Subgroups — C₁₉×#34909 #18040868

Order 4864.

2726 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2600	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2599	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2598	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2581	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2580	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2536	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2535	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2485	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2407	C₂	1	2	yes	maximal, complemented
12	C₁₉×#2395	C₂	1	2	yes	maximal, complemented
13	C₁₉×#2388	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₉×#121	C₂	1	2	yes	maximal, complemented
16	C₁₉×#2290	C₂	1	4	yes	maximal, complemented
17	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₉×#121	C₂²	1	2	yes	—
22	C₄×#41×C₁₉	—	2	8	no	—
23	C₄×#41×C₁₉	—	2	8	no	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
37	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#117	C₂²	1	2	yes	—
39	C₂×C₁₉×#117	C₂²	1	2	yes	—
40	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
42	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
43	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
44	C₁₉×#400	C₂²	1	2	yes	—
45	C₁₉×#399	C₂²	1	2	yes	—
46	C₁₉×#398	C₂²	1	2	yes	—
47	C₁₉×#397	C₂²	1	4	yes	—
48	C₁₉×#397	C₂²	1	2	yes	—
49	C₁₉×#395	C₂²	1	2	yes	—
50	C₁₉×#394	C₂²	1	4	yes	—
51	C₁₉×#394	C₂²	1	4	yes	—
52	C₁₉×#394	C₂²	1	2	yes	—
53	C₁₉×#393	C₂²	1	2	yes	—
54	C₁₉×#392	C₂²	1	4	yes	—
55	C₁₉×#392	C₂²	1	2	yes	—
56	C₁₉×#391	C₂²	1	2	yes	—
57	C₁₉×#390	C₂²	1	2	yes	—
58	C₁₉×#389	C₂²	1	2	yes	—
59	C₁₉×#389	C₂²	1	2	yes	—
60	C₁₉×#388	C₂²	1	4	yes	—
61	C₁₉×#388	C₂²	1	4	yes	—
62	C₁₉×#388	C₂²	1	4	yes	—
63	C₁₉×#387	C₂²	1	4	yes	—
64	C₁₉×#387	C₂²	1	4	yes	—
65	C₁₉×#387	C₂²	1	4	yes	—
66	C₁₉×#386	C₂²	1	4	yes	—
67	C₁₉×#386	C₂²	1	4	yes	—
68	C₁₉×#386	C₂²	1	4	yes	—
69	C₁₉×#385	C₂²	1	4	yes	—
70	C₁₉×#385	C₂²	1	4	yes	—
71	C₁₉×#385	C₂²	1	4	yes	—
72	C₁₉×#383	C₂²	1	2	yes	—
73	C₁₉×#382	C₂²	1	1	yes	characteristic
74	C₁₉×#382	C₂²	1	1	yes	characteristic
75	C₁₉×#381	C₂²	1	2	yes	—
76	C₁₉×#380	C₂²	1	2	yes	—
77	C₁₉×#380	C₂²	1	2	yes	—
78	C₁₉×#380	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
81	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
84	C₁₉×#376	C₂²	1	2	yes	—
85	C₂×#41×C₁₉	—	2	4	no	—
86	C₂×#41×C₁₉	—	2	4	no	—
87	C₂×#41×C₁₉	—	2	4	no	—
88	C₂×#41×C₁₉	—	2	4	no	—
89	C₂×#41×C₁₉	—	2	8	no	—
90	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
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	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
104	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×C₂²⋊Q₈	—	2	8	no	—
107	C₁₉×#121	—	2	8	no	—
108	C₄×Q₈×C₁₉	—	2	4	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	8	no	—
116	C₄×D₄×C₁₉	—	2	16	no	—
117	C₄×D₄×C₁₉	—	2	4	no	—
118	C₄×D₄×C₁₉	—	2	4	no	—
119	C₄×D₄×C₁₉	—	2	4	no	—
120	C₄×D₄×C₁₉	—	2	4	no	—
121	C₁₉×#117	—	2	4	no	—
122	C₁₉×#117	—	2	4	no	—
123	C₁₉×#117	—	2	8	no	—
124	C₁₉×#117	—	2	8	no	—
125	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	4	yes	—
134	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊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	4	yes	—
149	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
151	C₂×C₄²×C₁₉	—	2	8	no	—
152	C₂×C₄²×C₁₉	—	2	8	no	—
153	C₂×C₄²×C₁₉	D₄	1	8	yes	complemented
154	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
159	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
165	C₁₉×#95	C₂³	1	4	yes	—
166	C₁₉×#95	C₂³	1	2	yes	—
167	C₁₉×#95	C₂³	1	2	yes	—
168	C₁₉×#95	C₂³	1	4	yes	—
169	C₁₉×#95	C₂³	1	2	yes	—
170	C₁₉×#95	C₂³	1	2	yes	—
171	C₁₉×#95	C₂³	1	4	yes	—
172	C₁₉×#95	C₂³	1	4	yes	—
173	C₁₉×#95	C₂³	1	4	yes	—
174	C₁₉×#95	C₂³	1	4	yes	—
175	C₁₉×#95	C₂³	1	4	yes	—
176	C₁₉×#95	C₂³	1	4	yes	—
177	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
178	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
179	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
180	#41×C₁₉	—	2	32	no	—
181	#41×C₁₉	—	2	32	no	—
182	C₂×Q₈×C₁₉	—	2	2	no	—
183	C₂×Q₈×C₁₉	—	2	2	no	—
184	C₂×Q₈×C₁₉	—	2	4	no	—
185	C₂×Q₈×C₁₉	—	2	2	no	—
186	C₂×Q₈×C₁₉	#41	1	4	yes	complemented
187	C₂×D₄×C₁₉	—	2	4	no	—
188	C₂×D₄×C₁₉	—	2	4	no	—
189	C₂×D₄×C₁₉	—	2	4	no	—
190	C₂×D₄×C₁₉	—	2	4	no	—
191	C₂×D₄×C₁₉	—	2	4	no	—
192	C₂×D₄×C₁₉	—	2	8	no	—
193	C₂×D₄×C₁₉	—	2	8	no	—
194	C₂×D₄×C₁₉	—	2	2	no	—
195	C₂×D₄×C₁₉	—	2	2	no	—
196	C₂×D₄×C₁₉	—	2	4	no	—
197	C₂×D₄×C₁₉	—	2	4	no	—
198	C₂×D₄×C₁₉	—	2	2	no	—
199	C₂×D₄×C₁₉	—	4	4	no	—
200	C₂×D₄×C₁₉	#41	1	4	yes	complemented
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	2	no	—
206	C₂²×C₄×C₁₉	—	2	2	no	—
207	C₂²×C₄×C₁₉	—	2	4	no	—
208	C₂²×C₄×C₁₉	—	2	4	no	—
209	C₂²×C₄×C₁₉	—	2	4	no	—
210	C₂²×C₄×C₁₉	—	2	4	no	—
211	C₂²×C₄×C₁₉	—	2	4	no	—
212	C₂²×C₄×C₁₉	—	2	4	no	—
213	C₂²×C₄×C₁₉	—	2	8	no	—
214	C₂²×C₄×C₁₉	—	2	4	no	—
215	C₂²×C₄×C₁₉	—	2	4	no	—
216	C₂²×C₄×C₁₉	—	4	2	no	—
217	C₂²×C₄×C₁₉	—	4	2	no	—
218	C₂²×C₄×C₁₉	—	4	4	no	—
219	C₂²×C₄×C₁₉	—	4	2	no	—
220	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
221	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
222	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
223	C₂²×C₄×C₁₉	#41	1	8	yes	complemented
224	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
229	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
230	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	4	no	—
242	C₄⋊C₄×C₁₉	—	2	2	no	—
243	C₄⋊C₄×C₁₉	—	2	2	no	—
244	C₄⋊C₄×C₁₉	—	2	2	no	—
245	C₄⋊C₄×C₁₉	—	2	2	no	—
246	C₄⋊C₄×C₁₉	—	2	8	no	—
247	C₄⋊C₄×C₁₉	—	2	4	no	—
248	C₄⋊C₄×C₁₉	—	2	4	no	—
249	C₄⋊C₄×C₁₉	—	2	8	no	—
250	C₄⋊C₄×C₁₉	—	4	4	no	—
251	C₂²⋊C₄×C₁₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₉	—	2	8	no	—
254	C₂²⋊C₄×C₁₉	—	2	8	no	—
255	C₂²⋊C₄×C₁₉	—	2	4	no	—
256	C₂²⋊C₄×C₁₉	—	2	4	no	—
257	C₂²⋊C₄×C₁₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₉	—	2	4	no	—
259	C₂²⋊C₄×C₁₉	—	2	8	no	—
260	C₂²⋊C₄×C₁₉	—	2	8	no	—
261	C₂²⋊C₄×C₁₉	—	4	4	no	—
262	C₂²⋊C₄×C₁₉	—	4	4	no	—
263	C₂²⋊C₄×C₁₉	—	4	4	no	—
264	C₄²×C₁₉	—	2	4	no	—
265	C₄²×C₁₉	—	2	4	no	—
266	C₄²×C₁₉	—	2	4	no	—
267	C₄²×C₁₉	—	2	4	no	—
268	C₄²×C₁₉	—	2	4	no	—
269	C₄²×C₁₉	—	2	4	no	—
270	C₄²×C₁₉	—	2	8	no	—
271	C₄²×C₁₉	C₂×D₄	1	4	yes	—
272	C₄²×C₁₉	C₂×D₄	1	4	yes	—
273	C₄²×C₁₉	C₂×D₄	1	4	yes	—
274	C₄²×C₁₉	C₂×D₄	1	4	yes	—
275	#34909	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₁₉	—	2	2	no	—
277	C₂³×C₁₉	—	2	2	no	—
278	C₂³×C₁₉	—	2	2	no	—
279	C₂³×C₁₉	—	2	4	no	—
280	C₂³×C₁₉	—	2	1	no	—
281	C₂³×C₁₉	—	2	2	no	—
282	C₂³×C₁₉	—	2	1	no	—
283	C₂³×C₁₉	—	2	2	no	—
284	C₂³×C₁₉	—	2	2	no	—
285	C₂³×C₁₉	—	2	2	no	—
286	C₂³×C₁₉	—	2	2	no	—
287	C₂³×C₁₉	—	2	2	no	—
288	C₂³×C₁₉	—	2	4	no	—
289	C₂³×C₁₉	—	2	2	no	—
290	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
291	C₂³×C₁₉	C₂×#41	1	4	yes	—
292	C₂³×C₁₉	C₂×#41	1	4	yes	—
293	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
294	Q₈×C₁₉	—	2	8	no	—
295	Q₈×C₁₉	—	2	8	no	—
296	D₄×C₁₉	—	2	8	no	—
297	D₄×C₁₉	—	2	16	no	—
298	D₄×C₁₉	—	2	16	no	—
299	D₄×C₁₉	—	2	8	no	—
300	D₄×C₁₉	—	4	16	no	—
301	C₂×C₄×C₁₉	—	2	16	no	—
302	C₂×C₄×C₁₉	—	2	2	no	—
303	C₂×C₄×C₁₉	—	2	2	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	1	no	—
306	C₂×C₄×C₁₉	—	2	2	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	8	no	—
312	C₂×C₄×C₁₉	—	2	8	no	—
313	C₂×C₄×C₁₉	—	2	16	no	—
314	C₂×C₄×C₁₉	—	2	2	no	—
315	C₂×C₄×C₁₉	—	2	2	no	—
316	C₂×C₄×C₁₉	—	2	2	no	—
317	C₂×C₄×C₁₉	—	2	2	no	—
318	C₂×C₄×C₁₉	—	2	4	no	—
319	C₂×C₄×C₁₉	—	2	4	no	—
320	C₂×C₄×C₁₉	—	2	2	no	—
321	C₂×C₄×C₁₉	—	2	4	no	—
322	C₂×C₄×C₁₉	—	2	4	no	—
323	C₂×C₄×C₁₉	—	2	4	no	—
324	C₂×C₄×C₁₉	—	2	2	no	—
325	C₂×C₄×C₁₉	—	2	4	no	—
326	C₂×C₄×C₁₉	—	2	2	no	—
327	C₂×C₄×C₁₉	—	2	4	no	—
328	C₂×C₄×C₁₉	—	2	4	no	—
329	C₂×C₄×C₁₉	—	2	2	no	—
330	C₂×C₄×C₁₉	—	4	4	no	—
331	C₂×C₄×C₁₉	—	4	8	no	—
332	C₂×C₄×C₁₉	—	4	8	no	—
333	C₂×C₄×C₁₉	—	4	8	no	—
334	C₂×C₄×C₁₉	—	4	8	no	—
335	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
342	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
343	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
344	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
345	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
346	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
347	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#2600	C₂×C₁₉	1	4	yes	complemented
349	#2599	C₂×C₁₉	1	2	yes	complemented
350	#2598	C₂×C₁₉	1	2	yes	complemented
351	#2581	C₂×C₁₉	1	1	yes	characteristic, complemented
352	#2580	C₂×C₁₉	1	1	yes	characteristic, complemented
353	#2536	C₂×C₁₉	1	1	yes	characteristic, complemented
354	#2535	C₂×C₁₉	1	1	yes	characteristic, complemented
355	#2485	C₂×C₁₉	1	2	yes	complemented
356	#2407	C₂×C₁₉	1	2	yes	complemented
357	#2395	C₂×C₁₉	1	2	yes	complemented
358	#2388	C₂×C₁₉	1	2	yes	complemented
359	C₄×C₂²⋊Q₈	C₂×C₁₉	1	2	yes	complemented
360	C₄×#121	C₂×C₁₉	1	2	yes	complemented
361	#2290	C₂×C₁₉	1	4	yes	complemented
362	#2283	C₂×C₁₉	1	1	yes	characteristic, complemented
363	C₂²×C₁₉	—	2	2	no	—
364	C₂²×C₁₉	—	2	2	no	—
365	C₂²×C₁₉	—	2	4	no	—
366	C₂²×C₁₉	—	2	4	no	—
367	C₂²×C₁₉	—	2	2	no	—
368	C₂²×C₁₉	—	2	4	no	—
369	C₂²×C₁₉	—	2	8	no	—
370	C₂²×C₁₉	—	2	4	no	—
371	C₂²×C₁₉	—	4	2	no	—
372	C₂²×C₁₉	—	4	2	no	—
373	C₂²×C₁₉	—	4	2	no	—
374	C₂²×C₁₉	—	4	2	no	—
375	C₂²×C₁₉	—	4	2	no	—
376	C₂²×C₁₉	—	4	2	no	—
377	C₂²×C₁₉	—	4	2	no	—
378	C₂²×C₁₉	—	4	4	no	—
379	C₂²×C₁₉	—	4	2	no	—
380	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
381	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
382	C₂²×C₁₉	C₂²×#41	1	2	yes	—
383	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
384	C₂²×C₁₉	#585	1	2	yes	—
385	C₄×C₁₉	—	2	2	no	—
386	C₄×C₁₉	—	2	2	no	—
387	C₄×C₁₉	—	2	4	no	—
388	C₄×C₁₉	—	2	4	no	—
389	C₄×C₁₉	—	2	2	no	—
390	C₄×C₁₉	—	2	2	no	—
391	C₄×C₁₉	—	4	2	no	—
392	C₄×C₁₉	—	4	2	no	—
393	C₄×C₁₉	—	4	2	no	—
394	C₄×C₁₉	—	4	2	no	—
395	C₄×C₁₉	—	4	4	no	—
396	C₄×C₁₉	—	4	4	no	—
397	C₄×C₁₉	#525	1	4	yes	—
398	C₄×C₁₉	#525	1	4	yes	—
399	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
400	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
402	C₂×#121	C₂²×C₁₉	1	2	yes	—
403	C₄×#41	—	2	8	no	—
404	C₄×#41	—	2	8	no	—
405	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
406	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
407	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
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	2	yes	—
413	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
414	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
415	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
416	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
418	C₂×#117	C₂²×C₁₉	1	2	yes	—
419	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
420	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
421	C₂×#117	C₂²×C₁₉	1	2	yes	—
422	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
423	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
424	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
425	#400	C₂²×C₁₉	1	2	yes	—
426	#399	C₂²×C₁₉	1	2	yes	—
427	#398	C₂²×C₁₉	1	2	yes	—
428	#397	C₂²×C₁₉	1	2	yes	—
429	#397	C₂²×C₁₉	1	4	yes	—
430	#395	C₂²×C₁₉	1	2	yes	—
431	#394	C₂²×C₁₉	1	2	yes	—
432	#394	C₂²×C₁₉	1	4	yes	—
433	#394	C₂²×C₁₉	1	4	yes	—
434	#393	C₂²×C₁₉	1	2	yes	—
435	#392	C₂²×C₁₉	1	2	yes	—
436	#392	C₂²×C₁₉	1	4	yes	—
437	#391	C₂²×C₁₉	1	2	yes	—
438	#390	C₂²×C₁₉	1	2	yes	—
439	#389	C₂²×C₁₉	1	2	yes	—
440	#389	C₂²×C₁₉	1	2	yes	—
441	#388	C₂²×C₁₉	1	4	yes	—
442	#388	C₂²×C₁₉	1	4	yes	—
443	#388	C₂²×C₁₉	1	4	yes	—
444	#387	C₂²×C₁₉	1	4	yes	—
445	#387	C₂²×C₁₉	1	4	yes	—
446	#387	C₂²×C₁₉	1	4	yes	—
447	#386	C₂²×C₁₉	1	4	yes	—
448	#386	C₂²×C₁₉	1	4	yes	—
449	#386	C₂²×C₁₉	1	4	yes	—
450	#385	C₂²×C₁₉	1	4	yes	—
451	#385	C₂²×C₁₉	1	4	yes	—
452	#385	C₂²×C₁₉	1	4	yes	—
453	#383	C₂²×C₁₉	1	2	yes	—
454	#382	C₂²×C₁₉	1	1	yes	characteristic
455	#382	C₂²×C₁₉	1	1	yes	characteristic
456	#381	C₂²×C₁₉	1	2	yes	—
457	#380	C₂²×C₁₉	1	2	yes	—
458	#380	C₂²×C₁₉	1	2	yes	—
459	#380	C₂²×C₁₉	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
461	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
462	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
463	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
465	#376	C₂²×C₁₉	1	2	yes	—
466	C₂×C₁₉	—	4	2	no	—
467	C₂×C₁₉	—	4	4	no	—
468	C₂×C₁₉	—	4	4	no	—
469	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
470	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
471	C₂×C₁₉	#3449	1	1	yes	characteristic
472	C₂×C₁₉	#3475	1	2	yes	—
473	C₂×C₁₉	#3480	1	2	yes	—
474	C₂×#41	—	2	4	no	—
475	C₂×#41	—	2	4	no	—
476	C₂×#41	—	2	4	no	—
477	C₂×#41	—	2	4	no	—
478	C₂×#41	—	2	8	no	—
479	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
481	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
483	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
484	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
485	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
487	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
488	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
489	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
492	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
493	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
494	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
495	C₂²⋊Q₈	—	2	8	no	—
496	#121	—	2	8	no	—
497	C₄×Q₈	—	2	4	no	—
498	C₄×Q₈	—	2	4	no	—
499	C₄×Q₈	—	2	4	no	—
500	C₄×Q₈	—	2	4	no	—
501	C₄×D₄	—	2	8	no	—
502	C₄×D₄	—	2	8	no	—
503	C₄×D₄	—	2	8	no	—
504	C₄×D₄	—	2	8	no	—
505	C₄×D₄	—	2	16	no	—
506	C₄×D₄	—	2	4	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	—	2	4	no	—
510	#117	—	2	4	no	—
511	#117	—	2	4	no	—
512	#117	—	2	8	no	—
513	#117	—	2	8	no	—
514	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
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	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
526	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	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	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	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×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
540	C₂×C₄²	—	2	8	no	—
541	C₂×C₄²	—	2	8	no	—
542	C₂×C₄²	D₄×C₁₉	1	8	yes	complemented
543	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
544	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
545	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
546	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
547	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
549	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
550	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
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	2	yes	—
559	#95	C₂³×C₁₉	1	2	yes	—
560	#95	C₂³×C₁₉	1	4	yes	—
561	#95	C₂³×C₁₉	1	4	yes	—
562	#95	C₂³×C₁₉	1	4	yes	—
563	#95	C₂³×C₁₉	1	4	yes	—
564	#95	C₂³×C₁₉	1	4	yes	—
565	#95	C₂³×C₁₉	1	4	yes	—
566	C₁₉	#34909	1	1	yes	characteristic, direct product factor, Sylow
567	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
568	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
569	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
570	#41	—	2	32	no	—
571	#41	—	2	32	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	2	2	no	—
576	C₂×Q₈	#41×C₁₉	1	4	yes	complemented
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	8	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂×D₄	#41×C₁₉	1	4	yes	complemented
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	8	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	—	4	4	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
611	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
612	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
613	C₂²×C₄	#41×C₁₉	1	8	yes	complemented
614	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
615	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
616	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	8	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	8	no	—
640	C₄⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	8	no	—
644	C₂²⋊C₄	—	2	8	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	8	no	—
650	C₂²⋊C₄	—	2	8	no	—
651	C₂²⋊C₄	—	4	4	no	—
652	C₂²⋊C₄	—	4	4	no	—
653	C₂²⋊C₄	—	4	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	4	no	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	4	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	8	no	—
661	C₄²	C₂×D₄×C₁₉	1	4	yes	—
662	C₄²	C₂×D₄×C₁₉	1	4	yes	—
663	C₄²	C₂×D₄×C₁₉	1	4	yes	—
664	C₄²	C₂×D₄×C₁₉	1	4	yes	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	2	no	—
679	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
680	C₂³	C₂×#41×C₁₉	1	4	yes	—
681	C₂³	C₂×#41×C₁₉	1	4	yes	—
682	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
683	Q₈	—	2	8	no	—
684	Q₈	—	2	8	no	—
685	D₄	—	2	8	no	—
686	D₄	—	2	16	no	—
687	D₄	—	2	16	no	—
688	D₄	—	2	8	no	—
689	D₄	—	4	16	no	—
690	C₂×C₄	—	2	16	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	8	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	16	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	8	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
725	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
730	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
731	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
732	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
733	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
734	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	8	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	2	no	—
752	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
753	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
754	C₂²	C₂²×#41×C₁₉	1	2	yes	—
755	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
756	C₂²	C₁₉×#585	1	2	yes	—
757	C₄	—	2	2	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	4	no	—
768	C₄	—	4	4	no	—
769	C₄	C₁₉×#525	1	4	yes	—
770	C₄	C₁₉×#525	1	4	yes	—
771	C₂	—	4	2	no	—
772	C₂	—	4	4	no	—
773	C₂	—	4	4	no	—
774	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
775	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
776	C₂	C₁₉×#3449	1	1	yes	characteristic
777	C₂	C₁₉×#3475	1	2	yes	—
778	C₂	C₁₉×#3480	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×#41×C₁₉	C₂	semidirect
2. C₂×C₄×#41×C₁₉	C₂	semidirect
3. C₁₉×#2600	C₂	semidirect
4. C₁₉×#2599	C₂	semidirect
5. C₁₉×#2598	C₂	semidirect
6. C₁₉×#2581	C₂	semidirect
7. C₁₉×#2580	C₂	semidirect
8. C₁₉×#2536	C₂	semidirect
9. C₁₉×#2535	C₂	semidirect
10. C₁₉×#2485	C₂	semidirect
11. C₁₉×#2407	C₂	semidirect
12. C₁₉×#2395	C₂	semidirect
13. C₁₉×#2388	C₂	semidirect
14. C₄×C₁₉×C₂²⋊Q₈	C₂	semidirect
15. C₄×C₁₉×#121	C₂	semidirect
16. C₁₉×#2290	C₂	semidirect
17. C₁₉×#2283	C₂	semidirect
153. C₂×C₄²×C₁₉	D₄	semidirect
186. C₂×Q₈×C₁₉	#41	semidirect
200. C₂×D₄×C₁₉	#41	semidirect
223. C₂²×C₄×C₁₉	#41	semidirect
275. #34909	C₁₉	direct (N × H)
346. C₂×C₄×#41	C₂×C₁₉	semidirect
347. C₂×C₄×#41	C₂×C₁₉	semidirect
348. #2600	C₂×C₁₉	semidirect
349. #2599	C₂×C₁₉	semidirect
350. #2598	C₂×C₁₉	semidirect
351. #2581	C₂×C₁₉	semidirect
352. #2580	C₂×C₁₉	semidirect
353. #2536	C₂×C₁₉	semidirect
354. #2535	C₂×C₁₉	semidirect
355. #2485	C₂×C₁₉	semidirect
356. #2407	C₂×C₁₉	semidirect
357. #2395	C₂×C₁₉	semidirect
358. #2388	C₂×C₁₉	semidirect
359. C₄×C₂²⋊Q₈	C₂×C₁₉	semidirect
360. C₄×#121	C₂×C₁₉	semidirect
361. #2290	C₂×C₁₉	semidirect
362. #2283	C₂×C₁₉	semidirect
542. C₂×C₄²	D₄×C₁₉	semidirect
566. C₁₉	#34909	direct (N × H)
576. C₂×Q₈	#41×C₁₉	semidirect
590. C₂×D₄	#41×C₁₉	semidirect
613. C₂²×C₄	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₉	2
C₁₉×#2600	2
C₁₉×#2599	2
C₁₉×#2598	2
C₁₉×#2581	2
C₁₉×#2580	2
C₁₉×#2536	2
C₁₉×#2535	2
C₁₉×#2485	2
C₁₉×#2407	2
C₁₉×#2395	2
C₁₉×#2388	2
C₄×C₁₉×C₂²⋊Q₈	2
C₄×C₁₉×#121	2
C₁₉×#2290	2
C₁₉×#2283	2
#34909	19

Subgroups — C19×#34909 #18040868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34909 #18040868