Subgroups — C₁₉×#32637 #18038596

Order 4864.

694 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2592	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2067	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2024	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2023	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1984	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1934	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1926	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1921	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#124	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×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	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×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#398	—	2	1	no	—
33	C₁₉×#398	—	2	1	no	—
34	C₁₉×#397	—	2	1	no	—
35	C₁₉×#393	—	2	1	no	—
36	C₁₉×#391	—	2	1	no	—
37	C₁₉×#391	C₂²	1	1	yes	characteristic
38	C₁₉×#391	C₂²	1	1	yes	characteristic
39	C₁₉×#390	C₂²	1	1	yes	characteristic
40	C₁₉×#390	C₂²	1	1	yes	characteristic
41	C₁₉×#389	C₂²	1	1	yes	characteristic
42	C₁₉×#389	C₂²	1	1	yes	characteristic
43	C₁₉×#389	C₂²	1	1	yes	characteristic
44	C₁₉×#389	C₂²	1	1	yes	characteristic
45	C₁₉×#388	—	2	1	no	—
46	C₁₉×#388	—	2	1	no	—
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₉	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×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×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	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₁₉×C₄⋊Q₈	—	4	1	no	—
68	C₁₉×C₄⋊Q₈	—	4	1	no	—
69	C₁₉×C₄⋊Q₈	—	4	4	no	—
70	C₁₉×#124	—	4	1	no	—
71	C₁₉×#124	—	4	1	no	—
72	C₄×Q₈×C₁₉	—	4	1	no	—
73	C₄×Q₈×C₁₉	—	4	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	D₄	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×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	—	2	2	no	—
100	C₁₉×#106	—	2	2	no	—
101	C₁₉×C₄⋊C₈	—	4	1	no	—
102	C₁₉×#103	—	2	2	no	—
103	C₁₉×#103	—	2	2	no	—
104	C₁₉×#103	—	4	1	no	—
105	C₁₉×#103	—	4	1	no	—
106	C₁₉×#102	—	2	2	no	—
107	C₁₉×#102	—	2	2	no	—
108	C₁₉×#102	—	4	1	no	—
109	C₁₉×#102	—	4	1	no	—
110	C₄×C₈×C₁₉	—	4	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	C₁₉×#95	—	2	1	no	—
118	C₁₉×#95	—	2	1	no	—
119	C₁₉×#95	—	2	1	no	—
120	C₁₉×#95	—	2	1	no	—
121	C₂⁴×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	2	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×Q₈×C₁₉	—	2	1	no	—
129	C₂×Q₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	4	1	no	—
131	C₂×Q₈×C₁₉	—	4	2	no	—
132	C₂×Q₈×C₁₉	—	4	2	no	—
133	C₂×Q₈×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	—	2	1	no	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	1	no	—
138	C₂×D₄×C₁₉	—	2	1	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	1	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	2	1	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₂×C₈×C₁₉	—	2	1	no	—
163	C₂×C₈×C₁₉	—	2	1	no	—
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	4	1	no	—
177	C₄⋊C₄×C₁₉	—	4	1	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₄⋊C₄×C₁₉	—	4	2	no	—
180	C₄⋊C₄×C₁₉	—	4	2	no	—
181	C₄⋊C₄×C₁₉	—	4	2	no	—
182	C₄⋊C₄×C₁₉	—	4	2	no	—
183	C₄⋊C₄×C₁₉	—	4	2	no	—
184	C₄⋊C₄×C₁₉	#41	1	2	yes	—
185	C₄⋊C₄×C₁₉	#41	1	2	yes	—
186	C₂²⋊C₄×C₁₉	—	4	2	no	—
187	C₂²⋊C₄×C₁₉	—	4	2	no	—
188	C₂²⋊C₄×C₁₉	—	4	2	no	—
189	C₂²⋊C₄×C₁₉	—	4	2	no	—
190	C₂²⋊C₄×C₁₉	—	8	1	no	—
191	C₂²⋊C₄×C₁₉	—	8	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	2	1	no	—
195	C₄²×C₁₉	—	2	1	no	—
196	C₄²×C₁₉	—	2	1	no	—
197	C₄²×C₁₉	—	2	1	no	—
198	C₄²×C₁₉	—	4	2	no	—
199	C₄²×C₁₉	—	8	1	no	—
200	#32637	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂³×C₁₉	—	4	1	no	—
202	C₂³×C₁₉	—	4	1	no	—
203	C₂³×C₁₉	—	4	1	no	—
204	C₂³×C₁₉	—	4	1	no	—
205	C₂³×C₁₉	—	4	1	no	—
206	C₂³×C₁₉	—	4	1	no	—
207	C₂³×C₁₉	—	4	1	no	—
208	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₁₉	—	4	4	no	—
210	Q₈×C₁₉	—	4	1	no	—
211	Q₈×C₁₉	—	4	1	no	—
212	Q₈×C₁₉	—	4	1	no	—
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	8	4	no	—
215	D₄×C₁₉	—	4	1	no	—
216	D₄×C₁₉	—	4	1	no	—
217	D₄×C₁₉	—	4	1	no	—
218	D₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	4	1	no	—
250	C₂×C₄×C₁₉	—	4	1	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	1	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	#135	1	2	yes	—
257	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
258	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
261	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
264	C₈×C₁₉	—	4	1	no	—
265	C₈×C₁₉	—	4	1	no	—
266	C₈×C₁₉	—	4	1	no	—
267	C₈×C₁₉	—	4	1	no	—
268	#2592	C₂×C₁₉	1	1	yes	characteristic
269	#2546	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#2067	C₂×C₁₉	1	1	yes	characteristic
271	#2066	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#2042	C₂×C₁₉	1	1	yes	characteristic
273	#2042	C₂×C₁₉	1	1	yes	characteristic
274	#2024	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#2023	C₂×C₁₉	1	1	yes	characteristic
276	#1984	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#1934	C₂×C₁₉	1	1	yes	characteristic
278	#1933	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#1928	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#1926	C₂×C₁₉	1	1	yes	characteristic
281	#1921	C₂×C₁₉	1	1	yes	characteristic, complemented
282	#1920	C₂×C₁₉	1	1	yes	characteristic, complemented
283	C₂²×C₁₉	—	8	1	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	—	8	1	no	—
286	C₂²×C₁₉	—	8	1	no	—
287	C₂²×C₁₉	—	8	1	no	—
288	C₂²×C₁₉	—	8	1	no	—
289	C₂²×C₁₉	—	8	1	no	—
290	C₂²×C₁₉	#534	1	1	yes	characteristic
291	C₂²×C₁₉	#548	1	1	yes	characteristic
292	C₂²×C₁₉	#548	1	1	yes	characteristic
293	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
294	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
295	C₂²×C₁₉	#577	1	1	yes	characteristic
296	C₂²×C₁₉	#578	1	1	yes	characteristic
297	C₄×C₁₉	—	2	2	no	—
298	C₄×C₁₉	—	2	2	no	—
299	C₄×C₁₉	—	4	2	no	—
300	C₄×C₁₉	—	4	2	no	—
301	C₄×C₁₉	—	4	1	no	—
302	C₄×C₁₉	—	4	1	no	—
303	C₄×C₁₉	—	4	1	no	—
304	C₄×C₁₉	—	4	1	no	—
305	C₄×C₁₉	—	8	1	no	—
306	C₄×C₁₉	—	8	1	no	—
307	C₄×C₁₉	—	8	1	no	—
308	C₄×C₁₉	—	8	1	no	—
309	C₄×C₁₉	—	8	1	no	—
310	C₄×C₁₉	#542	1	1	yes	characteristic
311	C₄×C₁₉	#542	1	1	yes	characteristic
312	C₄×C₁₉	#555	1	1	yes	characteristic
313	C₄×C₁₉	#563	1	1	yes	characteristic
314	C₂×C₄⋊Q₈	—	2	1	no	—
315	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
325	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
326	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
330	#398	—	2	1	no	—
331	#398	—	2	1	no	—
332	#397	—	2	1	no	—
333	#393	—	2	1	no	—
334	#391	—	2	1	no	—
335	#391	C₂²×C₁₉	1	1	yes	characteristic
336	#391	C₂²×C₁₉	1	1	yes	characteristic
337	#390	C₂²×C₁₉	1	1	yes	characteristic
338	#390	C₂²×C₁₉	1	1	yes	characteristic
339	#389	C₂²×C₁₉	1	1	yes	characteristic
340	#389	C₂²×C₁₉	1	1	yes	characteristic
341	#389	C₂²×C₁₉	1	1	yes	characteristic
342	#389	C₂²×C₁₉	1	1	yes	characteristic
343	#388	—	2	1	no	—
344	#388	—	2	1	no	—
345	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
347	#340	C₂²×C₁₉	1	1	yes	characteristic
348	#340	C₂²×C₁₉	1	1	yes	characteristic
349	#340	C₂²×C₁₉	1	1	yes	characteristic
350	#340	C₂²×C₁₉	1	1	yes	characteristic
351	#340	C₂²×C₁₉	1	1	yes	characteristic
352	#340	C₂²×C₁₉	1	1	yes	characteristic
353	#336	C₂²×C₁₉	1	1	yes	characteristic
354	#336	C₂²×C₁₉	1	1	yes	characteristic
355	#336	C₂²×C₁₉	1	1	yes	characteristic
356	#336	C₂²×C₁₉	1	1	yes	characteristic
357	C₂×C₁₉	—	16	1	no	—
358	C₂×C₁₉	#2731	1	1	yes	characteristic
359	C₂×C₁₉	#3188	1	1	yes	characteristic
360	C₂×C₁₉	#3201	1	1	yes	characteristic
361	C₂×C₁₉	#3364	1	1	yes	characteristic
362	C₂×C₁₉	#3365	1	1	yes	characteristic
363	C₂×C₁₉	#3367	1	1	yes	characteristic
364	C₂×C₁₉	#3373	1	1	yes	characteristic
365	C₂²×Q₈	—	2	1	no	—
366	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
367	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
373	C₄⋊Q₈	—	4	1	no	—
374	C₄⋊Q₈	—	4	1	no	—
375	C₄⋊Q₈	—	4	4	no	—
376	#124	—	4	1	no	—
377	#124	—	4	1	no	—
378	C₄×Q₈	—	4	1	no	—
379	C₄×Q₈	—	4	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
405	#107	—	2	2	no	—
406	#106	—	2	2	no	—
407	C₄⋊C₈	—	4	1	no	—
408	#103	—	2	2	no	—
409	#103	—	2	2	no	—
410	#103	—	4	1	no	—
411	#103	—	4	1	no	—
412	#102	—	2	2	no	—
413	#102	—	2	2	no	—
414	#102	—	4	1	no	—
415	#102	—	4	1	no	—
416	C₄×C₈	—	4	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	C₁₉	#32637	1	1	yes	characteristic, direct product factor, Sylow
428	C₂⁴	—	2	1	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	4	1	no	—
438	C₂×Q₈	—	4	2	no	—
439	C₂×Q₈	—	4	2	no	—
440	C₂×Q₈	—	4	2	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	2	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	#41×C₁₉	1	2	yes	—
492	C₄⋊C₄	#41×C₁₉	1	2	yes	—
493	C₂²⋊C₄	—	4	2	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	—	4	2	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₂²⋊C₄	—	8	1	no	—
498	C₂²⋊C₄	—	8	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	4	2	no	—
506	C₄²	—	8	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
515	Q₈	—	4	4	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	8	4	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	C₁₉×#135	1	2	yes	—
563	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
564	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
565	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
566	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
569	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	C₁₉×#534	1	1	yes	characteristic
582	C₂²	C₁₉×#548	1	1	yes	characteristic
583	C₂²	C₁₉×#548	1	1	yes	characteristic
584	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
585	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
586	C₂²	C₁₉×#577	1	1	yes	characteristic
587	C₂²	C₁₉×#578	1	1	yes	characteristic
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	8	1	no	—
597	C₄	—	8	1	no	—
598	C₄	—	8	1	no	—
599	C₄	—	8	1	no	—
600	C₄	—	8	1	no	—
601	C₄	C₁₉×#542	1	1	yes	characteristic
602	C₄	C₁₉×#542	1	1	yes	characteristic
603	C₄	C₁₉×#555	1	1	yes	characteristic
604	C₄	C₁₉×#563	1	1	yes	characteristic
605	C₂	—	16	1	no	—
606	C₂	C₁₉×#2731	1	1	yes	characteristic
607	C₂	C₁₉×#3188	1	1	yes	characteristic
608	C₂	C₁₉×#3201	1	1	yes	characteristic
609	C₂	C₁₉×#3364	1	1	yes	characteristic
610	C₂	C₁₉×#3365	1	1	yes	characteristic
611	C₂	C₁₉×#3367	1	1	yes	characteristic
612	C₂	C₁₉×#3373	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂³
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
2. C₁₉×#2546	C₂	semidirect
4. C₁₉×#2066	C₂	semidirect
7. C₁₉×#2024	C₂	semidirect
9. C₁₉×#1984	C₂	semidirect
11. C₁₉×#1933	C₂	semidirect
12. C₁₉×#1928	C₂	semidirect
14. C₁₉×#1921	C₂	semidirect
15. C₁₉×#1920	C₂	semidirect
200. #32637	C₁₉	direct (N × H)
269. #2546	C₂×C₁₉	semidirect
271. #2066	C₂×C₁₉	semidirect
274. #2024	C₂×C₁₉	semidirect
276. #1984	C₂×C₁₉	semidirect
278. #1933	C₂×C₁₉	semidirect
279. #1928	C₂×C₁₉	semidirect
281. #1921	C₂×C₁₉	semidirect
282. #1920	C₂×C₁₉	semidirect
427. C₁₉	#32637	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×#2592	2
C₁₉×#2546	2
C₁₉×#2067	2
C₁₉×#2066	2
C₁₉×#2042	2
C₁₉×#2024	2
C₁₉×#2023	2
C₁₉×#1984	2
C₁₉×#1934	2
C₁₉×#1933	2
C₁₉×#1928	2
C₁₉×#1926	2
C₁₉×#1921	2
C₁₉×#1920	2
#32637	19

Subgroups — C19×#32637 #18038596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32637 #18038596