Subgroups — C₁₉×#22668 #18028627

Order 4864.

868 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×M₁₆×C₁₉	C₂	1	2	yes	maximal
2	C₂×C₁₉×#435	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1950	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1855	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1855	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1849	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1811	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1810	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1778	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#436	—	2	2	no	—
18	C₁₉×#435	—	2	2	no	—
19	C₁₉×#435	—	2	2	no	—
20	C₁₉×#435	C₄	1	4	yes	—
21	C₁₉×#435	C₄	1	4	yes	—
22	C₈×D₄×C₁₉	—	2	2	no	—
23	C₁₉×#430	—	2	4	no	—
24	C₂×C₁₉×#108	—	2	4	no	—
25	C₂×C₁₉×#108	C₂²	1	2	yes	—
26	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#108	C₂²	1	2	yes	—
28	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#108	C₂²	1	2	yes	—
31	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
32	C₁₉×#423	C₂²	1	2	yes	—
33	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₁₉×#407	C₂²	1	2	yes	—
35	C₁₉×#407	C₂²	1	2	yes	—
36	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
39	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
40	C₁₉×#341	C₂²	1	2	yes	—
41	C₁₉×#341	C₂²	1	2	yes	—
42	C₁₉×#341	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₉	Q₈	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	4	no	—
51	C₂×M₁₆×C₁₉	—	2	4	no	—
52	C₂×M₁₆×C₁₉	—	4	2	no	—
53	C₂×M₁₆×C₁₉	—	4	2	no	—
54	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	—
55	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
56	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
57	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
58	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₉	—	2	2	no	—
60	C₂²×C₈×C₁₉	—	2	2	no	—
61	C₂²×C₈×C₁₉	—	2	2	no	—
62	C₂²×C₈×C₁₉	—	2	2	no	—
63	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
70	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
71	C₄×D₄×C₁₉	D₄	1	2	yes	—
72	C₄×D₄×C₁₉	D₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#108	—	2	4	no	—
78	C₁₉×#108	—	2	4	no	—
79	C₁₉×#108	—	2	2	no	—
80	C₁₉×#108	—	2	2	no	—
81	C₁₉×#108	—	2	2	no	—
82	C₁₉×#108	—	4	2	no	—
83	C₁₉×#108	D₄	1	4	yes	complemented
84	C₁₉×C₄⋊C₈	—	2	2	no	—
85	C₁₉×C₄⋊C₈	—	2	2	no	—
86	C₁₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
87	C₁₉×C₂²⋊C₈	—	2	2	no	—
88	C₁₉×C₂²⋊C₈	—	2	2	no	—
89	C₁₉×C₂²⋊C₈	—	2	2	no	—
90	C₁₉×C₂²⋊C₈	—	2	2	no	—
91	C₁₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
92	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
94	C₁₉×#97	—	2	2	no	—
95	C₁₉×#97	C₂×C₄	1	4	yes	—
96	C₄×C₈×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
98	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
99	C₂×D₄×C₁₉	—	4	2	no	—
100	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
101	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
121	M₁₆×C₁₉	—	2	2	no	—
122	M₁₆×C₁₉	—	2	8	no	—
123	M₁₆×C₁₉	—	2	2	no	—
124	M₁₆×C₁₉	—	2	2	no	—
125	M₁₆×C₁₉	—	2	2	no	—
126	M₁₆×C₁₉	—	2	2	no	—
127	M₁₆×C₁₉	—	2	2	no	—
128	M₁₆×C₁₉	—	2	2	no	—
129	M₁₆×C₁₉	—	4	4	no	—
130	M₁₆×C₁₉	—	4	4	no	—
131	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	1	no	—
136	C₂×C₈×C₁₉	—	2	1	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	2	1	no	—
139	C₂×C₈×C₁₉	—	2	4	no	—
140	C₂×C₈×C₁₉	—	2	4	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₂×C₈×C₁₉	—	4	4	no	—
145	C₂×C₈×C₁₉	—	4	4	no	—
146	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₉	#41	1	2	yes	—
152	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
153	C₄⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
154	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
155	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
156	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
157	C₂²⋊C₄×C₁₉	C₄⋊C₄	1	2	yes	—
158	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
159	C₄²×C₁₉	C₂×D₄	1	2	yes	—
160	#22668	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂³×C₁₉	—	2	1	no	—
162	C₂³×C₁₉	—	2	1	no	—
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	4	1	no	—
167	C₂³×C₁₉	—	4	1	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
170	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
173	D₄×C₁₉	—	2	4	no	—
174	D₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	1	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
194	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
195	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
198	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
204	C₈×C₁₉	—	2	2	no	—
205	C₈×C₁₉	—	2	2	no	—
206	C₈×C₁₉	—	2	2	no	—
207	C₈×C₁₉	—	2	4	no	—
208	C₈×C₁₉	—	4	2	no	—
209	C₈×C₁₉	—	4	2	no	—
210	C₈×C₁₉	—	4	2	no	—
211	C₈×C₁₉	C₄×D₄	1	4	yes	—
212	D₄×M₁₆	C₂×C₁₉	1	2	yes	—
213	C₂×#435	C₂×C₁₉	1	1	yes	characteristic
214	C₂×#430	C₂×C₁₉	1	1	yes	characteristic, complemented
215	C₂²×#108	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#1950	C₂×C₁₉	1	2	yes	complemented
217	#1855	C₂×C₁₉	1	2	yes	complemented
218	#1855	C₂×C₁₉	1	2	yes	complemented
219	#1849	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1811	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#1810	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#1778	C₂×C₁₉	1	1	yes	characteristic, complemented
223	C₂²×C₁₉	—	2	1	no	—
224	C₂²×C₁₉	—	2	1	no	—
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	2	2	no	—
229	C₂²×C₁₉	—	2	2	no	—
230	C₂²×C₁₉	—	2	1	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	8	1	no	—
236	C₂²×C₁₉	—	8	1	no	—
237	C₂²×C₁₉	#430	1	2	yes	complemented
238	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
239	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
240	C₂²×C₁₉	#554	1	1	yes	characteristic
241	C₄×C₁₉	—	2	1	no	—
242	C₄×C₁₉	—	2	1	no	—
243	C₄×C₁₉	—	2	2	no	—
244	C₄×C₁₉	—	2	2	no	—
245	C₄×C₁₉	—	2	2	no	—
246	C₄×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
247	C₄×C₁₉	#520	1	1	yes	characteristic
248	C₄×C₁₉	D₄²	1	1	yes	characteristic
249	C₄×C₁₉	#547	1	1	yes	characteristic
250	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
251	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
252	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
253	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
255	#436	—	2	2	no	—
256	#435	—	2	2	no	—
257	#435	—	2	2	no	—
258	#435	C₄×C₁₉	1	4	yes	—
259	#435	C₄×C₁₉	1	4	yes	—
260	C₈×D₄	—	2	2	no	—
261	#430	—	2	4	no	—
262	C₂×#108	—	2	4	no	—
263	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
264	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×#108	C₂²×C₁₉	1	2	yes	—
267	C₂×#108	C₂²×C₁₉	1	2	yes	—
268	C₂×#108	C₂²×C₁₉	1	2	yes	—
269	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
270	#423	C₂²×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
272	#407	C₂²×C₁₉	1	2	yes	—
273	#407	C₂²×C₁₉	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
276	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
277	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
278	#341	C₂²×C₁₉	1	2	yes	—
279	#341	C₂²×C₁₉	1	2	yes	—
280	#341	C₂²×C₁₉	1	2	yes	—
281	C₂×C₁₉	—	2	1	no	—
282	C₂×C₁₉	—	2	1	no	—
283	C₂×C₁₉	—	2	2	no	—
284	C₂×C₁₉	—	4	1	no	—
285	C₂×C₁₉	—	4	2	no	—
286	C₂×C₁₉	D₄×C₄⋊C₄	1	1	yes	characteristic
287	C₂×C₁₉	C₂×#430	1	1	yes	characteristic
288	C₂×C₁₉	#2916	1	1	yes	characteristic
289	C₂²×D₄	Q₈×C₁₉	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	4	no	—
297	C₂×M₁₆	—	2	4	no	—
298	C₂×M₁₆	—	4	2	no	—
299	C₂×M₁₆	—	4	2	no	—
300	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	—
301	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
302	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
303	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
304	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
310	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
311	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
315	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
316	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
317	C₄×D₄	D₄×C₁₉	1	2	yes	—
318	C₄×D₄	D₄×C₁₉	1	2	yes	—
319	C₂×C₄⋊C₄	Q₈×C₁₉	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	Q₈×C₁₉	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	Q₈×C₁₉	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
323	#108	—	2	4	no	—
324	#108	—	2	4	no	—
325	#108	—	2	2	no	—
326	#108	—	2	2	no	—
327	#108	—	2	2	no	—
328	#108	—	4	2	no	—
329	#108	D₄×C₁₉	1	4	yes	complemented
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	C₂×C₄×C₁₉	1	4	yes	—
338	C₂²⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
339	C₂²⋊C₈	C₂×C₄×C₁₉	1	2	yes	—
340	#97	—	2	2	no	—
341	#97	C₂×C₄×C₁₉	1	4	yes	—
342	C₄×C₈	—	2	2	no	—
343	C₁₉	#22668	1	1	yes	characteristic, direct product factor, Sylow
344	C₂⁴	C₂×Q₈×C₁₉	1	1	yes	characteristic
345	C₂⁴	C₂×Q₈×C₁₉	1	1	yes	characteristic
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
348	C₂×D₄	C₄⋊C₄×C₁₉	1	2	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
363	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
364	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
368	M₁₆	—	2	2	no	—
369	M₁₆	—	2	8	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	4	4	no	—
377	M₁₆	—	4	4	no	—
378	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	4	4	no	—
392	C₂×C₈	—	4	4	no	—
393	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
394	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
395	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
396	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
397	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
398	C₂×C₈	#41×C₁₉	1	2	yes	—
399	C₄⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	—
400	C₄⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	—
401	C₂²⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	—
402	C₂²⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	—
403	C₂²⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	—
404	C₂²⋊C₄	C₄⋊C₄×C₁₉	1	2	yes	—
405	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
406	C₄²	C₂×D₄×C₁₉	1	2	yes	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
416	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
417	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
418	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
419	D₄	—	2	4	no	—
420	D₄	—	4	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
440	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
441	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
442	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
443	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
444	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
447	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
448	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	—	2	4	no	—
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	4	2	no	—
457	C₈	C₄×D₄×C₁₉	1	4	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	C₁₉×#430	1	2	yes	complemented
473	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
474	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
475	C₂²	C₁₉×#554	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	2	no	—
481	C₄	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
482	C₄	C₁₉×#520	1	1	yes	characteristic
483	C₄	D₄²×C₁₉	1	1	yes	characteristic
484	C₄	C₁₉×#547	1	1	yes	characteristic
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	4	2	no	—
490	C₂	D₄×C₄⋊C₄×C₁₉	1	1	yes	characteristic
491	C₂	C₂×C₁₉×#430	1	1	yes	characteristic
492	C₂	C₁₉×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₁₉	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₉×#430	C₂	semidirect
4. C₂²×C₁₉×#108	C₂	semidirect
5. C₁₉×#1950	C₂	semidirect
6. C₁₉×#1855	C₂	semidirect
7. C₁₉×#1855	C₂	semidirect
8. C₁₉×#1849	C₂	semidirect
9. C₁₉×#1811	C₂	semidirect
10. C₁₉×#1810	C₂	semidirect
11. C₁₉×#1778	C₂	semidirect
83. C₁₉×#108	D₄	semidirect
160. #22668	C₁₉	direct (N × H)
214. C₂×#430	C₂×C₁₉	semidirect
215. C₂²×#108	C₂×C₁₉	semidirect
216. #1950	C₂×C₁₉	semidirect
217. #1855	C₂×C₁₉	semidirect
218. #1855	C₂×C₁₉	semidirect
219. #1849	C₂×C₁₉	semidirect
220. #1811	C₂×C₁₉	semidirect
221. #1810	C₂×C₁₉	semidirect
222. #1778	C₂×C₁₉	semidirect
237. C₂²×C₁₉	#430	semidirect
329. #108	D₄×C₁₉	semidirect
343. C₁₉	#22668	direct (N × H)
472. C₂²	C₁₉×#430	semidirect

Maximal subgroups

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

subgroup	index
D₄×M₁₆×C₁₉	2
C₂×C₁₉×#435	2
C₂×C₁₉×#430	2
C₂²×C₁₉×#108	2
C₁₉×#1950	2
C₁₉×#1855	2
C₁₉×#1849	2
C₁₉×#1811	2
C₁₉×#1810	2
C₁₉×#1778	2
#22668	19

Subgroups — C19×#22668 #18028627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22668 #18028627