Subgroups — C₂×C₁₉×#2355 #18040077

Order 4864.

2638 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2355	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₉×#391	C₂	1	2	yes	maximal
4	C₂×C₁₉×#387	C₂	1	4	yes	maximal
5	C₂×C₁₉×#384	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#382	C₂	1	2	yes	maximal
7	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	2	yes	maximal
8	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	2	yes	maximal
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₉	C₄	1	16	yes	complemented
12	C₂×C₄×Q₈×C₁₉	C₂²	1	8	yes	—
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₉	C₂²	1	4	yes	—
22	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#391	C₂²	1	16	yes	—
25	C₁₉×#387	C₂²	1	32	yes	—
26	C₁₉×#384	C₂²	1	8	yes	—
27	C₁₉×#382	C₂²	1	16	yes	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	16	yes	—
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	16	yes	—
31	C₂×C₁₉×#95	C₂²	1	4	yes	—
32	C₂×C₁₉×#95	C₂²	1	2	yes	—
33	C₂×C₁₉×#95	C₂²	1	4	yes	—
34	C₂×C₁₉×#95	C₂²	1	4	yes	—
35	C₂²×Q₈×C₁₉	—	2	4	no	—
36	C₂²×Q₈×C₁₉	—	2	4	no	—
37	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	—
38	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₄×Q₈×C₁₉	C₂×C₄	1	64	yes	complemented
48	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
51	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
53	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₁₉	Q₈	1	8	yes	complemented
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
62	C₂×C₄²×C₁₉	—	2	8	no	—
63	C₂×C₄²×C₁₉	—	4	8	no	—
64	C₂×C₄²×C₁₉	C₂×C₄	1	16	yes	—
65	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	—
66	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
67	C₂×C₄²×C₁₉	C₂³	1	16	yes	—
68	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
69	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
70	C₁₉×#95	C₂³	1	16	yes	—
71	C₁₉×#95	C₂³	1	8	yes	—
72	C₁₉×#95	C₂³	1	16	yes	—
73	C₁₉×#95	C₂³	1	16	yes	—
74	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
75	C₂×Q₈×C₁₉	—	2	32	no	—
76	C₂×Q₈×C₁₉	—	2	8	no	—
77	C₂×Q₈×C₁₉	—	2	8	no	—
78	C₂×Q₈×C₁₉	C₂²×C₄	1	16	yes	—
79	C₂²×C₄×C₁₉	—	2	4	no	—
80	C₂²×C₄×C₁₉	—	2	4	no	—
81	C₂²×C₄×C₁₉	—	2	4	no	—
82	C₂²×C₄×C₁₉	—	2	4	no	—
83	C₂²×C₄×C₁₉	—	2	4	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	2	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	8	no	—
90	C₂²×C₄×C₁₉	—	2	8	no	—
91	C₂²×C₄×C₁₉	—	2	8	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
94	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
96	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
99	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
100	C₂²×C₄×C₁₉	#41	1	4	yes	—
101	C₂²×C₄×C₁₉	#41	1	4	yes	—
102	C₂²×C₄×C₁₉	#41	1	4	yes	—
103	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
104	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
111	C₄⋊C₄×C₁₉	—	2	16	no	—
112	C₄⋊C₄×C₁₉	—	2	8	no	—
113	C₄⋊C₄×C₁₉	—	2	16	no	—
114	C₄⋊C₄×C₁₉	—	4	8	no	—
115	C₄⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
116	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
117	C₄⋊C₄×C₁₉	C₂×Q₈	1	16	yes	complemented
118	C₄²×C₁₉	—	2	16	no	—
119	C₄²×C₁₉	—	4	16	no	—
120	C₄²×C₁₉	C₂²×C₄	1	32	yes	—
121	C₄²×C₁₉	C₂²×C₄	1	16	yes	—
122	C₂×#2355	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
124	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
125	C₂³×C₁₉	C₂×#41	1	2	yes	—
126	C₂³×C₁₉	C₂×#41	1	2	yes	—
127	C₂³×C₁₉	C₂×#41	1	2	yes	—
128	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
129	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
130	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
131	Q₈×C₁₉	—	2	32	no	—
132	C₂×C₄×C₁₉	—	2	16	no	—
133	C₂×C₄×C₁₉	—	2	16	no	—
134	C₂×C₄×C₁₉	—	2	8	no	—
135	C₂×C₄×C₁₉	—	2	16	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	2	4	no	—
138	C₂×C₄×C₁₉	—	2	4	no	—
139	C₂×C₄×C₁₉	—	2	4	no	—
140	C₂×C₄×C₁₉	—	2	4	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	4	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	—	2	8	no	—
147	C₂×C₄×C₁₉	—	2	8	no	—
148	C₂×C₄×C₁₉	—	2	8	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	4	8	no	—
151	C₂×C₄×C₁₉	—	4	16	no	—
152	C₂×C₄×C₁₉	#117	1	16	yes	—
153	C₂×C₄×C₁₉	C₄×Q₈	1	16	yes	—
154	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
155	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
156	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
157	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
158	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
159	C₂×C₄×C₁₉	C₂²×Q₈	1	8	yes	—
160	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
161	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
162	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
163	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
164	C₂²×C₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
165	#2355	C₂×C₁₉	1	16	yes	direct product factor
166	C₂×#391	C₂×C₁₉	1	2	yes	—
167	C₂×#387	C₂×C₁₉	1	4	yes	—
168	C₂×#384	C₂×C₁₉	1	1	yes	characteristic
169	C₂×#382	C₂×C₁₉	1	2	yes	—
170	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
171	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	2	yes	—
172	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	2	yes	—
173	C₂²×C₁₉	C₂×#117	1	4	yes	—
174	C₂²×C₁₉	C₂×C₄×Q₈	1	4	yes	—
175	C₂²×C₁₉	#520	1	4	yes	—
176	C₂²×C₁₉	#554	1	4	yes	—
177	C₂²×C₁₉	#556	1	4	yes	—
178	C₂²×C₁₉	#557	1	4	yes	—
179	C₂²×C₁₉	#559	1	4	yes	—
180	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
181	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
182	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
183	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
184	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
185	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
186	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
187	C₄×C₁₉	—	2	8	no	—
188	C₄×C₁₉	—	2	8	no	—
189	C₄×C₁₉	—	2	4	no	—
190	C₄×C₁₉	—	2	8	no	—
191	C₄×C₁₉	—	4	4	no	—
192	C₄×C₁₉	—	4	8	no	—
193	C₄×C₁₉	C₂×#117	1	8	yes	—
194	C₄×C₁₉	C₂×C₄×Q₈	1	8	yes	—
195	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
196	C₂×C₄×Q₈	C₄×C₁₉	1	16	yes	complemented
197	C₂×C₄×Q₈	C₂²×C₁₉	1	8	yes	—
198	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
199	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
200	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
201	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
202	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
203	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
204	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
205	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
206	C₂²×C₄²	C₂²×C₁₉	1	4	yes	—
207	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
208	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
209	#391	C₂²×C₁₉	1	16	yes	—
210	#387	C₂²×C₁₉	1	32	yes	—
211	#384	C₂²×C₁₉	1	8	yes	—
212	#382	C₂²×C₁₉	1	16	yes	—
213	C₄×C₄⋊C₄	C₂²×C₁₉	1	16	yes	—
214	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
215	C₄×C₄⋊C₄	C₂²×C₁₉	1	16	yes	—
216	C₂×#95	C₂²×C₁₉	1	4	yes	—
217	C₂×#95	C₂²×C₁₉	1	2	yes	—
218	C₂×#95	C₂²×C₁₉	1	4	yes	—
219	C₂×#95	C₂²×C₁₉	1	4	yes	—
220	C₂×C₁₉	#2355	1	8	yes	direct product factor
221	C₂×C₁₉	C₂²×#117	1	1	yes	characteristic
222	C₂×C₁₉	C₂²×C₄×Q₈	1	1	yes	characteristic
223	C₂×C₁₉	C₂×#520	1	1	yes	characteristic
224	C₂×C₁₉	C₂×#554	1	1	yes	characteristic
225	C₂×C₁₉	C₂×#556	1	1	yes	characteristic
226	C₂×C₁₉	C₂×#557	1	1	yes	characteristic
227	C₂×C₁₉	C₂×#559	1	1	yes	characteristic
228	C₂²×Q₈	—	2	4	no	—
229	C₂²×Q₈	—	2	4	no	—
230	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	—
231	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
232	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
233	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
234	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
236	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
237	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
238	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
240	C₄×Q₈	C₂×C₄×C₁₉	1	64	yes	complemented
241	C₂×C₄⋊C₄	—	2	8	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	8	no	—
244	C₂×C₄⋊C₄	—	4	4	no	—
245	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
246	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
247	C₂×C₄⋊C₄	Q₈×C₁₉	1	8	yes	complemented
248	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
252	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
253	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
254	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
255	C₂×C₄²	—	2	8	no	—
256	C₂×C₄²	—	4	8	no	—
257	C₂×C₄²	C₂×C₄×C₁₉	1	16	yes	—
258	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	—
259	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
260	C₂×C₄²	C₂³×C₁₉	1	16	yes	—
261	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
262	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
263	#95	C₂³×C₁₉	1	16	yes	—
264	#95	C₂³×C₁₉	1	8	yes	—
265	#95	C₂³×C₁₉	1	16	yes	—
266	#95	C₂³×C₁₉	1	16	yes	—
267	C₁₉	C₂×#2355	1	1	yes	characteristic, direct product factor, Sylow
268	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
269	C₂×Q₈	—	2	32	no	—
270	C₂×Q₈	—	2	8	no	—
271	C₂×Q₈	—	2	8	no	—
272	C₂×Q₈	C₂²×C₄×C₁₉	1	16	yes	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	2	8	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
288	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
289	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
290	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
291	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
292	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
293	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
294	C₂²×C₄	#41×C₁₉	1	4	yes	—
295	C₂²×C₄	#41×C₁₉	1	4	yes	—
296	C₂²×C₄	#41×C₁₉	1	4	yes	—
297	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
298	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
299	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
300	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
301	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
302	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
303	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
305	C₄⋊C₄	—	2	16	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	16	no	—
308	C₄⋊C₄	—	4	8	no	—
309	C₄⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
310	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
311	C₄⋊C₄	C₂×Q₈×C₁₉	1	16	yes	complemented
312	C₄²	—	2	16	no	—
313	C₄²	—	4	16	no	—
314	C₄²	C₂²×C₄×C₁₉	1	32	yes	—
315	C₄²	C₂²×C₄×C₁₉	1	16	yes	—
316	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
317	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
318	C₂³	C₂×#41×C₁₉	1	2	yes	—
319	C₂³	C₂×#41×C₁₉	1	2	yes	—
320	C₂³	C₂×#41×C₁₉	1	2	yes	—
321	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
322	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
323	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
324	Q₈	—	2	32	no	—
325	C₂×C₄	—	2	16	no	—
326	C₂×C₄	—	2	16	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	16	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	16	no	—
345	C₂×C₄	C₁₉×#117	1	16	yes	—
346	C₂×C₄	C₄×Q₈×C₁₉	1	16	yes	—
347	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
348	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
349	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
350	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
351	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
352	C₂×C₄	C₂²×Q₈×C₁₉	1	8	yes	—
353	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
354	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
355	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
356	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
357	C₂²	C₂×C₁₉×#117	1	4	yes	—
358	C₂²	C₂×C₄×Q₈×C₁₉	1	4	yes	—
359	C₂²	C₁₉×#520	1	4	yes	—
360	C₂²	C₁₉×#554	1	4	yes	—
361	C₂²	C₁₉×#556	1	4	yes	—
362	C₂²	C₁₉×#557	1	4	yes	—
363	C₂²	C₁₉×#559	1	4	yes	—
364	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
365	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
366	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
367	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
368	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
369	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
371	C₄	—	2	8	no	—
372	C₄	—	2	4	no	—
373	C₄	—	2	8	no	—
374	C₄	—	2	8	no	—
375	C₄	—	4	4	no	—
376	C₄	—	4	8	no	—
377	C₄	C₂×C₁₉×#117	1	8	yes	—
378	C₄	C₂×C₄×Q₈×C₁₉	1	8	yes	—
379	C₂	C₁₉×#2355	1	8	yes	direct product factor
380	C₂	C₂²×C₁₉×#117	1	1	yes	characteristic
381	C₂	C₂²×C₄×Q₈×C₁₉	1	1	yes	characteristic
382	C₂	C₂×C₁₉×#520	1	1	yes	characteristic
383	C₂	C₂×C₁₉×#554	1	1	yes	characteristic
384	C₂	C₂×C₁₉×#556	1	1	yes	characteristic
385	C₂	C₂×C₁₉×#557	1	1	yes	characteristic
386	C₂	C₂×C₁₉×#559	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2355	C₂	direct (N × H)
11. C₂×C₄×Q₈×C₁₉	C₄	semidirect
47. C₄×Q₈×C₁₉	C₂×C₄	semidirect
54. C₂×C₄⋊C₄×C₁₉	Q₈	semidirect
117. C₄⋊C₄×C₁₉	C₂×Q₈	semidirect
122. C₂×#2355	C₁₉	direct (N × H)
165. #2355	C₂×C₁₉	direct (N × H)
196. C₂×C₄×Q₈	C₄×C₁₉	semidirect
220. C₂×C₁₉	#2355	direct (N × H)
240. C₄×Q₈	C₂×C₄×C₁₉	semidirect
247. C₂×C₄⋊C₄	Q₈×C₁₉	semidirect
267. C₁₉	C₂×#2355	direct (N × H)
311. C₄⋊C₄	C₂×Q₈×C₁₉	semidirect
379. C₂	C₁₉×#2355	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×C₄×Q₈×C₁₉	2
C₁₉×#2355	2
C₂×C₁₉×#391	2
C₂×C₁₉×#387	2
C₂×C₁₉×#384	2
C₂×C₁₉×#382	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₂×#2355	19

Subgroups — C2×C19×#2355 #18040077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2355 #18040077