Subgroups — C₁₉×#60345 #18066304

Order 4864.

1744 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3482	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2993	C₂	1	6	yes	maximal, complemented
3	C₁₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2991	C₂	1	3	yes	maximal, complemented
5	C₁₉×#2986	C₂	1	3	yes	maximal, complemented
6	C₁₉×#2982	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2969	C₂	1	6	yes	maximal, complemented
8	C₁₉×#2965	C₂	1	3	yes	maximal, complemented
9	C₈×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₈×M₁₆×C₁₉	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2960	C₂	1	3	yes	maximal, complemented
12	C₁₉×#557	C₄	1	1	yes	characteristic
13	C₁₉×#556	C₄	1	3	yes	—
14	C₁₉×#552	C₄	1	6	yes	—
15	D₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
16	C₁₉×#548	C₄	1	2	yes	—
17	C₁₉×#547	C₄	1	3	yes	—
18	C₁₉×#533	C₂²	1	3	yes	—
19	C₁₉×#529	C₂²	1	6	yes	—
20	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
21	C₄×#41×C₁₉	C₂²	1	3	yes	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#446	C₂²	1	3	yes	—
24	C₁₉×#446	C₂²	1	6	yes	—
25	C₁₉×#446	C₂²	1	6	yes	—
26	C₁₉×#446	C₂²	1	3	yes	—
27	C₈×Q₈×C₁₉	C₂²	1	6	yes	—
28	C₈×Q₈×C₁₉	C₂²	1	6	yes	—
29	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₁₉	C₂²	1	2	yes	—
31	C₈×Q₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₈×Q₈×C₁₉	C₂²	1	6	yes	—
33	C₁₉×#436	C₂²	1	1	yes	characteristic
34	C₁₉×#436	C₂²	1	3	yes	—
35	C₁₉×#436	C₂²	1	6	yes	—
36	C₁₉×#436	C₂²	1	12	yes	—
37	C₁₉×#435	C₂²	1	6	yes	—
38	C₁₉×#435	C₂²	1	6	yes	—
39	C₈×D₄×C₁₉	C₂²	1	3	yes	—
40	C₈×D₄×C₁₉	C₂²	1	3	yes	—
41	C₁₉×#433	C₂²	1	12	yes	—
42	C₁₉×#431	C₂²	1	3	yes	—
43	C₁₉×#431	C₂²	1	6	yes	—
44	C₁₉×#431	C₂²	1	3	yes	—
45	C₁₉×#431	C₂²	1	6	yes	—
46	C₁₉×#424	C₂²	1	6	yes	—
47	C₁₉×#423	C₂²	1	3	yes	—
48	C₁₉×#423	C₂²	1	6	yes	—
49	C₁₉×#405	C₂²	1	6	yes	—
50	C₄×M₁₆×C₁₉	C₂²	1	6	yes	—
51	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
52	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₂×#41×C₁₉	C₂×C₄	1	3	yes	—
54	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
56	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
57	C₂×M₁₆×C₁₉	C₂³	1	6	yes	—
58	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
59	C₂²×C₈×C₁₉	C₂³	1	3	yes	—
60	C₁₉×C₄⋊Q₈	C₂×C₄	1	3	yes	—
61	C₁₉×C₄⋊Q₈	C₂×C₄	1	3	yes	—
62	C₁₉×#126	C₂×C₄	1	12	yes	—
63	C₁₉×#125	C₂×C₄	1	6	yes	—
64	C₁₉×#125	C₂×C₄	1	6	yes	—
65	C₁₉×#124	C₂×C₄	1	6	yes	—
66	C₁₉×#123	C₂×C₄	1	12	yes	—
67	C₁₉×C₂²⋊Q₈	C₂×C₄	1	6	yes	—
68	C₁₉×C₂²⋊Q₈	C₂×C₄	1	6	yes	—
69	C₁₉×C₂²⋊Q₈	C₂×C₄	1	6	yes	—
70	C₁₉×#121	C₂×C₄	1	6	yes	—
71	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
72	C₄×Q₈×C₁₉	C₂×C₄	1	6	yes	—
73	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₄×Q₈×C₁₉	C₂×C₄	1	3	yes	—
75	C₄×Q₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₄×Q₈×C₁₉	C₂³	1	6	yes	—
77	C₄×Q₈×C₁₉	C₂³	1	3	yes	—
78	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
79	C₄×D₄×C₁₉	C₂×C₄	1	3	yes	—
80	C₄×D₄×C₁₉	C₂×C₄	1	6	yes	—
81	C₄×D₄×C₁₉	C₂³	1	3	yes	—
82	C₄×D₄×C₁₉	C₂³	1	6	yes	—
83	C₄×D₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₁₉×#117	C₂×C₄	1	3	yes	—
85	C₁₉×#117	C₂×C₄	1	6	yes	—
86	C₁₉×#117	C₂×C₄	1	3	yes	—
87	C₁₉×#117	C₂³	1	6	yes	—
88	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	6	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	3	yes	—
90	C₂×C₄²×C₁₉	C₂³	1	6	yes	—
91	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
92	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
93	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
94	C₁₉×C₄⋊C₈	C₂³	1	12	yes	—
95	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
96	C₁₉×C₄⋊C₈	C₂³	1	3	yes	—
97	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₁₉×C₄⋊C₈	C₂³	1	6	yes	—
99	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
100	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
101	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
102	C₁₉×C₂²⋊C₈	C₂³	1	6	yes	—
103	C₁₉×#97	C₂³	1	6	yes	—
104	C₁₉×#97	C₂³	1	6	yes	—
105	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
106	C₄×C₈×C₁₉	C₂³	1	3	yes	—
107	C₄×C₈×C₁₉	C₂³	1	3	yes	—
108	C₄×C₈×C₁₉	C₂³	1	3	yes	—
109	C₄×C₈×C₁₉	C₂³	1	6	yes	—
110	C₄×C₈×C₁₉	C₂³	1	12	yes	—
111	#41×C₁₉	—	2	4	no	—
112	#41×C₁₉	—	4	6	no	—
113	C₂×Q₈×C₁₉	—	2	8	no	—
114	C₂×Q₈×C₁₉	C₂²×C₄	1	6	yes	—
115	C₂×Q₈×C₁₉	C₂²×C₄	1	3	yes	—
116	C₂×Q₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₄×C₁₉	C₂²×C₄	1	3	yes	—
119	C₂×D₄×C₁₉	C₂²×C₄	1	6	yes	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
123	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
124	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
126	M₁₆×C₁₉	—	2	4	no	—
127	M₁₆×C₁₉	—	4	6	no	—
128	M₁₆×C₁₉	—	4	6	no	—
129	C₂×C₈×C₁₉	—	2	6	no	—
130	C₂×C₈×C₁₉	—	4	3	no	—
131	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
132	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
133	C₂×C₈×C₁₉	C₂⁴	1	3	yes	—
134	C₂×C₈×C₁₉	C₂⁴	1	6	yes	—
135	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
136	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
137	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
138	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
139	C₄⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
140	C₄⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
142	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
143	C₄⋊C₄×C₁₉	C₂²×C₄	1	3	yes	—
144	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
145	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
146	C₄⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
147	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
148	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
149	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
150	C₂²⋊C₄×C₁₉	C₂²×C₄	1	6	yes	—
151	C₂²⋊C₄×C₁₉	C₂²×C₄	1	12	yes	—
152	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
153	C₄²×C₁₉	C₂²×C₄	1	6	yes	—
154	C₄²×C₁₉	C₂²×C₄	1	3	yes	—
155	C₄²×C₁₉	C₂²×C₄	1	6	yes	—
156	C₄²×C₁₉	C₂⁴	1	3	yes	—
157	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
158	C₄²×C₁₉	C₂⁴	1	6	yes	—
159	#60345	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₁₉	C₂³×C₄	1	3	yes	—
161	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
162	Q₈×C₁₉	—	2	12	no	—
163	Q₈×C₁₉	—	2	6	no	—
164	Q₈×C₁₉	#131	1	4	yes	—
165	D₄×C₁₉	—	2	6	no	—
166	D₄×C₁₉	—	2	2	no	—
167	D₄×C₁₉	—	4	6	no	—
168	C₂×C₄×C₁₉	—	2	12	no	—
169	C₂×C₄×C₁₉	—	2	6	no	—
170	C₂×C₄×C₁₉	—	2	6	no	—
171	C₂×C₄×C₁₉	—	2	3	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	3	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	4	6	no	—
176	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
177	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
179	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
180	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
181	C₂×C₄×C₁₉	C₂³×C₄	1	6	yes	—
182	C₂×C₄×C₁₉	C₂³×C₄	1	3	yes	—
183	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
185	C₈×C₁₉	—	2	3	no	—
186	C₈×C₁₉	—	2	2	no	—
187	C₈×C₁₉	—	2	1	no	—
188	C₈×C₁₉	—	2	3	no	—
189	C₈×C₁₉	—	2	6	no	—
190	C₈×C₁₉	2₋¹⁺⁴	1	2	yes	—
191	#3482	C₂×C₁₉	1	1	yes	characteristic
192	#2993	C₂×C₁₉	1	6	yes	complemented
193	#2991	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#2991	C₂×C₁₉	1	3	yes	complemented
195	#2986	C₂×C₁₉	1	3	yes	complemented
196	#2982	C₂×C₁₉	1	2	yes	complemented
197	#2969	C₂×C₁₉	1	6	yes	complemented
198	#2965	C₂×C₁₉	1	3	yes	complemented
199	C₈×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
200	Q₈×M₁₆	C₂×C₁₉	1	2	yes	complemented
201	#2960	C₂×C₁₉	1	3	yes	complemented
202	C₂²×C₁₉	—	2	3	no	—
203	C₂²×C₁₉	—	2	2	no	—
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	2	3	no	—
206	C₂²×C₁₉	—	2	3	no	—
207	C₂²×C₁₉	—	2	2	no	—
208	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
209	C₄×C₁₉	—	2	3	no	—
210	C₄×C₁₉	—	2	2	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	6	no	—
213	C₄×C₁₉	—	2	3	no	—
214	C₄×C₁₉	—	2	6	no	—
215	C₄×C₁₉	C₂×#131	1	6	yes	—
216	C₄×C₁₉	#568	1	2	yes	—
217	C₄×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
218	C₄×C₁₉	#585	1	1	yes	characteristic
219	#557	C₄×C₁₉	1	1	yes	characteristic
220	#556	C₄×C₁₉	1	3	yes	—
221	#552	C₄×C₁₉	1	6	yes	—
222	D₄×Q₈	C₄×C₁₉	1	1	yes	characteristic
223	#548	C₄×C₁₉	1	2	yes	—
224	#547	C₄×C₁₉	1	3	yes	—
225	#533	C₂²×C₁₉	1	3	yes	—
226	#529	C₂²×C₁₉	1	6	yes	—
227	C₄×#41	C₂²×C₁₉	1	1	yes	characteristic
228	C₄×#41	C₂²×C₁₉	1	3	yes	—
229	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
230	#446	C₂²×C₁₉	1	3	yes	—
231	#446	C₂²×C₁₉	1	6	yes	—
232	#446	C₂²×C₁₉	1	6	yes	—
233	#446	C₂²×C₁₉	1	3	yes	—
234	C₈×Q₈	C₂²×C₁₉	1	6	yes	—
235	C₈×Q₈	C₂²×C₁₉	1	6	yes	—
236	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
237	C₈×Q₈	C₂²×C₁₉	1	2	yes	—
238	C₈×Q₈	C₂²×C₁₉	1	1	yes	characteristic
239	C₈×Q₈	C₂²×C₁₉	1	6	yes	—
240	#436	C₂²×C₁₉	1	1	yes	characteristic
241	#436	C₂²×C₁₉	1	3	yes	—
242	#436	C₂²×C₁₉	1	6	yes	—
243	#436	C₂²×C₁₉	1	12	yes	—
244	#435	C₂²×C₁₉	1	6	yes	—
245	#435	C₂²×C₁₉	1	6	yes	—
246	C₈×D₄	C₂²×C₁₉	1	3	yes	—
247	C₈×D₄	C₂²×C₁₉	1	3	yes	—
248	#433	C₂²×C₁₉	1	12	yes	—
249	#431	C₂²×C₁₉	1	3	yes	—
250	#431	C₂²×C₁₉	1	6	yes	—
251	#431	C₂²×C₁₉	1	3	yes	—
252	#431	C₂²×C₁₉	1	6	yes	—
253	#424	C₂²×C₁₉	1	6	yes	—
254	#423	C₂²×C₁₉	1	3	yes	—
255	#423	C₂²×C₁₉	1	6	yes	—
256	#405	C₂²×C₁₉	1	6	yes	—
257	C₄×M₁₆	C₂²×C₁₉	1	6	yes	—
258	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	—
259	C₂×C₁₉	—	4	2	no	—
260	C₂×C₁₉	—	4	3	no	—
261	C₂×C₁₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
262	C₂×C₁₉	C₂²×#131	1	1	yes	characteristic
263	C₂×C₁₉	C₂×#568	1	1	yes	characteristic
264	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
265	C₂×#41	C₂×C₄×C₁₉	1	3	yes	—
266	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
267	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
268	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
269	C₂×M₁₆	C₂³×C₁₉	1	6	yes	—
270	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
271	C₂²×C₈	C₂³×C₁₉	1	3	yes	—
272	C₄⋊Q₈	C₂×C₄×C₁₉	1	3	yes	—
273	C₄⋊Q₈	C₂×C₄×C₁₉	1	3	yes	—
274	#126	C₂×C₄×C₁₉	1	12	yes	—
275	#125	C₂×C₄×C₁₉	1	6	yes	—
276	#125	C₂×C₄×C₁₉	1	6	yes	—
277	#124	C₂×C₄×C₁₉	1	6	yes	—
278	#123	C₂×C₄×C₁₉	1	12	yes	—
279	C₂²⋊Q₈	C₂×C₄×C₁₉	1	6	yes	—
280	C₂²⋊Q₈	C₂×C₄×C₁₉	1	6	yes	—
281	C₂²⋊Q₈	C₂×C₄×C₁₉	1	6	yes	—
282	#121	C₂×C₄×C₁₉	1	6	yes	—
283	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
284	C₄×Q₈	C₂×C₄×C₁₉	1	6	yes	—
285	C₄×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
286	C₄×Q₈	C₂×C₄×C₁₉	1	3	yes	—
287	C₄×Q₈	C₂³×C₁₉	1	1	yes	characteristic
288	C₄×Q₈	C₂³×C₁₉	1	6	yes	—
289	C₄×Q₈	C₂³×C₁₉	1	3	yes	—
290	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
291	C₄×D₄	C₂×C₄×C₁₉	1	3	yes	—
292	C₄×D₄	C₂×C₄×C₁₉	1	6	yes	—
293	C₄×D₄	C₂³×C₁₉	1	1	yes	characteristic
294	C₄×D₄	C₂³×C₁₉	1	3	yes	—
295	C₄×D₄	C₂³×C₁₉	1	6	yes	—
296	#117	C₂×C₄×C₁₉	1	3	yes	—
297	#117	C₂×C₄×C₁₉	1	6	yes	—
298	#117	C₂×C₄×C₁₉	1	3	yes	—
299	#117	C₂³×C₁₉	1	6	yes	—
300	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	6	yes	—
301	C₂×C₄²	C₂³×C₁₉	1	6	yes	—
302	C₂×C₄²	C₂³×C₁₉	1	3	yes	—
303	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
304	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
305	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
306	C₄⋊C₈	C₂³×C₁₉	1	12	yes	—
307	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
308	C₄⋊C₈	C₂³×C₁₉	1	3	yes	—
309	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
310	C₄⋊C₈	C₂³×C₁₉	1	6	yes	—
311	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
312	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
313	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
314	C₂²⋊C₈	C₂³×C₁₉	1	6	yes	—
315	#97	C₂³×C₁₉	1	6	yes	—
316	#97	C₂³×C₁₉	1	6	yes	—
317	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
318	C₄×C₈	C₂³×C₁₉	1	3	yes	—
319	C₄×C₈	C₂³×C₁₉	1	3	yes	—
320	C₄×C₈	C₂³×C₁₉	1	3	yes	—
321	C₄×C₈	C₂³×C₁₉	1	6	yes	—
322	C₄×C₈	C₂³×C₁₉	1	12	yes	—
323	C₁₉	#60345	1	1	yes	characteristic, direct product factor, Sylow
324	#41	—	2	4	no	—
325	#41	—	4	6	no	—
326	C₂×Q₈	—	2	8	no	—
327	C₂×Q₈	C₂²×C₄×C₁₉	1	6	yes	—
328	C₂×Q₈	C₂²×C₄×C₁₉	1	3	yes	—
329	C₂×Q₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
330	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
331	C₂×D₄	C₂²×C₄×C₁₉	1	3	yes	—
332	C₂×D₄	C₂²×C₄×C₁₉	1	6	yes	—
333	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
334	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
335	C₂²×C₄	C₂²×C₄×C₁₉	1	3	yes	—
336	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
337	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	4	6	no	—
341	M₁₆	—	4	6	no	—
342	C₂×C₈	—	2	6	no	—
343	C₂×C₈	—	4	3	no	—
344	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
345	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
346	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
347	C₂×C₈	C₂⁴×C₁₉	1	6	yes	—
348	C₂×C₈	C₂⁴×C₁₉	1	3	yes	—
349	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
350	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
351	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
352	C₄⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
353	C₄⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
354	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
355	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
356	C₄⋊C₄	C₂²×C₄×C₁₉	1	3	yes	—
357	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
358	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
359	C₄⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
360	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
361	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
362	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
363	C₂²⋊C₄	C₂²×C₄×C₁₉	1	6	yes	—
364	C₂²⋊C₄	C₂²×C₄×C₁₉	1	12	yes	—
365	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
366	C₄²	C₂²×C₄×C₁₉	1	6	yes	—
367	C₄²	C₂²×C₄×C₁₉	1	3	yes	—
368	C₄²	C₂²×C₄×C₁₉	1	6	yes	—
369	C₄²	C₂⁴×C₁₉	1	3	yes	—
370	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
371	C₄²	C₂⁴×C₁₉	1	6	yes	—
372	C₂³	C₂³×C₄×C₁₉	1	3	yes	—
373	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
374	Q₈	—	2	12	no	—
375	Q₈	—	2	6	no	—
376	Q₈	C₁₉×#131	1	4	yes	—
377	D₄	—	2	6	no	—
378	D₄	—	2	2	no	—
379	D₄	—	4	6	no	—
380	C₂×C₄	—	2	12	no	—
381	C₂×C₄	—	2	6	no	—
382	C₂×C₄	—	2	6	no	—
383	C₂×C₄	—	2	3	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	3	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	6	no	—
388	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
389	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
390	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
391	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
392	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
393	C₂×C₄	C₂³×C₄×C₁₉	1	6	yes	—
394	C₂×C₄	C₂³×C₄×C₁₉	1	3	yes	—
395	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
396	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
397	C₈	—	2	3	no	—
398	C₈	—	2	2	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	3	no	—
401	C₈	—	2	6	no	—
402	C₈	C₁₉×2₋¹⁺⁴	1	2	yes	—
403	C₂²	—	2	3	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	3	no	—
407	C₂²	—	2	3	no	—
408	C₂²	—	2	2	no	—
409	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
410	C₄	—	2	3	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	6	no	—
414	C₄	—	2	3	no	—
415	C₄	—	2	6	no	—
416	C₄	C₂×C₁₉×#131	1	6	yes	—
417	C₄	C₁₉×#568	1	2	yes	—
418	C₄	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
419	C₄	C₁₉×#585	1	1	yes	characteristic
420	C₂	—	4	2	no	—
421	C₂	—	4	3	no	—
422	C₂	C₄×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
423	C₂	C₂²×C₁₉×#131	1	1	yes	characteristic
424	C₂	C₂×C₁₉×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#3482	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×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×#2991	C₂	semidirect
4. C₁₉×#2991	C₂	semidirect
5. C₁₉×#2986	C₂	semidirect
6. C₁₉×#2982	C₂	semidirect
7. C₁₉×#2969	C₂	semidirect
8. C₁₉×#2965	C₂	semidirect
9. C₈×#41×C₁₉	C₂	semidirect
10. Q₈×M₁₆×C₁₉	C₂	semidirect
11. C₁₉×#2960	C₂	semidirect
159. #60345	C₁₉	direct (N × H)
192. #2993	C₂×C₁₉	semidirect
193. #2991	C₂×C₁₉	semidirect
194. #2991	C₂×C₁₉	semidirect
195. #2986	C₂×C₁₉	semidirect
196. #2982	C₂×C₁₉	semidirect
197. #2969	C₂×C₁₉	semidirect
198. #2965	C₂×C₁₉	semidirect
199. C₈×#41	C₂×C₁₉	semidirect
200. Q₈×M₁₆	C₂×C₁₉	semidirect
201. #2960	C₂×C₁₉	semidirect
323. C₁₉	#60345	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×#3482	2
C₁₉×#2993	2
C₁₉×#2991	2
C₁₉×#2986	2
C₁₉×#2982	2
C₁₉×#2969	2
C₁₉×#2965	2
C₈×#41×C₁₉	2
Q₈×M₁₆×C₁₉	2
C₁₉×#2960	2
#60345	19

Subgroups — C19×#60345 #18066304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60345 #18066304