Subgroups — C₁₉×#34614 #18040573

Order 4864.

2474 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2637	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2636	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2630	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2629	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2625	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2624	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2620	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2616	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2615	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#2396	C₂	1	2	yes	maximal, complemented
13	C₁₉×#2392	C₂	1	4	yes	maximal, complemented
14	C₁₉×#2392	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₉×#121	C₂	1	2	yes	maximal, complemented
17	C₁₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#529	—	2	8	no	—
20	C₂×C₁₉×#126	C₂²	1	2	yes	—
21	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#123	C₂²	1	2	yes	—
24	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#121	C₂²	1	2	yes	—
28	C₄×#41×C₁₉	—	2	8	no	—
29	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
39	C₂×C₁₉×#117	C₂²	1	2	yes	—
40	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#117	C₂²	1	2	yes	—
42	C₂×C₁₉×#117	C₂²	1	2	yes	—
43	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
44	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#400	C₂²	1	2	yes	—
46	C₁₉×#399	C₂²	1	2	yes	—
47	C₁₉×#398	C₂²	1	2	yes	—
48	C₁₉×#398	C₂²	1	4	yes	—
49	C₁₉×#398	C₂²	1	4	yes	—
50	C₁₉×#397	C₂²	1	2	yes	—
51	C₁₉×#397	C₂²	1	4	yes	—
52	C₁₉×#396	C₂²	1	4	yes	—
53	C₁₉×#396	C₂²	1	4	yes	—
54	C₁₉×#396	C₂²	1	4	yes	—
55	C₁₉×#396	C₂²	1	4	yes	—
56	C₁₉×#395	C₂²	1	2	yes	—
57	C₁₉×#394	C₂²	1	4	yes	—
58	C₁₉×#394	C₂²	1	2	yes	—
59	C₁₉×#394	C₂²	1	4	yes	—
60	C₁₉×#394	C₂²	1	4	yes	—
61	C₁₉×#394	C₂²	1	4	yes	—
62	C₁₉×#393	C₂²	1	2	yes	—
63	C₁₉×#392	C₂²	1	4	yes	—
64	C₁₉×#392	C₂²	1	2	yes	—
65	C₁₉×#391	C₂²	1	2	yes	—
66	C₁₉×#390	C₂²	1	2	yes	—
67	C₁₉×#389	C₂²	1	2	yes	—
68	C₁₉×#389	C₂²	1	2	yes	—
69	C₁₉×#388	C₂²	1	4	yes	—
70	C₁₉×#387	C₂²	1	4	yes	—
71	C₁₉×#386	C₂²	1	4	yes	—
72	C₁₉×#385	C₂²	1	4	yes	—
73	C₁₉×#384	C₂²	1	2	yes	—
74	C₁₉×#382	C₂²	1	2	yes	—
75	C₁₉×#380	C₂²	1	1	yes	characteristic
76	C₁₉×#380	C₂²	1	1	yes	characteristic
77	C₁₉×#380	C₂²	1	2	yes	—
78	C₁₉×#380	C₂²	1	2	yes	—
79	C₁₉×#380	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
84	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
85	C₂×#41×C₁₉	—	2	4	no	—
86	C₂×#41×C₁₉	—	2	8	no	—
87	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₁₉×#126	—	2	8	no	—
102	C₁₉×#125	—	2	4	no	—
103	C₁₉×#124	—	2	4	no	—
104	C₁₉×#123	—	2	8	no	—
105	C₁₉×C₂²⋊Q₈	—	2	4	no	—
106	C₁₉×C₂²⋊Q₈	—	2	8	no	—
107	C₁₉×#121	—	2	4	no	—
108	C₁₉×#121	—	2	8	no	—
109	C₄×Q₈×C₁₉	—	2	4	no	—
110	C₄×Q₈×C₁₉	—	2	4	no	—
111	C₄×Q₈×C₁₉	—	2	4	no	—
112	C₄×D₄×C₁₉	—	2	8	no	—
113	C₄×D₄×C₁₉	—	2	8	no	—
114	C₄×D₄×C₁₉	—	2	8	no	—
115	C₄×D₄×C₁₉	—	2	4	no	—
116	C₄×D₄×C₁₉	—	2	4	no	—
117	C₄×D₄×C₁₉	—	2	4	no	—
118	C₄×D₄×C₁₉	—	4	8	no	—
119	C₁₉×#117	—	2	4	no	—
120	C₁₉×#117	—	2	8	no	—
121	C₁₉×#117	—	2	8	no	—
122	C₁₉×#117	—	4	4	no	—
123	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
156	C₂×C₄²×C₁₉	—	2	8	no	—
157	C₂×C₄²×C₁₉	D₄	1	8	yes	complemented
158	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
161	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
167	C₁₉×#95	C₂³	1	4	yes	—
168	C₁₉×#95	C₂³	1	4	yes	—
169	C₁₉×#95	C₂³	1	4	yes	—
170	C₁₉×#95	C₂³	1	4	yes	—
171	C₁₉×#95	C₂³	1	4	yes	—
172	C₁₉×#95	C₂³	1	2	yes	—
173	C₁₉×#95	C₂³	1	2	yes	—
174	C₁₉×#95	C₂³	1	4	yes	—
175	C₁₉×#95	C₂³	1	4	yes	—
176	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
177	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
179	#41×C₁₉	—	2	32	no	—
180	C₂×Q₈×C₁₉	—	2	2	no	—
181	C₂×Q₈×C₁₉	—	2	2	no	—
182	C₂×Q₈×C₁₉	—	2	4	no	—
183	C₂×Q₈×C₁₉	—	2	4	no	—
184	C₂×D₄×C₁₉	—	2	4	no	—
185	C₂×D₄×C₁₉	—	2	4	no	—
186	C₂×D₄×C₁₉	—	2	4	no	—
187	C₂×D₄×C₁₉	—	2	4	no	—
188	C₂×D₄×C₁₉	—	2	8	no	—
189	C₂×D₄×C₁₉	—	2	2	no	—
190	C₂×D₄×C₁₉	—	2	2	no	—
191	C₂×D₄×C₁₉	—	2	4	no	—
192	C₂×D₄×C₁₉	—	2	4	no	—
193	C₂×D₄×C₁₉	—	4	4	no	—
194	C₂×D₄×C₁₉	—	4	4	no	—
195	C₂×D₄×C₁₉	—	4	4	no	—
196	C₂²×C₄×C₁₉	—	2	4	no	—
197	C₂²×C₄×C₁₉	—	2	4	no	—
198	C₂²×C₄×C₁₉	—	2	4	no	—
199	C₂²×C₄×C₁₉	—	2	2	no	—
200	C₂²×C₄×C₁₉	—	2	2	no	—
201	C₂²×C₄×C₁₉	—	2	4	no	—
202	C₂²×C₄×C₁₉	—	2	4	no	—
203	C₂²×C₄×C₁₉	—	2	4	no	—
204	C₂²×C₄×C₁₉	—	2	4	no	—
205	C₂²×C₄×C₁₉	—	2	4	no	—
206	C₂²×C₄×C₁₉	—	2	4	no	—
207	C₂²×C₄×C₁₉	—	2	4	no	—
208	C₂²×C₄×C₁₉	—	4	2	no	—
209	C₂²×C₄×C₁₉	—	4	2	no	—
210	C₂²×C₄×C₁₉	—	4	2	no	—
211	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₁₉	#41	1	8	yes	—
215	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
229	C₄⋊C₄×C₁₉	—	2	4	no	—
230	C₄⋊C₄×C₁₉	—	2	4	no	—
231	C₄⋊C₄×C₁₉	—	2	2	no	—
232	C₄⋊C₄×C₁₉	—	2	2	no	—
233	C₄⋊C₄×C₁₉	—	2	4	no	—
234	C₄⋊C₄×C₁₉	—	2	4	no	—
235	C₄⋊C₄×C₁₉	—	2	2	no	—
236	C₄⋊C₄×C₁₉	—	2	4	no	—
237	C₄⋊C₄×C₁₉	—	2	2	no	—
238	C₄⋊C₄×C₁₉	—	2	4	no	—
239	C₄⋊C₄×C₁₉	—	2	4	no	—
240	C₄⋊C₄×C₁₉	—	2	4	no	—
241	C₄⋊C₄×C₁₉	—	2	8	no	—
242	C₄⋊C₄×C₁₉	—	4	4	no	—
243	C₄⋊C₄×C₁₉	—	4	4	no	—
244	C₄⋊C₄×C₁₉	—	4	4	no	—
245	C₄⋊C₄×C₁₉	—	4	4	no	—
246	C₂²⋊C₄×C₁₉	—	2	4	no	—
247	C₂²⋊C₄×C₁₉	—	2	4	no	—
248	C₂²⋊C₄×C₁₉	—	2	8	no	—
249	C₂²⋊C₄×C₁₉	—	2	4	no	—
250	C₂²⋊C₄×C₁₉	—	2	4	no	—
251	C₂²⋊C₄×C₁₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₉	—	2	4	no	—
254	C₂²⋊C₄×C₁₉	—	2	4	no	—
255	C₂²⋊C₄×C₁₉	—	2	8	no	—
256	C₂²⋊C₄×C₁₉	—	4	4	no	—
257	C₂²⋊C₄×C₁₉	—	4	4	no	—
258	C₂²⋊C₄×C₁₉	—	4	2	no	—
259	C₂²⋊C₄×C₁₉	—	4	2	no	—
260	C₂²⋊C₄×C₁₉	—	4	4	no	—
261	C₂²⋊C₄×C₁₉	—	4	4	no	—
262	C₄²×C₁₉	—	2	4	no	—
263	C₄²×C₁₉	—	2	4	no	—
264	C₄²×C₁₉	—	2	4	no	—
265	C₄²×C₁₉	—	2	4	no	—
266	C₄²×C₁₉	—	2	8	no	—
267	C₄²×C₁₉	C₂×D₄	1	4	yes	—
268	C₄²×C₁₉	C₂×D₄	1	4	yes	—
269	C₄²×C₁₉	C₂×D₄	1	4	yes	—
270	C₄²×C₁₉	C₂×D₄	1	4	yes	—
271	#34614	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
272	C₂³×C₁₉	—	2	2	no	—
273	C₂³×C₁₉	—	2	2	no	—
274	C₂³×C₁₉	—	2	2	no	—
275	C₂³×C₁₉	—	2	1	no	—
276	C₂³×C₁₉	—	2	2	no	—
277	C₂³×C₁₉	—	2	1	no	—
278	C₂³×C₁₉	—	2	2	no	—
279	C₂³×C₁₉	—	2	2	no	—
280	C₂³×C₁₉	—	2	2	no	—
281	C₂³×C₁₉	—	2	2	no	—
282	C₂³×C₁₉	—	2	2	no	—
283	C₂³×C₁₉	—	2	4	no	—
284	C₂³×C₁₉	—	2	2	no	—
285	C₂³×C₁₉	—	2	2	no	—
286	C₂³×C₁₉	—	2	4	no	—
287	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
288	C₂³×C₁₉	C₂×#41	1	4	yes	—
289	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
290	Q₈×C₁₉	—	2	8	no	—
291	Q₈×C₁₉	—	4	4	no	—
292	D₄×C₁₉	—	2	8	no	—
293	D₄×C₁₉	—	2	16	no	—
294	D₄×C₁₉	—	4	8	no	—
295	D₄×C₁₉	—	4	16	no	—
296	D₄×C₁₉	—	4	4	no	—
297	C₂×C₄×C₁₉	—	2	2	no	—
298	C₂×C₄×C₁₉	—	2	2	no	—
299	C₂×C₄×C₁₉	—	2	2	no	—
300	C₂×C₄×C₁₉	—	2	1	no	—
301	C₂×C₄×C₁₉	—	2	1	no	—
302	C₂×C₄×C₁₉	—	2	2	no	—
303	C₂×C₄×C₁₉	—	2	2	no	—
304	C₂×C₄×C₁₉	—	2	8	no	—
305	C₂×C₄×C₁₉	—	2	16	no	—
306	C₂×C₄×C₁₉	—	2	8	no	—
307	C₂×C₄×C₁₉	—	2	2	no	—
308	C₂×C₄×C₁₉	—	2	2	no	—
309	C₂×C₄×C₁₉	—	2	2	no	—
310	C₂×C₄×C₁₉	—	2	2	no	—
311	C₂×C₄×C₁₉	—	2	2	no	—
312	C₂×C₄×C₁₉	—	2	4	no	—
313	C₂×C₄×C₁₉	—	2	4	no	—
314	C₂×C₄×C₁₉	—	2	4	no	—
315	C₂×C₄×C₁₉	—	2	4	no	—
316	C₂×C₄×C₁₉	—	2	4	no	—
317	C₂×C₄×C₁₉	—	2	2	no	—
318	C₂×C₄×C₁₉	—	2	2	no	—
319	C₂×C₄×C₁₉	—	2	2	no	—
320	C₂×C₄×C₁₉	—	2	2	no	—
321	C₂×C₄×C₁₉	—	2	2	no	—
322	C₂×C₄×C₁₉	—	2	4	no	—
323	C₂×C₄×C₁₉	—	2	4	no	—
324	C₂×C₄×C₁₉	—	2	4	no	—
325	C₂×C₄×C₁₉	—	2	2	no	—
326	C₂×C₄×C₁₉	—	4	4	no	—
327	C₂×C₄×C₁₉	—	4	8	no	—
328	C₂×C₄×C₁₉	—	4	8	no	—
329	C₂×C₄×C₁₉	—	4	8	no	—
330	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
337	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
338	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
339	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
340	C₂×#529	C₂×C₁₉	1	1	yes	characteristic, complemented
341	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
342	#2637	C₂×C₁₉	1	2	yes	complemented
343	#2636	C₂×C₁₉	1	2	yes	complemented
344	#2630	C₂×C₁₉	1	4	yes	complemented
345	#2629	C₂×C₁₉	1	2	yes	complemented
346	#2625	C₂×C₁₉	1	1	yes	characteristic, complemented
347	#2624	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#2620	C₂×C₁₉	1	2	yes	complemented
349	#2616	C₂×C₁₉	1	1	yes	characteristic, complemented
350	#2615	C₂×C₁₉	1	1	yes	characteristic
351	#2396	C₂×C₁₉	1	2	yes	complemented
352	#2392	C₂×C₁₉	1	2	yes	complemented
353	#2392	C₂×C₁₉	1	4	yes	complemented
354	C₄×C₂²⋊Q₈	C₂×C₁₉	1	2	yes	complemented
355	C₄×#121	C₂×C₁₉	1	2	yes	complemented
356	#2285	C₂×C₁₉	1	1	yes	characteristic, complemented
357	C₂²×C₁₉	—	2	2	no	—
358	C₂²×C₁₉	—	2	4	no	—
359	C₂²×C₁₉	—	2	2	no	—
360	C₂²×C₁₉	—	2	2	no	—
361	C₂²×C₁₉	—	2	4	no	—
362	C₂²×C₁₉	—	2	4	no	—
363	C₂²×C₁₉	—	4	2	no	—
364	C₂²×C₁₉	—	4	2	no	—
365	C₂²×C₁₉	—	4	2	no	—
366	C₂²×C₁₉	—	4	2	no	—
367	C₂²×C₁₉	—	4	2	no	—
368	C₂²×C₁₉	—	4	2	no	—
369	C₂²×C₁₉	—	4	2	no	—
370	C₂²×C₁₉	—	4	2	no	—
371	C₂²×C₁₉	—	4	2	no	—
372	C₂²×C₁₉	—	4	4	no	—
373	C₂²×C₁₉	—	4	4	no	—
374	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
375	C₂²×C₁₉	C₂²×#41	1	2	yes	—
376	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂²×C₁₉	#585	1	2	yes	—
379	C₄×C₁₉	—	2	2	no	—
380	C₄×C₁₉	—	2	4	no	—
381	C₄×C₁₉	—	2	2	no	—
382	C₄×C₁₉	—	2	2	no	—
383	C₄×C₁₉	—	2	2	no	—
384	C₄×C₁₉	—	4	2	no	—
385	C₄×C₁₉	—	4	2	no	—
386	C₄×C₁₉	—	4	2	no	—
387	C₄×C₁₉	—	4	2	no	—
388	C₄×C₁₉	—	4	2	no	—
389	C₄×C₁₉	—	4	4	no	—
390	C₄×C₁₉	—	4	4	no	—
391	C₄×C₁₉	#525	1	4	yes	—
392	C₄×C₁₉	#537	1	4	yes	—
393	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
394	#529	—	2	8	no	—
395	C₂×#126	C₂²×C₁₉	1	2	yes	—
396	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
397	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
398	C₂×#123	C₂²×C₁₉	1	2	yes	—
399	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
400	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
401	C₂×#121	C₂²×C₁₉	1	2	yes	—
402	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
403	C₄×#41	—	2	8	no	—
404	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
405	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
408	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
410	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
411	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
412	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
413	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
414	C₂×#117	C₂²×C₁₉	1	2	yes	—
415	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
416	C₂×#117	C₂²×C₁₉	1	2	yes	—
417	C₂×#117	C₂²×C₁₉	1	2	yes	—
418	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
419	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
420	#400	C₂²×C₁₉	1	2	yes	—
421	#399	C₂²×C₁₉	1	2	yes	—
422	#398	C₂²×C₁₉	1	2	yes	—
423	#398	C₂²×C₁₉	1	4	yes	—
424	#398	C₂²×C₁₉	1	4	yes	—
425	#397	C₂²×C₁₉	1	2	yes	—
426	#397	C₂²×C₁₉	1	4	yes	—
427	#396	C₂²×C₁₉	1	4	yes	—
428	#396	C₂²×C₁₉	1	4	yes	—
429	#396	C₂²×C₁₉	1	4	yes	—
430	#396	C₂²×C₁₉	1	4	yes	—
431	#395	C₂²×C₁₉	1	2	yes	—
432	#394	C₂²×C₁₉	1	4	yes	—
433	#394	C₂²×C₁₉	1	2	yes	—
434	#394	C₂²×C₁₉	1	4	yes	—
435	#394	C₂²×C₁₉	1	4	yes	—
436	#394	C₂²×C₁₉	1	4	yes	—
437	#393	C₂²×C₁₉	1	2	yes	—
438	#392	C₂²×C₁₉	1	4	yes	—
439	#392	C₂²×C₁₉	1	2	yes	—
440	#391	C₂²×C₁₉	1	2	yes	—
441	#390	C₂²×C₁₉	1	2	yes	—
442	#389	C₂²×C₁₉	1	2	yes	—
443	#389	C₂²×C₁₉	1	2	yes	—
444	#388	C₂²×C₁₉	1	4	yes	—
445	#387	C₂²×C₁₉	1	4	yes	—
446	#386	C₂²×C₁₉	1	4	yes	—
447	#385	C₂²×C₁₉	1	4	yes	—
448	#384	C₂²×C₁₉	1	2	yes	—
449	#382	C₂²×C₁₉	1	2	yes	—
450	#380	C₂²×C₁₉	1	1	yes	characteristic
451	#380	C₂²×C₁₉	1	2	yes	—
452	#380	C₂²×C₁₉	1	1	yes	characteristic
453	#380	C₂²×C₁₉	1	2	yes	—
454	#380	C₂²×C₁₉	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
457	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
459	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
460	C₂×C₁₉	—	4	2	no	—
461	C₂×C₁₉	—	4	4	no	—
462	C₂×C₁₉	—	8	2	no	—
463	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
464	C₂×C₁₉	C₂×#537	1	1	yes	characteristic
465	C₂×C₁₉	#3449	1	1	yes	characteristic
466	C₂×C₁₉	#3460	1	2	yes	—
467	C₂×C₁₉	#3461	1	2	yes	—
468	C₂×#41	—	2	4	no	—
469	C₂×#41	—	2	8	no	—
470	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
472	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
473	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
474	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
476	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
477	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
478	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
479	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
482	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
483	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
484	#126	—	2	8	no	—
485	#125	—	2	4	no	—
486	#124	—	2	4	no	—
487	#123	—	2	8	no	—
488	C₂²⋊Q₈	—	2	4	no	—
489	C₂²⋊Q₈	—	2	8	no	—
490	#121	—	2	4	no	—
491	#121	—	2	8	no	—
492	C₄×Q₈	—	2	4	no	—
493	C₄×Q₈	—	2	4	no	—
494	C₄×Q₈	—	2	4	no	—
495	C₄×D₄	—	2	8	no	—
496	C₄×D₄	—	2	8	no	—
497	C₄×D₄	—	2	8	no	—
498	C₄×D₄	—	2	4	no	—
499	C₄×D₄	—	2	4	no	—
500	C₄×D₄	—	2	4	no	—
501	C₄×D₄	—	4	8	no	—
502	#117	—	2	4	no	—
503	#117	—	2	8	no	—
504	#117	—	2	8	no	—
505	#117	—	4	4	no	—
506	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
539	C₂×C₄²	—	2	8	no	—
540	C₂×C₄²	D₄×C₁₉	1	8	yes	complemented
541	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
542	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
543	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
544	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
545	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
546	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
550	#95	C₂³×C₁₉	1	4	yes	—
551	#95	C₂³×C₁₉	1	4	yes	—
552	#95	C₂³×C₁₉	1	4	yes	—
553	#95	C₂³×C₁₉	1	4	yes	—
554	#95	C₂³×C₁₉	1	4	yes	—
555	#95	C₂³×C₁₉	1	2	yes	—
556	#95	C₂³×C₁₉	1	2	yes	—
557	#95	C₂³×C₁₉	1	4	yes	—
558	#95	C₂³×C₁₉	1	4	yes	—
559	C₁₉	#34614	1	1	yes	characteristic, direct product factor, Sylow
560	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
561	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
562	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
563	#41	—	2	32	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	8	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
596	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
597	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
598	C₂²×C₄	#41×C₁₉	1	8	yes	—
599	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
603	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	8	no	—
626	C₄⋊C₄	—	4	4	no	—
627	C₄⋊C₄	—	4	4	no	—
628	C₄⋊C₄	—	4	4	no	—
629	C₄⋊C₄	—	4	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	8	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	4	no	—
645	C₂²⋊C₄	—	4	4	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	4	no	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	8	no	—
651	C₄²	C₂×D₄×C₁₉	1	4	yes	—
652	C₄²	C₂×D₄×C₁₉	1	4	yes	—
653	C₄²	C₂×D₄×C₁₉	1	4	yes	—
654	C₄²	C₂×D₄×C₁₉	1	4	yes	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
671	C₂³	C₂×#41×C₁₉	1	4	yes	—
672	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
673	Q₈	—	2	8	no	—
674	Q₈	—	4	4	no	—
675	D₄	—	2	8	no	—
676	D₄	—	2	16	no	—
677	D₄	—	4	8	no	—
678	D₄	—	4	16	no	—
679	D₄	—	4	4	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	8	no	—
688	C₂×C₄	—	2	16	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	8	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
719	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
720	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
721	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
722	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	4	no	—
740	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
741	C₂²	C₂²×#41×C₁₉	1	2	yes	—
742	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
743	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
744	C₂²	C₁₉×#585	1	2	yes	—
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	4	no	—
756	C₄	—	4	4	no	—
757	C₄	C₁₉×#525	1	4	yes	—
758	C₄	C₁₉×#537	1	4	yes	—
759	C₂	—	4	2	no	—
760	C₂	—	4	4	no	—
761	C₂	—	8	2	no	—
762	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
763	C₂	C₂×C₁₉×#537	1	1	yes	characteristic
764	C₂	C₁₉×#3449	1	1	yes	characteristic
765	C₂	C₁₉×#3460	1	2	yes	—
766	C₂	C₁₉×#3461	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₁₉×#2615	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#529	C₂	semidirect
2. C₂×C₄×#41×C₁₉	C₂	semidirect
3. C₁₉×#2637	C₂	semidirect
4. C₁₉×#2636	C₂	semidirect
5. C₁₉×#2630	C₂	semidirect
6. C₁₉×#2629	C₂	semidirect
7. C₁₉×#2625	C₂	semidirect
8. C₁₉×#2624	C₂	semidirect
9. C₁₉×#2620	C₂	semidirect
10. C₁₉×#2616	C₂	semidirect
12. C₁₉×#2396	C₂	semidirect
13. C₁₉×#2392	C₂	semidirect
14. C₁₉×#2392	C₂	semidirect
15. C₄×C₁₉×C₂²⋊Q₈	C₂	semidirect
16. C₄×C₁₉×#121	C₂	semidirect
17. C₁₉×#2285	C₂	semidirect
157. C₂×C₄²×C₁₉	D₄	semidirect
271. #34614	C₁₉	direct (N × H)
340. C₂×#529	C₂×C₁₉	semidirect
341. C₂×C₄×#41	C₂×C₁₉	semidirect
342. #2637	C₂×C₁₉	semidirect
343. #2636	C₂×C₁₉	semidirect
344. #2630	C₂×C₁₉	semidirect
345. #2629	C₂×C₁₉	semidirect
346. #2625	C₂×C₁₉	semidirect
347. #2624	C₂×C₁₉	semidirect
348. #2620	C₂×C₁₉	semidirect
349. #2616	C₂×C₁₉	semidirect
351. #2396	C₂×C₁₉	semidirect
352. #2392	C₂×C₁₉	semidirect
353. #2392	C₂×C₁₉	semidirect
354. C₄×C₂²⋊Q₈	C₂×C₁₉	semidirect
355. C₄×#121	C₂×C₁₉	semidirect
356. #2285	C₂×C₁₉	semidirect
540. C₂×C₄²	D₄×C₁₉	semidirect
559. C₁₉	#34614	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×#529	2
C₂×C₄×#41×C₁₉	2
C₁₉×#2637	2
C₁₉×#2636	2
C₁₉×#2630	2
C₁₉×#2629	2
C₁₉×#2625	2
C₁₉×#2624	2
C₁₉×#2620	2
C₁₉×#2616	2
C₁₉×#2615	2
C₁₉×#2396	2
C₁₉×#2392	2
C₄×C₁₉×C₂²⋊Q₈	2
C₄×C₁₉×#121	2
C₁₉×#2285	2
#34614	19

Subgroups — C19×#34614 #18040573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34614 #18040573