Finite Group Databasebeta

← #14277125

Subgroups — #14277125

Order 1920.

368 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 88 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#11752415C211yesmaximal, characteristic
2C3×#65756C211yesmaximal, characteristic
3C2×#90955C211yesmaximal, characteristic
4#10598767—31nomaximal, Hall
5C22×C3×C4×D5C2211yescharacteristic
6C2×#6758—21no—
7C2×C3×#700—21no—
8C22×C3⋊#168C411yescharacteristic
9C22×C5×C3⋊C8C411yescharacteristic
10#91241—21no—
11#91232C412yes—
12C3×C22⋊#170—21no—
13C3×#4003C412yes—
14#90955—21no—
15#90955—21no—
16#67687—51nomaximal, Hall
17#65756—31no—
18#65756D311yescharacteristic
19C2×#3952—31no—
20C23×C3×D5Q811yescharacteristic
21C22×C3×C4×C5C2×C411yescharacteristic
22C22×C3×Dic5D411yescharacteristic
23C2×C3×C4×D5—41no—
24C2×C3×C4×D5—41no—
25C2×C3×C4×D5C2×C411yescharacteristic
26C2×C3×C4×D5C2×C411yescharacteristic
27C2×C3×C4×D5D411yescharacteristic
28C2×C3×C4×D5D411yescharacteristic
29C2×C3⋊#170—22no—
30#6758—41no—
31#6758—41no—
32C2×C3×#170—22no—
33C3×#700—41no—
34C3×#700—41no—
35C2×C3⋊#168—21no—
36C2×C3⋊#168—41no—
37C2×C5×C3⋊C8—21no—
38C2×C5×C3⋊C8—41no—
39C3×#407—51no—
40#5207—51no—
41C2×#830—51no—
42C22×C4×D5C2×D311yescharacteristic
43C2×#700—21no—
44C2×#700—61no—
45C22×C5×C8—31no—
46C22×#168—31no—
47C22⋊#170—21no—
48C22⋊#170—61no—
49#4003—32no—
50#4003Dic312yes—
51#3952—61no—
52#3952—61no—
53#1293—151noSylow
54C23×C3×C5C4⋊C411yescharacteristic
55C22×C3×D5—21no—
56C22×C3×D5—21no—
57C22×C3×D5—41no—
58C22×C3×D5—41no—
59C22×C3×D5C4⋊C411yescharacteristic
60C22×C3×D5C4⋊C411yescharacteristic
61C2×C3×C4×C5—21no—
62C2×C3×C4×C5—21no—
63C2×C3×C4×C5C4211yescharacteristic
64C2×C3×C4×C5C22⋊C411yescharacteristic
65C2×C3×Dic5—41no—
66C2×C3×Dic5C22⋊C411yescharacteristic
67C2×C3×Dic5C22⋊C411yescharacteristic
68C3×C4×D5—21no—
69C3×C4×D5—21no—
70C3×C4×D5—21no—
71C3×C4×D5—21no—
72C3×C4×D5—41no—
73C3×C4×D5—41no—
74C3⋊#170—42no—
75C3×#170—42no—
76C3⋊#168—41no—
77C5×C3⋊C8—41no—
78C23×C3×C4—51no—
79C2×C3×M16—101no—
80C2×#208—101no—
81C22×C3⋊C8—51no—
82C22×C3⋊C8AGL(1,𝔽5)11yescharacteristic
83C3×C22⋊C8—52no—
84C3×C22⋊C8—101no—
85#830—52no—
86#830—101no—
87#830—101no—
88#830—101no—
89C23×D5Dic611yescharacteristic
90C22×C4×C5C4×D311yescharacteristic
91C22×Dic5#6711yescharacteristic
92C2×C4×D5—41no—
93C2×C4×D5—41no—
94C2×C4×D5C4×D311yescharacteristic
95C2×C4×D5D1211yescharacteristic
96C2×C4×D5C2×Dic311yescharacteristic
97C2×C4×D5#6711yescharacteristic
98C2×#170—22no—
99C2×#170—62no—
100#700—41no—
101#700—41no—
102#700—121no—
103#700—121no—
104C2×C5×C8—61no—
105C2×C5×C8—121no—
106C2×#168—61no—
107C2×#168—121no—
108#407—51no—
109#407—151no—
110C2×C22⋊C8—151no—
111C22×C3×C5—21no—
112C22×C3×C5—21no—
113C22×C3×C5#9511yescharacteristic
114C22×C3×C5#10811yescharacteristic
115C22×C3×C5#10811yescharacteristic
116C2×C3×D5—21no—
117C2×C3×D5—21no—
118C2×C3×D5—21no—
119C2×C3×D5—21no—
120C2×C3×D5—21no—
121C2×C3×D5—21no—
122C2×C3×D5—42no—
123C2×C3×D5—42no—
124C3×C4×C5—21no—
125C3×C4×C5#9911yescharacteristic
126C3×C4×C5#9911yescharacteristic
127C3×Dic5—21no—
128C3×Dic5—21no—
129C24×C3—51no—
130C22×C3×C4—51no—
131C22×C3×C4—51no—
132C22×C3×C4—51no—
133C22×C3×C4—51no—
134C22×C3×C4—51no—
135C22×C3×C4—201no—
136C22×C3×C4—201no—
137C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
138C3×M16—201no—
139C3×M16—201no—
140C2×C3×C8—102no—
141#208—201no—
142#208—201no—
143C2×C3⋊C8—21no—
144C2×C3⋊C8—41no—
145C2×C3⋊C8—102no—
146C2×C3⋊C8—101no—
147C2×C3⋊C8—201no—
148C23×C5Dic3⋊C411yescharacteristic
149C22×D5—21no—
150C22×D5—21no—
151C22×D5—41no—
152C22×D5—41no—
153C22×D5Dic3⋊C411yescharacteristic
154C22×D5C4⋊Dic311yescharacteristic
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5C4×Dic311yescharacteristic
158C2×C4×C5(C2×D3)⋊C411yescharacteristic
159C2×Dic5—41no—
160C2×Dic5(C2×D3)⋊C411yescharacteristic
161C2×Dic5#21711yescharacteristic
162C4×D5—21no—
163C4×D5—21no—
164C4×D5—21no—
165C4×D5—21no—
166C4×D5—41no—
167C4×D5—41no—
168#170—42no—
169#170—122no—
170C5×C8—121no—
171#168—121no—
172C23×C4—51no—
173C2×M16—101no—
174C2×M16—301no—
175C22×C8—31no—
176C22×C8—151no—
177C22⋊C8—52no—
178C22⋊C8—101no—
179C22⋊C8—152no—
180C22⋊C8—301no—
181C22⋊C8—301no—
182C22⋊C8—301no—
183C2×C3×C5—21no—
184C2×C3×C5—21no—
185C2×C3×C5#33811yescharacteristic
186C2×C3×C5#34111yescharacteristic
187C2×C3×C5#34211yescharacteristic
188C3×D5—41no—
189C3×D5—41no—
190C23×C3—51no—
191C23×C3—51no—
192C23×C3—101no—
193C23×C3—101no—
194C23×C3—201no—
195C23×C3—201no—
196C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—51no—
200C2×C3×C4—51no—
201C2×C3×C4—101no—
202C2×C3×C4—101no—
203C2×C3×C4—101no—
204C2×C3×C4—101no—
205C2×C3×C4—201no—
206C2×C3×C4—201no—
207C2×C3×C4—201no—
208C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
209C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
210C3×C8—202no—
211C3⋊C8—41no—
212C3⋊C8—202no—
213C3⋊C8—201no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5#82211yescharacteristic
217C22×C5#82211yescharacteristic
218C22×C5C3⋊#9511yescharacteristic
219C2×D5—21no—
220C2×D5—21no—
221C2×D5—21no—
222C2×D5—21no—
223C2×D5—21no—
224C2×D5—21no—
225C2×D5—42no—
226C2×D5—42no—
227C4×C5—21no—
228C4×C5#80611yescharacteristic
229C4×C5#80611yescharacteristic
230Dic5—21no—
231Dic5—21no—
232C24—51no—
233C22×C4—51no—
234C22×C4—51no—
235C22×C4—51no—
236C22×C4—51no—
237C22×C4—51no—
238C22×C4—201no—
239C22×C4—201no—
240C22×C4D3×AGL(1,𝔽5)11yescharacteristic
241M16—201no—
242M16—201no—
243M16—601no—
244M16—601no—
245C2×C8—61no—
246C2×C8—102no—
247C2×C8—121no—
248C2×C8—302no—
249C2×C8—301no—
250C2×C8—601no—
251C3×C5#129311yescharacteristic, complemented, Hall
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—101no—
255C22×C3—101no—
256C22×C3—101no—
257C22×C3—101no—
258C22×C3—101no—
259C22×C3—101no—
260C22×C3—202no—
261C22×C3—202no—
262C22×C3#399511yescharacteristic
263C22×C3#399611yescharacteristic
264C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
265C3×C4—21no—
266C3×C4—101no—
267C3×C4—101no—
268C3×C4#399911yescharacteristic
269C3×C4#401111yescharacteristic
270C2×C5—21no—
271C2×C5—21no—
272C2×C5#452711yescharacteristic
273C2×C5#455811yescharacteristic
274C2×C5C3⋊#33811yescharacteristic
275D5—41no—
276D5—41no—
277C23—51no—
278C23—51no—
279C23—101no—
280C23—101no—
281C23—201no—
282C23—201no—
283C23Dic3⋊AGL(1,𝔽5)11yescharacteristic
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—51no—
287C2×C4—51no—
288C2×C4—101no—
289C2×C4—101no—
290C2×C4—101no—
291C2×C4—101no—
292C2×C4—201no—
293C2×C4—201no—
294C2×C4—201no—
295C2×C4Dic3×AGL(1,𝔽5)11yescharacteristic
296C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
297C8—121no—
298C8—202no—
299C8—602no—
300C8—601no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—201no—
304C2×C3—201no—
305C2×C3#6489611yescharacteristic
306C2×C3#6489711yescharacteristic
307C2×C3#6491711yescharacteristic
308C5#6768711yescharacteristic, complemented, Sylow
309C22—21no—
310C22—21no—
311C22—101no—
312C22—101no—
313C22—101no—
314C22—101no—
315C22—101no—
316C22—101no—
317C22—202no—
318C22—202no—
319C22#9116111yescharacteristic
320C22#9116211yescharacteristic
321C22(C2×AGL(1,𝔽5))⋊Dic311yescharacteristic
322C4—21no—
323C4—101no—
324C4—101no—
325C4#9117211yescharacteristic
326C4#9117311yescharacteristic
327C3#1059876711yescharacteristic, complemented, Sylow
328C2—21no—
329C2—21no—
330C2—201no—
331C2—201no—
332C2#1174652111yescharacteristic
333C2#1174653211yescharacteristic
334C2#1174657311yescharacteristic
subgroupG/H
centerC22(C2×AGL(1,𝔽5))⋊Dic3
commutatorC2×C3×C4×C5C42
Frattini, hypercenterC22×C4D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5#95
prime radicalC23×C3×D5Q8
cosocleC22×C3×C4×D5C22
hypocenterC3×C5#1293
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
251. C3×C5#1293semidirect
308. C5#67687semidirect
327. C3#10598767semidirect

Maximal subgroups

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

subgroupindex
#117524152
C3×#657562
C2×#909552
#105987673
#676875