Finite Group Databasebeta

← C3×#11756846 #72230061

Subgroups — C3×#11756846 #72230061

Order 2880.

1270 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#237C211yesmaximal, characteristic
2C3×D4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
3C32×D4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
4C3×#67⋊AGL(1,𝔽5)C212yesmaximal, complemented
5C3×AGL(1,𝔽5)×#67C212yesmaximal, complemented
6C2×C3×Dic3⋊AGL(1,𝔽5)C212yesmaximal, complemented
7C3×#91923C212yesmaximal, complemented
8C3×D3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
9C3×#91909C211yesmaximal, characteristic, complemented
10C3×ΓL(1,𝔽16)⋊Q8C211yesmaximal, characteristic, complemented
11C3×AGL(1,𝔽5)×Dic6C211yesmaximal, characteristic, complemented
12C3×#66266—31nomaximal
13#11756846C311yesmaximal, characteristic, direct product factor
14C22×C3×ΓL(1,𝔽16)C2212yes—
15C22×C32×AGL(1,𝔽5)C2212yes—
16C2×C3×D3×AGL(1,𝔽5)C2212yes—
17C3×#6819C411yescharacteristic, complemented
18C3×C5×#237C411yescharacteristic, complemented
19C32×D4×D5C2211yescharacteristic
20C3×D5×#67C2212yes—
21C3×#6780C412yescomplemented
22C3×#6779C412yescomplemented
23C2×C3×D5×Dic3C2212yes—
24C3×C4×D3×D5C2211yescharacteristic
25C3×#6766C411yescharacteristic, complemented
26C3×#6765C411yescharacteristic, complemented
27C3×D5×Dic6C2211yescharacteristic
28C3×#6763C2212yes—
29C3×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
30C3×C4×ΓL(1,𝔽16)C2211yescharacteristic
31C32×C22⋊AGL(1,𝔽5)C2212yes—
32C32×C4⋊AGL(1,𝔽5)C2211yescharacteristic
33C32×C4×AGL(1,𝔽5)C2211yescharacteristic
34C3×Dic3⋊AGL(1,𝔽5)C2212yes—
35C3×Dic3⋊AGL(1,𝔽5)C2212yes—
36C3×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
37C3×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
38C3×Dic3⋊AGL(1,𝔽5)C2212yes—
39C3×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
40C3×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
41C3×Dic3×AGL(1,𝔽5)C2212yes—
42C3×Dic3×AGL(1,𝔽5)C2212yes—
43C3×#5546—51nomaximal, Hall
44C3×D5×#41—31no—
45D5×#237C2×C311yescharacteristic
46D4×ΓL(1,𝔽16)C2×C311yescharacteristic, complemented
47C3×Q8×AGL(1,𝔽5)—31no—
48C3×Q8×AGL(1,𝔽5)—31no—
49C3×D4×AGL(1,𝔽5)—21no—
50C3×D4×AGL(1,𝔽5)—32no—
51C3×D4×AGL(1,𝔽5)—31no—
52C3×D4×AGL(1,𝔽5)—32no—
53C3×D4×AGL(1,𝔽5)D311yescharacteristic, complemented
54C3×D4×AGL(1,𝔽5)C2×C311yescharacteristic, complemented
55C3×#4130—32no—
56C3×#4130—31no—
57C2×C3×C4⋊AGL(1,𝔽5)—32no—
58C2×C3×C4⋊AGL(1,𝔽5)—31no—
59#67⋊AGL(1,𝔽5)C2×C312yescomplemented
60AGL(1,𝔽5)×#67C2×C312yescomplemented
61C2×Dic3⋊AGL(1,𝔽5)C2×C312yescomplemented
62#91923C2×C312yescomplemented
63D3×C4⋊AGL(1,𝔽5)C2×C311yescharacteristic, complemented
64#91909C2×C311yescharacteristic, complemented
65ΓL(1,𝔽16)⋊Q8C2×C311yescharacteristic, complemented
66AGL(1,𝔽5)×Dic6C2×C311yescharacteristic, complemented
67C22×C32×D5C2312yes—
68C2×C3×D3×D5C2311yescharacteristic
69C2×C3×ΓL(1,𝔽16)—42no—
70C2×C3×ΓL(1,𝔽16)C2312yes—
71C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
72C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
73C2×C32×AGL(1,𝔽5)—42no—
74C2×C32×AGL(1,𝔽5)C2312yes—
75C2×C32×AGL(1,𝔽5)C2311yescharacteristic
76C2×C32×AGL(1,𝔽5)C2311yescharacteristic
77C3×D3×AGL(1,𝔽5)—42no—
78C32×C5×D4C2×C411yescharacteristic, complemented
79C3×#1220C2×C412yescomplemented
80C2×C3×Dic15C2×C412yescomplemented
81C3×C4×D15C2×C411yescharacteristic, complemented
82C3×Dic30C2×C411yescharacteristic, complemented
83C3×C5×#67C2×C412yescomplemented
84C2×C3×C5×Dic3C2×C412yescomplemented
85C3×C4×C5×D3C2×C411yescharacteristic, complemented
86C3×C5×Dic6C2×C411yescharacteristic, complemented
87C32×C22⋊D5C2×C412yescomplemented
88C32×D20C2×C411yescharacteristic, complemented
89C32×C4×D5C2311yescharacteristic
90C3×#1204C2×C412yescomplemented
91C3×#1202C2×C412yescomplemented
92C3×#1201C2×C412yescomplemented
93C3×#1200C2×C411yescharacteristic, complemented
94C3×D3×Dic5C2×C411yescharacteristic, complemented
95C3×D5×Dic3C2×C412yescomplemented
96C3×D5×Dic3C2×C412yescomplemented
97C3×D5×Dic3C2312yes—
98C3×D5×Dic3C2311yescharacteristic
99#66266—31noHall
100C2×C3×#237—51no—
101C32×C4×D4—51no—
102C3×D4×Dic3—51no—
103C3×C4×#67—52no—
104C2×C3×Dic3⋊C4—52no—
105C3×D3×C4⋊C4—51no—
106C3×#887—51no—
107C3×#67⋊C4—52no—
108C3×#877—52no—
109C3×#872—51no—
110C3×C4×Dic6—51no—
111C22×ΓL(1,𝔽16)C22×C312yes—
112C22×C3×AGL(1,𝔽5)—22no—
113C22×C3×AGL(1,𝔽5)—32no—
114C22×C3×AGL(1,𝔽5)—32no—
115C22×C3×AGL(1,𝔽5)C2×D312yes—
116C22×C3×AGL(1,𝔽5)C22×C312yes—
117C2×D3×AGL(1,𝔽5)C22×C312yes—
118C3×C5×#41—31no—
119#6819C3×C411yescharacteristic, complemented
120C5×#237C3×C411yescharacteristic, complemented
121C3×#713—31no—
122C3×Q8×D5—31no—
123C3×#711—31no—
124C3×#711—32no—
125C3×D4×D5—21no—
126C3×D4×D5—32no—
127C3×D4×D5C2×D311yescharacteristic
128C3×D4×D5C22×C311yescharacteristic
129C3×#709—32no—
130C3×#709—31no—
131C2×C3×C4×D5—32no—
132C2×C3×C4×D5—31no—
133D5×#67C22×C312yes—
134#6780C3×C412yescomplemented
135#6779C3×C412yescomplemented
136C2×D5×Dic3C22×C312yes—
137C4×D3×D5C22×C311yescharacteristic
138#6766C3×C411yescharacteristic, complemented
139#6765C3×C411yescharacteristic, complemented
140D5×Dic6C22×C311yescharacteristic
141#6763C22×C312yes—
142C4⋊ΓL(1,𝔽16)C22×C311yescharacteristic
143C4×ΓL(1,𝔽16)C22×C311yescharacteristic
144C3×C22⋊AGL(1,𝔽5)—22no—
145C3×C22⋊AGL(1,𝔽5)—32no—
146C3×C22⋊AGL(1,𝔽5)—31no—
147C3×C22⋊AGL(1,𝔽5)—31no—
148C3×C22⋊AGL(1,𝔽5)C2×D312yes—
149C3×C22⋊AGL(1,𝔽5)C22×C312yes—
150C3×C4⋊AGL(1,𝔽5)—21no—
151C3×C4⋊AGL(1,𝔽5)—32no—
152C3×C4⋊AGL(1,𝔽5)—31no—
153C3×C4⋊AGL(1,𝔽5)—32no—
154C3×C4⋊AGL(1,𝔽5)—32no—
155C3×C4⋊AGL(1,𝔽5)—31no—
156C3×C4⋊AGL(1,𝔽5)—31no—
157C3×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
158C3×C4⋊AGL(1,𝔽5)C22×C311yescharacteristic
159C3×C4×AGL(1,𝔽5)—21no—
160C3×C4×AGL(1,𝔽5)—32no—
161C3×C4×AGL(1,𝔽5)—32no—
162C3×C4×AGL(1,𝔽5)—31no—
163C3×C4×AGL(1,𝔽5)C2×D311yescharacteristic
164C3×C4×AGL(1,𝔽5)C22×C311yescharacteristic
165Dic3⋊AGL(1,𝔽5)C22×C312yes—
166Dic3⋊AGL(1,𝔽5)C22×C312yes—
167Dic3⋊AGL(1,𝔽5)C22×C311yescharacteristic
168Dic3⋊AGL(1,𝔽5)C22×C311yescharacteristic
169Dic3⋊AGL(1,𝔽5)C22×C312yes—
170(C2×D3)⋊AGL(1,𝔽5)C22×C311yescharacteristic
171(C2×D3)⋊AGL(1,𝔽5)C22×C311yescharacteristic
172Dic3×AGL(1,𝔽5)C22×C312yes—
173Dic3×AGL(1,𝔽5)C22×C312yes—
174C3×#520—151no—
175#5546—51no—
176C22×C32×C5C22×C412yes—
177C2×C3×D15C22×C411yescharacteristic
178C2×C3×C5×D3C22×C411yescharacteristic
179C2×C32×D5—22no—
180C2×C32×D5—22no—
181C2×C32×D5C22×C412yes—
182C2×C32×D5C2411yescharacteristic
183C3×D3×D5—21no—
184C3×D3×D5—21no—
185C3×ΓL(1,𝔽16)—22no—
186C3×ΓL(1,𝔽16)—21no—
187C3×ΓL(1,𝔽16)—21no—
188C32×AGL(1,𝔽5)—21no—
189C32×AGL(1,𝔽5)—22no—
190C32×AGL(1,𝔽5)—21no—
191C32×C4×C5C22×C411yescharacteristic
192C3×Dic15C22×C411yescharacteristic
193C3×Dic15C22×C412yes—
194C3×C5×Dic3C22×C411yescharacteristic
195C3×C5×Dic3C22×C412yes—
196C32×Dic5C22×C411yescharacteristic
197D5×#41—31no—
198Q8×AGL(1,𝔽5)—31no—
199Q8×AGL(1,𝔽5)—31no—
200D4×AGL(1,𝔽5)—32no—
201D4×AGL(1,𝔽5)—31no—
202D4×AGL(1,𝔽5)—32no—
203D4×AGL(1,𝔽5)C3×D311yescharacteristic, complemented
204#4130—32no—
205#4130—31no—
206C2×C4⋊AGL(1,𝔽5)—32no—
207C2×C4⋊AGL(1,𝔽5)—31no—
208C2×C32×D4—51no—
209C22×C32×C4—52no—
210C2×C3×#67—52no—
211C22×C3×Dic3—52no—
212C22×C3×Dic3—52no—
213C3×#237—51no—
214C3×#237—52no—
215C3×#237—52no—
216C3×#237—51no—
217C3×#237—51no—
218C3×#237AGL(1,𝔽5)11yescharacteristic, complemented
219C2×C3×C4×D3—51no—
220C2×C3×C4×D3—52no—
221C2×C3×Dic6—51no—
222C32×C4⋊C4—51no—
223C32×C22⋊C4—52no—
224C32×C42—51no—
225C3×#217—52no—
226C3×(C2×D3)⋊C4—51no—
227C3×(C2×D3)⋊C4—51no—
228C3×C4⋊Dic3—51no—
229C3×Dic3⋊C4—51no—
230C3×Dic3⋊C4—52no—
231C3×Dic3⋊C4—52no—
232C3×Dic3⋊C4—51no—
233C3×Dic3⋊C4—52no—
234C3×C4×Dic3—52no—
235C3×C4×Dic3—52no—
236C3×C4×Dic3—51no—
237C22×C3×D5—22no—
238C22×C3×D5—31no—
239C22×C3×D5C22×D312yes—
240C22×C3×D5C23×C312yes—
241C2×D3×D5C23×C311yescharacteristic
242C2×ΓL(1,𝔽16)—42no—
243C2×ΓL(1,𝔽16)C23×C311yescharacteristic
244C2×ΓL(1,𝔽16)C23×C312yes—
245C2×ΓL(1,𝔽16)C23×C311yescharacteristic
246C2×C3×AGL(1,𝔽5)—21no—
247C2×C3×AGL(1,𝔽5)—21no—
248C2×C3×AGL(1,𝔽5)—22no—
249C2×C3×AGL(1,𝔽5)—31no—
250C2×C3×AGL(1,𝔽5)—32no—
251C2×C3×AGL(1,𝔽5)—31no—
252C2×C3×AGL(1,𝔽5)—42no—
253C2×C3×AGL(1,𝔽5)—42no—
254C2×C3×AGL(1,𝔽5)—42no—
255C2×C3×AGL(1,𝔽5)—42no—
256C2×C3×AGL(1,𝔽5)—122no—
257C2×C3×AGL(1,𝔽5)—122no—
258C2×C3×AGL(1,𝔽5)C22×D311yescharacteristic
259C2×C3×AGL(1,𝔽5)C22×D312yes—
260C2×C3×AGL(1,𝔽5)C22×D311yescharacteristic
261C2×C3×AGL(1,𝔽5)C23×C311yescharacteristic
262C2×C3×AGL(1,𝔽5)C23×C312yes—
263C2×C3×AGL(1,𝔽5)C23×C311yescharacteristic
264D3×AGL(1,𝔽5)—42no—
265C3×C5×Q8—31no—
266C3×C5×D4—21no—
267C3×C5×D4—32no—
268C3×C5×D4C4×D311yescharacteristic, complemented
269C3×C5×D4C2×C3×C411yescharacteristic, complemented
270C2×C3×C4×C5—32no—
271C2×C3×C4×C5—31no—
272#1220C2×C3×C412yescomplemented
273C2×Dic15C2×C3×C412yescomplemented
274C4×D15C2×C3×C411yescharacteristic, complemented
275Dic30C2×C3×C411yescharacteristic, complemented
276C5×#67C2×C3×C412yescomplemented
277C2×C5×Dic3C2×C3×C412yescomplemented
278C4×C5×D3C2×C3×C411yescharacteristic, complemented
279C5×Dic6C2×C3×C411yescharacteristic, complemented
280C3×C22⋊D5—22no—
281C3×C22⋊D5—32no—
282C3×C22⋊D5—32no—
283C3×C22⋊D5C4×D312yescomplemented
284C3×C22⋊D5C2×C3×C412yescomplemented
285C2×C3×Dic5—32no—
286C2×C3×Dic5—31no—
287C3×D20—21no—
288C3×D20—32no—
289C3×D20C4×D311yescharacteristic, complemented
290C3×D20C2×C3×C411yescharacteristic, complemented
291C3×C4×D5—21no—
292C3×C4×D5—32no—
293C3×C4×D5—32no—
294C3×C4×D5—32no—
295C3×C4×D5—31no—
296C3×C4×D5—31no—
297C3×C4×D5—31no—
298C3×C4×D5C22×D311yescharacteristic
299C3×C4×D5C23×C311yescharacteristic
300C3×Dic10—31no—
301C3×Dic10—32no—
302#1204C2×C3×C412yescomplemented
303#1202C2×C3×C412yescomplemented
304#1201C2×C3×C412yescomplemented
305#1200C2×C3×C411yescharacteristic, complemented
306D3×Dic5C2×C3×C411yescharacteristic, complemented
307D5×Dic3C2×C3×C412yescomplemented
308D5×Dic3C2×C3×C412yescomplemented
309D5×Dic3C23×C312yes—
310D5×Dic3C23×C311yescharacteristic
311C2×C3×#41—151no—
312C2×#237—51no—
313C3×C4×Q8—151no—
314C3×C4×Q8—151no—
315C3×C4×D4—51no—
316C3×C4×D4—51no—
317C3×C4×D4—101no—
318C3×C4×D4—152no—
319C3×C4×D4—152no—
320C3×C4×D4—151no—
321C3×#117—151no—
322C3×#117—152no—
323C2×C3×C4⋊C4—151no—
324C2×C3×C4⋊C4—152no—
325D4×Dic3—51no—
326C4×#67—52no—
327C2×Dic3⋊C4—52no—
328D3×C4⋊C4—51no—
329#887—51no—
330#67⋊C4—52no—
331#877—52no—
332#872—51no—
333C4×Dic6—51no—
334C2×C32×C5—22no—
335C2×C32×C5C23×C411yescharacteristic
336C3×D15—21no—
337C3×C5×D3—21no—
338C32×D5—22no—
339C32×D5H(5,𝔽2)11yescharacteristic
340C32×D52−1+411yescharacteristic
341C22×AGL(1,𝔽5)—32no—
342C22×AGL(1,𝔽5)—32no—
343C22×AGL(1,𝔽5)C2×C3×D312yes—
344C5×#41—31no—
345#713—31no—
346Q8×D5—31no—
347#711—31no—
348#711—32no—
349D4×D5—32no—
350D4×D5C2×C3×D311yescharacteristic
351#709—32no—
352#709—31no—
353C2×C4×D5—32no—
354C2×C4×D5—31no—
355C22⋊AGL(1,𝔽5)—32no—
356C22⋊AGL(1,𝔽5)—31no—
357C22⋊AGL(1,𝔽5)—31no—
358C22⋊AGL(1,𝔽5)C2×C3×D312yes—
359C4⋊AGL(1,𝔽5)—32no—
360C4⋊AGL(1,𝔽5)—31no—
361C4⋊AGL(1,𝔽5)—32no—
362C4⋊AGL(1,𝔽5)—32no—
363C4⋊AGL(1,𝔽5)—31no—
364C4⋊AGL(1,𝔽5)—31no—
365C4⋊AGL(1,𝔽5)C2×C3×D311yescharacteristic
366C4×AGL(1,𝔽5)—32no—
367C4×AGL(1,𝔽5)—32no—
368C4×AGL(1,𝔽5)—31no—
369C4×AGL(1,𝔽5)C2×C3×D311yescharacteristic
370C23×C32—52no—
371C22×C3×D3—51no—
372C32×D4—52no—
373C32×D4—51no—
374C32×D4C2×AGL(1,𝔽5)11yescharacteristic, complemented
375C2×C32×C4—51no—
376C2×C32×C4—51no—
377C2×C32×C4—52no—
378C2×C32×C4—51no—
379C2×C32×C4—202no—
380C3×#67—52no—
381C3×#67—52no—
382C3×#67—52no—
383C3×#67C2×AGL(1,𝔽5)12yescomplemented
384C2×C3×Dic3—52no—
385C2×C3×Dic3—52no—
386C2×C3×Dic3—52no—
387C2×C3×Dic3—52no—
388C2×C3×Dic3—51no—
389C2×C3×Dic3—51no—
390C2×C3×Dic3—51no—
391C2×C3×Dic3—52no—
392C2×C3×Dic3—202no—
393C2×C3×Dic3C2×AGL(1,𝔽5)12yescomplemented
394C3×C4×D3—51no—
395C3×C4×D3—51no—
396C3×C4×D3—51no—
397C3×C4×D3—202no—
398C3×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
399C3×Dic6—51no—
400C3×Dic6—52no—
401C3×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
402#520—151noSylow
403C22×C3×C5—22no—
404C22×C3×C5—31no—
405C22×C3×C5C2×C4×D312yes—
406C22×C3×C5C22×C3×C412yes—
407C2×D15C22×C3×C411yescharacteristic
408C2×C5×D3C22×C3×C411yescharacteristic
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5—22no—
413C2×C3×D5—21no—
414C2×C3×D5—22no—
415C2×C3×D5—31no—
416C2×C3×D5—42no—
417C2×C3×D5—42no—
418C2×C3×D5—61no—
419C2×C3×D5—61no—
420C2×C3×D5C2×C4×D312yes—
421C2×C3×D5C22×C3×C412yes—
422C2×C3×D5C23×D311yescharacteristic
423C2×C3×D5C24×C311yescharacteristic
424D3×D5—21no—
425D3×D5—21no—
426ΓL(1,𝔽16)—22no—
427ΓL(1,𝔽16)—21no—
428ΓL(1,𝔽16)—21no—
429C3×AGL(1,𝔽5)—21no—
430C3×AGL(1,𝔽5)—21no—
431C3×AGL(1,𝔽5)—21no—
432C3×AGL(1,𝔽5)—22no—
433C3×AGL(1,𝔽5)—21no—
434C3×AGL(1,𝔽5)—22no—
435C3×AGL(1,𝔽5)—21no—
436C3×AGL(1,𝔽5)—21no—
437C3×AGL(1,𝔽5)—41no—
438C3×AGL(1,𝔽5)—42no—
439C3×AGL(1,𝔽5)—62no—
440C3×AGL(1,𝔽5)—61no—
441C3×AGL(1,𝔽5)—61no—
442C3×C4×C5—21no—
443C3×C4×C5—32no—
444C3×C4×C5—31no—
445C3×C4×C5C2×C4×D311yescharacteristic
446C3×C4×C5C22×C3×C411yescharacteristic
447Dic15C22×C3×C411yescharacteristic
448Dic15C22×C3×C412yes—
449C3×Dic5—21no—
450C3×Dic5—32no—
451C3×Dic5—31no—
452C3×Dic5C2×C4×D311yescharacteristic
453C3×Dic5C22×C3×C411yescharacteristic
454C5×Dic3C22×C3×C411yescharacteristic
455C5×Dic3C22×C3×C412yes—
456C3×#41—31no—
457C3×#41—152no—
458C3×#41—151no—
459C3×#41—152no—
460C3×#41—151no—
461C3×#41—151no—
462C2×C3×Q8—151no—
463C2×C3×D4—51no—
464C2×C3×D4—51no—
465C2×C3×D4—101no—
466C2×C3×D4—152no—
467C22×C3×C4—52no—
468C22×C3×C4—52no—
469C22×C3×C4—102no—
470C22×C3×C4—151no—
471C22×C3×C4—152no—
472C22×C3×C4—152no—
473C22×C3×C4—152no—
474C2×#67—52no—
475C22×Dic3—52no—
476C22×Dic3—52no—
477#237—51no—
478#237—52no—
479#237—52no—
480#237—51no—
481#237—51no—
482#237C3×AGL(1,𝔽5)11yescharacteristic, complemented
483C2×C4×D3—51no—
484C2×C4×D3—52no—
485C2×Dic6—51no—
486C3×C4⋊C4—51no—
487C3×C4⋊C4—51no—
488C3×C4⋊C4—101no—
489C3×C4⋊C4—151no—
490C3×C4⋊C4—152no—
491C3×C4⋊C4—152no—
492C3×C4⋊C4—152no—
493C3×C4⋊C4—151no—
494C3×C4⋊C4—151no—
495C3×C22⋊C4—52no—
496C3×C22⋊C4—52no—
497C3×C22⋊C4—102no—
498C3×C22⋊C4—151no—
499C3×C22⋊C4—151no—
500C3×C22⋊C4—152no—
501C3×C42—51no—
502C3×C42—51no—
503C3×C42—101no—
504C3×C42—151no—
505C3×C42—152no—
506C3×C42—152no—
507#217—52no—
508(C2×D3)⋊C4—51no—
509(C2×D3)⋊C4—51no—
510C4⋊Dic3—51no—
511Dic3⋊C4—52no—
512Dic3⋊C4—51no—
513Dic3⋊C4—51no—
514Dic3⋊C4—52no—
515Dic3⋊C4—52no—
516C4×Dic3—52no—
517C4×Dic3—52no—
518C4×Dic3—51no—
519C32×C5#52011yescharacteristic, complemented, Hall
520C22×D5—31no—
521C22×D5C22×C3×D312yes—
522C2×AGL(1,𝔽5)—31no—
523C2×AGL(1,𝔽5)—32no—
524C2×AGL(1,𝔽5)—31no—
525C2×AGL(1,𝔽5)—42no—
526C2×AGL(1,𝔽5)—122no—
527C2×AGL(1,𝔽5)—122no—
528C2×AGL(1,𝔽5)C22×C3×D311yescharacteristic
529C2×AGL(1,𝔽5)C22×C3×D312yes—
530C2×AGL(1,𝔽5)C22×C3×D311yescharacteristic
531C5×Q8—31no—
532C5×D4—32no—
533C5×D4C3×C4×D311yescharacteristic, complemented
534C2×C4×C5—32no—
535C2×C4×C5—31no—
536C22⋊D5—32no—
537C22⋊D5—32no—
538C22⋊D5C3×C4×D312yescomplemented
539C2×Dic5—32no—
540C2×Dic5—31no—
541D20—32no—
542D20C3×C4×D311yescharacteristic, complemented
543C4×D5—32no—
544C4×D5—31no—
545C4×D5—32no—
546C4×D5—32no—
547C4×D5—31no—
548C4×D5—31no—
549C4×D5C22×C3×D311yescharacteristic
550Dic10—31no—
551Dic10—32no—
552C22×C32—51no—
553C22×C32—52no—
554C22×C32—102no—
555C22×C32—102no—
556C22×C32C22×AGL(1,𝔽5)12yes—
557C2×C3×D3—51no—
558C2×C3×D3—101no—
559C2×C3×D3—101no—
560C2×C3×D3C22×AGL(1,𝔽5)11yescharacteristic
561C32×C4—51no—
562C32×C4—101no—
563C32×C4—102no—
564C32×C4—101no—
565C32×C4C22×AGL(1,𝔽5)11yescharacteristic
566C3×Dic3—52no—
567C3×Dic3—51no—
568C3×Dic3—102no—
569C3×Dic3—101no—
570C3×Dic3—101no—
571C3×Dic3C22×AGL(1,𝔽5)12yes—
572C3×Dic3C22×AGL(1,𝔽5)11yescharacteristic
573C2×#41—151no—
574C4×Q8—151no—
575C4×Q8—151no—
576C4×D4—51no—
577C4×D4—152no—
578C4×D4—152no—
579C4×D4—151no—
580#117—151no—
581#117—152no—
582C2×C4⋊C4—151no—
583C2×C4⋊C4—152no—
584C2×C3×C5—22no—
585C2×C3×C5—22no—
586C2×C3×C5—21no—
587C2×C3×C5—42no—
588C2×C3×C5—61no—
589C2×C3×C5C22×C4×D311yescharacteristic
590C2×C3×C5C23×C3×C411yescharacteristic
591D15—21no—
592C3×D5—22no—
593C3×D5—22no—
594C3×D5—21no—
595C3×D5—21no—
596C3×D5—42no—
597C3×D5—61no—
598C3×D5#100411yescharacteristic
599C3×D5#101011yescharacteristic
600C3×D5C3×H(5,𝔽2)11yescharacteristic
601C3×D5C3×2−1+411yescharacteristic
602C5×D3—21no—
603C23×C3—52no—
604C23×C3—52no—
605C23×C3—102no—
606C23×C3—151no—
607C22×D3—51no—
608C3×Q8—31no—
609C3×Q8—152no—
610C3×Q8—151no—
611C3×D4—21no—
612C3×D4—32no—
613C3×D4—52no—
614C3×D4—52no—
615C3×D4—51no—
616C3×D4—51no—
617C3×D4—101no—
618C3×D4—102no—
619C3×D4—152no—
620C3×D4—152no—
621C3×D4—152no—
622C3×D4D3×AGL(1,𝔽5)11yescharacteristic, complemented
623C3×D4C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
624C2×C3×C4—32no—
625C2×C3×C4—31no—
626C2×C3×C4—51no—
627C2×C3×C4—51no—
628C2×C3×C4—51no—
629C2×C3×C4—51no—
630C2×C3×C4—52no—
631C2×C3×C4—51no—
632C2×C3×C4—52no—
633C2×C3×C4—51no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—102no—
638C2×C3×C4—151no—
639C2×C3×C4—152no—
640C2×C3×C4—151no—
641C2×C3×C4—152no—
642C2×C3×C4—152no—
643C2×C3×C4—151no—
644C2×C3×C4—152no—
645C2×C3×C4—151no—
646C2×C3×C4—151no—
647C2×C3×C4—151no—
648C2×C3×C4—152no—
649C2×C3×C4—202no—
650C2×C3×C4—202no—
651C2×C3×C4—202no—
652C2×C3×C4—202no—
653C2×C3×C4—602no—
654C2×C3×C4—602no—
655#67—52no—
656#67—52no—
657#67—52no—
658#67C2×C3×AGL(1,𝔽5)12yescomplemented
659C2×Dic3—52no—
660C2×Dic3—52no—
661C2×Dic3—52no—
662C2×Dic3—52no—
663C2×Dic3—51no—
664C2×Dic3—51no—
665C2×Dic3—51no—
666C2×Dic3—52no—
667C2×Dic3—202no—
668C2×Dic3C2×C3×AGL(1,𝔽5)12yescomplemented
669C4×D3—51no—
670C4×D3—51no—
671C4×D3—51no—
672C4×D3—202no—
673C4×D3C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
674Dic6—51no—
675Dic6—52no—
676Dic6C2×C3×AGL(1,𝔽5)11yescharacteristic, complemented
677C22×C5—31no—
678C22×C5C2×C3×C4×D312yes—
679C2×D5—22no—
680C2×D5—22no—
681C2×D5—31no—
682C2×D5—61no—
683C2×D5—61no—
684C2×D5C2×C3×C4×D312yes—
685C2×D5C23×C3×D311yescharacteristic
686AGL(1,𝔽5)—21no—
687AGL(1,𝔽5)—22no—
688AGL(1,𝔽5)—21no—
689AGL(1,𝔽5)—62no—
690AGL(1,𝔽5)—61no—
691AGL(1,𝔽5)—61no—
692C4×C5—32no—
693C4×C5—31no—
694C4×C5C2×C3×C4×D311yescharacteristic
695Dic5—32no—
696Dic5—31no—
697Dic5C2×C3×C4×D311yescharacteristic
698C2×C32—22no—
699C2×C32—51no—
700C2×C32—51no—
701C2×C32—102no—
702C2×C32C23×AGL(1,𝔽5)11yescharacteristic
703C3×D3—21no—
704C3×D3—101no—
705#41—31no—
706#41—152no—
707#41—151no—
708#41—152no—
709#41—151no—
710#41—151no—
711C2×Q8—151no—
712C2×D4—51no—
713C2×D4—152no—
714C22×C4—52no—
715C22×C4—151no—
716C22×C4—152no—
717C22×C4—152no—
718C22×C4—152no—
719C4⋊C4—51no—
720C4⋊C4—151no—
721C4⋊C4—152no—
722C4⋊C4—152no—
723C4⋊C4—152no—
724C4⋊C4—151no—
725C4⋊C4—151no—
726C22⋊C4—52no—
727C22⋊C4—151no—
728C22⋊C4—151no—
729C22⋊C4—152no—
730C42—51no—
731C42—151no—
732C42—152no—
733C42—152no—
734C3×C5—21no—
735C3×C5#554611yescharacteristic, complemented
736C3×C5C3×#52011yescharacteristic, complemented
737C22×C3—22no—
738C22×C3—31no—
739C22×C3—51no—
740C22×C3—51no—
741C22×C3—52no—
742C22×C3—52no—
743C22×C3—101no—
744C22×C3—102no—
745C22×C3—102no—
746C22×C3—102no—
747C22×C3—102no—
748C22×C3—102no—
749C22×C3—151no—
750C22×C3—202no—
751C22×C3—202no—
752C22×C3—301no—
753C22×C3—301no—
754C22×C3C2×D3×AGL(1,𝔽5)12yes—
755C22×C3C22×C3×AGL(1,𝔽5)12yes—
756C2×D3—51no—
757C2×D3—101no—
758C2×D3—101no—
759C2×D3C22×C3×AGL(1,𝔽5)11yescharacteristic
760C3×C4—21no—
761C3×C4—31no—
762C3×C4—32no—
763C3×C4—51no—
764C3×C4—51no—
765C3×C4—101no—
766C3×C4—102no—
767C3×C4—101no—
768C3×C4—101no—
769C3×C4—102no—
770C3×C4—101no—
771C3×C4—101no—
772C3×C4—101no—
773C3×C4—101no—
774C3×C4—151no—
775C3×C4—152no—
776C3×C4—202no—
777C3×C4—201no—
778C3×C4—302no—
779C3×C4—301no—
780C3×C4—301no—
781C3×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
782C3×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
783Dic3—52no—
784Dic3—51no—
785Dic3—102no—
786Dic3—101no—
787Dic3—101no—
788Dic3C22×C3×AGL(1,𝔽5)12yes—
789Dic3C22×C3×AGL(1,𝔽5)11yescharacteristic
790C2×C5—22no—
791C2×C5—61no—
792C2×C5C22×C3×C4×D311yescharacteristic
793D5—22no—
794D5—61no—
795D5C3×#100411yescharacteristic
796D5C3×#101011yescharacteristic
797C32#6626611yescharacteristic, complemented, Sylow
798C23—52no—
799C23—151no—
800Q8—31no—
801Q8—152no—
802Q8—151no—
803D4—32no—
804D4—52no—
805D4—51no—
806D4—152no—
807D4—152no—
808D4—152no—
809D4C3×D3×AGL(1,𝔽5)11yescharacteristic, complemented
810C2×C4—32no—
811C2×C4—31no—
812C2×C4—51no—
813C2×C4—51no—
814C2×C4—51no—
815C2×C4—52no—
816C2×C4—151no—
817C2×C4—152no—
818C2×C4—151no—
819C2×C4—152no—
820C2×C4—152no—
821C2×C4—151no—
822C2×C4—152no—
823C2×C4—151no—
824C2×C4—151no—
825C2×C4—151no—
826C2×C4—152no—
827C2×C4—202no—
828C2×C4—602no—
829C2×C4—602no—
830C2×C3—22no—
831C2×C3—22no—
832C2×C3—21no—
833C2×C3—42no—
834C2×C3—51no—
835C2×C3—51no—
836C2×C3—51no—
837C2×C3—51no—
838C2×C3—61no—
839C2×C3—101no—
840C2×C3—101no—
841C2×C3—102no—
842C2×C3—102no—
843C2×C3—202no—
844C2×C3—301no—
845C2×C3C22×D3×AGL(1,𝔽5)11yescharacteristic
846C2×C3C23×C3×AGL(1,𝔽5)11yescharacteristic
847D3—21no—
848D3—101no—
849C5C3×#554611yescharacteristic, complemented, Sylow
850C22—31no—
851C22—51no—
852C22—52no—
853C22—102no—
854C22—102no—
855C22—151no—
856C22—301no—
857C22—301no—
858C22C2×C3×D3×AGL(1,𝔽5)12yes—
859C4—31no—
860C4—32no—
861C4—51no—
862C4—101no—
863C4—102no—
864C4—101no—
865C4—151no—
866C4—152no—
867C4—302no—
868C4—301no—
869C4—301no—
870C4C2×C3×D3×AGL(1,𝔽5)11yescharacteristic
871C3—21no—
872C3#1175684611yescharacteristic, direct product factor
873C3C3×#6626611yescharacteristic, complemented
874C2—22no—
875C2—51no—
876C2—51no—
877C2—61no—
878C2—102no—
879C2—301no—
880C2C22×C3×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2×C3C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C23×C3×C4
FrattiniC2C22×C3×D3×AGL(1,𝔽5)
FittingC32×C5×D4C2×C4
socleC2×C32×C5C23×C4
prime radicalC3×D5×#237C2
cosocleC2×C3×D5C24×C3
hypercenterC3×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C3×#520
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×D4×ΓL(1,𝔽16)C2semidirect
3. C32×D4×AGL(1,𝔽5)C2semidirect
4. C3×#67⋊AGL(1,𝔽5)C2semidirect
5. C3×AGL(1,𝔽5)×#67C2semidirect
6. C2×C3×Dic3⋊AGL(1,𝔽5)C2semidirect
7. C3×#91923C2semidirect
8. C3×D3×C4⋊AGL(1,𝔽5)C2semidirect
9. C3×#91909C2semidirect
10. C3×ΓL(1,𝔽16)⋊Q8C2semidirect
11. C3×AGL(1,𝔽5)×Dic6C2semidirect
13. #11756846C3direct (N × H)
17. C3×#6819C4semidirect
18. C3×C5×#237C4semidirect
21. C3×#6780C4semidirect
22. C3×#6779C4semidirect
25. C3×#6766C4semidirect
26. C3×#6765C4semidirect
46. D4×ΓL(1,𝔽16)C2×C3semidirect
53. C3×D4×AGL(1,𝔽5)D3semidirect
54. C3×D4×AGL(1,𝔽5)C2×C3semidirect
59. #67⋊AGL(1,𝔽5)C2×C3semidirect
60. AGL(1,𝔽5)×#67C2×C3semidirect
61. C2×Dic3⋊AGL(1,𝔽5)C2×C3semidirect
62. #91923C2×C3semidirect
63. D3×C4⋊AGL(1,𝔽5)C2×C3semidirect
64. #91909C2×C3semidirect
65. ΓL(1,𝔽16)⋊Q8C2×C3semidirect
66. AGL(1,𝔽5)×Dic6C2×C3semidirect
78. C32×C5×D4C2×C4semidirect
79. C3×#1220C2×C4semidirect
80. C2×C3×Dic15C2×C4semidirect
81. C3×C4×D15C2×C4semidirect
82. C3×Dic30C2×C4semidirect
83. C3×C5×#67C2×C4semidirect
84. C2×C3×C5×Dic3C2×C4semidirect
85. C3×C4×C5×D3C2×C4semidirect
86. C3×C5×Dic6C2×C4semidirect
87. C32×C22⋊D5C2×C4semidirect
88. C32×D20C2×C4semidirect
90. C3×#1204C2×C4semidirect
91. C3×#1202C2×C4semidirect
92. C3×#1201C2×C4semidirect
93. C3×#1200C2×C4semidirect
94. C3×D3×Dic5C2×C4semidirect
95. C3×D5×Dic3C2×C4semidirect
96. C3×D5×Dic3C2×C4semidirect
119. #6819C3×C4semidirect
120. C5×#237C3×C4semidirect
134. #6780C3×C4semidirect
135. #6779C3×C4semidirect
138. #6766C3×C4semidirect
139. #6765C3×C4semidirect
203. D4×AGL(1,𝔽5)C3×D3semidirect
218. C3×#237AGL(1,𝔽5)semidirect
268. C3×C5×D4C4×D3semidirect
269. C3×C5×D4C2×C3×C4semidirect
272. #1220C2×C3×C4semidirect
273. C2×Dic15C2×C3×C4semidirect
274. C4×D15C2×C3×C4semidirect
275. Dic30C2×C3×C4semidirect
276. C5×#67C2×C3×C4semidirect
277. C2×C5×Dic3C2×C3×C4semidirect
278. C4×C5×D3C2×C3×C4semidirect
279. C5×Dic6C2×C3×C4semidirect
283. C3×C22⋊D5C4×D3semidirect
284. C3×C22⋊D5C2×C3×C4semidirect
289. C3×D20C4×D3semidirect
290. C3×D20C2×C3×C4semidirect
302. #1204C2×C3×C4semidirect
303. #1202C2×C3×C4semidirect
304. #1201C2×C3×C4semidirect
305. #1200C2×C3×C4semidirect
306. D3×Dic5C2×C3×C4semidirect
307. D5×Dic3C2×C3×C4semidirect
308. D5×Dic3C2×C3×C4semidirect
374. C32×D4C2×AGL(1,𝔽5)semidirect
383. C3×#67C2×AGL(1,𝔽5)semidirect
393. C2×C3×Dic3C2×AGL(1,𝔽5)semidirect
398. C3×C4×D3C2×AGL(1,𝔽5)semidirect
401. C3×Dic6C2×AGL(1,𝔽5)semidirect
482. #237C3×AGL(1,𝔽5)semidirect
519. C32×C5#520semidirect
533. C5×D4C3×C4×D3semidirect
538. C22⋊D5C3×C4×D3semidirect
542. D20C3×C4×D3semidirect
622. C3×D4D3×AGL(1,𝔽5)semidirect
623. C3×D4C2×C3×AGL(1,𝔽5)semidirect
658. #67C2×C3×AGL(1,𝔽5)semidirect
668. C2×Dic3C2×C3×AGL(1,𝔽5)semidirect
673. C4×D3C2×C3×AGL(1,𝔽5)semidirect
676. Dic6C2×C3×AGL(1,𝔽5)semidirect
735. C3×C5#5546semidirect
736. C3×C5C3×#520semidirect
797. C32#66266semidirect
809. D4C3×D3×AGL(1,𝔽5)semidirect
849. C5C3×#5546semidirect
872. C3#11756846direct (N × H)
873. C3C3×#66266semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#2372
C3×D4×ΓL(1,𝔽16)2
C32×D4×AGL(1,𝔽5)2
C3×#67⋊AGL(1,𝔽5)2
C3×AGL(1,𝔽5)×#672
C2×C3×Dic3⋊AGL(1,𝔽5)2
C3×#919232
C3×D3×C4⋊AGL(1,𝔽5)2
C3×#919092
C3×ΓL(1,𝔽16)⋊Q82
C3×AGL(1,𝔽5)×Dic62
C3×#662663
#117568463
C3×#55465