Subgroups — C₁₉×#34962 #18040921

Order 4864.

2198 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2593	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2586	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2574	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2572	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2555	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2554	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2518	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2467	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2459	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2456	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2396	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2392	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2388	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₉×#126	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₉×#124	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₉×#123	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₉×#121	C₂	1	2	yes	maximal, complemented
18	C₁₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×D₄×C₁₉	C₂	1	2	yes	maximal, complemented
20	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#126	C₂²	1	2	yes	—
22	C₂×C₁₉×#124	C₂²	1	2	yes	—
23	C₂×C₁₉×#123	C₂²	1	2	yes	—
24	C₂×C₁₉×#121	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
32	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
35	C₁₉×#400	C₂²	1	1	yes	characteristic
36	C₁₉×#399	C₂²	1	1	yes	characteristic
37	C₁₉×#398	C₂²	1	2	yes	—
38	C₁₉×#398	C₂²	1	1	yes	characteristic
39	C₁₉×#397	C₂²	1	1	yes	characteristic
40	C₁₉×#396	C₂²	1	2	yes	—
41	C₁₉×#396	C₂²	1	2	yes	—
42	C₁₉×#395	C₂²	1	1	yes	characteristic
43	C₁₉×#395	C₂²	1	2	yes	—
44	C₁₉×#394	C₂²	1	2	yes	—
45	C₁₉×#394	C₂²	1	2	yes	—
46	C₁₉×#394	C₂²	1	2	yes	—
47	C₁₉×#394	C₂²	1	2	yes	—
48	C₁₉×#394	C₂²	1	1	yes	characteristic
49	C₁₉×#393	C₂²	1	1	yes	characteristic
50	C₁₉×#393	C₂²	1	2	yes	—
51	C₁₉×#392	C₂²	1	1	yes	characteristic
52	C₁₉×#392	C₂²	1	2	yes	—
53	C₁₉×#392	C₂²	1	2	yes	—
54	C₁₉×#392	C₂²	1	2	yes	—
55	C₁₉×#391	C₂²	1	2	yes	—
56	C₁₉×#391	C₂²	1	1	yes	characteristic
57	C₁₉×#391	C₂²	1	1	yes	characteristic
58	C₁₉×#390	C₂²	1	2	yes	—
59	C₁₉×#390	C₂²	1	2	yes	—
60	C₁₉×#390	C₂²	1	1	yes	characteristic
61	C₁₉×#390	C₂²	1	1	yes	characteristic
62	C₁₉×#389	C₂²	1	2	yes	—
63	C₁₉×#388	C₂²	1	2	yes	—
64	C₁₉×#388	C₂²	1	2	yes	—
65	C₁₉×#388	C₂²	1	2	yes	—
66	C₁₉×#388	C₂²	1	2	yes	—
67	C₁₉×#388	C₂²	1	2	yes	—
68	C₁₉×#388	C₂²	1	2	yes	—
69	C₁₉×#388	C₂²	1	2	yes	—
70	C₁₉×#388	C₂²	1	2	yes	—
71	C₁₉×#388	C₂²	1	2	yes	—
72	C₁₉×#388	C₂²	1	2	yes	—
73	C₁₉×#388	C₂²	1	2	yes	—
74	C₁₉×#387	C₂²	1	2	yes	—
75	C₁₉×#387	C₂²	1	2	yes	—
76	C₁₉×#387	C₂²	1	2	yes	—
77	C₁₉×#387	C₂²	1	2	yes	—
78	C₁₉×#387	C₂²	1	2	yes	—
79	C₁₉×#386	C₂²	1	2	yes	—
80	C₁₉×#386	C₂²	1	2	yes	—
81	C₁₉×#386	C₂²	1	2	yes	—
82	C₁₉×#386	C₂²	1	2	yes	—
83	C₁₉×#386	C₂²	1	2	yes	—
84	C₁₉×#385	C₂²	1	2	yes	—
85	C₁₉×#383	C₂²	1	2	yes	—
86	C₁₉×#382	C₂²	1	2	yes	—
87	C₁₉×#381	C₂²	1	2	yes	—
88	C₁₉×#380	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
106	C₄³×C₁₉	C₂²	1	2	yes	—
107	C₂×#41×C₁₉	—	2	4	no	—
108	C₂×#41×C₁₉	—	4	2	no	—
109	C₂×#41×C₁₉	—	4	2	no	—
110	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
116	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
117	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
121	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
122	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
123	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₁₉×#126	—	2	8	no	—
125	C₁₉×#124	—	2	8	no	—
126	C₁₉×#123	—	2	8	no	—
127	C₁₉×#121	—	2	8	no	—
128	C₄×Q₈×C₁₉	—	4	2	no	—
129	C₄×D₄×C₁₉	—	2	8	no	—
130	C₄×D₄×C₁₉	—	2	8	no	—
131	C₄×D₄×C₁₉	—	2	8	no	—
132	C₄×D₄×C₁₉	—	4	4	no	—
133	C₄×D₄×C₁₉	—	4	2	no	—
134	C₄×D₄×C₁₉	—	4	4	no	—
135	C₁₉×#117	—	4	2	no	—
136	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
173	C₂×C₄²×C₁₉	—	4	2	no	—
174	C₂×C₄²×C₁₉	—	4	4	no	—
175	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
177	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
178	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
179	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
181	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
182	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
184	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
188	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
189	C₁₉×#95	C₂³	1	2	yes	—
190	C₁₉×#95	C₂³	1	2	yes	—
191	C₁₉×#95	C₂³	1	2	yes	—
192	C₁₉×#95	C₂³	1	2	yes	—
193	C₁₉×#95	C₂³	1	2	yes	—
194	C₁₉×#95	C₂³	1	2	yes	—
195	C₁₉×#95	C₂³	1	2	yes	—
196	C₁₉×#95	C₂³	1	2	yes	—
197	C₁₉×#95	C₂³	1	2	yes	—
198	C₁₉×#95	C₂³	1	2	yes	—
199	C₁₉×#95	C₂³	1	2	yes	—
200	C₁₉×#95	C₂³	1	2	yes	—
201	C₁₉×#95	C₂³	1	2	yes	—
202	C₁₉×#95	C₂³	1	2	yes	—
203	C₁₉×#95	C₂³	1	2	yes	—
204	C₁₉×#95	C₂³	1	2	yes	—
205	C₁₉×#95	C₂³	1	1	yes	characteristic
206	C₁₉×#95	C₂³	1	1	yes	characteristic
207	C₁₉×#95	C₂³	1	2	yes	—
208	C₁₉×#95	C₂³	1	1	yes	characteristic
209	C₁₉×#95	C₂³	1	2	yes	—
210	C₁₉×#95	C₂³	1	1	yes	characteristic
211	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
212	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
214	#41×C₁₉	—	4	16	no	—
215	C₂×Q₈×C₁₉	—	2	4	no	—
216	C₂×Q₈×C₁₉	—	2	2	no	—
217	C₂×Q₈×C₁₉	—	4	1	no	—
218	C₂×Q₈×C₁₉	—	4	1	no	—
219	C₂×Q₈×C₁₉	—	4	1	no	—
220	C₂×D₄×C₁₉	—	2	4	no	—
221	C₂×D₄×C₁₉	—	2	4	no	—
222	C₂×D₄×C₁₉	—	2	4	no	—
223	C₂×D₄×C₁₉	—	2	4	no	—
224	C₂×D₄×C₁₉	—	2	4	no	—
225	C₂×D₄×C₁₉	—	2	4	no	—
226	C₂×D₄×C₁₉	—	2	4	no	—
227	C₂×D₄×C₁₉	—	2	4	no	—
228	C₂×D₄×C₁₉	—	2	4	no	—
229	C₂×D₄×C₁₉	—	2	2	no	—
230	C₂×D₄×C₁₉	—	4	2	no	—
231	C₂×D₄×C₁₉	—	4	2	no	—
232	C₂×D₄×C₁₉	—	4	1	no	—
233	C₂×D₄×C₁₉	—	4	1	no	—
234	C₂×D₄×C₁₉	—	4	1	no	—
235	C₂×D₄×C₁₉	—	4	2	no	—
236	C₂×D₄×C₁₉	—	4	2	no	—
237	C₂²×C₄×C₁₉	—	2	2	no	—
238	C₂²×C₄×C₁₉	—	2	2	no	—
239	C₂²×C₄×C₁₉	—	2	4	no	—
240	C₂²×C₄×C₁₉	—	2	4	no	—
241	C₂²×C₄×C₁₉	—	2	4	no	—
242	C₂²×C₄×C₁₉	—	2	4	no	—
243	C₂²×C₄×C₁₉	—	2	4	no	—
244	C₂²×C₄×C₁₉	—	2	4	no	—
245	C₂²×C₄×C₁₉	—	2	4	no	—
246	C₂²×C₄×C₁₉	—	2	4	no	—
247	C₂²×C₄×C₁₉	—	2	4	no	—
248	C₂²×C₄×C₁₉	—	2	4	no	—
249	C₂²×C₄×C₁₉	—	2	4	no	—
250	C₂²×C₄×C₁₉	—	2	4	no	—
251	C₂²×C₄×C₁₉	—	4	2	no	—
252	C₂²×C₄×C₁₉	—	4	2	no	—
253	C₂²×C₄×C₁₉	—	4	2	no	—
254	C₂²×C₄×C₁₉	#41	1	4	yes	—
255	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
271	C₄⋊C₄×C₁₉	—	2	4	no	—
272	C₄⋊C₄×C₁₉	—	2	4	no	—
273	C₄⋊C₄×C₁₉	—	2	4	no	—
274	C₄⋊C₄×C₁₉	—	2	4	no	—
275	C₄⋊C₄×C₁₉	—	2	4	no	—
276	C₄⋊C₄×C₁₉	—	2	4	no	—
277	C₄⋊C₄×C₁₉	—	4	1	no	—
278	C₄⋊C₄×C₁₉	—	4	1	no	—
279	C₄⋊C₄×C₁₉	—	4	2	no	—
280	C₄⋊C₄×C₁₉	—	4	2	no	—
281	C₄⋊C₄×C₁₉	—	4	1	no	—
282	C₄⋊C₄×C₁₉	—	4	2	no	—
283	C₄⋊C₄×C₁₉	—	4	1	no	—
284	C₄⋊C₄×C₁₉	#41	1	8	yes	complemented
285	C₂²⋊C₄×C₁₉	—	2	4	no	—
286	C₂²⋊C₄×C₁₉	—	2	4	no	—
287	C₂²⋊C₄×C₁₉	—	2	4	no	—
288	C₂²⋊C₄×C₁₉	—	2	4	no	—
289	C₂²⋊C₄×C₁₉	—	2	4	no	—
290	C₂²⋊C₄×C₁₉	—	2	4	no	—
291	C₂²⋊C₄×C₁₉	—	2	4	no	—
292	C₂²⋊C₄×C₁₉	—	2	4	no	—
293	C₂²⋊C₄×C₁₉	—	2	4	no	—
294	C₂²⋊C₄×C₁₉	—	2	4	no	—
295	C₂²⋊C₄×C₁₉	—	2	4	no	—
296	C₂²⋊C₄×C₁₉	—	2	4	no	—
297	C₂²⋊C₄×C₁₉	—	2	4	no	—
298	C₂²⋊C₄×C₁₉	—	2	4	no	—
299	C₂²⋊C₄×C₁₉	—	2	4	no	—
300	C₂²⋊C₄×C₁₉	—	4	1	no	—
301	C₂²⋊C₄×C₁₉	—	4	1	no	—
302	C₂²⋊C₄×C₁₉	—	4	2	no	—
303	C₂²⋊C₄×C₁₉	—	4	2	no	—
304	C₂²⋊C₄×C₁₉	—	4	2	no	—
305	C₂²⋊C₄×C₁₉	—	4	2	no	—
306	C₂²⋊C₄×C₁₉	—	4	2	no	—
307	C₂²⋊C₄×C₁₉	#41	1	8	yes	complemented
308	C₄²×C₁₉	—	2	4	no	—
309	C₄²×C₁₉	—	2	4	no	—
310	C₄²×C₁₉	—	2	4	no	—
311	C₄²×C₁₉	—	2	4	no	—
312	C₄²×C₁₉	—	2	4	no	—
313	C₄²×C₁₉	—	2	4	no	—
314	C₄²×C₁₉	—	2	4	no	—
315	C₄²×C₁₉	—	2	2	no	—
316	C₄²×C₁₉	—	2	2	no	—
317	C₄²×C₁₉	—	2	4	no	—
318	C₄²×C₁₉	—	4	1	no	—
319	C₄²×C₁₉	—	4	1	no	—
320	C₄²×C₁₉	—	4	2	no	—
321	C₄²×C₁₉	—	4	2	no	—
322	#34962	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
323	C₂³×C₁₉	—	2	2	no	—
324	C₂³×C₁₉	—	2	2	no	—
325	C₂³×C₁₉	—	2	2	no	—
326	C₂³×C₁₉	—	2	2	no	—
327	C₂³×C₁₉	—	2	2	no	—
328	C₂³×C₁₉	—	2	2	no	—
329	C₂³×C₁₉	—	2	1	no	—
330	C₂³×C₁₉	—	2	2	no	—
331	C₂³×C₁₉	—	2	2	no	—
332	C₂³×C₁₉	—	2	1	no	—
333	C₂³×C₁₉	—	2	2	no	—
334	C₂³×C₁₉	—	2	2	no	—
335	C₂³×C₁₉	—	2	2	no	—
336	C₂³×C₁₉	—	2	2	no	—
337	C₂³×C₁₉	—	2	2	no	—
338	C₂³×C₁₉	—	2	2	no	—
339	C₂³×C₁₉	—	2	2	no	—
340	C₂³×C₁₉	C₂×#41	1	2	yes	—
341	C₂³×C₁₉	C₂×#41	1	4	yes	—
342	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
343	Q₈×C₁₉	—	4	4	no	—
344	Q₈×C₁₉	—	4	4	no	—
345	D₄×C₁₉	—	2	16	no	—
346	D₄×C₁₉	—	4	8	no	—
347	D₄×C₁₉	—	4	8	no	—
348	D₄×C₁₉	—	4	4	no	—
349	D₄×C₁₉	—	4	4	no	—
350	D₄×C₁₉	—	4	8	no	—
351	C₂×C₄×C₁₉	—	2	2	no	—
352	C₂×C₄×C₁₉	—	2	2	no	—
353	C₂×C₄×C₁₉	—	2	2	no	—
354	C₂×C₄×C₁₉	—	2	2	no	—
355	C₂×C₄×C₁₉	—	2	2	no	—
356	C₂×C₄×C₁₉	—	2	2	no	—
357	C₂×C₄×C₁₉	—	2	2	no	—
358	C₂×C₄×C₁₉	—	2	2	no	—
359	C₂×C₄×C₁₉	—	2	2	no	—
360	C₂×C₄×C₁₉	—	2	2	no	—
361	C₂×C₄×C₁₉	—	2	1	no	—
362	C₂×C₄×C₁₉	—	2	1	no	—
363	C₂×C₄×C₁₉	—	2	8	no	—
364	C₂×C₄×C₁₉	—	2	2	no	—
365	C₂×C₄×C₁₉	—	2	2	no	—
366	C₂×C₄×C₁₉	—	2	2	no	—
367	C₂×C₄×C₁₉	—	2	2	no	—
368	C₂×C₄×C₁₉	—	2	2	no	—
369	C₂×C₄×C₁₉	—	2	2	no	—
370	C₂×C₄×C₁₉	—	2	2	no	—
371	C₂×C₄×C₁₉	—	2	2	no	—
372	C₂×C₄×C₁₉	—	2	2	no	—
373	C₂×C₄×C₁₉	—	2	2	no	—
374	C₂×C₄×C₁₉	—	2	2	no	—
375	C₂×C₄×C₁₉	—	2	2	no	—
376	C₂×C₄×C₁₉	—	2	2	no	—
377	C₂×C₄×C₁₉	—	2	2	no	—
378	C₂×C₄×C₁₉	—	2	1	no	—
379	C₂×C₄×C₁₉	—	2	2	no	—
380	C₂×C₄×C₁₉	—	2	1	no	—
381	C₂×C₄×C₁₉	—	2	1	no	—
382	C₂×C₄×C₁₉	—	2	1	no	—
383	C₂×C₄×C₁₉	—	2	2	no	—
384	C₂×C₄×C₁₉	—	2	2	no	—
385	C₂×C₄×C₁₉	—	2	2	no	—
386	C₂×C₄×C₁₉	—	2	2	no	—
387	C₂×C₄×C₁₉	—	4	8	no	—
388	C₂×C₄×C₁₉	—	4	8	no	—
389	C₂×C₄×C₁₉	—	4	8	no	—
390	C₂×C₄×C₁₉	—	4	8	no	—
391	C₂×C₄×C₁₉	—	4	8	no	—
392	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
393	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
394	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
395	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
396	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
397	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
398	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
399	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
400	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
401	#2593	C₂×C₁₉	1	1	yes	characteristic, complemented
402	#2586	C₂×C₁₉	1	1	yes	characteristic, complemented
403	#2574	C₂×C₁₉	1	2	yes	complemented
404	#2572	C₂×C₁₉	1	1	yes	characteristic, complemented
405	#2555	C₂×C₁₉	1	1	yes	characteristic, complemented
406	#2554	C₂×C₁₉	1	2	yes	complemented
407	#2518	C₂×C₁₉	1	2	yes	complemented
408	#2467	C₂×C₁₉	1	2	yes	complemented
409	#2459	C₂×C₁₉	1	2	yes	complemented
410	#2456	C₂×C₁₉	1	2	yes	complemented
411	#2396	C₂×C₁₉	1	1	yes	characteristic, complemented
412	#2392	C₂×C₁₉	1	1	yes	characteristic, complemented
413	#2388	C₂×C₁₉	1	2	yes	complemented
414	C₄×#126	C₂×C₁₉	1	2	yes	complemented
415	C₄×#124	C₂×C₁₉	1	2	yes	complemented
416	C₄×#123	C₂×C₁₉	1	2	yes	complemented
417	C₄×#121	C₂×C₁₉	1	2	yes	complemented
418	#2297	C₂×C₁₉	1	1	yes	characteristic, complemented
419	C₄²×D₄	C₂×C₁₉	1	2	yes	complemented
420	C₂²×C₁₉	—	2	4	no	—
421	C₂²×C₁₉	—	2	4	no	—
422	C₂²×C₁₉	—	2	2	no	—
423	C₂²×C₁₉	—	2	4	no	—
424	C₂²×C₁₉	—	2	4	no	—
425	C₂²×C₁₉	—	4	2	no	—
426	C₂²×C₁₉	—	4	2	no	—
427	C₂²×C₁₉	—	4	2	no	—
428	C₂²×C₁₉	—	4	2	no	—
429	C₂²×C₁₉	—	4	1	no	—
430	C₂²×C₁₉	—	4	1	no	—
431	C₂²×C₁₉	—	4	2	no	—
432	C₂²×C₁₉	—	4	2	no	—
433	C₂²×C₁₉	—	4	2	no	—
434	C₂²×C₁₉	—	4	2	no	—
435	C₂²×C₁₉	—	4	2	no	—
436	C₂²×C₁₉	—	4	2	no	—
437	C₂²×C₁₉	—	4	2	no	—
438	C₂²×C₁₉	—	4	2	no	—
439	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
440	C₂²×C₁₉	C₂²×#41	1	2	yes	—
441	C₂²×C₁₉	C₂²×#41	1	2	yes	—
442	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
444	C₄×C₁₉	—	2	4	no	—
445	C₄×C₁₉	—	2	2	no	—
446	C₄×C₁₉	—	2	4	no	—
447	C₄×C₁₉	—	2	4	no	—
448	C₄×C₁₉	—	2	4	no	—
449	C₄×C₁₉	—	2	4	no	—
450	C₄×C₁₉	—	4	2	no	—
451	C₄×C₁₉	—	4	2	no	—
452	C₄×C₁₉	—	4	2	no	—
453	C₄×C₁₉	—	4	2	no	—
454	C₄×C₁₉	—	4	1	no	—
455	C₄×C₁₉	—	4	1	no	—
456	C₄×C₁₉	—	4	2	no	—
457	C₄×C₁₉	—	4	1	no	—
458	C₄×C₁₉	—	4	1	no	—
459	C₄×C₁₉	#538	1	4	yes	—
460	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
461	C₂×#126	C₂²×C₁₉	1	2	yes	—
462	C₂×#124	C₂²×C₁₉	1	2	yes	—
463	C₂×#123	C₂²×C₁₉	1	2	yes	—
464	C₂×#121	C₂²×C₁₉	1	2	yes	—
465	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
467	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
468	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
469	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
470	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
471	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
472	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
473	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
474	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
475	#400	C₂²×C₁₉	1	1	yes	characteristic
476	#399	C₂²×C₁₉	1	1	yes	characteristic
477	#398	C₂²×C₁₉	1	2	yes	—
478	#398	C₂²×C₁₉	1	1	yes	characteristic
479	#397	C₂²×C₁₉	1	1	yes	characteristic
480	#396	C₂²×C₁₉	1	2	yes	—
481	#396	C₂²×C₁₉	1	2	yes	—
482	#395	C₂²×C₁₉	1	2	yes	—
483	#395	C₂²×C₁₉	1	1	yes	characteristic
484	#394	C₂²×C₁₉	1	1	yes	characteristic
485	#394	C₂²×C₁₉	1	2	yes	—
486	#394	C₂²×C₁₉	1	2	yes	—
487	#394	C₂²×C₁₉	1	2	yes	—
488	#394	C₂²×C₁₉	1	2	yes	—
489	#393	C₂²×C₁₉	1	2	yes	—
490	#393	C₂²×C₁₉	1	1	yes	characteristic
491	#392	C₂²×C₁₉	1	2	yes	—
492	#392	C₂²×C₁₉	1	2	yes	—
493	#392	C₂²×C₁₉	1	2	yes	—
494	#392	C₂²×C₁₉	1	1	yes	characteristic
495	#391	C₂²×C₁₉	1	1	yes	characteristic
496	#391	C₂²×C₁₉	1	1	yes	characteristic
497	#391	C₂²×C₁₉	1	2	yes	—
498	#390	C₂²×C₁₉	1	1	yes	characteristic
499	#390	C₂²×C₁₉	1	2	yes	—
500	#390	C₂²×C₁₉	1	2	yes	—
501	#390	C₂²×C₁₉	1	1	yes	characteristic
502	#389	C₂²×C₁₉	1	2	yes	—
503	#388	C₂²×C₁₉	1	2	yes	—
504	#388	C₂²×C₁₉	1	2	yes	—
505	#388	C₂²×C₁₉	1	2	yes	—
506	#388	C₂²×C₁₉	1	2	yes	—
507	#388	C₂²×C₁₉	1	2	yes	—
508	#388	C₂²×C₁₉	1	2	yes	—
509	#388	C₂²×C₁₉	1	2	yes	—
510	#388	C₂²×C₁₉	1	2	yes	—
511	#388	C₂²×C₁₉	1	2	yes	—
512	#388	C₂²×C₁₉	1	2	yes	—
513	#388	C₂²×C₁₉	1	2	yes	—
514	#387	C₂²×C₁₉	1	2	yes	—
515	#387	C₂²×C₁₉	1	2	yes	—
516	#387	C₂²×C₁₉	1	2	yes	—
517	#387	C₂²×C₁₉	1	2	yes	—
518	#387	C₂²×C₁₉	1	2	yes	—
519	#386	C₂²×C₁₉	1	2	yes	—
520	#386	C₂²×C₁₉	1	2	yes	—
521	#386	C₂²×C₁₉	1	2	yes	—
522	#386	C₂²×C₁₉	1	2	yes	—
523	#386	C₂²×C₁₉	1	2	yes	—
524	#385	C₂²×C₁₉	1	2	yes	—
525	#383	C₂²×C₁₉	1	2	yes	—
526	#382	C₂²×C₁₉	1	2	yes	—
527	#381	C₂²×C₁₉	1	2	yes	—
528	#380	C₂²×C₁₉	1	2	yes	—
529	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
530	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
531	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
532	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
533	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
534	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
535	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
536	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
537	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
538	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
539	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
540	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
541	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
542	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
543	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
544	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
545	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
546	C₄³	C₂²×C₁₉	1	2	yes	—
547	C₂×C₁₉	—	4	2	no	—
548	C₂×C₁₉	—	4	4	no	—
549	C₂×C₁₉	—	8	2	no	—
550	C₂×C₁₉	#3444	1	2	yes	—
551	C₂×C₁₉	C₂×#538	1	1	yes	characteristic
552	C₂×C₁₉	#3481	1	2	yes	—
553	C₂×C₁₉	#3481	1	1	yes	characteristic
554	C₂×C₁₉	#3483	1	1	yes	characteristic
555	C₂×#41	—	2	4	no	—
556	C₂×#41	—	4	2	no	—
557	C₂×#41	—	4	2	no	—
558	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
560	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
561	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
562	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
563	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
564	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
565	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
567	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
568	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
569	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
570	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
571	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
572	#126	—	2	8	no	—
573	#124	—	2	8	no	—
574	#123	—	2	8	no	—
575	#121	—	2	8	no	—
576	C₄×Q₈	—	4	2	no	—
577	C₄×D₄	—	2	8	no	—
578	C₄×D₄	—	2	8	no	—
579	C₄×D₄	—	2	8	no	—
580	C₄×D₄	—	4	4	no	—
581	C₄×D₄	—	4	2	no	—
582	C₄×D₄	—	4	4	no	—
583	#117	—	4	2	no	—
584	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
621	C₂×C₄²	—	4	2	no	—
622	C₂×C₄²	—	4	4	no	—
623	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
626	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
627	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
628	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
629	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
631	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
632	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
633	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
634	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
636	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
637	#95	C₂³×C₁₉	1	2	yes	—
638	#95	C₂³×C₁₉	1	2	yes	—
639	#95	C₂³×C₁₉	1	2	yes	—
640	#95	C₂³×C₁₉	1	2	yes	—
641	#95	C₂³×C₁₉	1	2	yes	—
642	#95	C₂³×C₁₉	1	2	yes	—
643	#95	C₂³×C₁₉	1	2	yes	—
644	#95	C₂³×C₁₉	1	2	yes	—
645	#95	C₂³×C₁₉	1	2	yes	—
646	#95	C₂³×C₁₉	1	2	yes	—
647	#95	C₂³×C₁₉	1	2	yes	—
648	#95	C₂³×C₁₉	1	2	yes	—
649	#95	C₂³×C₁₉	1	2	yes	—
650	#95	C₂³×C₁₉	1	2	yes	—
651	#95	C₂³×C₁₉	1	2	yes	—
652	#95	C₂³×C₁₉	1	2	yes	—
653	#95	C₂³×C₁₉	1	1	yes	characteristic
654	#95	C₂³×C₁₉	1	1	yes	characteristic
655	#95	C₂³×C₁₉	1	2	yes	—
656	#95	C₂³×C₁₉	1	1	yes	characteristic
657	#95	C₂³×C₁₉	1	2	yes	—
658	#95	C₂³×C₁₉	1	1	yes	characteristic
659	C₁₉	#34962	1	1	yes	characteristic, direct product factor, Sylow
660	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
661	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
662	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
663	#41	—	4	16	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	4	1	no	—
667	C₂×Q₈	—	4	1	no	—
668	C₂×Q₈	—	4	1	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	4	no	—
675	C₂×D₄	—	2	4	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	4	2	no	—
680	C₂×D₄	—	4	2	no	—
681	C₂×D₄	—	4	1	no	—
682	C₂×D₄	—	4	1	no	—
683	C₂×D₄	—	4	1	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	#41×C₁₉	1	4	yes	—
704	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	4	1	no	—
727	C₄⋊C₄	—	4	1	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	1	no	—
733	C₄⋊C₄	#41×C₁₉	1	8	yes	complemented
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	4	1	no	—
750	C₂²⋊C₄	—	4	1	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	#41×C₁₉	1	8	yes	complemented
757	C₄²	—	2	4	no	—
758	C₄²	—	2	4	no	—
759	C₄²	—	2	4	no	—
760	C₄²	—	2	4	no	—
761	C₄²	—	2	4	no	—
762	C₄²	—	2	4	no	—
763	C₄²	—	2	4	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	4	no	—
767	C₄²	—	4	1	no	—
768	C₄²	—	4	1	no	—
769	C₄²	—	4	2	no	—
770	C₄²	—	4	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	C₂×#41×C₁₉	1	2	yes	—
789	C₂³	C₂×#41×C₁₉	1	4	yes	—
790	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
791	Q₈	—	4	4	no	—
792	Q₈	—	4	4	no	—
793	D₄	—	2	16	no	—
794	D₄	—	4	8	no	—
795	D₄	—	4	8	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	8	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	8	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	8	no	—
838	C₂×C₄	—	4	8	no	—
839	C₂×C₄	—	4	8	no	—
840	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
841	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
842	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
843	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
844	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
845	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
846	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
847	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
848	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
849	C₂²	—	2	4	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
869	C₂²	C₂²×#41×C₁₉	1	2	yes	—
870	C₂²	C₂²×#41×C₁₉	1	2	yes	—
871	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
872	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
873	C₄	—	2	4	no	—
874	C₄	—	2	2	no	—
875	C₄	—	2	4	no	—
876	C₄	—	2	4	no	—
877	C₄	—	2	4	no	—
878	C₄	—	2	4	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	1	no	—
888	C₄	C₁₉×#538	1	4	yes	—
889	C₂	—	4	2	no	—
890	C₂	—	4	4	no	—
891	C₂	—	8	2	no	—
892	C₂	C₁₉×#3444	1	2	yes	—
893	C₂	C₂×C₁₉×#538	1	1	yes	characteristic
894	C₂	C₁₉×#3481	1	2	yes	—
895	C₂	C₁₉×#3481	1	1	yes	characteristic
896	C₂	C₁₉×#3483	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2593	C₂	semidirect
2. C₁₉×#2586	C₂	semidirect
3. C₁₉×#2574	C₂	semidirect
4. C₁₉×#2572	C₂	semidirect
5. C₁₉×#2555	C₂	semidirect
6. C₁₉×#2554	C₂	semidirect
7. C₁₉×#2518	C₂	semidirect
8. C₁₉×#2467	C₂	semidirect
9. C₁₉×#2459	C₂	semidirect
10. C₁₉×#2456	C₂	semidirect
11. C₁₉×#2396	C₂	semidirect
12. C₁₉×#2392	C₂	semidirect
13. C₁₉×#2388	C₂	semidirect
14. C₄×C₁₉×#126	C₂	semidirect
15. C₄×C₁₉×#124	C₂	semidirect
16. C₄×C₁₉×#123	C₂	semidirect
17. C₄×C₁₉×#121	C₂	semidirect
18. C₁₉×#2297	C₂	semidirect
19. C₄²×D₄×C₁₉	C₂	semidirect
284. C₄⋊C₄×C₁₉	#41	semidirect
307. C₂²⋊C₄×C₁₉	#41	semidirect
322. #34962	C₁₉	direct (N × H)
401. #2593	C₂×C₁₉	semidirect
402. #2586	C₂×C₁₉	semidirect
403. #2574	C₂×C₁₉	semidirect
404. #2572	C₂×C₁₉	semidirect
405. #2555	C₂×C₁₉	semidirect
406. #2554	C₂×C₁₉	semidirect
407. #2518	C₂×C₁₉	semidirect
408. #2467	C₂×C₁₉	semidirect
409. #2459	C₂×C₁₉	semidirect
410. #2456	C₂×C₁₉	semidirect
411. #2396	C₂×C₁₉	semidirect
412. #2392	C₂×C₁₉	semidirect
413. #2388	C₂×C₁₉	semidirect
414. C₄×#126	C₂×C₁₉	semidirect
415. C₄×#124	C₂×C₁₉	semidirect
416. C₄×#123	C₂×C₁₉	semidirect
417. C₄×#121	C₂×C₁₉	semidirect
418. #2297	C₂×C₁₉	semidirect
419. C₄²×D₄	C₂×C₁₉	semidirect
659. C₁₉	#34962	direct (N × H)
733. C₄⋊C₄	#41×C₁₉	semidirect
756. C₂²⋊C₄	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#2593	2
C₁₉×#2586	2
C₁₉×#2574	2
C₁₉×#2572	2
C₁₉×#2555	2
C₁₉×#2554	2
C₁₉×#2518	2
C₁₉×#2467	2
C₁₉×#2459	2
C₁₉×#2456	2
C₁₉×#2396	2
C₁₉×#2392	2
C₁₉×#2388	2
C₄×C₁₉×#126	2
C₄×C₁₉×#124	2
C₄×C₁₉×#123	2
C₄×C₁₉×#121	2
C₁₉×#2297	2
C₄²×D₄×C₁₉	2
#34962	19

Subgroups — C19×#34962 #18040921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34962 #18040921