Subgroups — C₂×C₁₉×#2645 #18040577

Order 4864.

1830 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2645	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₁₉×#401	C₂	1	2	yes	maximal
3	C₂×C₁₉×#400	C₂	1	6	yes	maximal
4	C₂×C₁₉×#391	C₂	1	3	yes	maximal
5	C₂×C₁₉×#389	C₂	1	3	yes	maximal
6	C₂×C₁₉×#376	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
10	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
11	C₁₉×#401	C₂²	1	16	yes	—
12	C₁₉×#400	C₂²	1	48	yes	—
13	C₁₉×#391	C₂²	1	24	yes	—
14	C₁₉×#389	C₂²	1	24	yes	—
15	C₁₉×#376	C₂²	1	8	yes	—
16	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#95	C₂²	1	6	yes	—
18	C₂×C₁₉×#95	C₂²	1	6	yes	—
19	C₂×C₁₉×#95	C₂²	1	3	yes	—
20	C₂×C₁₉×#95	C₂²	1	6	yes	—
21	C₂²×Q₈×C₁₉	—	2	12	no	—
22	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
23	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
25	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
26	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₁₉	—	2	12	no	—
29	C₂×C₄⋊C₄×C₁₉	—	4	12	no	—
30	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
31	C₂×C₄⋊C₄×C₁₉	C₂³	1	24	yes	—
32	C₂×C₄²×C₁₉	—	2	12	no	—
33	C₂×C₄²×C₁₉	C₂³	1	12	yes	—
34	C₁₉×#95	C₂³	1	12	yes	—
35	C₁₉×#95	C₂³	1	4	yes	—
36	C₁₉×#95	C₂³	1	24	yes	—
37	C₁₉×#95	C₂³	1	24	yes	—
38	C₁₉×#95	C₂³	1	24	yes	—
39	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
40	C₂×Q₈×C₁₉	—	2	24	no	—
41	C₂×Q₈×C₁₉	—	4	16	no	—
42	C₂²×C₄×C₁₉	—	2	6	no	—
43	C₂²×C₄×C₁₉	—	2	6	no	—
44	C₂²×C₄×C₁₉	—	2	12	no	—
45	C₂²×C₄×C₁₉	—	2	12	no	—
46	C₂²×C₄×C₁₉	—	2	6	no	—
47	C₂²×C₄×C₁₉	—	2	12	no	—
48	C₂²×C₄×C₁₉	—	2	12	no	—
49	C₂²×C₄×C₁₉	—	2	6	no	—
50	C₂²×C₄×C₁₉	—	2	12	no	—
51	C₂²×C₄×C₁₉	#41	1	12	yes	—
52	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
53	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
54	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
55	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
56	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
57	C₄⋊C₄×C₁₉	—	2	24	no	—
58	C₄⋊C₄×C₁₉	—	4	24	no	—
59	C₄²×C₁₉	—	2	24	no	—
60	C₂×#2645	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂³×C₁₉	C₂×#41	1	6	yes	—
62	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
63	C₂³×C₁₉	2₋¹⁺⁴	1	6	yes	—
64	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
65	Q₈×C₁₉	—	4	16	no	—
66	C₂×C₄×C₁₉	—	2	6	no	—
67	C₂×C₄×C₁₉	—	2	6	no	—
68	C₂×C₄×C₁₉	—	2	12	no	—
69	C₂×C₄×C₁₉	—	2	12	no	—
70	C₂×C₄×C₁₉	—	2	6	no	—
71	C₂×C₄×C₁₉	—	2	12	no	—
72	C₂×C₄×C₁₉	—	2	12	no	—
73	C₂×C₄×C₁₉	—	2	6	no	—
74	C₂×C₄×C₁₉	—	2	12	no	—
75	C₂×C₄×C₁₉	—	4	8	no	—
76	C₂×C₄×C₁₉	—	4	12	no	—
77	C₂×C₄×C₁₉	—	4	12	no	—
78	C₂×C₄×C₁₉	—	4	24	no	—
79	C₂×C₄×C₁₉	#126	1	16	yes	—
80	C₂×C₄×C₁₉	C₂×#41	1	12	yes	—
81	#2645	C₂×C₁₉	1	16	yes	direct product factor
82	C₂×#401	C₂×C₁₉	1	2	yes	—
83	C₂×#400	C₂×C₁₉	1	6	yes	—
84	C₂×#391	C₂×C₁₉	1	3	yes	—
85	C₂×#389	C₂×C₁₉	1	3	yes	—
86	C₂×#376	C₂×C₁₉	1	1	yes	characteristic
87	C₂²×C₁₉	C₂×#126	1	4	yes	—
88	C₂²×C₁₉	#541	1	12	yes	—
89	C₂²×C₁₉	#542	1	12	yes	—
90	C₂²×C₁₉	C₂²×#41	1	3	yes	—
91	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
92	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	3	yes	—
93	C₄×C₁₉	—	4	4	no	—
94	C₄×C₁₉	—	4	6	no	—
95	C₄×C₁₉	—	4	6	no	—
96	C₄×C₁₉	—	4	12	no	—
97	C₄×C₁₉	C₂×#126	1	8	yes	—
98	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
99	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
100	C₂²×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
101	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
102	#401	C₂²×C₁₉	1	16	yes	—
103	#400	C₂²×C₁₉	1	48	yes	—
104	#391	C₂²×C₁₉	1	24	yes	—
105	#389	C₂²×C₁₉	1	24	yes	—
106	#376	C₂²×C₁₉	1	8	yes	—
107	C₂×#95	C₂²×C₁₉	1	3	yes	—
108	C₂×#95	C₂²×C₁₉	1	6	yes	—
109	C₂×#95	C₂²×C₁₉	1	6	yes	—
110	C₂×#95	C₂²×C₁₉	1	6	yes	—
111	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
112	C₂×C₁₉	#2645	1	8	yes	direct product factor
113	C₂×C₁₉	C₂²×#126	1	1	yes	characteristic
114	C₂×C₁₉	C₂×#541	1	3	yes	—
115	C₂×C₁₉	C₂×#542	1	3	yes	—
116	C₂²×Q₈	—	2	12	no	—
117	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
118	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
119	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
120	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
121	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
122	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
123	C₂×C₄⋊C₄	—	2	12	no	—
124	C₂×C₄⋊C₄	—	4	12	no	—
125	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
126	C₂×C₄⋊C₄	C₂³×C₁₉	1	24	yes	—
127	C₂×C₄²	—	2	12	no	—
128	C₂×C₄²	C₂³×C₁₉	1	12	yes	—
129	#95	C₂³×C₁₉	1	12	yes	—
130	#95	C₂³×C₁₉	1	4	yes	—
131	#95	C₂³×C₁₉	1	24	yes	—
132	#95	C₂³×C₁₉	1	24	yes	—
133	#95	C₂³×C₁₉	1	24	yes	—
134	C₁₉	C₂×#2645	1	1	yes	characteristic, direct product factor, Sylow
135	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
136	C₂×Q₈	—	2	24	no	—
137	C₂×Q₈	—	4	16	no	—
138	C₂²×C₄	—	2	6	no	—
139	C₂²×C₄	—	2	6	no	—
140	C₂²×C₄	—	2	12	no	—
141	C₂²×C₄	—	2	12	no	—
142	C₂²×C₄	—	2	12	no	—
143	C₂²×C₄	—	2	6	no	—
144	C₂²×C₄	—	2	12	no	—
145	C₂²×C₄	—	2	12	no	—
146	C₂²×C₄	—	2	6	no	—
147	C₂²×C₄	#41×C₁₉	1	12	yes	—
148	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
149	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
150	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
151	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
152	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
153	C₄⋊C₄	—	2	24	no	—
154	C₄⋊C₄	—	4	24	no	—
155	C₄²	—	2	24	no	—
156	C₂³	C₂×#41×C₁₉	1	6	yes	—
157	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
158	C₂³	C₁₉×2₋¹⁺⁴	1	6	yes	—
159	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
160	Q₈	—	4	16	no	—
161	C₂×C₄	—	2	6	no	—
162	C₂×C₄	—	2	6	no	—
163	C₂×C₄	—	2	12	no	—
164	C₂×C₄	—	2	12	no	—
165	C₂×C₄	—	2	6	no	—
166	C₂×C₄	—	2	12	no	—
167	C₂×C₄	—	2	12	no	—
168	C₂×C₄	—	2	6	no	—
169	C₂×C₄	—	2	12	no	—
170	C₂×C₄	—	4	8	no	—
171	C₂×C₄	—	4	12	no	—
172	C₂×C₄	—	4	12	no	—
173	C₂×C₄	—	4	24	no	—
174	C₂×C₄	C₁₉×#126	1	16	yes	—
175	C₂×C₄	C₂×#41×C₁₉	1	12	yes	—
176	C₂²	C₂×C₁₉×#126	1	4	yes	—
177	C₂²	C₁₉×#541	1	12	yes	—
178	C₂²	C₁₉×#542	1	12	yes	—
179	C₂²	C₂²×#41×C₁₉	1	3	yes	—
180	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
181	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	3	yes	—
182	C₄	—	4	4	no	—
183	C₄	—	4	6	no	—
184	C₄	—	4	6	no	—
185	C₄	—	4	12	no	—
186	C₄	C₂×C₁₉×#126	1	8	yes	—
187	C₂	C₁₉×#2645	1	8	yes	direct product factor
188	C₂	C₂²×C₁₉×#126	1	1	yes	characteristic
189	C₂	C₂×C₁₉×#541	1	3	yes	—
190	C₂	C₂×C₁₉×#542	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2645	C₂	direct (N × H)
60. C₂×#2645	C₁₉	direct (N × H)
81. #2645	C₂×C₁₉	direct (N × H)
112. C₂×C₁₉	#2645	direct (N × H)
134. C₁₉	C₂×#2645	direct (N × H)
187. C₂	C₁₉×#2645	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2645	2
C₂×C₁₉×#401	2
C₂×C₁₉×#400	2
C₂×C₁₉×#391	2
C₂×C₁₉×#389	2
C₂×C₁₉×#376	2
C₂×#2645	19

Subgroups — C2×C19×#2645 #18040577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2645 #18040577