Subgroups — C₄×C₅×#494 #11944408

Order 1280.

1086 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×Q₁₆	C₂	1	4	yes	maximal
3	C₄×C₅×C₄⋊Q₈	C₂	1	2	yes	maximal
4	C₅×#1969	C₂	1	4	yes	maximal
5	C₅×#1956	C₂	1	2	yes	maximal
6	C₅×#1845	C₂	1	1	yes	maximal, characteristic
7	C₄²×C₅×C₈	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₅×Q₁₆	C₂²	1	4	yes	—
9	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
10	C₂×C₄×C₅×Q₈	C₂²	1	4	yes	—
11	C₅×#494	C₄	1	8	yes	direct product factor
12	C₄×C₅×Q₁₆	—	2	16	no	—
13	C₂×C₅×#107	C₂²	1	4	yes	—
14	C₂×C₅×#103	C₂²	1	8	yes	—
15	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
17	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
19	C₅×#391	C₂²	1	4	yes	—
20	C₅×#389	—	2	4	no	—
21	C₅×#384	C₂²	1	2	yes	—
22	C₄×C₅×C₄⋊C₄	—	2	4	no	—
23	C₄³×C₅	C₂²	1	1	yes	characteristic
24	C₄×#494	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₅×Q₈	C₂³	1	4	yes	—
26	C₂×C₅×Q₁₆	—	2	8	no	—
27	C₂×C₅×Q₁₆	—	2	8	no	—
28	C₂×C₅×Q₁₆	C₂×C₄	1	16	yes	—
29	C₂²×C₅×C₈	C₂³	1	2	yes	—
30	C₂²×C₅×C₈	C₂³	1	2	yes	—
31	C₅×C₄⋊Q₈	—	2	4	no	—
32	C₅×C₄⋊Q₈	C₂×C₄	1	8	yes	—
33	C₄×C₅×Q₈	—	2	16	no	—
34	C₂×C₅×C₄⋊C₄	—	2	4	no	—
35	C₂×C₅×C₄⋊C₄	—	2	4	no	—
36	C₂×C₅×C₄⋊C₄	—	2	4	no	—
37	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
38	C₂×C₄²×C₅	—	2	4	no	—
39	C₂×C₄²×C₅	D₄	1	2	yes	—
40	C₂×C₄²×C₅	D₄	1	2	yes	—
41	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
43	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
44	C₅×#107	—	2	8	no	—
45	C₅×#103	—	2	16	no	—
46	C₄×C₅×C₈	—	2	4	no	—
47	C₄×C₅×C₈	—	2	2	no	—
48	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
49	C₄×C₅×C₈	D₄	1	8	yes	—
50	C₅×#95	—	2	8	no	—
51	C₂×#494	C₂×C₅	1	1	yes	characteristic
52	C₂×C₄×Q₁₆	C₂×C₅	1	4	yes	—
53	C₄×C₄⋊Q₈	C₂×C₅	1	2	yes	—
54	#1969	C₂×C₅	1	4	yes	—
55	#1956	C₂×C₅	1	2	yes	—
56	#1845	C₂×C₅	1	1	yes	characteristic
57	C₄²×C₈	C₂×C₅	1	1	yes	characteristic
58	C₂×C₅×Q₈	—	2	4	no	—
59	C₂×C₅×Q₈	—	2	8	no	—
60	C₂×C₅×Q₈	—	2	8	no	—
61	C₂×C₅×Q₈	C₂²×C₄	1	8	yes	—
62	C₂²×C₄×C₅	—	2	4	no	—
63	C₂²×C₄×C₅	—	2	4	no	—
64	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
67	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
69	C₅×Q₁₆	—	2	32	no	—
70	C₂×C₅×C₈	—	2	2	no	—
71	C₂×C₅×C₈	—	2	2	no	—
72	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
73	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
74	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
75	C₂×C₅×C₈	#41	1	4	yes	—
76	C₅×C₄⋊C₄	—	2	16	no	—
77	C₅×C₄⋊C₄	—	2	8	no	—
78	C₅×C₄⋊C₄	—	4	8	no	—
79	C₅×C₄⋊C₄	—	4	8	no	—
80	C₄²×C₅	—	2	4	no	—
81	C₄²×C₅	—	2	2	no	—
82	C₄²×C₅	—	4	8	no	—
83	C₄²×C₅	Q₁₆	1	8	yes	complemented
84	C₄²×C₅	C₂²×C₄	1	2	yes	—
85	C₄²×C₅	C₂×D₄	1	4	yes	—
86	C₄²×C₅	#41	1	2	yes	—
87	C₂²×Q₁₆	C₂²×C₅	1	4	yes	—
88	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
89	C₂×C₄×Q₈	C₂²×C₅	1	4	yes	—
90	#494	C₄×C₅	1	8	yes	direct product factor
91	C₄×Q₁₆	—	2	16	no	—
92	C₂×#107	C₂²×C₅	1	4	yes	—
93	C₂×#103	C₂²×C₅	1	8	yes	—
94	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
95	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
96	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
97	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
98	#391	C₂²×C₅	1	4	yes	—
99	#389	—	2	4	no	—
100	#384	C₂²×C₅	1	2	yes	—
101	C₄×C₄⋊C₄	—	2	4	no	—
102	C₄³	C₂²×C₅	1	1	yes	characteristic
103	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
104	C₅×Q₈	—	2	16	no	—
105	C₅×Q₈	—	4	8	no	—
106	C₂×C₄×C₅	—	2	2	no	—
107	C₂×C₄×C₅	—	2	2	no	—
108	C₂×C₄×C₅	—	2	2	no	—
109	C₂×C₄×C₅	—	2	8	no	—
110	C₂×C₄×C₅	—	4	4	no	—
111	C₂×C₄×C₅	—	4	4	no	—
112	C₂×C₄×C₅	—	4	4	no	—
113	C₂×C₄×C₅	—	4	8	no	—
114	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
115	C₂×C₄×C₅	#127	1	2	yes	—
116	C₂×C₄×C₅	#127	1	2	yes	—
117	C₂×C₄×C₅	C₂×Q₁₆	1	4	yes	—
118	C₂×C₄×C₅	C₂×Q₁₆	1	4	yes	—
119	C₂×C₄×C₅	C₂×Q₁₆	1	4	yes	—
120	C₂×C₄×C₅	#135	1	4	yes	—
121	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
122	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
123	C₂×C₄×C₅	C₂×#41	1	2	yes	—
124	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
125	C₅×C₈	—	2	4	no	—
126	C₅×C₈	C₄×D₄	1	8	yes	—
127	C₂²×Q₈	C₂³×C₅	1	4	yes	—
128	C₂×Q₁₆	—	2	8	no	—
129	C₂×Q₁₆	—	2	8	no	—
130	C₂×Q₁₆	C₂×C₄×C₅	1	16	yes	—
131	C₂²×C₈	C₂³×C₅	1	2	yes	—
132	C₂²×C₈	C₂³×C₅	1	2	yes	—
133	C₄⋊Q₈	—	2	4	no	—
134	C₄⋊Q₈	C₂×C₄×C₅	1	8	yes	—
135	C₄×Q₈	—	2	16	no	—
136	C₂×C₄⋊C₄	—	2	4	no	—
137	C₂×C₄⋊C₄	—	2	4	no	—
138	C₂×C₄⋊C₄	—	2	4	no	—
139	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
140	C₂×C₄²	—	2	4	no	—
141	C₂×C₄²	C₅×D₄	1	2	yes	—
142	C₂×C₄²	C₅×D₄	1	2	yes	—
143	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
144	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
145	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
146	#107	—	2	8	no	—
147	#103	—	2	16	no	—
148	C₄×C₈	—	2	4	no	—
149	C₄×C₈	—	2	2	no	—
150	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
151	C₄×C₈	C₅×D₄	1	8	yes	—
152	#95	—	2	8	no	—
153	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
154	C₂²×C₅	C₂×#127	1	1	yes	characteristic
155	C₂²×C₅	#532	1	1	yes	characteristic
156	C₂²×C₅	C₂²×Q₁₆	1	2	yes	—
157	C₂²×C₅	C₂×#135	1	2	yes	—
158	C₄×C₅	—	2	2	no	—
159	C₄×C₅	—	2	4	no	—
160	C₄×C₅	—	4	8	no	—
161	C₄×C₅	—	8	4	no	—
162	C₄×C₅	C₄×Q₁₆	1	8	yes	complemented
163	C₄×C₅	#494	1	4	yes	direct product factor
164	C₄×C₅	C₂×C₄×D₄	1	2	yes	—
165	C₄×C₅	#532	1	2	yes	—
166	C₂×Q₈	—	2	4	no	—
167	C₂×Q₈	—	2	8	no	—
168	C₂×Q₈	—	2	8	no	—
169	C₂×Q₈	C₂²×C₄×C₅	1	8	yes	—
170	C₂²×C₄	—	2	4	no	—
171	C₂²×C₄	—	2	4	no	—
172	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
173	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
174	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
175	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
176	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
177	Q₁₆	—	2	32	no	—
178	C₂×C₈	—	2	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
181	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
182	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
183	C₂×C₈	C₅×#41	1	4	yes	—
184	C₄⋊C₄	—	2	16	no	—
185	C₄⋊C₄	—	2	8	no	—
186	C₄⋊C₄	—	4	8	no	—
187	C₄⋊C₄	—	4	8	no	—
188	C₄²	—	2	4	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	4	8	no	—
191	C₄²	C₅×Q₁₆	1	8	yes	complemented
192	C₄²	C₂²×C₄×C₅	1	2	yes	—
193	C₄²	C₂×C₅×D₄	1	4	yes	—
194	C₄²	C₅×#41	1	2	yes	—
195	C₂×C₅	C₄×#127	1	1	yes	characteristic
196	C₂×C₅	C₂×C₄×Q₁₆	1	2	yes	—
197	C₂×C₅	C₂×#494	1	1	yes	characteristic
198	C₂×C₅	#3147	1	1	yes	characteristic
199	C₂×C₅	#3170	1	2	yes	—
200	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
201	Q₈	—	2	16	no	—
202	Q₈	—	4	8	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	8	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	4	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	—	4	8	no	—
211	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
212	C₂×C₄	C₅×#127	1	2	yes	—
213	C₂×C₄	C₅×#127	1	2	yes	—
214	C₂×C₄	C₂×C₅×Q₁₆	1	4	yes	—
215	C₂×C₄	C₂×C₅×Q₁₆	1	4	yes	—
216	C₂×C₄	C₂×C₅×Q₁₆	1	4	yes	—
217	C₂×C₄	C₅×#135	1	4	yes	—
218	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
219	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
220	C₂×C₄	C₂×C₅×#41	1	2	yes	—
221	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
222	C₈	—	2	4	no	—
223	C₈	C₄×C₅×D₄	1	8	yes	—
224	C₅	C₄×#494	1	1	yes	characteristic, direct product factor, Sylow
225	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
226	C₂²	C₂×C₅×#127	1	1	yes	characteristic
227	C₂²	C₅×#532	1	1	yes	characteristic
228	C₂²	C₂²×C₅×Q₁₆	1	2	yes	—
229	C₂²	C₂×C₅×#135	1	2	yes	—
230	C₄	—	2	2	no	—
231	C₄	—	2	4	no	—
232	C₄	—	4	8	no	—
233	C₄	—	8	4	no	—
234	C₄	C₄×C₅×Q₁₆	1	8	yes	complemented
235	C₄	C₅×#494	1	4	yes	direct product factor
236	C₄	C₂×C₄×C₅×D₄	1	2	yes	—
237	C₄	C₅×#532	1	2	yes	—
238	C₂	C₄×C₅×#127	1	1	yes	characteristic
239	C₂	C₂×C₄×C₅×Q₁₆	1	2	yes	—
240	C₂	C₂×C₅×#494	1	1	yes	characteristic
241	C₂	C₅×#3147	1	1	yes	characteristic
242	C₂	C₅×#3170	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle, prime radical	C₂³×C₅	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₅×#494	C₄	direct (N × H)
24. C₄×#494	C₅	direct (N × H)
83. C₄²×C₅	Q₁₆	semidirect
90. #494	C₄×C₅	direct (N × H)
162. C₄×C₅	C₄×Q₁₆	semidirect
163. C₄×C₅	#494	direct (N × H)
191. C₄²	C₅×Q₁₆	semidirect
224. C₅	C₄×#494	direct (N × H)
234. C₄	C₄×C₅×Q₁₆	semidirect
235. C₄	C₅×#494	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#494	2
C₂×C₄×C₅×Q₁₆	2
C₄×C₅×C₄⋊Q₈	2
C₅×#1969	2
C₅×#1956	2
C₅×#1845	2
C₄²×C₅×C₈	2
C₄×#494	5

Subgroups — C4×C5×#494 #11944408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#494 #11944408