101no—
646C22×C4—101no—
647C22×C4—101no—
648C22×C4—101no—
649C22×C4—101no—
650C22×C4—101no—
651C22×C4—101no—
652C22×C4—101no—
653C22×C4—101no—
654C22×C4—101no—
655C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
656C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
657C22×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
658C4⋊C4—108no—
659C42—108no—
660C3×C5#143611yescharacteristic, complemented, Hall
661C22×C3—51no—
662C22×C3—51no—
663C22×C3—51no—
664C22×C3—51no—
665C22×C3—51no—
666C22×C3—51no—
667C22×C3—51no—
668C22×C3—51no—
669C22×C3—51no—
670C22×C3—51no—
671C22×C3—51no—
672C22×C3—51no—
673C22×C3—51no—
674C22×C3—51no—
675C22×C3—51no—
676C22×C3—51no—
677C22×C3—51no—
678C22×C3—51no—
679C22×C3—51no—
680C22×C3—51no—
681C22×C3—51no—
682C22×C3—51no—
683C22×C3—51no—
684C22×C3—51no—
685C22×C3—51no—
686C22×C3—51no—
687C22×C3—51no—
688C22×C3—51no—
689C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
690C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
691C22×C3#413011yescharacteristic
692C22×C3D4×AGL(1,𝔽5)11yescharacteristic
693C22×C3D4×AGL(1,𝔽5)11yescharacteristic
694C22×C3D4×AGL(1,𝔽5)11yescharacteristic
695C22×C3Q8×AGL(1,𝔽5)11yescharacteristic
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—41no—
699C3×C4—104no—
700C3×C4—104no—
701C3×C4—102no—
702C3×C4—102no—
703C3×C4—202no—
704C3×C4—202no—
705C3×C4—201no—
706C2×C5C3×C4×C22⋊C411yescharacteristic
707C2×C5C3×C4×C4⋊C411yescharacteristic
708C2×C5C3×C4×C4⋊C411yescharacteristic
709C2×C5C3×#38511yescharacteristic
710C2×C5C3×#38711yescharacteristic
711C2×C5C3×#38811yescharacteristic
712C2×C5C3×#38911yescharacteristic
713D5C3×#38511yescharacteristic
714D5C3×#38611yescharacteristic
715D5C3×#38711yescharacteristic
716D5C3×#38711yescharacteristic
717D5C3×#38711yescharacteristic
718D5C3×#38811yescharacteristic
719D5C3×#38911yescharacteristic
720D5C3×#39111yescharacteristic
721C23—51no—
722C23—51no—
723C23—51no—
724C23—51no—
725C23—51no—
726C23—51no—
727C23—51no—
728C23—51no—
729C23—51no—
730C23—51no—
731C23—51no—
732C23—51no—
733C23—51no—
734C23—51no—
735C23C22×C3×AGL(1,𝔽5)11yescharacteristic
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—54no—
744C2×C4—54no—
745C2×C4—52no—
746C2×C4—52no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—102no—
763C2×C4—102no—
764C2×C4—102no—
765C2×C4—102no—
766C2×C4—102no—
767C2×C4—101no—
768C2×C4—101no—
769C2×C4—101no—
770C2×C4—101no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—101no—
778C2×C4—101no—
779C2×C4—101no—
780C2×C4—201no—
781C2×C4—201no—
782C2×C4—201no—
783C2×C4—201no—
784C2×C4—201no—
785C2×C4—201no—
786C2×C4—201no—
787C2×C4—201no—
788C2×C4—201no—
789C2×C4—201no—
790C2×C4—201no—
791C2×C4—201no—
792C2×C4C3×C4×AGL(1,𝔽5)12yescomplemented
793C2×C4C3×C4⋊AGL(1,𝔽5)12yescomplemented
794C2×C3—51no—
795C2×C3—51no—
796C2×C3—51no—
797C2×C3—51no—
798C2×C3—51no—
799C2×C3—51no—
800C2×C3—51no—
801C2×C3—51no—
802C2×C3C4×C4⋊AGL(1,𝔽5)11yescharacteristic
803C2×C3C22⋊C4×AGL(1,𝔽5)11yescharacteristic
804C2×C3#6569911yescharacteristic
805C2×C3#6570011yescharacteristic
806C2×C3C4⋊C4×AGL(1,𝔽5)11yescharacteristic
807C2×C3#6571111yescharacteristic
808C2×C3#6571211yescharacteristic
809C5C3×#143611yescharacteristic, complemented, Sylow
810C22—51no—
811C22—51no—
812C22—51no—
813C22—51no—
814C22—51no—
815C22—51no—
816C22—51no—
817C22—51no—
818C22—51no—
819C22—51no—
820C22—51no—
821C22—51no—
822C22—51no—
823C22—51no—
824C22—51no—
825C22—51no—
826C22—51no—
827C22—51no—
828C22—51no—
829C22—51no—
830C22—51no—
831C22—51no—
832C22—51no—
833C22—51no—
834C22—51no—
835C22—51no—
836C22—51no—
837C22—51no—
838C22C2×C3×C4×AGL(1,𝔽5)11yescharacteristic
839C22C2×C3×C4⋊AGL(1,𝔽5)11yescharacteristic
840C22C3×#413011yescharacteristic
841C22C3×D4×AGL(1,𝔽5)11yescharacteristic
842C22C3×D4×AGL(1,𝔽5)11yescharacteristic
843C22C3×D4×AGL(1,𝔽5)11yescharacteristic
844C22C3×Q8×AGL(1,𝔽5)11yescharacteristic
845C4—22no—
846C4—22no—
847C4—41no—
848C4—104no—
849C4—104no—
850C4—102no—
851C4—102no—
852C4—202no—
853C4—202no—
854C4—201no—
855C3#1060380111yescharacteristic, direct product factor, Sylow
856C2—51no—
857C2—51no—
858C2—51no—
859C2—51no—
860C2—51no—
861C2—51no—
862C2—51no—
863C2—51no—
864C2C3×C4×C4⋊AGL(1,𝔽5)11yescharacteristic
865C2C3×C22⋊C4×AGL(1,𝔽5)11yescharacteristic
866C2C3×#6569911yescharacteristic
867C2C3×#6570011yescharacteristic
868C2C3×C4⋊C4×AGL(1,𝔽5)11yescharacteristic
869C2C3×#6571111yescharacteristic
870C2C3×#6571211yescharacteristic
subgroupG/H
centerC23×C3C22×AGL(1,𝔽5)
commutatorC22×C5C2×C3×C42
FrattiniC23C22×C3×AGL(1,𝔽5)
FittingC3×C5×#95C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C23
cosocleC23×D5C23×C3
hypercenterC3×#95AGL(1,𝔽5)
hypocenterC5C3×#1436
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#95

Complements

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

NH ≅ G/Ntype
8. #10603801C3direct (N × H)
18. C2×C3×C4⋊AGL(1,𝔽5)C4semidirect
25. C3×(C2×AGL(1,𝔽5))⋊C4C4semidirect
26. C3×C5×#95C4semidirect
27. C3×#3963C4semidirect
28. C3×#3963C4semidirect
29. C3×#3963C4semidirect
109. C2×C4⋊AGL(1,𝔽5)C3×C4semidirect
116. (C2×AGL(1,𝔽5))⋊C4C3×C4semidirect
117. C5×#95C3×C4semidirect
118. #3963C3×C4semidirect
119. #3963C3×C4semidirect
120. #3963C3×C4semidirect
164. C2×C3×AGL(1,𝔽5)C4⋊C4semidirect
172. C2×C3×C4×C5C42semidirect
173. C2×C3×C4×C5C4⋊C4semidirect
181. C2×C3×Dic5C42semidirect
182. C2×C3×Dic5C4⋊C4semidirect
215. C3×#95AGL(1,𝔽5)semidirect
420. C2×AGL(1,𝔽5)C3×C4⋊C4semidirect
428. C2×C4×C5C3×C42semidirect
429. C2×C4×C5C3×C4⋊C4semidirect
437. C2×Dic5C3×C42semidirect
438. C2×Dic5C3×C4⋊C4semidirect
471. #95C3×AGL(1,𝔽5)semidirect
558. C2×C3×C4C4×AGL(1,𝔽5)semidirect
559. C2×C3×C4C4⋊AGL(1,𝔽5)semidirect
660. C3×C5#1436semidirect
792. C2×C4C3×C4×AGL(1,𝔽5)semidirect
793. C2×C4C3×C4⋊AGL(1,𝔽5)semidirect
809. C5C3×#1436semidirect
855. C3#10603801direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊AGL(1,𝔽5)2
C22×C3×C4×AGL(1,𝔽5)2
C2×C3×(C2×AGL(1,𝔽5))⋊C42
C3×D5×#952
#106038013
C3×#14365