Subgroups — C₄×C₁₉×#559 #18040127

Order 4864.

2564 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#559	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2374	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2367	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2366	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2357	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2355	C₂	1	2	yes	maximal, complemented
7	C₄×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
8	C₄×C₁₉×#124	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₉×#123	C₂	1	4	yes	maximal, complemented
10	C₄²×Q₈×C₁₉	C₂	1	2	yes	maximal, complemented
11	C₄²×D₄×C₁₉	C₂	1	4	yes	maximal, complemented
12	C₁₉×#559	C₄	1	16	yes	direct product factor
13	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#124	C₂²	1	4	yes	—
15	C₂×C₁₉×#123	C₂²	1	4	yes	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
23	C₂²×C₄²×C₁₉	C₂²	1	4	yes	—
24	C₁₉×#391	C₂²	1	4	yes	—
25	C₁₉×#390	C₂²	1	4	yes	—
26	C₁₉×#390	C₂²	1	4	yes	—
27	C₁₉×#390	C₂²	1	2	yes	—
28	C₁₉×#388	C₂²	1	8	yes	—
29	C₁₉×#388	C₂²	1	8	yes	—
30	C₁₉×#388	C₂²	1	8	yes	—
31	C₁₉×#387	C₂²	1	8	yes	—
32	C₁₉×#386	C₂²	1	4	yes	—
33	C₁₉×#385	C₂²	1	4	yes	—
34	C₁₉×#384	C₂²	1	1	yes	characteristic
35	C₁₉×#382	C₂²	1	4	yes	—
36	C₁₉×#381	C₂²	1	4	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
45	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
46	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
47	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
48	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
49	C₄³×C₁₉	C₂²	1	4	yes	—
50	C₄³×C₁₉	C₂²	1	1	yes	characteristic
51	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
53	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
57	C₁₉×#127	C₂×C₄	1	8	yes	—
58	C₁₉×#124	C₂×C₄	1	32	yes	complemented
59	C₁₉×#123	C₂×C₄	1	32	yes	complemented
60	C₄×Q₈×C₁₉	—	2	8	no	—
61	C₄×Q₈×C₁₉	—	2	8	no	—
62	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	complemented
63	C₄×D₄×C₁₉	—	2	16	no	—
64	C₄×D₄×C₁₉	—	2	16	no	—
65	C₄×D₄×C₁₉	—	4	4	no	—
66	C₄×D₄×C₁₉	C₂×C₄	1	32	yes	complemented
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
81	C₂×C₄²×C₁₉	—	4	8	no	—
82	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
85	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
91	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
94	C₁₉×#95	C₂³	1	4	yes	—
95	C₁₉×#95	C₂³	1	8	yes	—
96	C₁₉×#95	C₂³	1	8	yes	—
97	C₁₉×#95	C₂³	1	8	yes	—
98	C₁₉×#95	C₂³	1	4	yes	—
99	C₁₉×#95	C₂³	1	4	yes	—
100	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
101	C₂×Q₈×C₁₉	—	2	4	no	—
102	C₂×Q₈×C₁₉	—	2	4	no	—
103	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
104	C₂×D₄×C₁₉	—	2	8	no	—
105	C₂×D₄×C₁₉	—	2	8	no	—
106	C₂×D₄×C₁₉	—	4	2	no	—
107	C₂×D₄×C₁₉	—	4	2	no	—
108	C₂×D₄×C₁₉	C₂²×C₄	1	16	yes	—
109	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
110	C₂²×C₄×C₁₉	—	2	16	no	—
111	C₂²×C₄×C₁₉	—	2	16	no	—
112	C₂²×C₄×C₁₉	—	2	8	no	—
113	C₂²×C₄×C₁₉	—	4	4	no	—
114	C₂²×C₄×C₁₉	—	4	4	no	—
115	C₂²×C₄×C₁₉	—	4	4	no	—
116	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₁₉	—	2	8	no	—
128	C₄⋊C₄×C₁₉	—	2	8	no	—
129	C₄⋊C₄×C₁₉	—	2	8	no	—
130	C₄⋊C₄×C₁₉	—	2	4	no	—
131	C₄⋊C₄×C₁₉	—	4	2	no	—
132	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
133	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
134	C₄⋊C₄×C₁₉	#41	1	8	yes	—
135	C₂²⋊C₄×C₁₉	—	2	16	no	—
136	C₂²⋊C₄×C₁₉	—	2	16	no	—
137	C₂²⋊C₄×C₁₉	—	4	4	no	—
138	C₂²⋊C₄×C₁₉	—	4	4	no	—
139	C₂²⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
140	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
141	C₄²×C₁₉	—	2	8	no	—
142	C₄²×C₁₉	—	2	8	no	—
143	C₄²×C₁₉	—	2	4	no	—
144	C₄²×C₁₉	—	2	8	no	—
145	C₄²×C₁₉	—	2	8	no	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	4	8	no	—
148	C₄²×C₁₉	—	4	1	no	—
149	C₄²×C₁₉	—	4	4	no	—
150	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
151	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
152	C₄²×C₁₉	#41	1	8	yes	—
153	C₄×#559	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	—	2	8	no	—
155	C₂³×C₁₉	—	2	8	no	—
156	C₂³×C₁₉	—	2	4	no	—
157	C₂³×C₁₉	—	2	4	no	—
158	C₂³×C₁₉	C₂³×C₄	1	8	yes	—
159	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
160	Q₈×C₁₉	—	2	16	no	—
161	D₄×C₁₉	—	2	32	no	—
162	D₄×C₁₉	—	4	8	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	4	no	—
169	C₂×C₄×C₁₉	—	2	1	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	1	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	8	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	4	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	4	16	no	—
181	C₂×C₄×C₁₉	—	4	16	no	—
182	C₂×C₄×C₁₉	—	4	16	no	—
183	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
184	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
185	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
186	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
187	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
188	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
189	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
190	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
191	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
192	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
193	C₂×#559	C₂×C₁₉	1	1	yes	characteristic
194	#2374	C₂×C₁₉	1	4	yes	complemented
195	#2367	C₂×C₁₉	1	4	yes	complemented
196	#2366	C₂×C₁₉	1	1	yes	characteristic
197	#2357	C₂×C₁₉	1	4	yes	complemented
198	#2355	C₂×C₁₉	1	2	yes	complemented
199	C₄×#127	C₂×C₁₉	1	1	yes	characteristic
200	C₄×#124	C₂×C₁₉	1	4	yes	complemented
201	C₄×#123	C₂×C₁₉	1	4	yes	complemented
202	C₄²×Q₈	C₂×C₁₉	1	2	yes	complemented
203	C₄²×D₄	C₂×C₁₉	1	4	yes	complemented
204	C₂²×C₁₉	—	2	16	no	—
205	C₂²×C₁₉	—	2	8	no	—
206	C₂²×C₁₉	—	4	4	no	—
207	C₂²×C₁₉	—	4	8	no	—
208	C₂²×C₁₉	—	4	4	no	—
209	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
210	C₂²×C₁₉	C₂²×#41	1	2	yes	—
211	C₂²×C₁₉	C₂²×#41	1	2	yes	—
212	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
213	C₂²×C₁₉	#585	1	1	yes	characteristic
214	C₄×C₁₉	—	2	8	no	—
215	C₄×C₁₉	—	2	8	no	—
216	C₄×C₁₉	—	2	2	no	—
217	C₄×C₁₉	—	2	4	no	—
218	C₄×C₁₉	—	2	8	no	—
219	C₄×C₁₉	—	4	4	no	—
220	C₄×C₁₉	—	4	4	no	—
221	C₄×C₁₉	—	4	1	no	—
222	C₄×C₁₉	C₄×#41	1	8	yes	—
223	C₄×C₁₉	#559	1	4	yes	direct product factor
224	#559	C₄×C₁₉	1	16	yes	direct product factor
225	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
226	C₂×#124	C₂²×C₁₉	1	4	yes	—
227	C₂×#123	C₂²×C₁₉	1	4	yes	—
228	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
229	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
230	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
231	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
232	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
233	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
234	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
235	C₂²×C₄²	C₂²×C₁₉	1	4	yes	—
236	#391	C₂²×C₁₉	1	4	yes	—
237	#390	C₂²×C₁₉	1	4	yes	—
238	#390	C₂²×C₁₉	1	2	yes	—
239	#390	C₂²×C₁₉	1	4	yes	—
240	#388	C₂²×C₁₉	1	8	yes	—
241	#388	C₂²×C₁₉	1	8	yes	—
242	#388	C₂²×C₁₉	1	8	yes	—
243	#387	C₂²×C₁₉	1	8	yes	—
244	#386	C₂²×C₁₉	1	4	yes	—
245	#385	C₂²×C₁₉	1	4	yes	—
246	#384	C₂²×C₁₉	1	1	yes	characteristic
247	#382	C₂²×C₁₉	1	4	yes	—
248	#381	C₂²×C₁₉	1	4	yes	—
249	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
250	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
251	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
252	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
253	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
254	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
255	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
256	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
257	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
258	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
259	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
260	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
261	C₄³	C₂²×C₁₉	1	1	yes	characteristic
262	C₄³	C₂²×C₁₉	1	4	yes	—
263	C₂×C₁₉	—	4	8	no	—
264	C₂×C₁₉	C₂×C₄×#41	1	2	yes	—
265	C₂×C₁₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₁₉	C₂×#559	1	1	yes	characteristic
267	C₂×C₁₉	#3480	1	2	yes	—
268	C₂×C₁₉	#3481	1	1	yes	characteristic
269	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
270	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
271	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
272	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
273	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
274	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
275	#127	C₂×C₄×C₁₉	1	8	yes	—
276	#124	C₂×C₄×C₁₉	1	32	yes	complemented
277	#123	C₂×C₄×C₁₉	1	32	yes	complemented
278	C₄×Q₈	—	2	8	no	—
279	C₄×Q₈	—	2	8	no	—
280	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
281	C₄×D₄	—	2	16	no	—
282	C₄×D₄	—	2	16	no	—
283	C₄×D₄	—	4	4	no	—
284	C₄×D₄	C₂×C₄×C₁₉	1	32	yes	complemented
285	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
299	C₂×C₄²	—	4	8	no	—
300	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
302	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
303	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
304	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
305	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
306	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
307	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
309	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
310	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
312	#95	C₂³×C₁₉	1	4	yes	—
313	#95	C₂³×C₁₉	1	8	yes	—
314	#95	C₂³×C₁₉	1	8	yes	—
315	#95	C₂³×C₁₉	1	8	yes	—
316	#95	C₂³×C₁₉	1	4	yes	—
317	#95	C₂³×C₁₉	1	4	yes	—
318	C₁₉	C₄×#559	1	1	yes	characteristic, direct product factor, Sylow
319	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
320	C₂×Q₈	—	2	4	no	—
321	C₂×Q₈	—	2	4	no	—
322	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
323	C₂×D₄	—	2	8	no	—
324	C₂×D₄	—	2	8	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	C₂²×C₄×C₁₉	1	16	yes	—
328	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
329	C₂²×C₄	—	2	16	no	—
330	C₂²×C₄	—	2	16	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	4	4	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
336	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
337	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
338	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
343	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
352	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
353	C₄⋊C₄	#41×C₁₉	1	8	yes	—
354	C₂²⋊C₄	—	2	16	no	—
355	C₂²⋊C₄	—	2	16	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₂²⋊C₄	—	4	4	no	—
358	C₂²⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
359	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
360	C₄²	—	2	8	no	—
361	C₄²	—	2	8	no	—
362	C₄²	—	2	4	no	—
363	C₄²	—	2	8	no	—
364	C₄²	—	2	8	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	4	8	no	—
367	C₄²	—	4	1	no	—
368	C₄²	—	4	4	no	—
369	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
370	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
371	C₄²	#41×C₁₉	1	8	yes	—
372	C₂³	—	2	8	no	—
373	C₂³	—	2	8	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	4	no	—
376	C₂³	C₂³×C₄×C₁₉	1	8	yes	—
377	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
378	Q₈	—	2	16	no	—
379	D₄	—	2	32	no	—
380	D₄	—	4	8	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	16	no	—
399	C₂×C₄	—	4	16	no	—
400	C₂×C₄	—	4	16	no	—
401	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
402	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
403	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
404	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
405	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
406	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
407	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
408	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
409	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
410	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
411	C₂²	—	2	16	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	8	no	—
415	C₂²	—	4	4	no	—
416	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
417	C₂²	C₂²×#41×C₁₉	1	2	yes	—
418	C₂²	C₂²×#41×C₁₉	1	2	yes	—
419	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂²	C₁₉×#585	1	1	yes	characteristic
421	C₄	—	2	8	no	—
422	C₄	—	2	8	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	8	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	1	no	—
429	C₄	C₄×#41×C₁₉	1	8	yes	—
430	C₄	C₁₉×#559	1	4	yes	direct product factor
431	C₂	—	4	8	no	—
432	C₂	C₂×C₄×#41×C₁₉	1	2	yes	—
433	C₂	C₄×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
434	C₂	C₂×C₁₉×#559	1	1	yes	characteristic
435	C₂	C₁₉×#3480	1	2	yes	—
436	C₂	C₁₉×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂×C₁₉×#127	C₂²
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
2. C₁₉×#2374	C₂	semidirect
3. C₁₉×#2367	C₂	semidirect
5. C₁₉×#2357	C₂	semidirect
6. C₁₉×#2355	C₂	semidirect
8. C₄×C₁₉×#124	C₂	semidirect
9. C₄×C₁₉×#123	C₂	semidirect
10. C₄²×Q₈×C₁₉	C₂	semidirect
11. C₄²×D₄×C₁₉	C₂	semidirect
12. C₁₉×#559	C₄	direct (N × H)
58. C₁₉×#124	C₂×C₄	semidirect
59. C₁₉×#123	C₂×C₄	semidirect
62. C₄×Q₈×C₁₉	C₂×C₄	semidirect
66. C₄×D₄×C₁₉	C₂×C₄	semidirect
153. C₄×#559	C₁₉	direct (N × H)
194. #2374	C₂×C₁₉	semidirect
195. #2367	C₂×C₁₉	semidirect
197. #2357	C₂×C₁₉	semidirect
198. #2355	C₂×C₁₉	semidirect
200. C₄×#124	C₂×C₁₉	semidirect
201. C₄×#123	C₂×C₁₉	semidirect
202. C₄²×Q₈	C₂×C₁₉	semidirect
203. C₄²×D₄	C₂×C₁₉	semidirect
223. C₄×C₁₉	#559	direct (N × H)
224. #559	C₄×C₁₉	direct (N × H)
276. #124	C₂×C₄×C₁₉	semidirect
277. #123	C₂×C₄×C₁₉	semidirect
280. C₄×Q₈	C₂×C₄×C₁₉	semidirect
284. C₄×D₄	C₂×C₄×C₁₉	semidirect
318. C₁₉	C₄×#559	direct (N × H)
430. C₄	C₁₉×#559	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#559	2
C₁₉×#2374	2
C₁₉×#2367	2
C₁₉×#2366	2
C₁₉×#2357	2
C₁₉×#2355	2
C₄×C₁₉×#127	2
C₄×C₁₉×#124	2
C₄×C₁₉×#123	2
C₄²×Q₈×C₁₉	2
C₄²×D₄×C₁₉	2
C₄×#559	19

Subgroups — C4×C19×#559 #18040127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#559 #18040127