Subgroups — C₁₉×#60306 #18066265

Order 4864.

1902 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3460	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2993	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2989	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2981	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2976	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2966	C₂	1	4	yes	maximal, complemented
8	C₈×#41×C₁₉	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2931	C₂	1	4	yes	maximal, complemented
10	C₁₉×#2929	C₂	1	4	yes	maximal, complemented
11	C₂×C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#131	C₂²	1	4	yes	complemented
13	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
14	C₁₉×#544	C₄	1	1	yes	characteristic
15	C₁₉×#542	C₄	1	4	yes	—
16	C₁₉×#540	C₄	1	4	yes	—
17	C₁₉×#538	C₄	1	4	yes	—
18	C₁₉×#537	C₄	1	1	yes	characteristic
19	C₁₉×#535	C₄	1	2	yes	—
20	C₁₉×#532	C₂²	1	4	yes	—
21	C₁₉×#529	C₂²	1	4	yes	—
22	C₁₉×#525	C₂²	1	4	yes	—
23	C₄×#41×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#446	C₂²	1	4	yes	complemented
26	C₈×Q₈×C₁₉	C₂²	1	2	yes	complemented
27	C₈×Q₈×C₁₉	C₂²	1	2	yes	complemented
28	C₁₉×#436	C₂²	1	4	yes	—
29	C₁₉×#436	C₂²	1	4	yes	—
30	C₁₉×#436	C₂²	1	8	yes	complemented
31	C₁₉×#436	C₂²	1	4	yes	complemented
32	C₁₉×#435	C₂²	1	8	yes	—
33	C₁₉×#435	C₂²	1	8	yes	complemented
34	C₁₉×#435	C₂²	1	8	yes	complemented
35	C₈×D₄×C₁₉	C₂²	1	4	yes	—
36	C₈×D₄×C₁₉	C₂²	1	4	yes	—
37	C₈×D₄×C₁₉	C₂²	1	4	yes	—
38	C₈×D₄×C₁₉	C₂²	1	4	yes	—
39	C₈×D₄×C₁₉	C₂²	1	8	yes	complemented
40	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
41	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
42	C₁₉×#433	C₂²	1	8	yes	complemented
43	C₁₉×#432	C₂²	1	4	yes	complemented
44	C₁₉×#431	C₂²	1	2	yes	—
45	C₁₉×#431	C₂²	1	4	yes	complemented
46	C₁₉×#424	C₂²	1	4	yes	complemented
47	C₁₉×#423	C₂²	1	4	yes	complemented
48	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₁₉×#408	C₂²	1	4	yes	complemented
50	C₁₉×#408	C₂²	1	8	yes	complemented
51	C₁₉×#407	C₂²	1	4	yes	—
52	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
53	C₁₉×#405	C₂²	1	4	yes	complemented
54	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₁₉	C₂²	1	4	yes	complemented
56	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
57	C₂×#41×C₁₉	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
60	C₁₉×#131	—	4	8	no	—
61	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
62	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
63	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
64	C₂²×C₈×C₁₉	—	4	4	no	—
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
67	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
70	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
72	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
73	C₁₉×#127	C₂×C₄	1	4	yes	—
74	C₁₉×#126	C₂×C₄	1	8	yes	—
75	C₁₉×#125	C₂×C₄	1	4	yes	—
76	C₁₉×#124	C₂×C₄	1	4	yes	—
77	C₁₉×#124	C₂×C₄	1	8	yes	—
78	C₁₉×#123	C₂×C₄	1	8	yes	—
79	C₁₉×#123	C₂×C₄	1	8	yes	—
80	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
81	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
82	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
83	C₁₉×#121	C₂×C₄	1	4	yes	—
84	C₁₉×#121	C₂×C₄	1	4	yes	—
85	C₁₉×#121	C₂×C₄	1	4	yes	—
86	C₁₉×#121	C₂×C₄	1	4	yes	—
87	C₁₉×#121	C₂×C₄	1	4	yes	—
88	C₁₉×#121	C₂×C₄	1	8	yes	—
89	C₁₉×#120	C₂×C₄	1	8	yes	—
90	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
91	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
92	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
93	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
94	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
95	C₄×D₄×C₁₉	C₂³	1	4	yes	—
96	C₄×D₄×C₁₉	C₂³	1	4	yes	—
97	C₄×D₄×C₁₉	C₂³	1	2	yes	—
98	C₄×D₄×C₁₉	C₂³	1	8	yes	—
99	C₁₉×#117	C₂×C₄	1	2	yes	—
100	C₁₉×#117	C₂×C₄	1	4	yes	—
101	C₁₉×#117	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
106	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
107	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
108	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
109	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
110	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
111	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
112	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
113	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
114	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
115	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
116	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
117	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
118	C₁₉×#97	C₂³	1	8	yes	—
119	C₄×C₈×C₁₉	C₂³	1	2	yes	—
120	C₄×C₈×C₁₉	C₂³	1	4	yes	—
121	C₄×C₈×C₁₉	C₂³	1	4	yes	—
122	C₄×C₈×C₁₉	C₂³	1	2	yes	—
123	C₄×C₈×C₁₉	C₂³	1	4	yes	—
124	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
125	#41×C₁₉	—	2	8	no	—
126	#41×C₁₉	—	4	4	no	—
127	#41×C₁₉	—	4	4	no	—
128	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
129	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
132	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
133	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
134	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
135	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
136	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₁₉	—	4	2	no	—
138	C₂²×C₄×C₁₉	—	4	2	no	—
139	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
148	M₁₆×C₁₉	—	4	4	no	—
149	M₁₆×C₁₉	—	4	8	no	—
150	M₁₆×C₁₉	—	4	4	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	8	no	—
153	C₂×C₈×C₁₉	—	2	8	no	—
154	C₂×C₈×C₁₉	—	4	4	no	—
155	C₂×C₈×C₁₉	—	4	2	no	—
156	C₂×C₈×C₁₉	—	4	1	no	—
157	C₂×C₈×C₁₉	—	4	4	no	—
158	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
159	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
160	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
161	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
162	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
163	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
164	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
165	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
166	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
167	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
168	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
169	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
170	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
171	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
172	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
173	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
174	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
175	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
176	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
177	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
178	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
179	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
180	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
181	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
182	C₄²×C₁₉	C₂⁴	1	2	yes	—
183	C₄²×C₁₉	C₂⁴	1	4	yes	—
184	#60306	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂³×C₁₉	—	2	4	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
189	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
190	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
191	Q₈×C₁₉	—	2	4	no	—
192	Q₈×C₁₉	—	4	4	no	—
193	D₄×C₁₉	—	2	8	no	—
194	D₄×C₁₉	—	2	8	no	—
195	D₄×C₁₉	—	2	4	no	—
196	D₄×C₁₉	—	4	8	no	—
197	D₄×C₁₉	—	4	4	no	—
198	D₄×C₁₉	—	4	8	no	—
199	C₂×C₄×C₁₉	—	2	8	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	4	no	—
210	C₂×C₄×C₁₉	#131	1	4	yes	complemented
211	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
212	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
214	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
215	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
216	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
217	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
218	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
219	C₈×C₁₉	—	2	1	no	—
220	C₈×C₁₉	—	2	4	no	—
221	C₈×C₁₉	—	2	4	no	—
222	C₈×C₁₉	—	2	2	no	—
223	C₈×C₁₉	—	2	4	no	—
224	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
225	#3460	C₂×C₁₉	1	1	yes	characteristic
226	#2993	C₂×C₁₉	1	4	yes	complemented
227	#2989	C₂×C₁₉	1	2	yes	complemented
228	#2981	C₂×C₁₉	1	4	yes	complemented
229	#2976	C₂×C₁₉	1	4	yes	complemented
230	#2975	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#2966	C₂×C₁₉	1	4	yes	complemented
232	C₈×#41	C₂×C₁₉	1	2	yes	complemented
233	#2931	C₂×C₁₉	1	4	yes	complemented
234	#2929	C₂×C₁₉	1	4	yes	complemented
235	C₂×C₈×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	4	no	—
239	C₂²×C₁₉	—	2	4	no	—
240	C₂²×C₁₉	—	2	4	no	—
241	C₂²×C₁₉	—	2	4	no	—
242	C₂²×C₁₉	—	2	4	no	—
243	C₂²×C₁₉	—	2	4	no	—
244	C₂²×C₁₉	—	4	8	no	—
245	C₂²×C₁₉	C₂×#131	1	2	yes	—
246	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
247	C₄×C₁₉	—	2	1	no	—
248	C₄×C₁₉	—	2	4	no	—
249	C₄×C₁₉	—	2	4	no	—
250	C₄×C₁₉	—	2	4	no	—
251	C₄×C₁₉	—	2	2	no	—
252	C₄×C₁₉	—	2	4	no	—
253	C₄×C₁₉	C₂×#131	1	4	yes	—
254	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
255	C₄×C₁₉	#585	1	1	yes	characteristic
256	C₂×#131	C₂²×C₁₉	1	4	yes	complemented
257	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
258	#544	C₄×C₁₉	1	1	yes	characteristic
259	#542	C₄×C₁₉	1	4	yes	—
260	#540	C₄×C₁₉	1	4	yes	—
261	#538	C₄×C₁₉	1	4	yes	—
262	#537	C₄×C₁₉	1	1	yes	characteristic
263	#535	C₄×C₁₉	1	2	yes	—
264	#532	C₂²×C₁₉	1	4	yes	—
265	#529	C₂²×C₁₉	1	4	yes	—
266	#525	C₂²×C₁₉	1	4	yes	—
267	C₄×#41	C₂²×C₁₉	1	2	yes	—
268	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
269	#446	C₂²×C₁₉	1	4	yes	complemented
270	C₈×Q₈	C₂²×C₁₉	1	2	yes	complemented
271	C₈×Q₈	C₂²×C₁₉	1	2	yes	complemented
272	#436	C₂²×C₁₉	1	4	yes	—
273	#436	C₂²×C₁₉	1	4	yes	—
274	#436	C₂²×C₁₉	1	8	yes	complemented
275	#436	C₂²×C₁₉	1	4	yes	complemented
276	#435	C₂²×C₁₉	1	8	yes	—
277	#435	C₂²×C₁₉	1	8	yes	complemented
278	#435	C₂²×C₁₉	1	8	yes	complemented
279	C₈×D₄	C₂²×C₁₉	1	4	yes	—
280	C₈×D₄	C₂²×C₁₉	1	4	yes	—
281	C₈×D₄	C₂²×C₁₉	1	4	yes	—
282	C₈×D₄	C₂²×C₁₉	1	4	yes	—
283	C₈×D₄	C₂²×C₁₉	1	8	yes	complemented
284	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
285	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
286	#433	C₂²×C₁₉	1	8	yes	complemented
287	#432	C₂²×C₁₉	1	4	yes	complemented
288	#431	C₂²×C₁₉	1	2	yes	—
289	#431	C₂²×C₁₉	1	4	yes	complemented
290	#424	C₂²×C₁₉	1	4	yes	complemented
291	#423	C₂²×C₁₉	1	4	yes	complemented
292	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
293	#408	C₂²×C₁₉	1	4	yes	complemented
294	#408	C₂²×C₁₉	1	8	yes	complemented
295	#407	C₂²×C₁₉	1	4	yes	—
296	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
297	#405	C₂²×C₁₉	1	4	yes	complemented
298	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×C₄×C₈	C₂²×C₁₉	1	4	yes	complemented
300	C₂×C₁₉	—	2	2	no	—
301	C₂×C₁₉	—	4	4	no	—
302	C₂×C₁₉	—	4	4	no	—
303	C₂×C₁₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
304	C₂×C₁₉	C₂²×#131	1	1	yes	characteristic
305	C₂×C₁₉	#3573	1	1	yes	characteristic
306	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
307	C₂×#41	C₂³×C₁₉	1	4	yes	—
308	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
310	#131	—	4	8	no	—
311	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
312	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
313	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
314	C₂²×C₈	—	4	4	no	—
315	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
317	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
318	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
319	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
320	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
322	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
323	#127	C₂×C₄×C₁₉	1	4	yes	—
324	#126	C₂×C₄×C₁₉	1	8	yes	—
325	#125	C₂×C₄×C₁₉	1	4	yes	—
326	#124	C₂×C₄×C₁₉	1	4	yes	—
327	#124	C₂×C₄×C₁₉	1	8	yes	—
328	#123	C₂×C₄×C₁₉	1	8	yes	—
329	#123	C₂×C₄×C₁₉	1	8	yes	—
330	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
331	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
332	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
333	#121	C₂×C₄×C₁₉	1	4	yes	—
334	#121	C₂×C₄×C₁₉	1	4	yes	—
335	#121	C₂×C₄×C₁₉	1	4	yes	—
336	#121	C₂×C₄×C₁₉	1	4	yes	—
337	#121	C₂×C₄×C₁₉	1	4	yes	—
338	#121	C₂×C₄×C₁₉	1	8	yes	—
339	#120	C₂×C₄×C₁₉	1	8	yes	—
340	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
341	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
342	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
343	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
344	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
345	C₄×D₄	C₂³×C₁₉	1	4	yes	—
346	C₄×D₄	C₂³×C₁₉	1	4	yes	—
347	C₄×D₄	C₂³×C₁₉	1	2	yes	—
348	C₄×D₄	C₂³×C₁₉	1	8	yes	—
349	#117	C₂×C₄×C₁₉	1	2	yes	—
350	#117	C₂×C₄×C₁₉	1	4	yes	—
351	#117	C₂³×C₁₉	1	4	yes	—
352	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
354	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
356	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
357	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
358	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
359	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
360	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
361	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
362	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
363	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
364	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
365	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
366	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
367	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
368	#97	C₂³×C₁₉	1	8	yes	—
369	C₄×C₈	C₂³×C₁₉	1	2	yes	—
370	C₄×C₈	C₂³×C₁₉	1	2	yes	—
371	C₄×C₈	C₂³×C₁₉	1	4	yes	—
372	C₄×C₈	C₂³×C₁₉	1	4	yes	—
373	C₄×C₈	C₂³×C₁₉	1	4	yes	—
374	C₁₉	#60306	1	1	yes	characteristic, direct product factor, Sylow
375	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
376	#41	—	2	8	no	—
377	#41	—	4	4	no	—
378	#41	—	4	4	no	—
379	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
380	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
383	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
384	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
385	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
386	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
387	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
391	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
393	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
394	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
395	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
399	M₁₆	—	4	4	no	—
400	M₁₆	—	4	8	no	—
401	M₁₆	—	4	4	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	8	no	—
404	C₂×C₈	—	2	8	no	—
405	C₂×C₈	—	4	4	no	—
406	C₂×C₈	—	4	2	no	—
407	C₂×C₈	—	4	1	no	—
408	C₂×C₈	—	4	4	no	—
409	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
410	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
411	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
412	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
413	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
414	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
415	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
416	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
417	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
418	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
419	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
420	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
421	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
422	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
423	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
424	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
425	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
426	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
427	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
428	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
429	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
430	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
431	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
432	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
433	C₄²	C₂⁴×C₁₉	1	2	yes	—
434	C₄²	C₂⁴×C₁₉	1	4	yes	—
435	C₂³	—	2	4	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
439	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
440	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
441	Q₈	—	2	4	no	—
442	Q₈	—	4	4	no	—
443	D₄	—	2	8	no	—
444	D₄	—	2	8	no	—
445	D₄	—	2	4	no	—
446	D₄	—	4	4	no	—
447	D₄	—	4	8	no	—
448	D₄	—	4	8	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	C₁₉×#131	1	4	yes	complemented
461	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
462	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
463	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
464	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
465	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
466	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
467	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
468	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
469	C₈	—	2	1	no	—
470	C₈	—	2	4	no	—
471	C₈	—	2	4	no	—
472	C₈	—	2	2	no	—
473	C₈	—	2	4	no	—
474	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	4	8	no	—
484	C₂²	C₂×C₁₉×#131	1	2	yes	—
485	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
486	C₄	—	2	1	no	—
487	C₄	—	2	4	no	—
488	C₄	—	2	4	no	—
489	C₄	—	2	4	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	4	no	—
492	C₄	C₂×C₁₉×#131	1	4	yes	—
493	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
494	C₄	C₁₉×#585	1	1	yes	characteristic
495	C₂	—	2	2	no	—
496	C₂	—	4	4	no	—
497	C₂	—	4	4	no	—
498	C₂	C₄×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
499	C₂	C₂²×C₁₉×#131	1	1	yes	characteristic
500	C₂	C₁₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#3460	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2993	C₂	semidirect
3. C₁₉×#2989	C₂	semidirect
4. C₁₉×#2981	C₂	semidirect
5. C₁₉×#2976	C₂	semidirect
6. C₁₉×#2975	C₂	semidirect
7. C₁₉×#2966	C₂	semidirect
8. C₈×#41×C₁₉	C₂	semidirect
9. C₁₉×#2931	C₂	semidirect
10. C₁₉×#2929	C₂	semidirect
11. C₂×C₈×D₄×C₁₉	C₂	semidirect
12. C₂×C₁₉×#131	C₂²	semidirect
25. C₁₉×#446	C₂²	semidirect
26. C₈×Q₈×C₁₉	C₂²	semidirect
27. C₈×Q₈×C₁₉	C₂²	semidirect
30. C₁₉×#436	C₂²	semidirect
31. C₁₉×#436	C₂²	semidirect
33. C₁₉×#435	C₂²	semidirect
34. C₁₉×#435	C₂²	semidirect
39. C₈×D₄×C₁₉	C₂²	semidirect
40. C₈×D₄×C₁₉	C₂²	semidirect
41. C₈×D₄×C₁₉	C₂²	semidirect
42. C₁₉×#433	C₂²	semidirect
43. C₁₉×#432	C₂²	semidirect
45. C₁₉×#431	C₂²	semidirect
46. C₁₉×#424	C₂²	semidirect
47. C₁₉×#423	C₂²	semidirect
49. C₁₉×#408	C₂²	semidirect
50. C₁₉×#408	C₂²	semidirect
53. C₁₉×#405	C₂²	semidirect
55. C₂×C₄×C₈×C₁₉	C₂²	semidirect
184. #60306	C₁₉	direct (N × H)
210. C₂×C₄×C₁₉	#131	semidirect
226. #2993	C₂×C₁₉	semidirect
227. #2989	C₂×C₁₉	semidirect
228. #2981	C₂×C₁₉	semidirect
229. #2976	C₂×C₁₉	semidirect
230. #2975	C₂×C₁₉	semidirect
231. #2966	C₂×C₁₉	semidirect
232. C₈×#41	C₂×C₁₉	semidirect
233. #2931	C₂×C₁₉	semidirect
234. #2929	C₂×C₁₉	semidirect
235. C₂×C₈×D₄	C₂×C₁₉	semidirect
256. C₂×#131	C₂²×C₁₉	semidirect
269. #446	C₂²×C₁₉	semidirect
270. C₈×Q₈	C₂²×C₁₉	semidirect
271. C₈×Q₈	C₂²×C₁₉	semidirect
274. #436	C₂²×C₁₉	semidirect
275. #436	C₂²×C₁₉	semidirect
277. #435	C₂²×C₁₉	semidirect
278. #435	C₂²×C₁₉	semidirect
283. C₈×D₄	C₂²×C₁₉	semidirect
284. C₈×D₄	C₂²×C₁₉	semidirect
285. C₈×D₄	C₂²×C₁₉	semidirect
286. #433	C₂²×C₁₉	semidirect
287. #432	C₂²×C₁₉	semidirect
289. #431	C₂²×C₁₉	semidirect
290. #424	C₂²×C₁₉	semidirect
291. #423	C₂²×C₁₉	semidirect
293. #408	C₂²×C₁₉	semidirect
294. #408	C₂²×C₁₉	semidirect
297. #405	C₂²×C₁₉	semidirect
299. C₂×C₄×C₈	C₂²×C₁₉	semidirect
374. C₁₉	#60306	direct (N × H)
460. C₂×C₄	C₁₉×#131	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3460	2
C₁₉×#2993	2
C₁₉×#2989	2
C₁₉×#2981	2
C₁₉×#2976	2
C₁₉×#2975	2
C₁₉×#2966	2
C₈×#41×C₁₉	2
C₁₉×#2931	2
C₁₉×#2929	2
C₂×C₈×D₄×C₁₉	2
#60306	19

Subgroups — C19×#60306 #18066265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60306 #18066265