Finite Group Databasebeta

← #12000618

Subgroups — #12000618

Order 1280.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C5×#2822C211yesmaximal, characteristic
2C2×#65354C211yesmaximal, characteristic
3C2×#65358C211yesmaximal, characteristic
4C2×#64763C211yesmaximal, characteristic
5C2×#64763C211yesmaximal, characteristic
6#10600348C211yesmaximal, characteristic
7#10598121C211yesmaximal, characteristic
8C2×C5×#125C2211yescharacteristic
9C2×C5×#125C2211yescharacteristic
10C2×#4015C2211yescharacteristic
11C5×#400—21no—
12C5×#400—21no—
13C5×#398—22no—
14C5×#398—21no—
15C5×#398—21no—
16C5×#382C2211yescharacteristic
17#65358—22no—
18#65358—22no—
19#65354—22no—
20#65354—22no—
21C2×#3942—21no—
22C2×#3942—21no—
23C2×#3940—21no—
24C2×#3939—21no—
25C2×#3935C2211yescharacteristic
26C2×#3935C2211yescharacteristic
27C2×#3935C2211yescharacteristic
28#64763—22no—
29#64763—22no—
30#64749—22no—
31#10084—51nomaximal, Sylow
32C22×Dic10—21no—
33C5×#125—21no—
34C5×#125—21no—
35C5×#125—21no—
36C5×#125—21no—
37C5×#125—21no—
38C5×#125—21no—
39C5×#125—21no—
40C5×#125—21no—
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4—21no—
43C2×C5×C4⋊C4—21no—
44C2×C5×C4⋊C4—21no—
45C2×C5×C4⋊C4—22no—
46C2×C5×C4⋊C4D411yescharacteristic
47C2×C5×C4⋊C4D411yescharacteristic
48C2×C5×C4⋊C4D411yescharacteristic
49C2×C5×C4⋊C4D411yescharacteristic
50C2×C5×C4⋊C4D412yes—
51C2×C42×C5C2311yescharacteristic
52C2×C4⋊Dic5—21no—
53C2×C4⋊Dic5—21no—
54C22×#168—21no—
55C22×#168—21no—
56C22×#168—21no—
57#4015—21no—
58#4015—21no—
59#4015—21no—
60#4015D412yes—
61C5×#95—22no—
62C5×#95—22no—
63C5×#95—22no—
64C5×#95—21no—
65C5×#95—21no—
66#3942—24no—
67#3942—24no—
68#3940—24no—
69#3939—24no—
70#3935—21no—
71#3935—21no—
72#3935—21no—
73#3935—21no—
74#3935D412yes—
75#3935D412yes—
76C2×#501—51no—
77C2×#491—51no—
78#2822D511yescharacteristic
79#1993—51no—
80C2×#330—51no—
81C2×#330—51no—
82#1295—51no—
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5—21no—
86C22×C4×C5—21no—
87C22×C4×C5—22no—
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×Dic5—41no—
92C2×Dic10—22no—
93C2×Dic10—44no—
94C2×Dic10—41no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4—21no—
97C5×C4⋊C4—21no—
98C5×C4⋊C4—21no—
99C5×C4⋊C4—21no—
100C5×C4⋊C4—21no—
101C5×C4⋊C4—21no—
102C5×C4⋊C4—21no—
103C5×C4⋊C4—42no—
104C5×C4⋊C4—41no—
105C5×C4⋊C4—41no—
106C5×C4⋊C4—41no—
107C5×C4⋊C4—41no—
108C5×C4⋊C4—41no—
109C5×C4⋊C4—41no—
110C5×C4⋊C4—41no—
111C5×C4⋊C4—41no—
112C5×C4⋊C4—82no—
113C42×C5C2×D411yescharacteristic
114C42×C5C2×D411yescharacteristic
115C42×C5C2×D411yescharacteristic
116C42×C5#4111yescharacteristic
117C4⋊Dic5—22no—
118C4⋊Dic5—22no—
119C4⋊Dic5—41no—
120C4⋊Dic5—41no—
121C2×#168—24no—
122C2×#168—22no—
123C2×#168—22no—
124C2×#168—22no—
125C2×#168—42no—
126C2×#168—41no—
127C2×#168—41no—
128C2×C4⋊Q8—51no—
129C2×#125C2×D511yescharacteristic
130C2×#125C2×D511yescharacteristic
131#501—102no—
132#501—102no—
133#491—102no—
134#491—102no—
135C2×#107—101no—
136C2×#106—101no—
137C2×#103—101no—
138C2×#103—101no—
139C2×#97—51no—
140C2×#97—51no—
141C2×#97—51no—
142#400—21no—
143#400—21no—
144#398—22no—
145#398—21no—
146#398—21no—
147#382C2×D511yescharacteristic
148#340—102no—
149#330—102no—
150#330—102no—
151C23×C5#12011yescharacteristic
152C2×C4×C5—22no—
153C2×C4×C5—21no—
154C2×C4×C5—22no—
155C2×C4×C5—21no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—42no—
161C2×C4×C5—42no—
162C2×C4×C5—42no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—42no—
166C2×C4×C5—42no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5#12011yescharacteristic
170C2×C4×C5#12011yescharacteristic
171C2×C4×C5#12111yescharacteristic
172C2×C4×C5#12111yescharacteristic
173C2×C4×C5#12111yescharacteristic
174C2×C4×C5#12711yescharacteristic
175C2×Dic5—42no—
176C2×Dic5—82no—
177Dic10—44no—
178Dic10—82no—
179#168—24no—
180#168—42no—
181#168—42no—
182C22×Q8—101no—
183C22×C8—101no—
184C22×C8—101no—
185C22×C8—101no—
186C4⋊Q8—52no—
187C4⋊Q8—101no—
188C4⋊Q8—101no—
189C4⋊Q8—101no—
190#125—21no—
191#125—21no—
192#125—21no—
193#125—21no—
194#125—21no—
195#125—21no—
196#125—21no—
197#125—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—101no—
204C2×C4⋊C4—101no—
205C2×C4⋊C4C22⋊D511yescharacteristic
206C2×C4⋊C4C22⋊D511yescharacteristic
207C2×C4⋊C4C22⋊D511yescharacteristic
208C2×C4⋊C4C22⋊D511yescharacteristic
209C2×C4⋊C4C22⋊D512yes—
210C2×C42C22×D511yescharacteristic
211#107—104no—
212#106—104no—
213#103—104no—
214#103—104no—
215#97—52no—
216#97—52no—
217#97—101no—
218#97—101no—
219#97—101no—
220#97—101no—
221#95—22no—
222#95—22no—
223#95—22no—
224#95—21no—
225#95—21no—
226C22×C5#39211yescharacteristic
227C22×C5#45412yes—
228C22×C5#45511yescharacteristic
229C22×C5#45611yescharacteristic
230C22×C5#45612yes—
231C4×C5—21no—
232C4×C5—21no—
233C4×C5—21no—
234C4×C5—21no—
235C4×C5—21no—
236C4×C5—21no—
237C4×C5—82no—
238C4×C5—81no—
239C4×C5—81no—
240C4×C5—81no—
241C4×C5—81no—
242Dic5—82no—
243C2×Q8—102no—
244C2×Q8—204no—
245C2×Q8—201no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—201no—
252C22×C4C2×C22⋊D511yescharacteristic
253C22×C4C2×C22⋊D511yescharacteristic
254C22×C4C2×C22⋊D511yescharacteristic
255C2×C8—104no—
256C2×C8—102no—
257C2×C8—102no—
258C2×C8—102no—
259C2×C8—201no—
260C2×C8—202no—
261C2×C8—201no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—82no—
280C4⋊C4—102no—
281C4⋊C4—102no—
282C4⋊C4—201no—
283C4⋊C4—201no—
284C42D4×D511yescharacteristic
285C42D4×D511yescharacteristic
286C42D4×D511yescharacteristic
287C42#71111yescharacteristic
288C2×C5#166312yes—
289C2×C5#166412yes—
290C2×C5#200311yescharacteristic
291C2×C5#200511yescharacteristic
292C2×C5#200711yescharacteristic
293C23#409911yescharacteristic
294Q8—204no—
295Q8—402no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—202no—
314C2×C4—402no—
315C2×C4#408311yescharacteristic
316C2×C4#408311yescharacteristic
317C2×C4#408411yescharacteristic
318C2×C4#408511yescharacteristic
319C2×C4#408511yescharacteristic
320C2×C4#408611yescharacteristic
321C8—104no—
322C8—202no—
323C8—202no—
324C5#1008411yescharacteristic, complemented, Sylow
325C22#6551211yescharacteristic
326C22#6553111yescharacteristic
327C22#6553412yes—
328C22#6553511yescharacteristic
329C22#6553512yes—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—82no—
341C4—402no—
342C2#1060266011yescharacteristic
343C2#1060266111yescharacteristic
344C2#1060267411yescharacteristic
345C2#1060275012yes—
346C2#1060275412yes—
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2822C2
socle, prime radicalC23×C5#120
hypercenter#2822D5
hypocenterC5#10084
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
324. C5#10084semidirect

Maximal subgroups

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

subgroupindex
C5×#28222
C2×#653542
C2×#653582
C2×#647632
#106003482
#105981212
#100845