Subgroups — C₂×C₁₉×#2544 #18040845

Order 4864.

4174 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2544	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₉×#394	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#386	C₂	1	4	yes	maximal, complemented
10	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₉	C₂²	1	4	yes	—
14	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₁₉×#127	—	2	8	no	—
17	C₂×C₁₉×#127	C₂²	1	8	yes	—
18	C₂×C₁₉×#124	—	2	8	no	—
19	C₂×C₁₉×#124	—	2	8	no	—
20	C₂×C₁₉×#124	C₂²	1	8	yes	complemented
21	C₂×C₁₉×#124	C₂²	1	8	yes	complemented
22	C₂×C₄×D₄×C₁₉	—	2	8	no	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
28	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
31	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#394	C₂²	1	32	yes	complemented
35	C₁₉×#391	C₂²	1	8	yes	complemented
36	C₁₉×#390	C₂²	1	8	yes	complemented
37	C₁₉×#386	C₂²	1	32	yes	complemented
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	complemented
39	C₂×C₁₉×#95	C₂²	1	2	yes	—
40	C₂×C₁₉×#95	C₂²	1	4	yes	—
41	C₂⁵×C₁₉	C₂³	1	2	yes	—
42	C₂⁵×C₁₉	C₂³	1	2	yes	—
43	C₂²×Q₈×C₁₉	—	2	4	no	—
44	C₂²×Q₈×C₁₉	—	2	4	no	—
45	C₂²×Q₈×C₁₉	—	2	4	no	—
46	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
47	C₂²×D₄×C₁₉	—	2	16	no	—
48	C₂²×D₄×C₁₉	—	2	4	no	—
49	C₂²×D₄×C₁₉	—	2	4	no	—
50	C₂²×D₄×C₁₉	—	2	4	no	—
51	C₂²×D₄×C₁₉	—	2	4	no	—
52	C₂²×D₄×C₁₉	—	2	16	no	—
53	C₂²×D₄×C₁₉	—	2	4	no	—
54	C₂²×D₄×C₁₉	—	4	8	no	—
55	C₂²×D₄×C₁₉	D₄	1	8	yes	—
56	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₉	C₂³	1	16	yes	—
58	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₉	—	2	8	no	—
60	C₂³×C₄×C₁₉	—	4	8	no	—
61	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×#127	—	2	32	no	—
70	C₁₉×#124	—	2	32	no	—
71	C₁₉×#124	—	2	32	no	—
72	C₄×D₄×C₁₉	—	2	32	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
82	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
83	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
84	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
85	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
87	C₂×C₄²×C₁₉	—	2	4	no	—
88	C₂×C₄²×C₁₉	—	2	4	no	—
89	C₂×C₄²×C₁₉	D₄	1	8	yes	complemented
90	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
91	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
93	C₁₉×#95	C₂³	1	8	yes	—
94	C₁₉×#95	C₂³	1	16	yes	—
95	C₂⁴×C₁₉	—	2	4	no	—
96	C₂⁴×C₁₉	—	2	4	no	—
97	C₂⁴×C₁₉	—	2	8	no	—
98	C₂⁴×C₁₉	—	2	8	no	—
99	C₂⁴×C₁₉	—	2	4	no	—
100	C₂⁴×C₁₉	—	2	4	no	—
101	C₂⁴×C₁₉	—	2	4	no	—
102	C₂⁴×C₁₉	—	2	8	no	—
103	C₂⁴×C₁₉	—	2	8	no	—
104	C₂⁴×C₁₉	C₂×D₄	1	8	yes	—
105	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
106	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
107	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
108	C₂×Q₈×C₁₉	—	2	8	no	—
109	C₂×Q₈×C₁₉	—	2	8	no	—
110	C₂×Q₈×C₁₉	—	2	8	no	—
111	C₂×Q₈×C₁₉	—	4	16	no	—
112	C₂×D₄×C₁₉	—	2	32	no	—
113	C₂×D₄×C₁₉	—	2	32	no	—
114	C₂×D₄×C₁₉	—	2	8	no	—
115	C₂×D₄×C₁₉	—	2	8	no	—
116	C₂×D₄×C₁₉	—	2	8	no	—
117	C₂×D₄×C₁₉	—	2	8	no	—
118	C₂×D₄×C₁₉	—	2	32	no	—
119	C₂×D₄×C₁₉	—	2	8	no	—
120	C₂×D₄×C₁₉	—	4	16	no	—
121	C₂×D₄×C₁₉	—	4	64	no	—
122	C₂×D₄×C₁₉	—	4	16	no	—
123	C₂×D₄×C₁₉	C₂×D₄	1	16	yes	—
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	4	no	—
128	C₂²×C₄×C₁₉	—	2	4	no	—
129	C₂²×C₄×C₁₉	—	2	4	no	—
130	C₂²×C₄×C₁₉	—	2	4	no	—
131	C₂²×C₄×C₁₉	—	2	4	no	—
132	C₂²×C₄×C₁₉	—	2	4	no	—
133	C₂²×C₄×C₁₉	—	2	4	no	—
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	8	no	—
136	C₂²×C₄×C₁₉	—	2	16	no	—
137	C₂²×C₄×C₁₉	—	4	16	no	—
138	C₂²×C₄×C₁₉	—	4	32	no	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₉	#41	1	8	yes	—
144	C₂²×C₄×C₁₉	#41	1	4	yes	—
145	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
152	C₄⋊C₄×C₁₉	—	2	8	no	—
153	C₄⋊C₄×C₁₉	—	2	16	no	—
154	C₂²⋊C₄×C₁₉	—	2	32	no	—
155	C₂²⋊C₄×C₁₉	—	2	16	no	—
156	C₂²⋊C₄×C₁₉	—	2	16	no	—
157	C₂²⋊C₄×C₁₉	—	2	16	no	—
158	C₂²⋊C₄×C₁₉	—	4	16	no	—
159	C₄²×C₁₉	—	2	8	no	—
160	C₄²×C₁₉	—	2	8	no	—
161	C₄²×C₁₉	C₂×D₄	1	16	yes	complemented
162	C₂×#2544	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	2	16	no	—
164	C₂³×C₁₉	—	2	32	no	—
165	C₂³×C₁₉	—	2	4	no	—
166	C₂³×C₁₉	—	2	4	no	—
167	C₂³×C₁₉	—	2	8	no	—
168	C₂³×C₁₉	—	2	8	no	—
169	C₂³×C₁₉	—	2	4	no	—
170	C₂³×C₁₉	—	2	4	no	—
171	C₂³×C₁₉	—	2	4	no	—
172	C₂³×C₁₉	—	2	8	no	—
173	C₂³×C₁₉	—	2	8	no	—
174	C₂³×C₁₉	—	4	8	no	—
175	C₂³×C₁₉	—	4	8	no	—
176	C₂³×C₁₉	—	4	16	no	—
177	C₂³×C₁₉	—	4	8	no	—
178	C₂³×C₁₉	—	4	8	no	—
179	C₂³×C₁₉	—	4	8	no	—
180	C₂³×C₁₉	—	4	16	no	—
181	C₂³×C₁₉	—	4	16	no	—
182	C₂³×C₁₉	C₂²×D₄	1	8	yes	—
183	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
184	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
185	C₂³×C₁₉	C₂×#41	1	2	yes	—
186	C₂³×C₁₉	C₂×#41	1	4	yes	—
187	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
188	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
189	Q₈×C₁₉	—	4	16	no	—
190	D₄×C₁₉	—	2	32	no	—
191	D₄×C₁₉	—	4	64	no	—
192	D₄×C₁₉	—	4	16	no	—
193	C₂×C₄×C₁₉	—	2	8	no	—
194	C₂×C₄×C₁₉	—	2	8	no	—
195	C₂×C₄×C₁₉	—	2	16	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	4	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	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	2	8	no	—
208	C₂×C₄×C₁₉	—	4	32	no	—
209	C₂×C₄×C₁₉	—	4	8	no	—
210	C₂×C₄×C₁₉	—	4	8	no	—
211	C₂×C₄×C₁₉	—	4	8	no	—
212	C₂×C₄×C₁₉	#121	1	16	yes	—
213	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
214	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
215	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
216	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
218	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
219	C₂²×#127	C₂×C₁₉	1	1	yes	characteristic
220	C₂²×#124	C₂×C₁₉	1	1	yes	characteristic, complemented
221	C₂²×#124	C₂×C₁₉	1	1	yes	characteristic, complemented
222	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#2544	C₂×C₁₉	1	16	yes	direct product factor
224	C₂×#394	C₂×C₁₉	1	4	yes	complemented
225	C₂×#391	C₂×C₁₉	1	1	yes	characteristic, complemented
226	C₂×#390	C₂×C₁₉	1	1	yes	characteristic, complemented
227	C₂×#386	C₂×C₁₉	1	4	yes	complemented
228	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
229	C₂²×C₁₉	—	2	8	no	—
230	C₂²×C₁₉	—	2	16	no	—
231	C₂²×C₁₉	—	4	4	no	—
232	C₂²×C₁₉	—	4	4	no	—
233	C₂²×C₁₉	—	4	8	no	—
234	C₂²×C₁₉	—	4	32	no	—
235	C₂²×C₁₉	—	4	4	no	—
236	C₂²×C₁₉	—	4	4	no	—
237	C₂²×C₁₉	—	4	4	no	—
238	C₂²×C₁₉	—	4	8	no	—
239	C₂²×C₁₉	—	4	8	no	—
240	C₂²×C₁₉	—	8	16	no	—
241	C₂²×C₁₉	C₂×#121	1	4	yes	—
242	C₂²×C₁₉	#532	1	4	yes	—
243	C₂²×C₁₉	#535	1	4	yes	—
244	C₂²×C₁₉	#546	1	8	yes	—
245	C₂²×C₁₉	#559	1	8	yes	—
246	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
247	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
248	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
249	C₂²×C₁₉	C₂²×#41	1	2	yes	—
250	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
251	C₄×C₁₉	—	2	4	no	—
252	C₄×C₁₉	—	2	4	no	—
253	C₄×C₁₉	—	2	8	no	—
254	C₄×C₁₉	—	4	4	no	—
255	C₄×C₁₉	—	4	4	no	—
256	C₄×C₁₉	—	4	4	no	—
257	C₄×C₁₉	C₂×#121	1	8	yes	—
258	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
259	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
260	C₂³×D₄	C₂²×C₁₉	1	4	yes	—
261	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
262	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
263	C₂×#127	—	2	8	no	—
264	C₂×#127	C₂²×C₁₉	1	8	yes	—
265	C₂×#124	—	2	8	no	—
266	C₂×#124	—	2	8	no	—
267	C₂×#124	C₂²×C₁₉	1	8	yes	complemented
268	C₂×#124	C₂²×C₁₉	1	8	yes	complemented
269	C₂×C₄×D₄	—	2	8	no	—
270	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
271	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
272	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
273	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
274	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
275	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
276	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
277	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
278	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
279	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
280	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
281	#394	C₂²×C₁₉	1	32	yes	complemented
282	#391	C₂²×C₁₉	1	8	yes	complemented
283	#390	C₂²×C₁₉	1	8	yes	complemented
284	#386	C₂²×C₁₉	1	32	yes	complemented
285	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	complemented
286	C₂×#95	C₂²×C₁₉	1	4	yes	—
287	C₂×#95	C₂²×C₁₉	1	2	yes	—
288	C₂×C₁₉	—	4	8	no	—
289	C₂×C₁₉	—	8	4	no	—
290	C₂×C₁₉	#2544	1	8	yes	direct product factor
291	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
292	C₂×C₁₉	C₂×#532	1	1	yes	characteristic
293	C₂×C₁₉	C₂×#535	1	1	yes	characteristic
294	C₂×C₁₉	C₂×#546	1	2	yes	—
295	C₂×C₁₉	C₂×#559	1	2	yes	—
296	C₂⁵	C₂³×C₁₉	1	2	yes	—
297	C₂⁵	C₂³×C₁₉	1	2	yes	—
298	C₂²×Q₈	—	2	4	no	—
299	C₂²×Q₈	—	2	4	no	—
300	C₂²×Q₈	—	2	4	no	—
301	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
302	C₂²×D₄	—	2	16	no	—
303	C₂²×D₄	—	2	4	no	—
304	C₂²×D₄	—	2	4	no	—
305	C₂²×D₄	—	2	4	no	—
306	C₂²×D₄	—	2	4	no	—
307	C₂²×D₄	—	2	16	no	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	—	4	8	no	—
310	C₂²×D₄	D₄×C₁₉	1	8	yes	—
311	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
312	C₂²×D₄	C₂³×C₁₉	1	16	yes	—
313	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
314	C₂³×C₄	—	2	8	no	—
315	C₂³×C₄	—	4	8	no	—
316	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
317	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
318	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
319	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
322	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
323	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
324	#127	—	2	32	no	—
325	#124	—	2	32	no	—
326	#124	—	2	32	no	—
327	C₄×D₄	—	2	32	no	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	—	2	8	no	—
330	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
332	C₂×C₂²⋊C₄	—	2	16	no	—
333	C₂×C₂²⋊C₄	—	2	8	no	—
334	C₂×C₂²⋊C₄	—	2	8	no	—
335	C₂×C₂²⋊C₄	—	2	8	no	—
336	C₂×C₂²⋊C₄	—	4	8	no	—
337	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
342	C₂×C₄²	—	2	4	no	—
343	C₂×C₄²	—	2	4	no	—
344	C₂×C₄²	D₄×C₁₉	1	8	yes	complemented
345	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
346	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
347	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
348	#95	C₂³×C₁₉	1	8	yes	—
349	#95	C₂³×C₁₉	1	16	yes	—
350	C₁₉	C₂×#2544	1	1	yes	characteristic, direct product factor, Sylow
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	4	no	—
353	C₂⁴	—	2	8	no	—
354	C₂⁴	—	2	8	no	—
355	C₂⁴	—	2	4	no	—
356	C₂⁴	—	2	4	no	—
357	C₂⁴	—	2	4	no	—
358	C₂⁴	—	2	8	no	—
359	C₂⁴	—	2	8	no	—
360	C₂⁴	C₂×D₄×C₁₉	1	8	yes	—
361	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
362	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
363	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
364	C₂×Q₈	—	2	8	no	—
365	C₂×Q₈	—	2	8	no	—
366	C₂×Q₈	—	2	8	no	—
367	C₂×Q₈	—	4	16	no	—
368	C₂×D₄	—	2	32	no	—
369	C₂×D₄	—	2	32	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	8	no	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	2	32	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	4	16	no	—
377	C₂×D₄	—	4	64	no	—
378	C₂×D₄	—	4	16	no	—
379	C₂×D₄	C₂×D₄×C₁₉	1	16	yes	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	2	16	no	—
393	C₂²×C₄	—	4	16	no	—
394	C₂²×C₄	—	4	32	no	—
395	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
396	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
397	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
398	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
399	C₂²×C₄	#41×C₁₉	1	8	yes	—
400	C₂²×C₄	#41×C₁₉	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
406	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
407	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	16	no	—
410	C₂²⋊C₄	—	2	32	no	—
411	C₂²⋊C₄	—	2	16	no	—
412	C₂²⋊C₄	—	2	16	no	—
413	C₂²⋊C₄	—	2	16	no	—
414	C₂²⋊C₄	—	4	16	no	—
415	C₄²	—	2	8	no	—
416	C₄²	—	2	8	no	—
417	C₄²	C₂×D₄×C₁₉	1	16	yes	complemented
418	C₂³	—	2	16	no	—
419	C₂³	—	2	32	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	4	8	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	16	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	4	8	no	—
434	C₂³	—	4	8	no	—
435	C₂³	—	4	16	no	—
436	C₂³	—	4	16	no	—
437	C₂³	C₂²×D₄×C₁₉	1	8	yes	—
438	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
439	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
440	C₂³	C₂×#41×C₁₉	1	2	yes	—
441	C₂³	C₂×#41×C₁₉	1	4	yes	—
442	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
443	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
444	Q₈	—	4	16	no	—
445	D₄	—	2	32	no	—
446	D₄	—	4	64	no	—
447	D₄	—	4	16	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	16	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	4	32	no	—
464	C₂×C₄	—	4	8	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	8	no	—
467	C₂×C₄	C₁₉×#121	1	16	yes	—
468	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
469	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
470	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
471	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
472	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
473	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	16	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	8	no	—
479	C₂²	—	4	32	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	8	no	—
484	C₂²	—	4	8	no	—
485	C₂²	—	8	16	no	—
486	C₂²	C₂×C₁₉×#121	1	4	yes	—
487	C₂²	C₁₉×#532	1	4	yes	—
488	C₂²	C₁₉×#535	1	4	yes	—
489	C₂²	C₁₉×#546	1	8	yes	—
490	C₂²	C₁₉×#559	1	8	yes	—
491	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
492	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
493	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
494	C₂²	C₂²×#41×C₁₉	1	2	yes	—
495	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
496	C₄	—	2	4	no	—
497	C₄	—	2	4	no	—
498	C₄	—	2	8	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	4	no	—
502	C₄	C₂×C₁₉×#121	1	8	yes	—
503	C₂	—	4	8	no	—
504	C₂	—	8	4	no	—
505	C₂	C₁₉×#2544	1	8	yes	direct product factor
506	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
507	C₂	C₂×C₁₉×#532	1	1	yes	characteristic
508	C₂	C₂×C₁₉×#535	1	1	yes	characteristic
509	C₂	C₂×C₁₉×#546	1	2	yes	—
510	C₂	C₂×C₁₉×#559	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂²×C₁₉×#127	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. C₂²×C₁₉×#124	C₂	semidirect
3. C₂²×C₁₉×#124	C₂	semidirect
4. C₂²×C₄×D₄×C₁₉	C₂	semidirect
5. C₁₉×#2544	C₂	direct (N × H)
6. C₂×C₁₉×#394	C₂	semidirect
7. C₂×C₁₉×#391	C₂	semidirect
8. C₂×C₁₉×#390	C₂	semidirect
9. C₂×C₁₉×#386	C₂	semidirect
10. C₂×C₄×C₄⋊C₄×C₁₉	C₂	semidirect
20. C₂×C₁₉×#124	C₂²	semidirect
21. C₂×C₁₉×#124	C₂²	semidirect
23. C₂×C₄×D₄×C₁₉	C₂²	semidirect
34. C₁₉×#394	C₂²	semidirect
35. C₁₉×#391	C₂²	semidirect
36. C₁₉×#390	C₂²	semidirect
37. C₁₉×#386	C₂²	semidirect
38. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
89. C₂×C₄²×C₁₉	D₄	semidirect
161. C₄²×C₁₉	C₂×D₄	semidirect
162. C₂×#2544	C₁₉	direct (N × H)
220. C₂²×#124	C₂×C₁₉	semidirect
221. C₂²×#124	C₂×C₁₉	semidirect
222. C₂²×C₄×D₄	C₂×C₁₉	semidirect
223. #2544	C₂×C₁₉	direct (N × H)
224. C₂×#394	C₂×C₁₉	semidirect
225. C₂×#391	C₂×C₁₉	semidirect
226. C₂×#390	C₂×C₁₉	semidirect
227. C₂×#386	C₂×C₁₉	semidirect
228. C₂×C₄×C₄⋊C₄	C₂×C₁₉	semidirect
267. C₂×#124	C₂²×C₁₉	semidirect
268. C₂×#124	C₂²×C₁₉	semidirect
270. C₂×C₄×D₄	C₂²×C₁₉	semidirect
281. #394	C₂²×C₁₉	semidirect
282. #391	C₂²×C₁₉	semidirect
283. #390	C₂²×C₁₉	semidirect
284. #386	C₂²×C₁₉	semidirect
285. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
290. C₂×C₁₉	#2544	direct (N × H)
344. C₂×C₄²	D₄×C₁₉	semidirect
350. C₁₉	C₂×#2544	direct (N × H)
417. C₄²	C₂×D₄×C₁₉	semidirect
505. C₂	C₁₉×#2544	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#127	2
C₂²×C₁₉×#124	2
C₂²×C₄×D₄×C₁₉	2
C₁₉×#2544	2
C₂×C₁₉×#394	2
C₂×C₁₉×#391	2
C₂×C₁₉×#390	2
C₂×C₁₉×#386	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₂×#2544	19

Subgroups — C2×C19×#2544 #18040845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2544 #18040845