Subgroups — C₁₉×#14130 #18020089

Order 4864.

2366 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#389	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#385	C₂	1	2	yes	maximal
4	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1444	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1442	C₂	1	2	yes	maximal, complemented
8	C₁₉×C₄⋊#95	C₂	1	2	yes	maximal, complemented
9	C₁₉×C₂²⋊#95	C₂	1	2	yes	maximal
10	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	—	2	4	no	—
13	C₂²×C₄⋊C₄×C₁₉	—	2	8	no	—
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
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	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#389	—	2	8	no	—
24	C₁₉×#385	—	2	8	no	—
25	C₁₉×#380	C₄	1	8	yes	complemented
26	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
27	C₂×C₁₉×#95	C₂²	1	4	yes	—
28	C₂×C₁₉×#95	C₂²	1	4	yes	—
29	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#95	C₂²	1	4	yes	—
32	C₂×C₁₉×#95	C₂²	1	2	yes	—
33	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₁₉	—	2	4	no	—
35	C₂³×C₄×C₁₉	—	2	4	no	—
36	C₂³×C₄×C₁₉	—	2	4	no	—
37	C₂³×C₄×C₁₉	—	2	8	no	—
38	C₂³×C₄×C₁₉	—	2	4	no	—
39	C₂³×C₄×C₁₉	—	2	4	no	—
40	C₂³×C₄×C₁₉	—	4	4	no	—
41	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
42	C₂³×C₄×C₁₉	D₄	1	4	yes	—
43	C₂³×C₄×C₁₉	Q₈	1	4	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₉	—	2	32	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
61	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
62	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
63	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
71	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
72	C₂×C₂²⋊C₄×C₁₉	Q₈	1	4	yes	—
73	C₂×C₄²×C₁₉	—	2	2	no	—
74	C₂×C₄²×C₁₉	—	2	2	no	—
75	C₂×C₄²×C₁₉	—	2	4	no	—
76	C₂×C₄²×C₁₉	—	2	4	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	8	no	—
80	C₁₉×#95	—	2	8	no	—
81	C₁₉×#95	—	4	4	no	—
82	C₁₉×#95	C₂×C₄	1	8	yes	complemented
83	C₂⁴×C₁₉	—	2	2	no	—
84	C₂⁴×C₁₉	—	2	2	no	—
85	C₂⁴×C₁₉	—	2	2	no	—
86	C₂⁴×C₁₉	—	2	2	no	—
87	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
88	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
89	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
90	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
91	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
92	C₂⁴×C₁₉	#41	1	2	yes	—
93	C₂⁴×C₁₉	#41	1	2	yes	—
94	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	16	no	—
98	C₂²×C₄×C₁₉	—	2	8	no	—
99	C₂²×C₄×C₁₉	—	2	16	no	—
100	C₂²×C₄×C₁₉	—	2	8	no	—
101	C₂²×C₄×C₁₉	—	2	16	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	4	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	2	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	2	no	—
127	C₂²×C₄×C₁₉	—	2	4	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	4	16	no	—
131	C₂²×C₄×C₁₉	—	4	16	no	—
132	C₂²×C₄×C₁₉	—	4	8	no	—
133	C₂²×C₄×C₁₉	—	4	8	no	—
134	C₂²×C₄×C₁₉	C₄⋊C₄	1	16	yes	complemented
135	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
136	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂²×C₄	1	2	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	8	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
148	C₂²×C₄×C₁₉	#41	1	4	yes	—
149	C₄⋊C₄×C₁₉	—	2	16	no	—
150	C₄⋊C₄×C₁₉	—	2	16	no	—
151	C₄⋊C₄×C₁₉	—	2	16	no	—
152	C₄⋊C₄×C₁₉	—	4	16	no	—
153	C₂²⋊C₄×C₁₉	—	2	16	no	—
154	C₂²⋊C₄×C₁₉	—	2	8	no	—
155	C₂²⋊C₄×C₁₉	—	2	8	no	—
156	C₄²×C₁₉	—	4	4	no	—
157	C₄²×C₁₉	—	4	4	no	—
158	#14130	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	2	4	no	—
160	C₂³×C₁₉	—	2	4	no	—
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	2	4	no	—
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	—	2	2	no	—
166	C₂³×C₁₉	—	2	4	no	—
167	C₂³×C₁₉	—	2	4	no	—
168	C₂³×C₁₉	—	2	4	no	—
169	C₂³×C₁₉	—	2	4	no	—
170	C₂³×C₁₉	—	2	4	no	—
171	C₂³×C₁₉	—	2	4	no	—
172	C₂³×C₁₉	—	2	4	no	—
173	C₂³×C₁₉	—	2	4	no	—
174	C₂³×C₁₉	—	2	4	no	—
175	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
176	C₂³×C₁₉	C₄×D₄	1	4	yes	—
177	C₂³×C₁₉	C₄×Q₈	1	4	yes	—
178	C₂³×C₁₉	#121	1	4	yes	—
179	C₂³×C₁₉	C₂²⋊Q₈	1	4	yes	—
180	C₂³×C₁₉	#125	1	4	yes	—
181	C₂³×C₁₉	C₄⋊Q₈	1	4	yes	—
182	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
183	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
184	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
185	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
186	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
187	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
188	C₂³×C₁₉	C₂×#41	1	2	yes	—
189	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
190	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
191	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
192	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	32	no	—
198	C₂×C₄×C₁₉	—	2	8	no	—
199	C₂×C₄×C₁₉	—	2	8	no	—
200	C₂×C₄×C₁₉	—	2	8	no	—
201	C₂×C₄×C₁₉	—	2	8	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	2	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	8	no	—
208	C₂×C₄×C₁₉	—	2	8	no	—
209	C₂×C₄×C₁₉	—	2	4	no	—
210	C₂×C₄×C₁₉	—	2	4	no	—
211	C₂×C₄×C₁₉	—	2	4	no	—
212	C₂×C₄×C₁₉	—	4	32	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	4	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	4	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	4	no	—
224	C₂×C₄×C₁₉	—	4	4	no	—
225	C₂×C₄×C₁₉	—	4	2	no	—
226	C₂×C₄×C₁₉	—	4	4	no	—
227	C₂×C₄×C₁₉	—	4	4	no	—
228	C₂×C₄×C₁₉	—	4	4	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	4	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
234	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
235	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
236	C₂×C₄×C₁₉	#120	1	4	yes	—
237	C₂×C₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
238	C₂×C₄×C₁₉	#123	1	4	yes	—
239	C₂³×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
240	C₂×#389	C₂×C₁₉	1	2	yes	complemented
241	C₂×#385	C₂×C₁₉	1	2	yes	—
242	C₂×#380	C₂×C₁₉	1	1	yes	characteristic
243	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
244	#1444	C₂×C₁₉	1	2	yes	complemented
245	#1442	C₂×C₁₉	1	2	yes	complemented
246	C₄⋊#95	C₂×C₁₉	1	2	yes	complemented
247	C₂²⋊#95	C₂×C₁₉	1	2	yes	—
248	C₂²×C₁₉	—	2	4	no	—
249	C₂²×C₁₉	—	2	8	no	—
250	C₂²×C₁₉	—	2	8	no	—
251	C₂²×C₁₉	—	2	4	no	—
252	C₂²×C₁₉	—	2	4	no	—
253	C₂²×C₁₉	—	2	8	no	—
254	C₂²×C₁₉	—	2	8	no	—
255	C₂²×C₁₉	—	2	4	no	—
256	C₂²×C₁₉	—	2	4	no	—
257	C₂²×C₁₉	—	2	4	no	—
258	C₂²×C₁₉	#389	1	8	yes	complemented
259	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
260	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
261	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂²×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
263	C₂²×C₁₉	#520	1	2	yes	—
264	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
265	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
266	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
267	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
268	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
269	C₂²×C₁₉	C₂×#125	1	1	yes	characteristic
270	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
271	C₂²×C₁₉	#535	1	1	yes	characteristic
272	C₂²×C₁₉	#536	1	1	yes	characteristic
273	C₂²×C₁₉	#544	1	2	yes	—
274	C₂²×C₁₉	D₄²	1	2	yes	—
275	C₂²×C₁₉	#546	1	2	yes	—
276	C₂²×C₁₉	#547	1	2	yes	—
277	C₂²×C₁₉	#548	1	2	yes	—
278	C₂²×C₁₉	D₄×Q₈	1	2	yes	—
279	C₂²×C₁₉	#552	1	2	yes	—
280	C₂²×C₁₉	#553	1	2	yes	—
281	C₂²×C₁₉	#554	1	2	yes	—
282	C₄×C₁₉	—	2	4	no	—
283	C₄×C₁₉	—	4	8	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	4	8	no	—
286	C₄×C₁₉	—	4	2	no	—
287	C₄×C₁₉	—	4	2	no	—
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	#385	1	8	yes	complemented
290	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
291	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
292	C₂²×C₄⋊C₄	—	2	4	no	—
293	C₂²×C₄⋊C₄	—	2	8	no	—
294	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
295	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
296	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
297	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
298	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
299	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
300	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
301	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
302	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
303	#389	—	2	8	no	—
304	#385	—	2	8	no	—
305	#380	C₄×C₁₉	1	8	yes	complemented
306	C₄×C₂²⋊C₄	—	2	4	no	—
307	C₂×#95	C₂²×C₁₉	1	4	yes	—
308	C₂×#95	C₂²×C₁₉	1	4	yes	—
309	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×#95	C₂²×C₁₉	1	4	yes	—
312	C₂×#95	C₂²×C₁₉	1	2	yes	—
313	C₂×C₁₉	—	2	8	no	—
314	C₂×C₁₉	C₂×#385	1	1	yes	characteristic
315	C₂×C₁₉	C₂×#389	1	1	yes	characteristic
316	C₂×C₁₉	#2317	1	1	yes	characteristic
317	C₂×C₁₉	#2360	1	2	yes	—
318	C₂×C₁₉	#2361	1	2	yes	—
319	C₂×C₁₉	#2408	1	1	yes	characteristic
320	C₂×C₁₉	#2409	1	1	yes	characteristic
321	C₂×C₁₉	#2440	1	2	yes	—
322	C₂×C₁₉	#2442	1	2	yes	—
323	C₂×C₁₉	#2486	1	1	yes	characteristic
324	C₂×C₁₉	#2487	1	1	yes	characteristic
325	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
326	C₂³×C₄	—	2	4	no	—
327	C₂³×C₄	—	2	4	no	—
328	C₂³×C₄	—	2	4	no	—
329	C₂³×C₄	—	2	8	no	—
330	C₂³×C₄	—	2	4	no	—
331	C₂³×C₄	—	2	4	no	—
332	C₂³×C₄	—	4	4	no	—
333	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
334	C₂³×C₄	D₄×C₁₉	1	4	yes	—
335	C₂³×C₄	Q₈×C₁₉	1	4	yes	—
336	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
337	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
338	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
340	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	—	2	32	no	—
345	C₂×C₄⋊C₄	—	2	8	no	—
346	C₂×C₄⋊C₄	—	2	4	no	—
347	C₂×C₄⋊C₄	—	2	4	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	4	no	—
350	C₂×C₄⋊C₄	—	2	4	no	—
351	C₂×C₄⋊C₄	—	2	8	no	—
352	C₂×C₄⋊C₄	—	2	8	no	—
353	C₂×C₄⋊C₄	—	4	4	no	—
354	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
355	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	4	no	—
359	C₂×C₂²⋊C₄	—	2	4	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
363	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	—
364	C₂×C₂²⋊C₄	Q₈×C₁₉	1	4	yes	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	4	no	—
368	C₂×C₄²	—	2	4	no	—
369	#95	—	2	2	no	—
370	#95	—	2	2	no	—
371	#95	—	2	8	no	—
372	#95	—	2	8	no	—
373	#95	—	4	4	no	—
374	#95	C₂×C₄×C₁₉	1	8	yes	complemented
375	C₁₉	#14130	1	1	yes	characteristic, direct product factor, Sylow
376	C₂⁴	—	2	2	no	—
377	C₂⁴	—	2	2	no	—
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
381	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
382	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
383	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
384	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
385	C₂⁴	#41×C₁₉	1	2	yes	—
386	C₂⁴	#41×C₁₉	1	2	yes	—
387	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	16	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	2	16	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	2	16	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	4	16	no	—
424	C₂²×C₄	—	4	16	no	—
425	C₂²×C₄	—	4	8	no	—
426	C₂²×C₄	—	4	8	no	—
427	C₂²×C₄	C₄⋊C₄×C₁₉	1	16	yes	complemented
428	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
429	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
430	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
433	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
435	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
436	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
437	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
438	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
439	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
440	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
441	C₂²×C₄	#41×C₁₉	1	4	yes	—
442	C₄⋊C₄	—	2	16	no	—
443	C₄⋊C₄	—	2	16	no	—
444	C₄⋊C₄	—	2	16	no	—
445	C₄⋊C₄	—	4	16	no	—
446	C₂²⋊C₄	—	2	16	no	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	8	no	—
449	C₄²	—	4	4	no	—
450	C₄²	—	4	4	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	2	4	no	—
467	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
468	C₂³	C₄×D₄×C₁₉	1	4	yes	—
469	C₂³	C₄×Q₈×C₁₉	1	4	yes	—
470	C₂³	C₁₉×#121	1	4	yes	—
471	C₂³	C₁₉×C₂²⋊Q₈	1	4	yes	—
472	C₂³	C₁₉×#125	1	4	yes	—
473	C₂³	C₁₉×C₄⋊Q₈	1	4	yes	—
474	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
475	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
476	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
477	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
478	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
479	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
480	C₂³	C₂×#41×C₁₉	1	2	yes	—
481	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
482	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
483	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
484	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	32	no	—
490	C₂×C₄	—	2	8	no	—
491	C₂×C₄	—	2	8	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	8	no	—
500	C₂×C₄	—	2	8	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	4	32	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
526	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
527	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
528	C₂×C₄	C₁₉×#120	1	4	yes	—
529	C₂×C₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
530	C₂×C₄	C₁₉×#123	1	4	yes	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	8	no	—
534	C₂²	—	2	8	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	2	4	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	2	8	no	—
540	C₂²	—	2	8	no	—
541	C₂²	C₁₉×#389	1	8	yes	complemented
542	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
543	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
544	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
545	C₂²	C₂×C₄×Q₈×C₁₉	1	1	yes	characteristic
546	C₂²	C₁₉×#520	1	2	yes	—
547	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
548	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
549	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
550	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
551	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
552	C₂²	C₂×C₁₉×#125	1	1	yes	characteristic
553	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
554	C₂²	C₁₉×#535	1	1	yes	characteristic
555	C₂²	C₁₉×#536	1	1	yes	characteristic
556	C₂²	C₁₉×#544	1	2	yes	—
557	C₂²	D₄²×C₁₉	1	2	yes	—
558	C₂²	C₁₉×#546	1	2	yes	—
559	C₂²	C₁₉×#547	1	2	yes	—
560	C₂²	C₁₉×#548	1	2	yes	—
561	C₂²	D₄×Q₈×C₁₉	1	2	yes	—
562	C₂²	C₁₉×#552	1	2	yes	—
563	C₂²	C₁₉×#553	1	2	yes	—
564	C₂²	C₁₉×#554	1	2	yes	—
565	C₄	—	2	4	no	—
566	C₄	—	4	8	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	8	no	—
572	C₄	C₁₉×#385	1	8	yes	complemented
573	C₂	—	2	8	no	—
574	C₂	C₂×C₁₉×#385	1	1	yes	characteristic
575	C₂	C₂×C₁₉×#389	1	1	yes	characteristic
576	C₂	C₁₉×#2317	1	1	yes	characteristic
577	C₂	C₁₉×#2360	1	2	yes	—
578	C₂	C₁₉×#2361	1	2	yes	—
579	C₂	C₁₉×#2408	1	1	yes	characteristic
580	C₂	C₁₉×#2409	1	1	yes	characteristic
581	C₂	C₁₉×#2440	1	2	yes	—
582	C₂	C₁₉×#2442	1	2	yes	—
583	C₂	C₁₉×#2486	1	1	yes	characteristic
584	C₂	C₁₉×#2487	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
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. C₂×C₁₉×#389	C₂	semidirect
6. C₁₉×#1444	C₂	semidirect
7. C₁₉×#1442	C₂	semidirect
8. C₁₉×C₄⋊#95	C₂	semidirect
25. C₁₉×#380	C₄	semidirect
62. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
82. C₁₉×#95	C₂×C₄	semidirect
134. C₂²×C₄×C₁₉	C₄⋊C₄	semidirect
158. #14130	C₁₉	direct (N × H)
240. C₂×#389	C₂×C₁₉	semidirect
244. #1444	C₂×C₁₉	semidirect
245. #1442	C₂×C₁₉	semidirect
246. C₄⋊#95	C₂×C₁₉	semidirect
258. C₂²×C₁₉	#389	semidirect
289. C₄×C₁₉	#385	semidirect
305. #380	C₄×C₁₉	semidirect
354. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
374. #95	C₂×C₄×C₁₉	semidirect
375. C₁₉	#14130	direct (N × H)
427. C₂²×C₄	C₄⋊C₄×C₁₉	semidirect
541. C₂²	C₁₉×#389	semidirect
572. C₄	C₁₉×#385	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₁₉	2
C₂×C₁₉×#389	2
C₂×C₁₉×#385	2
C₂×C₁₉×#380	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1444	2
C₁₉×#1442	2
C₁₉×C₄⋊#95	2
C₁₉×C₂²⋊#95	2
#14130	19

Subgroups — C19×#14130 #18020089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14130 #18020089