Subgroups — C₁₉×#34235 #18040194

Order 4864.

2238 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2365	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2365	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2360	C₂	1	4	yes	maximal
5	C₁₉×#2356	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2351	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2343	C₂	1	4	yes	maximal
8	C₁₉×#2336	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2320	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₉×C₂²⋊Q₈	C₂	1	4	yes	maximal
11	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#2276	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#533	C₄	1	16	yes	complemented
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	C₂²	1	2	yes	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
24	C₂×C₁₉×#117	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
28	C₁₉×#391	C₂²	1	4	yes	—
29	C₁₉×#391	C₂²	1	4	yes	—
30	C₁₉×#389	C₂²	1	4	yes	—
31	C₁₉×#389	C₂²	1	4	yes	—
32	C₁₉×#389	C₂²	1	8	yes	—
33	C₁₉×#387	C₂²	1	8	yes	—
34	C₁₉×#387	C₂²	1	8	yes	—
35	C₁₉×#387	C₂²	1	8	yes	—
36	C₁₉×#387	C₂²	1	8	yes	—
37	C₁₉×#385	C₂²	1	8	yes	—
38	C₁₉×#383	C₂²	1	2	yes	—
39	C₁₉×#383	C₂²	1	4	yes	—
40	C₁₉×#382	C₂²	1	1	yes	characteristic
41	C₁₉×#382	C₂²	1	1	yes	characteristic
42	C₁₉×#382	C₂²	1	4	yes	—
43	C₁₉×#381	C₂²	1	2	yes	—
44	C₁₉×#380	C₂²	1	2	yes	—
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
50	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
53	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
54	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
55	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
56	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
57	C₁₉×#376	C₂²	1	2	yes	—
58	C₁₉×#376	C₂²	1	4	yes	—
59	C₂×C₁₉×#95	C₂²	1	2	yes	—
60	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
61	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
67	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
68	C₁₉×#125	C₂×C₄	1	16	yes	complemented
69	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
70	C₁₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
71	C₄×Q₈×C₁₉	—	2	16	no	—
72	C₄×Q₈×C₁₉	—	4	8	no	—
73	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	complemented
74	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	complemented
75	C₁₉×#117	C₂×C₄	1	16	yes	—
76	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	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	2	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₉	—	4	4	no	—
93	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
95	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
97	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
98	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×#95	C₂³	1	2	yes	—
106	C₁₉×#95	C₂³	1	2	yes	—
107	C₁₉×#95	C₂³	1	4	yes	—
108	C₁₉×#95	C₂³	1	2	yes	—
109	C₁₉×#95	C₂³	1	4	yes	—
110	C₁₉×#95	C₂³	1	2	yes	—
111	C₁₉×#95	C₂³	1	8	yes	—
112	C₁₉×#95	C₂³	1	2	yes	—
113	C₁₉×#95	C₂³	1	2	yes	—
114	C₁₉×#95	C₂³	1	8	yes	—
115	C₁₉×#95	C₂³	1	8	yes	—
116	C₁₉×#95	C₂³	1	4	yes	—
117	C₁₉×#95	C₂³	1	8	yes	—
118	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
119	C₂×Q₈×C₁₉	—	2	8	no	—
120	C₂×Q₈×C₁₉	—	2	4	no	—
121	C₂×Q₈×C₁₉	—	2	4	no	—
122	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
123	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
124	C₂²×C₄×C₁₉	—	2	4	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	8	no	—
129	C₂²×C₄×C₁₉	—	2	8	no	—
130	C₂²×C₄×C₁₉	—	4	4	no	—
131	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
133	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
146	C₄⋊C₄×C₁₉	—	2	8	no	—
147	C₄⋊C₄×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	—	2	16	no	—
149	C₄⋊C₄×C₁₉	—	2	4	no	—
150	C₄⋊C₄×C₁₉	—	2	4	no	—
151	C₄⋊C₄×C₁₉	—	4	8	no	—
152	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
153	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
154	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
155	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
156	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
157	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
158	C₄⋊C₄×C₁₉	#41	1	8	yes	—
159	C₂²⋊C₄×C₁₉	—	2	8	no	—
160	C₂²⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
161	C₄²×C₁₉	—	2	16	no	—
162	C₄²×C₁₉	—	2	8	no	—
163	C₄²×C₁₉	—	2	8	no	—
164	C₄²×C₁₉	—	4	2	no	—
165	C₄²×C₁₉	—	4	2	no	—
166	C₄²×C₁₉	—	4	8	no	—
167	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
168	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
169	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
170	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
171	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
172	#34235	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	2	1	no	—
175	C₂³×C₁₉	—	2	1	no	—
176	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
177	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
178	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
179	Q₈×C₁₉	—	2	16	no	—
180	Q₈×C₁₉	—	2	16	no	—
181	C₂×C₄×C₁₉	—	2	8	no	—
182	C₂×C₄×C₁₉	—	2	8	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	8	no	—
193	C₂×C₄×C₁₉	—	2	8	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	4	16	no	—
204	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
205	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
206	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
207	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
208	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
209	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
210	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
211	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
212	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
213	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
214	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
215	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
216	C₂×#533	C₂×C₁₉	1	1	yes	characteristic
217	#2365	C₂×C₁₉	1	2	yes	complemented
218	#2365	C₂×C₁₉	1	2	yes	complemented
219	#2360	C₂×C₁₉	1	4	yes	—
220	#2356	C₂×C₁₉	1	2	yes	complemented
221	#2351	C₂×C₁₉	1	2	yes	complemented
222	#2343	C₂×C₁₉	1	4	yes	—
223	#2336	C₂×C₁₉	1	4	yes	complemented
224	#2320	C₂×C₁₉	1	2	yes	complemented
225	C₄×C₂²⋊Q₈	C₂×C₁₉	1	4	yes	—
226	#2283	C₂×C₁₉	1	1	yes	characteristic
227	#2276	C₂×C₁₉	1	2	yes	complemented
228	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
229	C₂²×C₁₉	—	2	2	no	—
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	2	4	no	—
232	C₂²×C₁₉	—	2	4	no	—
233	C₂²×C₁₉	#519	1	4	yes	—
234	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
235	C₂²×C₁₉	C₂²×#41	1	2	yes	—
236	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
237	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
238	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
239	C₄×C₁₉	—	2	2	no	—
240	C₄×C₁₉	—	2	8	no	—
241	C₄×C₁₉	—	2	2	no	—
242	C₄×C₁₉	—	2	2	no	—
243	C₄×C₁₉	—	2	2	no	—
244	C₄×C₁₉	—	2	8	no	—
245	C₄×C₁₉	—	2	8	no	—
246	C₄×C₁₉	—	4	4	no	—
247	C₄×C₁₉	—	4	4	no	—
248	C₄×C₁₉	—	4	4	no	—
249	C₄×C₁₉	C₄×#41	1	4	yes	—
250	C₄×C₁₉	#520	1	4	yes	—
251	#533	C₄×C₁₉	1	16	yes	complemented
252	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
253	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×#125	C₂²×C₁₉	1	2	yes	—
255	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
256	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
257	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
258	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
259	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
260	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
261	C₂×#117	C₂²×C₁₉	1	2	yes	—
262	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
263	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
264	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
265	#391	C₂²×C₁₉	1	4	yes	—
266	#391	C₂²×C₁₉	1	4	yes	—
267	#389	C₂²×C₁₉	1	4	yes	—
268	#389	C₂²×C₁₉	1	8	yes	—
269	#389	C₂²×C₁₉	1	4	yes	—
270	#387	C₂²×C₁₉	1	8	yes	—
271	#387	C₂²×C₁₉	1	8	yes	—
272	#387	C₂²×C₁₉	1	8	yes	—
273	#387	C₂²×C₁₉	1	8	yes	—
274	#385	C₂²×C₁₉	1	8	yes	—
275	#383	C₂²×C₁₉	1	4	yes	—
276	#383	C₂²×C₁₉	1	2	yes	—
277	#382	C₂²×C₁₉	1	4	yes	—
278	#382	C₂²×C₁₉	1	1	yes	characteristic
279	#382	C₂²×C₁₉	1	1	yes	characteristic
280	#381	C₂²×C₁₉	1	2	yes	—
281	#380	C₂²×C₁₉	1	2	yes	—
282	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
284	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
285	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
286	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
287	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
288	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
289	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
290	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
291	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
292	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
293	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
294	#376	C₂²×C₁₉	1	2	yes	—
295	#376	C₂²×C₁₉	1	4	yes	—
296	C₂×#95	C₂²×C₁₉	1	2	yes	—
297	C₂×C₁₉	—	2	4	no	—
298	C₂×C₁₉	C₂×C₄×#41	1	1	yes	characteristic
299	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
300	C₂×C₁₉	C₂×#520	1	1	yes	characteristic
301	C₂×C₁₉	#3520	1	2	yes	—
302	C₂×C₁₉	#3523	1	2	yes	—
303	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
304	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
305	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
306	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
310	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
311	#125	C₂×C₄×C₁₉	1	16	yes	complemented
312	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
313	C₂²⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
314	C₄×Q₈	—	2	16	no	—
315	C₄×Q₈	—	4	8	no	—
316	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
317	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	complemented
318	#117	C₂×C₄×C₁₉	1	16	yes	—
319	C₂×C₄⋊C₄	—	2	8	no	—
320	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
335	C₂×C₄²	—	4	4	no	—
336	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
337	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
338	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
339	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
340	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
341	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
342	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
343	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
344	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
348	#95	C₂³×C₁₉	1	2	yes	—
349	#95	C₂³×C₁₉	1	2	yes	—
350	#95	C₂³×C₁₉	1	4	yes	—
351	#95	C₂³×C₁₉	1	2	yes	—
352	#95	C₂³×C₁₉	1	4	yes	—
353	#95	C₂³×C₁₉	1	2	yes	—
354	#95	C₂³×C₁₉	1	8	yes	—
355	#95	C₂³×C₁₉	1	2	yes	—
356	#95	C₂³×C₁₉	1	2	yes	—
357	#95	C₂³×C₁₉	1	8	yes	—
358	#95	C₂³×C₁₉	1	8	yes	—
359	#95	C₂³×C₁₉	1	4	yes	—
360	#95	C₂³×C₁₉	1	8	yes	—
361	C₁₉	#34235	1	1	yes	characteristic, direct product factor, Sylow
362	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
363	C₂×Q₈	—	2	8	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
367	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	8	no	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
376	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
377	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
378	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
379	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
380	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
381	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
385	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
386	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
388	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	16	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	4	8	no	—
396	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
397	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
398	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
399	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
400	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
401	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
402	C₄⋊C₄	#41×C₁₉	1	8	yes	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
405	C₄²	—	2	16	no	—
406	C₄²	—	2	8	no	—
407	C₄²	—	2	8	no	—
408	C₄²	—	4	2	no	—
409	C₄²	—	4	2	no	—
410	C₄²	—	4	8	no	—
411	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
412	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
413	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
414	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
415	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
420	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
421	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
422	Q₈	—	2	16	no	—
423	Q₈	—	2	16	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	4	16	no	—
447	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
448	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
449	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
450	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
451	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
452	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
453	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
454	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
455	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
456	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
457	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
458	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	C₁₉×#519	1	4	yes	—
464	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
465	C₂²	C₂²×#41×C₁₉	1	2	yes	—
466	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
468	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	8	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	8	no	—
475	C₄	—	2	8	no	—
476	C₄	—	4	4	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	4	no	—
479	C₄	C₄×#41×C₁₉	1	4	yes	—
480	C₄	C₁₉×#520	1	4	yes	—
481	C₂	—	2	4	no	—
482	C₂	C₂×C₄×#41×C₁₉	1	1	yes	characteristic
483	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
484	C₂	C₂×C₁₉×#520	1	1	yes	characteristic
485	C₂	C₁₉×#3520	1	2	yes	—
486	C₂	C₁₉×#3523	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
2. C₁₉×#2365	C₂	semidirect
3. C₁₉×#2365	C₂	semidirect
5. C₁₉×#2356	C₂	semidirect
6. C₁₉×#2351	C₂	semidirect
8. C₁₉×#2336	C₂	semidirect
9. C₁₉×#2320	C₂	semidirect
12. C₁₉×#2276	C₂	semidirect
14. C₁₉×#533	C₄	semidirect
66. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
67. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
68. C₁₉×#125	C₂×C₄	semidirect
73. C₄×Q₈×C₁₉	C₂×C₄	semidirect
74. C₄×Q₈×C₁₉	C₂×C₄	semidirect
172. #34235	C₁₉	direct (N × H)
217. #2365	C₂×C₁₉	semidirect
218. #2365	C₂×C₁₉	semidirect
220. #2356	C₂×C₁₉	semidirect
221. #2351	C₂×C₁₉	semidirect
223. #2336	C₂×C₁₉	semidirect
224. #2320	C₂×C₁₉	semidirect
227. #2276	C₂×C₁₉	semidirect
251. #533	C₄×C₁₉	semidirect
309. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
310. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
311. #125	C₂×C₄×C₁₉	semidirect
316. C₄×Q₈	C₂×C₄×C₁₉	semidirect
317. C₄×Q₈	C₂×C₄×C₁₉	semidirect
361. C₁₉	#34235	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×#533	2
C₁₉×#2365	2
C₁₉×#2360	2
C₁₉×#2356	2
C₁₉×#2351	2
C₁₉×#2343	2
C₁₉×#2336	2
C₁₉×#2320	2
C₄×C₁₉×C₂²⋊Q₈	2
C₁₉×#2283	2
C₁₉×#2276	2
C₂×C₄×C₄⋊C₄×C₁₉	2
#34235	19

Subgroups — C19×#34235 #18040194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34235 #18040194