Subgroups — C₄×#41×D₁₉ #14576812

Order 2432.

1728 conjugacy classes of subgroups.

The subgroup lattice has 282 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	#41×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#64545	C₂	1	2	yes	maximal, complemented
4	C₄×#64541	C₂	1	3	yes	maximal, complemented
5	#11927012	C₂	1	3	yes	maximal, complemented
6	C₄×#64543	C₂	1	6	yes	maximal, complemented
7	C₄×Q₈×D₁₉	C₂	1	2	yes	maximal, complemented
8	C₄×D₄×D₁₉	C₂	1	6	yes	maximal, complemented
9	#117×D₁₉	C₂	1	3	yes	maximal, complemented
10	C₂×C₄²×D₁₉	C₂	1	3	yes	maximal, complemented
11	C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
13	#41×D₁₉	C₄	1	16	yes	direct product factor
14	C₂×#64545	C₂²	1	1	yes	characteristic
15	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
16	C₂×#64543	C₂²	1	3	yes	—
17	C₂×D₄×D₁₉	C₂²	1	3	yes	—
18	C₂×#64541	C₂²	1	3	yes	—
19	C₂²×C₄×D₁₉	C₂²	1	6	yes	—
20	C₂²×C₄×D₁₉	C₂²	1	3	yes	—
21	C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
22	C₄×D₄×C₁₉	C₂²	1	6	yes	complemented
23	C₁₉×#117	C₂²	1	3	yes	complemented
24	C₂×C₄²×C₁₉	C₂²	1	3	yes	complemented
25	Q₈×Dic₁₉	C₂²	1	2	yes	complemented
26	D₄×Dic₁₉	C₂²	1	6	yes	complemented
27	C₄×C₂²⋊D₁₉	C₂²	1	12	yes	complemented
28	#10597372	C₂²	1	3	yes	complemented
29	C₂×C₄×Dic₁₉	C₂²	1	6	yes	complemented
30	C₂×C₄×Dic₁₉	C₂²	1	3	yes	complemented
31	#10597339	C₂²	1	6	yes	complemented
32	#10597338	C₂²	1	6	yes	complemented
33	C₄⋊C₄×D₁₉	C₂²	1	6	yes	—
34	#10597333	C₂²	1	6	yes	complemented
35	(C₂²⋊D₁₉)⋊C₄	C₂²	1	12	yes	complemented
36	C₂²⋊C₄×D₁₉	C₂²	1	6	yes	—
37	#10597323	C₂²	1	6	yes	complemented
38	C₄×D₇₆	C₂²	1	6	yes	complemented
39	#10597318	C₂²	1	6	yes	complemented
40	C₄²×D₁₉	C₂²	1	1	yes	characteristic
41	C₄²×D₁₉	C₂²	1	3	yes	—
42	C₄²×D₁₉	C₂²	1	6	yes	—
43	C₄²×D₁₉	C₂²	1	6	yes	complemented
44	C₄²×D₁₉	C₂²	1	3	yes	complemented
45	C₄²×D₁₉	C₂²	1	3	yes	complemented
46	C₄×Dic₃₈	C₂²	1	6	yes	complemented
47	C₂³×D₁₉	C₂³	1	3	yes	—
48	#41×C₁₉	C₂×C₄	1	8	yes	complemented
49	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×D₄×C₁₉	C₂³	1	3	yes	—
51	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
52	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
53	C₂×C₂²⋊D₁₉	C₂³	1	6	yes	—
54	C₂²×Dic₁₉	C₂³	1	6	yes	—
55	C₂²×Dic₁₉	C₂³	1	3	yes	—
56	#64545	C₂×C₄	1	8	yes	complemented
57	Q₈×D₁₉	C₂×C₄	1	8	yes	complemented
58	#64543	C₂×C₄	1	24	yes	complemented
59	D₄×D₁₉	C₂×C₄	1	24	yes	complemented
60	#64541	C₂×C₄	1	24	yes	complemented
61	C₂×D₇₆	C₂³	1	3	yes	—
62	C₂×C₄×D₁₉	—	2	24	no	—
63	C₂×C₄×D₁₉	C₂×C₄	1	24	yes	complemented
64	C₂×C₄×D₁₉	C₂³	1	6	yes	—
65	C₂×C₄×D₁₉	C₂³	1	6	yes	—
66	C₂×C₄×D₁₉	C₂³	1	6	yes	—
67	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄×D₁₉	C₂³	1	3	yes	—
69	C₂×C₄×D₁₉	C₂³	1	3	yes	—
70	C₂×C₄×D₁₉	C₂³	1	3	yes	—
71	C₂×C₄×D₁₉	C₂³	1	2	yes	—
72	C₂×Dic₃₈	C₂³	1	3	yes	—
73	C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
74	C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
75	C₄²×C₁₉	C₂³	1	3	yes	—
76	C₄²×C₁₉	C₂³	1	6	yes	—
77	C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²⋊Dic₁₉	C₂³	1	6	yes	—
79	(C₂×D₁₉)⋊C₄	C₂³	1	12	yes	—
80	C₄⋊Dic₁₉	C₂³	1	6	yes	—
81	Dic₁₉⋊C₄	C₂³	1	12	yes	—
82	C₄×Dic₁₉	C₂³	1	6	yes	—
83	C₄×Dic₁₉	C₂³	1	6	yes	—
84	C₄×Dic₁₉	C₂³	1	2	yes	—
85	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
86	C₄×Dic₁₉	C₂³	1	3	yes	—
87	C₄×Dic₁₉	C₂³	1	6	yes	—
88	C₄×Dic₁₉	C₂³	1	6	yes	—
89	C₂³×C₁₉	C₂⁴	1	3	yes	—
90	C₂²×D₁₉	—	2	12	no	—
91	C₂²×D₁₉	C₂²×C₄	1	12	yes	—
92	C₂²×D₁₉	C₂⁴	1	3	yes	—
93	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
94	Q₈×C₁₉	C₂²×C₄	1	4	yes	complemented
95	D₄×C₁₉	C₂²×C₄	1	12	yes	complemented
96	C₂×C₄×C₁₉	—	2	12	no	—
97	C₂×C₄×C₁₉	C₂²×C₄	1	12	yes	complemented
98	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
99	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
101	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
102	C₂²⋊D₁₉	C₂²×C₄	1	24	yes	complemented
103	C₂×Dic₁₉	—	2	12	no	—
104	C₂×Dic₁₉	C₂²×C₄	1	12	yes	complemented
105	C₂×Dic₁₉	C₂⁴	1	6	yes	—
106	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
107	C₂×Dic₁₉	C₂⁴	1	3	yes	—
108	C₂×Dic₁₉	C₂⁴	1	2	yes	—
109	D₇₆	C₂²×C₄	1	12	yes	complemented
110	C₄×D₁₉	—	2	12	no	—
111	C₄×D₁₉	—	2	12	no	—
112	C₄×D₁₉	—	2	12	no	—
113	C₄×D₁₉	C₂²×C₄	1	4	yes	—
114	C₄×D₁₉	C₂²×C₄	1	12	yes	—
115	C₄×D₁₉	C₂²×C₄	1	12	yes	complemented
116	C₄×D₁₉	C₂²×C₄	1	12	yes	complemented
117	C₄×D₁₉	#41	1	8	yes	direct product factor
118	Dic₃₈	C₂²×C₄	1	12	yes	complemented
119	C₂×C₄×#41	—	19	1	no	maximal, Sylow
120	C₂²×C₁₉	—	2	6	no	—
121	C₂²×C₁₉	C₂³×C₄	1	6	yes	—
122	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
123	C₂×D₁₉	—	2	6	no	—
124	C₂×D₁₉	—	2	24	no	—
125	C₂×D₁₉	C₂³×C₄	1	6	yes	—
126	C₂×D₁₉	C₂³×C₄	1	2	yes	—
127	C₂×D₁₉	C₂×#41	1	4	yes	—
128	C₄×C₁₉	—	2	6	no	—
129	C₄×C₁₉	C₂³×C₄	1	6	yes	—
130	C₄×C₁₉	C₂³×C₄	1	2	yes	—
131	C₄×C₁₉	C₂×#41	1	4	yes	complemented
132	Dic₁₉	—	2	6	no	—
133	Dic₁₉	C₂³×C₄	1	6	yes	—
134	Dic₁₉	C₂³×C₄	1	2	yes	—
135	Dic₁₉	C₂×#41	1	4	yes	complemented
136	C₂²×#41	—	19	1	no	—
137	C₄×#41	—	19	1	no	—
138	C₄×#41	—	19	2	no	—
139	C₄×#41	—	19	6	no	—
140	C₄×#41	—	19	3	no	—
141	C₄×#41	—	19	3	no	—
142	C₄×#41	D₁₉	1	1	yes	characteristic, direct product factor
143	C₂×C₄×Q₈	—	19	2	no	—
144	C₂×C₄×D₄	—	19	6	no	—
145	C₂×#117	—	19	3	no	—
146	C₂²×C₄²	—	19	3	no	—
147	C₂×C₁₉	—	2	6	no	—
148	C₂×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
149	C₂×C₁₉	C₂²×#41	1	2	yes	—
150	D₁₉	—	2	6	no	—
151	D₁₉	C₄×#41	1	4	yes	direct product factor
152	C₂×#41	—	19	16	no	—
153	C₂×#41	—	19	1	no	—
154	C₂×#41	—	19	3	no	—
155	C₂×#41	—	19	3	no	—
156	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
157	C₂²×Q₈	—	19	1	no	—
158	C₂²×D₄	—	19	3	no	—
159	C₂³×C₄	—	19	3	no	—
160	C₂³×C₄	—	19	6	no	—
161	C₄×Q₈	—	19	2	no	—
162	C₄×Q₈	—	19	6	no	—
163	C₄×Q₈	—	19	6	no	—
164	C₄×Q₈	C₂×D₁₉	1	2	yes	complemented
165	C₄×D₄	—	19	6	no	—
166	C₄×D₄	—	19	12	no	—
167	C₄×D₄	—	19	6	no	—
168	C₄×D₄	—	19	12	no	—
169	C₄×D₄	—	19	6	no	—
170	C₄×D₄	C₂×D₁₉	1	6	yes	complemented
171	#117	—	19	3	no	—
172	#117	—	19	6	no	—
173	#117	—	19	6	no	—
174	#117	—	19	6	no	—
175	#117	C₂×D₁₉	1	3	yes	complemented
176	C₂×C₄⋊C₄	—	19	6	no	—
177	C₂×C₂²⋊C₄	—	19	6	no	—
178	C₂×C₄²	—	19	6	no	—
179	C₂×C₄²	—	19	3	no	—
180	C₂×C₄²	—	19	3	no	—
181	C₂×C₄²	—	19	6	no	—
182	C₂×C₄²	—	19	6	no	—
183	C₂×C₄²	—	19	3	no	—
184	C₂×C₄²	—	19	3	no	—
185	C₂×C₄²	—	19	1	no	—
186	C₂×C₄²	C₂×D₁₉	1	3	yes	complemented
187	C₁₉	C₂×C₄×#41	1	1	yes	characteristic, complemented, Sylow
188	C₂⁴	—	19	3	no	—
189	#41	—	19	8	no	—
190	#41	—	19	24	no	—
191	#41	—	19	24	no	—
192	#41	C₄×D₁₉	1	8	yes	direct product factor
193	C₂×Q₈	—	19	8	no	—
194	C₂×Q₈	—	19	3	no	—
195	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
196	C₂×D₄	—	19	6	no	—
197	C₂×D₄	—	19	24	no	—
198	C₂×D₄	—	19	3	no	—
199	C₂×D₄	C₂²×D₁₉	1	3	yes	—
200	C₂²×C₄	—	19	3	no	—
201	C₂²×C₄	—	19	24	no	—
202	C₂²×C₄	—	19	1	no	—
203	C₂²×C₄	—	19	2	no	—
204	C₂²×C₄	—	19	3	no	—
205	C₂²×C₄	—	19	3	no	—
206	C₂²×C₄	—	19	3	no	—
207	C₂²×C₄	—	19	6	no	—
208	C₂²×C₄	—	19	6	no	—
209	C₂²×C₄	—	19	6	no	—
210	C₂²×C₄	—	19	6	no	—
211	C₂²×C₄	—	38	24	no	—
212	C₂²×C₄	C₂²×D₁₉	1	6	yes	—
213	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
214	C₄⋊C₄	—	19	12	no	—
215	C₄⋊C₄	—	19	6	no	—
216	C₄⋊C₄	C₂²×D₁₉	1	6	yes	—
217	C₂²⋊C₄	—	19	6	no	—
218	C₂²⋊C₄	—	19	12	no	—
219	C₂²⋊C₄	C₂²×D₁₉	1	6	yes	—
220	C₄²	—	19	1	no	—
221	C₄²	—	19	2	no	—
222	C₄²	—	19	6	no	—
223	C₄²	—	19	3	no	—
224	C₄²	—	19	6	no	—
225	C₄²	—	19	6	no	—
226	C₄²	—	19	6	no	—
227	C₄²	C₂²×D₁₉	1	3	yes	—
228	C₄²	C₂²×D₁₉	1	6	yes	—
229	C₄²	C₂²×D₁₉	1	1	yes	characteristic
230	C₂³	—	19	1	no	—
231	C₂³	—	19	12	no	—
232	C₂³	—	19	3	no	—
233	C₂³	—	38	12	no	—
234	C₂³	C₂³×D₁₉	1	3	yes	—
235	Q₈	—	19	12	no	—
236	Q₈	C₂×C₄×D₁₉	1	4	yes	complemented
237	D₄	—	19	24	no	—
238	D₄	—	19	12	no	—
239	D₄	C₂×C₄×D₁₉	1	12	yes	complemented
240	C₂×C₄	—	2	12	no	—
241	C₂×C₄	—	19	12	no	—
242	C₂×C₄	—	19	1	no	—
243	C₂×C₄	—	19	2	no	—
244	C₂×C₄	—	19	3	no	—
245	C₂×C₄	—	19	4	no	—
246	C₂×C₄	—	19	12	no	—
247	C₂×C₄	—	19	12	no	—
248	C₂×C₄	—	19	12	no	—
249	C₂×C₄	—	19	8	no	—
250	C₂×C₄	—	19	6	no	—
251	C₂×C₄	—	38	12	no	—
252	C₂×C₄	—	38	12	no	—
253	C₂×C₄	—	38	12	no	—
254	C₂×C₄	—	38	12	no	—
255	C₂×C₄	C₂×C₄×D₁₉	1	12	yes	complemented
256	C₂×C₄	C₂³×D₁₉	1	6	yes	—
257	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
258	C₂×C₄	C₂³×D₁₉	1	3	yes	—
259	C₂×C₄	C₂³×D₁₉	1	2	yes	—
260	C₂²	—	2	6	no	—
261	C₂²	—	19	2	no	—
262	C₂²	—	19	4	no	—
263	C₂²	—	19	6	no	—
264	C₂²	—	38	24	no	—
265	C₂²	—	38	6	no	—
266	C₂²	C₂²×C₄×D₁₉	1	6	yes	—
267	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
268	C₄	—	2	6	no	—
269	C₄	—	19	2	no	—
270	C₄	—	19	6	no	—
271	C₄	—	19	4	no	—
272	C₄	—	38	6	no	—
273	C₄	C₂²×C₄×D₁₉	1	2	yes	—
274	C₄	C₂²×C₄×D₁₉	1	6	yes	—
275	C₄	#41×D₁₉	1	4	yes	direct product factor
276	C₂	—	2	6	no	—
277	C₂	—	19	4	no	—
278	C₂	—	38	6	no	—
279	C₂	C₂³×C₄×D₁₉	1	1	yes	characteristic
280	C₂	C₂×#41×D₁₉	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂²×D₁₉
commutator	C₂×C₁₉	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₄×#41×C₁₉	C₂
socle, cosocle	C₂²×C₁₉	C₂⁵
prime radical	C₂×#41×D₁₉	C₂
hypercenter	C₄×#41	D₁₉
hypocenter	C₁₉	C₂×C₄×#41
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
2. #41×Dic₁₉	C₂	semidirect
3. C₄×#64545	C₂	semidirect
4. C₄×#64541	C₂	semidirect
5. #11927012	C₂	semidirect
6. C₄×#64543	C₂	semidirect
7. C₄×Q₈×D₁₉	C₂	semidirect
8. C₄×D₄×D₁₉	C₂	semidirect
9. #117×D₁₉	C₂	semidirect
10. C₂×C₄²×D₁₉	C₂	semidirect
11. C₄×#41×C₁₉	C₂	semidirect
13. #41×D₁₉	C₄	direct (N × H)
21. C₄×Q₈×C₁₉	C₂²	semidirect
22. C₄×D₄×C₁₉	C₂²	semidirect
23. C₁₉×#117	C₂²	semidirect
24. C₂×C₄²×C₁₉	C₂²	semidirect
25. Q₈×Dic₁₉	C₂²	semidirect
26. D₄×Dic₁₉	C₂²	semidirect
27. C₄×C₂²⋊D₁₉	C₂²	semidirect
28. #10597372	C₂²	semidirect
29. C₂×C₄×Dic₁₉	C₂²	semidirect
30. C₂×C₄×Dic₁₉	C₂²	semidirect
31. #10597339	C₂²	semidirect
32. #10597338	C₂²	semidirect
34. #10597333	C₂²	semidirect
35. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
37. #10597323	C₂²	semidirect
38. C₄×D₇₆	C₂²	semidirect
39. #10597318	C₂²	semidirect
43. C₄²×D₁₉	C₂²	semidirect
44. C₄²×D₁₉	C₂²	semidirect
45. C₄²×D₁₉	C₂²	semidirect
46. C₄×Dic₃₈	C₂²	semidirect
48. #41×C₁₉	C₂×C₄	semidirect
56. #64545	C₂×C₄	semidirect
57. Q₈×D₁₉	C₂×C₄	semidirect
58. #64543	C₂×C₄	semidirect
59. D₄×D₁₉	C₂×C₄	semidirect
60. #64541	C₂×C₄	semidirect
63. C₂×C₄×D₁₉	C₂×C₄	semidirect
94. Q₈×C₁₉	C₂²×C₄	semidirect
95. D₄×C₁₉	C₂²×C₄	semidirect
97. C₂×C₄×C₁₉	C₂²×C₄	semidirect
102. C₂²⋊D₁₉	C₂²×C₄	semidirect
104. C₂×Dic₁₉	C₂²×C₄	semidirect
109. D₇₆	C₂²×C₄	semidirect
115. C₄×D₁₉	C₂²×C₄	semidirect
116. C₄×D₁₉	C₂²×C₄	semidirect
117. C₄×D₁₉	#41	direct (N × H)
118. Dic₃₈	C₂²×C₄	semidirect
131. C₄×C₁₉	C₂×#41	semidirect
135. Dic₁₉	C₂×#41	semidirect
142. C₄×#41	D₁₉	direct (N × H)
151. D₁₉	C₄×#41	direct (N × H)
164. C₄×Q₈	C₂×D₁₉	semidirect
170. C₄×D₄	C₂×D₁₉	semidirect
175. #117	C₂×D₁₉	semidirect
186. C₂×C₄²	C₂×D₁₉	semidirect
187. C₁₉	C₂×C₄×#41	semidirect
192. #41	C₄×D₁₉	direct (N × H)
236. Q₈	C₂×C₄×D₁₉	semidirect
239. D₄	C₂×C₄×D₁₉	semidirect
255. C₂×C₄	C₂×C₄×D₁₉	semidirect
275. C₄	#41×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
#41×Dic₁₉	2
C₄×#64545	2
C₄×#64541	2
#11927012	2
C₄×#64543	2
C₄×Q₈×D₁₉	2
C₄×D₄×D₁₉	2
#117×D₁₉	2
C₂×C₄²×D₁₉	2
C₄×#41×C₁₉	2
C₂×C₄×#41	19

Subgroups — C4×#41×D19 #14576812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#41×D₁₉ #14576812