Subgroups — C₁₉×#34376 #18040335

Order 4864.

2630 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#123	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2376	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2359	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2345	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2342	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2342	C₂	1	2	yes	maximal, complemented
7	D₄×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal
8	C₁₉×#2335	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2322	C₂	1	4	yes	maximal, complemented
10	C₁₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2315	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2313	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2312	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#123	C₄	1	16	yes	complemented
19	C₂×C₁₉×#123	C₂²	1	2	yes	—
20	C₂×C₁₉×#123	C₂²	1	2	yes	—
21	C₂×C₁₉×#123	C₂²	1	2	yes	—
22	C₂×C₁₉×#123	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
24	C₂×C₁₉×#117	C₂²	1	2	yes	—
25	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
26	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
29	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#390	C₂²	1	4	yes	—
35	C₁₉×#389	C₂²	1	4	yes	complemented
36	C₁₉×#389	C₂²	1	4	yes	complemented
37	C₁₉×#389	C₂²	1	4	yes	complemented
38	C₁₉×#388	C₂²	1	4	yes	complemented
39	C₁₉×#388	C₂²	1	4	yes	complemented
40	C₁₉×#388	C₂²	1	4	yes	complemented
41	C₁₉×#388	C₂²	1	4	yes	complemented
42	C₁₉×#388	C₂²	1	4	yes	complemented
43	C₁₉×#388	C₂²	1	4	yes	complemented
44	C₁₉×#387	C₂²	1	4	yes	complemented
45	C₁₉×#387	C₂²	1	4	yes	complemented
46	C₁₉×#387	C₂²	1	4	yes	complemented
47	C₁₉×#387	C₂²	1	4	yes	complemented
48	C₁₉×#386	C₂²	1	4	yes	—
49	C₁₉×#386	C₂²	1	4	yes	—
50	C₁₉×#385	C₂²	1	4	yes	complemented
51	C₁₉×#385	C₂²	1	4	yes	complemented
52	C₁₉×#385	C₂²	1	4	yes	complemented
53	C₁₉×#385	C₂²	1	4	yes	complemented
54	C₁₉×#381	C₂²	1	2	yes	—
55	C₁₉×#381	C₂²	1	2	yes	complemented
56	C₁₉×#380	C₂²	1	1	yes	characteristic
57	C₁₉×#380	C₂²	1	1	yes	characteristic
58	C₁₉×#380	C₂²	1	2	yes	—
59	C₁₉×#380	C₂²	1	1	yes	characteristic
60	C₁₉×#380	C₂²	1	1	yes	characteristic
61	C₁₉×#380	C₂²	1	2	yes	—
62	C₁₉×#380	C₂²	1	2	yes	—
63	C₁₉×#380	C₂²	1	2	yes	complemented
64	C₁₉×#380	C₂²	1	2	yes	complemented
65	C₁₉×#380	C₂²	1	2	yes	complemented
66	C₁₉×#379	C₂²	1	2	yes	—
67	C₁₉×#379	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
69	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
74	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	complemented
75	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
76	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
77	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₉	—	4	4	no	—
79	C₂²×D₄×C₁₉	C₂×C₄	1	8	yes	—
80	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₉	—	4	4	no	—
83	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	complemented
84	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
88	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
89	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₁₉×#123	C₂×C₄	1	16	yes	complemented
96	C₁₉×#123	C₂×C₄	1	16	yes	complemented
97	C₁₉×#123	C₂×C₄	1	16	yes	complemented
98	C₁₉×#123	C₂×C₄	1	16	yes	complemented
99	C₄×D₄×C₁₉	—	4	8	no	—
100	C₁₉×#117	—	4	4	no	—
101	C₁₉×#117	—	4	4	no	—
102	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
103	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
104	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
118	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
119	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
120	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
121	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
122	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
141	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
142	C₁₉×#95	C₂³	1	4	yes	—
143	C₁₉×#95	C₂³	1	2	yes	—
144	C₁₉×#95	C₂³	1	2	yes	—
145	C₁₉×#95	C₂³	1	4	yes	—
146	C₁₉×#95	C₂³	1	4	yes	—
147	C₁₉×#95	C₂³	1	4	yes	—
148	C₁₉×#95	C₂³	1	2	yes	—
149	C₁₉×#95	C₂³	1	2	yes	—
150	C₁₉×#95	C₂³	1	4	yes	—
151	C₁₉×#95	C₂³	1	4	yes	—
152	C₁₉×#95	C₂³	1	4	yes	—
153	C₁₉×#95	C₂³	1	4	yes	—
154	C₂⁴×C₁₉	—	2	2	no	—
155	C₂⁴×C₁₉	—	2	4	no	—
156	C₂⁴×C₁₉	—	2	2	no	—
157	C₂⁴×C₁₉	—	2	2	no	—
158	C₂⁴×C₁₉	—	2	2	no	—
159	C₂⁴×C₁₉	—	4	2	no	—
160	C₂⁴×C₁₉	—	4	2	no	—
161	C₂⁴×C₁₉	—	4	2	no	—
162	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
163	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
164	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
165	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
166	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
168	C₂×D₄×C₁₉	—	2	8	no	—
169	C₂×D₄×C₁₉	—	4	4	no	—
170	C₂×D₄×C₁₉	—	4	16	no	—
171	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
172	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
173	C₂²×C₄×C₁₉	—	2	4	no	—
174	C₂²×C₄×C₁₉	—	2	2	no	—
175	C₂²×C₄×C₁₉	—	2	4	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	8	no	—
178	C₂²×C₄×C₁₉	—	4	16	no	—
179	C₂²×C₄×C₁₉	—	4	2	no	—
180	C₂²×C₄×C₁₉	—	4	2	no	—
181	C₂²×C₄×C₁₉	—	4	2	no	—
182	C₂²×C₄×C₁₉	—	4	2	no	—
183	C₂²×C₄×C₁₉	—	4	2	no	—
184	C₂²×C₄×C₁₉	—	4	2	no	—
185	C₂²×C₄×C₁₉	—	4	4	no	—
186	C₂²×C₄×C₁₉	—	4	4	no	—
187	C₂²×C₄×C₁₉	—	4	4	no	—
188	C₂²×C₄×C₁₉	—	4	4	no	—
189	C₂²×C₄×C₁₉	—	4	4	no	—
190	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
199	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
210	C₄⋊C₄×C₁₉	—	4	2	no	—
211	C₄⋊C₄×C₁₉	—	4	4	no	—
212	C₄⋊C₄×C₁₉	—	4	2	no	—
213	C₄⋊C₄×C₁₉	—	4	4	no	—
214	C₄⋊C₄×C₁₉	—	4	4	no	—
215	C₄⋊C₄×C₁₉	—	4	2	no	—
216	C₄⋊C₄×C₁₉	—	4	2	no	—
217	C₄⋊C₄×C₁₉	—	4	4	no	—
218	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
219	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
220	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
221	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₁₉	—	2	4	no	—
223	C₂²⋊C₄×C₁₉	—	2	4	no	—
224	C₂²⋊C₄×C₁₉	—	2	4	no	—
225	C₂²⋊C₄×C₁₉	—	2	8	no	—
226	C₂²⋊C₄×C₁₉	—	2	4	no	—
227	C₂²⋊C₄×C₁₉	—	4	4	no	—
228	C₂²⋊C₄×C₁₉	—	4	4	no	—
229	C₂²⋊C₄×C₁₉	—	4	4	no	—
230	C₂²⋊C₄×C₁₉	—	4	4	no	—
231	C₂²⋊C₄×C₁₉	—	4	4	no	—
232	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
233	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
234	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
235	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
236	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
237	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
238	C₄²×C₁₉	—	4	4	no	—
239	C₄²×C₁₉	—	4	4	no	—
240	C₄²×C₁₉	—	4	4	no	—
241	C₄²×C₁₉	—	4	4	no	—
242	#34376	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂³×C₁₉	—	2	1	no	—
244	C₂³×C₁₉	—	2	2	no	—
245	C₂³×C₁₉	—	2	1	no	—
246	C₂³×C₁₉	—	2	2	no	—
247	C₂³×C₁₉	—	2	2	no	—
248	C₂³×C₁₉	—	2	8	no	—
249	C₂³×C₁₉	—	2	8	no	—
250	C₂³×C₁₉	—	2	1	no	—
251	C₂³×C₁₉	—	2	2	no	—
252	C₂³×C₁₉	—	2	4	no	—
253	C₂³×C₁₉	—	2	2	no	—
254	C₂³×C₁₉	—	2	1	no	—
255	C₂³×C₁₉	—	2	2	no	—
256	C₂³×C₁₉	—	2	2	no	—
257	C₂³×C₁₉	—	2	4	no	—
258	C₂³×C₁₉	—	2	8	no	—
259	C₂³×C₁₉	—	4	4	no	—
260	C₂³×C₁₉	—	4	4	no	—
261	C₂³×C₁₉	—	4	4	no	—
262	C₂³×C₁₉	—	4	8	no	—
263	C₂³×C₁₉	—	4	8	no	—
264	C₂³×C₁₉	—	8	4	no	—
265	C₂³×C₁₉	—	8	4	no	—
266	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
267	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
268	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
269	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
270	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
271	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
272	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
273	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
274	D₄×C₁₉	—	2	16	no	—
275	D₄×C₁₉	—	4	8	no	—
276	C₂×C₄×C₁₉	—	2	8	no	—
277	C₂×C₄×C₁₉	—	2	8	no	—
278	C₂×C₄×C₁₉	—	2	8	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	2	no	—
281	C₂×C₄×C₁₉	—	2	4	no	—
282	C₂×C₄×C₁₉	—	2	2	no	—
283	C₂×C₄×C₁₉	—	2	2	no	—
284	C₂×C₄×C₁₉	—	2	2	no	—
285	C₂×C₄×C₁₉	—	2	2	no	—
286	C₂×C₄×C₁₉	—	2	4	no	—
287	C₂×C₄×C₁₉	—	2	4	no	—
288	C₂×C₄×C₁₉	—	2	4	no	—
289	C₂×C₄×C₁₉	—	2	4	no	—
290	C₂×C₄×C₁₉	—	2	4	no	—
291	C₂×C₄×C₁₉	—	2	4	no	—
292	C₂×C₄×C₁₉	—	2	4	no	—
293	C₂×C₄×C₁₉	—	2	4	no	—
294	C₂×C₄×C₁₉	—	2	4	no	—
295	C₂×C₄×C₁₉	—	2	4	no	—
296	C₂×C₄×C₁₉	—	2	4	no	—
297	C₂×C₄×C₁₉	—	2	4	no	—
298	C₂×C₄×C₁₉	—	2	4	no	—
299	C₂×C₄×C₁₉	—	4	4	no	—
300	C₂×C₄×C₁₉	—	4	4	no	—
301	C₂×C₄×C₁₉	—	4	4	no	—
302	C₂×C₄×C₁₉	—	4	4	no	—
303	C₂×C₄×C₁₉	—	4	4	no	—
304	C₂×C₄×C₁₉	—	4	4	no	—
305	C₂×C₄×C₁₉	—	8	8	no	—
306	C₂×C₄×C₁₉	—	8	8	no	—
307	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
309	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
310	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
311	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
313	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
314	C₂²×#123	C₂×C₁₉	1	1	yes	characteristic
315	#2376	C₂×C₁₉	1	4	yes	complemented
316	#2359	C₂×C₁₉	1	4	yes	complemented
317	#2345	C₂×C₁₉	1	2	yes	complemented
318	#2342	C₂×C₁₉	1	2	yes	complemented
319	#2342	C₂×C₁₉	1	2	yes	complemented
320	D₄×C₂²⋊C₄	C₂×C₁₉	1	2	yes	—
321	#2335	C₂×C₁₉	1	4	yes	complemented
322	#2322	C₂×C₁₉	1	4	yes	complemented
323	#2316	C₂×C₁₉	1	1	yes	characteristic, complemented
324	#2315	C₂×C₁₉	1	1	yes	characteristic, complemented
325	#2313	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#2312	C₂×C₁₉	1	1	yes	characteristic, complemented
327	#2280	C₂×C₁₉	1	1	yes	characteristic, complemented
328	C₂×#380	C₂×C₁₉	1	1	yes	characteristic, complemented
329	C₂²×C₁₉	—	2	2	no	—
330	C₂²×C₁₉	—	2	2	no	—
331	C₂²×C₁₉	—	2	2	no	—
332	C₂²×C₁₉	—	2	2	no	—
333	C₂²×C₁₉	—	2	4	no	—
334	C₂²×C₁₉	—	2	4	no	—
335	C₂²×C₁₉	—	2	4	no	—
336	C₂²×C₁₉	—	2	4	no	—
337	C₂²×C₁₉	—	2	2	no	—
338	C₂²×C₁₉	—	2	4	no	—
339	C₂²×C₁₉	—	2	2	no	—
340	C₂²×C₁₉	—	2	4	no	—
341	C₂²×C₁₉	—	2	2	no	—
342	C₂²×C₁₉	—	2	4	no	—
343	C₂²×C₁₉	—	4	16	no	—
344	C₂²×C₁₉	—	4	4	no	—
345	C₂²×C₁₉	—	4	2	no	—
346	C₂²×C₁₉	—	4	2	no	—
347	C₂²×C₁₉	—	4	4	no	—
348	C₂²×C₁₉	—	8	8	no	—
349	C₂²×C₁₉	#518	1	4	yes	—
350	C₂²×C₁₉	#520	1	4	yes	—
351	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
352	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
353	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
355	C₂²×C₁₉	#585	1	2	yes	—
356	C₄×C₁₉	—	2	2	no	—
357	C₄×C₁₉	—	2	2	no	—
358	C₄×C₁₉	—	2	2	no	—
359	C₄×C₁₉	—	2	2	no	—
360	C₄×C₁₉	—	2	4	no	—
361	C₄×C₁₉	—	2	4	no	—
362	C₄×C₁₉	—	2	4	no	—
363	C₄×C₁₉	—	4	4	no	—
364	C₄×C₁₉	—	4	4	no	—
365	C₄×C₁₉	—	4	4	no	—
366	C₄×C₁₉	—	4	4	no	—
367	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
368	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#123	C₄×C₁₉	1	16	yes	complemented
370	C₂×#123	C₂²×C₁₉	1	2	yes	—
371	C₂×#123	C₂²×C₁₉	1	2	yes	—
372	C₂×#123	C₂²×C₁₉	1	2	yes	—
373	C₂×#123	C₂²×C₁₉	1	2	yes	—
374	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
375	C₂×#117	C₂²×C₁₉	1	2	yes	—
376	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
377	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
378	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
379	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
380	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
381	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
382	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
383	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
384	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
385	#390	C₂²×C₁₉	1	4	yes	—
386	#389	C₂²×C₁₉	1	4	yes	complemented
387	#389	C₂²×C₁₉	1	4	yes	complemented
388	#389	C₂²×C₁₉	1	4	yes	complemented
389	#388	C₂²×C₁₉	1	4	yes	complemented
390	#388	C₂²×C₁₉	1	4	yes	complemented
391	#388	C₂²×C₁₉	1	4	yes	complemented
392	#388	C₂²×C₁₉	1	4	yes	complemented
393	#388	C₂²×C₁₉	1	4	yes	complemented
394	#388	C₂²×C₁₉	1	4	yes	complemented
395	#387	C₂²×C₁₉	1	4	yes	complemented
396	#387	C₂²×C₁₉	1	4	yes	complemented
397	#387	C₂²×C₁₉	1	4	yes	complemented
398	#387	C₂²×C₁₉	1	4	yes	complemented
399	#386	C₂²×C₁₉	1	4	yes	—
400	#386	C₂²×C₁₉	1	4	yes	—
401	#385	C₂²×C₁₉	1	4	yes	complemented
402	#385	C₂²×C₁₉	1	4	yes	complemented
403	#385	C₂²×C₁₉	1	4	yes	complemented
404	#385	C₂²×C₁₉	1	4	yes	complemented
405	#381	C₂²×C₁₉	1	2	yes	—
406	#381	C₂²×C₁₉	1	2	yes	complemented
407	#380	C₂²×C₁₉	1	1	yes	characteristic
408	#380	C₂²×C₁₉	1	1	yes	characteristic
409	#380	C₂²×C₁₉	1	1	yes	characteristic
410	#380	C₂²×C₁₉	1	1	yes	characteristic
411	#380	C₂²×C₁₉	1	2	yes	—
412	#380	C₂²×C₁₉	1	2	yes	—
413	#380	C₂²×C₁₉	1	2	yes	—
414	#380	C₂²×C₁₉	1	2	yes	complemented
415	#380	C₂²×C₁₉	1	2	yes	complemented
416	#380	C₂²×C₁₉	1	2	yes	complemented
417	#379	C₂²×C₁₉	1	2	yes	—
418	#379	C₂²×C₁₉	1	2	yes	—
419	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
420	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
422	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
424	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	complemented
425	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	complemented
426	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
427	C₂×C₁₉	—	2	4	no	—
428	C₂×C₁₉	—	2	4	no	—
429	C₂×C₁₉	—	4	2	no	—
430	C₂×C₁₉	—	4	4	no	—
431	C₂×C₁₉	C₂×#518	1	1	yes	characteristic
432	C₂×C₁₉	C₂×#520	1	1	yes	characteristic
433	C₂×C₁₉	#3428	1	1	yes	characteristic
434	C₂×C₁₉	#3534	1	2	yes	—
435	C₂×C₁₉	#3535	1	2	yes	—
436	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
437	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
438	C₂²×D₄	—	4	4	no	—
439	C₂²×D₄	C₂×C₄×C₁₉	1	8	yes	—
440	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
441	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
442	C₂³×C₄	—	4	4	no	—
443	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	complemented
444	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
448	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
449	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
455	#123	C₂×C₄×C₁₉	1	16	yes	complemented
456	#123	C₂×C₄×C₁₉	1	16	yes	complemented
457	#123	C₂×C₄×C₁₉	1	16	yes	complemented
458	#123	C₂×C₄×C₁₉	1	16	yes	complemented
459	C₄×D₄	—	4	8	no	—
460	#117	—	4	4	no	—
461	#117	—	4	4	no	—
462	C₂×C₄⋊C₄	—	4	4	no	—
463	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
464	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
465	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
477	C₂×C₂²⋊C₄	—	4	4	no	—
478	C₂×C₂²⋊C₄	—	4	4	no	—
479	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
480	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
481	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
482	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
498	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
499	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
500	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
501	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
502	#95	C₂³×C₁₉	1	4	yes	—
503	#95	C₂³×C₁₉	1	2	yes	—
504	#95	C₂³×C₁₉	1	2	yes	—
505	#95	C₂³×C₁₉	1	4	yes	—
506	#95	C₂³×C₁₉	1	4	yes	—
507	#95	C₂³×C₁₉	1	4	yes	—
508	#95	C₂³×C₁₉	1	2	yes	—
509	#95	C₂³×C₁₉	1	2	yes	—
510	#95	C₂³×C₁₉	1	4	yes	—
511	#95	C₂³×C₁₉	1	4	yes	—
512	#95	C₂³×C₁₉	1	4	yes	—
513	#95	C₂³×C₁₉	1	4	yes	—
514	C₁₉	#34376	1	1	yes	characteristic, direct product factor, Sylow
515	C₂⁴	—	2	2	no	—
516	C₂⁴	—	2	4	no	—
517	C₂⁴	—	2	2	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	2	no	—
520	C₂⁴	—	4	2	no	—
521	C₂⁴	—	4	2	no	—
522	C₂⁴	—	4	2	no	—
523	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
524	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
525	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
526	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
527	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
528	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
529	C₂×D₄	—	2	8	no	—
530	C₂×D₄	—	4	4	no	—
531	C₂×D₄	—	4	16	no	—
532	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
533	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	8	no	—
539	C₂²×C₄	—	4	16	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
552	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
553	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
554	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
555	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
556	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
557	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
558	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
559	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
561	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
563	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
564	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
571	C₄⋊C₄	—	4	2	no	—
572	C₄⋊C₄	—	4	4	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	4	no	—
575	C₄⋊C₄	—	4	4	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	4	2	no	—
578	C₄⋊C₄	—	4	4	no	—
579	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
580	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
581	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
582	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	4	4	no	—
589	C₂²⋊C₄	—	4	4	no	—
590	C₂²⋊C₄	—	4	4	no	—
591	C₂²⋊C₄	—	4	4	no	—
592	C₂²⋊C₄	—	4	4	no	—
593	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
594	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
595	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
596	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
597	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
598	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
599	C₄²	—	4	4	no	—
600	C₄²	—	4	4	no	—
601	C₄²	—	4	4	no	—
602	C₄²	—	4	4	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	2	8	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	8	no	—
619	C₂³	—	4	4	no	—
620	C₂³	—	4	4	no	—
621	C₂³	—	4	4	no	—
622	C₂³	—	4	8	no	—
623	C₂³	—	4	8	no	—
624	C₂³	—	8	4	no	—
625	C₂³	—	8	4	no	—
626	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
627	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
628	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
629	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
630	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
631	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
632	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
633	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
634	D₄	—	2	16	no	—
635	D₄	—	4	8	no	—
636	C₂×C₄	—	2	8	no	—
637	C₂×C₄	—	2	8	no	—
638	C₂×C₄	—	2	8	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	8	8	no	—
666	C₂×C₄	—	8	8	no	—
667	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
668	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
669	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
670	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
671	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
672	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
673	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	4	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	4	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	4	16	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	4	no	—
693	C₂²	—	8	8	no	—
694	C₂²	C₁₉×#518	1	4	yes	—
695	C₂²	C₁₉×#520	1	4	yes	—
696	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
697	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
698	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
699	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
700	C₂²	C₁₉×#585	1	2	yes	—
701	C₄	—	2	2	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	4	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	4	no	—
708	C₄	—	4	4	no	—
709	C₄	—	4	4	no	—
710	C₄	—	4	4	no	—
711	C₄	—	4	4	no	—
712	C₂	—	2	4	no	—
713	C₂	—	2	4	no	—
714	C₂	—	4	2	no	—
715	C₂	—	4	4	no	—
716	C₂	C₂×C₁₉×#518	1	1	yes	characteristic
717	C₂	C₂×C₁₉×#520	1	1	yes	characteristic
718	C₂	C₁₉×#3428	1	1	yes	characteristic
719	C₂	C₁₉×#3534	1	2	yes	—
720	C₂	C₁₉×#3535	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₉×#2376	C₂	semidirect
3. C₁₉×#2359	C₂	semidirect
4. C₁₉×#2345	C₂	semidirect
5. C₁₉×#2342	C₂	semidirect
6. C₁₉×#2342	C₂	semidirect
8. C₁₉×#2335	C₂	semidirect
9. C₁₉×#2322	C₂	semidirect
10. C₁₉×#2316	C₂	semidirect
11. C₁₉×#2315	C₂	semidirect
12. C₁₉×#2313	C₂	semidirect
13. C₁₉×#2312	C₂	semidirect
14. C₁₉×#2280	C₂	semidirect
15. C₂×C₁₉×#380	C₂	semidirect
18. C₂×C₁₉×#123	C₄	semidirect
25. C₂×C₁₉×#117	C₂²	semidirect
28. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
35. C₁₉×#389	C₂²	semidirect
36. C₁₉×#389	C₂²	semidirect
37. C₁₉×#389	C₂²	semidirect
38. C₁₉×#388	C₂²	semidirect
39. C₁₉×#388	C₂²	semidirect
40. C₁₉×#388	C₂²	semidirect
41. C₁₉×#388	C₂²	semidirect
42. C₁₉×#388	C₂²	semidirect
43. C₁₉×#388	C₂²	semidirect
44. C₁₉×#387	C₂²	semidirect
45. C₁₉×#387	C₂²	semidirect
46. C₁₉×#387	C₂²	semidirect
47. C₁₉×#387	C₂²	semidirect
50. C₁₉×#385	C₂²	semidirect
51. C₁₉×#385	C₂²	semidirect
52. C₁₉×#385	C₂²	semidirect
53. C₁₉×#385	C₂²	semidirect
55. C₁₉×#381	C₂²	semidirect
63. C₁₉×#380	C₂²	semidirect
64. C₁₉×#380	C₂²	semidirect
65. C₁₉×#380	C₂²	semidirect
68. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
75. C₂×C₁₉×#95	C₂²	semidirect
83. C₂³×C₄×C₁₉	C₂×C₄	semidirect
95. C₁₉×#123	C₂×C₄	semidirect
96. C₁₉×#123	C₂×C₄	semidirect
97. C₁₉×#123	C₂×C₄	semidirect
98. C₁₉×#123	C₂×C₄	semidirect
103. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
104. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
119. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
120. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
121. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
242. #34376	C₁₉	direct (N × H)
315. #2376	C₂×C₁₉	semidirect
316. #2359	C₂×C₁₉	semidirect
317. #2345	C₂×C₁₉	semidirect
318. #2342	C₂×C₁₉	semidirect
319. #2342	C₂×C₁₉	semidirect
321. #2335	C₂×C₁₉	semidirect
322. #2322	C₂×C₁₉	semidirect
323. #2316	C₂×C₁₉	semidirect
324. #2315	C₂×C₁₉	semidirect
325. #2313	C₂×C₁₉	semidirect
326. #2312	C₂×C₁₉	semidirect
327. #2280	C₂×C₁₉	semidirect
328. C₂×#380	C₂×C₁₉	semidirect
369. C₂×#123	C₄×C₁₉	semidirect
376. C₂×#117	C₂²×C₁₉	semidirect
379. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
386. #389	C₂²×C₁₉	semidirect
387. #389	C₂²×C₁₉	semidirect
388. #389	C₂²×C₁₉	semidirect
389. #388	C₂²×C₁₉	semidirect
390. #388	C₂²×C₁₉	semidirect
391. #388	C₂²×C₁₉	semidirect
392. #388	C₂²×C₁₉	semidirect
393. #388	C₂²×C₁₉	semidirect
394. #388	C₂²×C₁₉	semidirect
395. #387	C₂²×C₁₉	semidirect
396. #387	C₂²×C₁₉	semidirect
397. #387	C₂²×C₁₉	semidirect
398. #387	C₂²×C₁₉	semidirect
401. #385	C₂²×C₁₉	semidirect
402. #385	C₂²×C₁₉	semidirect
403. #385	C₂²×C₁₉	semidirect
404. #385	C₂²×C₁₉	semidirect
406. #381	C₂²×C₁₉	semidirect
414. #380	C₂²×C₁₉	semidirect
415. #380	C₂²×C₁₉	semidirect
416. #380	C₂²×C₁₉	semidirect
419. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
423. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
424. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
425. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
426. C₂×#95	C₂²×C₁₉	semidirect
443. C₂³×C₄	C₂×C₄×C₁₉	semidirect
455. #123	C₂×C₄×C₁₉	semidirect
456. #123	C₂×C₄×C₁₉	semidirect
457. #123	C₂×C₄×C₁₉	semidirect
458. #123	C₂×C₄×C₁₉	semidirect
463. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
464. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
479. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
480. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
481. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
514. C₁₉	#34376	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×#123	2
C₁₉×#2376	2
C₁₉×#2359	2
C₁₉×#2345	2
C₁₉×#2342	2
D₄×C₂²⋊C₄×C₁₉	2
C₁₉×#2335	2
C₁₉×#2322	2
C₁₉×#2316	2
C₁₉×#2315	2
C₁₉×#2313	2
C₁₉×#2312	2
C₁₉×#2280	2
C₂×C₁₉×#380	2
#34376	19

Subgroups — C19×#34376 #18040335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34376 #18040335