Subgroups — C₁₉×#23997 #18029956

Order 4864.

1210 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3491	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3026	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#458	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2883	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2032	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2022	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1913	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1913	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1899	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1890	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1828	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
13	C₁₉×#552	—	2	2	no	—
14	C₁₉×#552	—	2	2	no	—
15	C₁₉×#551	—	2	2	no	—
16	C₁₉×#551	—	2	2	no	—
17	C₁₉×#543	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#539	—	2	2	no	—
19	C₁₉×#534	C₂²	1	2	yes	—
20	C₁₉×#534	C₂²	1	1	yes	characteristic
21	C₁₉×#529	—	2	2	no	—
22	C₂×C₁₉×#123	C₂²	1	2	yes	—
23	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#123	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#518	C₂²	1	1	yes	characteristic
26	C₁₉×#518	C₂²	1	1	yes	characteristic
27	C₁₉×#518	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#458	—	2	2	no	—
30	C₁₉×#458	—	2	2	no	—
31	C₁₉×#458	—	2	2	no	—
32	C₁₉×B(4,𝔽₂)	—	2	2	no	—
33	C₁₉×#410	—	2	2	no	—
34	C₂×C₁₉×#99	—	2	2	no	—
35	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#99	C₂²	1	2	yes	—
37	C₂×C₁₉×#99	C₂²	1	2	yes	—
38	C₂×C₁₉×#99	C₂²	1	2	yes	—
39	C₂×C₁₉×#99	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#99	C₂²	1	2	yes	—
41	C₂×C₁₉×#99	C₂²	1	2	yes	complemented
42	C₁₉×#381	C₂²	1	2	yes	complemented
43	C₁₉×#342	C₂²	1	2	yes	complemented
44	C₁₉×#342	C₂²	1	2	yes	complemented
45	C₁₉×#342	C₂²	1	2	yes	complemented
46	C₁₉×#342	C₂²	1	2	yes	complemented
47	C₁₉×H(5,𝔽₂)	—	2	2	no	—
48	C₁₉×H(5,𝔽₂)	—	2	2	no	—
49	C₁₉×H(5,𝔽₂)	—	4	2	no	—
50	C₂×#41×C₁₉	—	2	1	no	—
51	C₂×#41×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	2	no	—
54	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#126	—	2	2	no	—
59	C₁₉×#126	—	2	2	no	—
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#125	—	2	2	no	—
63	C₁₉×#125	—	2	2	no	—
64	C₁₉×#125	—	2	2	no	—
65	C₁₉×#124	—	2	2	no	—
66	C₁₉×#123	—	2	2	no	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×#123	—	2	2	no	—
69	C₁₉×#123	—	2	1	no	—
70	C₁₉×#123	—	2	1	no	—
71	C₁₉×#123	—	2	1	no	—
72	C₁₉×#123	—	2	2	no	—
73	C₁₉×#123	—	2	2	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	2	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	4	2	no	—
78	C₁₉×#123	D₄	1	2	yes	—
79	C₁₉×#123	D₄	1	2	yes	complemented
80	C₁₉×#123	D₄	1	2	yes	complemented
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	4	2	no	—
88	C₁₉×#120	—	2	1	no	—
89	C₁₉×#120	—	2	2	no	—
90	C₁₉×#120	—	2	2	no	—
91	C₁₉×#120	D₄	1	2	yes	—
92	C₄×Q₈×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	4	2	no	—
99	C₁₉×#117	—	2	2	no	—
100	C₁₉×#117	—	2	2	no	—
101	C₁₉×#117	—	2	1	no	—
102	C₁₉×#117	—	2	2	no	—
103	C₁₉×#117	—	2	2	no	—
104	C₁₉×#117	—	2	1	no	—
105	C₁₉×#117	D₄	1	2	yes	complemented
106	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
115	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	complemented
116	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₉	—	2	1	no	—
124	C₁₉×#99	—	2	2	no	—
125	C₁₉×#99	—	2	2	no	—
126	C₁₉×#99	—	2	4	no	—
127	C₁₉×#99	—	2	4	no	—
128	C₁₉×#99	—	2	4	no	—
129	C₁₉×#99	—	2	4	no	—
130	C₁₉×#99	—	4	2	no	—
131	C₁₉×#95	—	4	2	no	—
132	C₂⁴×C₁₉	—	2	1	no	—
133	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂⁴×C₁₉	#41	1	2	yes	—
136	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
137	#41×C₁₉	—	4	4	no	—
138	#41×C₁₉	—	4	4	no	—
139	#41×C₁₉	—	4	2	no	—
140	#41×C₁₉	—	4	2	no	—
141	C₂×Q₈×C₁₉	—	2	1	no	—
142	C₂×Q₈×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	2	no	—
147	C₂×D₄×C₁₉	—	2	1	no	—
148	C₂×D₄×C₁₉	—	2	1	no	—
149	C₂×D₄×C₁₉	—	2	2	no	—
150	C₂×D₄×C₁₉	—	2	2	no	—
151	C₂×D₄×C₁₉	—	2	2	no	—
152	C₂×D₄×C₁₉	—	2	2	no	—
153	C₂×D₄×C₁₉	—	2	2	no	—
154	C₂×D₄×C₁₉	—	2	2	no	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	4	4	no	—
159	C₂×D₄×C₁₉	—	4	4	no	—
160	C₂×D₄×C₁₉	—	4	2	no	—
161	C₂×D₄×C₁₉	—	4	2	no	—
162	C₂×D₄×C₁₉	—	4	2	no	—
163	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
164	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	2	2	no	—
171	C₂²×C₄×C₁₉	—	2	2	no	—
172	C₂²×C₄×C₁₉	—	2	2	no	—
173	C₂²×C₄×C₁₉	—	2	1	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	1	no	—
177	C₂²×C₄×C₁₉	—	2	2	no	—
178	C₂²×C₄×C₁₉	—	2	2	no	—
179	C₂²×C₄×C₁₉	—	2	2	no	—
180	C₂²×C₄×C₁₉	—	4	1	no	—
181	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₉	#41	1	2	yes	—
186	C₄⋊C₄×C₁₉	—	2	2	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	2	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	2	no	—
198	C₄⋊C₄×C₁₉	—	4	2	no	—
199	C₄⋊C₄×C₁₉	—	4	2	no	—
200	C₄⋊C₄×C₁₉	—	4	2	no	—
201	C₄⋊C₄×C₁₉	—	4	1	no	—
202	C₂²⋊C₄×C₁₉	—	2	2	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	1	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	4	2	no	—
221	C₂²⋊C₄×C₁₉	—	4	2	no	—
222	C₂²⋊C₄×C₁₉	—	4	2	no	—
223	C₂²⋊C₄×C₁₉	—	4	2	no	—
224	C₂²⋊C₄×C₁₉	—	4	1	no	—
225	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
226	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
227	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
228	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
229	C₄²×C₁₉	—	2	2	no	—
230	C₄²×C₁₉	—	2	2	no	—
231	C₄²×C₁₉	—	2	2	no	—
232	C₄²×C₁₉	—	2	2	no	—
233	C₄²×C₁₉	—	4	1	no	—
234	#23997	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂³×C₁₉	—	2	1	no	—
236	C₂³×C₁₉	—	2	1	no	—
237	C₂³×C₁₉	—	2	1	no	—
238	C₂³×C₁₉	—	2	2	no	—
239	C₂³×C₁₉	—	2	2	no	—
240	C₂³×C₁₉	—	2	2	no	—
241	C₂³×C₁₉	—	2	2	no	—
242	C₂³×C₁₉	—	4	2	no	—
243	C₂³×C₁₉	—	8	1	no	—
244	C₂³×C₁₉	—	8	1	no	—
245	C₂³×C₁₉	—	8	1	no	—
246	C₂³×C₁₉	—	8	2	no	—
247	C₂³×C₁₉	—	16	1	no	—
248	C₂³×C₁₉	#120	1	2	yes	—
249	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
250	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
251	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
252	C₂³×C₁₉	C₂×#41	1	2	yes	—
253	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
254	Q₈×C₁₉	—	4	2	no	—
255	Q₈×C₁₉	—	8	2	no	—
256	D₄×C₁₉	—	2	4	no	—
257	D₄×C₁₉	—	2	4	no	—
258	D₄×C₁₉	—	4	2	no	—
259	D₄×C₁₉	—	4	4	no	—
260	D₄×C₁₉	—	4	2	no	—
261	D₄×C₁₉	—	4	1	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	4	2	no	—
264	D₄×C₁₉	—	4	2	no	—
265	D₄×C₁₉	—	4	2	no	—
266	D₄×C₁₉	—	4	2	no	—
267	D₄×C₁₉	—	8	2	no	—
268	D₄×C₁₉	—	16	2	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	2	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	2	no	—
279	C₂×C₄×C₁₉	—	2	2	no	—
280	C₂×C₄×C₁₉	—	2	2	no	—
281	C₂×C₄×C₁₉	—	2	2	no	—
282	C₂×C₄×C₁₉	—	2	2	no	—
283	C₂×C₄×C₁₉	—	2	2	no	—
284	C₂×C₄×C₁₉	—	4	4	no	—
285	C₂×C₄×C₁₉	—	4	2	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	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	—	4	2	no	—
292	C₂×C₄×C₁₉	—	8	1	no	—
293	C₂×C₄×C₁₉	—	8	2	no	—
294	C₂×C₄×C₁₉	—	8	2	no	—
295	C₂×C₄×C₁₉	—	8	1	no	—
296	C₂×C₄×C₁₉	—	8	1	no	—
297	C₂×C₄×C₁₉	—	8	1	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	—	16	1	no	—
302	C₂×C₄×C₁₉	#120	1	2	yes	—
303	#3491	C₂×C₁₉	1	1	yes	characteristic, complemented
304	#3026	C₂×C₁₉	1	1	yes	characteristic
305	C₂×#458	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#2883	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#2032	C₂×C₁₉	1	2	yes	complemented
308	#2022	C₂×C₁₉	1	2	yes	complemented
309	#1913	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#1913	C₂×C₁₉	1	2	yes	complemented
311	#1899	C₂×C₁₉	1	2	yes	complemented
312	#1890	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1828	C₂×C₁₉	1	1	yes	characteristic, complemented
314	C₂²×C₁₉	—	2	2	no	—
315	C₂²×C₁₉	—	4	1	no	—
316	C₂²×C₁₉	—	4	2	no	—
317	C₂²×C₁₉	—	4	1	no	—
318	C₂²×C₁₉	—	4	1	no	—
319	C₂²×C₁₉	—	4	2	no	—
320	C₂²×C₁₉	—	4	2	no	—
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	4	2	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	8	1	no	—
325	C₂²×C₁₉	—	8	1	no	—
326	C₂²×C₁₉	—	8	2	no	—
327	C₂²×C₁₉	—	8	2	no	—
328	C₂²×C₁₉	—	8	2	no	—
329	C₂²×C₁₉	—	8	2	no	—
330	C₂²×C₁₉	—	16	2	no	—
331	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
332	C₂²×C₁₉	#525	1	1	yes	characteristic
333	C₂²×C₁₉	#535	1	1	yes	characteristic
334	C₂²×C₁₉	#546	1	2	yes	—
335	C₂²×C₁₉	#546	1	2	yes	—
336	C₄×C₁₉	—	2	2	no	—
337	C₄×C₁₉	—	4	2	no	—
338	C₄×C₁₉	—	4	2	no	—
339	C₄×C₁₉	—	4	2	no	—
340	C₄×C₁₉	—	4	2	no	—
341	C₄×C₁₉	—	4	1	no	—
342	C₄×C₁₉	—	4	1	no	—
343	C₄×C₁₉	—	4	2	no	—
344	C₄×C₁₉	—	4	1	no	—
345	C₄×C₁₉	—	8	2	no	—
346	C₄×C₁₉	—	8	2	no	—
347	C₄×C₁₉	—	8	2	no	—
348	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
349	#552	—	2	2	no	—
350	#552	—	2	2	no	—
351	#551	—	2	2	no	—
352	#551	—	2	2	no	—
353	#543	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#539	—	2	2	no	—
355	#534	C₂²×C₁₉	1	2	yes	—
356	#534	C₂²×C₁₉	1	1	yes	characteristic
357	#529	—	2	2	no	—
358	C₂×#123	C₂²×C₁₉	1	2	yes	—
359	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×#123	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	#518	C₂²×C₁₉	1	1	yes	characteristic
362	#518	C₂²×C₁₉	1	1	yes	characteristic
363	#518	C₂²×C₁₉	1	1	yes	characteristic, complemented
364	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
365	#458	—	2	2	no	—
366	#458	—	2	2	no	—
367	#458	—	2	2	no	—
368	B(4,𝔽₂)	—	2	2	no	—
369	#410	—	2	2	no	—
370	C₂×#99	—	2	2	no	—
371	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×#99	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#99	C₂²×C₁₉	1	2	yes	—
374	C₂×#99	C₂²×C₁₉	1	2	yes	—
375	C₂×#99	C₂²×C₁₉	1	2	yes	—
376	C₂×#99	C₂²×C₁₉	1	2	yes	—
377	C₂×#99	C₂²×C₁₉	1	2	yes	complemented
378	#381	C₂²×C₁₉	1	2	yes	complemented
379	#342	C₂²×C₁₉	1	2	yes	complemented
380	#342	C₂²×C₁₉	1	2	yes	complemented
381	#342	C₂²×C₁₉	1	2	yes	complemented
382	#342	C₂²×C₁₉	1	2	yes	complemented
383	C₂×C₁₉	—	2	1	no	—
384	C₂×C₁₉	—	2	1	no	—
385	C₂×C₁₉	—	2	2	no	—
386	C₂×C₁₉	—	2	2	no	—
387	C₂×C₁₉	—	2	1	no	—
388	C₂×C₁₉	—	4	2	no	—
389	C₂×C₁₉	—	8	1	no	—
390	C₂×C₁₉	—	8	2	no	—
391	C₂×C₁₉	#2404	1	1	yes	characteristic
392	H(5,𝔽₂)	—	2	2	no	—
393	H(5,𝔽₂)	—	2	2	no	—
394	H(5,𝔽₂)	—	4	2	no	—
395	C₂×#41	—	2	1	no	—
396	C₂×#41	—	2	2	no	—
397	C₂²×D₄	—	2	1	no	—
398	C₂²×D₄	—	2	2	no	—
399	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
400	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
401	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
402	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
403	#126	—	2	2	no	—
404	#126	—	2	2	no	—
405	#126	—	2	2	no	—
406	#126	—	2	2	no	—
407	#125	—	2	2	no	—
408	#125	—	2	2	no	—
409	#125	—	2	2	no	—
410	#124	—	2	2	no	—
411	#123	—	2	2	no	—
412	#123	—	2	2	no	—
413	#123	—	2	2	no	—
414	#123	—	2	1	no	—
415	#123	—	2	1	no	—
416	#123	—	2	1	no	—
417	#123	—	2	2	no	—
418	#123	—	2	2	no	—
419	#123	—	2	2	no	—
420	#123	—	2	2	no	—
421	#123	—	2	2	no	—
422	#123	—	4	2	no	—
423	#123	D₄×C₁₉	1	2	yes	—
424	#123	D₄×C₁₉	1	2	yes	complemented
425	#123	D₄×C₁₉	1	2	yes	complemented
426	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	—	2	2	no	—
428	C₂²⋊Q₈	—	2	2	no	—
429	C₂²⋊Q₈	—	2	2	no	—
430	C₂²⋊Q₈	—	2	2	no	—
431	#121	—	2	2	no	—
432	#121	—	4	2	no	—
433	#120	—	2	1	no	—
434	#120	—	2	2	no	—
435	#120	—	2	2	no	—
436	#120	D₄×C₁₉	1	2	yes	—
437	C₄×Q₈	—	2	2	no	—
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	2	no	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	4	2	no	—
444	#117	—	2	2	no	—
445	#117	—	2	2	no	—
446	#117	—	2	1	no	—
447	#117	—	2	2	no	—
448	#117	—	2	2	no	—
449	#117	—	2	1	no	—
450	#117	D₄×C₁₉	1	2	yes	complemented
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	2	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	2	no	—
460	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	complemented
461	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
468	C₂×C₄²	—	2	1	no	—
469	#99	—	2	2	no	—
470	#99	—	2	2	no	—
471	#99	—	2	4	no	—
472	#99	—	2	4	no	—
473	#99	—	2	4	no	—
474	#99	—	2	4	no	—
475	#99	—	4	2	no	—
476	#95	—	4	2	no	—
477	C₁₉	#23997	1	1	yes	characteristic, direct product factor, Sylow
478	C₂⁴	—	2	1	no	—
479	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂⁴	#41×C₁₉	1	2	yes	—
482	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
483	#41	—	4	4	no	—
484	#41	—	4	4	no	—
485	#41	—	4	2	no	—
486	#41	—	4	2	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	2	no	—
489	C₂×D₄	—	2	2	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	4	4	no	—
505	C₂×D₄	—	4	4	no	—
506	C₂×D₄	—	4	2	no	—
507	C₂×D₄	—	4	2	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
510	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	4	1	no	—
527	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
528	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
530	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
531	C₂²×C₄	#41×C₁₉	1	2	yes	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	1	no	—
556	C₂²⋊C₄	—	2	1	no	—
557	C₂²⋊C₄	—	2	1	no	—
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	4	2	no	—
567	C₂²⋊C₄	—	4	2	no	—
568	C₂²⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	4	2	no	—
570	C₂²⋊C₄	—	4	1	no	—
571	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
572	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
573	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
574	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
575	C₄²	—	2	2	no	—
576	C₄²	—	2	2	no	—
577	C₄²	—	2	2	no	—
578	C₄²	—	2	2	no	—
579	C₄²	—	4	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	4	2	no	—
588	C₂³	—	8	1	no	—
589	C₂³	—	8	1	no	—
590	C₂³	—	8	1	no	—
591	C₂³	—	8	2	no	—
592	C₂³	—	16	1	no	—
593	C₂³	C₁₉×#120	1	2	yes	—
594	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
595	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
596	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
597	C₂³	C₂×#41×C₁₉	1	2	yes	—
598	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
599	Q₈	—	4	2	no	—
600	Q₈	—	8	2	no	—
601	D₄	—	2	4	no	—
602	D₄	—	2	4	no	—
603	D₄	—	4	2	no	—
604	D₄	—	4	4	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	1	no	—
609	D₄	—	4	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	2	no	—
612	D₄	—	8	2	no	—
613	D₄	—	16	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	2	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	8	1	no	—
638	C₂×C₄	—	8	2	no	—
639	C₂×C₄	—	8	2	no	—
640	C₂×C₄	—	8	1	no	—
641	C₂×C₄	—	8	1	no	—
642	C₂×C₄	—	8	1	no	—
643	C₂×C₄	—	8	2	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	—	8	2	no	—
646	C₂×C₄	—	16	1	no	—
647	C₂×C₄	C₁₉×#120	1	2	yes	—
648	C₂²	—	2	2	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	2	no	—
654	C₂²	—	4	2	no	—
655	C₂²	—	4	2	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	8	1	no	—
659	C₂²	—	8	1	no	—
660	C₂²	—	8	2	no	—
661	C₂²	—	8	2	no	—
662	C₂²	—	8	2	no	—
663	C₂²	—	8	2	no	—
664	C₂²	—	16	2	no	—
665	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
666	C₂²	C₁₉×#525	1	1	yes	characteristic
667	C₂²	C₁₉×#535	1	1	yes	characteristic
668	C₂²	C₁₉×#546	1	2	yes	—
669	C₂²	C₁₉×#546	1	2	yes	—
670	C₄	—	2	2	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	4	2	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	8	2	no	—
680	C₄	—	8	2	no	—
681	C₄	—	8	2	no	—
682	C₂	—	2	1	no	—
683	C₂	—	2	1	no	—
684	C₂	—	2	2	no	—
685	C₂	—	2	2	no	—
686	C₂	—	2	1	no	—
687	C₂	—	4	2	no	—
688	C₂	—	8	1	no	—
689	C₂	—	8	2	no	—
690	C₂	C₁₉×#2404	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2404
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₁₉×#3026	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3491	C₂	semidirect
3. C₂×C₁₉×#458	C₂	semidirect
4. C₁₉×#2883	C₂	semidirect
5. C₁₉×#2032	C₂	semidirect
6. C₁₉×#2022	C₂	semidirect
7. C₁₉×#1913	C₂	semidirect
8. C₁₉×#1913	C₂	semidirect
9. C₁₉×#1899	C₂	semidirect
10. C₁₉×#1890	C₂	semidirect
11. C₁₉×#1828	C₂	semidirect
17. C₁₉×#543	C₂²	semidirect
24. C₂×C₁₉×#123	C₂²	semidirect
27. C₁₉×#518	C₂²	semidirect
28. C₂×C₁₉×#117	C₂²	semidirect
41. C₂×C₁₉×#99	C₂²	semidirect
42. C₁₉×#381	C₂²	semidirect
43. C₁₉×#342	C₂²	semidirect
44. C₁₉×#342	C₂²	semidirect
45. C₁₉×#342	C₂²	semidirect
46. C₁₉×#342	C₂²	semidirect
79. C₁₉×#123	D₄	semidirect
80. C₁₉×#123	D₄	semidirect
105. C₁₉×#117	D₄	semidirect
115. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
234. #23997	C₁₉	direct (N × H)
303. #3491	C₂×C₁₉	semidirect
305. C₂×#458	C₂×C₁₉	semidirect
306. #2883	C₂×C₁₉	semidirect
307. #2032	C₂×C₁₉	semidirect
308. #2022	C₂×C₁₉	semidirect
309. #1913	C₂×C₁₉	semidirect
310. #1913	C₂×C₁₉	semidirect
311. #1899	C₂×C₁₉	semidirect
312. #1890	C₂×C₁₉	semidirect
313. #1828	C₂×C₁₉	semidirect
353. #543	C₂²×C₁₉	semidirect
360. C₂×#123	C₂²×C₁₉	semidirect
363. #518	C₂²×C₁₉	semidirect
364. C₂×#117	C₂²×C₁₉	semidirect
377. C₂×#99	C₂²×C₁₉	semidirect
378. #381	C₂²×C₁₉	semidirect
379. #342	C₂²×C₁₉	semidirect
380. #342	C₂²×C₁₉	semidirect
381. #342	C₂²×C₁₉	semidirect
382. #342	C₂²×C₁₉	semidirect
424. #123	D₄×C₁₉	semidirect
425. #123	D₄×C₁₉	semidirect
450. #117	D₄×C₁₉	semidirect
460. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
477. C₁₉	#23997	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3491	2
C₁₉×#3026	2
C₂×C₁₉×#458	2
C₁₉×#2883	2
C₁₉×#2032	2
C₁₉×#2022	2
C₁₉×#1913	2
C₁₉×#1899	2
C₁₉×#1890	2
C₁₉×#1828	2
#23997	19

Subgroups — C19×#23997 #18029956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23997 #18029956