Finite Group Databasebeta

← #14312884

Subgroups — #14312884

Order 1920.

456 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91286C211yesmaximal, characteristic
2C2×#91165C211yesmaximal, characteristic, complemented
3C2×D3×#674C211yesmaximal, characteristic, complemented
4#11746782C211yesmaximal, characteristic, complemented
5C3×C22⋊#674C211yesmaximal, characteristic, complemented
6(C2×D3)⋊#674C211yesmaximal, characteristic, complemented
7(C2×D3)⋊#674C211yesmaximal, characteristic, complemented
8#10605007—31nomaximal, Hall
9C2×C5×#235C411yescharacteristic
10C2×#6710C411yescharacteristic
11C22×C3×#168C2211yescharacteristic
12C2×#6650C411yescharacteristic
13C2×#6650C411yescharacteristic
14#91286—22no—
15#91286—22no—
16C2×D3×#168C2211yescharacteristic
17C2×D3×#168C2211yescharacteristic
18C2×C3⋊#674C2211yescharacteristic
19C2×C3⋊#674C2211yescharacteristic
20C2×C3×#674C2211yescharacteristic
21C2×C3×#674C2211yescharacteristic
22#91165—22no—
23D3×#674—22no—
24#69107—51nomaximal, Hall
25C2×#4094—31no—
26C2×#3998—31no—
27C22×#674—31no—
28C22⋊#674—31no—
29C22⋊#674—31no—
30C22⋊#674—31no—
31C22⋊#674D311yescharacteristic, complemented
32C22×C3×C4×C5C2×C411yescharacteristic
33C2×C5×#67C811yescharacteristic
34C2×C5×#67C811yescharacteristic
35C5×#235—22no—
36C5×#235—22no—
37C2×C5×D12C811yescharacteristic
38C2×C4×C5×D3C2×C411yescharacteristic
39C2×C4×C5×D3C2×C411yescharacteristic
40C2×C5×Dic6C811yescharacteristic
41#6710—22no—
42C2×C3⋊#168C2×C411yescharacteristic
43C2×C3⋊#168C2×C411yescharacteristic
44C2×C3×#168—21no—
45C2×C3×#168—21no—
46C2×C3×#168C2×C411yescharacteristic
47C2×C3×#168C2311yescharacteristic
48#6650—22no—
49#6650—22no—
50D3×#168—21no—
51D3×#168—21no—
52D3×#168D412yes—
53D3×#168D412yes—
54C3⋊#674—21no—
55C3⋊#674—21no—
56C3×#674—21no—
57C3×#674—21no—
58C2×#901—51no—
59C2×#798—51no—
60C2×D3×C16—51no—
61C3×C22⋊C16—51no—
62#4549—51no—
63(C2×D3)⋊C16—51no—
64(C2×D3)⋊C16—51no—
65C2×C5×#41—31no—
66#4094—62no—
67#4094—62no—
68C2×#681—31no—
69C2×#681—31no—
70C2×#681—31no—
71C22×#168—31no—
72C22×#168—31no—
73C22×#168C2×D311yescharacteristic
74#3998—62no—
75C2×#674—31no—
76C2×#674—31no—
77C2×#674—62no—
78C2×#674C2×D311yescharacteristic
79C2×#674C2×D311yescharacteristic
80#2113—151noSylow
81C23×C3×C5C2×C811yescharacteristic
82C22×C5×D3C2×C811yescharacteristic
83C22×C5×D3C2×C811yescharacteristic
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C2×C811yescharacteristic
87C2×C3×C4×C5C22×C411yescharacteristic
88C5×#67—22no—
89C5×#67—22no—
90C2×C5×Dic3C2×C811yescharacteristic
91C2×C5×Dic3C2×C811yescharacteristic
92C5×D12—22no—
93C4×C5×D3—21no—
94C4×C5×D3—21no—
95C4×C5×D3C22⋊C412yes—
96C4×C5×D3M1612yes—
97C5×Dic6—22no—
98C3⋊#168—21no—
99C3⋊#168C22⋊C412yes—
100C3×#168—21no—
101C3×#168C2×D411yescharacteristic
102C3×#168C2×D411yescharacteristic
103C2×#235AGL(1,𝔽5)11yescharacteristic
104C22×C3×C8—51no—
105C2×#208—51no—
106#901—102no—
107#901—102no—
108C2×ΓL(1,𝔽25)—51no—
109C2×ΓL(1,𝔽25)—51no—
110C2×D3×C8—51no—
111C2×D3×C8—51no—
112C2×C3×C16—51no—
113C2×C3×C16—51no—
114C2×C3⋊C16—51no—
115C2×C3⋊C16—51no—
116#798—102no—
117D3×C16—102no—
118C5×#41—62no—
119C5×#41—62no—
120C2×C5×Q8—31no—
121C2×C5×D4—31no—
122C2×C5×D4—31no—
123C2×C5×D4—31no—
124C22×C4×C5—31no—
125C22×C4×C5—31no—
126C22×C4×C5C4×D311yescharacteristic
127#681—62no—
128#681—62no—
129#681—62no—
130C2×#168—21no—
131C2×#168—21no—
132C2×#168—31no—
133C2×#168—32no—
134C2×#168—32no—
135C2×#168—31no—
136C2×#168—61no—
137C2×#168—61no—
138C2×#168C4×D311yescharacteristic
139C2×#168C22×D311yescharacteristic
140#674—21no—
141#674—21no—
142#674—61no—
143#674—61no—
144C2×#131—151no—
145C2×M32—151no—
146C22×C16—151no—
147C22⋊C16—51no—
148C22⋊C16—151no—
149C22⋊C16—151no—
150C22⋊C16—151no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5C22×C811yescharacteristic
155C2×C5×D3—21no—
156C2×C5×D3—21no—
157C2×C5×D3—21no—
158C2×C5×D3—21no—
159C2×C5×D3—21no—
160C2×C5×D3C22⋊C812yes—
161C3×C4×C5—21no—
162C3×C4×C5C2×C22⋊C411yescharacteristic
163C3×C4×C5C2×M1611yescharacteristic
164C5×Dic3—21no—
165C5×Dic3C22⋊C812yes—
166C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
167C2×#67#17011yescharacteristic
168C2×#67#17011yescharacteristic
169#235—22no—
170#235—22no—
171C2×D12#17011yescharacteristic
172C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
173C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
174C2×Dic6#17011yescharacteristic
175C2×C3×C8—51no—
176C2×C3×C8—51no—
177C2×C3×C8—101no—
178C2×C3×C8—101no—
179#208—102no—
180C2×C3⋊C8—51no—
181C2×C3⋊C8—51no—
182ΓL(1,𝔽25)—102no—
183ΓL(1,𝔽25)—102no—
184D3×C8—52no—
185D3×C8—52no—
186D3×C8—101no—
187D3×C8—101no—
188C3×C16—101no—
189C3×C16—101no—
190C3⋊C16—101no—
191C3⋊C16—101no—
192C23×C5—31no—
193C23×C5—31no—
194C23×C5D3×C811yescharacteristic
195C5×Q8—62no—
196C5×D4—62no—
197C5×D4—62no—
198C5×D4—62no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—31no—
202C2×C4×C5—32no—
203C2×C4×C5—32no—
204C2×C4×C5—31no—
205C2×C4×C5—61no—
206C2×C4×C5—61no—
207C2×C4×C5D3×C811yescharacteristic
208C2×C4×C5C2×C4×D311yescharacteristic
209#168—21no—
210#168—32no—
211#168—61no—
212#168D3×D411yescharacteristic
213#168D3×D411yescharacteristic
214C2×#41—31no—
215#131—302no—
216#131—302no—
217C2×M16—151no—
218C2×M16—151no—
219C2×M16—151no—
220C22×C8—51no—
221C22×C8—151no—
222C22×C8—151no—
223M32—302no—
224C2×C16—51no—
225C2×C16—51no—
226C2×C16—151no—
227C2×C16—151no—
228C2×C16—302no—
229C2×C3×C5—41no—
230C2×C3×C5C2×C22⋊C811yescharacteristic
231C2×C3×C5#50411yescharacteristic
232C2×C3×C5#50411yescharacteristic
233C5×D3—22no—
234C5×D3—41no—
235C23×C3C2×#17011yescharacteristic
236C22×D3C2×#17011yescharacteristic
237C22×D3C2×#17011yescharacteristic
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4C2×#17011yescharacteristic
241C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
242#67—22no—
243#67—22no—
244C2×Dic3C2×#17011yescharacteristic
245C2×Dic3C2×#17011yescharacteristic
246D12—22no—
247C4×D3—21no—
248C4×D3—21no—
249C4×D3#70412yes—
250C4×D3C22⋊AGL(1,𝔽5)12yes—
251Dic6—22no—
252C3×C8—51no—
253C3×C8—51no—
254C3×C8—101no—
255C3⋊C8—52no—
256C3⋊C8—101no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—32no—
261C22×C5—61no—
262C22×C5—61no—
263C22×C5—61no—
264C22×C5—61no—
265C22×C5—61no—
266C22×C5C2×D3×C811yescharacteristic
267C4×C5—21no—
268C4×C5—32no—
269C4×C5—61no—
270C4×C5D3×C22⋊C411yescharacteristic
271C4×C5D3×M1611yescharacteristic
272#41—62no—
273#41—62no—
274C2×Q8—31no—
275C2×D4—31no—
276C2×D4—31no—
277C2×D4—31no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4D3×AGL(1,𝔽5)11yescharacteristic
281M16—302no—
282M16—302no—
283M16—302no—
284C2×C8—51no—
285C2×C8—51no—
286C2×C8—101no—
287C2×C8—101no—
288C2×C8—152no—
289C2×C8—152no—
290C2×C8—151no—
291C2×C8—151no—
292C2×C8—301no—
293C2×C8—301no—
294C16—101no—
295C16—101no—
296C16—301no—
297C16—301no—
298C3×C5#211311yescharacteristic, complemented, Hall
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3C22×#17011yescharacteristic
303C2×D3—21no—
304C2×D3—21no—
305C2×D3—21no—
306C2×D3—21no—
307C2×D3—21no—
308C2×D3C22⋊#17012yes—
309C3×C4—21no—
310C3×C4C2×#70411yescharacteristic
311C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
312Dic3—21no—
313Dic3C22⋊#17012yes—
314C2×C5—41no—
315C2×C5—62no—
316C2×C5—121no—
317C2×C5D3×C22⋊C811yescharacteristic
318C2×C5#490111yescharacteristic
319C2×C5#490711yescharacteristic
320C23—31no—
321C23—31no—
322C23D3×#17011yescharacteristic
323Q8—62no—
324D4—62no—
325D4—62no—
326D4—62no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—31no—
330C2×C4—32no—
331C2×C4—32no—
332C2×C4—31no—
333C2×C4—61no—
334C2×C4—61no—
335C2×C4D3×#17011yescharacteristic
336C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
337C8—51no—
338C8—51no—
339C8—101no—
340C8—152no—
341C8—301no—
342C2×C3—41no—
343C2×C3#6579111yescharacteristic
344C2×C3#6579111yescharacteristic
345C2×C3C2×C22⋊#17011yescharacteristic
346D3—22no—
347D3—41no—
348C5#6910711yescharacteristic, complemented, Sylow
349C22—21no—
350C22—21no—
351C22—21no—
352C22—32no—
353C22—61no—
354C22—61no—
355C22—61no—
356C22—61no—
357C22—61no—
358C22C2×D3×#17011yescharacteristic
359C4—21no—
360C4—32no—
361C4—61no—
362C4D3×#70411yescharacteristic
363C4D3×C22⋊AGL(1,𝔽5)11yescharacteristic
364C3#1060500711yescharacteristic, complemented, Sylow
365C2—41no—
366C2—62no—
367C2—121no—
368C2#1175173611yescharacteristic
369C2#1175173811yescharacteristic
370C2D3×C22⋊#17011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C22×C8
FittingC22×C3×C4×C5C2×C4
prime radicalC2×C5×#235C4
cosocleC2×C3×#168C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2113
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91165C2semidirect
3. C2×D3×#674C2semidirect
4. #11746782C2semidirect
5. C3×C22⋊#674C2semidirect
6. (C2×D3)⋊#674C2semidirect
7. (C2×D3)⋊#674C2semidirect
31. C22⋊#674D3semidirect
298. C3×C5#2113semidirect
348. C5#69107semidirect
364. C3#10605007semidirect

Maximal subgroups

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

subgroupindex
C2×#912862
C2×#911652
C2×D3×#6742
#117467822
C3×C22⋊#6742
(C2×D3)⋊#6742
#106050073
#691075