Subgroups — C₁₉×#32690 #18038649

Order 4864.

646 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2584	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2546	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2088	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2087	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2059	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2059	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2058	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#2057	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1944	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1943	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1921	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1918	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
28	C₁₉×#398	—	2	1	no	—
29	C₁₉×#398	—	2	1	no	—
30	C₁₉×#398	—	2	1	no	—
31	C₁₉×#395	—	2	1	no	—
32	C₁₉×#391	—	2	1	no	—
33	C₁₉×#389	—	2	1	no	—
34	C₁₉×#389	—	2	1	no	—
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#389	C₂²	1	1	yes	characteristic
37	C₁₉×#389	C₂²	1	1	yes	characteristic
38	C₁₉×#389	C₂²	1	1	yes	characteristic
39	C₁₉×#389	C₂²	1	1	yes	characteristic
40	C₁₉×#389	C₂²	1	1	yes	characteristic
41	C₁₉×#389	C₂²	1	1	yes	characteristic
42	C₁₉×#389	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₁₉×#340	C₂²	1	1	yes	characteristic
46	C₁₉×#340	C₂²	1	1	yes	characteristic
47	C₁₉×#340	C₂²	1	1	yes	characteristic
48	C₁₉×#340	C₂²	1	1	yes	characteristic
49	C₁₉×#340	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#336	C₂²	1	1	yes	characteristic
56	C₁₉×#336	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	—	2	1	no	—
60	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₁₉×C₄⋊Q₈	—	4	1	no	—
66	C₁₉×C₄⋊Q₈	—	4	1	no	—
67	C₁₉×C₄⋊Q₈	—	4	4	no	—
68	C₁₉×#125	—	4	1	no	—
69	C₁₉×#125	—	4	1	no	—
70	C₄×Q₈×C₁₉	—	4	1	no	—
71	C₄×Q₈×C₁₉	—	4	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	—	2	1	no	—
95	C₂×C₄²×C₁₉	—	2	1	no	—
96	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₁₉×#107	—	4	1	no	—
100	C₁₉×#107	—	4	1	no	—
101	C₁₉×#107	Q₈	1	4	yes	complemented
102	C₁₉×#106	—	4	1	no	—
103	C₁₉×#106	—	4	1	no	—
104	C₁₉×#106	Q₈	1	4	yes	complemented
105	C₁₉×C₄⋊C₈	—	4	1	no	—
106	C₁₉×#97	—	4	1	no	—
107	C₁₉×#95	—	2	1	no	—
108	C₁₉×#95	—	2	1	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	2	no	—
118	C₂×Q₈×C₁₉	—	4	1	no	—
119	C₂×Q₈×C₁₉	—	4	1	no	—
120	C₂×Q₈×C₁₉	—	4	2	no	—
121	C₂×Q₈×C₁₉	—	4	2	no	—
122	C₂×Q₈×C₁₉	—	4	2	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	1	no	—
128	C₂²×C₄×C₁₉	—	2	1	no	—
129	C₂²×C₄×C₁₉	—	2	1	no	—
130	C₂²×C₄×C₁₉	—	2	1	no	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₁₉	—	2	1	no	—
139	C₂×C₈×C₁₉	—	2	1	no	—
140	C₂×C₈×C₁₉	—	2	1	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	2	1	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	1	no	—
148	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
149	C₂×C₈×C₁₉	C₂×Q₈	1	2	yes	—
150	C₄⋊C₄×C₁₉	—	2	1	no	—
151	C₄⋊C₄×C₁₉	—	2	1	no	—
152	C₄⋊C₄×C₁₉	—	2	1	no	—
153	C₄⋊C₄×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	1	no	—
155	C₄⋊C₄×C₁₉	—	2	1	no	—
156	C₄⋊C₄×C₁₉	—	2	1	no	—
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	4	1	no	—
163	C₄⋊C₄×C₁₉	—	4	1	no	—
164	C₄⋊C₄×C₁₉	—	4	1	no	—
165	C₄⋊C₄×C₁₉	—	4	2	no	—
166	C₄⋊C₄×C₁₉	—	4	2	no	—
167	C₄⋊C₄×C₁₉	—	4	2	no	—
168	C₄⋊C₄×C₁₉	—	4	2	no	—
169	C₄⋊C₄×C₁₉	—	4	2	no	—
170	C₄⋊C₄×C₁₉	—	4	2	no	—
171	C₄⋊C₄×C₁₉	—	4	2	no	—
172	C₄⋊C₄×C₁₉	—	4	2	no	—
173	C₄⋊C₄×C₁₉	—	4	2	no	—
174	C₄⋊C₄×C₁₉	—	8	1	no	—
175	C₄⋊C₄×C₁₉	—	8	1	no	—
176	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
177	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
178	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
179	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
180	C₄²×C₁₉	—	2	1	no	—
181	C₄²×C₁₉	—	2	1	no	—
182	C₄²×C₁₉	—	2	1	no	—
183	C₄²×C₁₉	—	2	1	no	—
184	C₄²×C₁₉	—	2	1	no	—
185	C₄²×C₁₉	—	2	1	no	—
186	C₄²×C₁₉	—	4	2	no	—
187	C₄²×C₁₉	—	8	1	no	—
188	#32690	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₁₉	—	4	4	no	—
191	Q₈×C₁₉	—	8	4	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	1	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	4	1	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
234	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
236	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
240	C₈×C₁₉	—	2	2	no	—
241	C₈×C₁₉	—	2	2	no	—
242	C₈×C₁₉	—	4	1	no	—
243	C₈×C₁₉	—	4	1	no	—
244	#2584	C₂×C₁₉	1	1	yes	characteristic
245	#2546	C₂×C₁₉	1	1	yes	characteristic
246	#2088	C₂×C₁₉	1	1	yes	characteristic
247	#2087	C₂×C₁₉	1	1	yes	characteristic
248	#2059	C₂×C₁₉	1	1	yes	characteristic
249	#2059	C₂×C₁₉	1	1	yes	characteristic
250	#2058	C₂×C₁₉	1	1	yes	characteristic
251	#2057	C₂×C₁₉	1	1	yes	characteristic
252	#1985	C₂×C₁₉	1	1	yes	characteristic
253	#1944	C₂×C₁₉	1	1	yes	characteristic
254	#1943	C₂×C₁₉	1	1	yes	characteristic
255	#1921	C₂×C₁₉	1	1	yes	characteristic
256	#1920	C₂×C₁₉	1	1	yes	characteristic
257	#1920	C₂×C₁₉	1	1	yes	characteristic
258	#1918	C₂×C₁₉	1	1	yes	characteristic
259	C₂²×C₁₉	#534	1	1	yes	characteristic
260	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
261	C₂²×C₁₉	D₄×Q₈	1	1	yes	characteristic
262	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₂²×C₁₉	#575	1	1	yes	characteristic
264	C₂²×C₁₉	#577	1	1	yes	characteristic
265	C₂²×C₁₉	#578	1	1	yes	characteristic
266	C₄×C₁₉	—	2	2	no	—
267	C₄×C₁₉	—	4	2	no	—
268	C₄×C₁₉	—	4	2	no	—
269	C₄×C₁₉	—	4	2	no	—
270	C₄×C₁₉	—	4	2	no	—
271	C₄×C₁₉	—	4	1	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	4	1	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	—	8	1	no	—
278	C₄×C₁₉	—	8	1	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	#544	1	1	yes	characteristic
281	C₄×C₁₉	#544	1	1	yes	characteristic
282	C₄×C₁₉	Q₈²	1	1	yes	characteristic
283	C₄×C₁₉	#563	1	1	yes	characteristic
284	C₂×C₄⋊Q₈	—	2	1	no	—
285	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
286	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
296	#398	—	2	1	no	—
297	#398	—	2	1	no	—
298	#398	—	2	1	no	—
299	#395	—	2	1	no	—
300	#391	—	2	1	no	—
301	#389	—	2	1	no	—
302	#389	—	2	1	no	—
303	#389	C₂²×C₁₉	1	1	yes	characteristic
304	#389	C₂²×C₁₉	1	1	yes	characteristic
305	#389	C₂²×C₁₉	1	1	yes	characteristic
306	#389	C₂²×C₁₉	1	1	yes	characteristic
307	#389	C₂²×C₁₉	1	1	yes	characteristic
308	#389	C₂²×C₁₉	1	1	yes	characteristic
309	#389	C₂²×C₁₉	1	1	yes	characteristic
310	#389	C₂²×C₁₉	1	1	yes	characteristic
311	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
312	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
313	#340	C₂²×C₁₉	1	1	yes	characteristic
314	#340	C₂²×C₁₉	1	1	yes	characteristic
315	#340	C₂²×C₁₉	1	1	yes	characteristic
316	#340	C₂²×C₁₉	1	1	yes	characteristic
317	#340	C₂²×C₁₉	1	1	yes	characteristic
318	#340	C₂²×C₁₉	1	1	yes	characteristic
319	#340	C₂²×C₁₉	1	1	yes	characteristic
320	#340	C₂²×C₁₉	1	1	yes	characteristic
321	#340	C₂²×C₁₉	1	1	yes	characteristic
322	#340	C₂²×C₁₉	1	1	yes	characteristic
323	#336	C₂²×C₁₉	1	1	yes	characteristic
324	#336	C₂²×C₁₉	1	1	yes	characteristic
325	#336	C₂²×C₁₉	1	1	yes	characteristic
326	#336	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×C₁₉	#2734	1	1	yes	characteristic
328	C₂×C₁₉	#3194	1	1	yes	characteristic
329	C₂×C₁₉	#3201	1	1	yes	characteristic
330	C₂×C₁₉	#3384	1	1	yes	characteristic
331	C₂×C₁₉	#3386	1	1	yes	characteristic
332	C₂×C₁₉	#3388	1	1	yes	characteristic
333	C₂×C₁₉	#3390	1	1	yes	characteristic
334	C₂²×Q₈	—	2	1	no	—
335	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₄⋊Q₈	—	4	1	no	—
341	C₄⋊Q₈	—	4	1	no	—
342	C₄⋊Q₈	—	4	4	no	—
343	#125	—	4	1	no	—
344	#125	—	4	1	no	—
345	C₄×Q₈	—	4	1	no	—
346	C₄×Q₈	—	4	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
360	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
374	#107	—	4	1	no	—
375	#107	—	4	1	no	—
376	#107	Q₈×C₁₉	1	4	yes	complemented
377	#106	—	4	1	no	—
378	#106	—	4	1	no	—
379	#106	Q₈×C₁₉	1	4	yes	complemented
380	C₄⋊C₈	—	4	1	no	—
381	#97	—	4	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	C₁₉	#32690	1	1	yes	characteristic, direct product factor, Sylow
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×Q₈	—	4	1	no	—
396	C₂×Q₈	—	4	2	no	—
397	C₂×Q₈	—	4	2	no	—
398	C₂×Q₈	—	4	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
425	C₂×C₈	C₂×Q₈×C₁₉	1	2	yes	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	4	1	no	—
439	C₄⋊C₄	—	4	1	no	—
440	C₄⋊C₄	—	4	1	no	—
441	C₄⋊C₄	—	4	2	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	4	2	no	—
446	C₄⋊C₄	—	4	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	—	4	2	no	—
450	C₄⋊C₄	—	8	1	no	—
451	C₄⋊C₄	—	8	1	no	—
452	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
453	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
454	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
455	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	4	2	no	—
463	C₄²	—	8	1	no	—
464	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
465	Q₈	—	4	4	no	—
466	Q₈	—	8	4	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
509	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
510	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
511	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
512	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
513	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
514	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	2	2	no	—
517	C₈	—	4	1	no	—
518	C₈	—	4	1	no	—
519	C₂²	C₁₉×#534	1	1	yes	characteristic
520	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
521	C₂²	D₄×Q₈×C₁₉	1	1	yes	characteristic
522	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
523	C₂²	C₁₉×#575	1	1	yes	characteristic
524	C₂²	C₁₉×#577	1	1	yes	characteristic
525	C₂²	C₁₉×#578	1	1	yes	characteristic
526	C₄	—	2	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	8	1	no	—
537	C₄	—	8	1	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	1	no	—
540	C₄	C₁₉×#544	1	1	yes	characteristic
541	C₄	C₁₉×#544	1	1	yes	characteristic
542	C₄	Q₈²×C₁₉	1	1	yes	characteristic
543	C₄	C₁₉×#563	1	1	yes	characteristic
544	C₂	C₁₉×#2734	1	1	yes	characteristic
545	C₂	C₁₉×#3194	1	1	yes	characteristic
546	C₂	C₁₉×#3201	1	1	yes	characteristic
547	C₂	C₁₉×#3384	1	1	yes	characteristic
548	C₂	C₁₉×#3386	1	1	yes	characteristic
549	C₂	C₁₉×#3388	1	1	yes	characteristic
550	C₂	C₁₉×#3390	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
101. C₁₉×#107	Q₈	semidirect
104. C₁₉×#106	Q₈	semidirect
188. #32690	C₁₉	direct (N × H)
376. #107	Q₈×C₁₉	semidirect
379. #106	Q₈×C₁₉	semidirect
392. C₁₉	#32690	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×#2584	2
C₁₉×#2546	2
C₁₉×#2088	2
C₁₉×#2087	2
C₁₉×#2059	2
C₁₉×#2058	2
C₁₉×#2057	2
C₁₉×#1985	2
C₁₉×#1944	2
C₁₉×#1943	2
C₁₉×#1921	2
C₁₉×#1920	2
C₁₉×#1918	2
#32690	19

Subgroups — C19×#32690 #18038649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32690 #18038649