Subgroups — C₁₉×#11089 #18017048

Order 4864.

1154 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#99	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#99	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₉×#99	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2315	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#99	—	2	2	no	—
16	C₂×C₁₉×#99	—	2	2	no	—
17	C₂×C₁₉×#99	—	2	2	no	—
18	C₂×C₁₉×#99	—	2	2	no	—
19	C₂×C₁₉×#99	—	2	2	no	—
20	C₂×C₁₉×#99	—	2	2	no	—
21	C₂×C₁₉×#99	—	2	2	no	—
22	C₂×C₁₉×#99	—	2	2	no	—
23	C₂×C₁₉×#99	C₄	1	4	yes	complemented
24	C₁₉×#385	—	2	2	no	—
25	C₁₉×#385	—	2	2	no	—
26	C₁₉×#380	—	2	2	no	—
27	C₁₉×#342	—	2	2	no	—
28	C₁₉×#342	—	2	2	no	—
29	C₁₉×#342	—	2	2	no	—
30	C₂⁵×C₁₉	Q₈	1	1	yes	characteristic
31	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	1	no	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₉	D₄	1	2	yes	—
46	C₂³×C₄×C₁₉	—	2	1	no	—
47	C₂³×C₄×C₁₉	—	2	1	no	—
48	C₂³×C₄×C₁₉	—	2	1	no	—
49	C₂³×C₄×C₁₉	—	2	1	no	—
50	C₂³×C₄×C₁₉	—	2	1	no	—
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	Q₈	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
88	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
90	C₁₉×#99	—	2	8	no	—
91	C₁₉×#99	—	2	8	no	—
92	C₁₉×#99	—	2	8	no	—
93	C₁₉×#95	—	2	4	no	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	C₂⁴×C₁₉	—	2	1	no	—
96	C₂⁴×C₁₉	—	2	1	no	—
97	C₂⁴×C₁₉	—	2	1	no	—
98	C₂⁴×C₁₉	—	2	1	no	—
99	C₂⁴×C₁₉	—	2	1	no	—
100	C₂⁴×C₁₉	—	8	2	no	—
101	C₂⁴×C₁₉	—	8	2	no	—
102	C₂⁴×C₁₉	C₄⋊C₄	1	2	yes	complemented
103	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
112	C₂⁴×C₁₉	#41	1	1	yes	characteristic
113	C₂⁴×C₁₉	#41	1	1	yes	characteristic
114	C₂⁴×C₁₉	#41	1	1	yes	characteristic
115	C₂⁴×C₁₉	#41	1	1	yes	characteristic
116	C₂⁴×C₁₉	#41	1	1	yes	characteristic
117	C₂⁴×C₁₉	#41	1	1	yes	characteristic
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	2	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	—	4	1	no	—
132	C₂×D₄×C₁₉	—	4	1	no	—
133	C₂×D₄×C₁₉	—	4	1	no	—
134	C₂×D₄×C₁₉	—	4	1	no	—
135	C₂×D₄×C₁₉	—	4	1	no	—
136	C₂×D₄×C₁₉	—	4	1	no	—
137	C₂×D₄×C₁₉	—	4	1	no	—
138	C₂×D₄×C₁₉	—	4	1	no	—
139	C₂×D₄×C₁₉	—	4	1	no	—
140	C₂×D₄×C₁₉	—	4	1	no	—
141	C₂×D₄×C₁₉	—	4	1	no	—
142	C₂×D₄×C₁₉	—	4	1	no	—
143	C₂×D₄×C₁₉	—	4	1	no	—
144	C₂×D₄×C₁₉	—	4	1	no	—
145	C₂×D₄×C₁₉	—	4	1	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	4	1	no	—
161	C₂²×C₄×C₁₉	—	4	1	no	—
162	C₂²×C₄×C₁₉	—	4	1	no	—
163	C₂²×C₄×C₁₉	—	4	1	no	—
164	C₂²×C₄×C₁₉	—	4	1	no	—
165	C₂²×C₄×C₁₉	—	4	1	no	—
166	C₂²×C₄×C₁₉	—	4	1	no	—
167	C₂²×C₄×C₁₉	—	4	1	no	—
168	C₂²×C₄×C₁₉	—	4	1	no	—
169	C₂²×C₄×C₁₉	—	4	1	no	—
170	C₂²×C₄×C₁₉	—	8	2	no	—
171	C₂²×C₄×C₁₉	—	8	2	no	—
172	C₂²×C₄×C₁₉	—	8	2	no	—
173	C₂²×C₄×C₁₉	—	8	2	no	—
174	C₂²×C₄×C₁₉	—	8	2	no	—
175	C₂²×C₄×C₁₉	—	8	2	no	—
176	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	complemented
177	C₄⋊C₄×C₁₉	—	8	4	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₂²⋊C₄×C₁₉	—	2	2	no	—
181	C₂²⋊C₄×C₁₉	—	2	2	no	—
182	C₂²⋊C₄×C₁₉	—	2	2	no	—
183	C₂²⋊C₄×C₁₉	—	2	2	no	—
184	C₂²⋊C₄×C₁₉	—	2	2	no	—
185	C₂²⋊C₄×C₁₉	—	2	2	no	—
186	C₂²⋊C₄×C₁₉	—	2	2	no	—
187	C₂²⋊C₄×C₁₉	—	2	2	no	—
188	C₂²⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	4	1	no	—
192	C₂²⋊C₄×C₁₉	—	4	1	no	—
193	C₂²⋊C₄×C₁₉	—	4	1	no	—
194	C₂²⋊C₄×C₁₉	—	4	1	no	—
195	C₂²⋊C₄×C₁₉	—	4	1	no	—
196	C₂²⋊C₄×C₁₉	—	4	1	no	—
197	C₂²⋊C₄×C₁₉	—	4	1	no	—
198	C₂²⋊C₄×C₁₉	—	4	1	no	—
199	C₂²⋊C₄×C₁₉	—	4	1	no	—
200	C₂²⋊C₄×C₁₉	—	4	1	no	—
201	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
202	#11089	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂³×C₁₉	—	2	2	no	—
204	C₂³×C₁₉	—	2	2	no	—
205	C₂³×C₁₉	—	2	2	no	—
206	C₂³×C₁₉	—	4	2	no	—
207	C₂³×C₁₉	—	4	2	no	—
208	C₂³×C₁₉	—	4	2	no	—
209	C₂³×C₁₉	—	4	2	no	—
210	C₂³×C₁₉	—	4	2	no	—
211	C₂³×C₁₉	—	4	2	no	—
212	C₂³×C₁₉	—	4	2	no	—
213	C₂³×C₁₉	—	4	1	no	—
214	C₂³×C₁₉	—	4	1	no	—
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	—	4	1	no	—
217	C₂³×C₁₉	—	8	2	no	—
218	C₂³×C₁₉	—	8	2	no	—
219	C₂³×C₁₉	—	8	2	no	—
220	C₂³×C₁₉	—	8	1	no	—
221	C₂³×C₁₉	—	8	1	no	—
222	C₂³×C₁₉	—	8	1	no	—
223	C₂³×C₁₉	—	8	1	no	—
224	C₂³×C₁₉	—	8	1	no	—
225	C₂³×C₁₉	—	8	1	no	—
226	C₂³×C₁₉	—	8	1	no	—
227	C₂³×C₁₉	—	8	1	no	—
228	C₂³×C₁₉	—	8	2	no	—
229	C₂³×C₁₉	—	8	2	no	—
230	C₂³×C₁₉	—	8	2	no	—
231	C₂³×C₁₉	—	8	2	no	—
232	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₂³×C₁₉	#117	1	1	yes	characteristic
235	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
236	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
237	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
238	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
239	C₂³×C₁₉	#120	1	1	yes	characteristic
240	C₂³×C₁₉	#120	1	1	yes	characteristic
241	C₂³×C₁₉	#120	1	1	yes	characteristic
242	C₂³×C₁₉	#121	1	1	yes	characteristic
243	C₂³×C₁₉	#121	1	1	yes	characteristic
244	C₂³×C₁₉	#121	1	1	yes	characteristic
245	C₂³×C₁₉	#121	1	1	yes	characteristic
246	C₂³×C₁₉	#121	1	1	yes	characteristic
247	C₂³×C₁₉	#121	1	1	yes	characteristic
248	C₂³×C₁₉	#121	1	1	yes	characteristic
249	C₂³×C₁₉	#121	1	1	yes	characteristic
250	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
251	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
252	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
255	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
256	C₂³×C₁₉	#123	1	1	yes	characteristic
257	C₂³×C₁₉	#123	1	1	yes	characteristic
258	C₂³×C₁₉	#123	1	1	yes	characteristic
259	C₂³×C₁₉	#123	1	1	yes	characteristic
260	C₂³×C₁₉	#123	1	1	yes	characteristic
261	C₂³×C₁₉	#124	1	1	yes	characteristic
262	C₂³×C₁₉	#124	1	1	yes	characteristic
263	C₂³×C₁₉	#124	1	1	yes	characteristic
264	C₂³×C₁₉	#126	1	1	yes	characteristic
265	C₂³×C₁₉	#126	1	1	yes	characteristic
266	C₂³×C₁₉	#127	1	1	yes	characteristic
267	D₄×C₁₉	—	4	2	no	—
268	D₄×C₁₉	—	4	2	no	—
269	D₄×C₁₉	—	4	2	no	—
270	D₄×C₁₉	—	4	2	no	—
271	D₄×C₁₉	—	4	2	no	—
272	D₄×C₁₉	—	4	2	no	—
273	D₄×C₁₉	—	4	2	no	—
274	D₄×C₁₉	—	4	2	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	2	no	—
278	C₂×C₄×C₁₉	—	2	4	no	—
279	C₂×C₄×C₁₉	—	4	4	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	4	no	—
285	C₂×C₄×C₁₉	—	4	4	no	—
286	C₂×C₄×C₁₉	—	4	2	no	—
287	C₂×C₄×C₁₉	—	4	2	no	—
288	C₂×C₄×C₁₉	—	4	2	no	—
289	C₂×C₄×C₁₉	—	4	2	no	—
290	C₂×C₄×C₁₉	—	4	2	no	—
291	C₂×C₄×C₁₉	—	8	2	no	—
292	C₂×C₄×C₁₉	—	8	2	no	—
293	C₂×C₄×C₁₉	—	8	2	no	—
294	C₂×C₄×C₁₉	—	8	2	no	—
295	C₂×C₄×C₁₉	—	8	2	no	—
296	C₂×C₄×C₁₉	—	8	2	no	—
297	C₂×C₄×C₁₉	—	8	2	no	—
298	C₂×C₄×C₁₉	—	8	2	no	—
299	C₂×C₄×C₁₉	—	8	2	no	—
300	C₂×C₄×C₁₉	—	8	2	no	—
301	C₂×C₄×C₁₉	—	8	2	no	—
302	C₂×C₄×C₁₉	—	8	2	no	—
303	C₂×C₄×C₁₉	—	8	2	no	—
304	C₂×C₄×C₁₉	—	8	2	no	—
305	C₂×C₄×C₁₉	—	8	2	no	—
306	C₂²×#99	C₂×C₁₉	1	1	yes	characteristic
307	C₂²×#99	C₂×C₁₉	1	1	yes	characteristic
308	C₂²×#99	C₂×C₁₉	1	1	yes	characteristic
309	#2315	C₂×C₁₉	1	1	yes	characteristic, complemented
310	C₂×#342	C₂×C₁₉	1	1	yes	characteristic, complemented
311	C₂×#342	C₂×C₁₉	1	1	yes	characteristic, complemented
312	C₂×#342	C₂×C₁₉	1	1	yes	characteristic, complemented
313	C₂²×C₁₉	—	2	2	no	—
314	C₂²×C₁₉	—	2	2	no	—
315	C₂²×C₁₉	—	2	2	no	—
316	C₂²×C₁₉	—	2	2	no	—
317	C₂²×C₁₉	—	2	2	no	—
318	C₂²×C₁₉	—	2	2	no	—
319	C₂²×C₁₉	—	2	2	no	—
320	C₂²×C₁₉	—	4	1	no	—
321	C₂²×C₁₉	—	4	1	no	—
322	C₂²×C₁₉	—	4	1	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	4	1	no	—
325	C₂²×C₁₉	—	4	1	no	—
326	C₂²×C₁₉	—	4	1	no	—
327	C₂²×C₁₉	—	4	1	no	—
328	C₂²×C₁₉	—	4	1	no	—
329	C₂²×C₁₉	—	4	1	no	—
330	C₂²×C₁₉	—	4	1	no	—
331	C₂²×C₁₉	—	4	1	no	—
332	C₂²×C₁₉	—	4	1	no	—
333	C₂²×C₁₉	—	4	1	no	—
334	C₂²×C₁₉	—	4	1	no	—
335	C₂²×C₁₉	—	4	1	no	—
336	C₂²×C₁₉	—	4	1	no	—
337	C₂²×C₁₉	—	4	1	no	—
338	C₂²×C₁₉	—	4	1	no	—
339	C₂²×C₁₉	—	4	1	no	—
340	C₂²×C₁₉	—	4	1	no	—
341	C₂²×C₁₉	—	4	1	no	—
342	C₂²×C₁₉	—	4	1	no	—
343	C₂²×C₁₉	—	4	1	no	—
344	C₂²×C₁₉	—	4	1	no	—
345	C₂²×C₁₉	—	4	1	no	—
346	C₂²×C₁₉	—	4	1	no	—
347	C₂²×C₁₉	—	4	1	no	—
348	C₂²×C₁₉	—	4	2	no	—
349	C₂²×C₁₉	—	8	2	no	—
350	C₂²×C₁₉	—	8	2	no	—
351	C₂²×C₁₉	—	8	2	no	—
352	C₂²×C₁₉	—	8	2	no	—
353	C₂²×C₁₉	—	8	2	no	—
354	C₂²×C₁₉	—	8	2	no	—
355	C₂²×C₁₉	—	8	2	no	—
356	C₂²×C₁₉	#380	1	1	yes	characteristic
357	C₂²×C₁₉	#385	1	1	yes	characteristic
358	C₂²×C₁₉	#385	1	1	yes	characteristic
359	C₂²×C₁₉	#386	1	1	yes	characteristic
360	C₂²×C₁₉	#388	1	1	yes	characteristic
361	C₂²×C₁₉	#388	1	1	yes	characteristic
362	C₂²×C₁₉	#390	1	1	yes	characteristic
363	C₂²×C₁₉	#392	1	1	yes	characteristic
364	C₂²×C₁₉	#393	1	1	yes	characteristic
365	C₂²×C₁₉	#394	1	1	yes	characteristic
366	C₂²×C₁₉	#394	1	1	yes	characteristic
367	C₂²×C₁₉	#396	1	1	yes	characteristic
368	C₂²×C₁₉	#396	1	1	yes	characteristic
369	C₂²×C₁₉	#397	1	1	yes	characteristic
370	C₂²×C₁₉	#399	1	1	yes	characteristic
371	C₄×C₁₉	—	4	4	no	—
372	C₄×C₁₉	—	4	2	no	—
373	C₄×C₁₉	—	8	2	no	—
374	C₄×C₁₉	—	8	2	no	—
375	C₄×C₁₉	—	8	2	no	—
376	C₄×C₁₉	—	8	2	no	—
377	C₄×C₁₉	—	8	2	no	—
378	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
379	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
380	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
381	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
382	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
383	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
384	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
385	C₂×#99	—	2	2	no	—
386	C₂×#99	—	2	2	no	—
387	C₂×#99	—	2	2	no	—
388	C₂×#99	—	2	2	no	—
389	C₂×#99	—	2	2	no	—
390	C₂×#99	—	2	2	no	—
391	C₂×#99	—	2	2	no	—
392	C₂×#99	—	2	2	no	—
393	C₂×#99	C₄×C₁₉	1	4	yes	complemented
394	#385	—	2	2	no	—
395	#385	—	2	2	no	—
396	#380	—	2	2	no	—
397	#342	—	2	2	no	—
398	#342	—	2	2	no	—
399	#342	—	2	2	no	—
400	C₂×C₁₉	—	2	1	no	—
401	C₂×C₁₉	—	2	1	no	—
402	C₂×C₁₉	—	2	1	no	—
403	C₂×C₁₉	—	2	1	no	—
404	C₂×C₁₉	—	2	1	no	—
405	C₂×C₁₉	—	2	1	no	—
406	C₂×C₁₉	—	2	1	no	—
407	C₂×C₁₉	—	2	1	no	—
408	C₂×C₁₉	—	2	1	no	—
409	C₂×C₁₉	—	2	1	no	—
410	C₂×C₁₉	—	2	1	no	—
411	C₂×C₁₉	—	2	1	no	—
412	C₂×C₁₉	—	2	1	no	—
413	C₂×C₁₉	—	2	1	no	—
414	C₂×C₁₉	—	8	2	no	—
415	C₂×C₁₉	#1439	1	1	yes	characteristic
416	C₂×C₁₉	#2032	1	2	yes	—
417	C₂⁵	Q₈×C₁₉	1	1	yes	characteristic
418	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
419	C₂²×D₄	—	2	1	no	—
420	C₂²×D₄	—	2	1	no	—
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	—	2	1	no	—
423	C₂²×D₄	—	2	1	no	—
424	C₂²×D₄	—	2	1	no	—
425	C₂²×D₄	—	2	1	no	—
426	C₂²×D₄	—	2	1	no	—
427	C₂²×D₄	—	2	1	no	—
428	C₂²×D₄	—	2	1	no	—
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	—	2	1	no	—
431	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
432	C₂²×D₄	D₄×C₁₉	1	2	yes	—
433	C₂³×C₄	—	2	1	no	—
434	C₂³×C₄	—	2	1	no	—
435	C₂³×C₄	—	2	1	no	—
436	C₂³×C₄	—	2	1	no	—
437	C₂³×C₄	—	2	1	no	—
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	Q₈×C₁₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	—	2	4	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
471	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
472	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
473	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
474	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
475	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
476	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
477	#99	—	2	8	no	—
478	#99	—	2	8	no	—
479	#99	—	2	8	no	—
480	#95	—	2	4	no	—
481	C₁₉	#11089	1	1	yes	characteristic, direct product factor, Sylow
482	C₂⁴	—	2	1	no	—
483	C₂⁴	—	2	1	no	—
484	C₂⁴	—	2	1	no	—
485	C₂⁴	—	2	1	no	—
486	C₂⁴	—	2	1	no	—
487	C₂⁴	—	2	1	no	—
488	C₂⁴	—	8	2	no	—
489	C₂⁴	—	8	2	no	—
490	C₂⁴	C₄⋊C₄×C₁₉	1	2	yes	complemented
491	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
492	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
493	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₂⁴	C₂×Q₈×C₁₉	1	1	yes	characteristic
500	C₂⁴	#41×C₁₉	1	1	yes	characteristic
501	C₂⁴	#41×C₁₉	1	1	yes	characteristic
502	C₂⁴	#41×C₁₉	1	1	yes	characteristic
503	C₂⁴	#41×C₁₉	1	1	yes	characteristic
504	C₂⁴	#41×C₁₉	1	1	yes	characteristic
505	C₂⁴	#41×C₁₉	1	1	yes	characteristic
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	—	2	2	no	—
515	C₂×D₄	—	2	2	no	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	4	1	no	—
519	C₂×D₄	—	4	1	no	—
520	C₂×D₄	—	4	1	no	—
521	C₂×D₄	—	4	1	no	—
522	C₂×D₄	—	4	1	no	—
523	C₂×D₄	—	4	1	no	—
524	C₂×D₄	—	4	1	no	—
525	C₂×D₄	—	4	1	no	—
526	C₂×D₄	—	4	1	no	—
527	C₂×D₄	—	4	1	no	—
528	C₂×D₄	—	4	1	no	—
529	C₂×D₄	—	4	1	no	—
530	C₂×D₄	—	4	1	no	—
531	C₂×D₄	—	4	1	no	—
532	C₂×D₄	—	4	1	no	—
533	C₂×D₄	—	4	1	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	4	1	no	—
549	C₂²×C₄	—	4	1	no	—
550	C₂²×C₄	—	4	1	no	—
551	C₂²×C₄	—	4	1	no	—
552	C₂²×C₄	—	4	1	no	—
553	C₂²×C₄	—	4	1	no	—
554	C₂²×C₄	—	4	1	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	4	1	no	—
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	—	8	2	no	—
559	C₂²×C₄	—	8	2	no	—
560	C₂²×C₄	—	8	2	no	—
561	C₂²×C₄	—	8	2	no	—
562	C₂²×C₄	—	8	2	no	—
563	C₂²×C₄	—	8	2	no	—
564	C₂²×C₄	C₄⋊C₄×C₁₉	1	2	yes	complemented
565	C₄⋊C₄	—	8	4	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	—	2	2	no	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	2	2	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	2	2	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	2	2	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	2	2	no	—
579	C₂²⋊C₄	—	4	1	no	—
580	C₂²⋊C₄	—	4	1	no	—
581	C₂²⋊C₄	—	4	1	no	—
582	C₂²⋊C₄	—	4	1	no	—
583	C₂²⋊C₄	—	4	1	no	—
584	C₂²⋊C₄	—	4	1	no	—
585	C₂²⋊C₄	—	4	1	no	—
586	C₂²⋊C₄	—	4	1	no	—
587	C₂²⋊C₄	—	4	1	no	—
588	C₂²⋊C₄	—	4	1	no	—
589	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	4	2	no	—
594	C₂³	—	4	2	no	—
595	C₂³	—	4	2	no	—
596	C₂³	—	4	2	no	—
597	C₂³	—	4	2	no	—
598	C₂³	—	4	2	no	—
599	C₂³	—	4	2	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	8	2	no	—
605	C₂³	—	8	2	no	—
606	C₂³	—	8	2	no	—
607	C₂³	—	8	1	no	—
608	C₂³	—	8	1	no	—
609	C₂³	—	8	1	no	—
610	C₂³	—	8	1	no	—
611	C₂³	—	8	1	no	—
612	C₂³	—	8	1	no	—
613	C₂³	—	8	1	no	—
614	C₂³	—	8	1	no	—
615	C₂³	—	8	2	no	—
616	C₂³	—	8	2	no	—
617	C₂³	—	8	2	no	—
618	C₂³	—	8	2	no	—
619	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
620	C₂³	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
621	C₂³	C₁₉×#117	1	1	yes	characteristic
622	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
623	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
624	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
625	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
626	C₂³	C₁₉×#120	1	1	yes	characteristic
627	C₂³	C₁₉×#120	1	1	yes	characteristic
628	C₂³	C₁₉×#120	1	1	yes	characteristic
629	C₂³	C₁₉×#121	1	1	yes	characteristic
630	C₂³	C₁₉×#121	1	1	yes	characteristic
631	C₂³	C₁₉×#121	1	1	yes	characteristic
632	C₂³	C₁₉×#121	1	1	yes	characteristic
633	C₂³	C₁₉×#121	1	1	yes	characteristic
634	C₂³	C₁₉×#121	1	1	yes	characteristic
635	C₂³	C₁₉×#121	1	1	yes	characteristic
636	C₂³	C₁₉×#121	1	1	yes	characteristic
637	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
638	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
639	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
640	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
641	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
642	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
643	C₂³	C₁₉×#123	1	1	yes	characteristic
644	C₂³	C₁₉×#123	1	1	yes	characteristic
645	C₂³	C₁₉×#123	1	1	yes	characteristic
646	C₂³	C₁₉×#123	1	1	yes	characteristic
647	C₂³	C₁₉×#123	1	1	yes	characteristic
648	C₂³	C₁₉×#124	1	1	yes	characteristic
649	C₂³	C₁₉×#124	1	1	yes	characteristic
650	C₂³	C₁₉×#124	1	1	yes	characteristic
651	C₂³	C₁₉×#126	1	1	yes	characteristic
652	C₂³	C₁₉×#126	1	1	yes	characteristic
653	C₂³	C₁₉×#127	1	1	yes	characteristic
654	D₄	—	4	2	no	—
655	D₄	—	4	2	no	—
656	D₄	—	4	2	no	—
657	D₄	—	4	2	no	—
658	D₄	—	4	2	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	2	no	—
661	D₄	—	4	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	4	2	no	—
675	C₂×C₄	—	4	2	no	—
676	C₂×C₄	—	4	2	no	—
677	C₂×C₄	—	4	2	no	—
678	C₂×C₄	—	8	2	no	—
679	C₂×C₄	—	8	2	no	—
680	C₂×C₄	—	8	2	no	—
681	C₂×C₄	—	8	2	no	—
682	C₂×C₄	—	8	2	no	—
683	C₂×C₄	—	8	2	no	—
684	C₂×C₄	—	8	2	no	—
685	C₂×C₄	—	8	2	no	—
686	C₂×C₄	—	8	2	no	—
687	C₂×C₄	—	8	2	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	—	8	2	no	—
690	C₂×C₄	—	8	2	no	—
691	C₂×C₄	—	8	2	no	—
692	C₂×C₄	—	8	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	8	2	no	—
730	C₂²	—	8	2	no	—
731	C₂²	—	8	2	no	—
732	C₂²	—	8	2	no	—
733	C₂²	—	8	2	no	—
734	C₂²	—	8	2	no	—
735	C₂²	—	8	2	no	—
736	C₂²	C₁₉×#380	1	1	yes	characteristic
737	C₂²	C₁₉×#385	1	1	yes	characteristic
738	C₂²	C₁₉×#385	1	1	yes	characteristic
739	C₂²	C₁₉×#386	1	1	yes	characteristic
740	C₂²	C₁₉×#388	1	1	yes	characteristic
741	C₂²	C₁₉×#388	1	1	yes	characteristic
742	C₂²	C₁₉×#390	1	1	yes	characteristic
743	C₂²	C₁₉×#392	1	1	yes	characteristic
744	C₂²	C₁₉×#393	1	1	yes	characteristic
745	C₂²	C₁₉×#394	1	1	yes	characteristic
746	C₂²	C₁₉×#394	1	1	yes	characteristic
747	C₂²	C₁₉×#396	1	1	yes	characteristic
748	C₂²	C₁₉×#396	1	1	yes	characteristic
749	C₂²	C₁₉×#397	1	1	yes	characteristic
750	C₂²	C₁₉×#399	1	1	yes	characteristic
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	8	2	no	—
754	C₄	—	8	2	no	—
755	C₄	—	8	2	no	—
756	C₄	—	8	2	no	—
757	C₄	—	8	2	no	—
758	C₂	—	2	1	no	—
759	C₂	—	2	1	no	—
760	C₂	—	2	1	no	—
761	C₂	—	2	1	no	—
762	C₂	—	2	1	no	—
763	C₂	—	2	1	no	—
764	C₂	—	2	1	no	—
765	C₂	—	2	1	no	—
766	C₂	—	2	1	no	—
767	C₂	—	2	1	no	—
768	C₂	—	2	1	no	—
769	C₂	—	2	1	no	—
770	C₂	—	2	1	no	—
771	C₂	—	2	1	no	—
772	C₂	—	8	2	no	—
773	C₂	C₁₉×#1439	1	1	yes	characteristic
774	C₂	C₁₉×#2032	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#393
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂⁵	C₂³×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₉×#2315	C₂	semidirect
5. C₂×C₁₉×#342	C₂	semidirect
6. C₂×C₁₉×#342	C₂	semidirect
7. C₂×C₁₉×#342	C₂	semidirect
23. C₂×C₁₉×#99	C₄	semidirect
102. C₂⁴×C₁₉	C₄⋊C₄	semidirect
176. C₂²×C₄×C₁₉	C₄⋊C₄	semidirect
202. #11089	C₁₉	direct (N × H)
309. #2315	C₂×C₁₉	semidirect
310. C₂×#342	C₂×C₁₉	semidirect
311. C₂×#342	C₂×C₁₉	semidirect
312. C₂×#342	C₂×C₁₉	semidirect
393. C₂×#99	C₄×C₁₉	semidirect
481. C₁₉	#11089	direct (N × H)
490. C₂⁴	C₄⋊C₄×C₁₉	semidirect
564. C₂²×C₄	C₄⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#99	2
C₁₉×#2315	2
C₂×C₁₉×#342	2
#11089	19

Subgroups — C19×#11089 #18017048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11089 #18017048