Subgroups — C₁₉×#62903 #18068862

Order 4864.

6628 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3564	C₂	1	6	yes	maximal, complemented
2	C₁₉×#3564	C₂	1	6	yes	maximal, complemented
3	C₁₉×#3561	C₂	1	6	yes	maximal, complemented
4	C₁₉×#3538	C₂	1	6	yes	maximal, complemented
5	C₁₉×#3535	C₂	1	6	yes	maximal, complemented
6	C₁₉×#3535	C₂	1	6	yes	maximal, complemented
7	C₁₉×#3520	C₂	1	6	yes	maximal, complemented
8	C₁₉×#3501	C₂	1	3	yes	maximal, complemented
9	C₁₉×#3495	C₂	1	6	yes	maximal, complemented
10	C₁₉×#3491	C₂	1	3	yes	maximal, complemented
11	C₁₉×#3490	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₉×#551	C₂	1	3	yes	maximal, complemented
13	C₁₉×#3459	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#3458	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#543	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#563	C₂²	1	12	yes	complemented
17	C₁₉×#563	C₂²	1	12	yes	complemented
18	C₁₉×#563	C₂²	1	12	yes	complemented
19	C₁₉×#562	C₂²	1	12	yes	complemented
20	C₁₉×#556	C₂²	1	12	yes	complemented
21	C₁₉×#556	C₂²	1	6	yes	complemented
22	C₁₉×#554	C₂²	1	12	yes	complemented
23	C₁₉×#554	C₂²	1	12	yes	complemented
24	C₁₉×#554	C₂²	1	12	yes	complemented
25	C₁₉×#552	C₂²	1	12	yes	complemented
26	C₁₉×#552	C₂²	1	12	yes	complemented
27	C₁₉×#552	C₂²	1	6	yes	complemented
28	C₁₉×#552	C₂²	1	12	yes	complemented
29	C₁₉×#552	C₂²	1	12	yes	complemented
30	C₁₉×#552	C₂²	1	6	yes	complemented
31	C₁₉×#551	C₂²	1	12	yes	complemented
32	C₁₉×#551	C₂²	1	12	yes	complemented
33	C₁₉×#551	C₂²	1	12	yes	complemented
34	C₁₉×#551	C₂²	1	12	yes	complemented
35	C₁₉×#551	C₂²	1	12	yes	complemented
36	C₁₉×#551	C₂²	1	12	yes	complemented
37	C₁₉×#551	C₂²	1	12	yes	complemented
38	C₁₉×#551	C₂²	1	12	yes	complemented
39	D₄×Q₈×C₁₉	C₂²	1	12	yes	complemented
40	D₄×Q₈×C₁₉	C₂²	1	6	yes	complemented
41	C₁₉×#548	C₂²	1	2	yes	complemented
42	C₁₉×#548	C₂²	1	6	yes	complemented
43	C₁₉×#547	C₂²	1	6	yes	complemented
44	C₁₉×#547	C₂²	1	6	yes	complemented
45	C₁₉×#546	C₂²	1	12	yes	complemented
46	C₁₉×#546	C₂²	1	12	yes	complemented
47	C₁₉×#544	C₂²	1	6	yes	complemented
48	C₁₉×#544	C₂²	1	6	yes	complemented
49	C₁₉×#544	C₂²	1	6	yes	complemented
50	C₁₉×#544	C₂²	1	6	yes	complemented
51	C₁₉×#543	C₂²	1	1	yes	characteristic
52	C₁₉×#543	C₂²	1	3	yes	—
53	C₁₉×#543	C₂²	1	3	yes	—
54	C₁₉×#543	C₂²	1	6	yes	complemented
55	C₁₉×#543	C₂²	1	6	yes	complemented
56	C₁₉×#543	C₂²	1	6	yes	complemented
57	C₁₉×#542	C₂²	1	6	yes	complemented
58	C₁₉×#542	C₂²	1	6	yes	complemented
59	C₁₉×#542	C₂²	1	12	yes	complemented
60	C₁₉×#542	C₂²	1	12	yes	complemented
61	C₁₉×#541	C₂²	1	6	yes	complemented
62	C₁₉×#541	C₂²	1	6	yes	complemented
63	C₁₉×#541	C₂²	1	12	yes	complemented
64	C₁₉×#539	C₂²	1	6	yes	complemented
65	C₁₉×#539	C₂²	1	6	yes	complemented
66	C₁₉×#539	C₂²	1	6	yes	complemented
67	C₁₉×#539	C₂²	1	12	yes	complemented
68	C₁₉×#539	C₂²	1	12	yes	complemented
69	C₁₉×#539	C₂²	1	12	yes	complemented
70	C₁₉×#538	C₂²	1	6	yes	—
71	C₁₉×#538	C₂²	1	6	yes	—
72	C₁₉×#538	C₂²	1	6	yes	complemented
73	C₁₉×#536	C₂²	1	6	yes	complemented
74	C₁₉×#536	C₂²	1	12	yes	complemented
75	C₁₉×#534	C₂²	1	3	yes	—
76	C₁₉×#533	C₂²	1	6	yes	complemented
77	C₁₉×#533	C₂²	1	6	yes	complemented
78	C₁₉×#533	C₂²	1	6	yes	complemented
79	C₁₉×#529	C₂²	1	6	yes	complemented
80	C₁₉×#529	C₂²	1	6	yes	complemented
81	C₁₉×#529	C₂²	1	6	yes	complemented
82	C₂×C₁₉×#126	C₂²	1	3	yes	complemented
83	C₂×C₁₉×#126	C₂²	1	3	yes	complemented
84	C₂×C₁₉×#124	C₂²	1	3	yes	complemented
85	C₁₉×#525	C₂²	1	6	yes	—
86	C₁₉×#525	C₂²	1	6	yes	—
87	C₁₉×#525	C₂²	1	6	yes	complemented
88	C₂×C₁₉×#123	C₂²	1	3	yes	—
89	C₂×C₁₉×#123	C₂²	1	3	yes	complemented
90	C₂×C₁₉×#123	C₂²	1	3	yes	complemented
91	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
92	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
93	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
94	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	complemented
95	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
96	C₂×C₁₉×#120	C₂²	1	3	yes	—
97	C₁₉×#520	C₂²	1	6	yes	complemented
98	C₁₉×#519	C₂²	1	2	yes	complemented
99	C₁₉×#518	C₂²	1	6	yes	—
100	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
101	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	complemented
102	C₂×C₁₉×#117	C₂²	1	3	yes	—
103	C₂×C₁₉×#117	C₂²	1	3	yes	complemented
104	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
105	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
106	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
107	C₂×#41×C₁₉	C₂³	1	6	yes	—
108	C₂×#41×C₁₉	C₂³	1	6	yes	—
109	C₂×#41×C₁₉	C₂³	1	2	yes	complemented
110	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
111	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
112	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
113	C₂²×Q₈×C₁₉	C₂³	1	6	yes	complemented
114	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
115	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
116	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
117	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
119	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
121	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
122	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	complemented
123	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	complemented
124	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	complemented
125	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	complemented
126	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	complemented
127	C₁₉×C₄⋊Q₈	C₂³	1	6	yes	complemented
128	C₁₉×C₄⋊Q₈	C₂³	1	12	yes	complemented
129	C₁₉×C₄⋊Q₈	C₂³	1	12	yes	complemented
130	C₁₉×#126	C₂³	1	12	yes	—
131	C₁₉×#126	C₂³	1	12	yes	—
132	C₁₉×#126	C₂³	1	12	yes	—
133	C₁₉×#126	C₂³	1	12	yes	—
134	C₁₉×#126	C₂³	1	12	yes	—
135	C₁₉×#126	C₂³	1	12	yes	—
136	C₁₉×#126	C₂³	1	12	yes	complemented
137	C₁₉×#126	C₂³	1	12	yes	complemented
138	C₁₉×#126	C₂³	1	12	yes	complemented
139	C₁₉×#126	C₂³	1	12	yes	complemented
140	C₁₉×#126	C₂³	1	12	yes	complemented
141	C₁₉×#125	C₂³	1	6	yes	complemented
142	C₁₉×#125	C₂³	1	6	yes	complemented
143	C₁₉×#125	C₂³	1	6	yes	complemented
144	C₁₉×#125	C₂³	1	12	yes	complemented
145	C₁₉×#125	C₂³	1	12	yes	complemented
146	C₁₉×#125	C₂³	1	12	yes	complemented
147	C₁₉×#125	C₂³	1	12	yes	complemented
148	C₁₉×#125	C₂³	1	12	yes	complemented
149	C₁₉×#125	C₂³	1	12	yes	complemented
150	C₁₉×#125	C₂³	1	12	yes	complemented
151	C₁₉×#124	C₂³	1	12	yes	—
152	C₁₉×#124	C₂³	1	12	yes	—
153	C₁₉×#124	C₂³	1	12	yes	—
154	C₁₉×#124	C₂³	1	12	yes	—
155	C₁₉×#124	C₂³	1	6	yes	complemented
156	C₁₉×#124	C₂³	1	6	yes	complemented
157	C₁₉×#124	C₂³	1	6	yes	complemented
158	C₁₉×#123	C₂³	1	12	yes	—
159	C₁₉×#123	C₂³	1	12	yes	—
160	C₁₉×#123	C₂³	1	12	yes	—
161	C₁₉×#123	C₂³	1	12	yes	—
162	C₁₉×#123	C₂³	1	12	yes	—
163	C₁₉×#123	C₂³	1	12	yes	—
164	C₁₉×#123	C₂³	1	12	yes	—
165	C₁₉×#123	C₂³	1	12	yes	—
166	C₁₉×#123	C₂³	1	12	yes	—
167	C₁₉×#123	C₂³	1	12	yes	—
168	C₁₉×#123	C₂³	1	12	yes	—
169	C₁₉×#123	C₂³	1	12	yes	complemented
170	C₁₉×#123	C₂³	1	12	yes	complemented
171	C₁₉×#123	C₂³	1	12	yes	complemented
172	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
173	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
174	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
175	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
176	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
177	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
178	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
179	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
180	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
181	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
182	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
183	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
184	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
185	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
186	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
187	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
188	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
189	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
190	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
191	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	—
192	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
193	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	—
194	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	complemented
195	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
196	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	complemented
197	C₁₉×C₂²⋊Q₈	C₂³	1	6	yes	complemented
198	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
199	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
200	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
201	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
202	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
203	C₁₉×C₂²⋊Q₈	C₂³	1	12	yes	complemented
204	C₁₉×#121	C₂³	1	6	yes	—
205	C₁₉×#121	C₂³	1	6	yes	—
206	C₁₉×#121	C₂³	1	6	yes	—
207	C₁₉×#121	C₂³	1	6	yes	—
208	C₁₉×#121	C₂³	1	12	yes	—
209	C₁₉×#121	C₂³	1	12	yes	—
210	C₁₉×#121	C₂³	1	6	yes	complemented
211	C₁₉×#120	C₂³	1	12	yes	—
212	C₁₉×#120	C₂³	1	12	yes	—
213	C₁₉×#120	C₂³	1	12	yes	—
214	C₄×Q₈×C₁₉	C₂³	1	2	yes	complemented
215	C₄×Q₈×C₁₉	C₂³	1	6	yes	complemented
216	C₄×Q₈×C₁₉	C₂³	1	2	yes	complemented
217	C₄×Q₈×C₁₉	C₂³	1	6	yes	complemented
218	C₄×Q₈×C₁₉	C₂³	1	6	yes	complemented
219	C₄×Q₈×C₁₉	C₂³	1	6	yes	complemented
220	C₄×Q₈×C₁₉	C₂³	1	6	yes	complemented
221	C₄×Q₈×C₁₉	C₂³	1	2	yes	complemented
222	C₄×Q₈×C₁₉	C₂³	1	6	yes	complemented
223	C₄×Q₈×C₁₉	C₂³	1	12	yes	complemented
224	C₄×D₄×C₁₉	C₂³	1	12	yes	—
225	C₄×D₄×C₁₉	C₂³	1	12	yes	—
226	C₄×D₄×C₁₉	C₂³	1	6	yes	—
227	C₄×D₄×C₁₉	C₂³	1	6	yes	—
228	C₄×D₄×C₁₉	C₂³	1	6	yes	—
229	C₄×D₄×C₁₉	C₂³	1	6	yes	—
230	C₄×D₄×C₁₉	C₂³	1	12	yes	—
231	C₄×D₄×C₁₉	C₂³	1	12	yes	—
232	C₄×D₄×C₁₉	C₂³	1	12	yes	—
233	C₄×D₄×C₁₉	C₂³	1	12	yes	—
234	C₄×D₄×C₁₉	C₂³	1	12	yes	—
235	C₄×D₄×C₁₉	C₂³	1	12	yes	—
236	C₄×D₄×C₁₉	C₂³	1	6	yes	complemented
237	C₄×D₄×C₁₉	C₂³	1	6	yes	complemented
238	C₄×D₄×C₁₉	C₂³	1	6	yes	complemented
239	C₁₉×#117	C₂³	1	12	yes	—
240	C₁₉×#117	C₂³	1	12	yes	—
241	C₁₉×#117	C₂³	1	6	yes	—
242	C₁₉×#117	C₂³	1	6	yes	—
243	C₁₉×#117	C₂³	1	6	yes	—
244	C₁₉×#117	C₂³	1	6	yes	—
245	C₁₉×#117	C₂³	1	12	yes	—
246	C₁₉×#117	C₂³	1	6	yes	—
247	C₁₉×#117	C₂³	1	6	yes	—
248	C₁₉×#117	C₂³	1	12	yes	complemented
249	C₁₉×#117	C₂³	1	6	yes	complemented
250	C₁₉×#117	C₂³	1	12	yes	complemented
251	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
252	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
253	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
254	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
255	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
256	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
257	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
258	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
259	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
260	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
261	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	complemented
262	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	complemented
263	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
264	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
265	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
266	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
267	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
268	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
269	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
270	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
271	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
272	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
273	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
274	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
275	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
276	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
277	C₂×C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
278	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
279	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
280	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
281	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
282	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
283	C₂⁴×C₁₉	—	2	4	no	—
284	C₂⁴×C₁₉	—	4	2	no	—
285	C₂⁴×C₁₉	—	8	1	no	—
286	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
287	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
288	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
289	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
290	#41×C₁₉	—	4	12	no	—
291	#41×C₁₉	—	8	6	no	—
292	#41×C₁₉	—	8	2	no	—
293	C₂×Q₈×C₁₉	—	4	4	no	—
294	C₂×Q₈×C₁₉	—	8	2	no	—
295	C₂×Q₈×C₁₉	—	8	3	no	—
296	C₂×Q₈×C₁₉	—	8	6	no	—
297	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
298	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
299	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
300	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
301	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
302	C₂×Q₈×C₁₉	C₂⁴	1	12	yes	—
303	C₂×Q₈×C₁₉	C₂⁴	1	6	yes	—
304	C₂×D₄×C₁₉	—	2	12	no	—
305	C₂×D₄×C₁₉	—	4	6	no	—
306	C₂×D₄×C₁₉	—	8	3	no	—
307	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
308	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
309	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
310	C₂×D₄×C₁₉	C₂⁴	1	12	yes	—
311	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
312	C₂×D₄×C₁₉	C₂⁴	1	6	yes	—
313	C₂²×C₄×C₁₉	—	2	4	no	—
314	C₂²×C₄×C₁₉	—	4	6	no	—
315	C₂²×C₄×C₁₉	—	8	1	no	—
316	C₂²×C₄×C₁₉	—	8	3	no	—
317	C₂²×C₄×C₁₉	—	8	3	no	—
318	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
319	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
320	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
321	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
322	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
323	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
324	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
325	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
326	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
327	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
328	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
329	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
330	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
331	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
332	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
333	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
334	C₂²×C₄×C₁₉	C₂⁴	1	12	yes	—
335	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
336	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
337	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
338	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
339	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
340	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
341	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
342	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
343	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
344	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
345	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
346	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
347	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
348	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
349	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
350	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
351	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
352	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
353	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
354	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
355	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
356	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
357	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
358	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
359	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
360	C₄⋊C₄×C₁₉	C₂⁴	1	6	yes	—
361	C₄⋊C₄×C₁₉	C₂⁴	1	12	yes	—
362	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
363	C₂²⋊C₄×C₁₉	C₂⁴	1	1	yes	characteristic
364	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
365	C₂²⋊C₄×C₁₉	C₂⁴	1	3	yes	—
366	C₂²⋊C₄×C₁₉	C₂⁴	1	3	yes	—
367	C₂²⋊C₄×C₁₉	C₂⁴	1	3	yes	—
368	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
369	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
370	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
371	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
372	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
373	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
374	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
375	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
376	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
377	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
378	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
379	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
380	C₂²⋊C₄×C₁₉	C₂⁴	1	6	yes	—
381	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
382	C₂²⋊C₄×C₁₉	C₂⁴	1	12	yes	—
383	C₄²×C₁₉	C₂⁴	1	6	yes	—
384	C₄²×C₁₉	C₂⁴	1	6	yes	—
385	C₄²×C₁₉	C₂⁴	1	6	yes	—
386	C₄²×C₁₉	C₂⁴	1	6	yes	—
387	C₄²×C₁₉	C₂⁴	1	6	yes	—
388	C₄²×C₁₉	C₂⁴	1	6	yes	—
389	C₄²×C₁₉	C₂⁴	1	12	yes	—
390	C₄²×C₁₉	C₂⁴	1	12	yes	—
391	#62903	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₂³×C₁₉	—	2	6	no	—
393	C₂³×C₁₉	—	2	6	no	—
394	C₂³×C₁₉	—	2	6	no	—
395	C₂³×C₁₉	—	2	6	no	—
396	C₂³×C₁₉	—	4	3	no	—
397	C₂³×C₁₉	—	4	1	no	—
398	C₂³×C₁₉	—	4	1	no	—
399	C₂³×C₁₉	—	4	3	no	—
400	C₂³×C₁₉	—	4	3	no	—
401	C₂³×C₁₉	—	4	3	no	—
402	C₂³×C₁₉	—	4	3	no	—
403	C₂³×C₁₉	—	8	8	no	—
404	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
405	C₂³×C₁₉	C₂⁵	1	3	yes	—
406	C₂³×C₁₉	C₂⁵	1	6	yes	—
407	C₂³×C₁₉	C₂⁵	1	3	yes	—
408	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
409	Q₈×C₁₉	—	4	6	no	—
410	Q₈×C₁₉	—	4	2	no	—
411	Q₈×C₁₉	—	4	6	no	—
412	Q₈×C₁₉	—	4	12	no	—
413	Q₈×C₁₉	—	4	2	no	—
414	Q₈×C₁₉	—	4	6	no	—
415	Q₈×C₁₉	—	4	6	no	—
416	D₄×C₁₉	—	2	24	no	—
417	D₄×C₁₉	—	2	12	no	—
418	D₄×C₁₉	—	4	6	no	—
419	D₄×C₁₉	—	4	12	no	—
420	D₄×C₁₉	—	4	6	no	—
421	D₄×C₁₉	—	4	6	no	—
422	C₂×C₄×C₁₉	—	2	6	no	—
423	C₂×C₄×C₁₉	—	2	6	no	—
424	C₂×C₄×C₁₉	—	2	6	no	—
425	C₂×C₄×C₁₉	—	2	12	no	—
426	C₂×C₄×C₁₉	—	4	3	no	—
427	C₂×C₄×C₁₉	—	4	6	no	—
428	C₂×C₄×C₁₉	—	4	3	no	—
429	C₂×C₄×C₁₉	—	4	3	no	—
430	C₂×C₄×C₁₉	—	4	3	no	—
431	C₂×C₄×C₁₉	—	4	6	no	—
432	C₂×C₄×C₁₉	—	4	6	no	—
433	C₂×C₄×C₁₉	—	4	3	no	—
434	C₂×C₄×C₁₉	—	4	3	no	—
435	C₂×C₄×C₁₉	—	4	6	no	—
436	C₂×C₄×C₁₉	—	4	6	no	—
437	C₂×C₄×C₁₉	—	4	3	no	—
438	C₂×C₄×C₁₉	—	4	3	no	—
439	C₂×C₄×C₁₉	—	4	12	no	—
440	C₂×C₄×C₁₉	—	4	12	no	—
441	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
442	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
443	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
444	C₂×C₄×C₁₉	C₂⁵	1	3	yes	—
445	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
446	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
447	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
448	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
449	C₂×C₄×C₁₉	C₂⁵	1	3	yes	—
450	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
451	C₂×C₄×C₁₉	C₂⁵	1	6	yes	—
452	#3564	C₂×C₁₉	1	6	yes	complemented
453	#3564	C₂×C₁₉	1	6	yes	complemented
454	#3561	C₂×C₁₉	1	6	yes	complemented
455	#3538	C₂×C₁₉	1	6	yes	complemented
456	#3535	C₂×C₁₉	1	6	yes	complemented
457	#3535	C₂×C₁₉	1	6	yes	complemented
458	#3520	C₂×C₁₉	1	6	yes	complemented
459	#3501	C₂×C₁₉	1	3	yes	complemented
460	#3495	C₂×C₁₉	1	6	yes	complemented
461	#3491	C₂×C₁₉	1	3	yes	complemented
462	#3490	C₂×C₁₉	1	3	yes	complemented
463	C₂×#551	C₂×C₁₉	1	3	yes	complemented
464	#3459	C₂×C₁₉	1	1	yes	characteristic, complemented
465	#3458	C₂×C₁₉	1	1	yes	characteristic, complemented
466	C₂×#543	C₂×C₁₉	1	1	yes	characteristic, complemented
467	C₂²×C₁₉	—	2	1	no	—
468	C₂²×C₁₉	—	2	3	no	—
469	C₂²×C₁₉	—	2	1	no	—
470	C₂²×C₁₉	—	2	3	no	—
471	C₂²×C₁₉	—	2	6	no	—
472	C₂²×C₁₉	—	2	3	no	—
473	C₂²×C₁₉	—	2	6	no	—
474	C₂²×C₁₉	—	2	3	no	—
475	C₂²×C₁₉	—	2	6	no	—
476	C₂²×C₁₉	—	2	3	no	—
477	C₂²×C₁₉	—	4	4	no	—
478	C₂²×C₁₉	—	4	12	no	—
479	C₂²×C₁₉	—	8	6	no	—
480	C₂²×C₁₉	—	8	6	no	—
481	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	6	yes	—
482	C₂²×C₁₉	#585	1	2	yes	—
483	C₂²×C₁₉	C₂⁶	1	1	yes	characteristic
484	C₄×C₁₉	—	2	1	no	—
485	C₄×C₁₉	—	2	3	no	—
486	C₄×C₁₉	—	2	6	no	—
487	C₄×C₁₉	—	2	6	no	—
488	C₄×C₁₉	—	2	6	no	—
489	C₄×C₁₉	—	2	6	no	—
490	C₄×C₁₉	—	2	1	no	—
491	C₄×C₁₉	—	2	6	no	—
492	C₄×C₁₉	—	2	3	no	—
493	C₄×C₁₉	—	2	6	no	—
494	C₄×C₁₉	—	2	6	no	—
495	#563	C₂²×C₁₉	1	12	yes	complemented
496	#563	C₂²×C₁₉	1	12	yes	complemented
497	#563	C₂²×C₁₉	1	12	yes	complemented
498	#562	C₂²×C₁₉	1	12	yes	complemented
499	#556	C₂²×C₁₉	1	12	yes	complemented
500	#556	C₂²×C₁₉	1	6	yes	complemented
501	#554	C₂²×C₁₉	1	12	yes	complemented
502	#554	C₂²×C₁₉	1	12	yes	complemented
503	#554	C₂²×C₁₉	1	12	yes	complemented
504	#552	C₂²×C₁₉	1	12	yes	complemented
505	#552	C₂²×C₁₉	1	12	yes	complemented
506	#552	C₂²×C₁₉	1	6	yes	complemented
507	#552	C₂²×C₁₉	1	12	yes	complemented
508	#552	C₂²×C₁₉	1	12	yes	complemented
509	#552	C₂²×C₁₉	1	6	yes	complemented
510	#551	C₂²×C₁₉	1	12	yes	complemented
511	#551	C₂²×C₁₉	1	12	yes	complemented
512	#551	C₂²×C₁₉	1	12	yes	complemented
513	#551	C₂²×C₁₉	1	12	yes	complemented
514	#551	C₂²×C₁₉	1	12	yes	complemented
515	#551	C₂²×C₁₉	1	12	yes	complemented
516	#551	C₂²×C₁₉	1	12	yes	complemented
517	#551	C₂²×C₁₉	1	12	yes	complemented
518	D₄×Q₈	C₂²×C₁₉	1	12	yes	complemented
519	D₄×Q₈	C₂²×C₁₉	1	6	yes	complemented
520	#548	C₂²×C₁₉	1	2	yes	complemented
521	#548	C₂²×C₁₉	1	6	yes	complemented
522	#547	C₂²×C₁₉	1	6	yes	complemented
523	#547	C₂²×C₁₉	1	6	yes	complemented
524	#546	C₂²×C₁₉	1	12	yes	complemented
525	#546	C₂²×C₁₉	1	12	yes	complemented
526	#544	C₂²×C₁₉	1	6	yes	complemented
527	#544	C₂²×C₁₉	1	6	yes	complemented
528	#544	C₂²×C₁₉	1	6	yes	complemented
529	#544	C₂²×C₁₉	1	6	yes	complemented
530	#543	C₂²×C₁₉	1	1	yes	characteristic
531	#543	C₂²×C₁₉	1	3	yes	—
532	#543	C₂²×C₁₉	1	3	yes	—
533	#543	C₂²×C₁₉	1	6	yes	complemented
534	#543	C₂²×C₁₉	1	6	yes	complemented
535	#543	C₂²×C₁₉	1	6	yes	complemented
536	#542	C₂²×C₁₉	1	6	yes	complemented
537	#542	C₂²×C₁₉	1	6	yes	complemented
538	#542	C₂²×C₁₉	1	12	yes	complemented
539	#542	C₂²×C₁₉	1	12	yes	complemented
540	#541	C₂²×C₁₉	1	6	yes	complemented
541	#541	C₂²×C₁₉	1	6	yes	complemented
542	#541	C₂²×C₁₉	1	12	yes	complemented
543	#539	C₂²×C₁₉	1	6	yes	complemented
544	#539	C₂²×C₁₉	1	6	yes	complemented
545	#539	C₂²×C₁₉	1	6	yes	complemented
546	#539	C₂²×C₁₉	1	12	yes	complemented
547	#539	C₂²×C₁₉	1	12	yes	complemented
548	#539	C₂²×C₁₉	1	12	yes	complemented
549	#538	C₂²×C₁₉	1	6	yes	—
550	#538	C₂²×C₁₉	1	6	yes	—
551	#538	C₂²×C₁₉	1	6	yes	complemented
552	#536	C₂²×C₁₉	1	6	yes	complemented
553	#536	C₂²×C₁₉	1	12	yes	complemented
554	#534	C₂²×C₁₉	1	3	yes	—
555	#533	C₂²×C₁₉	1	6	yes	complemented
556	#533	C₂²×C₁₉	1	6	yes	complemented
557	#533	C₂²×C₁₉	1	6	yes	complemented
558	#529	C₂²×C₁₉	1	6	yes	complemented
559	#529	C₂²×C₁₉	1	6	yes	complemented
560	#529	C₂²×C₁₉	1	6	yes	complemented
561	C₂×#126	C₂²×C₁₉	1	3	yes	complemented
562	C₂×#126	C₂²×C₁₉	1	3	yes	complemented
563	C₂×#124	C₂²×C₁₉	1	3	yes	complemented
564	#525	C₂²×C₁₉	1	6	yes	—
565	#525	C₂²×C₁₉	1	6	yes	—
566	#525	C₂²×C₁₉	1	6	yes	complemented
567	C₂×#123	C₂²×C₁₉	1	3	yes	—
568	C₂×#123	C₂²×C₁₉	1	3	yes	complemented
569	C₂×#123	C₂²×C₁₉	1	3	yes	complemented
570	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
571	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	complemented
572	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	complemented
573	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	complemented
574	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	6	yes	complemented
575	C₂×#120	C₂²×C₁₉	1	3	yes	—
576	#520	C₂²×C₁₉	1	6	yes	complemented
577	#519	C₂²×C₁₉	1	2	yes	complemented
578	#518	C₂²×C₁₉	1	6	yes	—
579	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
580	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	complemented
581	C₂×#117	C₂²×C₁₉	1	3	yes	—
582	C₂×#117	C₂²×C₁₉	1	3	yes	complemented
583	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
584	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
585	C₂×C₁₉	—	2	2	no	—
586	C₂×C₁₉	—	2	6	no	—
587	C₂×C₁₉	—	4	3	no	—
588	C₂×C₁₉	—	4	6	no	—
589	C₂×C₁₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
590	C₂×C₁₉	C₂×#585	1	1	yes	characteristic
591	C₂×C₁₉	H(7,𝔽₂)	1	1	yes	characteristic
592	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
593	C₂×#41	C₂³×C₁₉	1	6	yes	—
594	C₂×#41	C₂³×C₁₉	1	6	yes	—
595	C₂×#41	C₂³×C₁₉	1	2	yes	complemented
596	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
597	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
598	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
599	C₂²×Q₈	C₂³×C₁₉	1	6	yes	complemented
600	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
601	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
602	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
603	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
605	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
606	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
607	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
608	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
609	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
610	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
611	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
612	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
613	C₄⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
614	C₄⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
615	C₄⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
616	#126	C₂³×C₁₉	1	12	yes	—
617	#126	C₂³×C₁₉	1	12	yes	—
618	#126	C₂³×C₁₉	1	12	yes	—
619	#126	C₂³×C₁₉	1	12	yes	—
620	#126	C₂³×C₁₉	1	12	yes	—
621	#126	C₂³×C₁₉	1	12	yes	—
622	#126	C₂³×C₁₉	1	12	yes	complemented
623	#126	C₂³×C₁₉	1	12	yes	complemented
624	#126	C₂³×C₁₉	1	12	yes	complemented
625	#126	C₂³×C₁₉	1	12	yes	complemented
626	#126	C₂³×C₁₉	1	12	yes	complemented
627	#125	C₂³×C₁₉	1	6	yes	complemented
628	#125	C₂³×C₁₉	1	6	yes	complemented
629	#125	C₂³×C₁₉	1	6	yes	complemented
630	#125	C₂³×C₁₉	1	12	yes	complemented
631	#125	C₂³×C₁₉	1	12	yes	complemented
632	#125	C₂³×C₁₉	1	12	yes	complemented
633	#125	C₂³×C₁₉	1	12	yes	complemented
634	#125	C₂³×C₁₉	1	12	yes	complemented
635	#125	C₂³×C₁₉	1	12	yes	complemented
636	#125	C₂³×C₁₉	1	12	yes	complemented
637	#124	C₂³×C₁₉	1	12	yes	—
638	#124	C₂³×C₁₉	1	12	yes	—
639	#124	C₂³×C₁₉	1	12	yes	—
640	#124	C₂³×C₁₉	1	12	yes	—
641	#124	C₂³×C₁₉	1	6	yes	complemented
642	#124	C₂³×C₁₉	1	6	yes	complemented
643	#124	C₂³×C₁₉	1	6	yes	complemented
644	#123	C₂³×C₁₉	1	12	yes	—
645	#123	C₂³×C₁₉	1	12	yes	—
646	#123	C₂³×C₁₉	1	12	yes	—
647	#123	C₂³×C₁₉	1	12	yes	—
648	#123	C₂³×C₁₉	1	12	yes	—
649	#123	C₂³×C₁₉	1	12	yes	—
650	#123	C₂³×C₁₉	1	12	yes	—
651	#123	C₂³×C₁₉	1	12	yes	—
652	#123	C₂³×C₁₉	1	12	yes	—
653	#123	C₂³×C₁₉	1	12	yes	—
654	#123	C₂³×C₁₉	1	12	yes	—
655	#123	C₂³×C₁₉	1	12	yes	complemented
656	#123	C₂³×C₁₉	1	12	yes	complemented
657	#123	C₂³×C₁₉	1	12	yes	complemented
658	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
659	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
660	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
661	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
662	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
663	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
664	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
665	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
666	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
667	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
668	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
669	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
670	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
671	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
672	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
673	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
674	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
675	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
676	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
677	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	—
678	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
679	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	—
680	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
681	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
682	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
683	C₂²⋊Q₈	C₂³×C₁₉	1	6	yes	complemented
684	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
685	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
686	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
687	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
688	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
689	C₂²⋊Q₈	C₂³×C₁₉	1	12	yes	complemented
690	#121	C₂³×C₁₉	1	6	yes	—
691	#121	C₂³×C₁₉	1	6	yes	—
692	#121	C₂³×C₁₉	1	6	yes	—
693	#121	C₂³×C₁₉	1	6	yes	—
694	#121	C₂³×C₁₉	1	12	yes	—
695	#121	C₂³×C₁₉	1	12	yes	—
696	#121	C₂³×C₁₉	1	6	yes	complemented
697	#120	C₂³×C₁₉	1	12	yes	—
698	#120	C₂³×C₁₉	1	12	yes	—
699	#120	C₂³×C₁₉	1	12	yes	—
700	C₄×Q₈	C₂³×C₁₉	1	2	yes	complemented
701	C₄×Q₈	C₂³×C₁₉	1	6	yes	complemented
702	C₄×Q₈	C₂³×C₁₉	1	2	yes	complemented
703	C₄×Q₈	C₂³×C₁₉	1	6	yes	complemented
704	C₄×Q₈	C₂³×C₁₉	1	6	yes	complemented
705	C₄×Q₈	C₂³×C₁₉	1	6	yes	complemented
706	C₄×Q₈	C₂³×C₁₉	1	6	yes	complemented
707	C₄×Q₈	C₂³×C₁₉	1	2	yes	complemented
708	C₄×Q₈	C₂³×C₁₉	1	6	yes	complemented
709	C₄×Q₈	C₂³×C₁₉	1	12	yes	complemented
710	C₄×D₄	C₂³×C₁₉	1	12	yes	—
711	C₄×D₄	C₂³×C₁₉	1	12	yes	—
712	C₄×D₄	C₂³×C₁₉	1	6	yes	—
713	C₄×D₄	C₂³×C₁₉	1	6	yes	—
714	C₄×D₄	C₂³×C₁₉	1	6	yes	—
715	C₄×D₄	C₂³×C₁₉	1	6	yes	—
716	C₄×D₄	C₂³×C₁₉	1	12	yes	—
717	C₄×D₄	C₂³×C₁₉	1	12	yes	—
718	C₄×D₄	C₂³×C₁₉	1	12	yes	—
719	C₄×D₄	C₂³×C₁₉	1	12	yes	—
720	C₄×D₄	C₂³×C₁₉	1	12	yes	—
721	C₄×D₄	C₂³×C₁₉	1	12	yes	—
722	C₄×D₄	C₂³×C₁₉	1	6	yes	complemented
723	C₄×D₄	C₂³×C₁₉	1	6	yes	complemented
724	C₄×D₄	C₂³×C₁₉	1	6	yes	complemented
725	#117	C₂³×C₁₉	1	12	yes	—
726	#117	C₂³×C₁₉	1	12	yes	—
727	#117	C₂³×C₁₉	1	6	yes	—
728	#117	C₂³×C₁₉	1	6	yes	—
729	#117	C₂³×C₁₉	1	6	yes	—
730	#117	C₂³×C₁₉	1	6	yes	—
731	#117	C₂³×C₁₉	1	12	yes	—
732	#117	C₂³×C₁₉	1	6	yes	—
733	#117	C₂³×C₁₉	1	6	yes	—
734	#117	C₂³×C₁₉	1	12	yes	complemented
735	#117	C₂³×C₁₉	1	6	yes	complemented
736	#117	C₂³×C₁₉	1	12	yes	complemented
737	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
738	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
739	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
740	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
741	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
742	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
743	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
744	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
745	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
746	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
747	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	complemented
748	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	complemented
749	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₁₉	1	12	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
766	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
767	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
768	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
769	C₁₉	#62903	1	1	yes	characteristic, direct product factor, Sylow
770	C₂⁴	—	2	4	no	—
771	C₂⁴	—	4	2	no	—
772	C₂⁴	—	8	1	no	—
773	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
774	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
775	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
776	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
777	#41	—	4	12	no	—
778	#41	—	8	6	no	—
779	#41	—	8	2	no	—
780	C₂×Q₈	—	4	4	no	—
781	C₂×Q₈	—	8	2	no	—
782	C₂×Q₈	—	8	3	no	—
783	C₂×Q₈	—	8	6	no	—
784	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
785	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
786	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
787	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
788	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
789	C₂×Q₈	C₂⁴×C₁₉	1	12	yes	—
790	C₂×Q₈	C₂⁴×C₁₉	1	6	yes	—
791	C₂×D₄	—	2	12	no	—
792	C₂×D₄	—	4	6	no	—
793	C₂×D₄	—	8	3	no	—
794	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
795	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
796	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
797	C₂×D₄	C₂⁴×C₁₉	1	12	yes	—
798	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
799	C₂×D₄	C₂⁴×C₁₉	1	6	yes	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	4	6	no	—
802	C₂²×C₄	—	8	1	no	—
803	C₂²×C₄	—	8	3	no	—
804	C₂²×C₄	—	8	3	no	—
805	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
806	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
807	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
808	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
809	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
810	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
811	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
812	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
813	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
814	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
815	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
816	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
817	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
818	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
819	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
820	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
821	C₂²×C₄	C₂⁴×C₁₉	1	12	yes	—
822	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
823	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
824	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
825	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
826	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
827	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
828	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
829	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
830	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
831	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
832	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
833	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
834	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
835	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
836	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
837	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
838	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
839	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
840	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
841	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
842	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
843	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
844	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
845	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
846	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
847	C₄⋊C₄	C₂⁴×C₁₉	1	6	yes	—
848	C₄⋊C₄	C₂⁴×C₁₉	1	12	yes	—
849	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
850	C₂²⋊C₄	C₂⁴×C₁₉	1	1	yes	characteristic
851	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
852	C₂²⋊C₄	C₂⁴×C₁₉	1	3	yes	—
853	C₂²⋊C₄	C₂⁴×C₁₉	1	3	yes	—
854	C₂²⋊C₄	C₂⁴×C₁₉	1	3	yes	—
855	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
856	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
857	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
858	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
859	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
860	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
861	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
862	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
863	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
864	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
865	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
866	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
867	C₂²⋊C₄	C₂⁴×C₁₉	1	6	yes	—
868	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
869	C₂²⋊C₄	C₂⁴×C₁₉	1	12	yes	—
870	C₄²	C₂⁴×C₁₉	1	6	yes	—
871	C₄²	C₂⁴×C₁₉	1	6	yes	—
872	C₄²	C₂⁴×C₁₉	1	6	yes	—
873	C₄²	C₂⁴×C₁₉	1	6	yes	—
874	C₄²	C₂⁴×C₁₉	1	6	yes	—
875	C₄²	C₂⁴×C₁₉	1	6	yes	—
876	C₄²	C₂⁴×C₁₉	1	12	yes	—
877	C₄²	C₂⁴×C₁₉	1	12	yes	—
878	C₂³	—	2	6	no	—
879	C₂³	—	2	6	no	—
880	C₂³	—	2	6	no	—
881	C₂³	—	2	6	no	—
882	C₂³	—	4	3	no	—
883	C₂³	—	4	1	no	—
884	C₂³	—	4	1	no	—
885	C₂³	—	4	3	no	—
886	C₂³	—	4	3	no	—
887	C₂³	—	4	3	no	—
888	C₂³	—	4	3	no	—
889	C₂³	—	8	8	no	—
890	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
891	C₂³	C₂⁵×C₁₉	1	3	yes	—
892	C₂³	C₂⁵×C₁₉	1	6	yes	—
893	C₂³	C₂⁵×C₁₉	1	3	yes	—
894	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
895	Q₈	—	4	6	no	—
896	Q₈	—	4	2	no	—
897	Q₈	—	4	6	no	—
898	Q₈	—	4	12	no	—
899	Q₈	—	4	2	no	—
900	Q₈	—	4	6	no	—
901	Q₈	—	4	6	no	—
902	D₄	—	2	24	no	—
903	D₄	—	2	12	no	—
904	D₄	—	4	6	no	—
905	D₄	—	4	12	no	—
906	D₄	—	4	6	no	—
907	D₄	—	4	6	no	—
908	C₂×C₄	—	2	6	no	—
909	C₂×C₄	—	2	6	no	—
910	C₂×C₄	—	2	6	no	—
911	C₂×C₄	—	2	12	no	—
912	C₂×C₄	—	4	3	no	—
913	C₂×C₄	—	4	6	no	—
914	C₂×C₄	—	4	3	no	—
915	C₂×C₄	—	4	3	no	—
916	C₂×C₄	—	4	3	no	—
917	C₂×C₄	—	4	6	no	—
918	C₂×C₄	—	4	6	no	—
919	C₂×C₄	—	4	3	no	—
920	C₂×C₄	—	4	3	no	—
921	C₂×C₄	—	4	6	no	—
922	C₂×C₄	—	4	6	no	—
923	C₂×C₄	—	4	3	no	—
924	C₂×C₄	—	4	3	no	—
925	C₂×C₄	—	4	12	no	—
926	C₂×C₄	—	4	12	no	—
927	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
928	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
929	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
930	C₂×C₄	C₂⁵×C₁₉	1	3	yes	—
931	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
932	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
933	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
934	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
935	C₂×C₄	C₂⁵×C₁₉	1	3	yes	—
936	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
937	C₂×C₄	C₂⁵×C₁₉	1	6	yes	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	3	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	3	no	—
942	C₂²	—	2	6	no	—
943	C₂²	—	2	3	no	—
944	C₂²	—	2	6	no	—
945	C₂²	—	2	3	no	—
946	C₂²	—	2	6	no	—
947	C₂²	—	2	3	no	—
948	C₂²	—	4	4	no	—
949	C₂²	—	4	12	no	—
950	C₂²	—	8	6	no	—
951	C₂²	—	8	6	no	—
952	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	6	yes	—
953	C₂²	C₁₉×#585	1	2	yes	—
954	C₂²	C₂⁶×C₁₉	1	1	yes	characteristic
955	C₄	—	2	1	no	—
956	C₄	—	2	3	no	—
957	C₄	—	2	6	no	—
958	C₄	—	2	6	no	—
959	C₄	—	2	6	no	—
960	C₄	—	2	6	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	6	no	—
963	C₄	—	2	3	no	—
964	C₄	—	2	6	no	—
965	C₄	—	2	6	no	—
966	C₂	—	2	2	no	—
967	C₂	—	2	6	no	—
968	C₂	—	4	3	no	—
969	C₂	—	4	6	no	—
970	C₂	C₂²×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
971	C₂	C₂×C₁₉×#585	1	1	yes	characteristic
972	C₂	C₁₉×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3564	C₂	semidirect
2. C₁₉×#3564	C₂	semidirect
3. C₁₉×#3561	C₂	semidirect
4. C₁₉×#3538	C₂	semidirect
5. C₁₉×#3535	C₂	semidirect
6. C₁₉×#3535	C₂	semidirect
7. C₁₉×#3520	C₂	semidirect
8. C₁₉×#3501	C₂	semidirect
9. C₁₉×#3495	C₂	semidirect
10. C₁₉×#3491	C₂	semidirect
11. C₁₉×#3490	C₂	semidirect
12. C₂×C₁₉×#551	C₂	semidirect
13. C₁₉×#3459	C₂	semidirect
14. C₁₉×#3458	C₂	semidirect
15. C₂×C₁₉×#543	C₂	semidirect
16. C₁₉×#563	C₂²	semidirect
17. C₁₉×#563	C₂²	semidirect
18. C₁₉×#563	C₂²	semidirect
19. C₁₉×#562	C₂²	semidirect
20. C₁₉×#556	C₂²	semidirect
21. C₁₉×#556	C₂²	semidirect
22. C₁₉×#554	C₂²	semidirect
23. C₁₉×#554	C₂²	semidirect
24. C₁₉×#554	C₂²	semidirect
25. C₁₉×#552	C₂²	semidirect
26. C₁₉×#552	C₂²	semidirect
27. C₁₉×#552	C₂²	semidirect
28. C₁₉×#552	C₂²	semidirect
29. C₁₉×#552	C₂²	semidirect
30. C₁₉×#552	C₂²	semidirect
31. C₁₉×#551	C₂²	semidirect
32. C₁₉×#551	C₂²	semidirect
33. C₁₉×#551	C₂²	semidirect
34. C₁₉×#551	C₂²	semidirect
35. C₁₉×#551	C₂²	semidirect
36. C₁₉×#551	C₂²	semidirect
37. C₁₉×#551	C₂²	semidirect
38. C₁₉×#551	C₂²	semidirect
39. D₄×Q₈×C₁₉	C₂²	semidirect
40. D₄×Q₈×C₁₉	C₂²	semidirect
41. C₁₉×#548	C₂²	semidirect
42. C₁₉×#548	C₂²	semidirect
43. C₁₉×#547	C₂²	semidirect
44. C₁₉×#547	C₂²	semidirect
45. C₁₉×#546	C₂²	semidirect
46. C₁₉×#546	C₂²	semidirect
47. C₁₉×#544	C₂²	semidirect
48. C₁₉×#544	C₂²	semidirect
49. C₁₉×#544	C₂²	semidirect
50. C₁₉×#544	C₂²	semidirect
54. C₁₉×#543	C₂²	semidirect
55. C₁₉×#543	C₂²	semidirect
56. C₁₉×#543	C₂²	semidirect
57. C₁₉×#542	C₂²	semidirect
58. C₁₉×#542	C₂²	semidirect
59. C₁₉×#542	C₂²	semidirect
60. C₁₉×#542	C₂²	semidirect
61. C₁₉×#541	C₂²	semidirect
62. C₁₉×#541	C₂²	semidirect
63. C₁₉×#541	C₂²	semidirect
64. C₁₉×#539	C₂²	semidirect
65. C₁₉×#539	C₂²	semidirect
66. C₁₉×#539	C₂²	semidirect
67. C₁₉×#539	C₂²	semidirect
68. C₁₉×#539	C₂²	semidirect
69. C₁₉×#539	C₂²	semidirect
72. C₁₉×#538	C₂²	semidirect
73. C₁₉×#536	C₂²	semidirect
74. C₁₉×#536	C₂²	semidirect
76. C₁₉×#533	C₂²	semidirect
77. C₁₉×#533	C₂²	semidirect
78. C₁₉×#533	C₂²	semidirect
79. C₁₉×#529	C₂²	semidirect
80. C₁₉×#529	C₂²	semidirect
81. C₁₉×#529	C₂²	semidirect
82. C₂×C₁₉×#126	C₂²	semidirect
83. C₂×C₁₉×#126	C₂²	semidirect
84. C₂×C₁₉×#124	C₂²	semidirect
87. C₁₉×#525	C₂²	semidirect
89. C₂×C₁₉×#123	C₂²	semidirect
90. C₂×C₁₉×#123	C₂²	semidirect
92. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
93. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
94. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
95. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
97. C₁₉×#520	C₂²	semidirect
98. C₁₉×#519	C₂²	semidirect
101. C₂×C₄×D₄×C₁₉	C₂²	semidirect
103. C₂×C₁₉×#117	C₂²	semidirect
109. C₂×#41×C₁₉	C₂³	semidirect
113. C₂²×Q₈×C₁₉	C₂³	semidirect
122. C₁₉×C₄⋊Q₈	C₂³	semidirect
123. C₁₉×C₄⋊Q₈	C₂³	semidirect
124. C₁₉×C₄⋊Q₈	C₂³	semidirect
125. C₁₉×C₄⋊Q₈	C₂³	semidirect
126. C₁₉×C₄⋊Q₈	C₂³	semidirect
127. C₁₉×C₄⋊Q₈	C₂³	semidirect
128. C₁₉×C₄⋊Q₈	C₂³	semidirect
129. C₁₉×C₄⋊Q₈	C₂³	semidirect
136. C₁₉×#126	C₂³	semidirect
137. C₁₉×#126	C₂³	semidirect
138. C₁₉×#126	C₂³	semidirect
139. C₁₉×#126	C₂³	semidirect
140. C₁₉×#126	C₂³	semidirect
141. C₁₉×#125	C₂³	semidirect
142. C₁₉×#125	C₂³	semidirect
143. C₁₉×#125	C₂³	semidirect
144. C₁₉×#125	C₂³	semidirect
145. C₁₉×#125	C₂³	semidirect
146. C₁₉×#125	C₂³	semidirect
147. C₁₉×#125	C₂³	semidirect
148. C₁₉×#125	C₂³	semidirect
149. C₁₉×#125	C₂³	semidirect
150. C₁₉×#125	C₂³	semidirect
155. C₁₉×#124	C₂³	semidirect
156. C₁₉×#124	C₂³	semidirect
157. C₁₉×#124	C₂³	semidirect
169. C₁₉×#123	C₂³	semidirect
170. C₁₉×#123	C₂³	semidirect
171. C₁₉×#123	C₂³	semidirect
194. C₁₉×C₂²⋊Q₈	C₂³	semidirect
195. C₁₉×C₂²⋊Q₈	C₂³	semidirect
196. C₁₉×C₂²⋊Q₈	C₂³	semidirect
197. C₁₉×C₂²⋊Q₈	C₂³	semidirect
198. C₁₉×C₂²⋊Q₈	C₂³	semidirect
199. C₁₉×C₂²⋊Q₈	C₂³	semidirect
200. C₁₉×C₂²⋊Q₈	C₂³	semidirect
201. C₁₉×C₂²⋊Q₈	C₂³	semidirect
202. C₁₉×C₂²⋊Q₈	C₂³	semidirect
203. C₁₉×C₂²⋊Q₈	C₂³	semidirect
210. C₁₉×#121	C₂³	semidirect
214. C₄×Q₈×C₁₉	C₂³	semidirect
215. C₄×Q₈×C₁₉	C₂³	semidirect
216. C₄×Q₈×C₁₉	C₂³	semidirect
217. C₄×Q₈×C₁₉	C₂³	semidirect
218. C₄×Q₈×C₁₉	C₂³	semidirect
219. C₄×Q₈×C₁₉	C₂³	semidirect
220. C₄×Q₈×C₁₉	C₂³	semidirect
221. C₄×Q₈×C₁₉	C₂³	semidirect
222. C₄×Q₈×C₁₉	C₂³	semidirect
223. C₄×Q₈×C₁₉	C₂³	semidirect
236. C₄×D₄×C₁₉	C₂³	semidirect
237. C₄×D₄×C₁₉	C₂³	semidirect
238. C₄×D₄×C₁₉	C₂³	semidirect
248. C₁₉×#117	C₂³	semidirect
249. C₁₉×#117	C₂³	semidirect
250. C₁₉×#117	C₂³	semidirect
261. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
262. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
391. #62903	C₁₉	direct (N × H)
452. #3564	C₂×C₁₉	semidirect
453. #3564	C₂×C₁₉	semidirect
454. #3561	C₂×C₁₉	semidirect
455. #3538	C₂×C₁₉	semidirect
456. #3535	C₂×C₁₉	semidirect
457. #3535	C₂×C₁₉	semidirect
458. #3520	C₂×C₁₉	semidirect
459. #3501	C₂×C₁₉	semidirect
460. #3495	C₂×C₁₉	semidirect
461. #3491	C₂×C₁₉	semidirect
462. #3490	C₂×C₁₉	semidirect
463. C₂×#551	C₂×C₁₉	semidirect
464. #3459	C₂×C₁₉	semidirect
465. #3458	C₂×C₁₉	semidirect
466. C₂×#543	C₂×C₁₉	semidirect
495. #563	C₂²×C₁₉	semidirect
496. #563	C₂²×C₁₉	semidirect
497. #563	C₂²×C₁₉	semidirect
498. #562	C₂²×C₁₉	semidirect
499. #556	C₂²×C₁₉	semidirect
500. #556	C₂²×C₁₉	semidirect
501. #554	C₂²×C₁₉	semidirect
502. #554	C₂²×C₁₉	semidirect
503. #554	C₂²×C₁₉	semidirect
504. #552	C₂²×C₁₉	semidirect
505. #552	C₂²×C₁₉	semidirect
506. #552	C₂²×C₁₉	semidirect
507. #552	C₂²×C₁₉	semidirect
508. #552	C₂²×C₁₉	semidirect
509. #552	C₂²×C₁₉	semidirect
510. #551	C₂²×C₁₉	semidirect
511. #551	C₂²×C₁₉	semidirect
512. #551	C₂²×C₁₉	semidirect
513. #551	C₂²×C₁₉	semidirect
514. #551	C₂²×C₁₉	semidirect
515. #551	C₂²×C₁₉	semidirect
516. #551	C₂²×C₁₉	semidirect
517. #551	C₂²×C₁₉	semidirect
518. D₄×Q₈	C₂²×C₁₉	semidirect
519. D₄×Q₈	C₂²×C₁₉	semidirect
520. #548	C₂²×C₁₉	semidirect
521. #548	C₂²×C₁₉	semidirect
522. #547	C₂²×C₁₉	semidirect
523. #547	C₂²×C₁₉	semidirect
524. #546	C₂²×C₁₉	semidirect
525. #546	C₂²×C₁₉	semidirect
526. #544	C₂²×C₁₉	semidirect
527. #544	C₂²×C₁₉	semidirect
528. #544	C₂²×C₁₉	semidirect
529. #544	C₂²×C₁₉	semidirect
533. #543	C₂²×C₁₉	semidirect
534. #543	C₂²×C₁₉	semidirect
535. #543	C₂²×C₁₉	semidirect
536. #542	C₂²×C₁₉	semidirect
537. #542	C₂²×C₁₉	semidirect
538. #542	C₂²×C₁₉	semidirect
539. #542	C₂²×C₁₉	semidirect
540. #541	C₂²×C₁₉	semidirect
541. #541	C₂²×C₁₉	semidirect
542. #541	C₂²×C₁₉	semidirect
543. #539	C₂²×C₁₉	semidirect
544. #539	C₂²×C₁₉	semidirect
545. #539	C₂²×C₁₉	semidirect
546. #539	C₂²×C₁₉	semidirect
547. #539	C₂²×C₁₉	semidirect
548. #539	C₂²×C₁₉	semidirect
551. #538	C₂²×C₁₉	semidirect
552. #536	C₂²×C₁₉	semidirect
553. #536	C₂²×C₁₉	semidirect
555. #533	C₂²×C₁₉	semidirect
556. #533	C₂²×C₁₉	semidirect
557. #533	C₂²×C₁₉	semidirect
558. #529	C₂²×C₁₉	semidirect
559. #529	C₂²×C₁₉	semidirect
560. #529	C₂²×C₁₉	semidirect
561. C₂×#126	C₂²×C₁₉	semidirect
562. C₂×#126	C₂²×C₁₉	semidirect
563. C₂×#124	C₂²×C₁₉	semidirect
566. #525	C₂²×C₁₉	semidirect
568. C₂×#123	C₂²×C₁₉	semidirect
569. C₂×#123	C₂²×C₁₉	semidirect
571. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
572. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
573. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
574. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
576. #520	C₂²×C₁₉	semidirect
577. #519	C₂²×C₁₉	semidirect
580. C₂×C₄×D₄	C₂²×C₁₉	semidirect
582. C₂×#117	C₂²×C₁₉	semidirect
595. C₂×#41	C₂³×C₁₉	semidirect
599. C₂²×Q₈	C₂³×C₁₉	semidirect
608. C₄⋊Q₈	C₂³×C₁₉	semidirect
609. C₄⋊Q₈	C₂³×C₁₉	semidirect
610. C₄⋊Q₈	C₂³×C₁₉	semidirect
611. C₄⋊Q₈	C₂³×C₁₉	semidirect
612. C₄⋊Q₈	C₂³×C₁₉	semidirect
613. C₄⋊Q₈	C₂³×C₁₉	semidirect
614. C₄⋊Q₈	C₂³×C₁₉	semidirect
615. C₄⋊Q₈	C₂³×C₁₉	semidirect
622. #126	C₂³×C₁₉	semidirect
623. #126	C₂³×C₁₉	semidirect
624. #126	C₂³×C₁₉	semidirect
625. #126	C₂³×C₁₉	semidirect
626. #126	C₂³×C₁₉	semidirect
627. #125	C₂³×C₁₉	semidirect
628. #125	C₂³×C₁₉	semidirect
629. #125	C₂³×C₁₉	semidirect
630. #125	C₂³×C₁₉	semidirect
631. #125	C₂³×C₁₉	semidirect
632. #125	C₂³×C₁₉	semidirect
633. #125	C₂³×C₁₉	semidirect
634. #125	C₂³×C₁₉	semidirect
635. #125	C₂³×C₁₉	semidirect
636. #125	C₂³×C₁₉	semidirect
641. #124	C₂³×C₁₉	semidirect
642. #124	C₂³×C₁₉	semidirect
643. #124	C₂³×C₁₉	semidirect
655. #123	C₂³×C₁₉	semidirect
656. #123	C₂³×C₁₉	semidirect
657. #123	C₂³×C₁₉	semidirect
680. C₂²⋊Q₈	C₂³×C₁₉	semidirect
681. C₂²⋊Q₈	C₂³×C₁₉	semidirect
682. C₂²⋊Q₈	C₂³×C₁₉	semidirect
683. C₂²⋊Q₈	C₂³×C₁₉	semidirect
684. C₂²⋊Q₈	C₂³×C₁₉	semidirect
685. C₂²⋊Q₈	C₂³×C₁₉	semidirect
686. C₂²⋊Q₈	C₂³×C₁₉	semidirect
687. C₂²⋊Q₈	C₂³×C₁₉	semidirect
688. C₂²⋊Q₈	C₂³×C₁₉	semidirect
689. C₂²⋊Q₈	C₂³×C₁₉	semidirect
696. #121	C₂³×C₁₉	semidirect
700. C₄×Q₈	C₂³×C₁₉	semidirect
701. C₄×Q₈	C₂³×C₁₉	semidirect
702. C₄×Q₈	C₂³×C₁₉	semidirect
703. C₄×Q₈	C₂³×C₁₉	semidirect
704. C₄×Q₈	C₂³×C₁₉	semidirect
705. C₄×Q₈	C₂³×C₁₉	semidirect
706. C₄×Q₈	C₂³×C₁₉	semidirect
707. C₄×Q₈	C₂³×C₁₉	semidirect
708. C₄×Q₈	C₂³×C₁₉	semidirect
709. C₄×Q₈	C₂³×C₁₉	semidirect
722. C₄×D₄	C₂³×C₁₉	semidirect
723. C₄×D₄	C₂³×C₁₉	semidirect
724. C₄×D₄	C₂³×C₁₉	semidirect
734. #117	C₂³×C₁₉	semidirect
735. #117	C₂³×C₁₉	semidirect
736. #117	C₂³×C₁₉	semidirect
747. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
748. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
769. C₁₉	#62903	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3564	2
C₁₉×#3561	2
C₁₉×#3538	2
C₁₉×#3535	2
C₁₉×#3520	2
C₁₉×#3501	2
C₁₉×#3495	2
C₁₉×#3491	2
C₁₉×#3490	2
C₂×C₁₉×#551	2
C₁₉×#3459	2
C₁₉×#3458	2
C₂×C₁₉×#543	2
#62903	19

Subgroups — C19×#62903 #18068862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62903 #18068862