Subgroups — C₈×C₁₉×2₋¹⁺⁴ #18066288

Order 4864.

2190 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2988	C₂	1	10	yes	maximal, complemented
3	C₁₉×#2982	C₂	1	5	yes	maximal, complemented
4	C₈×#41×C₁₉	C₂	1	10	yes	maximal, complemented
5	C₂×C₈×Q₈×C₁₉	C₂	1	5	yes	maximal, complemented
6	C₂×C₁₉×2₋¹⁺⁴	C₄	1	1	yes	characteristic
7	C₁₉×#520	C₄	1	10	yes	—
8	C₁₉×#519	C₄	1	5	yes	—
9	C₄×#41×C₁₉	C₂²	1	10	yes	—
10	C₂×C₄×Q₈×C₁₉	C₂²	1	5	yes	—
11	C₈×Q₈×C₁₉	C₂²	1	10	yes	—
12	C₈×Q₈×C₁₉	C₂²	1	20	yes	—
13	C₈×Q₈×C₁₉	C₂²	1	10	yes	—
14	C₈×D₄×C₁₉	C₂²	1	10	yes	—
15	C₈×D₄×C₁₉	C₂²	1	30	yes	—
16	C₁₉×#431	C₂²	1	30	yes	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	15	yes	—
18	C₂×C₄×C₈×C₁₉	C₂²	1	15	yes	—
19	C₁₉×2₋¹⁺⁴	C₈	1	16	yes	direct product factor
20	C₂×#41×C₁₉	C₂×C₄	1	10	yes	—
21	C₂²×Q₈×C₁₉	C₂×C₄	1	5	yes	—
22	C₂²×C₈×C₁₉	C₂³	1	5	yes	—
23	C₂²×C₈×C₁₉	C₂³	1	15	yes	—
24	C₄×Q₈×C₁₉	C₂×C₄	1	20	yes	—
25	C₄×Q₈×C₁₉	C₂×C₄	1	10	yes	—
26	C₄×Q₈×C₁₉	C₂³	1	10	yes	—
27	C₄×D₄×C₁₉	C₂×C₄	1	30	yes	—
28	C₄×D₄×C₁₉	C₂³	1	10	yes	—
29	C₁₉×#117	C₂×C₄	1	30	yes	—
30	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	15	yes	—
31	C₂×C₄²×C₁₉	C₂³	1	15	yes	—
32	C₁₉×C₄⋊C₈	C₂³	1	30	yes	—
33	C₁₉×C₄⋊C₈	C₂³	1	10	yes	—
34	C₁₉×C₂²⋊C₈	C₂³	1	20	yes	—
35	C₄×C₈×C₁₉	C₂³	1	30	yes	—
36	C₄×C₈×C₁₉	C₂³	1	10	yes	—
37	#41×C₁₉	C₂×C₈	1	80	yes	complemented
38	C₂×Q₈×C₁₉	C₂×C₈	1	40	yes	complemented
39	C₂×Q₈×C₁₉	C₂²×C₄	1	10	yes	—
40	C₂×D₄×C₁₉	C₂²×C₄	1	10	yes	—
41	C₂²×C₄×C₁₉	C₂²×C₄	1	15	yes	—
42	C₂²×C₄×C₁₉	C₂²×C₄	1	15	yes	—
43	C₂²×C₄×C₁₉	C₂⁴	1	5	yes	—
44	C₂×C₈×C₁₉	—	2	10	no	—
45	C₂×C₈×C₁₉	—	4	15	no	—
46	C₂×C₈×C₁₉	C₂⁴	1	10	yes	—
47	C₂×C₈×C₁₉	C₂⁴	1	5	yes	—
48	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
49	C₄⋊C₄×C₁₉	C₂²×C₄	1	30	yes	—
50	C₄⋊C₄×C₁₉	C₂²×C₄	1	10	yes	—
51	C₂²⋊C₄×C₁₉	C₂²×C₄	1	20	yes	—
52	C₄²×C₁₉	C₂²×C₄	1	30	yes	—
53	C₄²×C₁₉	C₂⁴	1	10	yes	—
54	C₈×2₋¹⁺⁴	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂³×C₁₉	C₂³×C₄	1	5	yes	—
56	Q₈×C₁₉	C₂²×C₈	1	40	yes	—
57	D₄×C₁₉	C₂²×C₈	1	40	yes	—
58	C₂×C₄×C₁₉	—	2	5	no	—
59	C₂×C₄×C₁₉	—	2	5	no	—
60	C₂×C₄×C₁₉	—	4	15	no	—
61	C₂×C₄×C₁₉	C₂²×C₈	1	60	yes	—
62	C₂×C₄×C₁₉	C₂³×C₄	1	5	yes	—
63	C₂×C₄×C₁₉	C₂³×C₄	1	10	yes	—
64	C₂×C₄×C₁₉	C₂³×C₄	1	10	yes	—
65	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
66	C₈×C₁₉	—	2	5	no	—
67	C₈×C₁₉	—	2	10	no	—
68	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	direct product factor
69	C₄×2₋¹⁺⁴	C₂×C₁₉	1	1	yes	characteristic
70	#2988	C₂×C₁₉	1	10	yes	complemented
71	#2982	C₂×C₁₉	1	5	yes	complemented
72	C₈×#41	C₂×C₁₉	1	10	yes	complemented
73	C₂×C₈×Q₈	C₂×C₁₉	1	5	yes	complemented
74	C₂²×C₁₉	—	2	5	no	—
75	C₂²×C₁₉	—	2	5	no	—
76	C₂²×C₁₉	C₂³×C₈	1	10	yes	—
77	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
78	C₄×C₁₉	—	2	5	no	—
79	C₄×C₁₉	—	2	10	no	—
80	C₄×C₁₉	C₂³×C₈	1	20	yes	—
81	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
82	C₄×C₁₉	#585	1	1	yes	characteristic
83	C₂×2₋¹⁺⁴	C₄×C₁₉	1	1	yes	characteristic
84	#520	C₄×C₁₉	1	10	yes	—
85	#519	C₄×C₁₉	1	5	yes	—
86	C₄×#41	C₂²×C₁₉	1	10	yes	—
87	C₂×C₄×Q₈	C₂²×C₁₉	1	5	yes	—
88	C₈×Q₈	C₂²×C₁₉	1	10	yes	—
89	C₈×Q₈	C₂²×C₁₉	1	20	yes	—
90	C₈×Q₈	C₂²×C₁₉	1	10	yes	—
91	C₈×D₄	C₂²×C₁₉	1	10	yes	—
92	C₈×D₄	C₂²×C₁₉	1	30	yes	—
93	#431	C₂²×C₁₉	1	30	yes	—
94	C₂×C₄⋊C₈	C₂²×C₁₉	1	15	yes	—
95	C₂×C₄×C₈	C₂²×C₁₉	1	15	yes	—
96	C₂×C₁₉	—	2	10	no	—
97	C₂×C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
98	C₂×C₁₉	C₂⁴×C₈	1	1	yes	characteristic
99	C₂×C₁₉	#3573	1	1	yes	characteristic
100	2₋¹⁺⁴	C₈×C₁₉	1	16	yes	direct product factor
101	C₂×#41	C₂×C₄×C₁₉	1	10	yes	—
102	C₂²×Q₈	C₂×C₄×C₁₉	1	5	yes	—
103	C₂²×C₈	C₂³×C₁₉	1	5	yes	—
104	C₂²×C₈	C₂³×C₁₉	1	15	yes	—
105	C₄×Q₈	C₂×C₄×C₁₉	1	20	yes	—
106	C₄×Q₈	C₂×C₄×C₁₉	1	10	yes	—
107	C₄×Q₈	C₂³×C₁₉	1	10	yes	—
108	C₄×D₄	C₂×C₄×C₁₉	1	30	yes	—
109	C₄×D₄	C₂³×C₁₉	1	10	yes	—
110	#117	C₂×C₄×C₁₉	1	30	yes	—
111	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	15	yes	—
112	C₂×C₄²	C₂³×C₁₉	1	15	yes	—
113	C₄⋊C₈	C₂³×C₁₉	1	30	yes	—
114	C₄⋊C₈	C₂³×C₁₉	1	10	yes	—
115	C₂²⋊C₈	C₂³×C₁₉	1	20	yes	—
116	C₄×C₈	C₂³×C₁₉	1	10	yes	—
117	C₄×C₈	C₂³×C₁₉	1	30	yes	—
118	C₁₉	C₈×2₋¹⁺⁴	1	1	yes	characteristic, direct product factor, Sylow
119	#41	C₂×C₈×C₁₉	1	80	yes	complemented
120	C₂×Q₈	C₂×C₈×C₁₉	1	40	yes	complemented
121	C₂×Q₈	C₂²×C₄×C₁₉	1	10	yes	—
122	C₂×D₄	C₂²×C₄×C₁₉	1	10	yes	—
123	C₂²×C₄	C₂²×C₄×C₁₉	1	15	yes	—
124	C₂²×C₄	C₂²×C₄×C₁₉	1	15	yes	—
125	C₂²×C₄	C₂⁴×C₁₉	1	5	yes	—
126	C₂×C₈	—	2	10	no	—
127	C₂×C₈	—	4	15	no	—
128	C₂×C₈	C₂⁴×C₁₉	1	5	yes	—
129	C₂×C₈	C₂⁴×C₁₉	1	10	yes	—
130	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
131	C₄⋊C₄	C₂²×C₄×C₁₉	1	30	yes	—
132	C₄⋊C₄	C₂²×C₄×C₁₉	1	10	yes	—
133	C₂²⋊C₄	C₂²×C₄×C₁₉	1	20	yes	—
134	C₄²	C₂²×C₄×C₁₉	1	30	yes	—
135	C₄²	C₂⁴×C₁₉	1	10	yes	—
136	C₂³	C₂³×C₄×C₁₉	1	5	yes	—
137	Q₈	C₂²×C₈×C₁₉	1	40	yes	—
138	D₄	C₂²×C₈×C₁₉	1	40	yes	—
139	C₂×C₄	—	2	5	no	—
140	C₂×C₄	—	2	5	no	—
141	C₂×C₄	—	4	15	no	—
142	C₂×C₄	C₂²×C₈×C₁₉	1	60	yes	—
143	C₂×C₄	C₂³×C₄×C₁₉	1	5	yes	—
144	C₂×C₄	C₂³×C₄×C₁₉	1	10	yes	—
145	C₂×C₄	C₂³×C₄×C₁₉	1	10	yes	—
146	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
147	C₈	—	2	5	no	—
148	C₈	—	2	10	no	—
149	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	direct product factor
150	C₂²	—	2	5	no	—
151	C₂²	—	2	5	no	—
152	C₂²	C₂³×C₈×C₁₉	1	10	yes	—
153	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
154	C₄	—	2	5	no	—
155	C₄	—	2	10	no	—
156	C₄	C₂³×C₈×C₁₉	1	20	yes	—
157	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
158	C₄	C₁₉×#585	1	1	yes	characteristic
159	C₂	—	2	10	no	—
160	C₂	C₄×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
161	C₂	C₂⁴×C₈×C₁₉	1	1	yes	characteristic
162	C₂	C₁₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂⁴
commutator	C₂	C₂⁴×C₈×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₂×C₁₉×2₋¹⁺⁴	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2988	C₂	semidirect
3. C₁₉×#2982	C₂	semidirect
4. C₈×#41×C₁₉	C₂	semidirect
5. C₂×C₈×Q₈×C₁₉	C₂	semidirect
19. C₁₉×2₋¹⁺⁴	C₈	direct (N × H)
37. #41×C₁₉	C₂×C₈	semidirect
38. C₂×Q₈×C₁₉	C₂×C₈	semidirect
54. C₈×2₋¹⁺⁴	C₁₉	direct (N × H)
68. C₈×C₁₉	2₋¹⁺⁴	direct (N × H)
70. #2988	C₂×C₁₉	semidirect
71. #2982	C₂×C₁₉	semidirect
72. C₈×#41	C₂×C₁₉	semidirect
73. C₂×C₈×Q₈	C₂×C₁₉	semidirect
100. 2₋¹⁺⁴	C₈×C₁₉	direct (N × H)
118. C₁₉	C₈×2₋¹⁺⁴	direct (N × H)
119. #41	C₂×C₈×C₁₉	semidirect
120. C₂×Q₈	C₂×C₈×C₁₉	semidirect
149. C₈	C₁₉×2₋¹⁺⁴	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₉×2₋¹⁺⁴	2
C₁₉×#2988	2
C₁₉×#2982	2
C₈×#41×C₁₉	2
C₂×C₈×Q₈×C₁₉	2
C₈×2₋¹⁺⁴	19

Subgroups — C8×C19×2−1+4 #18066288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₁₉×2₋¹⁺⁴ #18066288