Subgroups — C₁₉×#61674 #18067633

Order 4864.

2032 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3500	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3313	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3311	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3270	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3266	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3215	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3202	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3200	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3116	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3011	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3009	C₂	1	2	yes	maximal, complemented
13	C₁₉×#2980	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#137	C₂²	1	2	yes	—
17	C₂×C₁₉×#137	C₂²	1	2	yes	complemented
18	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
19	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#563	—	2	1	no	—
21	C₁₉×#563	—	2	1	no	—
22	C₁₉×#559	—	2	1	no	—
23	Q₈²×C₁₉	—	2	1	no	—
24	C₁₉×#556	C₂²	1	4	yes	complemented
25	D₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
26	C₁₉×#548	C₂²	1	4	yes	—
27	C₁₉×#546	—	2	4	no	—
28	C₁₉×#546	C₂²	1	4	yes	—
29	C₁₉×#542	—	2	4	no	—
30	C₁₉×#536	—	2	1	no	—
31	C₁₉×#536	C₂²	1	1	yes	characteristic
32	C₁₉×#536	C₂²	1	2	yes	—
33	C₁₉×#536	C₂²	1	2	yes	complemented
34	C₁₉×#535	—	2	1	no	—
35	C₁₉×#535	C₂²	1	1	yes	characteristic
36	C₁₉×#533	C₂²	1	2	yes	complemented
37	C₁₉×#532	—	2	1	no	—
38	C₁₉×#532	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#124	—	2	1	no	—
40	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
41	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
42	C₁₉×#497	C₂²	1	4	yes	complemented
43	C₁₉×#489	C₂²	1	4	yes	complemented
44	C₁₉×#485	C₂²	1	4	yes	complemented
45	C₁₉×#485	C₂²	1	4	yes	complemented
46	C₁₉×#482	C₂²	1	4	yes	complemented
47	C₁₉×#477	C₂²	1	2	yes	complemented
48	C₁₉×#476	C₂²	1	2	yes	complemented
49	C₁₉×#470	C₂²	1	4	yes	complemented
50	C₁₉×#468	C₂²	1	4	yes	complemented
51	C₁₉×#467	C₂²	1	4	yes	complemented
52	C₁₉×#465	C₂²	1	4	yes	complemented
53	C₁₉×#464	C₂²	1	4	yes	complemented
54	C₁₉×#464	C₂²	1	4	yes	complemented
55	C₁₉×#462	C₂²	1	2	yes	complemented
56	C₁₉×#461	C₂²	1	2	yes	complemented
57	C₁₉×#452	C₂²	1	4	yes	—
58	C₁₉×#452	C₂²	1	4	yes	—
59	C₁₉×#452	C₂²	1	4	yes	complemented
60	C₁₉×#451	C₂²	1	4	yes	complemented
61	C₁₉×#451	C₂²	1	4	yes	complemented
62	C₁₉×#451	C₂²	1	4	yes	complemented
63	C₁₉×#450	C₂²	1	4	yes	—
64	C₁₉×#450	C₂²	1	4	yes	—
65	C₁₉×#448	C₂²	1	4	yes	complemented
66	C₁₉×#441	C₂²	1	4	yes	complemented
67	C₁₉×#440	C₂²	1	4	yes	complemented
68	C₁₉×#435	C₂²	1	4	yes	complemented
69	C₁₉×#435	C₂²	1	4	yes	complemented
70	C₁₉×#432	C₂²	1	2	yes	complemented
71	C₁₉×#419	C₂²	1	2	yes	complemented
72	C₁₉×#418	C₂²	1	2	yes	—
73	C₁₉×#416	C₂²	1	2	yes	—
74	C₁₉×#416	C₂²	1	2	yes	complemented
75	C₁₉×#408	C₂²	1	2	yes	—
76	C₁₉×#408	C₂²	1	2	yes	complemented
77	C₁₉×2₋¹⁺⁴	—	4	2	no	—
78	C₁₉×2₋¹⁺⁴	—	4	2	no	—
79	C₁₉×H(5,𝔽₂)	—	4	2	no	—
80	C₁₉×H(5,𝔽₂)	—	4	2	no	—
81	C₂×#41×C₁₉	—	2	1	no	—
82	C₂×#41×C₁₉	—	2	1	no	—
83	C₂×#41×C₁₉	—	2	2	no	—
84	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×#41×C₁₉	C₂³	1	2	yes	—
86	C₂×#41×C₁₉	C₂³	1	2	yes	—
87	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₉	—	2	1	no	—
90	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
91	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
92	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₉	—	2	1	no	—
95	C₂²×D₄×C₁₉	—	2	2	no	—
96	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×#137	—	4	4	no	—
99	C₁₉×#137	—	4	4	no	—
100	C₂×Q₁₆×C₁₉	—	4	4	no	—
101	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
102	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
103	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₁₉	—	4	4	no	—
105	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
108	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
109	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
110	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
111	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
112	C₁₉×C₄⋊Q₈	—	2	1	no	—
113	C₁₉×C₄⋊Q₈	—	2	2	no	—
114	C₁₉×C₄⋊Q₈	—	2	2	no	—
115	C₁₉×C₄⋊Q₈	—	2	4	no	—
116	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
117	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₉×#127	—	2	1	no	—
120	C₁₉×#127	D₄	1	1	yes	characteristic
121	C₁₉×#126	—	2	4	no	—
122	C₁₉×#126	—	2	4	no	—
123	C₁₉×#125	—	2	2	no	—
124	C₁₉×#124	—	2	1	no	—
125	C₁₉×#124	—	2	1	no	—
126	C₁₉×#124	—	2	2	no	—
127	C₁₉×#124	—	2	2	no	—
128	C₁₉×#124	—	2	4	no	—
129	C₁₉×#124	—	2	4	no	—
130	C₁₉×#124	—	2	1	no	—
131	C₁₉×#124	—	2	1	no	—
132	C₁₉×#124	D₄	1	1	yes	characteristic
133	C₁₉×#124	D₄	1	1	yes	characteristic
134	C₁₉×#124	C₂³	1	4	yes	—
135	C₁₉×#123	—	2	2	no	—
136	C₁₉×#123	—	2	2	no	—
137	C₁₉×#123	—	2	2	no	—
138	C₁₉×#123	—	2	2	no	—
139	C₁₉×#123	—	2	2	no	—
140	C₁₉×#123	—	2	4	no	—
141	C₁₉×C₂²⋊Q₈	—	2	2	no	—
142	C₁₉×C₂²⋊Q₈	—	2	4	no	—
143	C₁₉×C₂²⋊Q₈	—	2	4	no	—
144	C₁₉×C₂²⋊Q₈	—	2	4	no	—
145	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₁₉×#121	—	2	4	no	—
150	C₁₉×#121	—	2	4	no	—
151	C₁₉×#121	D₄	1	4	yes	—
152	C₁₉×#121	C₂³	1	4	yes	—
153	C₁₉×#120	—	2	4	no	—
154	C₁₉×#120	—	2	2	no	—
155	C₄×Q₈×C₁₉	—	2	4	no	—
156	C₄×Q₈×C₁₉	—	2	2	no	—
157	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
158	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
159	C₄×D₄×C₁₉	—	2	4	no	—
160	C₄×D₄×C₁₉	—	2	2	no	—
161	C₄×D₄×C₁₉	—	2	4	no	—
162	C₄×D₄×C₁₉	C₂³	1	2	yes	—
163	C₄×D₄×C₁₉	C₂³	1	4	yes	—
164	C₁₉×#117	—	2	2	no	—
165	C₁₉×#117	—	2	1	no	—
166	C₁₉×#117	C₂³	1	2	yes	—
167	C₁₉×#117	C₂³	1	2	yes	—
168	C₁₉×#117	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂×C₄²×C₁₉	—	2	1	no	—
172	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
173	C₁₉×#107	C₂³	1	4	yes	—
174	C₁₉×#106	C₂³	1	4	yes	—
175	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
176	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₉×#103	C₂³	1	4	yes	—
178	C₁₉×#103	C₂³	1	4	yes	—
179	C₁₉×#103	C₂³	1	4	yes	—
180	C₁₉×#103	C₂³	1	4	yes	—
181	C₁₉×#103	C₂³	1	4	yes	—
182	C₁₉×#102	C₂³	1	4	yes	—
183	C₁₉×#102	C₂³	1	4	yes	—
184	C₁₉×#102	C₂³	1	4	yes	—
185	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
186	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₁₉×#97	C₂³	1	4	yes	—
189	C₂⁴×C₁₉	—	2	2	no	—
190	C₂⁴×C₁₉	—	2	1	no	—
191	#41×C₁₉	—	2	2	no	—
192	#41×C₁₉	—	2	2	no	—
193	#41×C₁₉	—	2	4	no	—
194	#41×C₁₉	—	2	4	no	—
195	#41×C₁₉	—	4	1	no	—
196	#41×C₁₉	—	4	1	no	—
197	#41×C₁₉	—	4	1	no	—
198	#41×C₁₉	—	4	1	no	—
199	#41×C₁₉	—	4	2	no	—
200	#41×C₁₉	—	4	2	no	—
201	#41×C₁₉	—	4	4	no	—
202	#41×C₁₉	—	4	4	no	—
203	#41×C₁₉	—	4	8	no	—
204	C₂×Q₈×C₁₉	—	2	2	no	—
205	C₂×Q₈×C₁₉	—	2	2	no	—
206	C₂×Q₈×C₁₉	—	2	1	no	—
207	C₂×Q₈×C₁₉	—	2	2	no	—
208	C₂×Q₈×C₁₉	—	2	2	no	—
209	C₂×Q₈×C₁₉	—	2	4	no	—
210	C₂×Q₈×C₁₉	—	4	2	no	—
211	C₂×Q₈×C₁₉	—	4	1	no	—
212	C₂×Q₈×C₁₉	—	4	1	no	—
213	C₂×Q₈×C₁₉	—	4	4	no	—
214	C₂×Q₈×C₁₉	—	4	2	no	—
215	C₂×Q₈×C₁₉	—	4	2	no	—
216	C₂×Q₈×C₁₉	—	4	2	no	—
217	C₂×Q₈×C₁₉	—	4	2	no	—
218	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
221	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
222	C₂×Q₈×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₂×D₄×C₁₉	—	2	1	no	—
224	C₂×D₄×C₁₉	—	2	4	no	—
225	C₂×D₄×C₁₉	—	2	2	no	—
226	C₂×D₄×C₁₉	—	2	2	no	—
227	C₂×D₄×C₁₉	—	2	4	no	—
228	C₂×D₄×C₁₉	—	2	2	no	—
229	C₂×D₄×C₁₉	—	2	1	no	—
230	C₂×D₄×C₁₉	—	4	2	no	—
231	C₂×D₄×C₁₉	—	4	1	no	—
232	C₂×D₄×C₁₉	—	4	1	no	—
233	C₂×D₄×C₁₉	—	4	4	no	—
234	C₂×D₄×C₁₉	—	4	8	no	—
235	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
236	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
239	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
240	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
241	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₉	—	2	1	no	—
243	C₂²×C₄×C₁₉	—	2	1	no	—
244	C₂²×C₄×C₁₉	—	2	2	no	—
245	C₂²×C₄×C₁₉	—	2	2	no	—
246	C₂²×C₄×C₁₉	—	2	2	no	—
247	C₂²×C₄×C₁₉	—	2	2	no	—
248	C₂²×C₄×C₁₉	—	2	2	no	—
249	C₂²×C₄×C₁₉	—	2	2	no	—
250	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
254	Q₁₆×C₁₉	—	2	8	no	—
255	Q₁₆×C₁₉	—	4	4	no	—
256	Q₁₆×C₁₉	—	4	4	no	—
257	SD₁₆×C₁₉	—	2	8	no	—
258	SD₁₆×C₁₉	—	4	4	no	—
259	SD₁₆×C₁₉	—	4	4	no	—
260	M₁₆×C₁₉	—	4	2	no	—
261	M₁₆×C₁₉	—	4	2	no	—
262	C₂×C₈×C₁₉	—	4	2	no	—
263	C₂×C₈×C₁₉	—	4	2	no	—
264	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
265	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
266	C₄⋊C₄×C₁₉	—	2	2	no	—
267	C₄⋊C₄×C₁₉	—	2	2	no	—
268	C₄⋊C₄×C₁₉	—	2	2	no	—
269	C₄⋊C₄×C₁₉	—	2	2	no	—
270	C₄⋊C₄×C₁₉	—	2	4	no	—
271	C₄⋊C₄×C₁₉	—	2	4	no	—
272	C₄⋊C₄×C₁₉	—	2	4	no	—
273	C₄⋊C₄×C₁₉	—	2	4	no	—
274	C₄⋊C₄×C₁₉	—	2	4	no	—
275	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
276	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
277	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
278	C₂²⋊C₄×C₁₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₉	—	2	1	no	—
281	C₂²⋊C₄×C₁₉	—	2	2	no	—
282	C₂²⋊C₄×C₁₉	—	2	2	no	—
283	C₂²⋊C₄×C₁₉	—	2	4	no	—
284	C₂²⋊C₄×C₁₉	—	2	4	no	—
285	C₂²⋊C₄×C₁₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₉	—	2	2	no	—
289	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
290	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
291	C₄²×C₁₉	—	2	1	no	—
292	C₄²×C₁₉	—	2	2	no	—
293	C₄²×C₁₉	—	2	4	no	—
294	C₄²×C₁₉	—	2	2	no	—
295	C₄²×C₁₉	—	2	2	no	—
296	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₁₉	C₂⁴	1	2	yes	—
299	#61674	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
300	C₂³×C₁₉	—	2	1	no	—
301	C₂³×C₁₉	—	2	2	no	—
302	C₂³×C₁₉	—	4	4	no	—
303	C₂³×C₁₉	—	4	2	no	—
304	C₂³×C₁₉	—	8	2	no	—
305	C₂³×C₁₉	—	8	4	no	—
306	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
307	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
308	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
309	Q₈×C₁₉	—	2	1	no	—
310	Q₈×C₁₉	—	2	4	no	—
311	Q₈×C₁₉	—	2	4	no	—
312	Q₈×C₁₉	—	2	2	no	—
313	Q₈×C₁₉	—	2	2	no	—
314	Q₈×C₁₉	—	4	1	no	—
315	Q₈×C₁₉	—	4	1	no	—
316	Q₈×C₁₉	—	4	4	no	—
317	Q₈×C₁₉	—	4	4	no	—
318	Q₈×C₁₉	—	4	2	no	—
319	Q₈×C₁₉	—	8	2	no	—
320	Q₈×C₁₉	—	8	2	no	—
321	Q₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
322	D₄×C₁₉	—	2	4	no	—
323	D₄×C₁₉	—	2	1	no	—
324	D₄×C₁₉	—	2	2	no	—
325	D₄×C₁₉	—	2	2	no	—
326	D₄×C₁₉	—	4	1	no	—
327	D₄×C₁₉	—	4	2	no	—
328	D₄×C₁₉	—	4	4	no	—
329	D₄×C₁₉	—	4	1	no	—
330	D₄×C₁₉	—	4	2	no	—
331	D₄×C₁₉	—	4	4	no	—
332	D₄×C₁₉	—	4	4	no	—
333	D₄×C₁₉	—	4	2	no	—
334	D₄×C₁₉	—	4	4	no	—
335	D₄×C₁₉	—	8	4	no	—
336	D₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
337	C₂×C₄×C₁₉	—	2	4	no	—
338	C₂×C₄×C₁₉	—	2	1	no	—
339	C₂×C₄×C₁₉	—	2	2	no	—
340	C₂×C₄×C₁₉	—	2	2	no	—
341	C₂×C₄×C₁₉	—	2	2	no	—
342	C₂×C₄×C₁₉	—	2	2	no	—
343	C₂×C₄×C₁₉	—	2	1	no	—
344	C₂×C₄×C₁₉	—	2	1	no	—
345	C₂×C₄×C₁₉	—	2	4	no	—
346	C₂×C₄×C₁₉	—	2	2	no	—
347	C₂×C₄×C₁₉	—	2	4	no	—
348	C₂×C₄×C₁₉	—	2	2	no	—
349	C₂×C₄×C₁₉	—	4	2	no	—
350	C₂×C₄×C₁₉	—	4	4	no	—
351	C₂×C₄×C₁₉	—	4	4	no	—
352	C₂×C₄×C₁₉	—	4	4	no	—
353	C₂×C₄×C₁₉	—	4	2	no	—
354	C₂×C₄×C₁₉	—	8	2	no	—
355	C₂×C₄×C₁₉	—	8	2	no	—
356	C₂×C₄×C₁₉	—	8	2	no	—
357	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
361	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
363	C₈×C₁₉	—	2	4	no	—
364	C₈×C₁₉	—	2	4	no	—
365	#3550	C₂×C₁₉	1	1	yes	characteristic, complemented
366	#3500	C₂×C₁₉	1	1	yes	characteristic
367	#3313	C₂×C₁₉	1	4	yes	complemented
368	#3311	C₂×C₁₉	1	4	yes	complemented
369	#3270	C₂×C₁₉	1	4	yes	complemented
370	#3266	C₂×C₁₉	1	4	yes	complemented
371	#3215	C₂×C₁₉	1	2	yes	complemented
372	#3202	C₂×C₁₉	1	2	yes	complemented
373	#3200	C₂×C₁₉	1	2	yes	complemented
374	#3116	C₂×C₁₉	1	2	yes	complemented
375	#3011	C₂×C₁₉	1	2	yes	complemented
376	#3009	C₂×C₁₉	1	2	yes	complemented
377	#2980	C₂×C₁₉	1	1	yes	characteristic, complemented
378	C₂²×C₁₉	—	2	2	no	—
379	C₂²×C₁₉	—	2	4	no	—
380	C₂²×C₁₉	—	2	4	no	—
381	C₂²×C₁₉	—	2	2	no	—
382	C₂²×C₁₉	—	2	1	no	—
383	C₂²×C₁₉	—	2	2	no	—
384	C₂²×C₁₉	—	2	2	no	—
385	C₂²×C₁₉	—	4	2	no	—
386	C₂²×C₁₉	—	4	4	no	—
387	C₂²×C₁₉	—	4	2	no	—
388	C₂²×C₁₉	—	16	4	no	—
389	C₂²×C₁₉	—	16	2	no	—
390	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
391	C₄×C₁₉	—	2	2	no	—
392	C₄×C₁₉	—	2	2	no	—
393	C₄×C₁₉	—	2	1	no	—
394	C₄×C₁₉	—	2	2	no	—
395	C₄×C₁₉	—	2	2	no	—
396	C₄×C₁₉	—	2	2	no	—
397	C₄×C₁₉	—	4	2	no	—
398	C₄×C₁₉	—	4	4	no	—
399	C₄×C₁₉	—	4	2	no	—
400	C₄×C₁₉	—	4	4	no	—
401	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	1	yes	characteristic
404	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
405	C₂×#137	C₂²×C₁₉	1	2	yes	—
406	C₂×#137	C₂²×C₁₉	1	2	yes	complemented
407	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
408	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
409	#563	—	2	1	no	—
410	#563	—	2	1	no	—
411	#559	—	2	1	no	—
412	Q₈²	—	2	1	no	—
413	#556	C₂²×C₁₉	1	4	yes	complemented
414	D₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
415	#548	C₂²×C₁₉	1	4	yes	—
416	#546	—	2	4	no	—
417	#546	C₂²×C₁₉	1	4	yes	—
418	#542	—	2	4	no	—
419	#536	—	2	1	no	—
420	#536	C₂²×C₁₉	1	1	yes	characteristic
421	#536	C₂²×C₁₉	1	2	yes	—
422	#536	C₂²×C₁₉	1	2	yes	complemented
423	#535	—	2	1	no	—
424	#535	C₂²×C₁₉	1	1	yes	characteristic
425	#533	C₂²×C₁₉	1	2	yes	complemented
426	#532	—	2	1	no	—
427	#532	C₂²×C₁₉	1	1	yes	characteristic
428	C₂×#124	—	2	1	no	—
429	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
430	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
431	#497	C₂²×C₁₉	1	4	yes	complemented
432	#489	C₂²×C₁₉	1	4	yes	complemented
433	#485	C₂²×C₁₉	1	4	yes	complemented
434	#485	C₂²×C₁₉	1	4	yes	complemented
435	#482	C₂²×C₁₉	1	4	yes	complemented
436	#477	C₂²×C₁₉	1	2	yes	complemented
437	#476	C₂²×C₁₉	1	2	yes	complemented
438	#470	C₂²×C₁₉	1	4	yes	complemented
439	#468	C₂²×C₁₉	1	4	yes	complemented
440	#467	C₂²×C₁₉	1	4	yes	complemented
441	#465	C₂²×C₁₉	1	4	yes	complemented
442	#464	C₂²×C₁₉	1	4	yes	complemented
443	#464	C₂²×C₁₉	1	4	yes	complemented
444	#462	C₂²×C₁₉	1	2	yes	complemented
445	#461	C₂²×C₁₉	1	2	yes	complemented
446	#452	C₂²×C₁₉	1	4	yes	—
447	#452	C₂²×C₁₉	1	4	yes	—
448	#452	C₂²×C₁₉	1	4	yes	complemented
449	#451	C₂²×C₁₉	1	4	yes	complemented
450	#451	C₂²×C₁₉	1	4	yes	complemented
451	#451	C₂²×C₁₉	1	4	yes	complemented
452	#450	C₂²×C₁₉	1	4	yes	—
453	#450	C₂²×C₁₉	1	4	yes	—
454	#448	C₂²×C₁₉	1	4	yes	complemented
455	#441	C₂²×C₁₉	1	4	yes	complemented
456	#440	C₂²×C₁₉	1	4	yes	complemented
457	#435	C₂²×C₁₉	1	4	yes	complemented
458	#435	C₂²×C₁₉	1	4	yes	complemented
459	#432	C₂²×C₁₉	1	2	yes	complemented
460	#419	C₂²×C₁₉	1	2	yes	complemented
461	#418	C₂²×C₁₉	1	2	yes	—
462	#416	C₂²×C₁₉	1	2	yes	—
463	#416	C₂²×C₁₉	1	2	yes	complemented
464	#408	C₂²×C₁₉	1	2	yes	—
465	#408	C₂²×C₁₉	1	2	yes	complemented
466	C₂×C₁₉	—	4	2	no	—
467	C₂×C₁₉	—	4	1	no	—
468	C₂×C₁₉	—	4	2	no	—
469	C₂×C₁₉	—	4	2	no	—
470	C₂×C₁₉	—	8	2	no	—
471	C₂×C₁₉	#3484	1	1	yes	characteristic
472	C₂×C₁₉	#3586	1	2	yes	—
473	2₋¹⁺⁴	—	4	2	no	—
474	2₋¹⁺⁴	—	4	2	no	—
475	H(5,𝔽₂)	—	4	2	no	—
476	H(5,𝔽₂)	—	4	2	no	—
477	C₂×#41	—	2	1	no	—
478	C₂×#41	—	2	1	no	—
479	C₂×#41	—	2	2	no	—
480	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
481	C₂×#41	C₂³×C₁₉	1	2	yes	—
482	C₂×#41	C₂³×C₁₉	1	2	yes	—
483	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
484	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
485	C₂²×Q₈	—	2	1	no	—
486	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
487	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
488	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
489	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	2	no	—
492	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
493	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
494	#137	—	4	4	no	—
495	#137	—	4	4	no	—
496	C₂×Q₁₆	—	4	4	no	—
497	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
498	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
499	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
500	C₂×SD₁₆	—	4	4	no	—
501	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
502	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
503	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
504	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
505	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
506	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
507	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
508	C₄⋊Q₈	—	2	1	no	—
509	C₄⋊Q₈	—	2	2	no	—
510	C₄⋊Q₈	—	2	2	no	—
511	C₄⋊Q₈	—	2	4	no	—
512	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
514	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
515	#127	—	2	1	no	—
516	#127	D₄×C₁₉	1	1	yes	characteristic
517	#126	—	2	4	no	—
518	#126	—	2	4	no	—
519	#125	—	2	2	no	—
520	#124	—	2	1	no	—
521	#124	—	2	1	no	—
522	#124	—	2	2	no	—
523	#124	—	2	2	no	—
524	#124	—	2	4	no	—
525	#124	—	2	4	no	—
526	#124	—	2	1	no	—
527	#124	—	2	1	no	—
528	#124	D₄×C₁₉	1	1	yes	characteristic
529	#124	D₄×C₁₉	1	1	yes	characteristic
530	#124	C₂³×C₁₉	1	4	yes	—
531	#123	—	2	2	no	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	#123	—	2	2	no	—
535	#123	—	2	2	no	—
536	#123	—	2	4	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	4	no	—
539	C₂²⋊Q₈	—	2	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
542	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
543	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
544	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
545	#121	—	2	4	no	—
546	#121	—	2	4	no	—
547	#121	D₄×C₁₉	1	4	yes	—
548	#121	C₂³×C₁₉	1	4	yes	—
549	#120	—	2	4	no	—
550	#120	—	2	2	no	—
551	C₄×Q₈	—	2	4	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
554	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
555	C₄×D₄	—	2	4	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	4	no	—
558	C₄×D₄	C₂³×C₁₉	1	2	yes	—
559	C₄×D₄	C₂³×C₁₉	1	4	yes	—
560	#117	—	2	2	no	—
561	#117	—	2	1	no	—
562	#117	C₂³×C₁₉	1	1	yes	characteristic
563	#117	C₂³×C₁₉	1	2	yes	—
564	#117	C₂³×C₁₉	1	2	yes	—
565	C₂×C₂²⋊C₄	—	2	2	no	—
566	C₂×C₂²⋊C₄	—	2	4	no	—
567	C₂×C₄²	—	2	1	no	—
568	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
569	#107	C₂³×C₁₉	1	4	yes	—
570	#106	C₂³×C₁₉	1	4	yes	—
571	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
572	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
573	#103	C₂³×C₁₉	1	4	yes	—
574	#103	C₂³×C₁₉	1	4	yes	—
575	#103	C₂³×C₁₉	1	4	yes	—
576	#103	C₂³×C₁₉	1	4	yes	—
577	#103	C₂³×C₁₉	1	4	yes	—
578	#102	C₂³×C₁₉	1	4	yes	—
579	#102	C₂³×C₁₉	1	4	yes	—
580	#102	C₂³×C₁₉	1	4	yes	—
581	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
582	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
583	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
584	#97	C₂³×C₁₉	1	4	yes	—
585	C₁₉	#61674	1	1	yes	characteristic, direct product factor, Sylow
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	1	no	—
588	#41	—	2	2	no	—
589	#41	—	2	2	no	—
590	#41	—	2	4	no	—
591	#41	—	2	4	no	—
592	#41	—	4	1	no	—
593	#41	—	4	1	no	—
594	#41	—	4	1	no	—
595	#41	—	4	1	no	—
596	#41	—	4	2	no	—
597	#41	—	4	2	no	—
598	#41	—	4	4	no	—
599	#41	—	4	4	no	—
600	#41	—	4	8	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	2	2	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	4	no	—
607	C₂×Q₈	—	4	2	no	—
608	C₂×Q₈	—	4	1	no	—
609	C₂×Q₈	—	4	1	no	—
610	C₂×Q₈	—	4	4	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	4	2	no	—
615	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
616	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
617	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
618	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
619	C₂×Q₈	C₂⁴×C₁₉	1	1	yes	characteristic
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	4	1	no	—
629	C₂×D₄	—	4	1	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	4	8	no	—
632	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
633	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
634	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
635	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
636	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
637	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
638	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
651	Q₁₆	—	2	8	no	—
652	Q₁₆	—	4	4	no	—
653	Q₁₆	—	4	4	no	—
654	SD₁₆	—	2	8	no	—
655	SD₁₆	—	4	4	no	—
656	SD₁₆	—	4	4	no	—
657	M₁₆	—	4	2	no	—
658	M₁₆	—	4	2	no	—
659	C₂×C₈	—	4	2	no	—
660	C₂×C₈	—	4	2	no	—
661	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
662	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
673	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
674	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
687	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
688	C₄²	—	2	1	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	4	no	—
691	C₄²	—	2	2	no	—
692	C₄²	—	2	2	no	—
693	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
694	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
695	C₄²	C₂⁴×C₁₉	1	2	yes	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	4	2	no	—
700	C₂³	—	8	2	no	—
701	C₂³	—	8	4	no	—
702	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
703	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
704	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
705	Q₈	—	2	1	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	2	4	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	4	1	no	—
711	Q₈	—	4	1	no	—
712	Q₈	—	4	4	no	—
713	Q₈	—	4	2	no	—
714	Q₈	—	4	4	no	—
715	Q₈	—	8	2	no	—
716	Q₈	—	8	2	no	—
717	Q₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
718	D₄	—	2	4	no	—
719	D₄	—	2	1	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	4	1	no	—
723	D₄	—	4	2	no	—
724	D₄	—	4	1	no	—
725	D₄	—	4	2	no	—
726	D₄	—	4	4	no	—
727	D₄	—	4	4	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	2	no	—
730	D₄	—	4	4	no	—
731	D₄	—	8	4	no	—
732	D₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
733	C₂×C₄	—	2	4	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	4	4	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	4	no	—
749	C₂×C₄	—	4	2	no	—
750	C₂×C₄	—	8	2	no	—
751	C₂×C₄	—	8	2	no	—
752	C₂×C₄	—	8	2	no	—
753	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
754	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
756	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
757	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
758	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
759	C₈	—	2	4	no	—
760	C₈	—	2	4	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	4	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	4	no	—
771	C₂²	—	16	4	no	—
772	C₂²	—	16	2	no	—
773	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
774	C₄	—	2	1	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	4	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	4	no	—
784	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
785	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
786	C₂	—	4	1	no	—
787	C₂	—	4	2	no	—
788	C₂	—	4	2	no	—
789	C₂	—	4	2	no	—
790	C₂	—	8	2	no	—
791	C₂	C₁₉×#3484	1	1	yes	characteristic
792	C₂	C₁₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₁₉×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3550	C₂	semidirect
3. C₁₉×#3313	C₂	semidirect
4. C₁₉×#3311	C₂	semidirect
5. C₁₉×#3270	C₂	semidirect
6. C₁₉×#3266	C₂	semidirect
7. C₁₉×#3215	C₂	semidirect
8. C₁₉×#3202	C₂	semidirect
9. C₁₉×#3200	C₂	semidirect
10. C₁₉×#3116	C₂	semidirect
11. C₁₉×#3011	C₂	semidirect
12. C₁₉×#3009	C₂	semidirect
13. C₁₉×#2980	C₂	semidirect
17. C₂×C₁₉×#137	C₂²	semidirect
18. C₂²×Q₁₆×C₁₉	C₂²	semidirect
24. C₁₉×#556	C₂²	semidirect
25. D₄×Q₈×C₁₉	C₂²	semidirect
33. C₁₉×#536	C₂²	semidirect
36. C₁₉×#533	C₂²	semidirect
42. C₁₉×#497	C₂²	semidirect
43. C₁₉×#489	C₂²	semidirect
44. C₁₉×#485	C₂²	semidirect
45. C₁₉×#485	C₂²	semidirect
46. C₁₉×#482	C₂²	semidirect
47. C₁₉×#477	C₂²	semidirect
48. C₁₉×#476	C₂²	semidirect
49. C₁₉×#470	C₂²	semidirect
50. C₁₉×#468	C₂²	semidirect
51. C₁₉×#467	C₂²	semidirect
52. C₁₉×#465	C₂²	semidirect
53. C₁₉×#464	C₂²	semidirect
54. C₁₉×#464	C₂²	semidirect
55. C₁₉×#462	C₂²	semidirect
56. C₁₉×#461	C₂²	semidirect
59. C₁₉×#452	C₂²	semidirect
60. C₁₉×#451	C₂²	semidirect
61. C₁₉×#451	C₂²	semidirect
62. C₁₉×#451	C₂²	semidirect
65. C₁₉×#448	C₂²	semidirect
66. C₁₉×#441	C₂²	semidirect
67. C₁₉×#440	C₂²	semidirect
68. C₁₉×#435	C₂²	semidirect
69. C₁₉×#435	C₂²	semidirect
70. C₁₉×#432	C₂²	semidirect
71. C₁₉×#419	C₂²	semidirect
74. C₁₉×#416	C₂²	semidirect
76. C₁₉×#408	C₂²	semidirect
299. #61674	C₁₉	direct (N × H)
365. #3550	C₂×C₁₉	semidirect
367. #3313	C₂×C₁₉	semidirect
368. #3311	C₂×C₁₉	semidirect
369. #3270	C₂×C₁₉	semidirect
370. #3266	C₂×C₁₉	semidirect
371. #3215	C₂×C₁₉	semidirect
372. #3202	C₂×C₁₉	semidirect
373. #3200	C₂×C₁₉	semidirect
374. #3116	C₂×C₁₉	semidirect
375. #3011	C₂×C₁₉	semidirect
376. #3009	C₂×C₁₉	semidirect
377. #2980	C₂×C₁₉	semidirect
406. C₂×#137	C₂²×C₁₉	semidirect
407. C₂²×Q₁₆	C₂²×C₁₉	semidirect
413. #556	C₂²×C₁₉	semidirect
414. D₄×Q₈	C₂²×C₁₉	semidirect
422. #536	C₂²×C₁₉	semidirect
425. #533	C₂²×C₁₉	semidirect
431. #497	C₂²×C₁₉	semidirect
432. #489	C₂²×C₁₉	semidirect
433. #485	C₂²×C₁₉	semidirect
434. #485	C₂²×C₁₉	semidirect
435. #482	C₂²×C₁₉	semidirect
436. #477	C₂²×C₁₉	semidirect
437. #476	C₂²×C₁₉	semidirect
438. #470	C₂²×C₁₉	semidirect
439. #468	C₂²×C₁₉	semidirect
440. #467	C₂²×C₁₉	semidirect
441. #465	C₂²×C₁₉	semidirect
442. #464	C₂²×C₁₉	semidirect
443. #464	C₂²×C₁₉	semidirect
444. #462	C₂²×C₁₉	semidirect
445. #461	C₂²×C₁₉	semidirect
448. #452	C₂²×C₁₉	semidirect
449. #451	C₂²×C₁₉	semidirect
450. #451	C₂²×C₁₉	semidirect
451. #451	C₂²×C₁₉	semidirect
454. #448	C₂²×C₁₉	semidirect
455. #441	C₂²×C₁₉	semidirect
456. #440	C₂²×C₁₉	semidirect
457. #435	C₂²×C₁₉	semidirect
458. #435	C₂²×C₁₉	semidirect
459. #432	C₂²×C₁₉	semidirect
460. #419	C₂²×C₁₉	semidirect
463. #416	C₂²×C₁₉	semidirect
465. #408	C₂²×C₁₉	semidirect
585. C₁₉	#61674	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×#3550	2
C₁₉×#3500	2
C₁₉×#3313	2
C₁₉×#3311	2
C₁₉×#3270	2
C₁₉×#3266	2
C₁₉×#3215	2
C₁₉×#3202	2
C₁₉×#3200	2
C₁₉×#3116	2
C₁₉×#3011	2
C₁₉×#3009	2
C₁₉×#2980	2
#61674	19

Subgroups — C19×#61674 #18067633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#61674 #18067633