Subgroups — C₁₉×#34312 #18040271

Order 4864.

2960 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#548	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2367	C₂	1	3	yes	maximal, complemented
5	C₁₉×#2363	C₂	1	3	yes	maximal, complemented
6	C₁₉×#2360	C₂	1	3	yes	maximal, complemented
7	C₁₉×#2352	C₂	1	3	yes	maximal, complemented
8	C₁₉×#2351	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2341	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₈×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2324	C₂	1	3	yes	maximal, complemented
12	C₁₉×#2323	C₂	1	3	yes	maximal, complemented
13	C₄×C₁₉×#124	C₂	1	3	yes	maximal, complemented
14	C₁₉×#2293	C₂	1	3	yes	maximal, complemented
15	C₄²×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#548	C₄	1	16	yes	complemented
19	C₂×C₁₉×#124	C₂²	1	3	yes	—
20	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	3	yes	—
21	C₂×C₁₉×#121	C₂²	1	3	yes	—
22	C₁₉×#520	—	2	8	no	—
23	C₁₉×#519	—	2	8	no	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₉	C₂²	1	3	yes	—
27	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
32	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
33	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
34	C₂×C₁₉×#117	C₂²	1	3	yes	—
35	C₂×C₁₉×#117	C₂²	1	3	yes	—
36	C₂×C₁₉×#117	C₂²	1	3	yes	—
37	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
38	C₁₉×#391	C₂²	1	3	yes	—
39	C₁₉×#391	C₂²	1	3	yes	—
40	C₁₉×#390	C₂²	1	3	yes	—
41	C₁₉×#390	C₂²	1	3	yes	—
42	C₁₉×#390	C₂²	1	3	yes	—
43	C₁₉×#390	C₂²	1	3	yes	—
44	C₁₉×#389	C₂²	1	3	yes	—
45	C₁₉×#389	C₂²	1	3	yes	—
46	C₁₉×#389	C₂²	1	3	yes	—
47	C₁₉×#389	C₂²	1	3	yes	—
48	C₁₉×#388	C₂²	1	1	yes	characteristic
49	C₁₉×#388	C₂²	1	3	yes	—
50	C₁₉×#388	C₂²	1	3	yes	—
51	C₁₉×#388	C₂²	1	3	yes	—
52	C₁₉×#388	C₂²	1	6	yes	—
53	C₁₉×#388	C₂²	1	6	yes	—
54	C₁₉×#387	C₂²	1	6	yes	—
55	C₁₉×#386	C₂²	1	6	yes	—
56	C₁₉×#385	C₂²	1	6	yes	—
57	C₁₉×#382	C₂²	1	3	yes	—
58	C₁₉×#380	C₂²	1	3	yes	—
59	C₁₉×#380	C₂²	1	3	yes	—
60	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
61	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
62	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
63	C₄×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
64	C₄×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
65	C₄×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
66	C₄×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
67	C₄×C₂²⋊C₄×C₁₉	C₂²	1	6	yes	—
68	C₄³×C₁₉	C₂²	1	3	yes	—
69	C₂×#41×C₁₉	—	2	4	no	—
70	C₂×#41×C₁₉	—	2	4	no	—
71	C₂×#41×C₁₉	C₂×C₄	1	8	yes	—
72	C₂²×Q₈×C₁₉	—	2	4	no	—
73	C₂²×Q₈×C₁₉	—	2	4	no	—
74	C₂²×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
75	C₂²×Q₈×C₁₉	C₂³	1	3	yes	—
76	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
78	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
79	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
80	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
81	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
82	C₁₉×#124	C₂×C₄	1	24	yes	complemented
83	C₁₉×C₂²⋊Q₈	C₂×C₄	1	24	yes	complemented
84	C₁₉×#121	C₂×C₄	1	24	yes	complemented
85	C₄×Q₈×C₁₉	—	2	4	no	—
86	C₄×Q₈×C₁₉	—	2	4	no	—
87	C₄×Q₈×C₁₉	—	2	4	no	—
88	C₄×Q₈×C₁₉	—	2	12	no	—
89	C₄×Q₈×C₁₉	—	2	12	no	—
90	C₄×Q₈×C₁₉	C₂×C₄	1	8	yes	complemented
91	C₄×Q₈×C₁₉	D₄	1	8	yes	complemented
92	C₄×D₄×C₁₉	—	2	12	no	—
93	C₄×D₄×C₁₉	—	2	12	no	—
94	C₄×D₄×C₁₉	C₂×C₄	1	24	yes	complemented
95	C₁₉×#117	—	2	12	no	—
96	C₁₉×#117	—	2	12	no	—
97	C₁₉×#117	—	2	12	no	—
98	C₂×C₄⋊C₄×C₁₉	—	2	12	no	—
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
101	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
102	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
103	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
104	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
107	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
110	C₂×C₄⋊C₄×C₁₉	C₂³	1	3	yes	—
111	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
113	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
114	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
115	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
116	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
118	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
119	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
120	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
121	C₂×C₂²⋊C₄×C₁₉	C₂³	1	6	yes	—
122	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
125	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
126	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
127	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
128	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
129	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
130	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
131	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
132	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
133	C₁₉×#95	C₂³	1	1	yes	characteristic
134	C₁₉×#95	C₂³	1	3	yes	—
135	C₁₉×#95	C₂³	1	3	yes	—
136	C₁₉×#95	C₂³	1	3	yes	—
137	C₁₉×#95	C₂³	1	6	yes	—
138	C₁₉×#95	C₂³	1	6	yes	—
139	C₁₉×#95	C₂³	1	3	yes	—
140	C₁₉×#95	C₂³	1	6	yes	—
141	C₁₉×#95	C₂³	1	1	yes	characteristic
142	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
143	C₂⁴×C₁₉	C₂⁴	1	3	yes	—
144	#41×C₁₉	—	2	32	no	—
145	C₂×Q₈×C₁₉	—	2	32	no	—
146	C₂×Q₈×C₁₉	—	2	6	no	—
147	C₂×Q₈×C₁₉	—	2	6	no	—
148	C₂×Q₈×C₁₉	C₂²×C₄	1	12	yes	—
149	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
150	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
151	C₂×Q₈×C₁₉	#41	1	4	yes	—
152	C₂×D₄×C₁₉	—	2	6	no	—
153	C₂×D₄×C₁₉	—	2	6	no	—
154	C₂×D₄×C₁₉	—	4	3	no	—
155	C₂×D₄×C₁₉	—	4	3	no	—
156	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
157	C₂×D₄×C₁₉	C₂²×C₄	1	12	yes	—
158	C₂²×C₄×C₁₉	—	2	6	no	—
159	C₂²×C₄×C₁₉	—	2	6	no	—
160	C₂²×C₄×C₁₉	—	2	6	no	—
161	C₂²×C₄×C₁₉	—	2	6	no	—
162	C₂²×C₄×C₁₉	—	2	12	no	—
163	C₂²×C₄×C₁₉	—	4	6	no	—
164	C₂²×C₄×C₁₉	—	4	6	no	—
165	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
166	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
167	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
170	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
172	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
174	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
175	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
178	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
180	C₄⋊C₄×C₁₉	—	2	6	no	—
181	C₄⋊C₄×C₁₉	—	2	6	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	6	no	—
184	C₄⋊C₄×C₁₉	—	2	6	no	—
185	C₄⋊C₄×C₁₉	—	2	6	no	—
186	C₄⋊C₄×C₁₉	—	2	6	no	—
187	C₄⋊C₄×C₁₉	—	4	3	no	—
188	C₄⋊C₄×C₁₉	—	4	3	no	—
189	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
190	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
191	C₄⋊C₄×C₁₉	C₂×D₄	1	12	yes	—
192	C₂²⋊C₄×C₁₉	—	2	6	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	6	no	—
195	C₂²⋊C₄×C₁₉	—	2	6	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	6	no	—
198	C₂²⋊C₄×C₁₉	—	4	3	no	—
199	C₂²⋊C₄×C₁₉	—	4	6	no	—
200	C₂²⋊C₄×C₁₉	—	4	3	no	—
201	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
202	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
203	C₂²⋊C₄×C₁₉	C₂²×C₄	1	24	yes	—
204	C₄²×C₁₉	—	2	6	no	—
205	C₄²×C₁₉	—	2	12	no	—
206	C₄²×C₁₉	—	2	6	no	—
207	C₄²×C₁₉	—	2	6	no	—
208	C₄²×C₁₉	—	2	2	no	—
209	C₄²×C₁₉	—	4	3	no	—
210	C₄²×C₁₉	—	4	3	no	—
211	C₄²×C₁₉	—	4	3	no	—
212	C₄²×C₁₉	C₂²×C₄	1	12	yes	—
213	C₄²×C₁₉	C₂×D₄	1	12	yes	—
214	#34312	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	3	no	—
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	2	3	no	—
219	C₂³×C₁₉	—	2	1	no	—
220	C₂³×C₁₉	—	2	3	no	—
221	C₂³×C₁₉	—	2	1	no	—
222	C₂³×C₁₉	—	2	3	no	—
223	C₂³×C₁₉	—	2	3	no	—
224	C₂³×C₁₉	—	2	3	no	—
225	C₂³×C₁₉	—	2	1	no	—
226	C₂³×C₁₉	—	2	1	no	—
227	C₂³×C₁₉	C₂³×C₄	1	6	yes	—
228	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
229	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
230	Q₈×C₁₉	—	2	24	no	—
231	Q₈×C₁₉	C₄×D₄	1	16	yes	—
232	D₄×C₁₉	—	2	24	no	—
233	D₄×C₁₉	—	4	12	no	—
234	C₂×C₄×C₁₉	—	2	3	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	3	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	1	no	—
244	C₂×C₄×C₁₉	—	2	3	no	—
245	C₂×C₄×C₁₉	—	2	3	no	—
246	C₂×C₄×C₁₉	—	2	3	no	—
247	C₂×C₄×C₁₉	—	2	3	no	—
248	C₂×C₄×C₁₉	—	2	24	no	—
249	C₂×C₄×C₁₉	—	2	24	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	3	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	2	3	no	—
254	C₂×C₄×C₁₉	—	2	3	no	—
255	C₂×C₄×C₁₉	—	2	1	no	—
256	C₂×C₄×C₁₉	—	2	3	no	—
257	C₂×C₄×C₁₉	—	2	3	no	—
258	C₂×C₄×C₁₉	—	2	3	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	3	no	—
261	C₂×C₄×C₁₉	—	2	3	no	—
262	C₂×C₄×C₁₉	—	2	1	no	—
263	C₂×C₄×C₁₉	—	2	1	no	—
264	C₂×C₄×C₁₉	—	2	3	no	—
265	C₂×C₄×C₁₉	—	8	12	no	—
266	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
267	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
268	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
269	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
270	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
271	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
272	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
274	C₂×C₄×C₁₉	C₂×#41	1	6	yes	—
275	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
276	C₂×#548	C₂×C₁₉	1	1	yes	characteristic
277	C₂×#520	C₂×C₁₉	1	1	yes	characteristic, complemented
278	C₂×#519	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#2367	C₂×C₁₉	1	3	yes	complemented
280	#2363	C₂×C₁₉	1	3	yes	complemented
281	#2360	C₂×C₁₉	1	3	yes	complemented
282	#2352	C₂×C₁₉	1	3	yes	complemented
283	#2351	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#2341	C₂×C₁₉	1	1	yes	characteristic, complemented
285	Q₈×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
286	#2324	C₂×C₁₉	1	3	yes	complemented
287	#2323	C₂×C₁₉	1	3	yes	complemented
288	C₄×#124	C₂×C₁₉	1	3	yes	complemented
289	#2293	C₂×C₁₉	1	3	yes	complemented
290	C₄²×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	2	6	no	—
293	C₂²×C₁₉	—	2	2	no	—
294	C₂²×C₁₉	—	2	6	no	—
295	C₂²×C₁₉	—	2	2	no	—
296	C₂²×C₁₉	—	2	6	no	—
297	C₂²×C₁₉	—	4	1	no	—
298	C₂²×C₁₉	—	4	3	no	—
299	C₂²×C₁₉	—	4	3	no	—
300	C₂²×C₁₉	—	4	1	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	3	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	4	3	no	—
305	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
306	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
307	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
308	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
309	C₂²×C₁₉	#585	1	1	yes	characteristic
310	C₂²×C₁₉	#585	1	1	yes	characteristic
311	C₂²×C₁₉	#585	1	1	yes	characteristic
312	C₄×C₁₉	—	2	2	no	—
313	C₄×C₁₉	—	2	6	no	—
314	C₄×C₁₉	—	2	6	no	—
315	C₄×C₁₉	—	2	2	no	—
316	C₄×C₁₉	—	2	2	no	—
317	C₄×C₁₉	—	2	6	no	—
318	C₄×C₁₉	—	2	2	no	—
319	C₄×C₁₉	—	4	1	no	—
320	C₄×C₁₉	—	4	3	no	—
321	C₄×C₁₉	—	4	1	no	—
322	C₄×C₁₉	—	4	3	no	—
323	C₄×C₁₉	—	4	3	no	—
324	C₄×C₁₉	C₂×C₄×D₄	1	12	yes	—
325	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
326	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
327	#548	C₄×C₁₉	1	16	yes	complemented
328	C₂×#124	C₂²×C₁₉	1	3	yes	—
329	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	3	yes	—
330	C₂×#121	C₂²×C₁₉	1	3	yes	—
331	#520	—	2	8	no	—
332	#519	—	2	8	no	—
333	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
334	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
336	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
337	C₂×C₄×Q₈	C₂²×C₁₉	1	3	yes	—
338	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
339	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
340	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
341	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
342	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
343	C₂×#117	C₂²×C₁₉	1	3	yes	—
344	C₂×#117	C₂²×C₁₉	1	3	yes	—
345	C₂×#117	C₂²×C₁₉	1	3	yes	—
346	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
347	#391	C₂²×C₁₉	1	3	yes	—
348	#391	C₂²×C₁₉	1	3	yes	—
349	#390	C₂²×C₁₉	1	3	yes	—
350	#390	C₂²×C₁₉	1	3	yes	—
351	#390	C₂²×C₁₉	1	3	yes	—
352	#390	C₂²×C₁₉	1	3	yes	—
353	#389	C₂²×C₁₉	1	3	yes	—
354	#389	C₂²×C₁₉	1	3	yes	—
355	#389	C₂²×C₁₉	1	3	yes	—
356	#389	C₂²×C₁₉	1	3	yes	—
357	#388	C₂²×C₁₉	1	6	yes	—
358	#388	C₂²×C₁₉	1	6	yes	—
359	#388	C₂²×C₁₉	1	3	yes	—
360	#388	C₂²×C₁₉	1	3	yes	—
361	#388	C₂²×C₁₉	1	1	yes	characteristic
362	#388	C₂²×C₁₉	1	3	yes	—
363	#387	C₂²×C₁₉	1	6	yes	—
364	#386	C₂²×C₁₉	1	6	yes	—
365	#385	C₂²×C₁₉	1	6	yes	—
366	#382	C₂²×C₁₉	1	3	yes	—
367	#380	C₂²×C₁₉	1	3	yes	—
368	#380	C₂²×C₁₉	1	3	yes	—
369	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
370	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
371	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
372	C₄×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
373	C₄×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
374	C₄×C₂²⋊C₄	C₂²×C₁₉	1	3	yes	—
375	C₄×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
376	C₄×C₂²⋊C₄	C₂²×C₁₉	1	6	yes	—
377	C₄³	C₂²×C₁₉	1	3	yes	—
378	C₂×C₁₉	—	4	2	no	—
379	C₂×C₁₉	—	4	6	no	—
380	C₂×C₁₉	C₂²×C₄×D₄	1	1	yes	characteristic
381	C₂×C₁₉	#3428	1	1	yes	characteristic
382	C₂×C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
383	C₂×C₁₉	#3497	1	1	yes	characteristic
384	C₂×C₁₉	#3500	1	1	yes	characteristic
385	C₂×C₁₉	#3516	1	1	yes	characteristic
386	C₂×C₁₉	#3524	1	1	yes	characteristic
387	C₂×#41	—	2	4	no	—
388	C₂×#41	—	2	4	no	—
389	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
390	C₂²×Q₈	—	2	4	no	—
391	C₂²×Q₈	—	2	4	no	—
392	C₂²×Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
393	C₂²×Q₈	C₂³×C₁₉	1	3	yes	—
394	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
395	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
396	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
397	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
398	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
399	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
400	#124	C₂×C₄×C₁₉	1	24	yes	complemented
401	C₂²⋊Q₈	C₂×C₄×C₁₉	1	24	yes	complemented
402	#121	C₂×C₄×C₁₉	1	24	yes	complemented
403	C₄×Q₈	—	2	4	no	—
404	C₄×Q₈	—	2	4	no	—
405	C₄×Q₈	—	2	4	no	—
406	C₄×Q₈	—	2	12	no	—
407	C₄×Q₈	—	2	12	no	—
408	C₄×Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
409	C₄×Q₈	D₄×C₁₉	1	8	yes	complemented
410	C₄×D₄	—	2	12	no	—
411	C₄×D₄	—	2	12	no	—
412	C₄×D₄	C₂×C₄×C₁₉	1	24	yes	complemented
413	#117	—	2	12	no	—
414	#117	—	2	12	no	—
415	#117	—	2	12	no	—
416	C₂×C₄⋊C₄	—	2	12	no	—
417	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
419	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
426	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
427	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
428	C₂×C₄⋊C₄	C₂³×C₁₉	1	3	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
434	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₉	1	6	yes	—
441	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
442	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
443	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
444	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
445	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
447	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
448	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
449	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
450	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
451	#95	C₂³×C₁₉	1	1	yes	characteristic
452	#95	C₂³×C₁₉	1	3	yes	—
453	#95	C₂³×C₁₉	1	3	yes	—
454	#95	C₂³×C₁₉	1	3	yes	—
455	#95	C₂³×C₁₉	1	6	yes	—
456	#95	C₂³×C₁₉	1	6	yes	—
457	#95	C₂³×C₁₉	1	3	yes	—
458	#95	C₂³×C₁₉	1	6	yes	—
459	#95	C₂³×C₁₉	1	1	yes	characteristic
460	C₁₉	#34312	1	1	yes	characteristic, direct product factor, Sylow
461	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
462	C₂⁴	C₂⁴×C₁₉	1	3	yes	—
463	#41	—	2	32	no	—
464	C₂×Q₈	—	2	32	no	—
465	C₂×Q₈	—	2	6	no	—
466	C₂×Q₈	—	2	6	no	—
467	C₂×Q₈	C₂²×C₄×C₁₉	1	12	yes	—
468	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
469	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
470	C₂×Q₈	#41×C₁₉	1	4	yes	—
471	C₂×D₄	—	2	6	no	—
472	C₂×D₄	—	2	6	no	—
473	C₂×D₄	—	4	3	no	—
474	C₂×D₄	—	4	3	no	—
475	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
476	C₂×D₄	C₂²×C₄×C₁₉	1	12	yes	—
477	C₂²×C₄	—	2	6	no	—
478	C₂²×C₄	—	2	6	no	—
479	C₂²×C₄	—	2	6	no	—
480	C₂²×C₄	—	2	6	no	—
481	C₂²×C₄	—	2	12	no	—
482	C₂²×C₄	—	4	6	no	—
483	C₂²×C₄	—	4	6	no	—
484	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
485	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
486	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
487	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
488	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
490	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
493	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
494	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
496	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
498	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
499	C₄⋊C₄	—	2	6	no	—
500	C₄⋊C₄	—	2	6	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	6	no	—
503	C₄⋊C₄	—	2	6	no	—
504	C₄⋊C₄	—	2	6	no	—
505	C₄⋊C₄	—	2	6	no	—
506	C₄⋊C₄	—	4	3	no	—
507	C₄⋊C₄	—	4	3	no	—
508	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
509	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
510	C₄⋊C₄	C₂×D₄×C₁₉	1	12	yes	—
511	C₂²⋊C₄	—	2	6	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	6	no	—
514	C₂²⋊C₄	—	2	6	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	6	no	—
517	C₂²⋊C₄	—	4	3	no	—
518	C₂²⋊C₄	—	4	6	no	—
519	C₂²⋊C₄	—	4	3	no	—
520	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
521	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
522	C₂²⋊C₄	C₂²×C₄×C₁₉	1	24	yes	—
523	C₄²	—	2	6	no	—
524	C₄²	—	2	12	no	—
525	C₄²	—	2	6	no	—
526	C₄²	—	2	6	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	4	3	no	—
529	C₄²	—	4	3	no	—
530	C₄²	—	4	3	no	—
531	C₄²	C₂²×C₄×C₁₉	1	12	yes	—
532	C₄²	C₂×D₄×C₁₉	1	12	yes	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	3	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	3	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	3	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	3	no	—
541	C₂³	—	2	3	no	—
542	C₂³	—	2	3	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	C₂³×C₄×C₁₉	1	6	yes	—
546	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
547	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
548	Q₈	—	2	24	no	—
549	Q₈	C₄×D₄×C₁₉	1	16	yes	—
550	D₄	—	2	24	no	—
551	D₄	—	4	12	no	—
552	C₂×C₄	—	2	3	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	3	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	3	no	—
563	C₂×C₄	—	2	3	no	—
564	C₂×C₄	—	2	3	no	—
565	C₂×C₄	—	2	3	no	—
566	C₂×C₄	—	2	24	no	—
567	C₂×C₄	—	2	24	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	3	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	3	no	—
572	C₂×C₄	—	2	3	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	3	no	—
575	C₂×C₄	—	2	3	no	—
576	C₂×C₄	—	2	3	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	3	no	—
579	C₂×C₄	—	2	3	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	3	no	—
583	C₂×C₄	—	8	12	no	—
584	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
585	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
586	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
587	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
588	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
589	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
590	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
591	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
592	C₂×C₄	C₂×#41×C₁₉	1	6	yes	—
593	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	6	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	6	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	6	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	3	no	—
602	C₂²	—	4	3	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	3	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	3	no	—
608	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
609	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
610	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
611	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
612	C₂²	C₁₉×#585	1	1	yes	characteristic
613	C₂²	C₁₉×#585	1	1	yes	characteristic
614	C₂²	C₁₉×#585	1	1	yes	characteristic
615	C₄	—	2	6	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	6	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	6	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	3	no	—
624	C₄	—	4	3	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	3	no	—
627	C₄	C₂×C₄×D₄×C₁₉	1	12	yes	—
628	C₂	—	4	2	no	—
629	C₂	—	4	6	no	—
630	C₂	C₂²×C₄×D₄×C₁₉	1	1	yes	characteristic
631	C₂	C₁₉×#3428	1	1	yes	characteristic
632	C₂	C₄×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
633	C₂	C₁₉×#3497	1	1	yes	characteristic
634	C₂	C₁₉×#3500	1	1	yes	characteristic
635	C₂	C₁₉×#3516	1	1	yes	characteristic
636	C₂	C₁₉×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂×C₁₉×#548	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. C₂×C₁₉×#520	C₂	semidirect
3. C₂×C₁₉×#519	C₂	semidirect
4. C₁₉×#2367	C₂	semidirect
5. C₁₉×#2363	C₂	semidirect
6. C₁₉×#2360	C₂	semidirect
7. C₁₉×#2352	C₂	semidirect
8. C₁₉×#2351	C₂	semidirect
9. C₁₉×#2341	C₂	semidirect
10. Q₈×C₂²⋊C₄×C₁₉	C₂	semidirect
11. C₁₉×#2324	C₂	semidirect
12. C₁₉×#2323	C₂	semidirect
13. C₄×C₁₉×#124	C₂	semidirect
14. C₁₉×#2293	C₂	semidirect
15. C₄²×Q₈×C₁₉	C₂	semidirect
18. C₁₉×#548	C₄	semidirect
74. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
82. C₁₉×#124	C₂×C₄	semidirect
83. C₁₉×C₂²⋊Q₈	C₂×C₄	semidirect
84. C₁₉×#121	C₂×C₄	semidirect
90. C₄×Q₈×C₁₉	C₂×C₄	semidirect
91. C₄×Q₈×C₁₉	D₄	semidirect
94. C₄×D₄×C₁₉	C₂×C₄	semidirect
214. #34312	C₁₉	direct (N × H)
277. C₂×#520	C₂×C₁₉	semidirect
278. C₂×#519	C₂×C₁₉	semidirect
279. #2367	C₂×C₁₉	semidirect
280. #2363	C₂×C₁₉	semidirect
281. #2360	C₂×C₁₉	semidirect
282. #2352	C₂×C₁₉	semidirect
283. #2351	C₂×C₁₉	semidirect
284. #2341	C₂×C₁₉	semidirect
285. Q₈×C₂²⋊C₄	C₂×C₁₉	semidirect
286. #2324	C₂×C₁₉	semidirect
287. #2323	C₂×C₁₉	semidirect
288. C₄×#124	C₂×C₁₉	semidirect
289. #2293	C₂×C₁₉	semidirect
290. C₄²×Q₈	C₂×C₁₉	semidirect
327. #548	C₄×C₁₉	semidirect
392. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
400. #124	C₂×C₄×C₁₉	semidirect
401. C₂²⋊Q₈	C₂×C₄×C₁₉	semidirect
402. #121	C₂×C₄×C₁₉	semidirect
408. C₄×Q₈	C₂×C₄×C₁₉	semidirect
409. C₄×Q₈	D₄×C₁₉	semidirect
412. C₄×D₄	C₂×C₄×C₁₉	semidirect
460. C₁₉	#34312	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×#548	2
C₂×C₁₉×#520	2
C₂×C₁₉×#519	2
C₁₉×#2367	2
C₁₉×#2363	2
C₁₉×#2360	2
C₁₉×#2352	2
C₁₉×#2351	2
C₁₉×#2341	2
Q₈×C₂²⋊C₄×C₁₉	2
C₁₉×#2324	2
C₁₉×#2323	2
C₄×C₁₉×#124	2
C₁₉×#2293	2
C₄²×Q₈×C₁₉	2
#34312	19

Subgroups — C19×#34312 #18040271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34312 #18040271