Finite Group Databasebeta

← #14284028

Subgroups — #14284028

Order 1920.

452 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 102 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
1#11754615C211yesmaximal, characteristic
2C4×#6762C211yesmaximal, characteristic
3C3×C4×#704C211yesmaximal, characteristic
4#11746507C212yesmaximal, complemented
5#11746506C212yesmaximal, complemented
6#10604350—31nomaximal, Hall
7C2×#6762—21no—
8C2×C3×#704—21no—
9#91815C411yescharacteristic
10C5×#926C411yescharacteristic
11C2×C3×C4×Dic5C2211yescharacteristic
12#91574—21no—
13#91574—21no—
14#91468C411yescharacteristic
15#91468C411yescharacteristic
16C4×#1204—21no—
17C4×#1204—21no—
18#91388C2211yescharacteristic
19#91388C2211yescharacteristic
20#91231C2212yes—
21C4×C3⋊#170—21no—
22C3×#4002C2212yes—
23C3×C4×#170—21no—
24#69862—51nomaximal, Hall
25#65851—31no—
26C4×#704—31no—
27C4×#704D311yescharacteristic
28#64870—32no—
29#64870—32no—
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×Dic5D411yescharacteristic
32C22×C3×Dic5D411yescharacteristic
33C2×#1204—21no—
34C2×#1204—21no—
35#6762—24no—
36C2×C3⋊#170—22no—
37C3×#704—24no—
38C2×C3×#170—22no—
39#6719—21no—
40C4⋊Dic15C2×C411yescharacteristic
41C4⋊Dic15C2×C411yescharacteristic
42C4×Dic15—21no—
43C5×#217—21no—
44C5×C4⋊Dic3C2×C411yescharacteristic
45C5×C4⋊Dic3C2×C411yescharacteristic
46C4×C5×Dic3—21no—
47C3×C4×Dic5C2×C411yescharacteristic
48C3×C4×Dic5D411yescharacteristic
49C3×C4×Dic5D411yescharacteristic
50C3×C4×Dic5C2311yescharacteristic
51Dic3⋊Dic5—21no—
52Dic3⋊Dic5—21no—
53#6669—21no—
54#6669—21no—
55#6668—21no—
56#6668—21no—
57#5470—51no—
58C3×C4×M16—51no—
59C4×#208—51no—
60#4465—52no—
61#4465—52no—
62C2×#704—21no—
63C2×#704—61no—
64C5×#117—31no—
65#4072—31no—
66C2×C4×Dic5C2×D311yescharacteristic
67#4036—31no—
68#4036—31no—
69#4034—31no—
70#4034—31no—
71#4024—61no—
72#4024—61no—
73C4×Dic10—61no—
74C4×Dic10—61no—
75#4002—32no—
76#4002C2×D312yes—
77C4×#170—21no—
78C4×#170—61no—
79#1526—151noSylow
80C23×C3×C5C22⋊C411yescharacteristic
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5C22⋊C411yescharacteristic
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×Dic15—21no—
85C2×Dic15—21no—
86C2×C5×Dic3—21no—
87C2×C5×Dic3—21no—
88C2×C3×Dic5—22no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5C22⋊C411yescharacteristic
91C2×C3×Dic5C22⋊C411yescharacteristic
92C2×C3×Dic5C2×D411yescharacteristic
93C2×C3×Dic5C2×D411yescharacteristic
94#1204—42no—
95#1204—42no—
96C3⋊#170—24no—
97C3×#170—24no—
98C2×C3×M16—101no—
99C2×C3×C42—51no—
100#926—51no—
101#926AGL(1,𝔽5)11yescharacteristic
102#924—101no—
103#924—101no—
104C2×#208—101no—
105#870—51no—
106#870—51no—
107#869—51no—
108#869—51no—
109C4×Dic6—101no—
110C4×Dic6—101no—
111C3×#97—52no—
112C3×C4×C8—101no—
113#803—52no—
114C4×C3⋊C8—101no—
115C22×C4×C5C4×D311yescharacteristic
116C22×Dic5D1211yescharacteristic
117C22×Dic5#6711yescharacteristic
118C2×Dic10—61no—
119C2×Dic10—61no—
120#704—24no—
121#704—64no—
122C2×#170—22no—
123C2×#170—62no—
124C5×C4⋊C4—31no—
125C5×C4⋊C4—31no—
126C5×C22⋊C4—61no—
127C42×C5—61no—
128C22⋊Dic5—61no—
129C4⋊Dic5—31no—
130C4⋊Dic5—31no—
131C4⋊Dic5—61no—
132C4⋊Dic5—61no—
133#683—61no—
134#683—61no—
135#683—61no—
136#683—61no—
137C4×Dic5—61no—
138C4×Dic5C4×D311yescharacteristic
139C4×Dic5D1211yescharacteristic
140C4×Dic5#6711yescharacteristic
141C4×Dic5C22×D311yescharacteristic
142#533—151no—
143C4×M16—51no—
144C4×M16—151no—
145#330—152no—
146#330—152no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C3×C4×C5—21no—
152C3×C4×C5#10112yes—
153Dic15—41no—
154Dic15—41no—
155C3×Dic5—21no—
156C3×Dic5—21no—
157C3×Dic5#10412yes—
158C3×Dic5#10412yes—
159C5×Dic3—41no—
160C5×Dic3—41no—
161C22×C3×C4—51no—
162C22×C3×C4—51no—
163C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
164C2×Dic6—101no—
165C2×Dic6—101no—
166C3×M16—104no—
167C2×C3×C8—102no—
168C3×C42—51no—
169C3×C42—51no—
170C3×C42—51no—
171C3×C42—51no—
172#217—21no—
173#217—101no—
174C4⋊Dic3—51no—
175C4⋊Dic3—51no—
176C4⋊Dic3—101no—
177C4⋊Dic3—101no—
178C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
179C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
180Dic3⋊C4—101no—
181Dic3⋊C4—101no—
182Dic3⋊C4—101no—
183Dic3⋊C4—101no—
184C4×Dic3—21no—
185C4×Dic3—101no—
186#208—104no—
187C2×C3⋊C8—102no—
188C23×C5(C2×D3)⋊C411yescharacteristic
189C2×C4×C5—22no—
190C2×C4×C5—61no—
191C2×C4×C5—61no—
192C2×C4×C5(C2×D3)⋊C411yescharacteristic
193C2×C4×C5C2×C4×D311yescharacteristic
194C2×Dic5—22no—
195C2×Dic5—22no—
196C2×Dic5—61no—
197C2×Dic5—61no—
198C2×Dic5(C2×D3)⋊C411yescharacteristic
199C2×Dic5(C2×D3)⋊C411yescharacteristic
200C2×Dic5C2×D1211yescharacteristic
201C2×Dic5C2×#6711yescharacteristic
202Dic10—122no—
203Dic10—122no—
204#170—24no—
205#170—64no—
206C2×M16—101no—
207C2×M16—301no—
208C4⋊Q8—151no—
209C4⋊Q8—151no—
210#125—151no—
211#125—151no—
212C22⋊Q8—301no—
213C22⋊Q8—301no—
214C4×Q8—301no—
215C4×Q8—301no—
216#117—31no—
217#117—151no—
218C2×C42—51no—
219#97—52no—
220#97—152no—
221C4×C8—101no—
222C4×C8—301no—
223C2×C3×C5—41no—
224C2×C3×C5C2×#10111yescharacteristic
225C2×C3×C5C2×#10411yescharacteristic
226C2×C3×C5C2×#10411yescharacteristic
227C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
228C2×C3×C4—22no—
229C2×C3×C4—51no—
230C2×C3×C4—51no—
231C2×C3×C4—51no—
232C2×C3×C4—51no—
233C2×C3×C4—102no—
234C2×C3×C4—102no—
235C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
236C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—101no—
240C2×Dic3—101no—
241Dic6—202no—
242Dic6—202no—
243C3×C8—104no—
244C3⋊C8—104no—
245C22×C5—21no—
246C22×C5—21no—
247C22×C5—21no—
248C22×C5C2×(C2×D3)⋊C411yescharacteristic
249C4×C5—21no—
250C4×C5—121no—
251C4×C5—121no—
252C4×C5#82412yes—
253Dic5—21no—
254Dic5—21no—
255Dic5—121no—
256Dic5—121no—
257Dic5#80512yes—
258Dic5#82512yes—
259C2×Q8—301no—
260C2×Q8—301no—
261C22×C4—51no—
262C22×C4—51no—
263C22×C4D3×AGL(1,𝔽5)11yescharacteristic
264M16—104no—
265M16—304no—
266C2×C8—102no—
267C2×C8—302no—
268C4⋊C4—31no—
269C4⋊C4—31no—
270C4⋊C4—151no—
271C4⋊C4—151no—
272C4⋊C4—301no—
273C4⋊C4—301no—
274C4⋊C4—301no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C4⋊C4—301no—
278C22⋊C4—61no—
279C22⋊C4—301no—
280C42—51no—
281C42—51no—
282C42—51no—
283C42—51no—
284C42—61no—
285C42—301no—
286C3×C5#152611yescharacteristic, complemented, Hall
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
291C3×C4—21no—
292C3×C4—52no—
293C3×C4—52no—
294C3×C4—101no—
295C3×C4—101no—
296C3×C4#400512yes—
297Dic3—41no—
298Dic3—41no—
299Dic3—201no—
300Dic3—201no—
301C2×C5—41no—
302C2×C5C2×#80511yescharacteristic
303C2×C5C2×#82411yescharacteristic
304C2×C5C2×#82511yescharacteristic
305C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
306Q8—602no—
307Q8—602no—
308C2×C4—22no—
309C2×C4—51no—
310C2×C4—51no—
311C2×C4—51no—
312C2×C4—51no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—102no—
316C2×C4—102no—
317C2×C4—301no—
318C2×C4—301no—
319C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
320C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
321C8—104no—
322C8—304no—
323C2×C3—41no—
324C2×C3C2×#400511yescharacteristic
325C2×C3D5⋊#10411yescharacteristic
326C2×C3D5⋊#10411yescharacteristic
327C5#6986211yescharacteristic, complemented, Sylow
328C22—21no—
329C22—21no—
330C22—21no—
331C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
332C4—21no—
333C4—52no—
334C4—52no—
335C4—101no—
336C4—101no—
337C4—121no—
338C4—121no—
339C4—601no—
340C4—601no—
341C4#9117512yes—
342C3#1060435011yescharacteristic, complemented, Sylow
343C2—41no—
344C2D5⋊#82511yescharacteristic
345C2D5⋊#80511yescharacteristic
346C2C2×#9117511yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1526
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746507C2semidirect
5. #11746506C2semidirect
286. C3×C5#1526semidirect
327. C5#69862semidirect
342. C3#10604350semidirect

Maximal subgroups

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

subgroupindex
#117546152
C4×#67622
C3×C4×#7042
#117465072
#117465062
#106043503
#698625