Subgroups — C₁₉×#32844 #18038803

Order 4864.

590 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2660	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2644	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2094	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2092	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2085	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2084	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2073	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2071	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2025	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#2023	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1840	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#107	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×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₁₉×#398	—	2	1	no	—
27	C₁₉×#398	—	2	1	no	—
28	C₁₉×#397	—	2	1	no	—
29	C₁₉×#397	—	2	1	no	—
30	C₁₉×#397	—	2	1	no	—
31	C₁₉×#396	—	2	1	no	—
32	C₁₉×#395	—	2	1	no	—
33	C₁₉×#395	—	2	1	no	—
34	C₁₉×#390	C₂²	1	1	yes	characteristic
35	C₁₉×#390	C₂²	1	1	yes	characteristic
36	C₁₉×#390	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×#384	C₂²	1	1	yes	characteristic
41	C₁₉×#384	C₂²	1	1	yes	characteristic
42	C₁₉×#382	C₂²	1	1	yes	characteristic
43	C₁₉×#382	C₂²	1	1	yes	characteristic
44	C₁₉×#376	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×#336	C₂²	1	1	yes	characteristic
54	C₁₉×#336	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×D₄×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	—	4	1	no	—
66	C₁₉×C₄⋊Q₈	—	4	1	no	—
67	C₁₉×#125	—	4	1	no	—
68	C₁₉×#125	—	4	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	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×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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×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×#107	—	4	1	no	—
96	C₁₉×#106	—	4	1	no	—
97	C₁₉×#106	—	4	1	no	—
98	C₁₉×#106	—	4	1	no	—
99	C₁₉×#102	—	4	1	no	—
100	C₁₉×#102	—	4	1	no	—
101	C₁₉×#102	—	4	1	no	—
102	C₁₉×#102	—	4	1	no	—
103	C₁₉×#95	—	2	1	no	—
104	C₁₉×#95	—	2	1	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	D₄	1	1	yes	characteristic
111	C₁₉×#95	D₄	1	1	yes	characteristic
112	C₁₉×#95	D₄	1	1	yes	characteristic
113	C₁₉×#95	D₄	1	1	yes	characteristic
114	C₂⁴×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	4	2	no	—
116	C₂×Q₈×C₁₉	—	8	1	no	—
117	C₂×Q₈×C₁₉	—	8	1	no	—
118	C₂×D₄×C₁₉	—	2	1	no	—
119	C₂×D₄×C₁₉	—	2	1	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×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	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
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	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	4	2	no	—
165	C₄⋊C₄×C₁₉	—	4	2	no	—
166	C₄⋊C₄×C₁₉	—	4	2	no	—
167	C₄⋊C₄×C₁₉	—	8	1	no	—
168	C₄⋊C₄×C₁₉	—	8	1	no	—
169	C₄⋊C₄×C₁₉	—	8	1	no	—
170	C₄⋊C₄×C₁₉	—	8	1	no	—
171	C₄⋊C₄×C₁₉	—	8	1	no	—
172	C₄⋊C₄×C₁₉	—	8	1	no	—
173	C₄⋊C₄×C₁₉	—	8	1	no	—
174	C₂²⋊C₄×C₁₉	—	8	1	no	—
175	C₂²⋊C₄×C₁₉	—	8	1	no	—
176	C₂²⋊C₄×C₁₉	—	8	1	no	—
177	C₂²⋊C₄×C₁₉	—	8	1	no	—
178	C₂²⋊C₄×C₁₉	—	8	1	no	—
179	C₂²⋊C₄×C₁₉	—	8	1	no	—
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	#32844	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂³×C₁₉	—	4	1	no	—
188	C₂³×C₁₉	—	4	1	no	—
189	C₂³×C₁₉	—	4	1	no	—
190	C₂³×C₁₉	—	4	1	no	—
191	C₂³×C₁₉	—	4	1	no	—
192	C₂³×C₁₉	—	4	1	no	—
193	C₂³×C₁₉	—	4	1	no	—
194	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₁₉	—	8	4	no	—
196	D₄×C₁₉	—	4	1	no	—
197	D₄×C₁₉	—	4	1	no	—
198	D₄×C₁₉	—	4	1	no	—
199	D₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	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	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	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	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
245	C₈×C₁₉	—	4	1	no	—
246	C₈×C₁₉	—	4	1	no	—
247	C₈×C₁₉	—	4	1	no	—
248	C₈×C₁₉	—	4	1	no	—
249	#2660	C₂×C₁₉	1	1	yes	characteristic, complemented
250	#2644	C₂×C₁₉	1	1	yes	characteristic
251	#2101	C₂×C₁₉	1	1	yes	characteristic, complemented
252	#2099	C₂×C₁₉	1	1	yes	characteristic, complemented
253	#2094	C₂×C₁₉	1	1	yes	characteristic
254	#2092	C₂×C₁₉	1	1	yes	characteristic
255	#2085	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#2084	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#2073	C₂×C₁₉	1	1	yes	characteristic
258	#2071	C₂×C₁₉	1	1	yes	characteristic
259	#2059	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#2058	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#2025	C₂×C₁₉	1	1	yes	characteristic
262	#2023	C₂×C₁₉	1	1	yes	characteristic
263	#1840	C₂×C₁₉	1	1	yes	characteristic, complemented
264	C₂²×C₁₉	—	8	1	no	—
265	C₂²×C₁₉	—	8	1	no	—
266	C₂²×C₁₉	—	8	1	no	—
267	C₂²×C₁₉	—	8	1	no	—
268	C₂²×C₁₉	—	8	1	no	—
269	C₂²×C₁₉	—	8	1	no	—
270	C₂²×C₁₉	—	8	1	no	—
271	C₂²×C₁₉	#535	1	1	yes	characteristic
272	C₂²×C₁₉	#536	1	1	yes	characteristic
273	C₂²×C₁₉	#536	1	1	yes	characteristic
274	C₂²×C₁₉	#576	1	1	yes	characteristic
275	C₂²×C₁₉	#577	1	1	yes	characteristic
276	C₂²×C₁₉	#577	1	1	yes	characteristic
277	C₂²×C₁₉	#577	1	1	yes	characteristic
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	4	1	no	—
281	C₄×C₁₉	—	4	1	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	8	1	no	—
285	C₄×C₁₉	—	8	1	no	—
286	C₄×C₁₉	—	8	1	no	—
287	C₄×C₁₉	—	8	1	no	—
288	C₄×C₁₉	—	8	1	no	—
289	C₄×C₁₉	—	8	1	no	—
290	C₄×C₁₉	—	8	1	no	—
291	C₄×C₁₉	#563	1	1	yes	characteristic
292	C₄×C₁₉	#563	1	1	yes	characteristic
293	C₄×C₁₉	#563	1	1	yes	characteristic
294	C₄×C₁₉	#563	1	1	yes	characteristic
295	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
298	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
299	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
300	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
304	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
305	#398	—	2	1	no	—
306	#398	—	2	1	no	—
307	#397	—	2	1	no	—
308	#397	—	2	1	no	—
309	#397	—	2	1	no	—
310	#396	—	2	1	no	—
311	#395	—	2	1	no	—
312	#395	—	2	1	no	—
313	#390	C₂²×C₁₉	1	1	yes	characteristic
314	#390	C₂²×C₁₉	1	1	yes	characteristic
315	#390	C₂²×C₁₉	1	1	yes	characteristic
316	#389	C₂²×C₁₉	1	1	yes	characteristic
317	#389	C₂²×C₁₉	1	1	yes	characteristic
318	#389	C₂²×C₁₉	1	1	yes	characteristic
319	#384	C₂²×C₁₉	1	1	yes	characteristic
320	#384	C₂²×C₁₉	1	1	yes	characteristic
321	#382	C₂²×C₁₉	1	1	yes	characteristic
322	#382	C₂²×C₁₉	1	1	yes	characteristic
323	#376	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	#340	C₂²×C₁₉	1	1	yes	characteristic
329	#340	C₂²×C₁₉	1	1	yes	characteristic
330	#340	C₂²×C₁₉	1	1	yes	characteristic
331	#340	C₂²×C₁₉	1	1	yes	characteristic
332	#336	C₂²×C₁₉	1	1	yes	characteristic
333	#336	C₂²×C₁₉	1	1	yes	characteristic
334	#336	C₂²×C₁₉	1	1	yes	characteristic
335	#336	C₂²×C₁₉	1	1	yes	characteristic
336	#336	C₂²×C₁₉	1	1	yes	characteristic
337	#336	C₂²×C₁₉	1	1	yes	characteristic
338	C₂×C₁₉	—	16	1	no	—
339	C₂×C₁₉	#2821	1	1	yes	characteristic
340	C₂×C₁₉	#3221	1	1	yes	characteristic
341	C₂×C₁₉	#3224	1	1	yes	characteristic
342	C₂×C₁₉	#3241	1	1	yes	characteristic
343	C₂×C₁₉	#3241	1	1	yes	characteristic
344	C₂×C₁₉	#3244	1	1	yes	characteristic
345	C₂×C₁₉	#3244	1	1	yes	characteristic
346	C₂²×Q₈	—	2	1	no	—
347	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
352	C₄⋊Q₈	—	4	1	no	—
353	C₄⋊Q₈	—	4	1	no	—
354	#125	—	4	1	no	—
355	#125	—	4	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
382	#107	—	4	1	no	—
383	#106	—	4	1	no	—
384	#106	—	4	1	no	—
385	#106	—	4	1	no	—
386	#102	—	4	1	no	—
387	#102	—	4	1	no	—
388	#102	—	4	1	no	—
389	#102	—	4	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	1	no	—
396	#95	—	2	1	no	—
397	#95	D₄×C₁₉	1	1	yes	characteristic
398	#95	D₄×C₁₉	1	1	yes	characteristic
399	#95	D₄×C₁₉	1	1	yes	characteristic
400	#95	D₄×C₁₉	1	1	yes	characteristic
401	C₁₉	#32844	1	1	yes	characteristic, direct product factor, Sylow
402	C₂⁴	—	2	1	no	—
403	C₂×Q₈	—	4	2	no	—
404	C₂×Q₈	—	8	1	no	—
405	C₂×Q₈	—	8	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
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	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	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	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₄⋊C₄	—	4	2	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₄⋊C₄	—	8	1	no	—
456	C₄⋊C₄	—	8	1	no	—
457	C₄⋊C₄	—	8	1	no	—
458	C₄⋊C₄	—	8	1	no	—
459	C₄⋊C₄	—	8	1	no	—
460	C₄⋊C₄	—	8	1	no	—
461	C₄⋊C₄	—	8	1	no	—
462	C₂²⋊C₄	—	8	1	no	—
463	C₂²⋊C₄	—	8	1	no	—
464	C₂²⋊C₄	—	8	1	no	—
465	C₂²⋊C₄	—	8	1	no	—
466	C₂²⋊C₄	—	8	1	no	—
467	C₂²⋊C₄	—	8	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	1	no	—
481	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
482	Q₈	—	8	4	no	—
483	D₄	—	4	1	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	1	no	—
486	D₄	—	4	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	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	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	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
528	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
529	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
530	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
531	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	C₁₉×#535	1	1	yes	characteristic
544	C₂²	C₁₉×#536	1	1	yes	characteristic
545	C₂²	C₁₉×#536	1	1	yes	characteristic
546	C₂²	C₁₉×#576	1	1	yes	characteristic
547	C₂²	C₁₉×#577	1	1	yes	characteristic
548	C₂²	C₁₉×#577	1	1	yes	characteristic
549	C₂²	C₁₉×#577	1	1	yes	characteristic
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	—	8	1	no	—
560	C₄	—	8	1	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	C₁₉×#563	1	1	yes	characteristic
564	C₄	C₁₉×#563	1	1	yes	characteristic
565	C₄	C₁₉×#563	1	1	yes	characteristic
566	C₄	C₁₉×#563	1	1	yes	characteristic
567	C₂	—	16	1	no	—
568	C₂	C₁₉×#2821	1	1	yes	characteristic
569	C₂	C₁₉×#3221	1	1	yes	characteristic
570	C₂	C₁₉×#3224	1	1	yes	characteristic
571	C₂	C₁₉×#3241	1	1	yes	characteristic
572	C₂	C₁₉×#3241	1	1	yes	characteristic
573	C₂	C₁₉×#3244	1	1	yes	characteristic
574	C₂	C₁₉×#3244	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 ◁ C₁₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2660	C₂	semidirect
3. C₁₉×#2101	C₂	semidirect
4. C₁₉×#2099	C₂	semidirect
7. C₁₉×#2085	C₂	semidirect
8. C₁₉×#2084	C₂	semidirect
11. C₁₉×#2059	C₂	semidirect
12. C₁₉×#2058	C₂	semidirect
15. C₁₉×#1840	C₂	semidirect
186. #32844	C₁₉	direct (N × H)
249. #2660	C₂×C₁₉	semidirect
251. #2101	C₂×C₁₉	semidirect
252. #2099	C₂×C₁₉	semidirect
255. #2085	C₂×C₁₉	semidirect
256. #2084	C₂×C₁₉	semidirect
259. #2059	C₂×C₁₉	semidirect
260. #2058	C₂×C₁₉	semidirect
263. #1840	C₂×C₁₉	semidirect
401. C₁₉	#32844	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×#2660	2
C₁₉×#2644	2
C₁₉×#2101	2
C₁₉×#2099	2
C₁₉×#2094	2
C₁₉×#2092	2
C₁₉×#2085	2
C₁₉×#2084	2
C₁₉×#2073	2
C₁₉×#2071	2
C₁₉×#2059	2
C₁₉×#2058	2
C₁₉×#2025	2
C₁₉×#2023	2
C₁₉×#1840	2
#32844	19

Subgroups — C19×#32844 #18038803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32844 #18038803