Subgroups — C₅×#11493 #11934213

Order 1280.

342 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×#2162	C₂	1	2	yes	maximal
3	C₅×#1322	C₂	1	4	yes	maximal
4	C₂×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
5	C₅×C₈×Q₈	—	2	2	no	—
6	C₅×C₈×Q₈	—	2	2	no	—
7	C₂×C₅×C₄⋊C₈	C₄	1	1	yes	characteristic
8	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₄×C₅×C₈	C₄	1	2	yes	—
10	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₅×C₄⋊C₁₆	—	2	2	no	—
12	C₅×C₂²⋊C₁₆	C₂²	1	4	yes	—
13	C₄×C₅×C₁₆	—	2	2	no	—
14	#11493	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₅×Q₈	C₈	1	1	yes	characteristic
16	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
18	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
19	C₄×C₅×Q₈	—	2	2	no	—
20	C₄×C₅×Q₈	—	2	2	no	—
21	C₂×C₅×C₄⋊C₄	C₈	1	2	yes	—
22	C₂×C₅×C₄⋊C₄	C₈	1	1	yes	characteristic
23	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
25	C₂×C₅×C₁₆	—	2	4	no	—
26	C₅×C₄⋊C₈	—	2	4	no	—
27	C₅×C₄⋊C₈	—	2	2	no	—
28	C₄×C₅×C₈	—	2	2	no	—
29	C₄×C₅×C₈	—	2	2	no	—
30	C₄×C₅×C₈	D₄	1	2	yes	—
31	C₄×C₅×C₈	D₄	1	2	yes	—
32	C₂×C₈×Q₈	C₂×C₅	1	1	yes	characteristic
33	#2162	C₂×C₅	1	2	yes	—
34	#1322	C₂×C₅	1	4	yes	—
35	C₂×C₅×Q₈	—	2	2	no	—
36	C₂×C₅×Q₈	—	2	2	no	—
37	C₂×C₅×Q₈	C₁₆	1	4	yes	complemented
38	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
39	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
40	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
41	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
42	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₅×C₈	—	2	2	no	—
44	C₂×C₅×C₈	—	2	2	no	—
45	C₂×C₅×C₈	—	4	1	no	—
46	C₂×C₅×C₈	—	4	2	no	—
47	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
50	C₅×C₄⋊C₄	—	2	4	no	—
51	C₅×C₄⋊C₄	—	2	2	no	—
52	C₄²×C₅	—	2	2	no	—
53	C₄²×C₅	—	2	2	no	—
54	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
55	C₄²×C₅	M₁₆	1	2	yes	—
56	C₅×C₁₆	—	4	4	no	—
57	C₂×C₄×Q₈	C₄×C₅	1	1	yes	characteristic
58	C₈×Q₈	—	2	2	no	—
59	C₈×Q₈	—	2	2	no	—
60	C₂×C₄⋊C₈	C₄×C₅	1	1	yes	characteristic
61	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
62	C₂×C₄×C₈	C₄×C₅	1	2	yes	—
63	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
64	C₄⋊C₁₆	—	2	2	no	—
65	C₂²⋊C₁₆	C₂²×C₅	1	4	yes	—
66	C₄×C₁₆	—	2	2	no	—
67	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
68	C₅×Q₈	—	2	8	no	—
69	C₂×C₄×C₅	—	2	2	no	—
70	C₂×C₄×C₅	—	2	2	no	—
71	C₂×C₄×C₅	—	2	1	no	—
72	C₂×C₄×C₅	—	2	1	no	—
73	C₂×C₄×C₅	—	2	2	no	—
74	C₂×C₄×C₅	—	4	1	no	—
75	C₂×C₄×C₅	—	4	2	no	—
76	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
77	C₂×C₄×C₅	C₂²⋊C₈	1	2	yes	—
78	C₂×C₄×C₅	C₂×C₁₆	1	4	yes	—
79	C₂×C₄×C₅	C₂×C₁₆	1	2	yes	—
80	C₂×C₄×C₅	M₃₂	1	2	yes	—
81	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
83	C₅×C₈	—	2	2	no	—
84	C₅×C₈	—	2	1	no	—
85	C₅×C₈	—	4	2	no	—
86	C₅×C₈	#101	1	2	yes	—
87	C₂²×Q₈	C₅×C₈	1	1	yes	characteristic
88	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
89	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
90	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
91	C₄×Q₈	—	2	2	no	—
92	C₄×Q₈	—	2	2	no	—
93	C₂×C₄⋊C₄	C₅×C₈	1	2	yes	—
94	C₂×C₄⋊C₄	C₅×C₈	1	1	yes	characteristic
95	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
96	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
97	C₂×C₁₆	—	2	4	no	—
98	C₄⋊C₈	—	2	4	no	—
99	C₄⋊C₈	—	2	2	no	—
100	C₄×C₈	—	2	2	no	—
101	C₄×C₈	—	2	2	no	—
102	C₄×C₈	C₅×D₄	1	2	yes	—
103	C₄×C₈	C₅×D₄	1	2	yes	—
104	C₂²×C₅	—	2	1	no	—
105	C₂²×C₅	—	2	1	no	—
106	C₂²×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
107	C₂²×C₅	C₂²×C₁₆	1	1	yes	characteristic
108	C₂²×C₅	C₂×M₃₂	1	1	yes	characteristic
109	C₄×C₅	—	2	4	no	—
110	C₄×C₅	—	2	2	no	—
111	C₄×C₅	—	2	1	no	—
112	C₄×C₅	—	4	2	no	—
113	C₄×C₅	C₂²⋊C₁₆	1	4	yes	—
114	C₄×C₅	#410	1	1	yes	characteristic
115	C₄×C₅	C₂×#101	1	1	yes	characteristic
116	C₂×Q₈	—	2	2	no	—
117	C₂×Q₈	—	2	2	no	—
118	C₂×Q₈	C₅×C₁₆	1	4	yes	complemented
119	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
120	C₂²×C₄	C₂×C₅×C₈	1	2	yes	—
121	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
122	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
123	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	—	4	1	no	—
127	C₂×C₈	—	4	2	no	—
128	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
131	C₄⋊C₄	—	2	4	no	—
132	C₄⋊C₄	—	2	2	no	—
133	C₄²	—	2	2	no	—
134	C₄²	—	2	2	no	—
135	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
136	C₄²	C₅×M₁₆	1	2	yes	—
137	C₁₆	—	4	4	no	—
138	C₂×C₅	—	2	1	no	—
139	C₂×C₅	—	2	1	no	—
140	C₂×C₅	#1461	1	1	yes	characteristic
141	C₂×C₅	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
142	C₂×C₅	#2115	1	1	yes	characteristic
143	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
144	Q₈	—	2	8	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	4	1	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
153	C₂×C₄	C₅×C₂²⋊C₈	1	2	yes	—
154	C₂×C₄	C₂×C₅×C₁₆	1	4	yes	—
155	C₂×C₄	C₂×C₅×C₁₆	1	2	yes	—
156	C₂×C₄	C₅×M₃₂	1	2	yes	—
157	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
159	C₈	—	2	2	no	—
160	C₈	—	2	1	no	—
161	C₈	—	4	2	no	—
162	C₈	C₅×#101	1	2	yes	—
163	C₅	#11493	1	1	yes	characteristic, direct product factor, Sylow
164	C₂²	—	2	1	no	—
165	C₂²	—	2	1	no	—
166	C₂²	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
167	C₂²	C₂²×C₅×C₁₆	1	1	yes	characteristic
168	C₂²	C₂×C₅×M₃₂	1	1	yes	characteristic
169	C₄	—	2	4	no	—
170	C₄	—	2	2	no	—
171	C₄	—	2	1	no	—
172	C₄	—	4	2	no	—
173	C₄	C₅×C₂²⋊C₁₆	1	4	yes	—
174	C₄	C₅×#410	1	1	yes	characteristic
175	C₄	C₂×C₅×#101	1	1	yes	characteristic
176	C₂	—	2	1	no	—
177	C₂	—	2	1	no	—
178	C₂	C₅×#1461	1	1	yes	characteristic
179	C₂	C₂×C₅×C₂²⋊C₁₆	1	1	yes	characteristic
180	C₂	C₅×#2115	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	C₂²⋊C₄
commutator	C₂²	C₂²×C₅×C₁₆
Frattini, cosocle	C₂²×C₈	C₂³×C₅
socle	C₂²×C₅	C₂×C₂²⋊C₈
prime radical	C₂³×C₅	C₂²×C₈
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
14. #11493	C₅	direct (N × H)
37. C₂×C₅×Q₈	C₁₆	semidirect
118. C₂×Q₈	C₅×C₁₆	semidirect
163. C₅	#11493	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×#2162	2
C₅×#1322	2
#11493	5

Subgroups — C5×#11493 #11934213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11493 #11934213