Subgroups — C₁₉×#23444 #18029403

Order 4864.

2418 conjugacy classes of subgroups.

The subgroup lattice has 614 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, complemented
2	C₂×C₁₉×#534	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×#99	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2308	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2022	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2021	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
9	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#534	—	2	4	no	—
11	C₁₉×#534	—	2	8	no	—
12	C₁₉×#534	—	2	2	no	—
13	C₁₉×#534	—	2	8	no	—
14	C₁₉×#534	C₂²	1	4	yes	—
15	C₂×C₁₉×#123	—	2	2	no	—
16	C₂×C₁₉×#123	—	2	2	no	—
17	C₂×C₁₉×#123	C₂²	1	4	yes	complemented
18	C₂×C₁₉×#121	—	2	4	no	—
19	C₂×C₁₉×#121	—	2	2	no	—
20	C₂×C₁₉×#120	—	2	2	no	—
21	C₂×C₁₉×#120	—	2	2	no	—
22	C₂×C₁₉×#120	C₂²	1	4	yes	complemented
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₂×C₁₉×#99	—	2	8	no	—
27	C₂×C₁₉×#99	C₂²	1	8	yes	complemented
28	C₁₉×#386	—	2	2	no	—
29	C₁₉×#386	—	2	2	no	—
30	C₁₉×#381	C₂²	1	2	yes	complemented
31	C₁₉×#379	C₂²	1	2	yes	complemented
32	C₁₉×#342	C₂²	1	4	yes	complemented
33	C₂⁵×C₁₉	D₄	1	2	yes	complemented
34	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
35	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
36	C₂²×D₄×C₁₉	—	2	1	no	—
37	C₂²×D₄×C₁₉	—	2	1	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	2	no	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	4	no	—
46	C₂²×D₄×C₁₉	—	2	4	no	—
47	C₂²×D₄×C₁₉	—	2	4	no	—
48	C₂²×D₄×C₁₉	—	2	4	no	—
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	—	2	2	no	—
51	C₂²×D₄×C₁₉	—	2	4	no	—
52	C₂²×D₄×C₁₉	D₄	1	4	yes	complemented
53	C₂²×D₄×C₁₉	D₄	1	4	yes	complemented
54	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₉	—	2	2	no	—
56	C₂³×C₄×C₁₉	—	2	1	no	—
57	C₂³×C₄×C₁₉	D₄	1	2	yes	complemented
58	C₂³×C₄×C₁₉	D₄	1	2	yes	complemented
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₁₉×#123	—	2	16	no	—
61	C₁₉×#123	—	2	8	no	—
62	C₁₉×#123	—	2	8	no	—
63	C₁₉×#123	—	2	8	no	—
64	C₁₉×#123	—	2	8	no	—
65	C₁₉×#121	—	2	8	no	—
66	C₁₉×#121	—	2	32	no	—
67	C₁₉×#121	—	2	8	no	—
68	C₁₉×#120	—	2	16	no	—
69	C₁₉×#120	—	2	8	no	—
70	C₁₉×#120	—	2	8	no	—
71	C₁₉×#120	—	2	8	no	—
72	C₁₉×#120	—	2	8	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	complemented
86	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	complemented
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
88	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
90	C₁₉×#99	—	2	16	no	—
91	C₁₉×#95	—	2	4	no	—
92	C₂⁴×C₁₉	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	—	2	4	no	—
96	C₂⁴×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	—	2	4	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	—	2	1	no	—
100	C₂⁴×C₁₉	—	8	2	no	—
101	C₂⁴×C₁₉	—	8	2	no	—
102	C₂⁴×C₁₉	—	8	4	no	—
103	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
104	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
105	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
106	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
109	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
110	C₂⁴×C₁₉	C₂×D₄	1	2	yes	complemented
111	C₂⁴×C₁₉	#41	1	2	yes	—
112	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
113	C₂×D₄×C₁₉	—	2	8	no	—
114	C₂×D₄×C₁₉	—	2	4	no	—
115	C₂×D₄×C₁₉	—	2	8	no	—
116	C₂×D₄×C₁₉	—	2	8	no	—
117	C₂×D₄×C₁₉	—	2	4	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	4	no	—
125	C₂×D₄×C₁₉	—	2	4	no	—
126	C₂×D₄×C₁₉	—	2	4	no	—
127	C₂×D₄×C₁₉	—	2	16	no	—
128	C₂×D₄×C₁₉	—	2	8	no	—
129	C₂×D₄×C₁₉	—	4	2	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	—	4	1	no	—
132	C₂×D₄×C₁₉	—	4	4	no	—
133	C₂×D₄×C₁₉	—	4	4	no	—
134	C₂×D₄×C₁₉	—	4	4	no	—
135	C₂×D₄×C₁₉	—	4	4	no	—
136	C₂×D₄×C₁₉	—	4	4	no	—
137	C₂×D₄×C₁₉	—	4	4	no	—
138	C₂×D₄×C₁₉	—	4	4	no	—
139	C₂×D₄×C₁₉	—	4	4	no	—
140	C₂×D₄×C₁₉	—	4	2	no	—
141	C₂×D₄×C₁₉	—	4	2	no	—
142	C₂×D₄×C₁₉	—	4	4	no	—
143	C₂×D₄×C₁₉	—	4	4	no	—
144	C₂×D₄×C₁₉	—	8	8	no	—
145	C₂×D₄×C₁₉	—	8	4	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	4	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	4	no	—
151	C₂²×C₄×C₁₉	—	2	4	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	1	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	8	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	4	2	no	—
160	C₂²×C₄×C₁₉	—	8	2	no	—
161	C₂²×C₄×C₁₉	—	8	4	no	—
162	C₂²×C₄×C₁₉	—	8	2	no	—
163	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	complemented
166	C₄⋊C₄×C₁₉	—	2	16	no	—
167	C₄⋊C₄×C₁₉	—	2	8	no	—
168	C₂²⋊C₄×C₁₉	—	2	16	no	—
169	C₂²⋊C₄×C₁₉	—	2	16	no	—
170	C₂²⋊C₄×C₁₉	—	2	16	no	—
171	C₂²⋊C₄×C₁₉	—	2	8	no	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	2	4	no	—
174	C₂²⋊C₄×C₁₉	—	2	4	no	—
175	C₂²⋊C₄×C₁₉	—	2	4	no	—
176	C₂²⋊C₄×C₁₉	—	4	2	no	—
177	C₂²⋊C₄×C₁₉	—	8	4	no	—
178	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	complemented
179	#23444	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂³×C₁₉	—	2	4	no	—
181	C₂³×C₁₉	—	2	4	no	—
182	C₂³×C₁₉	—	2	4	no	—
183	C₂³×C₁₉	—	2	2	no	—
184	C₂³×C₁₉	—	2	4	no	—
185	C₂³×C₁₉	—	4	2	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	4	no	—
188	C₂³×C₁₉	—	4	4	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	8	no	—
191	C₂³×C₁₉	—	4	4	no	—
192	C₂³×C₁₉	—	4	8	no	—
193	C₂³×C₁₉	—	4	8	no	—
194	C₂³×C₁₉	—	4	1	no	—
195	C₂³×C₁₉	—	4	2	no	—
196	C₂³×C₁₉	—	4	1	no	—
197	C₂³×C₁₉	—	4	4	no	—
198	C₂³×C₁₉	—	4	4	no	—
199	C₂³×C₁₉	—	8	4	no	—
200	C₂³×C₁₉	—	8	2	no	—
201	C₂³×C₁₉	—	8	4	no	—
202	C₂³×C₁₉	—	8	2	no	—
203	C₂³×C₁₉	—	8	2	no	—
204	C₂³×C₁₉	—	8	8	no	—
205	C₂³×C₁₉	—	8	4	no	—
206	C₂³×C₁₉	—	8	2	no	—
207	C₂³×C₁₉	—	8	8	no	—
208	C₂³×C₁₉	#120	1	2	yes	—
209	C₂³×C₁₉	#120	1	1	yes	characteristic
210	C₂³×C₁₉	#120	1	1	yes	characteristic
211	C₂³×C₁₉	#120	1	4	yes	—
212	C₂³×C₁₉	#120	1	4	yes	—
213	C₂³×C₁₉	#121	1	4	yes	—
214	C₂³×C₁₉	#121	1	4	yes	—
215	C₂³×C₁₉	#121	1	2	yes	—
216	C₂³×C₁₉	#121	1	2	yes	—
217	C₂³×C₁₉	#127	1	2	yes	—
218	C₂³×C₁₉	#127	1	2	yes	—
219	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
220	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
222	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
223	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
224	D₄×C₁₉	—	4	4	no	—
225	D₄×C₁₉	—	4	4	no	—
226	D₄×C₁₉	—	4	4	no	—
227	D₄×C₁₉	—	4	4	no	—
228	D₄×C₁₉	—	4	4	no	—
229	D₄×C₁₉	—	4	8	no	—
230	D₄×C₁₉	—	4	8	no	—
231	D₄×C₁₉	—	4	8	no	—
232	D₄×C₁₉	—	4	4	no	—
233	D₄×C₁₉	—	8	16	no	—
234	D₄×C₁₉	—	8	8	no	—
235	C₂×C₄×C₁₉	—	2	8	no	—
236	C₂×C₄×C₁₉	—	2	4	no	—
237	C₂×C₄×C₁₉	—	2	4	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	4	no	—
240	C₂×C₄×C₁₉	—	2	4	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	4	8	no	—
243	C₂×C₄×C₁₉	—	4	4	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	2	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	4	no	—
248	C₂×C₄×C₁₉	—	4	4	no	—
249	C₂×C₄×C₁₉	—	4	4	no	—
250	C₂×C₄×C₁₉	—	4	4	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	8	2	no	—
253	C₂×C₄×C₁₉	—	8	8	no	—
254	C₂×C₄×C₁₉	—	8	4	no	—
255	C₂×#534	C₂×C₁₉	1	1	yes	characteristic, complemented
256	C₂×#534	C₂×C₁₉	1	2	yes	complemented
257	C₂²×#99	C₂×C₁₉	1	2	yes	complemented
258	#2308	C₂×C₁₉	1	1	yes	characteristic, complemented
259	#2022	C₂×C₁₉	1	4	yes	complemented
260	#2021	C₂×C₁₉	1	4	yes	complemented
261	C₂×#342	C₂×C₁₉	1	1	yes	characteristic, complemented
262	C₂²×C₁₉	—	2	2	no	—
263	C₂²×C₁₉	—	2	2	no	—
264	C₂²×C₁₉	—	2	4	no	—
265	C₂²×C₁₉	—	2	2	no	—
266	C₂²×C₁₉	—	2	4	no	—
267	C₂²×C₁₉	—	4	4	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	4	no	—
270	C₂²×C₁₉	—	4	4	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	—	4	2	no	—
275	C₂²×C₁₉	—	4	2	no	—
276	C₂²×C₁₉	—	4	4	no	—
277	C₂²×C₁₉	—	4	2	no	—
278	C₂²×C₁₉	—	4	8	no	—
279	C₂²×C₁₉	—	4	8	no	—
280	C₂²×C₁₉	—	4	4	no	—
281	C₂²×C₁₉	—	4	2	no	—
282	C₂²×C₁₉	—	4	4	no	—
283	C₂²×C₁₉	—	4	8	no	—
284	C₂²×C₁₉	—	8	4	no	—
285	C₂²×C₁₉	—	8	2	no	—
286	C₂²×C₁₉	—	8	4	no	—
287	C₂²×C₁₉	—	8	8	no	—
288	C₂²×C₁₉	—	8	8	no	—
289	C₂²×C₁₉	—	8	2	no	—
290	C₂²×C₁₉	#392	1	2	yes	—
291	C₂²×C₁₉	#392	1	4	yes	—
292	C₂²×C₁₉	#392	1	2	yes	—
293	C₂²×C₁₉	C₂×#120	1	2	yes	—
294	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
295	C₂²×C₁₉	C₂×#121	1	2	yes	—
296	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
297	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
298	C₄×C₁₉	—	4	8	no	—
299	C₄×C₁₉	—	4	4	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	4	no	—
302	C₄×C₁₉	—	8	2	no	—
303	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
304	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
305	#534	—	2	4	no	—
306	#534	—	2	8	no	—
307	#534	—	2	2	no	—
308	#534	—	2	8	no	—
309	#534	C₂²×C₁₉	1	4	yes	—
310	C₂×#123	—	2	2	no	—
311	C₂×#123	—	2	2	no	—
312	C₂×#123	C₂²×C₁₉	1	4	yes	complemented
313	C₂×#121	—	2	4	no	—
314	C₂×#121	—	2	2	no	—
315	C₂×#120	—	2	2	no	—
316	C₂×#120	—	2	2	no	—
317	C₂×#120	C₂²×C₁₉	1	4	yes	complemented
318	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
319	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
320	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
321	C₂×#99	—	2	8	no	—
322	C₂×#99	C₂²×C₁₉	1	8	yes	complemented
323	#386	—	2	2	no	—
324	#386	—	2	2	no	—
325	#381	C₂²×C₁₉	1	2	yes	complemented
326	#379	C₂²×C₁₉	1	2	yes	complemented
327	#342	C₂²×C₁₉	1	4	yes	complemented
328	C₂×C₁₉	—	2	2	no	—
329	C₂×C₁₉	—	2	1	no	—
330	C₂×C₁₉	—	2	1	no	—
331	C₂×C₁₉	—	2	2	no	—
332	C₂×C₁₉	—	2	2	no	—
333	C₂×C₁₉	—	2	4	no	—
334	C₂×C₁₉	—	2	2	no	—
335	C₂×C₁₉	—	8	2	no	—
336	C₂×C₁₉	—	8	4	no	—
337	C₂×C₁₉	C₂×#392	1	1	yes	characteristic
338	C₂×C₁₉	#3026	1	2	yes	—
339	C₂⁵	D₄×C₁₉	1	2	yes	complemented
340	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
341	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	2	2	no	—
347	C₂²×D₄	—	2	2	no	—
348	C₂²×D₄	—	2	4	no	—
349	C₂²×D₄	—	2	4	no	—
350	C₂²×D₄	—	2	4	no	—
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	—	2	1	no	—
353	C₂²×D₄	—	2	4	no	—
354	C₂²×D₄	—	2	4	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	2	no	—
357	C₂²×D₄	—	2	4	no	—
358	C₂²×D₄	D₄×C₁₉	1	4	yes	complemented
359	C₂²×D₄	D₄×C₁₉	1	4	yes	complemented
360	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
361	C₂³×C₄	—	2	2	no	—
362	C₂³×C₄	—	2	1	no	—
363	C₂³×C₄	D₄×C₁₉	1	2	yes	complemented
364	C₂³×C₄	D₄×C₁₉	1	2	yes	complemented
365	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
366	#123	—	2	8	no	—
367	#123	—	2	16	no	—
368	#123	—	2	8	no	—
369	#123	—	2	8	no	—
370	#123	—	2	8	no	—
371	#121	—	2	8	no	—
372	#121	—	2	32	no	—
373	#121	—	2	8	no	—
374	#120	—	2	8	no	—
375	#120	—	2	16	no	—
376	#120	—	2	8	no	—
377	#120	—	2	8	no	—
378	#120	—	2	8	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	4	no	—
381	C₂×C₂²⋊C₄	—	2	4	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₂²⋊C₄	—	2	4	no	—
386	C₂×C₂²⋊C₄	—	2	4	no	—
387	C₂×C₂²⋊C₄	—	2	4	no	—
388	C₂×C₂²⋊C₄	—	2	4	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	4	no	—
391	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	complemented
392	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	complemented
393	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
396	#99	—	2	16	no	—
397	#95	—	2	4	no	—
398	C₁₉	#23444	1	1	yes	characteristic, direct product factor, Sylow
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	1	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	2	4	no	—
405	C₂⁴	—	2	2	no	—
406	C₂⁴	—	2	1	no	—
407	C₂⁴	—	8	2	no	—
408	C₂⁴	—	8	2	no	—
409	C₂⁴	—	8	4	no	—
410	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
411	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
412	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
413	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
416	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
417	C₂⁴	C₂×D₄×C₁₉	1	2	yes	complemented
418	C₂⁴	#41×C₁₉	1	2	yes	—
419	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	8	no	—
425	C₂×D₄	—	2	8	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	16	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	2	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	4	4	no	—
443	C₂×D₄	—	4	4	no	—
444	C₂×D₄	—	4	4	no	—
445	C₂×D₄	—	4	4	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	—	4	4	no	—
448	C₂×D₄	—	4	4	no	—
449	C₂×D₄	—	4	2	no	—
450	C₂×D₄	—	4	2	no	—
451	C₂×D₄	—	8	8	no	—
452	C₂×D₄	—	8	4	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	8	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	—	8	2	no	—
468	C₂²×C₄	—	8	4	no	—
469	C₂²×C₄	—	8	2	no	—
470	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
471	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
472	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	complemented
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	2	16	no	—
475	C₂²⋊C₄	—	2	16	no	—
476	C₂²⋊C₄	—	2	16	no	—
477	C₂²⋊C₄	—	2	16	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	4	2	no	—
484	C₂²⋊C₄	—	8	4	no	—
485	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	complemented
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	8	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	4	8	no	—
499	C₂³	—	4	8	no	—
500	C₂³	—	4	4	no	—
501	C₂³	—	4	4	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	8	4	no	—
506	C₂³	—	8	2	no	—
507	C₂³	—	8	4	no	—
508	C₂³	—	8	2	no	—
509	C₂³	—	8	2	no	—
510	C₂³	—	8	8	no	—
511	C₂³	—	8	4	no	—
512	C₂³	—	8	2	no	—
513	C₂³	—	8	8	no	—
514	C₂³	C₁₉×#120	1	2	yes	—
515	C₂³	C₁₉×#120	1	1	yes	characteristic
516	C₂³	C₁₉×#120	1	1	yes	characteristic
517	C₂³	C₁₉×#120	1	4	yes	—
518	C₂³	C₁₉×#120	1	4	yes	—
519	C₂³	C₁₉×#121	1	4	yes	—
520	C₂³	C₁₉×#121	1	2	yes	—
521	C₂³	C₁₉×#121	1	2	yes	—
522	C₂³	C₁₉×#121	1	4	yes	—
523	C₂³	C₁₉×#127	1	2	yes	—
524	C₂³	C₁₉×#127	1	2	yes	—
525	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
526	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
527	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
528	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
529	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
530	D₄	—	4	4	no	—
531	D₄	—	4	8	no	—
532	D₄	—	4	8	no	—
533	D₄	—	4	8	no	—
534	D₄	—	4	4	no	—
535	D₄	—	4	4	no	—
536	D₄	—	4	4	no	—
537	D₄	—	4	4	no	—
538	D₄	—	4	4	no	—
539	D₄	—	8	16	no	—
540	D₄	—	8	8	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	8	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	4	8	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	—	8	8	no	—
560	C₂×C₄	—	8	4	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	4	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	8	no	—
578	C₂²	—	4	8	no	—
579	C₂²	—	4	4	no	—
580	C₂²	—	4	8	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	8	4	no	—
584	C₂²	—	8	2	no	—
585	C₂²	—	8	8	no	—
586	C₂²	—	8	4	no	—
587	C₂²	—	8	8	no	—
588	C₂²	—	8	2	no	—
589	C₂²	C₁₉×#392	1	2	yes	—
590	C₂²	C₁₉×#392	1	4	yes	—
591	C₂²	C₁₉×#392	1	2	yes	—
592	C₂²	C₂×C₁₉×#120	1	2	yes	—
593	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
594	C₂²	C₂×C₁₉×#121	1	2	yes	—
595	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
596	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
597	C₄	—	4	8	no	—
598	C₄	—	4	4	no	—
599	C₄	—	4	4	no	—
600	C₄	—	4	2	no	—
601	C₄	—	8	2	no	—
602	C₂	—	2	2	no	—
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	2	no	—
606	C₂	—	2	2	no	—
607	C₂	—	2	4	no	—
608	C₂	—	2	2	no	—
609	C₂	—	8	2	no	—
610	C₂	—	8	4	no	—
611	C₂	C₂×C₁₉×#392	1	1	yes	characteristic
612	C₂	C₁₉×#3026	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
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
1. C₂×C₁₉×#534	C₂	semidirect
2. C₂×C₁₉×#534	C₂	semidirect
3. C₂²×C₁₉×#99	C₂	semidirect
4. C₁₉×#2308	C₂	semidirect
5. C₁₉×#2022	C₂	semidirect
6. C₁₉×#2021	C₂	semidirect
7. C₂×C₁₉×#342	C₂	semidirect
17. C₂×C₁₉×#123	C₂²	semidirect
22. C₂×C₁₉×#120	C₂²	semidirect
27. C₂×C₁₉×#99	C₂²	semidirect
30. C₁₉×#381	C₂²	semidirect
31. C₁₉×#379	C₂²	semidirect
32. C₁₉×#342	C₂²	semidirect
33. C₂⁵×C₁₉	D₄	semidirect
52. C₂²×D₄×C₁₉	D₄	semidirect
53. C₂²×D₄×C₁₉	D₄	semidirect
57. C₂³×C₄×C₁₉	D₄	semidirect
58. C₂³×C₄×C₁₉	D₄	semidirect
85. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
86. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
110. C₂⁴×C₁₉	C₂×D₄	semidirect
165. C₂²×C₄×C₁₉	C₂×D₄	semidirect
178. C₂²⋊C₄×C₁₉	C₂×D₄	semidirect
179. #23444	C₁₉	direct (N × H)
255. C₂×#534	C₂×C₁₉	semidirect
256. C₂×#534	C₂×C₁₉	semidirect
257. C₂²×#99	C₂×C₁₉	semidirect
258. #2308	C₂×C₁₉	semidirect
259. #2022	C₂×C₁₉	semidirect
260. #2021	C₂×C₁₉	semidirect
261. C₂×#342	C₂×C₁₉	semidirect
312. C₂×#123	C₂²×C₁₉	semidirect
317. C₂×#120	C₂²×C₁₉	semidirect
322. C₂×#99	C₂²×C₁₉	semidirect
325. #381	C₂²×C₁₉	semidirect
326. #379	C₂²×C₁₉	semidirect
327. #342	C₂²×C₁₉	semidirect
339. C₂⁵	D₄×C₁₉	semidirect
358. C₂²×D₄	D₄×C₁₉	semidirect
359. C₂²×D₄	D₄×C₁₉	semidirect
363. C₂³×C₄	D₄×C₁₉	semidirect
364. C₂³×C₄	D₄×C₁₉	semidirect
391. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
392. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
398. C₁₉	#23444	direct (N × H)
417. C₂⁴	C₂×D₄×C₁₉	semidirect
472. C₂²×C₄	C₂×D₄×C₁₉	semidirect
485. C₂²⋊C₄	C₂×D₄×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
C₂²×C₁₉×#99	2
C₁₉×#2308	2
C₁₉×#2022	2
C₁₉×#2021	2
C₂×C₁₉×#342	2
#23444	19

Subgroups — C19×#23444 #18029403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23444 #18029403