Subgroups — C₁₉×#22322 #18028281

Order 4864.

652 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2396	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1924	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1924	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1923	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1923	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1917	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1916	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1771	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1750	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#400	C₄	1	1	yes	characteristic
33	C₁₉×#399	C₄	1	1	yes	characteristic
34	C₁₉×#398	C₄	1	1	yes	characteristic
35	C₁₉×#398	C₄	1	1	yes	characteristic
36	C₁₉×#396	C₄	1	1	yes	characteristic
37	C₁₉×#396	C₄	1	1	yes	characteristic
38	C₁₉×#395	C₄	1	1	yes	characteristic
39	C₁₉×#393	C₄	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#336	C₂²	1	1	yes	characteristic
46	C₁₉×#336	C₂²	1	1	yes	characteristic
47	C₁₉×#336	C₂²	1	1	yes	characteristic
48	C₁₉×#336	C₂²	1	1	yes	characteristic
49	C₁₉×#336	C₂²	1	1	yes	characteristic
50	C₁₉×#336	C₂²	1	1	yes	characteristic
51	C₁₉×#336	C₂²	1	1	yes	characteristic
52	C₁₉×#336	C₂²	1	1	yes	characteristic
53	C₁₉×#336	C₂²	1	1	yes	characteristic
54	C₁₉×#336	C₂²	1	1	yes	characteristic
55	C₁₉×#336	C₂²	1	1	yes	characteristic
56	C₁₉×#336	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
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×Q₈×C₁₉	—	4	1	no	—
70	C₄×Q₈×C₁₉	—	4	1	no	—
71	C₁₉×#117	—	4	1	no	—
72	C₁₉×#117	—	4	1	no	—
73	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×C₄⋊C₈	—	2	2	no	—
97	C₁₉×C₄⋊C₈	—	2	2	no	—
98	C₁₉×C₄⋊C₈	—	4	1	no	—
99	C₁₉×C₄⋊C₈	—	4	1	no	—
100	C₁₉×C₂²⋊C₈	—	2	2	no	—
101	C₁₉×C₂²⋊C₈	—	2	2	no	—
102	C₁₉×C₂²⋊C₈	—	4	1	no	—
103	C₁₉×C₂²⋊C₈	—	4	1	no	—
104	C₁₉×#97	—	2	2	no	—
105	C₁₉×#97	—	4	1	no	—
106	C₁₉×#97	—	4	1	no	—
107	C₄×C₈×C₁₉	—	2	2	no	—
108	C₄×C₈×C₁₉	—	4	1	no	—
109	C₄×C₈×C₁₉	—	4	1	no	—
110	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
111	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
112	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
113	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
114	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
115	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
116	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
117	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
118	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
119	C₁₉×#95	C₂×C₄	1	1	yes	characteristic
120	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×Q₈×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	4	1	no	—
123	C₂×Q₈×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	1	no	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	2	1	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	#41	1	2	yes	—
167	C₂×C₈×C₁₉	#41	1	2	yes	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	4	1	no	—
172	C₄⋊C₄×C₁₉	—	4	1	no	—
173	C₄⋊C₄×C₁₉	—	4	1	no	—
174	C₄⋊C₄×C₁₉	—	4	1	no	—
175	C₄⋊C₄×C₁₉	—	4	1	no	—
176	C₄⋊C₄×C₁₉	—	4	1	no	—
177	C₄⋊C₄×C₁₉	—	4	1	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂²⋊C₄×C₁₉	—	4	1	no	—
182	C₂²⋊C₄×C₁₉	—	4	1	no	—
183	C₂²⋊C₄×C₁₉	—	4	1	no	—
184	C₂²⋊C₄×C₁₉	—	4	1	no	—
185	C₄²×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	—	2	1	no	—
187	C₄²×C₁₉	—	2	1	no	—
188	C₄²×C₁₉	—	2	1	no	—
189	C₄²×C₁₉	—	2	1	no	—
190	C₄²×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	2	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	2	1	no	—
197	#22322	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂³×C₁₉	—	2	1	no	—
199	C₂³×C₁₉	—	2	1	no	—
200	C₂³×C₁₉	—	2	1	no	—
201	C₂³×C₁₉	—	2	1	no	—
202	C₂³×C₁₉	—	2	1	no	—
203	C₂³×C₁₉	—	2	1	no	—
204	C₂³×C₁₉	—	2	1	no	—
205	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
206	Q₈×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	#131	1	2	yes	—
249	C₂×C₄×C₁₉	#131	1	2	yes	—
250	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
253	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
256	C₈×C₁₉	—	2	2	no	—
257	C₈×C₁₉	—	2	2	no	—
258	C₈×C₁₉	—	4	1	no	—
259	C₈×C₁₉	—	4	1	no	—
260	C₈×C₁₉	—	4	1	no	—
261	C₈×C₁₉	—	4	1	no	—
262	C₈×C₁₉	—	4	1	no	—
263	C₈×C₁₉	—	4	1	no	—
264	#2396	C₂×C₁₉	1	1	yes	characteristic
265	#1985	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1984	C₂×C₁₉	1	1	yes	characteristic, complemented
267	#1924	C₂×C₁₉	1	1	yes	characteristic
268	#1924	C₂×C₁₉	1	1	yes	characteristic
269	#1923	C₂×C₁₉	1	1	yes	characteristic
270	#1923	C₂×C₁₉	1	1	yes	characteristic
271	#1917	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1917	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1917	C₂×C₁₉	1	1	yes	characteristic, complemented
274	#1916	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1818	C₂×C₁₉	1	1	yes	characteristic
276	#1771	C₂×C₁₉	1	1	yes	characteristic, complemented
277	C₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
278	#1750	C₂×C₁₉	1	1	yes	characteristic
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	—	4	1	no	—
283	C₂²×C₁₉	—	4	1	no	—
284	C₂²×C₁₉	—	4	1	no	—
285	C₂²×C₁₉	—	4	1	no	—
286	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
287	C₂²×C₁₉	#518	1	1	yes	characteristic
288	C₂²×C₁₉	#519	1	1	yes	characteristic
289	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
290	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
291	C₂²×C₁₉	#568	1	1	yes	characteristic
292	C₂²×C₁₉	#568	1	1	yes	characteristic
293	C₄×C₁₉	—	2	2	no	—
294	C₄×C₁₉	—	2	2	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	—	4	1	no	—
297	C₄×C₁₉	—	4	1	no	—
298	C₄×C₁₉	—	4	1	no	—
299	C₄×C₁₉	—	4	1	no	—
300	C₄×C₁₉	—	4	1	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	#539	1	1	yes	characteristic
307	C₄×C₁₉	#539	1	1	yes	characteristic
308	C₄×C₁₉	#542	1	1	yes	characteristic
309	C₄×C₁₉	#542	1	1	yes	characteristic
310	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
326	#400	C₄×C₁₉	1	1	yes	characteristic
327	#399	C₄×C₁₉	1	1	yes	characteristic
328	#398	C₄×C₁₉	1	1	yes	characteristic
329	#398	C₄×C₁₉	1	1	yes	characteristic
330	#396	C₄×C₁₉	1	1	yes	characteristic
331	#396	C₄×C₁₉	1	1	yes	characteristic
332	#395	C₄×C₁₉	1	1	yes	characteristic
333	#393	C₄×C₁₉	1	1	yes	characteristic
334	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
335	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
336	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
337	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
338	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
339	#336	C₂²×C₁₉	1	1	yes	characteristic
340	#336	C₂²×C₁₉	1	1	yes	characteristic
341	#336	C₂²×C₁₉	1	1	yes	characteristic
342	#336	C₂²×C₁₉	1	1	yes	characteristic
343	#336	C₂²×C₁₉	1	1	yes	characteristic
344	#336	C₂²×C₁₉	1	1	yes	characteristic
345	#336	C₂²×C₁₉	1	1	yes	characteristic
346	#336	C₂²×C₁₉	1	1	yes	characteristic
347	#336	C₂²×C₁₉	1	1	yes	characteristic
348	#336	C₂²×C₁₉	1	1	yes	characteristic
349	#336	C₂²×C₁₉	1	1	yes	characteristic
350	#336	C₂²×C₁₉	1	1	yes	characteristic
351	#336	C₂²×C₁₉	1	1	yes	characteristic
352	#336	C₂²×C₁₉	1	1	yes	characteristic
353	C₂×C₁₉	—	8	1	no	—
354	C₂×C₁₉	#2332	1	1	yes	characteristic
355	C₂×C₁₉	#2966	1	1	yes	characteristic
356	C₂×C₁₉	#2967	1	1	yes	characteristic
357	C₂×C₁₉	#2976	1	1	yes	characteristic
358	C₂×C₁₉	#2981	1	1	yes	characteristic
359	C₂×C₁₉	#2985	1	1	yes	characteristic
360	C₂×C₁₉	#2985	1	1	yes	characteristic
361	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
366	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
367	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
371	C₄×Q₈	—	4	1	no	—
372	C₄×Q₈	—	4	1	no	—
373	#117	—	4	1	no	—
374	#117	—	4	1	no	—
375	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
386	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
398	C₄⋊C₈	—	2	2	no	—
399	C₄⋊C₈	—	2	2	no	—
400	C₄⋊C₈	—	4	1	no	—
401	C₄⋊C₈	—	4	1	no	—
402	C₂²⋊C₈	—	2	2	no	—
403	C₂²⋊C₈	—	2	2	no	—
404	C₂²⋊C₈	—	4	1	no	—
405	C₂²⋊C₈	—	4	1	no	—
406	#97	—	2	2	no	—
407	#97	—	4	1	no	—
408	#97	—	4	1	no	—
409	C₄×C₈	—	2	2	no	—
410	C₄×C₈	—	4	1	no	—
411	C₄×C₈	—	4	1	no	—
412	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
413	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
414	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
415	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
416	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
417	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
418	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
419	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
420	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
421	#95	C₂×C₄×C₁₉	1	1	yes	characteristic
422	C₁₉	#22322	1	1	yes	characteristic, direct product factor, Sylow
423	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	4	1	no	—
426	C₂×Q₈	—	4	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
440	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
443	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
444	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	#41×C₁₉	1	2	yes	—
470	C₂×C₈	#41×C₁₉	1	2	yes	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	4	1	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
508	Q₈	—	4	4	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	C₁₉×#131	1	2	yes	—
551	C₂×C₄	C₁₉×#131	1	2	yes	—
552	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
553	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
554	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
555	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
556	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
557	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
558	C₈	—	2	2	no	—
559	C₈	—	2	2	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
574	C₂²	C₁₉×#518	1	1	yes	characteristic
575	C₂²	C₁₉×#519	1	1	yes	characteristic
576	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
577	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
578	C₂²	C₁₉×#568	1	1	yes	characteristic
579	C₂²	C₁₉×#568	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	C₁₉×#539	1	1	yes	characteristic
594	C₄	C₁₉×#539	1	1	yes	characteristic
595	C₄	C₁₉×#542	1	1	yes	characteristic
596	C₄	C₁₉×#542	1	1	yes	characteristic
597	C₂	—	8	1	no	—
598	C₂	C₁₉×#2332	1	1	yes	characteristic
599	C₂	C₁₉×#2966	1	1	yes	characteristic
600	C₂	C₁₉×#2967	1	1	yes	characteristic
601	C₂	C₁₉×#2976	1	1	yes	characteristic
602	C₂	C₁₉×#2981	1	1	yes	characteristic
603	C₂	C₁₉×#2985	1	1	yes	characteristic
604	C₂	C₁₉×#2985	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#1985	C₂	semidirect
3. C₁₉×#1984	C₂	semidirect
8. C₁₉×#1917	C₂	semidirect
9. C₁₉×#1917	C₂	semidirect
10. C₁₉×#1917	C₂	semidirect
11. C₁₉×#1916	C₂	semidirect
13. C₁₉×#1771	C₂	semidirect
14. C₈×C₄⋊C₄×C₁₉	C₂	semidirect
197. #22322	C₁₉	direct (N × H)
265. #1985	C₂×C₁₉	semidirect
266. #1984	C₂×C₁₉	semidirect
271. #1917	C₂×C₁₉	semidirect
272. #1917	C₂×C₁₉	semidirect
273. #1917	C₂×C₁₉	semidirect
274. #1916	C₂×C₁₉	semidirect
276. #1771	C₂×C₁₉	semidirect
277. C₈×C₄⋊C₄	C₂×C₁₉	semidirect
422. C₁₉	#22322	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×#2396	2
C₁₉×#1985	2
C₁₉×#1984	2
C₁₉×#1924	2
C₁₉×#1923	2
C₁₉×#1917	2
C₁₉×#1916	2
C₁₉×#1818	2
C₁₉×#1771	2
C₈×C₄⋊C₄×C₁₉	2
C₁₉×#1750	2
#22322	19

Subgroups — C19×#22322 #18028281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22322 #18028281