Subgroups — C₁₉×#23116 #18029075

Order 4864.

1076 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₉	C₂	1	2	yes	maximal, complemented
2	C₄×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1923	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1916	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1869	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1869	C₂	1	2	yes	maximal, complemented
7	C₈×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
12	C₂×C₁₉×#121	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₈×D₄×C₁₉	—	2	8	no	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
25	C₁₉×#390	C₄	1	1	yes	characteristic
26	C₁₉×#389	C₄	1	1	yes	characteristic
27	C₁₉×#388	C₄	1	2	yes	—
28	C₁₉×#386	C₄	1	2	yes	—
29	C₁₉×#380	C₄	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
32	C₁₉×#336	C₂²	1	2	yes	—
33	C₁₉×#336	C₂²	1	2	yes	—
34	C₁₉×#336	C₂²	1	2	yes	—
35	C₁₉×#336	C₂²	1	2	yes	—
36	C₁₉×#336	C₂²	1	1	yes	characteristic
37	C₁₉×#336	C₂²	1	1	yes	characteristic
38	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
39	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₉	—	2	4	no	—
45	C₂²×C₈×C₁₉	—	2	4	no	—
46	C₂²×C₈×C₁₉	—	2	4	no	—
47	C₂²×C₈×C₁₉	—	2	4	no	—
48	C₂²×C₈×C₁₉	—	4	2	no	—
49	C₂²×C₈×C₁₉	—	4	2	no	—
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
54	C₁₉×#121	C₈	1	8	yes	complemented
55	C₄×D₄×C₁₉	—	2	4	no	—
56	C₄×D₄×C₁₉	—	2	4	no	—
57	C₄×D₄×C₁₉	—	4	2	no	—
58	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₉	—	4	2	no	—
68	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×C₄⋊C₈	—	2	4	no	—
74	C₁₉×C₂²⋊C₈	—	2	2	no	—
75	C₁₉×C₂²⋊C₈	—	2	4	no	—
76	C₁₉×C₂²⋊C₈	—	2	4	no	—
77	C₁₉×C₂²⋊C₈	—	4	2	no	—
78	C₁₉×C₂²⋊C₈	D₄	1	4	yes	complemented
79	C₄×C₈×C₁₉	—	2	4	no	—
80	C₄×C₈×C₁₉	—	4	2	no	—
81	C₁₉×#95	C₂×C₄	1	2	yes	—
82	C₁₉×#95	C₂×C₄	1	2	yes	—
83	C₁₉×#95	C₂×C₄	1	2	yes	—
84	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	C₂×C₈	1	8	yes	complemented
91	C₂×D₄×C₁₉	C₂×C₈	1	4	yes	complemented
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	C₂×C₈	1	4	yes	complemented
106	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₉	#41	1	2	yes	—
116	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	4	8	no	—
128	C₂×C₈×C₁₉	—	4	8	no	—
129	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
130	C₂×C₈×C₁₉	#41	1	4	yes	—
131	C₄⋊C₄×C₁₉	—	2	4	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	—	4	1	no	—
134	C₄⋊C₄×C₁₉	C₂×C₈	1	4	yes	complemented
135	C₂²⋊C₄×C₁₉	—	2	4	no	—
136	C₂²⋊C₄×C₁₉	—	2	4	no	—
137	C₂²⋊C₄×C₁₉	—	2	4	no	—
138	C₂²⋊C₄×C₁₉	—	4	2	no	—
139	C₂²⋊C₄×C₁₉	C₂×C₈	1	8	yes	complemented
140	C₄²×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	—	2	2	no	—
142	C₄²×C₁₉	—	2	2	no	—
143	C₄²×C₁₉	—	2	2	no	—
144	C₄²×C₁₉	—	4	1	no	—
145	C₄²×C₁₉	—	4	1	no	—
146	#23116	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	1	no	—
150	C₂³×C₁₉	—	2	1	no	—
151	C₂³×C₁₉	—	2	2	no	—
152	C₂³×C₁₉	—	2	2	no	—
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	C₄×D₄	1	2	yes	—
158	C₂³×C₁₉	C₂²×C₈	1	4	yes	—
159	C₂³×C₁₉	C₂²×C₈	1	2	yes	—
160	C₂³×C₁₉	#131	1	2	yes	—
161	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
162	D₄×C₁₉	—	2	16	no	—
163	D₄×C₁₉	—	4	4	no	—
164	C₂×C₄×C₁₉	—	2	2	no	—
165	C₂×C₄×C₁₉	—	2	1	no	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	1	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	2	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	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
193	C₂×C₄×C₁₉	C₂²×C₈	1	4	yes	—
194	C₂×C₄×C₁₉	C₂²×C₈	1	2	yes	—
195	C₂×C₄×C₁₉	#131	1	2	yes	—
196	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
200	C₈×C₁₉	—	2	4	no	—
201	C₈×C₁₉	—	2	4	no	—
202	C₈×C₁₉	—	4	2	no	—
203	C₈×C₁₉	—	4	2	no	—
204	C₂×C₈×D₄	C₂×C₁₉	1	2	yes	complemented
205	C₄×#121	C₂×C₁₉	1	1	yes	characteristic
206	#1923	C₂×C₁₉	1	2	yes	complemented
207	#1916	C₂×C₁₉	1	2	yes	complemented
208	#1869	C₂×C₁₉	1	2	yes	complemented
209	#1869	C₂×C₁₉	1	2	yes	complemented
210	C₈×C₂²⋊C₄	C₂×C₁₉	1	2	yes	complemented
211	C₄×C₂²⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
212	C₂×#336	C₂×C₁₉	1	1	yes	characteristic, complemented
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	—	2	2	no	—
217	C₂²×C₁₉	—	2	2	no	—
218	C₂²×C₁₉	—	2	2	no	—
219	C₂²×C₁₉	—	2	4	no	—
220	C₂²×C₁₉	—	2	4	no	—
221	C₂²×C₁₉	—	2	4	no	—
222	C₂²×C₁₉	—	4	2	no	—
223	C₂²×C₁₉	—	4	2	no	—
224	C₂²×C₁₉	—	4	2	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	C₈×D₄	1	4	yes	—
227	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
229	C₂²×C₁₉	#518	1	1	yes	characteristic
230	C₂²×C₁₉	C₂³×C₈	1	1	yes	characteristic
231	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
232	C₂²×C₁₉	C₂×#131	1	1	yes	characteristic
233	C₂²×C₁₉	#568	1	1	yes	characteristic
234	C₄×C₁₉	—	2	2	no	—
235	C₄×C₁₉	—	2	4	no	—
236	C₄×C₁₉	—	2	2	no	—
237	C₄×C₁₉	—	2	2	no	—
238	C₄×C₁₉	—	2	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	1	no	—
242	C₄×C₁₉	#546	1	2	yes	—
243	C₄×C₁₉	#553	1	2	yes	—
244	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
245	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
246	C₂×#121	C₄×C₁₉	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
248	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
249	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
250	C₈×D₄	—	2	8	no	—
251	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
252	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
254	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
255	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
256	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
258	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
259	#390	C₄×C₁₉	1	1	yes	characteristic
260	#389	C₄×C₁₉	1	1	yes	characteristic
261	#388	C₄×C₁₉	1	2	yes	—
262	#386	C₄×C₁₉	1	2	yes	—
263	#380	C₄×C₁₉	1	1	yes	characteristic
264	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
265	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
266	#336	C₂²×C₁₉	1	2	yes	—
267	#336	C₂²×C₁₉	1	2	yes	—
268	#336	C₂²×C₁₉	1	2	yes	—
269	#336	C₂²×C₁₉	1	2	yes	—
270	#336	C₂²×C₁₉	1	1	yes	characteristic
271	#336	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×C₁₉	—	2	4	no	—
273	C₂×C₁₉	—	4	4	no	—
274	C₂×C₁₉	#2364	1	1	yes	characteristic
275	C₂×C₁₉	C₂×C₈×D₄	1	1	yes	characteristic
276	C₂×C₁₉	#2935	1	1	yes	characteristic
277	C₂×C₁₉	C₈×#41	1	1	yes	characteristic
278	C₂×C₁₉	#2968	1	1	yes	characteristic
279	C₂×C₁₉	#2972	1	1	yes	characteristic
280	C₂×C₁₉	#2977	1	1	yes	characteristic
281	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
282	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
283	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
284	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
286	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂²×C₈	—	2	4	no	—
288	C₂²×C₈	—	2	4	no	—
289	C₂²×C₈	—	2	4	no	—
290	C₂²×C₈	—	2	4	no	—
291	C₂²×C₈	—	4	2	no	—
292	C₂²×C₈	—	4	2	no	—
293	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
295	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
296	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
297	#121	C₈×C₁₉	1	8	yes	complemented
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	4	no	—
300	C₄×D₄	—	4	2	no	—
301	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
302	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
308	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
309	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
310	C₂×C₄²	—	4	2	no	—
311	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
312	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
315	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
316	C₄⋊C₈	—	2	4	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	—	2	4	no	—
319	C₂²⋊C₈	—	2	4	no	—
320	C₂²⋊C₈	—	4	2	no	—
321	C₂²⋊C₈	D₄×C₁₉	1	4	yes	complemented
322	C₄×C₈	—	2	4	no	—
323	C₄×C₈	—	4	2	no	—
324	#95	C₂×C₄×C₁₉	1	2	yes	—
325	#95	C₂×C₄×C₁₉	1	2	yes	—
326	#95	C₂×C₄×C₁₉	1	2	yes	—
327	C₁₉	#23116	1	1	yes	characteristic, direct product factor, Sylow
328	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
329	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	C₂×C₈×C₁₉	1	8	yes	complemented
335	C₂×D₄	C₂×C₈×C₁₉	1	4	yes	complemented
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	C₂×C₈×C₁₉	1	4	yes	complemented
350	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
353	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
356	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
357	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
359	C₂²×C₄	#41×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	8	no	—
372	C₂×C₈	—	4	8	no	—
373	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
374	C₂×C₈	#41×C₁₉	1	4	yes	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	C₂×C₈×C₁₉	1	4	yes	complemented
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	C₂×C₈×C₁₉	1	8	yes	complemented
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	4	1	no	—
389	C₄²	—	4	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	C₄×D₄×C₁₉	1	2	yes	—
401	C₂³	C₂²×C₈×C₁₉	1	4	yes	—
402	C₂³	C₂²×C₈×C₁₉	1	2	yes	—
403	C₂³	C₁₉×#131	1	2	yes	—
404	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
405	D₄	—	2	16	no	—
406	D₄	—	4	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
435	C₂×C₄	C₂²×C₈×C₁₉	1	2	yes	—
436	C₂×C₄	C₂²×C₈×C₁₉	1	4	yes	—
437	C₂×C₄	C₂²×C₈×C₁₉	1	2	yes	—
438	C₂×C₄	C₁₉×#131	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
441	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
442	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
443	C₈	—	2	4	no	—
444	C₈	—	2	4	no	—
445	C₈	—	4	2	no	—
446	C₈	—	4	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	C₈×D₄×C₁₉	1	4	yes	—
461	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
462	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
463	C₂²	C₁₉×#518	1	1	yes	characteristic
464	C₂²	C₂³×C₈×C₁₉	1	1	yes	characteristic
465	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
466	C₂²	C₂×C₁₉×#131	1	1	yes	characteristic
467	C₂²	C₁₉×#568	1	1	yes	characteristic
468	C₄	—	2	4	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	C₁₉×#546	1	2	yes	—
477	C₄	C₁₉×#553	1	2	yes	—
478	C₂	—	2	4	no	—
479	C₂	—	4	4	no	—
480	C₂	C₁₉×#2364	1	1	yes	characteristic
481	C₂	C₂×C₈×D₄×C₁₉	1	1	yes	characteristic
482	C₂	C₁₉×#2935	1	1	yes	characteristic
483	C₂	C₈×#41×C₁₉	1	1	yes	characteristic
484	C₂	C₁₉×#2968	1	1	yes	characteristic
485	C₂	C₁₉×#2972	1	1	yes	characteristic
486	C₂	C₁₉×#2977	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂³×C₁₉	C₂³×C₄
prime radical	C₂×C₁₉×#121	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×D₄×C₁₉	C₂	semidirect
3. C₁₉×#1923	C₂	semidirect
4. C₁₉×#1916	C₂	semidirect
5. C₁₉×#1869	C₂	semidirect
6. C₁₉×#1869	C₂	semidirect
7. C₈×C₂²⋊C₄×C₁₉	C₂	semidirect
8. C₄×C₁₉×C₂²⋊C₈	C₂	semidirect
9. C₂×C₁₉×#336	C₂	semidirect
54. C₁₉×#121	C₈	semidirect
78. C₁₉×C₂²⋊C₈	D₄	semidirect
90. C₂×D₄×C₁₉	C₂×C₈	semidirect
91. C₂×D₄×C₁₉	C₂×C₈	semidirect
105. C₂²×C₄×C₁₉	C₂×C₈	semidirect
134. C₄⋊C₄×C₁₉	C₂×C₈	semidirect
139. C₂²⋊C₄×C₁₉	C₂×C₈	semidirect
146. #23116	C₁₉	direct (N × H)
204. C₂×C₈×D₄	C₂×C₁₉	semidirect
206. #1923	C₂×C₁₉	semidirect
207. #1916	C₂×C₁₉	semidirect
208. #1869	C₂×C₁₉	semidirect
209. #1869	C₂×C₁₉	semidirect
210. C₈×C₂²⋊C₄	C₂×C₁₉	semidirect
211. C₄×C₂²⋊C₈	C₂×C₁₉	semidirect
212. C₂×#336	C₂×C₁₉	semidirect
297. #121	C₈×C₁₉	semidirect
321. C₂²⋊C₈	D₄×C₁₉	semidirect
327. C₁₉	#23116	direct (N × H)
334. C₂×D₄	C₂×C₈×C₁₉	semidirect
335. C₂×D₄	C₂×C₈×C₁₉	semidirect
349. C₂²×C₄	C₂×C₈×C₁₉	semidirect
378. C₄⋊C₄	C₂×C₈×C₁₉	semidirect
383. C₂²⋊C₄	C₂×C₈×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₁₉	2
C₄×C₁₉×#121	2
C₁₉×#1923	2
C₁₉×#1916	2
C₁₉×#1869	2
C₈×C₂²⋊C₄×C₁₉	2
C₄×C₁₉×C₂²⋊C₈	2
C₂×C₁₉×#336	2
#23116	19

Subgroups — C19×#23116 #18029075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23116 #18029075