Subgroups — C₁₉×#14134 #18020093

Order 4864.

4586 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#120	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#386	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1440	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1438	C₂	1	2	yes	maximal, complemented
6	C₁₉×C₂²⋊#95	C₂	1	4	yes	maximal, complemented
7	C₂⁶×C₁₉	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	4	yes	—
11	C₂×C₁₉×#120	—	2	8	no	—
12	C₂×C₁₉×#120	C₄	1	8	yes	complemented
13	C₂²×C₂²⋊C₄×C₁₉	—	2	8	no	—
14	C₂²×C₂²⋊C₄×C₁₉	—	2	16	no	—
15	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
19	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
20	C₁₉×#386	—	2	16	no	—
21	C₂×C₁₉×#95	C₂²	1	8	yes	complemented
22	C₂×C₁₉×#95	C₂²	1	4	yes	complemented
23	C₂⁵×C₁₉	—	2	8	no	—
24	C₂⁵×C₁₉	—	2	8	no	—
25	C₂⁵×C₁₉	—	4	4	no	—
26	C₂⁵×C₁₉	C₂×C₄	1	4	yes	—
27	C₂⁵×C₁₉	D₄	1	8	yes	—
28	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
29	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
30	C₂⁵×C₁₉	C₂³	1	2	yes	—
31	C₂²×D₄×C₁₉	—	2	8	no	—
32	C₂²×D₄×C₁₉	—	2	4	no	—
33	C₂²×D₄×C₁₉	—	2	4	no	—
34	C₂²×D₄×C₁₉	—	2	4	no	—
35	C₂²×D₄×C₁₉	—	2	8	no	—
36	C₂²×D₄×C₁₉	—	4	4	no	—
37	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	complemented
38	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	complemented
39	C₂³×C₄×C₁₉	—	2	8	no	—
40	C₂³×C₄×C₁₉	—	2	16	no	—
41	C₂³×C₄×C₁₉	—	2	8	no	—
42	C₂³×C₄×C₁₉	—	2	8	no	—
43	C₂³×C₄×C₁₉	—	4	8	no	—
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
47	C₁₉×#120	—	2	32	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	64	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
52	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
58	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
59	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
60	C₂×C₂²⋊C₄×C₁₉	D₄	1	16	yes	complemented
61	C₁₉×#95	—	2	16	no	—
62	C₁₉×#95	—	4	4	no	—
63	C₂⁴×C₁₉	—	2	4	no	—
64	C₂⁴×C₁₉	—	2	4	no	—
65	C₂⁴×C₁₉	—	2	8	no	—
66	C₂⁴×C₁₉	—	2	32	no	—
67	C₂⁴×C₁₉	—	2	16	no	—
68	C₂⁴×C₁₉	—	2	32	no	—
69	C₂⁴×C₁₉	—	2	16	no	—
70	C₂⁴×C₁₉	—	2	4	no	—
71	C₂⁴×C₁₉	—	2	4	no	—
72	C₂⁴×C₁₉	—	2	4	no	—
73	C₂⁴×C₁₉	—	2	4	no	—
74	C₂⁴×C₁₉	—	2	2	no	—
75	C₂⁴×C₁₉	—	2	4	no	—
76	C₂⁴×C₁₉	—	2	4	no	—
77	C₂⁴×C₁₉	—	4	8	no	—
78	C₂⁴×C₁₉	—	4	16	no	—
79	C₂⁴×C₁₉	—	4	16	no	—
80	C₂⁴×C₁₉	—	4	32	no	—
81	C₂⁴×C₁₉	—	4	16	no	—
82	C₂⁴×C₁₉	C₂²⋊C₄	1	16	yes	complemented
83	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
84	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
85	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
86	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
87	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
88	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
89	C₂⁴×C₁₉	C₂×D₄	1	8	yes	—
90	C₂⁴×C₁₉	#41	1	8	yes	—
91	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
92	C₂×D₄×C₁₉	—	2	8	no	—
93	C₂×D₄×C₁₉	—	2	16	no	—
94	C₂×D₄×C₁₉	—	2	32	no	—
95	C₂×D₄×C₁₉	—	4	8	no	—
96	C₂×D₄×C₁₉	—	4	16	no	—
97	C₂×D₄×C₁₉	—	4	8	no	—
98	C₂×D₄×C₁₉	—	4	16	no	—
99	C₂×D₄×C₁₉	—	4	8	no	—
100	C₂²×C₄×C₁₉	—	2	32	no	—
101	C₂²×C₄×C₁₉	—	2	8	no	—
102	C₂²×C₄×C₁₉	—	2	8	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	8	no	—
107	C₂²×C₄×C₁₉	—	2	4	no	—
108	C₂²×C₄×C₁₉	—	2	8	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	8	no	—
111	C₂²×C₄×C₁₉	—	2	8	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	4	32	no	—
114	C₂²×C₄×C₁₉	—	4	32	no	—
115	C₂²×C₄×C₁₉	—	4	16	no	—
116	C₂²×C₄×C₁₉	—	4	16	no	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	16	yes	—
120	C₂²⋊C₄×C₁₉	—	2	32	no	—
121	C₂²⋊C₄×C₁₉	—	2	8	no	—
122	C₂²⋊C₄×C₁₉	—	2	16	no	—
123	C₂²⋊C₄×C₁₉	—	2	32	no	—
124	C₂²⋊C₄×C₁₉	—	4	16	no	—
125	#14134	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₁₉	—	2	8	no	—
127	C₂³×C₁₉	—	2	8	no	—
128	C₂³×C₁₉	—	2	4	no	—
129	C₂³×C₁₉	—	2	8	no	—
130	C₂³×C₁₉	—	2	4	no	—
131	C₂³×C₁₉	—	2	8	no	—
132	C₂³×C₁₉	—	2	8	no	—
133	C₂³×C₁₉	—	2	16	no	—
134	C₂³×C₁₉	—	2	16	no	—
135	C₂³×C₁₉	—	2	16	no	—
136	C₂³×C₁₉	—	2	16	no	—
137	C₂³×C₁₉	—	2	8	no	—
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	2	4	no	—
140	C₂³×C₁₉	—	2	8	no	—
141	C₂³×C₁₉	—	2	4	no	—
142	C₂³×C₁₉	—	2	8	no	—
143	C₂³×C₁₉	—	2	64	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	2	8	no	—
146	C₂³×C₁₉	—	2	4	no	—
147	C₂³×C₁₉	—	4	16	no	—
148	C₂³×C₁₉	—	4	64	no	—
149	C₂³×C₁₉	—	4	64	no	—
150	C₂³×C₁₉	—	4	64	no	—
151	C₂³×C₁₉	—	4	4	no	—
152	C₂³×C₁₉	—	4	8	no	—
153	C₂³×C₁₉	—	4	4	no	—
154	C₂³×C₁₉	—	4	2	no	—
155	C₂³×C₁₉	—	4	4	no	—
156	C₂³×C₁₉	—	4	2	no	—
157	C₂³×C₁₉	—	4	4	no	—
158	C₂³×C₁₉	—	4	4	no	—
159	C₂³×C₁₉	—	4	8	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
162	C₂³×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
163	C₂³×C₁₉	C₄×D₄	1	16	yes	—
164	C₂³×C₁₉	#120	1	8	yes	—
165	C₂³×C₁₉	#121	1	16	yes	—
166	C₂³×C₁₉	#123	1	8	yes	—
167	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
168	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
169	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
170	C₂³×C₁₉	C₂×#41	1	4	yes	—
171	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
172	D₄×C₁₉	—	4	16	no	—
173	D₄×C₁₉	—	4	32	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	8	no	—
177	C₂×C₄×C₁₉	—	2	4	no	—
178	C₂×C₄×C₁₉	—	2	16	no	—
179	C₂×C₄×C₁₉	—	2	16	no	—
180	C₂×C₄×C₁₉	—	2	16	no	—
181	C₂×C₄×C₁₉	—	4	64	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	8	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	8	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	8	no	—
189	C₂×C₄×C₁₉	—	4	8	no	—
190	C₂²×#120	C₂×C₁₉	1	1	yes	characteristic
191	C₂³×C₂²⋊C₄	C₂×C₁₉	1	2	yes	complemented
192	C₂×#386	C₂×C₁₉	1	4	yes	complemented
193	#1440	C₂×C₁₉	1	2	yes	complemented
194	#1438	C₂×C₁₉	1	2	yes	complemented
195	C₂²⋊#95	C₂×C₁₉	1	4	yes	complemented
196	C₂²×C₁₉	—	2	8	no	—
197	C₂²×C₁₉	—	2	32	no	—
198	C₂²×C₁₉	—	2	16	no	—
199	C₂²×C₁₉	—	2	16	no	—
200	C₂²×C₁₉	—	2	16	no	—
201	C₂²×C₁₉	—	2	16	no	—
202	C₂²×C₁₉	—	2	8	no	—
203	C₂²×C₁₉	—	2	4	no	—
204	C₂²×C₁₉	—	2	8	no	—
205	C₂²×C₁₉	—	4	64	no	—
206	C₂²×C₁₉	—	4	8	no	—
207	C₂²×C₁₉	—	4	8	no	—
208	C₂²×C₁₉	—	4	8	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	4	8	no	—
211	C₂²×C₁₉	—	4	4	no	—
212	C₂²×C₁₉	—	8	4	no	—
213	C₂²×C₁₉	—	8	4	no	—
214	C₂²×C₁₉	#386	1	16	yes	complemented
215	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×C₁₉	C₂×C₄×D₄	1	4	yes	—
217	C₂²×C₁₉	#518	1	2	yes	—
218	C₂²×C₁₉	C₂×#120	1	2	yes	—
219	C₂²×C₁₉	C₂×#121	1	4	yes	—
220	C₂²×C₁₉	C₂×#123	1	2	yes	—
221	C₂²×C₁₉	#534	1	4	yes	—
222	C₂²×C₁₉	D₄²	1	4	yes	—
223	C₂²×C₁₉	#546	1	8	yes	—
224	C₂²×C₁₉	#551	1	4	yes	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	4	16	no	—
227	C₄×C₁₉	—	4	4	no	—
228	C₂⁶	C₂²×C₁₉	1	1	yes	characteristic
229	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
230	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
231	C₂⁴×C₄	C₂²×C₁₉	1	4	yes	—
232	C₂×#120	—	2	8	no	—
233	C₂×#120	C₄×C₁₉	1	8	yes	complemented
234	C₂²×C₂²⋊C₄	—	2	8	no	—
235	C₂²×C₂²⋊C₄	—	2	16	no	—
236	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
238	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
239	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
240	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
241	#386	—	2	16	no	—
242	C₂×#95	C₂²×C₁₉	1	8	yes	complemented
243	C₂×#95	C₂²×C₁₉	1	4	yes	complemented
244	C₂×C₁₉	—	2	16	no	—
245	C₂×C₁₉	—	4	4	no	—
246	C₂×C₁₉	—	8	2	no	—
247	C₂×C₁₉	C₂×#386	1	2	yes	—
248	C₂×C₁₉	#2308	1	1	yes	characteristic
249	C₂×C₁₉	#2358	1	4	yes	—
250	C₂×C₁₉	#2410	1	4	yes	—
251	C₂×C₁₉	#2412	1	4	yes	—
252	C₂⁵	—	2	8	no	—
253	C₂⁵	—	2	8	no	—
254	C₂⁵	—	4	4	no	—
255	C₂⁵	C₂×C₄×C₁₉	1	4	yes	—
256	C₂⁵	D₄×C₁₉	1	8	yes	—
257	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
258	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
259	C₂⁵	C₂³×C₁₉	1	2	yes	—
260	C₂²×D₄	—	2	4	no	—
261	C₂²×D₄	—	2	4	no	—
262	C₂²×D₄	—	2	4	no	—
263	C₂²×D₄	—	2	8	no	—
264	C₂²×D₄	—	2	8	no	—
265	C₂²×D₄	—	4	4	no	—
266	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	complemented
267	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	complemented
268	C₂³×C₄	—	2	8	no	—
269	C₂³×C₄	—	2	16	no	—
270	C₂³×C₄	—	2	8	no	—
271	C₂³×C₄	—	2	8	no	—
272	C₂³×C₄	—	4	8	no	—
273	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
274	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
276	#120	—	2	32	no	—
277	C₂×C₂²⋊C₄	—	2	64	no	—
278	C₂×C₂²⋊C₄	—	2	8	no	—
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	2	8	no	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	—	2	4	no	—
284	C₂×C₂²⋊C₄	—	2	16	no	—
285	C₂×C₂²⋊C₄	—	2	16	no	—
286	C₂×C₂²⋊C₄	—	4	4	no	—
287	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
288	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
289	C₂×C₂²⋊C₄	D₄×C₁₉	1	16	yes	complemented
290	#95	—	2	16	no	—
291	#95	—	4	4	no	—
292	C₁₉	#14134	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁴	—	2	4	no	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	—	2	8	no	—
296	C₂⁴	—	2	32	no	—
297	C₂⁴	—	2	16	no	—
298	C₂⁴	—	2	32	no	—
299	C₂⁴	—	2	16	no	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	4	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	4	no	—
306	C₂⁴	—	2	4	no	—
307	C₂⁴	—	4	8	no	—
308	C₂⁴	—	4	16	no	—
309	C₂⁴	—	4	16	no	—
310	C₂⁴	—	4	32	no	—
311	C₂⁴	—	4	16	no	—
312	C₂⁴	C₂²⋊C₄×C₁₉	1	16	yes	complemented
313	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
314	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
315	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
316	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
317	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
318	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
319	C₂⁴	C₂×D₄×C₁₉	1	8	yes	—
320	C₂⁴	#41×C₁₉	1	8	yes	—
321	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	16	no	—
324	C₂×D₄	—	2	32	no	—
325	C₂×D₄	—	4	8	no	—
326	C₂×D₄	—	4	16	no	—
327	C₂×D₄	—	4	8	no	—
328	C₂×D₄	—	4	16	no	—
329	C₂×D₄	—	4	8	no	—
330	C₂²×C₄	—	2	32	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	4	32	no	—
344	C₂²×C₄	—	4	32	no	—
345	C₂²×C₄	—	4	16	no	—
346	C₂²×C₄	—	4	16	no	—
347	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
348	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	16	yes	—
350	C₂²⋊C₄	—	2	32	no	—
351	C₂²⋊C₄	—	2	8	no	—
352	C₂²⋊C₄	—	2	16	no	—
353	C₂²⋊C₄	—	2	32	no	—
354	C₂²⋊C₄	—	4	16	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	8	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	16	no	—
363	C₂³	—	2	16	no	—
364	C₂³	—	2	16	no	—
365	C₂³	—	2	16	no	—
366	C₂³	—	2	64	no	—
367	C₂³	—	2	8	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	2	8	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	8	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	4	16	no	—
377	C₂³	—	4	64	no	—
378	C₂³	—	4	64	no	—
379	C₂³	—	4	64	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	4	8	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	4	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	4	8	no	—
389	C₂³	—	4	4	no	—
390	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
391	C₂³	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
392	C₂³	C₄×D₄×C₁₉	1	16	yes	—
393	C₂³	C₁₉×#120	1	8	yes	—
394	C₂³	C₁₉×#121	1	16	yes	—
395	C₂³	C₁₉×#123	1	8	yes	—
396	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
397	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
398	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
399	C₂³	C₂×#41×C₁₉	1	4	yes	—
400	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
401	D₄	—	4	16	no	—
402	D₄	—	4	32	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	16	no	—
408	C₂×C₄	—	2	16	no	—
409	C₂×C₄	—	2	16	no	—
410	C₂×C₄	—	4	64	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂²	—	2	16	no	—
420	C₂²	—	2	16	no	—
421	C₂²	—	2	16	no	—
422	C₂²	—	2	16	no	—
423	C₂²	—	2	8	no	—
424	C₂²	—	2	8	no	—
425	C₂²	—	2	32	no	—
426	C₂²	—	2	8	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	4	64	no	—
429	C₂²	—	4	8	no	—
430	C₂²	—	4	8	no	—
431	C₂²	—	4	8	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	8	4	no	—
436	C₂²	—	8	4	no	—
437	C₂²	C₁₉×#386	1	16	yes	complemented
438	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
439	C₂²	C₂×C₄×D₄×C₁₉	1	4	yes	—
440	C₂²	C₁₉×#518	1	2	yes	—
441	C₂²	C₂×C₁₉×#120	1	2	yes	—
442	C₂²	C₂×C₁₉×#121	1	4	yes	—
443	C₂²	C₂×C₁₉×#123	1	2	yes	—
444	C₂²	C₁₉×#534	1	4	yes	—
445	C₂²	D₄²×C₁₉	1	4	yes	—
446	C₂²	C₁₉×#546	1	8	yes	—
447	C₂²	C₁₉×#551	1	4	yes	—
448	C₄	—	4	16	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	2	no	—
451	C₂	—	2	16	no	—
452	C₂	—	4	4	no	—
453	C₂	—	8	2	no	—
454	C₂	C₂×C₁₉×#386	1	2	yes	—
455	C₂	C₁₉×#2308	1	1	yes	characteristic
456	C₂	C₁₉×#2358	1	4	yes	—
457	C₂	C₁₉×#2410	1	4	yes	—
458	C₂	C₁₉×#2412	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×#120	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. C₂³×C₂²⋊C₄×C₁₉	C₂	semidirect
3. C₂×C₁₉×#386	C₂	semidirect
4. C₁₉×#1440	C₂	semidirect
5. C₁₉×#1438	C₂	semidirect
6. C₁₉×C₂²⋊#95	C₂	semidirect
12. C₂×C₁₉×#120	C₄	semidirect
19. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
21. C₂×C₁₉×#95	C₂²	semidirect
22. C₂×C₁₉×#95	C₂²	semidirect
37. C₂²×D₄×C₁₉	C₂×C₄	semidirect
38. C₂²×D₄×C₁₉	C₂×C₄	semidirect
58. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
59. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
60. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
82. C₂⁴×C₁₉	C₂²⋊C₄	semidirect
125. #14134	C₁₉	direct (N × H)
191. C₂³×C₂²⋊C₄	C₂×C₁₉	semidirect
192. C₂×#386	C₂×C₁₉	semidirect
193. #1440	C₂×C₁₉	semidirect
194. #1438	C₂×C₁₉	semidirect
195. C₂²⋊#95	C₂×C₁₉	semidirect
214. C₂²×C₁₉	#386	semidirect
233. C₂×#120	C₄×C₁₉	semidirect
240. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
242. C₂×#95	C₂²×C₁₉	semidirect
243. C₂×#95	C₂²×C₁₉	semidirect
266. C₂²×D₄	C₂×C₄×C₁₉	semidirect
267. C₂²×D₄	C₂×C₄×C₁₉	semidirect
287. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
288. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
289. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
292. C₁₉	#14134	direct (N × H)
312. C₂⁴	C₂²⋊C₄×C₁₉	semidirect
437. C₂²	C₁₉×#386	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#120	2
C₂³×C₂²⋊C₄×C₁₉	2
C₂×C₁₉×#386	2
C₁₉×#1440	2
C₁₉×#1438	2
C₁₉×C₂²⋊#95	2
#14134	19

Subgroups — C19×#14134 #18020093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14134 #18020093