Subgroups — C₁₉×#14137 #18020096

Order 4864.

3158 conjugacy classes of subgroups.

The subgroup lattice has 554 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	C₂³×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#390	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#386	C₂	1	4	yes	maximal, complemented
5	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1439	C₂	1	4	yes	maximal, complemented
7	C₁₉×C₄⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#121	—	2	4	no	—
13	C₂×C₁₉×#121	—	2	4	no	—
14	C₂×C₁₉×#121	C₄	1	8	yes	complemented
15	C₂²×C₄⋊C₄×C₁₉	—	2	4	no	—
16	C₂²×C₄⋊C₄×C₁₉	—	2	8	no	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊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×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
24	C₁₉×#390	—	2	8	no	—
25	C₁₉×#386	—	2	16	no	—
26	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
27	C₂×C₁₉×#95	C₂²	1	8	yes	—
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂⁵×C₁₉	C₂³	1	2	yes	—
30	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
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	8	no	—
35	C₂²×D₄×C₁₉	—	2	4	no	—
36	C₂²×D₄×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	—	2	4	no	—
39	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	—
40	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	complemented
41	C₂³×C₄×C₁₉	—	2	4	no	—
42	C₂³×C₄×C₁₉	—	2	4	no	—
43	C₂³×C₄×C₁₉	—	2	4	no	—
44	C₂³×C₄×C₁₉	—	2	8	no	—
45	C₂³×C₄×C₁₉	—	2	8	no	—
46	C₂³×C₄×C₁₉	—	4	4	no	—
47	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
48	C₂³×C₄×C₁₉	D₄	1	4	yes	—
49	C₂³×C₄×C₁₉	D₄	1	4	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
52	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₁₉×#121	—	2	32	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	32	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
64	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	complemented
65	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
72	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
73	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	complemented
74	C₂×C₄²×C₁₉	—	2	4	no	—
75	C₂×C₄²×C₁₉	—	2	4	no	—
76	C₂×C₄²×C₁₉	—	2	4	no	—
77	C₁₉×#95	—	2	4	no	—
78	C₁₉×#95	—	2	16	no	—
79	C₂⁴×C₁₉	—	2	2	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	—	2	2	no	—
82	C₂⁴×C₁₉	—	2	2	no	—
83	C₂⁴×C₁₉	—	2	4	no	—
84	C₂⁴×C₁₉	—	2	4	no	—
85	C₂⁴×C₁₉	—	2	2	no	—
86	C₂⁴×C₁₉	—	2	2	no	—
87	C₂⁴×C₁₉	—	2	4	no	—
88	C₂⁴×C₁₉	—	2	4	no	—
89	C₂⁴×C₁₉	—	2	4	no	—
90	C₂⁴×C₁₉	—	2	4	no	—
91	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
92	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
93	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
94	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
95	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
96	C₂⁴×C₁₉	#41	1	4	yes	—
97	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
98	C₂×D₄×C₁₉	—	2	16	no	—
99	C₂×D₄×C₁₉	—	2	32	no	—
100	C₂×D₄×C₁₉	—	2	8	no	—
101	C₂×D₄×C₁₉	—	2	16	no	—
102	C₂×D₄×C₁₉	—	4	16	no	—
103	C₂×D₄×C₁₉	—	4	8	no	—
104	C₂×D₄×C₁₉	—	4	8	no	—
105	C₂×D₄×C₁₉	—	4	4	no	—
106	C₂×D₄×C₁₉	—	4	8	no	—
107	C₂×D₄×C₁₉	—	4	4	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	16	no	—
111	C₂²×C₄×C₁₉	—	2	8	no	—
112	C₂²×C₄×C₁₉	—	2	16	no	—
113	C₂²×C₄×C₁₉	—	2	8	no	—
114	C₂²×C₄×C₁₉	—	2	16	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	8	no	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
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	8	no	—
128	C₂²×C₄×C₁₉	—	2	4	no	—
129	C₂²×C₄×C₁₉	—	4	32	no	—
130	C₂²×C₄×C₁₉	—	4	8	no	—
131	C₂²×C₄×C₁₉	—	4	8	no	—
132	C₂²×C₄×C₁₉	C₂²⋊C₄	1	16	yes	complemented
133	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
137	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₉	#41	1	4	yes	—
144	C₄⋊C₄×C₁₉	—	2	16	no	—
145	C₄⋊C₄×C₁₉	—	2	8	no	—
146	C₄⋊C₄×C₁₉	—	2	16	no	—
147	C₂²⋊C₄×C₁₉	—	2	16	no	—
148	C₂²⋊C₄×C₁₉	—	2	16	no	—
149	C₂²⋊C₄×C₁₉	—	4	32	no	—
150	C₄²×C₁₉	—	4	8	no	—
151	#14137	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₁₉	—	2	4	no	—
153	C₂³×C₁₉	—	2	4	no	—
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	4	no	—
156	C₂³×C₁₉	—	2	2	no	—
157	C₂³×C₁₉	—	2	2	no	—
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	4	no	—
160	C₂³×C₁₉	—	2	8	no	—
161	C₂³×C₁₉	—	2	8	no	—
162	C₂³×C₁₉	—	2	8	no	—
163	C₂³×C₁₉	—	2	8	no	—
164	C₂³×C₁₉	—	2	4	no	—
165	C₂³×C₁₉	—	2	8	no	—
166	C₂³×C₁₉	—	2	8	no	—
167	C₂³×C₁₉	—	2	8	no	—
168	C₂³×C₁₉	—	4	2	no	—
169	C₂³×C₁₉	—	4	4	no	—
170	C₂³×C₁₉	—	4	4	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	—	4	2	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	4	4	no	—
177	C₂³×C₁₉	—	4	8	no	—
178	C₂³×C₁₉	—	4	8	no	—
179	C₂³×C₁₉	—	4	8	no	—
180	C₂³×C₁₉	—	4	8	no	—
181	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
182	C₂³×C₁₉	C₄×D₄	1	8	yes	—
183	C₂³×C₁₉	#121	1	8	yes	—
184	C₂³×C₁₉	#124	1	4	yes	—
185	C₂³×C₁₉	#127	1	4	yes	—
186	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
187	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
188	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
189	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
190	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
191	C₂³×C₁₉	C₂×#41	1	2	yes	—
192	C₂³×C₁₉	C₂×#41	1	2	yes	—
193	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
194	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
195	D₄×C₁₉	—	4	32	no	—
196	D₄×C₁₉	—	4	16	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	32	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	8	no	—
204	C₂×C₄×C₁₉	—	2	8	no	—
205	C₂×C₄×C₁₉	—	2	8	no	—
206	C₂×C₄×C₁₉	—	2	8	no	—
207	C₂×C₄×C₁₉	—	2	16	no	—
208	C₂×C₄×C₁₉	—	2	8	no	—
209	C₂×C₄×C₁₉	—	4	32	no	—
210	C₂×C₄×C₁₉	—	4	4	no	—
211	C₂×C₄×C₁₉	—	4	4	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	4	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	4	no	—
216	C₂×C₄×C₁₉	—	4	4	no	—
217	C₂×C₄×C₁₉	—	4	8	no	—
218	C₂×C₄×C₁₉	—	4	4	no	—
219	C₂×C₄×C₁₉	—	4	4	no	—
220	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
221	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
222	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
223	C₂×C₄×C₁₉	#120	1	4	yes	—
224	C₂×C₄×C₁₉	#121	1	8	yes	—
225	C₂×C₄×C₁₉	#123	1	4	yes	—
226	C₂²×#121	C₂×C₁₉	1	1	yes	characteristic
227	C₂³×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
228	C₂×#390	C₂×C₁₉	1	2	yes	complemented
229	C₂×#386	C₂×C₁₉	1	4	yes	complemented
230	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#1439	C₂×C₁₉	1	4	yes	complemented
232	C₄⋊#95	C₂×C₁₉	1	2	yes	complemented
233	C₂²×C₁₉	—	2	4	no	—
234	C₂²×C₁₉	—	2	16	no	—
235	C₂²×C₁₉	—	2	16	no	—
236	C₂²×C₁₉	—	2	4	no	—
237	C₂²×C₁₉	—	2	4	no	—
238	C₂²×C₁₉	—	2	4	no	—
239	C₂²×C₁₉	—	2	4	no	—
240	C₂²×C₁₉	—	2	4	no	—
241	C₂²×C₁₉	—	4	4	no	—
242	C₂²×C₁₉	—	4	16	no	—
243	C₂²×C₁₉	—	4	4	no	—
244	C₂²×C₁₉	—	4	4	no	—
245	C₂²×C₁₉	—	8	8	no	—
246	C₂²×C₁₉	—	8	2	no	—
247	C₂²×C₁₉	—	8	2	no	—
248	C₂²×C₁₉	—	8	2	no	—
249	C₂²×C₁₉	—	8	2	no	—
250	C₂²×C₁₉	#390	1	8	yes	complemented
251	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
253	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
254	C₂²×C₁₉	#520	1	2	yes	—
255	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
256	C₂²×C₁₉	C₂×#121	1	2	yes	—
257	C₂²×C₁₉	C₂×#121	1	2	yes	—
258	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
259	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
260	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
261	C₂²×C₁₉	#535	1	1	yes	characteristic
262	C₂²×C₁₉	#536	1	1	yes	characteristic
263	C₂²×C₁₉	#537	1	2	yes	—
264	C₂²×C₁₉	D₄²	1	4	yes	—
265	C₂²×C₁₉	#547	1	4	yes	—
266	C₂²×C₁₉	#548	1	4	yes	—
267	C₂²×C₁₉	#553	1	4	yes	—
268	C₄×C₁₉	—	2	4	no	—
269	C₄×C₁₉	—	4	8	no	—
270	C₄×C₁₉	—	4	8	no	—
271	C₄×C₁₉	—	4	4	no	—
272	C₄×C₁₉	#386	1	8	yes	complemented
273	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
274	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
275	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
276	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×#121	—	2	4	no	—
278	C₂×#121	—	2	4	no	—
279	C₂×#121	C₄×C₁₉	1	8	yes	complemented
280	C₂²×C₄⋊C₄	—	2	4	no	—
281	C₂²×C₄⋊C₄	—	2	8	no	—
282	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
283	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
284	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
285	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
286	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
287	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
288	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
289	#390	—	2	8	no	—
290	#386	—	2	16	no	—
291	C₄×C₂²⋊C₄	—	2	4	no	—
292	C₂×#95	C₂²×C₁₉	1	8	yes	—
293	C₂×#95	C₂²×C₁₉	1	2	yes	—
294	C₂×C₁₉	—	2	8	no	—
295	C₂×C₁₉	—	8	4	no	—
296	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
297	C₂×C₁₉	C₂×#390	1	1	yes	characteristic
298	C₂×C₁₉	#2311	1	1	yes	characteristic
299	C₂×C₁₉	#2361	1	4	yes	—
300	C₂×C₁₉	#2416	1	4	yes	—
301	C₂×C₁₉	#2433	1	1	yes	characteristic
302	C₂×C₁₉	#2436	1	1	yes	characteristic
303	C₂×C₁₉	#2501	1	1	yes	characteristic
304	C₂×C₁₉	#2504	1	1	yes	characteristic
305	C₂⁵	C₂³×C₁₉	1	2	yes	—
306	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
307	C₂²×D₄	—	2	4	no	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	—	2	8	no	—
310	C₂²×D₄	—	2	8	no	—
311	C₂²×D₄	—	2	2	no	—
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	—	2	4	no	—
314	C₂²×D₄	—	2	4	no	—
315	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	—
316	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	complemented
317	C₂³×C₄	—	2	4	no	—
318	C₂³×C₄	—	2	4	no	—
319	C₂³×C₄	—	2	4	no	—
320	C₂³×C₄	—	2	8	no	—
321	C₂³×C₄	—	2	8	no	—
322	C₂³×C₄	—	4	4	no	—
323	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
324	C₂³×C₄	D₄×C₁₉	1	4	yes	—
325	C₂³×C₄	D₄×C₁₉	1	4	yes	—
326	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
327	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
328	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
329	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
331	#121	—	2	32	no	—
332	C₂×C₄⋊C₄	—	2	32	no	—
333	C₂×C₄⋊C₄	—	2	8	no	—
334	C₂×C₄⋊C₄	—	2	4	no	—
335	C₂×C₄⋊C₄	—	2	4	no	—
336	C₂×C₄⋊C₄	—	2	4	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
340	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	complemented
341	C₂×C₂²⋊C₄	—	2	4	no	—
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₂²⋊C₄	—	2	4	no	—
344	C₂×C₂²⋊C₄	—	2	4	no	—
345	C₂×C₂²⋊C₄	—	2	16	no	—
346	C₂×C₂²⋊C₄	—	2	16	no	—
347	C₂×C₂²⋊C₄	—	4	8	no	—
348	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
349	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	complemented
350	C₂×C₄²	—	2	4	no	—
351	C₂×C₄²	—	2	4	no	—
352	C₂×C₄²	—	2	4	no	—
353	#95	—	2	4	no	—
354	#95	—	2	16	no	—
355	C₁₉	#14137	1	1	yes	characteristic, direct product factor, Sylow
356	C₂⁴	—	2	2	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	—	2	2	no	—
360	C₂⁴	—	2	4	no	—
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	2	no	—
363	C₂⁴	—	2	2	no	—
364	C₂⁴	—	2	4	no	—
365	C₂⁴	—	2	4	no	—
366	C₂⁴	—	2	4	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
369	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
370	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
371	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
372	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
373	C₂⁴	#41×C₁₉	1	4	yes	—
374	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
375	C₂×D₄	—	2	16	no	—
376	C₂×D₄	—	2	32	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	16	no	—
379	C₂×D₄	—	4	16	no	—
380	C₂×D₄	—	4	8	no	—
381	C₂×D₄	—	4	8	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	8	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	16	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	16	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	16	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	4	32	no	—
407	C₂²×C₄	—	4	8	no	—
408	C₂²×C₄	—	4	8	no	—
409	C₂²×C₄	C₂²⋊C₄×C₁₉	1	16	yes	complemented
410	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
411	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
412	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
414	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
415	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
416	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
417	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
420	C₂²×C₄	#41×C₁₉	1	4	yes	—
421	C₄⋊C₄	—	2	16	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	2	16	no	—
424	C₂²⋊C₄	—	2	16	no	—
425	C₂²⋊C₄	—	2	16	no	—
426	C₂²⋊C₄	—	4	32	no	—
427	C₄²	—	4	8	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	8	no	—
437	C₂³	—	2	8	no	—
438	C₂³	—	2	8	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	8	no	—
442	C₂³	—	2	8	no	—
443	C₂³	—	2	8	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	4	8	no	—
454	C₂³	—	4	8	no	—
455	C₂³	—	4	8	no	—
456	C₂³	—	4	8	no	—
457	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
458	C₂³	C₄×D₄×C₁₉	1	8	yes	—
459	C₂³	C₁₉×#121	1	8	yes	—
460	C₂³	C₁₉×#124	1	4	yes	—
461	C₂³	C₁₉×#127	1	4	yes	—
462	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
463	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
464	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
465	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
466	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
467	C₂³	C₂×#41×C₁₉	1	2	yes	—
468	C₂³	C₂×#41×C₁₉	1	2	yes	—
469	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
470	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
471	D₄	—	4	32	no	—
472	D₄	—	4	16	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	32	no	—
478	C₂×C₄	—	2	4	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	—	2	16	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	4	32	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
497	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
498	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
499	C₂×C₄	C₁₉×#120	1	4	yes	—
500	C₂×C₄	C₁₉×#121	1	8	yes	—
501	C₂×C₄	C₁₉×#123	1	4	yes	—
502	C₂²	—	2	16	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	16	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	16	no	—
514	C₂²	—	8	8	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	—	8	2	no	—
519	C₂²	C₁₉×#390	1	8	yes	complemented
520	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
521	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
522	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
523	C₂²	C₁₉×#520	1	2	yes	—
524	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
525	C₂²	C₂×C₁₉×#121	1	2	yes	—
526	C₂²	C₂×C₁₉×#121	1	2	yes	—
527	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
528	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
529	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
530	C₂²	C₁₉×#535	1	1	yes	characteristic
531	C₂²	C₁₉×#536	1	1	yes	characteristic
532	C₂²	C₁₉×#537	1	2	yes	—
533	C₂²	D₄²×C₁₉	1	4	yes	—
534	C₂²	C₁₉×#547	1	4	yes	—
535	C₂²	C₁₉×#548	1	4	yes	—
536	C₂²	C₁₉×#553	1	4	yes	—
537	C₄	—	2	4	no	—
538	C₄	—	4	8	no	—
539	C₄	—	4	8	no	—
540	C₄	—	4	4	no	—
541	C₄	C₁₉×#386	1	8	yes	complemented
542	C₂	—	2	8	no	—
543	C₂	—	8	4	no	—
544	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
545	C₂	C₂×C₁₉×#390	1	1	yes	characteristic
546	C₂	C₁₉×#2311	1	1	yes	characteristic
547	C₂	C₁₉×#2361	1	4	yes	—
548	C₂	C₁₉×#2416	1	4	yes	—
549	C₂	C₁₉×#2433	1	1	yes	characteristic
550	C₂	C₁₉×#2436	1	1	yes	characteristic
551	C₂	C₁₉×#2501	1	1	yes	characteristic
552	C₂	C₁₉×#2504	1	1	yes	characteristic

	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. C₂³×C₄⋊C₄×C₁₉	C₂	semidirect
3. C₂×C₁₉×#390	C₂	semidirect
4. C₂×C₁₉×#386	C₂	semidirect
5. C₂×C₄×C₂²⋊C₄×C₁₉	C₂	semidirect
6. C₁₉×#1439	C₂	semidirect
7. C₁₉×C₄⋊#95	C₂	semidirect
14. C₂×C₁₉×#121	C₄	semidirect
40. C₂²×D₄×C₁₉	C₂×C₄	semidirect
63. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
64. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
72. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
73. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
132. C₂²×C₄×C₁₉	C₂²⋊C₄	semidirect
151. #14137	C₁₉	direct (N × H)
227. C₂³×C₄⋊C₄	C₂×C₁₉	semidirect
228. C₂×#390	C₂×C₁₉	semidirect
229. C₂×#386	C₂×C₁₉	semidirect
230. C₂×C₄×C₂²⋊C₄	C₂×C₁₉	semidirect
231. #1439	C₂×C₁₉	semidirect
232. C₄⋊#95	C₂×C₁₉	semidirect
250. C₂²×C₁₉	#390	semidirect
272. C₄×C₁₉	#386	semidirect
279. C₂×#121	C₄×C₁₉	semidirect
316. C₂²×D₄	C₂×C₄×C₁₉	semidirect
339. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
340. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
348. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
349. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
355. C₁₉	#14137	direct (N × H)
409. C₂²×C₄	C₂²⋊C₄×C₁₉	semidirect
519. C₂²	C₁₉×#390	semidirect
541. C₄	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×#121	2
C₂³×C₄⋊C₄×C₁₉	2
C₂×C₁₉×#390	2
C₂×C₁₉×#386	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1439	2
C₁₉×C₄⋊#95	2
#14137	19

Subgroups — C19×#14137 #18020096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14137 #18020096