Subgroups — C₁₉×#34736 #18040695

Order 4864.

5758 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#525	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2409	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2408	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2407	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2406	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2405	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2404	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2403	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2388	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₉×#120	C₂	1	4	yes	maximal, complemented
13	C₁₉×#2297	C₂	1	2	yes	maximal, complemented
14	C₁₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₁₉	—	2	16	no	—
16	C₂²×#41×C₁₉	—	2	8	no	—
17	C₂²×#41×C₁₉	C₂²	1	2	yes	—
18	C₂²×#41×C₁₉	C₂²	1	2	yes	—
19	C₂²×#41×C₁₉	C₂²	1	2	yes	complemented
20	C₂²×#41×C₁₉	C₂²	1	2	yes	complemented
21	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
24	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
27	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	complemented
28	C₁₉×#525	—	2	16	no	—
29	C₂×C₁₉×#123	C₂²	1	4	yes	complemented
30	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
31	C₂×C₁₉×#121	C₂²	1	4	yes	complemented
32	C₂×C₁₉×#120	C₂²	1	4	yes	—
33	C₂×C₁₉×#120	C₂²	1	4	yes	complemented
34	C₂×C₄×D₄×C₁₉	—	2	8	no	—
35	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
39	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
40	C₂×C₁₉×#117	C₂²	1	2	yes	complemented
41	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#395	C₂²	1	4	yes	complemented
46	C₁₉×#394	C₂²	1	8	yes	complemented
47	C₁₉×#394	C₂²	1	4	yes	complemented
48	C₁₉×#393	C₂²	1	4	yes	complemented
49	C₁₉×#392	C₂²	1	8	yes	complemented
50	C₁₉×#392	C₂²	1	4	yes	complemented
51	C₁₉×#391	C₂²	1	4	yes	complemented
52	C₁₉×#390	C₂²	1	4	yes	complemented
53	C₁₉×#386	C₂²	1	4	yes	—
54	C₁₉×#386	C₂²	1	4	yes	complemented
55	C₁₉×#386	C₂²	1	4	yes	complemented
56	C₁₉×#386	C₂²	1	8	yes	complemented
57	C₁₉×#385	C₂²	1	4	yes	complemented
58	C₁₉×#385	C₂²	1	8	yes	complemented
59	C₁₉×#381	C₂²	1	2	yes	complemented
60	C₁₉×#380	C₂²	1	2	yes	complemented
61	C₁₉×#380	C₂²	1	2	yes	complemented
62	C₁₉×#379	C₂²	1	2	yes	—
63	C₁₉×#379	C₂²	1	4	yes	complemented
64	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	complemented
67	C₂⁵×C₁₉	C₂³	1	2	yes	—
68	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
69	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×#41×C₁₉	—	2	128	no	—
71	C₂×#41×C₁₉	—	2	8	no	—
72	C₂×#41×C₁₉	—	2	16	no	—
73	C₂×#41×C₁₉	—	2	8	no	—
74	C₂×#41×C₁₉	—	2	8	no	—
75	C₂×#41×C₁₉	—	2	8	no	—
76	C₂×#41×C₁₉	—	2	8	no	—
77	C₂×#41×C₁₉	—	2	8	no	—
78	C₂×#41×C₁₉	—	2	8	no	—
79	C₂×#41×C₁₉	—	2	16	no	—
80	C₂×#41×C₁₉	D₄	1	16	yes	complemented
81	C₂²×Q₈×C₁₉	—	2	8	no	—
82	C₂²×Q₈×C₁₉	—	2	4	no	—
83	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
84	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₉	—	2	4	no	—
86	C₂²×D₄×C₁₉	—	2	8	no	—
87	C₂²×D₄×C₁₉	—	2	16	no	—
88	C₂²×D₄×C₁₉	—	2	8	no	—
89	C₂²×D₄×C₁₉	—	2	8	no	—
90	C₂²×D₄×C₁₉	—	2	4	no	—
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	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
95	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
96	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₁₉	—	2	8	no	—
99	C₂³×C₄×C₁₉	—	2	8	no	—
100	C₂³×C₄×C₁₉	—	2	16	no	—
101	C₂³×C₄×C₁₉	—	2	4	no	—
102	C₂³×C₄×C₁₉	—	2	8	no	—
103	C₂³×C₄×C₁₉	D₄	1	8	yes	complemented
104	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
106	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
116	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
118	C₁₉×#123	—	2	16	no	—
119	C₁₉×C₂²⋊Q₈	—	2	16	no	—
120	C₁₉×#121	—	2	16	no	—
121	C₁₉×#120	—	2	16	no	—
122	C₁₉×#120	—	2	16	no	—
123	C₄×D₄×C₁₉	—	2	8	no	—
124	C₄×D₄×C₁₉	—	2	8	no	—
125	C₄×D₄×C₁₉	—	2	8	no	—
126	C₄×D₄×C₁₉	—	2	8	no	—
127	C₄×D₄×C₁₉	—	2	32	no	—
128	C₁₉×#117	—	2	8	no	—
129	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
130	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
133	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
138	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
141	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	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	4	yes	—
146	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
147	C₂×C₄²×C₁₉	—	2	4	no	—
148	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
151	C₁₉×#95	C₂³	1	4	yes	—
152	C₁₉×#95	C₂³	1	4	yes	—
153	C₁₉×#95	C₂³	1	8	yes	—
154	C₁₉×#95	C₂³	1	8	yes	—
155	C₂⁴×C₁₉	—	2	2	no	—
156	C₂⁴×C₁₉	—	2	8	no	—
157	C₂⁴×C₁₉	—	2	4	no	—
158	C₂⁴×C₁₉	—	2	4	no	—
159	C₂⁴×C₁₉	—	2	4	no	—
160	C₂⁴×C₁₉	—	2	4	no	—
161	C₂⁴×C₁₉	—	2	4	no	—
162	C₂⁴×C₁₉	—	2	8	no	—
163	C₂⁴×C₁₉	—	4	2	no	—
164	C₂⁴×C₁₉	—	4	2	no	—
165	C₂⁴×C₁₉	—	4	4	no	—
166	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
167	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
168	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
169	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
170	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
171	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
172	#41×C₁₉	—	2	64	no	—
173	#41×C₁₉	—	2	64	no	—
174	#41×C₁₉	—	2	64	no	—
175	#41×C₁₉	—	2	64	no	—
176	C₂×Q₈×C₁₉	—	2	32	no	—
177	C₂×Q₈×C₁₉	—	2	8	no	—
178	C₂×Q₈×C₁₉	—	2	4	no	—
179	C₂×Q₈×C₁₉	—	2	4	no	—
180	C₂×Q₈×C₁₉	—	2	4	no	—
181	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	complemented
182	C₂×D₄×C₁₉	—	2	32	no	—
183	C₂×D₄×C₁₉	—	2	64	no	—
184	C₂×D₄×C₁₉	—	2	32	no	—
185	C₂×D₄×C₁₉	—	2	4	no	—
186	C₂×D₄×C₁₉	—	2	4	no	—
187	C₂×D₄×C₁₉	—	2	8	no	—
188	C₂×D₄×C₁₉	—	2	8	no	—
189	C₂×D₄×C₁₉	—	2	8	no	—
190	C₂×D₄×C₁₉	—	2	8	no	—
191	C₂×D₄×C₁₉	—	2	8	no	—
192	C₂×D₄×C₁₉	—	2	4	no	—
193	C₂×D₄×C₁₉	—	2	4	no	—
194	C₂×D₄×C₁₉	—	2	16	no	—
195	C₂×D₄×C₁₉	—	2	16	no	—
196	C₂×D₄×C₁₉	—	2	8	no	—
197	C₂×D₄×C₁₉	—	2	4	no	—
198	C₂×D₄×C₁₉	—	2	4	no	—
199	C₂×D₄×C₁₉	—	2	4	no	—
200	C₂×D₄×C₁₉	—	2	4	no	—
201	C₂×D₄×C₁₉	—	4	8	no	—
202	C₂×D₄×C₁₉	C₂×D₄	1	16	yes	—
203	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	complemented
204	C₂×D₄×C₁₉	#41	1	8	yes	complemented
205	C₂²×C₄×C₁₉	—	2	64	no	—
206	C₂²×C₄×C₁₉	—	2	2	no	—
207	C₂²×C₄×C₁₉	—	2	4	no	—
208	C₂²×C₄×C₁₉	—	2	8	no	—
209	C₂²×C₄×C₁₉	—	2	4	no	—
210	C₂²×C₄×C₁₉	—	2	32	no	—
211	C₂²×C₄×C₁₉	—	2	4	no	—
212	C₂²×C₄×C₁₉	—	2	8	no	—
213	C₂²×C₄×C₁₉	—	2	4	no	—
214	C₂²×C₄×C₁₉	—	2	8	no	—
215	C₂²×C₄×C₁₉	—	2	8	no	—
216	C₂²×C₄×C₁₉	—	2	4	no	—
217	C₂²×C₄×C₁₉	—	2	4	no	—
218	C₂²×C₄×C₁₉	—	2	8	no	—
219	C₂²×C₄×C₁₉	—	2	8	no	—
220	C₂²×C₄×C₁₉	—	2	4	no	—
221	C₂²×C₄×C₁₉	—	2	2	no	—
222	C₂²×C₄×C₁₉	—	2	2	no	—
223	C₂²×C₄×C₁₉	—	2	4	no	—
224	C₂²×C₄×C₁₉	—	2	4	no	—
225	C₂²×C₄×C₁₉	—	2	8	no	—
226	C₂²×C₄×C₁₉	—	2	4	no	—
227	C₂²×C₄×C₁₉	—	2	8	no	—
228	C₂²×C₄×C₁₉	—	4	2	no	—
229	C₂²×C₄×C₁₉	—	4	16	no	—
230	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
231	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
236	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
237	C₂²×C₄×C₁₉	C₂×D₄	1	16	yes	complemented
238	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
240	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	2	16	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	16	no	—
255	C₂²⋊C₄×C₁₉	—	2	8	no	—
256	C₂²⋊C₄×C₁₉	—	2	4	no	—
257	C₂²⋊C₄×C₁₉	—	2	4	no	—
258	C₂²⋊C₄×C₁₉	—	2	16	no	—
259	C₂²⋊C₄×C₁₉	—	2	16	no	—
260	C₂²⋊C₄×C₁₉	—	4	8	no	—
261	C₂²⋊C₄×C₁₉	—	4	4	no	—
262	C₄²×C₁₉	—	2	4	no	—
263	C₄²×C₁₉	—	2	4	no	—
264	C₄²×C₁₉	—	2	8	no	—
265	#34736	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂³×C₁₉	—	2	2	no	—
267	C₂³×C₁₉	—	2	2	no	—
268	C₂³×C₁₉	—	2	2	no	—
269	C₂³×C₁₉	—	2	2	no	—
270	C₂³×C₁₉	—	2	16	no	—
271	C₂³×C₁₉	—	2	8	no	—
272	C₂³×C₁₉	—	2	8	no	—
273	C₂³×C₁₉	—	2	8	no	—
274	C₂³×C₁₉	—	2	2	no	—
275	C₂³×C₁₉	—	2	4	no	—
276	C₂³×C₁₉	—	2	4	no	—
277	C₂³×C₁₉	—	2	4	no	—
278	C₂³×C₁₉	—	2	2	no	—
279	C₂³×C₁₉	—	2	8	no	—
280	C₂³×C₁₉	—	2	2	no	—
281	C₂³×C₁₉	—	2	2	no	—
282	C₂³×C₁₉	—	2	2	no	—
283	C₂³×C₁₉	—	2	8	no	—
284	C₂³×C₁₉	—	2	4	no	—
285	C₂³×C₁₉	—	4	4	no	—
286	C₂³×C₁₉	—	4	16	no	—
287	C₂³×C₁₉	—	4	32	no	—
288	C₂³×C₁₉	—	4	16	no	—
289	C₂³×C₁₉	—	4	4	no	—
290	C₂³×C₁₉	—	4	8	no	—
291	C₂³×C₁₉	—	4	4	no	—
292	C₂³×C₁₉	—	4	8	no	—
293	C₂³×C₁₉	C₂²×D₄	1	8	yes	—
294	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
295	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
296	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
297	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
298	C₂³×C₁₉	C₂×#41	1	4	yes	—
299	C₂³×C₁₉	C₂×#41	1	4	yes	complemented
300	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
301	Q₈×C₁₉	—	2	16	no	—
302	Q₈×C₁₉	—	2	16	no	—
303	D₄×C₁₉	—	2	16	no	—
304	D₄×C₁₉	—	2	32	no	—
305	D₄×C₁₉	—	2	16	no	—
306	D₄×C₁₉	—	2	32	no	—
307	D₄×C₁₉	—	2	16	no	—
308	D₄×C₁₉	—	2	16	no	—
309	D₄×C₁₉	—	4	32	no	—
310	C₂×C₄×C₁₉	—	2	16	no	—
311	C₂×C₄×C₁₉	—	2	32	no	—
312	C₂×C₄×C₁₉	—	2	8	no	—
313	C₂×C₄×C₁₉	—	2	8	no	—
314	C₂×C₄×C₁₉	—	2	2	no	—
315	C₂×C₄×C₁₉	—	2	2	no	—
316	C₂×C₄×C₁₉	—	2	4	no	—
317	C₂×C₄×C₁₉	—	2	4	no	—
318	C₂×C₄×C₁₉	—	2	2	no	—
319	C₂×C₄×C₁₉	—	2	2	no	—
320	C₂×C₄×C₁₉	—	2	8	no	—
321	C₂×C₄×C₁₉	—	2	8	no	—
322	C₂×C₄×C₁₉	—	2	8	no	—
323	C₂×C₄×C₁₉	—	2	8	no	—
324	C₂×C₄×C₁₉	—	2	32	no	—
325	C₂×C₄×C₁₉	—	2	2	no	—
326	C₂×C₄×C₁₉	—	2	8	no	—
327	C₂×C₄×C₁₉	—	2	2	no	—
328	C₂×C₄×C₁₉	—	2	4	no	—
329	C₂×C₄×C₁₉	—	2	8	no	—
330	C₂×C₄×C₁₉	—	2	4	no	—
331	C₂×C₄×C₁₉	—	2	8	no	—
332	C₂×C₄×C₁₉	—	4	4	no	—
333	C₂×C₄×C₁₉	—	4	4	no	—
334	C₂×C₄×C₁₉	—	4	8	no	—
335	C₂×C₄×C₁₉	—	4	8	no	—
336	C₂×C₄×C₁₉	#120	1	16	yes	complemented
337	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
339	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
342	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₁₉	C₂×#41	1	4	yes	complemented
345	C₂³×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
346	C₂×#525	C₂×C₁₉	1	2	yes	complemented
347	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
348	#2409	C₂×C₁₉	1	2	yes	complemented
349	#2408	C₂×C₁₉	1	2	yes	complemented
350	#2407	C₂×C₁₉	1	4	yes	complemented
351	#2406	C₂×C₁₉	1	2	yes	complemented
352	#2405	C₂×C₁₉	1	2	yes	complemented
353	#2404	C₂×C₁₉	1	2	yes	complemented
354	#2403	C₂×C₁₉	1	2	yes	complemented
355	#2388	C₂×C₁₉	1	4	yes	complemented
356	C₄×#120	C₂×C₁₉	1	4	yes	complemented
357	#2297	C₂×C₁₉	1	2	yes	complemented
358	#2280	C₂×C₁₉	1	1	yes	characteristic, complemented
359	C₂²×C₁₉	—	2	2	no	—
360	C₂²×C₁₉	—	2	2	no	—
361	C₂²×C₁₉	—	2	2	no	—
362	C₂²×C₁₉	—	2	2	no	—
363	C₂²×C₁₉	—	2	8	no	—
364	C₂²×C₁₉	—	2	8	no	—
365	C₂²×C₁₉	—	2	8	no	—
366	C₂²×C₁₉	—	2	2	no	—
367	C₂²×C₁₉	—	2	2	no	—
368	C₂²×C₁₉	—	2	4	no	—
369	C₂²×C₁₉	—	2	2	no	—
370	C₂²×C₁₉	—	2	8	no	—
371	C₂²×C₁₉	—	2	16	no	—
372	C₂²×C₁₉	—	4	16	no	—
373	C₂²×C₁₉	—	4	32	no	—
374	C₂²×C₁₉	—	4	16	no	—
375	C₂²×C₁₉	—	4	2	no	—
376	C₂²×C₁₉	—	4	4	no	—
377	C₂²×C₁₉	—	4	2	no	—
378	C₂²×C₁₉	—	4	4	no	—
379	C₂²×C₁₉	—	4	4	no	—
380	C₂²×C₁₉	—	4	8	no	—
381	C₂²×C₁₉	—	4	4	no	—
382	C₂²×C₁₉	C₂×#120	1	4	yes	—
383	C₂²×C₁₉	#525	1	4	yes	complemented
384	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
385	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
386	C₂²×C₁₉	C₂²×#41	1	2	yes	—
387	C₂²×C₁₉	#585	1	2	yes	—
388	C₄×C₁₉	—	2	2	no	—
389	C₄×C₁₉	—	2	8	no	—
390	C₄×C₁₉	—	2	2	no	—
391	C₄×C₁₉	—	2	4	no	—
392	C₄×C₁₉	—	4	2	no	—
393	C₄×C₁₉	—	4	2	no	—
394	C₄×C₁₉	—	4	8	no	—
395	C₄×C₁₉	C₂×#120	1	4	yes	—
396	C₄×C₁₉	C₂×#120	1	4	yes	—
397	C₂²×#41	—	2	16	no	—
398	C₂²×#41	—	2	8	no	—
399	C₂²×#41	C₂²×C₁₉	1	2	yes	—
400	C₂²×#41	C₂²×C₁₉	1	2	yes	—
401	C₂²×#41	C₂²×C₁₉	1	2	yes	complemented
402	C₂²×#41	C₂²×C₁₉	1	2	yes	complemented
403	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
404	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
405	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
406	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
407	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
408	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	complemented
409	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
410	#525	—	2	16	no	—
411	C₂×#123	C₂²×C₁₉	1	4	yes	complemented
412	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
413	C₂×#121	C₂²×C₁₉	1	4	yes	complemented
414	C₂×#120	C₂²×C₁₉	1	4	yes	—
415	C₂×#120	C₂²×C₁₉	1	4	yes	complemented
416	C₂×C₄×D₄	—	2	8	no	—
417	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
419	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	complemented
420	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
421	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	complemented
422	C₂×#117	C₂²×C₁₉	1	2	yes	complemented
423	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
424	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
425	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
426	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
427	#395	C₂²×C₁₉	1	4	yes	complemented
428	#394	C₂²×C₁₉	1	8	yes	complemented
429	#394	C₂²×C₁₉	1	4	yes	complemented
430	#393	C₂²×C₁₉	1	4	yes	complemented
431	#392	C₂²×C₁₉	1	8	yes	complemented
432	#392	C₂²×C₁₉	1	4	yes	complemented
433	#391	C₂²×C₁₉	1	4	yes	complemented
434	#390	C₂²×C₁₉	1	4	yes	complemented
435	#386	C₂²×C₁₉	1	4	yes	—
436	#386	C₂²×C₁₉	1	4	yes	complemented
437	#386	C₂²×C₁₉	1	4	yes	complemented
438	#386	C₂²×C₁₉	1	8	yes	complemented
439	#385	C₂²×C₁₉	1	4	yes	complemented
440	#385	C₂²×C₁₉	1	8	yes	complemented
441	#381	C₂²×C₁₉	1	2	yes	complemented
442	#380	C₂²×C₁₉	1	2	yes	complemented
443	#380	C₂²×C₁₉	1	2	yes	complemented
444	#379	C₂²×C₁₉	1	2	yes	—
445	#379	C₂²×C₁₉	1	4	yes	complemented
446	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	complemented
447	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	complemented
448	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	complemented
449	C₂×C₁₉	—	2	4	no	—
450	C₂×C₁₉	—	2	4	no	—
451	C₂×C₁₉	—	4	2	no	—
452	C₂×C₁₉	—	4	8	no	—
453	C₂×C₁₉	—	4	4	no	—
454	C₂×C₁₉	C₂²×#120	1	1	yes	characteristic
455	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
456	C₂×C₁₉	#3449	1	1	yes	characteristic
457	C₂×C₁₉	D₄×#41	1	4	yes	—
458	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
459	C₂⁵	C₂³×C₁₉	1	2	yes	—
460	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
461	C₂×#41	—	2	128	no	—
462	C₂×#41	—	2	8	no	—
463	C₂×#41	—	2	16	no	—
464	C₂×#41	—	2	8	no	—
465	C₂×#41	—	2	8	no	—
466	C₂×#41	—	2	8	no	—
467	C₂×#41	—	2	8	no	—
468	C₂×#41	—	2	8	no	—
469	C₂×#41	—	2	8	no	—
470	C₂×#41	—	2	16	no	—
471	C₂×#41	D₄×C₁₉	1	16	yes	complemented
472	C₂²×Q₈	—	2	8	no	—
473	C₂²×Q₈	—	2	4	no	—
474	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
475	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
476	C₂²×D₄	—	2	4	no	—
477	C₂²×D₄	—	2	8	no	—
478	C₂²×D₄	—	2	16	no	—
479	C₂²×D₄	—	2	8	no	—
480	C₂²×D₄	—	2	8	no	—
481	C₂²×D₄	—	2	4	no	—
482	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
483	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
484	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
485	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
486	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
487	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
488	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
489	C₂³×C₄	—	2	8	no	—
490	C₂³×C₄	—	2	8	no	—
491	C₂³×C₄	—	2	16	no	—
492	C₂³×C₄	—	2	4	no	—
493	C₂³×C₄	—	2	8	no	—
494	C₂³×C₄	D₄×C₁₉	1	8	yes	complemented
495	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
498	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
499	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
500	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
501	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
506	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
507	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
509	#123	—	2	16	no	—
510	C₂²⋊Q₈	—	2	16	no	—
511	#121	—	2	16	no	—
512	#120	—	2	16	no	—
513	#120	—	2	16	no	—
514	C₄×D₄	—	2	8	no	—
515	C₄×D₄	—	2	8	no	—
516	C₄×D₄	—	2	8	no	—
517	C₄×D₄	—	2	8	no	—
518	C₄×D₄	—	2	32	no	—
519	#117	—	2	8	no	—
520	C₂×C₄⋊C₄	—	2	4	no	—
521	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
525	C₂×C₂²⋊C₄	—	2	4	no	—
526	C₂×C₂²⋊C₄	—	2	4	no	—
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	8	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
538	C₂×C₄²	—	2	4	no	—
539	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
540	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
541	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
542	#95	C₂³×C₁₉	1	4	yes	—
543	#95	C₂³×C₁₉	1	4	yes	—
544	#95	C₂³×C₁₉	1	8	yes	—
545	#95	C₂³×C₁₉	1	8	yes	—
546	C₁₉	#34736	1	1	yes	characteristic, direct product factor, Sylow
547	C₂⁴	—	2	2	no	—
548	C₂⁴	—	2	8	no	—
549	C₂⁴	—	2	4	no	—
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	2	4	no	—
553	C₂⁴	—	2	4	no	—
554	C₂⁴	—	2	8	no	—
555	C₂⁴	—	4	2	no	—
556	C₂⁴	—	4	2	no	—
557	C₂⁴	—	4	4	no	—
558	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
559	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
560	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
561	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
562	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
563	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
564	#41	—	2	64	no	—
565	#41	—	2	64	no	—
566	#41	—	2	64	no	—
567	#41	—	2	64	no	—
568	C₂×Q₈	—	2	32	no	—
569	C₂×Q₈	—	2	8	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	2	4	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	complemented
574	C₂×D₄	—	2	32	no	—
575	C₂×D₄	—	2	64	no	—
576	C₂×D₄	—	2	32	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	8	no	—
580	C₂×D₄	—	2	8	no	—
581	C₂×D₄	—	2	8	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	8	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	16	no	—
587	C₂×D₄	—	2	16	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	4	8	no	—
594	C₂×D₄	C₂×D₄×C₁₉	1	16	yes	—
595	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	complemented
596	C₂×D₄	#41×C₁₉	1	8	yes	complemented
597	C₂²×C₄	—	2	64	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	8	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	32	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	8	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	8	no	—
607	C₂²×C₄	—	2	8	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	8	no	—
611	C₂²×C₄	—	2	8	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	8	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	8	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	—	4	16	no	—
622	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
623	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
624	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
625	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
626	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
627	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
628	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
629	C₂²×C₄	C₂×D₄×C₁₉	1	16	yes	complemented
630	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
635	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	8	no	—
642	C₄⋊C₄	—	2	16	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	8	no	—
646	C₂²⋊C₄	—	2	16	no	—
647	C₂²⋊C₄	—	2	8	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	16	no	—
651	C₂²⋊C₄	—	2	16	no	—
652	C₂²⋊C₄	—	4	8	no	—
653	C₂²⋊C₄	—	4	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	8	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	16	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	8	no	—
664	C₂³	—	2	8	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	8	no	—
675	C₂³	—	2	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	16	no	—
678	C₂³	—	4	32	no	—
679	C₂³	—	4	16	no	—
680	C₂³	—	4	4	no	—
681	C₂³	—	4	8	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	4	8	no	—
684	C₂³	C₂²×D₄×C₁₉	1	8	yes	—
685	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
686	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
687	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
688	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
689	C₂³	C₂×#41×C₁₉	1	4	yes	—
690	C₂³	C₂×#41×C₁₉	1	4	yes	complemented
691	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
692	Q₈	—	2	16	no	—
693	Q₈	—	2	16	no	—
694	D₄	—	2	32	no	—
695	D₄	—	2	16	no	—
696	D₄	—	2	16	no	—
697	D₄	—	2	32	no	—
698	D₄	—	2	16	no	—
699	D₄	—	2	16	no	—
700	D₄	—	4	32	no	—
701	C₂×C₄	—	2	16	no	—
702	C₂×C₄	—	2	32	no	—
703	C₂×C₄	—	2	8	no	—
704	C₂×C₄	—	2	8	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	2	no	—
711	C₂×C₄	—	2	8	no	—
712	C₂×C₄	—	2	8	no	—
713	C₂×C₄	—	2	8	no	—
714	C₂×C₄	—	2	8	no	—
715	C₂×C₄	—	2	32	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	8	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	8	no	—
723	C₂×C₄	—	4	4	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	8	no	—
726	C₂×C₄	—	4	8	no	—
727	C₂×C₄	C₁₉×#120	1	16	yes	complemented
728	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
730	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
733	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
735	C₂×C₄	C₂×#41×C₁₉	1	4	yes	complemented
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	8	no	—
741	C₂²	—	2	8	no	—
742	C₂²	—	2	8	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	8	no	—
748	C₂²	—	2	16	no	—
749	C₂²	—	4	16	no	—
750	C₂²	—	4	32	no	—
751	C₂²	—	4	16	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	4	8	no	—
758	C₂²	—	4	4	no	—
759	C₂²	C₂×C₁₉×#120	1	4	yes	—
760	C₂²	C₁₉×#525	1	4	yes	complemented
761	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
762	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
763	C₂²	C₂²×#41×C₁₉	1	2	yes	—
764	C₂²	C₁₉×#585	1	2	yes	—
765	C₄	—	2	2	no	—
766	C₄	—	2	8	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	4	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	8	no	—
772	C₄	C₂×C₁₉×#120	1	4	yes	—
773	C₄	C₂×C₁₉×#120	1	4	yes	—
774	C₂	—	2	4	no	—
775	C₂	—	2	4	no	—
776	C₂	—	4	2	no	—
777	C₂	—	4	8	no	—
778	C₂	—	4	4	no	—
779	C₂	C₂²×C₁₉×#120	1	1	yes	characteristic
780	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
781	C₂	C₁₉×#3449	1	1	yes	characteristic
782	C₂	D₄×#41×C₁₉	1	4	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. C₂³×#41×C₁₉	C₂	semidirect
2. C₂×C₁₉×#525	C₂	semidirect
3. C₂²×C₄×D₄×C₁₉	C₂	semidirect
4. C₁₉×#2409	C₂	semidirect
5. C₁₉×#2408	C₂	semidirect
6. C₁₉×#2407	C₂	semidirect
7. C₁₉×#2406	C₂	semidirect
8. C₁₉×#2405	C₂	semidirect
9. C₁₉×#2404	C₂	semidirect
10. C₁₉×#2403	C₂	semidirect
11. C₁₉×#2388	C₂	semidirect
12. C₄×C₁₉×#120	C₂	semidirect
13. C₁₉×#2297	C₂	semidirect
14. C₁₉×#2280	C₂	semidirect
19. C₂²×#41×C₁₉	C₂²	semidirect
20. C₂²×#41×C₁₉	C₂²	semidirect
21. C₂³×Q₈×C₁₉	C₂²	semidirect
24. C₂³×D₄×C₁₉	C₂²	semidirect
26. C₂⁴×C₄×C₁₉	C₂²	semidirect
27. C₂⁴×C₄×C₁₉	C₂²	semidirect
29. C₂×C₁₉×#123	C₂²	semidirect
30. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₁₉×#121	C₂²	semidirect
33. C₂×C₁₉×#120	C₂²	semidirect
37. C₂×C₄×D₄×C₁₉	C₂²	semidirect
38. C₂×C₄×D₄×C₁₉	C₂²	semidirect
39. C₂×C₄×D₄×C₁₉	C₂²	semidirect
40. C₂×C₁₉×#117	C₂²	semidirect
41. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
44. C₂²×C₄²×C₁₉	C₂²	semidirect
45. C₁₉×#395	C₂²	semidirect
46. C₁₉×#394	C₂²	semidirect
47. C₁₉×#394	C₂²	semidirect
48. C₁₉×#393	C₂²	semidirect
49. C₁₉×#392	C₂²	semidirect
50. C₁₉×#392	C₂²	semidirect
51. C₁₉×#391	C₂²	semidirect
52. C₁₉×#390	C₂²	semidirect
54. C₁₉×#386	C₂²	semidirect
55. C₁₉×#386	C₂²	semidirect
56. C₁₉×#386	C₂²	semidirect
57. C₁₉×#385	C₂²	semidirect
58. C₁₉×#385	C₂²	semidirect
59. C₁₉×#381	C₂²	semidirect
60. C₁₉×#380	C₂²	semidirect
61. C₁₉×#380	C₂²	semidirect
63. C₁₉×#379	C₂²	semidirect
64. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
65. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
66. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
80. C₂×#41×C₁₉	D₄	semidirect
103. C₂³×C₄×C₁₉	D₄	semidirect
181. C₂×Q₈×C₁₉	C₂×D₄	semidirect
203. C₂×D₄×C₁₉	C₂×D₄	semidirect
204. C₂×D₄×C₁₉	#41	semidirect
237. C₂²×C₄×C₁₉	C₂×D₄	semidirect
265. #34736	C₁₉	direct (N × H)
299. C₂³×C₁₉	C₂×#41	semidirect
336. C₂×C₄×C₁₉	#120	semidirect
344. C₂×C₄×C₁₉	C₂×#41	semidirect
345. C₂³×#41	C₂×C₁₉	semidirect
346. C₂×#525	C₂×C₁₉	semidirect
347. C₂²×C₄×D₄	C₂×C₁₉	semidirect
348. #2409	C₂×C₁₉	semidirect
349. #2408	C₂×C₁₉	semidirect
350. #2407	C₂×C₁₉	semidirect
351. #2406	C₂×C₁₉	semidirect
352. #2405	C₂×C₁₉	semidirect
353. #2404	C₂×C₁₉	semidirect
354. #2403	C₂×C₁₉	semidirect
355. #2388	C₂×C₁₉	semidirect
356. C₄×#120	C₂×C₁₉	semidirect
357. #2297	C₂×C₁₉	semidirect
358. #2280	C₂×C₁₉	semidirect
383. C₂²×C₁₉	#525	semidirect
401. C₂²×#41	C₂²×C₁₉	semidirect
402. C₂²×#41	C₂²×C₁₉	semidirect
403. C₂³×Q₈	C₂²×C₁₉	semidirect
406. C₂³×D₄	C₂²×C₁₉	semidirect
408. C₂⁴×C₄	C₂²×C₁₉	semidirect
409. C₂⁴×C₄	C₂²×C₁₉	semidirect
411. C₂×#123	C₂²×C₁₉	semidirect
412. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
413. C₂×#121	C₂²×C₁₉	semidirect
415. C₂×#120	C₂²×C₁₉	semidirect
419. C₂×C₄×D₄	C₂²×C₁₉	semidirect
420. C₂×C₄×D₄	C₂²×C₁₉	semidirect
421. C₂×C₄×D₄	C₂²×C₁₉	semidirect
422. C₂×#117	C₂²×C₁₉	semidirect
423. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
425. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
426. C₂²×C₄²	C₂²×C₁₉	semidirect
427. #395	C₂²×C₁₉	semidirect
428. #394	C₂²×C₁₉	semidirect
429. #394	C₂²×C₁₉	semidirect
430. #393	C₂²×C₁₉	semidirect
431. #392	C₂²×C₁₉	semidirect
432. #392	C₂²×C₁₉	semidirect
433. #391	C₂²×C₁₉	semidirect
434. #390	C₂²×C₁₉	semidirect
436. #386	C₂²×C₁₉	semidirect
437. #386	C₂²×C₁₉	semidirect
438. #386	C₂²×C₁₉	semidirect
439. #385	C₂²×C₁₉	semidirect
440. #385	C₂²×C₁₉	semidirect
441. #381	C₂²×C₁₉	semidirect
442. #380	C₂²×C₁₉	semidirect
443. #380	C₂²×C₁₉	semidirect
445. #379	C₂²×C₁₉	semidirect
446. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
447. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
448. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
471. C₂×#41	D₄×C₁₉	semidirect
494. C₂³×C₄	D₄×C₁₉	semidirect
546. C₁₉	#34736	direct (N × H)
573. C₂×Q₈	C₂×D₄×C₁₉	semidirect
595. C₂×D₄	C₂×D₄×C₁₉	semidirect
596. C₂×D₄	#41×C₁₉	semidirect
629. C₂²×C₄	C₂×D₄×C₁₉	semidirect
690. C₂³	C₂×#41×C₁₉	semidirect
727. C₂×C₄	C₁₉×#120	semidirect
735. C₂×C₄	C₂×#41×C₁₉	semidirect
760. C₂²	C₁₉×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₁₉	2
C₂×C₁₉×#525	2
C₂²×C₄×D₄×C₁₉	2
C₁₉×#2409	2
C₁₉×#2408	2
C₁₉×#2407	2
C₁₉×#2406	2
C₁₉×#2405	2
C₁₉×#2404	2
C₁₉×#2403	2
C₁₉×#2388	2
C₄×C₁₉×#120	2
C₁₉×#2297	2
C₁₉×#2280	2
#34736	19

Subgroups — C19×#34736 #18040695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34736 #18040695