Subgroups — C₁₉×#34512 #18040471

Order 4864.

2576 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2375	C₂	1	3	yes	maximal, complemented
3	C₁₉×#2372	C₂	1	3	yes	maximal, complemented
4	C₁₉×#2367	C₂	1	6	yes	maximal, complemented
5	C₁₉×#2358	C₂	1	3	yes	maximal, complemented
6	C₁₉×#2337	C₂	1	6	yes	maximal, complemented
7	C₁₉×#2326	C₂	1	3	yes	maximal, complemented
8	C₁₉×#2321	C₂	1	3	yes	maximal, complemented
9	C₄×C₁₉×#120	C₂	1	3	yes	maximal, complemented
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
11	C₁₉×H(3,𝔽₄)	C₄	1	16	yes	complemented
12	C₂×C₁₉×#124	C₂²	1	3	yes	—
13	C₂×C₁₉×#124	C₂²	1	6	yes	—
14	C₂×C₁₉×#120	C₂²	1	3	yes	—
15	C₂×C₁₉×#120	C₂²	1	3	yes	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	complemented
17	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
18	C₂×C₄×D₄×C₁₉	C₂²	1	6	yes	—
19	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	complemented
20	C₁₉×#391	C₂²	1	3	yes	complemented
21	C₁₉×#391	C₂²	1	6	yes	complemented
22	C₁₉×#390	C₂²	1	6	yes	—
23	C₁₉×#390	C₂²	1	3	yes	—
24	C₁₉×#388	C₂²	1	6	yes	complemented
25	C₁₉×#388	C₂²	1	6	yes	complemented
26	C₁₉×#388	C₂²	1	6	yes	complemented
27	C₁₉×#388	C₂²	1	6	yes	complemented
28	C₁₉×#388	C₂²	1	6	yes	complemented
29	C₁₉×#388	C₂²	1	6	yes	complemented
30	C₁₉×#386	C₂²	1	6	yes	—
31	C₁₉×#386	C₂²	1	3	yes	—
32	C₁₉×#386	C₂²	1	3	yes	—
33	C₁₉×#386	C₂²	1	6	yes	—
34	C₁₉×#385	C₂²	1	6	yes	complemented
35	C₁₉×#385	C₂²	1	3	yes	complemented
36	C₁₉×#385	C₂²	1	3	yes	complemented
37	C₁₉×#385	C₂²	1	6	yes	complemented
38	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#383	C₂²	1	2	yes	complemented
40	C₁₉×#379	C₂²	1	3	yes	complemented
41	C₁₉×#379	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	complemented
43	C₄×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	complemented
44	C₄×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	complemented
45	C₄×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	complemented
46	C₄×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	complemented
47	C₁₉×#376	C₂²	1	3	yes	complemented
48	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
49	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
52	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
53	C₂³×C₄×C₁₉	—	4	6	no	—
54	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
55	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
58	C₁₉×#124	C₂×C₄	1	24	yes	complemented
59	C₁₉×#124	C₂×C₄	1	48	yes	complemented
60	C₁₉×#120	C₂×C₄	1	24	yes	complemented
61	C₁₉×#120	C₂×C₄	1	24	yes	complemented
62	C₄×Q₈×C₁₉	—	4	6	no	—
63	C₄×D₄×C₁₉	—	4	6	no	—
64	C₄×D₄×C₁₉	—	4	12	no	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
69	C₂×C₂²⋊C₄×C₁₉	—	4	6	no	—
70	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
71	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
72	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
73	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
74	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
75	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
80	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
81	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
82	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
84	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
85	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
88	C₁₉×#95	C₂³	1	6	yes	—
89	C₁₉×#95	C₂³	1	6	yes	—
90	C₁₉×#95	C₂³	1	6	yes	—
91	C₁₉×#95	C₂³	1	6	yes	—
92	C₁₉×#95	C₂³	1	6	yes	—
93	C₁₉×#95	C₂³	1	6	yes	—
94	C₂⁴×C₁₉	—	4	3	no	—
95	C₂⁴×C₁₉	—	4	3	no	—
96	C₂⁴×C₁₉	—	4	3	no	—
97	C₂⁴×C₁₉	—	4	3	no	—
98	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
99	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	complemented
100	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
101	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
102	C₂×Q₈×C₁₉	—	4	3	no	—
103	C₂×Q₈×C₁₉	—	4	3	no	—
104	C₂×Q₈×C₁₉	C₂²×C₄	1	12	yes	complemented
105	C₂×D₄×C₁₉	—	4	3	no	—
106	C₂×D₄×C₁₉	—	4	6	no	—
107	C₂×D₄×C₁₉	—	4	3	no	—
108	C₂×D₄×C₁₉	—	4	6	no	—
109	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
110	C₂×D₄×C₁₉	C₂²×C₄	1	24	yes	—
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	3	no	—
115	C₂²×C₄×C₁₉	—	4	6	no	—
116	C₂²×C₄×C₁₉	—	4	3	no	—
117	C₂²×C₄×C₁₉	—	4	6	no	—
118	C₂²×C₄×C₁₉	—	4	6	no	—
119	C₂²×C₄×C₁₉	—	4	16	no	—
120	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
121	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
122	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
123	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
125	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
126	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
127	C₄⋊C₄×C₁₉	—	2	12	no	—
128	C₄⋊C₄×C₁₉	—	4	6	no	—
129	C₄⋊C₄×C₁₉	—	4	3	no	—
130	C₄⋊C₄×C₁₉	—	4	3	no	—
131	C₂²⋊C₄×C₁₉	—	2	12	no	—
132	C₂²⋊C₄×C₁₉	—	4	6	no	—
133	C₂²⋊C₄×C₁₉	—	4	6	no	—
134	C₂²⋊C₄×C₁₉	—	4	3	no	—
135	C₂²⋊C₄×C₁₉	—	4	3	no	—
136	C₂²⋊C₄×C₁₉	—	4	3	no	—
137	C₂²⋊C₄×C₁₉	—	4	3	no	—
138	C₂²⋊C₄×C₁₉	—	4	6	no	—
139	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
140	C₂²⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
141	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	complemented
142	C₂²⋊C₄×C₁₉	C₂²×C₄	1	24	yes	complemented
143	C₄²×C₁₉	—	2	6	no	—
144	C₄²×C₁₉	—	4	3	no	—
145	C₄²×C₁₉	—	4	6	no	—
146	C₄²×C₁₉	—	4	6	no	—
147	C₄²×C₁₉	C₂²×C₄	1	4	yes	complemented
148	C₄²×C₁₉	C₂²×C₄	1	8	yes	complemented
149	#34512	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂³×C₁₉	—	2	6	no	—
151	C₂³×C₁₉	—	2	3	no	—
152	C₂³×C₁₉	—	2	6	no	—
153	C₂³×C₁₉	—	2	3	no	—
154	C₂³×C₁₉	—	2	6	no	—
155	C₂³×C₁₉	—	2	3	no	—
156	C₂³×C₁₉	—	2	3	no	—
157	C₂³×C₁₉	—	2	6	no	—
158	C₂³×C₁₉	—	4	12	no	—
159	C₂³×C₁₉	—	4	12	no	—
160	C₂³×C₁₉	—	4	4	no	—
161	C₂³×C₁₉	—	4	12	no	—
162	C₂³×C₁₉	—	8	2	no	—
163	C₂³×C₁₉	—	8	6	no	—
164	C₂³×C₁₉	C₂³×C₄	1	6	yes	—
165	C₂³×C₁₉	C₂³×C₄	1	6	yes	—
166	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
167	Q₈×C₁₉	—	4	12	no	—
168	D₄×C₁₉	—	4	12	no	—
169	D₄×C₁₉	—	4	24	no	—
170	C₂×C₄×C₁₉	—	2	3	no	—
171	C₂×C₄×C₁₉	—	2	6	no	—
172	C₂×C₄×C₁₉	—	2	6	no	—
173	C₂×C₄×C₁₉	—	2	3	no	—
174	C₂×C₄×C₁₉	—	2	6	no	—
175	C₂×C₄×C₁₉	—	2	3	no	—
176	C₂×C₄×C₁₉	—	2	6	no	—
177	C₂×C₄×C₁₉	—	2	6	no	—
178	C₂×C₄×C₁₉	—	2	3	no	—
179	C₂×C₄×C₁₉	—	2	3	no	—
180	C₂×C₄×C₁₉	—	2	6	no	—
181	C₂×C₄×C₁₉	—	2	6	no	—
182	C₂×C₄×C₁₉	—	2	6	no	—
183	C₂×C₄×C₁₉	—	4	12	no	—
184	C₂×C₄×C₁₉	—	4	12	no	—
185	C₂×C₄×C₁₉	—	8	6	no	—
186	C₂×C₄×C₁₉	—	8	6	no	—
187	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
188	C₂×C₄×C₁₉	C₂³×C₄	1	12	yes	—
189	C₂×C₄×C₁₉	H(5,𝔽₂)	1	6	yes	—
190	C₂×H(3,𝔽₄)	C₂×C₁₉	1	1	yes	characteristic
191	#2375	C₂×C₁₉	1	3	yes	complemented
192	#2372	C₂×C₁₉	1	3	yes	complemented
193	#2367	C₂×C₁₉	1	6	yes	complemented
194	#2358	C₂×C₁₉	1	3	yes	complemented
195	#2337	C₂×C₁₉	1	6	yes	complemented
196	#2326	C₂×C₁₉	1	3	yes	complemented
197	#2321	C₂×C₁₉	1	3	yes	complemented
198	C₄×#120	C₂×C₁₉	1	3	yes	complemented
199	C₂²×C₁₉	—	2	6	no	—
200	C₂²×C₁₉	—	2	12	no	—
201	C₂²×C₁₉	—	2	12	no	—
202	C₂²×C₁₉	—	2	6	no	—
203	C₂²×C₁₉	—	4	16	no	—
204	C₂²×C₁₉	—	4	3	no	—
205	C₂²×C₁₉	—	4	3	no	—
206	C₂²×C₁₉	—	4	3	no	—
207	C₂²×C₁₉	—	4	3	no	—
208	C₂²×C₁₉	—	4	6	no	—
209	C₂²×C₁₉	—	4	6	no	—
210	C₂²×C₁₉	—	8	8	no	—
211	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
212	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	3	yes	—
213	C₂²×C₁₉	#585	1	3	yes	—
214	C₄×C₁₉	—	2	6	no	—
215	C₄×C₁₉	—	2	12	no	—
216	C₄×C₁₉	—	2	6	no	—
217	C₄×C₁₉	—	4	1	no	—
218	C₄×C₁₉	—	4	3	no	—
219	C₄×C₁₉	—	4	3	no	—
220	C₄×C₁₉	—	4	6	no	—
221	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
222	H(3,𝔽₄)	C₄×C₁₉	1	16	yes	complemented
223	C₂×#124	C₂²×C₁₉	1	3	yes	—
224	C₂×#124	C₂²×C₁₉	1	6	yes	—
225	C₂×#120	C₂²×C₁₉	1	3	yes	—
226	C₂×#120	C₂²×C₁₉	1	3	yes	—
227	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	complemented
228	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
229	C₂×C₄×D₄	C₂²×C₁₉	1	6	yes	—
230	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	complemented
231	#391	C₂²×C₁₉	1	3	yes	complemented
232	#391	C₂²×C₁₉	1	6	yes	complemented
233	#390	C₂²×C₁₉	1	6	yes	—
234	#390	C₂²×C₁₉	1	3	yes	—
235	#388	C₂²×C₁₉	1	6	yes	complemented
236	#388	C₂²×C₁₉	1	6	yes	complemented
237	#388	C₂²×C₁₉	1	6	yes	complemented
238	#388	C₂²×C₁₉	1	6	yes	complemented
239	#388	C₂²×C₁₉	1	6	yes	complemented
240	#388	C₂²×C₁₉	1	6	yes	complemented
241	#386	C₂²×C₁₉	1	6	yes	—
242	#386	C₂²×C₁₉	1	3	yes	—
243	#386	C₂²×C₁₉	1	6	yes	—
244	#386	C₂²×C₁₉	1	3	yes	—
245	#385	C₂²×C₁₉	1	3	yes	complemented
246	#385	C₂²×C₁₉	1	6	yes	complemented
247	#385	C₂²×C₁₉	1	6	yes	complemented
248	#385	C₂²×C₁₉	1	3	yes	complemented
249	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
250	#383	C₂²×C₁₉	1	2	yes	complemented
251	#379	C₂²×C₁₉	1	1	yes	characteristic, complemented
252	#379	C₂²×C₁₉	1	3	yes	complemented
253	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	complemented
254	C₄×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	complemented
255	C₄×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	complemented
256	C₄×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	complemented
257	C₄×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	complemented
258	#376	C₂²×C₁₉	1	3	yes	complemented
259	C₂×C₁₉	—	4	6	no	—
260	C₂×C₁₉	—	4	6	no	—
261	C₂×C₁₉	C₄×H(5,𝔽₂)	1	3	yes	—
262	C₂×C₁₉	#3532	1	1	yes	characteristic
263	C₂×C₁₉	#3540	1	3	yes	—
264	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
265	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
266	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
267	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
268	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
269	C₂³×C₄	—	4	6	no	—
270	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
271	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
272	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
273	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
274	#124	C₂×C₄×C₁₉	1	24	yes	complemented
275	#124	C₂×C₄×C₁₉	1	48	yes	complemented
276	#120	C₂×C₄×C₁₉	1	24	yes	complemented
277	#120	C₂×C₄×C₁₉	1	24	yes	complemented
278	C₄×Q₈	—	4	6	no	—
279	C₄×D₄	—	4	6	no	—
280	C₄×D₄	—	4	12	no	—
281	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
285	C₂×C₂²⋊C₄	—	4	6	no	—
286	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
298	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
299	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
300	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
301	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
302	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
304	#95	C₂³×C₁₉	1	6	yes	—
305	#95	C₂³×C₁₉	1	6	yes	—
306	#95	C₂³×C₁₉	1	6	yes	—
307	#95	C₂³×C₁₉	1	6	yes	—
308	#95	C₂³×C₁₉	1	6	yes	—
309	#95	C₂³×C₁₉	1	6	yes	—
310	C₁₉	#34512	1	1	yes	characteristic, direct product factor, Sylow
311	C₂⁴	—	4	3	no	—
312	C₂⁴	—	4	3	no	—
313	C₂⁴	—	4	3	no	—
314	C₂⁴	—	4	3	no	—
315	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
316	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	complemented
317	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
318	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
319	C₂×Q₈	—	4	3	no	—
320	C₂×Q₈	—	4	3	no	—
321	C₂×Q₈	C₂²×C₄×C₁₉	1	12	yes	complemented
322	C₂×D₄	—	4	3	no	—
323	C₂×D₄	—	4	6	no	—
324	C₂×D₄	—	4	3	no	—
325	C₂×D₄	—	4	6	no	—
326	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
327	C₂×D₄	C₂²×C₄×C₁₉	1	24	yes	—
328	C₂²×C₄	—	2	12	no	—
329	C₂²×C₄	—	2	6	no	—
330	C₂²×C₄	—	2	6	no	—
331	C₂²×C₄	—	4	3	no	—
332	C₂²×C₄	—	4	6	no	—
333	C₂²×C₄	—	4	3	no	—
334	C₂²×C₄	—	4	6	no	—
335	C₂²×C₄	—	4	6	no	—
336	C₂²×C₄	—	4	16	no	—
337	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
338	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
340	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
341	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
342	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
343	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
344	C₄⋊C₄	—	2	12	no	—
345	C₄⋊C₄	—	4	6	no	—
346	C₄⋊C₄	—	4	3	no	—
347	C₄⋊C₄	—	4	3	no	—
348	C₂²⋊C₄	—	2	12	no	—
349	C₂²⋊C₄	—	4	6	no	—
350	C₂²⋊C₄	—	4	6	no	—
351	C₂²⋊C₄	—	4	3	no	—
352	C₂²⋊C₄	—	4	3	no	—
353	C₂²⋊C₄	—	4	3	no	—
354	C₂²⋊C₄	—	4	3	no	—
355	C₂²⋊C₄	—	4	6	no	—
356	C₂²⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
357	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
358	C₂²⋊C₄	C₂²×C₄×C₁₉	1	24	yes	complemented
359	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	complemented
360	C₄²	—	2	6	no	—
361	C₄²	—	4	3	no	—
362	C₄²	—	4	6	no	—
363	C₄²	—	4	6	no	—
364	C₄²	C₂²×C₄×C₁₉	1	4	yes	complemented
365	C₄²	C₂²×C₄×C₁₉	1	8	yes	complemented
366	C₂³	—	2	6	no	—
367	C₂³	—	2	3	no	—
368	C₂³	—	2	6	no	—
369	C₂³	—	2	3	no	—
370	C₂³	—	2	6	no	—
371	C₂³	—	2	3	no	—
372	C₂³	—	2	3	no	—
373	C₂³	—	2	6	no	—
374	C₂³	—	4	12	no	—
375	C₂³	—	4	12	no	—
376	C₂³	—	4	4	no	—
377	C₂³	—	4	12	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	6	no	—
380	C₂³	C₂³×C₄×C₁₉	1	6	yes	—
381	C₂³	C₂³×C₄×C₁₉	1	6	yes	—
382	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
383	Q₈	—	4	12	no	—
384	D₄	—	4	12	no	—
385	D₄	—	4	24	no	—
386	C₂×C₄	—	2	3	no	—
387	C₂×C₄	—	2	6	no	—
388	C₂×C₄	—	2	6	no	—
389	C₂×C₄	—	2	3	no	—
390	C₂×C₄	—	2	6	no	—
391	C₂×C₄	—	2	3	no	—
392	C₂×C₄	—	2	6	no	—
393	C₂×C₄	—	2	6	no	—
394	C₂×C₄	—	2	3	no	—
395	C₂×C₄	—	2	3	no	—
396	C₂×C₄	—	2	6	no	—
397	C₂×C₄	—	2	6	no	—
398	C₂×C₄	—	2	6	no	—
399	C₂×C₄	—	4	12	no	—
400	C₂×C₄	—	4	12	no	—
401	C₂×C₄	—	8	6	no	—
402	C₂×C₄	—	8	6	no	—
403	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
404	C₂×C₄	C₂³×C₄×C₁₉	1	12	yes	—
405	C₂×C₄	C₁₉×H(5,𝔽₂)	1	6	yes	—
406	C₂²	—	2	6	no	—
407	C₂²	—	2	12	no	—
408	C₂²	—	2	12	no	—
409	C₂²	—	2	6	no	—
410	C₂²	—	4	16	no	—
411	C₂²	—	4	3	no	—
412	C₂²	—	4	3	no	—
413	C₂²	—	4	3	no	—
414	C₂²	—	4	3	no	—
415	C₂²	—	4	6	no	—
416	C₂²	—	4	6	no	—
417	C₂²	—	8	8	no	—
418	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
419	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	3	yes	—
420	C₂²	C₁₉×#585	1	3	yes	—
421	C₄	—	2	6	no	—
422	C₄	—	2	12	no	—
423	C₄	—	2	6	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	3	no	—
426	C₄	—	4	6	no	—
427	C₄	—	4	3	no	—
428	C₂	—	4	6	no	—
429	C₂	—	4	6	no	—
430	C₂	C₄×C₁₉×H(5,𝔽₂)	1	3	yes	—
431	C₂	C₁₉×#3532	1	1	yes	characteristic
432	C₂	C₁₉×#3540	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂×C₁₉×H(3,𝔽₄)	C₂
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
2. C₁₉×#2375	C₂	semidirect
3. C₁₉×#2372	C₂	semidirect
4. C₁₉×#2367	C₂	semidirect
5. C₁₉×#2358	C₂	semidirect
6. C₁₉×#2337	C₂	semidirect
7. C₁₉×#2326	C₂	semidirect
8. C₁₉×#2321	C₂	semidirect
9. C₄×C₁₉×#120	C₂	semidirect
10. C₂⁴×C₄×C₁₉	C₂²	semidirect
11. C₁₉×H(3,𝔽₄)	C₄	semidirect
16. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
19. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
20. C₁₉×#391	C₂²	semidirect
21. C₁₉×#391	C₂²	semidirect
24. C₁₉×#388	C₂²	semidirect
25. C₁₉×#388	C₂²	semidirect
26. C₁₉×#388	C₂²	semidirect
27. C₁₉×#388	C₂²	semidirect
28. C₁₉×#388	C₂²	semidirect
29. C₁₉×#388	C₂²	semidirect
34. C₁₉×#385	C₂²	semidirect
35. C₁₉×#385	C₂²	semidirect
36. C₁₉×#385	C₂²	semidirect
37. C₁₉×#385	C₂²	semidirect
38. C₁₉×#384	C₂²	semidirect
39. C₁₉×#383	C₂²	semidirect
40. C₁₉×#379	C₂²	semidirect
41. C₁₉×#379	C₂²	semidirect
42. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
43. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
44. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
45. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
46. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
47. C₁₉×#376	C₂²	semidirect
58. C₁₉×#124	C₂×C₄	semidirect
59. C₁₉×#124	C₂×C₄	semidirect
60. C₁₉×#120	C₂×C₄	semidirect
61. C₁₉×#120	C₂×C₄	semidirect
99. C₂⁴×C₁₉	C₂²×C₄	semidirect
104. C₂×Q₈×C₁₉	C₂²×C₄	semidirect
141. C₂²⋊C₄×C₁₉	C₂²×C₄	semidirect
142. C₂²⋊C₄×C₁₉	C₂²×C₄	semidirect
147. C₄²×C₁₉	C₂²×C₄	semidirect
148. C₄²×C₁₉	C₂²×C₄	semidirect
149. #34512	C₁₉	direct (N × H)
191. #2375	C₂×C₁₉	semidirect
192. #2372	C₂×C₁₉	semidirect
193. #2367	C₂×C₁₉	semidirect
194. #2358	C₂×C₁₉	semidirect
195. #2337	C₂×C₁₉	semidirect
196. #2326	C₂×C₁₉	semidirect
197. #2321	C₂×C₁₉	semidirect
198. C₄×#120	C₂×C₁₉	semidirect
221. C₂⁴×C₄	C₂²×C₁₉	semidirect
222. H(3,𝔽₄)	C₄×C₁₉	semidirect
227. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
230. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
231. #391	C₂²×C₁₉	semidirect
232. #391	C₂²×C₁₉	semidirect
235. #388	C₂²×C₁₉	semidirect
236. #388	C₂²×C₁₉	semidirect
237. #388	C₂²×C₁₉	semidirect
238. #388	C₂²×C₁₉	semidirect
239. #388	C₂²×C₁₉	semidirect
240. #388	C₂²×C₁₉	semidirect
245. #385	C₂²×C₁₉	semidirect
246. #385	C₂²×C₁₉	semidirect
247. #385	C₂²×C₁₉	semidirect
248. #385	C₂²×C₁₉	semidirect
249. #384	C₂²×C₁₉	semidirect
250. #383	C₂²×C₁₉	semidirect
251. #379	C₂²×C₁₉	semidirect
252. #379	C₂²×C₁₉	semidirect
253. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
254. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
255. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
256. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
257. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
258. #376	C₂²×C₁₉	semidirect
274. #124	C₂×C₄×C₁₉	semidirect
275. #124	C₂×C₄×C₁₉	semidirect
276. #120	C₂×C₄×C₁₉	semidirect
277. #120	C₂×C₄×C₁₉	semidirect
310. C₁₉	#34512	direct (N × H)
316. C₂⁴	C₂²×C₄×C₁₉	semidirect
321. C₂×Q₈	C₂²×C₄×C₁₉	semidirect
358. C₂²⋊C₄	C₂²×C₄×C₁₉	semidirect
359. C₂²⋊C₄	C₂²×C₄×C₁₉	semidirect
364. C₄²	C₂²×C₄×C₁₉	semidirect
365. C₄²	C₂²×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×H(3,𝔽₄)	2
C₁₉×#2375	2
C₁₉×#2372	2
C₁₉×#2367	2
C₁₉×#2358	2
C₁₉×#2337	2
C₁₉×#2326	2
C₁₉×#2321	2
C₄×C₁₉×#120	2
#34512	19

Subgroups — C19×#34512 #18040471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34512 #18040471