Subgroups — C₂×#131×D₁₉ #14578338

Order 2432.

1504 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597353	C₂	1	3	yes	maximal, complemented
3	C₂×#10597394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597347	C₂	1	3	yes	maximal, complemented
5	#131×D₁₉	C₂	1	16	yes	maximal, direct product factor
6	C₂×M₁₆×D₁₉	C₂	1	3	yes	maximal, complemented
7	C₂²×C₈×D₁₉	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
10	#41×D₁₉	C₄	1	8	yes	—
11	#41×D₁₉	C₂²	1	8	yes	—
12	C₂×#64545	C₄	1	1	yes	characteristic
13	C₂×Q₈×D₁₉	C₄	1	1	yes	characteristic
14	C₂×#64543	C₄	1	3	yes	—
15	C₂×D₄×D₁₉	C₄	1	3	yes	—
16	C₂×#64541	C₂²	1	3	yes	—
17	C₂²×C₄×D₁₉	C₂²	1	3	yes	—
18	C₁₉×#131	C₂²	1	8	yes	complemented
19	C₂×M₁₆×C₁₉	C₂²	1	3	yes	complemented
20	C₂²×C₈×C₁₉	C₂²	1	3	yes	complemented
21	#10597394	C₂²	1	8	yes	complemented
22	C₂×#64520	C₂²	1	3	yes	complemented
23	C₂²×C₁₉⋊C₈	C₂²	1	3	yes	complemented
24	#10597353	C₂²	1	24	yes	complemented
25	M₁₆×D₁₉	C₂²	1	24	yes	complemented
26	#10597347	C₂²	1	24	yes	complemented
27	C₂×#64515	C₂²	1	6	yes	complemented
28	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₁₉	C₂²	1	3	yes	—
30	C₂×C₈×D₁₉	C₂²	1	24	yes	complemented
31	C₂×C₈×D₁₉	C₂²	1	3	yes	complemented
32	C₂×C₈×D₁₉	C₂²	1	3	yes	complemented
33	C₂³×D₁₉	C₂×C₄	1	3	yes	—
34	#41×C₁₉	C₂×C₄	1	4	yes	—
35	#41×C₁₉	C₂³	1	4	yes	—
36	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×D₄×C₁₉	C₂×C₄	1	3	yes	—
38	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
39	C₂×C₂²⋊D₁₉	C₂×C₄	1	6	yes	—
40	C₂²×Dic₁₉	C₂×C₄	1	3	yes	—
41	#64545	C₂×C₄	1	8	yes	—
42	Q₈×D₁₉	C₂×C₄	1	8	yes	—
43	#64543	C₂×C₄	1	24	yes	—
44	D₄×D₁₉	C₂×C₄	1	24	yes	—
45	#64541	C₂×C₄	1	12	yes	—
46	#64541	C₂³	1	12	yes	—
47	C₂×D₇₆	C₂×C₄	1	3	yes	—
48	C₂×C₄×D₁₉	C₂×C₄	1	3	yes	—
49	C₂×C₄×D₁₉	C₂×C₄	1	3	yes	—
50	C₂×C₄×D₁₉	C₂×C₄	1	12	yes	—
51	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
52	C₂×C₄×D₁₉	C₂³	1	3	yes	—
53	C₂×C₄×D₁₉	C₂³	1	12	yes	—
54	C₂×Dic₃₈	C₂×C₄	1	3	yes	—
55	M₁₆×C₁₉	C₂³	1	12	yes	complemented
56	C₂×C₈×C₁₉	C₂³	1	3	yes	—
57	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₈×C₁₉	C₂³	1	12	yes	complemented
59	#64520	C₂³	1	12	yes	complemented
60	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
61	C₂×C₁₉⋊C₈	C₂³	1	3	yes	—
62	C₂×C₁₉⋊C₈	C₂³	1	12	yes	complemented
63	#64515	C₂³	1	24	yes	complemented
64	C₈×D₁₉	C₂³	1	4	yes	—
65	C₈×D₁₉	C₂³	1	12	yes	—
66	C₈×D₁₉	C₂³	1	12	yes	complemented
67	C₈×D₁₉	C₂³	1	12	yes	complemented
68	C₂³×C₁₉	C₂²×C₄	1	3	yes	—
69	C₂²×D₁₉	—	2	12	no	—
70	C₂²×D₁₉	C₂²×C₄	1	3	yes	—
71	C₂²×D₁₉	C₂²×C₄	1	12	yes	—
72	C₂²×D₁₉	C₂²×C₄	1	1	yes	characteristic
73	Q₈×C₁₉	C₂²×C₄	1	4	yes	—
74	D₄×C₁₉	C₂²×C₄	1	12	yes	—
75	C₂×C₄×C₁₉	C₂²×C₄	1	3	yes	—
76	C₂×C₄×C₁₉	C₂²×C₄	1	6	yes	—
77	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
79	C₂²⋊D₁₉	C₂²×C₄	1	24	yes	—
80	C₂×Dic₁₉	C₂²×C₄	1	3	yes	—
81	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₂×Dic₁₉	C₂²×C₄	1	12	yes	—
83	D₇₆	C₂²×C₄	1	12	yes	—
84	C₄×D₁₉	C₂²×C₄	1	2	yes	—
85	C₄×D₁₉	C₂²×C₄	1	6	yes	—
86	C₄×D₁₉	C₂²×C₄	1	12	yes	—
87	C₄×D₁₉	C₂²×C₄	1	12	yes	—
88	C₄×D₁₉	C₂⁴	1	2	yes	—
89	C₄×D₁₉	C₂⁴	1	6	yes	—
90	Dic₃₈	C₂²×C₄	1	12	yes	—
91	C₈×C₁₉	C₂⁴	1	2	yes	—
92	C₈×C₁₉	C₂⁴	1	6	yes	—
93	C₁₉⋊C₈	C₂⁴	1	2	yes	—
94	C₁₉⋊C₈	C₂⁴	1	6	yes	—
95	C₂²×#131	—	19	1	no	maximal, Sylow
96	C₂²×C₁₉	—	2	6	no	—
97	C₂²×C₁₉	C₂³×C₄	1	6	yes	—
98	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
99	C₂×D₁₉	—	2	6	no	—
100	C₂×D₁₉	—	2	24	no	—
101	C₂×D₁₉	#131	1	4	yes	direct product factor
102	C₂×D₁₉	C₂³×C₄	1	6	yes	—
103	C₂×D₁₉	C₂³×C₄	1	2	yes	—
104	C₄×C₁₉	C₂³×C₄	1	6	yes	—
105	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
106	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
107	Dic₁₉	C₂³×C₄	1	6	yes	—
108	Dic₁₉	C₂³×C₄	1	2	yes	—
109	C₂²×#41	—	19	1	no	—
110	C₂×#131	—	19	1	no	—
111	C₂×#131	—	19	16	no	—
112	C₂×#131	—	19	3	no	—
113	C₂×#131	—	19	3	no	—
114	C₂×#131	D₁₉	1	1	yes	characteristic, direct product factor
115	C₂²×M₁₆	—	19	3	no	—
116	C₂³×C₈	—	19	3	no	—
117	C₂×C₁₉	—	2	6	no	—
118	C₂×C₁₉	C₂×#131	1	2	yes	complemented
119	C₂×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
120	D₁₉	—	2	6	no	—
121	D₁₉	C₂×#131	1	4	yes	direct product factor
122	C₂×#41	—	19	8	no	—
123	C₂×#41	—	19	8	no	—
124	C₂×#41	—	19	1	no	—
125	C₂×#41	—	19	3	no	—
126	C₂×#41	—	19	3	no	—
127	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
128	C₂²×Q₈	—	19	1	no	—
129	C₂²×D₄	—	19	3	no	—
130	C₂³×C₄	—	19	3	no	—
131	#131	—	19	8	no	—
132	#131	—	19	24	no	—
133	#131	—	19	24	no	—
134	#131	C₂×D₁₉	1	8	yes	direct product factor
135	C₂×M₁₆	—	19	3	no	—
136	C₂×M₁₆	—	19	24	no	—
137	C₂×M₁₆	—	19	6	no	—
138	C₂×M₁₆	C₂×D₁₉	1	3	yes	complemented
139	C₂²×C₈	—	19	3	no	—
140	C₂²×C₈	—	19	3	no	—
141	C₂²×C₈	—	19	3	no	—
142	C₂²×C₈	—	19	1	no	—
143	C₂²×C₈	—	19	3	no	—
144	C₂²×C₈	—	19	24	no	—
145	C₂²×C₈	C₂×D₁₉	1	3	yes	complemented
146	C₁₉	C₂²×#131	1	1	yes	characteristic, complemented, Sylow
147	C₂⁴	—	19	3	no	—
148	#41	—	19	8	no	—
149	#41	—	19	24	no	—
150	#41	—	19	12	no	—
151	#41	—	19	12	no	—
152	#41	C₄×D₁₉	1	4	yes	—
153	#41	C₂²×D₁₉	1	4	yes	—
154	C₂×Q₈	—	19	8	no	—
155	C₂×Q₈	—	19	3	no	—
156	C₂×Q₈	C₄×D₁₉	1	1	yes	characteristic
157	C₂×D₄	—	19	6	no	—
158	C₂×D₄	—	19	24	no	—
159	C₂×D₄	—	19	3	no	—
160	C₂×D₄	C₄×D₁₉	1	3	yes	—
161	C₂²×C₄	—	19	3	no	—
162	C₂²×C₄	—	19	3	no	—
163	C₂²×C₄	—	19	3	no	—
164	C₂²×C₄	—	19	12	no	—
165	C₂²×C₄	—	19	1	no	—
166	C₂²×C₄	—	19	3	no	—
167	C₂²×C₄	—	19	12	no	—
168	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
169	M₁₆	—	19	12	no	—
170	M₁₆	—	19	24	no	—
171	M₁₆	C₂²×D₁₉	1	12	yes	complemented
172	C₂×C₈	—	19	1	no	—
173	C₂×C₈	—	19	3	no	—
174	C₂×C₈	—	19	12	no	—
175	C₂×C₈	—	19	4	no	—
176	C₂×C₈	—	19	12	no	—
177	C₂×C₈	—	19	12	no	—
178	C₂×C₈	—	19	12	no	—
179	C₂×C₈	C₂²×D₁₉	1	3	yes	—
180	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
181	C₂×C₈	C₂²×D₁₉	1	12	yes	complemented
182	C₂³	—	19	1	no	—
183	C₂³	—	19	12	no	—
184	C₂³	—	19	3	no	—
185	C₂³	—	38	12	no	—
186	C₂³	C₂×C₄×D₁₉	1	3	yes	—
187	Q₈	—	19	12	no	—
188	Q₈	C₂×C₄×D₁₉	1	4	yes	—
189	D₄	—	19	24	no	—
190	D₄	—	19	12	no	—
191	D₄	C₂×C₄×D₁₉	1	12	yes	—
192	C₂×C₄	—	19	1	no	—
193	C₂×C₄	—	19	3	no	—
194	C₂×C₄	—	19	12	no	—
195	C₂×C₄	—	19	2	no	—
196	C₂×C₄	—	19	12	no	—
197	C₂×C₄	—	19	12	no	—
198	C₂×C₄	—	19	6	no	—
199	C₂×C₄	—	19	2	no	—
200	C₂×C₄	—	19	6	no	—
201	C₂×C₄	C₂×C₄×D₁₉	1	3	yes	—
202	C₂×C₄	C₂×C₄×D₁₉	1	6	yes	—
203	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
204	C₂×C₄	C₂³×D₁₉	1	6	yes	—
205	C₈	—	19	2	no	—
206	C₈	—	19	6	no	—
207	C₈	C₂³×D₁₉	1	2	yes	—
208	C₈	C₂³×D₁₉	1	6	yes	—
209	C₂²	—	2	6	no	—
210	C₂²	—	19	4	no	—
211	C₂²	—	19	2	no	—
212	C₂²	—	19	6	no	—
213	C₂²	—	38	24	no	—
214	C₂²	—	38	6	no	—
215	C₂²	C₂²×C₄×D₁₉	1	6	yes	—
216	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
217	C₄	—	19	2	no	—
218	C₄	—	19	6	no	—
219	C₄	C₂²×C₄×D₁₉	1	1	yes	characteristic
220	C₄	C₂²×C₄×D₁₉	1	6	yes	—
221	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
222	C₂	—	2	6	no	—
223	C₂	—	19	4	no	—
224	C₂	—	38	6	no	—
225	C₂	#131×D₁₉	1	2	yes	direct product factor
226	C₂	C₂³×C₄×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₁₉
commutator	C₂×C₁₉	C₂⁴×C₄
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂×C₁₉×#131	C₂
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₂×#41×D₁₉	C₂
cosocle	C₄×C₁₉	C₂⁵
hypercenter	C₂×#131	D₁₉
hypocenter	C₁₉	C₂²×#131
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
2. C₂×#10597353	C₂	semidirect
3. C₂×#10597394	C₂	semidirect
4. C₂×#10597347	C₂	semidirect
5. #131×D₁₉	C₂	direct (N × H)
6. C₂×M₁₆×D₁₉	C₂	semidirect
7. C₂²×C₈×D₁₉	C₂	semidirect
8. C₂×C₁₉×#131	C₂	semidirect
18. C₁₉×#131	C₂²	semidirect
19. C₂×M₁₆×C₁₉	C₂²	semidirect
20. C₂²×C₈×C₁₉	C₂²	semidirect
21. #10597394	C₂²	semidirect
22. C₂×#64520	C₂²	semidirect
23. C₂²×C₁₉⋊C₈	C₂²	semidirect
24. #10597353	C₂²	semidirect
25. M₁₆×D₁₉	C₂²	semidirect
26. #10597347	C₂²	semidirect
27. C₂×#64515	C₂²	semidirect
30. C₂×C₈×D₁₉	C₂²	semidirect
31. C₂×C₈×D₁₉	C₂²	semidirect
32. C₂×C₈×D₁₉	C₂²	semidirect
55. M₁₆×C₁₉	C₂³	semidirect
58. C₂×C₈×C₁₉	C₂³	semidirect
59. #64520	C₂³	semidirect
62. C₂×C₁₉⋊C₈	C₂³	semidirect
63. #64515	C₂³	semidirect
66. C₈×D₁₉	C₂³	semidirect
67. C₈×D₁₉	C₂³	semidirect
101. C₂×D₁₉	#131	direct (N × H)
114. C₂×#131	D₁₉	direct (N × H)
118. C₂×C₁₉	C₂×#131	semidirect
121. D₁₉	C₂×#131	direct (N × H)
134. #131	C₂×D₁₉	direct (N × H)
138. C₂×M₁₆	C₂×D₁₉	semidirect
145. C₂²×C₈	C₂×D₁₉	semidirect
146. C₁₉	C₂²×#131	semidirect
171. M₁₆	C₂²×D₁₉	semidirect
181. C₂×C₈	C₂²×D₁₉	semidirect
225. C₂	#131×D₁₉	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×#41×D₁₉	2
C₂×#10597353	2
C₂×#10597394	2
C₂×#10597347	2
#131×D₁₉	2
C₂×M₁₆×D₁₉	2
C₂²×C₈×D₁₉	2
C₂×C₁₉×#131	2
C₂²×#131	19

Subgroups — C2×#131×D19 #14578338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#131×D₁₉ #14578338