Subgroups — C₁₉×#62832 #18068791

Order 4864.

8650 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3543	C₂	1	24	yes	maximal, complemented
2	C₁₉×#3508	C₂	1	12	yes	maximal, complemented
3	C₁₉×#3498	C₂	1	12	yes	maximal, complemented
4	C₁₉×#3484	C₂	1	12	yes	maximal, complemented
5	C₁₉×#3444	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	12	yes	complemented
8	C₂³×D₄×C₁₉	C₂²	1	6	yes	complemented
9	C₁₉×#560	C₂²	1	32	yes	complemented
10	C₁₉×#559	C₂²	1	24	yes	complemented
11	C₁₉×#550	C₂²	1	48	yes	complemented
12	C₁₉×#546	C₂²	1	96	yes	complemented
13	D₄²×C₁₉	C₂²	1	96	yes	complemented
14	D₄²×C₁₉	C₂²	1	24	yes	complemented
15	C₁₉×#540	C₂²	1	48	yes	complemented
16	C₁₉×#535	C₂²	1	24	yes	complemented
17	C₁₉×#535	C₂²	1	48	yes	complemented
18	C₁₉×#534	C₂²	1	48	yes	complemented
19	C₁₉×#533	C₂²	1	6	yes	complemented
20	C₁₉×#532	C₂²	1	6	yes	complemented
21	C₁₉×#532	C₂²	1	24	yes	complemented
22	C₂×C₁₉×#127	C₂²	1	12	yes	complemented
23	C₂×C₁₉×#127	C₂²	1	12	yes	complemented
24	C₂×C₁₉×#127	C₂²	1	8	yes	complemented
25	C₁₉×#529	C₂²	1	24	yes	complemented
26	C₁₉×#525	C₂²	1	12	yes	complemented
27	C₂×C₁₉×#120	C₂²	1	16	yes	complemented
28	C₁₉×#518	C₂²	1	12	yes	complemented
29	C₄×#41×C₁₉	C₂²	1	12	yes	complemented
30	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₂⁵×C₁₉	C₂³	1	4	yes	—
32	C₁₉×H(5,𝔽₂)	—	4	48	no	—
33	C₂×#41×C₁₉	C₂³	1	12	yes	—
34	C₂×#41×C₁₉	C₂³	1	48	yes	complemented
35	C₂²×D₄×C₁₉	—	4	24	no	—
36	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
37	C₂²×D₄×C₁₉	C₂³	1	48	yes	—
38	C₂²×D₄×C₁₉	C₂³	1	12	yes	—
39	C₂²×D₄×C₁₉	C₂³	1	48	yes	—
40	C₂²×D₄×C₁₉	C₂³	1	48	yes	complemented
41	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
42	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	complemented
43	C₁₉×#127	C₂³	1	8	yes	—
44	C₁₉×#127	C₂³	1	24	yes	—
45	C₁₉×#127	C₂³	1	24	yes	—
46	C₁₉×#127	C₂³	1	8	yes	—
47	C₁₉×#127	C₂³	1	2	yes	complemented
48	C₁₉×#127	C₂³	1	48	yes	complemented
49	C₁₉×#126	C₂³	1	16	yes	complemented
50	C₁₉×#125	C₂³	1	12	yes	complemented
51	C₁₉×#124	C₂³	1	12	yes	complemented
52	C₁₉×#124	C₂³	1	48	yes	complemented
53	C₁₉×#123	C₂³	1	24	yes	—
54	C₁₉×#123	C₂³	1	96	yes	complemented
55	C₁₉×C₂²⋊Q₈	C₂³	1	24	yes	—
56	C₁₉×#121	C₂³	1	24	yes	—
57	C₁₉×#121	C₂³	1	96	yes	complemented
58	C₁₉×#121	C₂³	1	192	yes	complemented
59	C₁₉×#120	C₂³	1	8	yes	—
60	C₁₉×#120	C₂³	1	96	yes	—
61	C₁₉×#120	C₂³	1	96	yes	complemented
62	C₄×Q₈×C₁₉	C₂³	1	24	yes	complemented
63	C₄×D₄×C₁₉	C₂³	1	48	yes	—
64	C₄×D₄×C₁₉	C₂³	1	24	yes	complemented
65	C₄×D₄×C₁₉	C₂³	1	96	yes	complemented
66	C₁₉×#117	C₂³	1	12	yes	—
67	C₁₉×#117	C₂³	1	24	yes	complemented
68	C₂×C₂²⋊C₄×C₁₉	C₂³	1	48	yes	—
69	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	8	yes	complemented
72	C₂⁴×C₁₉	—	4	24	no	—
73	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
74	C₂⁴×C₁₉	C₂⁴	1	24	yes	—
75	C₂⁴×C₁₉	C₂⁴	1	16	yes	—
76	#41×C₁₉	—	2	48	no	—
77	#41×C₁₉	—	4	96	no	—
78	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
79	C₂×D₄×C₁₉	—	2	48	no	—
80	C₂×D₄×C₁₉	—	4	96	no	—
81	C₂×D₄×C₁₉	—	4	96	no	—
82	C₂×D₄×C₁₉	—	4	24	no	—
83	C₂×D₄×C₁₉	—	4	96	no	—
84	C₂×D₄×C₁₉	C₂⁴	1	24	yes	—
85	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
86	C₂×D₄×C₁₉	C₂⁴	1	48	yes	—
87	C₂×D₄×C₁₉	C₂⁴	1	96	yes	—
88	C₂×D₄×C₁₉	C₂⁴	1	48	yes	—
89	C₂²×C₄×C₁₉	—	2	12	no	—
90	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
91	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
92	C₂²×C₄×C₁₉	C₂⁴	1	24	yes	—
93	C₂²×C₄×C₁₉	C₂⁴	1	48	yes	—
94	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
95	C₄⋊C₄×C₁₉	C₂⁴	1	24	yes	—
96	C₄⋊C₄×C₁₉	C₂⁴	1	48	yes	—
97	C₂²⋊C₄×C₁₉	C₂⁴	1	24	yes	—
98	C₂²⋊C₄×C₁₉	C₂⁴	1	96	yes	—
99	C₂²⋊C₄×C₁₉	C₂⁴	1	48	yes	—
100	C₄²×C₁₉	C₂⁴	1	2	yes	—
101	C₄²×C₁₉	C₂⁴	1	6	yes	—
102	C₄²×C₁₉	C₂⁴	1	6	yes	—
103	C₄²×C₁₉	C₂⁴	1	2	yes	—
104	C₄²×C₁₉	C₂⁴	1	24	yes	—
105	#62832	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₁₉	—	2	6	no	—
107	C₂³×C₁₉	—	2	48	no	—
108	C₂³×C₁₉	—	4	48	no	—
109	C₂³×C₁₉	—	4	48	no	—
110	C₂³×C₁₉	—	8	32	no	—
111	C₂³×C₁₉	C₂⁵	1	8	yes	—
112	C₂³×C₁₉	C₂⁵	1	16	yes	—
113	C₂³×C₁₉	C₂⁵	1	3	yes	—
114	Q₈×C₁₉	—	2	24	no	—
115	D₄×C₁₉	—	2	48	no	—
116	D₄×C₁₉	—	2	96	no	—
117	D₄×C₁₉	—	2	24	no	—
118	D₄×C₁₉	—	4	48	no	—
119	D₄×C₁₉	—	4	96	no	—
120	C₂×C₄×C₁₉	—	2	6	no	—
121	C₂×C₄×C₁₉	—	2	24	no	—
122	C₂×C₄×C₁₉	—	2	48	no	—
123	C₂×C₄×C₁₉	—	4	48	no	—
124	C₂×C₄×C₁₉	H(5,𝔽₂)	1	12	yes	complemented
125	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
126	C₂×C₄×C₁₉	C₂⁵	1	24	yes	—
127	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
128	#3543	C₂×C₁₉	1	24	yes	complemented
129	#3508	C₂×C₁₉	1	12	yes	complemented
130	#3498	C₂×C₁₉	1	12	yes	complemented
131	#3484	C₂×C₁₉	1	12	yes	complemented
132	#3444	C₂×C₁₉	1	2	yes	complemented
133	C₂²×#127	C₂×C₁₉	1	1	yes	characteristic, complemented
134	C₂²×C₁₉	—	2	8	no	—
135	C₂²×C₁₉	—	2	6	no	—
136	C₂²×C₁₉	—	2	24	no	—
137	C₂²×C₁₉	—	2	48	no	—
138	C₂²×C₁₉	—	8	48	no	—
139	C₂²×C₁₉	—	16	16	no	—
140	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	6	yes	—
141	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
142	C₄×C₁₉	—	2	6	no	—
143	C₄×C₁₉	—	2	24	no	—
144	C₄×C₁₉	C₂×H(5,𝔽₂)	1	12	yes	—
145	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	12	yes	complemented
146	C₂³×D₄	C₂²×C₁₉	1	6	yes	complemented
147	#560	C₂²×C₁₉	1	32	yes	complemented
148	#559	C₂²×C₁₉	1	24	yes	complemented
149	#550	C₂²×C₁₉	1	48	yes	complemented
150	#546	C₂²×C₁₉	1	96	yes	complemented
151	D₄²	C₂²×C₁₉	1	96	yes	complemented
152	D₄²	C₂²×C₁₉	1	24	yes	complemented
153	#540	C₂²×C₁₉	1	48	yes	complemented
154	#535	C₂²×C₁₉	1	24	yes	complemented
155	#535	C₂²×C₁₉	1	48	yes	complemented
156	#534	C₂²×C₁₉	1	48	yes	complemented
157	#533	C₂²×C₁₉	1	6	yes	complemented
158	#532	C₂²×C₁₉	1	6	yes	complemented
159	#532	C₂²×C₁₉	1	24	yes	complemented
160	C₂×#127	C₂²×C₁₉	1	12	yes	complemented
161	C₂×#127	C₂²×C₁₉	1	12	yes	complemented
162	C₂×#127	C₂²×C₁₉	1	8	yes	complemented
163	#529	C₂²×C₁₉	1	24	yes	complemented
164	#525	C₂²×C₁₉	1	12	yes	complemented
165	C₂×#120	C₂²×C₁₉	1	16	yes	complemented
166	#518	C₂²×C₁₉	1	12	yes	complemented
167	C₄×#41	C₂²×C₁₉	1	12	yes	complemented
168	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
169	C₂×C₁₉	—	2	6	no	—
170	C₂×C₁₉	—	4	16	no	—
171	C₂×C₁₉	—	4	8	no	—
172	C₂×C₁₉	C₂²×H(5,𝔽₂)	1	3	yes	—
173	C₂⁵	C₂³×C₁₉	1	4	yes	—
174	H(5,𝔽₂)	—	4	48	no	—
175	C₂×#41	C₂³×C₁₉	1	12	yes	—
176	C₂×#41	C₂³×C₁₉	1	48	yes	complemented
177	C₂²×D₄	—	4	24	no	—
178	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
179	C₂²×D₄	C₂³×C₁₉	1	48	yes	—
180	C₂²×D₄	C₂³×C₁₉	1	12	yes	—
181	C₂²×D₄	C₂³×C₁₉	1	48	yes	—
182	C₂²×D₄	C₂³×C₁₉	1	48	yes	complemented
183	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
184	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
185	#127	C₂³×C₁₉	1	8	yes	—
186	#127	C₂³×C₁₉	1	24	yes	—
187	#127	C₂³×C₁₉	1	24	yes	—
188	#127	C₂³×C₁₉	1	8	yes	—
189	#127	C₂³×C₁₉	1	2	yes	complemented
190	#127	C₂³×C₁₉	1	48	yes	complemented
191	#126	C₂³×C₁₉	1	16	yes	complemented
192	#125	C₂³×C₁₉	1	12	yes	complemented
193	#124	C₂³×C₁₉	1	12	yes	complemented
194	#124	C₂³×C₁₉	1	48	yes	complemented
195	#123	C₂³×C₁₉	1	24	yes	—
196	#123	C₂³×C₁₉	1	96	yes	complemented
197	C₂²⋊Q₈	C₂³×C₁₉	1	24	yes	—
198	#121	C₂³×C₁₉	1	24	yes	—
199	#121	C₂³×C₁₉	1	96	yes	complemented
200	#121	C₂³×C₁₉	1	192	yes	complemented
201	#120	C₂³×C₁₉	1	8	yes	—
202	#120	C₂³×C₁₉	1	96	yes	—
203	#120	C₂³×C₁₉	1	96	yes	complemented
204	C₄×Q₈	C₂³×C₁₉	1	24	yes	complemented
205	C₄×D₄	C₂³×C₁₉	1	48	yes	—
206	C₄×D₄	C₂³×C₁₉	1	24	yes	complemented
207	C₄×D₄	C₂³×C₁₉	1	96	yes	complemented
208	#117	C₂³×C₁₉	1	12	yes	—
209	#117	C₂³×C₁₉	1	24	yes	complemented
210	C₂×C₂²⋊C₄	C₂³×C₁₉	1	48	yes	—
211	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
212	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
213	C₂×C₄²	C₂³×C₁₉	1	8	yes	complemented
214	C₁₉	#62832	1	1	yes	characteristic, direct product factor, Sylow
215	C₂⁴	—	4	24	no	—
216	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
217	C₂⁴	C₂⁴×C₁₉	1	24	yes	—
218	C₂⁴	C₂⁴×C₁₉	1	16	yes	—
219	#41	—	2	48	no	—
220	#41	—	4	96	no	—
221	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
222	C₂×D₄	—	2	48	no	—
223	C₂×D₄	—	4	96	no	—
224	C₂×D₄	—	4	96	no	—
225	C₂×D₄	—	4	24	no	—
226	C₂×D₄	—	4	96	no	—
227	C₂×D₄	C₂⁴×C₁₉	1	24	yes	—
228	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
229	C₂×D₄	C₂⁴×C₁₉	1	48	yes	—
230	C₂×D₄	C₂⁴×C₁₉	1	96	yes	—
231	C₂×D₄	C₂⁴×C₁₉	1	48	yes	—
232	C₂²×C₄	—	2	12	no	—
233	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
234	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
235	C₂²×C₄	C₂⁴×C₁₉	1	24	yes	—
236	C₂²×C₄	C₂⁴×C₁₉	1	48	yes	—
237	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
238	C₄⋊C₄	C₂⁴×C₁₉	1	24	yes	—
239	C₄⋊C₄	C₂⁴×C₁₉	1	48	yes	—
240	C₂²⋊C₄	C₂⁴×C₁₉	1	24	yes	—
241	C₂²⋊C₄	C₂⁴×C₁₉	1	96	yes	—
242	C₂²⋊C₄	C₂⁴×C₁₉	1	48	yes	—
243	C₄²	C₂⁴×C₁₉	1	2	yes	—
244	C₄²	C₂⁴×C₁₉	1	6	yes	—
245	C₄²	C₂⁴×C₁₉	1	6	yes	—
246	C₄²	C₂⁴×C₁₉	1	2	yes	—
247	C₄²	C₂⁴×C₁₉	1	24	yes	—
248	C₂³	—	2	6	no	—
249	C₂³	—	2	48	no	—
250	C₂³	—	4	48	no	—
251	C₂³	—	4	48	no	—
252	C₂³	—	8	32	no	—
253	C₂³	C₂⁵×C₁₉	1	8	yes	—
254	C₂³	C₂⁵×C₁₉	1	16	yes	—
255	C₂³	C₂⁵×C₁₉	1	3	yes	—
256	Q₈	—	2	24	no	—
257	D₄	—	2	48	no	—
258	D₄	—	2	96	no	—
259	D₄	—	2	24	no	—
260	D₄	—	4	48	no	—
261	D₄	—	4	96	no	—
262	C₂×C₄	—	2	6	no	—
263	C₂×C₄	—	2	24	no	—
264	C₂×C₄	—	2	48	no	—
265	C₂×C₄	—	4	48	no	—
266	C₂×C₄	C₁₉×H(5,𝔽₂)	1	12	yes	complemented
267	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
268	C₂×C₄	C₂⁵×C₁₉	1	24	yes	—
269	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
270	C₂²	—	2	8	no	—
271	C₂²	—	2	6	no	—
272	C₂²	—	2	24	no	—
273	C₂²	—	2	48	no	—
274	C₂²	—	8	48	no	—
275	C₂²	—	16	16	no	—
276	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	6	yes	—
277	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
278	C₄	—	2	6	no	—
279	C₄	—	2	24	no	—
280	C₄	C₂×C₁₉×H(5,𝔽₂)	1	12	yes	—
281	C₂	—	2	6	no	—
282	C₂	—	4	16	no	—
283	C₂	—	4	8	no	—
284	C₂	C₂²×C₁₉×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3543	C₂	semidirect
2. C₁₉×#3508	C₂	semidirect
3. C₁₉×#3498	C₂	semidirect
4. C₁₉×#3484	C₂	semidirect
5. C₁₉×#3444	C₂	semidirect
6. C₂²×C₁₉×#127	C₂	semidirect
7. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
8. C₂³×D₄×C₁₉	C₂²	semidirect
9. C₁₉×#560	C₂²	semidirect
10. C₁₉×#559	C₂²	semidirect
11. C₁₉×#550	C₂²	semidirect
12. C₁₉×#546	C₂²	semidirect
13. D₄²×C₁₉	C₂²	semidirect
14. D₄²×C₁₉	C₂²	semidirect
15. C₁₉×#540	C₂²	semidirect
16. C₁₉×#535	C₂²	semidirect
17. C₁₉×#535	C₂²	semidirect
18. C₁₉×#534	C₂²	semidirect
19. C₁₉×#533	C₂²	semidirect
20. C₁₉×#532	C₂²	semidirect
21. C₁₉×#532	C₂²	semidirect
22. C₂×C₁₉×#127	C₂²	semidirect
23. C₂×C₁₉×#127	C₂²	semidirect
24. C₂×C₁₉×#127	C₂²	semidirect
25. C₁₉×#529	C₂²	semidirect
26. C₁₉×#525	C₂²	semidirect
27. C₂×C₁₉×#120	C₂²	semidirect
28. C₁₉×#518	C₂²	semidirect
29. C₄×#41×C₁₉	C₂²	semidirect
30. C₂²×C₄²×C₁₉	C₂²	semidirect
34. C₂×#41×C₁₉	C₂³	semidirect
40. C₂²×D₄×C₁₉	C₂³	semidirect
42. C₁₉×C₄⋊Q₈	C₂³	semidirect
47. C₁₉×#127	C₂³	semidirect
48. C₁₉×#127	C₂³	semidirect
49. C₁₉×#126	C₂³	semidirect
50. C₁₉×#125	C₂³	semidirect
51. C₁₉×#124	C₂³	semidirect
52. C₁₉×#124	C₂³	semidirect
54. C₁₉×#123	C₂³	semidirect
57. C₁₉×#121	C₂³	semidirect
58. C₁₉×#121	C₂³	semidirect
61. C₁₉×#120	C₂³	semidirect
62. C₄×Q₈×C₁₉	C₂³	semidirect
64. C₄×D₄×C₁₉	C₂³	semidirect
65. C₄×D₄×C₁₉	C₂³	semidirect
67. C₁₉×#117	C₂³	semidirect
71. C₂×C₄²×C₁₉	C₂³	semidirect
105. #62832	C₁₉	direct (N × H)
124. C₂×C₄×C₁₉	H(5,𝔽₂)	semidirect
128. #3543	C₂×C₁₉	semidirect
129. #3508	C₂×C₁₉	semidirect
130. #3498	C₂×C₁₉	semidirect
131. #3484	C₂×C₁₉	semidirect
132. #3444	C₂×C₁₉	semidirect
133. C₂²×#127	C₂×C₁₉	semidirect
145. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
146. C₂³×D₄	C₂²×C₁₉	semidirect
147. #560	C₂²×C₁₉	semidirect
148. #559	C₂²×C₁₉	semidirect
149. #550	C₂²×C₁₉	semidirect
150. #546	C₂²×C₁₉	semidirect
151. D₄²	C₂²×C₁₉	semidirect
152. D₄²	C₂²×C₁₉	semidirect
153. #540	C₂²×C₁₉	semidirect
154. #535	C₂²×C₁₉	semidirect
155. #535	C₂²×C₁₉	semidirect
156. #534	C₂²×C₁₉	semidirect
157. #533	C₂²×C₁₉	semidirect
158. #532	C₂²×C₁₉	semidirect
159. #532	C₂²×C₁₉	semidirect
160. C₂×#127	C₂²×C₁₉	semidirect
161. C₂×#127	C₂²×C₁₉	semidirect
162. C₂×#127	C₂²×C₁₉	semidirect
163. #529	C₂²×C₁₉	semidirect
164. #525	C₂²×C₁₉	semidirect
165. C₂×#120	C₂²×C₁₉	semidirect
166. #518	C₂²×C₁₉	semidirect
167. C₄×#41	C₂²×C₁₉	semidirect
168. C₂²×C₄²	C₂²×C₁₉	semidirect
176. C₂×#41	C₂³×C₁₉	semidirect
182. C₂²×D₄	C₂³×C₁₉	semidirect
184. C₄⋊Q₈	C₂³×C₁₉	semidirect
189. #127	C₂³×C₁₉	semidirect
190. #127	C₂³×C₁₉	semidirect
191. #126	C₂³×C₁₉	semidirect
192. #125	C₂³×C₁₉	semidirect
193. #124	C₂³×C₁₉	semidirect
194. #124	C₂³×C₁₉	semidirect
196. #123	C₂³×C₁₉	semidirect
199. #121	C₂³×C₁₉	semidirect
200. #121	C₂³×C₁₉	semidirect
203. #120	C₂³×C₁₉	semidirect
204. C₄×Q₈	C₂³×C₁₉	semidirect
206. C₄×D₄	C₂³×C₁₉	semidirect
207. C₄×D₄	C₂³×C₁₉	semidirect
209. #117	C₂³×C₁₉	semidirect
213. C₂×C₄²	C₂³×C₁₉	semidirect
214. C₁₉	#62832	direct (N × H)
266. C₂×C₄	C₁₉×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3543	2
C₁₉×#3508	2
C₁₉×#3498	2
C₁₉×#3484	2
C₁₉×#3444	2
C₂²×C₁₉×#127	2
#62832	19

Subgroups — C19×#62832 #18068791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62832 #18068791