Subgroups — C₁₉×#20960 #18026919

Order 4864.

2126 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#534	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#99	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2308	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1890	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1889	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₉×#342	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#534	—	2	4	no	—
11	C₁₉×#534	C₄	1	8	yes	complemented
12	C₂×C₁₉×#123	—	2	1	no	—
13	C₂×C₁₉×#123	C₂²	1	2	yes	—
14	C₂×C₁₉×#121	—	2	2	no	—
15	C₂×C₁₉×#120	—	2	1	no	—
16	C₂×C₁₉×#120	C₂²	1	2	yes	—
17	C₁₉×#518	—	2	2	no	—
18	C₁₉×#518	—	2	4	no	—
19	C₁₉×#518	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₁₉	—	2	4	no	—
21	C₂×C₁₉×#117	—	2	1	no	—
22	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#99	—	2	4	no	—
27	C₂×C₁₉×#99	C₂²	1	4	yes	—
28	C₁₉×#386	—	2	4	no	—
29	C₁₉×#386	—	2	4	no	—
30	C₁₉×#381	C₂²	1	4	yes	complemented
31	C₁₉×#379	C₂²	1	4	yes	complemented
32	C₁₉×#342	C₂²	1	8	yes	complemented
33	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
34	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
35	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	—	2	2	no	—
38	C₂²×D₄×C₁₉	—	2	4	no	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	—	2	2	no	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	4	no	—
45	C₂²×D₄×C₁₉	—	2	2	no	—
46	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
47	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	complemented
48	C₂²×D₄×C₁₉	D₄	1	4	yes	—
49	C₂²×D₄×C₁₉	D₄	1	2	yes	—
50	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₉	—	2	2	no	—
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	D₄	1	4	yes	complemented
56	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₁₉×#123	—	2	4	no	—
58	C₁₉×#123	—	2	8	no	—
59	C₁₉×#123	C₂×C₄	1	8	yes	complemented
60	C₁₉×#121	—	2	16	no	—
61	C₁₉×#120	—	2	8	no	—
62	C₁₉×#120	—	2	4	no	—
63	C₁₉×#120	C₂×C₄	1	8	yes	complemented
64	C₄×D₄×C₁₉	—	2	16	no	—
65	C₄×D₄×C₁₉	—	2	16	no	—
66	C₁₉×#117	—	2	4	no	—
67	C₁₉×#117	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
85	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
86	C₂×C₂²⋊C₄×C₁₉	D₄	1	4	yes	complemented
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₉	—	2	2	no	—
91	C₁₉×#99	—	2	8	no	—
92	C₁₉×#95	—	2	8	no	—
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	—	2	1	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	—	2	1	no	—
98	C₂⁴×C₁₉	—	2	1	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	—	8	2	no	—
101	C₂⁴×C₁₉	—	8	2	no	—
102	C₂⁴×C₁₉	—	8	2	no	—
103	C₂⁴×C₁₉	C₂²⋊C₄	1	4	yes	complemented
104	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
105	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	complemented
106	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
107	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
110	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
111	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
112	C₂⁴×C₁₉	#41	1	4	yes	—
113	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
114	C₂×D₄×C₁₉	—	2	8	no	—
115	C₂×D₄×C₁₉	—	2	8	no	—
116	C₂×D₄×C₁₉	—	2	4	no	—
117	C₂×D₄×C₁₉	—	2	8	no	—
118	C₂×D₄×C₁₉	—	2	8	no	—
119	C₂×D₄×C₁₉	—	2	4	no	—
120	C₂×D₄×C₁₉	—	2	4	no	—
121	C₂×D₄×C₁₉	—	2	4	no	—
122	C₂×D₄×C₁₉	—	2	4	no	—
123	C₂×D₄×C₁₉	—	2	4	no	—
124	C₂×D₄×C₁₉	—	2	8	no	—
125	C₂×D₄×C₁₉	—	2	8	no	—
126	C₂×D₄×C₁₉	—	2	8	no	—
127	C₂×D₄×C₁₉	—	4	1	no	—
128	C₂×D₄×C₁₉	—	4	2	no	—
129	C₂×D₄×C₁₉	—	4	1	no	—
130	C₂×D₄×C₁₉	—	4	4	no	—
131	C₂×D₄×C₁₉	—	4	4	no	—
132	C₂×D₄×C₁₉	—	4	2	no	—
133	C₂×D₄×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	—	8	4	no	—
135	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	complemented
136	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
137	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	4	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	8	no	—
148	C₂²×C₄×C₁₉	—	2	4	no	—
149	C₂²×C₄×C₁₉	—	2	4	no	—
150	C₂²×C₄×C₁₉	—	2	4	no	—
151	C₂²×C₄×C₁₉	—	4	4	no	—
152	C₂²×C₄×C₁₉	—	8	4	no	—
153	C₂²×C₄×C₁₉	—	8	4	no	—
154	C₂²×C₄×C₁₉	—	8	2	no	—
155	C₂²×C₄×C₁₉	—	8	4	no	—
156	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	complemented
157	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	complemented
158	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
160	C₄⋊C₄×C₁₉	—	2	8	no	—
161	C₄⋊C₄×C₁₉	—	2	8	no	—
162	C₂²⋊C₄×C₁₉	—	2	8	no	—
163	C₂²⋊C₄×C₁₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₉	—	2	4	no	—
166	C₂²⋊C₄×C₁₉	—	2	4	no	—
167	C₂²⋊C₄×C₁₉	—	2	4	no	—
168	C₂²⋊C₄×C₁₉	—	2	4	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	8	no	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	4	4	no	—
174	C₂²⋊C₄×C₁₉	—	8	8	no	—
175	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	complemented
176	C₄²×C₁₉	—	2	8	no	—
177	#20960	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂³×C₁₉	—	2	2	no	—
179	C₂³×C₁₉	—	2	4	no	—
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	2	4	no	—
182	C₂³×C₁₉	—	2	2	no	—
183	C₂³×C₁₉	—	2	4	no	—
184	C₂³×C₁₉	—	4	4	no	—
185	C₂³×C₁₉	—	4	4	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	4	no	—
190	C₂³×C₁₉	—	4	4	no	—
191	C₂³×C₁₉	—	4	8	no	—
192	C₂³×C₁₉	—	4	4	no	—
193	C₂³×C₁₉	—	4	1	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	4	1	no	—
196	C₂³×C₁₉	—	8	2	no	—
197	C₂³×C₁₉	—	8	2	no	—
198	C₂³×C₁₉	—	8	2	no	—
199	C₂³×C₁₉	—	8	2	no	—
200	C₂³×C₁₉	—	8	4	no	—
201	C₂³×C₁₉	—	8	4	no	—
202	C₂³×C₁₉	—	8	4	no	—
203	C₂³×C₁₉	—	8	2	no	—
204	C₂³×C₁₉	—	8	4	no	—
205	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
206	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂³×C₁₉	C₄×D₄	1	4	yes	—
209	C₂³×C₁₉	C₄×D₄	1	4	yes	—
210	C₂³×C₁₉	#120	1	1	yes	characteristic
211	C₂³×C₁₉	#120	1	2	yes	—
212	C₂³×C₁₉	#120	1	1	yes	characteristic
213	C₂³×C₁₉	#121	1	4	yes	—
214	C₂³×C₁₉	#121	1	4	yes	—
215	C₂³×C₁₉	#123	1	2	yes	—
216	C₂³×C₁₉	#123	1	2	yes	—
217	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
218	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
219	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
220	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	C₂³×C₁₉	C₂×#41	1	2	yes	—
222	D₄×C₁₉	—	2	8	no	—
223	D₄×C₁₉	—	2	8	no	—
224	D₄×C₁₉	—	2	16	no	—
225	D₄×C₁₉	—	4	4	no	—
226	D₄×C₁₉	—	4	4	no	—
227	D₄×C₁₉	—	4	8	no	—
228	D₄×C₁₉	—	8	8	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	2	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	4	no	—
236	C₂×C₄×C₁₉	—	2	8	no	—
237	C₂×C₄×C₁₉	—	4	8	no	—
238	C₂×C₄×C₁₉	—	4	4	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	8	no	—
243	C₂×C₄×C₁₉	—	4	8	no	—
244	C₂×C₄×C₁₉	—	4	4	no	—
245	C₂×C₄×C₁₉	—	8	4	no	—
246	C₂×C₄×C₁₉	—	8	4	no	—
247	C₂×C₄×C₁₉	—	8	8	no	—
248	C₂×C₄×C₁₉	—	8	8	no	—
249	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
250	C₂×#534	C₂×C₁₉	1	1	yes	characteristic
251	C₂×#518	C₂×C₁₉	1	1	yes	characteristic, complemented
252	C₂²×#99	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#2308	C₂×C₁₉	1	2	yes	complemented
254	#1890	C₂×C₁₉	1	4	yes	complemented
255	#1889	C₂×C₁₉	1	4	yes	complemented
256	C₂×#342	C₂×C₁₉	1	2	yes	complemented
257	C₂²×C₁₉	—	2	2	no	—
258	C₂²×C₁₉	—	2	4	no	—
259	C₂²×C₁₉	—	2	2	no	—
260	C₂²×C₁₉	—	2	4	no	—
261	C₂²×C₁₉	—	2	2	no	—
262	C₂²×C₁₉	—	2	4	no	—
263	C₂²×C₁₉	—	4	2	no	—
264	C₂²×C₁₉	—	4	4	no	—
265	C₂²×C₁₉	—	4	2	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	1	no	—
268	C₂²×C₁₉	—	4	1	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	4	no	—
271	C₂²×C₁₉	—	4	4	no	—
272	C₂²×C₁₉	—	4	4	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	—	4	4	no	—
275	C₂²×C₁₉	—	4	8	no	—
276	C₂²×C₁₉	—	4	4	no	—
277	C₂²×C₁₉	—	4	8	no	—
278	C₂²×C₁₉	—	4	4	no	—
279	C₂²×C₁₉	—	4	2	no	—
280	C₂²×C₁₉	—	8	2	no	—
281	C₂²×C₁₉	—	8	4	no	—
282	C₂²×C₁₉	—	8	4	no	—
283	C₂²×C₁₉	—	8	2	no	—
284	C₂²×C₁₉	—	8	2	no	—
285	C₂²×C₁₉	#386	1	2	yes	—
286	C₂²×C₁₉	#386	1	2	yes	—
287	C₂²×C₁₉	#386	1	4	yes	—
288	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
290	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
291	C₂²×C₁₉	C₂×#121	1	2	yes	—
292	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
293	C₄×C₁₉	—	2	4	no	—
294	C₄×C₁₉	—	4	4	no	—
295	C₄×C₁₉	—	4	8	no	—
296	C₄×C₁₉	—	4	2	no	—
297	C₄×C₁₉	—	8	4	no	—
298	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
299	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
300	#534	—	2	4	no	—
301	#534	C₄×C₁₉	1	8	yes	complemented
302	C₂×#123	—	2	1	no	—
303	C₂×#123	C₂²×C₁₉	1	2	yes	—
304	C₂×#121	—	2	2	no	—
305	C₂×#120	—	2	1	no	—
306	C₂×#120	C₂²×C₁₉	1	2	yes	—
307	#518	—	2	2	no	—
308	#518	—	2	4	no	—
309	#518	C₂²×C₁₉	1	4	yes	—
310	C₂×C₄×D₄	—	2	4	no	—
311	C₂×#117	—	2	1	no	—
312	C₂²×C₂²⋊C₄	—	2	1	no	—
313	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
314	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
315	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×#99	—	2	4	no	—
317	C₂×#99	C₂²×C₁₉	1	4	yes	—
318	#386	—	2	4	no	—
319	#386	—	2	4	no	—
320	#381	C₂²×C₁₉	1	4	yes	complemented
321	#379	C₂²×C₁₉	1	4	yes	complemented
322	#342	C₂²×C₁₉	1	8	yes	complemented
323	C₂×C₁₉	—	2	1	no	—
324	C₂×C₁₉	—	2	2	no	—
325	C₂×C₁₉	—	2	2	no	—
326	C₂×C₁₉	—	2	2	no	—
327	C₂×C₁₉	—	2	1	no	—
328	C₂×C₁₉	—	2	2	no	—
329	C₂×C₁₉	—	2	4	no	—
330	C₂×C₁₉	—	4	4	no	—
331	C₂×C₁₉	—	8	2	no	—
332	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
333	C₂×C₁₉	#3026	1	2	yes	—
334	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
335	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
336	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
337	C₂²×D₄	—	2	2	no	—
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	—	2	4	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	4	no	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
348	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	complemented
349	C₂²×D₄	D₄×C₁₉	1	4	yes	—
350	C₂²×D₄	D₄×C₁₉	1	2	yes	—
351	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
352	C₂³×C₄	—	2	2	no	—
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	—	2	2	no	—
355	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
356	C₂³×C₄	D₄×C₁₉	1	4	yes	complemented
357	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
358	#123	—	2	4	no	—
359	#123	—	2	8	no	—
360	#123	C₂×C₄×C₁₉	1	8	yes	complemented
361	#121	—	2	16	no	—
362	#120	—	2	8	no	—
363	#120	—	2	4	no	—
364	#120	C₂×C₄×C₁₉	1	8	yes	complemented
365	C₄×D₄	—	2	16	no	—
366	C₄×D₄	—	2	16	no	—
367	#117	—	2	4	no	—
368	#117	—	2	4	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	4	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	4	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	4	no	—
383	C₂×C₂²⋊C₄	—	2	4	no	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₂²⋊C₄	—	2	8	no	—
386	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
387	C₂×C₂²⋊C₄	D₄×C₁₉	1	4	yes	complemented
388	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
391	C₂×C₄²	—	2	2	no	—
392	#99	—	2	8	no	—
393	#95	—	2	8	no	—
394	C₁₉	#20960	1	1	yes	characteristic, direct product factor, Sylow
395	C₂⁴	—	2	1	no	—
396	C₂⁴	—	2	1	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	2	1	no	—
400	C₂⁴	—	2	1	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	8	2	no	—
403	C₂⁴	—	8	2	no	—
404	C₂⁴	—	8	2	no	—
405	C₂⁴	C₂²⋊C₄×C₁₉	1	4	yes	complemented
406	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
407	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	complemented
408	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
409	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
412	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
413	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
414	C₂⁴	#41×C₁₉	1	4	yes	—
415	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	8	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	8	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	2	8	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	2	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	8	4	no	—
437	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	complemented
438	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
439	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	8	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	8	4	no	—
455	C₂²×C₄	—	8	4	no	—
456	C₂²×C₄	—	8	2	no	—
457	C₂²×C₄	—	8	4	no	—
458	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	complemented
459	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	complemented
460	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	4	4	no	—
476	C₂²⋊C₄	—	8	8	no	—
477	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	complemented
478	C₄²	—	2	8	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	4	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	4	8	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	8	2	no	—
498	C₂³	—	8	2	no	—
499	C₂³	—	8	2	no	—
500	C₂³	—	8	2	no	—
501	C₂³	—	8	4	no	—
502	C₂³	—	8	4	no	—
503	C₂³	—	8	4	no	—
504	C₂³	—	8	2	no	—
505	C₂³	—	8	4	no	—
506	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
507	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
508	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
509	C₂³	C₄×D₄×C₁₉	1	4	yes	—
510	C₂³	C₄×D₄×C₁₉	1	4	yes	—
511	C₂³	C₁₉×#120	1	1	yes	characteristic
512	C₂³	C₁₉×#120	1	2	yes	—
513	C₂³	C₁₉×#120	1	1	yes	characteristic
514	C₂³	C₁₉×#121	1	4	yes	—
515	C₂³	C₁₉×#121	1	4	yes	—
516	C₂³	C₁₉×#123	1	2	yes	—
517	C₂³	C₁₉×#123	1	2	yes	—
518	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
519	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
520	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
521	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
522	C₂³	C₂×#41×C₁₉	1	2	yes	—
523	D₄	—	2	16	no	—
524	D₄	—	2	8	no	—
525	D₄	—	2	8	no	—
526	D₄	—	4	4	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	8	no	—
529	D₄	—	8	8	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	8	no	—
538	C₂×C₄	—	4	8	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	8	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	8	4	no	—
547	C₂×C₄	—	8	4	no	—
548	C₂×C₄	—	8	8	no	—
549	C₂×C₄	—	8	8	no	—
550	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	4	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	8	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	8	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	8	2	no	—
575	C₂²	—	8	4	no	—
576	C₂²	—	8	4	no	—
577	C₂²	—	8	2	no	—
578	C₂²	—	8	2	no	—
579	C₂²	C₁₉×#386	1	2	yes	—
580	C₂²	C₁₉×#386	1	2	yes	—
581	C₂²	C₁₉×#386	1	4	yes	—
582	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
583	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
584	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
585	C₂²	C₂×C₁₉×#121	1	2	yes	—
586	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
587	C₄	—	2	4	no	—
588	C₄	—	4	4	no	—
589	C₄	—	4	8	no	—
590	C₄	—	4	2	no	—
591	C₄	—	8	4	no	—
592	C₂	—	2	1	no	—
593	C₂	—	2	2	no	—
594	C₂	—	2	2	no	—
595	C₂	—	2	2	no	—
596	C₂	—	2	1	no	—
597	C₂	—	2	2	no	—
598	C₂	—	2	4	no	—
599	C₂	—	4	4	no	—
600	C₂	—	8	2	no	—
601	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
602	C₂	C₁₉×#3026	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#534	C₂
LCS	G ▷ C₂³ ▷ 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
2. C₂×C₁₉×#518	C₂	semidirect
3. C₂²×C₁₉×#99	C₂	semidirect
4. C₁₉×#2308	C₂	semidirect
5. C₁₉×#1890	C₂	semidirect
6. C₁₉×#1889	C₂	semidirect
7. C₂×C₁₉×#342	C₂	semidirect
11. C₁₉×#534	C₄	semidirect
30. C₁₉×#381	C₂²	semidirect
31. C₁₉×#379	C₂²	semidirect
32. C₁₉×#342	C₂²	semidirect
47. C₂²×D₄×C₁₉	C₂×C₄	semidirect
55. C₂³×C₄×C₁₉	D₄	semidirect
59. C₁₉×#123	C₂×C₄	semidirect
63. C₁₉×#120	C₂×C₄	semidirect
85. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
86. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
103. C₂⁴×C₁₉	C₂²⋊C₄	semidirect
105. C₂⁴×C₁₉	C₂²×C₄	semidirect
135. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
156. C₂²×C₄×C₁₉	C₂²⋊C₄	semidirect
157. C₂²×C₄×C₁₉	C₂²×C₄	semidirect
175. C₂²⋊C₄×C₁₉	C₂²×C₄	semidirect
177. #20960	C₁₉	direct (N × H)
251. C₂×#518	C₂×C₁₉	semidirect
252. C₂²×#99	C₂×C₁₉	semidirect
253. #2308	C₂×C₁₉	semidirect
254. #1890	C₂×C₁₉	semidirect
255. #1889	C₂×C₁₉	semidirect
256. C₂×#342	C₂×C₁₉	semidirect
301. #534	C₄×C₁₉	semidirect
320. #381	C₂²×C₁₉	semidirect
321. #379	C₂²×C₁₉	semidirect
322. #342	C₂²×C₁₉	semidirect
348. C₂²×D₄	C₂×C₄×C₁₉	semidirect
356. C₂³×C₄	D₄×C₁₉	semidirect
360. #123	C₂×C₄×C₁₉	semidirect
364. #120	C₂×C₄×C₁₉	semidirect
386. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
387. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
394. C₁₉	#20960	direct (N × H)
405. C₂⁴	C₂²⋊C₄×C₁₉	semidirect
407. C₂⁴	C₂²×C₄×C₁₉	semidirect
437. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect
458. C₂²×C₄	C₂²⋊C₄×C₁₉	semidirect
459. C₂²×C₄	C₂²×C₄×C₁₉	semidirect
477. C₂²⋊C₄	C₂²×C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#534	2
C₂×C₁₉×#518	2
C₂²×C₁₉×#99	2
C₁₉×#2308	2
C₁₉×#1890	2
C₁₉×#1889	2
C₂×C₁₉×#342	2
#20960	19

Subgroups — C19×#20960 #18026919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20960 #18026919