Subgroups — C₁₉×#20606 #18026565

Order 4864.

3722 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#585	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#421	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×#104	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2879	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1789	C₂	1	8	yes	maximal, complemented
7	C₁₉×#585	—	2	8	no	—
8	C₁₉×#585	—	2	8	no	—
9	C₂×C₁₉×2₋¹⁺⁴	—	2	1	no	—
10	C₂×C₁₉×2₋¹⁺⁴	C₄	1	4	yes	complemented
11	C₂×C₁₉×H(5,𝔽₂)	—	2	2	no	—
12	C₂×C₁₉×H(5,𝔽₂)	—	2	1	no	—
13	C₂×C₁₉×H(5,𝔽₂)	C₄	1	4	yes	complemented
14	C₂²×#41×C₁₉	—	2	4	no	—
15	C₂²×#41×C₁₉	C₂²	1	2	yes	—
16	C₂²×#41×C₁₉	C₂²	1	4	yes	—
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#421	—	2	8	no	—
22	C₂×C₁₉×#104	—	2	8	no	—
23	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
24	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
25	C₁₉×#408	—	2	4	no	—
26	C₁₉×#407	C₂²	1	4	yes	complemented
27	C₁₉×#391	—	2	1	no	—
28	C₁₉×#390	—	2	1	no	—
29	C₁₉×#386	—	2	2	no	—
30	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
31	C₁₉×2₋¹⁺⁴	—	2	8	no	—
32	C₁₉×2₋¹⁺⁴	—	2	8	no	—
33	C₁₉×2₋¹⁺⁴	—	2	16	no	—
34	C₁₉×2₋¹⁺⁴	—	2	16	no	—
35	C₁₉×H(5,𝔽₂)	—	2	8	no	—
36	C₁₉×H(5,𝔽₂)	—	2	8	no	—
37	C₁₉×H(5,𝔽₂)	—	2	16	no	—
38	C₁₉×H(5,𝔽₂)	—	2	16	no	—
39	C₁₉×H(5,𝔽₂)	—	2	16	no	—
40	C₁₉×H(5,𝔽₂)	—	2	16	no	—
41	C₂×#41×C₁₉	—	2	32	no	—
42	C₂×#41×C₁₉	—	2	32	no	—
43	C₂×#41×C₁₉	—	2	16	no	—
44	C₂×#41×C₁₉	—	2	16	no	—
45	C₂×#41×C₁₉	—	2	4	no	—
46	C₂×#41×C₁₉	—	2	8	no	—
47	C₂×#41×C₁₉	—	2	4	no	—
48	C₂×#41×C₁₉	—	2	4	no	—
49	C₂×#41×C₁₉	—	2	2	no	—
50	C₂×#41×C₁₉	—	2	2	no	—
51	C₂×#41×C₁₉	—	2	4	no	—
52	C₂×#41×C₁₉	—	2	4	no	—
53	C₂×#41×C₁₉	—	2	4	no	—
54	C₂×#41×C₁₉	—	2	4	no	—
55	C₂×#41×C₁₉	—	2	4	no	—
56	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
57	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
58	C₂×#41×C₁₉	C₂×C₄	1	8	yes	complemented
59	C₂×#41×C₁₉	D₄	1	8	yes	—
60	C₂×#41×C₁₉	D₄	1	8	yes	—
61	C₂×#41×C₁₉	D₄	1	4	yes	—
62	C₂×#41×C₁₉	C₂³	1	4	yes	—
63	C₂²×Q₈×C₁₉	—	2	4	no	—
64	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
65	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	complemented
66	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
67	C₂²×D₄×C₁₉	—	2	2	no	—
68	C₂²×D₄×C₁₉	—	2	4	no	—
69	C₂²×D₄×C₁₉	—	2	4	no	—
70	C₂²×D₄×C₁₉	—	2	8	no	—
71	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
72	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	complemented
73	C₂²×D₄×C₁₉	D₄	1	2	yes	—
74	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
75	C₂³×C₄×C₁₉	—	2	4	no	—
76	C₂³×C₄×C₁₉	—	2	2	no	—
77	C₂³×C₄×C₁₉	—	2	1	no	—
78	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₁₉	—	2	2	no	—
81	C₂×M₁₆×C₁₉	—	2	4	no	—
82	C₂×M₁₆×C₁₉	—	2	4	no	—
83	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
84	C₂²×C₈×C₁₉	—	2	2	no	—
85	C₁₉×#117	—	2	4	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	—	2	4	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
93	C₁₉×#104	—	2	16	no	—
94	C₁₉×#104	—	2	16	no	—
95	C₁₉×C₂²⋊C₈	—	2	8	no	—
96	C₁₉×#95	—	2	4	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	4	no	—
99	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
100	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
101	#41×C₁₉	—	2	32	no	—
102	#41×C₁₉	—	2	16	no	—
103	#41×C₁₉	—	2	16	no	—
104	#41×C₁₉	—	2	64	no	—
105	#41×C₁₉	—	2	32	no	—
106	#41×C₁₉	—	2	32	no	—
107	#41×C₁₉	—	2	16	no	—
108	#41×C₁₉	—	2	16	no	—
109	#41×C₁₉	—	2	8	no	—
110	#41×C₁₉	—	2	8	no	—
111	#41×C₁₉	—	2	8	no	—
112	#41×C₁₉	—	2	8	no	—
113	#41×C₁₉	—	2	8	no	—
114	#41×C₁₉	—	2	8	no	—
115	#41×C₁₉	—	2	8	no	—
116	#41×C₁₉	—	2	8	no	—
117	#41×C₁₉	—	2	8	no	—
118	#41×C₁₉	—	2	4	no	—
119	#41×C₁₉	—	2	4	no	—
120	#41×C₁₉	C₂²⋊C₄	1	16	yes	complemented
121	#41×C₁₉	C₂×D₄	1	8	yes	—
122	#41×C₁₉	C₂×D₄	1	8	yes	—
123	C₂×Q₈×C₁₉	—	2	32	no	—
124	C₂×Q₈×C₁₉	—	2	16	no	—
125	C₂×Q₈×C₁₉	—	2	2	no	—
126	C₂×Q₈×C₁₉	—	2	4	no	—
127	C₂×Q₈×C₁₉	—	2	4	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
131	C₂×Q₈×C₁₉	C₂²⋊C₄	1	8	yes	complemented
132	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
133	C₂×D₄×C₁₉	—	2	16	no	—
134	C₂×D₄×C₁₉	—	2	16	no	—
135	C₂×D₄×C₁₉	—	2	64	no	—
136	C₂×D₄×C₁₉	—	2	32	no	—
137	C₂×D₄×C₁₉	—	2	4	no	—
138	C₂×D₄×C₁₉	—	2	8	no	—
139	C₂×D₄×C₁₉	—	2	8	no	—
140	C₂×D₄×C₁₉	—	2	8	no	—
141	C₂×D₄×C₁₉	—	2	4	no	—
142	C₂×D₄×C₁₉	—	2	4	no	—
143	C₂×D₄×C₁₉	—	2	4	no	—
144	C₂×D₄×C₁₉	—	2	16	no	—
145	C₂×D₄×C₁₉	—	2	2	no	—
146	C₂×D₄×C₁₉	—	2	4	no	—
147	C₂×D₄×C₁₉	—	2	4	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	—
151	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
152	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	complemented
153	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₁₉	—	2	32	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	4	no	—
157	C₂²×C₄×C₁₉	—	2	4	no	—
158	C₂²×C₄×C₁₉	—	2	8	no	—
159	C₂²×C₄×C₁₉	—	2	8	no	—
160	C₂²×C₄×C₁₉	—	2	8	no	—
161	C₂²×C₄×C₁₉	—	2	4	no	—
162	C₂²×C₄×C₁₉	—	2	4	no	—
163	C₂²×C₄×C₁₉	—	2	4	no	—
164	C₂²×C₄×C₁₉	—	2	2	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	4	4	no	—
167	C₂²×C₄×C₁₉	—	4	2	no	—
168	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
169	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
170	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	M₁₆×C₁₉	—	2	4	no	—
178	M₁₆×C₁₉	—	2	4	no	—
179	M₁₆×C₁₉	—	4	4	no	—
180	C₂×C₈×C₁₉	—	2	4	no	—
181	C₂×C₈×C₁₉	—	4	4	no	—
182	C₄⋊C₄×C₁₉	—	4	2	no	—
183	C₂²⋊C₄×C₁₉	—	4	8	no	—
184	C₂²⋊C₄×C₁₉	—	4	2	no	—
185	C₄²×C₁₉	—	2	4	no	—
186	C₄²×C₁₉	—	2	4	no	—
187	C₄²×C₁₉	—	4	2	no	—
188	#20606	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂³×C₁₉	—	2	16	no	—
190	C₂³×C₁₉	—	2	4	no	—
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	2	8	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	4	no	—
196	C₂³×C₁₉	—	8	4	no	—
197	C₂³×C₁₉	—	8	8	no	—
198	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
199	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂³×C₁₉	#120	1	2	yes	—
201	C₂³×C₁₉	#120	1	2	yes	—
202	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₁₉	—	2	16	no	—
204	Q₈×C₁₉	—	2	4	no	—
205	Q₈×C₁₉	—	2	8	no	—
206	Q₈×C₁₉	—	2	8	no	—
207	Q₈×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
208	D₄×C₁₉	—	2	32	no	—
209	D₄×C₁₉	—	2	16	no	—
210	D₄×C₁₉	—	2	8	no	—
211	D₄×C₁₉	—	2	8	no	—
212	D₄×C₁₉	—	2	16	no	—
213	D₄×C₁₉	—	2	16	no	—
214	D₄×C₁₉	—	2	4	no	—
215	D₄×C₁₉	—	2	8	no	—
216	D₄×C₁₉	—	2	8	no	—
217	D₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
218	C₂×C₄×C₁₉	—	2	16	no	—
219	C₂×C₄×C₁₉	—	2	32	no	—
220	C₂×C₄×C₁₉	—	2	4	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	8	no	—
224	C₂×C₄×C₁₉	—	2	8	no	—
225	C₂×C₄×C₁₉	—	2	8	no	—
226	C₂×C₄×C₁₉	—	2	8	no	—
227	C₂×C₄×C₁₉	—	2	8	no	—
228	C₂×C₄×C₁₉	—	2	16	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	8	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	4	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
236	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
237	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
238	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
239	C₂×C₄×C₁₉	#120	1	4	yes	—
240	C₂×C₄×C₁₉	#120	1	4	yes	—
241	C₂×C₄×C₁₉	#120	1	2	yes	—
242	C₂×C₄×C₁₉	#120	1	2	yes	—
243	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₈×C₁₉	—	4	4	no	—
248	C₂×#585	C₂×C₁₉	1	1	yes	characteristic
249	C₂×#421	C₂×C₁₉	1	2	yes	complemented
250	C₂²×#104	C₂×C₁₉	1	2	yes	complemented
251	#2879	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#2297	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#1789	C₂×C₁₉	1	8	yes	complemented
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	2	4	no	—
256	C₂²×C₁₉	—	2	8	no	—
257	C₂²×C₁₉	—	2	4	no	—
258	C₂²×C₁₉	—	2	8	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	2	no	—
261	C₂²×C₁₉	—	4	8	no	—
262	C₂²×C₁₉	—	8	2	no	—
263	C₂²×C₁₉	—	8	2	no	—
264	C₂²×C₁₉	—	8	8	no	—
265	C₂²×C₁₉	—	8	16	no	—
266	C₂²×C₁₉	#379	1	4	yes	—
267	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
269	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
270	C₄×C₁₉	—	2	8	no	—
271	C₄×C₁₉	—	2	4	no	—
272	C₄×C₁₉	—	4	4	no	—
273	C₄×C₁₉	—	8	2	no	—
274	C₄×C₁₉	#379	1	4	yes	—
275	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
276	C₄×C₁₉	C₂×#120	1	2	yes	—
277	#585	—	2	8	no	—
278	#585	—	2	8	no	—
279	C₂×2₋¹⁺⁴	—	2	1	no	—
280	C₂×2₋¹⁺⁴	C₄×C₁₉	1	4	yes	complemented
281	C₂×H(5,𝔽₂)	—	2	2	no	—
282	C₂×H(5,𝔽₂)	—	2	1	no	—
283	C₂×H(5,𝔽₂)	C₄×C₁₉	1	4	yes	complemented
284	C₂²×#41	—	2	4	no	—
285	C₂²×#41	C₂²×C₁₉	1	2	yes	—
286	C₂²×#41	C₂²×C₁₉	1	4	yes	—
287	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
288	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
289	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
290	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
291	#421	—	2	8	no	—
292	C₂×#104	—	2	8	no	—
293	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
294	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
295	#408	—	2	4	no	—
296	#407	C₂²×C₁₉	1	4	yes	complemented
297	#391	—	2	1	no	—
298	#390	—	2	1	no	—
299	#386	—	2	2	no	—
300	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
301	C₂×C₁₉	—	2	1	no	—
302	C₂×C₁₉	—	2	1	no	—
303	C₂×C₁₉	—	2	4	no	—
304	C₂×C₁₉	—	4	4	no	—
305	C₂×C₁₉	—	4	8	no	—
306	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
307	C₂×C₁₉	#2901	1	2	yes	—
308	2₋¹⁺⁴	—	2	8	no	—
309	2₋¹⁺⁴	—	2	8	no	—
310	2₋¹⁺⁴	—	2	16	no	—
311	2₋¹⁺⁴	—	2	16	no	—
312	H(5,𝔽₂)	—	2	8	no	—
313	H(5,𝔽₂)	—	2	8	no	—
314	H(5,𝔽₂)	—	2	16	no	—
315	H(5,𝔽₂)	—	2	16	no	—
316	H(5,𝔽₂)	—	2	16	no	—
317	H(5,𝔽₂)	—	2	16	no	—
318	C₂×#41	—	2	32	no	—
319	C₂×#41	—	2	32	no	—
320	C₂×#41	—	2	16	no	—
321	C₂×#41	—	2	16	no	—
322	C₂×#41	—	2	4	no	—
323	C₂×#41	—	2	8	no	—
324	C₂×#41	—	2	4	no	—
325	C₂×#41	—	2	4	no	—
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	—	2	4	no	—
329	C₂×#41	—	2	4	no	—
330	C₂×#41	—	2	4	no	—
331	C₂×#41	—	2	4	no	—
332	C₂×#41	—	2	4	no	—
333	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
334	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
335	C₂×#41	C₂×C₄×C₁₉	1	8	yes	complemented
336	C₂×#41	D₄×C₁₉	1	8	yes	—
337	C₂×#41	D₄×C₁₉	1	8	yes	—
338	C₂×#41	D₄×C₁₉	1	4	yes	—
339	C₂×#41	C₂³×C₁₉	1	4	yes	—
340	C₂²×Q₈	—	2	4	no	—
341	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
342	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
343	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	4	no	—
346	C₂²×D₄	—	2	4	no	—
347	C₂²×D₄	—	2	8	no	—
348	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
349	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	complemented
350	C₂²×D₄	D₄×C₁₉	1	2	yes	—
351	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
352	C₂³×C₄	—	2	4	no	—
353	C₂³×C₄	—	2	2	no	—
354	C₂³×C₄	—	2	1	no	—
355	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
356	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	—	2	4	no	—
359	C₂×M₁₆	—	2	4	no	—
360	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
361	C₂²×C₈	—	2	2	no	—
362	#117	—	2	4	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	4	no	—
366	C₂×C₄²	—	2	4	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
369	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
370	#104	—	2	16	no	—
371	#104	—	2	16	no	—
372	C₂²⋊C₈	—	2	8	no	—
373	#95	—	2	4	no	—
374	C₁₉	#20606	1	1	yes	characteristic, direct product factor, Sylow
375	C₂⁴	—	2	2	no	—
376	C₂⁴	—	2	4	no	—
377	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
378	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
379	#41	—	2	32	no	—
380	#41	—	2	64	no	—
381	#41	—	2	16	no	—
382	#41	—	2	16	no	—
383	#41	—	2	32	no	—
384	#41	—	2	32	no	—
385	#41	—	2	16	no	—
386	#41	—	2	16	no	—
387	#41	—	2	8	no	—
388	#41	—	2	8	no	—
389	#41	—	2	8	no	—
390	#41	—	2	8	no	—
391	#41	—	2	8	no	—
392	#41	—	2	8	no	—
393	#41	—	2	8	no	—
394	#41	—	2	8	no	—
395	#41	—	2	8	no	—
396	#41	—	2	4	no	—
397	#41	—	2	4	no	—
398	#41	C₂²⋊C₄×C₁₉	1	16	yes	complemented
399	#41	C₂×D₄×C₁₉	1	8	yes	—
400	#41	C₂×D₄×C₁₉	1	8	yes	—
401	C₂×Q₈	—	2	32	no	—
402	C₂×Q₈	—	2	16	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
409	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	complemented
410	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
411	C₂×D₄	—	2	64	no	—
412	C₂×D₄	—	2	16	no	—
413	C₂×D₄	—	2	16	no	—
414	C₂×D₄	—	2	32	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	16	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	—
429	C₂×D₄	C₂²⋊C₄×C₁₉	1	4	yes	—
430	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	complemented
431	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
432	C₂²×C₄	—	2	32	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	8	no	—
437	C₂²×C₄	—	2	8	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
447	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
448	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
450	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
452	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
453	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
455	M₁₆	—	2	4	no	—
456	M₁₆	—	2	4	no	—
457	M₁₆	—	4	4	no	—
458	C₂×C₈	—	2	4	no	—
459	C₂×C₈	—	4	4	no	—
460	C₄⋊C₄	—	4	2	no	—
461	C₂²⋊C₄	—	4	8	no	—
462	C₂²⋊C₄	—	4	2	no	—
463	C₄²	—	2	4	no	—
464	C₄²	—	2	4	no	—
465	C₄²	—	4	2	no	—
466	C₂³	—	2	16	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	8	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	8	4	no	—
474	C₂³	—	8	8	no	—
475	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
476	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
477	C₂³	C₁₉×#120	1	2	yes	—
478	C₂³	C₁₉×#120	1	2	yes	—
479	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
480	Q₈	—	2	16	no	—
481	Q₈	—	2	8	no	—
482	Q₈	—	2	8	no	—
483	Q₈	—	2	4	no	—
484	Q₈	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
485	D₄	—	2	32	no	—
486	D₄	—	2	16	no	—
487	D₄	—	2	16	no	—
488	D₄	—	2	16	no	—
489	D₄	—	2	8	no	—
490	D₄	—	2	8	no	—
491	D₄	—	2	8	no	—
492	D₄	—	2	8	no	—
493	D₄	—	2	4	no	—
494	D₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
495	C₂×C₄	—	2	16	no	—
496	C₂×C₄	—	2	32	no	—
497	C₂×C₄	—	2	8	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	16	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	8	no	—
505	C₂×C₄	—	2	8	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	8	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
513	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
514	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
515	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
516	C₂×C₄	C₁₉×#120	1	2	yes	—
517	C₂×C₄	C₁₉×#120	1	2	yes	—
518	C₂×C₄	C₁₉×#120	1	4	yes	—
519	C₂×C₄	C₁₉×#120	1	4	yes	—
520	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
522	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
523	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
524	C₈	—	4	4	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	8	no	—
529	C₂²	—	2	8	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	8	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	8	2	no	—
535	C₂²	—	8	8	no	—
536	C₂²	—	8	16	no	—
537	C₂²	C₁₉×#379	1	4	yes	—
538	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
539	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
540	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
541	C₄	—	2	8	no	—
542	C₄	—	2	4	no	—
543	C₄	—	4	4	no	—
544	C₄	—	8	2	no	—
545	C₄	C₁₉×#379	1	4	yes	—
546	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
547	C₄	C₂×C₁₉×#120	1	2	yes	—
548	C₂	—	2	1	no	—
549	C₂	—	2	1	no	—
550	C₂	—	2	4	no	—
551	C₂	—	4	4	no	—
552	C₂	—	4	8	no	—
553	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
554	C₂	C₁₉×#2901	1	2	yes	—

	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×C₂²⋊C₄
prime radical	C₂×C₁₉×#585	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#421	C₂	semidirect
3. C₂²×C₁₉×#104	C₂	semidirect
4. C₁₉×#2879	C₂	semidirect
5. C₁₉×#2297	C₂	semidirect
6. C₁₉×#1789	C₂	semidirect
10. C₂×C₁₉×2₋¹⁺⁴	C₄	semidirect
13. C₂×C₁₉×H(5,𝔽₂)	C₄	semidirect
18. C₂²×M₁₆×C₁₉	C₂²	semidirect
19. C₂×C₁₉×#117	C₂²	semidirect
20. C₂²×C₄²×C₁₉	C₂²	semidirect
23. C₂×C₁₉×#104	C₂²	semidirect
24. C₂×C₁₉×#104	C₂²	semidirect
26. C₁₉×#407	C₂²	semidirect
30. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
58. C₂×#41×C₁₉	C₂×C₄	semidirect
65. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
72. C₂²×D₄×C₁₉	C₂×C₄	semidirect
120. #41×C₁₉	C₂²⋊C₄	semidirect
131. C₂×Q₈×C₁₉	C₂²⋊C₄	semidirect
152. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
188. #20606	C₁₉	direct (N × H)
249. C₂×#421	C₂×C₁₉	semidirect
250. C₂²×#104	C₂×C₁₉	semidirect
251. #2879	C₂×C₁₉	semidirect
252. #2297	C₂×C₁₉	semidirect
253. #1789	C₂×C₁₉	semidirect
280. C₂×2₋¹⁺⁴	C₄×C₁₉	semidirect
283. C₂×H(5,𝔽₂)	C₄×C₁₉	semidirect
288. C₂²×M₁₆	C₂²×C₁₉	semidirect
289. C₂×#117	C₂²×C₁₉	semidirect
290. C₂²×C₄²	C₂²×C₁₉	semidirect
293. C₂×#104	C₂²×C₁₉	semidirect
294. C₂×#104	C₂²×C₁₉	semidirect
296. #407	C₂²×C₁₉	semidirect
300. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
335. C₂×#41	C₂×C₄×C₁₉	semidirect
342. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
349. C₂²×D₄	C₂×C₄×C₁₉	semidirect
374. C₁₉	#20606	direct (N × H)
398. #41	C₂²⋊C₄×C₁₉	semidirect
409. C₂×Q₈	C₂²⋊C₄×C₁₉	semidirect
430. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#585	2
C₂×C₁₉×#421	2
C₂²×C₁₉×#104	2
C₁₉×#2879	2
C₁₉×#2297	2
C₁₉×#1789	2
#20606	19

Subgroups — C19×#20606 #18026565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20606 #18026565