Subgroups — C₁₉×#60330 #18066289

Order 4864.

1710 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3461	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2993	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2992	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2989	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2985	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2983	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2966	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2966	C₂	1	4	yes	maximal, complemented
9	C₈×#41×C₁₉	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2960	C₂	1	4	yes	maximal, complemented
11	C₂×C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#544	C₄	1	1	yes	characteristic
13	C₁₉×#542	C₄	1	4	yes	—
14	C₁₉×#541	C₄	1	4	yes	—
15	C₁₉×#539	C₄	1	4	yes	—
16	C₁₉×#537	C₄	1	1	yes	characteristic
17	C₁₉×#536	C₄	1	2	yes	—
18	C₁₉×#533	C₂²	1	4	yes	—
19	C₁₉×#529	C₂²	1	4	yes	—
20	C₁₉×#529	C₂²	1	4	yes	—
21	C₄×#41×C₁₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#446	C₂²	1	4	yes	—
24	C₁₉×#446	C₂²	1	4	yes	—
25	C₁₉×#446	C₂²	1	8	yes	—
26	C₁₉×#446	C₂²	1	4	yes	—
27	C₁₉×#446	C₂²	1	4	yes	—
28	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
29	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
30	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
31	C₈×Q₈×C₁₉	C₂²	1	4	yes	—
32	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
33	C₁₉×#436	C₂²	1	4	yes	—
34	C₁₉×#436	C₂²	1	4	yes	—
35	C₁₉×#435	C₂²	1	8	yes	—
36	C₁₉×#435	C₂²	1	8	yes	—
37	C₈×D₄×C₁₉	C₂²	1	4	yes	—
38	C₈×D₄×C₁₉	C₂²	1	2	yes	—
39	C₈×D₄×C₁₉	C₂²	1	4	yes	—
40	C₈×D₄×C₁₉	C₂²	1	2	yes	—
41	C₈×D₄×C₁₉	C₂²	1	4	yes	—
42	C₁₉×#433	C₂²	1	8	yes	—
43	C₁₉×#433	C₂²	1	8	yes	—
44	C₁₉×#432	C₂²	1	4	yes	—
45	C₁₉×#432	C₂²	1	4	yes	—
46	C₁₉×#431	C₂²	1	2	yes	—
47	C₁₉×#431	C₂²	1	4	yes	—
48	C₁₉×#424	C₂²	1	8	yes	—
49	C₁₉×#423	C₂²	1	4	yes	—
50	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
52	C₁₉×#405	C₂²	1	8	yes	—
53	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	—
55	C₂×C₄×C₈×C₁₉	C₂²	1	4	yes	—
56	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
57	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
59	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
64	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
65	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
66	C₁₉×#126	C₂×C₄	1	8	yes	—
67	C₁₉×#126	C₂×C₄	1	8	yes	—
68	C₁₉×#125	C₂×C₄	1	4	yes	—
69	C₁₉×#125	C₂×C₄	1	4	yes	—
70	C₁₉×#125	C₂×C₄	1	8	yes	—
71	C₁₉×#124	C₂×C₄	1	4	yes	—
72	C₁₉×#124	C₂×C₄	1	4	yes	—
73	C₁₉×#123	C₂×C₄	1	8	yes	—
74	C₁₉×#123	C₂×C₄	1	8	yes	—
75	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
76	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
77	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
78	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
79	C₁₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
80	C₁₉×#121	C₂×C₄	1	4	yes	—
81	C₁₉×#121	C₂×C₄	1	4	yes	—
82	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
83	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
84	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
85	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
86	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
87	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
88	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
89	C₄×D₄×C₁₉	C₂³	1	4	yes	—
90	C₄×D₄×C₁₉	C₂³	1	2	yes	—
91	C₄×D₄×C₁₉	C₂³	1	4	yes	—
92	C₁₉×#117	C₂×C₄	1	2	yes	—
93	C₁₉×#117	C₂×C₄	1	4	yes	—
94	C₁₉×#117	C₂³	1	8	yes	—
95	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
100	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
101	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
102	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
103	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
104	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
105	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
106	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
107	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
108	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
109	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
110	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
111	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
112	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
113	C₁₉×#97	C₂³	1	8	yes	—
114	C₁₉×#97	C₂³	1	8	yes	—
115	C₄×C₈×C₁₉	C₂³	1	2	yes	—
116	C₄×C₈×C₁₉	C₂³	1	4	yes	—
117	C₄×C₈×C₁₉	C₂³	1	4	yes	—
118	C₄×C₈×C₁₉	C₂³	1	4	yes	—
119	C₄×C₈×C₁₉	C₂³	1	2	yes	—
120	C₄×C₈×C₁₉	C₂³	1	4	yes	—
121	C₄×C₈×C₁₉	C₂³	1	4	yes	—
122	#41×C₁₉	—	2	8	no	—
123	C₂×Q₈×C₁₉	—	2	4	no	—
124	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
125	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
126	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
127	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
128	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
129	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
138	M₁₆×C₁₉	—	4	8	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	2	8	no	—
141	C₂×C₈×C₁₉	—	4	1	no	—
142	C₂×C₈×C₁₉	—	4	4	no	—
143	C₂×C₈×C₁₉	—	4	2	no	—
144	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
145	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
146	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
147	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
148	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
149	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
150	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
151	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
152	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
153	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
154	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
155	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
156	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
157	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
158	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
159	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
160	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
161	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
162	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
163	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
164	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
165	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
166	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
167	C₄²×C₁₉	C₂²×C₄	1	2	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	C₂⁴	1	2	yes	—
172	C₄²×C₁₉	C₂⁴	1	4	yes	—
173	C₄²×C₁₉	C₂⁴	1	4	yes	—
174	#60330	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
176	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
177	Q₈×C₁₉	—	2	8	no	—
178	Q₈×C₁₉	—	2	4	no	—
179	Q₈×C₁₉	—	4	4	no	—
180	D₄×C₁₉	—	2	8	no	—
181	D₄×C₁₉	—	2	4	no	—
182	D₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	8	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	1	no	—
188	C₂×C₄×C₁₉	—	2	4	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	#131	1	4	yes	—
193	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
195	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
196	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
197	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
198	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
199	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
200	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
201	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
202	C₈×C₁₉	—	2	1	no	—
203	C₈×C₁₉	—	2	4	no	—
204	C₈×C₁₉	—	2	2	no	—
205	C₈×C₁₉	—	2	4	no	—
206	C₈×C₁₉	—	2	4	no	—
207	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
208	#3461	C₂×C₁₉	1	1	yes	characteristic
209	#2993	C₂×C₁₉	1	4	yes	complemented
210	#2992	C₂×C₁₉	1	4	yes	complemented
211	#2989	C₂×C₁₉	1	2	yes	complemented
212	#2985	C₂×C₁₉	1	4	yes	complemented
213	#2983	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#2966	C₂×C₁₉	1	4	yes	complemented
215	#2966	C₂×C₁₉	1	4	yes	complemented
216	C₈×#41	C₂×C₁₉	1	2	yes	complemented
217	#2960	C₂×C₁₉	1	4	yes	complemented
218	C₂×C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	2	4	no	—
222	C₂²×C₁₉	—	2	4	no	—
223	C₂²×C₁₉	—	2	4	no	—
224	C₂²×C₁₉	C₂×#131	1	2	yes	—
225	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
226	C₄×C₁₉	—	2	1	no	—
227	C₄×C₁₉	—	2	4	no	—
228	C₄×C₁₉	—	2	4	no	—
229	C₄×C₁₉	—	2	4	no	—
230	C₄×C₁₉	—	2	2	no	—
231	C₄×C₁₉	—	2	4	no	—
232	C₄×C₁₉	—	2	4	no	—
233	C₄×C₁₉	C₂×#131	1	4	yes	—
234	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
235	C₄×C₁₉	#585	1	1	yes	characteristic
236	#544	C₄×C₁₉	1	1	yes	characteristic
237	#542	C₄×C₁₉	1	4	yes	—
238	#541	C₄×C₁₉	1	4	yes	—
239	#539	C₄×C₁₉	1	4	yes	—
240	#537	C₄×C₁₉	1	1	yes	characteristic
241	#536	C₄×C₁₉	1	2	yes	—
242	#533	C₂²×C₁₉	1	4	yes	—
243	#529	C₂²×C₁₉	1	4	yes	—
244	#529	C₂²×C₁₉	1	4	yes	—
245	C₄×#41	C₂²×C₁₉	1	2	yes	—
246	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
247	#446	C₂²×C₁₉	1	4	yes	—
248	#446	C₂²×C₁₉	1	4	yes	—
249	#446	C₂²×C₁₉	1	8	yes	—
250	#446	C₂²×C₁₉	1	4	yes	—
251	#446	C₂²×C₁₉	1	4	yes	—
252	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
253	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
254	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
255	C₈×Q₈	C₂²×C₁₉	1	4	yes	—
256	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
257	#436	C₂²×C₁₉	1	4	yes	—
258	#436	C₂²×C₁₉	1	4	yes	—
259	#435	C₂²×C₁₉	1	8	yes	—
260	#435	C₂²×C₁₉	1	8	yes	—
261	C₈×D₄	C₂²×C₁₉	1	2	yes	—
262	C₈×D₄	C₂²×C₁₉	1	4	yes	—
263	C₈×D₄	C₂²×C₁₉	1	4	yes	—
264	C₈×D₄	C₂²×C₁₉	1	2	yes	—
265	C₈×D₄	C₂²×C₁₉	1	4	yes	—
266	#433	C₂²×C₁₉	1	8	yes	—
267	#433	C₂²×C₁₉	1	8	yes	—
268	#432	C₂²×C₁₉	1	4	yes	—
269	#432	C₂²×C₁₉	1	4	yes	—
270	#431	C₂²×C₁₉	1	2	yes	—
271	#431	C₂²×C₁₉	1	4	yes	—
272	#424	C₂²×C₁₉	1	8	yes	—
273	#423	C₂²×C₁₉	1	4	yes	—
274	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
276	#405	C₂²×C₁₉	1	8	yes	—
277	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	—
279	C₂×C₄×C₈	C₂²×C₁₉	1	4	yes	—
280	C₂×C₁₉	—	2	2	no	—
281	C₂×C₁₉	—	4	4	no	—
282	C₂×C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
283	C₂×C₁₉	C₂²×#131	1	1	yes	characteristic
284	C₂×C₁₉	#3573	1	1	yes	characteristic
285	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
286	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
287	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
288	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
290	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
292	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
293	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
294	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
295	#126	C₂×C₄×C₁₉	1	8	yes	—
296	#126	C₂×C₄×C₁₉	1	8	yes	—
297	#125	C₂×C₄×C₁₉	1	4	yes	—
298	#125	C₂×C₄×C₁₉	1	4	yes	—
299	#125	C₂×C₄×C₁₉	1	8	yes	—
300	#124	C₂×C₄×C₁₉	1	4	yes	—
301	#124	C₂×C₄×C₁₉	1	4	yes	—
302	#123	C₂×C₄×C₁₉	1	8	yes	—
303	#123	C₂×C₄×C₁₉	1	8	yes	—
304	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
305	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
306	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
307	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
308	C₂²⋊Q₈	C₂×C₄×C₁₉	1	8	yes	—
309	#121	C₂×C₄×C₁₉	1	4	yes	—
310	#121	C₂×C₄×C₁₉	1	4	yes	—
311	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
312	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
313	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
314	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
315	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
316	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
317	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
318	C₄×D₄	C₂³×C₁₉	1	4	yes	—
319	C₄×D₄	C₂³×C₁₉	1	2	yes	—
320	C₄×D₄	C₂³×C₁₉	1	4	yes	—
321	#117	C₂×C₄×C₁₉	1	2	yes	—
322	#117	C₂×C₄×C₁₉	1	4	yes	—
323	#117	C₂³×C₁₉	1	8	yes	—
324	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
326	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
328	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
329	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
330	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
331	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
332	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
333	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
334	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
335	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
336	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
337	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
338	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
339	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
340	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
341	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
342	#97	C₂³×C₁₉	1	8	yes	—
343	#97	C₂³×C₁₉	1	8	yes	—
344	C₄×C₈	C₂³×C₁₉	1	2	yes	—
345	C₄×C₈	C₂³×C₁₉	1	4	yes	—
346	C₄×C₈	C₂³×C₁₉	1	4	yes	—
347	C₄×C₈	C₂³×C₁₉	1	2	yes	—
348	C₄×C₈	C₂³×C₁₉	1	4	yes	—
349	C₄×C₈	C₂³×C₁₉	1	4	yes	—
350	C₄×C₈	C₂³×C₁₉	1	4	yes	—
351	C₁₉	#60330	1	1	yes	characteristic, direct product factor, Sylow
352	#41	—	2	8	no	—
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
355	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
356	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
357	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
358	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
359	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
360	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
361	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
362	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
364	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
365	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
368	M₁₆	—	4	8	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	8	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	4	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
375	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
376	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
377	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
378	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
379	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
380	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
381	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
382	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
383	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
384	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
385	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
386	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
387	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
388	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
389	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
390	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
391	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
392	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
393	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
394	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
395	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
396	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
397	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
398	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
399	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
400	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
401	C₄²	C₂⁴×C₁₉	1	2	yes	—
402	C₄²	C₂⁴×C₁₉	1	4	yes	—
403	C₄²	C₂⁴×C₁₉	1	4	yes	—
404	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
405	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
406	Q₈	—	2	8	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	4	no	—
409	D₄	—	2	8	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	C₁₉×#131	1	4	yes	—
422	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
423	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
424	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
425	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
426	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
427	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
428	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
429	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
430	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	4	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	4	no	—
435	C₈	—	2	4	no	—
436	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	C₂×C₁₉×#131	1	2	yes	—
443	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	4	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	4	no	—
450	C₄	—	2	4	no	—
451	C₄	C₂×C₁₉×#131	1	4	yes	—
452	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
453	C₄	C₁₉×#585	1	1	yes	characteristic
454	C₂	—	2	2	no	—
455	C₂	—	4	4	no	—
456	C₂	C₄×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
457	C₂	C₂²×C₁₉×#131	1	1	yes	characteristic
458	C₂	C₁₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#537	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2993	C₂	semidirect
3. C₁₉×#2992	C₂	semidirect
4. C₁₉×#2989	C₂	semidirect
5. C₁₉×#2985	C₂	semidirect
6. C₁₉×#2983	C₂	semidirect
7. C₁₉×#2966	C₂	semidirect
8. C₁₉×#2966	C₂	semidirect
9. C₈×#41×C₁₉	C₂	semidirect
10. C₁₉×#2960	C₂	semidirect
11. C₂×C₈×Q₈×C₁₉	C₂	semidirect
174. #60330	C₁₉	direct (N × H)
209. #2993	C₂×C₁₉	semidirect
210. #2992	C₂×C₁₉	semidirect
211. #2989	C₂×C₁₉	semidirect
212. #2985	C₂×C₁₉	semidirect
213. #2983	C₂×C₁₉	semidirect
214. #2966	C₂×C₁₉	semidirect
215. #2966	C₂×C₁₉	semidirect
216. C₈×#41	C₂×C₁₉	semidirect
217. #2960	C₂×C₁₉	semidirect
218. C₂×C₈×Q₈	C₂×C₁₉	semidirect
351. C₁₉	#60330	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3461	2
C₁₉×#2993	2
C₁₉×#2992	2
C₁₉×#2989	2
C₁₉×#2985	2
C₁₉×#2983	2
C₁₉×#2966	2
C₈×#41×C₁₉	2
C₁₉×#2960	2
C₂×C₈×Q₈×C₁₉	2
#60330	19

Subgroups — C19×#60330 #18066289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60330 #18066289