Subgroups — C₁₉×#34250 #18040209

Order 4864.

3106 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2351	C₂	1	2	yes	maximal, complemented
5	Q₈×C₄⋊C₄×C₁₉	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2349	C₂	1	6	yes	maximal, complemented
7	D₄×C₄⋊C₄×C₁₉	C₂	1	6	yes	maximal, complemented
8	C₁₉×#2317	C₂	1	3	yes	maximal, complemented
9	C₁₉×#2316	C₂	1	3	yes	maximal, complemented
10	C₁₉×#2296	C₂	1	3	yes	maximal, complemented
11	C₂×C₁₉×#389	C₂	1	3	yes	maximal, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#520	—	2	8	no	—
14	C₁₉×#520	C₄	1	16	yes	complemented
15	C₄×#41×C₁₉	—	2	8	no	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	—
23	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	—
24	C₂×C₁₉×#117	C₂²	1	3	yes	—
25	C₂×C₁₉×#117	C₂²	1	3	yes	—
26	C₂×C₁₉×#117	C₂²	1	3	yes	—
27	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
28	C₂²×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
29	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
30	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
31	C₁₉×#389	C₂²	1	3	yes	—
32	C₁₉×#389	C₂²	1	6	yes	—
33	C₁₉×#389	C₂²	1	6	yes	—
34	C₁₉×#389	C₂²	1	6	yes	—
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#389	C₂²	1	3	yes	—
37	C₁₉×#389	C₂²	1	3	yes	—
38	C₁₉×#389	C₂²	1	6	yes	—
39	C₁₉×#389	C₂²	1	6	yes	—
40	C₁₉×#385	C₂²	1	6	yes	—
41	C₁₉×#385	C₂²	1	6	yes	—
42	C₁₉×#385	C₂²	1	12	yes	—
43	C₁₉×#384	C₂²	1	6	yes	—
44	C₁₉×#382	C₂²	1	6	yes	—
45	C₁₉×#380	C₂²	1	12	yes	—
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
48	C₂×C₁₉×#95	C₂²	1	6	yes	—
49	C₂×#41×C₁₉	C₂×C₄	1	8	yes	—
50	C₂×#41×C₁₉	D₄	1	8	yes	—
51	C₂×#41×C₁₉	Q₈	1	8	yes	—
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
59	C₄×Q₈×C₁₉	—	2	4	no	—
60	C₄×Q₈×C₁₉	—	2	4	no	—
61	C₄×Q₈×C₁₉	—	2	8	no	—
62	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	complemented
63	C₄×D₄×C₁₉	—	2	12	no	—
64	C₄×D₄×C₁₉	—	2	12	no	—
65	C₄×D₄×C₁₉	—	2	24	no	—
66	C₄×D₄×C₁₉	C₂×C₄	1	48	yes	complemented
67	C₁₉×#117	—	2	12	no	—
68	C₁₉×#117	—	2	12	no	—
69	C₁₉×#117	C₂×C₄	1	24	yes	complemented
70	C₂×C₄⋊C₄×C₁₉	—	2	12	no	—
71	C₂×C₄⋊C₄×C₁₉	—	4	12	no	—
72	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	24	yes	complemented
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
88	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
89	C₂×C₄²×C₁₉	—	2	12	no	—
90	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
91	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
95	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
96	C₁₉×#95	C₂³	1	6	yes	—
97	C₁₉×#95	C₂³	1	12	yes	—
98	C₁₉×#95	C₂³	1	2	yes	—
99	C₁₉×#95	C₂³	1	6	yes	—
100	C₁₉×#95	C₂³	1	6	yes	—
101	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
102	#41×C₁₉	C₄⋊C₄	1	64	yes	complemented
103	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
104	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
105	C₂×Q₈×C₁₉	C₂×Q₈	1	4	yes	—
106	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
107	C₂×D₄×C₁₉	C₂×D₄	1	12	yes	—
108	C₂×D₄×C₁₉	C₂×Q₈	1	12	yes	—
109	C₂²×C₄×C₁₉	—	2	6	no	—
110	C₂²×C₄×C₁₉	—	2	6	no	—
111	C₂²×C₄×C₁₉	—	2	12	no	—
112	C₂²×C₄×C₁₉	—	2	6	no	—
113	C₂²×C₄×C₁₉	—	2	6	no	—
114	C₂²×C₄×C₁₉	—	4	6	no	—
115	C₂²×C₄×C₁₉	—	4	6	no	—
116	C₂²×C₄×C₁₉	—	4	3	no	—
117	C₂²×C₄×C₁₉	—	4	3	no	—
118	C₂²×C₄×C₁₉	—	4	6	no	—
119	C₂²×C₄×C₁₉	—	4	6	no	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	24	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	12	yes	—
123	C₂²×C₄×C₁₉	C₂×Q₈	1	12	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
126	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
130	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
134	C₄⋊C₄×C₁₉	—	2	6	no	—
135	C₄⋊C₄×C₁₉	—	2	12	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	6	no	—
138	C₄⋊C₄×C₁₉	—	2	6	no	—
139	C₄⋊C₄×C₁₉	—	2	12	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	4	12	no	—
142	C₄⋊C₄×C₁₉	—	4	6	no	—
143	C₄⋊C₄×C₁₉	—	4	6	no	—
144	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
145	C₄⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
146	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
147	C₂²⋊C₄×C₁₉	—	2	12	no	—
148	C₂²⋊C₄×C₁₉	—	2	12	no	—
149	C₂²⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
150	C₄²×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	—	2	6	no	—
152	C₄²×C₁₉	—	2	6	no	—
153	C₄²×C₁₉	—	2	6	no	—
154	C₄²×C₁₉	—	2	12	no	—
155	C₄²×C₁₉	C₂²×C₄	1	24	yes	—
156	#34250	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂³×C₁₉	—	2	3	no	—
158	C₂³×C₁₉	—	2	3	no	—
159	C₂³×C₁₉	—	2	3	no	—
160	C₂³×C₁₉	—	2	3	no	—
161	C₂³×C₁₉	C₂³×C₄	1	6	yes	—
162	C₂³×C₁₉	C₂²×D₄	1	6	yes	—
163	C₂³×C₁₉	C₂²×Q₈	1	6	yes	—
164	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
165	Q₈×C₁₉	C₂×C₄⋊C₄	1	16	yes	complemented
166	D₄×C₁₉	C₂×C₄⋊C₄	1	48	yes	complemented
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	6	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	6	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	2	3	no	—
177	C₂×C₄×C₁₉	—	2	3	no	—
178	C₂×C₄×C₁₉	—	2	6	no	—
179	C₂×C₄×C₁₉	—	2	6	no	—
180	C₂×C₄×C₁₉	—	2	3	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	3	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	3	no	—
185	C₂×C₄×C₁₉	—	2	3	no	—
186	C₂×C₄×C₁₉	—	2	6	no	—
187	C₂×C₄×C₁₉	—	4	24	no	—
188	C₂×C₄×C₁₉	—	4	12	no	—
189	C₂×C₄×C₁₉	—	4	12	no	—
190	C₂×C₄×C₁₉	—	8	12	no	—
191	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	48	yes	complemented
192	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
193	C₂×C₄×C₁₉	C₂³×C₄	1	12	yes	—
194	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
195	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
196	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
198	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
199	C₂×C₄×C₁₉	C₂²×Q₈	1	6	yes	—
200	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
201	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
202	C₂×#520	C₂×C₁₉	1	1	yes	characteristic
203	C₂×#520	C₂×C₁₉	1	1	yes	characteristic
204	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic
205	#2351	C₂×C₁₉	1	2	yes	complemented
206	Q₈×C₄⋊C₄	C₂×C₁₉	1	2	yes	complemented
207	#2349	C₂×C₁₉	1	6	yes	complemented
208	D₄×C₄⋊C₄	C₂×C₁₉	1	6	yes	complemented
209	#2317	C₂×C₁₉	1	3	yes	complemented
210	#2316	C₂×C₁₉	1	3	yes	complemented
211	#2296	C₂×C₁₉	1	3	yes	complemented
212	C₂×#389	C₂×C₁₉	1	3	yes	complemented
213	C₂²×C₁₉	—	2	6	no	—
214	C₂²×C₁₉	—	2	6	no	—
215	C₂²×C₁₉	—	2	6	no	—
216	C₂²×C₁₉	—	2	6	no	—
217	C₂²×C₁₉	—	2	6	no	—
218	C₂²×C₁₉	—	2	6	no	—
219	C₂²×C₁₉	C₂²×C₄⋊C₄	1	12	yes	—
220	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
221	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
222	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
223	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
224	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
225	C₂²×C₁₉	#585	1	1	yes	characteristic
226	C₂²×C₁₉	#585	1	1	yes	characteristic
227	C₄×C₁₉	—	2	12	no	—
228	C₄×C₁₉	—	2	4	no	—
229	C₄×C₁₉	—	2	2	no	—
230	C₄×C₁₉	—	2	2	no	—
231	C₄×C₁₉	—	4	3	no	—
232	C₄×C₁₉	—	4	6	no	—
233	C₄×C₁₉	—	4	2	no	—
234	C₄×C₁₉	—	4	3	no	—
235	C₄×C₁₉	C₂²×C₄⋊C₄	1	4	yes	—
236	C₄×C₁₉	C₂²×C₄⋊C₄	1	12	yes	—
237	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
238	#520	—	2	8	no	—
239	#520	C₄×C₁₉	1	16	yes	complemented
240	C₄×#41	—	2	8	no	—
241	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
243	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
246	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	—
247	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
248	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	—
249	C₂×#117	C₂²×C₁₉	1	3	yes	—
250	C₂×#117	C₂²×C₁₉	1	3	yes	—
251	C₂×#117	C₂²×C₁₉	1	3	yes	—
252	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
253	C₂²×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
254	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
255	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
256	#389	C₂²×C₁₉	1	3	yes	—
257	#389	C₂²×C₁₉	1	6	yes	—
258	#389	C₂²×C₁₉	1	6	yes	—
259	#389	C₂²×C₁₉	1	6	yes	—
260	#389	C₂²×C₁₉	1	3	yes	—
261	#389	C₂²×C₁₉	1	6	yes	—
262	#389	C₂²×C₁₉	1	6	yes	—
263	#389	C₂²×C₁₉	1	3	yes	—
264	#389	C₂²×C₁₉	1	1	yes	characteristic
265	#385	C₂²×C₁₉	1	12	yes	—
266	#385	C₂²×C₁₉	1	6	yes	—
267	#385	C₂²×C₁₉	1	6	yes	—
268	#384	C₂²×C₁₉	1	6	yes	—
269	#382	C₂²×C₁₉	1	6	yes	—
270	#380	C₂²×C₁₉	1	12	yes	—
271	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
272	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
273	C₂×#95	C₂²×C₁₉	1	6	yes	—
274	C₂×C₁₉	—	2	12	no	—
275	C₂×C₁₉	C₂³×C₄⋊C₄	1	1	yes	characteristic
276	C₂×C₁₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
278	C₂×C₁₉	#3488	1	1	yes	characteristic
279	C₂×C₁₉	#3489	1	1	yes	characteristic
280	C₂×C₁₉	#3503	1	1	yes	characteristic
281	C₂×C₁₉	#3504	1	1	yes	characteristic
282	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
283	C₂×#41	D₄×C₁₉	1	8	yes	—
284	C₂×#41	Q₈×C₁₉	1	8	yes	—
285	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
286	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
287	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
288	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
289	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
290	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
291	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
292	C₄×Q₈	—	2	4	no	—
293	C₄×Q₈	—	2	4	no	—
294	C₄×Q₈	—	2	8	no	—
295	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
296	C₄×D₄	—	2	12	no	—
297	C₄×D₄	—	2	12	no	—
298	C₄×D₄	—	2	24	no	—
299	C₄×D₄	C₂×C₄×C₁₉	1	48	yes	complemented
300	#117	—	2	12	no	—
301	#117	—	2	12	no	—
302	#117	C₂×C₄×C₁₉	1	24	yes	complemented
303	C₂×C₄⋊C₄	—	2	12	no	—
304	C₂×C₄⋊C₄	—	4	12	no	—
305	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	24	yes	complemented
306	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₉	1	12	yes	—
314	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
322	C₂×C₄²	—	2	12	no	—
323	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
324	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
325	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
326	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
327	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
329	#95	C₂³×C₁₉	1	6	yes	—
330	#95	C₂³×C₁₉	1	12	yes	—
331	#95	C₂³×C₁₉	1	2	yes	—
332	#95	C₂³×C₁₉	1	6	yes	—
333	#95	C₂³×C₁₉	1	6	yes	—
334	C₁₉	#34250	1	1	yes	characteristic, direct product factor, Sylow
335	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
336	#41	C₄⋊C₄×C₁₉	1	64	yes	complemented
337	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
338	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
339	C₂×Q₈	C₂×Q₈×C₁₉	1	4	yes	—
340	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
341	C₂×D₄	C₂×D₄×C₁₉	1	12	yes	—
342	C₂×D₄	C₂×Q₈×C₁₉	1	12	yes	—
343	C₂²×C₄	—	2	6	no	—
344	C₂²×C₄	—	2	6	no	—
345	C₂²×C₄	—	2	12	no	—
346	C₂²×C₄	—	2	6	no	—
347	C₂²×C₄	—	2	6	no	—
348	C₂²×C₄	—	4	6	no	—
349	C₂²×C₄	—	4	6	no	—
350	C₂²×C₄	—	4	3	no	—
351	C₂²×C₄	—	4	3	no	—
352	C₂²×C₄	—	4	6	no	—
353	C₂²×C₄	—	4	6	no	—
354	C₂²×C₄	C₂²×C₄×C₁₉	1	24	yes	—
355	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
356	C₂²×C₄	C₂×D₄×C₁₉	1	12	yes	—
357	C₂²×C₄	C₂×Q₈×C₁₉	1	12	yes	—
358	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
359	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
361	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
362	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
364	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
367	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
368	C₄⋊C₄	—	2	6	no	—
369	C₄⋊C₄	—	2	12	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	6	no	—
372	C₄⋊C₄	—	2	6	no	—
373	C₄⋊C₄	—	2	12	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	4	12	no	—
376	C₄⋊C₄	—	4	6	no	—
377	C₄⋊C₄	—	4	6	no	—
378	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
379	C₄⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
380	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
381	C₂²⋊C₄	—	2	12	no	—
382	C₂²⋊C₄	—	2	12	no	—
383	C₂²⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	6	no	—
386	C₄²	—	2	6	no	—
387	C₄²	—	2	6	no	—
388	C₄²	—	2	12	no	—
389	C₄²	C₂²×C₄×C₁₉	1	24	yes	—
390	C₂³	—	2	3	no	—
391	C₂³	—	2	3	no	—
392	C₂³	—	2	3	no	—
393	C₂³	—	2	3	no	—
394	C₂³	C₂³×C₄×C₁₉	1	6	yes	—
395	C₂³	C₂²×D₄×C₁₉	1	6	yes	—
396	C₂³	C₂²×Q₈×C₁₉	1	6	yes	—
397	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
398	Q₈	C₂×C₄⋊C₄×C₁₉	1	16	yes	complemented
399	D₄	C₂×C₄⋊C₄×C₁₉	1	48	yes	complemented
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	6	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	6	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	3	no	—
410	C₂×C₄	—	2	3	no	—
411	C₂×C₄	—	2	6	no	—
412	C₂×C₄	—	2	6	no	—
413	C₂×C₄	—	2	3	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	3	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	3	no	—
418	C₂×C₄	—	2	3	no	—
419	C₂×C₄	—	2	6	no	—
420	C₂×C₄	—	4	24	no	—
421	C₂×C₄	—	4	12	no	—
422	C₂×C₄	—	4	12	no	—
423	C₂×C₄	—	8	12	no	—
424	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	48	yes	complemented
425	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
426	C₂×C₄	C₂³×C₄×C₁₉	1	12	yes	—
427	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
428	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
431	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
432	C₂×C₄	C₂²×Q₈×C₁₉	1	6	yes	—
433	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
434	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
435	C₂²	—	2	6	no	—
436	C₂²	—	2	6	no	—
437	C₂²	—	2	6	no	—
438	C₂²	—	2	6	no	—
439	C₂²	—	2	6	no	—
440	C₂²	—	2	6	no	—
441	C₂²	C₂²×C₄⋊C₄×C₁₉	1	12	yes	—
442	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
443	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
444	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
445	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
447	C₂²	C₁₉×#585	1	1	yes	characteristic
448	C₂²	C₁₉×#585	1	1	yes	characteristic
449	C₄	—	2	12	no	—
450	C₄	—	2	4	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	4	3	no	—
454	C₄	—	4	6	no	—
455	C₄	—	4	3	no	—
456	C₄	—	4	2	no	—
457	C₄	C₂²×C₄⋊C₄×C₁₉	1	4	yes	—
458	C₄	C₂²×C₄⋊C₄×C₁₉	1	12	yes	—
459	C₂	—	2	12	no	—
460	C₂	C₂³×C₄⋊C₄×C₁₉	1	1	yes	characteristic
461	C₂	C₄×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂	C₄×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
463	C₂	C₁₉×#3488	1	1	yes	characteristic
464	C₂	C₁₉×#3489	1	1	yes	characteristic
465	C₂	C₁₉×#3503	1	1	yes	characteristic
466	C₂	C₁₉×#3504	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
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×#2351	C₂	semidirect
5. Q₈×C₄⋊C₄×C₁₉	C₂	semidirect
6. C₁₉×#2349	C₂	semidirect
7. D₄×C₄⋊C₄×C₁₉	C₂	semidirect
8. C₁₉×#2317	C₂	semidirect
9. C₁₉×#2316	C₂	semidirect
10. C₁₉×#2296	C₂	semidirect
11. C₂×C₁₉×#389	C₂	semidirect
14. C₁₉×#520	C₄	semidirect
62. C₄×Q₈×C₁₉	C₂×C₄	semidirect
66. C₄×D₄×C₁₉	C₂×C₄	semidirect
69. C₁₉×#117	C₂×C₄	semidirect
72. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
102. #41×C₁₉	C₄⋊C₄	semidirect
156. #34250	C₁₉	direct (N × H)
165. Q₈×C₁₉	C₂×C₄⋊C₄	semidirect
166. D₄×C₁₉	C₂×C₄⋊C₄	semidirect
191. C₂×C₄×C₁₉	C₂×C₄⋊C₄	semidirect
205. #2351	C₂×C₁₉	semidirect
206. Q₈×C₄⋊C₄	C₂×C₁₉	semidirect
207. #2349	C₂×C₁₉	semidirect
208. D₄×C₄⋊C₄	C₂×C₁₉	semidirect
209. #2317	C₂×C₁₉	semidirect
210. #2316	C₂×C₁₉	semidirect
211. #2296	C₂×C₁₉	semidirect
212. C₂×#389	C₂×C₁₉	semidirect
239. #520	C₄×C₁₉	semidirect
295. C₄×Q₈	C₂×C₄×C₁₉	semidirect
299. C₄×D₄	C₂×C₄×C₁₉	semidirect
302. #117	C₂×C₄×C₁₉	semidirect
305. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
334. C₁₉	#34250	direct (N × H)
336. #41	C₄⋊C₄×C₁₉	semidirect
398. Q₈	C₂×C₄⋊C₄×C₁₉	semidirect
399. D₄	C₂×C₄⋊C₄×C₁₉	semidirect
424. C₂×C₄	C₂×C₄⋊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×#520	2
C₂×C₄×#41×C₁₉	2
C₁₉×#2351	2
Q₈×C₄⋊C₄×C₁₉	2
C₁₉×#2349	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2317	2
C₁₉×#2316	2
C₁₉×#2296	2
C₂×C₁₉×#389	2
#34250	19

Subgroups — C19×#34250 #18040209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34250 #18040209