Finite Group Databasebeta

← #13017535

Subgroups — #13017535

Order 1280.

1030 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Q8C211yesmaximal, characteristic
2C2×#64873C214yesmaximal, complemented
3#10604183C211yesmaximal, characteristic
4#10604183C211yesmaximal, characteristic
5C22×Q8×D5—21no—
6C2×C5×C4⋊Q8C411yescharacteristic
7C2×#4090—21no—
8D5×C4⋊Q8—28no—
9C2×D5×C4⋊C4—21no—
10C2×D5×C4⋊C4C412yes—
11C2×#4034—21no—
12C2×#4034C2212yes—
13C2×C42×D5C2211yescharacteristic
14C2×#4015C411yescharacteristic
15C2×#4004C2212yes—
16C2×#4004C2212yes—
17C2×#4003—21no—
18C2×#4003—21no—
19#64918—21no—
20#64918—21no—
21#64873—28no—
22#8340—51nomaximal, Sylow
23C22×C5×Q8—21no—
24C2×Q8×D5—28no—
25C2×Q8×D5—44no—
26C2×Q8×D5—42no—
27C2×Q8×D5—42no—
28C22×C4×D5—22no—
29C22×C4×D5C2×C411yescharacteristic
30C22×C4×D5D411yescharacteristic
31C22×C4×D5D411yescharacteristic
32C22×Dic10—21no—
33C22×Dic10—22no—
34C22×#170—22no—
35C22×#170—22no—
36C5×C4⋊Q8—24no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4C2×C412yes—
39C2×C42×C5C2×C411yescharacteristic
40#4090—28no—
41C2×C4⋊Dic5—21no—
42C2×C4⋊Dic5C2×C412yes—
43C2×#683—22no—
44C2×#683—22no—
45C2×C4×Dic5D411yescharacteristic
46C2×C4×Dic5D411yescharacteristic
47C2×C4×Dic5C2311yescharacteristic
48D5×C4⋊C4—28no—
49D5×C4⋊C4—24no—
50D5×C4⋊C4—24no—
51#4034—28no—
52#4034—24no—
53#4034D418yes—
54C42×D5—24no—
55#4015—24no—
56#4004—24no—
57#4004—24no—
58#4003—42no—
59#4003—42no—
60C22×C4⋊Q8—51no—
61#1797—51no—
62#1797—51no—
63C2×#332—54no—
64C23×D5C22⋊C411yescharacteristic
65C2×C5×Q8—24no—
66C2×C5×Q8—42no—
67C2×C5×Q8—42no—
68C22×C4×C5—22no—
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22×C411yescharacteristic
72C22×Dic5—22no—
73C22×Dic5C22⋊C411yescharacteristic
74C22×Dic5C2×D411yescharacteristic
75C22×Dic5C2×D411yescharacteristic
76Q8×D5—416no—
77Q8×D5—416no—
78C2×C4×D5—22no—
79C2×C4×D5—22no—
80C2×C4×D5—22no—
81C2×C4×D5—22no—
82C2×C4×D5—22no—
83C2×C4×D5—22no—
84C2×C4×D5—22no—
85C2×C4×D5—28no—
86C2×C4×D5—44no—
87C2×C4×D5—44no—
88C2×C4×D5D812yes—
89C2×C4×D5SD1612yes—
90C2×C4×D5SD1612yes—
91C2×C4×D5Q1612yes—
92C2×Dic10—24no—
93C2×Dic10—28no—
94C2×Dic10—42no—
95C2×Dic10—42no—
96C2×Dic10—42no—
97C2×Dic10—42no—
98C2×Dic10—44no—
99C2×#170—42no—
100C2×#170—42no—
101C2×#170—42no—
102C2×#170—42no—
103C2×#170—42no—
104C2×#170—42no—
105C5×C4⋊C4—24no—
106C5×C4⋊C4—22no—
107C5×C4⋊C4C22⋊C414yes—
108C42×C5—22no—
109C4⋊Dic5—24no—
110C4⋊Dic5—22no—
111C4⋊Dic5C22⋊C414yes—
112#683—28no—
113#683—28no—
114C4×Dic5—22no—
115C4×Dic5—22no—
116C4×Dic5C2×D414yes—
117C23×Q8—101no—
118C2×C4⋊Q8—52no—
119C2×C4⋊Q8—51no—
120C2×C4⋊Q8—101no—
121C2×C4⋊Q8—101no—
122C2×C4⋊Q8—108no—
123C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
124C22×C4⋊C4—52no—
125C22×C4⋊C4—101no—
126C22×C42—51no—
127C2×C4⋊C8—52no—
128C2×C4⋊C8—52no—
129C2×C22⋊C8—101no—
130C2×C22⋊C8—101no—
131#336—101no—
132#336—101no—
133#332—108no—
134C23×C5C2×C22⋊C411yescharacteristic
135C22×D5—21no—
136C22×D5—21no—
137C22×D5—21no—
138C22×D5—21no—
139C22×D5#10112yes—
140C22×D5#10212yes—
141C22×D5#10312yes—
142C5×Q8—48no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—24no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
152C2×C4×C5#10212yes—
153C2×C4×C5#10312yes—
154C2×C4×C5C2×C22⋊C412yes—
155C2×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5—24no—
158C2×Dic5—42no—
159C2×Dic5—42no—
160C2×Dic5#10112yes—
161C2×Dic5#12012yes—
162C2×Dic5#12012yes—
163C2×Dic5C2×D811yescharacteristic
164C2×Dic5C2×SD1611yescharacteristic
165C2×Dic5C2×SD1611yescharacteristic
166C2×Dic5C2×Q1611yescharacteristic
167C2×Dic5AGL(1,ℤ/8)12yes—
168C2×Dic5#13712yes—
169C4×D5—28no—
170C4×D5—24no—
171C4×D5—24no—
172C4×D5—24no—
173C4×D5—24no—
174C4×D5—416no—
175Dic10—48no—
176Dic10—48no—
177Dic10—48no—
178#170—82no—
179#170—82no—
180C22×Q8—21no—
181C22×Q8—102no—
182C22×Q8—108no—
183C22×Q8—101no—
184C22×Q8—202no—
185C22×Q8—202no—
186C22×Q8—204no—
187C23×C4—51no—
188C23×C4—51no—
189C23×C4—51no—
190C23×C4—102no—
191C22×C8—102no—
192C22×C8—102no—
193C4⋊Q8—24no—
194C4⋊Q8—58no—
195C4⋊Q8—104no—
196C4⋊Q8—104no—
197C4⋊Q8—108no—
198C4⋊Q8—108no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—52no—
201C2×C4⋊C4—104no—
202C2×C4⋊C4—108no—
203C2×C4⋊C4—102no—
204C2×C4⋊C4—102no—
205C2×C4⋊C4—101no—
206C2×C4⋊C4—104no—
207C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
208C2×C42—51no—
209C2×C42—51no—
210C2×C42—51no—
211C2×C42—104no—
212C2×C42C2×AGL(1,𝔽5)11yescharacteristic
213C4⋊C8—104no—
214C4⋊C8—104no—
215C22⋊C8—202no—
216C22⋊C8—202no—
217C22×C5#37911yescharacteristic
218C22×C5C2×#10111yescharacteristic
219C22×C5C2×#10111yescharacteristic
220C22×C5C2×#10211yescharacteristic
221C22×C5C2×#10311yescharacteristic
222C22×C5#41811yescharacteristic
223C22×C5#41911yescharacteristic
224C2×D5—22no—
225C2×D5—22no—
226C2×D5—22no—
227C2×D5—22no—
228C2×D5—22no—
229C2×D5—22no—
230C2×D5#33214yescomplemented
231C4×C5—22no—
232C4×C5—22no—
233C4×C5—22no—
234C4×C5—44no—
235Dic5—22no—
236Dic5—44no—
237Dic5#44712yes—
238Dic5#44812yes—
239Dic5#45012yes—
240Dic5#45112yes—
241C24—51no—
242C2×Q8—24no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—108no—
246C2×Q8—104no—
247C2×Q8—202no—
248C2×Q8—202no—
249C2×Q8—202no—
250C2×Q8—204no—
251C2×Q8—2016no—
252C2×Q8—2016no—
253C2×Q8—202no—
254C22×C4—22no—
255C22×C4—51no—
256C22×C4—51no—
257C22×C4—51no—
258C22×C4—52no—
259C22×C4—52no—
260C22×C4—52no—
261C22×C4—52no—
262C22×C4—102no—
263C22×C4—102no—
264C22×C4—102no—
265C22×C4—102no—
266C22×C4—102no—
267C22×C4—102no—
268C22×C4—108no—
269C22×C4—102no—
270C22×C4—102no—
271C22×C4—204no—
272C22×C4—204no—
273C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
274C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
275C22×C4C22×AGL(1,𝔽5)11yescharacteristic
276C2×C8—202no—
277C2×C8—202no—
278C2×C8—202no—
279C2×C8—202no—
280C2×C8—202no—
281C2×C8—202no—
282C4⋊C4—24no—
283C4⋊C4—22no—
284C4⋊C4—54no—
285C4⋊C4—108no—
286C4⋊C4—108no—
287C4⋊C4—104no—
288C4⋊C4—102no—
289C4⋊C4C22⋊AGL(1,𝔽5)14yes—
290C42—22no—
291C42—54no—
292C42—102no—
293C42—102no—
294C2×C5C2×#33211yescharacteristic
295C2×C5#154611yescharacteristic
296C2×C5#154911yescharacteristic
297C2×C5#155611yescharacteristic
298C2×C5#178411yescharacteristic
299C2×C5#178611yescharacteristic
300C2×C5#178711yescharacteristic
301D5—24no—
302C23—52no—
303C23—52no—
304C23—52no—
305C23—101no—
306C23—101no—
307C23—101no—
308C23—101no—
309C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
310Q8—48no—
311Q8—208no—
312Q8—208no—
313Q8—208no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—24no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—52no—
324C2×C4—52no—
325C2×C4—51no—
326C2×C4—51no—
327C2×C4—52no—
328C2×C4—51no—
329C2×C4—51no—
330C2×C4—52no—
331C2×C4—52no—
332C2×C4—104no—
333C2×C4—104no—
334C2×C4—104no—
335C2×C4—104no—
336C2×C4—108no—
337C2×C4—101no—
338C2×C4—101no—
339C2×C4—104no—
340C2×C4—2016no—
341C2×C4—202no—
342C2×C4—202no—
343C2×C4#400712yes—
344C2×C4#400912yes—
345C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
346C8—402no—
347C8—402no—
348C5#834011yescharacteristic, complemented, Sylow
349C22—54no—
350C22—102no—
351C22—102no—
352C22—102no—
353C22—102no—
354C22—102no—
355C22—102no—
356C22C2×#400711yescharacteristic
357C22#6576711yescharacteristic
358C22C2×#400911yescharacteristic
359C22#6578211yescharacteristic
360C22D5⋊#10111yescharacteristic
361C22D5⋊#10111yescharacteristic
362C22#6580011yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—44no—
367C4—52no—
368C4—52no—
369C4—52no—
370C4—52no—
371C4—102no—
372C4—204no—
373C2—104no—
374C2D5⋊#33211yescharacteristic
375C2#1060465811yescharacteristic
376C2#1060466011yescharacteristic
377C2#1060466111yescharacteristic
378C2#1060492811yescharacteristic
379C2#1060497311yescharacteristic
380C2#1060498611yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socleC23×C5C2×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5#8340
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#64873C2semidirect
230. C2×D5#332semidirect
348. C5#8340semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Q82
C2×#648732
#106041832
#83405