Subgroups — C₄×C₁₉×#557 #18040128

Order 4864.

2220 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#557	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2370	C₂	1	6	yes	maximal
3	C₁₉×#2365	C₂	1	3	yes	maximal
4	C₁₉×#2355	C₂	1	3	yes	maximal
5	C₁₉×#2351	C₂	1	2	yes	maximal
6	Q₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
7	C₄×C₁₉×C₄⋊Q₈	C₂	1	3	yes	maximal
8	C₄×C₁₉×#125	C₂	1	6	yes	maximal
9	C₄²×Q₈×C₁₉	C₂	1	2	yes	maximal
10	C₄²×Q₈×C₁₉	C₂	1	3	yes	maximal
11	C₄²×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#557	C₄	1	16	yes	direct product factor
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
14	C₂×C₁₉×#125	C₂²	1	6	yes	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#391	C₂²	1	6	yes	—
24	C₁₉×#389	C₂²	1	6	yes	—
25	C₁₉×#389	C₂²	1	6	yes	—
26	C₁₉×#389	C₂²	1	6	yes	—
27	C₁₉×#389	C₂²	1	6	yes	—
28	C₁₉×#387	C₂²	1	12	yes	—
29	C₁₉×#387	C₂²	1	12	yes	—
30	C₁₉×#384	C₂²	1	3	yes	—
31	C₁₉×#382	C₂²	1	6	yes	—
32	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	6	yes	—
45	C₄³×C₁₉	C₂²	1	6	yes	—
46	C₄³×C₁₉	C₂²	1	3	yes	—
47	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
48	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₁₉×C₄⋊Q₈	C₂×C₄	1	24	yes	—
50	C₁₉×#125	C₂×C₄	1	48	yes	—
51	C₄×Q₈×C₁₉	—	2	8	no	—
52	C₄×Q₈×C₁₉	—	2	4	no	—
53	C₄×Q₈×C₁₉	—	2	12	no	—
54	C₄×Q₈×C₁₉	—	2	12	no	—
55	C₄×Q₈×C₁₉	C₂×C₄	1	16	yes	—
56	C₄×Q₈×C₁₉	C₂×C₄	1	24	yes	—
57	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	—
58	C₄×Q₈×C₁₉	Q₈	1	8	yes	complemented
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
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	6	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	6	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
73	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
75	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
76	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
78	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
79	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
80	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
81	C₂×C₄²×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	1	yes	characteristic
85	C₁₉×#95	C₂³	1	2	yes	—
86	C₁₉×#95	C₂³	1	6	yes	—
87	C₁₉×#95	C₂³	1	6	yes	—
88	C₁₉×#95	C₂³	1	6	yes	—
89	C₁₉×#95	C₂³	1	12	yes	—
90	C₁₉×#95	C₂³	1	12	yes	—
91	C₂×Q₈×C₁₉	—	2	6	no	—
92	C₂×Q₈×C₁₉	—	2	6	no	—
93	C₂×Q₈×C₁₉	C₂²×C₄	1	12	yes	—
94	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
95	C₂×Q₈×C₁₉	C₂×Q₈	1	4	yes	—
96	C₂×Q₈×C₁₉	#41	1	4	yes	—
97	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
98	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
99	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
101	C₂²×C₄×C₁₉	C₂⁴	1	6	yes	—
102	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
103	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
106	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₁₉	—	2	12	no	—
109	C₄⋊C₄×C₁₉	—	2	12	no	—
110	C₄⋊C₄×C₁₉	—	2	6	no	—
111	C₄⋊C₄×C₁₉	—	2	12	no	—
112	C₄⋊C₄×C₁₉	—	2	6	no	—
113	C₄⋊C₄×C₁₉	—	4	6	no	—
114	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
115	C₄⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
116	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
117	C₄⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
118	C₄⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
119	C₄⋊C₄×C₁₉	C₂×Q₈	1	12	yes	—
120	C₄⋊C₄×C₁₉	#41	1	4	yes	—
121	C₄²×C₁₉	—	2	12	no	—
122	C₄²×C₁₉	—	2	6	no	—
123	C₄²×C₁₉	—	2	12	no	—
124	C₄²×C₁₉	—	2	6	no	—
125	C₄²×C₁₉	—	2	12	no	—
126	C₄²×C₁₉	—	2	4	no	—
127	C₄²×C₁₉	—	2	6	no	—
128	C₄²×C₁₉	—	4	3	no	—
129	C₄²×C₁₉	—	4	6	no	—
130	C₄²×C₁₉	C₂²×C₄	1	24	yes	—
131	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
132	C₄²×C₁₉	C₂×Q₈	1	12	yes	—
133	C₄²×C₁₉	#41	1	4	yes	—
134	C₄×#557	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
136	Q₈×C₁₉	—	2	24	no	—
137	Q₈×C₁₉	C₄×Q₈	1	16	yes	complemented
138	C₂×C₄×C₁₉	—	2	3	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	6	no	—
142	C₂×C₄×C₁₉	—	2	6	no	—
143	C₂×C₄×C₁₉	—	2	2	no	—
144	C₂×C₄×C₁₉	—	2	3	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	3	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	3	no	—
150	C₂×C₄×C₁₉	—	2	6	no	—
151	C₂×C₄×C₁₉	—	2	6	no	—
152	C₂×C₄×C₁₉	—	2	3	no	—
153	C₂×C₄×C₁₉	—	2	3	no	—
154	C₂×C₄×C₁₉	—	2	3	no	—
155	C₂×C₄×C₁₉	—	2	6	no	—
156	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
157	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
158	C₂×C₄×C₁₉	C₂³×C₄	1	12	yes	—
159	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
160	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
161	C₂×C₄×C₁₉	C₂²×Q₈	1	6	yes	—
162	C₂×C₄×C₁₉	C₂²×Q₈	1	6	yes	—
163	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
164	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
165	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
166	C₂×C₄×C₁₉	C₂×#41	1	6	yes	—
167	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
168	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
169	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
170	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
171	C₂×#557	C₂×C₁₉	1	1	yes	characteristic
172	#2370	C₂×C₁₉	1	6	yes	—
173	#2365	C₂×C₁₉	1	3	yes	—
174	#2355	C₂×C₁₉	1	3	yes	—
175	#2351	C₂×C₁₉	1	2	yes	—
176	Q₈×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
177	C₄×C₄⋊Q₈	C₂×C₁₉	1	3	yes	—
178	C₄×#125	C₂×C₁₉	1	6	yes	—
179	C₄²×Q₈	C₂×C₁₉	1	3	yes	—
180	C₄²×Q₈	C₂×C₁₉	1	2	yes	—
181	C₄²×Q₈	C₂×C₁₉	1	1	yes	characteristic
182	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
183	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
184	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
185	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
186	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
188	C₂²×C₁₉	#585	1	1	yes	characteristic
189	C₄×C₁₉	—	2	12	no	—
190	C₄×C₁₉	—	2	4	no	—
191	C₄×C₁₉	—	2	6	no	—
192	C₄×C₁₉	—	2	6	no	—
193	C₄×C₁₉	—	2	2	no	—
194	C₄×C₁₉	—	2	4	no	—
195	C₄×C₁₉	—	4	6	no	—
196	C₄×C₁₉	—	4	3	no	—
197	C₄×C₁₉	C₂×C₄×Q₈	1	12	yes	—
198	C₄×C₁₉	C₄×#41	1	4	yes	—
199	C₄×C₁₉	#557	1	4	yes	direct product factor
200	#557	C₄×C₁₉	1	16	yes	direct product factor
201	C₂×C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
202	C₂×#125	C₂²×C₁₉	1	6	yes	—
203	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
204	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
205	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
206	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
207	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
209	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
210	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
211	#391	C₂²×C₁₉	1	6	yes	—
212	#389	C₂²×C₁₉	1	6	yes	—
213	#389	C₂²×C₁₉	1	6	yes	—
214	#389	C₂²×C₁₉	1	6	yes	—
215	#389	C₂²×C₁₉	1	6	yes	—
216	#387	C₂²×C₁₉	1	12	yes	—
217	#387	C₂²×C₁₉	1	12	yes	—
218	#384	C₂²×C₁₉	1	3	yes	—
219	#382	C₂²×C₁₉	1	6	yes	—
220	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
221	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
222	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
223	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
224	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
225	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
226	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
227	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
228	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
229	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
230	C₄×C₄⋊C₄	C₂²×C₁₉	1	6	yes	—
231	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
232	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
233	C₄³	C₂²×C₁₉	1	6	yes	—
234	C₄³	C₂²×C₁₉	1	3	yes	—
235	C₂×C₁₉	C₂²×C₄×Q₈	1	1	yes	characteristic
236	C₂×C₁₉	C₂×C₄×#41	1	1	yes	characteristic
237	C₂×C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
238	C₂×C₁₉	C₂×#557	1	1	yes	characteristic
239	C₂×C₁₉	Q₈×#41	1	1	yes	characteristic
240	C₂×C₁₉	#3480	1	1	yes	characteristic
241	C₂×C₁₉	#3482	1	1	yes	characteristic
242	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
243	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
244	C₄⋊Q₈	C₂×C₄×C₁₉	1	24	yes	—
245	#125	C₂×C₄×C₁₉	1	48	yes	—
246	C₄×Q₈	—	2	8	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	12	no	—
249	C₄×Q₈	—	2	12	no	—
250	C₄×Q₈	C₂×C₄×C₁₉	1	16	yes	—
251	C₄×Q₈	C₂×C₄×C₁₉	1	24	yes	—
252	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	—
253	C₄×Q₈	Q₈×C₁₉	1	8	yes	complemented
254	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
255	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
258	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
259	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₉	1	6	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
268	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
269	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
270	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
271	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
272	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
273	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
274	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
275	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
276	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
277	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
278	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
279	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
280	#95	C₂³×C₁₉	1	2	yes	—
281	#95	C₂³×C₁₉	1	6	yes	—
282	#95	C₂³×C₁₉	1	6	yes	—
283	#95	C₂³×C₁₉	1	6	yes	—
284	#95	C₂³×C₁₉	1	12	yes	—
285	#95	C₂³×C₁₉	1	12	yes	—
286	C₁₉	C₄×#557	1	1	yes	characteristic, direct product factor, Sylow
287	C₂×Q₈	—	2	6	no	—
288	C₂×Q₈	—	2	6	no	—
289	C₂×Q₈	C₂²×C₄×C₁₉	1	12	yes	—
290	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
291	C₂×Q₈	C₂×Q₈×C₁₉	1	4	yes	—
292	C₂×Q₈	#41×C₁₉	1	4	yes	—
293	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
294	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
295	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
297	C₂²×C₄	C₂⁴×C₁₉	1	6	yes	—
298	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
299	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
300	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
302	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
304	C₄⋊C₄	—	2	12	no	—
305	C₄⋊C₄	—	2	12	no	—
306	C₄⋊C₄	—	2	6	no	—
307	C₄⋊C₄	—	2	12	no	—
308	C₄⋊C₄	—	2	6	no	—
309	C₄⋊C₄	—	4	6	no	—
310	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
311	C₄⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
312	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
313	C₄⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
314	C₄⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
315	C₄⋊C₄	C₂×Q₈×C₁₉	1	12	yes	—
316	C₄⋊C₄	#41×C₁₉	1	4	yes	—
317	C₄²	—	2	12	no	—
318	C₄²	—	2	6	no	—
319	C₄²	—	2	12	no	—
320	C₄²	—	2	6	no	—
321	C₄²	—	2	12	no	—
322	C₄²	—	2	4	no	—
323	C₄²	—	2	6	no	—
324	C₄²	—	4	3	no	—
325	C₄²	—	4	6	no	—
326	C₄²	C₂²×C₄×C₁₉	1	24	yes	—
327	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
328	C₄²	C₂×Q₈×C₁₉	1	12	yes	—
329	C₄²	#41×C₁₉	1	4	yes	—
330	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
331	Q₈	—	2	24	no	—
332	Q₈	C₄×Q₈×C₁₉	1	16	yes	complemented
333	C₂×C₄	—	2	3	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	6	no	—
337	C₂×C₄	—	2	6	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	3	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	3	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	3	no	—
345	C₂×C₄	—	2	6	no	—
346	C₂×C₄	—	2	6	no	—
347	C₂×C₄	—	2	3	no	—
348	C₂×C₄	—	2	3	no	—
349	C₂×C₄	—	2	3	no	—
350	C₂×C₄	—	2	6	no	—
351	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
352	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
353	C₂×C₄	C₂³×C₄×C₁₉	1	12	yes	—
354	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
355	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
356	C₂×C₄	C₂²×Q₈×C₁₉	1	6	yes	—
357	C₂×C₄	C₂²×Q₈×C₁₉	1	6	yes	—
358	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
359	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
360	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
361	C₂×C₄	C₂×#41×C₁₉	1	6	yes	—
362	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
363	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
364	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
365	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
366	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
367	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
368	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
369	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
370	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
371	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
372	C₂²	C₁₉×#585	1	1	yes	characteristic
373	C₄	—	2	12	no	—
374	C₄	—	2	4	no	—
375	C₄	—	2	6	no	—
376	C₄	—	2	6	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	4	no	—
379	C₄	—	4	6	no	—
380	C₄	—	4	3	no	—
381	C₄	C₂×C₄×Q₈×C₁₉	1	12	yes	—
382	C₄	C₄×#41×C₁₉	1	4	yes	—
383	C₄	C₁₉×#557	1	4	yes	direct product factor
384	C₂	C₂²×C₄×Q₈×C₁₉	1	1	yes	characteristic
385	C₂	C₂×C₄×#41×C₁₉	1	1	yes	characteristic
386	C₂	C₄×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
387	C₂	C₂×C₁₉×#557	1	1	yes	characteristic
388	C₂	Q₈×#41×C₁₉	1	1	yes	characteristic
389	C₂	C₁₉×#3480	1	1	yes	characteristic
390	C₂	C₁₉×#3482	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
12. C₁₉×#557	C₄	direct (N × H)
58. C₄×Q₈×C₁₉	Q₈	semidirect
134. C₄×#557	C₁₉	direct (N × H)
137. Q₈×C₁₉	C₄×Q₈	semidirect
199. C₄×C₁₉	#557	direct (N × H)
200. #557	C₄×C₁₉	direct (N × H)
253. C₄×Q₈	Q₈×C₁₉	semidirect
286. C₁₉	C₄×#557	direct (N × H)
332. Q₈	C₄×Q₈×C₁₉	semidirect
383. C₄	C₁₉×#557	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×#557	2
C₁₉×#2370	2
C₁₉×#2365	2
C₁₉×#2355	2
C₁₉×#2351	2
Q₈×C₄⋊C₄×C₁₉	2
C₄×C₁₉×C₄⋊Q₈	2
C₄×C₁₉×#125	2
C₄²×Q₈×C₁₉	2
C₄×#557	19

Subgroups — C4×C19×#557 #18040128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#557 #18040128