Subgroups — C₁₉×#34360 #18040319

Order 4864.

2714 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#525	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2376	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2358	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2352	C₂	1	4	yes	maximal, complemented
5	D₄×C₄⋊C₄×C₁₉	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2329	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2325	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2314	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2311	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₉×#380	C₂	1	2	yes	maximal, complemented
11	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#525	C₄	1	16	yes	complemented
14	C₂×C₁₉×#123	C₂²	1	2	yes	—
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₉×#121	C₂²	1	2	yes	—
17	C₂×C₁₉×#120	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
26	C₁₉×#391	C₂²	1	4	yes	complemented
27	C₁₉×#390	C₂²	1	4	yes	—
28	C₁₉×#389	C₂²	1	8	yes	complemented
29	C₁₉×#388	C₂²	1	8	yes	—
30	C₁₉×#388	C₂²	1	8	yes	complemented
31	C₁₉×#387	C₂²	1	8	yes	complemented
32	C₁₉×#387	C₂²	1	8	yes	complemented
33	C₁₉×#386	C₂²	1	4	yes	—
34	C₁₉×#386	C₂²	1	8	yes	—
35	C₁₉×#386	C₂²	1	4	yes	complemented
36	C₁₉×#385	C₂²	1	8	yes	—
37	C₁₉×#385	C₂²	1	8	yes	complemented
38	C₁₉×#384	C₂²	1	2	yes	complemented
39	C₁₉×#382	C₂²	1	2	yes	complemented
40	C₁₉×#380	C₂²	1	4	yes	—
41	C₁₉×#380	C₂²	1	4	yes	—
42	C₁₉×#380	C₂²	1	4	yes	—
43	C₁₉×#380	C₂²	1	4	yes	—
44	C₁₉×#380	C₂²	1	4	yes	complemented
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
46	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
47	C₂×C₁₉×#95	C₂²	1	4	yes	—
48	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×#41×C₁₉	—	4	2	no	—
50	C₂×#41×C₁₉	—	4	2	no	—
51	C₂×#41×C₁₉	C₂×C₄	1	8	yes	complemented
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
54	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
55	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₉	—	4	2	no	—
57	C₂³×C₄×C₁₉	—	4	2	no	—
58	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	complemented
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
64	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₁₉×#123	C₂×C₄	1	16	yes	complemented
68	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
69	C₁₉×#121	C₂×C₄	1	16	yes	complemented
70	C₁₉×#120	C₂×C₄	1	16	yes	complemented
71	C₄×D₄×C₁₉	—	4	16	no	—
72	C₄×D₄×C₁₉	C₂×C₄	1	32	yes	complemented
73	C₁₉×#117	—	4	4	no	—
74	C₁₉×#117	C₂×C₄	1	8	yes	complemented
75	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
76	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
77	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
95	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
96	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
97	C₁₉×#95	C₂³	1	8	yes	—
98	C₁₉×#95	C₂³	1	8	yes	—
99	C₁₉×#95	C₂³	1	8	yes	—
100	C₁₉×#95	C₂³	1	8	yes	—
101	C₁₉×#95	C₂³	1	8	yes	—
102	C₂⁴×C₁₉	—	2	4	no	—
103	C₂⁴×C₁₉	—	2	4	no	—
104	C₂⁴×C₁₉	—	4	1	no	—
105	C₂⁴×C₁₉	—	4	1	no	—
106	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
107	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
108	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
109	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
110	#41×C₁₉	—	4	16	no	—
111	C₂×Q₈×C₁₉	—	4	1	no	—
112	C₂×Q₈×C₁₉	—	4	1	no	—
113	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
114	C₂×D₄×C₁₉	—	2	8	no	—
115	C₂×D₄×C₁₉	—	2	8	no	—
116	C₂×D₄×C₁₉	—	4	2	no	—
117	C₂×D₄×C₁₉	—	4	2	no	—
118	C₂×D₄×C₁₉	—	4	1	no	—
119	C₂×D₄×C₁₉	—	4	1	no	—
120	C₂×D₄×C₁₉	C₂²×C₄	1	16	yes	—
121	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
122	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₁₉	—	2	4	no	—
124	C₂²×C₄×C₁₉	—	2	4	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	4	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	8	no	—
130	C₂²×C₄×C₁₉	—	2	8	no	—
131	C₂²×C₄×C₁₉	—	4	16	no	—
132	C₂²×C₄×C₁₉	—	4	1	no	—
133	C₂²×C₄×C₁₉	—	4	1	no	—
134	C₂²×C₄×C₁₉	—	4	2	no	—
135	C₂²×C₄×C₁₉	—	4	2	no	—
136	C₂²×C₄×C₁₉	—	4	4	no	—
137	C₂²×C₄×C₁₉	—	4	4	no	—
138	C₂²×C₄×C₁₉	—	4	4	no	—
139	C₂²×C₄×C₁₉	—	4	4	no	—
140	C₂²×C₄×C₁₉	—	4	4	no	—
141	C₂²×C₄×C₁₉	—	4	8	no	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
144	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
145	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
146	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
149	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
154	C₄⋊C₄×C₁₉	—	2	8	no	—
155	C₄⋊C₄×C₁₉	—	2	8	no	—
156	C₄⋊C₄×C₁₉	—	4	4	no	—
157	C₄⋊C₄×C₁₉	—	4	4	no	—
158	C₄⋊C₄×C₁₉	—	4	4	no	—
159	C₄⋊C₄×C₁₉	—	4	8	no	—
160	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
161	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
162	C₂²⋊C₄×C₁₉	—	2	16	no	—
163	C₂²⋊C₄×C₁₉	—	4	8	no	—
164	C₂²⋊C₄×C₁₉	—	4	4	no	—
165	C₂²⋊C₄×C₁₉	—	4	8	no	—
166	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
167	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
168	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
169	C₄²×C₁₉	—	4	4	no	—
170	C₄²×C₁₉	—	4	8	no	—
171	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
172	#34360	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	2	16	no	—
178	C₂³×C₁₉	—	2	2	no	—
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	2	4	no	—
181	C₂³×C₁₉	—	2	2	no	—
182	C₂³×C₁₉	—	2	1	no	—
183	C₂³×C₁₉	—	2	1	no	—
184	C₂³×C₁₉	—	2	4	no	—
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	4	4	no	—
187	C₂³×C₁₉	—	4	8	no	—
188	C₂³×C₁₉	—	4	4	no	—
189	C₂³×C₁₉	—	4	4	no	—
190	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
191	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
192	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
193	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
194	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
195	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
196	Q₈×C₁₉	—	4	4	no	—
197	D₄×C₁₉	—	2	32	no	—
198	D₄×C₁₉	—	4	4	no	—
199	D₄×C₁₉	—	4	8	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	16	no	—
209	C₂×C₄×C₁₉	—	2	8	no	—
210	C₂×C₄×C₁₉	—	2	16	no	—
211	C₂×C₄×C₁₉	—	2	8	no	—
212	C₂×C₄×C₁₉	—	2	8	no	—
213	C₂×C₄×C₁₉	—	2	8	no	—
214	C₂×C₄×C₁₉	—	2	8	no	—
215	C₂×C₄×C₁₉	—	2	8	no	—
216	C₂×C₄×C₁₉	—	2	8	no	—
217	C₂×C₄×C₁₉	—	4	4	no	—
218	C₂×C₄×C₁₉	—	4	8	no	—
219	C₂×C₄×C₁₉	—	8	8	no	—
220	C₂×C₄×C₁₉	—	8	8	no	—
221	C₂×C₄×C₁₉	—	8	8	no	—
222	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
223	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
224	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
225	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
226	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
227	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
228	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
229	C₂×#525	C₂×C₁₉	1	1	yes	characteristic
230	#2376	C₂×C₁₉	1	4	yes	complemented
231	#2358	C₂×C₁₉	1	4	yes	complemented
232	#2352	C₂×C₁₉	1	4	yes	complemented
233	D₄×C₄⋊C₄	C₂×C₁₉	1	4	yes	complemented
234	#2329	C₂×C₁₉	1	4	yes	complemented
235	#2325	C₂×C₁₉	1	4	yes	complemented
236	#2314	C₂×C₁₉	1	2	yes	complemented
237	#2311	C₂×C₁₉	1	2	yes	complemented
238	C₂×#380	C₂×C₁₉	1	2	yes	complemented
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	—	2	4	no	—
245	C₂²×C₁₉	—	2	2	no	—
246	C₂²×C₁₉	—	2	4	no	—
247	C₂²×C₁₉	—	2	8	no	—
248	C₂²×C₁₉	—	2	4	no	—
249	C₂²×C₁₉	—	4	16	no	—
250	C₂²×C₁₉	—	4	4	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	1	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	—	4	1	no	—
256	C₂²×C₁₉	#520	1	8	yes	—
257	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
258	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
259	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
260	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
261	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
262	C₄×C₁₉	—	2	4	no	—
263	C₄×C₁₉	—	2	2	no	—
264	C₄×C₁₉	—	2	4	no	—
265	C₄×C₁₉	—	2	8	no	—
266	C₄×C₁₉	—	4	8	no	—
267	C₄×C₁₉	—	4	8	no	—
268	C₄×C₁₉	#518	1	4	yes	—
269	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
270	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
271	#525	C₄×C₁₉	1	16	yes	complemented
272	C₂×#123	C₂²×C₁₉	1	2	yes	—
273	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
274	C₂×#121	C₂²×C₁₉	1	2	yes	—
275	C₂×#120	C₂²×C₁₉	1	2	yes	—
276	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	—
277	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
278	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
280	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
281	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
282	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
283	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
284	#391	C₂²×C₁₉	1	4	yes	complemented
285	#390	C₂²×C₁₉	1	4	yes	—
286	#389	C₂²×C₁₉	1	8	yes	complemented
287	#388	C₂²×C₁₉	1	8	yes	—
288	#388	C₂²×C₁₉	1	8	yes	complemented
289	#387	C₂²×C₁₉	1	8	yes	complemented
290	#387	C₂²×C₁₉	1	8	yes	complemented
291	#386	C₂²×C₁₉	1	4	yes	—
292	#386	C₂²×C₁₉	1	8	yes	—
293	#386	C₂²×C₁₉	1	4	yes	complemented
294	#385	C₂²×C₁₉	1	8	yes	—
295	#385	C₂²×C₁₉	1	8	yes	complemented
296	#384	C₂²×C₁₉	1	2	yes	complemented
297	#382	C₂²×C₁₉	1	2	yes	complemented
298	#380	C₂²×C₁₉	1	4	yes	—
299	#380	C₂²×C₁₉	1	4	yes	—
300	#380	C₂²×C₁₉	1	4	yes	—
301	#380	C₂²×C₁₉	1	4	yes	—
302	#380	C₂²×C₁₉	1	4	yes	complemented
303	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
304	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
305	C₂×#95	C₂²×C₁₉	1	4	yes	—
306	C₂×C₁₉	—	2	8	no	—
307	C₂×C₁₉	—	4	4	no	—
308	C₂×C₁₉	—	4	2	no	—
309	C₂×C₁₉	C₂×#518	1	1	yes	characteristic
310	C₂×C₁₉	C₂×#520	1	2	yes	—
311	C₂×C₁₉	#3536	1	2	yes	—
312	C₂×C₁₉	#3537	1	1	yes	characteristic
313	C₂×C₁₉	#3538	1	1	yes	characteristic
314	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
315	C₂×#41	—	4	2	no	—
316	C₂×#41	—	4	2	no	—
317	C₂×#41	C₂×C₄×C₁₉	1	8	yes	complemented
318	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
319	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
320	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
321	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
322	C₂³×C₄	—	4	2	no	—
323	C₂³×C₄	—	4	2	no	—
324	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	complemented
325	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
326	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
327	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
328	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
329	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
330	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
331	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
332	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
333	#123	C₂×C₄×C₁₉	1	16	yes	complemented
334	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
335	#121	C₂×C₄×C₁₉	1	16	yes	complemented
336	#120	C₂×C₄×C₁₉	1	16	yes	complemented
337	C₄×D₄	—	4	16	no	—
338	C₄×D₄	C₂×C₄×C₁₉	1	32	yes	complemented
339	#117	—	4	4	no	—
340	#117	C₂×C₄×C₁₉	1	8	yes	complemented
341	C₂×C₄⋊C₄	—	4	4	no	—
342	C₂×C₄⋊C₄	—	4	4	no	—
343	C₂×C₄⋊C₄	—	4	4	no	—
344	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
352	C₂×C₂²⋊C₄	—	4	8	no	—
353	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
360	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
361	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
362	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
363	#95	C₂³×C₁₉	1	8	yes	—
364	#95	C₂³×C₁₉	1	8	yes	—
365	#95	C₂³×C₁₉	1	8	yes	—
366	#95	C₂³×C₁₉	1	8	yes	—
367	#95	C₂³×C₁₉	1	8	yes	—
368	C₁₉	#34360	1	1	yes	characteristic, direct product factor, Sylow
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	2	4	no	—
371	C₂⁴	—	4	1	no	—
372	C₂⁴	—	4	1	no	—
373	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
374	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
375	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
376	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
377	#41	—	4	16	no	—
378	C₂×Q₈	—	4	1	no	—
379	C₂×Q₈	—	4	1	no	—
380	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
381	C₂×D₄	—	2	8	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	—	4	1	no	—
387	C₂×D₄	C₂²×C₄×C₁₉	1	16	yes	—
388	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
389	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	8	no	—
397	C₂²×C₄	—	2	8	no	—
398	C₂²×C₄	—	4	16	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	4	no	—
404	C₂²×C₄	—	4	4	no	—
405	C₂²×C₄	—	4	4	no	—
406	C₂²×C₄	—	4	4	no	—
407	C₂²×C₄	—	4	4	no	—
408	C₂²×C₄	—	4	8	no	—
409	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
410	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
411	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
412	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
413	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
415	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
416	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	4	4	no	—
424	C₄⋊C₄	—	4	4	no	—
425	C₄⋊C₄	—	4	4	no	—
426	C₄⋊C₄	—	4	8	no	—
427	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
428	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
429	C₂²⋊C₄	—	2	16	no	—
430	C₂²⋊C₄	—	4	8	no	—
431	C₂²⋊C₄	—	4	4	no	—
432	C₂²⋊C₄	—	4	8	no	—
433	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
434	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
435	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
436	C₄²	—	4	4	no	—
437	C₄²	—	4	8	no	—
438	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	16	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	4	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	4	8	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	4	no	—
456	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
457	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
458	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
459	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
460	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
461	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
462	Q₈	—	4	4	no	—
463	D₄	—	2	32	no	—
464	D₄	—	4	4	no	—
465	D₄	—	4	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	8	no	—
475	C₂×C₄	—	2	16	no	—
476	C₂×C₄	—	2	16	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	4	8	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	8	8	no	—
486	C₂×C₄	—	8	8	no	—
487	C₂×C₄	—	8	8	no	—
488	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
489	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
490	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
491	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
492	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
493	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
494	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	8	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	4	16	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	C₁₉×#520	1	8	yes	—
513	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
514	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
517	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
518	C₄	—	2	2	no	—
519	C₄	—	2	4	no	—
520	C₄	—	2	4	no	—
521	C₄	—	2	8	no	—
522	C₄	—	4	8	no	—
523	C₄	—	4	8	no	—
524	C₄	C₁₉×#518	1	4	yes	—
525	C₂	—	2	8	no	—
526	C₂	—	4	2	no	—
527	C₂	—	4	4	no	—
528	C₂	C₂×C₁₉×#518	1	1	yes	characteristic
529	C₂	C₂×C₁₉×#520	1	2	yes	—
530	C₂	C₁₉×#3536	1	2	yes	—
531	C₂	C₁₉×#3537	1	1	yes	characteristic
532	C₂	C₁₉×#3538	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂×C₁₉×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2376	C₂	semidirect
3. C₁₉×#2358	C₂	semidirect
4. C₁₉×#2352	C₂	semidirect
5. D₄×C₄⋊C₄×C₁₉	C₂	semidirect
6. C₁₉×#2329	C₂	semidirect
7. C₁₉×#2325	C₂	semidirect
8. C₁₉×#2314	C₂	semidirect
9. C₁₉×#2311	C₂	semidirect
10. C₂×C₁₉×#380	C₂	semidirect
13. C₁₉×#525	C₄	semidirect
21. C₂×C₁₉×#117	C₂²	semidirect
24. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
26. C₁₉×#391	C₂²	semidirect
28. C₁₉×#389	C₂²	semidirect
30. C₁₉×#388	C₂²	semidirect
31. C₁₉×#387	C₂²	semidirect
32. C₁₉×#387	C₂²	semidirect
35. C₁₉×#386	C₂²	semidirect
37. C₁₉×#385	C₂²	semidirect
38. C₁₉×#384	C₂²	semidirect
39. C₁₉×#382	C₂²	semidirect
44. C₁₉×#380	C₂²	semidirect
45. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
51. C₂×#41×C₁₉	C₂×C₄	semidirect
58. C₂³×C₄×C₁₉	C₂×C₄	semidirect
67. C₁₉×#123	C₂×C₄	semidirect
68. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
69. C₁₉×#121	C₂×C₄	semidirect
70. C₁₉×#120	C₂×C₄	semidirect
72. C₄×D₄×C₁₉	C₂×C₄	semidirect
74. C₁₉×#117	C₂×C₄	semidirect
172. #34360	C₁₉	direct (N × H)
230. #2376	C₂×C₁₉	semidirect
231. #2358	C₂×C₁₉	semidirect
232. #2352	C₂×C₁₉	semidirect
233. D₄×C₄⋊C₄	C₂×C₁₉	semidirect
234. #2329	C₂×C₁₉	semidirect
235. #2325	C₂×C₁₉	semidirect
236. #2314	C₂×C₁₉	semidirect
237. #2311	C₂×C₁₉	semidirect
238. C₂×#380	C₂×C₁₉	semidirect
271. #525	C₄×C₁₉	semidirect
279. C₂×#117	C₂²×C₁₉	semidirect
282. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
284. #391	C₂²×C₁₉	semidirect
286. #389	C₂²×C₁₉	semidirect
288. #388	C₂²×C₁₉	semidirect
289. #387	C₂²×C₁₉	semidirect
290. #387	C₂²×C₁₉	semidirect
293. #386	C₂²×C₁₉	semidirect
295. #385	C₂²×C₁₉	semidirect
296. #384	C₂²×C₁₉	semidirect
297. #382	C₂²×C₁₉	semidirect
302. #380	C₂²×C₁₉	semidirect
303. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
317. C₂×#41	C₂×C₄×C₁₉	semidirect
324. C₂³×C₄	C₂×C₄×C₁₉	semidirect
333. #123	C₂×C₄×C₁₉	semidirect
334. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
335. #121	C₂×C₄×C₁₉	semidirect
336. #120	C₂×C₄×C₁₉	semidirect
338. C₄×D₄	C₂×C₄×C₁₉	semidirect
340. #117	C₂×C₄×C₁₉	semidirect
368. C₁₉	#34360	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#525	2
C₁₉×#2376	2
C₁₉×#2358	2
C₁₉×#2352	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2329	2
C₁₉×#2325	2
C₁₉×#2314	2
C₁₉×#2311	2
C₂×C₁₉×#380	2
#34360	19

Subgroups — C19×#34360 #18040319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34360 #18040319