Subgroups — C₁₉×#14136 #18020095

Order 4864.

2742 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	C₂²×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#390	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1438	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1437	C₂	1	4	yes	maximal, complemented
7	C₁₉×C₄⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#121	—	2	4	no	—
12	C₂×C₁₉×#121	—	2	4	no	—
13	C₂×C₁₉×#121	C₄	1	8	yes	complemented
14	C₂×C₁₉×#117	—	2	4	no	—
15	C₂×C₁₉×#117	—	2	8	no	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
21	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
24	C₁₉×#390	—	2	8	no	—
25	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
26	C₂×C₁₉×#95	C₂²	1	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	8	yes	—
28	C₂⁵×C₁₉	C₂³	1	2	yes	—
29	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×D₄×C₁₉	—	2	4	no	—
31	C₂²×D₄×C₁₉	—	2	4	no	—
32	C₂²×D₄×C₁₉	—	2	4	no	—
33	C₂²×D₄×C₁₉	—	2	2	no	—
34	C₂²×D₄×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	—	2	4	no	—
36	C₂²×D₄×C₁₉	—	4	8	no	—
37	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
38	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	—
39	C₂³×C₄×C₁₉	—	2	4	no	—
40	C₂³×C₄×C₁₉	—	2	4	no	—
41	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
42	C₂³×C₄×C₁₉	D₄	1	4	yes	—
43	C₂³×C₄×C₁₉	D₄	1	4	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₁₉×#121	—	2	32	no	—
50	C₁₉×#117	—	2	32	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	complemented
57	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
66	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
67	C₂×C₄²×C₁₉	—	2	8	no	—
68	C₂×C₄²×C₁₉	—	2	4	no	—
69	C₂×C₄²×C₁₉	—	2	4	no	—
70	C₂×C₄²×C₁₉	—	2	4	no	—
71	C₂×C₄²×C₁₉	—	2	4	no	—
72	C₁₉×#95	—	2	4	no	—
73	C₁₉×#95	—	4	8	no	—
74	C₂⁴×C₁₉	—	2	2	no	—
75	C₂⁴×C₁₉	—	2	4	no	—
76	C₂⁴×C₁₉	—	2	2	no	—
77	C₂⁴×C₁₉	—	2	4	no	—
78	C₂⁴×C₁₉	—	2	4	no	—
79	C₂⁴×C₁₉	—	2	2	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	—	2	8	no	—
82	C₂⁴×C₁₉	—	2	4	no	—
83	C₂⁴×C₁₉	—	2	8	no	—
84	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
85	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
86	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
87	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
88	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
89	C₂×D₄×C₁₉	—	2	16	no	—
90	C₂×D₄×C₁₉	—	2	8	no	—
91	C₂×D₄×C₁₉	—	2	16	no	—
92	C₂×D₄×C₁₉	—	4	16	no	—
93	C₂×D₄×C₁₉	—	4	16	no	—
94	C₂×D₄×C₁₉	—	4	16	no	—
95	C₂×D₄×C₁₉	—	4	4	no	—
96	C₂×D₄×C₁₉	—	4	8	no	—
97	C₂×D₄×C₁₉	—	4	4	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	16	no	—
101	C₂²×C₄×C₁₉	—	2	8	no	—
102	C₂²×C₄×C₁₉	—	2	16	no	—
103	C₂²×C₄×C₁₉	—	2	8	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	2	4	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	4	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	8	no	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	8	no	—
115	C₂²×C₄×C₁₉	—	2	8	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	C₂²⋊C₄	1	16	yes	complemented
118	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₉	#41	1	8	yes	—
128	C₂²×C₄×C₁₉	#41	1	4	yes	—
129	C₄⋊C₄×C₁₉	—	2	8	no	—
130	C₄⋊C₄×C₁₉	—	2	16	no	—
131	C₂²⋊C₄×C₁₉	—	2	16	no	—
132	C₂²⋊C₄×C₁₉	—	2	16	no	—
133	C₂²⋊C₄×C₁₉	—	2	16	no	—
134	C₂²⋊C₄×C₁₉	—	4	32	no	—
135	C₄²×C₁₉	—	2	16	no	—
136	C₄²×C₁₉	—	4	8	no	—
137	#14136	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	2	4	no	—
140	C₂³×C₁₉	—	2	4	no	—
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	4	no	—
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	2	4	no	—
145	C₂³×C₁₉	—	2	4	no	—
146	C₂³×C₁₉	—	2	4	no	—
147	C₂³×C₁₉	—	2	4	no	—
148	C₂³×C₁₉	—	2	4	no	—
149	C₂³×C₁₉	—	2	8	no	—
150	C₂³×C₁₉	—	2	8	no	—
151	C₂³×C₁₉	—	2	8	no	—
152	C₂³×C₁₉	—	4	4	no	—
153	C₂³×C₁₉	—	4	4	no	—
154	C₂³×C₁₉	—	4	4	no	—
155	C₂³×C₁₉	—	4	4	no	—
156	C₂³×C₁₉	—	4	2	no	—
157	C₂³×C₁₉	—	4	4	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	4	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	—	4	4	no	—
162	C₂³×C₁₉	—	4	4	no	—
163	C₂³×C₁₉	—	4	8	no	—
164	C₂³×C₁₉	—	4	8	no	—
165	C₂³×C₁₉	—	4	8	no	—
166	C₂³×C₁₉	—	4	8	no	—
167	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
168	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
169	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
170	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
171	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
172	C₂³×C₁₉	C₂×#41	1	2	yes	—
173	C₂³×C₁₉	C₂×#41	1	4	yes	—
174	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
175	D₄×C₁₉	—	4	32	no	—
176	D₄×C₁₉	—	4	16	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	32	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	2	8	no	—
184	C₂×C₄×C₁₉	—	2	8	no	—
185	C₂×C₄×C₁₉	—	2	8	no	—
186	C₂×C₄×C₁₉	—	2	8	no	—
187	C₂×C₄×C₁₉	—	2	16	no	—
188	C₂×C₄×C₁₉	—	2	8	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	4	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	4	4	no	—
196	C₂×C₄×C₁₉	—	4	8	no	—
197	C₂×C₄×C₁₉	—	4	4	no	—
198	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
199	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
200	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
201	C₂×C₄×C₁₉	#120	1	4	yes	—
202	C₂×C₄×C₁₉	#121	1	8	yes	—
203	C₂×C₄×C₁₉	#123	1	4	yes	—
204	C₂²×#121	C₂×C₁₉	1	1	yes	characteristic
205	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic, complemented
206	C₂×#390	C₂×C₁₉	1	2	yes	complemented
207	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#1438	C₂×C₁₉	1	4	yes	complemented
209	#1437	C₂×C₁₉	1	4	yes	complemented
210	C₄⋊#95	C₂×C₁₉	1	2	yes	complemented
211	C₂²×C₁₉	—	2	4	no	—
212	C₂²×C₁₉	—	2	4	no	—
213	C₂²×C₁₉	—	2	4	no	—
214	C₂²×C₁₉	—	4	8	no	—
215	C₂²×C₁₉	—	4	8	no	—
216	C₂²×C₁₉	—	4	4	no	—
217	C₂²×C₁₉	—	4	4	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	—	4	16	no	—
220	C₂²×C₁₉	—	4	4	no	—
221	C₂²×C₁₉	—	4	4	no	—
222	C₂²×C₁₉	—	8	8	no	—
223	C₂²×C₁₉	—	8	4	no	—
224	C₂²×C₁₉	—	8	4	no	—
225	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
226	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
227	C₂²×C₁₉	C₄×#41	1	2	yes	—
228	C₂²×C₁₉	#518	1	2	yes	—
229	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
230	C₂²×C₁₉	C₂×#121	1	2	yes	—
231	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
232	C₂²×C₁₉	#525	1	2	yes	—
233	C₂²×C₁₉	#532	1	2	yes	—
234	C₂²×C₁₉	#535	1	2	yes	—
235	C₂²×C₁₉	#535	1	2	yes	—
236	C₂²×C₁₉	#546	1	4	yes	—
237	C₂²×C₁₉	#550	1	4	yes	—
238	C₂²×C₁₉	#553	1	4	yes	—
239	C₂²×C₁₉	#555	1	4	yes	—
240	C₄×C₁₉	—	2	4	no	—
241	C₄×C₁₉	—	4	4	no	—
242	C₄×C₁₉	—	4	8	no	—
243	C₄×C₁₉	—	4	8	no	—
244	C₄×C₁₉	#386	1	8	yes	—
245	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
246	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
247	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×#121	—	2	4	no	—
249	C₂×#121	—	2	4	no	—
250	C₂×#121	C₄×C₁₉	1	8	yes	complemented
251	C₂×#117	—	2	4	no	—
252	C₂×#117	—	2	8	no	—
253	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
254	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
255	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
256	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
257	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
258	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
259	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
260	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
261	#390	—	2	8	no	—
262	C₄×C₂²⋊C₄	—	2	4	no	—
263	C₂×#95	C₂²×C₁₉	1	2	yes	—
264	C₂×#95	C₂²×C₁₉	1	8	yes	—
265	C₂×C₁₉	—	4	4	no	—
266	C₂×C₁₉	—	8	4	no	—
267	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
268	C₂×C₁₉	#2297	1	1	yes	characteristic
269	C₂×C₁₉	#2309	1	1	yes	characteristic
270	C₂×C₁₉	#2363	1	4	yes	—
271	C₂×C₁₉	#2414	1	4	yes	—
272	C₂×C₁₉	#2431	1	2	yes	—
273	C₂×C₁₉	#2500	1	2	yes	—
274	C₂⁵	C₂³×C₁₉	1	2	yes	—
275	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
276	C₂²×D₄	—	2	4	no	—
277	C₂²×D₄	—	2	4	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	—	2	4	no	—
281	C₂²×D₄	—	2	4	no	—
282	C₂²×D₄	—	4	8	no	—
283	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
284	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	—
285	C₂³×C₄	—	2	4	no	—
286	C₂³×C₄	—	2	4	no	—
287	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
288	C₂³×C₄	D₄×C₁₉	1	4	yes	—
289	C₂³×C₄	D₄×C₁₉	1	4	yes	—
290	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
291	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
292	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
293	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
295	#121	—	2	32	no	—
296	#117	—	2	32	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
302	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	complemented
303	C₂×C₂²⋊C₄	—	2	4	no	—
304	C₂×C₂²⋊C₄	—	2	4	no	—
305	C₂×C₂²⋊C₄	—	2	8	no	—
306	C₂×C₂²⋊C₄	—	2	4	no	—
307	C₂×C₂²⋊C₄	—	2	4	no	—
308	C₂×C₂²⋊C₄	—	2	8	no	—
309	C₂×C₂²⋊C₄	—	2	16	no	—
310	C₂×C₂²⋊C₄	—	2	16	no	—
311	C₂×C₂²⋊C₄	—	4	8	no	—
312	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
313	C₂×C₄²	—	2	8	no	—
314	C₂×C₄²	—	2	4	no	—
315	C₂×C₄²	—	2	4	no	—
316	C₂×C₄²	—	2	4	no	—
317	C₂×C₄²	—	2	4	no	—
318	#95	—	2	4	no	—
319	#95	—	4	8	no	—
320	C₁₉	#14136	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁴	—	2	2	no	—
322	C₂⁴	—	2	4	no	—
323	C₂⁴	—	2	2	no	—
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	2	4	no	—
326	C₂⁴	—	2	2	no	—
327	C₂⁴	—	2	2	no	—
328	C₂⁴	—	2	8	no	—
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	2	8	no	—
331	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
332	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
333	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
334	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
335	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
336	C₂×D₄	—	2	16	no	—
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	16	no	—
339	C₂×D₄	—	4	16	no	—
340	C₂×D₄	—	4	16	no	—
341	C₂×D₄	—	4	16	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	—	4	8	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	16	no	—
348	C₂²×C₄	—	2	8	no	—
349	C₂²×C₄	—	2	16	no	—
350	C₂²×C₄	—	2	8	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	C₂²⋊C₄×C₁₉	1	16	yes	complemented
365	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
366	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
367	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
369	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
374	C₂²×C₄	#41×C₁₉	1	8	yes	—
375	C₂²×C₄	#41×C₁₉	1	4	yes	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	16	no	—
378	C₂²⋊C₄	—	2	16	no	—
379	C₂²⋊C₄	—	2	16	no	—
380	C₂²⋊C₄	—	2	16	no	—
381	C₂²⋊C₄	—	4	32	no	—
382	C₄²	—	2	16	no	—
383	C₄²	—	4	8	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	2	8	no	—
396	C₂³	—	2	8	no	—
397	C₂³	—	2	8	no	—
398	C₂³	—	4	4	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	4	4	no	—
401	C₂³	—	4	4	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	4	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	4	no	—
406	C₂³	—	4	4	no	—
407	C₂³	—	4	4	no	—
408	C₂³	—	4	4	no	—
409	C₂³	—	4	8	no	—
410	C₂³	—	4	8	no	—
411	C₂³	—	4	8	no	—
412	C₂³	—	4	8	no	—
413	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
414	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
415	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
416	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
417	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
418	C₂³	C₂×#41×C₁₉	1	2	yes	—
419	C₂³	C₂×#41×C₁₉	1	4	yes	—
420	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
421	D₄	—	4	32	no	—
422	D₄	—	4	16	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	32	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	16	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	8	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
445	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
446	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
447	C₂×C₄	C₁₉×#120	1	4	yes	—
448	C₂×C₄	C₁₉×#121	1	8	yes	—
449	C₂×C₄	C₁₉×#123	1	4	yes	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	4	no	—
453	C₂²	—	4	8	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	8	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	16	no	—
461	C₂²	—	8	8	no	—
462	C₂²	—	8	4	no	—
463	C₂²	—	8	4	no	—
464	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
465	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
466	C₂²	C₄×#41×C₁₉	1	2	yes	—
467	C₂²	C₁₉×#518	1	2	yes	—
468	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
469	C₂²	C₂×C₁₉×#121	1	2	yes	—
470	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
471	C₂²	C₁₉×#525	1	2	yes	—
472	C₂²	C₁₉×#532	1	2	yes	—
473	C₂²	C₁₉×#535	1	2	yes	—
474	C₂²	C₁₉×#535	1	2	yes	—
475	C₂²	C₁₉×#546	1	4	yes	—
476	C₂²	C₁₉×#550	1	4	yes	—
477	C₂²	C₁₉×#553	1	4	yes	—
478	C₂²	C₁₉×#555	1	4	yes	—
479	C₄	—	2	4	no	—
480	C₄	—	4	8	no	—
481	C₄	—	4	8	no	—
482	C₄	—	4	4	no	—
483	C₄	C₁₉×#386	1	8	yes	—
484	C₂	—	4	4	no	—
485	C₂	—	8	4	no	—
486	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
487	C₂	C₁₉×#2297	1	1	yes	characteristic
488	C₂	C₁₉×#2309	1	1	yes	characteristic
489	C₂	C₁₉×#2363	1	4	yes	—
490	C₂	C₁₉×#2414	1	4	yes	—
491	C₂	C₁₉×#2431	1	2	yes	—
492	C₂	C₁₉×#2500	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#117	C₂	semidirect
3. C₂×C₁₉×#390	C₂	semidirect
4. C₂×C₄×C₂²⋊C₄×C₁₉	C₂	semidirect
5. C₁₉×#1438	C₂	semidirect
6. C₁₉×#1437	C₂	semidirect
7. C₁₉×C₄⋊#95	C₂	semidirect
13. C₂×C₁₉×#121	C₄	semidirect
56. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
117. C₂²×C₄×C₁₉	C₂²⋊C₄	semidirect
137. #14136	C₁₉	direct (N × H)
205. C₂²×#117	C₂×C₁₉	semidirect
206. C₂×#390	C₂×C₁₉	semidirect
207. C₂×C₄×C₂²⋊C₄	C₂×C₁₉	semidirect
208. #1438	C₂×C₁₉	semidirect
209. #1437	C₂×C₁₉	semidirect
210. C₄⋊#95	C₂×C₁₉	semidirect
250. C₂×#121	C₄×C₁₉	semidirect
302. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
320. C₁₉	#14136	direct (N × H)
364. C₂²×C₄	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
C₂²×C₁₉×#121	2
C₂²×C₁₉×#117	2
C₂×C₁₉×#390	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1438	2
C₁₉×#1437	2
C₁₉×C₄⋊#95	2
#14136	19

Subgroups — C19×#14136 #18020095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14136 #18020095