Subgroups — C₄×C₁₉×#562 #18040311

Order 4864.

2248 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#562	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2382	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2379	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2378	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2377	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2376	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₁₉×#124	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₉×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
10	C₄×C₁₉×#123	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₉×#121	C₂	1	4	yes	maximal, complemented
12	C₁₉×#562	C₄	1	16	yes	direct product factor
13	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#124	C₂²	1	2	yes	—
15	C₂×C₁₉×#123	C₂²	1	4	yes	—
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
17	C₂×C₁₉×#121	C₂²	1	4	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	2	yes	—
21	C₂²×C₄²×C₁₉	C₂²	1	4	yes	—
22	C₁₉×#391	C₂²	1	4	yes	—
23	C₁₉×#391	C₂²	1	2	yes	—
24	C₁₉×#390	C₂²	1	4	yes	—
25	C₁₉×#390	C₂²	1	2	yes	—
26	C₁₉×#389	C₂²	1	4	yes	—
27	C₁₉×#389	C₂²	1	4	yes	—
28	C₁₉×#389	C₂²	1	2	yes	—
29	C₁₉×#388	C₂²	1	4	yes	—
30	C₁₉×#388	C₂²	1	4	yes	—
31	C₁₉×#388	C₂²	1	4	yes	—
32	C₁₉×#388	C₂²	1	4	yes	—
33	C₁₉×#388	C₂²	1	4	yes	—
34	C₁₉×#388	C₂²	1	4	yes	—
35	C₁₉×#387	C₂²	1	4	yes	—
36	C₁₉×#387	C₂²	1	4	yes	—
37	C₁₉×#387	C₂²	1	4	yes	—
38	C₁₉×#387	C₂²	1	4	yes	—
39	C₁₉×#387	C₂²	1	4	yes	—
40	C₁₉×#386	C₂²	1	4	yes	—
41	C₁₉×#386	C₂²	1	4	yes	—
42	C₁₉×#386	C₂²	1	4	yes	—
43	C₁₉×#385	C₂²	1	4	yes	—
44	C₁₉×#385	C₂²	1	4	yes	—
45	C₁₉×#385	C₂²	1	4	yes	—
46	C₁₉×#382	C₂²	1	2	yes	—
47	C₁₉×#382	C₂²	1	1	yes	characteristic
48	C₁₉×#381	C₂²	1	4	yes	—
49	C₁₉×#380	C₂²	1	4	yes	—
50	C₁₉×#380	C₂²	1	4	yes	—
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
53	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
54	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
55	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
56	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
57	C₄³×C₁₉	C₂²	1	1	yes	characteristic
58	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
64	C₁₉×#125	C₂×C₄	1	8	yes	complemented
65	C₁₉×#124	C₂×C₄	1	16	yes	complemented
66	C₁₉×#123	C₂×C₄	1	32	yes	complemented
67	C₁₉×C₂²⋊Q₈	C₂×C₄	1	32	yes	complemented
68	C₁₉×#121	C₂×C₄	1	32	yes	complemented
69	C₄×Q₈×C₁₉	—	4	4	no	—
70	C₄×D₄×C₁₉	—	4	8	no	—
71	C₄×D₄×C₁₉	—	4	4	no	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
83	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
91	C₂×C₄²×C₁₉	—	4	8	no	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
95	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
99	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#95	C₂³	1	4	yes	—
102	C₁₉×#95	C₂³	1	4	yes	—
103	C₁₉×#95	C₂³	1	4	yes	—
104	C₁₉×#95	C₂³	1	4	yes	—
105	C₁₉×#95	C₂³	1	4	yes	—
106	C₁₉×#95	C₂³	1	4	yes	—
107	C₁₉×#95	C₂³	1	4	yes	—
108	C₁₉×#95	C₂³	1	4	yes	—
109	C₁₉×#95	C₂³	1	4	yes	—
110	C₁₉×#95	C₂³	1	4	yes	—
111	C₁₉×#95	C₂³	1	4	yes	—
112	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
113	C₂×Q₈×C₁₉	—	4	2	no	—
114	C₂×Q₈×C₁₉	—	4	2	no	—
115	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
116	C₂×D₄×C₁₉	—	4	4	no	—
117	C₂×D₄×C₁₉	—	4	2	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	—	4	4	no	—
120	C₂×D₄×C₁₉	C₂²×C₄	1	16	yes	—
121	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
122	C₂²×C₄×C₁₉	—	2	8	no	—
123	C₂²×C₄×C₁₉	—	2	8	no	—
124	C₂²×C₄×C₁₉	—	2	8	no	—
125	C₂²×C₄×C₁₉	—	4	4	no	—
126	C₂²×C₄×C₁₉	—	4	4	no	—
127	C₂²×C₄×C₁₉	—	4	4	no	—
128	C₂²×C₄×C₁₉	—	4	4	no	—
129	C₂²×C₄×C₁₉	—	4	4	no	—
130	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
131	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
141	C₄⋊C₄×C₁₉	—	4	2	no	—
142	C₄⋊C₄×C₁₉	—	4	4	no	—
143	C₄⋊C₄×C₁₉	—	4	4	no	—
144	C₄⋊C₄×C₁₉	—	4	4	no	—
145	C₄⋊C₄×C₁₉	—	4	2	no	—
146	C₄⋊C₄×C₁₉	—	4	4	no	—
147	C₄⋊C₄×C₁₉	—	4	2	no	—
148	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
149	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
150	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
151	C₂²⋊C₄×C₁₉	—	4	4	no	—
152	C₂²⋊C₄×C₁₉	—	4	4	no	—
153	C₂²⋊C₄×C₁₉	—	4	4	no	—
154	C₂²⋊C₄×C₁₉	—	4	4	no	—
155	C₂²⋊C₄×C₁₉	—	4	4	no	—
156	C₂²⋊C₄×C₁₉	—	4	4	no	—
157	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
158	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
159	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
160	C₄²×C₁₉	—	2	8	no	—
161	C₄²×C₁₉	—	2	8	no	—
162	C₄²×C₁₉	—	2	4	no	—
163	C₄²×C₁₉	—	2	2	no	—
164	C₄²×C₁₉	—	4	4	no	—
165	C₄²×C₁₉	—	4	4	no	—
166	C₄²×C₁₉	—	4	1	no	—
167	C₄²×C₁₉	—	4	2	no	—
168	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
169	C₄×#562	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	4	no	—
176	C₂³×C₁₉	C₂³×C₄	1	8	yes	—
177	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
178	Q₈×C₁₉	—	4	8	no	—
179	D₄×C₁₉	—	4	16	no	—
180	D₄×C₁₉	—	4	8	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	4	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	4	16	no	—
204	C₂×C₄×C₁₉	—	4	16	no	—
205	C₂×C₄×C₁₉	—	4	16	no	—
206	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
207	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
208	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
209	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
210	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
211	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
212	C₂×#562	C₂×C₁₉	1	1	yes	characteristic
213	#2382	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#2379	C₂×C₁₉	1	2	yes	complemented
215	#2378	C₂×C₁₉	1	4	yes	complemented
216	#2377	C₂×C₁₉	1	4	yes	complemented
217	#2376	C₂×C₁₉	1	4	yes	complemented
218	C₄×#125	C₂×C₁₉	1	1	yes	characteristic, complemented
219	C₄×#124	C₂×C₁₉	1	2	yes	complemented
220	C₄×C₂²⋊Q₈	C₂×C₁₉	1	4	yes	complemented
221	C₄×#123	C₂×C₁₉	1	4	yes	complemented
222	C₄×#121	C₂×C₁₉	1	4	yes	complemented
223	C₂²×C₁₉	—	2	8	no	—
224	C₂²×C₁₉	—	2	8	no	—
225	C₂²×C₁₉	—	2	8	no	—
226	C₂²×C₁₉	—	4	4	no	—
227	C₂²×C₁₉	—	4	4	no	—
228	C₂²×C₁₉	—	4	4	no	—
229	C₂²×C₁₉	—	4	4	no	—
230	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
231	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
232	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
233	C₂²×C₁₉	#585	1	2	yes	—
234	C₂²×C₁₉	#585	1	1	yes	characteristic
235	C₄×C₁₉	—	2	8	no	—
236	C₄×C₁₉	—	2	8	no	—
237	C₄×C₁₉	—	2	4	no	—
238	C₄×C₁₉	—	2	2	no	—
239	C₄×C₁₉	—	4	4	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	4	no	—
242	C₄×C₁₉	—	4	4	no	—
243	C₄×C₁₉	—	4	1	no	—
244	C₄×C₁₉	#562	1	4	yes	direct product factor
245	#562	C₄×C₁₉	1	16	yes	direct product factor
246	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
247	C₂×#124	C₂²×C₁₉	1	2	yes	—
248	C₂×#123	C₂²×C₁₉	1	4	yes	—
249	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
250	C₂×#121	C₂²×C₁₉	1	4	yes	—
251	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
252	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
253	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
254	C₂²×C₄²	C₂²×C₁₉	1	4	yes	—
255	#391	C₂²×C₁₉	1	2	yes	—
256	#391	C₂²×C₁₉	1	4	yes	—
257	#390	C₂²×C₁₉	1	4	yes	—
258	#390	C₂²×C₁₉	1	2	yes	—
259	#389	C₂²×C₁₉	1	2	yes	—
260	#389	C₂²×C₁₉	1	4	yes	—
261	#389	C₂²×C₁₉	1	4	yes	—
262	#388	C₂²×C₁₉	1	4	yes	—
263	#388	C₂²×C₁₉	1	4	yes	—
264	#388	C₂²×C₁₉	1	4	yes	—
265	#388	C₂²×C₁₉	1	4	yes	—
266	#388	C₂²×C₁₉	1	4	yes	—
267	#388	C₂²×C₁₉	1	4	yes	—
268	#387	C₂²×C₁₉	1	4	yes	—
269	#387	C₂²×C₁₉	1	4	yes	—
270	#387	C₂²×C₁₉	1	4	yes	—
271	#387	C₂²×C₁₉	1	4	yes	—
272	#387	C₂²×C₁₉	1	4	yes	—
273	#386	C₂²×C₁₉	1	4	yes	—
274	#386	C₂²×C₁₉	1	4	yes	—
275	#386	C₂²×C₁₉	1	4	yes	—
276	#385	C₂²×C₁₉	1	4	yes	—
277	#385	C₂²×C₁₉	1	4	yes	—
278	#385	C₂²×C₁₉	1	4	yes	—
279	#382	C₂²×C₁₉	1	1	yes	characteristic
280	#382	C₂²×C₁₉	1	2	yes	—
281	#381	C₂²×C₁₉	1	4	yes	—
282	#380	C₂²×C₁₉	1	4	yes	—
283	#380	C₂²×C₁₉	1	4	yes	—
284	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
285	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
286	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
287	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
288	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
289	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
290	C₄³	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×C₁₉	—	4	8	no	—
292	C₂×C₁₉	C₄×H(5,𝔽₂)	1	2	yes	—
293	C₂×C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
294	C₂×C₁₉	C₂×#562	1	1	yes	characteristic
295	C₂×C₁₉	#3529	1	2	yes	—
296	C₂×C₁₉	#3531	1	1	yes	characteristic
297	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
298	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
299	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
300	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
301	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
302	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
303	#125	C₂×C₄×C₁₉	1	8	yes	complemented
304	#124	C₂×C₄×C₁₉	1	16	yes	complemented
305	#123	C₂×C₄×C₁₉	1	32	yes	complemented
306	C₂²⋊Q₈	C₂×C₄×C₁₉	1	32	yes	complemented
307	#121	C₂×C₄×C₁₉	1	32	yes	complemented
308	C₄×Q₈	—	4	4	no	—
309	C₄×D₄	—	4	8	no	—
310	C₄×D₄	—	4	4	no	—
311	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
330	C₂×C₄²	—	4	8	no	—
331	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
332	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
333	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
334	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
336	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
338	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
339	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
340	#95	C₂³×C₁₉	1	4	yes	—
341	#95	C₂³×C₁₉	1	4	yes	—
342	#95	C₂³×C₁₉	1	4	yes	—
343	#95	C₂³×C₁₉	1	4	yes	—
344	#95	C₂³×C₁₉	1	4	yes	—
345	#95	C₂³×C₁₉	1	4	yes	—
346	#95	C₂³×C₁₉	1	4	yes	—
347	#95	C₂³×C₁₉	1	4	yes	—
348	#95	C₂³×C₁₉	1	4	yes	—
349	#95	C₂³×C₁₉	1	4	yes	—
350	#95	C₂³×C₁₉	1	4	yes	—
351	C₁₉	C₄×#562	1	1	yes	characteristic, direct product factor, Sylow
352	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
353	C₂×Q₈	—	4	2	no	—
354	C₂×Q₈	—	4	2	no	—
355	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	C₂²×C₄×C₁₉	1	16	yes	—
361	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
371	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
373	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
377	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
379	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
380	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	4	4	no	—
384	C₄⋊C₄	—	4	4	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
389	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
390	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₂²⋊C₄	—	4	4	no	—
397	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
398	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
399	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
400	C₄²	—	2	8	no	—
401	C₄²	—	2	8	no	—
402	C₄²	—	2	4	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	4	4	no	—
405	C₄²	—	4	4	no	—
406	C₄²	—	4	1	no	—
407	C₄²	—	4	2	no	—
408	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
409	C₂³	—	2	4	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	4	no	—
415	C₂³	C₂³×C₄×C₁₉	1	8	yes	—
416	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
417	Q₈	—	4	8	no	—
418	D₄	—	4	16	no	—
419	D₄	—	4	8	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	4	16	no	—
443	C₂×C₄	—	4	16	no	—
444	C₂×C₄	—	4	16	no	—
445	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
446	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
447	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
448	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
449	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
450	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
451	C₂²	—	2	8	no	—
452	C₂²	—	2	8	no	—
453	C₂²	—	2	8	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
459	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
460	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
461	C₂²	C₁₉×#585	1	2	yes	—
462	C₂²	C₁₉×#585	1	1	yes	characteristic
463	C₄	—	2	8	no	—
464	C₄	—	2	8	no	—
465	C₄	—	2	4	no	—
466	C₄	—	2	2	no	—
467	C₄	—	4	4	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	1	no	—
472	C₄	C₁₉×#562	1	4	yes	direct product factor
473	C₂	—	4	8	no	—
474	C₂	C₄×C₁₉×H(5,𝔽₂)	1	2	yes	—
475	C₂	C₄×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
476	C₂	C₂×C₁₉×#562	1	1	yes	characteristic
477	C₂	C₁₉×#3529	1	2	yes	—
478	C₂	C₁₉×#3531	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×#562	C₂
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×#2382	C₂	semidirect
3. C₁₉×#2379	C₂	semidirect
4. C₁₉×#2378	C₂	semidirect
5. C₁₉×#2377	C₂	semidirect
6. C₁₉×#2376	C₂	semidirect
7. C₄×C₁₉×#125	C₂	semidirect
8. C₄×C₁₉×#124	C₂	semidirect
9. C₄×C₁₉×C₂²⋊Q₈	C₂	semidirect
10. C₄×C₁₉×#123	C₂	semidirect
11. C₄×C₁₉×#121	C₂	semidirect
12. C₁₉×#562	C₄	direct (N × H)
64. C₁₉×#125	C₂×C₄	semidirect
65. C₁₉×#124	C₂×C₄	semidirect
66. C₁₉×#123	C₂×C₄	semidirect
67. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
68. C₁₉×#121	C₂×C₄	semidirect
169. C₄×#562	C₁₉	direct (N × H)
213. #2382	C₂×C₁₉	semidirect
214. #2379	C₂×C₁₉	semidirect
215. #2378	C₂×C₁₉	semidirect
216. #2377	C₂×C₁₉	semidirect
217. #2376	C₂×C₁₉	semidirect
218. C₄×#125	C₂×C₁₉	semidirect
219. C₄×#124	C₂×C₁₉	semidirect
220. C₄×C₂²⋊Q₈	C₂×C₁₉	semidirect
221. C₄×#123	C₂×C₁₉	semidirect
222. C₄×#121	C₂×C₁₉	semidirect
244. C₄×C₁₉	#562	direct (N × H)
245. #562	C₄×C₁₉	direct (N × H)
303. #125	C₂×C₄×C₁₉	semidirect
304. #124	C₂×C₄×C₁₉	semidirect
305. #123	C₂×C₄×C₁₉	semidirect
306. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
307. #121	C₂×C₄×C₁₉	semidirect
351. C₁₉	C₄×#562	direct (N × H)
472. C₄	C₁₉×#562	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×#562	2
C₁₉×#2382	2
C₁₉×#2379	2
C₁₉×#2378	2
C₁₉×#2377	2
C₁₉×#2376	2
C₄×C₁₉×#125	2
C₄×C₁₉×#124	2
C₄×C₁₉×C₂²⋊Q₈	2
C₄×C₁₉×#123	2
C₄×C₁₉×#121	2
C₄×#562	19

Subgroups — C4×C19×#562 #18040311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#562 #18040311