Subgroups — C₁₉×#34371 #18040330

Order 4864.

2238 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2381	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2365	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2345	C₂	1	4	yes	maximal
5	Q₈×C₂²⋊C₄×C₁₉	C₂	1	4	yes	maximal
6	C₁₉×#2331	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2327	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2313	C₂	1	4	yes	maximal
9	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
11	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
12	C₂×C₁₉×C₄⋊Q₈	C₄	1	16	yes	complemented
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	8	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#391	C₂²	1	8	yes	—
22	C₁₉×#391	C₂²	1	16	yes	—
23	C₁₉×#389	C₂²	1	8	yes	—
24	C₁₉×#387	C₂²	1	16	yes	—
25	C₁₉×#387	C₂²	1	16	yes	—
26	C₁₉×#387	C₂²	1	16	yes	—
27	C₁₉×#383	C₂²	1	2	yes	—
28	C₁₉×#383	C₂²	1	2	yes	—
29	C₁₉×#382	C₂²	1	2	yes	—
30	C₁₉×#382	C₂²	1	2	yes	—
31	C₁₉×#381	C₂²	1	2	yes	—
32	C₁₉×#381	C₂²	1	2	yes	—
33	C₁₉×#380	C₂²	1	2	yes	—
34	C₁₉×#380	C₂²	1	2	yes	—
35	C₁₉×#380	C₂²	1	8	yes	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
39	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
40	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
41	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
42	C₁₉×#376	C₂²	1	2	yes	—
43	C₁₉×#376	C₂²	1	2	yes	—
44	C₂²×Q₈×C₁₉	—	4	8	no	—
45	C₂²×Q₈×C₁₉	C₂×C₄	1	16	yes	—
46	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
47	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
52	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
53	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
54	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
55	C₁₉×C₄⋊Q₈	C₂×C₄	1	16	yes	—
56	C₄×Q₈×C₁₉	—	4	16	no	—
57	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
66	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
68	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
69	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
70	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	16	yes	—
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×#95	C₂³	1	4	yes	—
77	C₁₉×#95	C₂³	1	4	yes	—
78	C₁₉×#95	C₂³	1	4	yes	—
79	C₁₉×#95	C₂³	1	4	yes	—
80	C₁₉×#95	C₂³	1	4	yes	—
81	C₁₉×#95	C₂³	1	4	yes	—
82	C₁₉×#95	C₂³	1	16	yes	—
83	C₁₉×#95	C₂³	1	16	yes	—
84	C₁₉×#95	C₂³	1	4	yes	—
85	C₁₉×#95	C₂³	1	4	yes	—
86	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
87	C₂×Q₈×C₁₉	—	2	16	no	—
88	C₂×Q₈×C₁₉	—	4	8	no	—
89	C₂×Q₈×C₁₉	—	4	32	no	—
90	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	—
91	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	4	8	no	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
100	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
101	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
102	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
103	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
109	C₄⋊C₄×C₁₉	—	2	8	no	—
110	C₄⋊C₄×C₁₉	—	2	8	no	—
111	C₄⋊C₄×C₁₉	—	4	16	no	—
112	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
113	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
114	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
115	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
116	C₂²⋊C₄×C₁₉	—	2	8	no	—
117	C₂²⋊C₄×C₁₉	—	2	8	no	—
118	C₄²×C₁₉	—	2	8	no	—
119	C₄²×C₁₉	—	2	8	no	—
120	C₄²×C₁₉	—	4	16	no	—
121	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
122	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
123	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
124	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
125	#34371	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	—	2	2	no	—
128	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
129	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
130	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
131	Q₈×C₁₉	—	2	32	no	—
132	Q₈×C₁₉	—	4	16	no	—
133	C₂×C₄×C₁₉	—	2	8	no	—
134	C₂×C₄×C₁₉	—	2	16	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	8	no	—
140	C₂×C₄×C₁₉	—	2	8	no	—
141	C₂×C₄×C₁₉	—	2	8	no	—
142	C₂×C₄×C₁₉	—	2	8	no	—
143	C₂×C₄×C₁₉	—	2	8	no	—
144	C₂×C₄×C₁₉	—	2	8	no	—
145	C₂×C₄×C₁₉	—	2	8	no	—
146	C₂×C₄×C₁₉	—	2	8	no	—
147	C₂×C₄×C₁₉	—	4	16	no	—
148	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
149	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
150	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
151	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
152	C₂×C₄×C₁₉	C₂³×C₄	1	16	yes	—
153	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
154	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
155	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
156	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
157	C₂²×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
158	#2381	C₂×C₁₉	1	4	yes	complemented
159	#2365	C₂×C₁₉	1	4	yes	complemented
160	#2345	C₂×C₁₉	1	4	yes	—
161	Q₈×C₂²⋊C₄	C₂×C₁₉	1	4	yes	—
162	#2331	C₂×C₁₉	1	4	yes	complemented
163	#2327	C₂×C₁₉	1	4	yes	complemented
164	#2313	C₂×C₁₉	1	4	yes	—
165	#2283	C₂×C₁₉	1	1	yes	characteristic
166	#2283	C₂×C₁₉	1	1	yes	characteristic
167	C₂²×C₁₉	—	2	2	no	—
168	C₂²×C₁₉	—	2	2	no	—
169	C₂²×C₁₉	—	2	8	no	—
170	C₂²×C₁₉	#519	1	4	yes	—
171	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
172	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
173	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
174	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
175	C₄×C₁₉	—	2	2	no	—
176	C₄×C₁₉	—	2	16	no	—
177	C₄×C₁₉	—	2	2	no	—
178	C₄×C₁₉	—	2	2	no	—
179	C₄×C₁₉	—	2	2	no	—
180	C₄×C₁₉	—	4	8	no	—
181	C₄×C₁₉	—	4	8	no	—
182	C₄×C₁₉	#518	1	4	yes	—
183	C₄×C₁₉	#519	1	4	yes	—
184	C₂³×Q₈	C₂²×C₁₉	1	2	yes	—
185	C₂×C₄⋊Q₈	C₄×C₁₉	1	16	yes	complemented
186	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
187	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
188	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
189	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
190	C₂×C₄×Q₈	C₂²×C₁₉	1	8	yes	—
191	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
192	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
193	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
194	#391	C₂²×C₁₉	1	8	yes	—
195	#391	C₂²×C₁₉	1	16	yes	—
196	#389	C₂²×C₁₉	1	8	yes	—
197	#387	C₂²×C₁₉	1	16	yes	—
198	#387	C₂²×C₁₉	1	16	yes	—
199	#387	C₂²×C₁₉	1	16	yes	—
200	#383	C₂²×C₁₉	1	2	yes	—
201	#383	C₂²×C₁₉	1	2	yes	—
202	#382	C₂²×C₁₉	1	2	yes	—
203	#382	C₂²×C₁₉	1	2	yes	—
204	#381	C₂²×C₁₉	1	2	yes	—
205	#381	C₂²×C₁₉	1	2	yes	—
206	#380	C₂²×C₁₉	1	8	yes	—
207	#380	C₂²×C₁₉	1	2	yes	—
208	#380	C₂²×C₁₉	1	2	yes	—
209	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
210	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
211	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
212	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
213	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
214	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
215	#376	C₂²×C₁₉	1	2	yes	—
216	#376	C₂²×C₁₉	1	2	yes	—
217	C₂×C₁₉	—	2	4	no	—
218	C₂×C₁₉	C₂×#518	1	1	yes	characteristic
219	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
220	C₂×C₁₉	C₂×#519	1	1	yes	characteristic
221	C₂×C₁₉	#3552	1	4	yes	—
222	C₂²×Q₈	—	4	8	no	—
223	C₂²×Q₈	C₂×C₄×C₁₉	1	16	yes	—
224	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
225	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
226	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
227	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
230	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
231	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
232	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
233	C₄⋊Q₈	C₂×C₄×C₁₉	1	16	yes	—
234	C₄×Q₈	—	4	16	no	—
235	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
237	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
240	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
244	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
245	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
246	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
247	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
248	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
249	C₂×C₄²	C₂³×C₁₉	1	16	yes	—
250	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
254	#95	C₂³×C₁₉	1	4	yes	—
255	#95	C₂³×C₁₉	1	4	yes	—
256	#95	C₂³×C₁₉	1	4	yes	—
257	#95	C₂³×C₁₉	1	4	yes	—
258	#95	C₂³×C₁₉	1	4	yes	—
259	#95	C₂³×C₁₉	1	4	yes	—
260	#95	C₂³×C₁₉	1	16	yes	—
261	#95	C₂³×C₁₉	1	16	yes	—
262	#95	C₂³×C₁₉	1	4	yes	—
263	#95	C₂³×C₁₉	1	4	yes	—
264	C₁₉	#34371	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
266	C₂×Q₈	—	2	16	no	—
267	C₂×Q₈	—	4	8	no	—
268	C₂×Q₈	—	4	32	no	—
269	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	—
270	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	4	8	no	—
275	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
276	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
277	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
278	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
279	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
280	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
281	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
286	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
288	C₄⋊C₄	—	2	8	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	4	16	no	—
291	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
292	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
293	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
294	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
295	C₂²⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	2	8	no	—
297	C₄²	—	2	8	no	—
298	C₄²	—	2	8	no	—
299	C₄²	—	4	16	no	—
300	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
301	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
302	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
303	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
307	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
308	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
309	Q₈	—	2	32	no	—
310	Q₈	—	4	16	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	2	16	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	4	16	no	—
326	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
327	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
328	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
329	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
330	C₂×C₄	C₂³×C₄×C₁₉	1	16	yes	—
331	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
332	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
333	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
334	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	8	no	—
338	C₂²	C₁₉×#519	1	4	yes	—
339	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
340	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
341	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
342	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
343	C₄	—	2	2	no	—
344	C₄	—	2	16	no	—
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	2	2	no	—
348	C₄	—	4	8	no	—
349	C₄	—	4	8	no	—
350	C₄	C₁₉×#518	1	4	yes	—
351	C₄	C₁₉×#519	1	4	yes	—
352	C₂	—	2	4	no	—
353	C₂	C₂×C₁₉×#518	1	1	yes	characteristic
354	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
355	C₂	C₂×C₁₉×#519	1	1	yes	characteristic
356	C₂	C₁₉×#3552	1	4	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×#2381	C₂	semidirect
3. C₁₉×#2365	C₂	semidirect
6. C₁₉×#2331	C₂	semidirect
7. C₁₉×#2327	C₂	semidirect
12. C₂×C₁₉×C₄⋊Q₈	C₄	semidirect
125. #34371	C₁₉	direct (N × H)
158. #2381	C₂×C₁₉	semidirect
159. #2365	C₂×C₁₉	semidirect
162. #2331	C₂×C₁₉	semidirect
163. #2327	C₂×C₁₉	semidirect
185. C₂×C₄⋊Q₈	C₄×C₁₉	semidirect
264. C₁₉	#34371	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₄⋊Q₈	2
C₁₉×#2381	2
C₁₉×#2365	2
C₁₉×#2345	2
Q₈×C₂²⋊C₄×C₁₉	2
C₁₉×#2331	2
C₁₉×#2327	2
C₁₉×#2313	2
C₁₉×#2283	2
#34371	19

Subgroups — C19×#34371 #18040330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34371 #18040330