Subgroups — C₁₉×#34420 #18040379

Order 4864.

1974 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#541	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2383	C₂	1	4	yes	maximal
3	C₁₉×#2373	C₂	1	4	yes	maximal
4	C₁₉×#2370	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2365	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2356	C₂	1	2	yes	maximal, complemented
7	Q₈×C₄⋊C₄×C₁₉	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2336	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2330	C₂	1	4	yes	maximal, complemented
10	C₁₉×#2323	C₂	1	2	yes	maximal
11	C₁₉×#2314	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₉×C₂²⋊Q₈	C₂	1	2	yes	maximal
13	C₁₉×#2296	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#541	C₄	1	16	yes	complemented
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#126	C₂²	1	4	yes	—
17	C₂×C₁₉×#125	C₂²	1	4	yes	—
18	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#391	C₂²	1	2	yes	—
27	C₁₉×#391	C₂²	1	2	yes	—
28	C₁₉×#389	C₂²	1	2	yes	—
29	C₁₉×#389	C₂²	1	2	yes	—
30	C₁₉×#389	C₂²	1	2	yes	—
31	C₁₉×#389	C₂²	1	4	yes	—
32	C₁₉×#389	C₂²	1	2	yes	—
33	C₁₉×#389	C₂²	1	4	yes	—
34	C₁₉×#389	C₂²	1	4	yes	—
35	C₁₉×#389	C₂²	1	4	yes	—
36	C₁₉×#389	C₂²	1	4	yes	—
37	C₁₉×#388	C₂²	1	4	yes	—
38	C₁₉×#388	C₂²	1	4	yes	—
39	C₁₉×#388	C₂²	1	4	yes	—
40	C₁₉×#387	C₂²	1	4	yes	—
41	C₁₉×#387	C₂²	1	4	yes	—
42	C₁₉×#387	C₂²	1	4	yes	—
43	C₁₉×#387	C₂²	1	4	yes	—
44	C₁₉×#387	C₂²	1	4	yes	—
45	C₁₉×#387	C₂²	1	4	yes	—
46	C₁₉×#387	C₂²	1	4	yes	—
47	C₁₉×#387	C₂²	1	4	yes	—
48	C₁₉×#387	C₂²	1	4	yes	—
49	C₁₉×#385	C₂²	1	2	yes	—
50	C₁₉×#385	C₂²	1	2	yes	—
51	C₁₉×#385	C₂²	1	4	yes	—
52	C₁₉×#384	C₂²	1	1	yes	characteristic
53	C₁₉×#384	C₂²	1	4	yes	—
54	C₁₉×#383	C₂²	1	4	yes	—
55	C₁₉×#382	C₂²	1	1	yes	characteristic
56	C₁₉×#380	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
60	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
64	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
65	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
66	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
67	C₁₉×#376	C₂²	1	4	yes	—
68	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
73	C₁₉×#126	C₂×C₄	1	32	yes	—
74	C₁₉×#125	C₂×C₄	1	8	yes	complemented
75	C₁₉×#125	C₂×C₄	1	32	yes	complemented
76	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
77	C₄×Q₈×C₁₉	—	4	4	no	—
78	C₄×Q₈×C₁₉	—	4	4	no	—
79	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	complemented
80	C₁₉×#117	—	4	2	no	—
81	C₁₉×#117	C₂×C₄	1	8	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
103	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₉	—	4	2	no	—
106	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
107	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
109	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
112	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
113	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
115	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
117	C₁₉×#95	C₂³	1	2	yes	—
118	C₁₉×#95	C₂³	1	4	yes	—
119	C₁₉×#95	C₂³	1	4	yes	—
120	C₁₉×#95	C₂³	1	4	yes	—
121	C₁₉×#95	C₂³	1	4	yes	—
122	C₁₉×#95	C₂³	1	2	yes	—
123	C₁₉×#95	C₂³	1	4	yes	—
124	C₁₉×#95	C₂³	1	2	yes	—
125	C₁₉×#95	C₂³	1	4	yes	—
126	C₁₉×#95	C₂³	1	4	yes	—
127	C₁₉×#95	C₂³	1	4	yes	—
128	C₁₉×#95	C₂³	1	4	yes	—
129	C₁₉×#95	C₂³	1	2	yes	—
130	C₁₉×#95	C₂³	1	4	yes	—
131	C₁₉×#95	C₂³	1	4	yes	—
132	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
133	C₂×Q₈×C₁₉	—	2	4	no	—
134	C₂×Q₈×C₁₉	—	2	4	no	—
135	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	2	no	—
138	C₂²×C₄×C₁₉	—	2	4	no	—
139	C₂²×C₄×C₁₉	—	4	1	no	—
140	C₂²×C₄×C₁₉	—	4	1	no	—
141	C₂²×C₄×C₁₉	—	4	2	no	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	C₄⋊C₄×C₁₉	—	2	4	no	—
156	C₄⋊C₄×C₁₉	—	2	4	no	—
157	C₄⋊C₄×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	4	no	—
159	C₄⋊C₄×C₁₉	—	4	2	no	—
160	C₄⋊C₄×C₁₉	—	4	4	no	—
161	C₄⋊C₄×C₁₉	—	4	4	no	—
162	C₄⋊C₄×C₁₉	—	4	2	no	—
163	C₄⋊C₄×C₁₉	—	4	4	no	—
164	C₄⋊C₄×C₁₉	—	4	1	no	—
165	C₄⋊C₄×C₁₉	—	4	1	no	—
166	C₄⋊C₄×C₁₉	—	4	4	no	—
167	C₄⋊C₄×C₁₉	—	4	4	no	—
168	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
169	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
170	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
171	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
172	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
173	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
174	C₂²⋊C₄×C₁₉	—	4	4	no	—
175	C₂²⋊C₄×C₁₉	—	4	2	no	—
176	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
177	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
178	C₄²×C₁₉	—	2	4	no	—
179	C₄²×C₁₉	—	2	4	no	—
180	C₄²×C₁₉	—	2	8	no	—
181	C₄²×C₁₉	—	4	2	no	—
182	C₄²×C₁₉	—	4	4	no	—
183	C₄²×C₁₉	—	4	4	no	—
184	C₄²×C₁₉	—	4	4	no	—
185	C₄²×C₁₉	—	4	4	no	—
186	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
187	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
188	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
189	#34420	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂³×C₁₉	—	2	1	no	—
191	C₂³×C₁₉	—	2	1	no	—
192	C₂³×C₁₉	—	2	2	no	—
193	C₂³×C₁₉	—	2	2	no	—
194	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
195	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
196	Q₈×C₁₉	—	2	16	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	2	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	4	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	8	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	4	no	—
214	C₂×C₄×C₁₉	—	2	4	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	4	no	—
218	C₂×C₄×C₁₉	—	2	4	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	4	no	—
221	C₂×C₄×C₁₉	—	2	4	no	—
222	C₂×C₄×C₁₉	—	2	2	no	—
223	C₂×C₄×C₁₉	—	2	2	no	—
224	C₂×C₄×C₁₉	—	2	2	no	—
225	C₂×C₄×C₁₉	—	4	4	no	—
226	C₂×C₄×C₁₉	—	4	4	no	—
227	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
228	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
229	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
230	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
231	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
232	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
233	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
234	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
235	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
236	C₂×#541	C₂×C₁₉	1	1	yes	characteristic
237	#2383	C₂×C₁₉	1	4	yes	—
238	#2373	C₂×C₁₉	1	4	yes	—
239	#2370	C₂×C₁₉	1	2	yes	complemented
240	#2365	C₂×C₁₉	1	2	yes	complemented
241	#2356	C₂×C₁₉	1	2	yes	complemented
242	Q₈×C₄⋊C₄	C₂×C₁₉	1	2	yes	complemented
243	#2336	C₂×C₁₉	1	4	yes	complemented
244	#2330	C₂×C₁₉	1	4	yes	complemented
245	#2323	C₂×C₁₉	1	2	yes	—
246	#2314	C₂×C₁₉	1	1	yes	characteristic
247	C₄×C₂²⋊Q₈	C₂×C₁₉	1	2	yes	—
248	#2296	C₂×C₁₉	1	1	yes	characteristic
249	C₂²×C₁₉	—	2	2	no	—
250	C₂²×C₁₉	—	2	4	no	—
251	C₂²×C₁₉	—	4	1	no	—
252	C₂²×C₁₉	—	4	1	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
255	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
256	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
257	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
258	C₂²×C₁₉	#585	1	2	yes	—
259	C₄×C₁₉	—	2	2	no	—
260	C₄×C₁₉	—	2	8	no	—
261	C₄×C₁₉	—	2	8	no	—
262	C₄×C₁₉	—	2	4	no	—
263	C₄×C₁₉	—	2	4	no	—
264	C₄×C₁₉	—	2	4	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	4	4	no	—
268	C₄×C₁₉	—	4	2	no	—
269	C₄×C₁₉	—	4	4	no	—
270	C₄×C₁₉	#520	1	4	yes	—
271	#541	C₄×C₁₉	1	16	yes	complemented
272	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
273	C₂×#126	C₂²×C₁₉	1	4	yes	—
274	C₂×#125	C₂²×C₁₉	1	4	yes	—
275	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
277	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
278	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
279	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
280	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
281	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
282	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
283	#391	C₂²×C₁₉	1	2	yes	—
284	#391	C₂²×C₁₉	1	2	yes	—
285	#389	C₂²×C₁₉	1	4	yes	—
286	#389	C₂²×C₁₉	1	2	yes	—
287	#389	C₂²×C₁₉	1	2	yes	—
288	#389	C₂²×C₁₉	1	4	yes	—
289	#389	C₂²×C₁₉	1	4	yes	—
290	#389	C₂²×C₁₉	1	4	yes	—
291	#389	C₂²×C₁₉	1	2	yes	—
292	#389	C₂²×C₁₉	1	4	yes	—
293	#389	C₂²×C₁₉	1	2	yes	—
294	#388	C₂²×C₁₉	1	4	yes	—
295	#388	C₂²×C₁₉	1	4	yes	—
296	#388	C₂²×C₁₉	1	4	yes	—
297	#387	C₂²×C₁₉	1	4	yes	—
298	#387	C₂²×C₁₉	1	4	yes	—
299	#387	C₂²×C₁₉	1	4	yes	—
300	#387	C₂²×C₁₉	1	4	yes	—
301	#387	C₂²×C₁₉	1	4	yes	—
302	#387	C₂²×C₁₉	1	4	yes	—
303	#387	C₂²×C₁₉	1	4	yes	—
304	#387	C₂²×C₁₉	1	4	yes	—
305	#387	C₂²×C₁₉	1	4	yes	—
306	#385	C₂²×C₁₉	1	2	yes	—
307	#385	C₂²×C₁₉	1	2	yes	—
308	#385	C₂²×C₁₉	1	4	yes	—
309	#384	C₂²×C₁₉	1	1	yes	characteristic
310	#384	C₂²×C₁₉	1	4	yes	—
311	#383	C₂²×C₁₉	1	4	yes	—
312	#382	C₂²×C₁₉	1	1	yes	characteristic
313	#380	C₂²×C₁₉	1	2	yes	—
314	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
315	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
316	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
317	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
318	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
319	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
320	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
321	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
322	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
323	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
324	#376	C₂²×C₁₉	1	4	yes	—
325	C₂×C₁₉	—	4	2	no	—
326	C₂×C₁₉	C₂×#520	1	1	yes	characteristic
327	C₂×C₁₉	C₄×2₋¹⁺⁴	1	2	yes	—
328	C₂×C₁₉	#3538	1	1	yes	characteristic
329	C₂×C₁₉	#3539	1	1	yes	characteristic
330	C₂×C₁₉	#3555	1	2	yes	—
331	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
332	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
335	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
336	#126	C₂×C₄×C₁₉	1	32	yes	—
337	#125	C₂×C₄×C₁₉	1	8	yes	complemented
338	#125	C₂×C₄×C₁₉	1	32	yes	complemented
339	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
340	C₄×Q₈	—	4	4	no	—
341	C₄×Q₈	—	4	4	no	—
342	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
343	#117	—	4	2	no	—
344	#117	C₂×C₄×C₁₉	1	8	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
368	C₂×C₄²	—	4	2	no	—
369	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
370	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
371	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
372	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
373	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
374	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
375	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
376	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
377	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
380	#95	C₂³×C₁₉	1	2	yes	—
381	#95	C₂³×C₁₉	1	4	yes	—
382	#95	C₂³×C₁₉	1	4	yes	—
383	#95	C₂³×C₁₉	1	4	yes	—
384	#95	C₂³×C₁₉	1	4	yes	—
385	#95	C₂³×C₁₉	1	2	yes	—
386	#95	C₂³×C₁₉	1	4	yes	—
387	#95	C₂³×C₁₉	1	2	yes	—
388	#95	C₂³×C₁₉	1	4	yes	—
389	#95	C₂³×C₁₉	1	4	yes	—
390	#95	C₂³×C₁₉	1	4	yes	—
391	#95	C₂³×C₁₉	1	4	yes	—
392	#95	C₂³×C₁₉	1	2	yes	—
393	#95	C₂³×C₁₉	1	4	yes	—
394	#95	C₂³×C₁₉	1	4	yes	—
395	C₁₉	#34420	1	1	yes	characteristic, direct product factor, Sylow
396	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	—	4	2	no	—
406	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
407	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
413	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	4	4	no	—
425	C₄⋊C₄	—	4	4	no	—
426	C₄⋊C₄	—	4	2	no	—
427	C₄⋊C₄	—	4	4	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₄⋊C₄	—	4	1	no	—
430	C₄⋊C₄	—	4	4	no	—
431	C₄⋊C₄	—	4	4	no	—
432	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
433	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
434	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
435	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
436	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
437	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
438	C₂²⋊C₄	—	4	4	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
441	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
442	C₄²	—	2	4	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	2	8	no	—
445	C₄²	—	4	2	no	—
446	C₄²	—	4	4	no	—
447	C₄²	—	4	4	no	—
448	C₄²	—	4	4	no	—
449	C₄²	—	4	4	no	—
450	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
451	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
452	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
453	C₂³	—	2	1	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
458	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
459	Q₈	—	2	16	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
491	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
492	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
493	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
494	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
495	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
496	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
497	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
498	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	2	no	—
504	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
505	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
506	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
507	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
508	C₂²	C₁₉×#585	1	2	yes	—
509	C₄	—	2	2	no	—
510	C₄	—	2	8	no	—
511	C₄	—	2	8	no	—
512	C₄	—	2	4	no	—
513	C₄	—	2	4	no	—
514	C₄	—	2	4	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	4	no	—
520	C₄	C₁₉×#520	1	4	yes	—
521	C₂	—	4	2	no	—
522	C₂	C₂×C₁₉×#520	1	1	yes	characteristic
523	C₂	C₄×C₁₉×2₋¹⁺⁴	1	2	yes	—
524	C₂	C₁₉×#3538	1	1	yes	characteristic
525	C₂	C₁₉×#3539	1	1	yes	characteristic
526	C₂	C₁₉×#3555	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₁₉×#2370	C₂	semidirect
5. C₁₉×#2365	C₂	semidirect
6. C₁₉×#2356	C₂	semidirect
7. Q₈×C₄⋊C₄×C₁₉	C₂	semidirect
8. C₁₉×#2336	C₂	semidirect
9. C₁₉×#2330	C₂	semidirect
14. C₁₉×#541	C₄	semidirect
72. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
74. C₁₉×#125	C₂×C₄	semidirect
75. C₁₉×#125	C₂×C₄	semidirect
79. C₄×Q₈×C₁₉	C₂×C₄	semidirect
189. #34420	C₁₉	direct (N × H)
239. #2370	C₂×C₁₉	semidirect
240. #2365	C₂×C₁₉	semidirect
241. #2356	C₂×C₁₉	semidirect
242. Q₈×C₄⋊C₄	C₂×C₁₉	semidirect
243. #2336	C₂×C₁₉	semidirect
244. #2330	C₂×C₁₉	semidirect
271. #541	C₄×C₁₉	semidirect
335. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
337. #125	C₂×C₄×C₁₉	semidirect
338. #125	C₂×C₄×C₁₉	semidirect
342. C₄×Q₈	C₂×C₄×C₁₉	semidirect
395. C₁₉	#34420	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×#541	2
C₁₉×#2383	2
C₁₉×#2373	2
C₁₉×#2370	2
C₁₉×#2365	2
C₁₉×#2356	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#2336	2
C₁₉×#2330	2
C₁₉×#2323	2
C₁₉×#2314	2
C₄×C₁₉×C₂²⋊Q₈	2
C₁₉×#2296	2
#34420	19

Subgroups — C19×#34420 #18040379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34420 #18040379