Subgroups — C₁₉×#32739 #18038698

Order 4864.

764 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2854	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2088	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2083	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2076	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2071	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2067	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2034	C₂	1	2	yes	maximal
10	C₁₉×#2023	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#123	—	2	1	no	—
14	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#107	C₂²	1	2	yes	—
18	C₂×C₁₉×#106	C₂²	1	2	yes	—
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₉×#102	C₂²	1	2	yes	—
21	C₂×C₁₉×#102	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₁₉×#391	—	2	1	no	—
24	C₁₉×#390	C₂²	1	1	yes	characteristic
25	C₁₉×#390	C₂²	1	1	yes	characteristic
26	C₁₉×#389	—	2	1	no	—
27	C₁₉×#389	C₂²	1	1	yes	characteristic
28	C₁₉×#389	C₂²	1	2	yes	—
29	C₁₉×#389	C₂²	1	1	yes	characteristic
30	C₁₉×#388	—	2	1	no	—
31	C₁₉×#388	—	2	1	no	—
32	C₁₉×#386	—	2	1	no	—
33	C₁₉×#384	C₂²	1	1	yes	characteristic
34	C₁₉×#380	—	2	1	no	—
35	C₁₉×#380	C₂²	1	2	yes	—
36	C₁₉×#380	C₂²	1	1	yes	characteristic
37	C₁₉×#340	C₂²	1	2	yes	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#336	C₂²	1	1	yes	characteristic
42	C₁₉×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₁₉×C₄⋊Q₈	—	4	2	no	—
52	C₁₉×#123	—	4	4	no	—
53	C₁₉×C₂²⋊Q₈	—	4	4	no	—
54	C₁₉×#121	—	4	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄²×C₁₉	—	4	2	no	—
74	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	C₁₉×#107	—	4	2	no	—
79	C₁₉×#106	—	4	2	no	—
80	C₁₉×C₄⋊C₈	—	4	2	no	—
81	C₁₉×#102	—	4	2	no	—
82	C₁₉×#102	—	4	2	no	—
83	C₁₉×C₂²⋊C₈	—	4	2	no	—
84	C₁₉×#95	—	2	2	no	—
85	C₁₉×#95	—	2	1	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₁₉×#95	—	2	1	no	—
88	C₁₉×#95	—	2	1	no	—
89	C₂⁴×C₁₉	—	2	1	no	—
90	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂×Q₈×C₁₉	—	4	2	no	—
92	C₂×Q₈×C₁₉	—	4	2	no	—
93	C₂×Q₈×C₁₉	—	4	2	no	—
94	C₂×D₄×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	—	2	1	no	—
96	C₂×D₄×C₁₉	—	2	2	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	4	2	no	—
99	C₂×D₄×C₁₉	—	4	2	no	—
100	C₂×D₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	1	no	—
110	C₂²×C₄×C₁₉	—	2	1	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	1	no	—
113	C₂²×C₄×C₁₉	—	2	2	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	—	4	1	no	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	2	1	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	2	no	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	4	2	no	—
137	C₄⋊C₄×C₁₉	—	4	2	no	—
138	C₄⋊C₄×C₁₉	—	4	2	no	—
139	C₄⋊C₄×C₁₉	—	4	2	no	—
140	C₄⋊C₄×C₁₉	—	4	4	no	—
141	C₄⋊C₄×C₁₉	—	4	2	no	—
142	C₂²⋊C₄×C₁₉	—	4	2	no	—
143	C₂²⋊C₄×C₁₉	—	4	2	no	—
144	C₂²⋊C₄×C₁₉	—	4	4	no	—
145	C₂²⋊C₄×C₁₉	—	4	2	no	—
146	C₂²⋊C₄×C₁₉	—	4	2	no	—
147	C₂²⋊C₄×C₁₉	—	4	2	no	—
148	C₂²⋊C₄×C₁₉	—	4	2	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	—	4	1	no	—
152	C₄²×C₁₉	—	4	1	no	—
153	#32739	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	—	2	1	no	—
155	C₂³×C₁₉	—	2	1	no	—
156	C₂³×C₁₉	—	2	1	no	—
157	C₂³×C₁₉	—	2	1	no	—
158	C₂³×C₁₉	—	2	1	no	—
159	C₂³×C₁₉	—	2	1	no	—
160	C₂³×C₁₉	—	4	1	no	—
161	C₂³×C₁₉	—	4	1	no	—
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	—	4	1	no	—
164	C₂³×C₁₉	—	4	1	no	—
165	C₂³×C₁₉	—	4	1	no	—
166	C₂³×C₁₉	—	4	1	no	—
167	C₂³×C₁₉	#137	1	2	yes	—
168	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₁₉	—	8	4	no	—
170	D₄×C₁₉	—	4	2	no	—
171	D₄×C₁₉	—	4	2	no	—
172	D₄×C₁₉	—	8	4	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	1	no	—
176	C₂×C₄×C₁₉	—	2	1	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	1	no	—
180	C₂×C₄×C₁₉	—	2	1	no	—
181	C₂×C₄×C₁₉	—	2	1	no	—
182	C₂×C₄×C₁₉	—	2	1	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	4	4	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	#135	1	2	yes	—
205	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
207	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
209	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
210	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
211	C₈×C₁₉	—	4	2	no	—
212	C₈×C₁₉	—	4	2	no	—
213	#2857	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#2854	C₂×C₁₉	1	1	yes	characteristic
215	#2088	C₂×C₁₉	1	2	yes	complemented
216	#2083	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#2076	C₂×C₁₉	1	2	yes	complemented
218	#2071	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#2067	C₂×C₁₉	1	2	yes	complemented
220	#2058	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#2034	C₂×C₁₉	1	2	yes	—
222	#2023	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂²×C₁₉	—	2	2	no	—
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	2	2	no	—
227	C₂²×C₁₉	—	4	1	no	—
228	C₂²×C₁₉	—	4	1	no	—
229	C₂²×C₁₉	—	4	1	no	—
230	C₂²×C₁₉	—	4	1	no	—
231	C₂²×C₁₉	—	8	1	no	—
232	C₂²×C₁₉	—	8	1	no	—
233	C₂²×C₁₉	—	8	1	no	—
234	C₂²×C₁₉	—	8	1	no	—
235	C₂²×C₁₉	—	8	1	no	—
236	C₂²×C₁₉	—	8	1	no	—
237	C₂²×C₁₉	—	8	1	no	—
238	C₂²×C₁₉	#534	1	1	yes	characteristic
239	C₂²×C₁₉	#536	1	1	yes	characteristic
240	C₂²×C₁₉	#537	1	1	yes	characteristic
241	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
242	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
244	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
245	C₄×C₁₉	—	2	2	no	—
246	C₄×C₁₉	—	2	2	no	—
247	C₄×C₁₉	—	2	2	no	—
248	C₄×C₁₉	—	4	1	no	—
249	C₄×C₁₉	—	4	1	no	—
250	C₄×C₁₉	—	8	2	no	—
251	C₄×C₁₉	—	8	1	no	—
252	C₄×C₁₉	—	8	1	no	—
253	C₄×C₁₉	—	8	1	no	—
254	C₄×C₁₉	—	8	2	no	—
255	C₄×C₁₉	#562	1	2	yes	—
256	C₄×C₁₉	#563	1	2	yes	—
257	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
258	C₂×#123	—	2	1	no	—
259	C₂×C₂²⋊Q₈	—	2	1	no	—
260	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
261	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×#107	C₂²×C₁₉	1	2	yes	—
263	C₂×#106	C₂²×C₁₉	1	2	yes	—
264	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
265	C₂×#102	C₂²×C₁₉	1	2	yes	—
266	C₂×#102	C₂²×C₁₉	1	2	yes	—
267	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
268	#391	—	2	1	no	—
269	#390	C₂²×C₁₉	1	1	yes	characteristic
270	#390	C₂²×C₁₉	1	1	yes	characteristic
271	#389	—	2	1	no	—
272	#389	C₂²×C₁₉	1	1	yes	characteristic
273	#389	C₂²×C₁₉	1	2	yes	—
274	#389	C₂²×C₁₉	1	1	yes	characteristic
275	#388	—	2	1	no	—
276	#388	—	2	1	no	—
277	#386	—	2	1	no	—
278	#384	C₂²×C₁₉	1	1	yes	characteristic
279	#380	—	2	1	no	—
280	#380	C₂²×C₁₉	1	1	yes	characteristic
281	#380	C₂²×C₁₉	1	2	yes	—
282	#340	C₂²×C₁₉	1	2	yes	—
283	#340	C₂²×C₁₉	1	2	yes	—
284	#340	C₂²×C₁₉	1	2	yes	—
285	#340	C₂²×C₁₉	1	2	yes	—
286	#336	C₂²×C₁₉	1	1	yes	characteristic
287	#336	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₁₉	—	4	2	no	—
289	C₂×C₁₉	—	16	1	no	—
290	C₂×C₁₉	#2814	1	1	yes	characteristic
291	C₂×C₁₉	#3188	1	1	yes	characteristic
292	C₂×C₁₉	#3193	1	1	yes	characteristic
293	C₂×C₁₉	#3228	1	1	yes	characteristic
294	C₂×C₁₉	#3239	1	1	yes	characteristic
295	C₂×C₁₉	#3248	1	1	yes	characteristic
296	C₂×C₁₉	#3253	1	1	yes	characteristic
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×D₄	—	2	1	no	—
299	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
300	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
301	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
304	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
305	C₄⋊Q₈	—	4	2	no	—
306	#123	—	4	4	no	—
307	C₂²⋊Q₈	—	4	4	no	—
308	#121	—	4	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₄²	—	4	2	no	—
328	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
329	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
332	#107	—	4	2	no	—
333	#106	—	4	2	no	—
334	C₄⋊C₈	—	4	2	no	—
335	#102	—	4	2	no	—
336	#102	—	4	2	no	—
337	C₂²⋊C₈	—	4	2	no	—
338	#95	—	2	2	no	—
339	#95	—	2	1	no	—
340	#95	—	2	2	no	—
341	#95	—	2	1	no	—
342	#95	—	2	1	no	—
343	C₁₉	#32739	1	1	yes	characteristic, direct product factor, Sylow
344	C₂⁴	—	2	1	no	—
345	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	—	4	2	no	—
348	C₂×Q₈	—	4	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	2	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	1	no	—
370	C₂²×C₄	—	4	1	no	—
371	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
376	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	—	4	4	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	2	no	—
398	C₂²⋊C₄	—	4	2	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	2	no	—
401	C₂²⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	4	1	no	—
407	C₄²	—	4	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	C₁₉×#137	1	2	yes	—
422	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
423	Q₈	—	8	4	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	8	4	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	C₁₉×#135	1	2	yes	—
459	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
460	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
461	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
463	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
464	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
465	C₈	—	4	2	no	—
466	C₈	—	4	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	—	8	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	C₁₉×#534	1	1	yes	characteristic
482	C₂²	C₁₉×#536	1	1	yes	characteristic
483	C₂²	C₁₉×#537	1	1	yes	characteristic
484	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
485	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
487	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	8	2	no	—
494	C₄	—	8	1	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	1	no	—
497	C₄	—	8	2	no	—
498	C₄	C₁₉×#562	1	2	yes	—
499	C₄	C₁₉×#563	1	2	yes	—
500	C₂	—	4	2	no	—
501	C₂	—	16	1	no	—
502	C₂	C₁₉×#2814	1	1	yes	characteristic
503	C₂	C₁₉×#3188	1	1	yes	characteristic
504	C₂	C₁₉×#3193	1	1	yes	characteristic
505	C₂	C₁₉×#3228	1	1	yes	characteristic
506	C₂	C₁₉×#3239	1	1	yes	characteristic
507	C₂	C₁₉×#3248	1	1	yes	characteristic
508	C₂	C₁₉×#3253	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2857	C₂	semidirect
3. C₁₉×#2088	C₂	semidirect
4. C₁₉×#2083	C₂	semidirect
5. C₁₉×#2076	C₂	semidirect
6. C₁₉×#2071	C₂	semidirect
7. C₁₉×#2067	C₂	semidirect
8. C₁₉×#2058	C₂	semidirect
10. C₁₉×#2023	C₂	semidirect
11. C₁₉×#1797	C₂	semidirect
153. #32739	C₁₉	direct (N × H)
213. #2857	C₂×C₁₉	semidirect
215. #2088	C₂×C₁₉	semidirect
216. #2083	C₂×C₁₉	semidirect
217. #2076	C₂×C₁₉	semidirect
218. #2071	C₂×C₁₉	semidirect
219. #2067	C₂×C₁₉	semidirect
220. #2058	C₂×C₁₉	semidirect
222. #2023	C₂×C₁₉	semidirect
223. #1797	C₂×C₁₉	semidirect
343. C₁₉	#32739	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×#2857	2
C₁₉×#2854	2
C₁₉×#2088	2
C₁₉×#2083	2
C₁₉×#2076	2
C₁₉×#2071	2
C₁₉×#2067	2
C₁₉×#2058	2
C₁₉×#2034	2
C₁₉×#2023	2
C₁₉×#1797	2
#32739	19

Subgroups — C19×#32739 #18038698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32739 #18038698