Subgroups — C₁₉×#22478 #18028437

Order 4864.

1132 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#552	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2344	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1996	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1899	C₂	1	4	yes	maximal
5	C₁₉×#1820	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1799	C₂	1	1	yes	maximal, characteristic
7	C₄×C₁₉×#99	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1740	C₂	1	2	yes	maximal, complemented
9	C₁₉×#552	—	2	2	no	—
10	C₁₉×#552	—	2	4	no	—
11	C₁₉×#552	—	2	2	no	—
12	C₂×C₁₉×#126	C₄	1	2	yes	complemented
13	C₂×C₁₉×#125	C₄	1	2	yes	complemented
14	C₂×C₁₉×#125	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₉×#123	C₂²	1	2	yes	—
16	C₂×C₁₉×C₂²⋊Q₈	C₄	1	1	yes	characteristic, complemented
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
19	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₄	1	1	yes	characteristic, complemented
21	C₂×C₁₉×#117	C₂²	1	4	yes	—
22	C₂×C₁₉×#117	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#99	C₂²	1	2	yes	—
25	C₂×C₁₉×#99	C₂²	1	2	yes	—
26	C₁₉×#389	—	2	2	no	—
27	C₁₉×#387	—	2	4	no	—
28	C₁₉×#381	C₂²	1	4	yes	—
29	C₁₉×#380	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
32	C₁₉×#342	C₂²	1	4	yes	—
33	C₁₉×#342	C₂²	1	4	yes	—
34	C₁₉×#342	C₂²	1	1	yes	characteristic
35	C₁₉×#342	C₂²	1	2	yes	—
36	C₁₉×#342	C₂²	1	1	yes	characteristic
37	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₁₉×#126	—	2	4	no	—
43	C₁₉×#126	—	2	4	no	—
44	C₁₉×#125	—	2	4	no	—
45	C₁₉×#125	—	2	4	no	—
46	C₁₉×#125	—	2	2	no	—
47	C₁₉×#125	—	2	2	no	—
48	C₁₉×#123	—	2	4	no	—
49	C₁₉×#123	—	2	4	no	—
50	C₁₉×C₂²⋊Q₈	—	2	2	no	—
51	C₁₉×C₂²⋊Q₈	—	2	2	no	—
52	C₁₉×C₂²⋊Q₈	—	2	2	no	—
53	C₁₉×C₂²⋊Q₈	—	2	2	no	—
54	C₄×Q₈×C₁₉	—	2	2	no	—
55	C₄×Q₈×C₁₉	—	2	1	no	—
56	C₄×Q₈×C₁₉	—	2	1	no	—
57	C₄×D₄×C₁₉	—	2	2	no	—
58	C₄×D₄×C₁₉	—	2	2	no	—
59	C₁₉×#117	—	2	4	no	—
60	C₁₉×#117	—	2	4	no	—
61	C₁₉×#117	—	2	2	no	—
62	C₁₉×#117	—	2	1	no	—
63	C₁₉×#117	—	2	1	no	—
64	C₁₉×#117	—	2	8	no	—
65	C₁₉×#117	—	4	4	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
84	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
85	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
88	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
89	C₂×C₄²×C₁₉	—	2	2	no	—
90	C₂×C₄²×C₁₉	—	2	4	no	—
91	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
92	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
93	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
94	C₁₉×#99	—	2	4	no	—
95	C₁₉×#99	—	4	2	no	—
96	C₁₉×#95	—	2	2	no	—
97	C₁₉×#95	—	2	4	no	—
98	C₁₉×#95	—	2	2	no	—
99	C₁₉×#95	—	2	4	no	—
100	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	1	no	—
104	C₂×Q₈×C₁₉	—	4	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	2	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	4	2	no	—
119	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	1	no	—
134	C₄⋊C₄×C₁₉	—	2	1	no	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	4	8	no	—
142	C₄⋊C₄×C₁₉	—	4	4	no	—
143	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
144	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
145	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
147	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
148	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
149	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
150	C₂²⋊C₄×C₁₉	—	2	2	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	2	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₉	—	2	4	no	—
157	C₂²⋊C₄×C₁₉	—	2	4	no	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	#41	1	4	yes	—
162	C₄²×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	—	2	2	no	—
164	C₄²×C₁₉	—	2	2	no	—
165	C₄²×C₁₉	—	2	2	no	—
166	C₄²×C₁₉	—	2	1	no	—
167	C₄²×C₁₉	—	2	1	no	—
168	C₄²×C₁₉	—	4	8	no	—
169	C₄²×C₁₉	—	4	4	no	—
170	#22478	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	1	no	—
177	C₂³×C₁₉	—	4	1	no	—
178	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
179	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
180	C₂³×C₁₉	C₂×#41	1	2	yes	—
181	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
183	Q₈×C₁₉	—	4	2	no	—
184	Q₈×C₁₉	—	4	2	no	—
185	D₄×C₁₉	—	4	2	no	—
186	D₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	2	no	—
216	C₂×C₄×C₁₉	—	4	4	no	—
217	C₂×C₄×C₁₉	—	4	4	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	4	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
222	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
225	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×#552	C₂×C₁₉	1	1	yes	characteristic
228	#2344	C₂×C₁₉	1	2	yes	complemented
229	#1996	C₂×C₁₉	1	2	yes	complemented
230	#1899	C₂×C₁₉	1	4	yes	—
231	#1820	C₂×C₁₉	1	2	yes	complemented
232	#1799	C₂×C₁₉	1	1	yes	characteristic
233	C₄×#99	C₂×C₁₉	1	1	yes	characteristic
234	#1740	C₂×C₁₉	1	2	yes	complemented
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	—	4	1	no	—
241	C₂²×C₁₉	—	4	1	no	—
242	C₂²×C₁₉	—	4	1	no	—
243	C₂²×C₁₉	—	4	1	no	—
244	C₂²×C₁₉	—	4	1	no	—
245	C₂²×C₁₉	—	8	1	no	—
246	C₂²×C₁₉	—	8	1	no	—
247	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₁₉	C₄×#41	1	1	yes	characteristic
249	C₂²×C₁₉	#520	1	1	yes	characteristic
250	C₂²×C₁₉	#546	1	2	yes	—
251	C₂²×C₁₉	#547	1	2	yes	—
252	C₄×C₁₉	—	2	2	no	—
253	C₄×C₁₉	—	2	4	no	—
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	2	1	no	—
256	C₄×C₁₉	—	2	2	no	—
257	C₄×C₁₉	—	4	4	no	—
258	C₄×C₁₉	—	4	1	no	—
259	C₄×C₁₉	—	4	1	no	—
260	C₄×C₁₉	—	4	2	no	—
261	C₄×C₁₉	—	4	1	no	—
262	C₄×C₁₉	—	4	2	no	—
263	C₄×C₁₉	—	8	4	no	—
264	C₄×C₁₉	—	8	2	no	—
265	C₄×C₁₉	#410	1	2	yes	—
266	#552	—	2	2	no	—
267	#552	—	2	4	no	—
268	#552	—	2	2	no	—
269	C₂×#126	C₄×C₁₉	1	2	yes	complemented
270	C₂×#125	C₄×C₁₉	1	2	yes	complemented
271	C₂×#125	C₄×C₁₉	1	1	yes	characteristic, complemented
272	C₂×#123	C₂²×C₁₉	1	2	yes	—
273	C₂×C₂²⋊Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
274	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
276	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×#117	C₄×C₁₉	1	1	yes	characteristic, complemented
278	C₂×#117	C₂²×C₁₉	1	4	yes	—
279	C₂×#117	C₂²×C₁₉	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×#99	C₂²×C₁₉	1	2	yes	—
282	C₂×#99	C₂²×C₁₉	1	2	yes	—
283	#389	—	2	2	no	—
284	#387	—	2	4	no	—
285	#381	C₂²×C₁₉	1	4	yes	—
286	#380	C₂²×C₁₉	1	2	yes	—
287	C₄×C₄⋊C₄	—	2	2	no	—
288	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
289	#342	C₂²×C₁₉	1	2	yes	—
290	#342	C₂²×C₁₉	1	1	yes	characteristic
291	#342	C₂²×C₁₉	1	4	yes	—
292	#342	C₂²×C₁₉	1	4	yes	—
293	#342	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×C₁₉	—	2	2	no	—
295	C₂×C₁₉	—	2	2	no	—
296	C₂×C₁₉	—	2	1	no	—
297	C₂×C₁₉	—	2	1	no	—
298	C₂×C₁₉	—	8	1	no	—
299	C₂×C₁₉	#2339	1	1	yes	characteristic
300	C₂×C₁₉	C₂×#410	1	1	yes	characteristic
301	C₂×C₁₉	#2884	1	1	yes	characteristic
302	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
303	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
304	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
306	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
307	#126	—	2	4	no	—
308	#126	—	2	4	no	—
309	#125	—	2	4	no	—
310	#125	—	2	4	no	—
311	#125	—	2	2	no	—
312	#125	—	2	2	no	—
313	#123	—	2	4	no	—
314	#123	—	2	4	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	#117	—	2	4	no	—
325	#117	—	2	4	no	—
326	#117	—	2	2	no	—
327	#117	—	2	1	no	—
328	#117	—	2	1	no	—
329	#117	—	2	8	no	—
330	#117	—	4	4	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
335	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
336	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
338	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
339	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
343	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
344	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
345	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
346	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
347	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
354	C₂×C₄²	—	2	4	no	—
355	C₂×C₄²	—	2	2	no	—
356	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
357	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
358	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
359	#99	—	2	4	no	—
360	#99	—	4	2	no	—
361	#95	—	2	2	no	—
362	#95	—	2	4	no	—
363	#95	—	2	2	no	—
364	#95	—	2	4	no	—
365	C₁₉	#22478	1	1	yes	characteristic, direct product factor, Sylow
366	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
367	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
387	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
389	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
392	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
393	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
396	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	4	8	no	—
408	C₄⋊C₄	—	4	4	no	—
409	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
410	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
411	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
412	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
413	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
414	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
415	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	#41×C₁₉	1	4	yes	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	4	8	no	—
435	C₄²	—	4	4	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
444	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
445	C₂³	C₂×#41×C₁₉	1	2	yes	—
446	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
448	Q₈	—	4	2	no	—
449	Q₈	—	4	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
487	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
488	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
489	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
490	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
491	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
492	C₂²	—	2	2	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
505	C₂²	C₄×#41×C₁₉	1	1	yes	characteristic
506	C₂²	C₁₉×#520	1	1	yes	characteristic
507	C₂²	C₁₉×#546	1	2	yes	—
508	C₂²	C₁₉×#547	1	2	yes	—
509	C₄	—	2	2	no	—
510	C₄	—	2	4	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	2	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	8	4	no	—
521	C₄	—	8	2	no	—
522	C₄	C₁₉×#410	1	2	yes	—
523	C₂	—	2	2	no	—
524	C₂	—	2	2	no	—
525	C₂	—	2	1	no	—
526	C₂	—	2	1	no	—
527	C₂	—	8	1	no	—
528	C₂	C₁₉×#2339	1	1	yes	characteristic
529	C₂	C₂×C₁₉×#410	1	1	yes	characteristic
530	C₂	C₁₉×#2884	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2344	C₂	semidirect
3. C₁₉×#1996	C₂	semidirect
5. C₁₉×#1820	C₂	semidirect
8. C₁₉×#1740	C₂	semidirect
12. C₂×C₁₉×#126	C₄	semidirect
13. C₂×C₁₉×#125	C₄	semidirect
14. C₂×C₁₉×#125	C₄	semidirect
16. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
18. C₂×C₄×Q₈×C₁₉	C₄	semidirect
20. C₂×C₁₉×#117	C₄	semidirect
170. #22478	C₁₉	direct (N × H)
228. #2344	C₂×C₁₉	semidirect
229. #1996	C₂×C₁₉	semidirect
231. #1820	C₂×C₁₉	semidirect
234. #1740	C₂×C₁₉	semidirect
269. C₂×#126	C₄×C₁₉	semidirect
270. C₂×#125	C₄×C₁₉	semidirect
271. C₂×#125	C₄×C₁₉	semidirect
273. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
275. C₂×C₄×Q₈	C₄×C₁₉	semidirect
277. C₂×#117	C₄×C₁₉	semidirect
365. C₁₉	#22478	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#552	2
C₁₉×#2344	2
C₁₉×#1996	2
C₁₉×#1899	2
C₁₉×#1820	2
C₁₉×#1799	2
C₄×C₁₉×#99	2
C₁₉×#1740	2
#22478	19

Subgroups — C19×#22478 #18028437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22478 #18028437