Subgroups — C₅×#33498 #11956218

Order 1280.

494 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#2183	C₂	1	6	yes	maximal, complemented
3	C₅×Q₈×C₁₆	C₂	1	2	yes	maximal, complemented
4	C₅×#2163	C₂	1	3	yes	maximal
5	C₅×#2162	C₂	1	3	yes	maximal
6	C₂×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
7	C₅×C₈×Q₈	C₄	1	3	yes	—
8	C₅×C₈×Q₈	C₄	1	1	yes	characteristic
9	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
10	C₅×C₈×Q₈	C₂²	1	3	yes	—
11	C₂×C₅×C₄⋊C₈	C₄	1	3	yes	—
12	C₂×C₄×C₅×C₈	C₂²	1	3	yes	—
13	C₅×C₄⋊C₁₆	C₂²	1	6	yes	—
14	C₅×C₄⋊C₁₆	C₂²	1	6	yes	—
15	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₅×C₂²⋊C₁₆	C₂²	1	3	yes	—
17	C₅×#346	C₂²	1	6	yes	—
18	C₄×C₅×C₁₆	C₂²	1	6	yes	—
19	#33498	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂²×C₅×Q₈	C₈	1	1	yes	characteristic
21	C₂²×C₅×C₈	C₂×C₄	1	3	yes	—
22	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
23	C₄×C₅×Q₈	C₈	1	3	yes	—
24	C₄×C₅×Q₈	C₈	1	1	yes	characteristic
25	C₄×C₅×Q₈	C₂×C₄	1	3	yes	—
26	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
27	C₂×C₅×C₄⋊C₄	C₈	1	3	yes	—
28	C₂×C₄²×C₅	C₂×C₄	1	3	yes	—
29	C₂×C₅×C₁₆	C₂³	1	2	yes	—
30	C₂×C₅×C₁₆	C₂³	1	6	yes	—
31	C₅×C₄⋊C₈	C₂×C₄	1	3	yes	—
32	C₅×C₄⋊C₈	C₂×C₄	1	6	yes	—
33	C₅×C₄⋊C₈	C₂×C₄	1	3	yes	—
34	C₄×C₅×C₈	C₂×C₄	1	3	yes	—
35	C₄×C₅×C₈	C₂×C₄	1	3	yes	—
36	C₄×C₅×C₈	C₂³	1	3	yes	—
37	C₄×C₅×C₈	C₂³	1	3	yes	—
38	C₂×C₈×Q₈	C₂×C₅	1	1	yes	characteristic
39	#2183	C₂×C₅	1	6	yes	complemented
40	Q₈×C₁₆	C₂×C₅	1	2	yes	complemented
41	#2163	C₂×C₅	1	3	yes	—
42	#2162	C₂×C₅	1	3	yes	—
43	C₂×C₅×Q₈	—	2	4	no	—
44	C₂×C₅×Q₈	C₂×C₈	1	3	yes	—
45	C₂×C₅×Q₈	C₂×C₈	1	1	yes	characteristic
46	C₂²×C₄×C₅	C₂×C₈	1	3	yes	—
47	C₂²×C₄×C₅	C₂×C₈	1	3	yes	—
48	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₅×C₈	—	2	2	no	—
50	C₂×C₅×C₈	—	4	3	no	—
51	C₂×C₅×C₈	C₂²×C₄	1	3	yes	—
52	C₂×C₅×C₈	C₂²×C₄	1	3	yes	—
53	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
55	C₅×C₄⋊C₄	C₂×C₈	1	6	yes	—
56	C₅×C₄⋊C₄	C₂×C₈	1	3	yes	—
57	C₅×C₄⋊C₄	C₂×C₈	1	3	yes	—
58	C₄²×C₅	C₂×C₈	1	3	yes	—
59	C₄²×C₅	C₂×C₈	1	3	yes	—
60	C₄²×C₅	C₂²×C₄	1	3	yes	—
61	C₄²×C₅	C₂²×C₄	1	3	yes	—
62	C₅×C₁₆	—	2	2	no	—
63	C₅×C₁₆	—	2	6	no	—
64	C₂×C₄×Q₈	C₄×C₅	1	1	yes	characteristic
65	C₈×Q₈	C₄×C₅	1	3	yes	—
66	C₈×Q₈	C₄×C₅	1	1	yes	characteristic
67	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
68	C₈×Q₈	C₂²×C₅	1	3	yes	—
69	C₂×C₄⋊C₈	C₄×C₅	1	3	yes	—
70	C₂×C₄×C₈	C₂²×C₅	1	3	yes	—
71	C₄⋊C₁₆	C₂²×C₅	1	6	yes	—
72	C₄⋊C₁₆	C₂²×C₅	1	6	yes	—
73	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
74	C₂²⋊C₁₆	C₂²×C₅	1	3	yes	—
75	#346	C₂²×C₅	1	6	yes	—
76	C₄×C₁₆	C₂²×C₅	1	6	yes	—
77	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
78	C₅×Q₈	—	2	6	no	—
79	C₅×Q₈	M₃₂	1	4	yes	—
80	C₂×C₄×C₅	—	2	6	no	—
81	C₂×C₄×C₅	—	2	1	no	—
82	C₂×C₄×C₅	—	2	1	no	—
83	C₂×C₄×C₅	—	2	6	no	—
84	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
85	C₂×C₄×C₅	C₂²×C₈	1	3	yes	—
86	C₂×C₄×C₅	C₂²×C₈	1	3	yes	—
87	C₂×C₄×C₅	C₂²×C₈	1	3	yes	—
88	C₂×C₄×C₅	C₂²×C₈	1	3	yes	—
89	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
90	C₅×C₈	—	2	1	no	—
91	C₅×C₈	—	2	3	no	—
92	C₅×C₈	—	2	3	no	—
93	C₅×C₈	2₋¹⁺⁴	1	2	yes	—
94	C₂²×Q₈	C₅×C₈	1	1	yes	characteristic
95	C₂²×C₈	C₂×C₄×C₅	1	3	yes	—
96	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
97	C₄×Q₈	C₅×C₈	1	3	yes	—
98	C₄×Q₈	C₅×C₈	1	1	yes	characteristic
99	C₄×Q₈	C₂×C₄×C₅	1	3	yes	—
100	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
101	C₂×C₄⋊C₄	C₅×C₈	1	3	yes	—
102	C₂×C₄²	C₂×C₄×C₅	1	3	yes	—
103	C₂×C₁₆	C₂³×C₅	1	2	yes	—
104	C₂×C₁₆	C₂³×C₅	1	6	yes	—
105	C₄⋊C₈	C₂×C₄×C₅	1	3	yes	—
106	C₄⋊C₈	C₂×C₄×C₅	1	6	yes	—
107	C₄⋊C₈	C₂×C₄×C₅	1	3	yes	—
108	C₄×C₈	C₂×C₄×C₅	1	3	yes	—
109	C₄×C₈	C₂×C₄×C₅	1	3	yes	—
110	C₄×C₈	C₂³×C₅	1	3	yes	—
111	C₄×C₈	C₂³×C₅	1	3	yes	—
112	C₂²×C₅	—	2	1	no	—
113	C₂²×C₅	—	2	1	no	—
114	C₂²×C₅	#504	1	2	yes	—
115	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
116	C₄×C₅	—	2	3	no	—
117	C₄×C₅	—	2	3	no	—
118	C₄×C₅	—	2	3	no	—
119	C₄×C₅	—	2	1	no	—
120	C₄×C₅	C₂×M₃₂	1	6	yes	—
121	C₄×C₅	#519	1	1	yes	characteristic
122	C₄×C₅	#568	1	1	yes	characteristic
123	C₂×Q₈	—	2	4	no	—
124	C₂×Q₈	C₂×C₅×C₈	1	3	yes	—
125	C₂×Q₈	C₂×C₅×C₈	1	1	yes	characteristic
126	C₂²×C₄	C₂×C₅×C₈	1	3	yes	—
127	C₂²×C₄	C₂×C₅×C₈	1	3	yes	—
128	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
129	C₂×C₈	—	2	2	no	—
130	C₂×C₈	—	4	3	no	—
131	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
132	C₂×C₈	C₂²×C₄×C₅	1	3	yes	—
133	C₂×C₈	C₂²×C₄×C₅	1	3	yes	—
134	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
135	C₄⋊C₄	C₂×C₅×C₈	1	6	yes	—
136	C₄⋊C₄	C₂×C₅×C₈	1	3	yes	—
137	C₄⋊C₄	C₂×C₅×C₈	1	3	yes	—
138	C₄²	C₂×C₅×C₈	1	3	yes	—
139	C₄²	C₂×C₅×C₈	1	3	yes	—
140	C₄²	C₂²×C₄×C₅	1	3	yes	—
141	C₄²	C₂²×C₄×C₅	1	3	yes	—
142	C₁₆	—	2	2	no	—
143	C₁₆	—	2	6	no	—
144	C₂×C₅	—	2	2	no	—
145	C₂×C₅	#2982	1	1	yes	characteristic
146	C₂×C₅	C₂²×M₃₂	1	1	yes	characteristic
147	C₂×C₅	C₂×#504	1	1	yes	characteristic
148	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
149	Q₈	—	2	6	no	—
150	Q₈	C₅×M₃₂	1	4	yes	—
151	C₂×C₄	—	2	6	no	—
152	C₂×C₄	—	2	6	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
156	C₂×C₄	C₂²×C₅×C₈	1	3	yes	—
157	C₂×C₄	C₂²×C₅×C₈	1	3	yes	—
158	C₂×C₄	C₂²×C₅×C₈	1	3	yes	—
159	C₂×C₄	C₂²×C₅×C₈	1	3	yes	—
160	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
161	C₈	—	2	1	no	—
162	C₈	—	2	3	no	—
163	C₈	—	2	3	no	—
164	C₈	C₅×2₋¹⁺⁴	1	2	yes	—
165	C₅	#33498	1	1	yes	characteristic, direct product factor, Sylow
166	C₂²	—	2	1	no	—
167	C₂²	—	2	1	no	—
168	C₂²	C₅×#504	1	2	yes	—
169	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
170	C₄	—	2	1	no	—
171	C₄	—	2	3	no	—
172	C₄	—	2	3	no	—
173	C₄	—	2	3	no	—
174	C₄	C₂×C₅×M₃₂	1	6	yes	—
175	C₄	C₅×#519	1	1	yes	characteristic
176	C₄	C₅×#568	1	1	yes	characteristic
177	C₂	—	2	2	no	—
178	C₂	C₅×#2982	1	1	yes	characteristic
179	C₂	C₂²×C₅×M₃₂	1	1	yes	characteristic
180	C₂	C₂×C₅×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂³×C₈
prime radical	C₂³×C₅	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2183	C₂	semidirect
3. C₅×Q₈×C₁₆	C₂	semidirect
19. #33498	C₅	direct (N × H)
39. #2183	C₂×C₅	semidirect
40. Q₈×C₁₆	C₂×C₅	semidirect
165. C₅	#33498	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×C₈×Q₈	2
C₅×#2183	2
C₅×Q₈×C₁₆	2
C₅×#2163	2
C₅×#2162	2
#33498	5

Subgroups — C5×#33498 #11956218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33498 #11956218