Subgroups — C₁₉×#34321 #18040280

Order 4864.

2452 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#555	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2369	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2367	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2363	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2361	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2354	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2347	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2347	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2337	C₂	1	4	yes	maximal, complemented
11	C₁₉×#2324	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₉×#121	C₂	1	2	yes	maximal, complemented
14	C₁₉×#2296	C₂	1	2	yes	maximal, complemented
15	C₁₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#2274	C₂	1	2	yes	maximal, complemented
17	C₄²×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×#555	C₄	1	16	yes	complemented
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#124	C₂²	1	4	yes	—
21	C₂×C₁₉×#121	C₂²	1	2	yes	—
22	C₂×C₁₉×#121	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#117	C₂²	1	2	yes	—
31	C₂×C₁₉×#117	C₂²	1	2	yes	—
32	C₂×C₁₉×#117	C₂²	1	2	yes	—
33	C₂×C₁₉×#117	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
36	C₁₉×#391	C₂²	1	2	yes	—
37	C₁₉×#391	C₂²	1	4	yes	—
38	C₁₉×#390	C₂²	1	1	yes	characteristic
39	C₁₉×#390	C₂²	1	1	yes	characteristic
40	C₁₉×#390	C₂²	1	2	yes	—
41	C₁₉×#390	C₂²	1	4	yes	—
42	C₁₉×#389	C₂²	1	1	yes	characteristic
43	C₁₉×#389	C₂²	1	1	yes	characteristic
44	C₁₉×#389	C₂²	1	2	yes	—
45	C₁₉×#389	C₂²	1	2	yes	—
46	C₁₉×#389	C₂²	1	2	yes	—
47	C₁₉×#389	C₂²	1	2	yes	—
48	C₁₉×#389	C₂²	1	2	yes	—
49	C₁₉×#388	C₂²	1	2	yes	—
50	C₁₉×#388	C₂²	1	2	yes	—
51	C₁₉×#388	C₂²	1	4	yes	—
52	C₁₉×#388	C₂²	1	4	yes	—
53	C₁₉×#388	C₂²	1	4	yes	—
54	C₁₉×#388	C₂²	1	4	yes	—
55	C₁₉×#388	C₂²	1	4	yes	—
56	C₁₉×#386	C₂²	1	4	yes	—
57	C₁₉×#386	C₂²	1	4	yes	—
58	C₁₉×#385	C₂²	1	4	yes	—
59	C₁₉×#385	C₂²	1	4	yes	—
60	C₁₉×#385	C₂²	1	4	yes	—
61	C₁₉×#384	C₂²	1	1	yes	characteristic
62	C₁₉×#383	C₂²	1	4	yes	—
63	C₁₉×#380	C₂²	1	2	yes	—
64	C₁₉×#380	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
67	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
68	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
69	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
72	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
75	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
79	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
81	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
82	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
83	C₄³×C₁₉	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
88	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
92	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
93	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
94	C₁₉×#124	C₂×C₄	1	32	yes	complemented
95	C₁₉×#121	C₂×C₄	1	16	yes	complemented
96	C₁₉×#121	C₂×C₄	1	16	yes	complemented
97	C₄×Q₈×C₁₉	—	4	4	no	—
98	C₄×D₄×C₁₉	—	2	4	no	—
99	C₄×D₄×C₁₉	—	2	4	no	—
100	C₄×D₄×C₁₉	—	4	4	no	—
101	C₄×D₄×C₁₉	—	4	8	no	—
102	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	complemented
103	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	complemented
104	C₁₉×#117	—	2	8	no	—
105	C₁₉×#117	—	4	4	no	—
106	C₁₉×#117	C₂×C₄	1	16	yes	complemented
107	C₁₉×#117	C₂×C₄	1	16	yes	complemented
108	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₉	—	4	4	no	—
139	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
149	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
150	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
151	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
153	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
154	C₁₉×#95	C₂³	1	2	yes	—
155	C₁₉×#95	C₂³	1	2	yes	—
156	C₁₉×#95	C₂³	1	2	yes	—
157	C₁₉×#95	C₂³	1	4	yes	—
158	C₁₉×#95	C₂³	1	2	yes	—
159	C₁₉×#95	C₂³	1	4	yes	—
160	C₁₉×#95	C₂³	1	4	yes	—
161	C₁₉×#95	C₂³	1	2	yes	—
162	C₁₉×#95	C₂³	1	4	yes	—
163	C₁₉×#95	C₂³	1	4	yes	—
164	C₁₉×#95	C₂³	1	4	yes	—
165	C₁₉×#95	C₂³	1	2	yes	—
166	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
167	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
168	C₂×Q₈×C₁₉	—	4	2	no	—
169	C₂×Q₈×C₁₉	—	4	2	no	—
170	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
171	C₂×D₄×C₁₉	—	2	2	no	—
172	C₂×D₄×C₁₉	—	2	2	no	—
173	C₂×D₄×C₁₉	—	2	2	no	—
174	C₂×D₄×C₁₉	—	2	2	no	—
175	C₂×D₄×C₁₉	—	4	4	no	—
176	C₂×D₄×C₁₉	—	4	4	no	—
177	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
178	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
179	C₂×D₄×C₁₉	C₂²×C₄	1	16	yes	—
180	C₂²×C₄×C₁₉	—	2	4	no	—
181	C₂²×C₄×C₁₉	—	2	4	no	—
182	C₂²×C₄×C₁₉	—	2	4	no	—
183	C₂²×C₄×C₁₉	—	2	4	no	—
184	C₂²×C₄×C₁₉	—	2	4	no	—
185	C₂²×C₄×C₁₉	—	2	4	no	—
186	C₂²×C₄×C₁₉	—	2	4	no	—
187	C₂²×C₄×C₁₉	—	2	8	no	—
188	C₂²×C₄×C₁₉	—	4	2	no	—
189	C₂²×C₄×C₁₉	—	4	2	no	—
190	C₂²×C₄×C₁₉	—	4	2	no	—
191	C₂²×C₄×C₁₉	—	4	4	no	—
192	C₂²×C₄×C₁₉	—	4	4	no	—
193	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
194	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
195	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
210	C₄⋊C₄×C₁₉	—	2	8	no	—
211	C₄⋊C₄×C₁₉	—	2	4	no	—
212	C₄⋊C₄×C₁₉	—	2	4	no	—
213	C₄⋊C₄×C₁₉	—	2	4	no	—
214	C₄⋊C₄×C₁₉	—	2	2	no	—
215	C₄⋊C₄×C₁₉	—	2	2	no	—
216	C₄⋊C₄×C₁₉	—	2	4	no	—
217	C₄⋊C₄×C₁₉	—	2	8	no	—
218	C₄⋊C₄×C₁₉	—	2	2	no	—
219	C₄⋊C₄×C₁₉	—	4	4	no	—
220	C₄⋊C₄×C₁₉	—	4	2	no	—
221	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
222	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
223	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
224	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
225	C₄⋊C₄×C₁₉	#41	1	4	yes	—
226	C₂²⋊C₄×C₁₉	—	2	4	no	—
227	C₂²⋊C₄×C₁₉	—	2	4	no	—
228	C₂²⋊C₄×C₁₉	—	2	4	no	—
229	C₂²⋊C₄×C₁₉	—	2	4	no	—
230	C₂²⋊C₄×C₁₉	—	2	4	no	—
231	C₂²⋊C₄×C₁₉	—	4	2	no	—
232	C₂²⋊C₄×C₁₉	—	4	4	no	—
233	C₂²⋊C₄×C₁₉	—	4	4	no	—
234	C₂²⋊C₄×C₁₉	—	4	4	no	—
235	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
236	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
237	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
238	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
239	C₄²×C₁₉	—	2	4	no	—
240	C₄²×C₁₉	—	2	2	no	—
241	C₄²×C₁₉	—	2	2	no	—
242	C₄²×C₁₉	—	2	4	no	—
243	C₄²×C₁₉	—	2	2	no	—
244	C₄²×C₁₉	—	2	2	no	—
245	C₄²×C₁₉	—	4	2	no	—
246	C₄²×C₁₉	—	4	2	no	—
247	C₄²×C₁₉	—	4	1	no	—
248	C₄²×C₁₉	—	4	4	no	—
249	C₄²×C₁₉	—	4	4	no	—
250	C₄²×C₁₉	—	4	4	no	—
251	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
252	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
253	C₄²×C₁₉	#41	1	4	yes	—
254	#34321	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂³×C₁₉	—	2	2	no	—
256	C₂³×C₁₉	—	2	2	no	—
257	C₂³×C₁₉	—	2	2	no	—
258	C₂³×C₁₉	—	2	2	no	—
259	C₂³×C₁₉	—	2	2	no	—
260	C₂³×C₁₉	—	2	2	no	—
261	C₂³×C₁₉	—	2	2	no	—
262	C₂³×C₁₉	—	2	2	no	—
263	C₂³×C₁₉	—	2	2	no	—
264	C₂³×C₁₉	—	2	2	no	—
265	C₂³×C₁₉	—	2	2	no	—
266	C₂³×C₁₉	—	2	2	no	—
267	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
268	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
269	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
270	Q₈×C₁₉	—	4	8	no	—
271	D₄×C₁₉	—	2	8	no	—
272	D₄×C₁₉	—	2	8	no	—
273	D₄×C₁₉	—	4	16	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	2	1	no	—
280	C₂×C₄×C₁₉	—	2	2	no	—
281	C₂×C₄×C₁₉	—	2	1	no	—
282	C₂×C₄×C₁₉	—	2	2	no	—
283	C₂×C₄×C₁₉	—	2	4	no	—
284	C₂×C₄×C₁₉	—	2	2	no	—
285	C₂×C₄×C₁₉	—	2	1	no	—
286	C₂×C₄×C₁₉	—	2	2	no	—
287	C₂×C₄×C₁₉	—	2	1	no	—
288	C₂×C₄×C₁₉	—	2	1	no	—
289	C₂×C₄×C₁₉	—	2	4	no	—
290	C₂×C₄×C₁₉	—	2	16	no	—
291	C₂×C₄×C₁₉	—	2	16	no	—
292	C₂×C₄×C₁₉	—	2	1	no	—
293	C₂×C₄×C₁₉	—	2	2	no	—
294	C₂×C₄×C₁₉	—	2	2	no	—
295	C₂×C₄×C₁₉	—	2	2	no	—
296	C₂×C₄×C₁₉	—	2	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	4	no	—
301	C₂×C₄×C₁₉	—	2	4	no	—
302	C₂×C₄×C₁₉	—	2	1	no	—
303	C₂×C₄×C₁₉	—	2	2	no	—
304	C₂×C₄×C₁₉	—	2	1	no	—
305	C₂×C₄×C₁₉	—	2	2	no	—
306	C₂×C₄×C₁₉	—	2	2	no	—
307	C₂×C₄×C₁₉	—	4	8	no	—
308	C₂×C₄×C₁₉	—	4	8	no	—
309	C₂×C₄×C₁₉	—	8	8	no	—
310	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
311	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
312	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
313	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
314	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
315	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
316	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
317	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
318	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
319	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
320	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
321	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
322	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
323	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
324	C₂×#555	C₂×C₁₉	1	1	yes	characteristic
325	#2369	C₂×C₁₉	1	1	yes	characteristic, complemented
326	#2367	C₂×C₁₉	1	4	yes	complemented
327	#2363	C₂×C₁₉	1	2	yes	complemented
328	#2361	C₂×C₁₉	1	2	yes	complemented
329	#2354	C₂×C₁₉	1	1	yes	characteristic, complemented
330	D₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
331	#2347	C₂×C₁₉	1	2	yes	complemented
332	#2347	C₂×C₁₉	1	2	yes	complemented
333	#2337	C₂×C₁₉	1	4	yes	complemented
334	#2324	C₂×C₁₉	1	2	yes	complemented
335	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
336	C₄×#121	C₂×C₁₉	1	2	yes	complemented
337	#2296	C₂×C₁₉	1	2	yes	complemented
338	#2293	C₂×C₁₉	1	1	yes	characteristic, complemented
339	#2274	C₂×C₁₉	1	2	yes	complemented
340	C₄²×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
341	C₂²×C₁₉	—	2	4	no	—
342	C₂²×C₁₉	—	2	4	no	—
343	C₂²×C₁₉	—	2	4	no	—
344	C₂²×C₁₉	—	2	4	no	—
345	C₂²×C₁₉	—	2	4	no	—
346	C₂²×C₁₉	—	2	4	no	—
347	C₂²×C₁₉	—	4	2	no	—
348	C₂²×C₁₉	—	4	2	no	—
349	C₂²×C₁₉	—	4	2	no	—
350	C₂²×C₁₉	—	4	2	no	—
351	C₂²×C₁₉	—	4	2	no	—
352	C₂²×C₁₉	—	4	2	no	—
353	C₂²×C₁₉	—	4	2	no	—
354	C₂²×C₁₉	—	4	2	no	—
355	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
356	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
357	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
358	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
359	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
361	C₂²×C₁₉	#585	1	1	yes	characteristic
362	C₄×C₁₉	—	2	4	no	—
363	C₄×C₁₉	—	2	4	no	—
364	C₄×C₁₉	—	2	8	no	—
365	C₄×C₁₉	—	2	2	no	—
366	C₄×C₁₉	—	2	2	no	—
367	C₄×C₁₉	—	2	2	no	—
368	C₄×C₁₉	—	2	2	no	—
369	C₄×C₁₉	—	2	4	no	—
370	C₄×C₁₉	—	4	2	no	—
371	C₄×C₁₉	—	4	2	no	—
372	C₄×C₁₉	—	4	2	no	—
373	C₄×C₁₉	—	4	1	no	—
374	C₄×C₁₉	—	4	4	no	—
375	C₄×C₁₉	C₄×#41	1	4	yes	—
376	C₄×C₁₉	#520	1	4	yes	—
377	#555	C₄×C₁₉	1	16	yes	complemented
378	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
379	C₂×#124	C₂²×C₁₉	1	4	yes	—
380	C₂×#121	C₂²×C₁₉	1	2	yes	—
381	C₂×#121	C₂²×C₁₉	1	2	yes	—
382	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
384	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
386	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
387	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
388	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
389	C₂×#117	C₂²×C₁₉	1	2	yes	—
390	C₂×#117	C₂²×C₁₉	1	2	yes	—
391	C₂×#117	C₂²×C₁₉	1	2	yes	—
392	C₂×#117	C₂²×C₁₉	1	2	yes	—
393	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
394	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
395	#391	C₂²×C₁₉	1	2	yes	—
396	#391	C₂²×C₁₉	1	4	yes	—
397	#390	C₂²×C₁₉	1	2	yes	—
398	#390	C₂²×C₁₉	1	4	yes	—
399	#390	C₂²×C₁₉	1	1	yes	characteristic
400	#390	C₂²×C₁₉	1	1	yes	characteristic
401	#389	C₂²×C₁₉	1	2	yes	—
402	#389	C₂²×C₁₉	1	2	yes	—
403	#389	C₂²×C₁₉	1	2	yes	—
404	#389	C₂²×C₁₉	1	1	yes	characteristic
405	#389	C₂²×C₁₉	1	2	yes	—
406	#389	C₂²×C₁₉	1	2	yes	—
407	#389	C₂²×C₁₉	1	1	yes	characteristic
408	#388	C₂²×C₁₉	1	4	yes	—
409	#388	C₂²×C₁₉	1	2	yes	—
410	#388	C₂²×C₁₉	1	4	yes	—
411	#388	C₂²×C₁₉	1	4	yes	—
412	#388	C₂²×C₁₉	1	4	yes	—
413	#388	C₂²×C₁₉	1	4	yes	—
414	#388	C₂²×C₁₉	1	2	yes	—
415	#386	C₂²×C₁₉	1	4	yes	—
416	#386	C₂²×C₁₉	1	4	yes	—
417	#385	C₂²×C₁₉	1	4	yes	—
418	#385	C₂²×C₁₉	1	4	yes	—
419	#385	C₂²×C₁₉	1	4	yes	—
420	#384	C₂²×C₁₉	1	1	yes	characteristic
421	#383	C₂²×C₁₉	1	4	yes	—
422	#380	C₂²×C₁₉	1	2	yes	—
423	#380	C₂²×C₁₉	1	2	yes	—
424	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
425	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
426	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
427	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
428	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
429	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
430	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
431	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
432	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
435	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
436	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
437	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
438	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
439	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
440	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
441	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
442	C₄³	C₂²×C₁₉	1	1	yes	characteristic
443	C₂×C₁₉	—	4	4	no	—
444	C₂×C₁₉	—	4	4	no	—
445	C₂×C₁₉	C₂×C₄×#41	1	1	yes	characteristic
446	C₂×C₁₉	C₂×#520	1	1	yes	characteristic
447	C₂×C₁₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂×C₁₉	#3506	1	1	yes	characteristic
449	C₂×C₁₉	#3511	1	1	yes	characteristic
450	C₂×C₁₉	#3518	1	1	yes	characteristic
451	C₂×C₁₉	#3519	1	1	yes	characteristic
452	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
453	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
454	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
455	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
456	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
457	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
458	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
459	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
460	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
461	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
462	#124	C₂×C₄×C₁₉	1	32	yes	complemented
463	#121	C₂×C₄×C₁₉	1	16	yes	complemented
464	#121	C₂×C₄×C₁₉	1	16	yes	complemented
465	C₄×Q₈	—	4	4	no	—
466	C₄×D₄	—	2	4	no	—
467	C₄×D₄	—	2	4	no	—
468	C₄×D₄	—	4	4	no	—
469	C₄×D₄	—	4	8	no	—
470	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	complemented
471	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	complemented
472	#117	—	2	8	no	—
473	#117	—	4	4	no	—
474	#117	C₂×C₄×C₁₉	1	16	yes	complemented
475	#117	C₂×C₄×C₁₉	1	16	yes	complemented
476	C₂×C₄⋊C₄	—	2	8	no	—
477	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
506	C₂×C₄²	—	4	4	no	—
507	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
508	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
510	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
512	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
513	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
514	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
515	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
516	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
517	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
518	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
519	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
520	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
522	#95	C₂³×C₁₉	1	2	yes	—
523	#95	C₂³×C₁₉	1	2	yes	—
524	#95	C₂³×C₁₉	1	2	yes	—
525	#95	C₂³×C₁₉	1	4	yes	—
526	#95	C₂³×C₁₉	1	2	yes	—
527	#95	C₂³×C₁₉	1	4	yes	—
528	#95	C₂³×C₁₉	1	4	yes	—
529	#95	C₂³×C₁₉	1	2	yes	—
530	#95	C₂³×C₁₉	1	4	yes	—
531	#95	C₂³×C₁₉	1	4	yes	—
532	#95	C₂³×C₁₉	1	4	yes	—
533	#95	C₂³×C₁₉	1	2	yes	—
534	C₁₉	#34321	1	1	yes	characteristic, direct product factor, Sylow
535	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
536	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
537	C₂×Q₈	—	4	2	no	—
538	C₂×Q₈	—	4	2	no	—
539	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂×D₄	—	4	4	no	—
546	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
547	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
548	C₂×D₄	C₂²×C₄×C₁₉	1	16	yes	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	8	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	2	no	—
560	C₂²×C₄	—	4	4	no	—
561	C₂²×C₄	—	4	4	no	—
562	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
563	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
564	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
569	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
572	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
579	C₄⋊C₄	—	2	8	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	8	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	4	4	no	—
589	C₄⋊C₄	—	4	2	no	—
590	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
591	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
592	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
593	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
594	C₄⋊C₄	#41×C₁₉	1	4	yes	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	4	2	no	—
601	C₂²⋊C₄	—	4	4	no	—
602	C₂²⋊C₄	—	4	4	no	—
603	C₂²⋊C₄	—	4	4	no	—
604	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
605	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
606	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
607	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
608	C₄²	—	2	4	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	4	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	2	no	—
614	C₄²	—	4	2	no	—
615	C₄²	—	4	2	no	—
616	C₄²	—	4	1	no	—
617	C₄²	—	4	4	no	—
618	C₄²	—	4	4	no	—
619	C₄²	—	4	4	no	—
620	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
621	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
622	C₄²	#41×C₁₉	1	4	yes	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
636	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
637	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
638	Q₈	—	4	8	no	—
639	D₄	—	2	8	no	—
640	D₄	—	2	8	no	—
641	D₄	—	4	16	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	16	no	—
659	C₂×C₄	—	2	16	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	8	no	—
677	C₂×C₄	—	8	8	no	—
678	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
679	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
680	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
681	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
682	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
683	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
684	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
685	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
686	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
687	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
688	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
689	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
690	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
691	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
692	C₂²	—	2	4	no	—
693	C₂²	—	2	4	no	—
694	C₂²	—	2	4	no	—
695	C₂²	—	2	4	no	—
696	C₂²	—	2	4	no	—
697	C₂²	—	2	4	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
707	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
708	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
709	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
710	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
711	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
712	C₂²	C₁₉×#585	1	1	yes	characteristic
713	C₄	—	2	4	no	—
714	C₄	—	2	4	no	—
715	C₄	—	2	8	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	4	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	4	no	—
726	C₄	C₄×#41×C₁₉	1	4	yes	—
727	C₄	C₁₉×#520	1	4	yes	—
728	C₂	—	4	4	no	—
729	C₂	—	4	4	no	—
730	C₂	C₂×C₄×#41×C₁₉	1	1	yes	characteristic
731	C₂	C₂×C₁₉×#520	1	1	yes	characteristic
732	C₂	C₄×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
733	C₂	C₁₉×#3506	1	1	yes	characteristic
734	C₂	C₁₉×#3511	1	1	yes	characteristic
735	C₂	C₁₉×#3518	1	1	yes	characteristic
736	C₂	C₁₉×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂×C₁₉×#555	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2369	C₂	semidirect
3. C₁₉×#2367	C₂	semidirect
4. C₁₉×#2363	C₂	semidirect
5. C₁₉×#2361	C₂	semidirect
6. C₁₉×#2354	C₂	semidirect
7. D₄×C₄⋊C₄×C₁₉	C₂	semidirect
8. C₁₉×#2347	C₂	semidirect
9. C₁₉×#2347	C₂	semidirect
10. C₁₉×#2337	C₂	semidirect
11. C₁₉×#2324	C₂	semidirect
12. C₄×C₁₉×C₄⋊Q₈	C₂	semidirect
13. C₄×C₁₉×#121	C₂	semidirect
14. C₁₉×#2296	C₂	semidirect
15. C₁₉×#2293	C₂	semidirect
16. C₁₉×#2274	C₂	semidirect
17. C₄²×D₄×C₁₉	C₂	semidirect
18. C₁₉×#555	C₄	semidirect
93. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
94. C₁₉×#124	C₂×C₄	semidirect
95. C₁₉×#121	C₂×C₄	semidirect
96. C₁₉×#121	C₂×C₄	semidirect
102. C₄×D₄×C₁₉	C₂×C₄	semidirect
103. C₄×D₄×C₁₉	C₂×C₄	semidirect
106. C₁₉×#117	C₂×C₄	semidirect
107. C₁₉×#117	C₂×C₄	semidirect
254. #34321	C₁₉	direct (N × H)
325. #2369	C₂×C₁₉	semidirect
326. #2367	C₂×C₁₉	semidirect
327. #2363	C₂×C₁₉	semidirect
328. #2361	C₂×C₁₉	semidirect
329. #2354	C₂×C₁₉	semidirect
330. D₄×C₄⋊C₄	C₂×C₁₉	semidirect
331. #2347	C₂×C₁₉	semidirect
332. #2347	C₂×C₁₉	semidirect
333. #2337	C₂×C₁₉	semidirect
334. #2324	C₂×C₁₉	semidirect
335. C₄×C₄⋊Q₈	C₂×C₁₉	semidirect
336. C₄×#121	C₂×C₁₉	semidirect
337. #2296	C₂×C₁₉	semidirect
338. #2293	C₂×C₁₉	semidirect
339. #2274	C₂×C₁₉	semidirect
340. C₄²×D₄	C₂×C₁₉	semidirect
377. #555	C₄×C₁₉	semidirect
461. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
462. #124	C₂×C₄×C₁₉	semidirect
463. #121	C₂×C₄×C₁₉	semidirect
464. #121	C₂×C₄×C₁₉	semidirect
470. C₄×D₄	C₂×C₄×C₁₉	semidirect
471. C₄×D₄	C₂×C₄×C₁₉	semidirect
474. #117	C₂×C₄×C₁₉	semidirect
475. #117	C₂×C₄×C₁₉	semidirect
534. C₁₉	#34321	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×#555	2
C₁₉×#2369	2
C₁₉×#2367	2
C₁₉×#2363	2
C₁₉×#2361	2
C₁₉×#2354	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2347	2
C₁₉×#2337	2
C₁₉×#2324	2
C₄×C₁₉×C₄⋊Q₈	2
C₄×C₁₉×#121	2
C₁₉×#2296	2
C₁₉×#2293	2
C₁₉×#2274	2
C₄²×D₄×C₁₉	2
#34321	19

Subgroups — C19×#34321 #18040280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34321 #18040280