Subgroups — C₁₉×#62272 #18068231

Order 4864.

1896 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3536	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3338	C₂	1	2	yes	maximal, complemented
3	C₁₉×#3334	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3314	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3308	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3285	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3280	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3262	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3203	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3193	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3175	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3061	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#135	C₂²	1	2	yes	complemented
17	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#562	—	2	4	no	—
22	C₁₉×#554	C₂²	1	4	yes	—
23	C₁₉×#548	C₂²	1	4	yes	complemented
24	C₁₉×#547	C₂²	1	4	yes	complemented
25	C₁₉×#546	—	2	4	no	—
26	C₁₉×#546	C₂²	1	4	yes	—
27	C₁₉×#543	—	2	2	no	—
28	C₁₉×#542	C₂²	1	4	yes	complemented
29	C₁₉×#539	—	2	2	no	—
30	C₁₉×#538	—	2	2	no	—
31	C₁₉×#537	—	2	2	no	—
32	C₁₉×#537	C₂²	1	4	yes	complemented
33	C₁₉×#525	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₁₉×#121	C₂²	1	2	yes	—
36	C₁₉×#500	C₂²	1	2	yes	complemented
37	C₁₉×#495	C₂²	1	2	yes	complemented
38	C₁₉×#489	C₂²	1	4	yes	complemented
39	C₁₉×#484	C₂²	1	4	yes	—
40	C₁₉×#484	C₂²	1	4	yes	complemented
41	C₁₉×#480	C₂²	1	4	yes	complemented
42	C₁₉×#480	C₂²	1	4	yes	complemented
43	C₁₉×#477	C₂²	1	4	yes	complemented
44	C₁₉×#474	C₂²	1	4	yes	complemented
45	C₁₉×#468	C₂²	1	4	yes	complemented
46	C₁₉×#468	C₂²	1	4	yes	complemented
47	C₁₉×#468	C₂²	1	4	yes	complemented
48	C₁₉×#467	C₂²	1	2	yes	—
49	C₁₉×#467	C₂²	1	2	yes	—
50	C₁₉×#467	C₂²	1	2	yes	complemented
51	C₁₉×#467	C₂²	1	2	yes	complemented
52	C₁₉×#467	C₂²	1	2	yes	complemented
53	C₁₉×#466	C₂²	1	2	yes	—
54	C₁₉×#466	C₂²	1	2	yes	—
55	C₁₉×#466	C₂²	1	2	yes	—
56	C₁₉×#466	C₂²	1	2	yes	—
57	C₁₉×#466	C₂²	1	2	yes	complemented
58	C₁₉×#464	C₂²	1	4	yes	complemented
59	C₁₉×#463	C₂²	1	4	yes	complemented
60	C₁₉×#452	C₂²	1	4	yes	complemented
61	C₁₉×#450	C₂²	1	4	yes	—
62	C₁₉×#449	C₂²	1	4	yes	complemented
63	C₁₉×#448	C₂²	1	4	yes	complemented
64	C₁₉×#440	C₂²	1	4	yes	complemented
65	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
66	C₄×D₈×C₁₉	C₂²	1	2	yes	complemented
67	C₁₉×#435	C₂²	1	2	yes	—
68	C₁₉×#435	C₂²	1	2	yes	complemented
69	C₈×D₄×C₁₉	C₂²	1	2	yes	—
70	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
71	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
72	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
74	C₁₉×#424	C₂²	1	1	yes	characteristic, complemented
75	C₁₉×#417	C₂²	1	4	yes	complemented
76	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
77	C₂×C₁₉×#102	C₂²	1	2	yes	—
78	C₁₉×#408	C₂²	1	1	yes	characteristic, complemented
79	C₁₉×#407	C₂²	1	1	yes	characteristic
80	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
81	C₂×#41×C₁₉	—	2	4	no	—
82	C₂×#41×C₁₉	C₂³	1	4	yes	—
83	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₉	—	2	2	no	—
86	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₁₉×#135	—	4	4	no	—
89	C₂×Q₁₆×C₁₉	—	4	2	no	—
90	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
91	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
92	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
94	C₂×D₈×C₁₉	—	4	2	no	—
95	C₂×D₈×C₁₉	C₂³	1	2	yes	—
96	C₂×D₈×C₁₉	C₂³	1	2	yes	—
97	C₁₉×#131	—	4	2	no	—
98	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
101	C₂²×C₈×C₁₉	—	4	2	no	—
102	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
105	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
109	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₁₉×#126	—	2	4	no	—
111	C₁₉×#125	—	2	4	no	—
112	C₁₉×#124	—	2	4	no	—
113	C₁₉×#124	—	2	4	no	—
114	C₁₉×#124	C₂³	1	4	yes	—
115	C₁₉×#123	—	2	4	no	—
116	C₁₉×#123	—	2	4	no	—
117	C₁₉×#123	—	2	4	no	—
118	C₁₉×#123	—	2	4	no	—
119	C₁₉×#123	D₄	1	2	yes	—
120	C₁₉×C₂²⋊Q₈	—	2	4	no	—
121	C₁₉×C₂²⋊Q₈	—	2	2	no	—
122	C₁₉×C₂²⋊Q₈	—	2	2	no	—
123	C₁₉×C₂²⋊Q₈	—	2	4	no	—
124	C₁₉×C₂²⋊Q₈	—	2	4	no	—
125	C₁₉×C₂²⋊Q₈	—	2	4	no	—
126	C₁₉×C₂²⋊Q₈	—	2	4	no	—
127	C₁₉×C₂²⋊Q₈	—	2	4	no	—
128	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
129	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
130	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
131	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₁₉×#121	—	2	4	no	—
134	C₁₉×#121	—	2	4	no	—
135	C₁₉×#121	—	2	4	no	—
136	C₁₉×#121	—	2	4	no	—
137	C₁₉×#121	—	2	2	no	—
138	C₁₉×#121	—	2	2	no	—
139	C₁₉×#121	—	2	4	no	—
140	C₁₉×#121	D₄	1	1	yes	characteristic
141	C₁₉×#121	D₄	1	1	yes	characteristic
142	C₁₉×#121	C₂³	1	4	yes	—
143	C₁₉×#121	C₂³	1	4	yes	—
144	C₁₉×#121	C₂³	1	4	yes	—
145	C₁₉×#120	—	2	4	no	—
146	C₁₉×#120	D₄	1	2	yes	—
147	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
148	C₄×D₄×C₁₉	—	2	4	no	—
149	C₄×D₄×C₁₉	—	2	4	no	—
150	C₄×D₄×C₁₉	C₂³	1	4	yes	—
151	C₄×D₄×C₁₉	C₂³	1	2	yes	—
152	C₄×D₄×C₁₉	C₂³	1	2	yes	—
153	C₁₉×#117	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
160	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
161	C₁₉×#107	C₂³	1	2	yes	—
162	C₁₉×#107	C₂³	1	2	yes	—
163	C₁₉×#107	C₂³	1	2	yes	—
164	C₁₉×#107	C₂³	1	2	yes	—
165	C₁₉×#107	C₂³	1	4	yes	—
166	C₁₉×#107	C₂³	1	4	yes	—
167	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
168	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
169	C₁₉×#103	C₂³	1	4	yes	—
170	C₁₉×#103	C₂³	1	4	yes	—
171	C₁₉×#103	C₂³	1	4	yes	—
172	C₁₉×#103	C₂³	1	4	yes	—
173	C₁₉×#102	C₂³	1	4	yes	—
174	C₁₉×#102	C₂³	1	4	yes	—
175	C₁₉×#102	C₂³	1	4	yes	—
176	C₁₉×#102	C₂³	1	4	yes	—
177	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
178	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
179	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
180	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
181	C₁₉×#97	C₂³	1	2	yes	—
182	C₄×C₈×C₁₉	C₂³	1	2	yes	—
183	C₂⁴×C₁₉	—	2	2	no	—
184	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
185	#41×C₁₉	—	4	1	no	—
186	#41×C₁₉	—	4	1	no	—
187	#41×C₁₉	—	4	4	no	—
188	#41×C₁₉	—	4	4	no	—
189	#41×C₁₉	—	8	8	no	—
190	C₂×Q₈×C₁₉	—	2	2	no	—
191	C₂×Q₈×C₁₉	—	2	4	no	—
192	C₂×Q₈×C₁₉	—	4	2	no	—
193	C₂×Q₈×C₁₉	—	4	2	no	—
194	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
196	C₂×D₄×C₁₉	—	2	4	no	—
197	C₂×D₄×C₁₉	—	2	4	no	—
198	C₂×D₄×C₁₉	—	2	4	no	—
199	C₂×D₄×C₁₉	—	2	4	no	—
200	C₂×D₄×C₁₉	—	2	2	no	—
201	C₂×D₄×C₁₉	—	4	2	no	—
202	C₂×D₄×C₁₉	—	4	2	no	—
203	C₂×D₄×C₁₉	—	8	4	no	—
204	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
205	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
206	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₉	—	2	2	no	—
210	C₂²×C₄×C₁₉	—	2	2	no	—
211	C₂²×C₄×C₁₉	—	2	2	no	—
212	C₂²×C₄×C₁₉	—	2	4	no	—
213	C₂²×C₄×C₁₉	—	2	4	no	—
214	C₂²×C₄×C₁₉	—	2	4	no	—
215	C₂²×C₄×C₁₉	—	4	1	no	—
216	C₂²×C₄×C₁₉	—	4	1	no	—
217	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
224	Q₁₆×C₁₉	—	2	4	no	—
225	Q₁₆×C₁₉	—	4	2	no	—
226	SD₁₆×C₁₉	—	4	4	no	—
227	SD₁₆×C₁₉	—	4	4	no	—
228	D₈×C₁₉	—	2	4	no	—
229	D₈×C₁₉	—	4	2	no	—
230	M₁₆×C₁₉	—	4	1	no	—
231	M₁₆×C₁₉	—	4	2	no	—
232	M₁₆×C₁₉	—	4	1	no	—
233	C₂×C₈×C₁₉	—	2	2	no	—
234	C₂×C₈×C₁₉	—	2	2	no	—
235	C₂×C₈×C₁₉	—	2	2	no	—
236	C₂×C₈×C₁₉	—	2	4	no	—
237	C₂×C₈×C₁₉	—	4	1	no	—
238	C₂×C₈×C₁₉	—	4	1	no	—
239	C₂×C₈×C₁₉	—	4	1	no	—
240	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
244	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
245	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
246	C₄⋊C₄×C₁₉	—	2	4	no	—
247	C₄⋊C₄×C₁₉	—	2	4	no	—
248	C₄⋊C₄×C₁₉	—	2	2	no	—
249	C₄⋊C₄×C₁₉	—	2	4	no	—
250	C₄⋊C₄×C₁₉	—	2	2	no	—
251	C₄⋊C₄×C₁₉	—	2	4	no	—
252	C₄⋊C₄×C₁₉	—	2	4	no	—
253	C₄⋊C₄×C₁₉	—	2	4	no	—
254	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
255	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
259	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
260	C₂²⋊C₄×C₁₉	—	2	4	no	—
261	C₂²⋊C₄×C₁₉	—	2	4	no	—
262	C₂²⋊C₄×C₁₉	—	2	4	no	—
263	C₂²⋊C₄×C₁₉	—	2	4	no	—
264	C₂²⋊C₄×C₁₉	—	2	4	no	—
265	C₂²⋊C₄×C₁₉	—	2	4	no	—
266	C₂²⋊C₄×C₁₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
270	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
273	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
274	C₄²×C₁₉	—	2	4	no	—
275	C₄²×C₁₉	C₂⁴	1	2	yes	—
276	#62272	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂³×C₁₉	—	2	2	no	—
278	C₂³×C₁₉	—	2	2	no	—
279	C₂³×C₁₉	—	2	4	no	—
280	C₂³×C₁₉	—	4	1	no	—
281	C₂³×C₁₉	—	4	4	no	—
282	C₂³×C₁₉	—	8	2	no	—
283	C₂³×C₁₉	—	8	2	no	—
284	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
285	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
286	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
287	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
288	Q₈×C₁₉	—	2	4	no	—
289	Q₈×C₁₉	—	2	4	no	—
290	Q₈×C₁₉	—	4	1	no	—
291	Q₈×C₁₉	—	8	2	no	—
292	Q₈×C₁₉	—	8	4	no	—
293	D₄×C₁₉	—	2	4	no	—
294	D₄×C₁₉	—	2	4	no	—
295	D₄×C₁₉	—	2	4	no	—
296	D₄×C₁₉	—	2	4	no	—
297	D₄×C₁₉	—	4	1	no	—
298	D₄×C₁₉	—	4	2	no	—
299	D₄×C₁₉	—	4	8	no	—
300	D₄×C₁₉	—	8	2	no	—
301	D₄×C₁₉	—	8	4	no	—
302	D₄×C₁₉	—	8	4	no	—
303	D₄×C₁₉	—	8	4	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	1	no	—
307	C₂×C₄×C₁₉	—	2	2	no	—
308	C₂×C₄×C₁₉	—	2	1	no	—
309	C₂×C₄×C₁₉	—	2	1	no	—
310	C₂×C₄×C₁₉	—	2	1	no	—
311	C₂×C₄×C₁₉	—	2	2	no	—
312	C₂×C₄×C₁₉	—	2	4	no	—
313	C₂×C₄×C₁₉	—	2	4	no	—
314	C₂×C₄×C₁₉	—	2	4	no	—
315	C₂×C₄×C₁₉	—	4	1	no	—
316	C₂×C₄×C₁₉	—	4	1	no	—
317	C₂×C₄×C₁₉	—	4	1	no	—
318	C₂×C₄×C₁₉	—	4	4	no	—
319	C₂×C₄×C₁₉	—	8	4	no	—
320	C₂×C₄×C₁₉	—	8	4	no	—
321	C₂×C₄×C₁₉	—	8	2	no	—
322	C₂×C₄×C₁₉	—	8	2	no	—
323	C₂×C₄×C₁₉	—	8	4	no	—
324	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
331	C₈×C₁₉	—	2	1	no	—
332	C₈×C₁₉	—	2	1	no	—
333	C₈×C₁₉	—	2	1	no	—
334	C₈×C₁₉	—	2	2	no	—
335	C₈×C₁₉	—	2	2	no	—
336	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
337	#3536	C₂×C₁₉	1	2	yes	complemented
338	#3338	C₂×C₁₉	1	2	yes	complemented
339	#3334	C₂×C₁₉	1	2	yes	complemented
340	#3314	C₂×C₁₉	1	4	yes	complemented
341	#3308	C₂×C₁₉	1	4	yes	complemented
342	#3285	C₂×C₁₉	1	2	yes	complemented
343	#3280	C₂×C₁₉	1	2	yes	complemented
344	#3262	C₂×C₁₉	1	2	yes	complemented
345	#3203	C₂×C₁₉	1	2	yes	complemented
346	#3193	C₂×C₁₉	1	2	yes	complemented
347	#3175	C₂×C₁₉	1	2	yes	complemented
348	#3061	C₂×C₁₉	1	2	yes	complemented
349	C₂×#467	C₂×C₁₉	1	1	yes	characteristic, complemented
350	C₂×#466	C₂×C₁₉	1	1	yes	characteristic, complemented
351	#2929	C₂×C₁₉	1	1	yes	characteristic, complemented
352	C₂²×C₁₉	—	2	1	no	—
353	C₂²×C₁₉	—	2	1	no	—
354	C₂²×C₁₉	—	2	1	no	—
355	C₂²×C₁₉	—	2	1	no	—
356	C₂²×C₁₉	—	2	1	no	—
357	C₂²×C₁₉	—	2	2	no	—
358	C₂²×C₁₉	—	2	2	no	—
359	C₂²×C₁₉	—	2	1	no	—
360	C₂²×C₁₉	—	2	2	no	—
361	C₂²×C₁₉	—	2	1	no	—
362	C₂²×C₁₉	—	4	4	no	—
363	C₂²×C₁₉	—	4	4	no	—
364	C₂²×C₁₉	—	4	4	no	—
365	C₂²×C₁₉	—	4	4	no	—
366	C₂²×C₁₉	—	16	4	no	—
367	C₂²×C₁₉	#576	1	2	yes	—
368	C₂²×C₁₉	#578	1	2	yes	—
369	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
370	C₄×C₁₉	—	2	1	no	—
371	C₄×C₁₉	—	2	1	no	—
372	C₄×C₁₉	—	2	1	no	—
373	C₄×C₁₉	—	2	2	no	—
374	C₄×C₁₉	—	2	2	no	—
375	C₄×C₁₉	—	2	2	no	—
376	C₄×C₁₉	—	4	4	no	—
377	C₄×C₁₉	—	4	4	no	—
378	C₄×C₁₉	—	4	4	no	—
379	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
380	C₄×C₁₉	#585	1	1	yes	characteristic
381	C₂×#135	C₂²×C₁₉	1	2	yes	complemented
382	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
383	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic, complemented
385	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
386	#562	—	2	4	no	—
387	#554	C₂²×C₁₉	1	4	yes	—
388	#548	C₂²×C₁₉	1	4	yes	complemented
389	#547	C₂²×C₁₉	1	4	yes	complemented
390	#546	—	2	4	no	—
391	#546	C₂²×C₁₉	1	4	yes	—
392	#543	—	2	2	no	—
393	#542	C₂²×C₁₉	1	4	yes	complemented
394	#539	—	2	2	no	—
395	#538	—	2	2	no	—
396	#537	—	2	2	no	—
397	#537	C₂²×C₁₉	1	4	yes	complemented
398	#525	C₂²×C₁₉	1	1	yes	characteristic
399	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
400	C₂×#121	C₂²×C₁₉	1	2	yes	—
401	#500	C₂²×C₁₉	1	2	yes	complemented
402	#495	C₂²×C₁₉	1	2	yes	complemented
403	#489	C₂²×C₁₉	1	4	yes	complemented
404	#484	C₂²×C₁₉	1	4	yes	—
405	#484	C₂²×C₁₉	1	4	yes	complemented
406	#480	C₂²×C₁₉	1	4	yes	complemented
407	#480	C₂²×C₁₉	1	4	yes	complemented
408	#477	C₂²×C₁₉	1	4	yes	complemented
409	#474	C₂²×C₁₉	1	4	yes	complemented
410	#468	C₂²×C₁₉	1	4	yes	complemented
411	#468	C₂²×C₁₉	1	4	yes	complemented
412	#468	C₂²×C₁₉	1	4	yes	complemented
413	#467	C₂²×C₁₉	1	2	yes	—
414	#467	C₂²×C₁₉	1	2	yes	—
415	#467	C₂²×C₁₉	1	2	yes	complemented
416	#467	C₂²×C₁₉	1	2	yes	complemented
417	#467	C₂²×C₁₉	1	2	yes	complemented
418	#466	C₂²×C₁₉	1	2	yes	—
419	#466	C₂²×C₁₉	1	2	yes	—
420	#466	C₂²×C₁₉	1	2	yes	—
421	#466	C₂²×C₁₉	1	2	yes	—
422	#466	C₂²×C₁₉	1	2	yes	complemented
423	#464	C₂²×C₁₉	1	4	yes	complemented
424	#463	C₂²×C₁₉	1	4	yes	complemented
425	#452	C₂²×C₁₉	1	4	yes	complemented
426	#450	C₂²×C₁₉	1	4	yes	—
427	#449	C₂²×C₁₉	1	4	yes	complemented
428	#448	C₂²×C₁₉	1	4	yes	complemented
429	#440	C₂²×C₁₉	1	4	yes	complemented
430	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
431	C₄×D₈	C₂²×C₁₉	1	2	yes	complemented
432	#435	C₂²×C₁₉	1	2	yes	—
433	#435	C₂²×C₁₉	1	2	yes	complemented
434	C₈×D₄	C₂²×C₁₉	1	2	yes	—
435	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
436	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
437	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
438	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
439	#424	C₂²×C₁₉	1	1	yes	characteristic, complemented
440	#417	C₂²×C₁₉	1	4	yes	complemented
441	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
442	C₂×#102	C₂²×C₁₉	1	2	yes	—
443	#408	C₂²×C₁₉	1	1	yes	characteristic, complemented
444	#407	C₂²×C₁₉	1	1	yes	characteristic
445	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
446	C₂×C₁₉	—	2	2	no	—
447	C₂×C₁₉	—	2	2	no	—
448	C₂×C₁₉	—	4	2	no	—
449	C₂×C₁₉	—	4	1	no	—
450	C₂×C₁₉	—	8	4	no	—
451	C₂×C₁₉	#3496	1	1	yes	characteristic
452	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
453	C₂×C₁₉	C₂×#578	1	1	yes	characteristic
454	C₂×#41	—	2	4	no	—
455	C₂×#41	C₂³×C₁₉	1	4	yes	—
456	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
457	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
458	C₂²×D₄	—	2	2	no	—
459	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
460	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
461	#135	—	4	4	no	—
462	C₂×Q₁₆	—	4	2	no	—
463	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
464	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
465	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
466	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
467	C₂×D₈	—	4	2	no	—
468	C₂×D₈	C₂³×C₁₉	1	2	yes	—
469	C₂×D₈	C₂³×C₁₉	1	2	yes	—
470	#131	—	4	2	no	—
471	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
472	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
473	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
474	C₂²×C₈	—	4	2	no	—
475	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
479	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
482	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
483	#126	—	2	4	no	—
484	#125	—	2	4	no	—
485	#124	—	2	4	no	—
486	#124	—	2	4	no	—
487	#124	C₂³×C₁₉	1	4	yes	—
488	#123	—	2	4	no	—
489	#123	—	2	4	no	—
490	#123	—	2	4	no	—
491	#123	—	2	4	no	—
492	#123	D₄×C₁₉	1	2	yes	—
493	C₂²⋊Q₈	—	2	4	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
502	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
503	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
504	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
505	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
506	#121	—	2	4	no	—
507	#121	—	2	4	no	—
508	#121	—	2	4	no	—
509	#121	—	2	4	no	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	2	4	no	—
513	#121	D₄×C₁₉	1	1	yes	characteristic
514	#121	D₄×C₁₉	1	1	yes	characteristic
515	#121	C₂³×C₁₉	1	4	yes	—
516	#121	C₂³×C₁₉	1	4	yes	—
517	#121	C₂³×C₁₉	1	4	yes	—
518	#120	—	2	4	no	—
519	#120	D₄×C₁₉	1	2	yes	—
520	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
521	C₄×D₄	—	2	4	no	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	C₂³×C₁₉	1	4	yes	—
524	C₄×D₄	C₂³×C₁₉	1	2	yes	—
525	C₄×D₄	C₂³×C₁₉	1	2	yes	—
526	#117	C₂³×C₁₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	—	2	2	no	—
528	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
531	C₂×C₂²⋊C₄	—	2	2	no	—
532	C₂×C₂²⋊C₄	—	2	2	no	—
533	C₂×C₂²⋊C₄	—	2	4	no	—
534	#107	C₂³×C₁₉	1	2	yes	—
535	#107	C₂³×C₁₉	1	2	yes	—
536	#107	C₂³×C₁₉	1	2	yes	—
537	#107	C₂³×C₁₉	1	2	yes	—
538	#107	C₂³×C₁₉	1	4	yes	—
539	#107	C₂³×C₁₉	1	4	yes	—
540	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
541	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
542	#103	C₂³×C₁₉	1	4	yes	—
543	#103	C₂³×C₁₉	1	4	yes	—
544	#103	C₂³×C₁₉	1	4	yes	—
545	#103	C₂³×C₁₉	1	4	yes	—
546	#102	C₂³×C₁₉	1	4	yes	—
547	#102	C₂³×C₁₉	1	4	yes	—
548	#102	C₂³×C₁₉	1	4	yes	—
549	#102	C₂³×C₁₉	1	4	yes	—
550	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
551	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
552	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
553	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
554	#97	C₂³×C₁₉	1	2	yes	—
555	C₄×C₈	C₂³×C₁₉	1	2	yes	—
556	C₁₉	#62272	1	1	yes	characteristic, direct product factor, Sylow
557	C₂⁴	—	2	2	no	—
558	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
559	#41	—	4	1	no	—
560	#41	—	4	1	no	—
561	#41	—	4	4	no	—
562	#41	—	4	4	no	—
563	#41	—	8	8	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	4	2	no	—
567	C₂×Q₈	—	4	2	no	—
568	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
569	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	8	4	no	—
578	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
579	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
580	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
581	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
582	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	4	1	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
598	Q₁₆	—	2	4	no	—
599	Q₁₆	—	4	2	no	—
600	SD₁₆	—	4	4	no	—
601	SD₁₆	—	4	4	no	—
602	D₈	—	2	4	no	—
603	D₈	—	4	2	no	—
604	M₁₆	—	4	1	no	—
605	M₁₆	—	4	2	no	—
606	M₁₆	—	4	1	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	2	no	—
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	2	4	no	—
611	C₂×C₈	—	4	1	no	—
612	C₂×C₈	—	4	1	no	—
613	C₂×C₈	—	4	1	no	—
614	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
615	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
616	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
617	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
618	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
619	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
629	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
630	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
631	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
633	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
644	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
645	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
646	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
647	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
648	C₄²	—	2	4	no	—
649	C₄²	C₂⁴×C₁₉	1	2	yes	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	4	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	8	2	no	—
656	C₂³	—	8	2	no	—
657	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
658	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
659	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
660	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
661	Q₈	—	2	4	no	—
662	Q₈	—	2	4	no	—
663	Q₈	—	4	1	no	—
664	Q₈	—	8	2	no	—
665	Q₈	—	8	4	no	—
666	D₄	—	2	4	no	—
667	D₄	—	2	4	no	—
668	D₄	—	2	4	no	—
669	D₄	—	2	4	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	2	no	—
672	D₄	—	4	8	no	—
673	D₄	—	8	2	no	—
674	D₄	—	8	4	no	—
675	D₄	—	8	4	no	—
676	D₄	—	8	4	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	8	4	no	—
693	C₂×C₄	—	8	4	no	—
694	C₂×C₄	—	8	2	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
698	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
703	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
704	C₈	—	2	1	no	—
705	C₈	—	2	1	no	—
706	C₈	—	2	1	no	—
707	C₈	—	2	2	no	—
708	C₈	—	2	2	no	—
709	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	4	4	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	4	4	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	16	4	no	—
725	C₂²	C₁₉×#576	1	2	yes	—
726	C₂²	C₁₉×#578	1	2	yes	—
727	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	2	no	—
734	C₄	—	4	4	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	4	no	—
737	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
738	C₄	C₁₉×#585	1	1	yes	characteristic
739	C₂	—	2	2	no	—
740	C₂	—	2	2	no	—
741	C₂	—	4	1	no	—
742	C₂	—	4	2	no	—
743	C₂	—	8	4	no	—
744	C₂	C₁₉×#3496	1	1	yes	characteristic
745	C₂	C₂×C₁₉×#576	1	1	yes	characteristic
746	C₂	C₂×C₁₉×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3536	C₂	semidirect
2. C₁₉×#3338	C₂	semidirect
3. C₁₉×#3334	C₂	semidirect
4. C₁₉×#3314	C₂	semidirect
5. C₁₉×#3308	C₂	semidirect
6. C₁₉×#3285	C₂	semidirect
7. C₁₉×#3280	C₂	semidirect
8. C₁₉×#3262	C₂	semidirect
9. C₁₉×#3203	C₂	semidirect
10. C₁₉×#3193	C₂	semidirect
11. C₁₉×#3175	C₂	semidirect
12. C₁₉×#3061	C₂	semidirect
13. C₂×C₁₉×#467	C₂	semidirect
14. C₂×C₁₉×#466	C₂	semidirect
15. C₁₉×#2929	C₂	semidirect
16. C₂×C₁₉×#135	C₂²	semidirect
17. C₂²×Q₁₆×C₁₉	C₂²	semidirect
19. C₂×C₁₉×#131	C₂²	semidirect
23. C₁₉×#548	C₂²	semidirect
24. C₁₉×#547	C₂²	semidirect
28. C₁₉×#542	C₂²	semidirect
32. C₁₉×#537	C₂²	semidirect
36. C₁₉×#500	C₂²	semidirect
37. C₁₉×#495	C₂²	semidirect
38. C₁₉×#489	C₂²	semidirect
40. C₁₉×#484	C₂²	semidirect
41. C₁₉×#480	C₂²	semidirect
42. C₁₉×#480	C₂²	semidirect
43. C₁₉×#477	C₂²	semidirect
44. C₁₉×#474	C₂²	semidirect
45. C₁₉×#468	C₂²	semidirect
46. C₁₉×#468	C₂²	semidirect
47. C₁₉×#468	C₂²	semidirect
50. C₁₉×#467	C₂²	semidirect
51. C₁₉×#467	C₂²	semidirect
52. C₁₉×#467	C₂²	semidirect
57. C₁₉×#466	C₂²	semidirect
58. C₁₉×#464	C₂²	semidirect
59. C₁₉×#463	C₂²	semidirect
60. C₁₉×#452	C₂²	semidirect
62. C₁₉×#449	C₂²	semidirect
63. C₁₉×#448	C₂²	semidirect
64. C₁₉×#440	C₂²	semidirect
65. C₄×Q₁₆×C₁₉	C₂²	semidirect
66. C₄×D₈×C₁₉	C₂²	semidirect
68. C₁₉×#435	C₂²	semidirect
70. C₈×D₄×C₁₉	C₂²	semidirect
72. C₂×C₁₉×#107	C₂²	semidirect
73. C₂×C₁₉×#107	C₂²	semidirect
74. C₁₉×#424	C₂²	semidirect
75. C₁₉×#417	C₂²	semidirect
76. C₂×C₁₉×#103	C₂²	semidirect
78. C₁₉×#408	C₂²	semidirect
80. C₁₉×#405	C₂²	semidirect
276. #62272	C₁₉	direct (N × H)
337. #3536	C₂×C₁₉	semidirect
338. #3338	C₂×C₁₉	semidirect
339. #3334	C₂×C₁₉	semidirect
340. #3314	C₂×C₁₉	semidirect
341. #3308	C₂×C₁₉	semidirect
342. #3285	C₂×C₁₉	semidirect
343. #3280	C₂×C₁₉	semidirect
344. #3262	C₂×C₁₉	semidirect
345. #3203	C₂×C₁₉	semidirect
346. #3193	C₂×C₁₉	semidirect
347. #3175	C₂×C₁₉	semidirect
348. #3061	C₂×C₁₉	semidirect
349. C₂×#467	C₂×C₁₉	semidirect
350. C₂×#466	C₂×C₁₉	semidirect
351. #2929	C₂×C₁₉	semidirect
381. C₂×#135	C₂²×C₁₉	semidirect
382. C₂²×Q₁₆	C₂²×C₁₉	semidirect
384. C₂×#131	C₂²×C₁₉	semidirect
388. #548	C₂²×C₁₉	semidirect
389. #547	C₂²×C₁₉	semidirect
393. #542	C₂²×C₁₉	semidirect
397. #537	C₂²×C₁₉	semidirect
401. #500	C₂²×C₁₉	semidirect
402. #495	C₂²×C₁₉	semidirect
403. #489	C₂²×C₁₉	semidirect
405. #484	C₂²×C₁₉	semidirect
406. #480	C₂²×C₁₉	semidirect
407. #480	C₂²×C₁₉	semidirect
408. #477	C₂²×C₁₉	semidirect
409. #474	C₂²×C₁₉	semidirect
410. #468	C₂²×C₁₉	semidirect
411. #468	C₂²×C₁₉	semidirect
412. #468	C₂²×C₁₉	semidirect
415. #467	C₂²×C₁₉	semidirect
416. #467	C₂²×C₁₉	semidirect
417. #467	C₂²×C₁₉	semidirect
422. #466	C₂²×C₁₉	semidirect
423. #464	C₂²×C₁₉	semidirect
424. #463	C₂²×C₁₉	semidirect
425. #452	C₂²×C₁₉	semidirect
427. #449	C₂²×C₁₉	semidirect
428. #448	C₂²×C₁₉	semidirect
429. #440	C₂²×C₁₉	semidirect
430. C₄×Q₁₆	C₂²×C₁₉	semidirect
431. C₄×D₈	C₂²×C₁₉	semidirect
433. #435	C₂²×C₁₉	semidirect
435. C₈×D₄	C₂²×C₁₉	semidirect
437. C₂×#107	C₂²×C₁₉	semidirect
438. C₂×#107	C₂²×C₁₉	semidirect
439. #424	C₂²×C₁₉	semidirect
440. #417	C₂²×C₁₉	semidirect
441. C₂×#103	C₂²×C₁₉	semidirect
443. #408	C₂²×C₁₉	semidirect
445. #405	C₂²×C₁₉	semidirect
556. C₁₉	#62272	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×#3536	2
C₁₉×#3338	2
C₁₉×#3334	2
C₁₉×#3314	2
C₁₉×#3308	2
C₁₉×#3285	2
C₁₉×#3280	2
C₁₉×#3262	2
C₁₉×#3203	2
C₁₉×#3193	2
C₁₉×#3175	2
C₁₉×#3061	2
C₂×C₁₉×#467	2
C₂×C₁₉×#466	2
C₁₉×#2929	2
#62272	19

Subgroups — C19×#62272 #18068231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62272 #18068231