Subgroups — C₁₉×#26035 #18031994

Order 4864.

660 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2550	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2355	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2066	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2066	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2026	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2024	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1989	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1987	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1940	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1919	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1836	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1763	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
29	C₁₉×#398	—	2	1	no	—
30	C₁₉×#395	—	2	1	no	—
31	C₁₉×#391	—	2	1	no	—
32	C₁₉×#391	C₂²	1	1	yes	characteristic
33	C₁₉×#391	C₂²	1	1	yes	characteristic
34	C₁₉×#389	—	2	1	no	—
35	C₁₉×#389	C₂²	1	1	yes	characteristic
36	C₁₉×#389	C₂²	1	1	yes	characteristic
37	C₁₉×#387	—	2	1	no	—
38	C₁₉×#387	—	2	1	no	—
39	C₁₉×#384	C₂²	1	1	yes	characteristic
40	C₁₉×#382	—	2	1	no	—
41	C₁₉×#382	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₉	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×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	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	C₂³	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	—	2	2	no	—
66	C₁₉×C₄⋊Q₈	—	4	1	no	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#125	—	4	1	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×Q₈×C₁₉	Q₈	1	4	yes	complemented
71	C₂×C₄⋊C₄×C₁₉	—	2	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	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	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×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	—	2	1	no	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
95	C₁₉×#106	—	2	2	no	—
96	C₁₉×#106	—	2	2	no	—
97	C₁₉×C₄⋊C₈	—	2	2	no	—
98	C₁₉×C₄⋊C₈	—	4	1	no	—
99	C₁₉×C₄⋊C₈	—	4	1	no	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#103	—	2	2	no	—
102	C₁₉×#103	—	4	1	no	—
103	C₁₉×#103	—	4	1	no	—
104	C₁₉×#97	—	2	2	no	—
105	C₁₉×#95	—	2	1	no	—
106	C₁₉×#95	—	2	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	D₄	1	1	yes	characteristic
117	C₁₉×#95	D₄	1	1	yes	characteristic
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	4	2	no	—
124	C₂×Q₈×C₁₉	—	4	2	no	—
125	C₂×Q₈×C₁₉	—	8	1	no	—
126	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
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	—	2	1	no	—
132	C₂²×C₄×C₁₉	—	2	1	no	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₄⋊C₄×C₁₉	—	2	4	no	—
155	C₄⋊C₄×C₁₉	—	2	2	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	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	4	1	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	—	8	1	no	—
174	C₄⋊C₄×C₁₉	—	8	1	no	—
175	C₄⋊C₄×C₁₉	C₂×Q₈	1	2	yes	—
176	C₄⋊C₄×C₁₉	#41	1	2	yes	—
177	C₄⋊C₄×C₁₉	#41	1	2	yes	—
178	C₄²×C₁₉	—	2	4	no	—
179	C₄²×C₁₉	—	2	1	no	—
180	C₄²×C₁₉	—	2	1	no	—
181	C₄²×C₁₉	—	2	1	no	—
182	C₄²×C₁₉	—	2	1	no	—
183	C₄²×C₁₉	—	8	1	no	—
184	C₄²×C₁₉	—	8	1	no	—
185	C₄²×C₁₉	—	8	1	no	—
186	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
187	C₄²×C₁₉	#41	1	2	yes	—
188	#26035	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₁₉	—	2	2	no	—
191	Q₈×C₁₉	—	2	2	no	—
192	Q₈×C₁₉	—	4	1	no	—
193	Q₈×C₁₉	—	4	1	no	—
194	Q₈×C₁₉	—	8	4	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	1	no	—
200	C₂×C₄×C₁₉	—	2	1	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	2	no	—
207	C₂×C₄×C₁₉	—	2	2	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	—	2	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	—	4	1	no	—
234	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
235	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
236	C₂×C₄×C₁₉	#137	1	2	yes	—
237	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
243	C₈×C₁₉	—	4	1	no	—
244	C₈×C₁₉	—	4	1	no	—
245	C₈×C₁₉	—	4	1	no	—
246	C₈×C₁₉	—	4	1	no	—
247	#2550	C₂×C₁₉	1	1	yes	characteristic
248	#2355	C₂×C₁₉	1	1	yes	characteristic
249	#2066	C₂×C₁₉	1	1	yes	characteristic
250	#2066	C₂×C₁₉	1	1	yes	characteristic
251	#2026	C₂×C₁₉	1	1	yes	characteristic
252	#2024	C₂×C₁₉	1	1	yes	characteristic
253	#1989	C₂×C₁₉	1	1	yes	characteristic
254	#1987	C₂×C₁₉	1	1	yes	characteristic
255	#1948	C₂×C₁₉	1	1	yes	characteristic
256	#1940	C₂×C₁₉	1	1	yes	characteristic
257	#1920	C₂×C₁₉	1	1	yes	characteristic
258	#1919	C₂×C₁₉	1	1	yes	characteristic
259	#1836	C₂×C₁₉	1	1	yes	characteristic
260	#1805	C₂×C₁₉	1	1	yes	characteristic
261	#1763	C₂×C₁₉	1	1	yes	characteristic
262	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
263	C₂²×C₁₉	#546	1	1	yes	characteristic
264	C₂²×C₁₉	#548	1	1	yes	characteristic
265	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
266	C₂²×C₁₉	#575	1	1	yes	characteristic
267	C₂²×C₁₉	#577	1	1	yes	characteristic
268	C₂²×C₁₉	#577	1	1	yes	characteristic
269	C₄×C₁₉	—	2	2	no	—
270	C₄×C₁₉	—	2	2	no	—
271	C₄×C₁₉	—	2	2	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	4	2	no	—
274	C₄×C₁₉	—	4	2	no	—
275	C₄×C₁₉	—	4	1	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	4	2	no	—
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	—	8	1	no	—
281	C₄×C₁₉	—	8	1	no	—
282	C₄×C₁₉	—	8	1	no	—
283	C₄×C₁₉	#533	1	1	yes	characteristic
284	C₄×C₁₉	#544	1	1	yes	characteristic
285	C₄×C₁₉	#555	1	1	yes	characteristic
286	C₄×C₁₉	#556	1	1	yes	characteristic
287	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
291	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
300	#398	—	2	1	no	—
301	#395	—	2	1	no	—
302	#391	—	2	1	no	—
303	#391	C₂²×C₁₉	1	1	yes	characteristic
304	#391	C₂²×C₁₉	1	1	yes	characteristic
305	#389	—	2	1	no	—
306	#389	C₂²×C₁₉	1	1	yes	characteristic
307	#389	C₂²×C₁₉	1	1	yes	characteristic
308	#387	—	2	1	no	—
309	#387	—	2	1	no	—
310	#384	C₂²×C₁₉	1	1	yes	characteristic
311	#382	—	2	1	no	—
312	#382	C₂²×C₁₉	1	1	yes	characteristic
313	C₄×C₄⋊C₄	—	2	1	no	—
314	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
315	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
316	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
317	C₄×C₄⋊C₄	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	#340	C₂²×C₁₉	1	1	yes	characteristic
324	#340	C₂²×C₁₉	1	1	yes	characteristic
325	#340	C₂²×C₁₉	1	1	yes	characteristic
326	#340	C₂²×C₁₉	1	1	yes	characteristic
327	#340	C₂²×C₁₉	1	1	yes	characteristic
328	#336	C₂²×C₁₉	1	1	yes	characteristic
329	#336	C₂²×C₁₉	1	1	yes	characteristic
330	C₂×C₁₉	#2439	1	1	yes	characteristic
331	C₂×C₁₉	#3078	1	1	yes	characteristic
332	C₂×C₁₉	#3084	1	1	yes	characteristic
333	C₂×C₁₉	#3311	1	1	yes	characteristic
334	C₂×C₁₉	#3316	1	1	yes	characteristic
335	C₂×C₁₉	#3371	1	1	yes	characteristic
336	C₂×C₁₉	#3372	1	1	yes	characteristic
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
343	C₄⋊Q₈	—	2	2	no	—
344	C₄⋊Q₈	—	4	1	no	—
345	#125	—	2	2	no	—
346	#125	—	4	1	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	Q₈×C₁₉	1	4	yes	complemented
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	D₄×C₁₉	1	1	yes	characteristic
358	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×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×C₄²	—	2	1	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
373	#106	—	2	2	no	—
374	#106	—	2	2	no	—
375	C₄⋊C₈	—	2	2	no	—
376	C₄⋊C₈	—	4	1	no	—
377	C₄⋊C₈	—	4	1	no	—
378	#103	—	2	2	no	—
379	#103	—	2	2	no	—
380	#103	—	4	1	no	—
381	#103	—	4	1	no	—
382	#97	—	2	2	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	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	D₄×C₁₉	1	1	yes	characteristic
395	#95	D₄×C₁₉	1	1	yes	characteristic
396	C₁₉	#26035	1	1	yes	characteristic, direct product factor, Sylow
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	4	2	no	—
403	C₂×Q₈	—	4	2	no	—
404	C₂×Q₈	—	8	1	no	—
405	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	—	4	2	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	—	8	1	no	—
453	C₄⋊C₄	—	8	1	no	—
454	C₄⋊C₄	C₂×Q₈×C₁₉	1	2	yes	—
455	C₄⋊C₄	#41×C₁₉	1	2	yes	—
456	C₄⋊C₄	#41×C₁₉	1	2	yes	—
457	C₄²	—	2	4	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	8	1	no	—
463	C₄²	—	8	1	no	—
464	C₄²	—	8	1	no	—
465	C₄²	C₂×Q₈×C₁₉	1	2	yes	—
466	C₄²	#41×C₁₉	1	2	yes	—
467	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
468	Q₈	—	2	2	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	4	1	no	—
471	Q₈	—	4	1	no	—
472	Q₈	—	8	4	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	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	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
513	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
514	C₂×C₄	C₁₉×#137	1	2	yes	—
515	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
517	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
518	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
519	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
520	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
521	C₈	—	4	1	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
526	C₂²	C₁₉×#546	1	1	yes	characteristic
527	C₂²	C₁₉×#548	1	1	yes	characteristic
528	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
529	C₂²	C₁₉×#575	1	1	yes	characteristic
530	C₂²	C₁₉×#577	1	1	yes	characteristic
531	C₂²	C₁₉×#577	1	1	yes	characteristic
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	2	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	8	1	no	—
543	C₄	—	8	1	no	—
544	C₄	—	8	1	no	—
545	C₄	—	8	1	no	—
546	C₄	C₁₉×#533	1	1	yes	characteristic
547	C₄	C₁₉×#544	1	1	yes	characteristic
548	C₄	C₁₉×#555	1	1	yes	characteristic
549	C₄	C₁₉×#556	1	1	yes	characteristic
550	C₂	C₁₉×#2439	1	1	yes	characteristic
551	C₂	C₁₉×#3078	1	1	yes	characteristic
552	C₂	C₁₉×#3084	1	1	yes	characteristic
553	C₂	C₁₉×#3311	1	1	yes	characteristic
554	C₂	C₁₉×#3316	1	1	yes	characteristic
555	C₂	C₁₉×#3371	1	1	yes	characteristic
556	C₂	C₁₉×#3372	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 ◁ C₄×C₄⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
70. C₄×Q₈×C₁₉	Q₈	semidirect
188. #26035	C₁₉	direct (N × H)
348. C₄×Q₈	Q₈×C₁₉	semidirect
396. C₁₉	#26035	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×#2550	2
C₁₉×#2355	2
C₁₉×#2066	2
C₁₉×#2026	2
C₁₉×#2024	2
C₁₉×#1989	2
C₁₉×#1987	2
C₁₉×#1948	2
C₁₉×#1940	2
C₁₉×#1920	2
C₁₉×#1919	2
C₁₉×#1836	2
C₁₉×#1805	2
C₁₉×#1763	2
#26035	19

Subgroups — C19×#26035 #18031994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#26035 #18031994