Subgroups — C₁₉×#14820 #18020779

Order 4864.

3350 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#397	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#379	C₂	1	2	yes	maximal
5	C₁₉×#1440	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1439	C₂	1	2	yes	maximal, complemented
7	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
9	C₂⁶×C₁₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₂²⋊C₄×C₁₉	—	2	4	no	—
15	C₂²×C₂²⋊C₄×C₁₉	—	2	8	no	—
16	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
20	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
22	C₁₉×#397	—	2	8	no	—
23	C₁₉×#380	—	2	4	no	—
24	C₁₉×#379	—	2	8	no	—
25	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
26	C₂×C₁₉×#95	C₂²	1	4	yes	complemented
27	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
28	C₂×C₁₉×#95	C₂²	1	4	yes	complemented
29	C₂×C₁₉×#95	C₂²	1	2	yes	complemented
30	C₂⁵×C₁₉	—	2	4	no	—
31	C₂⁵×C₁₉	—	2	2	no	—
32	C₂⁵×C₁₉	—	2	4	no	—
33	C₂⁵×C₁₉	—	2	2	no	—
34	C₂⁵×C₁₉	—	2	4	no	—
35	C₂⁵×C₁₉	—	2	4	no	—
36	C₂⁵×C₁₉	—	4	2	no	—
37	C₂⁵×C₁₉	—	4	2	no	—
38	C₂⁵×C₁₉	D₄	1	4	yes	—
39	C₂⁵×C₁₉	C₂³	1	2	yes	—
40	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₉	—	2	2	no	—
42	C₂³×C₄×C₁₉	—	2	4	no	—
43	C₂³×C₄×C₁₉	—	2	4	no	—
44	C₂³×C₄×C₁₉	—	2	4	no	—
45	C₂³×C₄×C₁₉	—	2	4	no	—
46	C₂³×C₄×C₁₉	—	4	2	no	—
47	C₂³×C₄×C₁₉	—	4	2	no	—
48	C₂³×C₄×C₁₉	D₄	1	4	yes	—
49	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	32	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
77	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
78	C₁₉×#95	—	2	4	no	—
79	C₁₉×#95	—	2	8	no	—
80	C₁₉×#95	—	2	4	no	—
81	C₁₉×#95	—	4	4	no	—
82	C₁₉×#95	—	4	2	no	—
83	C₂⁴×C₁₉	—	2	2	no	—
84	C₂⁴×C₁₉	—	2	2	no	—
85	C₂⁴×C₁₉	—	2	2	no	—
86	C₂⁴×C₁₉	—	2	2	no	—
87	C₂⁴×C₁₉	—	2	8	no	—
88	C₂⁴×C₁₉	—	2	8	no	—
89	C₂⁴×C₁₉	—	2	16	no	—
90	C₂⁴×C₁₉	—	2	16	no	—
91	C₂⁴×C₁₉	—	2	8	no	—
92	C₂⁴×C₁₉	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	2	no	—
94	C₂⁴×C₁₉	—	2	2	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	—	2	4	no	—
97	C₂⁴×C₁₉	—	2	4	no	—
98	C₂⁴×C₁₉	—	2	4	no	—
99	C₂⁴×C₁₉	—	2	4	no	—
100	C₂⁴×C₁₉	—	2	16	no	—
101	C₂⁴×C₁₉	—	4	8	no	—
102	C₂⁴×C₁₉	—	4	16	no	—
103	C₂⁴×C₁₉	—	4	16	no	—
104	C₂⁴×C₁₉	—	4	16	no	—
105	C₂⁴×C₁₉	—	4	16	no	—
106	C₂⁴×C₁₉	—	4	4	no	—
107	C₂⁴×C₁₉	—	4	4	no	—
108	C₂⁴×C₁₉	—	4	8	no	—
109	C₂⁴×C₁₉	—	4	4	no	—
110	C₂⁴×C₁₉	—	4	4	no	—
111	C₂⁴×C₁₉	—	4	8	no	—
112	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
113	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
114	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
115	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
116	C₂⁴×C₁₉	#41	1	4	yes	—
117	C₂⁴×C₁₉	#41	1	2	yes	—
118	C₂⁴×C₁₉	#41	1	4	yes	—
119	C₂⁴×C₁₉	#41	1	4	yes	—
120	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	8	no	—
124	C₂²×C₄×C₁₉	—	2	8	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	4	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	4	no	—
132	C₂²×C₄×C₁₉	—	2	8	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	4	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	2	4	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	4	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	4	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	4	no	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	2	4	no	—
146	C₂²×C₄×C₁₉	—	2	4	no	—
147	C₂²×C₄×C₁₉	—	2	4	no	—
148	C₂²×C₄×C₁₉	—	2	4	no	—
149	C₂²×C₄×C₁₉	—	2	4	no	—
150	C₂²×C₄×C₁₉	—	4	4	no	—
151	C₂²×C₄×C₁₉	—	4	16	no	—
152	C₂²×C₄×C₁₉	—	4	16	no	—
153	C₂²×C₄×C₁₉	—	4	4	no	—
154	C₂²×C₄×C₁₉	—	4	4	no	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
159	C₄⋊C₄×C₁₉	—	4	4	no	—
160	C₄⋊C₄×C₁₉	—	4	4	no	—
161	C₂²⋊C₄×C₁₉	—	2	16	no	—
162	C₂²⋊C₄×C₁₉	—	2	16	no	—
163	C₂²⋊C₄×C₁₉	—	4	16	no	—
164	C₂²⋊C₄×C₁₉	—	4	16	no	—
165	C₂²⋊C₄×C₁₉	—	4	8	no	—
166	C₂²⋊C₄×C₁₉	—	4	8	no	—
167	#14820	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	4	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	4	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	4	no	—
174	C₂³×C₁₉	—	2	2	no	—
175	C₂³×C₁₉	—	2	4	no	—
176	C₂³×C₁₉	—	2	8	no	—
177	C₂³×C₁₉	—	2	8	no	—
178	C₂³×C₁₉	—	2	8	no	—
179	C₂³×C₁₉	—	2	8	no	—
180	C₂³×C₁₉	—	2	32	no	—
181	C₂³×C₁₉	—	2	4	no	—
182	C₂³×C₁₉	—	2	4	no	—
183	C₂³×C₁₉	—	2	4	no	—
184	C₂³×C₁₉	—	2	8	no	—
185	C₂³×C₁₉	—	2	4	no	—
186	C₂³×C₁₉	—	2	4	no	—
187	C₂³×C₁₉	—	2	4	no	—
188	C₂³×C₁₉	—	2	8	no	—
189	C₂³×C₁₉	—	2	8	no	—
190	C₂³×C₁₉	—	2	8	no	—
191	C₂³×C₁₉	—	2	8	no	—
192	C₂³×C₁₉	—	2	8	no	—
193	C₂³×C₁₉	—	4	64	no	—
194	C₂³×C₁₉	—	4	16	no	—
195	C₂³×C₁₉	—	4	16	no	—
196	C₂³×C₁₉	—	4	16	no	—
197	C₂³×C₁₉	—	4	16	no	—
198	C₂³×C₁₉	—	4	64	no	—
199	C₂³×C₁₉	—	4	16	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	—	4	2	no	—
202	C₂³×C₁₉	—	4	4	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	—	4	2	no	—
205	C₂³×C₁₉	—	4	4	no	—
206	C₂³×C₁₉	—	4	4	no	—
207	C₂³×C₁₉	—	4	4	no	—
208	C₂³×C₁₉	—	4	4	no	—
209	C₂³×C₁₉	—	4	4	no	—
210	C₂³×C₁₉	—	4	16	no	—
211	C₂³×C₁₉	#121	1	8	yes	—
212	C₂³×C₁₉	#121	1	4	yes	—
213	C₂³×C₁₉	#123	1	8	yes	—
214	C₂³×C₁₉	#123	1	4	yes	—
215	C₂³×C₁₉	#124	1	4	yes	—
216	C₂³×C₁₉	#126	1	8	yes	—
217	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
218	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
219	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
220	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
221	C₂³×C₁₉	C₂×#41	1	2	yes	—
222	C₂³×C₁₉	C₂×#41	1	2	yes	—
223	C₂³×C₁₉	C₂×#41	1	2	yes	—
224	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
225	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₄×C₁₉	—	2	2	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	8	no	—
229	C₂×C₄×C₁₉	—	2	2	no	—
230	C₂×C₄×C₁₉	—	2	4	no	—
231	C₂×C₄×C₁₉	—	2	2	no	—
232	C₂×C₄×C₁₉	—	2	2	no	—
233	C₂×C₄×C₁₉	—	2	8	no	—
234	C₂×C₄×C₁₉	—	4	16	no	—
235	C₂×C₄×C₁₉	—	4	16	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	2	no	—
238	C₂×C₄×C₁₉	—	4	4	no	—
239	C₂×C₄×C₁₉	—	4	4	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	4	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	4	4	no	—
245	C₂×C₄×C₁₉	—	4	4	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	4	no	—
248	C₂×C₄×C₁₉	—	4	4	no	—
249	C₂×C₄×C₁₉	—	4	4	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	2	no	—
252	C₂×C₄×C₁₉	—	4	4	no	—
253	C₂×C₄×C₁₉	—	4	4	no	—
254	C₂×C₄×C₁₉	—	4	4	no	—
255	C₂×C₄×C₁₉	—	4	4	no	—
256	C₂×C₄×C₁₉	—	4	4	no	—
257	C₂×C₄×C₁₉	#120	1	4	yes	—
258	C₂³×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
259	C₂×#397	C₂×C₁₉	1	2	yes	complemented
260	C₂×#380	C₂×C₁₉	1	1	yes	characteristic, complemented
261	C₂×#379	C₂×C₁₉	1	2	yes	—
262	#1440	C₂×C₁₉	1	4	yes	complemented
263	#1439	C₂×C₁₉	1	2	yes	complemented
264	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic, complemented
265	C₂²⋊#95	C₂×C₁₉	1	2	yes	complemented
266	C₂²×C₁₉	—	2	4	no	—
267	C₂²×C₁₉	—	2	4	no	—
268	C₂²×C₁₉	—	2	4	no	—
269	C₂²×C₁₉	—	2	4	no	—
270	C₂²×C₁₉	—	2	16	no	—
271	C₂²×C₁₉	—	2	4	no	—
272	C₂²×C₁₉	—	2	16	no	—
273	C₂²×C₁₉	—	2	4	no	—
274	C₂²×C₁₉	—	2	8	no	—
275	C₂²×C₁₉	—	2	16	no	—
276	C₂²×C₁₉	—	4	64	no	—
277	C₂²×C₁₉	—	4	4	no	—
278	C₂²×C₁₉	—	4	4	no	—
279	C₂²×C₁₉	—	4	4	no	—
280	C₂²×C₁₉	—	4	4	no	—
281	C₂²×C₁₉	—	4	8	no	—
282	C₂²×C₁₉	—	4	4	no	—
283	C₂²×C₁₉	—	4	8	no	—
284	C₂²×C₁₉	—	4	8	no	—
285	C₂²×C₁₉	—	4	4	no	—
286	C₂²×C₁₉	#397	1	8	yes	complemented
287	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
288	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
289	C₂²×C₁₉	C₂×#121	1	2	yes	—
290	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
291	C₂²×C₁₉	C₂×#123	1	2	yes	—
292	C₂²×C₁₉	#525	1	1	yes	characteristic
293	C₂²×C₁₉	#525	1	2	yes	—
294	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
295	C₂²×C₁₉	C₂×#126	1	2	yes	—
296	C₂²×C₁₉	#534	1	1	yes	characteristic
297	C₂²×C₁₉	#534	1	2	yes	—
298	C₂²×C₁₉	#535	1	1	yes	characteristic
299	C₂²×C₁₉	#538	1	2	yes	—
300	C₂²×C₁₉	#546	1	4	yes	—
301	C₂²×C₁₉	#546	1	4	yes	—
302	C₂²×C₁₉	#551	1	4	yes	—
303	C₂²×C₁₉	#551	1	4	yes	—
304	C₄×C₁₉	—	2	4	no	—
305	C₄×C₁₉	—	4	2	no	—
306	C₄×C₁₉	—	4	4	no	—
307	C₄×C₁₉	—	8	2	no	—
308	C₄×C₁₉	—	8	2	no	—
309	C₄×C₁₉	—	8	4	no	—
310	C₂⁶	C₂²×C₁₉	1	1	yes	characteristic
311	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
312	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
313	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
314	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
315	C₂²×C₂²⋊C₄	—	2	4	no	—
316	C₂²×C₂²⋊C₄	—	2	8	no	—
317	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
318	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
319	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
320	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
321	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
322	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
323	#397	—	2	8	no	—
324	#380	—	2	4	no	—
325	#379	—	2	8	no	—
326	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
327	C₂×#95	C₂²×C₁₉	1	4	yes	complemented
328	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
329	C₂×#95	C₂²×C₁₉	1	4	yes	complemented
330	C₂×#95	C₂²×C₁₉	1	2	yes	complemented
331	C₂×C₁₉	—	2	8	no	—
332	C₂×C₁₉	—	4	8	no	—
333	C₂×C₁₉	C₂×#397	1	1	yes	characteristic
334	C₂×C₁₉	#2405	1	1	yes	characteristic
335	C₂×C₁₉	#2412	1	4	yes	—
336	C₂×C₁₉	#2435	1	1	yes	characteristic
337	C₂×C₁₉	#2480	1	4	yes	—
338	C₂×C₁₉	#2482	1	1	yes	characteristic
339	C₂×C₁₉	#2561	1	1	yes	characteristic
340	C₂×C₁₉	#2617	1	1	yes	characteristic
341	C₂×C₁₉	#2847	1	1	yes	characteristic
342	C₂⁵	—	2	4	no	—
343	C₂⁵	—	2	2	no	—
344	C₂⁵	—	2	4	no	—
345	C₂⁵	—	2	2	no	—
346	C₂⁵	—	2	4	no	—
347	C₂⁵	—	2	4	no	—
348	C₂⁵	—	4	2	no	—
349	C₂⁵	—	4	2	no	—
350	C₂⁵	D₄×C₁₉	1	4	yes	—
351	C₂⁵	C₂³×C₁₉	1	2	yes	—
352	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
353	C₂³×C₄	—	2	2	no	—
354	C₂³×C₄	—	2	4	no	—
355	C₂³×C₄	—	2	4	no	—
356	C₂³×C₄	—	2	4	no	—
357	C₂³×C₄	—	2	4	no	—
358	C₂³×C₄	—	4	2	no	—
359	C₂³×C₄	—	4	2	no	—
360	C₂³×C₄	D₄×C₁₉	1	4	yes	—
361	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
362	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
364	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
366	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
367	C₂×C₄⋊C₄	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	—	4	2	no	—
371	C₂×C₂²⋊C₄	—	2	32	no	—
372	C₂×C₂²⋊C₄	—	2	4	no	—
373	C₂×C₂²⋊C₄	—	2	4	no	—
374	C₂×C₂²⋊C₄	—	2	4	no	—
375	C₂×C₂²⋊C₄	—	2	4	no	—
376	C₂×C₂²⋊C₄	—	2	4	no	—
377	C₂×C₂²⋊C₄	—	2	8	no	—
378	C₂×C₂²⋊C₄	—	2	8	no	—
379	C₂×C₂²⋊C₄	—	2	4	no	—
380	C₂×C₂²⋊C₄	—	2	4	no	—
381	C₂×C₂²⋊C₄	—	2	4	no	—
382	C₂×C₂²⋊C₄	—	2	8	no	—
383	C₂×C₂²⋊C₄	—	2	8	no	—
384	C₂×C₂²⋊C₄	—	2	4	no	—
385	C₂×C₂²⋊C₄	—	2	4	no	—
386	C₂×C₂²⋊C₄	—	2	4	no	—
387	C₂×C₂²⋊C₄	—	4	4	no	—
388	C₂×C₂²⋊C₄	—	4	4	no	—
389	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
390	#95	—	2	4	no	—
391	#95	—	2	4	no	—
392	#95	—	2	8	no	—
393	#95	—	4	4	no	—
394	#95	—	4	2	no	—
395	C₁₉	#14820	1	1	yes	characteristic, direct product factor, Sylow
396	C₂⁴	—	2	2	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	2	8	no	—
401	C₂⁴	—	2	8	no	—
402	C₂⁴	—	2	16	no	—
403	C₂⁴	—	2	16	no	—
404	C₂⁴	—	2	8	no	—
405	C₂⁴	—	2	2	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	2	2	no	—
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	—	2	16	no	—
414	C₂⁴	—	4	8	no	—
415	C₂⁴	—	4	16	no	—
416	C₂⁴	—	4	16	no	—
417	C₂⁴	—	4	16	no	—
418	C₂⁴	—	4	16	no	—
419	C₂⁴	—	4	4	no	—
420	C₂⁴	—	4	4	no	—
421	C₂⁴	—	4	8	no	—
422	C₂⁴	—	4	4	no	—
423	C₂⁴	—	4	4	no	—
424	C₂⁴	—	4	8	no	—
425	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
426	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
427	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
428	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
429	C₂⁴	#41×C₁₉	1	4	yes	—
430	C₂⁴	#41×C₁₉	1	2	yes	—
431	C₂⁴	#41×C₁₉	1	4	yes	—
432	C₂⁴	#41×C₁₉	1	4	yes	—
433	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	8	no	—
437	C₂²×C₄	—	2	8	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	4	4	no	—
464	C₂²×C₄	—	4	16	no	—
465	C₂²×C₄	—	4	16	no	—
466	C₂²×C₄	—	4	4	no	—
467	C₂²×C₄	—	4	4	no	—
468	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
469	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
470	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
471	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
472	C₄⋊C₄	—	4	4	no	—
473	C₄⋊C₄	—	4	4	no	—
474	C₂²⋊C₄	—	2	16	no	—
475	C₂²⋊C₄	—	2	16	no	—
476	C₂²⋊C₄	—	4	16	no	—
477	C₂²⋊C₄	—	4	16	no	—
478	C₂²⋊C₄	—	4	8	no	—
479	C₂²⋊C₄	—	4	8	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	8	no	—
489	C₂³	—	2	8	no	—
490	C₂³	—	2	8	no	—
491	C₂³	—	2	8	no	—
492	C₂³	—	2	32	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	8	no	—
501	C₂³	—	2	8	no	—
502	C₂³	—	2	8	no	—
503	C₂³	—	2	8	no	—
504	C₂³	—	2	8	no	—
505	C₂³	—	4	64	no	—
506	C₂³	—	4	16	no	—
507	C₂³	—	4	16	no	—
508	C₂³	—	4	64	no	—
509	C₂³	—	4	16	no	—
510	C₂³	—	4	16	no	—
511	C₂³	—	4	16	no	—
512	C₂³	—	4	16	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	4	no	—
519	C₂³	—	4	4	no	—
520	C₂³	—	4	4	no	—
521	C₂³	—	4	4	no	—
522	C₂³	—	4	4	no	—
523	C₂³	C₁₉×#121	1	8	yes	—
524	C₂³	C₁₉×#121	1	4	yes	—
525	C₂³	C₁₉×#123	1	8	yes	—
526	C₂³	C₁₉×#123	1	4	yes	—
527	C₂³	C₁₉×#124	1	4	yes	—
528	C₂³	C₁₉×#126	1	8	yes	—
529	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
530	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
531	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
532	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
533	C₂³	C₂×#41×C₁₉	1	2	yes	—
534	C₂³	C₂×#41×C₁₉	1	2	yes	—
535	C₂³	C₂×#41×C₁₉	1	2	yes	—
536	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
537	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	8	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	8	no	—
546	C₂×C₄	—	4	16	no	—
547	C₂×C₄	—	4	16	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	C₁₉×#120	1	4	yes	—
570	C₂²	—	2	4	no	—
571	C₂²	—	2	16	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	16	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	16	no	—
579	C₂²	—	2	8	no	—
580	C₂²	—	4	64	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	8	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	8	no	—
585	C₂²	—	4	8	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	4	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	4	no	—
590	C₂²	C₁₉×#397	1	8	yes	complemented
591	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
592	C₂²	C₂×C₁₉×#121	1	2	yes	—
593	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
594	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
595	C₂²	C₂×C₁₉×#123	1	2	yes	—
596	C₂²	C₁₉×#525	1	2	yes	—
597	C₂²	C₁₉×#525	1	1	yes	characteristic
598	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
599	C₂²	C₂×C₁₉×#126	1	2	yes	—
600	C₂²	C₁₉×#534	1	1	yes	characteristic
601	C₂²	C₁₉×#534	1	2	yes	—
602	C₂²	C₁₉×#535	1	1	yes	characteristic
603	C₂²	C₁₉×#538	1	2	yes	—
604	C₂²	C₁₉×#546	1	4	yes	—
605	C₂²	C₁₉×#546	1	4	yes	—
606	C₂²	C₁₉×#551	1	4	yes	—
607	C₂²	C₁₉×#551	1	4	yes	—
608	C₄	—	2	4	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	4	no	—
611	C₄	—	8	4	no	—
612	C₄	—	8	2	no	—
613	C₄	—	8	2	no	—
614	C₂	—	2	8	no	—
615	C₂	—	4	8	no	—
616	C₂	C₂×C₁₉×#397	1	1	yes	characteristic
617	C₂	C₁₉×#2405	1	1	yes	characteristic
618	C₂	C₁₉×#2412	1	4	yes	—
619	C₂	C₁₉×#2435	1	1	yes	characteristic
620	C₂	C₁₉×#2480	1	4	yes	—
621	C₂	C₁₉×#2482	1	1	yes	characteristic
622	C₂	C₁₉×#2561	1	1	yes	characteristic
623	C₂	C₁₉×#2617	1	1	yes	characteristic
624	C₂	C₁₉×#2847	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁶×C₁₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#397	C₂	semidirect
3. C₂×C₁₉×#380	C₂	semidirect
5. C₁₉×#1440	C₂	semidirect
6. C₁₉×#1439	C₂	semidirect
7. C₁₉×C₂²⋊#95	C₂	semidirect
8. C₁₉×C₂²⋊#95	C₂	semidirect
12. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
13. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
25. C₂×C₁₉×#95	C₂²	semidirect
26. C₂×C₁₉×#95	C₂²	semidirect
27. C₂×C₁₉×#95	C₂²	semidirect
28. C₂×C₁₉×#95	C₂²	semidirect
29. C₂×C₁₉×#95	C₂²	semidirect
167. #14820	C₁₉	direct (N × H)
259. C₂×#397	C₂×C₁₉	semidirect
260. C₂×#380	C₂×C₁₉	semidirect
262. #1440	C₂×C₁₉	semidirect
263. #1439	C₂×C₁₉	semidirect
264. C₂²⋊#95	C₂×C₁₉	semidirect
265. C₂²⋊#95	C₂×C₁₉	semidirect
286. C₂²×C₁₉	#397	semidirect
313. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
314. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
326. C₂×#95	C₂²×C₁₉	semidirect
327. C₂×#95	C₂²×C₁₉	semidirect
328. C₂×#95	C₂²×C₁₉	semidirect
329. C₂×#95	C₂²×C₁₉	semidirect
330. C₂×#95	C₂²×C₁₉	semidirect
395. C₁₉	#14820	direct (N × H)
590. C₂²	C₁₉×#397	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₂²⋊C₄×C₁₉	2
C₂×C₁₉×#397	2
C₂×C₁₉×#380	2
C₂×C₁₉×#379	2
C₁₉×#1440	2
C₁₉×#1439	2
C₁₉×C₂²⋊#95	2
#14820	19

Subgroups — C19×#14820 #18020779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14820 #18020779