Subgroups — C₂×C₁₉×#3309 #18067096

Order 4864.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3309	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×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#449	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×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#553	—	2	4	no	—
25	C₁₉×#553	C₂²	1	8	yes	complemented
26	C₁₉×#550	—	2	4	no	—
27	C₁₉×#550	C₂²	1	8	yes	complemented
28	C₂×C₁₉×#127	—	2	1	no	—
29	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#126	—	2	1	no	—
31	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#123	—	2	1	no	—
33	C₂×C₁₉×#121	—	2	1	no	—
34	C₂×C₁₉×#121	—	2	1	no	—
35	C₂×C₁₉×#121	—	2	1	no	—
36	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
39	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₁₉	—	2	1	no	—
42	C₂×C₄×D₄×C₁₉	—	2	1	no	—
43	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
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×#479	C₂²	1	8	yes	complemented
51	C₁₉×#469	C₂²	1	8	yes	complemented
52	C₁₉×#466	C₂²	1	8	yes	complemented
53	C₁₉×#459	C₂²	1	8	yes	complemented
54	C₁₉×#449	C₂²	1	8	yes	complemented
55	C₁₉×#449	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
59	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
60	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
61	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₉×#417	C₂²	1	8	yes	complemented
63	C₁₉×#416	C₂²	1	8	yes	complemented
64	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
65	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
66	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
67	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
68	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
69	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
70	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
71	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
72	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
73	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
74	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
77	C₂×#41×C₁₉	—	2	2	no	—
78	C₂×#41×C₁₉	—	2	2	no	—
79	C₂×#41×C₁₉	—	2	4	no	—
80	C₂×#41×C₁₉	—	2	4	no	—
81	C₂×#41×C₁₉	—	4	2	no	—
82	C₂×#41×C₁₉	—	4	2	no	—
83	C₂×#41×C₁₉	C₂³	1	4	yes	—
84	C₂×#41×C₁₉	C₂³	1	4	yes	—
85	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₉	—	2	1	no	—
87	C₂²×D₄×C₁₉	—	2	1	no	—
88	C₂²×D₄×C₁₉	—	2	1	no	—
89	C₂²×D₄×C₁₉	—	2	1	no	—
90	C₂²×D₄×C₁₉	—	2	1	no	—
91	C₂²×D₄×C₁₉	—	2	1	no	—
92	C₂²×D₄×C₁₉	—	2	1	no	—
93	C₂²×D₄×C₁₉	—	2	1	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	1	yes	characteristic
98	C₂³×C₄×C₁₉	—	2	1	no	—
99	C₂³×C₄×C₁₉	—	2	1	no	—
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	C₂³	1	4	yes	—
106	C₂×D₈×C₁₉	—	4	2	no	—
107	C₂×D₈×C₁₉	—	4	2	no	—
108	C₂×D₈×C₁₉	C₂³	1	4	yes	—
109	C₂×D₈×C₁₉	C₂³	1	4	yes	—
110	C₂×M₁₆×C₁₉	—	4	2	no	—
111	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
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	—
118	C₁₉×#127	—	2	8	no	—
119	C₁₉×#127	—	2	2	no	—
120	C₁₉×#127	C₂³	1	4	yes	—
121	C₁₉×#126	—	2	8	no	—
122	C₁₉×#125	—	2	2	no	—
123	C₁₉×#125	C₂³	1	4	yes	—
124	C₁₉×#123	—	2	8	no	—
125	C₁₉×#121	—	2	8	no	—
126	C₁₉×#121	—	2	2	no	—
127	C₁₉×#121	—	2	2	no	—
128	C₁₉×#121	—	2	2	no	—
129	C₁₉×#121	—	2	2	no	—
130	C₁₉×#121	—	2	8	no	—
131	C₁₉×#121	—	2	8	no	—
132	C₁₉×#121	C₂³	1	4	yes	—
133	C₁₉×#121	C₂³	1	4	yes	—
134	C₁₉×#121	C₂³	1	4	yes	—
135	C₁₉×#121	C₂³	1	4	yes	—
136	C₄×Q₈×C₁₉	—	2	2	no	—
137	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
138	C₄×D₄×C₁₉	—	2	8	no	—
139	C₄×D₄×C₁₉	—	2	8	no	—
140	C₄×D₄×C₁₉	—	2	2	no	—
141	C₄×D₄×C₁₉	D₄	1	4	yes	—
142	C₄×D₄×C₁₉	C₂³	1	4	yes	—
143	C₄×D₄×C₁₉	C₂³	1	4	yes	—
144	C₁₉×#117	—	2	2	no	—
145	C₁₉×#117	C₂³	1	4	yes	—
146	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₂×C₄⋊C₄×C₁₉	—	2	2	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	D₄	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₁₉	C₂³	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	4	yes	—
157	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₁₉	—	2	1	no	—
166	C₂×C₄²×C₁₉	—	2	1	no	—
167	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
168	C₁₉×#107	C₂³	1	4	yes	—
169	C₁₉×#107	C₂³	1	4	yes	—
170	C₁₉×#106	C₂³	1	4	yes	—
171	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
172	C₁₉×#103	C₂³	1	4	yes	—
173	C₁₉×#103	C₂³	1	4	yes	—
174	C₁₉×#103	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	—
178	C₁₉×#102	C₂³	1	4	yes	—
179	C₁₉×#102	C₂³	1	4	yes	—
180	C₁₉×#102	C₂³	1	4	yes	—
181	C₁₉×#102	C₂³	1	4	yes	—
182	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
183	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₁₉×#97	C₂³	1	4	yes	—
185	C₂⁴×C₁₉	—	2	1	no	—
186	C₂⁴×C₁₉	—	2	1	no	—
187	C₂⁴×C₁₉	—	2	1	no	—
188	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
190	#41×C₁₉	—	2	8	no	—
191	#41×C₁₉	—	2	8	no	—
192	#41×C₁₉	—	4	4	no	—
193	#41×C₁₉	—	4	4	no	—
194	#41×C₁₉	—	4	8	no	—
195	#41×C₁₉	—	4	8	no	—
196	C₂×Q₈×C₁₉	—	2	1	no	—
197	C₂×Q₈×C₁₉	—	2	2	no	—
198	C₂×Q₈×C₁₉	#41	1	4	yes	—
199	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
200	C₂×D₄×C₁₉	—	2	4	no	—
201	C₂×D₄×C₁₉	—	2	4	no	—
202	C₂×D₄×C₁₉	—	2	4	no	—
203	C₂×D₄×C₁₉	—	2	4	no	—
204	C₂×D₄×C₁₉	—	2	4	no	—
205	C₂×D₄×C₁₉	—	2	4	no	—
206	C₂×D₄×C₁₉	—	2	1	no	—
207	C₂×D₄×C₁₉	—	2	4	no	—
208	C₂×D₄×C₁₉	—	2	1	no	—
209	C₂×D₄×C₁₉	—	2	1	no	—
210	C₂×D₄×C₁₉	—	2	4	no	—
211	C₂×D₄×C₁₉	—	2	2	no	—
212	C₂×D₄×C₁₉	—	2	2	no	—
213	C₂×D₄×C₁₉	—	2	2	no	—
214	C₂×D₄×C₁₉	—	2	2	no	—
215	C₂×D₄×C₁₉	—	2	2	no	—
216	C₂×D₄×C₁₉	—	2	2	no	—
217	C₂×D₄×C₁₉	—	4	2	no	—
218	C₂×D₄×C₁₉	—	4	4	no	—
219	C₂×D₄×C₁₉	—	4	4	no	—
220	C₂×D₄×C₁₉	—	4	4	no	—
221	C₂×D₄×C₁₉	—	4	4	no	—
222	C₂×D₄×C₁₉	—	8	2	no	—
223	C₂×D₄×C₁₉	—	8	2	no	—
224	C₂×D₄×C₁₉	—	8	2	no	—
225	C₂×D₄×C₁₉	—	8	2	no	—
226	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
227	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
228	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
229	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₉	—	2	1	no	—
231	C₂²×C₄×C₁₉	—	2	2	no	—
232	C₂²×C₄×C₁₉	—	2	2	no	—
233	C₂²×C₄×C₁₉	—	2	2	no	—
234	C₂²×C₄×C₁₉	—	2	2	no	—
235	C₂²×C₄×C₁₉	—	2	1	no	—
236	C₂²×C₄×C₁₉	—	2	1	no	—
237	C₂²×C₄×C₁₉	—	2	1	no	—
238	C₂²×C₄×C₁₉	—	2	1	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	—	4	4	no	—
244	C₂²×C₄×C₁₉	—	4	4	no	—
245	C₂²×C₄×C₁₉	—	8	2	no	—
246	C₂²×C₄×C₁₉	—	8	2	no	—
247	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
248	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
249	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
256	SD₁₆×C₁₉	—	2	8	no	—
257	D₈×C₁₉	—	4	4	no	—
258	D₈×C₁₉	—	4	4	no	—
259	M₁₆×C₁₉	—	4	4	no	—
260	C₂×C₈×C₁₉	—	2	2	no	—
261	C₂×C₈×C₁₉	—	2	2	no	—
262	C₂×C₈×C₁₉	—	2	2	no	—
263	C₂×C₈×C₁₉	—	2	2	no	—
264	C₂×C₈×C₁₉	—	4	4	no	—
265	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
266	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
267	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
268	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₁₉	—	2	1	no	—
270	C₄⋊C₄×C₁₉	—	2	1	no	—
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	1	no	—
276	C₄⋊C₄×C₁₉	—	2	1	no	—
277	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
278	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₁₉	C₂⁴	1	2	yes	—
282	C₂²⋊C₄×C₁₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₉	—	2	4	no	—
284	C₂²⋊C₄×C₁₉	—	2	4	no	—
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	C₂×D₄	1	4	yes	—
289	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
290	C₄²×C₁₉	—	2	4	no	—
291	C₄²×C₁₉	—	2	4	no	—
292	C₄²×C₁₉	C₂×D₄	1	2	yes	—
293	C₄²×C₁₉	C₂⁴	1	2	yes	—
294	C₂×#3309	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂³×C₁₉	—	2	2	no	—
296	C₂³×C₁₉	—	2	2	no	—
297	C₂³×C₁₉	—	2	2	no	—
298	C₂³×C₁₉	—	2	2	no	—
299	C₂³×C₁₉	—	2	2	no	—
300	C₂³×C₁₉	—	2	2	no	—
301	C₂³×C₁₉	—	2	2	no	—
302	C₂³×C₁₉	—	2	2	no	—
303	C₂³×C₁₉	—	2	2	no	—
304	C₂³×C₁₉	—	4	2	no	—
305	C₂³×C₁₉	—	4	2	no	—
306	C₂³×C₁₉	—	4	2	no	—
307	C₂³×C₁₉	—	4	2	no	—
308	C₂³×C₁₉	—	4	2	no	—
309	C₂³×C₁₉	—	4	2	no	—
310	C₂³×C₁₉	—	4	2	no	—
311	C₂³×C₁₉	—	4	2	no	—
312	C₂³×C₁₉	—	4	2	no	—
313	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
314	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
315	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
316	Q₈×C₁₉	—	2	4	no	—
317	Q₈×C₁₉	—	2	2	no	—
318	Q₈×C₁₉	C₂×#41	1	4	yes	—
319	D₄×C₁₉	—	2	2	no	—
320	D₄×C₁₉	—	2	2	no	—
321	D₄×C₁₉	—	2	2	no	—
322	D₄×C₁₉	—	2	2	no	—
323	D₄×C₁₉	—	2	2	no	—
324	D₄×C₁₉	—	2	2	no	—
325	D₄×C₁₉	—	4	4	no	—
326	D₄×C₁₉	—	4	8	no	—
327	D₄×C₁₉	—	4	8	no	—
328	D₄×C₁₉	—	4	8	no	—
329	D₄×C₁₉	—	4	8	no	—
330	D₄×C₁₉	—	4	2	no	—
331	D₄×C₁₉	—	4	2	no	—
332	D₄×C₁₉	—	4	2	no	—
333	D₄×C₁₉	—	8	4	no	—
334	D₄×C₁₉	—	8	4	no	—
335	D₄×C₁₉	—	8	4	no	—
336	D₄×C₁₉	—	8	4	no	—
337	C₂×C₄×C₁₉	—	2	2	no	—
338	C₂×C₄×C₁₉	—	2	2	no	—
339	C₂×C₄×C₁₉	—	2	4	no	—
340	C₂×C₄×C₁₉	—	2	2	no	—
341	C₂×C₄×C₁₉	—	2	2	no	—
342	C₂×C₄×C₁₉	—	2	2	no	—
343	C₂×C₄×C₁₉	—	2	4	no	—
344	C₂×C₄×C₁₉	—	2	4	no	—
345	C₂×C₄×C₁₉	—	2	2	no	—
346	C₂×C₄×C₁₉	—	2	2	no	—
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	2	no	—
352	C₂×C₄×C₁₉	—	2	2	no	—
353	C₂×C₄×C₁₉	—	4	8	no	—
354	C₂×C₄×C₁₉	—	4	8	no	—
355	C₂×C₄×C₁₉	—	4	2	no	—
356	C₂×C₄×C₁₉	—	4	2	no	—
357	C₂×C₄×C₁₉	—	4	2	no	—
358	C₂×C₄×C₁₉	—	4	2	no	—
359	C₂×C₄×C₁₉	—	8	4	no	—
360	C₂×C₄×C₁₉	—	8	4	no	—
361	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
367	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
368	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
369	C₈×C₁₉	—	2	2	no	—
370	C₈×C₁₉	—	2	2	no	—
371	C₈×C₁₉	—	2	2	no	—
372	C₈×C₁₉	—	2	2	no	—
373	C₂×#553	C₂×C₁₉	1	1	yes	characteristic, complemented
374	C₂×#550	C₂×C₁₉	1	1	yes	characteristic, complemented
375	#3309	C₂×C₁₉	1	16	yes	direct product factor
376	C₂×#490	C₂×C₁₉	1	1	yes	characteristic, complemented
377	C₂×#482	C₂×C₁₉	1	1	yes	characteristic, complemented
378	C₂×#480	C₂×C₁₉	1	1	yes	characteristic, complemented
379	C₂×#479	C₂×C₁₉	1	1	yes	characteristic, complemented
380	C₂×#469	C₂×C₁₉	1	1	yes	characteristic, complemented
381	C₂×#466	C₂×C₁₉	1	1	yes	characteristic, complemented
382	C₂×#459	C₂×C₁₉	1	1	yes	characteristic, complemented
383	C₂×#449	C₂×C₁₉	1	1	yes	characteristic, complemented
384	C₂×#449	C₂×C₁₉	1	1	yes	characteristic, complemented
385	C₂×#440	C₂×C₁₉	1	1	yes	characteristic, complemented
386	C₂×#435	C₂×C₁₉	1	1	yes	characteristic, complemented
387	C₂×#417	C₂×C₁₉	1	1	yes	characteristic, complemented
388	C₂×#416	C₂×C₁₉	1	1	yes	characteristic, complemented
389	C₂²×C₁₉	—	2	2	no	—
390	C₂²×C₁₉	—	2	2	no	—
391	C₂²×C₁₉	—	2	2	no	—
392	C₂²×C₁₉	—	2	2	no	—
393	C₂²×C₁₉	—	2	2	no	—
394	C₂²×C₁₉	—	2	2	no	—
395	C₂²×C₁₉	—	4	4	no	—
396	C₂²×C₁₉	—	4	4	no	—
397	C₂²×C₁₉	—	4	2	no	—
398	C₂²×C₁₉	—	4	2	no	—
399	C₂²×C₁₉	—	4	2	no	—
400	C₂²×C₁₉	—	4	2	no	—
401	C₂²×C₁₉	—	4	2	no	—
402	C₂²×C₁₉	—	4	2	no	—
403	C₂²×C₁₉	—	4	2	no	—
404	C₂²×C₁₉	—	4	2	no	—
405	C₂²×C₁₉	—	4	2	no	—
406	C₂²×C₁₉	—	8	4	no	—
407	C₂²×C₁₉	—	8	4	no	—
408	C₂²×C₁₉	—	8	4	no	—
409	C₂²×C₁₉	#546	1	2	yes	—
410	C₂²×C₁₉	#575	1	2	yes	—
411	C₂²×C₁₉	#576	1	2	yes	—
412	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
413	C₄×C₁₉	—	2	2	no	—
414	C₄×C₁₉	—	2	2	no	—
415	C₄×C₁₉	—	2	4	no	—
416	C₄×C₁₉	—	2	2	no	—
417	C₄×C₁₉	—	2	2	no	—
418	C₄×C₁₉	—	4	2	no	—
419	C₄×C₁₉	—	4	2	no	—
420	C₄×C₁₉	—	4	2	no	—
421	C₄×C₁₉	—	4	2	no	—
422	C₄×C₁₉	#546	1	2	yes	—
423	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
424	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
426	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
427	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
428	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
429	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
430	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
431	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
432	#553	—	2	4	no	—
433	#553	C₂²×C₁₉	1	8	yes	complemented
434	#550	—	2	4	no	—
435	#550	C₂²×C₁₉	1	8	yes	complemented
436	C₂×#127	—	2	1	no	—
437	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
438	C₂×#126	—	2	1	no	—
439	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
440	C₂×#123	—	2	1	no	—
441	C₂×#121	—	2	1	no	—
442	C₂×#121	—	2	1	no	—
443	C₂×#121	—	2	1	no	—
444	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
445	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
446	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
447	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
448	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
449	C₂×C₄×D₄	—	2	1	no	—
450	C₂×C₄×D₄	—	2	1	no	—
451	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
452	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
453	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
454	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
455	#490	C₂²×C₁₉	1	8	yes	complemented
456	#482	C₂²×C₁₉	1	8	yes	complemented
457	#480	C₂²×C₁₉	1	8	yes	complemented
458	#479	C₂²×C₁₉	1	8	yes	complemented
459	#469	C₂²×C₁₉	1	8	yes	complemented
460	#466	C₂²×C₁₉	1	8	yes	complemented
461	#459	C₂²×C₁₉	1	8	yes	complemented
462	#449	C₂²×C₁₉	1	8	yes	complemented
463	#449	C₂²×C₁₉	1	8	yes	complemented
464	#440	C₂²×C₁₉	1	8	yes	complemented
465	#435	C₂²×C₁₉	1	8	yes	complemented
466	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
467	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
468	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
469	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
470	#417	C₂²×C₁₉	1	8	yes	complemented
471	#416	C₂²×C₁₉	1	8	yes	complemented
472	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
473	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
474	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
475	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
476	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
477	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
478	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
479	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
480	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
481	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
482	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
483	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
484	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
485	C₂×C₁₉	—	4	2	no	—
486	C₂×C₁₉	—	4	2	no	—
487	C₂×C₁₉	—	8	2	no	—
488	C₂×C₁₉	—	8	2	no	—
489	C₂×C₁₉	—	8	2	no	—
490	C₂×C₁₉	#3309	1	4	yes	direct product factor
491	C₂×C₁₉	C₂×#546	1	1	yes	characteristic
492	C₂×C₁₉	C₂×#575	1	1	yes	characteristic
493	C₂×C₁₉	C₂×#576	1	1	yes	characteristic
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	4	no	—
497	C₂×#41	—	2	4	no	—
498	C₂×#41	—	4	2	no	—
499	C₂×#41	—	4	2	no	—
500	C₂×#41	C₂³×C₁₉	1	4	yes	—
501	C₂×#41	C₂³×C₁₉	1	4	yes	—
502	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	—	2	1	no	—
511	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
512	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
513	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
514	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
521	C₂×SD₁₆	—	2	4	no	—
522	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
523	C₂×D₈	—	4	2	no	—
524	C₂×D₈	—	4	2	no	—
525	C₂×D₈	C₂³×C₁₉	1	4	yes	—
526	C₂×D₈	C₂³×C₁₉	1	4	yes	—
527	C₂×M₁₆	—	4	2	no	—
528	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
529	C₂²×C₈	—	4	2	no	—
530	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
531	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
532	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
533	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
534	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
535	#127	—	2	8	no	—
536	#127	—	2	2	no	—
537	#127	C₂³×C₁₉	1	4	yes	—
538	#126	—	2	8	no	—
539	#125	—	2	2	no	—
540	#125	C₂³×C₁₉	1	4	yes	—
541	#123	—	2	8	no	—
542	#121	—	2	8	no	—
543	#121	—	2	2	no	—
544	#121	—	2	2	no	—
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	8	no	—
548	#121	—	2	8	no	—
549	#121	C₂³×C₁₉	1	4	yes	—
550	#121	C₂³×C₁₉	1	4	yes	—
551	#121	C₂³×C₁₉	1	4	yes	—
552	#121	C₂³×C₁₉	1	4	yes	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
555	C₄×D₄	—	2	8	no	—
556	C₄×D₄	—	2	8	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	D₄×C₁₉	1	4	yes	—
559	C₄×D₄	C₂³×C₁₉	1	4	yes	—
560	C₄×D₄	C₂³×C₁₉	1	4	yes	—
561	#117	—	2	2	no	—
562	#117	C₂³×C₁₉	1	4	yes	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	2	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
572	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
582	C₂×C₄²	—	2	1	no	—
583	C₂×C₄²	—	2	1	no	—
584	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
585	#107	C₂³×C₁₉	1	4	yes	—
586	#107	C₂³×C₁₉	1	4	yes	—
587	#106	C₂³×C₁₉	1	4	yes	—
588	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
589	#103	C₂³×C₁₉	1	4	yes	—
590	#103	C₂³×C₁₉	1	4	yes	—
591	#103	C₂³×C₁₉	1	4	yes	—
592	#102	C₂³×C₁₉	1	4	yes	—
593	#102	C₂³×C₁₉	1	4	yes	—
594	#102	C₂³×C₁₉	1	4	yes	—
595	#102	C₂³×C₁₉	1	4	yes	—
596	#102	C₂³×C₁₉	1	4	yes	—
597	#102	C₂³×C₁₉	1	4	yes	—
598	#102	C₂³×C₁₉	1	4	yes	—
599	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
601	#97	C₂³×C₁₉	1	4	yes	—
602	C₁₉	C₂×#3309	1	1	yes	characteristic, direct product factor, Sylow
603	C₂⁴	—	2	1	no	—
604	C₂⁴	—	2	1	no	—
605	C₂⁴	—	2	1	no	—
606	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
607	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
608	#41	—	2	8	no	—
609	#41	—	2	8	no	—
610	#41	—	4	4	no	—
611	#41	—	4	4	no	—
612	#41	—	4	8	no	—
613	#41	—	4	8	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	2	no	—
616	C₂×Q₈	#41×C₁₉	1	4	yes	—
617	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	4	2	no	—
636	C₂×D₄	—	4	4	no	—
637	C₂×D₄	—	4	4	no	—
638	C₂×D₄	—	4	4	no	—
639	C₂×D₄	—	4	4	no	—
640	C₂×D₄	—	8	2	no	—
641	C₂×D₄	—	8	2	no	—
642	C₂×D₄	—	8	2	no	—
643	C₂×D₄	—	8	2	no	—
644	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
645	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
646	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
647	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	4	4	no	—
662	C₂²×C₄	—	4	4	no	—
663	C₂²×C₄	—	8	2	no	—
664	C₂²×C₄	—	8	2	no	—
665	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
666	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
669	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
670	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
674	SD₁₆	—	2	8	no	—
675	D₈	—	4	4	no	—
676	D₈	—	4	4	no	—
677	M₁₆	—	4	4	no	—
678	C₂×C₈	—	2	2	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	—	2	2	no	—
681	C₂×C₈	—	2	2	no	—
682	C₂×C₈	—	4	4	no	—
683	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
684	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
685	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
686	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
696	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₁₉	1	2	yes	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
707	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
708	C₄²	—	2	4	no	—
709	C₄²	—	2	4	no	—
710	C₄²	C₂×D₄×C₁₉	1	2	yes	—
711	C₄²	C₂⁴×C₁₉	1	2	yes	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	4	2	no	—
722	C₂³	—	4	2	no	—
723	C₂³	—	4	2	no	—
724	C₂³	—	4	2	no	—
725	C₂³	—	4	2	no	—
726	C₂³	—	4	2	no	—
727	C₂³	—	4	2	no	—
728	C₂³	—	4	2	no	—
729	C₂³	—	4	2	no	—
730	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
731	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
732	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
733	Q₈	—	2	4	no	—
734	Q₈	—	2	2	no	—
735	Q₈	C₂×#41×C₁₉	1	4	yes	—
736	D₄	—	2	2	no	—
737	D₄	—	2	2	no	—
738	D₄	—	2	2	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	2	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	8	no	—
744	D₄	—	4	8	no	—
745	D₄	—	4	8	no	—
746	D₄	—	4	8	no	—
747	D₄	—	4	2	no	—
748	D₄	—	4	2	no	—
749	D₄	—	4	2	no	—
750	D₄	—	8	4	no	—
751	D₄	—	8	4	no	—
752	D₄	—	8	4	no	—
753	D₄	—	8	4	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	4	8	no	—
771	C₂×C₄	—	4	8	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	8	4	no	—
777	C₂×C₄	—	8	4	no	—
778	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
779	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
780	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
781	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
782	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
783	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
784	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
785	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
786	C₈	—	2	2	no	—
787	C₈	—	2	2	no	—
788	C₈	—	2	2	no	—
789	C₈	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	4	4	no	—
797	C₂²	—	4	4	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	8	4	no	—
808	C₂²	—	8	4	no	—
809	C₂²	—	8	4	no	—
810	C₂²	C₁₉×#546	1	2	yes	—
811	C₂²	C₁₉×#575	1	2	yes	—
812	C₂²	C₁₉×#576	1	2	yes	—
813	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	4	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	C₁₉×#546	1	2	yes	—
824	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
825	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
826	C₂	—	4	2	no	—
827	C₂	—	4	2	no	—
828	C₂	—	8	2	no	—
829	C₂	—	8	2	no	—
830	C₂	—	8	2	no	—
831	C₂	C₁₉×#3309	1	4	yes	direct product factor
832	C₂	C₂×C₁₉×#546	1	1	yes	characteristic
833	C₂	C₂×C₁₉×#575	1	1	yes	characteristic
834	C₂	C₂×C₁₉×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
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×#553	C₂	semidirect
2. C₂×C₁₉×#550	C₂	semidirect
3. C₁₉×#3309	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×#479	C₂	semidirect
8. C₂×C₁₉×#469	C₂	semidirect
9. C₂×C₁₉×#466	C₂	semidirect
10. C₂×C₁₉×#459	C₂	semidirect
11. C₂×C₁₉×#449	C₂	semidirect
12. C₂×C₁₉×#449	C₂	semidirect
13. C₂×C₁₉×#440	C₂	semidirect
14. C₂×C₁₉×#435	C₂	semidirect
15. C₂×C₁₉×#417	C₂	semidirect
16. C₂×C₁₉×#416	C₂	semidirect
25. C₁₉×#553	C₂²	semidirect
27. C₁₉×#550	C₂²	semidirect
47. C₁₉×#490	C₂²	semidirect
48. C₁₉×#482	C₂²	semidirect
49. C₁₉×#480	C₂²	semidirect
50. C₁₉×#479	C₂²	semidirect
51. C₁₉×#469	C₂²	semidirect
52. C₁₉×#466	C₂²	semidirect
53. C₁₉×#459	C₂²	semidirect
54. C₁₉×#449	C₂²	semidirect
55. C₁₉×#449	C₂²	semidirect
56. C₁₉×#440	C₂²	semidirect
57. C₁₉×#435	C₂²	semidirect
62. C₁₉×#417	C₂²	semidirect
63. C₁₉×#416	C₂²	semidirect
294. C₂×#3309	C₁₉	direct (N × H)
373. C₂×#553	C₂×C₁₉	semidirect
374. C₂×#550	C₂×C₁₉	semidirect
375. #3309	C₂×C₁₉	direct (N × H)
376. C₂×#490	C₂×C₁₉	semidirect
377. C₂×#482	C₂×C₁₉	semidirect
378. C₂×#480	C₂×C₁₉	semidirect
379. C₂×#479	C₂×C₁₉	semidirect
380. C₂×#469	C₂×C₁₉	semidirect
381. C₂×#466	C₂×C₁₉	semidirect
382. C₂×#459	C₂×C₁₉	semidirect
383. C₂×#449	C₂×C₁₉	semidirect
384. C₂×#449	C₂×C₁₉	semidirect
385. C₂×#440	C₂×C₁₉	semidirect
386. C₂×#435	C₂×C₁₉	semidirect
387. C₂×#417	C₂×C₁₉	semidirect
388. C₂×#416	C₂×C₁₉	semidirect
433. #553	C₂²×C₁₉	semidirect
435. #550	C₂²×C₁₉	semidirect
455. #490	C₂²×C₁₉	semidirect
456. #482	C₂²×C₁₉	semidirect
457. #480	C₂²×C₁₉	semidirect
458. #479	C₂²×C₁₉	semidirect
459. #469	C₂²×C₁₉	semidirect
460. #466	C₂²×C₁₉	semidirect
461. #459	C₂²×C₁₉	semidirect
462. #449	C₂²×C₁₉	semidirect
463. #449	C₂²×C₁₉	semidirect
464. #440	C₂²×C₁₉	semidirect
465. #435	C₂²×C₁₉	semidirect
470. #417	C₂²×C₁₉	semidirect
471. #416	C₂²×C₁₉	semidirect
490. C₂×C₁₉	#3309	direct (N × H)
602. C₁₉	C₂×#3309	direct (N × H)
831. C₂	C₁₉×#3309	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×#553	2
C₂×C₁₉×#550	2
C₁₉×#3309	2
C₂×C₁₉×#490	2
C₂×C₁₉×#482	2
C₂×C₁₉×#480	2
C₂×C₁₉×#479	2
C₂×C₁₉×#469	2
C₂×C₁₉×#466	2
C₂×C₁₉×#459	2
C₂×C₁₉×#449	2
C₂×C₁₉×#440	2
C₂×C₁₉×#435	2
C₂×C₁₉×#417	2
C₂×C₁₉×#416	2
C₂×#3309	19

Subgroups — C2×C19×#3309 #18067096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3309 #18067096