Subgroups — C₂×C₁₉×#3310 #18067086

Order 4864.

2578 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#3310	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₉×#490	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#418	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₁₉	—	2	1	no	—
18	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#552	—	2	4	no	—
26	C₁₉×#552	C₂²	1	8	yes	complemented
27	D₄²×C₁₉	—	2	4	no	—
28	D₄²×C₁₉	C₂²	1	8	yes	—
29	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#126	—	2	1	no	—
31	C₂×C₁₉×#125	—	2	1	no	—
32	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₉×#123	—	2	1	no	—
34	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₉×#121	—	2	1	no	—
37	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#120	—	2	1	no	—
40	C₂×C₁₉×#120	—	2	1	no	—
41	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
44	C₂×C₁₉×#117	—	2	1	no	—
45	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#490	C₂²	1	8	yes	complemented
48	C₁₉×#482	C₂²	1	8	yes	complemented
49	C₁₉×#480	C₂²	1	8	yes	complemented
50	C₁₉×#478	C₂²	1	8	yes	complemented
51	C₁₉×#468	C₂²	1	8	yes	complemented
52	C₁₉×#465	C₂²	1	8	yes	complemented
53	C₁₉×#460	C₂²	1	8	yes	complemented
54	C₁₉×#450	C₂²	1	8	yes	complemented
55	C₁₉×#450	C₂²	1	8	yes	complemented
56	C₁₉×#440	C₂²	1	8	yes	complemented
57	C₁₉×#435	C₂²	1	8	yes	complemented
58	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₁₉×#418	C₂²	1	8	yes	complemented
63	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
65	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
66	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
67	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₁₉×#102	C₂²	1	8	yes	complemented
74	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₁₉	—	2	1	no	—
78	C₂⁵×C₁₉	—	2	1	no	—
79	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₉	—	2	4	no	—
81	C₂²×D₄×C₁₉	—	2	4	no	—
82	C₂²×D₄×C₁₉	—	2	1	no	—
83	C₂²×D₄×C₁₉	—	2	1	no	—
84	C₂²×D₄×C₁₉	—	2	8	no	—
85	C₂²×D₄×C₁₉	—	2	1	no	—
86	C₂²×D₄×C₁₉	—	2	1	no	—
87	C₂²×D₄×C₁₉	—	2	1	no	—
88	C₂²×D₄×C₁₉	—	2	2	no	—
89	C₂²×D₄×C₁₉	—	2	2	no	—
90	C₂²×D₄×C₁₉	—	2	1	no	—
91	C₂²×D₄×C₁₉	—	4	2	no	—
92	C₂²×D₄×C₁₉	—	4	2	no	—
93	C₂²×D₄×C₁₉	—	4	8	no	—
94	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
95	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
98	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
99	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₉	—	2	1	no	—
101	C₂³×C₄×C₁₉	—	2	1	no	—
102	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×SD₁₆×C₁₉	—	2	4	no	—
105	C₂×SD₁₆×C₁₉	—	4	2	no	—
106	C₂×SD₁₆×C₁₉	—	4	2	no	—
107	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	complemented
109	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	complemented
110	C₂×M₁₆×C₁₉	—	4	2	no	—
111	C₂×M₁₆×C₁₉	C₂³	1	4	yes	complemented
112	C₂²×C₈×C₁₉	—	4	2	no	—
113	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₁₉	C₂³	1	4	yes	complemented
118	C₁₉×#127	—	2	2	no	—
119	C₁₉×#127	C₂³	1	4	yes	—
120	C₁₉×#126	—	2	8	no	—
121	C₁₉×#125	—	2	8	no	—
122	C₁₉×#125	—	2	2	no	—
123	C₁₉×#125	C₂³	1	4	yes	complemented
124	C₁₉×#123	—	2	8	no	—
125	C₁₉×C₂²⋊Q₈	—	2	2	no	—
126	C₁₉×C₂²⋊Q₈	—	2	2	no	—
127	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	complemented
128	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	complemented
129	C₁₉×#121	—	2	2	no	—
130	C₁₉×#121	—	2	2	no	—
131	C₁₉×#121	—	2	8	no	—
132	C₁₉×#121	C₂³	1	4	yes	—
133	C₁₉×#121	C₂³	1	4	yes	—
134	C₁₉×#120	—	2	8	no	—
135	C₁₉×#120	—	2	8	no	—
136	C₄×Q₈×C₁₉	—	2	2	no	—
137	C₄×Q₈×C₁₉	C₂³	1	4	yes	complemented
138	C₄×D₄×C₁₉	—	2	2	no	—
139	C₄×D₄×C₁₉	D₄	1	4	yes	—
140	C₄×D₄×C₁₉	C₂³	1	4	yes	—
141	C₄×D₄×C₁₉	C₂³	1	4	yes	—
142	C₁₉×#117	—	2	2	no	—
143	C₁₉×#117	—	2	8	no	—
144	C₁₉×#117	C₂³	1	4	yes	complemented
145	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	complemented
158	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₁₉	—	2	1	no	—
167	C₂×C₄²×C₁₉	—	2	1	no	—
168	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
169	C₁₉×#107	C₂³	1	4	yes	complemented
170	C₁₉×#107	C₂³	1	4	yes	complemented
171	C₁₉×#106	C₂³	1	4	yes	complemented
172	C₁₉×C₄⋊C₈	C₂³	1	4	yes	complemented
173	C₁₉×#103	C₂³	1	4	yes	complemented
174	C₁₉×#102	C₂³	1	4	yes	—
175	C₁₉×#102	C₂³	1	4	yes	—
176	C₁₉×#102	C₂³	1	4	yes	—
177	C₁₉×#102	C₂³	1	4	yes	complemented
178	C₁₉×#102	C₂³	1	4	yes	complemented
179	C₁₉×#102	C₂³	1	4	yes	complemented
180	C₁₉×#102	C₂³	1	4	yes	complemented
181	C₁₉×#102	C₂³	1	4	yes	complemented
182	C₁₉×#102	C₂³	1	4	yes	complemented
183	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	complemented
184	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	complemented
185	C₁₉×#97	C₂³	1	4	yes	complemented
186	C₂⁴×C₁₉	—	2	1	no	—
187	C₂⁴×C₁₉	—	2	1	no	—
188	C₂⁴×C₁₉	—	2	1	no	—
189	C₂⁴×C₁₉	—	2	4	no	—
190	C₂⁴×C₁₉	—	2	4	no	—
191	C₂⁴×C₁₉	—	4	4	no	—
192	C₂⁴×C₁₉	—	4	4	no	—
193	C₂⁴×C₁₉	—	4	4	no	—
194	C₂⁴×C₁₉	—	4	4	no	—
195	C₂⁴×C₁₉	—	8	2	no	—
196	C₂⁴×C₁₉	—	8	2	no	—
197	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
198	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂×Q₈×C₁₉	—	2	1	no	—
200	C₂×Q₈×C₁₉	—	2	2	no	—
201	C₂×Q₈×C₁₉	—	2	2	no	—
202	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
203	C₂×D₄×C₁₉	—	2	4	no	—
204	C₂×D₄×C₁₉	—	2	8	no	—
205	C₂×D₄×C₁₉	—	2	8	no	—
206	C₂×D₄×C₁₉	—	2	4	no	—
207	C₂×D₄×C₁₉	—	2	4	no	—
208	C₂×D₄×C₁₉	—	2	1	no	—
209	C₂×D₄×C₁₉	—	2	4	no	—
210	C₂×D₄×C₁₉	—	2	4	no	—
211	C₂×D₄×C₁₉	—	2	1	no	—
212	C₂×D₄×C₁₉	—	2	1	no	—
213	C₂×D₄×C₁₉	—	2	4	no	—
214	C₂×D₄×C₁₉	—	2	4	no	—
215	C₂×D₄×C₁₉	—	2	2	no	—
216	C₂×D₄×C₁₉	—	2	2	no	—
217	C₂×D₄×C₁₉	—	2	2	no	—
218	C₂×D₄×C₁₉	—	2	2	no	—
219	C₂×D₄×C₁₉	—	2	2	no	—
220	C₂×D₄×C₁₉	—	4	4	no	—
221	C₂×D₄×C₁₉	—	4	4	no	—
222	C₂×D₄×C₁₉	—	4	8	no	—
223	C₂×D₄×C₁₉	—	4	8	no	—
224	C₂×D₄×C₁₉	—	4	4	no	—
225	C₂×D₄×C₁₉	—	4	4	no	—
226	C₂×D₄×C₁₉	—	4	4	no	—
227	C₂×D₄×C₁₉	—	4	32	no	—
228	C₂×D₄×C₁₉	—	4	4	no	—
229	C₂×D₄×C₁₉	—	4	4	no	—
230	C₂×D₄×C₁₉	—	8	2	no	—
231	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₁₉	#41	1	4	yes	—
233	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
234	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
235	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₉	—	2	2	no	—
237	C₂²×C₄×C₁₉	—	2	2	no	—
238	C₂²×C₄×C₁₉	—	2	2	no	—
239	C₂²×C₄×C₁₉	—	2	2	no	—
240	C₂²×C₄×C₁₉	—	2	4	no	—
241	C₂²×C₄×C₁₉	—	2	1	no	—
242	C₂²×C₄×C₁₉	—	2	1	no	—
243	C₂²×C₄×C₁₉	—	2	1	no	—
244	C₂²×C₄×C₁₉	—	2	1	no	—
245	C₂²×C₄×C₁₉	—	2	1	no	—
246	C₂²×C₄×C₁₉	—	2	4	no	—
247	C₂²×C₄×C₁₉	—	4	4	no	—
248	C₂²×C₄×C₁₉	—	4	4	no	—
249	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
258	SD₁₆×C₁₉	—	2	8	no	—
259	SD₁₆×C₁₉	—	4	4	no	—
260	SD₁₆×C₁₉	—	4	4	no	—
261	M₁₆×C₁₉	—	4	4	no	—
262	C₂×C₈×C₁₉	—	2	2	no	—
263	C₂×C₈×C₁₉	—	2	2	no	—
264	C₂×C₈×C₁₉	—	2	2	no	—
265	C₂×C₈×C₁₉	—	2	2	no	—
266	C₂×C₈×C₁₉	—	4	4	no	—
267	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
268	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
269	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
270	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₁₉	—	2	1	no	—
272	C₄⋊C₄×C₁₉	—	2	1	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	—	2	4	no	—
278	C₄⋊C₄×C₁₉	—	2	4	no	—
279	C₄⋊C₄×C₁₉	—	2	1	no	—
280	C₄⋊C₄×C₁₉	—	2	1	no	—
281	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
282	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
285	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
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	C₂×D₄	1	4	yes	—
293	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
294	C₄²×C₁₉	—	2	4	no	—
295	C₄²×C₁₉	—	2	4	no	—
296	C₄²×C₁₉	C₂×D₄	1	2	yes	—
297	C₄²×C₁₉	C₂⁴	1	2	yes	—
298	C₂×#3310	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
299	C₂³×C₁₉	—	2	2	no	—
300	C₂³×C₁₉	—	2	2	no	—
301	C₂³×C₁₉	—	2	2	no	—
302	C₂³×C₁₉	—	2	4	no	—
303	C₂³×C₁₉	—	2	2	no	—
304	C₂³×C₁₉	—	2	2	no	—
305	C₂³×C₁₉	—	2	2	no	—
306	C₂³×C₁₉	—	2	2	no	—
307	C₂³×C₁₉	—	2	2	no	—
308	C₂³×C₁₉	—	4	8	no	—
309	C₂³×C₁₉	—	4	8	no	—
310	C₂³×C₁₉	—	4	8	no	—
311	C₂³×C₁₉	—	4	2	no	—
312	C₂³×C₁₉	—	4	2	no	—
313	C₂³×C₁₉	—	4	2	no	—
314	C₂³×C₁₉	—	4	2	no	—
315	C₂³×C₁₉	—	4	8	no	—
316	C₂³×C₁₉	—	4	2	no	—
317	C₂³×C₁₉	—	4	2	no	—
318	C₂³×C₁₉	—	4	2	no	—
319	C₂³×C₁₉	—	4	2	no	—
320	C₂³×C₁₉	—	8	4	no	—
321	C₂³×C₁₉	—	8	4	no	—
322	C₂³×C₁₉	—	8	16	no	—
323	C₂³×C₁₉	—	8	16	no	—
324	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
325	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
326	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
327	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
328	Q₈×C₁₉	—	2	2	no	—
329	Q₈×C₁₉	—	2	2	no	—
330	Q₈×C₁₉	—	4	2	no	—
331	D₄×C₁₉	—	2	8	no	—
332	D₄×C₁₉	—	2	4	no	—
333	D₄×C₁₉	—	2	2	no	—
334	D₄×C₁₉	—	2	2	no	—
335	D₄×C₁₉	—	2	2	no	—
336	D₄×C₁₉	—	2	2	no	—
337	D₄×C₁₉	—	2	2	no	—
338	D₄×C₁₉	—	4	8	no	—
339	D₄×C₁₉	—	4	8	no	—
340	D₄×C₁₉	—	4	8	no	—
341	D₄×C₁₉	—	4	8	no	—
342	D₄×C₁₉	—	4	8	no	—
343	D₄×C₁₉	—	4	2	no	—
344	D₄×C₁₉	—	4	2	no	—
345	D₄×C₁₉	—	8	4	no	—
346	D₄×C₁₉	C₂×#41	1	4	yes	—
347	C₂×C₄×C₁₉	—	2	2	no	—
348	C₂×C₄×C₁₉	—	2	2	no	—
349	C₂×C₄×C₁₉	—	2	2	no	—
350	C₂×C₄×C₁₉	—	2	2	no	—
351	C₂×C₄×C₁₉	—	2	4	no	—
352	C₂×C₄×C₁₉	—	2	4	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	2	no	—
362	C₂×C₄×C₁₉	—	4	8	no	—
363	C₂×C₄×C₁₉	—	4	2	no	—
364	C₂×C₄×C₁₉	—	4	8	no	—
365	C₂×C₄×C₁₉	—	4	2	no	—
366	C₂×C₄×C₁₉	—	4	2	no	—
367	C₂×C₄×C₁₉	—	4	2	no	—
368	C₂×C₄×C₁₉	—	4	2	no	—
369	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
372	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
373	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
375	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
376	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
377	C₈×C₁₉	—	2	2	no	—
378	C₈×C₁₉	—	2	2	no	—
379	C₈×C₁₉	—	2	2	no	—
380	C₈×C₁₉	—	2	2	no	—
381	C₂×#552	C₂×C₁₉	1	1	yes	characteristic, complemented
382	C₂×D₄²	C₂×C₁₉	1	1	yes	characteristic
383	#3310	C₂×C₁₉	1	16	yes	direct product factor
384	C₂×#490	C₂×C₁₉	1	1	yes	characteristic, complemented
385	C₂×#482	C₂×C₁₉	1	1	yes	characteristic, complemented
386	C₂×#480	C₂×C₁₉	1	1	yes	characteristic, complemented
387	C₂×#478	C₂×C₁₉	1	1	yes	characteristic, complemented
388	C₂×#468	C₂×C₁₉	1	1	yes	characteristic, complemented
389	C₂×#465	C₂×C₁₉	1	1	yes	characteristic, complemented
390	C₂×#460	C₂×C₁₉	1	1	yes	characteristic, complemented
391	C₂×#450	C₂×C₁₉	1	1	yes	characteristic, complemented
392	C₂×#450	C₂×C₁₉	1	1	yes	characteristic, complemented
393	C₂×#440	C₂×C₁₉	1	1	yes	characteristic, complemented
394	C₂×#435	C₂×C₁₉	1	1	yes	characteristic, complemented
395	C₂×#418	C₂×C₁₉	1	1	yes	characteristic, complemented
396	C₂²×#102	C₂×C₁₉	1	1	yes	characteristic, complemented
397	C₂²×C₁₉	—	2	2	no	—
398	C₂²×C₁₉	—	2	8	no	—
399	C₂²×C₁₉	—	2	2	no	—
400	C₂²×C₁₉	—	2	2	no	—
401	C₂²×C₁₉	—	2	4	no	—
402	C₂²×C₁₉	—	2	2	no	—
403	C₂²×C₁₉	—	2	2	no	—
404	C₂²×C₁₉	—	4	4	no	—
405	C₂²×C₁₉	—	4	8	no	—
406	C₂²×C₁₉	—	4	2	no	—
407	C₂²×C₁₉	—	4	2	no	—
408	C₂²×C₁₉	—	4	2	no	—
409	C₂²×C₁₉	—	4	2	no	—
410	C₂²×C₁₉	—	4	2	no	—
411	C₂²×C₁₉	—	4	2	no	—
412	C₂²×C₁₉	—	4	2	no	—
413	C₂²×C₁₉	—	4	2	no	—
414	C₂²×C₁₉	—	8	16	no	—
415	C₂²×C₁₉	—	8	16	no	—
416	C₂²×C₁₉	—	8	4	no	—
417	C₂²×C₁₉	—	8	4	no	—
418	C₂²×C₁₉	#546	1	2	yes	—
419	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
420	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
421	C₂²×C₁₉	#577	1	2	yes	—
422	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
423	C₄×C₁₉	—	2	2	no	—
424	C₄×C₁₉	—	2	2	no	—
425	C₄×C₁₉	—	2	2	no	—
426	C₄×C₁₉	—	2	2	no	—
427	C₄×C₁₉	—	4	2	no	—
428	C₄×C₁₉	—	4	2	no	—
429	C₄×C₁₉	—	4	2	no	—
430	C₄×C₁₉	—	4	2	no	—
431	C₄×C₁₉	—	4	2	no	—
432	C₄×C₁₉	#546	1	2	yes	—
433	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
434	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂³×D₄	—	2	1	no	—
436	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
437	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
438	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
439	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
440	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
441	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
442	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
443	#552	—	2	4	no	—
444	#552	C₂²×C₁₉	1	8	yes	complemented
445	D₄²	—	2	4	no	—
446	D₄²	C₂²×C₁₉	1	8	yes	—
447	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
448	C₂×#126	—	2	1	no	—
449	C₂×#125	—	2	1	no	—
450	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic, complemented
451	C₂×#123	—	2	1	no	—
452	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
453	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
454	C₂×#121	—	2	1	no	—
455	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
456	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
457	C₂×#120	—	2	1	no	—
458	C₂×#120	—	2	1	no	—
459	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
460	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
461	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
462	C₂×#117	—	2	1	no	—
463	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
464	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
465	#490	C₂²×C₁₉	1	8	yes	complemented
466	#482	C₂²×C₁₉	1	8	yes	complemented
467	#480	C₂²×C₁₉	1	8	yes	complemented
468	#478	C₂²×C₁₉	1	8	yes	complemented
469	#468	C₂²×C₁₉	1	8	yes	complemented
470	#465	C₂²×C₁₉	1	8	yes	complemented
471	#460	C₂²×C₁₉	1	8	yes	complemented
472	#450	C₂²×C₁₉	1	8	yes	complemented
473	#450	C₂²×C₁₉	1	8	yes	complemented
474	#440	C₂²×C₁₉	1	8	yes	complemented
475	#435	C₂²×C₁₉	1	8	yes	complemented
476	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
477	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
478	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic, complemented
479	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
480	#418	C₂²×C₁₉	1	8	yes	complemented
481	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic, complemented
482	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
483	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
484	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
485	C₂×#102	C₂²×C₁₉	1	8	yes	complemented
486	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
487	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
488	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
489	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
490	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
491	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic, complemented
492	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
493	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
494	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
495	C₂×C₁₉	—	2	4	no	—
496	C₂×C₁₉	—	4	2	no	—
497	C₂×C₁₉	—	4	4	no	—
498	C₂×C₁₉	—	8	2	no	—
499	C₂×C₁₉	—	8	2	no	—
500	C₂×C₁₉	#3310	1	4	yes	direct product factor
501	C₂×C₁₉	C₂×#546	1	1	yes	characteristic
502	C₂×C₁₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
503	C₂×C₁₉	C₂×#577	1	1	yes	characteristic
504	C₂⁵	—	2	1	no	—
505	C₂⁵	—	2	1	no	—
506	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
507	C₂²×D₄	—	2	4	no	—
508	C₂²×D₄	—	2	4	no	—
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	—	2	1	no	—
511	C₂²×D₄	—	2	8	no	—
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	—	2	2	no	—
516	C₂²×D₄	—	2	2	no	—
517	C₂²×D₄	—	2	1	no	—
518	C₂²×D₄	—	4	2	no	—
519	C₂²×D₄	—	4	2	no	—
520	C₂²×D₄	—	4	8	no	—
521	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
522	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
523	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
524	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
525	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
526	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
527	C₂³×C₄	—	2	1	no	—
528	C₂³×C₄	—	2	1	no	—
529	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
531	C₂×SD₁₆	—	2	4	no	—
532	C₂×SD₁₆	—	4	2	no	—
533	C₂×SD₁₆	—	4	2	no	—
534	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
535	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	complemented
536	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	complemented
537	C₂×M₁₆	—	4	2	no	—
538	C₂×M₁₆	C₂³×C₁₉	1	4	yes	complemented
539	C₂²×C₈	—	4	2	no	—
540	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
541	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
542	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
543	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
544	C₂²×C₈	C₂³×C₁₉	1	4	yes	complemented
545	#127	—	2	2	no	—
546	#127	C₂³×C₁₉	1	4	yes	—
547	#126	—	2	8	no	—
548	#125	—	2	8	no	—
549	#125	—	2	2	no	—
550	#125	C₂³×C₁₉	1	4	yes	complemented
551	#123	—	2	8	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	complemented
555	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	complemented
556	#121	—	2	2	no	—
557	#121	—	2	2	no	—
558	#121	—	2	8	no	—
559	#121	C₂³×C₁₉	1	4	yes	—
560	#121	C₂³×C₁₉	1	4	yes	—
561	#120	—	2	8	no	—
562	#120	—	2	8	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	C₂³×C₁₉	1	4	yes	complemented
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	D₄×C₁₉	1	4	yes	—
567	C₄×D₄	C₂³×C₁₉	1	4	yes	—
568	C₄×D₄	C₂³×C₁₉	1	4	yes	—
569	#117	—	2	2	no	—
570	#117	—	2	8	no	—
571	#117	C₂³×C₁₉	1	4	yes	complemented
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	2	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	complemented
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
593	C₂×C₄²	—	2	1	no	—
594	C₂×C₄²	—	2	1	no	—
595	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
596	#107	C₂³×C₁₉	1	4	yes	complemented
597	#107	C₂³×C₁₉	1	4	yes	complemented
598	#106	C₂³×C₁₉	1	4	yes	complemented
599	C₄⋊C₈	C₂³×C₁₉	1	4	yes	complemented
600	#103	C₂³×C₁₉	1	4	yes	complemented
601	#102	C₂³×C₁₉	1	4	yes	—
602	#102	C₂³×C₁₉	1	4	yes	—
603	#102	C₂³×C₁₉	1	4	yes	—
604	#102	C₂³×C₁₉	1	4	yes	complemented
605	#102	C₂³×C₁₉	1	4	yes	complemented
606	#102	C₂³×C₁₉	1	4	yes	complemented
607	#102	C₂³×C₁₉	1	4	yes	complemented
608	#102	C₂³×C₁₉	1	4	yes	complemented
609	#102	C₂³×C₁₉	1	4	yes	complemented
610	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	complemented
611	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	complemented
612	#97	C₂³×C₁₉	1	4	yes	complemented
613	C₁₉	C₂×#3310	1	1	yes	characteristic, direct product factor, Sylow
614	C₂⁴	—	2	1	no	—
615	C₂⁴	—	2	1	no	—
616	C₂⁴	—	2	1	no	—
617	C₂⁴	—	2	4	no	—
618	C₂⁴	—	2	4	no	—
619	C₂⁴	—	4	4	no	—
620	C₂⁴	—	4	4	no	—
621	C₂⁴	—	4	4	no	—
622	C₂⁴	—	4	4	no	—
623	C₂⁴	—	8	2	no	—
624	C₂⁴	—	8	2	no	—
625	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
626	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	2	2	no	—
630	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	8	no	—
633	C₂×D₄	—	2	8	no	—
634	C₂×D₄	—	2	4	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	4	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	8	no	—
651	C₂×D₄	—	4	8	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	4	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂×D₄	—	4	32	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	8	2	no	—
659	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
660	C₂×D₄	#41×C₁₉	1	4	yes	—
661	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
662	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
663	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	4	4	no	—
676	C₂²×C₄	—	4	4	no	—
677	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
682	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
686	SD₁₆	—	2	8	no	—
687	SD₁₆	—	4	4	no	—
688	SD₁₆	—	4	4	no	—
689	M₁₆	—	4	4	no	—
690	C₂×C₈	—	2	2	no	—
691	C₂×C₈	—	2	2	no	—
692	C₂×C₈	—	2	2	no	—
693	C₂×C₈	—	2	2	no	—
694	C₂×C₈	—	4	4	no	—
695	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
696	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
697	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
698	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
710	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
711	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
712	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
713	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
721	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
722	C₄²	—	2	4	no	—
723	C₄²	—	2	4	no	—
724	C₄²	C₂×D₄×C₁₉	1	2	yes	—
725	C₄²	C₂⁴×C₁₉	1	2	yes	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	4	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	4	8	no	—
736	C₂³	—	4	8	no	—
737	C₂³	—	4	8	no	—
738	C₂³	—	4	2	no	—
739	C₂³	—	4	2	no	—
740	C₂³	—	4	2	no	—
741	C₂³	—	4	2	no	—
742	C₂³	—	4	8	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	4	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	—	8	4	no	—
748	C₂³	—	8	4	no	—
749	C₂³	—	8	16	no	—
750	C₂³	—	8	16	no	—
751	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
752	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
753	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
754	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
755	Q₈	—	2	2	no	—
756	Q₈	—	2	2	no	—
757	Q₈	—	4	2	no	—
758	D₄	—	2	8	no	—
759	D₄	—	2	4	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	2	2	no	—
764	D₄	—	2	2	no	—
765	D₄	—	4	8	no	—
766	D₄	—	4	8	no	—
767	D₄	—	4	8	no	—
768	D₄	—	4	8	no	—
769	D₄	—	4	8	no	—
770	D₄	—	4	2	no	—
771	D₄	—	4	2	no	—
772	D₄	—	8	4	no	—
773	D₄	C₂×#41×C₁₉	1	4	yes	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	4	8	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	4	8	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
797	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
798	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
801	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
802	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
803	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
804	C₈	—	2	2	no	—
805	C₈	—	2	2	no	—
806	C₈	—	2	2	no	—
807	C₈	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	8	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	4	4	no	—
816	C₂²	—	4	8	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	8	16	no	—
826	C₂²	—	8	16	no	—
827	C₂²	—	8	4	no	—
828	C₂²	—	8	4	no	—
829	C₂²	C₁₉×#546	1	2	yes	—
830	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	4	yes	—
831	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
832	C₂²	C₁₉×#577	1	2	yes	—
833	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	C₁₉×#546	1	2	yes	—
844	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
845	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
846	C₂	—	2	4	no	—
847	C₂	—	4	2	no	—
848	C₂	—	4	4	no	—
849	C₂	—	8	2	no	—
850	C₂	—	8	2	no	—
851	C₂	C₁₉×#3310	1	4	yes	direct product factor
852	C₂	C₂×C₁₉×#546	1	1	yes	characteristic
853	C₂	C₂²×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
854	C₂	C₂×C₁₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂×D₄²×C₁₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#552	C₂	semidirect
3. C₁₉×#3310	C₂	direct (N × H)
4. C₂×C₁₉×#490	C₂	semidirect
5. C₂×C₁₉×#482	C₂	semidirect
6. C₂×C₁₉×#480	C₂	semidirect
7. C₂×C₁₉×#478	C₂	semidirect
8. C₂×C₁₉×#468	C₂	semidirect
9. C₂×C₁₉×#465	C₂	semidirect
10. C₂×C₁₉×#460	C₂	semidirect
11. C₂×C₁₉×#450	C₂	semidirect
12. C₂×C₁₉×#450	C₂	semidirect
13. C₂×C₁₉×#440	C₂	semidirect
14. C₂×C₁₉×#435	C₂	semidirect
15. C₂×C₁₉×#418	C₂	semidirect
16. C₂²×C₁₉×#102	C₂	semidirect
21. C₂²×SD₁₆×C₁₉	C₂²	semidirect
22. C₂²×SD₁₆×C₁₉	C₂²	semidirect
23. C₂²×M₁₆×C₁₉	C₂²	semidirect
24. C₂³×C₈×C₁₉	C₂²	semidirect
26. C₁₉×#552	C₂²	semidirect
32. C₂×C₁₉×#125	C₂²	semidirect
34. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
35. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
41. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
45. C₂×C₁₉×#117	C₂²	semidirect
46. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
47. C₁₉×#490	C₂²	semidirect
48. C₁₉×#482	C₂²	semidirect
49. C₁₉×#480	C₂²	semidirect
50. C₁₉×#478	C₂²	semidirect
51. C₁₉×#468	C₂²	semidirect
52. C₁₉×#465	C₂²	semidirect
53. C₁₉×#460	C₂²	semidirect
54. C₁₉×#450	C₂²	semidirect
55. C₁₉×#450	C₂²	semidirect
56. C₁₉×#440	C₂²	semidirect
57. C₁₉×#435	C₂²	semidirect
58. C₂×C₁₉×#107	C₂²	semidirect
59. C₂×C₁₉×#107	C₂²	semidirect
60. C₂×C₁₉×#106	C₂²	semidirect
61. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
62. C₁₉×#418	C₂²	semidirect
63. C₂×C₁₉×#103	C₂²	semidirect
67. C₂×C₁₉×#102	C₂²	semidirect
68. C₂×C₁₉×#102	C₂²	semidirect
69. C₂×C₁₉×#102	C₂²	semidirect
70. C₂×C₁₉×#102	C₂²	semidirect
71. C₂×C₁₉×#102	C₂²	semidirect
72. C₂×C₁₉×#102	C₂²	semidirect
73. C₂×C₁₉×#102	C₂²	semidirect
74. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
75. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
76. C₂×C₁₉×#97	C₂²	semidirect
108. C₂×SD₁₆×C₁₉	C₂³	semidirect
109. C₂×SD₁₆×C₁₉	C₂³	semidirect
111. C₂×M₁₆×C₁₉	C₂³	semidirect
117. C₂²×C₈×C₁₉	C₂³	semidirect
123. C₁₉×#125	C₂³	semidirect
127. C₁₉×C₂²⋊Q₈	C₂³	semidirect
128. C₁₉×C₂²⋊Q₈	C₂³	semidirect
137. C₄×Q₈×C₁₉	C₂³	semidirect
144. C₁₉×#117	C₂³	semidirect
157. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
169. C₁₉×#107	C₂³	semidirect
170. C₁₉×#107	C₂³	semidirect
171. C₁₉×#106	C₂³	semidirect
172. C₁₉×C₄⋊C₈	C₂³	semidirect
173. C₁₉×#103	C₂³	semidirect
177. C₁₉×#102	C₂³	semidirect
178. C₁₉×#102	C₂³	semidirect
179. C₁₉×#102	C₂³	semidirect
180. C₁₉×#102	C₂³	semidirect
181. C₁₉×#102	C₂³	semidirect
182. C₁₉×#102	C₂³	semidirect
183. C₁₉×C₂²⋊C₈	C₂³	semidirect
184. C₁₉×C₂²⋊C₈	C₂³	semidirect
185. C₁₉×#97	C₂³	semidirect
298. C₂×#3310	C₁₉	direct (N × H)
381. C₂×#552	C₂×C₁₉	semidirect
383. #3310	C₂×C₁₉	direct (N × H)
384. C₂×#490	C₂×C₁₉	semidirect
385. C₂×#482	C₂×C₁₉	semidirect
386. C₂×#480	C₂×C₁₉	semidirect
387. C₂×#478	C₂×C₁₉	semidirect
388. C₂×#468	C₂×C₁₉	semidirect
389. C₂×#465	C₂×C₁₉	semidirect
390. C₂×#460	C₂×C₁₉	semidirect
391. C₂×#450	C₂×C₁₉	semidirect
392. C₂×#450	C₂×C₁₉	semidirect
393. C₂×#440	C₂×C₁₉	semidirect
394. C₂×#435	C₂×C₁₉	semidirect
395. C₂×#418	C₂×C₁₉	semidirect
396. C₂²×#102	C₂×C₁₉	semidirect
439. C₂²×SD₁₆	C₂²×C₁₉	semidirect
440. C₂²×SD₁₆	C₂²×C₁₉	semidirect
441. C₂²×M₁₆	C₂²×C₁₉	semidirect
442. C₂³×C₈	C₂²×C₁₉	semidirect
444. #552	C₂²×C₁₉	semidirect
450. C₂×#125	C₂²×C₁₉	semidirect
452. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
453. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
459. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
463. C₂×#117	C₂²×C₁₉	semidirect
464. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
465. #490	C₂²×C₁₉	semidirect
466. #482	C₂²×C₁₉	semidirect
467. #480	C₂²×C₁₉	semidirect
468. #478	C₂²×C₁₉	semidirect
469. #468	C₂²×C₁₉	semidirect
470. #465	C₂²×C₁₉	semidirect
471. #460	C₂²×C₁₉	semidirect
472. #450	C₂²×C₁₉	semidirect
473. #450	C₂²×C₁₉	semidirect
474. #440	C₂²×C₁₉	semidirect
475. #435	C₂²×C₁₉	semidirect
476. C₂×#107	C₂²×C₁₉	semidirect
477. C₂×#107	C₂²×C₁₉	semidirect
478. C₂×#106	C₂²×C₁₉	semidirect
479. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
480. #418	C₂²×C₁₉	semidirect
481. C₂×#103	C₂²×C₁₉	semidirect
485. C₂×#102	C₂²×C₁₉	semidirect
486. C₂×#102	C₂²×C₁₉	semidirect
487. C₂×#102	C₂²×C₁₉	semidirect
488. C₂×#102	C₂²×C₁₉	semidirect
489. C₂×#102	C₂²×C₁₉	semidirect
490. C₂×#102	C₂²×C₁₉	semidirect
491. C₂×#102	C₂²×C₁₉	semidirect
492. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
493. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
494. C₂×#97	C₂²×C₁₉	semidirect
500. C₂×C₁₉	#3310	direct (N × H)
535. C₂×SD₁₆	C₂³×C₁₉	semidirect
536. C₂×SD₁₆	C₂³×C₁₉	semidirect
538. C₂×M₁₆	C₂³×C₁₉	semidirect
544. C₂²×C₈	C₂³×C₁₉	semidirect
550. #125	C₂³×C₁₉	semidirect
554. C₂²⋊Q₈	C₂³×C₁₉	semidirect
555. C₂²⋊Q₈	C₂³×C₁₉	semidirect
564. C₄×Q₈	C₂³×C₁₉	semidirect
571. #117	C₂³×C₁₉	semidirect
584. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
596. #107	C₂³×C₁₉	semidirect
597. #107	C₂³×C₁₉	semidirect
598. #106	C₂³×C₁₉	semidirect
599. C₄⋊C₈	C₂³×C₁₉	semidirect
600. #103	C₂³×C₁₉	semidirect
604. #102	C₂³×C₁₉	semidirect
605. #102	C₂³×C₁₉	semidirect
606. #102	C₂³×C₁₉	semidirect
607. #102	C₂³×C₁₉	semidirect
608. #102	C₂³×C₁₉	semidirect
609. #102	C₂³×C₁₉	semidirect
610. C₂²⋊C₈	C₂³×C₁₉	semidirect
611. C₂²⋊C₈	C₂³×C₁₉	semidirect
612. #97	C₂³×C₁₉	semidirect
613. C₁₉	C₂×#3310	direct (N × H)
851. C₂	C₁₉×#3310	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×#552	2
C₂×D₄²×C₁₉	2
C₁₉×#3310	2
C₂×C₁₉×#490	2
C₂×C₁₉×#482	2
C₂×C₁₉×#480	2
C₂×C₁₉×#478	2
C₂×C₁₉×#468	2
C₂×C₁₉×#465	2
C₂×C₁₉×#460	2
C₂×C₁₉×#450	2
C₂×C₁₉×#440	2
C₂×C₁₉×#435	2
C₂×C₁₉×#418	2
C₂²×C₁₉×#102	2
C₂×#3310	19

Subgroups — C2×C19×#3310 #18067086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3310 #18067086